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dissertation entitled

DISTRIBUTIONAL EFFECTS OF CURRENCY DEVALUATION
ON HOUSEHOLDS TN RWANDA:
AN APPLICATION OF WILLINGNESS-TO-PAY
WELFARE MEASURES

presented by

Nicholas W. Minot

has been accepted towards fulfillment
of the requirements for

 

 

 

Ph.D. degree in Agricultural Economics
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DISTRIBUTIONAL EFFECTS OF CURRENCY DEVALUATION
ON HOUSEHOLDS IN RWANDA:
AN APPLICATION OF WILLINGNESS-TO-PAY
WELFARE MEASURES

BY

Nicholas w. Minot

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Agricultural Economics

1992

ABSTRACT
Distributional Effects of Currency Devaluation
on Households in Rwanda:

An Application of Willingness-To-Pay
Welfare Measures

BY

Nicholas W. Minot

Currency devaluation is a controversial policy measure in develop-
ing countries. One of the most common criticisms is that devaluation
causes disproportionate suffering among the poor. This study investi-
gates theléggggggutional impact of price changes associated with devalu-
ation in Rwanda. It uses a simpiifiEdflhouseholdefirm model based on
household budget data and both hypothetical and historical prices to
simulate the effect of devaluation on demand, real income, and nutrition.
l/,l\ Two aspects of the research approach deserve note. First,<;3ther;
<than>using the standard method of simulating the impact on a handful of
"archetypal" households, this study approximates the effect of price
changes on each household in the sample, allowing the results to be
aggregated to any desired sub-group of the population Second, in
addition to the standard measures of welfare impact iconsumer surplus and
the Laspeyres price index), the two "willingness-to-pay" measures are
calculated using the method suggested by Vartia (1983).

The results indicate that the ..{£.‘...g§..“.....iated with devalu-
ation have a proportionately greater negative impact on the real income
of urban and high-income households than on rural and low—income house—
holds, principally because the latter are insulated from all price
changes by the importance of home production. These results highlight

the risks of simple generalizations about the distributional impact of

devaluation.

ii

Cbpynghtby
NICHOLAS WILLIAM MINOT

1992

DEDICATION

I dedicate this work to Lisa,
my wife, colleague, and friend

iii

ACKNOWLEDGEMENTS

In the course of my graduate program, I have benefited greatly
from the support and encouragement of a wide range of people. First and
foremost, I would like to thank Dr. Donald Mead, my thesis advisor, and
Dr. Michael Weber, my major professor. Dr. Mead has been a constant
source of professional guidance and moral support, both in Rwanda where
he was my research supervisor (and neighbor) for two years and back at
Michigan State University where he helped me develop the dissertation
topic. In addition, he has inspired me by his ability to combine tech-
nical skills as an economist with a personal commitment to "making a
difference."

Dr. Weber has provided valuable support ever since my first con-
tact with Michigan State University in 1982. Dr. Weber has been instru-
mental in arranging the financial and material resources necessary for
my research. Even more importantly, he has served a valuable role
through his skill at asking the right questions and by continually refo-
cusing my attention on the policy—relevance of the results.

I have also benefited from the other members of my thesis and
guidance committes. Dr. Tom Reardon provided valuable comments on vari-
ous aspects of the dissertation, occasionally recharging my interest in
the topic. The econometric modelling was ably guided by Dr. Peter
Schmidt, who was always available for my questions. Dr. James Shaffer
was a source of healthy skepticism about all my neoclassical preconcep-
tions. And Dr. Carl Eicher, like Dr. Weber, has supported my studies
and professional development in various ways over the past decade.

I would also like to thank a number of collegues from my time in
Rwanda. Bonaventure Niyibizi, my fellow-analyst and good friend at the
Ministry of Planning, almost single—handedly made my stay in Rwanda

enjoyable. Dr. Francois Kanimba, then the Director General of Planning,

iv

originally suggested the dissertation topic. Théodomir Muligo, Director
of Surveys at the Ministry, protected me from bureacratic "turf bat-
tles," allowing me to carry out the research. Dr. Greg Lassiter facili-
tated my continuing involvement in the ENBC analysis on a short-term
basis after 1988. And Jim Otto, computer programmer par excellance, got
the ENBC data processing off the ground in 1985-86 with his hard work
and sense of humor.

The ENBC analysis was also assisted by computer programer Nsengim-
ana Elie, statisticians Philip Rees and Paul-Henri Wirrankoski, demogra-
pher Michel Simonet, and Drs. Victor Smith and James Ansoanuur, both
economists. The data cleaning was facilitated by the cooperation of
Albert Munyankumburwa and his crew of coding agents. Even Christophe
Muller helped make my experience at the Ministry of Planning "memora-
ble."

My two-year contract in Rwanda was funded by the Employment and
Enterprise Policy Analysis project, while the short-term consultancies
and my research assistantship at Michigan State University were paid for
by the Agricultural Survey and Policy Analysis Project. Both projects
were funded by the United States Agency for International Development,
and thus, ultimately, by the U.S. taxpayers.

Most of all, I would like to express my deep gratitude to my wife,
Lisa Daniels, who somehow managed to make the last three years of gradu-
ate school actually enjoyable. Perhaps I could have done it without her
unwavering support and good humor, but it would not have been nearly as

much fun!

\J 4.

TABLE OF CONTENTS

CHAPTER ONE: INTRODUCTION . . . . . . . . . . . .

Background . . . . . . . . . . . . . .
Objectives of the study . . . . . . . . . .
Organization of the study . . . . . . . . .

CHAPTER TWO: BACKGROUND ON RWANDA . . . . . . . .

2.1

Description of Rwanda . . . . . .
2.1.1 Geography and climate . .
2.1.2 People and history . . . .
2.1.3 Structure of the economy .
Background of the crisis . . . .
2.2.1 Economic policy . . . . .
2.2.2 External sector . . . . .
Structural adjustment program . .
2.3.1 Trade and exchange rate policy
2.3.2 Fiscal and monetary policy . .
2.3.3 Structural reforms . . . . . .

CHAPTER THREE: REVIEW OF LITERATURE . . . . . . .

3.1
3.2.

3.3

Introduction . . . . . . . . . . . . . . .
Impact of currency devaluation . . . . .
3.2.1 Theory of devaluation . . . . .
Empirical studies of devaluation .
s of household behavior . . . . . .
Theory of consumer demand . . . .
Functional form of demand equations
Issues in the estimation of consumer
Household-firm models . . . . . . .
Summary . . . . . . . . . . . . . .
re effects of price and income changes
Producer surplus . . . . . . . . .
Consumer surplus . . . . . . . . .

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Summary . . . . . . . . . . . . . .

CHAPTER FOUR: RESEARCH METHODS . . . . . .

¥\4.1.
-}4.2.

Overview of research approach .

Household as consumer . . . . . . .
4.3.1 Assumptions about preferences .
4. 3. 2 Functional form of demand equations
3.3 Estimation of demand . . . . . . .
.4 Derivation of elasticities of demand

Data sources . . . . . . . . . . . . . .
4.2.1 Survey sample . . . . . . . . .
4. 2. 2 Data collection methods . . . . . .
4. 2. 3 Data processing methods . . . . . .

5
ehold as producer . . . . . . . . . . .
1 Effect of prices and income . . . .
2 Supply response of agriculture . . .

vi

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Additional issues in demand estimation

Compensating variation and equivalent varia
Methods of estimating willingness to pay

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TABLE or CONTENTS (cont.)

4.5. Price changes associated with devaluation . . . . . .
4.5.1 Historical price data . . . . . . . . . . . .
4 5 2 Hypothetical prices . . . . . . . . . . . . .
4.6 Effect of price changes
4 6.1 Effect of price changes on demand . . . . . .
4 6 2 Effect of price changes on nutrition . . . .
4.6.3 Effect of price changes on household welfare
\/'5 CHAPTER FIVE: HOUSEHOLD BUDGET PATTERNS IN RWANDA . . . . .

‘1 5.1 Characteristics of Rwandan households . . . . . . . .
./5.2 Composition of household income . . . . . . . . . .
5.2.1 Definition of net income . . . . . .
5.2.2 Proportion of income from different activities
5.2.3 Proportion of households by primary occupation
5.2.4 Proportion of households involved in different
activities . . . . . . . . . . . . . . . . . . . .
\/5.3. Composition of household expenditure . . . . . . . .
5.3.1 Definition of expenditure . . . . . . . . . .
5.3.2 Average expenditure and size-distribution . .
5.3.3 Expenditure for different types of households

5.3. 4 Composition of expenditure . . . . . . . . . .
5.4 Agricultural production in the rural sector . . . .
5.4.1 Land . . . .
5.4.2 Purchased inputs . . . . . . . . . . . . . .
5.4.3 Agricultural production and marketing . . . .
5.5 Effect of price changes on households . . . . . . . .
5.5.1 Participation in the market . . . . . . . . .
5.5.2 Net position in agricultural commodities
5.5.3 Tradeable component of expenditure and income
5.5.4 Summary . . . . . . . . . . . . . . . . . . .
6 CHAPTER SIX: MODEL OF HOUSEHOLD DEMAND . . . . . . . . . .
6.1 Selection of the appropriate model . . . . . . . .
6.1.1 Treatment of rural and urban samples . . . . .
6.1.2 Commodity Categories . . . . . . . . . . . .
6.1.3 Estimation method: OLS vs SUR . . . . . . .
6.2 Unrestricted SUR model of rural demand . . . . . . .
6.2.1 Overall goodness-of-fit and significance . .
6.2.2 Effect of total expenditure . . . . . . . .
6. 2. 3 Effect of household composition . . . . . . .
6. 2. 4 Effect of prices . . . . . . . . . . . . .
6.3 SUR model of rural demand with symmetry imposed .
6.4 Unrestricted SUR model of urban demand . . . . . . .
6.4.1 Overall goodness—of—fit and significance . . .
6.4.2 Effect of total expenditure . . . . . . . .
6.4.3 Effect of household composition . . . . . . .
6.4.4 Effect of prices . . . . . . . . . . . . . . .
6.5 SUR model of urban demand with symmetry imposed . . .
6.6 Effect of zero-expenditures on the model . . . . . .
6.7 Measurement error and quality effects . . . . . . .

vii

TABLE OF CONTENTS (cont.)

CHAPTER SEVEN: IMPACT OF CURRENCY DEVALUATION . . . . . . . 193
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . 193
7.2 Effects of hypothetical currency devaluation:
base scenario . . . . . . . . . . . . . . . . . . . . . 194
7.2.1 Assumptions used in base scenario . . . . . .
7. 2. 2 Aggregate demand and caloric intake . . . . . 197
7. L 3 Distributional effects of the hypothetical
devaluation . . . . . . . . . . . . . . . . . . 202

7.3 Effects of historical prices . . . . . . . . . . . . . 210
7.3.1 General price trends over 1989-90 . . . . . . . 211
7.3.2 Prices used in the simulation . . . . . . . . . 214
7.3.3 Aggregate demand and caloric intake . . . . . . 216

7.3.4 Distributional effects of historical price
changes . . . . . . . . . . . . . . . . . . . . 221

.4 Alternative assumptions about wage rates . . . . . . . 224
5 Alternative assumptions about agricultural supply

response O O O O O O O O O O O O O O O O O O O O O O O 225

.6 Demand response assumption . . . . . . . . . . . . . . 231
.7 Comparison of welfare measures . . . . . . . . . . . . 232
.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . 237

CHAPTER EIGHT: CONCLUSIONS AND POLICY IMPLICATIONS . . . . . 239

v/8.1 Summary of results . . . . . . . . . . . . . . . . . . 239
~L8.1.1 Income and expenditure patterns . . . . . . .
8.1.2 Model of consumer demand . . . . . . . . . . . . 243

8.1.3 Impact of price changes associated with

devaluation . . . . . . . . . . . . . . . . . . 245

8.2 Implications for policy . . . . . . 247
8.2.1 Magnitude of the impact of devaluation . . . . . 247

8. 2. 2 Alleviation of the impact of devaluation . . . . 248

8.3 Implications for research methods . . . . . . . . . . 250
8.3.1 Advantages of micro-simulation . . . . . . . . 250

8. 3. 2 Factors affecting the impact of devaluation . . 251

8.3.3 Alternative welfare measures . . . .
fx8.4 Limitations of the study and suggestions
for further research . . . . . . . . .

. . . . . . 252

. . . . . . . . 253

LIST OF REFERENCES . . . . . . . . . . . . . . . . 256

APPENDIX A: Devaluation and bean prices . . . . . . . . . 264

APPENDIX B: Adult equivalence scales . . . . . . . . . . 266

APPENDIX C: Regression coefficients and t statistics . . . . 267

viii

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LIST OF TABLES

Single-equation hypotheses to be tested . . . . .
Cross-equation hypotheses to be tested . . . . .
Selected welfare measures . . . . . . . . . . . .
Characteristics of rural and urban households . .
Sources of net income for rural and urban househo
Distribution of households by primary occupation
Proportion of households earning

any income from each source . . . . . . . . . . .
Mean level of expenditure in rural and urban areas . .
Cumulative distribution of households

by expenditure level . . . . . . . . . . . . . . . .
Real expenditure of different types of households . .
Composition of expenditure in rural and urban areas .
Rural expenditure and caloric intake by farm size .
Life cycle patterns in farm size in the rural sector
Factors which ameliorate the disparity in farm size
Rural expenditure and caloric intake by farm size
Composition of agricultural production and sales .
Agricultural production and marketed share . . . .
Importance of cash expenditure in rural and urban

lds

sectors . . . . . . . . . . . . . . . . . . . . . . .
Importance of cash expenditure by quintile . . . . . .
Importance of cash expenditure by rural and

urban quintile . . . . . . . . . . . . . . . . . . . .
Rural production, marketing, and consumption

of six crops . . . . . . . . . . . . . . . . . . . . .
Rural net sales and urban demand . . . . . . . . . . .
Distribution of households by market participation . .

Correlation of net sales of different commodities
Characteristics of rural households by net sales
position . . . . . . . . . . . . . . . . . . . . . . .
Tradeable component of rural and urban cash expenditure
Composition of rural and urban tradeable cash

expenditure . . . . . . . . . . . . . . . . . . . . .
Importance of tradeables in rural income and
expenditure by expenditure quintile . . . . . . . . . .
Importance of tradeables in urban income and
expenditure by expenditure quintile . . . . . . . . . .

Test of equality of urban and rural coefficients . . .
Description of food products in rural and urban models
Description of non-food categories in rural and urban

models O O O O O O O O O O O O O O O O O O O O O O O O
Summary of unrestricted SUR model of rural demand . .
Caloric cost of various food items . . . . . . . . .

Effect of household expenditure on rural demand . . .
Effect of household composition on rural demand . . .
Effect of prices on rural food demand . . . . . . . .
Derived rural non-food price elasticities . . . . . .
Summary of rural model with symmetry imposed . . . . .
Effect of expenditure on rural demand under symmetry .
Effect of prices on rural food demand under symmetry .
Derived rural non-food price elasticities

under symmetry . . . . . . . . . . . . . . . . . . . .
Summary of unrestricted SUR model of urban demand .
Effect of household expenditure on urban demand . . .
Effect of household composition on urban demand . . .

ix

128

131
132

139

141
144

146
146

147
151
153

154
157
159
160
163
166
168
170
171
172

172
174
175
178

Table

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LIST OF TABLES (cont.)

Page

Effect of prices on urban food demand . . . . . . . . 180
Derived effect of prices on urban non-food demand . . 181
Summary of urban model with symmetry imposed . . . . 183
Effect of expenditure on urban demand under symmetry . 184
Effect of prices on urban food demand with symmetry

imposed . . . . . . . . . . . . . . . . . . . . . . . . 185
Derived non-food price elasticities under symmetry . . 186
Comparison of elasticities estimated with Tobit and OLS 187
Quality and measurement error effects in rural

food demand . . . . . . . . . . . . . . . . . . . . . . 189
Quality and measurement error effects in urban

food demand . . . . . . . . . . . . . . . . . . . . . . 191
Assumed tradeable component of each budget category . . 195
Effect of hypothetical devaluation on rural demand . . 199
Effect of hypothetical devaluation on rural food consump-
tion . . . . . . . . . . . . . . . . . . . . . . . . . 200
Effect of hypothetical devaluation on urban demand . . 201
Effect of hypothetical devaluation on urban food consump-
tion . . . . . . . . . . . . . . . . . . . . . . . . . 202
Effect of hypothetical devaluation on households . . . 204
Effect of hypothetical devaluation on rural households 208
Effect of hypothetical devaluation on urban households 210
Food prices in Kigali before and after devaluation . . 215
Non-food prices in Kigali before and after devaluation 216
Effect of historical price changes on rural budgets . . 217
Effect of historical prices on rural food consumption . 218
Effect of historical price changes on urban budgets . . 219

Effect of historical prices on urban food consumption 220
Effect of historical price changes on households . . 221
Effect of hypothetical devaluation on households

assuming real wage remains constant . . . . . . . . . . 224
Estimated agricultural supply elasticities . . . . . 227
Effect of hypothetical devaluation on rural households,

asuming medium agricultural supply elasticities . . . . 228

Effect of hypothetical devaluation on rural
households, assuming high agricultural supply

elasticities . . . . . . . . . . . . 230

Effect of hypothetical devaluation on households

using the unrestricted demand model . . . . . . . . . 231

Welfare impact of hypothetical devaluation according

to different welfare measures . . . . . . . . . . . . . 233

Correlation across households of different welfare

measures . . . . . . . . . . . . . . . . . . . . . . . 234

Comparison of alternative welfare measures . . . . . . 234

Adult equivalence scales . . . . . . . . . . . . 266

Coefficients of the unrestricted SUR model of

rural demand . . . . . . . . . . . . . . . . . 267

Coefficients of the SUR model of rural demand

under symmetry restrictions . . . . . . . . . . . . . 270

Coefficients of the unrestricted SUR model of

urban demand . . . . . . . . . . . . . . . . . . . 273

Coefficients of the SUR model of urban demand

under symmetry restrictions . . . . . . . . . . . . . . 277
x

 

Figure

3-1:
3-2:
3-3:
5-1:
5-2:
5-3:

LIST OF FIGURES

Compensating variation and equivalent variation
First-order approximations of willingness to pay
Second-order approximations of willingness to pay

Distribution of
Distribution of
Distribution of
potatoes . .

Distribution of
potatoes . .

Distribution of
Distribution of
Distribution of
Distribution of
crops expressed

households by
households by
households by

households by
households by
households by

households by
households by

net
net
net
net
net
net

sales
sales
sales
sales
sales
sales

of sorghum
of cassava
of sweet
of white
of bananas
of beans

coffee sales . . .

net sales of six stapl

in caloric terms
Consumer price index for Rwanda (1989= 100) . . .
Tradeable and nontradeable price indexes (1989= -100)

xi

O O O O

e

135
136
137
138
138
140

213

CHAPTER ONE

INTRODUCTION

1.1 W

Since the early 19809, an increasing number of less developed
countries have been forced to implement macroeconomic adjustment
policies to deal with large current account deficits, inflation, and
stagnant economic growth. The reasons for these difficulties vary from
country to country, but they include international events such as
falling commodity prices and the world recession in the early 19803, as
well internal factors such as overly expansionary economic policies. In
sub-Saharan Africa, these problems have been exacerbated by increasing
variable rainfall and, in some countries, civil unrest (World Bank/UNDP,
1989).

In a number of countries, the historically high commodities prices
of the mid- and late-19709 allowed a significant expansion of government
revenue and spending. The fall in commodity prices in the early 19805,
generated both budget and trade deficits. Initially, these deficits
were financed by external borrowing, a policy based on both unjustified
optimism about commodity prices and political resistance to reductions
in imports and government spending. When low commodity prices proved
not to be transitory, governments often resorted to excessive monetary
expansion to finance the budget deficits. The resulting inflation, in
the context of a fixed exchange rate, exacerbated the current account
deficit, leading to import restrictions and controls on foreign exchange
transactions (Zulu and Nsouli, 1985).

The standard economic prescription for trade imbalances in a
fixed-exchange-rate regime is to adjust the exchange rate, devaluing the
local currency with respect to those of its trading partners. When

successful, devaluation raises the local returns to import substitution

2

and export activities, while dampening the demand for exportable goods
and imports. At the same time, it often serves to restore confidence in
the currency, reducing the incentives for capital flight.

For these reasons, devaluation is frequently a key element in
structural adjustment packages promoted by the World Bank and the
International Monetary Fund (IMF). Approximately two thirds of the
countries in sub-Saharan Africa devalued between 1983 and 1987. Most of
these devaluations were implemented as part of World Bank structural
adjustment loan programs (Sahn, 1990: 249).

At the same time, devaluation is a highly controversial policy
measure. .Policy-makers in less developed countries often postpone
devaluation as long as possible, appearing to implement it only under
pressure from the international financial organizations. Critics argue
that devaluation has a contractionary effect on the economy, is
ineffective in reducing external deficits, and has a regressive impact
on income distribution (Godfrey, 1985; Cornia, Jolly, and Stewart,
1987).

One result of this controversy is that the World Bank and other
donor agencies have given greater attention to designing complementary
programs to alleviate the impact on vulnerable groups, particularly the
poor (World Bank, 1990b). These programs are defended both on
humanitarian grounds and on the grounds that the sustainability of the
reforms often depends on maintaining a minimum degree of political
support during the difficult initial stages.

Another by-product of the controversy is that devaluation has been
the subject of numerous theoretical and empirical studies. The effect
of devaluation on aggregate demand, the price level, and the external
balance has been extensively studied using a variety of research
approaches (see section 3.2.2). On the other hand, the distributional
impact of devaluation, although powerful, is less well understood. Part

of the explanation is that indicators of income distribution are not

3

regularly collected, thus limiting the possibilities for cross-country
or time-series analysis. In addition, the distributional impact of
devaluation is quite sensitive to the structure of the economy (whether
staple food crops are imported, who produces the export commodities, and
so on). .Thus, it is difficult to generalize across countries.

This is unfortunate because knowledge of the distributional impact
of devaluation would assist the design of complementary policies to
alleviate the impact on those harmed. Furthermore, better knowledge
about the distributional impact may help explain the political economy

of currency devaluation.

1.2 Objectives of the study

The principle objective of this research is to use household
budget data from Rwanda to estimate the short-run distributional impact
of relative price changes associated with currency devaluation.
Household budget data are used to estimate income and price elasticities
of demand. The survey results, combined with projected changes in
prices, will provide a picture of the impact of devaluation along three
dimensions: real income, the composition of demand, and the nutritional
intake of households. The distributional impact will be evaluated by
disaggregating the results by location of residence, by income level, by
occupation, and by sex of head of household.

Because we examine only the short-run impact of one aspect of
devaluation, no attempt is made to judge the overall desirability of
devaluation. Nonetheless, the results should address concerns about the
distributional impact of devaluation.

A second objective of the study is to provide some generalizations
about the impact of devaluation in less developed countries. As
mentioned above, the distributional effect of devaluation varies greatly

among countries depending on the structure of the economy, but this

4

research may help specify the variables that are most important in
determining the outcome.

Third, the methods developed in this study could have applications
elsewhere. In spite of the growing recognition of the importance of
addressing the distributional effects of devaluation, most of the
empirical work done thus far is merely suggestive. Household budget
data, available in many less developed countries, are a rich source of
information for this type of policy analysis.

Two methodological issues are of particular interest. First, in
most applied studies, the welfare impact of alternative price scenarios
is approximated using simple price indexes or, in some cases} consumer
surplus. At the same time, several approaches to estimating the "exact"
welfare impact have been developed in the literature (McKenzie, 1983;
Vartia, 1983). These "willingness-to-pay" measures are theoretically
superior to consumer surplus and yet require no more information about
the shape of the demand curves. Thus, one of the methodological
objectives of this study is to compare alternative "willingness-to-pay"
measures and to evaluate their usefulness relative to simpler but less
accurate measures.

Second, aggregate household behavior is generally analyzed by
classifying households into three to seven categories such as small
farmers, large farmers, wage earners, and so on. Then, models of each
type are constructed and allowed to interact, usually with weights to
represent the relative importance of each group in the population.
However, such an approach does not take full advantage of the
information available in any household budget survey. Nor does it
reflect the diversity of household income and expenditure patterns.
This study makes use of "micro-simulation" in which the behavior of each
household in the sample is simulated (Smith and Strauss, 1986).

Although this approach involves somewhat more computation, it allows the

 

a‘XE‘II—

 

L_Ir_'

 

5

researcher to estimate the impact on any sub-group of the population,

making full use of the diversity found in the survey data base.

1.3 Organization of the study
This study comprises eight chapters. Chapter 2 provides a brief

overview of the geography, history, and economy of the Republic of
Rwanda. In addition, the background of the current economic crisis and
the response of the government are described.

In Chapter 3, a fairly diverse body of previous research is
reviewed. First, theoretical and empirical studies of the impact
currency devaluation are discussed. Second, models of consumer behavior
are considered, with emphasis on the theory of consumer demand and
various problems in estimating demand. Finally, an overview is provided
on the theory and practice of measuring the welfare impact of price
changes on individual households.

Chapter 4 outlines the methods of the study. This includes a
description of the Rwandan household budget survey which forms the basis
of the study. In addition, the estimation of the demand model is
discussed, along with the implied behavioral assumptions. Next, the
methods of obtaining the price changes associated with devaluation are
explained. And finally, we describe the process of using the demand
model to calculate the welfare and nutritional impact of the price
changes.

The results of the study are presented in Chapters 5, 6, and 7.
Chapter 5 presents some basic descriptive results from the household
budget survey. The sources of income, patterns of expenditure, and
variation across different types of households are described. Because
of the importance of agriculture in the Rwandan economy, special
attention is given to the patterns of agricultural production and

marketing patterns in the rural sector. The importance of subsistence

 

6

production, the patterns of net sales of staple crops, and the tradeable
component in household income and expenditure are considered.

In Chapter 6, the results of the econometric analysis of household
demand are described. Budget shares of some 25 categories of goods and
services are estimated as a function of total household expenditure, the
demographic characteristics of the household, and food prices.

Chapter 7 uses the demand model to simulate the impact on each
household in the sample of various price changes associated with
currency devaluation. The welfare and nutritional impact of these
changes is discussed.

Finally, in Chapter 8, we summarize the results of the study and
draw implications for economic policy in Rwanda and similar countries.
In addition, the results of the study are examined in light of the need

to improve the methods used in similar studies in the future.

 

CHAPTER 2

BACKGROUND ON RWANDA

This chapter provides a brief description of Rwanda and the developments
leading up to the recent economic problems in order to set the stage for
the analysis in later chapters. Section 2.1 provides an overview of the
geography, climate, people, and economy of Rwanda. Section 2.2 de-
scribes the external events and economic policies which precipitated the
current economic crisis. And section 2.3 reviews the most important
elements of the structural adjustment program, implemented to confront
the economic problems.
2-1 W

2.1-1 W

The Republic of Rwanda is a small landlocked country in

the highland region of east-central Africa. It covers just 26,338
square kilometers (10,169 square miles), virtually all of which is over
1000 meters (3250 feet) above sea level. The country is surrounded by
Tanzania on the east, Uganda to the north, Zaire across Lake Kivu to the
east, and Burundi to the south. Mombassa, the port through which most
international trade flows, lies about 1700 kilometers (650 miles) to the
east by road.

Although quite close to the equator (l—3° 8.), Rwanda enjoys a
mild temperature, averaging about 20° C. (68° F.) with relatively little
seasonal variation. Rainfall follows a bi-modal pattern, with the long
rainy season being between March and May and a less pronounced rainy
season from October to November. Most parts of the country receive 900-
1300 mm of rainfall annually.

In spite of its small size (less than that of Maryland), Rwanda
has a variety of geo-climatic zones. The eastern third of the country

is dominated by rolling savannah, being lower (1000-1500 m), drier (800-

 

 

 

8

1000 mm), and warmer (21-22° C) than most of Rwanda. The central
plateau lies between 1500 and 1900 meters and has intermediate tempera-
tures and rainfall. To the west is the Zaire-Nile Ridge which runs
north-south, separating the Nile watershed to the east and Lake Kivu to
the west. These mountains generally have altitudes from 2000 to 3000 m,
although several volcanic peaks in the northern portion of the range are
over 3500 m., including Mt. Karisimbi (4500 m). Thus, much of the
western third of Rwanda is cool (ls-17° C.) and damp (more than 1300 mm
rainfall) (Sirven et al., 1974).

2.1.2 W,

' Rwanda is the most densely populated country in sub-

Saharan Africa and has one of the highest population growth rates in the
world. The mid-1988 population was estimated at 6.7 million, yielding a
population density of 254 persons per square kilometer (approximately
650 per square mile). This density is higher than that of most Asian
countries including India and the Philippines. The World Bank estimates
that the population growth will average 3.8% through the 1990s, reaching
10 million by the year 2000 (World Bank, 1990a).

The high population density is even more surprising given the
small proportion of the population living in urban areas, around 7%.
The principal urban center is the capital, Kigali, with around 150,000
residents. In the rural areas, there are very few towns or even
hamlets, almost all dwellings being dispersed throughout the hills. The
population density is lowest in the eastern savannah and highest in the
fertile volcanic zone of the northwest. Most of the population,
however, lives in the intermediate altitudes of 1500 to 1900 meters
(Sirven, 1974).

Ethnically, the population of Rwanda is composed of the Hutu (87-
89% of the population), the Tutsi (10-12%), and the Twa (barely 1%).
The Twa were the original hunter-gatherer inhabitants of the region.

The Hutu are said to have arrived between the 7th and 10th century,

 

 

9

bringing sedentary agriculture with them as part of the great Bantu
migrations. The pastoral Tutsis migrated into the area in the 13th and
14th century, establishing feudalistic control over the existing
population. The network of kingdoms expanded slowly, encompassing by
1900 much of what is today Rwanda and Burundi (Heremans, 1988).

Although Germany occupied Rwanda and Burundi from the turn of the
century until World War I, their presence was minimal. Belgium seized
the territory in 1916 and received a League of Nations mandate to
administer it three years later. The Belgian administration concentrat-
ed on road building, reforestation, the promotion of sweet potatoes and
manioc as anti-famine measures, the introduction of coffee, and the
expansion of internal trade. Devoting only a small staff to the
territory (numbering just 205 in 1945), Belgium ruled through the
existing Tutsi monarchy (Leurquin, 1963). In the 19503, educated Hutus
began demanding a greater role in the political process, culminating in
a violent rebellion in 1959. This led to Belgian-organized elections in
1960-1961 and independence in 1962 under a Hutu-dominated government.

In 1964, Burundi and Rwanda separated from each other, the former being
ruled by minority Tutsi governments to this day (Heremans, 1988).

In Rwanda, the "First Republic," under President Gregoire Kayi-
banda, lasted from independence in 1962 until 1973. His rule ended when
the current president, Major General Juvenal Habyarimana, took control
in a bloodless coup, establishing the "Second Republic." While the
First Republic was explicitly pro-Hutu, President Habyarimana has
attempted to reduce ethnic tensions by incorporating Tutsis in the
government in numbers roughly proportional to their population.

Some have argued that the Hutus and Tutsis are not, strictly
speaking, ethnic groups since they share the same territory, language,
and culture. Furthermore, intermarriage has somewhat blurred the
physical differences between the two groups. On the other hand,

tensions between the groups have been an important factor in the history

0".

 

 

10

of Rwanda and Burundi, which has been punctuated by periods of violence.
In 1974, an estimated 100 thousand people were killed in ethnic conflict
in the two countries. In 1988, perhaps 10,000 were killed in an ethnic
uprising in Burundi.

And most recently, in October 1990, exiled Tutsis in Uganda
mounted an invasion of Rwanda from Uganda. Although unsuccessful, the
invasion and subsequent skirmishes have heightened ethnic tension and
greatly weakened the economy. At the same time, these events may have
accelerated the gradual democratization process already underway. In
1991, opposition political parties were legalized and press freedoms
greatly expanded. An interim government has been formed to pave the way
for presidential elections.

2-1-3 Wm

Rwanda is one of the 20 poorest countries in the world,
with the gross national product (GNP) per capita estimated at $ 320 in
1988. On the other hand, its performance in terms of economic growth
has been fairly good, particularly by sub-Saharan African standards.
Per capita GNP grew at 1.5% annually over the period 1965-1988, a rate
higher than almost three quarters of the sub-Saharan African countries
for which data are available (World Bank, 1990).

Agriculture represents 40% of the gross domestic product and
employs 90% of the economically active population (Ministére des
Finances et de l'Economie, 1987). There are over a million farm
households in Rwanda, over half of whom cultivate less than one hectare
of land (World Bank, 1991). In terms of volume, the most important
crops are plantains, sweet potatoes, manioc, beans, sorghum, and white
potatoes. Arabica coffee is grown by about 40% of the smallholders and
is the principal export commodity of Rwanda (Ministére de l'Agriculture,
1987).

Until the mid-19803, Rwanda was able to increase food production

to meet the needs of the growing population. This was accomplished by

 

 

 

11

expanding production in swampy valley bottoms, on steep hillsides, and
in the less populated eastern region of the country. Some intensifica-
tion has taken place, primarily by changing the production mix toward
crops with high caloric output per hectare. In recent years, however,
food production appears to have lagged behind the population growth.
Localized outbreaks of weather-induced famine in 1989-90 may be a
manifestation of the increasingly fragile food security of the rural
population in Rwanda.

The industrial sector represents about 23% of gross domestic
product. This category includes manufacturing (15% of GDP), construc-
tion, a small mining sector, hydro-electric production, and water (World
Bank, 1990). The manufacturing sector includes a large-scale "modern"
sector and a small-scale ”informal" sector. The large-scale manufactur-
ing sector produces a relatively wide range of goods: beer, carbonated
drinks, soap, paint, fruit products, foam rubber, matches, cigarettes,
radios, corrugated metal sheets, and plastic consumer products. Small-
scale manufacturing includes traditional beer brewing, metalwork,
woodwork, tailoring, and brick-making.

Services account for about 40% of gross domestic product. This
includes commerce, tourism, transport, banking, insurance, and public
administration. Tourism is a small but growing source of foreign
exchange, particularly since the initiation of "gorilla tourism" in 1985
(Ministere des Finances et de l'Economie, 1987) .

Because of the cost of transporting merchandise overland to the
coast, international trade is limited: official exports represent only
8-9% of GNP. Coffee accounts for 75-85% of the value of exports, while
other crops such as tea constitute another 10-15%. Minerals and animal
skins are also exported. Official Rwandan imports include consumer
goods (44% of the value), fuel and lubricants (17%), equipment (23%),
and raw materials (16%). Officially imported food products include

rice, sugar, powdered milk, vegetable oil, and processed foods (Mini-

 

 

12

stere des Finances et de 1'Economie, 1987). There is also evidence of
informal trade with neighboring countries, notably imports of palm oil,
beans, and coffee, and export of consumer goods and possibly white

potatoes (Loveridge, 1989 and Ngirumwami, 1989).

2.2 Background of crisis

In order to understand the nature of the recent economic crisis,
it is useful to review briefly the economic policies and external events
that preceded it. In general terms, the crisis can be attributed to the
fall in coffee prices, compounded by poor weather and inappropriate
policy response.

2-2-1 w

A consistent theme in Rwandan economic policy has been
fiscal and monetary conservatism. The public sector of Rwanda is
relatively small, with current expenditures accounting for just 10-13%
of GNP. Until recently, budget surpluses were as common as deficits,
and the deficits rarely surpassed 2% of GNP. With a modest public
deficit, there was little pressure to finance it through monetary
expansion. Expansion of the supply of (narrow) money over the period
1966-86 was thus kept to 14% per year. The result was only moderate
inflation, averaging just 7% over the 20-year period (Ministere des
Finances et de l'Economie, 1987).

Public investment in roads, schools, and health centers in the
rural areas has been significant. Agricultural research and extension
efforts has also been supported by public investment. Direct government
intervention in agricultural markets, however, has been largely focused
on the export crops. Some efforts have been made to control food crop
marketing by setting "official prices" and through the operations of a
‘parastatal marketing board, OPROVIA. Neither has had much influence,

and these efforts have been scaled back (Loveridge, 1989).

 

 

 

13

Paradoxically, the policies with the most significant impact on
the rural population may be those promoting import-substitution indus—
trialization. Most of the "modern-sector" industries involve a single
firm, established with government participation and import protection.
Their dependence on imported inputs is such that the domestic value
added is often only a small portion of the value of output. In fact, a
few have been shown to have negative value added at international prices
(World Bank, 1985; Ngirabatware, Murembya, and Mead, 1988). Such
policies raise the price of manufactured goods and implicitly tax
exports, most of which are agricultural commodities.

2-2-2. W

In 1987, the international price of coffee began to fall
from the heights it had reached in the mid-19809. In Rwanda, this
resulted in stagnating real gross national product in 1987-88. A
further decline of coffee prices in 1989, combined with reduced coffee
output and poor weather, resulted in a sharp decline (-6.6%) in real
GNP. The current account deficit (excluding official aid) rose to 10.7%
of GNP. At the same time, since the producer price of coffee had been
fixed at 120 FRw/kg, the coffee sector changed from a source of govern-
ment revenue to a drain on the treasury.

The external deficit was financed by borrowing and by depletion of
foreign reserves, which were reduced from the equivalent of five months
of imports in 1987 to less than one month in 1990. The government
responded by placing tighter controls on import licenses and foreign
exchange allocation and by reducing the producer price of coffee to 100
FRw/kg in March 1990. In addition, new taxes were imposed on cigarettes
and beer, but these caused a reduction in demand so large that govern-

ment revenue also fell, forcing the abandonment of the new taxes.

 

14

L3 Structural adjustment program

In September 1990, the details of the structural adjustment
gmogram were published in two documents. One document described the
policies to be implemented in the first year of the program (Republique
Rwandaise, 1990a), while a second one outlined economic policies for the
medium term (Republique Rwandaise, 1990b). As of October 1991, most of
the reforms mentioned had been implemented. The program involves trade
policy, fiscal policy, monetary policy, and structural reforms, each of

which are described below.

2.3.1 Trade and exchange rate policy

Trade policy reforms include currency devaluation and
import liberalization. On 10 November 1990, the Rwandan franc (FRw) was
devalued by 40% relative to the International Monetary Fund's Special
Drawing Right (SDR), so that the rate rose from 102.71 FRw/SDR to 171.18
FRw/SDR. At the same time, all export taxes except those on coffee were
eliminated in December 1990.

The system for allocating (rationing) foreign exchange to import-
ers was to be reformed to make it less arbitrary and more transparent,
thus reducing uncertainty and the risk of corruption. In the first
phase, initiated in June 1991, foreign exchange is allocated each month
at the official rate according to requests made by importers. If the
sum of the requests exceeds the available supply, allocations "will be
determined by reducing proportionately for each importer the amounts
requested" (Republique Rwandaise, 1990a: 6). A fee of 5% of the value
of the request discourages importers from exaggerating their needs. The
only goods exempted from these proportionate reductions are goods of
"primary necessity," including petroleum products, sugar, salt, milk
powder, vegetable oil, fertilizer, and pharmaceutical products. To
render the system more transparent, the amount available and the values

requested and received by each importer are published each month.

 

15

In the second phase, import licenses will be granted without
restriction (except for health and safety considerations) and foreign
exchange will be allocated to all at a "realistic" exchange rate. This
phase was to be implemented by January 1992, or earlier if foreign
exchange availability allows (Republique Rwandaise, 1990a).

A number of reforms have been undertaken to simplify the tariff
structure and reduce the level of protection. In December 1990, import
quotas and prohibitions were converted to ad-valorem tariffs, the
minimum tariff was raised from 5% to 10%, and the number of exemptions
reduced. In August 1991, the maximum tariff was reduced to 100%, and
the number of tariff rates was reduced to six. The list of imports
exempted from tariffs will be progressively shortened and the maximum
rate reduced over time.

2.3.2 Fiscal and monetary policy

Fiscal policy changes include measures to increase
revenue and restrict expenditure. In addition to raising the minimum
tariff, as mentioned above, business taxes have been raised from 2-6% of
gross revenue to 5-10%. Expenditures is being limited by the reduction
of the coffee support price payments, reduction in indirect subsidies to
state enterprises, and a freeze on public sector employment except for
teachers. In January 1991, public transport fares were raised 20%, and
in July 1991 water and electricity rates were increased by 50%.

Monetary policy is to be restrictive, with the money supply growth
being kept below the rate of increase of nominal GNP. In addition, the
structure of interest rates will be simplified, eliminating preferential
rates and ensuring that term-deposit rates are positive in real terms.
Interest rates on loans and demand-deposits will also be deregulated.

2.3.3 Structural reforms

A number of "structural" reforms are also envisaged. The
government has eliminated the regulation of profit margins (except those

of public utilities) and prices (except those of petroleum products and

 

16

export crops). The prices of petroleum products have risen 100% to
reflect the devaluation, higher international prices, and higher taxes.
In addition, indirect subsidies to state enterprises will be gradually
removed. Government shares will be sold for three state enterprises:
SONATUBE (a PVC tube manufacturer), STIR (a trucking firm), and RWAN-
TEXCO (a textile company). Privatization or liquidation is planned for
state enterprises in printing, metal products, paper products, regional
development, and hotels.

Other policy reforms include liberalization of coffee export
marketing, measures to improve coffee quality, rehabilitation of the tea
and mining sectors, reorganization of the agricultural extension.
service, simplification of administrative procedures for registering
small enterprises, and extension of family planning services to the
entire network of health centers.

This study concentrates on the distributional impact of one
component of the structural adjustment program, the currency devalua-
tion. Furthermore, as mentioned in section 1.2, we examine only the

short-run impact of the change in relative prices due to devaluation.

 

CHAPTER 3

REVIEW OF THE LITERATURE

3-1 W

Because this study attempts to analyze the household-level impact
of macro-economic policy, it is necessary to review a fairly diverse
body of literature to serve as background for the analysis. Section 3.2
reviews previous research, both theoretical and empirical, on the topic
of currency devaluation. The principal topics to be addressed in this
section are the mechanism by which devaluation influences the economy
and the effects of devaluation on prices, output, and income
distribution.

In section 3.3, models of household behavior will be discussed.
The household-firm model, which incorporates the role of the household
as both consumer and producer, will be described. The theory of
consumer behavior helps to identify some restrictions on the functional
form of the regression model, but there are a number of issues outstan-
ding.

Finally, in section 3.4, the measurement of welfare effects on
households is considered. The traditional consumer surplus measure is
compared to more sophisticated "willingness-to-pay" concepts. In
addition, some approaches to estimating these welfare measures are

reviewed.

3.2 W

This section will review recent research on the impact of
devaluation, with particularly emphasis on the case of less develOped
countries. First, various theoretical approaches to understanding
devaluation will be discussed. Then, the results of empirical research

on the impact of devaluation are considered.

17

18
3-2-1 W

Currency devaluation is a discrete increase in the
nominal exchange rate in the context of a fixed-rate regime, where the
exchange rate is expressed as the number of local currency units per
foreign currency unit. Devaluation is designed to raise the real
exchange rate, defined here as the price of tradeable goods (imports,
import substitutes, exports, and exportable goods) relative to the price
of non-tradeable goods. In theory, an increase in the real exchange
rate encourages the production and discourages consumption of tradeable
goods, improving the external balance, while a decrease in the real
exchange rate does the reverse, causing a deterioration in the trade
balance.

The above implies that there is an equilibrium real exchange rate
at which external balance is achievedl. As Edwards (1989) demon-
strates, the equilibrium real exchange rate will vary with real
variables: the terms of trade, trade policies, technology, exogenous
shifts in demand, interest rates, and other factors. On the other hand,
the actual real exchange rate varies (in spite of the fixed nominal
rate) with monetary variables such as the price level. For example, if
domestic inflation is higher than international inflation, the local
currency prices of non-tradeables rise relative to those of tradeables,
so the real exchange rate falls.

A common response to external deficits is import restrictions and
exchange controls. However, this is likely to create severe distortions
in the external sector. Another possible response is to allow ad-
justment to occur automatically: as international reserves are depleted,
the money supply contracts, and deflation reduces nontradeable prices
relative to tradeable prices. With flexible prices and full employment,

this would be identical to devaluation. But given sticky prices and

 

1. External equilibrium does not necessarily imply exact
balance of payments, but rather that any net capital flows are sus-
tainable and correspond to intertemporal preferences.

‘ul
6.

CC:

Ex»

‘ C
‘4

€f‘

e
“.9

l9
unemployed resources, adjustment under devaluation will be more rapid
and expansionary (or less contractionary) than automatic deflationary
adjustment.

Three approaches have been developed to look at the impact of
devaluation. The elasticity approach focuses on the impact of relative
price changes on the supply and demand of tradeable goods. Although it
allows derivation of the conditions under which devaluation improves the
trade balance, it assumes no changes in incomez, no money market, and
no capital flows (Niehans, 1984). The expenditure approach is based on
the idea that a current account deficit results from an excess of
expenditure (including imports) over output (including exports). Thus,
for devaluation to improve the trade balance it must cause either
"expenditure switching" (from tradeables to non-tradeables) or "expe-
nditure reducing" (Alexander, 1952). The monetary approach concentrates
on the impact of devaluation on the demand for money. Since tradeable
prices rise, consumers attempt to restore the real value of their cash
balances by temporarily ”hoarding" money, so that spending declines
relative to income. This improves the trade balance for as long as is
required to restore the initial real value of cash balances (Frenkel and
Johnson, 1976).

These approaches are different perspectives on devaluation rather
than rival interpretations. The expenditure approach is correct in
focusing on the gap between expenditure and output, but has, by itself,
little explanatory power. The elasticity approach helps explain
expenditure switching, but ignores expenditure reducing by assuming
constant income. Similarly, the monetary approach provides an

eXplanation for expenditure reducing, but de-emphasizes the composition

 

 

. This is true if the parameters are partial elasticities.
If they are interpreted as "total" elasticities, including all income
e”-:1:e<=‘t:s, then the theory "incorporates" income changes but the elas-

Eicrties are unobservable, thus eliminating the predictive capacity of
he theory .

20

of demand for goods by concentrating on money demand (Tsiang, 1961;
Cooper, 1971; Niehans, 1984). .

Traditionally, devaluation was considered expansionary. In the
standard Keynesian model, nominal wages are sticky so that an increase
in tradeable goods prices reduces real wages, inducing firms to expand
employment and output. However, several mechanisms by which devaluation
may be contractionary have been identified: 1) by the increase in the
cost of imported inputs for domestic production (Krugman and Taylor,
1978), 2) by redistributing income toward households with higher propen-
sities to save or to import (Diaz Alejandro, 1963), or 3) by deteriorat-
ing the terms of trade of a "large" country (Alexander,-l952). The
first mechanism is probably the most common, being particularly relevant
to semi-industrialized‘middle-income countries.

The impact of devaluation on income distribution depends heavily
on the structure of the economy. In a classical flexible-price model,
there is no unemployment and devaluation cannot affect the level of
output. In the short run with immobile factors of production, expendi-
ture switching benefits both labor and owners of capital in the trade-
able goods sector and hurts those in the non-tradeable goods sector. In
the medium term, labor will flow toward the tradeable sector and the
returns to labor will rise relative to non-tradeable prices and fall
relative to tradeable prices. And in the long run, with both factors
mobile, labor (capital) will gain if tradeable goods are more labor
intensive (capital intensive) than non-tradeable goods (Johnson and
Salope, 1980).

However, the distribution of income between labor and capital is
not closely linked to the size distribution of income in less developed
countries. This is because "owners of capital" often include large
numbers of small-scale entrepreneurs and independent farmers, while

”labor" includes relatively high-income employees of larger urban firms.

21

In a Keynesian model, devaluation may affect the aggregate level
of output and employment. Since, as mentioned above, it is not clear
whether the net effect of devaluation will be expansionary or contrac-
tionary, this further complicates the analysis of the distributional
impact., Addison and Demery (1990: 122) conclude:

While theory provides an essential framework for tracking the

distributional effects of adjustment, it does not yield unam-

biguous predictions... Researchers must therefore go beyond pure
theory to empirical analysis.

3-2-2 WW

Empirical analysis of devaluation is complicated by two
factors. First, devaluation is generally implemented as part of a
package of reforms which may include import liberalization, removal of
exchange controls, contraction of domestic credit, and so on. Second,
the appropriate comparison is between devaluation and an alternate
policy which addresses the external imbalance. Simple before-after
comparisons ignore the fact that the pre-devaluation situation was
unsustainable. These problems can be addressed in part by controlling
for other variables using regression analysis (e.g. Edwards, 1989) or by
comparing results to a control group (e.g. Kamin, 1988).

Currency devaluation is usually implemented as a last resort after
other measures to control the external imbalance have failed. The pre-
devaluation situation is generally characterized by accumulated ap-
preciation of the real exchange rate, reduced export growth, depletion
of international reserves, increasing restrictions on imports and
foreign exchange transactions, and slower economic growth (Cooper, 1971;
Connolly and Taylor, 1978; Edwards, 1989; Kamin, 1988).

Devaluation and prices: Some critics of devaluation have
questioned whether devaluation affects the real exchange rate. For
example, Godfrey (1985) argues that a devaluation may raise non-
tradeable prices enough to "negate itself within less than a year."

Indeed, it is easy to find cases in which inflation negates the effect

22

of devaluation in a short period. However, studies which isolate the
price increases attributable to devaluation (as opposed to excessive
monetary expansion and other factors) have not found any cases of
devaluation "negating" itself. Cooper's (1971) study of 36 cases of
devaluation over 1953-1969 showed that "devaluation does lead to price
increases, but not by amounts great enough to undermine the devalua-
tion.” Similar results are found by Connolly and Taylor (1976) in a
study of 18 devaluations, Donovan's (1981) review of 12 IMF
stabilization programs, and an analysis of 72 cases of devaluation by
Kamin (1988). Regression analyses by Edwards (1989) and Connolly and
Taylor (1976) confirm, however, that the effect of devaluation is
diluted by expansionary monetary policy.

Devaluation and tgggg: If devaluation is able to
influence relative prices, the next question is whether this improves
the balance of payments. Most studies find that the balance of payments
improves in two thirds to three quarters of the cases (Cooper, 1971;
Connolly and Taylor, 1976; Donovan, 1981; Kamin, 1988; Edwards, 1989).
Only Miles (1979), in a study of 16 devaluation episodes, failed to find
any impact. These studies indicate that devaluation fairly consistently
increases export growth, but the pattern of imports is more mixed,
presumably due to concurrent import liberalization programs. Because
devaluation may encourage capital inflow (or discourage capital flight),
some studies report improvements in the balance of payments even when
the trade balance does not.

Devaluation and output: The impact of devaluation on the
level of aggregate output has been addressed by a number of studies with
mixed results. Cooper (1971) found "some depression in economic
activity is frequently found" after devaluation. On the other hand,
Donovan (1981) reports that devaluation was associated with higher
growth rates, particularly when accompanied by import liberalization.

Edwards (1986) found a mild contractionary effect in the first year

 

23

after devaluation, offset by an expansionary effect in the second year.
Similarly, Kamin (1988) identified falling growth rates in the year
before and the year of devaluation, with output rebounding the year
after.

Although devaluation is often associated with temporary reduction
in growth rates, avoiding devaluation when the currency is overvalued
probably restricts growth as well. Edwards (1989) and Schafer (1989)
find a negative correlation between the degree of currency overvaluation
and economic growth.

Devaluation and income distribution: The distributional
impact of devaluation is more difficult to study because of the lack of
regularly collected indicators. Several studies report that, following
devaluation, nominal wages rise but real wages fall (Cooper, 1971;
Heller et a1., 1988, and Edwards, 1988). The implications of this
result for income distribution are not clear for several reasons.

First, published wage data generally refer to official minimum wages or
formal-sector urban wages. These figures may not reflect wages in the
rural areas and in the informal sector. Indeed, in most cases, official
wages are significantly higher than average rural incomes. Second, many
workers, particularly among the poor, are self-employed. And third,
even households with wage-earnings have diversified sources of income
(Sahn, 1990).

Heller et a1. (1988), in a study of nine structural adjustment
programs, draw tentative conclusions about income distribution from the
characteristics of the major export crops. They argue that devaluation
may have reduced income inequality in Kenya and Ghana (where small farms
produce most of the major export), but contributed to greater rural
inequality in the Dominican Republic and the Philippines (where export-
oriented plantations are important).

Bleijer and Guerrero (1988) use monthly data from the Philippines

and a three-equation model to estimate income distribution as a function

24

of macroeconomic variables. They find that unemployment and inflation
hit the poor the hardest, while the relative price effect of devaluation
and fiscal contraction tended to reduce income disparities.

Glewwe and de Tray (1988) discuss the impact of structural
adjustment in Cate d'Ivoire by examining household budget data. In
particular, they look at the characteristics of the poorest 10% and 30%
of Ivorian households, including the occupation of the household head,
the budget shares allocated to three imported foods, and the proportion
of poor households growing different crops. They conclude that bulk of
the poor, being predominantly rural and self-employed, should either
benefit from higher agricultural prices or be unaffected. The urban
poor, on the other hand, are more likely to be hurt. Similar results
are obtained from a study of household budgets in Peru (Glewwe and de
Tray, 1989).

The comparison of poor and non-poor household is further
elaborated in the "poverty profiles" developed by the Social Dimensions
of Adjustment Unit at the World Bank (see Boateng et a1., 1990 and
Kanbur, 1990). These methods are useful for examining the impact of
individual price changes, but they are only suggestive of the combined
effect of relative price increases for tradeable goods.

By contrast, Sahn and Sarris (1991) combine income and expenditure
data from five African countries and historical price data before and
after structural adjustment to calculate an index of real income for the
rural poorl. The index is a ratio of fixed-weight Laspeyres indexes of
nominal income and consumer prices. Income is divided into three
tradeable and two non-tradeable categories, while expenditure is broken

down into five tradeable and three non-tradeable groups. The results

 

1. The countries are Céte d'Ivoire, Ghana, Tanzania, Malawi,
and Madagascar. The budgets were based on the poorest 20% of households
in two regions each for Cate d'Ivoire and Ghana, small farms in three
regions in Madagascar, the Zomba district in Malawi, and rural
households in general in Tanzania.

25

indicate a mixture of gains and losses on the order of 5-10%. The
authors conclude:

that there is no unequivocal pattern of increase or decline in the
real welfare of the rural poor but that there are marked differen—
ces among countries and regions... earlier efforts which arrived
at simplified statements on the harmful or beneficial effects of
adjustment based on stylized facts were not useful. They failed
to account for sources of income, patterns of expenditure, and

movements in relative prices (Sahn and Sarris, 1991: 281-282).

The impact of devaluation has also been analyzed using context of
computable general equilibrium (CGE) modelsl. Dervis, de Melo, and
Robinson (1982) develop CGE models of three "archetypal” economies, each
with eight production sectors and seven household types. In each case,
the devaluation increases the income share of farmers, but landless
farmers and unorganized urban workers lose.

CGE models of Morocco, India, and Egypt confirm that the
distributional impact of stabilization programs are highly dependent on
the assumptions used. The impact on the urban poor is generally
negative, while the impact on the rural poor depends on the structure of
production (de Janvry et a1., 1988).

To summarize the empirical studies, devaluation does influence the
real exchange rate, although the effect is diluted by excessive monetary
expansion. Devaluation stimulates export growth, though its impact on
import growth is mixed. The trade balance and the overall balance of
payments generally improve. The impact on growth is mixed, but any
negative impact is usually temporary. Finally, the distributional

impact of devaluation depends on the structure of the economy, but the

urban poor are more likely to suffer than the rural poor.

 

1. CGE models involve a set of equations describing factor
markets, product markets, and the behavior of households and the
government. Although similar to input-output models, they incorporate
neoclassical production functions which allow substitution rather than
fixed-coefficient technology. See Dervis, de Melo, and Robinson (1982)
for a description of CGE models and Thorbecke and Berrian (1990) for a
review of applications to macroeconomic adjustment.

26

3.3 Modglpiof houggpplg_p§pgyigp

This section provides an overview of attempts to model household
behavior. It begins with a brief summary of the theory of consumer
demand. Next, various issues in the estimation of demand systems are
considered. Finally, household-firm models, which integrate the
consumption and production decisions of the semi-subsistence household
are described. Greater emphasis is given to consumer behavior than
producer behavior because the data base on household demand in Rwanda is
much richer and justifies a more sophisticated analytical treatment.

3.3.1 Theory of consumer demand

The theory of consumer demand is an attempt to model how
the consumer chooses between alternative bundles of goods subject to a
budget constraint. In its classical form, the model is static and
assumes perfect information on the part of the consumer. It is also
assumes that the consumer takes prices and income as given.
Epeferences: Several assumptions are made about

preferences to ensure that they are well-behaved (more precise
definitions are provided in Varian, 1984: 111-113):
1) Reflexivity: each bundle is as good as itself.
2) Completeness: preferences exist between any two bundles, so

that either bundle A is preferred to B, or B is preferred to
A, or the consumer is indifferent between them.

3) Transitivity: if bundle A is preferred to B and B is
preferred to C, then A is preferred to C.

4) Continuity: if bundle A is preferred to B and bundle C is close
enough to A, it too will be preferred to B.

5) Local non-satiation: even with small changes in the bundle of
goods, one can always make it better to the consumer.

6) Strict convexity: if bundles A and B are preferred to C, then a

weighted average of A and B will also be preferred to C.
Given the first four assumptions, preferences can be described by a
utility function, in which utility is a function of the quantities of

each good. This can be written as follows:

u = f(q1.q2---q,,) (3-1)
where u = utility
91 = quantity of good i

27
The final two assumptions restrict the shape of the utility function:
the fifth ensures that there are no local maxima, while the sixth
corresponds to the assumption of diminishing marginal rates of
substitution.

It is important to note that a given utility function describes
the ordering of preferences, but it is not the only function to describe
the same preferences. More specifically, any monotonic transformation
of the utility function will correspond to the same preferences, and
will thus constitute an equally valid representation of preferences in
the absence of some cardinal measure of utility.

The consumer problem is to maximize utility subject to prices (p)
and income or total expenditure (x). The solution to this constrained
maximization problem is a set of Marshallian (or uncompensated) demand
equations, which describe the demand for each good as a function of

prices and income. If these equations, denoted by q3(p,x), are

substituted into the direct utility equation, we get the indirect

utility function, v(p,x):

v(phx)==max u(q) :Ltz,pq=x
= utq1 (12.x) . q2 (17.x) . . .q,,(p.x)] (3-2)
= u‘(p.x)

The indirect utility function gives the maximum level of utility
attainable as a function of prices and income. Given the assumptions
about preferences described above, the indirect utility function must
have certain properties:

v(p,x) is continuous for all positive prices and incomes

v(p,x) is nonincreasing in prices

v(p,x) is nondecreasing in income

v(p,x) is quasi-convex in p

v(p,x) is homogeneous of degree 0 in p and x

Duality: The dual of the utility maximization problem is

the cost minimization problem. Here, the cost of a bundle of goods is

minimized subject to the requirement that a given level of utility (u')

be maintained. The solution of this constrained minimization problem

28

generates demand functions for each good, but in this case they are the
Hicksian (or compensated) demand equations, expressed in terms of prices
and utility. When these demand functions, denoted h1(p,u), are
substituted into the budget constraint, the result is the minimum cost

of attaining a given utility at given prices, known as the expenditure

function, e(p,u):

e(p,u) min pg s.t. u(q) = u

(3'3)

p1h1(p' U) + P2h2(Pr U) + - - - + pNhN(pI U)

The expenditure function can also be obtained by inverting the indirect
utility function, that is, by solving the indirect utility function for
income (total expenditure). The assumptions about preferences also
imply certain properties of the expenditure function:

e(p,u) is continuous for all positive prices

e(p,u) is nondecreasing in prices

e(p,u) is concave in p

e(p,u) is homogeneous of degree 1 in p

If preferences satisfy the standard assumptions listed earlier,
maximization of utility subject to a given level of income yields the

same solution as minimization of the cost of the consumption bundle

subject to a given level of utility. In other words,

V‘P: e(pl 11)) U

(3'4)

e(p. V(p.x)) x

The Hicksian and Marshallian demand functions can be derived
directly from the expenditure function and the indirect utility
function, respectively. In the first case, the Hicksian (or compen-
sated) demand can be obtained by applying Shephard's lemma1 to the

expenditure function:

 

1. For a proof of Shephard's lemma, see Deaton and Meulbauer
(1980a: 40).

29

ae(p, u)

api = hi(p.u) (3-5)

The Marshallian (or uncompensated) demand function can be derived from

the indirect utility function using Roy’s identityl:

__6v(2,x)
3P1
av(p,x)
6x

q1(p.x) = (3'5)

For a given level of prices and income (or prices and utility), the

Marshallian and Hicksian demand is the same. In other words,

111(17: U) ' q1(P, 8(1), 11))
(3-7)
h,(p.v(p.x)) = q1(p.x)

However, the partials derivatives with respect to price are different
because the Marshallian partial describes the impact of price holding
income constant, while the Hicksian partial assumes that utility is
unchanged. The Slutsky equation? gives the relationship between the
two partial derivatives:

aqi<p.x) = 6121 (p, u) _ aql.
apj apj ax qj

 

 

(3'3)

This equation decomposes the effect of a price change on Marshallian
demand into a substitution effect (the first term) and an income effect
(the second term). This equation can also be expressed in terms of

elasticities:

 

l. Roy's identity can be demonstrated by taking the
derivative of equation (3-4b) with respect to p1: applying Shephard's
lemma, and solving for qi (see Deaton and Meulbauer, 1980a: 41).

2. The Slutsky equation can be derived by taking the partial
of equation (3-7) and applying Shephard's lemma.

30
e“ = (521 - eisj (3‘9)

where 5%, ==the Marshallian price elasticity
514 = the Hicksian price elasticity
£1 = the expenditure elasticity of demand

Epoperties of demand: The properties of the demand
function, which are the result of the assumptions made about preferen-

ces, are the following:

1) Adding up: The total value of demand is equal to total expen-
‘diture. In other words, 2 q1(p,x)pi = 2 h1(p,u)p1 =‘ x.
2) Homogeneity: h(p,u) is homogeneous of degree 0 in p, and q(p,x)
is homogeneous of degree 0 in p and x together. ,
3) Symmetry: The substitution matrix (defined as the matrix of

Hicksian partials with respect to price) is symmetric. In other
words, 813 = S“, where Si) is the partial of hi with respect to pj.
4) Negativity: The substitution matrix is negative semi-definite.
It is useful to briefly review some of the implications of these
properties. The adding-up property appears trivial, but this property
is violated by a number of functional forms which are often used to
estimate demand (e.g. the double logarithmic form). In addition, the

adding-up property can be used to derive two useful equations: the

Engels and Cournot aggregation conditionsl:

I
H

N
hrs _
{I 1 ‘ (3-10)
N
;W1€u + wj = 0
u

The property of homogeneity implies that only relative prices and
incomes matter. In other words, it rules out "money illusion" in the
behavior of the consumer. Symmetry is merely a reflection of the fact
that consistency has been imposed on consumer behavior. With regard to

negativity, the most important implication is that the diagonal elements

 

1. These two equations are obtained by taking the partial
derivative of the adding-up property with respect to total expenditure
and the price of good j, respectively, and then converting the results
into elasticity form.

 

31
of the substitution matrix must be negative. This means that the
Hicksian own-price elasticities are negative.

Duality theory shows that, if the preferences obey the assumptions
made earlier, each direct utility function is associated with a unique
indirect utility function, an expenditure function, and set of demand
functions. Furthermore, any expenditure function, indirect utility
function, or set of demand functions which satisfies the properties
listed above will correspond to a direct utility function and thus to a
well-ordered set of preferences. This is useful in empirical work
because it is easier to derive demand functions from expenditure
functions and indirect utility functions than from direct utility
functions.

Consumer theory, as described so far, concerns the allocation of
income among well-defined goods by a single utility-maximizing entity.
Empirical research, however, is generally interested in results for
commodity categories (e.g. meat) and for household groups (e.g. rural
households). The issues of aggregation over goods and over consumers
are discussed in turn.

Aggregation over qoodg: In theory, it would be quite
possible to disaggregate "goods” into thousands of categories. In
practice, however, it is generally necessary to limit them to several
dozen at most, both because of data limitations and because of proces-
sing complexity. The issue then arises how to divide goods into
categories (this section is based on Deaton and Muelbauer, 1980a and
Phlip, 1983).

The composite commodity theory states that a set of goods can be
treated as a single good if their prices move together (Hicks, 1936).
In practical terms, this means that close substitutes (e.g. imported
rice and domestic rice) can be combined into a single category.

In order to justify further grouping, it is necessary to make some

assumptions about the structure of preferences. For example, it is

32

often assumed that preferences are weakly separable between commodity
groups. Under weak separability, the direct utility function has the

following structure:

u = f[g1(q1...q,), g,(q,.1...qb), gn(qz...q,,)] (3-11)

where u a utility
f is a function (f1 > 0 for all i)
91 is the sub-utility functions for group i

Weak separability may be understood in terms of "two-stage budgeting,"
in which the household first maximizes utility by allocating expenditure
among the commodity groups, and then allocates group expenditure among
the goods comprising each group. The implication in terms of the
substitution matrix is that:

.= 32:32.2:
‘1 “'6x 6x

0)

(3-12)

where q1 = the quantity of good i in group G
qJ = the quantity of good j in group H
Pea = a constant

A common application of this assumption is the case in which only food
expenditure data are available. By assuming weak separability between
food and non-food, the composition of the food budget can be analyzed
without reference to non-food spending patterns.

A much more restrictive assumption is strong (or additive)
separability. Under this assumption, the direct utility function has

the following structure:

u=f[g1(q1...q,) +gz(qa.1...qb) + +gn(qz...qN)] (3-13)

where u = utility
f is a function (f1 > 0 for all i)
91 is the sub-utility function for group i

lBecause it is expressed as a monotonic function of the sum of the sub-
latilities, even a utility function in which the sub-utility functions

Eire multiplied together would fit into this definition. One implication

33

of strong separability is that the substitution matrix has the following

restriction:

(3-14)

 

where qi = the quantity of good i in group G

q3 = the quantity of good j in group H

u = a constant

This equation differs from that corresponding to weak separability in
that the constant, p, does not vary among pairs of commodity groups. An
even more important implication of strong (or additive) separability is
that there is a fixed relationship between the expenditure elasticity
and the price elasticity, as first noted by Frisch (1959). This
explains the popularity of strong separability in the context of
empirical work. Nonetheless, Deaton and Meulbauer (1980a: 139) caution
that the powerful results come at the cost of strong, often unrealistic,
restrictions on preferences.

Aggregation over consumers: The next issue is concerns
aggregation of demand across consumers. In particular, under what
conditions can aggregate consumer behavior be described as if it were
the result of decisions made by a utility-maximizing representative
consumer? The simplest case is that of exact linear aggregation, in
which the average demand across consumers is a function of prices and
the average level of total expenditure. It is possible to show that
this property can only exist if 1) the demand is a linear function of
total expenditure and 2) the marginal propensities to consume a given
good are the same across consumers. Although aggregate demand in such a
model is consistent with utility maximization, the restrictions on
preferences are quite strong and unrealistic (Deaton and Muelbauer,
1980a).

Exact non-linear aggregation requires that average demand across
consumers be a function of prices and some representative level of total

expenditure. This representative level of expenditure could be a

34

function of prices and the distribution of expenditure. It turns out
that this implies that, for a given household, the marginal propensity
to consume (MPC) of each good varies linearly with the MPC of other
goods. A special case of exact non-linear aggregation occurs when the
representative expenditure level is independent of price. Under these
conditions, called Price Independent Generalized Linearity (PIGL), the
representative expenditure function and the demand function take the

following forms:

e(U.p) = [(1-u) [a1(p)]' + uta,(p)1¢]“‘ (3-15)

wi = bu-(p) + bu(p)(%‘)" (3-16)

where k and a are parameters
u is utility
a1(p) and b1(p) are functions of prices
As a approaches zero, the exponents become logarithms and the form is
thus known as PIGLOG. The expenditure and demand functions are as

follows:

e(U.p) = (1-U) log[d1(p)] + u log[d2(p)] (3-17)

kg = f1(p) + f, (p) 1096(5) (3-18)
where d1(p) and fi(p) are functions of prices
u is utility
In summary, the advantage of exact aggregation is that it

simplifies the calculation of aggregate responses to changes in income
or prices. Exact aggregations, however, imposes some restrictions on
the shape of the demand curves. The decision whether to use a model
characterized by exact aggregation must depend on 1) the degree to which
the restrictions of exact aggregation are violated by the data and 2)
the additional calculation costs involved in using models that do not

have exact aggregation.

35

3.3.2 Eppgpippgl form of demand ggpgpigpg

Economic theory does not specify the functional form of
the demand equations. Early studies, such as Allen and Bowley (1935),
estimated demand assuming a linear relationship between demand for a
given commodity and total expenditure. Prais and Houthaker (1955)
compare a variety of functional forms, suggesting that the choice among
them be based on goodness-of-fit. The double-logarithmic form has been
used often because the estimated parameters are directly interpreted as
elasticities. This procedure is acceptable when only one or a small
number of commodities is being estimated, but is inappropriate for
estimating a complete system because the equations do not satisfy the
properties of demand. For example, the double-log form does not even
satisfy adding up. This has led to the development of functional forms
which are appropriate for a system of demand equations.

Systems of dgmgnd egpations: The linear expenditure
system (LES), developed by Stone (1954), was the first demand system to
satisfy all the general properties of demand: adding-up, homogeneity,
symmetry, and negativity. The LES is highly restrictive, however,
prohibiting inferior goods and complements. Furthermore, it is based on
an additive utility function, which imposes a relationship between
expenditure and price elasticities. In spite of these restrictions (or
perhaps because of the advantages they yield), the LES has been a
Vfrequent choice of researchers (see for example Lluch, Powell, and
Williams, 1977).

The Rotterdam model is similar to the LES, but instead of imposing
homogeneity and symmetry algebraically, it allows them to be imposed
(and thus tested) statistically. Most empirical studies have rejected
symmetry and homogeneity, but it is not clear if this is a rejection of
the consistency of consumer behavior or some misspecification of the

demand model (Deaton and Muelbauer, 1980a).

36

In the 1970s, duality theory suggested the possibility of deriving
new "flexible" demand functions from direct utility functions, indirect
utility functions, and expenditure functions. For example, using an
indirect utility function in the form of the transcendental logarithmic
function, the ”indirect translog" demand system can be derived using
Roy’s Identity. The ”direct translog" system is similarly derived from
a translog direct utility function. However, these systems are non-
linear in the parameters and are thus difficult to estimate (Deaton and
Muelbauer, 1980a and Phlips, 1983).

Almost Ideal Demand System (AIDS): The flexible demand
function which has been most widely used in recent years is the Almost
Ideal Demand System (AIDS), proposed by Deaton and Muelbauer (1980b).
It is based on an expenditure function in the PIGLOG class, permitting
exact aggregation over consumers. By applying Shephard's Lemma to the

expenditure function, the following demand function is obtained:

"1 = [310 + Billogfi-fi) + Z$¢xijlog<pfl (3-19)

where wi is the budget share of good i, pi is the price of good i, and P

is the price index. In the true AIDS, the price index is defined as

follows:

log(P) = a0 + gaklogmk) + é-gZykjlog (pylog (p1) (3-20)
1:

However, the use of the true price index makes the system non-linear,
thus complicating estimation. In most applications, researchers have
followed Deaton and Muelbauer's (1980b) practice of replacing the true
price index by Stone's index, which is a geometric average of prices,

weighted by budget shares:

37

log P = E wilog(p1)
1

or (3‘21)
P = Um"
This allows the AIDS to be estimated equation-by-equation using ordinary
least squares (OLS). The advantages of the AIDS are summarized by
Deaton and Muelbauer (1980b: 312):
[The AIDS] gives an arbitrary first-order approximation to any
demand system; it satisfies the axioms of choice exactly; it
aggregates perfectly over consumers without invoking parallel
linear Engel curves; it has a functional form which is consistent
with known household-budget data; it is simple to estimate,
largely avoiding the need for non-linear estimation (provided the
Stone’s price index is used]; and it can be used to test the
restrictions of homogeneity and symmetry through linear restric-
tions on fixed parameters.
One restriction of the AIDS is that budget share is linear in log
expenditure, so that budget share cannot, for example, rise and then
fall as total expenditure increases.
Quadratic extension of the AIDS: In order to render the
AIDS more flexible, Swamy and Binswager (1983) add a quadratic term
(squared log expenditure). This modification means that the model no
longer has the property of "exact aggregation," by which the aggregation
of demand over many households can be represented by a single rational
consumer. In addition, the demand system does not correspond to an
explicit expenditure function.
0n the other hand, it allows more flexible consumer behavior,
allowing a good to be a ”luxury" (6 > 1) over some range of expenditure
and a "necessity" or "inferior" (e < 1) over another range. This
property is particularly important when the system includes a large
number of disaggregated commodities. In addition, the quadratic version
retains most of the advantages of the AIDS: it is linear in the
parameters when Stone's index is used, adding-up is imposed automatical-

ly when estimated with OLS, and homogeneity and symmetry can be imposed

and/or tested using linear restrictions on the parameters.

38

The restrictions necessary to impose adding-up if the model is not

estimated with OLS are as follows:

2:916 = 0' $911 = 0' $91: = 0, 22“” = 0 (3-22)

The restrictions to impose homogeneity and symmetry are the same as

those for the AIDS:

I
0

gen” - (homogeneity)
(3-23)
“11 = a” (symmetry)

Swamy and Binswanger (1983) find the coefficient on the quadratic
term to be statistically significant in a model of food demand in India.
Deaton and Case (1988) use the quadratic version of the AIDS in estimat-
ing demand in Indonesia and Sri Lanka. Similarly, Thomas, Strauss, and
Barbosa (1989) find the quadratic term significant for 15 of 20 products
in a demand model for Brazil. And in preliminary estimates of demand
from the Rwandan data, the quadratic terms were significant for many
budget categories, particularly in the urban areas (Ministere du Plan,
1988 and 1991).

3.3.3 Issues in the estimation of consumer demand

The simplest approach to estimating demand equations is
to use single-equation ordinary least squares (OLS). According to the
Gauss-Markov theorem, OLS yields the "best" (least variance) linear
unbiased estimates of the true parameters under conditions of classical
linear regression. These conditions are described in terms of the le
vector of error terms (6) and the ka matrix of independent variables

(X):

1) E(e) = 0

2) E(ee’) a 02 IN

3) x is of rank k (the number of variables) where k<N

4) x is non-stochastic

5) (X'X)/N approaches a finite non-singular matrix as the

number of observations, N, approaches infinity
The standard statistical tests are based on either the additional

assumption that the errors are normally distributed or, in "large"

39

samples, the application of the central limit theorem (see Schmidt,
1976: 2-7 and Judge et a1., 1988: 202-205).

As mentioned in section 3.3.2, the AIDS and the quadratic exten-
sion of the AIDS can be estimated using single-equation ordinary least
squares_(OLS) if the true price index is approximated with Stone's
index. Five issues related to the methods used to estimate the demand
parameters deserve mention.

Qpalitv and measurement grror effects: Until recently,
it was assumed that the price elasticities of demand could not be
estimated using cross-sectional data because of the lack of variation in
prices across the sample. However, a number of recent studies, starting
with Timmer and Alderman (1979), have estimated price elasticities,
making use of the fact that there may be significant spatial variation
in prices due to transportation costs, particularly in less developed
countries.

One problem with this procedure is that most household surveys
collect quantities and values but not prices per se. Unit values
(value/quantity) differ from prices in two ways. First, unit values
reflect both quality and price variation. Since higher prices might
induce consumers to choose a lower quality, the variation in unit value
will generally understate the variation in price. Thus, "price"
elasticities derived from unit values are likely to be biased upward.
Second, measurement error is likely to introduce spurious negative
correlation between quantity and unit value. For example, a positive
error in measuring quantity generates a negative error in the calculated
unit value, so the two may be negatively correlated even in the absence
of price variation (Deaton, 1987a).

One approach is to use average market prices across regions and
perhaps across seasons. For example, Strauss (1983) uses village-level
average prices instead of prices observed by individual households in a

study of demand in Sierra Leone. This reduces the quality component of

40

price variation to the extent that quality varies within the village and
reduces the measurement error in proportion to the number of transac-
tions observed within the village.

A more elaborate method of dealing with these problem is suggested
by Deaton (1987a and 1988). The procedure makes use of the fact that
household budget data are generally based on a clustered sample. If
prices are assumed constant in the cluster, then quality effects and
measurement error can be estimated from within-cluster variation. These
effects are then used to adjust the estimates of price elasticities.
Deaton (1989) compares several applications of these procedures, noting
that quality effects were relatively small in a study of demand in
Indonesia, but large in a demand study of the United States.

Estimating price response for non-food categories: In
addition to the problems related to unit values, estimating price
response is difficult when the commodity categories are highly diverse.
This is the case for most non-food categories such as clothing or
transportation. In principle, one could either disaggregate these
categories into more specific products (e.g shirts and bus trips) or
construct price indices for each category based on a subset of goods
within the category. These approaches rely on the availability of a
large number of observations of non-food purchases. This may be
difficult when such purchases are relatively infrequent, as is the case
in the rural areas of less developed countries.

An alternative is to derive price response more indirectly by
imposing restrictions on the structure of non-food preferences. As
discussed in section 3.1, strong (or additive) separability of utility
implies that the Hicksian substitution term is a function of the
marginal propensity to consume (MPC) each good and a fixed parameter
(Frisch, 1959). The MPCs of non-food categories can be estimated

econometrically, while the fixed parameter can be estimated from price

41

and expenditure elasticities of food. This is the approach used by
Newberry (1987) in a model of the agricultural sector in Korea.

Deaton and Muelbauer (1980a) argue that the assumption of additive
utility should be avoided in empirical work. Nonetheless, estimating
food price elasticities directly and deriving non-food price response
from strong assumptions is more justifiable than the widely-used linear
expenditure system which assumes strong separability among all goods.
Furthermore, even a very rough approximation of non-food price elas-
ticities is preferable to the alternative of implicitly assuming no
price response.

Zero-expenditure observations: Not all households
consume all goods during the recall period of a household budget survey.
Thus, cross-sectional demand studies typically contain a number of zero
values for the dependent variables, particularly when the commodity
categories are highly disaggregated. To the extent that the obser-
vations of the dependent variable are "clumped" at zero, the errors are
not normally distributed. More importantly, the expected value of the
error term is positive, violating one of the classical assumptions. In
this circumstance, OLS estimates are biased (see Judge et a1., 1988:
796).

The most obvious ”solution" to this problem is simply to exclude
from the regression the households that did not consume the good being
modeled. This approach, however, is not acceptable because the resul-
ting parameter estimates would suffer from sample selectivity bias. In
other words, the model would not represent the behavior of all
households (Alderman, 1986; Deaton and Case, 1988).

Another approach might be to aggregate across commodities to
eliminate the zero observations. Unfortunately, this would greatly
reduce the value of the results and even categories as broad as "animal
products" and "cereals" would still have some zero observations. A

Similar strategy would be to aggregate over groups of households. This

42
reduces the precision of the estimates and is generally only practical
when the sample size is quite large (see Gray, 1982).
An econometric solution is to adopt a "censored dependent
variable” (CDV) model which compensates for the bias due to the non-
normal error. This model takes the following form:

1'= z6-+e
(3-24)

WWW £328
The first equation determines whether the observed dependent variable
(w) will be zero or positive and the second gives the expected value of
w conditional on its being positive.

The original and most common type of CDV model is the "Tobit"
model, developed by Tobin (1958) to estimate durable good expenditures.
The Tobit model is a special case in which the two equations have the
same independent variables (x = Z) and the same coefficients (8 = 6).
More recently, Heckman suggested a two-step procedure which uses OLS to
obtain consistent parameter estimates when the dependent variable is
censored (Fomby, Hill, and Johnson, 1984: 358-364).

Several studies have used censored dependent models to estimate
demand systems, although the results have been mixed. Pitt (1983)
estimates food demand in Bangladesh using a Tobit model. He avoids
using expenditure or budget share as the dependent variable because of
the Tobit restriction that B be equal to 6. He notes that:

[if] expenditure or expenditure share is the dependent variable in

a tobit demand model and if demand is inelastic, an increase in

own-price necessarily implies an increase in the probability of

Eggsuming (positive) quantities of the commodity. (Pitt, 1983:

At the same time, the price coefficients of these goods are likely to be
biased downward by the negative effect of price on the probability of
consumption (an unrestricted CDV model would avoid these problems).

Deaton and Irish (1984) attempt to apply a version of the Tobit

model on data from the United Kingdom. They find that zero observations

43

are significantly less frequent than would be suggested by the Tobit
model. Deaton is skeptical of the validity of CDV models in demand
analysis. He notes that it is difficult to give a theoretical jus-
tification for the latent variable, particularly since zero expenditure
may be caused by non-consumption or by consumption outside the survey
recall period (Deaton and Case, 1987: 78).

Heien and Wessells (1990) estimate US dairy demand using an AIDS
with the Heckman two-step correction for zero observations. In spite of
their claim that homogeneity and symmetry are ”readily" imposed, the
standard linear restrictions that they adopt ignore the effect of prices
on the probability of zero expenditure. As McDonald and Moffit (1980)
show, the relationship between E(w) and X, and hence the restrictions
necessary to impose symmetry, are highly non-linear. Pudney (1989)
describes various complications that arise in attempting to reconcile
consumer choice and CDV models. Even adding-up cannot be readily
imposed on a set of equations in a CDV model.

In summary, CDV models would appear to be an attractive solution
to the problem of zero expenditures, but they may introduce a new set of
problems: it is difficult or impossible to impose the standard restric-
tions of economic theory, combining Tobit with the AIDS will bias the
coefficients for price inelastic goods, and the theoretical jus-
tification is not well established.

Using panel data for demand estimation: The fourth issue
is the possible use of the variation in consumption behavior within the
household across seasons. In order to avoid seasonal bias, household
budget data are often collected in several visits or "rounds." Although
ordinary least squares estimates based on annual averages for each
household are unbiased in this case, they are not efficient because they
do not incorporate the additional information provided by variation
across rounds. The fixed-effect model uses only the within-household

variation in the dependent and independent variables, whereas the

44

random-effect model uses both the variation among households and the
variation among rounds for the same household (Fomby, Hill, and Johnson,
1984: Chapter 15).

There are several limitations, however, to using this cross-round
within-household variation in household budget analysis. First, some
independent variables, such as the demographic characteristics of the
household, do not vary (or vary little) across time. For these
variables, the random effect model would yield (virtually) the same
results as a regression based on annual averages. Second, budget share
is thought to be influenced by "permanent income," for which annual
expenditure is a good proxy. Seasonal expenditure would be a less
accurate proxy for permanent income and is thus less desirable as an
independent variable. Thus, the value of cross-round variation in
demand analysis is generally limited to the estimation of price
response.

Simultaneous egpation ggtimation: Another type of
information which is not used by single-equation OLS estimation is the
correlation of error terms across equations for the same household. If
such correlation exists, OLS estimates are still unbiased but they are
not efficient because they do not use all available information. In
this case, the estimating the entire system simultaneously using the
seemingly unrelated regressions (SUR)1 model generates more efficient
parameter estimatesz.

In the two-step estimation procedure suggested by Zellner (1962),
the residuals from single-equation ordinary least squares estimation are

used to estimate the cross-equation covariance matrix. This matrix is

 

1. Although related through the correlation of error terms,
they are "seemingly unrelated" because each equation has only one
endogenous variable.

2. .One exception is the case where the independent variables
are the same in all equations. This does not apply to our model since

th: food equations contain price terms while the non-food equations do
no .

45

then used in a generalized least squares estimation of the entire system
(see Judge et a1., 1988: 444-452 and Fomby, Hill, and Johnson, 1988:
155-162).

The SUR model may be useful even when the error terms are not
correlated across equations since, unlike single-equation estimation,
SUR allows cross—equation restrictions to be tested or imposed. For
example, the symmetry of the Hicksian substitution matrix can be imposed
in the context of a SUR model. Furthermore, SUR must be used if we wish
to carry out cross-equation tests of significance, such as a test of the
joint hypothesis that 82:0 in every equation.

In summary, the SUR model is necessary to impose symmetry, and it

may be appropriate even for unrestricted estimates of the parameters.
In the latter case, the magnitude of these correlations is an empirical
issue and is subject to testing. The SUR model and associated tests are
described further in section 4.3.3.

3.3.4 fippgghold-firm modglp

Empirical models of consumer demand using cross-sectional
data have a relatively long history, extending back into the 19th
centuryl. In the context of the industrial economies where income
generally takes the form of wages and salaries, it was natural to
exclude the production side of household behavior. However, the
situation is quite different in less developed economies, particularly
in the rural sector, for several reasons. First, since agricultural
commodities are an important part of household output as well as
consumption, a given price change may affect production decisions and
income as well as consumption choices. Second, the issue of how prices
influence marketed output cannot be determined without a model that
integrates both consumption and production behavior. And third, since

agricultural households are generally self-employed, labor-leisure

1. A historical overview of demand analysis is provided by
Deaton and Brown (1972).

46

decisions are an important element of household behavior. Thus, a model
which allows labor input to vary is desirable.

One of the earliest treatments of time allocation and subsistence
production decisions is that of Chayanov (1966). He described household
behavior in terms of a subjective equilibrium between the "drudgery" of
alternate tasks and the consumption needs of the households. He drew
implications from this theory for the influence of household size and
structure on production patterns.

Becker (1965) formalized a model of time allocation which has
become the basis for modern household-firm theory. In Becker's model,
household utility is a function of "commodities," which are produced by
the household using time and purchased goods. The household must
allocate time among various work and leisure activities, and they must
distribute income from wages and other sources among various purchased
goods. Thus, they maximize utility subject to a time constraint and a
cash budget constraint. This model has been used to interpret a wide
variety of phenomena relating to the demand for convenience goods,
fertility decisions, intra-household division of labor, and queuing
behavior under rationing.

A similar model is developed by Hymer and Resnick (1969) in which
utility is a function of home-produced "z-goods" (artisanal goods and
services), home-produced food, and market goods purchased with revenue
from crop sales. Since the production choices are expressed in terms of
a production possibility frontier, time is not explicitly modeled, and
leisure is assumed constant. A key element of the model is the as-
sumption that z-goods are inferior, an assumption which is not supported
by empirical evidence (see King and Byerlee, 1978 and Liedhom and Mead,
1987).

Barnum and Squire (1979) generalize the Hymer and Resnick model by
allowing the purchase and sale of labor and by allowing total labor

input (and hence leisure) to vary. The assumption of z—good inferiority

 

47

is dropped, allowing it to be absorbed into ”leisure." The model can be

expressed as follows:

maximize:
U = U(L,C,M)
subject to:
(3-25)
p,(F-C) + wN = pMM

I.+.N-*I{= T

1v= F(H)
where L = leisure time
C = the value of agricultural output retained for
consumption . ‘
M = the value of market goods purchased
pw = the price of agricultural output
p” = the price of market goods
w = the wage rate
F s the value of agricultural output
N = sales of labor time (negative if labor is purchased)
H = time devoted to agricultural production
T = total available time

By successive substitution, the three constraints can be combined to an
expression which equates "full income" (farm profits and the value of
total available time) and the total value of consumption (the value of

goods consumed plus the opportunity cost of leisure):

(pr? - WH) + W = p,.C + pMM + wL (3-26)

The model is recursive in the sense that the profit-maximizing
production decisions can be derived without reference to consumption
decisions. The first-order conditions for profit maximization require
that the marginal value product (MVP) of labor in agricultural produc-

tion must be equal to the MVP of wage labor:

pF-g—S = w (3-27)

This expression defines the level of agricultural output and thus farm
profits and "full income." Utility maximizing consumption decisions can
then be made on the basis of prices, preferences, and the level of full

income obtained from the production decisions. The recursiveness of the

 

33-15;. A. '_.J at. .1

 

1"}

 

48

model depends on several assumptions: that there is a market for the
purchase and sale of labor, that family labor and hired labor are
perfect substitutes, and that risk is not an issue (Singh et a1., 1986).
A key result of this model is that prices affect demand for goods
and labor not just.through the familiar income and substitution effects,
but also through a "profit effect." In other words, prices influence
the level of farm profits and thus the level of income, which in turn
alters the pattern of demand. The total effect of price on consumption

can be decomposed as follows:

dC' _’ ac + ac'ax'

dpp 3}: 8x . app

 

(3-28)

where x' is the value of full income associated with profit-maximizing

behavior. The first term on the right side is the partial of Marshal-
lian demand and is negative except in the case of Giffen goods. The
second term is the profit effect and is positive for any normal good.
Thus, in the case of a household-firm, the profit effect will dampen,
and may even reverse, the negative effect of traditional demand theory.
The profit effect is particularly important when 1) the commodity is an
important source of income for the household and 2) the income elas-
ticity of the commodity is large.

The total effect of price on marketed output is written in a

similar way:

(3-29)

arm-C) . 2: -(22 . £2:
dpp app app ax‘ app

If the supply response of the commodity (the first term on the right
side) is small and the effect of price on consumption (in parentheses)
is positive due to the profit effect, then a price increase could
actually reduce marketed output.

Various approaches have been adopted for modeling the demand and

supply sides of household-firm models. Barnum and Squire (1979) use

49

data from the Muda River Valley in Malaysia where rice is the dominant
crop and model rice production with a Cobb-Douglas production function.
Demand for rice, manufactured goods, and leisure is estimated using a
modified linear expenditure system. Lau, Lin, and Yotopoulos (1978)
analyze Taiwan data using a linear-logarithmic expenditure system on the
demand side and a profit-function approach on the production side.
Strauss (1983) extends the model by disaggregating agricultural output
and purchased goods into various categories and by adopting a more
flexible demand specification. Using data from Sierra Leone, farm-
households are modeled with a quadratic expenditure function and a
constant-elasticity-of—transformation production function.

The estimated profit effect is large enough to make the impact of
price on consumption positive in four of the seven studies reviewed by
Singh, Squire, and Strauss (1986). In all of these cases, the commodity
in question was the dominant staple in the region (e.g rice in Korea and
sorghum in northern Nigeria). On the other hand, in none of the studies
did the profit effect make the elasticity of marketed output negative.

The model has been used to explore a number of issues. Pitt and
Rosenweig (1986) use the household-firm model to look at the impact of
price changes on health. Iqbal (1986) develops a two-period household-
firm model to analyze credit. Roe and Graham-Tomasi (1986) show that
the recursive nature of household-firm models disappears when risk is
introduced. Household behavior and intra-household division of labor
are discussed in the context of a household-firm model (albeit less
formally) by Low (1986) and Jones (1986), among others.

3.3.5 Summary

Models of household behavior are generally based on the
assumption of utility maximization subject to a budget constraint. If
preferences are assumed to be rational and consistent, then demand
functions will satisfy several properties: adding up, homogeneity,

symmetry, and negative semi-definiteness. A number of functional forms

 

 

50

either satisfy these restrictions or allow the restrictions to be tested
and imposed statistically.

One of the more popular models is the Almost Ideal Demand System.
Adding a quadratic income term makes the AIDS more flexible, although it
loses the convenient property of exact aggregation and no longer
corresponds to an explicit expenditure function.

Several issues in the estimation of demand systems include: 1)
adjustment for quality effects and measurement error in estimating price
response, 2) estimating price response for non-food categories, 3) the
appropriate treatment of zero-expenditure observations, 4) whether to
use the across-round variation in estimating parameters, and 5) whether
to use single-equation estimation or model the system with an SUR model.

The household-firm model integrates production and consumption
decisions, providing a more realistic view of the behavior of semi-
subsistence farm households. At the same time, these models have very

heavy data requirements.

3.4 ngfgpg effects of price and income changes

Household survey data has frequently been used to evaluate the
welfare impact of alternative policies in less developed countries. For
example, household budget data were used to evaluate the distributional
impact of wheat subsidies in Morocco (Laraki, 1988), food price policy
in Nepal (Pakpahan, 1988), rice policy in Indonesia (Mudbhary, 1988),
sugarcane-for-ethanol promotion policies in Brazil (Gray, 1982), and
structural adjustment policies in C6te d'Ivoire and Peru (Glewwe and de
Tray, 1988 and 1989).

However, these studies have generally adopted fairly rough
measures of welfare impact. Often the impact of a price increase is
assessed purely in terms of the budget share of the good in question.
This measure over-estimates the welfare impact of price increases

because it does not take into account the ability of household to

51

substitute away from the now more expensive goods. Other studies rely
on consumer surplus to measure welfare impact. Although this measure
has been shown to be seriously flawed, it remains popular among prac-
titioners because of its simplicity and the (erroneous) view that it
requires less information than do more precise measures. This section
discusses producer and consumer surplus, the more modern "willingness-
to-pay" measures, and several methods of calculating willingness to pay.

3-4-1 2£2222§£_§E£ELE§

Producer surplus is the amount of money a producer

receives for her output above and beyond the minimum she would accept
for it. Since the minimum acceptable amount is the cost of production,
the change in producer surplus is the change in net income. This can be

expressed as follows:

N 911

25 = Ax = )3 [F1 (p) dp (3-30)
1'1 p“
where F3(p) is the supply function of good i. A first-order approxima-

tions of producer surplus can be obtained from:

N
Ax-;F°1 Api (3'31)
'1

In the short run, before output has adjusted, this expression is exact.

More common is the second-order approximation of producer surplus:

N
1
A}: I 12.; 2- (F°1+F11)Ap1 (3‘32)

where the subscripts refer to time (0 is before, 1 is after).

A change in producer surplus implies a simple change in net income
which has an unambiguous affect on welfare. It is consistent with
either of the two willingness-to-pay concepts, which are discussed in
section 3.4.3. Unlike consumer surplus, producer surplus generates

little controversy.

 

 

52
3.4.2 Consumer supplus

Although welfare measures are implicitly based on the
concept of utility, the concept of consumer surplus actually predates
the formalization of the theory of consumer preferences. In 1844, Jules
Dupuit, a French engineer, developed the concept of consumer surplus to
evaluate the benefits associated with the construction of a bridge.
Consumer surplus may be defined as the amount a consumer is willing to
pay for a good above and beyond the amount actually paid for it. In
practice, we are generally interested in the change in consumer surplus

associated with a price change, defined as follows:

N p“

CS = {‘2 fq, (p) dp, (3‘33)

'1 Pu

where q3(p) is the Marshallian demand for good i. The most common way

to calculate consumer surplus is with the following approximation:

N
1
CS I 2 3(q°1+qu)Ap (3-34)

Several criticisms have been made of consumer surplus. First,
when consumer surplus is calculated from market demand curves, it
represents the unweighted sum of the consumer surplus of individual
consumers. In effect, it assumes the marginal utility of money is the
same for all consumers. Second, Samuelson (1942) showed that with
changes in more than one price, the concept of consumer surplus is not
well-defined because the result is generally path-dependent. In other
words, the value of consumer surplus varies depending on the order that
the different price changes are introduced into the calculations. Path
independence would require that the matrix of uncompensated (Marsha-

llian) price effects be symmetric:

53

6g, (p. x) = 6q2- (p. x)

for all i,’ 3-35
6 p1 6p! .7 ( )

It can be shown that this implies that preferences must be homothetic
and, hence, that budget shares must not vary with income (McKenzie,
1983). This condition is, of course, highly unrealistic in light of
empirical evidence.

3.4.3 Compensating variation and egpivalent variation

Hicks (1940) introduced the concepts of compensating
variation and equivalent variationl. These two "willingess-to-pay"
measures are defined, interpreted graphically, and compared in this
section.

Definitions: Compensating variation (CV) is the amount
of money which exactly compensates the individual for the price and
income changes, thus restoring her original level of utility. For a
price decrease, CV is the amount she is willing to pay for the change,
and for a price increase, it is minus the amount she would have to

receive to be willing to accept the change. CV can be expressed in

terms of the expenditure function as follows:

CV = e(Pi'uo) ' e(PiIui) (3’36)

where the subscripts refer to time (0 is before, 1 is after).

Equivalent variation (EV) is the amount of money which would have
to be given to a consumer in order to create a change in utility
equivalent to the price and income changes. For a price decrease, it is
the amount of money the consumer would have to receive to be willing to

give up the price change, and for a price increase it is minus the

 

1.. These concepts were first discussed in Hicks (1940), but
it was Henderson (1940), commenting on Hicks' paper, that first recog-
nized that consumer surplus, compensating variation, and equivalent
variation are different concepts (except in special cases). Henderson
also provided the graphic interpretation of these measures using utility
curves,

LIA-“v.7. ' I. m.“

I'FJ‘p-

 

54

amount she would be willing to pay to avoid the change. This can be

expressed as follows:

EV = e(po,uo) - e(p°,u1) (3-37)

where again the subscripts refer to time. Both CV and EV are defined
here as having the same sign as the welfare impact of the price and
income changesl.

Graphic interpretation: Both willingness-to-pay measures
can be divided into an income effect and a relative price effect. The
relative price effect can be interpreted as the area to the left of the
compensated (Hicksian) demand curve. To see this, we add and subtract

e(p1,u1) to equation 3-37:

EV = 9(90. U1) -e(P°I ”0) = e(Por U1) +e(P1I U1) '9(P1: U1) -e(P°I 110)
= e(p..u1) +x1-¢-:'(pl.u,)-xo (3-38)

3 AX + e(po, H1) -e(p10u1)

The first term is the change in income, while the second two terms
represent the change in income which is equivalent to the relative price
changes. If we take the derivative and the integral of the second two

terms with respect to p and then apply Shephard's lemma, we get:

EV

AX + e(Po: U1)'9(P1: “1)

9° 2:
69(p1.u)
Ax + ____1L_dp
I}; 6"! 1 (3-39)

”In
Ax -!°; 1214191, U1) dpi

By similar manipulation of equation 3-36, compensating variation can be
divided into income and relative price terms and expressed in terms of

the Hicksian demand function:

 

1. Some authors define CV and EV with opposite signs from
the definitions provided here, but it is convenient to have the sign of
CV and EV equal to the direction of welfare change.

55
AN
CV = Ax -f; hfipo, uo) dpi (3'40)
p. -1

Thus, the relative price effect of both willingness-to-pay measures can
be interpreted as the area to the left of the Hicksian demand curve over
the relevant price range. In the case of CV, the original Hicksian
demand curve is used, while for EV the final Hicksian demand curve is
used. This is illustrated in Figure 3-1 for a single price increase
from p0 to p1. The Marshallian demand curve is represented by D, while
the original and final Hicksian demand curves are ho and h1, respective-

ly.

 

 

 

Q

gov [HIHHIIEV

Figure 3-1: Compensating variation and equivalent variation

 

 

 

Comparison of measures: These two willingness-to-pay
measures are superior to consumer surplus in that they are well defined
for a consumer with consistent preferences. For CV and EV, the condi-
tions for path independence are that compensated (Hicksian) price
effects be symmetric. This, of course, is the same symmetry discussed
in section 3.3.1,-which is required under consistent ordering of

preferences (see McKenzie, 1983 and Johansson, 1987).

56

The choice between CV and EV must be based on the situation being
analyzed. If actual compensation is planned or if the "compensation
principle" is adopted as a criteria for social choice, then the compen-
sating variation is appropriate. On the other hand, if no compensation
is planned or if the goal is to minimize the welfare effect on con-
sumers, then the equivalent variation is appropriate. Some have argued
that this decision corresponds to the assumptions made about property
rights: if consumers have a "right" to the prior situation, then
compensating variation should be used, while equivalent variation is
more correct if they are assumed to have a right to the post-change
situation.

Because of its relationship to the compensation principle, CV has
been more often used than EV. On the other hand, McKenzie and Pearce
(1982) and McKenzie (1983) make a strong case for EV, arguing that it
allows multiple scenarios to be compared to the initial period since the
base period prices are used to evaluate all the alternatives. By
comparison, alternative outcomes cannot be compared using CV because the
prices differ. Thus, EV is a better measure of utility because it is
ordinally related to utility while CV is not.

The willingness-to-pay measures have been extended in various
ways. Blackorbry, Donaldson, and Maloney (1984) consider intertemporal
measurement of welfare. They show that the sum of discounted instan-
taneous surpluses cannot be an exact measure of welfare change, but it
can provide bounds on the true value. Helms (1985) discusses wil-
lingness to pay in the context of risk, demonstrating that expected CV
is a valid measure of welfare only under highly restrictive conditions.
Johansson (1987) reviews a wide body of literature on the use of welfare
measures to evaluate environmental benefits. And de Borger (1989)
adapts the concepts of CV and EV to the case of government programs

which provide in-kind transfers to consumers.

57

In spite of the theoretical superiority of CV and EV, many
practitioners continue to use consumer surplus as a welfare measure in
spite of its problems. For example, in a review of the trade
literature, Jeon and von Furstenberg (1986) were not able to find a
single case of CV or EV being used in calculations of the cost of
protection. One reason for this is that:

there appears to be a widespread impression in the literature that

computation of CV or EV is intrinsically more difficult or re-

quires more information than calculating the area under Marshal-
lian demand functions... In fact, this is not so... (Deaton and

Muelbauer, 1980a: 188- -189)

This brings us to the methods of estimating compensating variation and
equivalent variation.

3.4.4 Mephods of estimating willingness to pay

There are essentially four strategies which have been

 

proposed to estimate willingness to pay, given observable Marshallian*x

\
I

 

 

1‘. , . .r' 2"”4
demand equations. The first is to derive an explicit form of they” ./ g
.i. -101MWM.~~w«~~~«w~~wMW““”” iii;
(Egpggdituregfunction from the demand functions. The second method is to ‘
r N -

 

 

, ”i”,
use a Taylor-series expansion to estimate th indirect utility function.

_,._...,.,.. MC», -

 

’nfl- -ww- ‘

The third approach uses a Taylor-series expansion to estimate thqg)

”,me
”w,"

rexpenditure function} And the fourth strategy is to numerically_ C 7

integrate the Hicksian demand function. Each of these is described

“xiv—moo... ‘ Haw-«W "“"vI-..,--

briefly below.

P»- -1“ ~--

gaussman method: The most obvious strategy is to derive

_an explicit form of the expenditure function. /Hausm:h (1981)

“k. H-
,_ t u..- --—-

 

.- MW—IW

demonstrates how to do this with a single price change. The first step

is to combine Roy's identity and the observed demand function to form a
W“ ~~~~~~~~~~~~~~~~ .__

differential equation, the solution of which is the igdiEEEt~utility

Mu". . "

.efEEEEEEE. Solving the indirect utility function for income yields the

expenditure function, which can be used to calculate EV and CV exactly.

 

Unfortunately, this procedure has limited applicability. De Borger

(1989: 216) notes that:

58

[Hausman's method] is difficult to generalize to a many-commodity
world, and even in a two-good framework it will not always be
useful as for many demand functions the corresponding differential
equation will not have a close-form solution.
Obviously, these steps are unnecessary if the demand function is derived
from an explicit expenditure function, as is the Almost Ideal Demand
System. The fact remains, however, that only a few demand functions
correspond to explicit expenditure functions.
McKenzie method: The second approach involves a Taylor-

series expansion of the indirect utility function (McKenzie and Pearce,

1982 and McKenzie, 1983). The money-metric function, M(p1,x;p°),
defined as the cost of reaching the level of satisfaction, v(p1,x), at
base prices, p0. Thus, equivalent variation is simply the change in the

money metric function resulting from income and price changes. This
change is approximated using the Taylor-series expansion (shown here

expanded to the second order):

(3-41)

  

M(dX)2

 

N N N
1 3%! day 1
+ _ + _—.d dx + _
2;; .1 apiapj _1 apiax pl 23

where M = money metric function
x = income or total expenditure
pi a price of good i

By defining the money metric appropriately, this equation can be
converted into a function of observed demand parameters (shown again to

the second order):

N
AM(p,X) - -; qldpl + (TX
.1

1 aql
- d fld
2 N1;_1(q‘aax 6p:]dp p‘pj Ea):

where qi = quantity of good i

(3-42)

The third-order terms are rather involved, and McKenzie (1983: 48)

admits that it "may appear to be a highly tedious procedure." He

 

59

correctly notes that computer procedures can simplify the task, but
higher-order derivatives of the demand function must be derived by hand,
the order increasing with the desired level of precision. Furthermore,
as discussed later, Dumagen and Mount (1991) show that McKenzie's
approximation of the money metric may not be as accurate as alternative
approaches. \
Hicks metng: The third method is to approximate the
expenditure function/using a Taylor-series expansion. Deaton (1980) and
McKenzie (1983) illustrate this approximation up to the second-order
approximation, although the idea is attributed to Hicks. Dumagen and
Mount (1991) extend the expression to include the third-order term.

The first step is to decompose the two willingness-to-pay measures
into income and price effects, as shown in equation 3-38. The differ-
ence between the two expenditure function terms can then be approximated
as a Taylor-series expansion. In this way, the first-order approxi-

mations of EV and CV can be expressed as:

1); N
1 89 (P1, U1)
EW’I Axr+ ——- —————-———( - ) = Axr- A
l! .1 5P1- P01 p11 1:; qli p1
(3-43)
N N
CV II Ax + -l_" #- (PM‘Pu) = Ax ’ p qoxApi
' .1 i .1

by applying Shephard's lemma and defining Ap

pn-po. From this expres-
sion, it is clear that Laspeyres and Paasche price indexes are first-
order approximations of CV and EV, respectively1 (see Deaton, 1980).
Figure 3-2 illustrates the first-order approximations of compen-
sating variation (CV1) and equivalent variation (EVl) for a single price
increase. The graph shows that the first-order approximations are more
accurate when the Hicksian demand is highly inelastic. It also demon-

strates that, in absolute value, EVI is a lower bound for equivalent

variation, and CV1 is an upper bound for compensating variation.

 

1. Specifically, if nominal income (x) is constant, then the
Laspeyres index is 100(x-CV1)/x and the Paasche index is 100(x-EV1)/x.

'v—r-

60

 

 

 

Q

E CV1 M1111] EV1

Figure 3-2: First—order approximations of willingness to pay

 

 

 

The Taylor-series can be expanded further to obtain a second—order

approximation of equivalent variation as follows:

ae(p ,u)
EV ' AX + .17; —a:D-—1 (poi-p11)

4}

63e(p , u)

2! —; ; ap -——3———pj 1 (P01'P11)(p°j‘plj) (3‘44)
N N N

‘ Ax ' 2 91113191 + %' 1 ; SllepiApJ

where 5111 is the Hicksian substitution term evaluated at the final

position. Similarly, the second-order approximation of the compensating

variation can be expressed as:

N 1 N N
CV s Ax — z: qMApi — .2; ZSOHAplApJ (3-45)
-1 -1 j-1

The only difference between these two equations is that the expression
for EV is based on demand parameters evaluated at the end point (after
the price and income changes), whereas the CV equation is based on

parameters evaluated at the initial point (before the changes).

61
Figure 3-3 illustrates the second-order approximations of EV and
CV for a single price increase (labeled EVZ and CV2, respectively). The
slope of the right-hand edge of each area is equal to the slope of the

compensated (Hicksian) demand curve at the respective reference points.

 

 

 

 

 

E CV2 M EV2

Figure 3-3: Second—order approximations of willingness to pay

 

 

 

The expenditure function approximation, like the approximation of
the money metric, yields estimates of any desired degree of accuracy,
although increasing precision requires increasingly higher-order
derivatives of the demand function. However, the expenditure function
approximation is easier to derive because there is only one income term;
the money metric approximation involves various income-price interaction
terms. In addition, Dumagen and Mount (1991) show that a third—order
approximation of the expenditure function is generally more accurate
than a third-order money metric approximation, at least when tested
using a two-good model with quasi-linear demand.

Vartia method: The fourth approach to estimating wil-
lingness-to-pay, proposed by Vartia (1983), uses numerical integration

of the compensated (Hicksian) demand curve. This method uses the fact

62

that willingness to pay can be interpreted as the area "under" the
compensated demand curve as price changes. Although the compensated
demand curve is not directly observed, Vartia suggests an iterative
procedure: the price change is divided into small increments and for
each increment, consumer income is adjusted by an amount to compensate
for the price change, leaving utility constant. This compensation
increases the demand for the good (provided it is normal), so that with
each iteration we trace the steeper compensated demand curve rather than
the uncompensated demand curve.

The amount to compensate the consumer for each price increment can
be estimated "crudely“ (using CV1) cause as the change in price ap-
proaches zero, the difference between various approximations also
approaches zero. If we start at the initial point, utility is held at
its original level so the sum of the adjustments to income is the
compensating variation. Likewise, if we start at the final point and
work backwards, the utility is held constant at its final level, so that
the equivalent variation is calculated.

The Vartia method has a distinct computational advantage over the
two Taylor-series approaches: once the computer routine has been
written, increasing the level of precision is just a matter of raising
the number of iterations (hence diminishing the size of the price
increments). Unlike the Taylor expansions, no additional (human) effort
is needed to improve accuracy.

3.4.5 Summary

Consumer surplus remains the most common welfare measure
in applied economic research, in spite of the fact that it is not well
defined for multiple price changes due to the problem of path-depen-
dence. Although the two willingness-to-pay measures, compensating
variation and equivalent variation, are well defined, they have not

enjoyed widespread adoption.

 

63

Although the willingness-to-pay measures are based on unobserved
compensated demand functions, they do not require more information than
is needed to calculate consumer surplus. Several estimation approaches
have been suggested. In cases where the demand function corresponds to
an explicit expenditure function or indirect utility function, wil-
lingness to pay can be calculated exactly. When this is not possible,
the indirect utility function or the expenditure function can be
approximated using a Taylor-series expansion. The result is an expres-
sion for willingess to pay in terms of observed demand parameters.
Finally, willingness to pay can be estimated through a numerical

integration of the estimated compensated demand function.

 

CHAPTER 4

RESEARCH METHODS

4.1 erv'ew o esearch a roac

The research approach of this study can be divided into three
phases. In the first phase, data from the Rwandan National Budget and
Consumption Survey (ENBC) is used to model household behavior. Section
4.2 describes the data collection and processing methods of the ENBC.
In section 4.3, the procedures for estimating demand as a function of
income, prices, and household characteristics using the ENBC are
reviewed. Section 4.4 describes the modeling of the supply side of
household behavior, relying on both ENBC data and outside estimates of
agricultural supply elasticities.

In the second phase of the study, the impact of devaluation on
prices will be modeled using 1) hypothetical prices based on the
distinction between tradeable and non-tradeable goods and 2) historical
prices for the seven months after devaluation. This phase is described
in section 4.5.

The third phase combines the price changes and the model of
household behavior to estimate the effect of devaluation on different
types of households. The impact on demand, on nutritional intake, and
on household welfare are simulated. The methods used in this phase of

the study are described in section 4.6.

4.2 W

The National Household Budget and Consumption Survey (ENBC) was
carried out over the period 1983 to 1985 by the Ministry of Planning of
the Republic of Rwanda. Technical and financial assistance during the
data collection was provided by French agency for development assis-

tance, while the data analysis and publication of results was supported

64

65

primarily by the U.S. Agency for International Development, with
additional contributions by the Cooperation Francaise, the Food and
Agriculture Organization of the United Nations, and UNICEF.

The objectives of the survey were to provide information on

household economic activities to government organizations and inter- I
t

M
Two specific goals of the ENBC were 1) to provide more accuratewweights

national agencies in order to improve policy making and project design.

 

 

(based on the composition of expenditures) for the construction of price
indices and 2) to improve national accounts, particularly with regard to
agricultural production for own consumption in the rural areas.

4-2-1 W

The ENBC sampling method makes use of the administrative
units of Rwanda. The country is divided into ten prefectures, 149
communes, and roughly 1500 secteurs. The ENBC defined 36 secteurs as
urban, following their designation as ”predominantly urban" by the 1981
Demographic Survey. Only one commune, Nyarugenege, which contains the
city of Kigali, is entirely urban.

For the rural sample, 90 of the 148 rural communes were selected
using a complex system of multiple stratification: repeated samples were
drawn until one of them was "representative" according to several agro-
ecological variables. A few communes in the Zaire-Nile Ridge were
reportedly excluded because of their remoteness. In spite of these
manipulations, Scott (1985) recommended treating it as a random sample
in devising the weighting system.

In each selected commune, one secteur was randomly chosen, and in
each secteur, one census district was selected. An exhaustive list of
households in each district was assembled and three randomly selected
households were interviewed for the full set of questionnaires. Thus,

the sample size in the rural area is 270 householdsl.

 

l. A subset of the questionnaires was administered to a
larger sample, but the budget data were too incomplete to use.

66

The urban area was separated into two strata: the commune of
Nyarugenge (including Kigali proper) and the rest of the urban area
(including Butare, Ruhengheri, Gisenyi, and some outskirts of Kigali).
In the first stratum, 15 of 49 "Observation Zones" were selected with
probability proportional to the population as estimated by the National
Fertility Survey of 1983. Ten households were randomly selected from an
exhaustive list of households in each "Observation Zone." These f
households would receive the full set of questionnaires. In the second
stratum, 20 of the 60 census districts were selected with equal
probability. An exhaustive list of households in each district was
prepared and between two and ten households were randomly selected,

depending on the total number in each districtl.

4-2-2 222s.221122£i22.ms£fls§a
The data collection in the rural areas took place from
November 1982 to December 1983, while the urban data collection covered
the period October 1984 to January 1986. In both the rural and urban
areas, the data collection was conducted in four rounds, each one
involving two weeks of daily visits.

The survey used six main questionnaires, as well as some smaller
supplemental questionnaires. These questionnaires are described briefly
below (more complete descriptions can be found in Ministere du Plan,
1987 and 1988).

Daily transactions: This questionnaire recorded all transactions
carried out by members of the household during the day of the interview.
The transactions included purchases and sales (including those of
labor), loans made and received, and transfers given and received. Both
cash and in-kind transactions were included. The data collected
included the quantity, value, place of transaction, which member of the

household carried it out, and with whom the transaction took place.

 

1. As in the rural survey, a larger sample was used for a
few of the questionnaires, but the budget data for these households was
too incomplete to allow analysis.

AI

67

This information was collected daily for two weeks each round, making 56
days per household.

Retrospective transactions: This questionnaire was almost
identical to the daily transaction questionnaire, but it was adminis-
tered differently. The interview was carried out only once each round,
but the respondent was to recall all "large" transactions since the last
interview three months before.

Food consumption: The components of every meal consumed by
members of the household were recorded in this questionnaire. In
theory, the enumerator was to weigh each component during preparation.
Since this was not always possible, recall was used on occasion. Also
recorded were the origin of the food (purchased, gift, or own produc-
tion), the number of people present, and food consumed by family members
away from home. These data were collected over seven days during each
round for a total of 28 days per household.

Structure and activities of the household: This questionnaire
provided information on the various members of each household surveyed,
including age, sex, level of education, and occupation. This informa-
tion was collected in one visit per round.

Daily activities of the household: Each activity occupying more
than 15 minutes carried out by each member of the household was recorded
in this questionnaire. This information was collected daily for two
weeks during each of the four rounds of the survey.

Household assets: This questionnaire recorded a variety of types
of physical assets including livestock, farm tools, furniture, kitchen
equipment, and other household effects. Information on the size,
layout, and construction of the house and any other buildings was also
collected. This questionnaire was completed in one visit.

Supplemental questionnaires were also used. For example, surveys
of local markets were used to collect information on prices and the size

Of traditional units of measure.

68

4-2-3 W

In order to make the budget and consumption data useable,
several processing tasks were necessary. These included cleaning,
weighting, and valuing transactions in kind. These tasks are briefly
described in this sub-section.

Cleaning the data: The data cleaning phase involved the
usual tests of logical coherence between different variables. The data
were checked for inconsistencies between product and unit (e.g. liters
of cloth), between product and quantity (e.g. 5,000 kg of spices),
between product and price (e.g. one potato costing S 10), and between
product and type of transaction (e.g. a sale of a watch from "own
production"), among others.

In addition, careful attention was devoted to matching business
expenses and types of revenue generated. It was discovered that many
purchases of bananas and sorghum for beer brewing were mistakenly
classified as "commercial purchases” rather than "production expenses."
At a higher level, the transactions of households with serious imbal-
ances between cash revenue and cash expenditures were verified in the
questionnaires. In a number of cases, it was found that business
expenses were wrongly classified as consumption expenses.

In all the cleaning efforts, however, a conservative approach was
adopted, in which corrections were limited to cases in which an obvious
data-entry mistake had occurred or an unambiguous case could be made
that the enumerator miscoded certain transactions. Thus, although the
corgegpppdepfe~pefweepfigcome and expenditure is quite close on average,
there are a few households‘with no repdrtedwgghrzes of income and a
handful of merchants with apparently large operating losses.

Designing the weighting system: The spatial weighting
(or expansion) factors were calculated to allow extrapolation from the
sample to the universe. These were calculated as the inverse of the

probability of selection of a given household. This, in turn, is the

69

product of the proportion of households selected in the district, the
proportion of districts selected in the sector, and so on. In the urban
area, the formula varies between the two strata, but the principle is
the same. Throughout this study, weighted averages and percentages are
used, with the sole exception of the regression analysis where weighting
observations is not appropriate (see Deaton and Case, 1988).

The temporal weighting is used to extrapolate from sample data to
annual estimates. This factor is the inverse of the proportion of days
in the year which were covered by the survey recall period. Thus, it is
based on the proportion of days for which data exist in a given quarter
and the proportion of quarters for which data exists (normally four).
For small transactions, the daily transaction questionnaire is used, so
the temporal weight is generally around 6.5 (365 days per year divided
by 56 days covered). For large transactions, both the daily and
retrospective budget questionnaires are used, covering most of the year,
so the weight is around 1.0 in most cases. The threshold between small
and large transactions was set at 200 FRw (about US $2.00) for the rural
areas and 500 FRw for the urban areas. In both cases, the bulk of
transactions are recorded in the daily budget questionnaire.

Valuing transactions in kind: Budget data invariably
includes various types of non-monetary transactions such as gifts,
barter, and consumption of own roduction. In theory, one would like to
value these transactions according to their opportunity cost, as
reflected in the prices perceived by the household for those same goods.
In practice, there are two complications in applying this procedure.

The first issue is whether to measure opportunity costs by
purchase prices or by sale prices (the two differ significantly due to
transportation and transaction costs). In principle, the purchase price
is a better measure of the opportunity cost for a household which is a
net buyer of the good in question, while the sales price is more

appropriate for a net seller. Nonetheless, the purchase price was

70

adopted to value all in-kind transactions for two practical reasons: 1)
purchase price data are more abundant since purchases are smaller and
more frequent than sales, and 2) valuing home production with purchase
prices allows more direct comparison with the cash expenditures.

The second issue is at what level of geographic and temporal
aggregation to calculate the average purchase prices to be used in
valuing transactions in kind. After some experimentation, it was

decided to adopt a system with the following priorities:

1. ‘ Average purchase price within the same region and round
of the survey, provided 10 transactions are available;

2. Average purchase price within the same region over the
year of the survey, provided 10 transactions are avail-
able;

3. Average purchase price in the sector (urban or rural)
over the year of the survey, provided 10 transactions are
available;

4. Average sale price in the sector (urban or rural) over
the year of the survey multiplied by 1.1;

5. A ”plausible" price based on experience.

In the rural sector, the ”region" refers to the geographic zone, of
which there are five. In the urban area, "region" refers to the city,
of which the four largest are covered by the survey. The largest number
of transactions in kind were valued at the first level. Less than 10%
of the transactions had to be valued using the fourth and fifth methods.
The use of "plausible" prices at the fifth level was only necessary for
such unusual items as the gift of a dog and the loss of a dugout canoe.
These represented a very small portion of the total value of transac-

tions.

43 W
4.3.1 Assumptions about preferences
Any effort to estimate consumer demand must rely on
assumptions, whether explicit or implicit, about the structure of
preferences. Although in theory, these assumptions should be based on a
priori knowledge, in practice, it is often necessary to impose restric-

tions on preferences to compensate for deficiencies in the data.

 

71

Nonetheless, it is important to 1) avoid unnecessary restrictions, 2)
ensure that the restrictions are not seriously contradicted by the data,
and 3) make explicit the assumptions behind the restrictions.

It is assumed that households are a single decision-making unit
which maximizes utility subject to time constraints, production technol-
ogy, and market prices. Household utility is assumed to be an increas-
ing function of the quantity of goods and services it consumes and of
non-material qualities of life such as leisure time and health. In the
absence of data on these "quality of life” variables, it is necessary to
assume that leisure and other "quality of life” characteristics are
weakly separable from the consumption of goods and services. This
allows the demand for goods and services to be modeled without reference
to other determinants of utility.

Price variables for non-food categories are also unavailable. The
categories are too broad to be represented by a single price, and the
small number of observations for any specific good make it impossible to
construct a price index for each category. In order to obtain estimates
of non-food price elasticities, we assume strong separability between
food and non-food categories, as well as between the various non-food
categories. This procedure satisfies the argument that strong separa-
bility be limited to broad categories of goods (Phlips, 1983:70),
although Deaton (1974) argues that it is not justified even in this

1

case 0

These separability assumptions can be summarized in terms of the

form of the direct utility function.

 

1. On the other hand, Deaton (1987b: 100) appears to accept
additive preferences as a plausible restriction in applied demand
analysis.

 

72

U= U{¢{f(qfl.qu...qm) +;gj(q,,,) . 16(2)” (4-1)
where U(°) a utility
¢(-) = any monotonic increasing function
f(°) = the food sub-utility function
qfl_ = quantity of food i
gJ(°) a the sub-utility function for non-food
category j
qnj a quantity of non-food category j
k(°) = the sub-utility function for non-
material characteristics
2 = vector of non-material characteristics

of household which affect utility
The arbitrary monotonic increasing function, ¢, is necessary to ensure
that utility is represented ordinally and not cardinally.

The functional form of the sub-utility function f is directly
related to the functional form of the food demand equations. Rather
than start with an explicit sub-utility function and derive the corre-
sponding demand function, a demand function is adopted which, when
estimated in restricted form, satisfies the demand properties discussed
in section 3.3.1. By duality theory, we know that this corresponds to a
well-behaved utility function, although in this case the utility
function cannot be expressed in an explicit form.

4.3.2 Functional form of demand egpations

The functional form used to estimate consumer demand for
food is the quadratic extension of the Almost Ideal Demand System (AIDS)
with Stone's price index to deflate total expenditure. The food

equation thus takes the following form:

"1 ‘ 510 4‘ pilln(%) ‘* Bu{ln(%)]2 *‘ £171ka + g‘Hjhl (P1) (4‘2)

where wi a budget share of good i
x = total expenditure of the household
P = Stone's index, defined by
ln(P) = 2 W1 log(pi)
zk = household characteristic k
gf = number of food equations in model
pj = price of good j where there are N goods
8 y a = estimated parameters

73

The functional form used to estimate the demand for non-food categories
is the same except that the price terms are dropped for the reasons
described in section 4.3.1.

It is worth describing briefly each of these variables. The

dependent variable, wt, is the budget share: the annual value of con-

sumption of good i divided by total expenditure over the year (defined
below). The assumption behind this model is that the quantities
consumed (including consumption of own-produced food) are influenced by
the level of total expenditure (including home production), market
prices, and the demographic composition of the households.

Total expenditure, x, is the sum of cash expenditures on final
consumption, the value of home produced agricultural products, the value
of gifts received in kind for consumption, and the value of goods and 4
services received through barter. Two types of expenditure were
intentionally excluded: 1) business expenses such as seed, hoes, bananas
for making wine, hired labor for production activities, and goods
purchased for resale, and 2) large durable expenditures such as the
purchase of land, buildings, and vehicles. Excluded for lack of data
was the value of non-agricultural home production. Evidence from the
rural household asset questionnaire indicates that home production of
baskets, mats, and wood utensils averages less than 0.5 % of total
expenditure. On the other hand, the value of wood collected for
household use in the rural sector may be on the order of 10% of total
expenditure (see Ministere du Plan, 1988: 34).

Total expenditure is deflated using Stone’s price index, P, which
is essentially a geometric weighted average with budget shares as the
weights. The index is based on prices for a set of 35 food and non-food
items. The weights used to calculate the urban and rural indices are
based on the average budget shares in the urban and rural areas,

respectively.

74
The three demographic variables, 2k, are the number of household

members aged 16 or older, the number of members under 16 years of age,
and a dummy variable to identify the sex of the head of household.
Although the definition of the "head of household” was originally
intended to reflect the division of labor, in practice the enumerators
named the husband/father as the head whenever one was present. Thus, a
female head of household represents a woman who is single, divorced, or
widowed, or a woman whose husband lives elsewhere for whatever reason.
Finally, the food prices, PJ' are a combination of unit values,
when the household reported buying the good in question, and imputed
values, where no purchases were reported by the household. The imputed
prices are based on the system described in section 4.2.3. As mentioned
above, prices are not included in the equations that estimate non-food
demand.
4.3.3 Estimatiop of demand
Based on the discussion in section 3.3.3, several deci-
sions were made regarding the estimation methods. First, the model will
be estimated both in unrestricted form and under the symmetry restric-
tions in order to compare results. Second, quality and measurement
error effects will be investigated, but will not be the primary focus of
the analysis (see section 4.3.5). Third, a Tobit model will be estimat-
ed on part of the data for the purposes of comparison, but the welfare
analysis will be based on the linear models (see section 4.3.5).
Fourth, the variables used will be annual averages, ignoring across-
round variation. And finally, the cross-equation correlation of error
terms will be tested and, if indicated, the seemingly unrelated regres-
sion (SUR) model will be adopted.
I This section describes the methods used to estimate demand using
single-equation OLS and using the SUR model, as well as the methods to

impose symmetry on the SUR model and to test hypotheses. The derivation

75

of demand elasticities from the estimated coefficients is discussed in

section 4.3.4.

Single-egpation OLS estimation: We start by converting
the functional form of the food demand equation, equation (4-2), into a
statistical relationship by adding an error term to represent the effect
of missing variables and the measurement error in the dependent vari-

able. Then, it can be put into matrix notation as follows:

gt

wi = $01 4' pizln(%) + piz{1n(%)]2 + 231711;): + ; ajjln (Pj) "' ei

'1

. 5 £2 "

Pm5>m%naaaflga+e (M,
11

pi:
Y1:
Y1:
Y1:

3‘11.

 

 

= budget share of good i
x = total expenditure of the household
= Stone's index, defined by
ln(P) = 2 W1 109(p1)
price of good j where there are 9 goods

gf = number of food equations in system
zk = household characteristic k

B y a = estimated parameters

'0
LA.
II

The dimensions of these matrices can be described in terms of the number

of observations (N), the number of food categories in the system (g5),
and the number of independent variables (k¢=g£+6)1. The first set of

brackets represents the independent variables, where each element is an

le vector except p which is an ngt matrix. The second set of brackets

 

1. In the rural model, N=270, gf=17, and kf=23, while in the
urban model, N=297, g£=21, and kf=27.

 

76

contains the coefficients, each element being a scalar except for a
which is a gtxl vector.
The non-food demand equations can be expressed in a similar way

except that prices are omitted from the independent variables:

“’1 = 910 "’ pnln(%) + Bu{ln(%)]2 * £271ka + e1

= [1 ln(%) [ln(—:)]2 Z1 Z2 Z3] '90; + e1. (4-4)
911
9:1
Yu
Va:
.731.

 

 

 

where the notation is the same as in equation (4-3). Each element in
the first set of brackets is an le vector, while those in the second
set are scalars. The number of estimated parameters in the non-food
equations, kn, is six.

The independent variables can be combined into one ka matrix
called X, while the parameters can be represented by a kxl vector called

B1 (k=k£ for food equations and k=kn in the non-food equations). The

demand equation can be expressed as follows:

The ordinary least squares (OLS) estimate of Bi can be written as:
B, = (X'X)'1x'w, (4-6)

Ordinary least squares provides the best unbiased linear estimate
under the classical regression assumptions discussed in section 3.3.3.
However, single-equation OLS estimation does not allow cross-equation

restrictions or hypothesis tests. Furthermore, it is not efficient if

77

the error terms are correlated across equations. In this case, we need
to use seemingly unrelated regression (SUR).

Seemingly unrelated regression: The seemingly unrelated
regression model combines g equations into one regression model in order
to use information about 1) cross-equation correlation of the error
terms or 2) cross-equation restrictions on the parameters. The vari-

ables and coefficients are assembled as follows:

 

 

 

W1 ’}(1 o . 01 ’3] "e11
:5 0 A; 0 B2 e2
w3 = 0 X3 B3 + e3 (4_7)
wg‘ LO 0 0 XS, th‘ e94

 

 

 

 

 

The subscript identifies the commodity equation; for example, x1 refers

to the ka matrix of independent variables for equation i. The system

can be rewritten more concisely as:

w = 78 + e (4'8)

where

t
I

a Ngxl vector of budget shares for g goods
and N households

an Ngxgk block diagonal matrix with an ka
matrix, X1, in each block

B - an gkxl vector of parameters for g goods
and k variables

an Ngxl vector of error terms for g goods
and N households

XI
II

(D
II

The standard assumptions concerning the error terms in the SUR model are

that:

E(e) =0 and E[ee']=2®IN (4-9)

where E = a gxg matrix, each element of which
represents the covariance between the
error terms of equations i and j for the
same household
IN = an NxN identity matrix

 

78

In other words, the demand equation for each good has a different
variance, and there is a positive covariance between equations for the
same household but zero covariance between equations across households.
The SUR model is estimated in two steps. First, the OLS residuals
are used to estimate the 2 matrix. Specifically, each element of the 2

matrix, denoted 013, is consistently estimated by (éi'éj)/(N-k*), where
61 is an le vector of OLS residuals from equation i and k' is the

average number of estimated parameters per equationl. In the second
step, the estimated covariance matrix is used in a feasible generalized

least squares format to calculate the SUR estimate of B:
B" = [ 'X' (2'1®I,,)3? ]'1 7' (2'1®I,,) 91 (4'10)
The estimated covariance matrix of this estimate, designated 5, is:
6' = cov(§) = ['2' (2'1®I,,)'X' 1'1 (4‘11)

The Breusch-Pagan test can be used to determine whether the cross-
equation correlation of error terms is significant, which would suggest
the use of the SUR model even for models without cross-equation restric-
tions. This test is described at the end of section 4.3.3.

Imposing symmetry: Symmetry requires that the compensat-
ed effect of the price of good j on the demand for good i be equal to
the compensated effect of the price of good i on demand for good j. In
other words, the Hicksian substitution matrix must be symmetric. The

symmetry restriction can be expressed in terms of the estimated parame—

ters as follows:

 

l. The adjustment for degrees of freedom in the denominator
is not necessary for consistent estimation of an, but this adjustment

may reduce bias in finite samples (see Judge et a1., 1988: 450).

79

$11 3 511

Q‘ . Q’ .
—l€11 ‘ 33611

Eifiil+wj—5 321(EJJ4-w1-5)
P1 “'1 P1 "’1

where 8 is the Kronecker delta (equal to 1 when i-j and 0 otherwise) and
62” is the Hicksian elasticity of demand for good i with respect to the
price of good j. The expression for the Hicksian elasticity is derived
in section 4.3.4. Because we are interested in the case where i is not
equal to j, the Kronecker delta, 6, is equal to zero.‘ Using the

definition of budget share, w1=p1q1/x, we can write the condition for

symmetry as:

 

 

211;: .wj .sz(:a .wi
F5 ”3 ‘pl “9
(4-13)
3.1. x¢1j+gi_l_lpq =31 x¢fl+gl__p1q1
Pj quj P1 X P1 Pij P; X
After canceling terms, this expression reduces to the following:
“11 3 “11 (4-14)

In other words, symmetry of the matrix of price coefficients, a, is
. necessary and sufficient for symmetry of the Hicksian substitution
terms.

Because symmetry involves restrictions involving parameters in
different equations, imposing or testing symmetry must be carried out
within a seemingly unrelated regression (SUR) model. A set of m linear
restrictions can be written in the form RB-r=0, where R is an mxk
matrix, B is the kxl matrix of parameters, and r is an mxl vector.
Using the notation of equations 4-10 and 4-11, the restricted SUR
estimator can be written in terms of the unrestricted SUR parameters as

follows:

80

~

3‘ = B" + 612' (R CR')‘1(r-R§) . (4-15)

Imposing symmetry on the gtxgt matrix of price coefficients, :2, involves
gf(gf-l)/2 restrictions on the parameters.

e s s : It is useful to test various hypoth-
eses concerning the estimated coefficients. These tests are based on
the assumption that the error terms are normally distributed. If the
errors are not normally distributed, then the tests will hold "approxi-
mately" for large samples, making use of the central limit theorem (see
Judge et a1., 1988: 268-270).

A group of m linear hypotheses can be expressed as RB-r=0, where R
is an mxk matrix of constants, B is the kxl vector of parameters, and r
is an mxl vector of constants. For single-equation linear hypotheses in
the context of single-equation OLS estimation, we can use the standard F
test:

(RE-r)’ [R(x’X)'1R’ rims-r) /m

(§’§)/Tfi-k) " F(m,N-k) (4-16)

 

To test linear hypotheses in the SUR model of the demand system, we can
use the following Wald test where the estimated covariance matrix, C, is

defined in equation 4-11:
(RE-IO’LRCR0‘4(R§-r) ~ x; (4‘17)

This expression is only asymptotically distributed as chi squared
because the covariance matrix, C, is not known and must be estimated.
Judge at al. (1988) recommend an extended F-test as being somewhat more
cautious than the chi-squared test. It is similar to the single-
equation F-test except that the numerator includes the cross-equation

covariance matrix, 2 (within C), and the denominator collapses to 1.0.

81

(R8-r)’(RCR’)'1(R§-r)

m

 

' F(m.N9'9k') “'18)
By defining the R matrix and the r vector appropriately, these

tests can be used to test the single-equation null hypotheses presented

in Table 4-1. Similarly, the cross-equation hypotheses in Table 4-2 can

be tested in the context of the SUR model using the latter two tests.

Table 4-1: Single-equation hypotheses to be tested
IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII-I-I-II-IIII-I-I-I-I-l

 

Parameter re- Number of Explanation

strictions - restrictions

311881280 2 Total household expenditure has no

. effect on budget share of good i

812:0 1 Budget share of good i is linear
in log expenditure

yn=0 9 Sex of head of household has no
effect on the budget share for
good i

mu=0 for all j 9: Prices have no effect on the bud-

get share for good i

Finally, in order to determine whether the SUR is appropriate for
the unrestricted version of the model, we need to determine the statis-
tical significance of the off-diagonal elements of 2. The Breusch-Pagan
test uses the fact that, under the null hypothesis that 2 is a diagonal

matrix, the following asymptotic distribution is true:

9 1-1

2
;: 01
'2 ;-1 .11 j]

The test expression is the number of observation times the sum of cross-

 

equation correlation coefficients for each pair of equations. If the
value of this expression exceeds the appropriate critical value, the

null hypothesis is rejected and the SUR model should be adopted.

82

Table 4-2: Cross-equation hypotheses to be tested
—

 

Parameter re- Number of Explanation

strictions restrictions

811-81220 29 Total expenditure has no effect on
for all i budget share of all goods

812-0 9 Budget share is linear in log ex-
for all 1 penditure for all goods

711'712'0 29 Household size has no effect on the
for 311 1 budget share for all goods

711-0 9 Sex of head of household has no ef-
for all i feet on budget share for all goods
auao 9,2 Prices have no effect on the budget
for all i,j share for all goods

«13 - a“ (gf—gfl/Z Hicksian (compensated) price ef-
for all i,j facts are symmetric

4.3.4 perivapion of elasticities of demand

In the previous section, the methods for estimating the
demand coefficients was discussed. In this section, the price and
expenditure elasticities of demand are expressed in terms of these
coefficients. The expenditure (income) elasticities and food price
elasticities are calculated directly from estimated parameters. Non-
food price elasticities are derived from the other elasticities and the
assumption of additivity in preferences. Finally, the demand elastici-
ties for the excluded category, "other food," are derived using the
homogeneity and adding up from consumer theory. Each of these are
discussed below.

Elasticity of demand with respect to expenditure: The
elasticity of demand with respect to income (total expenditure) can be
derived by noting that:

ln(wi) = 145%) = 1an + lnqi - lnx (4-20)

Taking the partial of equation (4-20) with respect to ln x, we get:

83

alnwx _ alnpi + 31nq1 _ alnx
alnx ’ 791m: alnx alnx

 

= O + 61' - 1 (4'21)

where 51 is the income elasticity for good i. Rearranging terms and

using equation (4-2), we obtain the expression for the income elastici-

ty:

 

 

ei=1+Zi§=1+aigé=l+%+%1n{g) (4-22)
Since the expenditure elasticity varies with the budget share and the
level of total expenditure, it is normally evaluated at the mean values
of these variables.

at od em nd w t s ect to rices: The

compensated (or Hicksian) elasticity of demand for good i with respect
to the price of good j can be similarly derived. First, we take the
partial of equation (4-20) with respect to p3:

alnwi _ amp, + 311193 _ alnx _ 6 + - alnx

alnpj - dlnpj alnpj amp, _ U - 61an (4-23)

where 6 is the Kroenecker delta (equal to 1 if i=j and 0 otherwise) and
5x; is the compensated price elasticity of demand. The last term in
equation (4-23) is not zero because nominal income (x) must change to

compensate for the price change. Using the definition of Stene's index

and the fact that real income (x/P) must remain constant:

N
312(5) 62 wilnpl

 

= P = alnx _ 1.1 = alnx . w. (4'24)
Therefore,
alnx _
_—alnpj ' “'1' (4-25)

Solving equation (4-23) for epf and substituting in equation (4-25), we

get the following:

84

 

. alnug 8w; 1
. . = —_ . - = — - " 4'26
5" alnpj + w] alnpj w! + "J b ( )

Using the expression for wi in equation (4-2):

611 = $1 + Wj ' 5 (4-27)
1
where 8 is the Kroenecker delta. By substituting equations (4-22) and

(4-27) into the Slutsky equation, we obtain the uncompensated (Marsh-

allian) own-price elasticity:

. a. O 2
a“ = e“ - wje“I = T: + "1 - 1 - will + LB: +—£:’ln(%)]

(4-28)
a
7,1}! ' 1 ’ Bl: + 251956;)

The uncompensated cross-price elasticity is derived in a similar way:

_ - .. “1‘ 511 2912 x
611 - 3x1 ' W15: ‘ 7;“ ” "1 " WJ{1 * '71-‘71"(79)

(4-29)
1 x

Green and Alston (1990) suggest that the above method for deriving
the price elasticities is incorrect. Specifically, they argue that the
partial of Stone’s index with respect to p3 is not simply wJ, as shown
in equation (4-24). Rather, it should also include the influence of pi
on W} because the budget share is itself a function of prices. Because
they view the price index and the budget share as functions of each
other, Green and Alston hold that it is necessary to solve a system of
simultaneous equations to derive the elasticities.

This argument appears to overlook the fact that the budget share
in the Stone's price index is not a function of prices, but rather a
constant base-period weight for averaging the prices in the index. Just
as the base-period quantities in the (arithmetic) Laspeyre index do not

change, so the base-period shares in the (geometric) Stone's index are

85

constant. Indeed, a price index with variable weights would not be
well-defined: if demand were sufficiently price elastic, price increases
for a set of goods could reduce their budget shares enough to result in
a decrease in the price index.

D r ved - d e ast‘c ’e : The price elastici-
ties of non-food categories are approximated by assuming strong (or
additive) separability both among non-food categories and between food
and non-food categories. As discussed in section 3.3.1, strong separa-

bility implies the following relationship between income and price

elasticities:
6,1 = 6 4) e1 - eiwju + «1) (4-30)
where 613 a price elasticity of good i with respect
to the price of j
6 - the Kronecker delta (equal to one if i=j
and zero otherwise
¢ = -u/x
£1 = income elasticity of good i
wi = budget share of good i

This implies a fixed relationship, which depends on the parameter m,
between the income and price elasticities of each strongly separable
categoryl. Setting i=j, this equation can be solved for ¢ to get the

following expression:

511 * ‘1“9
= 4-31
¢ 51(1'WIG1) ( )
Following the procedure used by Newberry (1987), we can obtain an
estimate of ¢ using equation (4-31) with the estimated price and income
elasticities of food. Then, this parameter and the non-food income
elasticities can be combined in equation (4-30) to derive values for the

non-food price elasticities under the assumption of strongly separable

Preferences.

 

 

1. Additive preferences imply symmetry among separable
grOLIps and price homogeneity of non-food demand equations.

86

Degived coefficients for ”other food": The coefficients
for ”other food" are derived by using some of the restrictions of
consumer theory: adding up and homogeneity. Adding up requires that the
budget shares add up to one. Given the functional form used in this
study, adding-up is ensured when the sum of each coefficient across
equations is zero. Thus, the expenditure and household composition
coefficients of "other food" are each defined as minus the sum of the
corresponding coefficients in the g modeled equations. From these
coefficients, the elasticity of demand for "other food” with respect to
household expenditure can be calculated (Phlip, 1983).

Homogeneity requires that a proportionate increase (or decrease)
in all prices and incomes not affect the estimated budget shares. Such
a change will affect equally the numerator and denominator of (x/P),
leaving deflated expenditure unchanged. Thus, the only parameter

restrictions necessary for homogeneity are on the price terms, “13° In

particular,

9

32a” = 0 (4-32)
n

is necessary and sufficient for homogeneity.

The price terms associated with ”other foods" are derived as
follows. Starting with the homogeneity condition, we separate the
coefficient representing the effect of the price of ”other foods" on the

demand for good i, “an and move the summation of the remaining terms to

the right side:

9%

u
(the subscript 0 refers to ”other foods"). The coefficients represent-
ing the effect of other prices on the demand for ”other food" are
obtained by assuming a limited symmetry: ¢°1=¢1°. Finally, the own-price

termifor "other foods” can be obtained by again applying homogeneity:

87

9'1

coo = - a0 (4-34)
Z; 1

It should be noted that the price parameters for "other food" can be
derived only after all the other price parameters, both food and non-
food, have been obtained.

4.3.5 dd tiona ssu s n demand estimation

In Chapter 3, two sources of bias in the estimation of
household demand were discussed. In this section, we describe some
methods to evaluate the importance of these problems in the context of
the present model., The first topic is the potential bias of using unit
values in place of true prices as independent variables. The second is
the effect of zero-expenditures on the estimated income and price
elasticities.

Qpality and measuremegp error effects: Deaton (1987a,
1988) points out that the use of unit values (the value of a transaction
divided by the number of units purchased) to estimate price elasticities
may generate biased estimates of price and income elasticities. As
discussed in section 3.3.3, the biases are caused by quality effects and
measurement error. The correction methods devised by Deaton are complex
and this is not the focus of the present study. Nonetheless, it is
worth investigating the magnitude of these biases in the case of the
Rwandan budget data.

The method suggested by Deaton relies on the assumption that true
prices do not vary within the "cluster" of nearby households into which
the samples of many household surveys are organized. First, measurement
error effects can be detected by estimating the impact of "price" on
demand within the cluster. Second, the income elasticity of quality can
be estimated by regressing unit values on total expenditure within each
cluster. These two tests can be implemented with the Rwandan ENBC data

since it was collected using cluster sampling (there are 90 rural

88

clusters of three households each and 35 urban clusters averaging 8.5
households each).

In order to look for ”price” effects on demand within the cluster,
the basic food demand equation is modified by replacing the constant

term with a set of dummy variables, one for each cluster in the sample:

www;

where G a an Nxc matrix of c dummy variables, each one
representing a cluster
c - the number of clusters
Because we are not interested in the numerous coefficients on the dummy
variables, the estimation can be simplified by subtracting the cluster

means from each variable. The "within cluster” estimates are obtained

by:

9,, . (X’MGX) 'lx’Mcw, (4-36)

where an.‘ a kxl.vector of ”within" parameter estimates
for food commodity i
MG =- an NxN matrix = IN-Gm'crlc'

As Deaton (1988: 420) explains:

Since the model is supposedly one of spatial price variation, and

the since price variation within clusters should be absent, the

subtraction of the cluster means should make estimation of a price

elasticity impossible.
Thus, the presence of measurement error effects is tested by the
significance of the price coefficients in this regression.

The second test focuses on the quality effect. Since true prices
are assumed constant within each cluster, any within-cluster relation-
ship between unit value and the level of income (total expenditure) must

be a reflection of quality differences. The following regression

identifies this relationship:

89

ln(pi) - c; + (3,1111%) + fin{ln(-%)]z + $732,: + 91 (4-37)

k-l

where G - an Nxc matrix of dummy variables for the
clusters
c I the number of clusters
The elasticity of quality with respect to income can be derived by

taking the partial of unit values (p) with respect to income (x):

alnpi B i .x 4-38
3111): 911 + 231-311%?) ( )

 

The null hypothesis that the expenditure coefficients are zero (Ho:
811-812-0) is equivalent to the hypothesis of no quality effects for good

i. If a quality elasticity is significantly different than zero, we

would expect it to be positive.

2 r -e t bs tions: For reasons discussed in
section 3.3.3, a censored dependent variable model was not adopted for
this study. Nonetheless, it is worth comparing the price and income
elasticities derived from the standard linear regression model and those
derived from a limited dependent variable model which explicitly

incorporates zero-expenditures.

The Tobit model, discussed in section 3.3.3, is based on the

following log likelihood function:

lnL = 1 F(-x’B,02) + —-llna2 - i( -x’B)2 (4-39)
’2 n[ 1 1 y; 2 202 5’1 1

where F(-) a the cumulative normal distribution function
xi'B - the predicted value of the dependent
variable (y) for observation i
y1 = the actual value of the dependent variable

The first summation is over observations where the dependent variable is

zero, assuming that probability of such an observation is equal to the

probability of the latent variable being negative. The second summation

is over observations where the dependent variable takes a positive value

and.follows the form of a standard likelihood function.

90

Because the likelihood function is non-linear, it must be maxi-
mized using iterative techniques. The software package, LIMDEP,
performs this non-linear maximization, generating estimates of the
parameters, B, and their corresponding standard errors.

. The coefficients of this model must be interpreted carefully since
a change in an independent variable alters both the probability of the
dependent variable being positive and the expected value conditional on
its being positive. In order to derive the partial of y with respect to

x3, we start with the unconditional expected value of the i"h observa-

tion of dependent variable:
E(y,) - F(x{fl/O)E(y1|y>0) (4-40)

The first term on the right side is the probability that y is positive,
while the second is the expected value of y given that it is positive.

Taking the derivative with respect to an independent variable, x3, we

 

get:
arm) , 32ml y>0) amxgp/a)
= F(x /0) + E(y >0) (4-41)
5x” ‘3 6x1, 1' y x11

McDonald and Moffitt (1980) show that this can be expressed in terms of

estimated parameters as follows:

arm) _ _ £,_ff , f, 2
——a—xj—- ‘Fip[l 21}: E + Xijp 4' a? in

f f2 f

where F1 8 F(zi) a the cumulative normal density
function evaluated at 21
f1 = f(zi) = the normal density function
evaluated at z,
21 = xi'B/O

(4-42)
4’

 

The standard income and price elasticities can thus be calculated by
substituting this expression into the corresponding coefficients (8 and

4:} in the elasticity equations 4-22, 4-28, and 4-29. These elasticities

91

can then be compared to the results obtained using the standard linear

model.

4-4 WW

As discussed in section 3.3.4, household-firm models incorporate
the impact of agricultural price changes on household income, and thus
on consumption and marketed output. This ”profit effect" tends to
dampen, or even make positive, the elasticity of food consumption with
respect to own price. The elasticity of marketed output, although
'reduced, usually remains positive.

4.4.1 . c o ces 0 come

In the household-firm model, prices affect the income
level of the household. In section 3.4.1, it was shown that this effect
can be calculated using first- or second-order approximations of
producer surplus. These approximations may be considered the short- and
long-term effects of prices on income, respectively, since the first-
order approximation does not incorporate any change in output, as would
be appropriate in the short term.

There are three practical complications in using these equations.
First, the concept of "quantity" is not meaningful for many income
categories such as ”commerce" and "other artisanal activity." Fortu-
nately, the expressions for the short- and long-run effect of prices on
income can be rewritten in terms of values, the proportional change in

price, and (for the long-run effect) the proportional change in output:

 

N N AP
Ax ' z: Q1Ap1 '3 z Q1p1 i (4'43)
-1 1-1 pi
v u
1 1 q Ap
Ax-;—(q +q)Ap=;—q .1+—E——‘- (4-44)
_1 2 01 11 1 .1 2 011901 q“ P01

A second issue concerns the assumptions about business expenses.

In this study, we assume these costs change in the same proportion as

92

revenue (this is done by replacing gross revenue in these equations with
net revenue). This may be somewhat unrealistic in the case of agricul-
ture, although variable costs are relatively minor in this case,
representing only 9% of the value of agricultural output (Ministers du
Plan, 1988). This assumption is more realistic for commerce, a sector
in which intermediate expenses are quite important.

The third issue is how to deal with imbalances between net income
and total expenditure at the household level. Although income and
expenditure are highly correlated, there are important differences due
to saving and dissaving, transfers, and measurement error. Perhaps the
most conservative approach is to assume that-a given change in net
income results in a change in expenditure of the same proportion.

Under these assumptions, the short-run effect of prices on income
is simulated using the proportion of net income for each household
obtained from each type of activity. This information is available from
the ENBC data. Urban income was classified into 15 categories, while
rural income was divided into 24 groups.

4.4.2 Su r o s of a riculture

Simulating the long-run effect of prices on income
requires data on the supply response, particularly for agricultural
commodities. The ENBC data set is not appropriate for estimating
agricultural-supply elasticities because land, labor, and input use are
not available at the level of individual crops.

In this study, we make use of agricultural price supply elastici-
ties estimated for Rwanda by Ansoanuur (1991). The estimates are based
on time-series data covering the period 1971-1989. Production data were
assembled from the Ministry of Agriculture and the export marketing
boards, while price information was obtained from Ministry of Planning
sources. The double-log functional form was used in most cases,

although the semi-log form was adopted in a few cases where it yielded a

closer fit.

93

The dependent variable was the volume of production in most cases,
although the number of trees was used in the coffee equation. The
independent variables (expressed in log form) included the price of the
commodity, the legal minimum wage deflated by the consumer price index,
the real price of hoes, and the level of rainfall. In the case of
coffee and tea, three years of lagged prices were added to reflect the
lag between new planting and new production. The price of other crops
was also added in the case of a few pairs of close substitutes (white
potatoes and pyrethrum, bananas and coffee, and beans and sorghum).

There are a number of limitations of this approach to modeling the
household as produCer: l) labor-leisure decisions are not explicitly
modeled, 2) estimates are based on single-equation regressions using
only a few prices, and 3) few of the estimated elasticities are signifie
cantly different from zero, perhaps reflecting the low quality of the
original data.

On the other hand, the supply elasticities are well within the
range of those estimated for the same crops in other less developed
countries (see Askari and Cummings, 1976). Furthermore, the direct
price effect on income, which is estimated more accurately, is likely to

be more important than the output effect.

4.5 Price changes associated with devaluation

The next phase involves adopting some set of price changes
associated with devaluation. This information is combined with the
model of household behavior described in sections 4.3 and 4.4 to
simulate the impact on household welfare and nutritional intake, as
described in section 4.6. Both historical and hypothetical prices are
used, each with their own advantages and limitations. Each is discussed

in turn.

94

4.5.1 Historicai ppice data

The historical prices are based on monthly data collected
by the Ministry of Planning in the capital city of Kigali during the
year before and the six months after the October 1990 devaluation. This
data source has the obvious advantage of simulating the actual price
trends in the country.

There are, however, several drawbacks to using these data. The
most important complication is that an unsuccessful military invasion of
the country took place in October 1990, making it difficult to isolate
the effect of each event on prices. The invasion has resulted in
significant security measures within the country and strained relations
with neighboring countries, particularly Uganda and Burundi. The
security measures have affected prices in various ways, particularly by
impeding the internal flow of people and goods with checkpoints. The
strained relations with Uganda have restricted trade between the two
countries, as well as international trade which normally flows through
Uganda to and from the coast.

A second problem is that only five months of post-devaluation
price data from Kigali are available. A longer time series and a sample
of rural prices would be desirable. To the extent that the proportional
change in prices varied across the country, this simulation may be
biased.

4.5.2 Hypothetical prices

The alternative approach is to adopt hypothetical prices
according to a priori knowledge of the impact of devaluation and the
nature of different goods and services in Rwanda. The literature on
devaluation, reviewed in Chapter 3, focuses on the distinction between
tradeable and non-tradeable goods. The rural component of the Rwandan
household budget survey contains codes for 405 goods and services, while
the urban component has codes for 825 goods and services. Each product

was classified as tradeable or non-tradeable based on a judgement as to

95

whether the price of the product is determined by international markets
or by domestic demand and supply. Although the judgement is somewhat
arbitrary, in most cases the appropriate choice was obvious.

Most of the staple food crops were considered non-tradeable
because their low value/bulk ratio prevents any significant amount of
international trade in these commodities. Export crops such as coffee,
tea, and pyrethrum are obviously tradeable, as are imported foods such
as rice, wheat flour, vegetable oil, and most processed items.

Beans represent perhaps an intermediate case. 'First, imports
represent around half of all marketed volume but only 15% of domestic

consumption. Second, beans are imported informally so that the price is

 

partly a function of the parallel exchange rate. In this study, it is
assumed that the price increase for beans is one quarter that of pure
tradeables (see Appendix A).

All services were considered to be non-tradeable, while most
manufactured goods were considered tradeable. Although a number of
manufactured goods are produced in Rwanda, as described in Chapter 2,
many of them compete directly or indirectly with imported products.

Since the demand analysis is done at a much more aggregated level,
with only 17 to 20 food categories and nine non-food groups, it was
necessary to aggregate the tradeable-nontradeable information to this
level. The price change for a given category is set equal to the
weighted average of the assumed price change of tradeables and non-
tradeables, with the weights equal to the tradeable and non-tradeable
components of the category.

The relationship between nominal devaluation and the relative

Enrica of tradeables and non-tradeables is studied by Edwards (1989).
UB:ing pooled time-series data for 12 less developed countries and a
fixed-effect model, he estimates coefficients between 0.49 and 0.68,
meaning that "with all other things as given, a nominal devaluation has

been transferred in a less than one-to-one real devaluation in the first

 

96

year" (p. 141). Using a different specification and 29 devaluation
episodes, he obtains an estimate of 0.60 for the year after devaluation
(p. 268). In this study, we will adopt the latter figure. Thus, the
November 1991 increase of 67% in the Rwandan exchange rate (expressed in
francs per US dollar) would result in a 40% increase in the relative
price of tradables within a year of devaluation.

Although this study focuses on the effect of price changes
associated with devaluation, the same methods could be used to simulate
the effect of other hypothetical price changes. For example, changes in
the administratively-set rates for water and electricity or variations
in the price of individual food commodities could be modeled. Of
course, the price changes would have to be at the level of aggregation

of the budget categories used in the demand model.

4.6 ct of c han 3

At this point, we have described the methods for estimating a
model of consumer demand, an approach for incorporating the effect of
prices on income, and the use of both historical and hypothetical
prices. In this section, we describe the methods for measuring the
welfare impact and the nutritional impact of price changes on house-
.holds.

4.6.1 Efifecp of pgice cganges on demand

Because the functional form being used in this study does

not have the property of exact aggregation, we cannot simulate the
change in demand using a single demand equation of a representative
household. Instead, the demand must be calculated for each household
and then summed. For household h and good i, the quantity consumed can

be written as follows:

97
X x

q,”- = arm-(J .91.. z.) —” (4-45)
P F51

where q“, - quantity of good i consumed by
household h
wufi-)- demand function describing budget share
' for good i and household h

xh - total expenditure for household h

P a Stone's price index to deflate
expenditure

ph s gxl vector of prices for household h

zh a 3x1 vector of household characteristics

for household h
put a price of good i for household h

The quantities can then be summed over households for.each good to
obtain the aggregate quantities. .Prices affect demand in three ways: 1)

directly through the price vector, ph, 2) indirectly through the price
index, P, and 3) indirectly through total expenditure, xh, since income

is a function of the prices of output. These three types of influence
represent the substitution effect, the income effect, and the profit
effect, respectively.
4.6.2 ct r ce c n es on utr tion
The impact of price and income changes on nutritional
intake is calculated by combining simulated changes in food consumption
with the nutritional coefficients for each category of food. This can

be expressed as follows:

9 _
ACb = 2 c, AgM (4-45)
1-1

where Dch = change in caloric or protein intake for
household h
c1 a coefficient relating the caloric or
protein content per unit of good i

dqm a change in consumption of good i by
household h
The precision of this method is related to the degree of disaggregation
of the food categories. In this study, we use 17 food categories in the

rural areas and 21 in the urban areas. Although the degree of disaggre-

98

gation is quite high for a demand analysis, it does contain some
heterogeneous categories such as ”other meats" and "prepared meals.”

A more finely disaggregated analysis of the Rwandan ENBC food
consumption data was carried out using 180 food categories (see Mini-
sters du Plan, 1988). Although the demand analysis cannot be carried
out at this level of disaggregation, we can use these results to obtain
average nutritional coefficients for the broader categories. Thus, the
nutritional coefficient for "other meat" is based on a quantity-weighted
average of 20 types of meat other than beef.

Once again, the nutritional impact is calculated for each house-
hold, based on the diet of that household, the sources of income, and
the estimated food demand elasticities for that household. This allows
us to make full use of the diversity of household behavior as reflected
in the survey sample.

4.6.3 e o ‘ e cha es on ouseho d we fare

In section 3.4, a number of approaches to measuring
welfare impact were compared. In this study, we make use of seven
measures: consumer surplus, three approximations of compensating
variation, and three approximations of equivalent variations. They are
summarized in Table 4-3.

The first-order approximation of compensating variation (CV1) is

the simplest and most commonly used welfare measure. It is the only
measure which does not require any knowledge of the shape of the demand
curve, relying entirely on the price and quantity data at the original
position before the price change. The first-order approximation of the
equivalent variation (EVI) is similar, but it uses the "after” quantity
rather than the ”before" quantity. The expressions for CV1 and EV1 are
given in equations 3-43. Graphically, these measures may be considered
"rectangular” approximations of EV and CV, as shown in Figure 3-2.

Consumer surplus (CS) is approximated as a trapezoid, that is, as

a Second-order approximation of the "true” consumer surplus. Although

99

Table 4-3: Selected welfare measures
IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII-I-I-I-I-I-I-I-I-I-II

 

Symbol Measure Approximation method

CV1 .Compensating variation First-order approximation
CV2 Compensating variation Second-order approximation
cvi Compensating variation Vartia method (n iterations)
CS Consumer surplus Second-order approximation
Eva Equivalent variation Vartia method (n iterations)
EV; Equivalent variation ‘ Second-order approximation
EV1 Equivalent variation Firstforder approximation

this measure is not well-defined for multiple price and income changes,

as discussed in the previous chapter, it is calculated in this study as

a basis of comparison with the willingness-to-pay measures. Equation 3-
34 is used to calculated consumer surplus.

The two second-order approximations (EV: and CV2) are calculated

using the Hicks method which involves a Taylor-series expansion of the
expenditure function. The expressions for these two welfare measures
are given in equations 3-44 and 3-45. Graphically, these may be thought
of as "trapezoidal" approximations of CV and EV, as illustrated in
Figure 3-3.

The Vartia approximation of compensating variation (CVh) and

equivalent variation (svn) involve an interactive procedure, as de-

scribed in section 3.4.4, so it cannot be expressed as an equation. In
this study, twenty iterations are used to calculate this welfare
measure, although some experimentation is done with 50 iterations.

Each of these measures includes a term for the change in net
income (or profit) due to changes in output prices. This term (Ax) can
be calculated using short-term producer surplus or long-term producer

surplus, given in equations 3-31 and 3-32 respectively. Because of

100

uncertainty regarding the supply elasticities, most of the results are
calculated using the short-term producer surplus which assumes no supply
response. However, sensitivity analysis is used to explore the impact
of incorporating supply response in the model.

Consumer surplus and the two 'willingess-to—pay” measures are
expressed in monetary terms, yet clearly the utility derived from one
Rwandan franc is not the same across households. No attempt is made to
measure or assume a relationship between the marginal utility of money
and household income. Nonetheless, in order to incorporate, at least in
a rough way, the idea that the marginal utility of money declines with
income, the results are presented as a percentage of household expendi-
ture.

For example, substituting equation 3-31 into 3-45, we can write
CV1 as a proportion of expenditure as follows:

CV1.”

531 N 4%1
x ‘4‘?! X; 7A?!

.1 x

(4-47)
N

Ap " Ap
3 2:131 1 ‘ zz'GI——i
.1 pl .1 pi

where f0, is the base-period share of net income from good i and wb1.is

 

the base-period share of total expenditure allocated to good i1. This
is the measure used by Sahn and Sarris (1991). As they note, this
measure overestimates the welfare loss of consumer price increases and
underestimates the welfare gain from output price increases because it
does not incorporate household response to price changes.

Expressing the welfare impact as a percentage of household
expenditure allows for an intuitively simply interpretation of the
results. EV/x is the percentage change in real income equivalent to the

price changes being simulated. Similarly, CV/x is the percentage of

 

1. Strictly speaking, this interpretation requires the
assumption that expenditure is equal to net income.

101

real income which would be necessary to compensate the household for the
price changes.

Each of these welfare measures is calculated for each household in
the sample, based on the sources of net income, the structure of
consumption, and the demographic composition of the individual house-
holds. Only then are the welfare measures averaged over different
groups of households defined by region, occupation, or income. In this

way, the full diversity of households in the sample is exploited.

CHAPTER 5

HOUSEHOLD BUDGET PATTERNS IN RWANDA

In this chapter, the basic results of the National Household
Budget and Consumption Survey (ENBC) are presented to provide context
for the discussion in the chapters to follow. Section 5.1 reviews the
characteristics of Rwandan households. In section 5.2, the composition
of household income is described. Section 5.3 analyzes the level of
total expenditure which is used as an indicator of household welfare and
the composition of expenditure across different types of households.
Finally, section 5.4 provides additional analysis of the agricultural

economy of Rwanda.

5.1 wa d 0 1d

This sections presents a brief overview of the basic demographic
characteristics of Rwandan households. For the purposes of the ENBC,
the household is defined as a group of people, generally related, that
live and eat together. Under this definition, semi-permanent "guests"
and domestic employees are included in the household, but family members
who live elsewhere are not.
. . The average household in Rwanda has 4.9 people, including 2.7
adults and 2.3 children, as shown in Table 5-1. The heads of household
average somewhat less than 48 years of age, and about one fifth of the
heads of household are female. These national averages are determined
primarily by the rural sector, which accounts for about 95% of the
total. It is useful to compare urban and rural households.

Urban households tend to be younger than rural households, as
shown in Table 5-1. Less than a tenth of the urban heads of household
are over 60 years of age, whereas almost a quarter of the rural heads of

household are. As a consequence, urban households are more likely to be

102

103

in the child-bearing years: 57% of the heads of household in the cities
are 40 years or less in age, while only 36% of the rural heads are in

this age group.

Table 5-1: Characteristics of rural and urban households

 

Rural Urban Total
Avg age of head of household 48.2 40.4 47.8
Pct of households by age
30 or under 16.8 % 29.3 % 17.4 %
31-40 years 19.3 % 27.3 % 19.7 %
41-50 years 22.1 % 22.4 % 22.1 %
51-60 years “ 17.3 % 12.1 % 17.2 %
Over 60 years 24.5 % 9.0 % 23.7 %
Total . 100.0 % 100.0 % 100.0 %
Average size of household 4.9 -5.6 4.9
Number of adults 2.7 2.4 2.7
Number of children 2.3 3.2 2.3
Pct households by size
1-3 people 26.2 % 28.2 % 26.3 %
4 people 13.8 % 18.4 % 14.0 %
5 people 12.5 % 15.3 % 12.6 %
6 people 10.6 % 15.0 % 10.8 %
7 or more people 36.9 % 23.1 % 36.2 %
Total 100.0 % 100.0 % 100.0 %
Pct of households with
female head of household 20.6 % 16.6 % 20.4 %

 

Source: Rwandan ENBC.

Urban households are also larger than rural households, on
average. As shown in Table 5-1, this difference is due to the larger
number of children in urban households. One explanation for this
pattern is that a higher proportion of urban households are in child-
bearing years, as discussed above. Another factor is that children and
adolescents from rural households often migrate to the city, staying
with relatives while attending school or looking for work.

Urban households are somewhat less likely to be female-headed.

In both urban and rural areas, female heads of household are, on

average, older and have smaller households than their male counterparts.

104

About 38% of urban female head are 40 years or under in age, and just
12% of rural female heads are in this age group. This may reflect the
importance of widows among the female-headed households, particularly in

the rural sector.

5.2 Compggitiop of household income
5.2.1 Qgiinition of net igcome

For the purposes of this study, net income is the value
of production minus the value of business expenses. Production includes
agricultural home production, cash sales of goods and services, goods
and services "sold" through barter, and goods and services offered as
transfers. The sale or transfer of household assets is excluded
intentionally, while the value of non-agricultural home production is
excluded for lack of data. Business expenses include the value of
labor, raw materials, inputs, and land rental, whether purchased in cash
or through barter. In the case of merchants, it also includes the goods
purchased for resale. The purchase of vehicles, land, or commercial
property is excluded from business expensesl.

Net income is less suitable than total expenditure as an indicator
of household welfare for three reasons. First, welfare is a function of
material well-being (among other factors) and is thus more directly
measured by expenditure than income. _Second, net income is calculated
as the difference between two estimated values (gross income and
business expenses), so it is less accurately measured than expenditure.
Third, households probably "smooth" expenditure relative to income by
means of saving and dissaving. Seasonal smoothing implies that annual

expenditure is more accurately measured than annual income, while year-

 

1. These transactions would properly be included in a
capital account category. However, because infrequent transactions are

not well measured in this type of survey, no analysis of capital
accounts was attempted.

105

to-year smoothing implies that expenditure is an estimate of "permanent
income" as perceived by the household.

Given the fact that net income is less appropriate for measuring
household welfare, household welfare and distributional issues will be
discussed in the context of household expenditure in section 5.3. This
section concentrates on the sources of income for Rwandan households.

5.2.2 r io ncom om d’f e e t ct'v t‘es

The agricultural sector, which includes both crop and
animal production, is the most important source of net income in Rwanda.
It represents 55% of the net income of Rwandan households, according to
the ENBC data presented in Table 5-2. Of course, most of this
production is in the rural areas, where agriculture represents 62% of
net income, but agriculture exists on a small scale in the cities as
well.

The importance of agriculture would be even greater under a
broader definition. In Table 5-2, beer income is calculated by
implicitly including the value of the raw materials (bananas and
sorghum),when they are grown by the same household that brews the beer.
Reclassifying this banana and sorghum production as agriculture would
raise the share of agriculture to approximately 74% of rural net income
(Ministry of Planning, 1988: Annex D).

Manufacturing and services includes the output of selfeemployed
non-agricultural producers and service providers such as beer brewers,
tailors, wood- and metal-workers, masons, mechanics, bar and restaurant
owners, and truck drivers. The importance of this sector does not vary
much between the rural and urban areas (24% and 30%, respectively), but
these figures mask important differences in composition. In the
countryside, beer brewing is the dominant activity within this sector.
Banana beer alone accounts for over 60% of the value of rural
manufacturing and services. In the cities, by contrast, beer brewing is

a minor activity compared to construction, repair work, transportation,

106

Table 5-2: Sources of net income for rural and urban households
—

 

Source of income Rural Urban Total
TOTAL 100.0 % 100.0 % 100 %
Agricultural production 62.1 % 5.3 % 55.1
Manufacturing and services 23.7 % 30.4 % 24.5
Beer brewing 17.5 % 2.3 % 15.6
Other 6.2 % 28.0 % 8.9
Commerce 5.4 % 20.4 % 7.3
Wage employment 8.7 % 44.0 % 13.1
Agricultural wages 4.0 % 0.7 % 3.6
Public sector _ 2.9 % 19.2 % 4.9
Other 1.8 % 24.0 % 4.6

 

Source: Rwandan ENBC.

—

food preparation, and wood working.

This pattern of locational specialization in manufacturing can be
attributed, in part, to the geographic distribution of demand. As a
result of higher urban income and the consequent larger shares allocated
to non-food items, real non-food expenditure per household in the urban
areas is 6.2 times higher than in the rural areas. According to the
ENBC data, urban households represent just 5% of the population, but
account for over a quarter of the non-food demand.

Another factor in the geographic distribution of manufacturing is
that banana beer brewing is a weight-reducing process. _On average,
three kilograms of bananas are needed for one kilogram of banana beer.
Thus, transportation costs are reduced by brewing the beer on the farm
where the bananas are grown. Indeed, over 90% of the bananas used in
rural beer production are grown by the brewer household.

By contrast, sorghum beer brewing is a weight-adding activity,
with less than 100 grams of sorghum being needed for one kilogram of
sorghum beer. This helps explain why only half of the sorghum used in
rural sorghum beer production is grown by the brewer household. It also

explains the fact that rural brewing activity is dominated by banana

107

beer, while urban beer production is primarily in the form of sorghum
beer (Ministry of Planning, 1988: Annex D).

Commerce refers to the purchase and resale of goods with little or
no physical transformation of the product. This category includes the
entrepreneurial income of all types of traders, from large-scale
diversified importer-wholesalers to small-scale retailers without
employees. As presented in Table 5-2, commerce is almost four times as
important as a source of household income in the urban sector as in the
rural sector. This is not surprising given the fact that much of rural
production is not marketed. The level of commercial income as a
proportion of the value of cash expenditures is similar in rural and
urban sectors (15% and 21% respectively).

Wage income is defined as income earned on a per-hour or per-
month basis. Table 5-2 demonstrates that this is an important source of
income in the urban areas, representing 44% of the total. Somewhat more
than half of urban wage income is earned through non-agricultural
private sector employment, while public sector employment accounts for
almost all the remainder. By contrast, wage income is much less
important in the rural areas, contributing less than 9% of the total.
Almost half of this take the form of agricultural wage labor.

5.2.3 zgopoptiop of households by primapy occupation

.Another way to evaluate the importance of different
sources of income is to look at the distribution of households according
to the primary source of income, defined as that which contributes over
50% of household net income. Table 5-3 indicates that almost three-
quarters of all Rwandan households derive most of their income from
farming. In absolute terms, by this definition, there are approximately
800,000 farm households in Rwandal. About 10% of Rwandan households

are self-employed in manufacturing and services, while the remaining 16%

 

1. To fully appreciate the farming intensity in Rwanda, it
is worth noting that by a similar definition there are approximately
600,000 farm households in the United States (Tweeten, 1989).

108

of the households are more or less equally divided among commerce, wage

employment, and ”diverse” (i.e. households for which no single source of
income accounts for over half the total). Overall, about 88% of Rwandan
households obtain at least half of their net income from self-

employment.

Table 5-3: Distribution of households by primary occupation

 

Principal occupation Rural Urban Total

TOTAL ' . ' 100.0 % 100.0 % 100.0 %
Agriculture 76.9 % 14.0 % 73.7 %
Manufacturing and services 8.7 % 28.6 % 9.7 %
Commerce 3.7 % 11.5 % 4.1 %
Wage employment 4.4 % 35.3 % 5.9 %
Diverse 6.3 % 10.5 % 6.5 %

 

Source: Rwandan ENBC.

In the rural sector, 77% of the households depend primarily on
agriculture to earn their living. Furthermore, the prOportion would be
even higher if the banana and sorghum production of brewers were counted
as agriculture. Nonetheless, it is important to note that even in this
semifisubsistence low-income rural economy, almost one quarter of the
households derive most of their income from non-agricultural activities.

In the cities, wage employment is the most common primary
occupation, but only 35% of the households fall into this category.

This statistic highlights the danger of using wage rates as an indicator
of well-being in Rwanda, even among the urban population. Furthermore,
as discussed below, households whose primary source of income is wage
income tend to have higher-than-average incomes. Over half (54%) of the
urban households derive most of their income from self-employment in

agriculture, manufacturing and services, and commerce. For the

109

remaining 10% of the households, no one activity accounts for over half
of net income.

5.2.4 ort' f households 'nvolved in d erent activities

Having reviewed the distribution of households according

to the primary source of income, it is useful to consider supplemental
sources of income. Table 5-4 shows the proportion of households
obtaining any income from each source. The ENBC data indicate that all
the rural households and three-quarters of the urban households have
some agricultural production. The latter figure may seem high, but it
should be recalled that households with a garden, fruit trees, or a plot
outside the city are included. Virtually all rural households and about
half the urban household brew banana or sorghum beer, whether or not it
is marketed. Although wage employment is a secondary source of income
for most rural households, about 44% of them obtain some income from

agricultural wage labor.

Table 5-4: Proportion of households earning any income from each source
—

 

Source of income Rural Urban Total
Agricultural production 100.0 %' 75.5 % 98.7 %
Manufacturing and services 97.7 % 83.2 % 97.0 %
Beer brewing 96.5 % 49.3 % 94.1 %
Other . 42.3 % 70.4 % 43.7 %
Commerce 27.3 % 51.0 % 28.5 %
Wage employment 52.1 % 67.3 % 52.9 %
Agricultural wages 44.1 % 13.3 % 42.5 %
Public sector 5.0 % 24.6 % 6.0 %
Other 14.9 % 48.2 % 16.6 %

 

Source: Rwandan ENBC.

An index of the diversity of income sources is the sum of the

‘—

percentsges of households obtaining income from each source. If the
list of sources is exclusive and exhaustive, this sum represents the

average number of sources of income per household. Dividing the sources

110

into five categories (agriculture, brewing, other manufacturing and
services, commerce, and wage employment), the sum is over 300% in both
urban and rural sectors. This means that Rwandan households, on
average, obtain income from slightly more than three of these five

income sources.

5.3 Compggitiog gf household eipendipuge
5.3.1 Definition of expgnditupg

For the present purposes, total expenditure is defined as
the sum of cash consumption expenditures and the imputed value of
agricultural home production, gifts received in kind, and goods received
in barter transactions. Cash consumption expenditures includes current
consumption expenditures (e.g. food) and expenditure on durables (e.g.
household effects), but excludes purchases of vehicles, land, and
buildings. It also excludes goods purchased to be used as gifts for
other households to avoid double countingl. Non-agricultural home
production was not recorded in the ENBC, although estimates derived from
the Household Asset questionnaire indicate that this is negligible, even
in the rural areas. The collection of firewood, on the other hand, may
be a significant type of non-agricultural home production (see Ministers
du Plan, 1988).

Household expenditures need to be adjusted for household size and
composition in order to more accurately reflect the average standard of
living in the household. For the present purposes, we use both
expenditure per capita and expenditure per adult equivalent (ae), where

the latter is defined on the basis of caloric requirementsz. The

 

1. In the rural areas, ”product use" codes allowed the
exclusion of goods purchased to be used as gifts. In the urban areas,
the value of gifts given was subtracted from consumption expenditures
for the appropriate budget category.

2. 'Each member of the household is assigned a value, based
on age and gender, to reflect his or her caloric requirements as a
fraction of those of an adult male. For example, a five-year-old girl

111

estimation of adult-equivalence scales based on the budget data is a
more theoretically justifiable approach, but there is little agreement
on the correct method (see Deaton and Case, 1988).

And finally, nominal figures need to be adjusted for the price
level in each region. Price indices were calculated based on the prices
recorded in the ENBC of 32 products, representing about 70% of the value
of household expenditures nation-wide. A price index was calculated for
each of the five geographic zones in the rural areas and each of the
four urban centers. Kigali is used as the base region.

5.3.2 vera e end e d st b

The average level of expenditure in Rwanda according to
the ENBC is 13,422 Rwandan francs (FRw) per person per year at current
prices (1983 for rural expenditure and 1985 for urban) or 18,670 FRw per
capita at Kigali prices of 1985. Given the 1985 official exchange rate
of 100 Frw per U.S. dollar, nominal expenditure is equivalent to $ 134
per capita. The World Bank estimate of 1982 per capita gross national
product is $ 260 (World Bank, 1984). The difference is partly due to
the fact that gross national product includes several categories
excluded from this estimate, such as savings and government expenditure.
One study compared over a dozen household budget surveys and found that
survey estimates of income (or expenditure) were almost always lower
that those of national accounts (Brown et a1., 1978).

As shown in Table 5-5, the level of real expenditure per capita is
about 2.4 times higher in the urban areas than in the rural areas. When
household size is measured using adult equivalents, the ratio is almost
the same. The urban/rural ratio of real expenditure per capita (2.4) is
considerably lower than that of nominal expenditure per household
(almost 4.0) for two reasons. First, the average household size in the

cities (5.6 persons) is greater than that in the country (4.9). Second,

 

is given a value of 0.76 since her caloric needs are roughly three
quarters those of an adult male (see Appendix A for the equivalence
scale).

112
prices are about 50% higher in the urban areas, particularly those of
domestically produced food. These results highlight the importance of
adjusting for prices and household size when comparing urban and rural

expenditure.

Table 5-5: Mean level of expenditure in rural and urban areas
—

 

Urban/
Rural Urban rural National
average average ratio average
Nominal expenditure
FRw/household/year 54,360 214,807 3.95 62,543
FRw/person/year 11,763 44,302 3.77 13,422
FRw/ae/year 13,095 49,026 3.74 14,934
Real expenditure
FRw/household/year 80,245 210,706 2.63 86,923
FRw/person/year 17,396 42,285 2.43 18,670
FRw/ae/year 19,352 46,846 2.42 20,759

 

Note: ”as" refers to adult-equivalent, where the number of adult
equivalents in the household reflects the caloric requirements
of the household, based on the age and sex of its members

Source: Rwandan ENBC.

A brief examination of the distribution of expenditure among
households demonstrates that the gap between the urban and rural
averages is not just the result of a few high-income households in the
urban areas. Table 5-6 shows, for example, that scarcely one quarter of
the rural households reach the level of 20,000 FRw/person/year, whereas
almost three quarters of the urban households exceed this level.
Another illustration of the generally higher incomes in the cities is
that 73% of the urban households have per capita expenditure levels
above that of the national median (18,250 FRw/person/year).

According to various measures of concentration, expenditure is
more concentrated in the urban areas than in the rural areas. For

example, the poorest 20% of the rural households account for 14% of

113
Table 5-6: Cumulative distribution of households by expenditure level

 

Real expenditure Rural Urban National
(FRw/person/year)

5,000 - 9,999 13.9 % 4.6 % 13.4 %
10,000 - 14,999 51.7 % 12.9 % 49.9 %
15,000 - 19,999 72.4 % 26.3 % 70.0 %
20,000 - 24,999 82.9 % 39.4 % 81.9 %
25,000 - 29,999 90.0 % 49.0 % 87.9 %
30,000 - 34,999 95.2 % 56.0 % 93.2 %
35,000 - 39,999 97.9 % 63.3 % 96.1 %

40,000 and above 100.0 % 100.0 % 100.0 %

 

Source: Rwandan ENBC.

—

total expenditures in the rural areas, whereas the poorest 20% of the
urban households represent just 7% of the urban total. Similarly, the
Gini coefficient for the rural areas is 0.27, while the urban
coefficient is 0.42.

Because the overwhelming majority (roughly 95%) of the Rwandan
population is rural, the distribution of expenditure is largely
determined by the rural patterns. Thus, the poorest 20% of the
households in Rwanda, according to the ENBC, represent 13% of total
household expenditures and the Gini coefficient is 0.29. This indicates
that Rwanda has one of the least concentrated expenditure distributions
‘in the world, albeit at one of the lowest levels of average expenditure
(income) in the world.

5.3.3 Expenditure for different typgg of households

The level of per capita expenditure varies as a function
of a number of household characteristics, most importantly occupation,
size of household, and sex of head of household. The households in the
ENBC were divided into different five occupations depending on the most
important source of net income: agriculture, manufacturing and services,
cOmmerce, wage employment, and ”diverse” (the last category was for

INDuseholds for which no one source represented at least 50% of the

tOtal) .

114

In both urban and rural areas, the wage earners have the highest
incomes and expenditures, as shown in Table 5-7. Although there are
some day laborers and other low-income wage earners, most of the wage
earners are teachers, civil servants, and other relatively well-paid
occupations. Artisans and merchants tend to have expenditure levels
close to the average of their regions. Although merchants are perceived
in Rwanda as wealthy, the ENBC results imply that there are a large
number of small-scale (lower—income) merchants. Farmers and
"diversified earners” have the lowest level of expenditure and income.
Although these patterns hold in'both urban and rural areas, urban
households have higher levels of expenditure within the same
occupational category.

The level of per capita expenditure is also correlated with the
size of household, as shown in Table 5-7. In both urban and rural
areas, larger households have lower average per capita expenditure.
Deaton and Case (1988) note that this pattern exists in most household
budget surveys and caution against interpretingthis~a7 a sign that
household welfare falls with larger families-. First there may be

I

economies of scale in household size.(;Secon9,/larger households usually

have a larger proportion of children, of’whom expenditure requirements
are lower. This issue cannot be solved without more in-depth analysis,
but it is worth noting that, if adulteequivalents are defined by caloric
requirements, then expenditure per adult-equivalent also falls with
larger households.

Third, the sex of the head of household is a determinant of
expenditure per capita. As shown in Table 5-7, male-headed households
in the urban areas have per capita expenditure levels substantially
higher than those of female-headed households. Part of this is due to
the fact that female—headed households in the urban areas tend to be

involved in less remunerative occupations, such as farming and small-

scale commerce. This in turn could be the result of lower education and

115
Table 5-7: Real expenditure of different types of households

Real expenditure (Frw/person/year)

 

Rural Urban National
average average average
Principal occupation
Agriculture 16,491 19,740 16,523
Manuf./services 20,583 46,208 24,443
Commerce 18,251 37,994 21,073
Wage employment 24,668 53,509 33,444
Diverse 18,517 28,691 19,363
Household size
1-3 members 21,742 56,356 23,393
4 members 17,250 46,820 18,399
5 members 16,193 38,375 17,133
6 members 14,930 36,912 15,737
Over 6 members 14,597 _ 33,465 ' 16,095
Sex of head of hh .
Male 17,247 44,888 18,729
Female , 17,967 29,243 18,437
Overall mean 17,396 42,285 18,670

 

Note: Expenditure is evaluated at 1985 Kigali prices.
Source: Rwandan ENBC.

—

literacy levels, limited access to credit, discrimination by employers,
and/or social norms against participation in some occupations.

Interestingly, there is no gap between the expenditure levels of
male- and female-headed households in the rural areas. Perhaps this is
because, although rural women probably face the same problems as urban
women, education, credit, and discrimination are less constraining in
farming, which is the predominant activity in the rural sectorl.

5.3.4 Composipion of expenditure

Household expenditures in Rwanda are dominated by food,

particularly tubers, plantains, and beans. Nationwide, over three

m

quarters of household expenditures (including the value of home

 

.-
"“‘“"‘""hfi~s~ . - 1.
.mmr.ammo v p-“nnnmw‘i. ‘I'. It a J
“L" ‘ 'M M term. mm-jn\g‘|_-

1. The use of purchased inputs, and hence the need for
credit, is very limited in Rwanda. Expenditure on all agricultural
inputs including labor is only 8% of the gross value of crop production.

116

production) are devoted to food products, as shown in Table 5-8. Tubers
and bananas represent fully one quarter of expenditures, while legumes
(primarily beans) account for almost one fifth. The next most important
category is beverages, primarily traditional beers, which account for
15% of the value of expenditure. Animal products and grains, by
contrast, are relatively minor items in the Rwandan budget, representing
about 7% and 4% respectively. Only 22% of expenditure is allocated to
non-food categories, the most important of which are housing (8%) and

clothing (5%).

Table 5-8: Composition of expenditure in rural and urban areas

 

 

 

Expenditure category Rural Urban National
Total 100.0 100.0 100.0
Food 80.7 54.2 77.4
Grains 3.4 5.0 3.6

. ers and plantains 27.2 12.6 25.4
egumes 21.3 6.9 19.5
Fruits and vegetables 1 3.4 3.1 3.3
Meat, eggs, and dairy 6.7 8.5 6.9
TKBeverages 15.9 11.2 15.4
Other 2.7 6.9 3.3
Non-food 19.3 45.9 22.6
Clothing 5.0 4.9 5.0
Housing 7.1 14.3 8.0
Household equipment 1.9 3.9 2.1
Energy and water 1.0 5.7 1.6
Health and hygiene 1.6 3.4 1.8
.Education 0.5 1.4 0.6
Transportation 1.1 7J8 1.9
Tobacco 0.6 1.1 0.7
Leisure and services 0.5 3.3 0.8

Source: Rwandan ENBC.

Naturally, the composition of expenditure varies sharply between
urban and rural areas. In the urban areas, barely one half (54%) of
expenditures are allocated to food, whereas over four fifths (81%) of
rural expenditures are on food. This difference is almost entirely due

to the significantly larger shares of the rural budget allocated to

117

tubers, bananas, and legumes. These food categories account for 48% of
the rural budget, but less than 20% of the urban budget. In contrast,
the urban households allocate a larger share of their expenditures to
housing, transportation, and energy and water than do rural households.
In interpreting these figures, it is important to recall that real
per capita expenditure is about 2.4 times greater among urban households
than among rural households. Thus, even when the urban budget share is
smaller than the rural share, the absolute level of expenditure on a
given item is often higher in the urban areas. For example, the only
category for which rural households spend more in absolute terms than

urban households is legumes.

5.4 c e n u a sector

5.4.1 Lgng

Given the overwhelming importance of agriculture in

Rwanda and the high population density, access to arable land is
obviously an important factor in the well-being of rural households.
Data on the farm size is available for the rural sample of the ENBCI.
These data indicate that the average farm size in the ENBC sample was
1.28 hectares. Almost 60% of the households in the sample had less than
one hectare. Furthermore, the situation today is undoubtedly worse: in
the decade.since these measurements were made, the population of Rwanda
has probably grown by roughly 40%.

The Gini coefficient of the distribution of land in the rural
sector of Rwanda is 0.48.‘ This coefficient means that the degree of
concentration of land ownership in Rwanda is somewhat above the African

average, but far below that of most Latin American countries. In more

 

1. In 1982, the pilot survey of the Agricultural Census
measured land area for 450 rural households. The following year, a
subsample of 270 households was used for the rural portion of the ENBC.
However, no land area information is available for four of the
households in the rural ENBC sample. Thus, the farm size figures
presented here are based on the remaining 266 rural households.

118

concrete terms, 52% of the farm land is farmed by one fifth of the rural
households.

Surprisingly, there no clear positive relationship between total
farm size and household well-being, whether the latter is measured in
caloric intake or expenditure per adult equivalent. Table 5-9 shows
that the relationship is, if anything, curvilinear, with the smallest

and largest farms being better off.

Table 5-93‘ Rural expenditure and caloric intake by farm size
—

 

Real Caloric
Parm size expenditure intake
(hectares) (FRw/person/yr) (kcal/ae/day)
Under 0.38 17,898 2,546
0.38 to 0.65 16,808 2,455
0.66 to 1.07 15,955 2,351
1.08 to 1.90 18,923 2,309
Over 1.90 17,832 2,573

 

Note: Farm size categories represent quintiles
(each contains 20% of the rural households).

Source: Rwandan ENBC/Rural sector.

Three factors can be cited to explain this result. First, part of
the Variability in farm size is due to life-cycle patterns. Average
farm size increases and then decreases with the age of the head of
household, tracking the growth and later decline of household size, as
shown in Table 5-10. In other words, land ownership per capita is
somewhat more equal than land ownership per household. The Gini
coefficient for farm size per adult equivalent is 0.45, compared to 0.48

for total farm size.

119

Table 5-10: Life cycle patterns in farm size in the rural sector

 

Age of head of Average Average size
household size of of farm
(years) household (hectares)
Under 30 years 3.9 0.7
31-40 years 5.4 1.5
41-50 years 6.0 1.4
51-60 years 5.8 1.7
Over 60 years 3.7 1.1

 

Source: Rwandan ENBC/Rural sector.

Second, the land is more intensively cultivated on small farms.
Although net agricultural income1 per household rises with farm size,
it does not increase proportionately. As shown in Table 5-11, the
agricultural return per hectare is over six times as great on the
smallest 20% of farms compared to the largest 20%. Much of the reason
for this is related to soil fertility, which is probably inversely
related to farm size. Average farm size is the greatest in the drier
and less fertile eastern lowlands and the lowest in the fertile volcanic
zones to the northwest. In addition, small farms tend to have more
family labor per hectare of farmland (see Table 5-11). Thus, they are
able to plant-more labor-intensive crops and use more labor-intensive
techniques to increase return to the scarce factor, land.

A third factor which reduces the importance of unequal land
distribution is the fact that small farms rely more heavily on non-

agricultural income. The last column in Table 5-11 indicates that the

 

1. Net agricultural income is the value of agricultural
production (including home production) minus agricultural operating
expenses, such as seed, hoes, chemicals, and hired labor.

120

Table 5-11: Factors which ameliorate the disparity in farm size
—

Avg size Persons Ag return Pct income

 

Farm size household per per hect from non-
(hectares) (persons) hectare (Frw/ha) ag source
Under 0.38 3.6 17.5 104,731 35.5 t
0.38 to 0.65 4.6 9.6 56,631 19.6 t
0.66 to 1.07. 4.8 5.9 39,634 23.8 t
1.08 to 1.90 5.6 3.9 26,584 17.6 %
Over 1.90 6.2 2.1 17,126 9.6 s

 

Note: Farm size categories represent quintiles.
Source: Rwandan ENBC/Rural sector.

importance of income other than from agriculture and beer brewing1
increases from less than 10% among the largest 20% of farms to over 35%
among the smallest 20\ of farms. It seems likely that farm size and
non-agricultural income influence each other: small farmers are forced
to supplement their income with non—farm activities and households with
non-farm income are more likely to sell farm land they cannot adequately
tend.

Although total farm size is not related to household welfare, farm
size per adult equivalent is positively related to welfare. As shown in
the first pair of columns in Table 5-12, the mean expenditure level of
the rural quintile under the least land pressure is 33% higher than that
of the rural quintile under the greatest land pressure. Similarly, the
mean caloric intake of the first group of households is 24% higher than
that of the second.

If we restrict our attention to rural households which obtain at
least half of their net income from agriculture and beer brewing, then
the relationship between farm size per adult equivalent and household

welfare becomes stronger. This is particularly true if we use caloric

 

1. Since virtually all banana beer producers grow their own
bananas, beer brewing is closely linked to banana production and thus to
the availability of land.

121

Table 5-12: Rural expenditure and caloric intake by farm size

Among rural households Among rural agricul-

tural households

 

Farm size Real Caloric Real Caloric
per adult expenditure intake expenditure intake
equivalent (FRw/person/ (kcal/ae/ (FRw/person (kcal/ae/
(hect/ae) year) day) /year) day)
Under 0.10 15,725 2,230 14,538 2,151
0.11 to 0.18 16,089 2,352 15,568 2,319
0.19 to 0.27 17,209 2,594 17,025 2,596
0.28 to 0.47 18,194 2,389 17,173 2,398
Over 0.47 20,997 2,772 20,267 2,802
Note: Farm size categories represent quintiles. ”Agricultural”

households are those that obtain at least 50% of net income from
agriculture and beer brewing.

Source: Rwandan ENBC/Rural sector.

intake as the welfare indicator. One implication is that the situation
of agricultural households under the greatest land pressure is
especially acute, as shown in second pair of columns in Table 5-12.

In summary, there is no relationship between total farm size and

household welfare because 1) small farms
households, 2) small farms have a higher
and 3) small farms rely more on non-farm
there is a positive relationship between
and welfare, particularly for households
agriculture for their income.

5.4.2 Purchased inputs

Purchased inputs,

services bought, either in cash or through barter,

production (including livestock production).

seeds, hoes, agricultural chemicals,

 

1.

as defined here,

agricultural labor,

tend to be operated by small
economic return per hectare,
income. 0n the other hand,

farm size per adult equivalent

which rely primarily on

refer to goods and
for agricultural
This category includes

livestockl,

Livestock were counted as a purchased input only when the

household appeared to have a regular business of buying animals to

fatten them for resale.

122

and rental of land. Although the vast majority of rural households
(92%) purchase agricultural inputs, the value of these purchases is
equivalent to only 9% of the value of agricultural production. This
represents about USS 34 per household per year.

Of the amount spent on purchased inputs, the largest share (40%)
goes toward hired laborl. This is equivalent to about 17 days of hired
labor per rural household per year. Since less than half the rural
households (44%) hire labor, the average number of days of hired labor
among those households is greater, about 39 days. Slightly less than
half of rural households (46%) had members who worked as agricultural
laborers for someone else.

Livestock purchases are the second largest component, representing
about 19% of the value of purchased inputs. The remaining 41% is split I
more or less evenly among seeds and planting material, hoes and
chemicals, and land rental. In spite of the land pressure in Rwanda,
less than one quarter of the rural households purchase manure,
fertilizer, or other chemicals. The average expenditure among users is
roughly USS 6 per year.

5.4.3 Agricultural production and marketing

As described in section 5.2, agriculture represents 62%
of net income in the rural sector, and 77% of rural households earn over
half their net income from crop and livestock production. Table 5-13
shows the percentage contribution of each commodity to the gross value
of agricultural productionz. According to the ENBC data, the most
important crops in terms of the value of production are bananas, beans,

sweet potatoes, cassava, and white potatoes. It is interesting to note

 

1. This category also includes payment for specialist
services such as veterinarians, but this component is negligible.

2. ‘It is "gross" in the sense that the cost of purchased
inputs has not been subtracted. The contribution of each commodity to
net income cannot be calculated because the ENBC data do not allow the
input costs to be allocated among different crops.

123

that coffee, the predominant export commodity in Rwanda, is not among

the top five crops.

Table 5-13: Composition of agricultural production and sales
—

Pct of value Pct of value

 

of of
agricultural agricultural
Commodity production sales
Sorghum ‘ 4.4 6.5
Cassava 7.0 4.8
Sweet potatoes 12.7 3.8
White potatoes 6.2 . 7.9
Bananas ' 21.9 7.7
Beans 20.4 5.0
Fruits and vegetables 4.2 2.7
Coffee - y 4.3 21.7
Livestock ' 11.6 29.3
Other 7.3 10.6
TOTAL 100.0 100.0

 

Source: Rwandan ENBC/Rural sector.

However, most of the agricultural output is retained on the farm
for own-consumption. In value terms, more than three quarters (76%) of
agricultural output is not marketed (the importance of home production
is discussed further in section 5.5.1). The composition of agricultural
sales is quite different, as shown in the second column in Table 5-13.
Coffee and livestock alone account for one half of the value of
agricultural sales by Rwandan households. Bananas, beans, and sweet
potatoes, which represent 55% of the value of agricultural output,
account for barely 16% of the cash revenue from agriculture. At the
same time, it is worth pointing out that "food crops” as a whole
contribute almost half of agricultural cash income, while "cash crops"
barely account for one quarter.

The proportion of the staple food production which is marketed
varies considerably from one commodity to another, as shown in Table 5-

14. Less than 10% of the sweet potatoes, bananas, and beans produced in

124

Rwanda reach the market. The marketed shares of sorghum, cassava, white
potatoes, and fruits and vegetables are greater but still less than one
third of production.

Table 5-14: Agricultural production and marketed share
—

 

Production Pct of output
Commodity (kg/hh/yr) which is sold
Sorghum 125.8 31.0
Cassava 306.3 20.5
Sweet potatoes 888.3 7.8
White potatoes 271.6 31.1
Bananas 1590.8 0.8
Beans 361.1 6.3
Fruits and vegetables 102.1 15.2
Coffee 16.8 100.0
Livestock 77.7 40.8

 

Source: Rwandan ENBC/Rural sector.

Concerning sorghum and bananas, it should be noted that a portion
of the "non-marketed" output is used by the same household to
manufacture traditional beer, which may in turn be sold. Based on the
volume of beer production, it appears that around 1,150 kilograms of
bananas per household per year may be used directly in beer brewing by
the producer. Roughly two thirds of the banana beer is marketed.
Similarly, about 75 kilograms of sorghum per household per year are used
to manufacture traditional beer by the grower. Slightly over half the

sorghum beer production is sold.

5.5 Effect of prige changes on households

In this section, we begin to examine the impact on households of

 

the price changes associated with devaluation. Although a more rigorous
model of household-level impact is developed in Chapter 7, the
descriptive statistics presented in this section will facilitate the

interpretation of the results of that chapter.

125

The effect on a given household of a price changes associated with
devaluation can be crudely measured by considering the proportionate
change in price, the composition of expenditure, and the sources of
income. This type of analysis does not incorporate the effect of the
adjustment of households as consumers and as producers, but it may serve
as a first-round approximation. Thus, the absolute impact of a price
increase of a given commodity would be the proportionate change in price
times the difference between the value of production of that good and
the value of consumption of the goodl. Of course, in subtracting the
value of consumption (including home production) from the value of
production (including home production), the result is the net cash sales
of the good. The relative impact of the price increase can be
approximated by the net cash sales as a proportion of total expenditure -
(including home production).

This discussion suggests that the effect of price changes
associated with devaluation on a given household depends on 1) the level
of participation in the market economy, 2) the net sales position of the
household with respect to agricultural commodities, and 3) the tradeable
component of cash expenditure and cash income. Each of these topics is
explored in the following subsections.

5.5.1 a i ation 'n the market

.The portion of total expenditure which is in the form of
purchases (both cash and barter) clearly influences the vulnerability of
the household to price changes. In other words, the larger the home
produced component of expenditure (income), the more insulated the

household is from fluctuations in pricesz.

 

1. This is the first-order estimate of compensating
variation, i.e. the amount by which nominal income would have to be
increased to restore the initial level of utility if (compensated)
demand were completely inelastic (see equation 4-47).

2. The appropriate treatment for gifts and other transfers
is not clear. In this section, we have included the value of transfers
received with home production, since both are non-market acquisitions.

126

The first column of Table 5-15 indicates that, not surprisingly,
home production represents a much larger share of rural food consumption
than urban. Rural households produce over three quarters of their own
food, as measured in terms of monetary value. The rate of food self-
sufficiency in the urban sector is barely 20%, although this seems

fairly high compared to the conventional view of urban life.

Table 5-15: Importance of cash expenditure in rural and urban sectors
—

 

Home prod— .Food cons- Heme prod-' [Cash pur-

uction as a umption as a. uction as a chases as a

pct of food pct of total pct of total pct of total
Sector' expenditure expenditure expenditure expenditure
Rural 75.9 83.7 64.8 35.2
Urban 21.2 66.7 16.9 83.1
Rwanda 73.1 82.8 62.4 37.6

 

Source: Rwandan ENBC.

The second column provides the mean share of total expenditure
allocated to food consumption. The food share is, of course, higher in
the rural areas, reflecting Engle's Law and the lower levels of
expenditure in the countryside. _Food represents five sixths of the
average rural budget, but only two thirds of the average urban budget.

The product of these two ratios at the household level is the
share of home-produced food in total expenditure, the average of which
is presented in the third column of Table 5-15. Since data on non-food
home production are not available from the survey data, this is our
measure of the overall importance of home production. The portion of
total expenditure in the form of cash purchases is thus one minus the
home production share, as shown in the fourth column. Thus, purchases
represent 35% of the expenditure of an average rural household and 83%

of the expenditure of an average urban household.

127

The same information is disaggregated by expenditure quintile in
Table 5-16. This table demonstrates that the role of home production in
food consumption declines as income (expenditure per adult equivalent)
rises. Similarly, the food share in the budget falls from 87% in the
poorest fifth of households to 63% in the richest. These two factors
together explain the sharp drop in the importance of home production
from 62% of the budget in the first quintile to 19% in the fifth.
Examined from another perspective, the importance of market purchases
rises from somewhat more than one third to over four fifths of the total

expenditure.

Table 5-16: Importance of cash expenditure by expenditure quintile

 

Home prod- Food cons- Home prod- Cash pur-
Expendi- uction as a umption as a uction as a chases as a
ture pct of food pct of total pct of total pct of total
quintile expenditure expenditure expenditure expenditure
lst 70.1 87.4 62.5 37.5
2nd 68.2 84.2 58.6 41.4
3rd 62.5 82.0 53.2 46.8
4th 55.8 80.0 46.8 53.2
5th 24.5 63.2 18.9 81.1
Rwanda 73.1 82.8 . 62.4 37.6

 

Source: Rwandan ENBC.

The largest change in Table 5-16 occurs between the fourth and
fifth quintiles. This raises the question as to whether the observed
decline in the importance of home production is simply the result of
urban households being clustered in the fifth quintile or whether this
pattern exists separately in rural and urban sectors. In order to
address this issue, Table 5-17 disaggregates the variables by rural

quintile and urban quintile.

128

Table 5-17 reveals that the rate of food self-sufficiency does not
vary appreciably across expenditure quintiles within the rural sector.
In other words, relatively better off households in the rural sector are
no more food self-sufficient than their poorer neighbors, nor do they
depend any more on market purchases to obtain food. At the same time,
the value of food consumption as a percentage of total expenditure does
decrease as income rises, although the decline is fairly modest. The
food share falls from 86% among the richest quintile to 80% in the
poorest.

Combining these two patterns, the share of home production in
total expenditure declines gradually across expenditure quintiles. The
importance of market purchases correspondingly rises from 32% among the

poorest rural households to 38% among the richest.

Table 5-17: Importance of cash expenditure by rural and urban

expenditure quintiles
_

 

Home prod- Food cons- Home prod- Cash pur-

Expendi- uction as a umption as a uction as a chases as a
ture pct of food pct of total pct of total pct of total
quintile expenditure expenditure expenditure expenditure
Rural sector

lst 77.1 86.0 67.8 32.2

2nd 74.8 85.3 64.3 35.7

3rd 77.4 83.7 65.9 . 34.1

4th 75.1 - 83.1 63.5 36.5

5th 74.9 80.0 62.0 38.0

Urban sector

lst 38.0 80.7 32.4 67.6

2nd 24.2 73.2 19.5 80.5

3rd 18.3 66.0 13.7 86.3

4th 14.3 59.3 11.5 88.5

5th 9.6 53.7 6.2 93.8

 

Source: Rwandan ENBC.

—

Turning our attention to the urban section, it is important to

recall that the quintiles are defined relative to the income

129

distribution in each sector. For example, 60% of the urban households
would qualify to be in the fifth rural quintile. Similarly, over half
the rural households would be classified in the poorest urban quintile
(see Table 5-6).

According to Table 5-17, the patterns in the urban sector are much
more marked than those in the rural sector. The importance of home
production in food consumption drops sharply across expenditure
quintiles, from 38% for the poorest fifth of urban households to under
10% for the richest. Likewise, food shares fall from almost 81% to 54%.
As a result, the share of market purchases in total expenditure rises
from two thirds among the poorest urban households to almost 94% among
the richest.

In summary, the importance of market purchases in total
expenditure is positively related to the level of expenditure per adult
equivalent. Furthermore, this pattern exists in both rural and urban
areas. In the rural sector, the pattern is weak and is determined
solely by the falling food share. In the cities, the pattern is strong
and is determined by both a falling food share and falling food self-
sufficiency as expenditure rises. As a result of these patterns, we can
expect a given price change to have an effect on urban households at
least twice as great as that on rural households. Furthermore, other
things being equal, the impact will be fairly similar across rural
households, but it will vary considerably among urban households.

5.5.2 Net position in agricultural commodities

Even if two households have the same proportion of
expenditure in the form of home production, the impact of a given price
change will vary depending on the degree to which the hOuseholds are net
sellers (or net buyers) of the good in question. Until recently, it was
generally believed that rural households benefited from higher
agricultural prices, with the possible exception of landless households

that rely on wage-labor. However, recent research in Senegal (Goetz,

130

1990), Mali (Dione, 1989), and Rwanda (Loveridge, 1989) indicated that
significant numbers of farmers are net buyers of staple crops (this
research is summarized in Weber et al, 1988). This unexpected diversity
in the rural sector indicates the need for more careful consideration of
the net sales position of rural households. In particular, the welfare
impact of various types of agricultural policy depends greatly on the
distribution of households by their net sales position in different
commodities. This applies to agricultural price policy, agricultural
research priorities, and trade policy (including devaluation), among
others.

In the case of Rwanda, Loveridge (1989) found that 73% of Rwandan
farmers were net buyers of beans and that 6% of the farmers accounted
for over half of the net sales. Net buyers of beans depended more
heavily on coffee and tea sales than net sellers. Furthermore, based on
the imbalance between purchases and sales, he estimated that 15% of the
national consumption of beans (and 60% of purchases) must have been
imported. The survey data also indicated the existence of informal
imports of sorghum. These conclusions were based on agricultural
surveys of some 1000 farm households in 1985-86.

Although the ENBC data set is older (1983) and based on a smaller
sample (270 households) than that used by Loveridge, the breadth of the
ENBC survey allows it to address some additional issues. In this
section, we examine the net sales position for six principal crops, the
degree of correlation in net position across crops, and the relationship
between net sales and standard of living.

Average net sales in the rural sector: Table 5-18
presents information on rural production, marketing, and consumption for
seven crops, expressed in kilograms per rural household per year
(kg/hh/yr). These results support the finding of Loveridge (1989) that
rural purchases exceed sales for beans and sorghum. The ENBC figures

imply that been imports represent 10% of rural consumption and 64% of

131

rural market purchases, estimates generally in line with those of
Loveridge. In the case of sorghum, the calculation is complicated by
the fact that a large portion of sorghum output is used in beer
production, frequently by the same household. Based on ENBC estimates
of traditional beer output and accepted transformation coefficients,
self-supplied sorghum for beer brewing represents 75 kg/hh/yr on average
(see Ministry of Planning, 1988, Appendix D). Taking this into account,
apparent imports are 19% of rural usage (including that for beer

brewing) and 43% of market purchases.

Table 5-18: Rural production, marketing, and consumption of six crops
_

Consumption
of own
Production production Sales Purchases Net sales Consumption
Comodity (kg/hh/yr) (kg/hh/yr) (kg/hh/yr) (kg/hh/yr) (kg/hh/yr) (kg/hh/yr)

 

Sorghum 121 8 38 67 -29 150
Maniac 298 236 62 30 32 266
Sweet pot. 854 790 64 48 16 838
White pot. 260 177 83 24 59 201
Banana 1691 520 115 77 38 1653
Beans 354 333 21 59 -38 392
Coffee 17 0 17 0 17 0

 

Note: Production is the sum of home production and sales. Consumption is the sum of home
production and purchases. In the case of sorghum and banana, both production and consumption
figures include the amounts used by the grower in the manufacture of traditional beer. This
represents an estimated 1056 kg of bananas and 75 kg of sorghum per household per year. No
allowance for self-stored seed is made in these calculations.

Source: Rwandan ENBC/Rural sector.

e

In contrast, rural sales of the other staple food crops exceed
rural purchases, according to the ENBC data. The surpluses (positive
net sales) range from 16 to 59 kg/hh/year, depending on the crop. In
order to assess the hypothesis that these surpluses are the volumes
shipped to the urban areas of Rwanda, Table 5-19 presents the estimated
rural surpluses (net sales) and urban market demand, both expressed in
total tonnage. These figures are based on the extrapolation of ENBC

figures to the national level.

132

Table 5-19: Rural net sales and urban demand

 

Rural mkt Rural Urban mkt National

demand surplus demand surplus as
Commodity (1000 mt) (1000 mt) (1000 mt) % of cone.
Sorghum 69.4 -30.1 8.5 -23 %
Cassava 31.2 33.2 10.2 8 %
Sweet potatoes 49.9 16.6 7.3 1 %
White potatoes 24.8 61.2 37.2 10 %
Bananas 80.0 39.4 11.8 2 %
Beans 61.6 -39.4 9.6 -12 %

 

Source: Rwandan ENBC.

The national surplus (rural surplus minus urban market demand) is .
under 10% of national consumption for manioc, sweet potatoes, and
bananasl. This is probably within the margin of error for these
estimates. In the case of white potatoes, the results may indicate
exports to neighboring countries. This result confirms the conclusions
of Ngirumwami (1989) who found frequent references to potato exports in
interviews with Rwandan traders (see also Scott, 1988: 77).

Table 5-19 also illustrates the fact that the bulk of the market
demand for the basic staple crops is by rural households. It is often
assumed that, because rural households rely on the market for only a
small portion of their food consumption, agricultural sales must be
destined for urban markets. For all the basic staples except white
potatoes, rural market demand is three to eight times are great as urban
demand. Thus, the principal agricultural marketing channels are rural-

rural, with only relatively small volumes being siphoned off to meet

urban demand.

 

- 1. These calculations do not take into account agricultural
sales by urban households. The value of urban agricultural sales
indicates that the total volume for all crops is probably around six
thousand metric tons.

133

White potatoes are the exception in that the cities account for
60% of the national market demand. This is related to the fact that
white potatoes are a relatively expensive source of calories and are
actually a ”luxury" good in the rural sector (see Tables 6-4 and 6-5).

Qisppibutiog of householdg by net sales: Until now, the
discussion has been confined to the net sales of different commodities
for the "average" household. In this section, we explore the
distribution of rural households according to their net sales position
and examine the characteristics of net buyers and net sellers.

Table 5-20 shows the percentage of rural households according to
the type of participation in the markets for the six principal
commodities. The proportion of rural households that participate in one
way or another is around half for most commodities, but in the case of
beans it is over 90%. The bean market is also unusual for the large
percentage of rural households that are only purchasers (54%) and for
the relatively small numbers of households that only sell (14%).

Table 5-20: Distribution of households by market participation

Percentage of households by market participation

 

Buy and Neither buy
Commodity Only buy Only sell ' sell nor sell
Sorghum 32.7 23.7 5.8 37.8
Cassava 28.0 18.6 9.3 44.1
Sweet potatoes 26.8 22.2 2.6 48.4
White potatoes 32.2 11.9 2.1 53.9
Bananas 13.2 29.7 3.8 53.2
Beans 54.4 13.8 22.4 9.3

 

Only a small proportion of rural households both purchase and sell
the same commodity: with the exception of beans, each commodity is both
purchased and sold by less than 10% of rural households. This
<=ontradicts the common belief that many farmers are forced to sell their

<=xop at low harvest prices, only to buy some of it back at high prices

134

later in the season. Even in the case of beans, there is no evidence
from the ENBC that households that buy and sell beans are poor
households forced to make ”distress" salesl.

More detailed information on net sales is provided in Figures 5-1
through 5-7 which show the cumulative percentage of rural households
according to net sales of the six staple crops and coffee. Figure 5-1
provides the distribution for net sales of sorghum. Roughly half of the
rural households are net buyers and one quarter are net sellers. The
sharp "point" in the lower left portion of the graph indicates that net
purchases are highly concentrated among a small number of households.
This is due to the influence of relatively large-scale sorghum beer
brewers who purchase their raw materials. The area above the curve and
below the center line represents the total volume of net purchases,
while the area under the curve and above the center line represents net
sales. The fact that former exceeds the latter reflects the excess of
purchases over sales in Rwanda, presumably made possible by informal
sorghum imports.

The distribution of households by net sales of cassava is quite
different, as shown in Figure 5-2. About 30% of rural households are
net buyers and 25% are net sellers, with close to half of the households
having no net sales or net purchases. Purchases of cassava are less
concentrated than those of sorghum, which is expected since most cassava
purchases are for direct consumption.

Sweet potatoes follow a similar pattern, as shown in Figure 5-3.
One quarter of the rural households are net sellers, one quarter net
buyers, and the remainder do not participate in the sweet potato market.
Since virtually all rural households (94%) grow sweet potatoes, most of

these non-participants grow sweet potatoes for their own consumption.

 

1. 'Bouseholds that both buy and sell beans in the rural
sector tend to have average levels of expenditure and caloric intake and
above-average levels of home production of beans.

 

 

 

M eelee (WWW)
(MI-ll“)
I
e
e
I

 

 

 

hunk— I 0' mo.

 

 

 

Figure 5-1: Distribution of households by net sales of sorghum

 

 

1..
1.-
.J
1.:J
1 a
me-
0.0-1

0.4 -

(men)

0.: _.

let eelee (WWW)

 

-0.I -
.OA -.

 

'°'. I I I I I I I I I

 

 

hall‘ In. I 0' ml-

 

 

 

Figure 5—2: Distribution of households by net sales of cassava

According to Figure 5—4, white potatoes have a relatively even
distribution of purchases among the 25% of rural households that buy
them, but only 15% of rural households have net sales. Among the net
sellers, a small proportion of households account for a large portion of

the total volume. This concentration of production is due to the agro-

 

 

 

m eelee (Wer)
(MI-em)
I
o
.I
l

 

 

 

“all..- I d ”I.

 

 

 

Figure 5-3: Distribution of households by net sales of sweet potatoes ,

climatic requirements of potatoes which restrict them to fields above
1800 meters. In addition, there are a number of relatively large—scale
commercial growers in the northwest (Scott, 1988: 61, 68). The overall
rural surpluses in white potatoes is reflected in the greater area above
the center line than below it.

The distribution of rural households by net sales of bananas is
shown in Figure 5-5. A relatively large portion of households (30%)
have net sales. On the other hand, the net purchases of bananas are
highly concentrated. As in the case of sorghum, this is the result of
large-scale banana beer producers who need to purchase large quantities
of raw materials.

The net sales of beans are shown in Figure 5-6. There are several
distinctive aspects of the pattern of net beans sales. First, the total
volume of net purchases exceeds by a considerable margin the volume of
net sales. As noted in the previous section, this appears to indicate
informal imports of beans. Second, a large majority of rural households
(70%) are net buyers of beans. Perhaps only one quarter of rural

households have net sales. And third, unlike the other staple crops,

 

 

MeeleetWWWJ
(mm
one
um»
I I l

 

 

 

 

uni-else . e! her-duet.

 

 

 

Figure 5-4: Distribution of households by net sales of white potatoes

 

 

P
u

 

let eelee (WWW)
(nausea)

 

'3', I I I I I I I
N 40 ”

B-IIICIVI. I .9 ml-

 

 

81
5

 

 

 

Figure 5-5: Distribution of households by net sales of bananas

beans are bOught and/or sold by almost all rural households. About 20%
of all rural households have net purchases over 100 kg/yr, a quantity
that represents roughly one quarter of the average household

consumption.

138

 

 

am-

mi

 

-“1

ht eeIee (WWW)

-mq F

«no:

 

 

 

I I I r I I I j
0 so 40 n_ O 1m

“lens- I d var-l m0.

 

 

 

 

Figure 5-6: Distribution of households by net sales of beans

Finally, the distribution of rural households by the volume of
coffee sales is presented in Figure 5-7. According to the ENBC data,
about one third of the rural households sold coffee. Most coffee
growers sell less than 100 kg/yr, but about five percent of rural
households sell more than this amount. However, the ENBC may have
underestimated coffee sales. The 1984 Agricultural Census, using a much
larger sample, estimated that 44% of rural households were producing
coffee. The Agricultural Census also estimated coffee production to be
almost twice as high (32 compared to 17 kg/household/yr).

These graphs have several implications for the impact of price
changes on rural households. First, an increase in the price of beans
will harm a large majority of rural households (70%), benefiting only
one quarter of them. Second, changes in the price of the other staple
crops (sorghum, cassava, sweet potatoes, white potatoes, and bananas)
will generally benefit one quarter of the households, hurt another
quarter, and not directly affect half of the rural households. Third,
the impact (both positive and negative) will be relatively concentrated

among a small number of households. This is particularly true in the

139

 

 

ht eelee (Whflw)
l

 

 

 

”a
n-I
40¢
”a
o I _ I T T fl f T I U
0 20 40 m ' n '100'

Cami-elm I 0' mo.

 

 

 

Figure 5-7: Distribution of households by coffee sales

case of net sellers of white potatoes and the beer brewers who are net
buyers of bananas and sorghum.

Coprelation of pet sales across crops: The results in the
previous section raise the question whether net buyers of one commodity
tend to be net buyers of other commodities as well. One approach to
answering this question is to consider the correlation of net sales, in
volume terms, across commodities, shown in Table 5-21. In general, the
correlation coefficients are fairly low: only three of the commodity
pairs have net sales correlations greater than 0.15 in absolute value.
The highest coefficient is that between net sales of beans and net sales
of sorghum, although even this correlation is relatively weak (0.168).

Another way to address this question is to consider the
distribution of households according to their net sales of staple crops
as a group. For this purpose, net sales of the six staple food crops,

expressed in calories per adult equivalent (ae), have been summed for

140

Table 5-21: Correlation of net sales of different commodities
—

Sorghum Cassava Sw pot Wh pot Banana Beans Coffee
Sorghum 1.000

Cassava .056 _1.000

Sw pot -.052 .044 1.000

Wh pot -.155 -.040 -.006 1.000

Banana .076 .135 -.164 .006 1.000

Beans .168 .133 .128 -.033 .147 1.000

Coffee .064 .125 -.003 -.089 -.008 .014 1.000

 

Source: Rwandan ENBC/Rural sector.

—

each householdl. Sorghum and banana purchases for beer brewing have
been excluded in order to focus on food consumption. Figure 5-8 shows
the cumulative distribution of households by the net sales (in

kcal/ae/day) of the six staple food crops.

 

 

 

Vbt eelee e! ecolee (Mel/eelw)
(New
0
e
1

 

 

 

Gut-thee l of he‘s-reel-

 

 

 

Figure 5-8: Distribution of households by net sales of six staple crops
expressed in caloric terms

This graph reveals that fully 45% of the rural households are net

buyers of the six staple goods. However, many of the net buyers are

 

1. ' Net sales are expressed in calories to reflect more
accurately the importance of each kilogram of the different crops and in
per-adult-equivalent terms to adjust for household size.

141

purchasing relatively small amounts of these crops. Only about 5% of
the rural households purchase more than 500 kcal/ae/day worth of the six
staple crops. As a basis for comparison, the mean level of caloric
intake in the rural sector is 2444 kcal/ae/day, according to the ENBC
data.

ghagaoteristics of net buvgpg: The distributional impact

of a change in the price of an agricultural commodity obviously depends

 

on the characteristics of net buyers and net sellers. It seems :
plausible that net buyers could include poor households with g
insufficient land to meet their own food needs and/or households with E
relatively well-paying non-agricultural occupations. Table 5-22 5
provides some figures to help address these questions. a

With respect to net sales of sorghum, it appears that households
selling more than 100 kg/yr are relatively well-off. On the other hand,
net buyers are better off in terms of expenditure and caloric intake
than small-scale net sellers. This may be due to the influence of
sorghum beer producers among the net buyersl.

In the case of cassava and sweet potatoes, there is some evidence
that the 15-20% of households with net purchases over 50 kg/yr have

lower levels of food self-sufficiency, caloric intake, and expenditure.

Net buyers of cassava tend to have smaller farms, but this is not the
case for net buyers of sweet potatoes. However, it should be recalled
that even among net buyers, home production is more important than
purchases as a source of the commodity.

White potatoes present a quite different pattern in which net
buyers tend to be, if anything, better off than the 54% of rural
household that neither buy nor sell potatoes. Large-scale net sellers

(those with net sales of more than 100 kg/yr) have even higher levels of

 

1. The home production figures in this section of the table
refer only to consumption of own production, excluding production
retained for the manufacture of sorghum beer.

JJIZ

Table 5-22: Characteristics of rural households by net sales position
IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII
Pct
Farm food Home
Pct Expend Nbr size self Kca] Sales Purch prod
hh (F/ae) pers (ha) suff /ae (kg) (kg) (kg)
Net sales of sorghum
< -100 kg 16.0 13,551 5.3 1.5 66 2,502 3 292 10
-100 to -50 kg 9.3 13,933 4.6 .7 71 2,709 4 73 7
-50 to -1 kg 25.6 13,313 5.0 1.1 67 2,473 4 30 8
0 kg 24.5 11,907 3.9 1.1 64 2,279 0 O 4
1 to 100 kg 13.6 11,857 5.7 1.6 70 2,262 53 15 11
> 100 kg 10.9 15,418 5.9 2.1 74 2,659 268 32 14
Net sales of cassava
< -100 kg 9.9 11,597 6.0 1.1 61 2,135 5 194 217
-100 to -50 kg 5.9 9,651 5.6 1.1 54 1,872 13 82 186
-50 to -1 kg 16.6 13,212 4.5 .9 65 2.523 4 26 173
0 kg 44.1 13,933 4.5 1.4 71 2,622 0 0 141
1 to 100 kg 10.0 14,415 5.0 1.4 68 2,244 62 7 419
> 100 kg 13.5 11,833 5.6 1.6 70 2,387 402 7 520
Net sales of sweet potatoes
< -100 kg 12.9 10,799 6.1 1.4 67 2,092 3 306 905
-100 to -50 kg 7.9 10,049 5.4 1.3 71 2,210 0 77 685
-50 to -1 kg 6.5 14,478 5.5 1.0 65 2,480 0 24 494
0 kg 48.4 13,651 4.6 1.3 67 2,497 0 0 624
1 to 100 kg 9.8 14,313 4.8 1.4 66 2,471 84 9 757
> 100 kg 14.4 13,514 4.6 1.2 70 2,671 387 0 1,457
Net sales of white potatoes
< -100 kg 8.7 13,701 5.9 1.5 59 2,435 2 141 75
-100 to ~50 kg 8.8 14,458 5.5 1.3 70 2.558 1 71 60
-50 to -1 kg 15.7 14,691 4.9 1.3 69 2,509 l 30 47
0 kg 53.9 12,020 4.7 1.3 67 2,344 0 0 43
1 to 100 kg 3.7 12,263 5.4 1.1 73 2,519 71 9 793
> 100 kg 9.3 15,111 5.0 1.3 71 2,782 865 4 1,137
Net sales of bananas
< -100 kg 9.3 15,466 5.9 1.0 59 2,386 1 664 580
-100 to -50 kg 5.4 9,997 5.4 1.3 65 2,283 19 91 353
-50 to -1 kg 8.7 13,792 5.0 1.2 60 2,430 5 21 297
0 kg 45.1 11,907 4.7 1.2 68 2,380 0 0 208
1 to 100 kg 9.5 11,797 4.6 1.0 65 2,503 72 20 454
> 100 kg 22.0 15,582 5.0 1.8 74 2,617 488 32 1,294
Net sales of beans
. < -100 kg 18.8 11,814 6.1 1.5 59 2,281 8 176 315
-100 to -50 kg 17.8 11,751 5.2 1.2 68 2,381 5 77 303
-50 to -1 kg 33.3 13,356 4.4 .9 68 2,504 6 30 291
0 kg 9.3 13,241 4.2 1.5 63 2,260 0 O 251
1 to 100 kg 15.2 13,098 4.8 1.7 75 2,539 54 15 450
> 100 kg 5.6 19,923 4.9 1.9 72 2,881 150 S 553
Sales of coffee
0 kg 67.2 13,354 4.7 1.2 68 2,593 0 0 0
1 to 100 kg 30.0 12,296 5.3 1.4 66 2,138 35 0 0
> 100 kg 2.8 15,427 6.9 1.8 68 2,143 205 0 0
Rura] means 100.0 13,095 4.9 1.3 67 2,444 115 77 520

143

expenditure and caloric intake. The characteristics of net buyers are
explained by the fact that potatoes are a relatively costly source of
calories.

Concerning the net position in bananas, large-scale net buyers are
relatively well off, in spite of the small average farm size and low
level of food self-sufficiency. As in the case of sorghum, this is
probably due to the presence of important banana beer producers among
the net buyers. Large-scale net sellers are also relatively well-off,
although they tend to have above average farm sizes and rates of food
self-sufficiency.

Beans present the clearest case in which net sales are correlated
with the level of expenditure per adult equivalent, caloric intake, and
food self-sufficiency. Households buying over 50 kg/yr do not have
particularly small farms, but they are larger in number than the average
rural household.

Finally, Table 5-22 seems to indicate that ”large-scale" coffee
growers (those selling over 100 kg/yr) are better off than the average
rural household in terms of expenditure (though not in terms of caloric
intake), but small-scale coffee growers are less well off. This is
plausible, but the sample size for the ”large-scale" growers is too
(small to draw firm conclusions. Interestingly, the rate of food self-
sufficiency is the same between growers and non-growers.

5.5.3 Tpadeable component of expenditure and income

In this section, we concentrate on the composition of
cash expenditure and cash income with particular emphasis on the
tradeable and nontradeable components. As discussed in section 4.5.2,
the rural budget survey used a system of 405 codes for goods and
services, while the urban survey relied on an even more disaggregated
system of 825 codes. Each code was classified as tradeable or non-
tradeable, based on a judgement as to whether the domestic price is

determined by international prices or by domestic supply and demand.

144

Tradeable goods include export crops, rice, cooking oil, wheat
products, sugar, processed foods, and most manufactured consumer items.
Host staple food crops, building materials, and other bulky low-value
products were considered non-tradeable, as were all services. As
discussed earlier, factory beer is considered 50% tradeable, while beans
are counted as 25% tradeable (see Appendix A).

Table 5-23 gives the proportion of tradeable goods in cash
expenditure on each budget category. For example, tradeable goods
account for 16% of rural cash expenditure on food, but tradeables
represent almost twice as high a percentage of urban cash food
expenditure (30%). Part of this difference is due to the fact that non-
tradeable categories, such as tubers/bananas, play a larger role in the
cash budget of rural households than urban. In addition, the
composition of each category is more heavily weighted toward tradeable
goods in the urban sector, particularly in the case of grains, animal
products, and beverages. With respect to grains, rural households
purchase primarily (nontradeable) sorghum and maize, while urban
households buy mostly (tradeable) rice and wheat products. With regard
to beverages, the differences is due to the fact that factory beer is
much more important in the cities. Non-tradeable traditional beers
dominate beverage purchases in the countryside.

Among-non-food categories, rural cash expenditure has a larger
tradeable component (57%) than does urban cash expenditure (47%). This
is primarily due to the composition of energy/water, education, and
leisure/services. In general terms, this is because urban spending is
more concentrated on services (e.g. water, electricity, school fees, and
leisure services), while rural spending tends to have a larger share of
goods, including tradeable goods (e.g. kerosene, school uniforms, and
consumer goods). In addition, a much larger share of rural non-food

_spending is allocated to clothing, which is almost entirely tradeable.

145
Table 5-23: Tradeable component of rural and urban cash expenditure
IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII-I-I-I-I-I-I-I-I-I-Il

 

Budget category Rural Urban
We). 36.6 39.2
Food 16.0 29.6
Grain 36.1 85.9
Tubers/bananas .0 .0
Legumes 23.0 22.2
Fruits/vegetables 1.0 4.5
Animal products 2.2 17.9
Beverages 7.3 37.7
Other 47.0 52.3
Non-food sub-total 56.9 47.3
Clothing 96.4 94.0
Housing 14.1 15.7
Household equipment 64.2 76.2
Energy/water 82.1 26.8
Health/hygiene - 50.4 72.9
Education 33.7 15.5
Transportation 51.2 84.0
Tobacco ' .0 .0
Leisure/services 50.7 29.8

Interestingly, the tradeable share in overall spending is almost
the same in rural and urban areas (37% and 39%, respectively). This is
somewhat surprising given the conventional wisdom that imported goods
play a much larger role in urban (and high-income) household budgets.

If the prices of all tradeable goods increase in the same
proportion, which price increases will have the greatest effect on
household budgets? In order to address this question, we need to
examine the composition of tradeable goods spending, as shown in Table
5-24. The most striking aspect of this table is that almost half (46%)
of all tradeable goods spending in the rural sector is on clothing. The
ENBC data indicate that imported used clothing accounts for roughly one
third of rural clothing expenditure. Bolts of cloth and African print
wraps, also imported for the most part, represents another third (see
Ministry of Planning, 1988: 33).

Household equipment and "other food" represent the second and

third largest categories of rural tradeable spending. Each of these

 

146

Table 5-24: Composition of rural and urban tradeable cash expenditure
IIIIIIIIIIIIIImIIIIIIIIIIIIIIIIIIIIIIIIIIImIIImum-IIIIIIIII-Imuuummmma

 

Budget category Rural Urban ’

56ml 100.0 100.0
Food 21.6 34.5
Grain 3.3 9.7
Tubers/bananas .0 .0
Legumes 5.9 2.5
Fruits/vegetables .0 .3
Animal products .4 3.6
Beverages 3.4 9.5
Other 8.5 8.9
Non-food 78.4 65.5
Clothing 46.2 13.9
Housing 5.5 7.5
Household equipment 8.7 7.5
Energy/water 5.4 3.9
Health/hygiene 5.8 6.4
Education 1.0 .6
Transportation 44.3' 23.2
Tobacco .0 .0
Leisure/services 1.5 2.5

categories accounts for 8-9% of tradeable spending.

In the urban areas, transportation represents almost one quarter
(23%) of tradeable spending. This includes taxi and bus fare, fuel,
spare parts, and lubricants, but bus fares represent almost half of the
total. Other important components of tradeable spending are grains
(wheat products and rice) and beverages (primarily factory beer).

Having discussed the tradeable component in the average budget of
rural and urban households, it is now worth examining how the tradeable
component varies across households. Tables 5-25 and 5-26 give the
proportion of cash expenditure and of net cash income which is
associated with tradeable goods in the rural and urban sectors,
respectively.

According to Table 5-25, the tradeable portion of rural cash
expenditure does not show any consistent pattern with respect to total
expenditure, although it is highest for the third quintile. The net
cash income pattern is only somewhat more regular, with a "peak” in the

second and third quintiles. This peak corresponds to a larger number of

147

coffee producers in the third quintile, although this may be merely a
characteristic of the sample.

Table 5-25: Importance of tradeables in rural income and expenditure by
expenditure quintile

Tradeable share Tradeable share
Rural in cash in cash net
quintile expenditure (%) income (%)

lat 36.9 7.3
2nd 35.9 ' 17.0
3rd 42.4 20.5
4th 38.8 . 7.5
5th ‘ 32.1 8.2

 

Table 5-26 gives the corresponding results for the urban sector.
The importance of tradeable goods in urban cash expenditures rises from
31% in the first (poorest) quintile to over 40% in the last two
quintiles. The pattern for net income is irregular, but it appears that
the poorest 40% in the urban sector rely primarily on non-tradeable
types of income. This would indicate that the urban poor would be hurt
by devaluation, in spite of their relatively low spending on tradeables,

because of their overwhelmingly non-tradeable sources of income.

 

ls

148

Table 5-26: Importance of tradeables in urban income and expenditure by
expenditure quintile

Tradeable share Tradeable share

 

Urban in cash in cash net
quintile expenditure (%) income (%)
1st 31.1 5.6
‘2nd 34.7 5.7
3rd 36.8 30.3
4th 43.6 16.2
5th 40.2 22.1

The results in Tables 5-25 and 5-26 should be regarded with some
skepticism. It should be recalled that in the rural areas, cash
transactions are modest in absolute terms and may be greatly influenced
by a single large transaction. In addition, net income is subject to
greater measurement error than expenditure, a fact which is more serious
when the data are disaggregated. Finally, the classification of income
sources into tradeable and nontradeable groups is more difficult than

the classification of expenditure.

5.5.4 §ppmgpy
With regard to the impact of price changes on Rwandan
households, three topics were examined: the importance of market
transactions within the overall budget, the net sales position with
respect to the principal crops, and the tradeable component of cash
income and expenditure.

The importance of market purchases in total expenditure is
positively related to the level of expenditure per adult equivalent in
both rural and urban areas. As a result of these patterns, we can
expect a given price change to have an effect on urban households at

least twice as great as that on rural households. Furthermore, other

149

things being equal, the impact will be fairly similar across rural
households, but it will vary considerably among urban households.

The net sales information indicate that the rural sector of Rwanda
purchases more beans than it sells, implying the existence of informal
imports. Almost three quarters of the rural households are net buyers.
The data also imply the existence of sorghum imports. For the other
staple food crops, as a rule of thumb, price increases will benefit the
25% of rural households who are net sellers, harm another quarter of the
households, and leave unaffected the remaining 50% of rural households
who do not have market transactions in that commodity.

A household with net sales in one commodity shows no significant
tendency to have net sales in other commodities. In the case of beans
and possibly cassava and sweet potatoes, net purchases are correlated
with reduced caloric intake and expenditure levels.

The proportion of cash expenditure spent on tradeable good is
roughly the same in rural and urban sectors. In the rural sector,
clothing accounts for almost half of cash expenditure on tradeables,
while transportation is the most important type of tradeable spending
among urban households. The tradeable share in cash expenditure is
greater among high-income urban households than low-income, but it shows
no strong trend in the rural sector.

Thus, the impact of devaluation is expected to be less among rural
households and among the poor, not because they purchase fewer
tradeables, but because purchases are a smaller part of their overall
expenditure. However, these results are only suggestive in that the
analysis has not combined the various factors into one welfare measure,
nor does the analysis incorporate the adaptation of households as

consumers and as producers. This is the task of the next two chapters.

 

CHAPTER SIX

MODEL OF HOUSEHOLD DEMAND

In this section, we describe the results of the estimation of
rural and urban food demand as a function of total expenditure (income),
household characteristics, and prices. Sections 6.1 describes several
aspects of model selection: whether to estimate separate rural and urban
models or combine them, what commodity categories to use, and whether
single-equation ordinary least squares (OLS) or the seemingly unrelated
regression (SUR) model is more appropriate.. Sections 6.2 and 6.3
describe the results of the rural model with and without imposing
symmetry, while 6.4 and 6.5 provide the corresponding results from the
urban model. The final two sections digress somewhat to cover two
topics: 1) a comparison of OLS and Tobit results in estimating rural
food demand and 2) an analysis of the possible influence of quality and

measurement error in the elasticity estimates.

6.1 e ect o the a ro 'a e model

6.1.1 tme o a a d ba sam e

The first question to address is whether urban consumer

behavior is sufficiently different from rural behavior to justify
separating urban and rural samples to estimate demand from each.
Statistically, the question is whether there are variables missing from
the demand equations (such as tastes and assets) which vary between
rural and urban households and are correlated with the independent
variables, thus biasing the combined-sample parameter estimates.

We can use the F test (see equation 4-16) to statistically test
the joint null hypothesis that all rural coefficients are equal to the
corresponding urban coefficients (this is also called a Chow test). The

test is carried out equation-by-equation using ordinary least squares.

150

 

151

Table 6-1: Test of equality of urban and rural coefficients

Category F stat Prob

 

The results in Table 6-1 indicate that,

 

at the 90% confidence

soaca 1.41 0.10
arcs 1.17 0.27
SWPOT 3.67 0.00
wspor 3.03 0.00
BANAN 5.43 0.00
BEANS 2.67 0.00
PEAS 1.46 0.09
sass 1.57 0.05 _
MEAT 1.72 0.02
asses 1.46 0.09
ssEBR 3.99 0.00
FBEER 1.33 0.15
OIL 1.64 0.04
. SALT 1.66 0.03
SUGAR 1.67 0.03
cross 2.06 0.06
30083 0.59 0.74
EQUIP 0.26 0.96 4
snsac 14.33 0.00 -
HEALT 6.16 0.00
EDUCA 1.67 0.13
TRANS 4.30 0.00
TOBAC 8.89 0.00
LEISU 8.12 0.00

level, we can reject the null hypothesis that rural and urban coeffi-
cients are equal for 20 out of the 24 budget categories tested. Only in
the equations for rice, housing, education, and household equipment are
the differences statistically insignificant at the 90% level. At the
95% level, we can reject the hypothesis of rural-urban equality for 16
out of the 24 equations (sorghum, peas, banana beer, and clothing).

Taking the commodities as a group, it is clear that urban and
rural coefficients are significantly different. Thus, it is appropriate
to estimate separately rural and urban demand.

6.1.2 Commodity categories

Twenty-one food categories were considered for inclusion

in the rural model. The F statistic was used to test the joint null

152

hypothesis that all the coefficients (other than the constant) were
equal to zero. The hypothesis could not be rejected for several minor
commodities. After some experimentation, it was decided to drop four
goods from the rural model (eggplant, cabbage, onion, and prepared
meals) and to combine goat meat and fish into an "other meat" category.
The price of ”other meat” was calculated as the weighted average of goat
and fish prices. The impact of these changes is relatively minor since
the four dropped goods account for only 1.7% of rural expenditures,
while ”other meat" represents 1.8%. The 17 food commodities included in
the rural model are presented in Table 6—2. On average, they represent
74% of household expenditure and 87% of household food expenditure among
rural households.

In the urban system, 26 food products were originally included.
Based on the F-test of the joint significance of the independent
variables, it was decided to combine four vegetables (eggplant, cabbage,
tomatoes, and onions) into a "vegetables" category, to combine goat meat
and fish into "other meat," and to collapse liquid and powder milk
categories. Again, the prices of the combined categories were calculat-
ed as a weighted average of the various components of each.

The 21 food commodities in the urban model are briefly described
in Table 6-2. On average, they comprise about 59% of total expenditure
and 90% of food expenditure by households. The greater coverage of food
expenditure in the urban model is due to the inclusion of three catego-
ries not in the rural model: bread, milk, and prepared meals. Other
differences are that the urban model disaggregates cassava into cassava
root and cassava flour and that it includes the category "vegetables,"
while the rural model has just "tomatoes."

In both the rural and urban models, non-food expenditure was
divided into nine categories for the purpose of demand estimation.
Although the joint significance of the independent variables was low for

some non-food categories, all nine were retained in the final model to

 

153

Table 6-2: Description of food products in rural and urban models
_

 

Food Rural Urban Description

Code model model

SORGH Yes Yes Sorghum in grain or porridge
RICE Yes Yes Rice in grain or other form
BREAD No Yes Bread, cake, or other wheat product
CASSA Yes Yes Cassava root and, in rural model,

cassava flour

SWPOT Yes Yes Sweet potato

WHPOT Yes Yes White potato

BANAN Yes Yes Bananas and plantains

CASFL No Yes Cassava flour

BEANS Yes Yes Dry beans in any form
PEAS Yes ‘ Yes Peas

TOMAT Yes No Fresh tomatoes

VEGET No Yes Cabbage, onion, tomato, & eggplant
BEEF . Yes Yes Beef and related products‘

OTHMT Yes Yes Goat meat or any type of fish
MILK No Yes Liquid milk or milk powder

BBEER Yes Yes Banana beer

SBEER Yes Yes Sorghum beer

FBEER Yes Yes Factory beer
OIL Yes Yes Palm oil, other oils and fats
SALT Yes Yes Salt

SUGAR Yes Yes Sugar, candy, and other sweets

MEALS No Yes Prepared meals outside home

OTHER No No Millet, yams, groundnuts, greens,

other vegetables, fruit, other
meat, other beverages, canned or
processed goods

allow finer disaggregation between tradeable and nontradeable goods.
Table 6-3 provides a brief description of the goods and services which
comprise each non—food category.
6.1.3 Efipiggpigp_m§thod: OLS vg SUR

As described in Chapter 4, there are two situations in
which the seemingly unrelated regression (SUR) model does not improve on
the estimates obtained from single-equation ordinary least squares
(OLS): 1) when all the equations in the model have the same independent
variables and 2) when there is no correlation among errors in different
equations. The first condition is not fulfilled because the food

equations have price terms while the non-food equations do not. The

154

Table 6-3: Description of non-food categories in rural and urban models
—

Rural Urban

 

Category model model Description

CLOTH ‘Yes Yes Clothing, shoes, hats, accessories,
cloth, sewing materials, tailor
services

HOUSE Yes Yes Building materials, construction

labor (excludes rent and the
purchase of buildings and land)

EQUIP ‘Yes Yes Furniture, kitchenware, bedding,
floor mats, decorations

ENERG ‘Yes Yes Firewood, charcoal, water, kerosene,
electricity, batteries

HEALT , Yes Yes Medication, clinic fees, traditional
healers

EDUCA Yes Yes School fees, school uniforms, school
materials

TRANS ‘Yes Yes Buses, taxis, spare parts, operating

cost of vehicles (excludes
purchase of vehicles)

TOBAC ‘Yes Yes Cigarettes, tobacco leaf, tobacco
powder
LEISU ‘Yes Yes Radios, cassettes, games, sporting

equipment, domestic employees

second condition can be tested using the Breush-Pagan test of diagon-
ality.

The first step in the test is to estimate food and non-food demand
using single-equation OLS regression. The residuals are then used to
estimate the covariance matrix of errors across equations and within
households. The Breush-Pagan statistic tests the null hypothesis that
the covariance matrix is diagonal (i.e. that there is no correlation in
the error terms across equations).

The Breusch-Pagan test of the 26x26 cross-equation covariance
matrix of the rural model indicates that we can reject the null hypothe-
sis of diagonality at the 99.9% confidence level.

Null hypothesis: Cross-equation covariance matrix of

residuals is diagonal in rural model.

Chi squared - 762.845 with d.f.= 325
Prob under Ho - 0.000

he.

38:
301
$91

155

In the presence of cross-equation correlation of error terms, the SUR
model is more efficient than single-equation OLS because it uses
information regarding the correlated error terms to improve the parame-
ter estimates.

The Breusch-Pagan test was also applied to the 30x30 cross-
equation covariance matrix of the urban model. Again, the chi-squared
statistic was quite high, allowing us to reject the hypothesis of ,
diagonality at the 99.9% confidence level.

Null hypothesis: Cross-equation covariance matrix of

residuals is diagonal in urban model.

Chi squared = 1572.461 with d.f.= 435

Prob under Ho - 0.000

Thus, the SUR model is more appropriate for the urban demand system as

 

well.

It should be noted, however, that in spite of the non-diagonality
of the cross-equation covariance matrix, the parameter estimates
obtained using SUR are quite similar to those obtained using OLS. For
example, the expenditure and price elasticities at the mean differ by
0.02 or less for almost every food category. In the case of non-food
categories, OLS and SUR estimates are identical because the non-food
equations exclude prices and are thus over-identified. If the computa-
tional costs of SUR were high, single-equation OLS would be sufficiently

accurate for most purposes.

6.2 Unpestpicped SUR model of rurgl demand

 

The unrestricted SUR model of rural demand involves the simulta-
neous estimation of 445 parameters (six coefficients common to all 26
equation, plus 17 price terms in each of the 17 food equations).
Because of the large number of coefficients and because many of them are
not easily interpretable in original form, this section presents only
selected results. A complete listing of the coefficients and their

corresponding t statistics is found in Appendix C.

156

First, overall measures of the goodness-of-fit and significance of
the equations are discussed. Then, we consider the impact of different
groups of independent variables: the two expenditure terms, the three
household composition variables, and the price terms.

6.2.1 Overal oodness- f- t and si n cance

1

Table 6-4 presents the mean budget share , the correla-

tion coefficient (R2), the F statistic for the equation as a whole, and E
the probability corresponding to the F statistic.. The correlation :
coefficient indicates the proportion of the variance in the dependent E

variable (budget share) which is."exp1ained” by the set of independent

 

variables. The value of R2 varies from 0.01 for three non-food catego- - E

ries (health, tobacco, and leisure/services) to 0.39 for sweet potatoes.
Although these values may seem low, this is normal for cross-sectional -
demand studies, particularly when budget share, rather than quantity, is
the dependent variable.

The values of the correlation coefficient are generally higher for
food categories than for non-food categories. The low correlation
coefficients of non-food regression equations reflects the smaller
number of independent variables (six compared to 23 in the food equa-
tions). In addition, non-food expenditure is probably less predictable
than food expenditure because the budget shares are small and the
purchases are often lumpy and infrequent. For example, a single 5 20
radio would represent ten times the mean expenditure per household on
leisure and services.

The F statistic in Table 6-4 tests the hypothesis that all

coefficients except the constant are equal to zero. In other words, the

 

1. These budget shares do not agree exactly with those
presented in Chapter 5 because of different calculation methods. First,
these are unweighted averages, whereas the figures in Chapter 5 use the
expansion factors based on the sampling method. Second, these figures
are averages shares, while the figures in Chapter 5 represent the share
of total expenditure allocated to each category. The latter figures
give more weight to high-expenditure households.

157

 

Table 6-4: Summary of unrestricted SUR model of rural demand
—
Mean F stat Prob
Budget budget for all under
category share R2 variab Ho
SORGH 1.41 0.16 2.28 0.00
RICE 0.49 0.10 1.24 0.19
CASSA 5.92 0.13 1.65 0.03
SWPOT 12.54 0.39 7.93 0.00
WHPOT 4.02 0.30 4.82 0.00
BANAN 5.86 0.34 5.87 0.00
BEANS 21.61 0.28 4.25 0.00
PEAS 1.39 0.12 1.59 0.04
TOMAT 0.13 0.15 1.94 0.00
BEEF 1.39 0.14 1.87 0.01
MEAT 1.91 0.14 1.95 0.00
BBEER ” 10.15 -0.17 2.49 0.00
SBEER 3.91 0.21 3.29 0.00
FBEER 0.80 0.20 3.07 0.00
OIL 0.96 0.20 2.97 0.00
SALT 1.02 0.18 2.81 0.00
SUGAR 0.31 0.12 1.76 0.01
CLOTH 6.30 0.06 3.37 0.00
HOUSE 3.31 0.18 10.87 0.00
EQUIP 1.54 0.04 2.08 0.05
ENERG 1.19 0.03 1.58 0.15
HEALT 1.68 0.01 0.52 0.79
EDUCA 0.42 0.03 1.44 0.20
TRANS 0.80 0.07 3.64 0.00
TOBAC 0.71 0.01 0.73 0.63
LEISU 0.36 0.01 0.67 0.67

 

null hypothesis is that the budget share does not vary with total

expenditure, price, or household composition. The last column gives the

probability of obtaining the corresponding value of F if the null

hypothesis is true. The results show that the null hypothesis can be

rejected at the 95% confidence level for 20 of the 26 equations (17 of

these are significant at the 99% level). Rice is the only food commodi—

ty for which the coefficients are not significantly different from zero

at the 95% level. This category, which represents only 0.5 % of the
rural budget, was retained because it is one of a few tradeable foods

and thus will be important in subsequent analysis.

clc
car
all
wit

are

sha

ODE

as e
The

Easy
(T189
EXPQ
at a
gene

Dace

QCCU'
is
‘31/1
fOun

e

 

158

Among the non-food categories, the budget shares allocated to
clothing, housing, household equipment, and transportation vary signifi-
cantly with the five independent variables. In contrast, the shares
allocated to the other non-food categories do not vary significantly
with the independent variables. Health, tobacco, and leisure/services
are the least predictable budget categories.

6-2-2 W

Engel's Law states that, as income rises, the budget

share of food in general, and starchy staple foods in particular, falls.
In other words, food should have an expenditure elasticity less than
one, and the cheapest sources of calories should have the lowest
elasticities. Table 6-5 presents the average cost (in Rwandan francs of
1983) per 100 kilocalories of the most important foods. This table
demonstrates that sorghum, sweet potato, cassava, and bananas are the
least expensive sources of calories. Rice, white potatoes, and banana
beer are at least twice as costly on a per calorie basis, but are still
considerably less expensive than beef, goat meat, and factory beer.

The impact of total household expenditure on rural budget shares,
as estimated with the unrestricted SUR model, is shown in Table 6-6.

The estimated coefficients on the expenditure terms, 81 and 82, are not
easy to interpret by themselves. If both 81 and 82 have positive

(negative) signs then budget share increases (decreases) with total
expenditure, so the item is a luxury good (necessity or inferior good)

at all levels of income. When 81 and 82 have different signs, as is

generally the case, goods may change from luxury to necessity (or

necessity to luxury) as household expenditure increasesl.

 

1. The transition from luxury to necessity (or vice versa)
occurs when the budget share curve reaches a maximum (or minimum), that
is, when the expenditure elasticity is 1.0. At this point, log(x/P) 8
-81/282. If 8i and 82 have different signs, then the extremum will be

found at a positive level of expenditure, but it may still be outside
the relevant range.

 

159

Table 6-5: Caloric cost of various food items
_

 

Calories Price Caloric cost

Product (kcal/100 g) (F/kg) (F/100 kcal)
SORGH 345 20.9 0.61
RICE 363 80.4 2.21
CASSA 130 10.5 0.81
SWPOT 96 6.0 0.63
WHPOT 71 12.9 1.82
BANAN 89 7.3 0.83
BEANS 323 29.6 0.92
PEAS 339 35.5 1.05
TOMAT 20 24.2 12.10
BEEF 237 116.8 4.93
GOAT 141 113.5 8.05
BBEER 87 30.5 3.51
SBEER 173 14.1 0.82
FBEER 43 123.7 28.77
OIL 884 154.9 1.75

SALT 0 “47.0 not defined

SUGAR 380 97.3 2.56

The elasticity of demand with respect to total household expendi-

ture is easier to interpret. These elasticities are calculated from 81

and 8? using the following expression (derived in section 4.3.4):

61 = 1 + .911 + _2912 ln(i‘) (6-1)

w, 83 P
The rural expenditure elasticities of demand for food were evaluated at
the mean level of expenditure and are presented in the fifth column of
Table 6-6.

The sixth column provides the F statistic for the null

hypothesis that 81=Bz=0. Under the null hypothesis, budget share does

not vary with household expenditure, so that the expenditure elasticity
is equal to 1.0 at all levels of expenditure. The last column of Table
6-6 gives the probability of obtaining this value of F by chance if the
null hypothesis is true.

The food elasticities conform, in general, to a priori expecta-
tions. First, the expenditure elasticity of food as a whole is 0.85

(this is calculated as the share-weighted average of individual elastic-

 

160

Table 6-6: Effect of household expenditure on rural demand
—

 

ln(exp) F stat Prob
Budget ln(exp) sqrd expend for under
category 81 t 82 t elast expend Ho
SORGH -16.19 -1.75 0.79 1.69 0.48 3.02 0.05
RICE 5.79 0.89 -0.28 -0.84 1.80 1.48 0.23
CASSA 22.14 0.69 -1.30 ~0.80 0.45 5.24 0.01
.SWPOT -98.44 -2.64 4.41 2.33 0.02 40.99 0.00
WHPOT 68.33 2.33 -3.33 -2.24 1.83 5.95 0.00
BANAN -15.77 -0.52 0.82 0.54 1.04 0.21 0.81
BEANS 70.83 1.47 -4.03 -1.65 0.63 14.99 0.00
PEAS 11.62 0.86 -0.59 -0.86 1.09 0.37 0.69
TOMAT 0.20 0.11 -0.01 -0.13 0.70 0.20 0.82
BEEF -1.14 -0.12 0.11 0.22 1.66 4.10 0.02
MEAT 7.48 0.39 -0.30 -0.32 1.80 2.53 0.08
BBEER 4.32 0.11 -0.04 -0.02 1.34 2.97 0.05
SBEER 26.46 1.18 -1.30 -1.15 1.25 1.09 0.34
FBEER -15.23 -1.39 0.86 1.54 2.85 10.49 0.00
OIL 10.71 1.58 -0.52 -1.52 1.58 2.96 '0.05
SALT 3.55 0.99 -0.20 -1.13 0.56 8.22 0.00
SUGAR 3.55 0.71 -0.16 -0.64 2.24 2.23 0.11
CLOTH 2.63 0.12 -0.09 -0.08 1.15 0.80 0.45
HOUSE -92.54 -2.95 5.04 3.17 2.77 26.07 0.00
EQUIP 6.74 0.39 -0.25 -0.29 2.17 4.68 0.01
ENERG 1.69 0.18 -0.10 -0.21 0.72 0.61 0.55
HEALT 3.30 0.37 -0.17 -0.38 0.96 0.12 0.88
EDUCA 4.30 0.62 -0.21 -0.61 1.25 0.22 0.80
TRANS -5.33 -0.64 0.33 0.78 2.35 8.52 0.00
TOBAC -0.41 -0.08 0.01 0.05 0.80 0.31 0.74
LEISU 3.34 0.47 -0.15 -0.42 1.97 0.96 0.38

 

ities). In other words, a 1% increase in total household expenditure is

associated with a 0.85% rise in food expenditure. This implies, of
course, that food is a "necessity" and that the budget share allocated
to food declines with increasing total expenditure.

In addition, the highest expenditure elasticity (2.85) is that of
factory beer, the most expensive source of calories among the products
considered: compared to traditional beers, it is seven times as expen-
sive on a calorie basis and four times as costly on a volume basis.
Other foods with elasticities significantly greater than 1.0 are beef,
white potatoes, banana beer, and cooking oil, all relatively expensive

sources of calories in Rwanda (the elasticities of rice, other meat, and

sugar are also high, but are not significantly greater than 1.0).

in

t1:

C8

161

By contrast, the three cheapest sources of calories (sorghum,
sweet potatoes, and cassava) have expenditure elasticities below 0.5;
all three are significantly less than 1.0. Beans and salt also qualify
as "necessities“ with elasticities significantly less than 1.0. It is
worth noting that, at the mean expenditure level in the rural areas,
there are no inferior goods. Sweet potatoes come the closest to being
inferior with an expenditure elasticity of 0.02. This means that, at
the mean level of expenditure, sweet potato expenditures remain practi-
cally constant as total household expenditure rises.

Among the non-food categories, the highest expenditure elastici-
ties are those of housing (2.77), transportation (2.35), and household
equipment (2.17). Although the expenditure terms in these three
equations are significant at the 99% confidence level, none of the other
non-food equations has statistically significant expenditure coeffi-
cients. In other words, we cannot reject the hypothesis that rural
budget shares are constant across income for the other six non-food
categories.

Looking at both food and non-food categories in Table 6-6, the F
test indicates that the two expenditure terms are jointly significant at
the 95% level in 13 of the 26 equations. A cross-equation test of all

52 expenditure coefficients in the rural model yields an F statistic of
5.4, which is significant at the 99% confidence level. Thus, we can
reject the null hypothesis that rural budget shares are constant across
household expenditure levels.

The t statistic on the quadratic term, 32, is significant at the
95% level in only three equations (sweet potatoes, white potatoes, and
housing) and at the 90% level for two more (sorghum and beans)‘. A

cross-equation test of the joint significance of all 26 quadratic terms

 

1. The critical value of the t statistic with 246 degrees of
freedom at the two-tailed 95% confidence level is 1.96. At the two-
tailed 90% level, the critical value is 1.65.

162

rejects the null hypothesis only at the 90% level. When the test is
restricted to the 17 food equations within the system, the quadratic
terms are significantly different from zero at the 99% confidence level.
This result indicates that using the standard AIDS (without the quadrat-
ic term) to model demand in rural Rwanda would not allow sufficient
flexibility in the relationship between food budget share and total
expenditure (income).
6.2.3 Effect of household composition

7 The three demographic variables are the number of adults,

the number of children, and a dummy variable to indicate a female-headed

household. The first two demographic coefficients (71 and 72) in Table

6-7 indicate the effect on budget share of each additional member of the
household, holding prices and real expenditure per adult-equivalent -
constant. The third demographic coefficient (73) shows the change in
budget share associated with a female-headed household.

Few of the demographic variables are statistically significant in
the rural demand model, as indicated by the t-statistics in Table 6-7.
Only seven of the 81 demographic coefficients are statistically signifi-
cant at the 95% confidence level and nine more are significant at the
90% level.

The coefficients associated with household size (71 and 72) which

are significant at the 90% level provide weak support for the hypothesis
of "economies of scale" in household size. In this case, large house-
holds with the Same expenditure per adult equivalent consume more
luxuries (oil, sugar, other meat, and housing) and relatively less of
the necessities (sweet potatoes, beans, salt, and energy). This is a
common pattern in household budget data and is generally attributed to
economies of scale in non-food consumption such as housing (see Deaton
and Case, 1987).

Not surprisingly, the number of children is negatively associated

with the budget share allocated to tobacco. Contrary to expectations,

163

Table 6-7: Effect of household composition on rural demand

 

 

number number female
Budget adults children head
category 71 t 72 t 73 t
sofics* -0.04 -0.31 0.00 0.04 -0.37 -1.12
RICE -0.05 -0.63 0.08 1.44 0.40 1.75
CASSA -0.18 -0.46 -0.07 -0.23 0.56 0.49
SWPOT -0.84 -1.78 -0.25 -0.74 0.88 0.66
WHPOT 0.20 0.55 0.30 1.13 0.12 0.11
BANAN 0.09 0.24 0.16 0.59 0.93 0.87 m
BEANS -l.66 -2.73 -0.85 -1.95 1.47 0.86 i
PEAS -0.17 -1.00 -0.12 -0.99 -0.24 -0.50 '
TOMAT -0.02 -0.67 0.01 0.56 0.09 1.39
BEEF 0.09 0.78 0.04 0.47 0.28 0.83
MEAT -0.10 -0.43 0.35 2.04 -1.11 -1.64 I
BBEER 0.15 ' 0.29 -0.37 -1.00 -4;62 -3.20 7
SBEER 0.42 1.47 -0.11 -0.57 -0.61 -0.77
FBEER 0.07 0.54 0.03 0.33 -0.58 -1.48
OIL 0.15 1.71 0.05 0.83 -0.25 -1.04
SALT -0.10 -2.20 -0.05 -1.54 -0.05 -0.36 F
SUGAR 0.05 0.75 0.08 1.72 0.17 0.94 '
CLOTH 0.93 3.46 -0.37 -1.93 -0.02 -0.03
HOUSE 0.74 1.90 0.82 2.93 1.55 1.41
EQUIP 0.08 0.39 0.12 0.80 -0.38 -0.62
ENERG -0.07 -0.61 -0.23 -2.62 -0.11 -0.32
HEALT 0.15 1.37 -0.06 -0.74 0.03 0.11
EDUCA 0.14 1.60 0.10 1.62 -0.03 -0.10
TRANS -0.03 -0.31 0.09 1.14 0.21 0.73
TOBAC 0.03 0.43 -0.08 —1.73 -0.19 -1.01
LEISU -0.03 -0.28 0.02 0.31 -0.25 -0.99

—

the number of children is not significantly related to the portion of
the budget.allocated to beer. Perhaps the fact that children consume
less beer is offset by the economies of household size since beer is a
”luxury.” With regard to the impact of children on education spending,
although the sign is correct (positive), the coefficient is not quite
significant at the 90% confidence level.

Testing the cross-equation hypothesis that the numbers of adults
and of children do not affect budget shares in the rural sector
(1427220), the F statistic indicates that we can reject the hypothesis

at the 99% level of confidence. In other words, budget shares in the

164

rural sector are influenced by the number of adults and children in the
household, holding other variables constant. .

The sex of the head of household is represented by a dummy
variable which takes the value 1 for a female head and 0 for a male
head. At the 95% confidence level, the results show that female-headed
households allocate a significantly smaller portion of their budget (4.6
percentage points less) to banana beer. This finding probably reflects
social norms against banana beer consumption by women. By contrast,
sorghum beer is considered more appropriate for women (see Haggblade,
1988). _

If we accept a 90% confidence level, then female-headed household
allocate a somewhat larger share of the budget to rice and a smaller
share to ”other meat" (goat and fish). The former result may be related‘
to the greater time pressure of female heads and the ease of rice
preparation compared to alternative staples. It should be noted,
however, that rice constitutes a very minor portion of the budget (less
than 1%) in rural households, regardless of the gender of the household
head. The weak tendency of female headed households to consume less of
”other meat” may be due to traditional beliefs that discourage women
from consuming goat meatl.

Testing the cross-equation hypothesis that the sex of head of

household does not affect budget allocations (y3=0 in all equations),

the F statistic indicates that we can reject the null hypothesis only at
the 90% confidence level. Further analysis reveals that the gender of
the head of household is a significant determinant of food allocations

but that it does not influence non-food budget shares.

 

1. A common belief in Rwanda is that eating goat meat
contributes to facial hair in women.

 

165

6.2.4 Effect of prices

The effect of food prices on the demand for food is
estimated directly as part of the SUR model. Non-food price effects are
not estimated but derived under the assumptions of strongly separable
preferences. The results of each procedure are discussed in turn.

Estimated food price elasticities: The estimated price
parameter, a“, represents the compensated effect of the log of the F
price of food item j on the budget share of food item i. The interpre- ,

tation of these coefficients is complicated by the fact that even if a Q

price increase in good j does not affect the budget share of good i

 

(i.e. mU-O), the compensated demand will increase slightly due to the i

adjustment in nominal income to maintain a constant real incomel. i
Because the coefficients cannot be directly interpreted, they are
relegated to Appendix C, and we will move directly to the discussion of
price elasticities.
The uncompensated (Marshallian) price elasticities are calculated
from the estimated parameters using the following equation (derived in

section 4.3.4):

= 111 - _ 2'1 - _“_’1 if -
511 w! 6 W, 911 2 “pal-1% P) (6 2)

In general, we expect price elasticities (in absolute value) to be
positively correlated with expenditure (income) elasticities. In other
words, the demand for a good which is a "luxury" in the sense of being
consumed disproportionately by high-income consumers is likely to be

more sensitive to changes in price.

 

1. If Cufo, then the compensated own-price elasticity is
wi-l, where w, is the budget share of good i. If 613:0, then the compen-
sated cross-price elasticity is wJ. These price elasticities correspond
to the most plausible null hypothesis: that budget shares are not

affected by prices. In a disaggregated system, the budget shares will
be small and these elasticities will be close to -1 and 0, respectively.

166

A comparison of the expenditure elasticities in Table 6-6 and the
price elasticities in Table 6-8 confirms this intuition. Factory beer,
rice, and white potatoes, all luxuries in the rural sector, have price
elasticities (in absolute value) of 2.0 or greater. Other luxuries with
price elastic demand include traditional beers, "other meat,” and sugar.
Most of the necessities, such as bananas, beans, sorghum, salt, and
sweet potatoes, are relatively unresponsive to price. The most counter-
intuitive result is the low price elasticity of demand for beef (-0.20).

Although only three of the 17 own-price coefficients are signifi-

cant at the 95% level, as shown in Table 6-7, the cross-equation joint

 

 

Table 6-8: Effect of prices on rural food demand
—
own
price own F stat Prob
Budget coeff price for all under
category “11 t elast prices Ho
sofifis 0.23 0.24 -0.83 2.39 0.00
RICE -0.76 -0.76 -2.53 1.34 0.16
CASSA -0.56 -0.42 -1.06 1.41 0.12
SWPOT -1.20 -0.73 -0.97 2.92 0.00
WHPOT -5.75 -2.30 -2.46 5.46 0.00
BANAN 0.92 1.07 -0.85 7.35 . 0.00
BEANS 2.13 0.62 -0.82 4.06 0.00
PEAS -0.69 -0.69 -1.50 1.85 0.02
TOMAT -0.09 -1.19 -1.72 2.32 0.00
BEEF 1.12 1.36 -0.20 1.82 0.02
MEAT -0.46 -0.26 -1.25 1.80 0.02
BBEER -5.84 -2.60 -1.61 1.80 0.02
SBEER -3.96 -l.94 -2.02 4.01 0.00
FBEER -6.19 -2.09 -8.77 2.54 0.00
OIL 0.15 0.26 -0.85 3.32 0.00
SALT 0.38 0.95 -0.62 2.39 0.00
SUGAR -0.13 -0.62 -1.43 2.05 0.01

 

167

test of all 17 own-price coefficients is significant at the 95% confi-
dence level. Furthermore, in 15 of the 17 food equations, the vector of
price coefficients is significantly different than zero at the 95%
level. Not surprisingly, the cross-equation test of the joint signifi-
cance of all 289 price coefficients rejects at the 99$ level the
hypothesis that prices have no effect on the budget shares of food (see
Appendix B).

Derived non-food pficg elasticities: Following Frisch
(1959) and Newberry (1987), we derive non-food price elasticities using
the assumption of strongly separable preferences, the price and expendi-
ture elasticities for food, and the expenditure elasticities for each
non-food category. The elasticity of demand for food with respect to
household expenditure is 0.85, while the price elasticity of food as a
whole is -0.82, and the budget share of food is 0.741. Using equation
4-31, we can calculate the value of o as follows:

4,, fizz+ézwz . -.82 + (.85)(.74)

= -0.60 6-
efZI-wfet) .ESII-(.7Z)(.ES)I ( 3)

By substituting ¢ and the appropriate budget shares and expenditure
elasticities into equation 4-30, we can derive the own- and cross-price
elasticities of demand for non-food items in the rural area.

The uncompensated price elasticities of demand for non-food items
in the rural sector are presented in Table 6-9. These should be treated
as highly tentative given the particularly strong assumptions required
to obtain them. Nonetheless, the high price elasticity of demand for
”luxury" goods such a housing, transportation, and leisure/services is
certainly plausible, as is the inelastic demand for tobacco and energy.

The expenditure elasticities shown in Table 6-9 have been re-

estimated adding food prices to the model but restricting the price

 

1. Strictly speaking, these figures refer only to the 17
modeled food commodities, thus excluding ”other food" for which no price
information is available. The average budget share allocated to "other
food” is 9.8%.

168

 

Table 6-9: Derived rural non-food price elasticities
Budget elasticities
category share expend price

CLOT'IT 6 . 30 1 . 14 -0 FIT
HOUSE 3.31 2.78 -1.61
EQUIP 1.54 2.18 -1.30
ENERG 1.19 0.71 -0.44
HEALT 1.68 0.96 -0.59
EDUCA 0.42 1.25 -0.76
TRANS 0.80 2.35 -1.41
TOBAC 0.71 0.79 -0.48
LEISU 0.36 1.97 -1.18
OTHERF 9.87 1.17 -0.74

—

coefficients to correspond to the cross-price elasticities derived under

 

additivity assumptionsl.

This step causes only slight modification of ‘ E
the expenditure elasticities: comparing Tables 6-6 and 6-9, the largest
difference in the expenditure elasticities is 0.01.

The last line in Table 6-9 shows the price and expenditure
elasticities of the omitted category, "other food.” The expenditure and
demographic coefficients are defined in such a way to satisfy adding up,
while the price coefficients are defined to satisfy homogeneity for the
entire system. These results are presented here only because the non-
food coefficients must be determined before the coefficients for the

excluded "other food" category can be defined.

6.3 $23 mode; of rural demand with symmetry imposed
Consistent consumer behavior requires that the matrix of compen-

sated substitution effects be symmetric. In Chapter 4, it was shown

that, for the demand function used here, symmetric substitution effects

imply that the matrix of price coefficients, a”, must be symmetric.

 

1. This is done by regressing wn-anfpt on the same set of
five independent variables plus the constant, where wh is the budget
share of non-food category n, 051 is the matrix of food-non-food cross-
price coefficients derived using additivity, and p, is the vector of
food prices.

169

Since the a matrix is 17x17, imposing symmetry requires 136 restrictions
on the estimated coefficientsl.

The discussion of the rural model with symmetry will be relatively
brief, focusing on the price and expenditure elasticities. The effect
of household composition will not be reviewed, and the various joint
hypotheses will not be retested. The complete set of coefficients and t
statistics from the restricted rural model are presented in Appendix C.

Table 6-10 provides the correlation coefficients obtained for the
rural demand model with symmetry imposed. Comparing these results with
those of the unrestricted rural model (Table_6-4), imposing symmetry

appears to reduce the value of R? by 4-6% for most food items. The

equations for bananas, beans, and traditional beers suffer the most from
the imposition of symmetry. On the other hand, the non-food correlation‘
coefficients remain unchanged in the restricted rural model.

The expenditure elasticities from the SUR model with symmetry,
presented in Table 6-11, are similar to those without symmetry (see
Table 6-6). The expenditure elasticity for sweet potatoes changes from
barely positive in the unrestricted model to barely negative in the
restricted version. Only one commodity (peas) changes from luxury to
necessity, and no commodity switches in the reverse direction. The
expenditure elasticities for food commodities are almost all within 0.20
of the unrestricted value, and many are within 0.05. The coefficients‘
and the expenditure elasticities for the non-food categories do not
change at all with the symmetry restriction, presumably because these
equations do not contain any restricted parameters.

By contrast, the estimated food price elasticities in the re-
stricted model, presented in Table 6-12, differ considerably from those

in the unrestricted model (see Table 6-7). Although factory beer and

 

1. There are 17:17:289 elements in the matrix, 289-178272
off-diagonal elements, and thus 272/2=136 elements in each off-diagonal
triangle.

 

170
Table 6-10: Summary of rural model with symmetry imposed
—

 

Mean
Budget budget
category share R2

SORGH 1.41 0.11
RICE 0.49 0.06
CASSA 5.92 0.07
SWPOT 12.54 0.32
WHPOT 4.02 0.26
BANAN 5.86 0.06
BEANS 21.61 0.17

PEAS 1.39 0.05
TOMAT 0.13 0.12

BEEF 1.39 0.09
MEAT 1.91 0.10
BBEER 10.15 0.10
SBEER 3.91 0.14
FBEER- 0.80 . 0.19

OIL 0.96 0.17

SALT 1.02 0.17
SUGAR 0.31 0.07
CLOTH 6.30 0.06
HOUSE 3.31 0.18
EQUIP 1.54 0.04
ENERG 1.19 0.03
HEALT 1.68 0.01
EDUCA 0.42 0.03
TRANS 0.80 0.07
TOBAC 0.71 0.01
LEISU 0.36 0.01

 

 

white potatoes are the most price-elastic food commodities in both
versions, rice and oil become highly inelastic in the restricted
version, while beans and sugar become considerably more price elastic.
Although such a judgement is necessarily subjective, the price elastici-
ties estimated with symmetry restrictions seem, on the whole, less
credible than do the unrestricted price elasticities. This is most
notable in the cases of oil, rice, and beans.

Under symmetry, the expenditure elasticity of food (0.86) is
almost the same as in the unrestricted version (0.85). The price
elasticity of food (-0.90) is more elastic than the corresponding figure
from the unrestricted model (-0.82). Substituting these values into

equation 6-3, the value of O for the rural model under symmetry is

171
Table 6-11: Effect of expenditure on rural demand under symmetry

 

ln(exp)
Budget ln(exp) sqrd expend

category 31 t B; t elast
SORGH -17.48 -1.91 0.84 1.83 0.30
RICE 3.29 0.51 -0.15 -0.46 1.71
CASSA 20.83 0.66 -1.21 -0.76 0.54
SWPOT -105.13 -2.88 4.69 2.54 -0.08
WHPOT 67.42 2.35 -3.30 -2.27 1.72
BANAN 9.05 0.31 -0.38 -0.25 1.28
BEANS 85.34 1.81 -4.68 -l.96 0.72
PEAS 8.24 0.62 --0.44 -0.65 0.77
TOMAT 0.53 0.28 -0.03 -0.30 0.86
BEEF -1.22 -0.13 0.12 0.25 1.77
MEAT 2.24 0.12 -0.04 - -0.04 1.75
BBEER 3.41 0.09 0.01 0.01 1.36
SBEER 24.31 1.11 -1.22 -1.10 1.13
FBEER -16.03 -1.47 0.89 1.62 2.78
OIL 9.37 1.40 . -0.45 -1.33 1.62
SALT 3.16 0.88 -0.18 -1.01 0.59
SUGAR 1.68 0.34 -0.07 -0.27 2.22
CLOTH 2.63 0.12 -0.09 -0.08 1.15
HOUSE -92.54 -2.95 5.04 3.17 2.77
EQUIP 6.74 0.39 -0.25 -0.29 2.17
ENERG 1.69 0.18 -0.10 -0.21 0.72
HEALT 3.30 0.37 -0.17 -0.38 0.96
EDUCA 4.30 0.62 -0.21 -0.61 1.25
TRANS -5.33 -0.64 0.33 0.78 2.35
TOBAC -0.41 -0.08 0.01 0.05 0.80
LEISU 3.34 0.47 -0.15 -0.42 1.97

-0.83. Under the assumption of additive preferences, this parameter is
used to derive the non-food price elasticities shown in Table 6-13.

A comparison of the rural non-food elasticities in the unrestrict-
ed and restricted versions of the model reveals that the restricted non-
food price elasticities follow roughly the same rank order as the
unrestricted elasticities.i In both versions, the most price elastic
categories are housing, transportation, and household equipment, while
the least price responsive are tobacco and energy.

On the other hand, the restricted figures are consistently more
price elastic. This pattern reflects the fact that imposing symmetry
increases the price elasticity of food without changing appreciably the

expenditure elasticity of food. Under the assumption of additive

“new '5 3: ‘.

(Fun-2v

Table

6-12:

172
Effect of prices on rural food demand under symmetry

 

 

own
price own
Budget coeff price
category “11 t elast
SORGH 0.08 0109 -0.93
RICE 0.46 0.50 -0.08
CASSA -2.08 -1.80 -1.32
SWPOT -1.22 -0.80 -0.96
WHPOT -6.10 —3.25 -2.55
BANAN 2.63 3.80 -0.57
BEANS -3.78 -1.14 -1.11
PEAS -2.00 -2.53 -2.43
TOMAT —0.04 -0.62 -1.34
BEEF 0.31 0.41 -0.79
MEAT -1.00 -0.64 -1.54
BBEER -1.66 -0.82 -1.20
SBEER -1.87 -1.04 -1.48
FBEER -6.46 -2.36 -9.12
OIL 0.70 1.37 -0.28
SALT 0.42 1.14 -0.58
SUGAR -0.41 -2.17 -2.32

“I?!”

 

Table 6-13:

Derived rural non-food price elasticities under symmetry

 

Budget elasticities
category share expend price
CLOTH 6.30 1.15 -0.96
HOUSE 3.31 2.79 -2.19
EQUIP 1.54 2.18 -1.78
ENERG 1.19 0.72 -0.61
HEALT 1.68 0.96 -0.81
EDUCA 0.42 1.25 -1.04
TRANS 0.80 2.36 -1.94
TOBAC 0.71 0.79 -0.66
LEISU 0.36 1.97 -l.63
OTHFO 9.87 1.06 -0.90

preferences, the relationship between price and expenditure elasticities

is assumed constant across strongly separable categories.

173

6.4 Un st cte UR model of urban demand

This section reviews the results of the model of urban demand
without symmetry. As noted in section 6.1.2, the urban food classifica-
tion is similar to the rural classification except that the former
includes bread, milk, and prepared meals, and it disaggregates cassava
into cassava root and cassava flour. In addition, the urban model
includes the category ”vegetables," where the rural model has only
"tomatoes." Thus, the urban model includes 21 food equations and 9 non-
food equations.

With six coefficients common to all 30 equations and 21 price
terms in each of the 21 food equations, the unrestricted urban model
involves the simultaneous estimation of 621 coefficients. As in the
case of the rural model, only selected results are presented here. The
full set of coefficients and t statistics is given in Appendix C.

6.4.1 ngpgll ggogpess-gf-fft apd gfgpfffggpgp

In general, the urban model provides a better fit to the
data than does the rural model. As shown in Table 6-14, three commodity
equations in the urban model (beans, sweet potatoes, and white potatoes)

have correlation coefficients (R2) above 0.35, but only one equation in

the rural model (sweet potatoes) reaches this level. Similarly, five of
the nine non-food categories have R2 values above 0.10 in the urban
model, whereas only one does in the rural model.

Another indication of the better fit of the urban model is the
fact that the independent variables are jointly significant in almost
every equation. Table 6-14 shows that for 27 out of 30 commodity
equations, we can reject the hypothesis that all the coefficients are
zero at the 99% confidence level. The null hypothesis can be rejected
at the 95% confidence level for two more goods. Only in the case of
clothing are the coefficients jointly insignificant.

The higher level of explanatory power of the urban demand model is

probably due to the greater variability in income and household expendi-

 

I'_‘. .‘I .

174

Table 6-14: Summary of unrestricted SUR model of urban demand
—

 

Mean F stat Prob
Budget budget for all under
category share R2 variab Ho
SORGH 0.92 0.14 1.57 0.03
RICE 2.37 0.15 2.06 0.00
BREAD 0.67 0.21 2.78 0.00
'CASSA 1.79 0.31 5.06 0.00
SWPOT 3.84 0.49 10.37 0.00
WHPOT 6.24 0.38 6.50 0.00
BANAN 2.93 0.18 2.56 0.00
CASFL 2.40 0.26 3.73 0.00
BEANS 10.37 0.51 11.01 0.00
PEAS 0.41 0.20 2.62 ' 0.00
VEGET 1.57 0.17 2.27 0.00-
BEEF 2.90 0.21 2.93 0.00
MEAT 2.11 0.13 1.69 _0.02
MILK 2.30’ 0.19 2.76 0.00
BBEER 4.82 0.35 5.74 0.00
SBEER 1.16 0.23 3.08 0.00
FBEER 4.17 0.23 3.43 0.00
OIL 2.07 0.19 2.65 0.00
SALT 0.54 0.32 4.99 0.00
SUGAR 2.59 0.26 4.26 0.00
MEALS 2.76 0.19 2.77 0.00
CLOTH 5.50 0.02 1.18 0.24
HOUSE 10.04 0.34 27.86 0.00
EQUIP 2.87 0.16 10.80 0.00
ENERG 4.62 0.11 6.50 0.00
HEALT 3.05 0.07 4.36 0.00
EDUCA 1.07 0.06 3.57 0.00
TRANS 4.84 0.18 12.32 0.00
TOBAC 1.51 0.09 5.50 0.00
LEISU 1.88 0.29 23.01 0.00

 

ture (see section 5.3.2). In addition, the ”lumpiness” of non-food
spending is less of a problem in the urban areas because household
expenditure is generally greater and the percentage allocated to non-
food categories is higher. A S 20 radio represents ”only" one half the
annual expenditure on leisure/services of an average urban household,
compared to 10 times the leisure/services spending of a typical rural
household. 7
6.4.2 Effect of total expenditure

The expenditure elasticities for the unrestricted model

of urban food demand are shown in Table 6-15. Comparing the urban and

175

rural expenditure elasticities, it is interesting that the rank order of
the products is quite similar, but that the elasticities are generally

lower in the urban sector.

Table 6-15: Effect of household expenditure on urban demand
—

 

 

ln(exp) F stat Prob
Budget ln(exp) sqrd expend for under
category 81 t 8? t elast expend Ho
30368 -1.95 -0.71 0.07 0.58 0.59 2.85 0.06
RICE 17.19 3.96 -0.81 -3.95 1.10 7.83 0.00
BREAD 5.27 3.36 -0.24 -3.22 1.42 8.57 0.00
CASSA 3.27 0.76 -0.21 -1.05 0.34 . 13.10 0.00
SWPOT ~28.57 -3.75 1.20 3.35 0.12 31.59 0.00
WHPOT 10.28 1.45 -0.56 -1.69 0.75 10.18 0.00
BANAN -1.47 -0.25 -0.00 -0.01 0.47 10.82 0.00
CASFL -4.20. -0.86 0.13 0.57 0.40 13.09 0.00
BEANS -23.30 -1.84 0.77 1.29 0.31 48.48 0.00
PEAS 0.43 0.24 -0.02 -0.28 0.86 0.24 0.79
VEGET 3.98 1.98 -0.19 -2.02 0.98 2.27 0.10
BEEF 18.83 4.15 -0.90 -4.22 0.96 9.57 0.00
MEAT 5.53 1.29 -0.26 -1.26 1.08 0.91 0.40
MILK 10.18 1.82 -0.49 -1.86 0.97 1.89 0.15
BBEER 19.19 1.93 -0.98 -2.11 0.69 6.68 0.00
SBEER -0.10 -0.03 -0.01 -0.07 0.68 1.47 0.23
FBEER 13.07 1.30 -0.50 -1.06 1.60 9.25 0.00
OIL 10.29 4.05 -0.49 -4.08 1.02 8.43 0.00
SALT -0.36 -0.49 0.00 0.15 0.53 18.75 0.00
SUGAR 11.59 2.91 -0.55 -2.94 1.00 4.48 0.01
MEALS -19.41 -1.43 0.90 1.41 0.82 1.07 0.34
CLOTH 9.81 1.35 -0.46 -1.33 1.04 0.94 0.39
HOUSE -63.88 -3.26 3.49 3.77 1.94 53.91 0.00
EQUIP 1.41 0.24 0.03 0.11 1.72 22.31 0.00
ENERG 22.05 2.98 -0.98 -2.80 1.33 10.19 0.00
HEALT 7.42 1.71 --0.34 -1.65 1.10 1.97 0.14
EDUCA 5.25 1.00 -0.23 -0.93 1.36 1.25 0.29
TRANS -14.90 -1.25 0.88 _1.56 1.72 18.25 0.00
TOBAC 7.59 2.13 -0.38 -2.28 0.68 6.73 0.00
LEISU -4.25 -1.04 0.26 1.35 1.66 18.67 0.00

 

For example, among food categories, in both urban and rural areas
the highest expenditure elasticities are those of factory beer, sugar,
rice, oil, and animal products, while the lowest are those of cassava
root, sweet potatoes, beans, bananas, and salt. Bread, a category not

included in the rural model, is a "luxury" good, with an expenditure

176
elasticity second only to factory beer among food commodities. This is
not surprising given the fact that, on a per calorie basis, bread is
three times as expensive as sweet potatoes in the urban sector.

Among the non-food categories, the highest expenditure elastici-
ties in both rural and urban areas are those of housing, household
equipment, and transportation. In both cases, tobacco has one of the
lowest expenditure elasticities of the non-food categories. One
important difference is that energy is a luxury among urban households
but a necessity among rural households (although the latter elasticity
is not significantly below 1.0). .

As mentioned above, the urban expenditure elasticities are
generally lower than in the rural elasticities. For example, none of
the urban budget categories has an elasticities over 2.0, while there
are five such categories in the rural model. One implication is that
some of the goods that are ”luxuries" in the countryside, such as white
potatoes and traditional beers, are "necessities" in the cities.

In the urban model, the expenditure elasticities of food and non-
food are 0.72 and 1.52, respectively. By contrast, the corresponding
expenditure elasticities in the rural model are 0.85 and 1.591. It may
seem paradoxical that both food and non-food categories have lower
expenditure elasticities in the urban model, since the weighted average
of all expenditure elasticities must be 1.0 in any system, according to
the Engel aggregation condition. The explanation is that the non-food
elasticities, which are higher on average, are weighted more heavily in
the urban model because non-food categories represent a much larger
share of the urban budgets.

According to the F test in Table 6-15, the two expenditure terms

are jointly significant at the 99% level in 20 of the 30 equations (for

 

1. .The average food elasticities cited here exclude the
category "other food,“ whose expenditure elasticity is derived as a

residual. Thus, the weighted average of the two elasticities presented
here is not exactly equal to 1.0.

r ’.'-'.

 

11.314 .nl‘. x
I

 

177

the other ten, we cannot reject the null hypothesis that budget share is
constant across expenditure levels). Given this result, it is not
surprising that the 60 expenditure terms in the complete model are
jointly significant at the 99% confidence level (F a 10.47).

Finally, Table 6-15 indicates that there is significant curvature
in the relationship between budget share and log expenditure. The

quadratic expenditure coefficient (82) is significant in eleven of the

30 equations, as indicated by the t statistic. Furthermore, this
coefficient is jointly significant in the system at the 99% confidence
level (F = 2.94).
6.4.3 'Effect of household composition

Of the 90 coefficients representing the effect of house-
hold composition on urban food budget shares, about one third (31) are
significantly different than zero at the 95% confidence level, as shown
in Table 6-16. The two household size variables are jointly significant
for the unrestricted urban model as a whole (F s 5.06), as is the sex of
the head of household (F a 3.32).

The coefficients for number of adults and number of children (71
and 72) indicate the effect of an additional family member given the

same prices and real expenditure per adult-equivalent. These results
show that, at the 95% confidence level, a larger family allocates a
greater share of its budget to bread, cassava flour, "other meat,” milk,
oil, sugar, and most of the non-food categories, while devoting a
smaller share to cassava root, beans, traditional beers, meals away from
home, and tobacco. The first group has expenditure elasticities close
to or above 1.0, while every good in the second group has an elasticity
below 1.0. Thus, an increase in household size while holding expendi-
ture per adult equivalent constant has an effect on budget allocations
similar to an increase in total expenditure. These results correspond
to the hypothesis of economies of scale in household size, as discussed

in section 6.2.3.

 

178
Table 6-16: Effect of household composition on urban demand
IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII-I-I-I-III-I-l-IIII-I
number number sex of
Budget adults childr head
category 71 t 12 t 73' t

SORGH -0.10 -1.26 -0.03 -0.78 -0.06 -0.23
RICE -0.13 -1.06 0.12 1.73 -0.06 -0.14
BREAD 0.09 1.95 0.06 2.55 0.07 0.48
CASSA -0.32 -2.54 0.12 1.82 -0.72 -1.76
SWPOT —0.37 -1.70 -0.14 -1.18 0.39 0.54
WHPOT -0.19 -0.95 0.07 0.66 0.36 0.53
BANAN -0.05 —0.32 0.04 0.39 1.03 1.83
CASFL 0.00 0.00 0.17 2.22 0.50 1.07
BEANS -1.26 -3.49 -0.45 -2.29 -0.75 -0.62
PEAS -0.00 -0.03 0.01 0.20 -0.17 -1.02
VEGET 0.13 2.29 0.01 0.32 0.53 2.80
BEEF -0.12 -0.90 0.10 1.40 -0.45 -1.05
MEAT 0.29 2.35 0.09 1.33 0.03 0.07
MILK 0.33 2.06 0.09 1.08 0.76 1.43
BBEER -1.19 -4.17 -0.63 -4.12 -4.46 -4.74‘
SBEER -0.15 -1.33 -0.13 -2.19 -0.63 -1.71
FBEER -0.30 -1.05 -0.08 -0.52 -2.08 -2.18

OIL -0.00 -0.02 0.11 2.74 0.50 2.08
SALT -0.01 -0.34 -0.02 -1.36 0.12 1.76
SUGAR -0.01 -0.12 0.14 2.25 1.33 3.51
MEALS -1.15 -2.93 -0.82 -3.93 -2.89 -2.25
CLOTH 0.22 1.13 0.09 0.83 -0.36 -0.53
HOUSE 1.26 2.42 0.22 0.73 1.67 0.91
EQUIP 0.21 1.32 0.17 1.87 0.37 0.67
ENERG 0.44 2.25 0.22 1.98 0.92 1.33
HEALT 0.38 3.29 0.11 1.63 0.69 1.69
EDUCA 0.12 0.85 0.26 3.20 1.32 2.68
TRANS 1.22 3.86 0.35 1.91 1.39 1.25
TOBAC -0.16 -1.71 -0.19 -3.46 —1.03 -3.09
LEISU 0.79 7.28 0.04 0.69 0.40 1.04

 

 

Turning our attention to the effect of the gender of the head of
household, Table 6-16 reveals that, other things equal, female-headed
households allocate a smaller portion of their budget to banana beer,
factory beer, meals away from home, and tobacco, while spending a larger
share on vegetables, cooking oil, sugar, and education. In the case of

banana beer and prepared meals, the coefficients (Ya) are close in

magnitude to the corresponding mean budget shares, implying that
spending on these items by female-headed household is virtually non-

existent.

179

The smaller shares allocated to banana beer, factory beer, and
tobacco clearly reflect social norms. Similarly, eating at restaurants
and bars is less acceptable for women in Rwanda. The lower spending on
sugar and cooking oil by male-headed household may be simply the result
of under-reporting in these households: women generally do the shopping
but the interviews were more often carried out with the (male) heads of
household.

6.4-4 W

As in the rural model, the effect of food prices on the
demand for food is estimated directly as part of.the SUR model. Non-
food price effects are not estimated but derived under the assumptions
of strongly separable preferences. The results of each procedure are
discussed in turn.

Estimated food price elasticities: The uncompensated
own-price elasticities in the urban areas, shown in Table 6-17, are
similar to those in the rural areas, although there are a few unexpected
differences. As in the rural model, rice and traditional beer are
relatively price elastic, while salt, cassava root, and beans are price
inelastic. In fact, the estimated own-price elasticities of salt and
cassava root are positive, although they are not significantly greater
than zerol. Somewhat surprising are the low price elasticities of
bread and factory beer. Since neither elasticities is significantly
less than one, this may be simply the result of insufficient variability
in price within the urban areas. Also unexpected were the relatively
high price elasticities of sweet potatoes, cassava flour, and sorghum.
One possible explanation is that the greater degree of choice among

staples in the cities makes demand more sensitive to price.

 

1. The t statistic associated with a“ tests the null hypoth-
esis that the budget share does not vary with own-price. For goods with
a small budget share, like cassava root and salt, this essentially
corresponds to a test of the null hypothesis that the uncompensated own-
price elasticity is -1 (see footnote in section 6.2.4).

180
The t test on the own-price coefficients in the urban model,
presented in the second and third columns of Table 6-17, reveal that six
of the 21 goods have own-price terms which are significant at the 95%
confidence level. The F test of the joint effect of all 21 own-price
terms indicates that they are statistically significant at the 99%

confidence level (F = 5.23).

 

The F tests shown in the last two columns of Table 6-17 indicate F”
that the price vector is significantly different than zero at the 95%

confidence level in 13 of the 21 equations. Looking at the model as a

Table

6-17:

Effect of prices on urban food demand
IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII-I-I-I-I-I-I-I-I-I-II

 

own

price own F stat Prob
Budget coeff price for all under

category a“ t elast prices Ho
SORGH -0.48 -1.37 -1.52 0.93 0.55
RICE -3.77 -3.00 -2.59 1.53 0.06
BREAD 0.23 1.47 -0.65 1.47 0.07
CASSA 2.01 4.15 0.13 3.96 0.00
SWPOT -1.88 -2.11 -1.46 4.36 0.00
WHPOT -1.61 -0.90 -l.24 4.75 0.00
BANAN -0.90 —1.89 -1.29 1.31 0.15
CASFL -1.19 -l.95 -1.48 1.67 0.03
BEANS 2.98 1.26 -0.64 2.43 0.00
PEAS -0.16 -0.69 -1.38 3.02 0.00
VEGET -0.21 -0.84 -1.13 1.61 0.04
BEEF -0.25 -0.51 -1.08 1.91 0.01
MEAT -0.34 -0.74 -1.16 1.45 0.09
MILK 0.71 1.20 -0.69 2.31 0.00
BBEER -6.30 -6.03 -2.29 3.08 0.00
SBEER -0.98 -2.08 -1.84 2.56 0.00
FBEER 0.74 0.41 -0.85 1.37 0.12
OIL 0.21 1.13 -0.90 1.22 0.22
SALT 0.60 4.26 0.12 1.42 0.10
SUGAR 0.19 0.62 -0.93 3.04 0.00
MEALS -0.99 -1.17 -1.35 1.77 0.02

 

 

181

whole, the price terms are jointly significant at the 99% confidence
level.

Derived non-food price elasticities: The non-food price
elasticities for the urban sector are derived under the assumption of
strongly separable preferences. Substituting into equation 6-3 the
average urban food share (0.59), the expenditure elasticity of food
(0.72), and the price elasticity of food (-0.91), the value of 6 is F?“
calculated as -1.17. Combining this parameter with the non-food ‘
expenditure elasticities, the non-food price elasticities are calculated

as shown in Table 6-18.

Table 6-18: Derived effect of prices on urban non-food demand
_.

 

Budget elasticities
category share expend price

 

CLOTH 5.50 1.04 -1.20
HOUSE 10.04 1.93 -2.02
EQUIP 2.87 1.72 -1.97
ENERG 4.62 1.33 -1.52
HEALT 3.05 1.10 -1.28
EDUCA 1.07 1.36 -1.59
TRANS 4.84 1.72 -1.93
TOBAC 1.51 0.69 -O.80
LEISU 1.88 1.66 -1.92
OTHERF 5.69 0.69 -O.80

 

As in the rural model, these elasticities must be considered
highly tentative. Housing, household equipment, transportation, and
leisure/services are price elastic, while tobacco is the only price
inelastic non-food category, according to these calculations.

As explained in section 6.2.4, the expenditure elasticities in
this table reflect minor changes due to the re-estimation of the non-
food categories imposing the price terms derived under additive prefer-
ences. Only in the case of tobacco is the adjustment noticeable at the

level of precision presented in Table 6-18.

182

Finally, having completed the estimation of the 26 food and non-
food categories, we derive the coefficients for the excluded budget
category, "other food." The expenditure and household composition
coefficients are defined so as to satisfy adding up, while the price
terms are defined to satisfy homogeneity in the complete system. It is
difficult to evaluate the plausibility of the estimates for ”other
food," but it is worth noting that the price and expenditure elastici-
ties (-0.80 and 0.69) are similar to the averages for the explicitly

modeled food categories (-0.91 and 0.72).

6.5 SUR model of urban demgnd with symmetry impoggg

In this section, we briefly consider the results of the urban
model when symmetry of compensated cross-price substitution effects is
imposed. Since the estimated price terms form a 21x21 matrix, symmetry
requires imposing 210 restrictions on the urban SUR model.

The correlation coefficients (R2) for the urban equations are

presented in Table 6-19. The non-food equations are unaffected by the
restrictions placed on the food price terms. With regard to the food
equations, except in a few cases (beans, sweet potatoes, and white

potatoes), the reduction in the value of R2 is generally around 3-5

percentage points. A Wald test of the 210 restrictions rejects the null
hypothesis of symmetry at the 99% confidence level. However, we retain
the symmetric demand model as one alternative because the willingness-
to-pay calculations used in Chapter 7 require symmetry to qualify as
well-defined measures of welfare.

The expenditure elasticities in the urban model with symmetry
imposed are presented in Table 6-20. Under symmetry, the expenditure
elasticities of sweet potatoes, beans, and prepared meals fall, with
sweet potatoes becoming slightly inferior. On the whole, however, the
expenditure elasticities are not greatly affected by the symmetry

restriction.

 

 

 

Table 6-19: Summary of urban model with symmetry imposed
IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII-I-I-I-I-I-I-I-I-I-II
Mean
Budget budget
category share R2

SORGH 0.92 0.11
RICE 2.37 0.12
BREAD 0.67 0.19
CASSA 1.79 0.27
SWPOT 3.84 0.39
WHPOT 6.24 0.29
BANAN 2.93 0.14
CASFL 2.40 0.22
BEANS 10.37 0.45
PEAS 0.41 0.15
VEGET 1.57 0.16
BEEF 2.90 0.17
MEAT 2.11 0.07
MILK 2.30 0.13
BBEER 4.82 0.28
SBEER 1.16 0.14
FBEER 4.17 0.18
OIL 2.07 0.16
SALT 0.54 0.31
SUGAR 2.59 0.22
MEALS 2.76 0.12
CLOTH 5.50 0.02
HOUSE 10.04 0.34
EQUIP 2.87 0.16
ENERG 4.62 0.11
HEALT 3.05 0.07
EDUCA 1.07 0.06
TRANS 4.84 0.18
TOBAC 1.51 0.09
LEISU 1.88 0.29

183

 

 

 

The estimated price elasticities, on the other hand, are substan-
tially affected by imposing symmetry, as shown in Table 6-21. The price
elasticities of sweet potatoes and salt, which were slightly positive in
the unrestricted model, become slightly negative in the model with
symmetry. Six other food price elasticities change by at least 0.20:
rice and factory beer become more price responsive under symmetry, while
sorghum, white potatoes, milk, and sorghum beer become less so.

Symmetry does not affect the urban expenditure elasticity for food
as a whole (0.72), but it does increase the price elasticity of food

somewhat (from -0.87 to -0.91). Because of the fixed relationship

184
Table 6-20: Effect of expenditure on urban demand under symmetry

 

ln(exp)

Budget ln(exp) sqrd expend
category 32 t 82 t elast
SORGH -1.59 -0.59 0.06 0.44 0.56
RICE 18.87 4.39 -0.88 -4.34 1.18
BREAD 5.24 3.37 -0.24 -3.23 1.41
CASSA 4.49 1.06 -0.26 -1.33 0.40
SWPOT -35.19 -4.72 1.48 4.22 -0.06
WHPOT 8.50 1.22 -0.49 -1.50 0.70
BANAN -1.06 -0.19 -0.02 -0.07 0.51
CASFL -5.32 -1.11 0.18 0.81 0.39
BEANS -25.85 -2.09 0.86 1.47 0.24
PEAS 0.02 0.01 -0.01 -0.07 0.75
VEGET ,4.29 2.16 -0.20 - -2.19 0.99
BEEF 22.18 4.99 -1.05 -5.02 1.03
MEAT 5.36 1.27 -0.24 -1.23 1.11
MILK 9.42 1.72 -0.45 -1.75 0.97
BBEER 22.52 2.34 _ -1.14 -2.51 0.69
SBEER -0.98 -O.26 0.02 0.13 0.57
FBEER 12.18 1.24 -0.45 -0.98 1.64
OIL 11.15 4.46 -0.53 -4.47 1.05
SALT -0.45 -0.62 0.01 0.26 0.50
SUGAR 11.41 2.92 -0.54 -2.94 1.01
MEALS -17.51 -1.34 0.84 1.36 1.04
CLOTH 9.81 1.35 -0.46 -1.33 1.04
HOUSE -63.88 -3.26 3.49 3.77 1.94
EQUIP 1.41 0.24 0.03 0.11 1.72
ENERG 22.05 2.98 -0.98 -2.80 1.33
HEALT 7.42 1.71 -0.34 -1.65 1.10
EDUCA 5.25 1.00 -0.23 -0.93 1.36
TRANS -14.90 -1.25 0.88 1.56 1.72
TOBAC 7.59 2.13 -0.38 -2.28 0.68
LEISU -4.25 -1.04 0.26 1.35 1.66

between price and expenditure elasticities of strongly separable
commodity groups, this result make the non-food price elasticities
somewhat greater under symmetry than in the unrestricted model. As
shown in Table 6-22, the derived non-food price elasticities for the
urban model with symmetry are roughly 0.10 greater than those without
the symmetry restrictions. The relatively high price elasticity of
demand for housing, household equipment, and transportation and the
relatively inelastic demand for tobacco remain unchanged, however.

The coefficients of "other food," defined to satisfy adding up and

homogeneity, generate elasticities which are roughly the same as those

185
Table 6-21: Effect of prices on urban food demand with symmetry imposed
—

 

 

 

own
price own
Budget coeff price
category “11 t elast
SORGH -0.28 -0.88 -1.30
RICE -3.04 -2.91 -2.29
BREAD 0.15 1.03 -0.77
CASSA 1.50 3.33 -0.15
SWPOT -2.60 -3.17 -1.64
WHPOT -0.16 -0.11 -1.01
BANAN -0.85 -1.91 -1.27
CASFL -0.96 —1.72 -1.38
BEANS 1.59 0.79 -0.77
PEAS -0.13 -0.62 -1.31
VEGET -0.12 -0.59 -1.08
BEEF -0.07 -0.18 -1.03
MEAT -0.43 -1.05 -1.20
MILK 1.25 2.32 -0.46~
BBEER -5.51 -5.72 -2.13 .
SBEER -O.39 -O.93 -1.33 .
FBEER -0.54 -0.34 -1.16 L
OIL 0.04 0.26 -0.98
SALT 0.49 3.86 -0.09
SUGAR 0.04 0.14 -0.99
MEALS -1.25 -1.57 -1.45

obtained in the unrestricted model.

6.6 Effgct of zero expenditures on model

This section presents a brief digression to compare the rural food
results obtained from the linear model with those of the Tobit model
which adjusts for the fact that the dependent variable (budget share) is
limited to being non-negative. We do not adopt the Tobit model for
subsequent analysis because of the problems discussed in section 3.3.3,
primarily the difficulty in imposing adding up and symmetry on the
system.‘ The test is limited to comparing OLS estimation of rural food
demand estimation and Tobit estimation of rural food demand (single-
equation OLS results are used for compariSon because the Tobit model is

also estimated equation-by-equation).

186
Table 6-22: Derived non-food price elasticities under symmetry

 

Budget elasticities

category share expend price
croia 5.50 1.04 -1.11
HOUSE 10.04 1.93 -1.88
EQUIP 2.87 1.72 -1.82
ENERG 4.62 1.33 -1.41
HEALT 3.05 1.10 -1.18
EDUCA 1.07 1.36 -1.47
TRANS 4.84 1.72 -1.79
TOBAC 1.51 0.69 -0.74
LEISU 1.88 1.66 -1.77
OTHFO 5.69 0.74 -0.81

The software package LIMDEP is used to implement the Tobit
estimation of rural food demand. The marginal effect of each indepen-4
dent variable on the dependent variable is calculated using the expres-
sion given in MacDonald and Moffitt (1980). These partial derivatives
are then used to evaluate the price and income elasticities at the
means. Table 6-23 compares elasticities obtained with the Tobit model
to those obtained from the unrestricted linear model.

Several patterns can be identified from this table. First, as
expected, for goods consumed by a high proportion of the households, the
differences between the two models is negligible. This is the case for
the basic staple commodities such as sweet potatoes, cassava, bananas,
and beans, as well as banana beer and salt. Overall, eight of the 17
expenditure elasticities differ by less than 0.10, while nine of the 17
price elasticities differ by less than 0.20.

The divergence between the two models is greatest for the goods
consumed by less than a quarter of the sample: tomatoes, rice, and
sugar. Only one good (tomatoes) is a luxury in one model and a necessi-
ty in the other (none change in the other direction). And just one
commodity (sugar) is price inelastic in one model and price elastic in

the other (none switch from elastic to inelastic).

187

Table 6-23: Comparison of elasticities estimated with Tobit and OLS
—

 

Mean % hhs expenditure price
budget consum- elasticities elasticities
Product share ing Tobit OLS Tobit OLS
SORGH 1.41 58.9 0.70 0.48 -0.90 -0.77
RICE 0.49 23.7 2.11 1.83 -1.86 -3.15
CASSA 5.92 79.6 0.58 0.45 -1.09 -1.05
SWPOT 12.54 96.7 0.04 -0.00 -0.96 -0.96
WHPOT 4.02 64.4 1.78 1.82 -1.86 -2.41
BANAN 5.86 80.7 1.09 1.02 -0.80 -0.81
BEANS 21.86 100.0 0.62 0.62 -0.89 -0.89
PEAS 1.39 44.8 1.37 1.07 -1.03 -1.84
TOMAT 0.13 21.9 1.63 0.68 -1.17 -1.77
BEEF 1.39 63.0 1.82 1.66 -0.61 -0.18
OTHMT 1.91 44.4 2.06 1.79 -1.52 -1.37
BBEER 10.15 90.4 1.42 1.36 -1.59 -1.65
SBEER 3.91 72.2 1.19 1.23 -1.68 -1.97
FBEER 0.80 26.7 2.74 2.87 -1.11 -8.49
OIL 0.96 45.9 1.82 1.58 -0.96 -0.94
SALT 1.02 87.0 0.56 0.55 -0.62 -0.55
SUGAR 0.31 21.5 2.22 2.28 -0.86 -1.25

 

 

Second, the divergence between the two models is greater for the
price elasticities than for the expenditure elasticities. For example,
among expenditure elasticities, the gap between the two estimates is
greater than 0.35 for only one good (tomatoes). By contrast, among
price elasticities, the divergence is larger than this for seven
commodities (factory beer, rice, peas, tomatoes, white potatoes, beef,
and sugar).

Third, the price elasticities tend to be closer to -1.0 in the
Tobit model. In the case of goods with price inelastic demand, this is
may be the result of the bias in the Tobit model identified by Pitt
(1983). He notes that, by forcing the same parameters to predict both
the probability of positive budget shares and the expected budget share
among consumers, the Tobit estimates are biased when the signs of these

effects are different. This occurs with price insensitive goods since
an increase in price lowers the probability of consumption but raises

the expected budget share among those who consume it. In this case, the

188
price parameter, «1;: is biased toward zero and the price elasticity is

biased toward -1. This bias may explain the fact that the Tobit price
elasticities for the three most price-insensitive goods (sorghum, salt,
and beef) are considerably closer to -1.0 than the corresponding OLS
estimates.

In summary, the differences between the elasticity estimates of
the Tobit model and the OLS model are relatively small, particularly for
staple commodities and other goods consumed by a majority of the
households. In the case of price insensitive goods, the differences
between the two models may be due to biases in the Tobit model. For the
purposes of this analysis, the arguable statistical advantages of the
Tobit model do not seem to outweigh the problem that restrictions from
economic theory (adding up and symmetry) cannot be imposed. As dis-
cussed in Chapter 3, symmetry is necessary for the "willingness-to-pay"

measures to be well-defined.

6-7 W

In this section, we briefly explore the possibility that the
estimated price elasticities are affected by quality effects and/or
measurement error. Following Deaton (1987 and 1988), it is assumed that
there is no true price variation within the sample cluster. This
assumption means that quality and measurement error effects can be
tested in two ways which are explained in turn. In order to simplify
the analysis, the results are based on single—equation OLS regression.

6.7.1 Effgct of household expenditure on prices paid

Any significant (positive) effect of household expendi-

ture on the average "price" (unit value) paid for a good within the
cluster must be the result of quality effects since true prices are
presumed constant in each cluster. Thus, the elasticity of unit value

with respect to household expenditure within the cluster may be inter-

 

1r

 

189

preted as the "elasticity of quality with respect to household expendi-
ture.”

This relationship is tested by regressing ”unit values" on total
expenditure and household composition, using only within-cluster
variation in each variable (this is equivalent to adding a dummy

variable for each cluster in the sample). The first column of Table 6-

 

24 shows the estimated quality elasticities for the rural sector, while
the second and third columns give the F statistic for the joint impact

of the two expenditure terms and the corresponding probability under the

 

null hypothesis.

The rural quality elasticities are relatively low: 13 of the 17

 

are 0.05 or less and six are even negative. The highest values are for E
tomatoes (0.14), bananas (0.09), and banana beer (0.08). Furthermore,
in none of the equations can we reject the null hypothesis that there
are no expenditure effects, even at the 90% confidence level. Thus,
there is little or no evidence of quality effects in rural food demand.
Table 6-25 presents the results for the urban food demand model.
Here, the estimated quality elasticities are even lower: all but one is
below 0.05 and nine of the 21 are negative. And again, in none of the
equations are the expenditure terms statistically significant, even at
the 90% confidence levell. Thus, urban food demand also reveals little

or no sign of quality effects.

6.7.2 Effect of within-cluster unit value on budget share

 

Assuming that prices do not vary within the cluster, a
significant effect of "price" (unit value) on demand within the cluster
is probably due to measurement error. Measurement error can generate

this pattern since, for a given monetary value of a transaction, a

 

1. The largest quality elasticity is for prepared meals,
0.23. This product also comes closest to being statistically signifi-
cant at the 90% confidence level.

190
Table 6-24: Quality and measurement error effects in rural food demand
—

Estimation of
budget share2

Estimation of
unit values1

 

 

 

Impact of Impact of
expenditure unit values
Prod elast F prob F prob
SORGH -0.03 0.55 0.84 1.30 0.27
RICE 0.03 8.72 0.11 0.90 0.65
CASSA 0.04 0.61 0.80 1.24 0.32 ii
SWPOT 0.03 0.64 0.79 0.42 1.00
WHPOT 0.05 1.71 0.44 0.73 0.85
BANAN 0.09 0.60 0.81 0.52 0.98
BEANS -0.06 1.65 0.45 0.67 0.90
PEAS -0.01 0.24 0.98 0.95 0.59
TOMAT 0.14 1.87 0.41 0.88 0.68
BEEF 0.01 0.05 1.00 0.96 0.58
MEAT 0.02 0.38 0.92 0.56 0.97
BBEER 0.08 2.61 0.32 1.70 0.10
SBEER 0.05 1.67 0.45 0.50 0.99
FBEER -0.01 0.58 0.82 1.02 0.51 E:
OIL 0.07 2.35 0.35 0.89 0.66
SALT -0.02 1.13 0.58 1.24 0.32
SUGAR -0.00 0.21 0.99 2.37 0.02
1. Price (unit value) is regressed on log expenditure, log

expenditure squared, number of adults, number of children, a dummy
for female-headed household and dummy variables for each sample
cluster.

2. Budget share is regressed on log expenditure, log expenditure
squared, number of adults, number of children, a dummy for female-
headed households, prices (unit values), and dummy variables for
each sample cluster.

positive error in quantity generates a negative error in ”pricel."
The test is implemented by estimating the standard demand equa-
tion, but using the deviations from the cluster mean as observations
(this is equivalent to including dummy variables for each sample
cluster). If the price vector is statistically significant within

clusters, then measurement error is a likely cause.

 

1. This relationship could also result from quality effects
if richer households spend the same portion of their budget on a good as
do poorer households but purchase a smaller quantity of higher quality
(higher priced) goods. However, this seems a less likely cause.

Table

1.

for female-headed household

6-25:

Estimation

191
Quality and measurement error effects in urban food demand

of unit valuel

Estimation

of budget sharez

 

Impact of Impact of

expenditure unit value

Prod elast F prob F prob
SORGH -0.04 0.88 0.68 0.60 0.96
RICE -0.03 2.50 0.33 0.96 0.59
BREAD 0.02 0.56 0.83 1.55 0.12
CASSA 0.02 3.50 0.25 1.78 0.06
SWPOT 0.02 0.51 0.86 1.22 0.31
WHPOT -0.01 0.38 0.93 1.58 0.11
BANAN -0.02 0.10 1.00 0.73 0.87
CASFL 0.01 0.35 0.94 1.29 0.25
BEANS 0.02 0.43 0.90 0.68 0.91
PEAS -0.01 1.02 0.62 1.33 0.22
VEGET 0.05 1.88 0.41 0.66 0.92
BEEF 0.00 0.02 1.00 0.80 0.79
MEAT 0.05 1.02 0.62 1.85 0.05
MILK 0.02 1.14 0.58 1.57 0.11
BBEER -0.04 0.79 0.72 2.11 0.02
SBEER 0.03 1.58 0.47 1.37 0.20
FBEER -0.01 0.40 0.91 0.83 0.75
OIL -0.02 0.13 1.00 0.90 0.66
SALT -0.04 3.07 0.28 1.58 0.11
SUGAR 0.05 0.46 0.88 1.36 0.21
MEALS 0.23 7.77 0.12 1.14 0.38

Price (unit value) is
expenditure squared, number

cluster.

2.

each sample cluster.

regressed on log expenditure,

of adults,
and dummy variables for each sample

number of children,

 

log
a dummy

Budget share is regressed on log expenditure, log expenditure
squared, number of adults, number of children, a dummy for female-
headed households, prices (unit values), and dummy variables for

The last two columns Table 6-24 give the F statistic and the

corresponding probability under the null hypothesis that there are no

"within cluster" price effects on budget share in the rural sector. The

null hypothesis cannot be rejected at the 95% confidence level for 16 of

the 17 equations; only sugar shows some "within cluster" effects which

indicate measurement error effects.

results from the urban demand model.

The last two columns of Table 6-25 provide the corresponding

In this case, the null hypothesis

 

 

192

cannot be rejected at the 95% level in 19 out of 21 equations; "other
meat" and banana beer are the only goods which show signs of measurement
error effects.

In summary, although quality effects and measurement error may
exist in the ENBC data, these tests indicate that they are not statisti-
cally significant and that the quality elasticities are generally below
0.05. The measurement error is probably reduced by several factors.
First, the ENBC involved 56 days of transaction data, thus including in
many cases multiple observations for the same good and the same house-
hold. The measurement error would be reduced by calculating the average

unit value over several purchases. Second, because home prdduction is

 

so important in the rural sector, many of the unit values for food were i,
in fact average prices at the region—round level, again diluting i i
measurement error.
The small size of the quality effects is probably the result of
the generally low level of income in Rwanda and the high degree of
disaggregation in this demand study. For much of the population,
additional income is allocated to increasing the quantity of food
consumption rather than improving the quality. Nonetheless, the

estimated elasticities are similar in magnitude to previous estimates.

 

Using 1979 data from the C6te d'Ivoire, Deaton (1988) estimated quality
elasticities which ranged from 0.023 to 0.065. Similarly, Deaton (1990)
estimated quality elasticities from 1981 Indonesian data and obtained
values from -0.04 to 0.22. Thus, it is possible that with a larger
sample, some of the Rwandan quality elasticities may have been statisti-

cally significant.

CHAPTER SEVEN

 

WELFARE AND NUTRITIONAL IMPACT OF DEVALUATION

7.1 Introduction

This chapter uses information about household demand and the
sources of household income to evaluate the welfare and nutritional
effects of price changes associated with currency devaluation. In
carrying out the simulation, various assumptions can be made about the
supply response of agriculture and about the prices and wages associated

with devaluation. In order to reduce the number of alternative scenari-

 

os, a set of base assumptions is adopted, and the sensitivity analysis

is limited to studying the effects of changing each assumption one at a

 

time. In addition, various measures of welfare impact are compared.
In the base scenario, household demand is simulated using the
demand parameters estimated under the restrictions associated with
consumer theory: adding up, symmetry, and homogeneity. The effect of
price changes on income (the ”profit effect") is modeled using survey
data on the composition of income, but no agricultural supply response
is assumed. The price changes for both consumers and producers are
hypothesized based on the tradeability of each good. Real wages are
assumed to follow the average trend of other countries undergoing
currency devaluation, as studied by Edwards (1989). And welfare impact
is measured using equivalent variation (EV) and compensating variation
(CV), calculated using the Vartia method with 20 iterations. The
results of this base scenario are presented in section 7.2.
Alternative scenarios will also be considered to determine the
sensitivity of the results to changes in assumptions about demand,
supply, prices, and wages. In section 7.3, the base scenario is
compared to the simulated impact of the historical prices observed in

Rwanda over the seven months following devaluation. Section 7.4 tests

193

194

the sensitivity of the results to alternative assumptions about real
wage trends. Section 7.5 considers the implications of a more sophisti-
cate model which incorporates agricultural supply response and a simpler
model which ignores the profit effect completely. The last variant,
presented in section 7.6, analyzes the results when the unrestricted
parameters are used to model consumer demand. Finally, in section 7.7
we compare the various methods of calculating welfare impact, including
consumer surplus, first- and second-order approximations of EV and CV,

and two levels of precision in implementing the Vartia method.

7.2 Effects of hypothetical currency devaluation: base scenario

7.2.1 Assumption used in base scenario

On November 20, 1990, the Rwandan franc was devalued 40%-
relative to the International Monetary Fund Special Drawing Right. In
other words, the local cost of foreign currency increased by two thirds
(the inverse of 0.6 is 1.667). As discussed in section 4.2.5, we adopt
the results of econometric analysis of devaluation episodes in 29
countries by Edwards (1989) and assume a rate of effectiveness of 0.6 in
the first year after devaluation. Thus, a 67% increase in the local
cost of foreign currency is translated into a increase in the ratio of
tradeable to non-tradeable prices by 40%.

In Rwanda, the tradeable food commodities are limited to rice,
wheat products, cooking oil, sugar, and most processed foods. Factory
beer and beans are intermediate cases. The beer uses imported malt, but
these imports represent a small portion of the total cost to consumers
(Haggblade, 1987). Beans are imported to Rwanda, but these imports
represent perhaps 10-15% of national bean consumption. In addition,
beans are imported informally so that devaluation affects bean prices
only indirectly through its effect on the parallel exchange rate. For

the purpose of this analysis, factory beer is considered 50% tradeable

 

 

195

and beans are considered 25% tradeable. These assumptions are summa-

rized in Table 7-1.

Table 7-1: Assumed tradeable component of each budget category
IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII-I-I-I-II-I-I-I-I-I-l

 

 

 

Budget Tradeable component
category Rural Urban
SORGH 0.00 0.00
RICE 1.00 1.00 '—
BREAD — 1.00 g
CASSA 0.00 0.00
SWPOT 0.00 0.00
WHPOT 0.00 0.00
BANAN 0.00 0.00
CASFL - 0.00
BEANS 0.25 0.25
PEAS '0.00 0.00
TOMAT 0.00 -
vscs'r 0.00 0.00 is
BEEF 0.00 0.00
MEAT 0.00 0.00
MILK - 0.00
BBEER 0.00 0.00
SBEER 0.00 0.00
FBEER 0.50 0.50
OIL 1.00 1.00
SALT 0.00 0.00
SUGAR 1.00 1.00
MEALS - 0.00
CLOTH 0.96 0.94
HOUSE 0.14 0.16
EQUIP 0.64 0.76
ENERG 0.82 0.27
HEALT 0.50 0.73
EDUCA 0.34 0.16
TRANS 0.51 0.84
TOBAC 0.00 0.00
LEISU 0.51 0.30
OTHFO 0.10 0.21

For the non-food categories, a highly disaggregated list of non-
food goods and services was classified into tradeable and non-tradeable.
Then the proportion of expenditure on each category which goes to
tradeable goods was calculated. The price of each non-food category was
assumed to rise in proportion with the share of tradeable good expendi-

ture in that category. This procedure was carried out separately in the

196

rural and urban areas to allow for the fact that the tradeable component
of each non-food category varies somewhat between them.

As shown in Table 7-1, among the non-food categories, the trade-
able component is highest for clothing and lowest for tobacco. Not
surprisingly, the tradeable component is greater among urban consumers
than rural for household equipment, health/hygiene, and transportation.
Presumably, the higher incomes of urban consumers make them more likely
to purchase imported goods which are generally of a higher quality and
more expensive. In contrast, the tradeable component is higher among
rural consumers for educational expenditures. 'This is due to the large
share of rural education spending which is allocated to school uniforms,
which are classified as tradeable. Because private schools are more
common in the cities, urban households spend a greater portion of
educational expenses on school fees which are considered non-tradeable
services. Similarly, rural energy/water spending has a higher tradeable
component because of the importance of kerosenel; most urban spending
on energy/water is allocated to charcoal and electrical services, both
of which are classified as non-tradeable.

In order to express the price changes in real terms, we normalize
prices so that the budget share weighted average is 1.0. The result is
that the price of pure non-tradeable goods and services falls about 7%,
while that of pure tradeables rises by 30%. It is assumed that the
percentage changes in price for a given commodity are the same through-

out the countryz.

 

1. Firewood is the primary source of energy in the rural
areas, but it is generally gathered by families for their own consump-
tion. Information on firewood use is not available for this analysis.

2. Since transportation depends on tradeable goods (fuel and
vehicles), we would expect marketing margins to increase somewhat
following devaluation. A more sophisticated modelling approach would
use data on the regional flows of goods and transportation costs to
incorporate this effect. ‘

 

 

 

197

On the income side, agricultural producer prices are assumed to
change in proportion to the consumer prices of the same commodities.
Similarly, beer brewer income is assumed to reflect banana beer prices.
Coffee prices are assumed to follow tradeable good patterns. Although
coffee prices have not risen since devaluation due to international
price trends, this assumption reflects the fact that, in the absence of
devaluation, local coffee prices would certainly have had to decline. '7

Regarding real wages, Edwards (1989: 335-336) analysis of devalua-
tion episodes reveals that, on average, real agricultural wages fall
3.5%, while real non-agricultural wages decline 8.5% over the year
following devaluation. These figures are adopted for artisanal, commer-

cial, and wage income. These assumptions cover only 20% of net income

1 —I- IECTE e

in rural areas, but they account for 92% of urban net income (see Table-
5-2). Thus, the impact of devaluation on urban income is fairly crudely
modeled, so that the distributional results within the urban sector
reflect primarily different expenditure patterns among households.

As noted above, household demand in the base scenario is simulated
using the demand parameters estimated under the restrictions of consumer
theory: symmetry and homogeneity. These results were presented in
sections 6.4 and 6.6. On the supply side, the base scenario assumes no
agricultural supply response. This does not mean that there is no
”profit effect,” but rather that the profit effect is limited to the
change in price multiplied by the original quantity of output. This can
be considered an estimate of the short-term impact of price changes,
before supply has time to adjust, or as a first-order estimate of the
long-term impact of the price change (see section 3.4.1).

7.2.2 Aggregate demand and caloric intake

The assumptions described in the previous section are
used to simulate the change in income and prices affecting each house-

hold in the sample, allowing us to predict the change in demand for each

198

household. In this section, the aggregate results for the rural and
urban sectors are considered.

Table 7-2 shows the change in mean budget shares resulting from
the hypothesized price changes. These figures differ from those that
would be obtained using the individual price elasticities presented in
Chapter 6 for several reasons. First, these figures incorporate the
effect of all prices, not just own-price, on demand for a given commodi-
ty. Second, this table incorporates the "profit effect" in which prices
influence income which in turn affects demand. Third, the elasticities
in Chapter 6 are valid for a household "at the mean" but do not neces-
sarily represent the response of aggregate demand to price changes.
Finally, the estimated elasticities are applicable only for marginal
changes in prices, whereas non-marginal changes are simulated here.

It should be recalled that an increase (decrease) in budget share
does not always correspond to an increase (decrease) in quantity
demanded. For example, in the case of cooking oil, the budget share
increases roughly 10% in response to a 30% increase in price; this
implies a reduction in quantity demanded.

The last two columns of Table 7-2 provide a rough indicator of the
welfare impact of each price change on the expenditure side (the effect
of price changes on agricultural income is not included in this mea-

sure). CV1 is the first-order approximation of compensating variation

expressed as percentage of household expenditure: the percentage price

change times the old budget share. EVI, the first-order approximation

of equivalent variation is similarly calculated except that the new
budget share is used. These numbers show that, among the consumer price
increases, the one with the most serious impact on rural welfare by far
is the 30% increase in the price of clothing. This is particularly true
when we consider that the welfare impact of changes in food prices is

offset by simultaneous effects on agricultural income.

 

 

199

Table 7-2: Effect of hypothetical devaluation on rural demand
—

 

 

 

 

price budget share
change (percent) CV1 EVl

Prod (pct) old new (pct) (pct)
SORGH -7.0 1.4 1.6 0.1 0.1
RICE 30.0 0.5 0.8 -0.1 -0.2
CASSA -7.0 5.9 6.0 0.4 0.4
SWPOT -7.0 12.5 12.4 0.9 0.9
WHPOT -7.0 4.0 4.6 0.3 0.3
BANAN -7.0 5.9 6.1 0.4 0.4
BEANS 2.0 21.6 22.0 -0.4 -0.4
PEAS -7.0 1.4 1.8 0.1 0.1 F“
TOMAT -7.0 0.1 0.2 0.0 0.0
BEEF -7.0 1.4 1.9 0.1 0.1
MEAT -7.0 1.9 2.0 0.1 - 0.1
BBEER -7.0 10.1 9.5 0.7 0.7
SBEER -7.0 3.9 3.9 0.3 -0.3
FBEER 11.0 0.8 0.8 -0.1 -0.1

OIL 30.0 1.0 1.1 -0.3 -0.3
SALT -7.0 1.0 0.9 0.1 0.1
SUGAR 30.0 0.3 0.2 -0.1 -0.1 .
orsro -3.0 9.9 7.8 0.3 0.2 :
CLOTH 29.0 6.3 6.4 -1.8 -1.8
HOUSE -2.0 3.3 3.3 0.1 0.1
EQUIP 17.0 1.5 1.4 -0.3 -0.2
ENERG 23.0 1.2 1.3 -0.3 -0.3
HEALT 12.0 1.7 1.7 -0.2 -0.2
EDUCA 5.0 0.4 0.4 -0.0 -0.0
TRANS 12.0 0.8 0.8 -0.1 -0.1
TOBAC -7.0 0.7 0.7 0.0 0.0
LEISU 12.0 0.4 0.4 -0.0 -0.0
TOTAL —0.1 100.0 100.0 0.1 -0.0
Source: Simulation based on ENBC data.

Table 7-3 focuses on food consumption and caloric intake. Price
increases result in reduced demand for beans, factory beer, cooking oil,
and sugar. However, this is more than offset by increased consumption
of tubers and bananas, with the result that the volume of food consump-
tion and caloric intake rise slightly.

The aggregate impact of devaluation is simulated for the urban
sector in the same manner as for the rural sector. Table 7-4 shows the
mean budget shares among urban households before and after the relative
price changes associated with devaluation. Higher prices reduce the

average share allocated to rice, factory beer, cooking oil, sugar,

200
Table 7-3: Effect of hypothetical devaluation on rural food consumption

 

 

 

price quantity consumed caloric intake
change (kilograms/ae/yr) (kcal/ae/day)
Prod (pct) old ‘ new % change old new % change
SORGH -7.0 7.7 8.8 14.2 69.2 79.0 14.2
RICE 30.0 0.8 1.0 17.3 7.6 8.9 17.3
CASSA —7.0 72.1 76.5 6.2 333.6 354.3 6.2
SWPOT -7.0 208.4 211.8 1.6 439.6 446.8 1.6
WHPOT -7.0 43.7 51.1 16.9 79.1 92.5 16.9
BANAN -7.0 20.8 22.7 9.0 40.4 44.1 9.0
BEANS 2.0 92.2 89.6 -2.8 818.4 795.6 -2.8
PEAS -7.0 5.4 7.2 32.8 38.4 51.0 32.8 r—
TOMAT -7.0 0.6 0.9 66.6 0.3 0.5 66.6
BEEF -7.0 1.8 2.5 38.4 10.9 15.1 38.4 ‘
MEAT -7.0 2.2 2.3 4.8 7.7 8.1 4.8
BBEER -7.0 51.9 50.2 -3.4 122.4 118.3 -3.4
SBEER -7.0 37.7 39.4 4.6 175.4 183.5 4.6
FBEER 11.0 1.2 '1.0 -18{4 1.6 1.3 -18.4
OIL 30.0 0.8 0.7 -16.1 22.6 18.9 -16.1
SALT -7.0 2.5 2.3 -11.6 0.0 0.0 -11.6 i
SUGAR 30.0 0.6 0.3 -40.6 5.9 3.5 —40.6 E
OTHFO -3.0 35.0 27.4 -21.7 114.0 89.3 -21.7
TOTAL -0.1 585.3 595.6 1.8 2287.1 2310.6 1.0

 

Source: Simulation based on ENBC data.

household equipment, and transportation. The last two columns of Table
7-4 indicate that the price increases in clothing and transportation
have the greatest impact on the average urban household. Among the food
categories, the most damaging price increases are those of sugar,
cooking oil, and rice. By comparison, price increases in bread, beans,
and factory beer are less important, at least to the average household.

It is worth noting that urban prices rise by 4.4% using a base
weighted average. Although prices were normalized for the country as a
whole, the higher budget shares of tradeable goods among urban consumers
mean that the weighted average price change is positive (reflecting the
same pattern, the weighted average rural price change is slightly

negative).

201
Table 7-4: Effect of hypothetical devaluation on urban demand

—’

 

 

price budget share
change (percent) CV1 EVl
Prod (pct) old new (pct) (pct)
SORGH —7.0 0.92 1.01 0.06 0.07
RICE 30.0 2.37 1.71 -0.71 -0.51
BREAD 30.0 0.67 0.73 -0.20 -0.22
CASSA -7.0 1.79 1.47 0.13 0.10
SWPOT -7.0 3.84 4.82 0.27 0.34
WHPOT -7.0 6.24 6.43 0.44 0.45
BANAN -7.0 2.93 2.84 0.20 0.20
CASFL -7.0 2.40 2.73 0.17 0.19
BEANS 2.0 10.37 11.35 -0.21 -0.23
PEAS -7.0 0.41 0.75 0.03 0.05
VEGET -7.0 1.57 1.45 0.11 0.10
BEEF -7.0 2.90 2.83 0.20 0.20
MEAT -7.0 2.11 2.25 0.15 , 0.16
MILK -7.0 2.30' 2.12 ' 0.16 0.15
BBEER -7.0 4.82 5.65 0.34 0.40
SBEER -7.0 1.16 1.35 0.08 0.09
FBEER 11.0 4.17 3.95 -0.46 -0.43
OIL 30.0 2.07 1.98 -0.62 -0.59
SALT -7.0 0.54 0.53 0.04 0.04
SUGAR 30.0 2.59 2.49 -0.78 -0.75
MEALS -7.0 2.76 3.16 0.19 0.22
OTHFO 1.0 5.69 4.53 -0.06 -0.05
CLOTH 28.0 5.50 5.43 -1.54 -1.52
HOUSE -1.0 10.04 9.89 0.10 0.10
EQUIP 21.0 2.87 2.48 -0.60 -0.52
ENERG 3.0 4.62 4.60 -0.14 -0.14
HEALT 20.0 3.05 3.00 -0.61 -0.60
EDUCA -1.0 1.07 1.09 0.01 0.01
TRANS 24.0 4.84 4.00 -1.16 -0.96
TOBAC -7.0 1.51 1.56 0.11 0.11
LEISU 4.0 1.88 1.80 -0.08 -0.07
TOTAL 4.4 100.00 100.00 . -4.38 -3.62

 

 

Source: Simulation based on ENBC data.

Table 7-5 concentrates on food demand and caloric intake in the

urban areas. There appears to be substitution away from rice and bread

and toward sweet potatoes, white potatoes, and cassava flour, as well as

substitution away from factory beer and toward sorghum beer. The total

volume of food consumption rises somewhat (2.8%), but the caloric intake

falls slightly (1.1%). The fall in caloric intake is due primarily to

the reduced consumption of cooking oil and rice.

202

 

Table 7-5: Effect of hypothetical devaluation on urban food consumption

 

 

price quantity consumed caloric intake
change (kilograms/ae/yr) (kcal/ae/day)
Prod (pct) old new % change old new % change
SORGH -7.0 8.71 9.59 10.11 78.50 86.44 10.11
RICE 30.0 11.38 5.95 -47.71 103.82 54.29 -47.71
BREAD 30.0 2.67 2.13 -20.06 29.25 23.38 -20.06
CASSA -7.0 21.74 16.48 -24.21 100.66 76.29 -24.21
SWPOT -7.0 70.56 97.46 38.14 148.86 205.63 38.14
WHPOT -7.0 150.64 158.45 5.18 272.43 286.53 5.18
BANAN -7.0 58.91 57.52 -2.35 114.60 111.90 -2.35 F7
CASFL -7.0 20.21 23.88 18.17 190.45 225.06 18.17
BEANS 2.0 65.05 69.00 6.07 577.49 612.56 6.07 .
PEAS -7.0 2.95 5.46 85.09 20.78 38.45 85.09
VEGET -7.0 18.73 17.39 -7.18 12.83 11.91 -7.18
BEEF -7.0 10.88 10.77 -0.96 65.56 64.93 -0.96
MEAT -7.0 5.50 5.88 6.98. 19.44 20.80 6.98
MILK -7.0 7.33 6.68 -8.84 15.66 14.28 -8.84
BBEER -7.0 206.65 214.06 3.59 486.95 504.42 3.59
SBEER -7.0 20.87 25.29 21.19 97.20 117.80 21.19 ‘
FBEER 11.0 21.39 16.93 -20.87 29.31 23.19 -20.87 p-
OIL 30.0 8.57 5.96 -30.47 234.81 163.26 -30.47 "
SALT -7.0 3.25 3.20 -1.50 0.00 0.00 -1.50
SUGAR 30.0 13.54 9.37 -30.83 140.99 97.53 -30.83
MEALS -7.0 5.97 6.19 3.71 26.35 27.33 3.71
OTHFO 1.0 33.06 22.76 -31.14 102.36 70.48 -31.14
TOTAL 4.4 768.54 790.40 2.84 2868.29 2836.46 -1.11

 

Source: Simulation based on ENBC data.

7.2.3 Distributional effegge of hypothetical devaluation

Until this point, we have only considered the effects of
the hypothetical devaluation on aggregate demand, food consumption, and
caloric intake for the urban and rural sectors. In this section, the
impact on different types of households will be considered. In this
analysis, households are disaggregated by region, total expenditure
(income), principal occupation, and sex of head of household. The

welfare impact is calculated using the Vartia method to approximate the

203

equivalent variation (EV) and the compensating variation (CV). As

mentioned above, the Vartia method is applied with 20 iterationsl.

 

The welfare impact of price and income changes can be separated
into the effect of changes in income and the effect of changes in
consumer prices, as shown in section 3.4.4. The first component is the
effect of the price changes on the household as producer, measured by
producer surplusz. The second component is the impact on the house- , F;
hold as consumer, measured as the CV or EV associated with the change in
consumer pricesa. Combining the producer and consumer impact, we get

the total welfare impact of the price and income changes.

Table 746 shows the producer impact, the two measures of consumer

 

impact, and the total impact of the hypothetical prices on different
groups of households. For example, the value -3.5 under EV means that
the price and income changes associated with devaluation are, on
average, equivalent to a 3.5% decrease in the level of real expenditure
(income) per adult equivalent. This figure is the sum of a negative
producer impact (-4.0) and a smaller positive consumer impact (0.5).
Similarly, the CV value of -3.6 means that, on average, compensation
equal to 3.6% of their original level of expenditure would be necessary
to make Rwandan households as well of as before devaluation.

This result should be interpreted with some caution. The fact
that the average impact is negative has little bearing on the desirabil-

ity of devaluation as a policy option. First, as mentioned in Chapter

 

1. Price changes are divided into 20 increments and after
each increment, household income is adjusted to compensate for the price
change. Willingness to pay is approximated by the sum of these adjust-
ments (Vartia, 1983).

2. In the base scenario, no supply response is assumed so
the percentage change in producer surplus is simply the weighted average
of output price increases, where the weights are the proportion of
output from each source (see equation 3-31).

3. This is measured as the area under the compensated demand
function, h(p,u), over the range of price movement (see equation 3-42).
CV uses the "before" demand function, while EV uses the "after" func-
tion.

204

Table 7-6: Effect of hypothetical devaluation on households

 

Producer Consumer Consumer Net Net Pct change
impact impact impact impact impact in caloric
(PS) (EV-PS) (CV-PS) (EV) (CV) intake
Sector
Rural -3.8 0.7 0.6 -3.1 -3.2 1.3
Urban -7.8 -2.7 -3.5 -10.4 -1l.3 0.8
Mean -4.0 0.5 0.4 -3.5 -3.6 1.3
Expenditure quintile
1st -4.0 1.5 1.4 -2.5 -2.6 0.4
2d -4.0 1.0 0.9 -2.9 -3.0 0.7
3d -2.6 -0.0 -0.1 -2.6 -2.8 1.9
4th -4.3 0.7 0.6 -3.6 -3.8 0.7
5th ’ -5.1 -0.6 -0.9 -5.7 -6.0 2.6
Mean -4.0 0.5 0.4 -3.5 -3.6 1.3
Principal occupation
Farmer -3.4 1.0 0.9 —2.5 -2.6 1.1
Artisan -6.5 -0.2 -0.5 -6.7 -7.0 1.5
Merchant -3.2 -1.6 -1.9 -4.8 ~5.1 2.3
Employee -6.9 -1.7 -2.2 -8.6 -9.1 2.7
Various -4.8 -0.1 -0.3 -4.9 -5.1 1.0
Mean -4.0 0.5 0.4 -3.5 -3.6 1.3
Sex of head of household
Male -3.9 0.5 0.4 —3.4 -3.5 1.5
Female -4.5 0.5 0.4 -4.0 -4.1 0.5
Mean -4.0 0.5 0.4 -3.5 -3.6 1.3

 

Source: Simulation based on ENBC data.

2, the pre-devaluation situation is generally unsustainable so that
maintaining the original condition is not an option. Second, this model
simulates only the short-term relative price effect, ignoring any impact
on aggregate output and all long-term effects. Third, since price
changes are expressed in relative terms, the negative impact is primari-
ly a function of the assumption that real wages fall. In fact, given
the size of the assumed drop in real wages, it is somewhat surprising
that the average welfare impact is so modest.

Turning our attention to the distributional effects, the first
part of Table 7—6 makes it clear that, under the assumptions of the base
scenario, the proportional reduction in real income due to currency
devaluation is over three times as great for urban households as for

rural households. For urban households, the prices associated with

 

 

 

Ir

205

devaluation imply a 10% decline in standard of living on average. For

 

their rural counterparts, the decline is only about 3%1. Rural house-

holds face moderately lower incomes partially offset by small reductions

in consumer prices. Urban households, by contrast, experience sharply

reduced income, exacerbated by somewhat higher consumer pricesz.
It is worth noting that these results overestimate the proportion-

al impact on rural households to the extent that non-food home produc-

tion (excluded from our calculation of expenditure) is important. As fi‘

noted in section 5.3.1, the value of collected firewood is probably the

most significant component of rural non-food home production. Since

non-food home production is likely to be much more important in the

rural areas than in the cities, this omission also implies that, if

 

m" v'a

anything, the results in Table 7-6 understate the difference between
rural and urban impact.

Interestingly, the caloric impact is, on average, slightly
positive, in spite of the reduction in real income. This may be the
result of the fact that the food prices fall relative to non-food prices
(see Tables 7-2 and 7-4). This, in turn, is a result of the greater
tradeable component of non-food items compared to food (see Table 5-23).
In addition, the tradeable food items whose prices increase (rice,
bread, factory beer, and cooking oil) tend to be relatively expensive
sources of calories compared to the non-tradeable staples (cassava,

sweet potatoes, bananas, and so on).

 

1. Without some assumptions about the marginal utility of
money for different households, we cannot say which group is "hurt" more
by the price changes. For example, we cannot be sure that a 3% reduc-
tion in the real income of a rural household would be less "painful"
than a 10% reduction in the income of an urban household. Nonetheless,
these figures provide useful information and contribute to a more
informed application of the value judgements necessary to policy making.

2. The simulation assumes that the percentage price changes
for a given commodity are equal or similar across households (compare
Tables 7.2 and 7.4). However, the average price faced by a household is
also a function of the composition of expenditure, which varies across
households. Thus, saying that consumer prices rise more for urban
households than rural means that they consume proportionately more of
the (tradeable) goods whose prices increased.

206

The second part of Table 7-6 disaggregates the results by quintil-
es of real expenditure per adult equivalent. This section indicates
that the price changes associated with devaluation affect higher-income
households more seriously than lower-income households. The percentage
reduction in real income is more than twice as great for the richest 20%
of households as for the poorest 20% of them. Although the patterns are
not clear-cut, it seems that the richest fifth of Rwandan households
purchase more tradeables and sell more non-tradeables as a proportion of
income (expenditure) than other households. Given the weak relationship
between the tradeable share of the budget and total.expenditure (see
Tables 5—25 and 5-26), this pattern seems to be attributable to the
greater market participation of high-income households. In other words,
low income households are insulated from price changes by their relianCe
on home production.

With regard to principal occupation, farmers are the least
affected by currency devaluation. Under the assumptions of the base
scenario, households whose primary source of income is agriculture
experience a 3% reduction in their standard of living, on average.

These households account for 74% of all Rwandan households (see Table 5-
3). At the other extreme, wage earners are the most severely affected
by devaluation. For the 6% of Rwandan households whose primary source
of income is wage employment, the price changes associated with devalua-
tion are equivalent to an 8.6% decline in real income. This is due to a
large reduction in income and the fact that they purchase more tradeable
goods, whose prices rise.

It is worth noting that although non-agricultural income is
assumed to fall 8.5%, the actual reduction in income among artisans,
merchants, and employees ranges from 3.2% to 6.9%. The effect of wage
reductions on household income is softened by the fact that most house-

holds have other sources of income.

 

 

207

Given the common practice of using a small number of socio-
professional categories to analyze the distributional aspects of policy,
it is worth asking how much of the variation in welfare impact is
captured by this type of classification. Analysis of variance was used
to determine the proportion of the variance in EV which can be "ex-
plained" by the principal occupation of the households. The results
indicate that 50% of the variance occurs among occupations and 50%
exists within each occupation. One implication of this result is that
models which analyze policy impact using average characteristics of,
say, half a dozen socio-professional categories may be ignoring 50% of
the variation in welfare impact. .This suggests that the micro-simula-
tion approach adopted in this study merits wider application when
sufficient data are available.

Table 7-6 also confirms, as a result of the price changes associ-
ated with devaluation, that female-headed households experience a
slightly greater percentage reduction in real income than male-headed
households. This is the result of different sources of income rather
than different spending patterns. Nonetheless, it is worth noting that
the difference is not very great: devaluation is equivalent to a 4%
decrease in real income for female-headed households and it is equiva-
lent to a 3.4% decline in real income for male—headed households.

At this point, we separate the rural and urban samples to analyze
each one more closely. Table 7-7 shows the welfare impact on different
categories of rural households. The first part of the table disaggrega-
tes the households according to rural expenditure quintiles (the fifth
quintile represents the 20% of rural households with the highest
expenditure per adult equivalent). The negative effect of devaluation
is greatest among the high-income households and lowest among the
poorest. Both spending and income patterns appear to contribute to this

result.

 

 

1}

 

208

Table 7-7: Effect of hypothetical devaluation on rural households

 

Producer Consumer Consumer Net Net Pct change
impact impact impact impact impact in caloric
(PS) (EV-PS) (CV-PS) (EV) (CV) intake
Rural expenditure quintile
lst -3.9 1.5 1.4 -2.4 -2.5 0.4
2d -4.0 1.2 1.1 -2.8 -2.8 0.7
3d -2.7 -0.1 -0.3 -2.8 -2.9 2.0
4th -4.0 0.7 0.6 -3.3 -3.4 0.9
5th -4.5 0.1 -0.0 -4.4 -4.5 2.5
Mean -3.8 0.7 0.6 -3.1 -3.2 1.3
Region
N West -4.5 1.0 0.8 -3.5 -3.7 2.0
S West -3.6 -0.0 '-0.1 -3.6 -3.8 1.8
N Centr -3.9 0.8 0.7 -3.1 -3.2— 0.4
S Centr -4.1 0.4 0.3 -3.7 -3.8 1.5
East -3.2 1.1 1.0 -2.2 -2.2 1.1
Mean -3.8 0.7 0.6 -3.1 -3.2 1.3
Principal occupation
Farmer -3.4 1.0 0.9 -2.4 -2.5 1.1
Artisan -6.2 0.1 -0.1 -6.1 -6.3 1.6
Merchant -2.4 -l.2 -1.4 -3.6 -3.8 2.4
Employee -6.3 -0.7 -l.0 -7.0 -7.3 3.1
Various -4.6 0.0 -0.1 -4.6 -4.7 1.1
Mean -3.8 0.7 0.6 -3.1 -3.2 1.3
Sex of head of households
Male -3.7 0.7 0.6 -3.0 -3.1 1.5
Female -4.4 0.7 0.5 -3.7 -3.8 0.7
Mean -3.8 0.7 0.6 -3.1 -3.2 1.3

 

Source: Simulation based on ENBC data.

The second section of Table 7-7 disaggregates rural households by
region. These figures reveal that there is little geographic variation
in the impact of devaluation, except that the East is less hurt than
other rural regions. The Eastern zone is relatively low-density, drier
area of the country. The farms in the East tend to be larger, averaging

2.0 hectares compared to 1.3 ha. for the country as a wholel. The East

 

1. These figures are from the Pilot Agricultural Census of
1982. Although average farm size has undoubtedly fallen since then, the
East is still less densely populated than the rest of Rwanda.

 

If

 

 

 

a!

(1

wk

t1

IE

81‘:

01

t}

209

is even more specialized in agriculture than the rest of rural Rwanda,
and it is the most important surplus producing area of the country
(Ministry of Planning, 1988).

The impression that farmers are relatively shielded from the
impact of devaluation is confirmed in the third section of Table 7-7
which separates rural households by principal occupation. Farmers are
the least affected, the welfare impact being equivalent to a 2.4%
reduction in real expenditure. In contrast, the impact on salaried

employees and artisans in the rural sector is over twice as great. Most

 

of the difference between them is due to the sources of income rather
than spending patterns.

The last part of Table 7-7 breaks down the welfare impact by sex

 

of head of household. The impact of devaluation is greater for female-
headed households, although again the difference is rather small.
Turning to the impact of prices associated with devaluation on
urban households, Table 7-8 reveals many of the same patterns found in
the rural sector. The relative effect of devaluation appears to be the
most serious for high-income households, salaried employees, merchants,
and residents of Kigali. The effect is less severe for the poor,
farmers (about 14% of the "urban” households), and residents of Cities
other than Kigali. In contrast to the rural results, there is little
difference between male- and female-headed households in the urban
sector; if anything, male-headed households are more severely affected

by the prices associated with devaluation.

 

210

Table 7-8: Effect of hypothetical devaluation on urban households

 

Producer Consumer Consumer Net Net Pct change
impact impact impact impact impact in caloric
(PS) (EV-PS) (CV-PS) (EV) (CV) intake
Urban expenditure quintile
lst -6.9 -0.6 -l.1 -7.6 -8.1 -2.2
2d -7.6 -1.5 -2.1 -9. -9.7 -3.1
3d -8.0 -3.2 -4.1 -11.2 -12.1 -0.6
4th -8.1 -4.4 -5.5 -12.5 -13.6 -0.3
Sth -8.3 -3.6 -4.6 -11.9 -12.9 10.0
Mean. -7.8 -2.7 -3.5 -10.4 -11.3 0.8
City
Kigali -8.0 -2.9 -3.7 -10.9 -11.7 1.6
Other -7.1 -2.2 -2.9 -9.3 -10.0 -1.3
Mean -7.8 —2.7 -3.5 -10.4 -11.3 0.8
Principal occupation
Farmer -6.0 -0.0 -0.4 -6.0 -6.4 -2.9
Artisan -8.2 -2.1 -2.8 -10.3 -11.0 1.1
Merchant -8.2 -3.9 -5.0 -12.1 -13.2 1.7
Employee -8.2 -4.0 -5.1 -12.2 -13.3 1.7
Various -7.0 -1.9 -2.6 -8.9 -9.6 0.5
Mean -7.8 -2.7 -3.5 -10.4 -11.3 0.8
Sex of head of household
Male -7.9 -2.7 -3.5 -10.6 -11.4 1.4
Female -6.9 -2.7 -3.6 -9.7 -10.5 -2.5
Mean -7.8 -2.7 -3.5 -10.4 -11.3 0.8

 

 

 

Source: Simulation based on ENBC data.

7.3 Effects of hietoricel pricefchanges

This section analyzes the historical price changes associated with
the November 1990 devaluation and simulates the effect of these changes
on different types of households in Rwanda. This allows us to compare
the hypothetical prices changes which "should have" accompanied devalua-
tion with the price changes that actually occurred. In addition, it
provides some information on changes in the standard of living among
Rwandan households over the period 1989-1991 during which devaluation

took place.

211

On the other hand, historical prices reflect not just the devalua-
tion but also a variety of factors from seasonal cycles and economic
policy to trends in international prices. This is a particular problem
in the case of the Rwandan devaluation because it occurred just one
month after an unsuccessful invasion of the country by rebels in Uganda.
Security measures impeded the flow of goods and labor within the
country, as well as restricting international trade through Ugandal.

7.3.1 General prige trends over 1989-1991

Using prices collected by the Ministry of Planning and
the budget shares from the ENBC, a monthly consumer price index (CPI)
was constructed for the period from October 1989 to June 1991. As shown
in Figure 7-1, the CPI rose significantly in May and June 1989, declined
gradually over the following year. This pattern probably reflects the
crop failures in the south and southwest of Rwanda which led to scat-
tered outbreaks of famine. In October 1990, the CPI increased sharply,
rising 17% above the September level. Since the devaluation did not
occur until 20 November, much of this increase would seem to be attrib-
utable to the invasionz. Based on the limited data available, the
October increase appears to have been a discrete increase in price level
rather than an increase in the rate of inflation.

The impact of devaluation can be observed by constructing separate
indexes for tradeable and non-tradeable goods, as shown in Figure 7-2.
This graph makes it Clear that the 1989 increase was principally the
result of higher non-tradeable prices. Since this category is dominated
by the starchy staples, this seems to confirm the idea that the 1989

increase was linked to the localized crop failure. Regarding the

 

1. In normal times, the most direct route to the coast is
through Uganda to Mombassa, Kenya. As a result of attacks on trucks in
Uganda, much of Rwandan overland trade is rerouted through Tanzania.

2. Although prices often increase in anticipation of devalu-
ation, it should be noted that devaluation had been expected for over a
year and yet the price hikes did not occur until November.

 

 

I“ I

212

 

150
140
’130
120
110

100

 

 

 

 

 

so 55"
g 80
E 70
60
50
40
30 .
20 E;-
10
0
o N DJBSF u A M J J A s 0 N 0390: M A N J J A s 0 N 0351: M A M J
Month
Figure 7-1: Consumer price index for Rwanda (1989:100)

October 1990 price increase, Figure 7-2 reveals that tradeable and non-
tradeable prices increased in similar measure (14% and 17% respec-
tively). However, the two indexes diverge substantially starting in
November 1990. Non-tradeable prices fluctuate around the 110 level,
while tradeable prices continue rising, reaching almost 130 by June
1991. From October 1990 to June 1991, the real exchange rate (RER),
defined as the ratio of tradeable to non-tradeable prices, rose 31%.
Given the 66.7% increase in the official cost of foreign exchange,
this increase in the RER implies an effectiveness ratio of 47%, short of
the 60% average calculated by Edwards (1989) and adopted for the hypo-
thetical devaluation in section 7.2. However, Edwards’ figure repre-
sented the average for the calendar year following devaluation, so more

recent price data would be necessary to make an appropriate comparison.

 

 

213

 

150
140
130

420

100
90
80

Index

70
60
SO
40
3O
20

1O

 

0
0 N 0J89F M A M J J A S 0 N 0J90F M A M J J A S 0 N DJ91F N A M J

Month

 

D Tradeable prices Nontradeable prices

 

 

 

Figure 7-2: Tradeable and nontradeable price indexes (1989=100)

As noted above, historical prices are influenced by a variety of
factors. The real exchange rate may have been affected by the war. For
example, if internal security measures raised the prices of non-trade-
able more than those of imports, the effect of devaluation on the RER
would be dampened. On the other hand, if guerrilla activity in Uganda
raised the price of tradeables disproportionately, the shift in RER may
be strengthened by the war. Finally, it should be recalled that the
import liberalization policies initiated at the end of 1990 probably

dampened the effect of devaluation on the real exchange rate.

 

214

7.3-2 W
In order to evaluate the impact of historical price

changes on Rwandan households, the first step is to choose a "before"
and "after" period. Because of the significant fluctuations in monthly
prices, particularly those of agricultural commodities, it was decided
to use a three-month average for both periods. To avoid the potential
interference of seasonal patterns, it seemed preferable to compare the
same quarter in two different years. Thus, the second quarter of 1990
was chosen to represent the situation before devaluation, while the
second quarter of 1991 represents the prices after devaluation. These
two periods are centered six months before and six months after November
1990 when the Rwandan franc was devalued.

The food indexes are based on unpublished product-level prices for
Kigali collected by the Office of Prices within the Ministry of Plan-
ning. These prices, along with the average prices from the urban
portion of the ENBC, are presented in Table 7-9.

For the non-food categories, price indexes published by the
Ministry of Planning (1991) were used. These indexes were calculated by
Ministry personnel based on the prices of representative products and
services within each category. These indexes are shown in Table 7-10.

As in the hypothetical case, the producer prices of agricultural
commodities are assumed to change in the same proportion as the Kigali
consumer price for the same good. As before, agricultural wages are
assumed to decline by 3.5% in real terms, while non-agricultural wages
fall by 8.5% in real terms. Coffee and tea prices are assumed to remain
constant in nominal terms. This reduction in real coffee prices is a
delayed reaction to the fall in international coffee prices in the late
19803.

Tables 7-9 and 7-10 bear little resemblance to the price changes
expected on the basis of the tradeability of each budget category (see

Table 7-2). Even taking into account the fact that the hypothetical

 

Table 7-9:

215

Food prices in Kigali before and after devaluation
IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII-I-III-I-I-I-I-I-I-I-I

Nominal prices (FRw/kg)

 

 

ENBC/U May-July May-July % change
Food category 1985 1989 1990 ’89-'90
Sorghum 22.9 33.7 45.3 34.7
Rice 90.2 109.3 122.0 11.6
Bread 65.4 50.0 54.3 8.7
Cassava 19.6 16.0 23.7 47.9
Cassava flour 34.1 43.7 50.3 15.3
Sweet potato 15.5 15.3 16.0 4.3
White potato 15.0 14.7 17.3 18.2
Banana 13.2 16.7 27.0 62.0 v
Beans (dry) 48.4 36.0 42.7 18.5 F—
Peas (dry) 51.2 65.3 59.0 -9.7
Groundnuts 143.9 125.3 148.0 18.1
Cabbage 17.2 12.0 13.7 13.9
Eggplant 32.0 26.0 29.7 14.1
Onion 60.7 80.7 128.7 59.5
Tomato ' 42.7 . 26.0 34.3 32.1
Beef 141.5 191.3 192.7 0.7
Goat meat 141.7 250.7 248.0 -1.1
Fish (indagala) 162.9 189.3 255.0 34.7 5_
Banana wine 29.7 45.7 50.7 10.9 I
Sorghum beer 15.0 18.3 22.3 21.8
Factory beer 90.0 95.0 86.7 -8.8
Carbonated soda 24.7 28.3 37.0 30.6
Palm oil 156.0 159.3 180.0 13.0
Salt 55.7 48.3 65.0 34.5
Sugar 87.8 113.7 142.3 25.2
Prepared meal 55.3 127.3 116.0 -8.9

 

Source: Unpublished data collected by the Ministry of Planning.

prices are normalized while the historical prices are not, it is clear
that prices cannot be reliably predicted at this level of disaggrega-
tion. Tradeable goods such as rice, beans, and factory beer registered
modest increases, while some non-tradeable commodities such as bananas
and cassava experienced sharp increases.

There a number of possible explanations. First, these are Kigali
prices so that the price increases for bananas and cassava may reflect
in part the increased cost of transporting them to the capital (on the
other hand, if this were a factor, we would expect the price of sweet
potatoes to increase as well). Second, some prices were set by adminis-

trative decision rather than by market forces. An initial increase in

the government-set price of factory beer was rescinded when tax revenue

 

 

 

216
Table 7-10: Non-food prices in Kigali before and after devaluation
—
Price index (1989=100) Price
2d quart 2d quart change
Budget category 1990 1991 (pct)
Clothing 101.8 130.1 33.1
Household equipment 96.4 137.1 41.3
Energy 96.8 168.1 76.2
Water 101.5 101.5 2.4
Health 93.9 110.3 8.5
Hygiene 93.7 140.3 43.7
Education 109.4 133.3 31.1
Transport 94.1 117.8 23.7 F"
Tobacco 122.7 148.6 21.1
Leisure/services 97.7 106.9 9.3

 

Source: Ministers du Plan, 1991.

 

fell as a result. Another example is water and electricity rates, which ' i-
were raised significantly to more closely reflect costs. This policy is
part of the structural adjustment program but not a result of devalua-
tion per 58. Third, it may be that there is simply too much natural
variability in commodity prices to pick up the impact of devaluation at
this level of disaggregation and in this short a period of time. It is
worth recalling that when aggregated into tradeable and non-tradeable
groups, the price trends follow the expected patterns.

In spite of the divergence between anticipated price changes and
the historical price trends, the model is run using historical prices.
This simulation does not isolate the impact of devaluation, but it does
give an idea of the probable effect on households of the all price
changes that occurred over 1990-1991, regardless of their cause.

7.3.3 Aggregate demand and caloric intake

The simulated effect of the historical price changes on
rural budgets is shown in Table 7-11. The budget shares of cassava and
bananas rise but by less than the increase in price, implying reduced
quantity demanded. The share allocated to factory beer rises signifi-
cantly, though starting from a very low base. The non-food budget

shares are relatively unaffected by the price changes. According to the

217

last two columns in Table 7-11, the most serious impact on rural
households as consumers were caused by the large price increase for
bananas and the more moderate increase in bean prices. However, it
should be noted that the welfare impact of these price changes is offset
by their influence on rural households as producers. Among non-food

categories, the increase in clothing price has the greatest effect on

rural households.

 

 

In

’J

’1

f1

218

Table 7-11: Effect of historical price changes on rural budgets

 

price budget share

change (percent) CV1 EVl

Prod (pct) old new (pct) (pct)
SORGH 34.7 1.4 1.6 -0.5 -0.5
RICE 11.6 0.5 0.3 -0.1 -0.0
CASSA 47.9 5.9 6.0 -2.8 -2.9
SWPOT 4.3 12.5 12.4 -0.5 -0.5
WHPOT 18.2 4.0 3.7 -0.7 -0.7
BANAN 62.0 5.9 6.6 -3.6 —4.1
BEANS 18.5 21.6 23.0 -4.0 -4.3
PEAS -9.7 1.4 1.4 0.1 0.1
TOMAT 32.1 0.1 0.1 -0.0 -0.0
BEEF 0.7 .1.4 0.8 -0.0 --0.0
MEAT -0.2 1.9 2.7 0.0 0.0
BBEER 10.9 10.1 9.0 -1.1 -1.0
SBEER 21.8 3.9 3.4 -0.9 -0.7
FBEER -8.8 0.8 2.0 0.1 0.2
OIL 30.6 1.0 0.6 -0.3 -0.2
SALT 34.5 1.0 0.6 -0.4 -0.2
SUGAR 25.2 0.3 0.5 -0.1 -0.1
OTHFO 23.0 9.9 9.5 -2.3 -2.2
CLOTH 33.1 6.3 6.2 -2.1 -2.1
HOUSE 23.0 3.3 3.1 -0.8 -0.7
EQUIP 41.3 1.5 1.4 -0.6 -0.6
ENERG 76.2 1.2 1.4 -0.9 -1.0
HEALT 8.5 1.7 1.6 -0.1 -0.1
EDUCA 31.1 0.4 0.4 -0.1 -0.1
TRANS 23.? 0.8 0.8 —0.2 -0.2
TOBAC 21.1 0.7 0.7 -0.1 -0.1
LEISU 9.3 0.4 0.4 -0.0 -0.0
TOTAL 22.1 100.0 100.0 -22.1 -22.2

 

 

(mu-Ema

Source: Simulation based on ENBC data.

Table 7-12 presents the aggregate changes in the quantity of food
consumed and caloric intake by rural households. There is substitution
away from cassava, white potatoes, and bananas, whose prices rose
significantly, and toward beans and sweet potatoes, whose price increas-
es were more modest. The price increase of cassava has the greatest
negative impact on caloric intake, but this is offset by increased
reliance on beans. The net effect is that the volume of food consump-

tion and caloric intake fall by less than 2%. The small size of the

219

fall in caloric intake is due to the fact that participation in the

market is limited. In addition, the increases in food prices are offset

 

by increased revenue for surplus food producers.

Table 7-12: Effect of historical prices on rural food consumption
—

 

 

 

price quantity consumed caloric intake
change (kilograms/ae/yr) (kcal/ae/day) ”a.
Prod (pct) old new % change old new % Change
SORGH 34.7 7.7 7.3 -4.3 69.2 66.2 -4.3
RICE 11.6 0.8 0.5 —38.5 7.6 4.7 -38.5 p
CASSA 47.9 72.1 58.6 -18.7 333.6 271.1 -18.7
SWPOT 4.3 208.4 224.6 7.8 439.6 . 473.9 7.8 F
WHPOT 18.2 43.7 39.0 -10.7 79.1 70.6 -10.7 f
BANAN 62.0 20.8 17.8 -14.5 40.4 34.6 -14.5 '
BEANS 18.5 92.2 97.8 6.1 818.4 868.6 6.1 .
PEAS -9.7 5.4 6.9 25.9 38.4 48.3 25.9 _
TOMAT 32.1 0.6 0.4 -21.0 0.3 0.2 -21.0 r:
BEEF 0.7 1.8 1.2 -36.3 10.9 6.9 -36.3
MEAT -0.2 2.2 3.4 55.4 7.7 12.0 55.4
BBEER 10.9 51.9 49.2 -5.3 122.4 115.9 -5.3
SBEER 21.8 37.7 30.7 -18.4 175.4 143.1 -18.4
FBEER -8.8 1.2 2.9 143.2 1.6 4.0 143.2
OIL 30.6 0.8 0.5 -44.2 22.6 12.6 -44.2
SALT 34.5 2.5 1.4 -46.1 0.0 0.0 -46.1
SUGAR 25.2 0.6 0.7 27.9 5.9 7.5 27.9
OTHFO 23.0 35.0 31.4 -10.1 114.0 102.5 -10.1
TOTAL 22.1 585.3 574.3 -1.9 2287.1 2242.7 -1.9
Source: Simulation based on ENBC data.

The simulated impact of historical price changes on urban budgets
is shown in Table 7-13. On average, prices increased about 20% in the
urban areas. The shifts in budget allocations seem to be driven more by
reductions in real income than by the individual price changes. Larger
shares of the budget are spent on necessities such as beans, sweet
potatoes, cassava root, and cassava flour, while smaller shares are
allocated to luxuries such as factory beer, rice, bread, sugar, and most
non-food categories. The price increases which put the largest dent in

urban living standards are those of energy/water, housing, beans, and

clothing.

220

Table 7-13: Effect of historical price changes on urban budgets
_

 

price budget share
change (percent) CV1 EVl

Prod (pct) old new (pct) (pct)
SORGH 34.7 0.9 0.9 -0.3 -0.3
RICE 11.6 2.4 1.9 -0.3 -0.2
BREAD 8.7 0.7 0.5 -0.1 -0.0
CASSA 47.9 1.8 2.3 -0.9 -1.1
SWPOT 4.3 3.8 4.1 -0.2 -0.2
WHPOT 18.2 6.2 8.2 -1.1 -1.5
BANAN 62.0 2.9 2.5 -1.8 -1.6
CASFL 0.0 2.4 2.8 0.0 0.0
BEANS 18.5 10.4 11.8 -1.9 -2.2

PEAS -9.7 0.4 0.5 0.0 0.1
VEGET 0.0 1.6 1.4 0.0 0.0

BEEF 0.7 2.9 3.1 -0.0 -0.0
MEAT -0.2 2.1 1.9 0.0 0.0
MILK 0.0 2.3 1.9 0.0 0.0
BBEER 10.9 4.8 5.4 -0.5 -0.6
SBEER 21.8 1.2 1.2 -0.3 -0.3
FBEER -8.8 4.2 4.0 0.4 0.3

OIL 30.6 2.1 2.0 -0.6 -0.6

SALT 34.5 0.5 0.6 -0.2 -0.2
SUGAR 25.2 2.6 2.4 -0.7 -0.6
MEALS -8.9 2.8 2.9 0.2 0.3
OTHFO 23.0 5.7 6.0 -1.3 -1.4
CLOTH 33.1 5.5 5.3 -1.8 -1.8
HOUSE 23.0 10.0 8.6 -2.3 -2.0
EQUIP 41.3 2.9 2.3 -1.2 -1.0
ENERG 76.2 4.6 3.7 -3.5 -2.8
HEALT 8.5 3.1 3.0 -0.3 -0.3
EDUCA 31.1 1.1 1.0 -0.3 -0.3
TRANS 23.7 4.8 4.2 -1.1 -1.0
TOBAC 21.1 1.5 1.6 -0.3 -0.3
LEISU 9.3 1.9 1.8 ~0.2 -0.2
TOTAL 20.5 100.0 100.0 -20.5 -19.7

 

Table 7-14 concentrates on the effect of the historical price
changes on urban food consumption. In caloric terms, the largest
reductions in consumption are those of bananas, cooking oil, and sugar,
but this is offset by increase caloric intake from white potatoes,
cassava flour, and beans. The net effect is that urban caloric intake

declines by less than 3%.

221

Table 7-14: Effect of historical prices on urban food consumption
—

 

price quantity consumed caloric intake
change (kilograms/ae/yr) (kcal/ae/day)

Prod (pct) old new % change old new % change
’SORGH 34.7 8.7 6.1 -30.4 78.5 54.6 -30.4
RICE 11.6 11.4 8.4 -25.9 103.8 76.9 -25.9
BREAD 8.7 2.7 1.9 -29.6 29.2 20.6 -29.6
CASSA 47.9 21.7 23.4 7.5 100.7 108.2 7.5
SWPOT 4.3 70.6 73.2 3.7 148.9 154.4 3.7
WHPOT 18.2 150.6 184.7 22.6 272.4 334.0 22.6
BANAN 62.0 58.9 31.1 -47.2 114.6 60.5 -47.2
CASFL 0.0 20.2 25.0 23.8 190.5 235.7 23.8
BEANS 18.5 65.1 69.6 7.1 577.5 618.3 7.1
PEAS -9.7 3.0 4.3 45.1 20.8 >30.1 45.1
VEGET 0.0 18.7 17.5 -6.7 12.8 12.0 -6.7
BEEF '0.7 10.9 >12.1 11.1 65.6 72.8 11.1
MEAT -0.2 5.5 5.0 -10.0 19.4 17.5 -10.0
MILK 0.0 7.3 6.0 -17.5 15.7 12.9 -17.5
BBEER 10.9 206.6 192.9 -6.7 486.9 454.5 -6.7
SBEER 21.8 20.9 19.4 -7.2 97.2 90.2 -7.2
FBEER -8.8 21.4 22.5 5.4 29.3 30.9 5.4
OIL 30.6 8.6 6.8 -20.4 234.8 186.8 -20.4
SALT 34.5 3.2 3.0 -6.2 0.0 0.0 -6.2
SUGAR 25.2 13.5 10.2 -24.9 141.0 105.9 -24.9
MEALS -8.9 6.0 6.5 9.3 26.4 28.8 9.3
OTHFO 23.0 33.1 28.5 -13.8 102.4 88.2 -13.8
TOTAL 20.5 768.5 758.1 -1.4 2868.3 2794.0 -2.6

 

 

Source: Simulation based on ENBC data.

7.3.4 Distributional effects of historical price Changes

This section considers the effect of the historical price
changes on different groups of households. As explained above, the
welfare and caloric impact are calculated for each household in the
sample and then averaged over the household category. Table 7-15
presents the producer impact, the two measures of consumer impact, and
the net impact, as well as the percentage change in caloric intake for
each group.

The net effect of the price changes between the second quarter of
1990 and a year later is equivalent, for the average household, to a

reduction in real income of 4.7%. Compensation of 5.8% of household

 

Table 7-15:

222

Effect of historical price changes on households

 

Producer Consumer Consumer Net Net Pct change
impact impact impact impact impact in caloric
(PS) (EV-PS) (CV-PS) (EV) (CV) intake
Sector
Rural 16.2 -20.3 -21.4 -4.1 -5.1 -2.5
Urban 1.4 -16.0 -19.1 -14.6 -17.8 0.8
Mean 15.5 -20.1 -21.3 -4.7 -5.8 -2.3
Expenditure quintile
lst 16.7 -20.2 -21.2 -3.6 -4.5 -3.3
2d 16.7 -20.0 -20.8 -3.3 -4.1 -2.6
3d 15.8 -20.7 -22.0 -5.0 -6.3 -2.8
4th 16.0 -20.5 -21.6 -4.5 -5.6 -3.0
5th 12.1 -19.1 -20.6 -6.9 -8.5 -0.2
Mean 15.5 -20.1 -21.3 -4.7 -5.8 -2.3
Principal occupation
Farmer 17.2 -20.7 ~21.5 -3.4 —4.3 -2.2
Artisan 10.6 -19.2 -21.2 -8.6 -10.6 -3.3
Merchant 12.1 -17.5 -18.8 -5.4 -6.7 -3.1
Employee 4.4 -16.4 -19.1 -12.0 -14.7 -2.2
Various 15.0 ~20.4 -21.7 -5.3 -6.6 -2.1
Mean 15.5 ~20.1 -21.3 -4.7 -5.8 -2.3
Sex of head of household
Male 15.2 -20.0 -21.1 -4.8 —6.0 -2.3
Female 16.6 -20.7 -21.8 -4.1 -5.1 -2.4
Mean 15.5 -20.1 -21.3 -4.7 -5.8 -2.3

 

Source: Simulation based on ENBC data.

expenditure would be necessary to restore the original living standard.
However, this figure varies considerably from one type of household to
another. The relative impact on urban households is over three times as
great as the impact on rural households (the absolute equivalent
variation or compensating variation would be much greater). Most of
this difference is due to the fact that urban income, based heavily on
wages and services, rises only slightly (1.4%). By contrast, a large
portion of rural incomes is tied to commodity prices and rise signifi-
cantly (16%).

The second part of Table 7-15 divides households according to the
level of expenditure per adult equivalent. These results indicate that

low-income households are much less affected by the price changes over

 

 

223
1990-91 than high-income households. For the poorest 20% of the
households, the price changes were equivalent to a 3.6% reduction in
real income, while for the richest 20%, they were equivalent to a 6.9%
reduction. This difference is due primarily to the relative importance
of different sources of income rather than to the composition of

expenditure.

 

The third part of the table disaggregates the households by
principal occupation. Again, employees are the hardest hit, and farmers
are relatiVely insulated from the price changes. This is consistent
with the quintile results since salaried workers earn high incomes on.
average, while farmers tend to be the poorest segment of the population.

Finally, male-headed households appear to have been more affected é

 

by the price trends than female-headed households, although the differ-
ences are quite modest.

In the interest of space, the rural and urban results will not be
presented here. However, it is worth briefly reviewing some of the
results. In the rural areas, the households least affected by the
historical price changes were poor households, farmers, and those in the
Eastern zone. Employees were particularly hard hit. In the urban
areas, poor households are again less affected than others (though the
relationship is weaker than in the rural sector). Farmers and urban
residents outside Kigali were also relatively protected from the price
changes. Differences in impact according to the sex of head of house-
hold were weak or non-existent.

Thus, in spite of the fact that the historical price trends were
quite different than the expected "hypothetical" price changes, the
results of the simulation in terms of distributional impact were quite
similar. One possible explanation is that the similarity is due to the
wage assumptions, which were the same in the two simulations. An

alternative explanation is that semi-subsistence households (and by

224

extension, poor households) are somewhat insulated from price changes by

virtue of their limited participation in the market.

7.4 Wage rate assumptions

As described in section 5.2, only 6% of Rwandan households depend
on wages for a majority of their income, but over half of both urban and
rural households have some wage income. This section tests the hypothe-
sis that the results obtained in sections 7.2 and 7.3 were primarily the
result of the assumption that real wages decline. In particular, the
greater impact of devaluation on high income households may have
resulted from the assumption that real wages fall, since wages are an
important source of income for these households. The base scenario of
is rerun except that now it is assumed that wages and salaries are held
constant in real terms.

Table 7-16 shows the welfare and caloric impact of the hypotheti-
cal devaluation with nominal wages allowed to rise at the same level as
commodity prices. Not surprisingly, both urban and rural households are
better off in this simulation than in the base scenario. The effect of
the hypothetical devaluation is equivalent to a 1.7% increase in real
income for the average Rwandan household. Once again, urban households
are more negatively affected than rural households: the impact for rural
households is equivalent to a 2% increase in real income, while for
urban households it is equivalent to a 4% decrease in real income.

The table reveals that urban incomes fall while urban consumer
prices rise, whereas in the rural sector average income increases while
average prices fall. Another way to express this is that urban income
is more heavily dependent on non-tradeables (particularly services) than
rural income, and urban spending is more heavily weighted to tradeable
goods (particularly non-food spending) than rural spending.

The second part of Table 7-16 divides households according to

their expenditure quintile. As in previous scenarios, the poorest

 

Table 7-16: Effect of hypotheticalzzdsevaluation on households

assuming real wage remains constant
—

 

 

Producer Consumer Consumer Net Net Pct change
impact impact impact impact impact in caloric
(PS) (EV-PS) (CV-PS) (EV) (CV) intake
Sector
Rural 1.3 0.7 0.6 2.0 1.9 4.6
Urban -1.1 -3.1 -3.5 -4.1 -4.6 3.1
Mean 1.2 0.5 0.4 1.7 1.6 4.5
Expenditure quintile
1st 1.0 1.4 1.4 2.5 2.4 4.4
2d 1.1 1.0 0.9 2.1 2.1 4.4
3d 2.2 -0.1 -0.1 2.1 2.0 4.9
4th 0.8 0.7 0.6 1.5 1.4 4.1
5th 0.9 -0.7 -0.9 0.1 -0.0 4.9
Mean 1.2 0.5 _0.4 1.7 1.6 4.5
Principal occupation
Farmer 1.4 1.0 0.9 2.4 2.3 4.4
Artisan 0.3 -0.4 -0.5 -0.1 -0.2 5.0
Merchant 2.1 -1.8 -1.9 0.3 0.2 5.1
Employee -0.0 -2.0 -2.2 -2.0 -2.3 5.3
Various 0.5 -0.2 -0.3 0.3 0.2 4.1
Mean 1.2 0.5 0.4 1.7 1.6 4.5
Sex of head of household
Male 1.4 0.5 0.4 1.8 1.7 4.7
Female 0.5 0.5 0.4 1.0 0.9 3.9
Mean 1.2 0.5 0.4 1.7 1.6 4.5

 

Source: Simulation based on ENBC data.

households are the least harmed by the hypothetical price changes. In
this case, the price changes are equivalent to a 2.5% increase in real
income. As household expenditure rises, the benefits of the hypotheti-
cal devaluation decline, until they are essentially zero for the richest

20% of households.

The third part of Table 7-16 separates households according to the
principal occupation. As in the base scenario, employees are the most
seriously affected by the price and income changes, while farmers are
the least negatively affected. In this case, farmers actually gain from
the hypothetical devaluation. The other occupations remain in an

intermediate position, neither gaining nor losing.

 

226

According to the last section of Table 7-16, male-headed house-
holds benefit more under this scenario than female-headed households.
The table also indicates that the difference is due to income patterns
rather than to spending patterns. This result is probably related to
the fact that wage income is less common for female-headed households
than for male-headed households.

Most of these patterns are repeated in the rural and urban sub-
samples (see Appendix X). In the rural sector, the poor benefit the
most and the rich the least from this devaluation scenario. In the
cities, the pattern is lees Clear, but the poorest 40% are certainly
less negatively affected than the rest of the urban population.

In summary, most of the patterns observed in the base scenario and
the historical price scenario have been repeated in this simulation with
real wages held constant. Thus, these results appear not to be due
simply to the real wage assumptions. Rather, they seem to be a reflec-
tion of the different spending and income patterns among Rwandan

households.

7.5 Supply pesponse assumptions

In the base scenario, the producer impact (the effect of prices on
income) is simply the change in price multiplied by the level of output.
This can be described as a first-order estimate of producer surplus or
the short-term effect of prices on income. In this section, we consider
the sensitivity of the results to changes in the way the effects on
producers are specified.

The first question is whether it is important to include the
producer impact at all. Brief inspection of Tables 7-6 and 7-15 make it
clear that ignoring the producer impact would seriously distort the
results. This is particularly true when nominal price changes are
modeled since the implicit assumption behind omitting the producer

impact in this case is that nominal income remains constant. For

 

 

 

exam

sirm

the

the:

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(D
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that
real
unde
simu
demo

the

227

example, if we ignored the producer impact in the historical price
simulation of Table 7-15, we would conclude that the welfare effect of
the price changes was equivalent to a 20% fall in real income rather
than the actual figure of less than 5%.

Omitting the producer impact is probably less distorting when
deflated prices are used, since in this case the implicit assumption is
that real income is constant. 0n the other hand, to the extent that
real wages tend to fall as a result of devaluation, this procedure would
underestimate the negative effect. For example, the base scenario
simulates a hypothetical devaluation using normalized prices. Table 7-6
demonstrates that the consumer effect gives an overly optimistic view of
the net effect of the price changes.

The next question concerns the possible improvement in the
simulation by incorporating supply response. In the medium- to long-
term, producers adapt to price changes, substituting away from goods
whose prices have declined and toward those with higher returns.
Clearly, a model which incorporates supply response will generate a more
positive (or less negative) welfare impact than one which holds output
constant. But it is an empirical issue whether the magnitude of this
change is important.

Ansoanuur (1991) estimated the supply elasticities for a number of
agricultural commodities. The elasticities ranged from 0.02 for bananas
to 1.92 for the long-run response of coffee, as shown in Table 7-17.
Since these elasticities were estimated using deflated prices, the
supply response was calculated using the relative price Changes of
agricultural commodities. In carrying out these calculations for each
household, we assume that the supply elasticity of each household is the

same, and that each household changes the output of existing crops but

‘17 '.-

 

l!

‘rlt-nfle .v. '.

 

e)
5:

ir.

228
Table 7-17: Estimated agricultural supply elasticities

Estimated supply

 

Crop elasticity
Sorghum 0.167
Rice 0.069
Cassava 0.121
Sweet potatoes 0.081
White potatoes 0.394
Bananas 0.018
Beans 0.094
Coffee (short term) _ 0.385
Coffee (long term) 1.925
Tea (short term) 0.046
Tea (long term) 0.250

 

Source: Ansoanuur (1991).

 

does not change the crop mixl.

Since supply response information is only available for agricul-
tural commodities, the analysis in this section will focus on the rural
sector. Table 7-18 shows the distributional impact of the hypothetical
devaluation on rural households with agricultural supply response as
estimated by Ansoanuur (1990). Comparing this table with Table 7-7 from
the base scenario (without supply response), it appears that the
introduction of these supply elasticities makes virtually no difference
in the results. The average producer impact is -3.7% of household
expenditure, only a very slight improvement from -3.8% in the base
scenario. The other sets of corresponding figures are equal close or
indistinguishable at this level of precision.

Certainly part of the explanation for the fact that incorporating
these supply elasticities has virtually no effect on the results is that
the elasticities are quite small, particularly for beans, sweet pota-
toes, and bananas. Thus, another simulation was run setting all the

agricultural supply elasticities to 1.0. In view of agricultural supply

 

1. This assumption is a necessary result of using time-
series data to model supply response. Modeling crop mix would require
cross-sectional data, perhaps in conjunction with a tobit model.

229

response studies from other less developed countries, this probably
represents an probably upper bound for the actual supply elasticities.

Table 7-18: Effect of hypothetical devaluation on rural households,
assuming medium agricultural supply elasticities
IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII-II-I-I-I-I-IIIIIIIII-I

 

Producer Consumer Consumer Net Net Pct change
impact impact impact impact impact in caloric
(PS) (Ev-PS) (CV-PS) (EV) (CV) intake
Rural expenditure quintile
1st -3.9 1.5 1.4 -2.4 -2.4 0.6
2d -3.9 1.2 1.1 -2.7 -2.8 0.8
3d -2.6 -0.2 -0.3 -2.7 -2.8 2.3
4th ~3.9 0.7 0.6 -3.2 -3.3 1.0
5th -4.4 0.1 -0.0 -4.3 -4.5 2.3
Mean -3.7 0.7 0.6 -3.1 -3.2 1.4
Region
N West -4.4 1.0 0.8 -3.5 -3.6 1.8
S West -3.5 -0.0 -0.1 -3.6 -3.7 2.0
N Centr -3.8 0.8 0.7 -3.0 -3.1 0.6
S Centr -4.0 0.4 0.3 -3.6 -3.7 1.8
East -3.1 1.1 1.0 -2.1 -2.1 1.3
Mean -3.7 0.7 0.6 -3.1 -3.2 1.4
Principal occupation
Farmer -3.3 1.0 0.9 -2.4 -2.4 1.3
Artisan -6.1 0.1 -0.1 -6.1 -6.3 1.6
Merchant -2.2 -1.2 -1.4 -3.5 -3.6 2.8
Employee -6.3 -0.7 -1.0 -7.0 -7.3 3.1
Various -4.6 0.0 -0.1 -4.5 -4.7 1.2
Mean -3.7 0.7 0.6 -3.1 -3.2 1.4
Sex of head of household
Male —3.6 0.7 0.6 -2.9 -3.0 1.6
Female -4.4 0.7 0.5 -3.7 -3.8 0.6
Mean -3.7 0.7 0.6 -3.1 -3.2 1.4

 

 

 

' Source: Simulation based on ENBC data.

Table 7-19 shows the simulated impact of a hypothetical devalua-
tion with agricultural supply elasticities set at 1.0. Again comparing
the results to the base scenario presented in Table 7-7, the incorpora-
tion of an elastic supply response reduces the average producer impact
from -3.8% of household expenditure to -3.5%. The net impact, as
measured with equivalent variation, declines from -3.1% without supply

response to -2.8% with supply response. Of course, the position of

 

230

farmers relative to other occupations improves since it is only agricul-
tural production that is allowed to respond to price changes in this
simulation. But all of the basic patterns with respect to expenditure
quintile, region, occupation, and sex of head of household remain

essentially unchanged.

Table 7-19: Effect of hypothetical devaluation on rural households,
assuming high agricultural supply elasticities

 

 

Producer Consumer Consumer Net Net Pct change
impact impact impact impact impact in caloric
(PS) (EV-PS) (CV-PS) (EV) (CV) intake
Rural expenditure quintile
1st -3.7 1.5 1.4 -2.2 —2.3 0.2
2d -3.7 1.2 1.1 -2.5 -2.6 0.3
3d -2.3 -0.1 -0.3 -2.4 -2.5 2.5
4th -3.8 0.7 0.6 -3.0 -3.1 0.6
5th -4.2 0.2 -0.0 -4.1 -4.3 1.8
Mean -3.5 0.7 0.6 -2.8 -3.0 1.1
Region
N West -4.2 1.0 0.8 -3.2 -3.4 1.9
S West -3.2 -0.0 —0.1 -3.3 -3.4 1.9
N Centr -3.7 0.8 0.7 -2.8 -2.9 0.1
S Centr -3.9 0.5 0.3 -3.4 -3.6 1.2
East -2.9 1.1 1.0 -1.8 -1.9 0.9
Mean -3.5 0.7 0.6 -2.8 -3.0 1.1
Principal occupation
Farmer —3.1 1.0 0.9 -2.1 -2.2 1.0
Artisan —6.1 0.1 —0.1 -5.9 -6.2 1.2
Merchant -1.9 -1.2 -1.4 -3.2 -3.3 2.7
Employee -6.2 -0.7 -l.0 -6.9 -7.2 2.7
Various -4.4 0.1 -0.1 -4.4 -4.5 0.5
Mean -3.5 0.7 0.6 -2.8 —3.0 1.1
Sex of head of household
Male -3.4 0.7 0.6 -2.7 -2.8 1.4
Female -4.2 0.7 0.5 —3.5 -3.7 -0.1
Mean -3.5 0.7 0.6 -2.8 -3.0 1.1

 

Source: Simulation based on ENBC data.

In summary, the effect of incorporating agricultural supply
response into the simulation is modest to negligible. Even with
agricultural production is assumed to be quite responsive to price, the

distributional patterns of the hypothetical devaluation are not affect-

 

1F"

 

231

ed. Although incorporating some kind of producer impact is critical in
such a model, it appears that a first-order approximation of producer

surplus is sufficient for most purposes.

7.6 Demand response essumptions

In the base scenario, demand was modeled using the parameters
estimated under the restrictions of consumer theory. It is worth asking
whether the results change appreciably when the unrestricted demand
parameters are used instead. These demand parameters, and their
corresponding price and income elasticities, are described in sections
6.3 and 6.5.

Table 7-20 indicates that the consumer effect and hence the net
impact is somewhat greater, in absolute value, when the unrestricted
demand model is adopted. This presumably reflects the fact that
imposing symmetry made demand somewhat more price responsive, allowing
greater adaptation on the part of consumers to changes in price.
Nonetheless, all the basic results obtained when using the restricted
model hold as well when the unrestricted model is adopted.

The relative insensitivity of the results to changes in demand
response is illustrated by the considering the extreme case when there
is no demand response. If compensated demand is perfectly inelastic,
then the area under the curve (willingness to pay) is simply the
original quantity times the price change. This is equal to_the first-
order approximation of compensating variation for an arbitrary demand
system. Thus, we can use CV1 under the base scenario to indicate the
exact compensating variation in the extreme case in which consumer
demand is completely inflexible.

As shown in Table 7-21, CV1 is greater (in absolute magnitude)

than the other welfare measures. At the same time, CV1 is closely

correlated with the other measures, in the sense that it gives the same

results regarding the relative impact on rural and urban households,

 

 

232

rich and poor households, and so on. In other words, the results
concerning the relative impact of devaluation on different households

are fairly insensitive to the responsiveness of demand to price changes.

Table 7-20: Effect of hypothetical devaluation on households using the
unrestricted demand model
lIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII-Il-I-I-I-II-I-I-I-II

Producer Consumer Consumer Net Net Pct change

 

 

impact impact impact impact impact in caloric
(PS) (EV-PS) (CV-PS) (EV) (CV) intake
Sector a
Rural -3.8 0.8 0.7 -3.0 -3.1 -1.7 1
Urban -7.8 -2.6 -3.5 -10.4 -11.3 2.2 i
Mean -4.0 0.7 0.5 -3.4 -3.6 -1.5 1
Rural expenditure quintile
lst —4.0. 1.6 1.5 -2.4 -2.5 -3.1 1:
2d -4.0 1.2 1.0 -2.8 -2.9 -1.8
3d -2.6 0.1 -0.0 -2.5 -2.7 -1.1
4th -4.3 0.8 0.7 -3.5 -3.7 -2.6
5th -5.1 -0.5 -0.9 -5.6 -6.0 1.0
Mean -4.0 0.7 0.5 -3.4 -3.6 -1.5
Principal occupation
Farmer -3.4 1.1 1.0 -2.3 -2.5 -2.1
Artisan -6.5 -0.1 -0.4 -6.6 -6.9 -0.5
Merchant -3.2 -1.4 -1.8 -4.7 -5.0 1.4
Employee -6.9 -1.6 -2.2 -8.5 -9.0 2.1
Various -4.8 0.0 -0.2 -4.8 -5.0 -2.2
Mean -4.0 0.7 0.5 -3.4 -3.6 -1.5
Sex of head of household
Male -3.9 0.7 0.5 -3.2 -3.4 -1.3
Female -4.5 0.7 0.5 —3.8 -4.0 -2.4
Mean -4.0 0.7 0.5 -3.4 -3.6 -l.5

 

Source: Simulation based on ENBC data.

 

7.7 Comparison of alternative welfare measures

Until this point, the only welfare measures used were the Vartia
estimates of equivalent variation (EV) and compensating variation (CV).
In implementing the Vartia method, 20 iterations were used to approxi-
mate EV and CV. In this section, these measures are compared to both

more and less accurate approximations. More accurate approximations can

233

be obtained by increasing the number of iterations used in the Vartia
method. Less accurate measures can be calculated using first- and
second-order Taylor series approximations of the expenditure function.
In addition, consumer surplus is a frequently used measure of welfare
impact, in spite of the theoretical problems described in section 3.4.2.

Returning to the base scenario, nine measures of welfare impact
are calculated for each group of households and presented in Table 7-21.
To conserve space, the producer and consumer impact are not listed
separately; the figures in the table represent the net impact of the
hypothetical devaluation.

Three conclusions can be drawn from this table. First, there are
consistent differences in the magnitude of the welfare measures. The

first-order approximation of compensating variation (CV1) consistently

overestimates by about 10% the magnitude of CV as measured by the 50-

iteration Vartia estimate (Cvfln. This is because it uses the ”before"

quantities as weights in averaging price changes, thus ignoring adapta-

tion of consumers to price changes. In contrast, EVl, which uses the

"after" quantities as weights, underestimates the most accurate approxi-
mation of EV by about 10%. Consumer surplus falls between EVI and CV1,
as expected.

SeCond, the 20-iteration Vartia estimates and the Second-order
Taylor approximations tend to be more accurate (compared to the 50-
iteration Vartia estimate) than the first-order Taylor approximation and
consumer surplus.

And third, the order of different groups of households is virtual-
ly the same, no matter which welfare measure is used. In other words,
all seven measures show the same relative patterns of welfare impact by
location (urban or rural), expenditure quintile, principal occupation,
or sex of head of household.

The high degree of correlation of different welfare measures

across households is dramatically confirmed in Table 7-22. In every

 

 

 

ea

Table 7-21: Welfare impact of hypd¥hgtical devaluation according to

different welfare measures
—

EV, EV, EV“ EV” cs cvm cv,. cv, cv,

 

Sector
Rural -2.8 -3.2 -3.1 -3.1 -3.3 -3.2 -3.2 -3.2 -3.7
Urban -9.8 -10.4 -10.4 -10 5 -11.0 —11.2 -11.3 -11.1 -12.2
Mean -3.2 -3.6 -3.5 -3.5 -3.6 -3.6 -3.6 ~3.6 -4.1
Expenditure quintile
lst -2.3 -2.6 -2.5 -2.6 -2.6 -2.6 -2.6 -2.6 -3.0
20 -2.7 -3.0 -2.9 -3.0 -3.1 -3.0 -3.0 -3.0 -3.5
3d -2.3 -Z.7 -2.6 -2.7 -2.8 -2.8 -2.8 -2.7 -3.3
4th —3.4 -3.7 -3.6 -3.7 -3.8 -3.7 -3.8 -3.7 -4.2
5th -5.3 -5.7 -5.7 -5.7 -6.0 -6.0 -6.0 -6.0 -6.6
Mean -3.2 -3.6 -3.5 -3.5 -3.6 -3.6 —3.6 -3.6 -4.1
Principal occupation
Farmer -2.2 -2.5 -2.5 -2.5 -2.6 —2.5 -2.6 -2.5 -3.0
Artisan -6.3 -6.8 -6.7 -6.7 -7.0 —7.0 -7.0 -6.9 -7.6
Merchant -4.3 -4.8 -4.8 -4.8 -5.0 -5.1 -5.1 -5.1 -5.7
Employee -8.1 -8.6 -8.6 -8.6 -8.9 -9.1 -9.1 -9.0 -9.8
Various ~4.6 -5.0 -4.9 -5.0 -5.1 -5.1 -5.1 -S.1 -5.7
Mean -3.2 -3.6 -3.5 -3.5 -3.6 -3.6 -3.6 -3.6 -4.1
Sex of head of household
Male -3.1 -3.4 -3.4 -3.4 -3.5 -3.5 -3.5 -3.5 -4.0
Female -3.7 -4.0 -4.0 -4.0 -4.1 -4.1 -4.1 -4.1 -4.6
Mean -3.2 -3.6 -3.5 -3.5 -3.6 -3.6 -3.6 -3.6 -4.1

 

NOTE: EV1 = first-order approximation of equivalent variation
EVZ - second-order approximation of equivalent variation
EVZO = Vartia estimate of equivalent variation (20 iterations)
EVSO c Vartia estimate of equivalent variation (50 iterations)
CS I consumer surplus
CV50 - Vartia estimate of compensating variation (50 iterations)
CV20 = Vartia estimate of compensating variation (20 iterations)
CV2 8 second-order approximation of compensating variation

CV1 = first-order approximation of compensating variation
All figures are expressed as a percentage of expenditure.

Source: Simulation based on ENBC data.

pair-wise comparison, the correlation coefficient (R2) is over 0.99.

This result does not mean that every measure is accurate but rather the
ranking of households by impact is very similar across measures.

Table 7-23 compares each of the seven rougher approximations of
relative welfare impact to the corresponding value of the 50-iteration
Vartia estimate. The first line shows the mean difference, or bias, of

each measure relative to the reference measure (EV50 or CV50). For

 

qmi'. I. .- " _

 

Table 7-22:

235

Correlation across households of different welfare measures
—

 

 

EV1 EVz EV20 EVso CS CVso CV20 CV2 CV1

EV1 100.00 99.96 99.92 99.91 99.86 99.71 99.71 99.73 99.54
EV2 99.96 100.00 99.97 99.97 99.95 99.81 99.81 99.82 99.73
EV20 99.92 99.97 100.00 100.00 99.96 99.86 99.86 99.85 99.79
EV50 99.91 99.97 100.00 100.00 99.96 99.86 99.86 99.85 99.79
CS 99.86 99.95 99.96 99.96 100.00 99.95 99.95 99.95 99.91
CV50 99.71 99.81 99.86 99.86 99.95 100.00 100.00 99.99 99.95
CV20 99.71 99.81 99.86 99.86 99.95 100.00 100.00 99.99 99.95
CV2 99.73 99.82 99.85 99.85 99.95 99.99 99.99 100.00 99.93
CV1 99.54 99.73 99.79 99.79 99.91 99.95 99.95 99.93 100.00
Source: Calculated from simulations based on ENBC data.

example, EV1 is, on average, half a percentage point (0.51) smaller, in
absolute value, than Evflr

sponds to a 7.4% error.

mate by almost 10%.

measure either equivalent variation or compensating variation is smaller

(4.6% and 1.6%, respectively).

As shown in the second line, this corre-

Similarly, CV1 overestimates the Vartia esti-

The second-order estimates of CV and EV

and the 20-iteration Vartia estimates are even more accurate.

four measures have mean biases of less than 1%.

The percentage error in using consumer surplus to

These

 

 

I-Lr'r-ur-o .'

 

 

236

Table 7-23: Comparison of alternative welfare measures
—

Comparison with EVso Comparison with CV,

 

 

EV, EV. EV” CS CS CV” CV, CV,

 

Difference in

mean value 0.51 -0.01 0.02 -O.32 0.12 -0.02 0.06- 0.71
Pct difference
in mean value -7.38 0.10 -0.27 4.63 -1.63 0.29 -0.79 9.66
Mean absolute r
deviation 0.52 0.08 0.02 0.32 0.19 0.02 0.08 0.71
Mean difference
in rank 4.42 2.01 0.13 2.05 1.72 0.15 1.49 3.66

 

Source: Calculated from simulations based on ENBC data.

 

IlIr-«- :

A measure may be very inaccurate, yet be unbiased, if the positive
and negative errors offset each other. Thus, it is useful to look at
the mean absolute value of the error, as shown in the third line of

Table 7-23. For example, even though EV2 has a smaller bias than svm”
its mean absolute deviation is greater. In other words, EV20 consis-
tently provides a slight underestimate, while EV2 is less accurate but

has both positive and negative errors.
The last line in Table 7-23 shows the mean difference between the
order of the household when ranked by different measures. For example,

if households are ranked first by EV2 and then by EV30, a household will

change only two places, on average, out of the 567 possible rankings.
The first—order approximations of welfare impact would be much less
accurate, ranking households roughly four places away from their ”true"
place, on average. In contrast, the 20-iteration Vartia estimates give
virtually the same ranking, household by household, as the SO-iteration
Vartia estimates.

In summary, for the purpose of ranking household by welfare
impact, there is little difference among the alternative welfare

measures. However, if the magnitude of the welfare impact is of

 

inte:

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7.8

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237

interest, then a second-order approximation or a Vartia approximation

would be necessary to reduce the bias to less than 5%.

7-8 W

This chapter presents simulations of the relative price changes

 

associated with devaluation and describes their impact on household
welfare. Given the structure of the Rwandan economy, it appears that rm;

the adverse effect of these changes on urban households is three times

1".

as great as the effect on rural households. Furthermore, even within

each sector, the higher income households are more adversely affected

 

than the poor. This pattern is due to the sources of income and the

M3. slug-a -
,.

composition of expenditure. Farmers are relatively insulated from these
impacts because of the importance of subsistence production, while wage-
earners are the most affected. Furthermore, the poor spend a larger
share of their income on staple foods, which tend to be non-tradeables.
There is little difference in impact between male- and female-headed
households.

In the rural areas, price increases of clothing and kerosene
probably had the most serious impact on household welfare. In the urban
sector, price increases in clothing, transportation, rice and sugar were
expected to have the greatest impact. Instead, the higher rates for
water and electricity, housing, and beans were the most significant for
the average urban household.

These results are relatively robust to changes in the assumptions
of the model. The conclusions are not significantly affected when
historical prices are used rather than hypothetical price, when real
wages are assumed to remain constant rather than decline, when alternate
demand parameters are used, and when agricultural supply response is
assumed to be positive instead of zero.

In comparing various welfare measures, the simplest approximations

of welfare impact performed relatively well in ranking households by the

leve

are

for ‘

 

 

238

level of impact resulting from price changes. However, these measures
are generally biased, with the magnitude of bias being between 8 and 10%

for the modeled price changes.

 

 

 

CHAPTER EIGHT

SUMMARY AND CONCLUSIONS

This chapter reviews the principal results of the study and
discusses the implications for policy and for research methods. In

addition, a number of limitations of the study are listed and used to

 

make suggestions for extending and improving the approach in future

research.

8.1 Summafy of results

8.1.1 Income and expenditure patterns
The results of the National Household Budget and

 

Consumption Survey (ENBC) in Rwanda confirm the general view that Rwanda
is a predominantly rural, predominantly agricultural, semi-subsistence -
economy. Farming is the principal occupation of almost three quarters

of Rwandan households. Even in the urban sector, which accounts for 6%
of the population, one household in seven relies on agriculture for most

of its net income. Subsistence (or non-marketed2vproduction accounts

W or“ “W
*7" C-e. e.

V5.9.”

 

w”

for three quarters of the value of food consumption in the rural areas,
nAI:E“IE‘€E:E“I§“S3Z§AEEQM3Ewtgta{WSEEEKEEEEEET”HSQen in the cities,
home production represents a non-negligible source of food (21% of the
value of food consumption, 17% of total expenditure).

At the same time, the surVey reveals that there is considerable
diversity of income sources in both rural and urban sectors. In the
rural sector, 10% of the households obtain most of their income from
self-employment in manufacturing and services, the largest sub-sector
being the production of traditional beers. Another 15% are primarily
occupied as traders, as employees, or in a variety of activities, no one
of which accounts for over 50% of total income. In addition, rural

households often have three or more income generating activities.

Virtually all households brew traditional beer, 40% of them have other

239

240

manufacturing or service activities, a quarter are involved in trading,
and half of them earn some form of wage or salary income.

Urban households, like their rural counterparts, have diverse
sources of income and one-job households are rare. In contrast to the
view that the cities are composed primarily of wage-earners, the survey

indicates that only 35% of the urban households obtain most of their

 

income from wages and salaries. Over half of the urban household earn

most of their income from self-employment. FF—

The ENBC results also confirm that urban residents are generally

 

better off than their rural counterparts. Although prices are higher in E
the cities, particularly the prices of unprocessed local foods, urban :
households have higher levels of expenditure per capita than do rural i

households even after taking into account the difference in prices. In
the urban sector, the average level of expenditure is 2.4 times that of

the rural sector. Furthermore, 87% of the urban household have per

 

capita expenditure levels above the rural median.

One surprising result of the ENBC is the absence of a positive
relationship between total farm size on the one hand and expenditure and
caloric intake on the other. Three reasons for this patterns can be
identified. First, small farms tend to be operated by small families
due to life cycle patterns. Second, small farms have much higher
economic returns per hectare than large farms. Presumably, this results
from more intensive cultivation and the fact that, over time, farms have
fragmented to smaller sizes in areas where agro-climatic conditions are
the best. Third, small farms rely to a larger degree on non-farm
sources of income. At the same time, the ENBC data indicate that there
is a positive relationship between farm size per adult equivalent and
measures of well-being. Not surprisingly, this relationship is stronger
among households in which agriculture is the dominant activity.

The survey confirms the conventional view that only a small

portion of agricultural production is marketed. For all the staple food

241

crops, less than one third of total production reaches the market. In
the case of sweet potatoes, bananas, and beans, the proportion is less
than 10%. This implies that coffee and other export crops represent a
larger percentage of agricultural sales than of agricultural production.
In fact, coffee is by far the most important source of cash income among

individual crops. Less well recognized, however, is the fact that food

 

crops sales as a whole are twice as important as cash crop sales.

Furthermore, most of the food crop sales are destined, not for the urban
sector, but for other rural consumers. In other words, in spite of low
levels of rural expenditure and the small share of expenditure which is

in the form of cash purchases, rural households still account for the

 

bulk of the market demand for food crops in Rwanda.

The effect of the price changes associated with devaluation on
households is a function of several factors. First, the larger the
proportion of total expenditure which is in the form of cash purchases,
the more sensitive a household is to any fluctuations in market prices,
including devaluation. The ENBC data indicate that market transactions
account for 83% of the average urban budget but only 35% of the average
rural budget. Furthermore, for the country as a whole and within each
sector, market transactions are a larger share of total expenditure (and
income) among high-income households than low-income households. The
implication is that a price change will affect urban households over
twice as much as rural households even in the absence of any difference
in the composition of cash expenditure. Similarly, the richest 20% of

households would be affected more than twice as much as the poorest 20%.

 

Second, to the extent that devaluation affects food prices, the
impact on urban household is unambiguous, but the impact on rural
households is less clear. The effect depends, in part, on the direction
of change in relative prices and whether a household is a net seller or
net buyer of the commodity in question. Analysis of the distribution of

rural households by their net sales position in several key food crops

H»

242

reveals that, for most crops, about one quarter of the households are
net buyers, one quarter net sellers, and half neither buy nor sell.
Beans, and to a lesser degree sorghum, present a different pattern in
which most rural households are net buyers. Furthermore, supporting the
finding of Loveridge (1988), total purchases appear to exceed total

sales for beans and sorghum, implying informal imports of these two

 

crops from neighboring countries.

The correlation of net sales across commodities is weak and, for a
number of commodity pairs, negative. In other words, net buyers of one
staple food are not necessarily net buyers of others. At the same time,
45% of rural households are overall net buyers (expressed in caloric

terms) of the six major food crops. With regard to the question whether

 

net buyers tend to be poor, the answer is that it depends on the crop.
This pattern is most evident in the case of beans, and appears weaker
for cassava and sweet potatoes. In the case of white potatoes, net
buyers may be better off than net sellers, on average.

The third factor influencing the effect of devaluation on
households is the percentage of expenditure and of income which can be
considered tradeable. Since a successful devaluation raises the price
of tradeables relative to non-tradeables, a household gains to the
extent that it produces tradeables and consumes non-tradeables. In the
rural sector of Rwanda, almost half of all tradeable spending is on
clothing, mostly imported cloth and used clothing. In the urban sector,
transportation, Clothing, and rice are the most important types of
tradeable spending. The tradeable component of cash expenditure is,
somewhat surprisingly, the same in rural and urban areas. It varies
positively with income in the urban sector but apparently not in the
rural sector. On the income side, tradeable production is somewhat
erratic, possibly due to measurement and definitional problems.
However, among the urban poor, their somewhat lower spending on

tradeables is more than offset by very low levels of tradeable output.

 

243

However, the above measures of welfare impact are incomplete and
do not take into account the adaptation of households as consumers and
as producers to changing prices. When the demand for a good is highly
elastic, the welfare impact of a price increase is less, reflecting the
fact that there are substitutes in consumption or that the good is not

essential. Similarly, if the supply is price elastic, then a price

 

decrease has a less severe welfare impact, reflecting the fact that

there are substitutes in production. The construction of more

sophisticated welfare measures depends on estimating a demand model and,

for measuring long-term welfare impact, estimating supply response.
8.1.2 Model of consumer demand

Separate rural and urban demand models were constructed

 

using seemingly unrelated regression. The functional form used was the
Almost Ideal Demand System (AIDS) augmented with a squared income term.
Prices were included for all food items in the system, but no non-food
prices were available. Three household composition variables were
included: number of adults, number of children, and sex of head of
household. The rural model included 17 food categories, while the urban
model contained 21. Each model had nine non-food categories. Food own-
price and cross-price elasticities were estimated directly, while non-
food price elasticities were derived using Frisch's method which assumes
strong separability of preferences.

The estimated elasticities of food demand with respect to total
expenditure are closely correlated with the cost per calorie of the food
product. The least expensive sources of calories (sorghum, cassava,
sweet potatoes, bananas, and beans) have the lowest expenditure
elasticities in both rural and urban sectors. 'Sweet potatoes have the
lowest expenditure elasticity, but are not an inferior good at the mean
expenditure level in either sector. More expensive sources of calories
such as white potatoes, rice, and banana beer have higher expenditure

elasticities. The highest expenditure elasticities are those of factory

 

 

 

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244

beer, animal products, and sugar, all quite costly sources of calories.
Expenditure elasticities are generally lower in the urban sector than in
the rural sector. For example, white potatoes and banana beer are
"luxuries" in the countryside, but they are classified as "necessities"
in the cities. Most of the tradeable food items such as rice, bread,
sugar, and factory beer are ”luxuries,” implying that they are consumed
disproportionately by higher-income households.

With regard to non-food categories, housing, household equipment,
and transportation are "luxuries" in both urban and rural sectors, while
tobacco has the lowest expenditure elasticity. In the case of clothing,
education, and health/hygiene, the budget shares are relatively constant
across expenditure levels within each sector.

The household composition variables reveal that, other things
being equal, larger households consume more "luxuries" and fewer
"necessities.” This pattern is consistent with the hypothesis of
economies of scale in household size, often found in household budget
studies. Female-headed households spend significantly less on banana
beer in both sectors. In the cities, they also spend less on factory
beer, tobacco, and meals away from home, while allocating larger budget
shares to vegetables and education.

The estimated food price elasticities are roughly proportional to
the expenditure elasticities for the same items. In the rural sector,
the demand for factory beer, rice, and white potatoes is quite
responsive to prices, while that of the staple food commodities is less
so. The pattern is less clear in the urban sector, with factory beer
being less price-responsive and several staples having price elastic
demand, perhaps due to greater substitution possibilities in the cities.
By assumption, the derived non-food price elasticities are generally
proportional to the corresponding expenditure elasticities.

Imposing symmetry of compensated cross-price effects naturally

influences the price elasticities more than expenditure elasticities.

 

 

245
Nonetheless, the basic conclusions, as discussed above, apply equally to
the unrestricted and restricted versions of the model.

Quality and measurement error effects were investigated using the
within-cluster variation in the variables, as proposed by Deaton (1987
and 1988). Quality effects were tested by analyzing the within-cluster
effect of household expenditure on the average price paid for different
food items. For no commodity was the quality effect statistically
significant, and in a third of the equations, the sign was wrong
(negative). Measurement error was tested by examining the within-
cluster effect of prices on budget shares. Of the 37 rural and urban
food equations, only three showed any sign of significant measurement
error effects.

8.1.3 Impact of price changes associated with devaluation

In the base scenario, the price of each budget category
is assumed to rise in proportion with the tradeable content of the
category. Wages are assumed to fall by 4-8%, in accordance with the
historical patterns of other devaluation episodes, as analyzed by
Edwards (1989). Demand response is simulated using the parameters from
the restricted model (with symmetry imposed). Although supply response
is not included in the base scenario, the effect of price changes on
income and the consequent effect of income on demand (the profit effect)
is simulated. The welfare impaCt, in the form of equivalent variation
and compensating variation, is measured using Vartia's method with 50
iterations. In order to make full use of the sample data, the demand
response, profit effect, and the welfare and nutritional impact are
simulated for each household in the sample and then aggregated to the
appropriate group.

The most striking result of the simulation under the base scenario
is that the negative welfare impact (expressed as a percentage of total
expenditure) is over three times greater for urban households than for

rural households. The price changes associated with devaluation are

246

equivalent to a 3% reduction in the real income of rural households and
a 10% drop in real income for urban households. In addition, it is
twice as great for the richest 20% of households as it is for the
poorest 20%. Households whose primary occupation is farming are least
affected, while wage earners are the most severely affected. Female-
headed households are slightly more affected than male-headed
households. Caloric intake rises slightly, presumably because the
(nontradeable) staple foods have become less expensive relative to many
(tradeable) non-food items.

Within the rural sector, households which are poor, agricultural,
male-headed and/or in the Eastern region are more insulated from the
devaluation than others. In the urban sector, households which are
poor, agricultural, female-headed, and/or in cities other than Kigali
are least affected. This confirms the conventional wisdom that the
urban poor are harder hit than the rural poor, but it is at odds with
the common perception that low-income urban households are affected more
than higher-income households in the city.

Historical prices were examined for the two years before and the
seven months after the Rwandan franc was devalued on November 20, 1990.
An index of consumer prices based on 35 goods showed that prices rose
sharply during October 1990. This rise is probably the result of the
outbreak of guerilla warfare during that month. Developing separate
indexes for tradeable and non-tradeable goods shows that both rose in
parallel fashion in October, but in November tradeable good prices
continued rising while non-tradeable prices fell. The real exchange
rate, defined as the ratio of tradeable to nontradeable prices, rose 31%
from one month before to seven months after the devaluation.

The average prices during the second quarter of 1990 were used to
simulate the ”before" situation, while those of the second quarter of
1991 were used to represent the "after" situation. Although the

individual price changes bore little resemblance to the hypothesized

247

price changes, the welfare impact was similar in the two cases.
Historical prices affected rural, poor, and agricultural households the
least, while the effect on urban, high-income, and wage-earning
households was the greatest.

These results are relatively robust to changes in the assumptions
of the model. The relative impact on different types of households is
no different in any meaningful way when 1) real wages are assumed to
remain constant rather than decline, 2) agricultural supply response is
introduced, and 3) alterative demand parameters are adopted.

A comparison of alternative measures of welfare impact revealed
that the simplest first-order approximations performed relatively well
in ranking household by impact. On the other hand, these measures are
generally biased by 8-10%. For example, the first-order approximation
of compensating variation overstates the welfare impact of price

changes.

8.2 Implications for policy

Several policy implications can be drawn from the results of this
study. Some apply to Rwanda alone, while others may be applicable to
other less developed countries with similar economies.

.8.2.l Magnitude of the impact of devaluation

In Rwanda, and by extension in similar semi-subsistence
agricultural economies, the expenditure-switching effect of devaluation
has a relatively moderate impact on rural households and the poor in
general. In all the scenarios considered, the effect on the poor was
equivalent to a reduction in real income of 4% or less. The impact on
caloric intake is even less, perhaps slightly positive. In one sense,
this may represent an overstatement of the impact, since the model does
account for substitution within each budget category. For example, the

effect of higher prices for petroleum products may induce substitution

 

248

within energy expenditures, but these cannot be captured in a model
which does not disaggregate energy spending.

On the other hand, these results apply only to the relative price
(or ”expenditure switching”) effects of devaluation. The simulation
does not incorporate any change in aggregate output (”expenditure-
reducing"). In particular, the short-term contractionary effect,
identified in some devaluation episodes, could result in unemployment.
Nor does it take into account other aspects of the structural adjustment
program such as reductions in government expenditure, restrained growth
of public sector employment, trade liberalization, and so on.

The results of the simulations are consistent with political
explanations of resistance to currency devaluation. It is sometimes
argued that policy makers are reluctant to devalue the currency because
of a direct stake they have in access to ”cheap" foreign exchange. Only
weak support was found for the idea that higher-income households
consume more tradeables, whose relative price rises with devaluation.
However, the simulation indicates that rural farmers, who represent 73%
of Rwandan households, experience price changes equivalent to a small
(2.4%) reduction in real income, but urban wage-earners, who account for
less than 2% of all households, face price changes which are equivalent
to a 12% reduction in real income.

8.2.2 Alleviation of the impact of devaluation

With respect to the rural sector, there are no simple
ways to alleviate the impact of devaluation on rural households. The
same factor that protects them from the devaluation, limited
participation in the market economy, also insulates them from the
benefits of price policies. Manipulation of food prices, even if it
were practical, would leave many rural households unaffected and have
mixed effects on the remainder.

One exception is bean prices, reduction of which would benefit

Over 70% of the rural households. Furthermore, because net purchases

 

 

 

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249

represent a larger share of the expenditure of the poor than other
households, lower bean prices would benefit the poor disproportionately.
These results confirm the wisdom of the government's decision to
discontinue efforts to support bean prices. They also suggest that
restrictions on bean imports would, by raising prices, be particularly
harmful to the poor. Furthermore, it suggests that efforts to remove
impediments to ”informal” regional trade would yield significant
benefits for poor rural households. To the extent that the informal
trade is subject to additional costs because it is not officially
recognized, legalization of this trade could well reduce marketing
costs.

In addition, hypothetical and the historical simulation indicated
that increased prices for clothing account for a large portion of the
negative impact on rural households. Actual subsidies may not be
feasible, given budget constraints, but reduction or elimination of
import duties on clothing could be considered. In order to target the
benefits toward the poor, the tax reduction could be restricted to used
clothing, which is purchased disproportionately by the poor.

Although the effect of agricultural price policy is constrained by
the limited market participation of most rural households, the impact of
cost-reducing agricultural technology is much deeper and more widely
distributed. For example, an increase in the price of sweet potatoes
benefits roughly a quarter of the rural households, with a small number
of households capturing much of the gains. By contrast, a reduction in
the cost of producing sweet potatoes benefits over 85% of the rural
households. Furthermore, for a given change in cost/price, the benefits
of cost-reducing technology are much greater because they apply to the
volume of production rather than the small portion which is marketed.

The scope for assisting the urban poor is greater, since cash
purchases are an important part of expenditure (68% for the poorest 20%

Of the urban households). In the early stages of the structural

250

adjustment program, the government of Rwanda gave special access to
foreign exchange for the importation of sugar, cooking oil, and wheat
flour. Since these are the food items with the highest expenditure
elasticities in the urban areas, the benefits of such a policy accrue
disproportionately to higher-income urban residentsl. Subsidies on an
inferior good would be self-targeting in the sense that the absolute
benefits of subsidies would be greater for the poor than other
households. But the ENBC data indicate that there are no inferior goods
at the mean level of expenditure in the urban sector. Nonetheless, a
subsidy on sweet potatoes would be more targeted than any other food
subsidy: the absolute benefit would be relatively constant across
households, but it would represent a larger share of the budget of poor

households.

8.3 Implications for research methods
8.3.1 Advantages of micgo-simglation

In order to make full use of the sample data, the demand
response, profit effect, and the welfare and nutritional impact are
simulated for each household in the sample and then aggregated to the
appropriate group. This ”micro-simulation" approach is in contrast to
the usual practice of simulating the impact of price change on a small
number of "representative" or "archetypal" households. Micro-simulation
allows the analyst to examine the impact on any sub-group of the
population, rather than being limited to the selected ”representative"
households. For example, it allows the results to be disaggregated by
expenditure quintile, by region, by sex of head of household, or any
other classification.

In addition, this approach provides some information about the

variation within each group. For example, it was shown that the five

 

l. The expenditure elasticities of these items range from
0.97 to 1.42. Thus, the benefits as a percentage of expenditure are
constant or increasing as a function of household expenditure.

251

occupational groups explain about one half of the variation in welfare
impact across households. Combined with household expenditure, sex of
head of household, and urban/rural residence, 65% of the variation is
explained. This type of information is not available when the
simulation is run for a small number of ”representative" households.

A third advantage of micro-simulation is that it allows the use of
a demand specification without the property of exact aggregation. The
Almost Ideal Demand System, which does allow exact aggregation, was
shown to be insufficiently flexible in representing the relationship
between budget share and total expenditure. Yet adding a quadratic
expenditure term is not an option unless micro-simulation is used
because the resulting functional form does not have exact aggregation.

Naturally, the cost of micro-simulation is that it is
computationally more burdensome. The additional programming time is not
that significant since it only involves iterating the same procedure for
each household in the sample. And the additional computational time
becomes less important with each advance in micro-computer technology.

8.3.2 Factors affeCting the impact of devaluation

Various approaches have been used to analyze the

distributional impact of devaluation. Cross-country econometric studies
tend to focus on wage rates, since time-series data are available for a
number of countries (e.g. Edwards, 1989). For countries like Rwanda,
wage rates are a highly deceptive measure of the welfare of the poor.
As noted above, only 6% of the households in Rwanda obtain most of their
income from wages. Furthermore, these households are disproportionately
located in the urban sector. Even within the urban sector, employees
have income levels significantly above the mean.

The other approach is to examine the average composition of
spending and income (e.g. Sahn, 1990 and Glewwe and de Tray, 1988 and
1989). This is the core of the method used in this study, but several

caveats must be mentioned. First, as mentioned above, the use of

 

 

(I)

m

bx

3L

Va

Si

us

252

averages hides a large amount of variation within the population.
Second, it is not always clear whether cash budgets or total expenditure
are being analyzed. This study indicates that the importance of home
production in the budget may be at least as important as the tradeable
component of the budget in determining the effect of price changes,
including those associated with devaluation.

8.3.3 W

The conclusions with regard to alternative welfare
measures is mixed. The simplest welfare measure is the first-order
approximation of compensating variation. This measure uses only the
”before" budget and income shares, thus avoiding completely the need to
estimate demand. This measure is highly correlated with the most
sophisticated welfare measures and performs quite well in ranking
households by welfare impact. If the only objective of a study is to
determine which groups are most benefited or least hurt, then this is a
very cost-effective approach.

The reason for this is that demand response is a second-order
effect, while the budget shares are first order effects. In geometric
terms, the budget shares are the rectangle portion of the trapezoid,
while the demand response determines the size of the triangle at the end
of the trapezoid. In the same fashion, the income shares are first-
order effects while the supply response is a second-order effect. In
other words, a respectable approximation of the ”profit effect" can be
obtained without estimating supply response. This is fortunate, because
budget and income shares are much more widely available than demand and
supply response parameters.

On the other hand, the first-order approximation of compensating
variation overestimates the "true" welfare impact. In the base
simulation of this study, the magnitude of the overestimate was 8-10%.
If price and income elasticities are to be estimated, then it is worth

using the Vartia method to estimate willingness-to-pay. As Deaton

If?!“

 

253

argues, willingness to pay requires no information beyond what is needed
to calculate consumer surplus, yet it is conceptually superior to
consumer surplus. Furthermore, the intuitive meaning of willingness to
pay is arguably easier to explain to the non-specialist reader than is
the meaning of consumer surplus.

Equivalent variation (EV) appears to be better suited to applied
policy analysis than compensating variation, in spite of the popularity
of the latter. The principal advantage is the ability of EV to rank

alternative policy outcomes.

8.4 mi ation t e stud u e t s fo u u e research

Perhaps the greatest weakness of this study is the use of
exogenous price changes to simulate devaluation. This study made use of-
price trends observed in other countries after currency devaluation.
Nonetheless, a number of somewhat arbitrary judgements had to be made in
classifying tradeable and nontradeable goods, most notably in the case
of beans and factory beer. The most serious implication of this
approach is that there is no mechanism to equilibrate supply and demand.

One alternative would be to set the new price of tradeable goods
exogenously, since by definition their price is set by the international
market, and allow non-tradeable prices to be set endogenously such that
supply and demand are equatedl. Although it is not at all clear that
such a method would be more successful in predicting price changes, it
would have the advantage of being internally consistent.

A related problem is that prices were assumed to change by the
same percentage throughout the country. However, devaluation usually
involves sharp increases in transportation costs. To the extent that

transportation costs rise more than the price of a given commodity, the

 

1. This approach was attempted in the present study, but the
lack of exact aggregation in the demand specification meant that it was
difficult to reliably predict the direction of price change necessary to
reduce the gap between supply and demand. As a result, the system
tended to "explode" after seven or eight iterations.

254

percentage increase in price will be lower where it is produced than
elsewhere. The magnitude of this difference depends on 1) the share of
transportation costs in the final consumer price and 2) how much higher
transportation costs rose relative to the commodity. Following this
logic, the geographic variation in the percentage price increase should
be greatest for nontradeable goods with a low value/bulk ratio, such as
cassava and sweet potatoes. The incorporation of this effect, such as
with a spatial equilibrium model, would be more important in a large
country with a poor road network.

A third limitation of the study is the use of strong separability
assumptions to derive non-food price elasticities. Although this method
produced highly plausible elasticities, it would have been preferable to
estimate non-food price elasticities directly. This, however, would
require a much larger data base which would permit the construction of
price indexes for each non-food category. Nonetheless, the analysis in
section 7.6 demonstrates that the basic results of this study are not
very sensitive to changes in the demand parameters.

One more weakness of the study is that only seven months of prices
after devaluation were available for the analysis. If the devaluation
is ultimately unsuccessful in addressing the external imbalance, then
the devaluation may well have been insufficient. In this case, the
relatively weak welfare impact (at least for rural households) may be
attributed to the overly modest exchange rate adjustment.

This study confined its attention to the expenditure-switching
effects of devaluation. The research approach used could be extended to
incorporate the impact of change in employment or the impact of other
aspects of the structural adjustment program. The only constraint on
the application of this method to other policy changes is that the
policies must be able to be translated into price and income changes.

Thus, the doubling of oil prices or alternative taxes on factory beer

255

could be modeled more easily than the impact of reductions in public
health spending.

Finally, as was mentioned earlier, the distributional impact of
devaluation is highly dependent on the structure of the economy.
Nonetheless, many aspects of the structure of the Rwandan economy are
similar to those in other semi-subsistence agricultural economies. This
study has demonstrated the feasibility of calculating "exact" measures
of welfare impact in the context of micro-simulation. However, the
generalizability of these results to other countries cannot be

determined until similar studies are carried out elsewhere.

 

“1--.-. r..- .Kj

 

 

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APPENDICES

APPENDIX A

DEVALUATION AND BEAN PRICES

APPENDIX A

DEVALUATION AND BEAN PRICES

We expect devaluation to raise the price of beans less than the
increase in the local price of devaluation for two reasons. First, if
the international supply of beans is perfectly elastic, then the price
of beans will increase in the same proportion as the parallel exchange
rate, since beans are imported unofficially. Most studies (e.g.
Edwards, 1989) show that the parallel market premium declines following
devaluation. This implies that the cost of foreign exchange on the
parallel market rises less than the cost of foreign exchange in the
official market.

Second, the increase in the price of beans will be less than the
increase in the parallel exchange rate if the regional supply of beans
are not perfectly elastic. It is probably more realistic to assume that
Rwandan demand is "large" relative to the regionally traded volumes of
beans so that the supply of imported beans is not perfectly elastic. In
this case, the price increase will be dampened in proportion to the
price elasticity of market demand for beans in Rwanda. The market
demand for beans is likely to be highly price-responsive because the
market is "thin" in the sense that only a small portion (16% according
to the ENBC) of the total demand for beans is in the form of market
purchases. If the elasticity of demand for beans is somewhat around 0.8
(see Chapter 6), then the elasticity of market demand will be almost
5.0 (0.8/0.16 = 4.8). Thus, a 5% reduction in the volume of imported
beans would be necessary to raise the domestic price by 1%.

In summary, the increase in the price of Rwandan beans is likely
to be less than the increase in the price of foreign currency in the

official market. This is because 1) devaluation tends to raise the

264

265

parallel market rate less than the official rate and 2) if the regional
supplies of beans are not perfectly elastic, then bean prices will rise
proportionately less than the parallel exchange rate, particularly given
the thinness of the bean market in Rwanda.

At the same time, it should be recognized that any increase in the
price of beans reduces the real income of perhaps 70% of rural
households. Furthermore, such a price increase is likely to have a
regressive impact even within the rural sector, reducing the real income
of low-income households more than that of other households (see Table

5"21).

APPENDIX B

ADULT EQUIVALENCE SCALES

266

APPENDIX B

ADULT EQUIVALENCE SCALES

Adult equivalence scales are used to measure the "size" of a
household in terms of consumption requirements. The simplest approach
to calculating adult equivalence scales is to define them in terms of
the caloric requirements of household members. Although calorie-based
equivalence scales do not take into account non-food consumption needs,
this is a less serious bias in a country like Rwanda in which food
represents a large share of the value of total expenditure. The

equivalence scales used in this study are presented below.

Table B-1: Adult equivalence scale
—

Age category Male Female
Less than 1 year 0.41 0.41
l - 3 years 0.56 0.56
4 - 6 years 0.76 0.76
7 - 9 years 0.91 0.91
10 - 12 years 0.97 1.08
13 - 15 years 0.97 1.13
16 - 19 years 1.02 1.05
20 - 39 years 1.00 1.00
40 - 49 years 0.95 0.95
50 - 59 years 0.90 0.90
60 — 69 years 0.90 0.80
70 and older 0.70 0.70

 

Source: Calculated from caloric requirements for
"moderate activity" established by the World
Health Organization and the Food and Agriculture
Organization (see Ministere du Plan, 1998:

Annex B).

APPENDIX C

COEFFICIENTS AND T STATISTICS FOR REGRESSION MODELS

267

 

Table C-1: Coefficients of the unrestricted SUR model of rural demand
Dependent
variable constant lnexp lnexp2 adults children fem hh
(share) 80 81 32 71 72 73
SORGH 115.82 -l6.19 0.79 -0.04 0.00 -0.37
t 2.35 -1.75 1.69 -0.31 0.04 -1.12
RICE -37.86 5.79 -0.28 -0.05 0.08 0.40
t -l.09 0.89 -0.84 -0.63 1.44 1.75
CASSA -125.78 22.14 -1.30 -0.18 -0.07 0.56
t -0.74 0.69 -0.80 -0.46 -0.23 0.49
SWPOT 604.61 -98.44 4.41 -0.84 -0.25 0.88
T 3.05 -2.64 2.33 -l.78 -0.74 0.66
WHPOT -29l.40 68.33 -3.33 0.20 0.30 0.12
t -1.87 2.33 -2.24 0.55 1.13 0.11
BANAN 51.98 -15.77 0.82 0.09 0.16 0.93
t 0.32 -0.52 0.54 0.24 0.59 0.87
BEANS -308.30 70.83 -4.03 -l.66 -0.85 1.47
t -1.21 1.47 -1.65 -2.73 -l.95 0.86
PEAS -30.56 11.62 -0.59 -0.17 —0.12 -0.24
t -0.42 0.86 -0.86 -l.00 -0.99 -0.50
TOMAT -2.75 0.20 -0.01 -0.02 0.01 0.09
t -0.28 0.11 -0.13 -0.67 0.56 1.39
BEEF -10.59 -l.14 0.11 0.09 0.04 0.28
t -0.21 -0.12 0.22 0.78 0.47 0.83
MEAT -52.93 7.48 -0.30 -0.10 0.35 -l.ll
t -0.52 0.39 -0.32 -0.43 2.04 -l.64
BBEER -101.47 4.32 -0.04 0.15 -0.37 -4.62
t -0.47 0.11 -0.02 0.29 —l.00 -3.20
SBEER -103.13 26.46 -l.30 0.42 -0.11 -0.61
t -0.87 1.18 -l.15 1.47 -0.57 -0.77
FBEER 50.98 -15.23 0.86 0.07 0.03 -0.58
t 0.88 -1.39 1.54 0.54 0.33 -1.48
OIL -54.17 10.71 -0.52 0.15 0.05 -0.25
t -l.51 1.58 -l.52 1.71 0.83 -l.04
SALT -13.79 3.55 -0.20 -0.10 -0.05 -0.05
t -0.73 0.99 -l.l3 -2.20 -1.54 -0.36
SUGAR -lO.36 3.55 -0.16 0.05 0.08 0.17
t -0.39 0.71 -0.64 0.75 1.72 0.94
CLOTH -12.78 2.63 —0.09 0.93 -0.37 -0.02
t -0.12 0.12 -0.08 3.46 -1.93 -0.03
HOUSE 421.36 -92.54 5.04 0.74 0.82 1.55
t 2.73 -2.95 3.17 1.90 2.93 1.41
EQUIP -40.57 6.74 -0.25 0.08 0.12 -0.38
t -0.48 0.39 -0.29 0.39 0.80 -0.62
ENERG -4.67 1.69 -0.10 -0.07 -0.23 -0.11
t -0.10 0.18 -0.21 -0.61 -2.62 -0.32
HEALT -l4.39 3.30 -0.17 0.15 -0.06 0.03
t -0.33 0.37 -0.38 1.37 -0.74 0.11
EDUCA -21.66 4.30 -0.21 0.14 0.10 -0.03
t -0.63 0.62 -0.61 1.60 1.62 —0.10
TRANS 21.38 -5.33 0.33 —0.03 0.09 0.21
t 0.52 -0.64 0.78 -0.31 1.14 0.73
TOBAC 3.58 -0.41 0.01 0.03 -0.08 -0.19
t 0.13 -0.08 0.05 0.43 -l.73 -1.01
LEISU -l7.54 3.34 -0.15 -0.03 0.02 -0.25
t -0.50 0.47 -0.42 -0.28 0.31 -0.99

268

 

Dependent

variable SOR RICE CAS SWPT WHPT BAN BEAN PEAS
(share) ail ¢i2 ai3 ai4 ai5 ai6 ai7 ai8
SORGH 0.23 -0.58 -0.48 -0.88 -l.10 -0.63 0.77 0.13
t 0.24 -0.41 —1.22 -2.10 -l.40 -2.33 1.13 0.19
RICE 0.76 -0.76 0.11 -0.19 0.83 0.05 0.88 0.37
t 1.10 -0.76 0.40 -0.66 1.50 0.28 1.84 0.77
CASSA 1.83 -1.18 -0.56 —0.84 2.90 0.72 -1.69 0.94
t 0.54 -0.24 -0.42 -0.58 1.07 0.78 -0.72 0.40
SWPOT 2.48 1.93 -l.62 -l.20 4.14 1.01 —0.00 0.89
t 0.64 0.35 -l.05 -0.73 1.33 0.96 -0.00 0.33
WHPOT -1.63 -2.03 1.61 -0.89 -5.75 -2.54 -l.85 2.59
t -0.53 -0.46 1.29 -0.67 -2.30 -3.00 -0.86 1.19
BANAN -3.11 0.76 -2.03 1.32 0.57 0.92 0.84 -3.73
t -0.99 0.17 -l.6l 0.98 0.22 1.07 0.38 -1.69
BEANS -8.18 3.74 6.96 -0.18 -2.33 3.35 2.13-11.54
t —1.65 0.52 3.50 -0.08 -0.58 2.46 0.62 -3.31
PEAS -0.48 -2.66 0.44 -0.59 -0.92 -0.38 0.52 -0.69
t -0.34 -l.30 0.78 -0.96 -0.80 -0.97 0.52 -0.69
TOMAT 0.18 -0.08 0.03 -0.03 0.24 -0.07 0.10 0.00
t 0.92 —0.27 0.39 -0.38 1.50 -1.32 0.76 0.01
BEEF 0.05 0.26 0.32 1.12 0.85 -0.02 0.45 1.29
t 0.05 0.18 0.79 2.62 1.06 -0.06 0.65 1.83
MEAT 6.66 -4.70 -0.77 0.48 -2.06 0.27 0.17 -l.02
t 3.32 -1.63 -0.96 0.56 -1.27 0.50 0.12 -0.72
BBEER -3.19 11.73 -3.08 2.51 2.58 2.12 0.01 3.98
t -0.76 1.95 -l.83 1.40 0.76 1.85 0.00 1.35
SBEER 1.30 2.03 -1.60 -0.51 0.87 -l.21 -2.85 2.50
t 0.55 0.59 -1.68 -0.50 0.45 -1.86 -1.72 1.50
FBEER -0.64 4.13 -0.02 -0.16 0.53 0.15 0.28 1.18
t -0.56 2.51 -0.05 -0.33 0.57 0.49 0.35 1.47

OIL 0.77 -2.52 0.07 0.32 0.84 -0.09 0.12 0.62

t 1.08 -2.47 0.23 1.07 1.47 -0.48 0.24 1.24
SALT -0.54 -l.36 0.16 0.11 0.14 0.14 -0.21 0.01
t —1.46 -2.56 1.05 0.68 0.48 1.42 —0.80 0.04
SUGAR 0.74 -2.69 -0.40 0.11 -0.15 -0.03 0.20 -0.38
t 1.42 -3.59 -l.90 0.50 -0.37 -0.24 0.56 -1.05

269

 

Dependent
variable TOM BEEF MEAT BBR SBR FBR OIL SALT SUGR
(share) ai9 ailO aill ai12 ail3 ai14 ails ai16 ail7
SORGH 0.28 —2.03 0.55 0.08 -0.14 -l.73 -2.01 -0.46 0.30
t 0.74 -2.52 0.64 0.15 -0.17 -0.68 -2.50 -0.44 0.75
RICE 0.28 -0.51 -0.03 —0.49 0.11 0.90 0.30 0.17 -0.24
t 1.03 -0.90 -0.05 -1.32 0.19 0.50 0.53 0.24 -0.86
CASSA -1.84 2.78 2.78 2.00 1.07 -0.70 -1.97 2.11 2.30
t -l.40 1.00 0.93 1.11 0.37 -0.08 -0.71 0.58 1.67
SWPOT 3.27 -4.83 -4.03 6.53 -4.86 -2.61 1.49-10.02 -2.76
t 2.19 -1.53 -1.17 3.16 -1.47 -0.26 0.47 -2.44 -1.76
WHPOT -1.43 -3.10 0.43 5.35 -1.14-11.38 3.47 5.92 -0.82
t -1.19 -1.22 0.16 3.22 -0.43 -1.42 1.37 1.79 -0.65
BANAN -0.61 0.97 -l.65-ll.10 3.02 17.37 2.10 -6.48 1.76
t —0.50 0.38 -0.59 -6.59 1.12 2.14 0.81 -1.93 1.37
BEANS -0.62 0.37 5.54 2.86 -1.79 -1.88 -0.52 4.43 2.72
t -0.32 0.09 1.25 1.08 -0.42 -0.15 -0.13 0.84 1.34
PEAS -0.61 -1.52 -0.23 2.13 -0.84 0.71 0.74 -0.97 -0.98
t —l.11 -1.30 -0.18 2.79 -0.69 0.19 0.63 -0.64 -1.68
TOMAT —0.09 -0.11 0.32 -0.27 0.21 0.22 0.16 -0.40 0.11
t —l.19 -0.67 1.81 -2.58 1.27 0.43 0.99 -l.92 1.35
BEEF 0.47 1.12 0.80 -1.11 -0.15 -l.72 0.72 -l.53 0.88
t 1.21 1.36 0.90 -2.08 -0.17 -0.67 0.88 -1.43 2.16
MEAT 0.36 0.93 -0.46 -3.18 0.76 4.35 -0.44 1.60 -0.07
t 0.46 0.56 -0.26 -2.96 0.44 0.84 -0.27 0.75 -0.08
BBEER —l.12 6.05 -6.63 -5.84 6.97 3.33 0.00 1.43 -l.32
t -0.69 1.76 -l.78 -2.60 1.94 0.31 0.00 0.32 -0.77
SBEER 0.19 —5.96 -2.47 4.41 -3.96 -2.56 1.10 1.76 0.54
t 0.21 -3.05 -l.17 3.46 -l.94 -0.42 0.56 0.69 0.56
FBEER 0.44 2.87 -0.94 -0.26 1.62 -6.19 1.38 1.74 -0.92
t 0.99 3.04 -0.92 -0.43 1.65 -2.09 1.47 1.42 —l.97
OIL 0.07 1.62 0.34 -0.21 -0.88 -0.42 0.15 -0.43 -0.05
t 0.26 2.78 0.54 -0.56 -l.45 -0.23 0.26 -0.57 -0.17
SALT -0.27 0.01 0.37 0.10 0.07 1.15 -0.16 0.38 -0.13
t —1.91 0.04 1.13 0.50 0.22 1.20 -0.54 0.95 -0.87
SUGAR 0.26 -0.50 0.85 -0.53 -0.49 0.20 0.54 0.02 -0.13
t 1.30 -1.16 1.83 -l.9l -l.10 0.15 1.27 0.03 -0.62

270

 

Table C-2: Coefficients of the SUR model of rural demand
under symmetry restrictions
Dependent
variable constant lnexp lnexp2 adults children fem hh
(share) 80 81 32 71 72 73
SORGH 101.92 -l7.48 0.84 -0.03 -0.03 -0.31
t 2.21 -1.91 1.83 -0.29 -0.41 -0.97
RICE -30.60 3.29 -0.15 -0.03 0.06 0.43
t -0.92 0.51 -0.46 -0.41 1.03 1.88
CASSA -79.99 20.83 -1.21 -0.09 0.06 0.15
t -0.52 0.66 -0.76 -0.24 0.20 0.14
SWPOT 586.48 -105.13 4.69 -0.86 -0.44 1.53
t 3.25 -2.88 2.54 -1.89 -l.33 1.19
WHPOT -332.08 67.42 -3.30 0.22 0.18 0.13
t -2.34 2.35 -2.27 0.62 0.68 0.13
BANAN -58.35 9.05 -0.38 -0.38 0.34 0.10
t -0.40 0.31 -0.25 -1.03 1.28 0.10
BEANS -366.15 85.34 -4.68 -l.51 -0.55 1.62
t -1.57 1.81 -1.96 -2.55 -1.30 0.97
PEAS -34.63 8.24 -0.44 -0.16 -0.21 -0.26
t -0.52 0.62 -0.65 —0.94 -1.71 -0.55
TOMAT -5.40 0.53 -0.03 -0.02 0.01 0.07
t -0.57 0.28 -0.30 -l.04 0.56 1.07
BEEF -17.76 -1.22 0.12 0.09 0.05 0.27
t -0.38 -0.13 0.25 0.75 0.54 0.82
MEAT -1.02 2.24 -0.04 -0.05 0.32 -l.l3
t -0.01 0.12 -0.04 -0.20 1.88 -1.72
BBEER -8.32 3.41 0.01 0.25 -0.32 -4.89
t -0.04 0.09 0.01 0.51 -0.89 -3.47
SBEER -110.06 24.31 -1.22 0.31 -0.21 -0.55
t -l.01 1.11 -l.10 1.13 -1.08 -0.71
FBEER 67.20 -l6.03 0.89 0.09 0.04 -0.48
t 1.18 -1.47 1.62 0.63 0.40 -l.25
OIL -59.23 9.37 —0.45 0.17 0.04 -0.25
t -1.75 1.40 -l.33 2.02 0.74 -1.06
SALT -l4.66 3.16 -0.18 -0.09 -0.05 -0.05
t -0.79 0.88 -l.01 -1.99 —1.59 -0.41
SUGAR -5.06 1.68 -0.07 0.05 0.06 0.15
t -0.20 0.34 -0.27 0.84 1.33 0.89
CLOTH -12.78 2.63 -0.09 0.93 -0.37 -0.02
t -0.12 0.12 -0.08 3.46 -1.93 -0.03
HOUSE 421.36 -92.54 5.04 0.74 0.82 1.55
t 2.73 -2.95 3.17 1.90 2.93 1.41
EQUIP -40.57 6.74 -0.25 0.08 0.12 -0.38
t -0.48 0.39 —0.29 0.39 0.80 -0.62
ENERG -4.67 1.69 -0.10 -0.07 -0.23 -0.11
t -0.10 0.18 -0.21 -0.61 -2.62 -0.32
HEALT -14.39 3.30 -0.17 0.15 -0.06 0.03
t -0.33 0.37 -0.38 1.37 -0.74 0.11
EDUCA -21.66 4.30 -0.21 0.14 0.10 -0.03
t -0.63 0.62 -0.61 1.60 1.62 -0.10
TRANS 21.38 -5.33 0.33 -0.03 0.09 0.21
t 0.52 -0.64 0.78 -0.31 1.14 0.73
TOBAC 3.58 -0.41 0.01 0.03 -0.08 -0.19
t 0.13 -0.08 0.05 0.43 -l.73 -l.01
LEISU -l7.54 3.34 -0.15 -0.03 0.02 -0.25
t -0.50 0.47 -0.42 —0.28 0.31 -0.99

271

 

Dependent
variable SOR RICE CAS SWPT WHPT BAN BEAN PEAS
(share) ail ai2 ai3 ai4 ai5 ai6 ai7 ai8
SORGH 0.08 0.25 —0.43 -0.70 -l.20 -0.65 0.29 -0.12
t 0.09 0.43 -1.17 -1.73 -l.78 -2.56 0.45 -0.23
RICE 0.25 0.46 0.12 -0.16 0.67 0.09 1.12 0.08
t 0.43 0.50 0.45 -0.54 1.31 0.47 2.38 0.20
CASSA -0.43 0.12 -2.08 -l.68 2.95 1.04 1.53 0.23
t -l.l7 0.45 -l.80 -1.68 3.05 1.65 1.10 0.46
SWPOT -0.70 -0.16 -l.68 -l.22 0.12 0.84 -0.98 -0.24
t -l.73 -0.54 -1.68 -0.80 0.11 1.18 -0.62 -0.44
WHPOT -1.20 0.67 2.95 0.12 -6.10 -2.39 -l.96 -0.40
t -l.78 1.31 3.05 0.11 -3.25 -3.46 -l.15 -0.49
BANAN -0.65 0.09 1.04 0.84 -2.39 2.63 4.20 -l.00
t -2.56 0.47 1.65 1.18 -3.46 3.80 4.14 -2.83
BEANS 0.29 1.12 1.53 -0.98 -l.96 4.20 -3.78 -1.49
t 0.45 2.38 1.10 -0.62 -1.15 4.14 -1.14 -1.64
PEAS -0.12 0.08 0.23 -0.24 -0.40 -1.00 -1.49 -2.00
t -0.23 0.20 0.46 -0.44 -0.49 -2.83 -1.64 -2.53
TOMAT 0.13 0.15 0.08 -0.03 0.14 -0.05 0.23 -0.02
t 0.81 0.85 1.11 -0.42 0.99 -0.89 1.76 -0.16
BEEF -0.91 -0.21 0.16 1.00 0.20 0.18 0.47 1.04
t -1.59 -0.42 0.42 2.44 0.29 0.69 0.71 2.01
MEAT 1.15 -0.45 -0.24 0.26 -1.26 0.10 1.52 -0.72
t 1.64 -0.81 -0.32 0.33 -1.03 0.20 1.18 -0.91
BBEER -0.37 -0.57 -2.60 3.33 5.42 -l.53 -l.36 1.36
t -0.75 -l.59 -2.39 2.63 4.16 -1.88 -0.72 1.99
SBEER 0.32 0.52 -0.42 -0.17 -l.62 -0.50 -2.00 -0.13
t 0.44 0.94 -0.51 -0.19 -1.29 -0.87 -l.37 -0.l6
FBEER -l.04 2.91 0.12 -0.27 0.79 0.24 0.58 1.08
t -1.07 2.59 0.28 -0.56 0.90 0.80 0.74 1.50
OIL -0.22 -0.36 -0.09 0.31 1.18 -0.08 0.33 1.10
t -0.47 -0.80 -0.35 1.07 2.43 -0.46 0.71 2.88
SALT -0.43 -0.65 0.07 0.10 0.29 0.08 -0.31 0.12
t -1.31 -1.61 0.48 0.65 1.03 0.78 -l.20 0.49
SUGAR 0.50 -0.52 -0.27 0.06 -0.31 0.04 0.74 -0.41
t 1.77 -2.10 -l.36 0.26 -0.91 0.33 2.12 -l.55

272

 

Dependent
variable TOM BEEF MEAT BBR SBR FBR OIL SALT SUGR
(share) ai9 ai10 aill ai12 ai13 ai14 ai15 ai16 ail7
SORGH 0.13 -0.91 1.15 -0.37 0.32 -l.04 -0.22 -0.43 0.50
t 0.81 -l.59 1.64 -0.75 0.44 -l.07 -0.47 -1.31 1.77
RICE 0.15 -0.21 -0.45 -0.57 0.52 2.91 -0.36 -0.65 -0.52
t 0.85 -0.42 -0.81 -l.59 0.94 2.59 -0.80 -1.61 -2.10
CASSA 0.08 0.16 -0.24 -2.60 -0.42 0.12 -0.09 0.07 -0.27
t 1.11 0.42 -0.32 -2.39 -0.51 0.28 -0.35 0.48 -l.36
SWPOT -0.03 1.00 0.26 3.33 -0.17 -0.27 0.31 0.10 0.06
t -0.42 2.44 0.33 2.63 -0.19 -0.56 1.07 0.65 0.26
WHPOT 0.14 0.20 -1.26 5.42 -l.62 0.79 1.18 0.29 -0.31
t 0.99 0.29 -1.03 4.16 -1.29 0.90 2.43 1.03 -0.91
BANAN —0.05 0.18 0.10 -l.53 -0.50 0.24 -0.08 0.08 0.04
t -0.89 0.69 0.20 -l.88 -0.87 0.80 -0.46 0.78 0.33
BEANS 0.23 0.47 1.52 -1.36 -2.00 0.58 0.33 -0.31 0.74
t 1.76 0.71 1.18 -0.72 -1.37 0.74 0.71 -1.20 2.12
PEAS -0.02 1.04 -0.72 1.36 -0.13 1.08 1.10 0.12 -0.41
t -0.16 2.01 -0.91 1.99 -0.16 1.50 2.88 0.49 -1.55
TOMAT -0.04 0.01 0.25 -0.15 0.15 0.04 0.09 -0.26 0.06
t -0.62 0.10 1.67 -l.47 0.99 0.13 0.68 -2.34 0.88
BEEF 0.01 0.31 0.80 -0.53 -l.31 1.64 1.05 -0.11 0.34
t 0.10 0.41 1.16 -l.05 -1.79 1.97 2.48 -0.38 1.26
MEAT 0.25 0.80 -1.00 -3.78 -0.51 -0.44 -0.55 0.12 0.47
t 1.67 1.16 -0.64 -3.88 -0.43 -0.46 -l.ll 0.40 1.33
BBEER -0.15 -0.53 -3.78 -l.66 4.32 -0.14 -0.42 0.14 -0.54
t -1.47 -1.05 -3.88 -0.82 3.89 -0.24 -1.19 0.74 -2.05
SBEER 0.15 -l.31 -0.51 4.32 -1.87 1.57 -0.86 -0.02 -0.11
t 0.99 -1.79 -0.43 3.89 -l.04 1.69 -l.63 -0.06 -0.28
FBEER 0.04 1.64 -0.44 -0.14 1.57 -6.46 0.97 1.45 -0.52
t 0.13 1.97 -0.46 -0.24 1.69 -2.36 1.26 2.06 -1.28
OIL 0.09 1.05 -0.55 -0.42 -0.86 0.97 0.70 -0.25 -0.20
t 0.68 2.48 -1.11 -1.19 —1.63 1.26 1.37 -0.94 -0.96
SALT -0.26 -0.11 0.12 0.14 -0.02 1.45 -0.25 0.42 -0.19
t -2.34 -0.38 0.40 0.74 -0.06 2.06 -0.94 1.14 -1.36
SUGAR 0.06 0.34 0.47 -0.54 -0.11 -0.52 -0.20 -0.19 -0.41
t 0.88 1.26 1.33 -2.05 -0.28 -l.28 -0.96 -1.36 -2.17

273

 

Table C-3: Coefficients of the unrestricted SUR model of urban demand
Dependent
variable constant lnexp lnexp2 adults children fem hh
(share) 30 B1 B2 71 72 73
SORGH 14.39 -1.95 0.07 -0.10 -0.03 -0.06
t 0.92 -0.71 0.58 -1.26 -0.78 -0.23
RICE -89.51 17.19 -0.81 -0.13 0.12 -0.06
t -3.63 3.96 -3.95 -1.06 1.73 -0.14
BREAD -37.32 5.27 -0.24 0.09 0.06 0.07
t -4.21 3.36 -3.22 1.95 2.55 0.48
CASSA -15.78 3.27 -0.21 -0.32 0.12 -0.72
t -0.65 0.76 -1.05 -2.54 1.82 -1.76
SWPOT 157.83 —28.57 1.20 -0.37 -0.14 0.39
t 3.65 -3.75 3.35 -l.70 -l.l8 0.54
WHPOT 4.44 10.28 -0.56 -0.19 0.07 0.36
t 0.11 1.45 -l.69 -0.95 0.66 0.53
BANAN 6.21 -1.47 -0.00 -0.05 0.04 1.03
t 0.19 -0.25 -0.01 -0.32 0.39 1.83
CASFL 18.15 -4.20 0.13 0.00 0.17 0.50
t 0.65 -0.86 0.57 0.00 2.22 1.07
BEANS 214.25 —23.30 0.77 -1.26 -0.45 -0.75
t 3.00 -l.84 1.29 -3.49 -2.29 -0.62
PEAS 7.78 0.43 -0.02 -0.00 0.01 —0.17
t 0.76 0.24 -0.28 -0.03 0.20 —l.02
VEGET -24.50 3.98 -0.19 0.13 0.01 0.53
t -2.16 1.98 -2.02 2.29 0.32 2.80
BEEF -102.49 18.83 -0.90 -0.12 0.10 -0.45
t -3.97 4.15 -4.22 -0.90 1.40 -l.05
MEAT -18.28 5.53 -0.26 0.29 0.09 0.03
t —0.75 1.29 -l.26 2.35 1.33 0.07
MILK -88.82 10.18 -0.49 0.33 0.09 0.76
t -2.81 1.82 -l.86 2.06 1.08 1.43
BBEER -98.58 19.19 -0.98 -1.19 -0.63 -4.46
t -l.76 1.93 -2.11 -4.17 -4.12 ~4.74
SBEER 8.92 -0.10 -0.01 -0.15 -0.13 -0.63
t 0.41 -0.03 -0.07 -l.33 -2.19 -1.71
FBEER -73.32 13.07 -0.50 -0.30 -0.08 -2.08
t -1.28 1.30 -l.06 -1.05 -0.52 -2.18
OIL -49.59 10.29 -0.49 -0.00 0.11 0.50
t -3.45 4.05 -4.08 -0.02 2.74 2.08
SALT 2.86 -0.36 0.00 -0.01 -0.02 0.12
t 0.69 -0.49 0.15 -0.34 -1.36 1.76
SUGAR -52.71 11.59 -0.55 -0.01 0.14 1.33
t -2.33 2.91 -2.94 -0.12 2.25 3.51
MEALS 141.19 -l9.41 0.90 -1.15 -0.82 -2.89
t 1.83 -1.43 1.41 —2.93 -3.93 -2.25

274

 

Dependent
variable constant lnexp lnexp2 adults children fem hh
(share) 30 B1 B2 71 72 73
CLOTH -47.60 9.81 -0.46 0.22 0.09 -0.36
t -1.24 1.35 -1.33 1.13 0.83 -0.53
HOUSE 290.47 -63.88 3.49 1.26 0.22 1.67
t 2.81 -3.26 3.77 2.42 0.73 0.91
EQUIP -16.53 1.41 0.03 0.21 0.17 0.37
t -0.53 0.24 0.11 1.32 1.87 0.67
ENERG -120.65 22.05 -0.98 0.44 0.22 0.92
t -3.09 2.98 -2.80 2.25 1.98 1.33
HEALT -38.72 7.42 -0.34 0.38 0.11 0.69
t -1.69 1.71 -l.65 3.29 1.63 1.69
EDUCA -29.75 5.25 -0.23 0.12 0.26 1.32
t —1.07 1.00 -0.93 0.85 3.20 2.68
TRANS 60.02 -14.90 0.88 1.22 0.35 1.39
t 0.96 -1.25 1.56 3.86 1.91 1.25
TOBAC -34.51 7.59 -0.38 -0.16 -0.19 -1.03
t -1.83 2.13 -2.28 -1.71 -3.46 -3.09
LEISU 15.45 -4.25 0.26 0.79 0.04 0.40
t 0.72 -1.04 1.35 7.28 0.69 1.04

 

275

 

Dependent

variable SOR RICE BRD CAS SWPT WHPT BAN CSFL BEAN PEAS VEG
(share) ail ui2 ai3 ai4 aiS ai6 ai7 ai8 ai9 ailO aill
SORGH -0.48 0.20 -0.03 0.09 0.07 0.59 -0.36 0.13 0.70 -0.19 -0.30
t -l.37 0.26 -0.09 0.29 0.22 0.84 -1.64 0.38 1.29 -0.55 —0.87
RICE 0.46 -3.77 0.26 -0.56 1.32 -0.89 0.11 0.13 2.09 0.00 0.32
t 0.82 —3.00 0.57 -1.14 2.54 -0.79 0.31 0.25 2.41 0.00 0.58
BREAD 0.18 0.25 0.23 0.01 0.16 -0.51 -0.05 0.39 0.40 0.34 -0.18
t 0.92 0.56 1.47 0.06 0.89 -1.30 -0.39 2.06 1.33 1.79 -0.94
CASSA -0.30 -1.94 -0.36 2.01 -0.15 1.73 -0.22 0.20 -1.03 -0.31 0.20
t -0.55 -1.56 -0.79 4.15 -0.29 1.55 -0.64 0.38 -l.20 -0.57 0.37
SWPOT -2.82 3.79 0.02 0.52 -1.88 5.84 -0.91 -0.06 -0.88 3.36 -l.15
t -2.95 1.76 0.03 0.62 -2.11 3.03 -l.51 -0.07 -0.60 3.58 -1.20
WHPOT -0.03 1.69 0.47 -0.01 -1.07 -1.61 -0.70 -1.80 2.50 -2.93 -1.45
t -0.04 0.84 0.65 -0.01 -1.29 -0.90 -1.24 —2.09 1.80 -3.34 -1.62
BANAN -0.35 0.53 0.14 -0.28 -0.96 1.38 -0.90 0.54 0.29 -0.02 -0.22
t -0.46 0.31 0.23 -0.42 -1.37 0.91 -1.89 0.74 0.25 -0.02 -0.29
CASFL 0.67 0.42 0.01 -0.35 0.80 1.10 -0.35 -l.l9 -0.35 0.03 0.27
t 1.06 0.29 0.01 -0.64 1.36 0.86 -0.89 -l.95 -0.35 0.05 0.43
BEANS -2.06 -0.67 —0.39 -0.45 -3.45 1.19 -0.99 -0.18 2.98 -2.63 0.14
t -1.35 -0.19 -0.31 -0.34 -2.42 0.39 -1.03 -0.12 1.26 -1.76 0.09
PEAS -0.03 0.20 -0.16 -0.00 0.07 -1.75 -0.10 -0.52 0.48 -0.16 -0.16
t -0.14 0.39 -0.84 -0.00 0.33 —3.74 -0.71 -2.35 1.34 -0.69 -0.67
VEGET 0.43 -0.60 0.20 -0.11 0.45 0.45 0.06 -0.16 0.29 0.15 -0.21‘
t 1.72 -1.08 1.01 -0.51 1.95 0.90 0.38 -0.67 0.77 0.63 -0.84
BEEF 0.20 -0.53 0.44 1.26 1.70 ~0.30 -0.36 0.28 0.22 -0.80 0.19
t 0.34 -0.40 0.93 2.48 3.15 -0.26 -0.99 0.51 0.24 -l.40 0.33
MEAT 0.83 -3.20 -1.24 0.07 0.53 0.52 0.28 -0.10 -0.94 -0.57 0.17
t 1.53 -2.60 -2.79 0.14 1.03 0.47 0.80 -0.19 -l.ll -1.06 0.31
MILK -0.67 2.55 0.28 1.41 -0.22 -1.06 -1.03 -0.12 3.18 1.22 -0.08
t -0.95 1.62 0.49 2.29 -0.34 —0.75 -2.33 -0.18 2.92 1.78 -0.11
BBEER —0.41 7.06 0.66 0.86 1.13 3.17 0.85 3.25 -2.83 0.42 -0.52
t -0.34 2.55 0.66 0.80 0.99 1.28 1.10 2.74 -1.49 0.35 -0.43
SBEER -0.20 -1.15 0.06 0.03 -0.98 0.28 0.20 0.81 0.48 -l.02 -0.62
t -0.42 -1.05 0.15 0.07 -2.16 0.29 0.66 1.74 0.64 -2.15 -1.29
FBEER 0.78 0.14 -0.88 -2.78 0.90 -3.04 1.00 0.46 -3.53 -0.80 0.18
t 0.62 0.05 -0.86 -2.52 0.76 -1.20 1.26 0.38 -1.81 -0.65 0.15
OIL 0.45 -0.70 -0.14 0.23 0.71 0.14 -0.26 -0.10 0.28 -0.00 -0.24
t 1.40 -0.98 -0.55 0.82 2.39 0.22 -l.29 —0.33 0.56 -0.01 -0.77
SALT —0.11 0.10 -0.01 0.01 0.05 0.00 -0.09 0.05 -0.01 -0.07 -0.12
t -1.17 0.49 -0.08 0.12 0.61 0.02 -l.46 0.59 -0.06 -0.77 -l.24
SUGAR 0.69 -2.04 0.50 -0.09 1.08 -0.74 —0.87 -l.00 0.88 0.86 -0.25
t 1.37 -l.81 1.22 -0.20 2.32 -0.73 -2.76 -2.09 1.13 1.75 —0.49
MEALS 3.13 -2.58 0.09 -0.59 0.61 -6.09 3.73 -1.26 -4.43 2.31 3.79
t 1.79 -0.66 0.06 -0.38 0.37 -1.73 3.38 -0.75 -1.63 1.35 2.17

276

 

Dependent
variable BEEF MEAT MILK BBR SBR FBR OIL SALT SUGR MEAL
(share) ai12 ai13 ail4 ailS ail6 ai17 ai18 ail9 ai20 ai21
SORGH 0.11 0.10 -0.06 0.17 -0.65 0.15 -0.47 0.03 0.13 -0.12
t 0.36 0.33 -0.20 0.57 -l.92 0.30 —2.35 0.06 0.61 -0.74
RICE 0.56 -0.04 0.43 0.51 -0.91 0.43 0.08 -0.57 0.35 -0.01
t 1.19 -0.08 0.91 1.08 -1.67 0.54 0.25 -0.67 1.02 -0.02
BREAD -0.02 0.14 0.25 -0.01 -0.23 -0.07 0.15 0.06 -0.04 0.22
t -0.13 0.84 1.53 -0.06 -1.20 -0.26 1.34 0.20 -0.30 2.32
CASSA —0.69 -0.27 1.02 0.26 1.98 0.31 0.22 0.08 0.36 0.12
t —1.48 -0.58 2.18 0.55 3.67 0.39 0.70 0.10 1.05 0.47
SWPOT -0.14 -0.26 -0.20 -0.22 -l.06 —1.58 -0.29 0.61 0.71 0.34
t ~0.18 -0.32 -0.25 -0.27 -1.13 ~1.15 -0.54 0.42 1.20 0.74
WHPOT 0.03 -0.91 -1.17 -0.75 -0.29 -2.55 0.39 1.55 -1.00 -1.12
t 0.04 -1.22 -1.55 -0.98 -0.34 ~1.99 0.76 1.14 -l.81 -2.59
BANAN 0.93 -0.35 -0.52 0.93 2.09 0.10 -0.33 0.10 -0.20 0.40
t 1.46 -0.56 -0.82 1.44 2.84 0.09 ~0.76 0.08 -0.44 1.09
CASFL -0.34 -0.03 -0.32 0.04 1.36 -0.45 -0.03 2.59 0.60 -0.21
t -0.64 -0.06 -0.59 0.08 2.20 -0.49 -0.08 2.69 1.55 -0.68
BEANS 1.08 0.39 -0.17 0.05 -5.43 -1.87 0.29 2.51 -0.30 -1.36
t 0.85 0.30 -0.14 0.04 -3.65 -0.85 0.33 1.08 -0.32 -1.84
PEAS -0.05 -0.09 -0.06 -0.03 -0.40 -0.24 0.10 -0.23 0.15 0.02
t -0.24 -0.45 -0.29 -0.15 -1.75 -0.73 0.73 -0.65 1.07 0.13
VEGET 0.05 0.05 0.25 0.34 -0.09 -0.28 -0.05 -0.19 0.19 0.22
t 0.24 0.23 1.18 1.63 -0.38 -0.80 -0.35 -0.51 1.26 1.84
BEEF -0.25 -0.18 0.23 0.28 -0.19 -0.78 0.39 -0.04 0.01 0.59
t —0.51 -0.38 0.46 0.57 -0.34 —0.94 1.19 -0.05 0.03 2.11
MEAT -0.35 -0.34 0.46 0.38 -l.03 1.68 0.05 0.65 0.23 -0.04
t -0.76 -0.74 0.99 0.82 -1.93 2.15 0.16 0.78 0.69 -0.14
MILK 0.65 -0.58 0.71 0.49 1.73 -0.95 -0.01 0.79 -0.60 0.88
t 1.11 -0.99 1.20 0.83 2.53 -0.95 -0.02 0.74 -1.40 2.61
BBEER -1.67 -1.49 -0.48 -6.30 2.98 1.11 0.24 -l.57 0.04 -0.53
t -1.62 -l.45 -0.47 -6.03 2.49 0.63 0.34 -0.84 0.05 —0.90
SBEER -0.19 -0.10 -0.26 -0.31 -0.98 2.29 0.06 —0.50 0.65 -0.22
t -0.47 -0.24 -0.63 -0.75 -2.08 3.30 0.21 -0.68 2.20 -0.95
FBEER 0.46 2.64 1.12 1.11 -0.71 0.74 -0.15 -2.75 0.62 1.09
t 0.44 2.51 1.06 1.04 -0.58 0.41 -0.21 -1.44 0.80 1.80
OIL 0.11 -0.07 -0.21 0.20 -0.10 -0.66 0.21 -0.65 0.24 0.24
t 0.41 -0.25 -0.79 0.74 -0.33 -1.45 1.13 -l.33 1.22 1.56
SALT 0.03 -0.05 0.01 -0.03 -0.09 -0.05 -0.00 0.60 0.05 -0.08
t 0.38 -0.64 0.19 -0.35 -l.00 -0.36 -0.01 4.26 0.82 -1.73
SUGAR 0.25 -0.19 -1.42 0.55 1.27 -0.91 0.15 -0.38 0.19 0.52
t 0.61 -0.46 -3.38 1.31 2.61 -1.27 0.53 -0.50 0.62 2.16
MEALS -l.27 -0.03 0.97 0.56 1.43 0.10 -0.53 -2.86 -2.11 —0.99
t -0.86 -0.02 0.66 0.38 0.84 0.04 -0.53 -1.08 -1.97 -1.17

277

 

Table C-4: Coefficients of the SUR model of urban demand
under symmetry restrictions
Dependent
variable constant lnexp lnexp2 adults children fem hh
(share) BO 31 82 71 72 73
SORGH 12.43 -1.59 0.06 -0.13 -0.03 -0.07
t 0.85 -0.59 0.44 -1.67 -0.80 -0.28
RICE -99.28 18.87 -0.88 -0.05 0.13 -0.02
t -4.23 4.39 -4.34 -0.41 1.99 -0.05
BREAD -33.80 5.24 -0.24 0.09 0.06 0.11
t -3.99 3.37 -3.23 1.97 2.47 0.77
CASSA -20.51 4.49 -0.26 -0.35 0.14 -0.69
t -0.91 1.06 -1.33 -3.01 2.12 -l.76
SWPOT 200.36 -35.19 1.48 -0.49 -0.19 -0.06
t 5.05 -4.72 4.22 -2.40 -1.67 -0.08
WHPOT -2.46 8.50 -0.49 -0.31 0.10 0.19
t -0.07 1.22 -l.50 -1.59 0.93 0.29
BANAN 15.19 -1.06 -0.02 -0.12 0.04 0.88
t 0.50 -0.19 -0.07 -0.77 0.48 1.64
CASFL 36.55 -5.32 0.18 -0.02 0.15 0.64
t 1.42 -1.11 0.81 -0.12 2.08 1.42
BEANS 196.84 -25.85 0.86 -l.35 -0.48 -0.82
t 2.99 -2.09 1.47 -4.00 -2.55 -0.71
PEAS 4.61 0.02 -0.01 -0.03 0.01 -0.20
t 0.48 0.01 -0.07 -0.68 0.22 -1.20
VEGET -25.46 4.29 -0.20 0.13 0.01 0.57
t -2.36 2.16 -2.19 2.35 0.45 3.04
BEEF -112.44 22.18 -1.05 -0.10 0.11 -0.37
t —4.74 4.99 -5.02 -0.84 1.57 -0.89
MEAT -24.00 5.36 -0.24 0.28 0.08 0.28
t -1.07 1.27 -l.23 2.41 1.24 0.70
MILK -60.41 9.42 -0.45 0.29 0.09 0.63
t -2.07 1.72 -1.75 1.95 1.02 1.23
BBEER -92.91 22.52 -1.14 -1.46 -0.63 -5.03
t -1.82 2.34 -2.51 -5.59 -4.26 -5.57
SBEER 6.49 -0.98 0.02 -0.24 -0.15 -0.65
t 0.32 —0.26 0.13 -2.29 —2.54 -1.84
FBEER -66.84 12.18 -0.45 -0.10 -0.14 -1.93
t -1.27 1.24 -0.98 -0.36 -0.95 -2.09
OIL -57.60 11.15 -0.53 -0.01 0.11 0.55
t -4.29 4.46 -4.47 -0.11 2.98 2.35
SALT 3.49 -0.45 0.01 -0.01 -0.01 0.11
t 0.86 -0.62 0.26 -0.44 -l.34 1.54
SUGAR -58.70 11.41 -0.54 0.00 0.17 1.40
t -2.82 2.92 -2.94 0.01 2.80 3.83
MEALS 99.00 -17.51 0.84 -0.79 -0.75 -2.24
t 1.44 -l.34 1.36 -2.24 -3.75 -1.82

278

 

Dependent
variable constant lnexp lnexp2 adults children fem hh
(share) BO 31 82 71 72 73
CLOTH -47.60 9.81 —0.46 0.22 0.09 -0.36
t -1.24 1.35 -l.33 1.13 0.83 -0.53
HOUSE 290.47 -63.88 3.49 1.26 0.22 1.67
t 2.81 -3.26 3.77 2.42 0.73 0.91
EQUIP -l6.53 1.41 0.03 0.21 0.17 0.37
t -0.53 0.24 0.11 1.32 1.87 0.67
ENERG -120.65 22.05 -0.98 0.44 0.22 0.92
t -3.09 2.98 -2.80 2.25 1.98 1.33
HEALT -38.72 7.42 -0.34 0.38 0.11 0.69
t -1.69 1.71 -1.65 3.29 1.63 1.69
EDUCA -29.75 5.25 -0.23 0.12 0.26 1.32
t -l.07 1.00 -0.93 0.85 3.20 2.68
TRANS 60.02 -14.90 0.88 1.22 0.35 1.39
t 0.96 -l.25 1.56 3.86 1.91 1.25
TOBAC -34.51 7.59 -0.38 -0.16 -0.19 -1.03
t —l.83 2.13 -2.28 -1.71 -3.46 -3.09
LEISU 15.45 -4.25 0.26 0.79 0.04 0.40
t 0.72 -l.04 1.35 7.28 0.69 1.04

279

 

Dependent

variable SOR RICE BRD CAS SWPT WHPT BAN CSFL BEAN PEAS VEG
(share) ail ai2 ai3 ai4 ai5 ai6 ai7 ai8 ai9 ailO aill
SORGH -0.28 0.03 -0.07 0.00 -0.19 0.32 -0.23 0.16 0.41 -0.08 0.11
t -0.88 0.07 -0.45 0.01 -0.65 0.67 -l.14 0.59 0.85 -0.43 0.63
RICE 0.03 -3.04 0.22 -0.93 1.19 0.37 0.06 0.50 1.92 0.23 -0.07
t 0.07 -2.91 0.79 -2.28 2.55 0.45 0.20 1.12 2.46 0.70 -0.21
BREAD -0.07 0.22 0.15 -0.02 0.16 -0.14 -0.03 0.39 0.18 0.06 0.08
t -0.45 0.79 1.03 -0.15 0.95 -0.44 -0.28 2.30 0.65 0.51 0.63
CASSA 0.00 -0.93 -0.02 1.50 -0.10 0.98 -0.25 —0.49 0.63 0.23 -0.20
t 0.01 -2.28 -0.15 3.33 -0.25 1.77 -0.86 -1.39 0.97 1.28 -l.12
SWPOT -0.19 1.19 0.16 -0.10 -2.60 1.06 -0.08 0.48 2.66 0.42 0.35
t -0.65 2.55 0.95 -0.25 -3.17 1.54 -0.18 1.04 2.92 2.09 1.73
WHPOT 0.32 0.37 -0.14 0.98 1.06 -0.16 0.07 0.04 1.57 -l.89 0.10
t 0.67 0.45 -0.44 1.77 1.54 -0.11 0.15 0.07 1.43 -4.94 0.27
BANAN -0.23 0.06 -0.03 -0.25 -0.08 0.07 -0.85 -0.12 0.01 0.03 0.14
t -1.14 0.20 -0.28 -0.86 -0.18 0.15 -l.9l -0.35 0.02 0.21 0.97
CASFL 0.16 0.50 0.39 -0.49 0.48 0.04 -0.12 -0.96 0.03 -0.18 -0.07
t 0.59 1.12 2.30 -1.39 1.04 0.07 -0.35 -1.72 0.04 -0.93 -0.36
BEANS 0.41 1.92 0.18 -0.63 -2.66 1.57 0.01 0.03 1.59 0.06 0.33
t 0.85 2.46 0.65 -0.97 -2.92 1.43 0.02 0.04 0.79 0.20 0.98
PEAS -0.08 0.23 0.06 0.23 0.42 -1.89 0.03 -0.18 0.06 -0.13 0.16
t -0.43 0.70 0.51 1.28 2.09 -4.94 0.21 -0.93 0.20 -0.62 1.07
VEGET 0.11 -0.07 0.08 -0.20 0.35 0.10 0.14 -0.07 0.33 0.16 -0.12
t 0.63 -0.21 0.63 -1.12 1.73 0.27 0.97 -0.36 0.98 1.07 -0.59
BEEF -0.03 0.19 -0.04 0.32 0.72 -0.64 -0.13 -0.31 0.48 -0.04 0.03
t -0.15 0.49 -0.27 1.04 1.77 -l.20 -0.47 -0.89 0.74 -0.25 0.20
MEAT 0.10 -0.42 0.01 -0.22 0.53 -l.05 0.24 -0.12 0.69 -O.21 0.04
t 0.42 -1.10 0.08 -0.73 1.35 -1.98 0.85 -0.36 1.09 -1.22 0.22
MILK -0.18 0.47 0.21 1.09 0.49 -1.26 -0.65 -0.06 0.50 0.05 0.25
t -0.69 1.15 1.43 3.18 1.04 -2.15 -l.92 -0.15 0.67 0.29 1.40
BBEER 0.14 0.68 -0.01 0.39 -0.13 -0.55 1.06 0.58 0.86 -0.05 0.41
t 0.51 1.54 -0.03 0.96 -0.22 -0.83 2.31 1.27 0.91 -0.27 2.11
SBEER -0.39 -0.80 -0.30 1.05 -0.90 —0.08 0.70 1.33 0.96 -0.45 -0.05
t -l.55 -1.86 —l.86 3.40 -2.36 -0.15 2.66 3.92 1.56 -2.38 -0.27
FBEER 0.12 0.49 -0.17 -l.07 -0.4l -l.24 0.26 -0.33 1.87 0.01 -0.35
t 0.28 0.70 -0.65 -l.82 -0.51 -1.25 0.45 -0.50 1.45 0.02 -1.15

OIL -0.25 -0.12 0.09 0.26 0.67 0.07 -0.18 0.01 0.08 0.07 -0.14

t -l.62 -0.44 0.90 1.36 2.81 0.22 -1.06 0.05 0.21 0.62 -1.24
SALT -0.01 0.01 0.00 -0.02 0.12 0.03 -0.05 0.09 0.03 -0.05 -0.11
t -0.15 0.06 0.04 -0.21 1.41 0.18 -0.86 1.11 0.21 -0.60 -1.41
SUGAR 0.19 -0.17 0.05 0.14 1.43 -1.03 -0.52 0.13 0.44 0.24 0.10
t 1.02 -0.59 0.44 0.57 4.34 -2.48 -2.21 0.49 0.83 1.84 0.77
MEALS -0.04 -0.10 0.20 -0.01 0.30 -0.83 0.55 -0.37 0.49 0.04 0.16
t -0.27 -0.38 2.19 -0.06 0.71 -2.02 1.69 -1.28 0.73 0.38 1.40

280

 

Dependent
variable BEEF MEAT MILK BBR SBR FBR OIL SALT SUGR MEAL
(share) ai12 ail3 ail4 ails ai16 ail7 ai18 ail9 ai20 ai21
SORGH -0.03 0.10 -0.18 0.14 -0.39 0.12 -0.25 -0.01 0.19 -0.04
t -0.15 0.42 -0.69 0.51 -1.55 0.28 -1.62 -0.15 1.02 -0.27
RICE 0.19 -0.42 0.47 0.68 -0.80 0.49 -0.12 0.01 -0.17 -0.10
t 0.49 -l.10 1.15 1.54 -l.86 0.70 -0.44 0.06 —0.59 -0.38
BREAD -0.04 0.01 0.21 -0.01 -0.30 -0.17 0.09 0.00 0.05 0.20
t -0.27 0.08 1.43 -0.03 -1.86 -0.65 0.90 0.04 0.44 2.19
CASSA 0.32 -0.22 1.09 0.39 1.05 -1.07 0.26 -0.02 0.14 -0.01
t 1.04 -0.73 3.18 0.96 3.40 -1.82 1.36 -0.21 0.57 -0.06
SWPOT 0.72 0.53 0.49 -0.13 -0.90 -0.41 0.67 0.12 1.43 0.30
t 1.77 1.35 1.04 -0.22 -2.36 -0.51 2.81 1.41 4.34 0.71
WHPOT -0.64 -1.05 -1.26 -0.55 -0.08 -l.24 0.07 0.03 -l.03 -0.83
t -1.20 -l.98 -2.15 -0.83 -0.15 -1.25 0.22 0.18 -2.48 -2.02
BANAN -0.13 0.24 -0.65 1.06 0.70 0.26 -0.18 -0.05 -0.52 0.55
t -0.47 0.85 -1.92 2.31 2.66 0.45 -1.06 -0.86 -2.21 1.69
CASFL -0.31 -0.12 -0.06 0.58 1.33 -0.33 0.01 0.09 0.13 -0.37
t -0.89 —0.36 -0.15 1.27 3.92 -0.50 0.05 1.11 0.49 -1.28
BEANS 0.48 -0.69 0.50 -0.86 -0.96 -l.87 0.08 -0.03 -0.44 -0.49
t 0.74 -1.09 0.67 -0.91 -1.56 -l.45 0.21 -0.21 -0.83 -0.73
PEAS -0.04 -0.21 0.05 -0.05 -0.45 0.01 0.07 -0.05 0.24 0.04
t -0.25 -l.22 0.29 -0.27 -2.38 0.02 0.62 -0.60 1.84 0.38
VEGET 0.03 0.04 0.25 0.41 -0.05 -0.35 -0.14 -0.11 0.10 0.16
t 0.20 0.22 1.40 2.11 -0.27 -1.15 -l.24 -l.41 0.77 1.40
BEEF -0.07 -O.28 0.18 0.36 -0.03 -1.27 0.13 0.02 -0.18 0.45
t —0.18 -0.97 0.54 0.89 -0.08 -2.22 0.73 0.22 -0.74 1.71
MEAT -0.28 -0.43 0.18 0.41 -0.75 1.62 -0.12 -0.05 -0.03 -0.14
t -0.97 -l.05 0.56 1.04 -2.59 2.90 -0.67 -0.66 -0.15 -0.56
MILK 0.18 0.18 1.25 0.40 0.12 -0.46 -0.02 0.04 -0.87 0.67
t 0.54 0.56 2.32 0.83 0.38 -0.69 -0.09 0.52 -3.18 2.15
BBEER 0.36 0.41 0.40 -5.51 -0.38 0.91 0.31 -0.01 0.45 -0.63
t 0.89 1.04 0.83 -5.72 -1.03 1.08 1.31 -0.09 1.34 -1.21
SBEER -0.03 -0.75 0.12 -0.38 -0.39 2.31 -0.07 -0.10 0.89 -0.06
t -0.08 -2.59 0.38 -1.03 -0.93 4.24 -0.38 -1.17 3.88 -0.27
FBEER -l.27 1.62 -0.46 0.91 2.31 -0.54 -0.61 -0.05 -0.27 1.00
t -2.22 2.90 -0.69 1.08 4.24 -0.34 -l.80 -0.37 -0.58 1.78
OIL 0.13 -0.12 -0.02 0.31 -0.07 -0.61 0.04 -0.01 0.05 0.11
t 0.73 -0.67 -0.09 1.31 -0.38 -1.80 0.26 -0.14 0.38 0.79
SALT 0.02 -0.05 0.04 -0.01 -0.10 -0.05 -0.01 0.49 0.01 -0.07
t 0.22 -0.66 0.52 -0.09 -l.l7 -0.37 -0.14 3.86 0.14 -l.52
SUGAR -0.18 -0.03 -0.87 0.45 0.89 -0.27 0.05 0.01 0.04 0.35
t -0.74 -0.15 -3.18 1.34 3.88 -0.58 0.38 0.14 0.14 1.55
MEALS 0.45 -0.14 0.67 -0.63 -0.06 1.00 0.11 -0.07 0.35 -1.25
t 1.71 -0.56 2.15 -l.21 -0.27 1.78 0.79 -1.52 1.55 -1.57

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