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THE INFLUENCE OF DEMAND MODEL SELECTION ON
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THE INFLUENCE OF DEMAND MODEL SELECTION ON HOUSEHOLD
WELFARE ESTIMATES: AN APPLICATION TO SOUTH AFRICAN FOOD
EXPENDITURES
By

Lesiba Elias Bopape

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

DOCTOR OF PHILOSOPHY
Department of Agricultural Economics

2006

ABSTRACT

THE INFLUENCE OF DEMAND MODEL SELECTION ON HOUSEHOLD
WELFARE ESTIMATES: AN APPLICATION TO SOUTH AFRICAN FOOD
EXPENDITURES

By

Lesiba Elias Bopape

This study analyzes food expenditure patterns in South Africa, taking into account
differences in demand behavior across rural and urban households, as well as across
income groups. The study makes three main contributions from this study. First, it
develops a Lagrange Multiplier (LM) test that can be used to determine whether the
demand model should be speciﬁed with a quadratic or a linear expenditure term. The
advantage of this test over the Wald test, which is based on the signiﬁcance of the
quadratic expenditure term in the demand model, is that it can be conducted without
having to explicitly estimate the quadratic (in expenditure) demand model, which tends to
be highly nonlinear. Second, the study examines the effects on household welfare of an
indirect food tax reform, and evaluates the magnitude of the biases in the welfare
estimates due to demand model is misspeciﬁcation. The tax reform evaluated is the zero-
rating of value-added tax (VAT) on meat products. Lastly, this study examines the
differences in the consumption patterns between rural and urban households, and across
households in different income groups. The study makes use of panel data on household
food consumption in South Africa, collected as part of the KwaZulu-Natal Income

Dynamics Study.

Results from both the LM and the Wald tests support the inclusion of the
quadratic expenditure term. The implication of this ﬁnding is that popular functional
forms such as the almost ideal demand system (AIDS), which have Engel curves that are
linear in expenditure, would not give an accurate picture of demand behavior of the
households considered in this study. Given these ﬁndings, this study estimates the
quadratic almost ideal demand system (QUAIDS), which a generalization of AIDS that
allows for a quadratic relationship between budget shares and expenditure. The QUAIDS
model is used to estimate demand functions for seven food groups—grains, meat and
ﬁsh, fruits and vegetables, dairy, oils and fats, sugar, and other foods. The endogeneity of
expenditure in the demand model is explicitly tested and, where necessary, corrected for
using the control function approach. The model is also adjusted to account for a large
fraction of observed zero expenditures using a two-step procedure appropriate for
equation system estimation.

Five of the seven food groups were found to be expenditure elastic, the exceptions
being meat and ﬁsh and other foods. Demand behavior differs signiﬁcantly between rural
and urban households, as well as across income groups, implying that an accurate
analysis of expenditure patterns in South Africa requires a disaggregated analysis that
takes into account this heterogeneity in demand behavior. All households gain from the
removal of VAT on meat, with welfare gains being larger for high-income households.
On average, the AIDS expenditure elasticity estimates tend to be larger than the estimates
based on QUAIDS. The AIDS model was also found to systematically overstate the
welfare gains of the tax reform considered on this study, particularly for households with

large expenditure levels.

Copyright by
LESIBA ELIAS BOPAPE
2006

To My Family
For Your Encouragement and Support

ACKNOWLEDGEMENTS

This dissertation is the product of joint efforts by many individuals, to whom I
owe sincere gratitude. I am greatly indebted to the chair of my guidance committee,
Professor Robert Myers, whose technical and professional advice most students can only
hope for. The ingenious comments and suggestions from Professor Jeffrey Wooldridge
greatly improved the quality of the methods used in this study. I also thank Professors
John Staatz and Kellie Raper for their invaluable comments and suggestions during the
various stages of this dissertation.

The technical support from Dr. Brian Poi of StataCorp greatly expedited the
completion of this research. Professors Michael Carter of the University of Wisconsin,
Julian May of the University of KwaZulu-Natal, and Ingrid Woolard of the University of
Cape Town facilitated my access to the KIDS dataset. Dr. Jorge Agiiero answered many
of the questions I had on the technical details of the dataset.

This research was made possible by the ﬁnancial support from the Department Of '
Agricultural Economics at Michigan State University, Mandela Economics Scholars
Program, the National Research Foundation of South Aﬁica, and the Agricultural
Research Council of South Africa.

I am greatly indebted to my friends and colleagues whose support during the four
years I spent in Michigan greatly lightened the task of completing my studies. We
trekked through the heavy Michigan snow with Gerald Nyambane for stimulating and
intellectual discussions at the Peanut Barrel. My study partners, Lilian Kirimi and Mary

Mathenge, still have to convince me on the workings of the Law of Iterated Expectations.

vi

At last, I was able to convince my friend Elan Satriawan that I tackled endogeneity
adequately in my model. I admire the ingenuity of Khathutshelo Sikhitha. Special
mention also goes to the following individuals: Yanyan Liu, Anthony Chapoto, Wei
Zhang, Ben Moholwa, Hikuepi Katjiuongua, Sindi Kirimi, Shauﬁque Sidique, Rui
Benﬁca, Zhiying Xu, Vandana Yadav, Nomalanga Grootboom, and Annah Molosiwa.

I am deeply thankful to the love, support, and encouragement of my wife, Letta,
and our two beautiful daughters, Napyadi and Pheladi. My family in South Africa made
huge sacriﬁces during the long years of my graduate studies. My mother and late father
have always believed in the power of education to transform lives. The weekend calls to
my brothers Simon, Jonas, and Tshepo, and my sisters Maria and Monene, sustained my

motivation.

vii

TABLE OF CONTENTS

LIST OF TABLES .............................................................................................................. x
LIST OF FIGURES ......................................................................................................... xiii
CHAPTER ONE: INTRODUCTION .............................................................................. l
1 . 1 Introduction .................................................................................................... 1
1.2 Research Gap and Study Motivation ............................................................. 2
1.3 Objectives of the study ................................................................................... 6
1.4 Organization of the Dissertation .................................................................... 7
CHAPTER TWO: REVIEW OF RELATED LITERATURE ......................................... 8
2. 1 Introduction .................................................................................................... 8
2.2 Commodity Grouping and Separability ......................................................... 8
2.3 Modeling Preferences .................................................................................. 11
2.4 Demographic Variables in Demand ............................................................. 17
2.5 Observed Zero Expenditures ........................................................................ 22
2.6 Chapter Summary ........................................................................................ 29
CHAPTER THREE: EMPIRICAL MODEL ................................................................. 3O
3. 1 Introduction .................................................................................................. 30
3.2 Empirical Model .......................................................................................... 30
3.2.1 Quadratic Almost Ideal Demand System: The General Form ..................... 31
3.2.2 Quadratic Almost Ideal Demand System: The Estimation Form ................ 35

3.3 Estimation .................................................................................................... 38
3.3.1 A Test for Nonlinearity of the Demand Model ............................................ 41
3.3.2 Nonlinear Estimation ................................................................................... 44

3.4 Econometric Issues ...................................................................................... 45
3.4.1 Attrition ........................................................................................................ 45
3.4.2 Expenditure Endogeneity ............................................................................. 49
3.4.3 Observed Zero Expenditures ........................................................................ 51

3.5 Chapter Summary ........................................................................................ 54
CHAPTER FOUR: DATA SOURCES AND DESCRIPTION ..................................... 55
4. 1 Introduction .................................................................................................. 55
4.2 Surveys and Data Description ...................................................................... 55
4.3 Background Information: KwaZulu-Natal Province ................................... 59
4.4 Descriptive Statistics .................................................................................... 60
4.5 Zero-Expenditure ......................................................................................... 67
4.6 Chapter Summary ........................................................................................ 68
CHAPTER FIVE: _EMPIRICAL RESULTS ................................................................. 7O
5. 1 Introduction .................................................................................................. 70
5.2 Attrition ........................................................................................................ 70

viii

5.2.1 Difference-of-means tests for major outcomes and control variables ......... 71
5.2.2 A probit model for probability of attrition ................................................... 74
5.2.3 Difference-of-coefﬁcient tests: attritors versus nonattritors ........................ 76

5.3 Nonlinearity ................................................................................................. 78
5.3.1 LM test results: OLS and SUR estimations ..................................................... 78
5.3.2 LM test results: IV-ZSLS and 3SLS estimations ............................................. 80

5.4 Demand Model Results ................................................................................ 85
5.4.1. The effects of controlling for expenditure endogeneity ............................ 94
5.4.2. The effects of home production ................................................................ 94
5.4.3. The effects of attrition ............................................................................... 95
5.4.4. The effects of excluding the quadratic expenditure term .......................... 95
5.4.5. The effect of imposing linearity ................................................................ 99

5.5 Rural-Urban and Income-Groups Differences ........................................... 100
5.6 The Problem of Observed Zero Expenditures ........................................... 109
5.7 Implications of demand model selection for welfare measures ................. 111
5.8 Comparison with previous studies ............................................................. 119
5.9 Chapter summary ....................................................................................... 123
APPENDIX A ................................................................................................................. 125
ADDITIONAL RESULTS FOR CHAPTER FIVE ....................................................... 125
CHAPTER SIX: SUMMARY AND CONCLUSIONS .............................................. 148
6.1 Summary .................................................................................................... 148
6.2 Conclusions ................................................................................................ 152
REFERENCES ............................................................................................................... 154

ix

Table 4.1

Table 4.2

Table 4.3

Table 4.4

Table 4.5

Table 4.6

Table 5.1

Table 5.2

Table 5.3

Table 5.4

Table 5.5

Table 5.6

Table 5.7

Table 5.8

Table 5.9

Table 5.10

LIST OF TABLES

Average Budget Shares of Broad Consumption Goods ................................ 61
The Composition of Composite Food Commodity Groups .......................... 63
Average Budget Shares and Prices of the Food Groups ............................... 63
Income-groups and Rural-urban differences: Budget shares and prices ...... 65

Summary statistics of household composition variables .............................. 66

Proportions of households with zero consumption for various food groups

...................................................................................................................... 68
Differences-of-Means Tests between the Attritors and Nonattritors in KIDS
1993 .............................................................................................................. 72
A Selection Probit Model for analyzing Attrition between KIDS Panel
Waves ........................................................................................................... 75
Testing Impact of Attrition on the Coefﬁcients of the Budget Share
Equations for the Individual Food Groups ................................................... 78
Tests for Nonlinearity of the Demand System based on Statistical
Signiﬁcance of ............................................................................................. 79
Results of the Test for the Endogeneity of Expenditure ............................... 83

Tests Endogeneity of Expenditure, and for the Statistical Signiﬁcance of
Lambda in the demographically-extended QUAIDS Model ....................... 88

Results of the Wald Tests for Demographic effects, Structural Change, and
Seasonality ................................................................................................... 91

Expenditure Elasticities estimated from QUAIDS Models with and without
Endogeneity Adjustments ............................................................................ 92

Own-price elasticities estimated from QUAIDS models with and without
endogeneity adjustments .............................................................................. 93

Expenditure Elasticities estimated from LA/AIDS and AIDS models with
and without endogeneity adj ustrnents .......................................................... 96

Table 5.1 1

Table 5.14

Table 5.15

Table 5.16

Table 5.17

Table 5.18

Table 5.19
Table 5.20
Table A1
Table A2
Table A3

Table A4

Own-price elasticities estimated from LA/AIDS and AIDS models with and

without endogeneity adjustments ................................................................. 98
Estimated Expenditure Elasticities: Rural-Urban and Income Group
Differences ................................................................................................. 106
Estimated Marshallian and Hicksian Own Price Elasticities ...................... 108
Expenditure and Own Price Elasticities for the Dairy Commodity with
adjustment for the Zero-Expenditure Problem .......................................... 111
Average Welfare Effects of Zero-Rating VAT on Meat ............................ 115
Average Welfare Gains of Zero-Rating VAT on Meat: Rural-Urban and
Income Group Differences ......................................................................... 118
Estimates of Elasticities in South Aﬁica: Previous Studies ....................... 120

Comparison of elasticities from different demand model speciﬁcations.... 121

The estimated reduced forms for expenditure and expenditure—squared 125

The estimated reduced forms for individual commodity groups ................ 126
Parameter estimates for QUAIDS with and without endogeneity-
adjustrnent .................................................................................................. 127
Own and Cross Price Elasticities estimated from the QUAIDS Mmodel with

and without Endogeneity Adjustment ........................................................ 130

Table A5 (Part I) Expenditure and Price Elasticities estimated using Data from only

Households who do not engage in Own-production .................................. 132

Table A5 (Part II) Expenditure and Price Elasticities estimated using Data on all

Table A6

Table A7

Table A8

Table A9

Table A10

Households including those who Attrited .................................................. 133
Parameter Estimates from the AIDS Model with and without Endogeneity
Ajustment ................................................................................................... 134
Own and Cross Price Elasticities estimated from the AIDS Model with and
without Endogeneity-Adjustment .............................................................. 136
Parameter Estimates for QUAIDS: Rural-Urban Differences .................... 138
Own and Cross Price Elasticities: Rural-Urban Differences ...................... 140

Parameter Estimates of the QUAIDS Model: Income-Groups Differences 142

xi

Table All Own and Cross Price Elasticities: Income-Group Differences ................... 145

xii

LIST OF FIGURES

Figure 5.1 Welfare Gain due to Removal of 14% VAT on Meat: Compensated
Variation .................................................................................................... 114

Figure 5.2 Welfare Gain due to Removal of 14% VAT on Meat: Equivalent Variation

.................................................................................................................... 114
Figure 5.3 The Distribution of Welfare Gains ............................................................. 116
Figure 5.4 Bias in Welfare Gain from Using the Nonlinear AIDS Model ................... 117
Figure 5.5 Bias in Welfare Gain from Using the LA/AIDS Model ............................. 117

xiii

CHAPTER ONE

INTRODUCTION

1.1 Introduction

Aggregate per capita availability data suggest that South Africa is food secure in
almost all basic foodstuffs. Furthermore, South Africa has the highest per capita income
in Sub-Saharan Africa, and is categorized as a middle-income country with average per
capita gross national income of US $3,650 in 2004 (World Bank, 2004). These facts
suggest that hunger and food security should not be major policy issues in the country.
However, these aggregate data mask a highly unequal distribution Of income and a huge
divide between relatively affluent urban areas and destitute conditions in many rural
communities. The richest 20% of the population receives over 60% of the income while
the poorest 20% receives less than 3% (World Development Report, 2002). At the
household level, over 30% of the population is categorized as vulnerable to food
insecurity and over 20% of the children are estimated to be stunted and vitamin A
deﬁcient (Human Science Research Council, 2004).

Policies designed to reduce income inequality, hunger, and malnutrition, have had
mixed results. Major social, economic, and political reforms introduced since the demise
of apartheid and the emergence of democratic government in 1994 have obviously
redistributed wealth. But income inequality and household food insecurity remain. One of
the problems is that little is known about how food expenditure patterns differ across
different income groups, and across different geographic regions. Without a thorough

understanding of the heterogeneity of food expenditure patterns, and how these patterns

are changing over time, it will continue to be difﬁcult to design policies that improve
food security effectively over a broad range of heterogeneous low-income households.
An accurate assessment of the distributional impacts of policies such as commodity tax
reform requires accurate estimates of price and income effects, and how these differ
across households in different socioeconomic groups.

This study seeks to improve knowledge and understanding of the heterogeneity in
food expenditure patterns in South Africa. The study makes use of an unusually rich
panel dataset on household food consumption, collected as part of the KwaZulu-Natal
Income Dynamics Study (KIDS). The KIDS dataset contains detailed information on
household socioeconomic and demographic characteristics, which permit heterogeneity
effects to be analyzed. The dataset followed the same households over a ten-year period,
with surveys in 1993, 1998, and 2004, to study changes in their incomes, expenditures,
and poverty levels. Data on prices and expenditures on various food products consumed
by households were also collected.

This study utilizes the KIDS data to estimate demand functions for seven food
groups—grains, meat and ﬁsh, fruits and vegetables, dairy, oils and fats, sugar, and all
other foods. Household locations, socioeconomic characteristics, and income levels are

used to explain heterogeneity in food expenditure patterns.

1.2 Research Gap and Study Motivation
This study makes three main contributions. First, to the best of our knowledge
this study is the only theoretically consistent panel data study of food consumption in

South Africa done to date. Previous studies on food consumption in South Aﬁica have

either been limited to examining only one commodity (e. g., Taljaard, 2003; Nieuwoudt,
1998; Poonyth et al., 2001) or have used highly aggregated composite commodity
deﬁnitions, and typically ignored any impact of demographic factors on food demand
(Bowmaker and Nieuwoudt, 1990; Liebenberg and Groenewald, 1997). The only
theoretically consistent study of food demand in South Africa we are aware of that uses
micro-level data incorporating household demographic characteristics is by Agbola
(2003). However, Agbola uses cross-sectional data that was collected in 1993—one year
prior to South Africa’s ﬁrst democratic government. Clearly, such data do not capture
periods of important social and economic reforms that affect households’ proﬁles and,
hence, their food consumption patterns. As earlier mentioned, South Aﬁica became a
democracy in 1994 and as a result major policies were implemented with implications
that the study by Agbola (2003) does not capture. The KIDS panel dataset allows for
greater price variability across the sample, and also covers most of the period associated
with major policy reforms in South Africa.

Unlike most previous food demand studies, this study explicitly tests for the
endogeneity of expenditure in the budget share equations, and then controls for it. Among
existing food demand studies, only LaFrance (1991) and Dhar et al. (2003) consider the
problem of expenditure endogeneity. Expenditure endogeneity may arise whenever the
household expenditure allocation process across food groups is correlated with other
factors not captured by the explanatory variables used in demand estimation (i.e., bundled
in the error term). In this case, least squares estimation of the demand model gives

inconsistent parameter estimates. This study takes advantage of recent advances in

econometric methods designed to overcome this problem, and to enhance demand
estimation with micro level panel data.

We estimate a quadratic almost ideal demand system (QUAIDS) controlling for
expenditure endogeneity, and explicitly accounting for the problem of observed zero-
expenditures. Most of the previous food demand studies in South Africa use the almost
ideal demand system (AIDS) model. The shortcoming of the AIDS model is that it
assumes linear Engel curves and constant expenditure elasticity. Such assumptions have
been shown to be restrictive, even in developing countries (examples include Meekashi
and Ray (1999) and Abdulai (2004)).

Furthermore, because of high income inequality and large disparities in the
economic conditions between rural and urban households in South Africa, pooling data
across all households obscures important information on variability in demand behavior
across households in different socioeconomic and demographic groups. To determine the
impact of this household heterogeneity on demand, this study analyzes separately the
food expenditure patterns of rural and urban households, as well as households in
different income groups.

Second, this study builds on the work of Banks et al. (1997) to develop a test that
can be used to determine whether the demand model should be speciﬁed with a quadratic
(QUAIDS) or a linear (AIDS) expenditure variable. In particular, the implication of
corollary 2 in Banks et al. (p.533) is that a utility-derived demand system that is rank 3

and exactly aggregable cannot have coefficients on both the linear and the quadratic

expenditure terms that are independent of prices.l In other words, if such a demand model
has a coefﬁcient on the linear expenditure term that is independent of prices, then it must
have a coefﬁcient on the quadratic expenditure term that is price dependent. This study
uses Bank et al.’s corollary 2 to develop a Lagrange Multiplier (LM) test that allows one
to determine whether or not a QUAIDS speciﬁcation is necessary. No other study was
found to have explicitly conducted this test, certainly not with South Aﬁican data. Hence,
this study provides richer information on food consumption behavior in South Africa than
has been obtained from existing studies.

Finally, the study examines the effects on household welfare of zero-rating the
value-added tax (VAT) on meat products.2 While most of the basic food commodities
such as grains, milk, fruits and vegetables are zero-rated in South Africa, meat is not.
Meat is taxed at the standard VAT rate of 14%. Whether or not meat should be zero-rated
has been a subject of contention between the government and lobby groups (most notably
the Congress of South African Trade Unions) since the introduction of VAT in 1991
(Watkinson and Makgetla, 2002). This study contributes to this issue by providing
quantitative measures of the impacts of this tax reform on household welfare. We use the
QUAIDS parameter estimates to calculate indirect utilities before and aﬁer the tax
reform. These are then used to compute two money metric welfare measures of the tax
effect, namely compensating variation and equivalent variation. To determine the

sensitivity of these welfare measures to demand model selection, and the bias that results

 

' As will be made clearer below, the rank of a demand system has implications for aggregation and the non-
linearity of Engel curves. Higher rank models are well suited to approximate non-linear Engel curves oﬁen
found in empirical analyses. QUAIDS has a rank of 3.

2 A commodity is zero-rated if it is taxable, but taxed at a rate of 0%. Zero-rating a commodity is different
from exempting it; by law, exempted commodities cannot be taxed (i.e., they are not taxable).

when a restrictive functional form is used, we also estimate these welfare measures using
parameters from the (nonlinear and linear) AIDS model. There are no studies we are
aware of that compute these welfare measures for South Africa, certainly not with this

dataset.

1.3 Objectives of the study

The broad objective of this study is to analyze the responsiveness of South
African households to food price and income changes as well as other relevant
socioeconomic factors, particularly focusing on the KwaZulu-Natal Province. This
objective is accomplished by estimating a food demand model using appropriate
econometric techniques.
The speciﬁc objectives are:

1. To estimate a household food demand model for South Africa. The
model accounts for the effects of demographic and socioeconomic
characteristics, and explicitly controls for expenditure endogeneity and
observed zero expenditures.

2. To determine how food expenditure patterns differ across rural and
urban households, as well as across income groups.

3. To estimate price and expenditure elasticities of demand for food using
the model from objective (1), and to evaluate how these differ across
rural and urban households as well as across households in different

income groups.

4. To examine the effects on household welfare of zero-rating the value-

added tax (VAT) on meat products

The results of this study will provide important insights into food policy
formulation and implementation in South Aﬁica. In particular, accounting for household
heterogeneity in demand has implications on the likely effects of alternative policies on
food consumption and food safety nets. These results should be particularly useful in
implementation of the national food security strategy—the Integrated Food Security
Strategy, established in 2002 by the South African cabinet—which emphasizes
improvements in household-level nutrition and increases in the provision of food safety
nets. These policies can be made more effective if they are based on behavioral

parameters speciﬁc to particular demographic and socioeconomic groups.

1.4 Organization of the Dissertation

The rest of the dissertation is organized as follows. The next chapter presents a
review of related literature. The relationship between utility maximization theory and
demand functional forms is discussed, and a review of alternative approaches to
modeling preferences is provided. Chapter three presents the empirical model and
discusses various econometric tests to be implemented. Chapter four describes the survey
and data sources, and then presents a descriptive analysis of expenditure patterns across
time and household groups. Chapter ﬁve presents the empirical results, while Chapter six

concludes with a summary and conclusions.

CHAPTER TWO

REVIEW OF RELATED LITERATURE

2.1 Introduction

This chapter reviews the literature on the theory and empirical estimation of
consumer demand. The ﬁrst section discusses various approaches to restricting a large
number of goods in the consumer’s utility maximization problem to a smaller number,
more manageable for empirical estimation. This is followed by section 2.3 which
discusses demand system functional forms, and the assumptions about their underlying
preferences. The various methods for incorporating demographic variables are discussed
in section 2.4. This is followed by a review of the literature on censored demand

modeling. The ﬁnal section summarizes the key points in this chapter.

2.2 Commodity Grouping and Separability

In the standard utility maximization problem, a consumer makes budget allocation
decisions on large numbers of goods with different relative prices. The solution to this
problem gives the amount demanded of each good as a function of its price, prices of
other goods, and the consumer’s income. However, when the number of goods involved
is too large, the consumer’s allocation problem becomes complex for the empirical
analyst. The problem of ﬁnding theoretically appealing approaches to reducing this large
number of goods to a relatively small and more manageable number has attracted, and
continues to attract, attention in the demand literature. The literature proposes two

alternative approaches; one that groups commodities based on the behavior of their

relative prices—the composite commodity theorem—; and another that makes
assumptions about the consumers’ preferences—separability and two-stage budgeting.

Originally proposed by Hicks (1936) and Leontief (1936), the composite
commodity theorem asserts that, if a group of prices move in parallel, then the
corresponding group of commodities can be treated as a single good. The price and
quantity indices of the commodity groups are used to derive an expenditure function that
satisﬁes the usual properties of expenditure functions (increasing in utility and prices,
concave in prices, and linearly homogenous).

The usefulness of the composite commodity theorem in constructing commodity
groupings for empirical analysis is limited (Deaton and Muellbauer, 1980a). One source
of limitation is that relative prices ﬂuctuate considerably in practice. Also, it would be
difﬁcult to justify some of the aggregates that are imposed. For example, a relatively
volatile price of meat would prevent it being grouped with other foods whose prices are
relatively stable.

In an attempt to circumvent some of these limitations, Lewbel (1996) develops a
generalized composite commodity theorem, which is an extension of original Hicks-
Leontief idea. The generalized composite commodity theorem relaxes the assumption of
perfect correlation among group prices and instead allows for less than perfect co-
movement among intra-group prices. It assumes that the distribution of an individual
commodity’s price is independent of the composite group price, and tests for the
generalized composite commodity theorem are based on cointegration relationships
between each of the good’s prices and the price indices of groups to which they belong.

Interesting applications of Lewbel’s generalized composite commodity theorem are by

Davis (2003) and Reed et al. (2005). Davis extends Lewbel’s bivariate Engel-Granger
testing approach to a multivatiate framework, while Reed et al. applies the generalized
composite commodity theorem to nonlinear demand systems.

In contrast to the composite commodity theorem which relies on an external
factor (namely, the constancy of relative prices) to deﬁne commodity groups, separability
deﬁnes commodity groups using consumer preferences themselves. If preferences are
weakly separable, then commodities can be partitioned into groups so that preferences
within groups can be described independently of consumption in other groups. This
implies that a subutility function can be deﬁned for each group, so that the values of each
of these subutilities can be added to give total utility. The concept of a utility tree,
proposed by Strotz (1957, 1959), allows consumers to break a decision into multiple
steps. A closely related concept is two-stage budgeting, which hypothesizes that
consumers ﬁrst allocate total expenditure to broad groups of goods (the ﬁrst stage) and
then allocate each group expenditure to the individual commodities in that group (the
second stage). Weak separability is both necessary and sufﬁcient for the second stage of
two-stage budgeting (Deaton and Muellbauer, 1980a).

Several studies attempt to empirically test the restrictions imposed by separability
within ﬂexible demand systems. These studies derive functional relationships that must
hold between goods that belong to the same group and goods that belong to other groups,
expressed in terms of price and expenditure elasticities. They then econometrically test
for whether these relationships are supported by data. Included in these studies are those
by Bales and Unnevehr (1988), Moschini (1992), Moschini et al. (1994), Nayga and

Capps (1994), Edgerton (1997), and Carpentier and Guyomard (2001).

10

However, there are a number of problems associated with the tests mentioned
above. One of the problems, as mentioned by Lewbel (1996), is that weak separability
restrictions require that group prices depend on the parameters of the individual’s utility
function. Also, separability restrictions are difﬁcult to test powerfully due to the
multicollinearity of aggregate price data. In the context of this study, a more important
problem with both the tests for separability and commodity groupings is that they have
been developed within the context of time series data. Their implementability in the
context of cross-sectional or panel data is limited. Given that this study uses panel data,
we will follow the ‘traditional’ approach of maintaining the assumption of weak
separability between foods and all other broad consumption goods. The food items that
are closely related will then be grouped together into composite food commodities, where

a group comprises items that are closely substitutable.

2.3 Modeling Preferences

The preference-based approach to modeling choice behavior treats the
individual’s tastes, summarized by a preference relation, as his or her primitive
characteristic. The theory is developed by ﬁrst imposing rationality axioms on the
individual’s preferences and then analyzing the consequences of these preferences on his
or her choice behavior.

The preference-based approach to modeling choice behavior provides a useful
framework for analyzing data on demand. Functional forms proposed for the econometric
analysis of these data can be evaluated in terms of whether they are consistent with

theory. Failure of data to conform to theoretical predictions may indicate excessive

11

restrictiveness of the chosen functional form. It may also mean that people do not behave
as theory suggests. When the chosen functional form gives meaningful results, then it
becomes the basis for estimating such demand behavioral parameters as price and income
elasticities.

The earliest empirical demand studies are characterized by extensive use of single
equation methodology. At the center of these analyses has been the measurement of
elasticities. The requirement that demand systems satisfy properties such as adding-up
was ignored and perhaps unimportant because these early studies considered only a
fraction of the total budget (Deaton and Muellbauer, 1980a). This made it tempting to
choose explanatory variables pragmatically with the goal of getting better model ﬁts.

The single equation approach to demand modeling changed with the introduction
by Stone (1954) of the linear expenditure system (LES). The LES was among the ﬁrst
attempts to derive utility-based demand models. The derivation of LES imposes
theoretical restrictions of adding-up, homogeneity, and symmetry. Among the
implications of the LES are that goods cannot be inferior and that all goods must be
substitutes, which obviously makes it too restrictive a functional form to model demand,
except for cases where commodities are grouped into very broad categories so that it is
reasonable not to expect inferiority or complementarity among them. Also, while the
imposition of the theoretical restrictions helps generate degrees of freedom, it also forces
the analyst to take theoretical restrictions as given (because these restrictions are
embedded in the model). An interesting alternative is one that allows restrictions to be

tested empirically.

12

The Rotterdam model proposed by Theil (1965) and estimated by Barten (1969)
allows for restrictions to be tested statistically. In many ways, the approach followed in
deriving the Rotterdam model is similar to Stone’s, except the Rotterdam model is
speciﬁed using variables in ﬁrst-differences. Like the LES, the derivation of the
Rotterdam model emphasized the use of theoretical restrictions to generate degrees of
ﬁ'eedom. Among the limitations of the Rotterdam model are that it imposes constant price
and expenditure elasticities and that it typically does not satisfy theoretical restrictions
when applied to data (Deaton and Muellbauer, 1980a).

It became apparent that specifying functional forms using theoretical restrictions
to generate degrees of freedom did not offer much promise. It was partly for this reason
that research in the 19705 focused on developing ﬂexible functional forms. This approach
entailed approximating the direct utility function, the indirect utility ﬁtnction, or the cost
function with some speciﬁc functional form that has enough parameters to be regarded as
a reasonable approximation to whatever the true unknown function might be. Important
contributions in this regard were the transcendental logarithmic (translog) model of
Christensen, J orgensen, and Lau (1975) and the almost ideal demand system (AIDS)
model of Deaton and Muellbauer (1980b).

The indirect translog model (as originally proposed by Christensen et al. (1975))
is derived by applying Roy’s identity to a function that approximates the unknown
indirect utility function by a quadratic form in the logarithms of the price to expenditure
ratios. Unfortunately, the demand functions derived from this indirect utility function are

complicated and difﬁcult to estimate. Its modiﬁed version (J orgenson et al., 1982), the

13

direct translog model, makes the discomforting assumption that, for all goods, prices are
determined by quantities rather than the other way round.

Deaton and Muellbauer’s AIDS model marked an important breakthrough in the
quest for ﬂexible functional forms. In fact, no dramatic advances have been made since
its introduction in 1980, although some reﬁnements (discussed next) have been made.
The particularly desirable properties of AIDS are that it satisﬁes the axioms of choice
exactly and can be interpreted in terms of economic models of consumer behavior when
applied to either aggregate or disaggregate (e. g., household) data. It also allows for
consistent aggregation of individual demands to market demands.

Both AIDS and J orgenson et al.’s translog models are members of the Price-
Independent Generalized Logarithmic (PIGLOG) class of demand models (Muellbauer,
1976), which have budget shares that are linear functions of log total expenditure.
Speciﬁcation of Engel curves (i.e., relationships between a commodity’s budget share
and total expenditure) that are linear functions of log total expenditure are extensions of
the earlier work by Working (1943) and Lesser (1963).

For many commodities, however, there is increasing evidence that Engel curve
analysis based on this Working-Lesser form does not provide an accurate picture of
behavior. Empirical Engel curve studies indicate that further terms in total expenditure
are required for some, if not all, expenditure share equations (Lewbel, 1991; Blundell et
al., 1993). Also, Engel curves may vary with the labor market status and region
(Browning and Meghir, 1991). Banks et al. (1997) generalize PIGLOG preferences to

allow for nonlinearities in total expenditure. We discuss in general terms the differences

l4

in approach to modeling preferences using the PIGLOG class vis-a-vis other general
classes.

Let w,- denote expenditure share of good i (i = 1, , K), x denote total
expenditure, and a(p) denote a price index used to deﬂate total expenditure, where p is a

K-vector of prices. A general form that nest those derived from the PIGLOG class is

w.- = Alp) + B.(p)lnx + C.(p)g(x) (2.1)

where A,(p), B,(p) , C, (p), and g(x) are differentiable functions. Equation (2.1) says that

expenditure shares are linear in log total expenditure and another function of total

expenditure, represented by g(x). Thus, the C ,(p)g(x) term allows for potential
nonlinearity in demands. Engel curves of the PIGLOG class have C, (p) equal to zero, so

that for this class of preferences, demands are modeled as linear functions of In x. Lewbel
(1991) deﬁnes the rank of a demand system as the dimension of the space spanned by its
Engel curves. Based on this deﬁnition, the rank of equation system (2.1) equals the rank

of the N X 3 matrix of Engel curve coefﬁcients, having rows [A,. (p): B,(p): C ,(p)] for

good i (Banks et al., 1997). This matrix has three columns, so 3 is the maximum possible
rank of equation system (2.1). Exactly aggregable demand systems are deﬁned as demand
systems that are linear in functions of x. Gorman (1981) proved that the maximum
possible rank of any exactly aggregable demand system (with any number of terms) is 3.
Thus, based on this theoretical result, there would be little or no gain in adding additional

terms of the form D, (p)h(x) if exact aggregation is desired. In fact, Banks et al. show that

15

all rank 3 exactly aggregable utility-derived demand systems of the form represented by
equation (2.1) have g(x) = (In x)2 . So, given that rank 3 forces g(x) to have this speciﬁc

functional form, budget shares of form (2.1) are quadratic in In x, and therefore, are
quadratic in In x itself.

Banks et al. (1997) also show that rank 3 exactly aggregable demand systems

cannot have both 8, (p) and C, (p) independent of prices. So, the AIDS model has the
form of equation (2.1) with each B, constant (that is, independent of prices) and

every C, = 0. To allow for potential nonlinearity in expenditure, it may be tempting to
consider extending the AIDS model by simply adding a squared expenditure term with a
constant, nonzero coefﬁcient C,. In fact, a number of studies do this (Blundell et.al.,
1993; Labeaga and Puig, 2002; Christensen, 2004; Browing and Collado, 2004).
However, as Banks et al. show (Corollary 2, p. 53 3), B, and C, cannot both be constants

for all commodities i in a rank 3 demand system. Based on these algebraic facts and
restrictions from utility theory, Banks et al. derive an exactly aggregable rank 3 demand
system —the Quadratic Almost Ideal Demand System (QUAIDS).

The QUAIDS model is of the form represented by equation (2.1), with the

- nonlinear expenditure term set to quadratic and its coefﬁcient, C, (p), dependent on prices

via the inverse of a Cobb-Douglas price aggregator. Hence, the QUAIDS model nests the

AIDS model. Due to the restriction by AIDS that B, is constant and C, = 0 , its

expenditure elasticities are constant. In contrast, QUAIDS permits goods to be luxuries at
some expenditure levels and to be necessities at others. In this study, we estimate the

demand parameters and the price and income elasticities using the QUAIDS model, given

16

its generality over AIDS and its other desirable properties to be explained in detail in the
next chapter.

Recently, several demand studies have emerged that conﬁrm the appropriateness
of QUAIDS in modeling preferences. Examples using developed country data include
Abdulai (2002) who applies QUAIDS to the food expenditure data from Switzerland,
Moro and Sckokai (2000) who use Italian food expenditure data, Banks et al. (1997) and
Blundell and Robin (1999) who both use expenditure data on broad consumption goods
from the UK, and Fisher et al. (2001) who apply QUAIDS to the US. aggregate
consumption data. A number of studies in developing countries are also emerging that
support QUAIDS. However, these studies are fewer compared to those from developed
countries. Examples include Abdulai and Aubert (2004) using Tanzanian food
expenditure data, Meenkashi and Ray (1999) using Indian food expenditure data, Gould
and Villarreal (2006) using food expenditure data from urban China, and Molina and Gil

(2005) using aggregate consumption data from Peru.

2.4 Demographic Variables in Demand

Demographic variables such as household size and age composition play an
important role in determining household demand patterns. The treatment of demographic
effects in the context of theoretically plausible demand systems dates back to Barten
(1964). Since Barten’s work, studies proliferated that were aimed at ﬁnding theoretically
consistent techniques to incorporate demographic effects into demand analysis (for a

review, see Pollak and Wales (1992)).

17

Ideally, there are two ways to incorporate demographic effects into a demand
system; one is to use unpooled data and the other to use pooled data (Pollak and Wales,
1978). The ﬁrst approach involves separating the entire dataset into sub-samples with
identical demographic proﬁles and then estimating a demand system for each sub-sample
separately. This approach allows all of the parameters of the demand system to depend on
the demographic variables, so that there is no need to specify the form of the relationship
between the parameters and the demographic variables. The major drawback of this
approach, apart from its apparent inefﬁciency, is that it does not make it possible to draw
inferences about households with one demographic proﬁle from observations on the
behavior of households with different proﬁles.

The second approach, which uses pooled data, involves three separate but
interrelated steps (Pollak and Wales, 1980). The ﬁrst step involves specifying a class of
demand systems for every admissible demographic proﬁle. The second involves
specifying which parameters depend on the demographic variables and which do not, and
the third involves speciﬁcation of a functional form for each parameter which depends on
the demographic variable.

Earlier attempts to incorporate demographic effects into complete demand
systems using pooled data have led to the development of ﬁve general procedures: (i)
demographic scaling of Barten (1964); (ii) Gorman’s (1976) speciﬁcation; (iii) the
reverse-German speciﬁcation; (iv) the modiﬁed Prais-Houthakker procedure; and (iv)
demographic translating of Pollak and Wales (1981). The procedures are general in the
sense that they do not assume the original demand system has a particular functional

form, but can be used in conjunction with any complete demand system.

18

Demographic translation replaces the original demand system, w, (p, m), by
w, (p,m)= 6, + W, (p,m —Z:, p ,6 j ), where the 5’s are translation parameters. Hence,

specifying demographic variables using translation can be viewed as allowing
“subsistence” (typically the intercept) parameters of a demand system to depend on the
demographic variables. Linear demographic translation, speciﬁes demographic variables

as intercept shiﬁers

S
19,-(1): 251%. (2.2)

3:]

where z = (21 , ..., Z5) is a vector of demographic variables, and the 8’s are parameters to be

estimated. Linear demographic translation is the most common speciﬁcation in empirical
demand studies.

Demographic scaling involves applying scaling functions to prices and quantities.
The scaling functions depend on demographic variables, and are interpreted as reﬂecting
the number of ‘equivalent adults” in the household (when the same scaling functions are
the same for all goods), or as measuring the number of equivalent adults on a scale
appropriate to each good (when the scaling functions differ from one good to another).
This procedure leads to the interpretation of the household’s preferences as depending not
on the quantity of the raw commodities it consumes, but on the quantity per equivalent
adult. The challenge when using demographic scaling is the criteria for choosing scaling
functions or for choosing numerical scaling values. The criteria for specifying scaling

functions have been based on such factors as nutritional and physiological needs, poverty

19

measures, and expenditure behavior of households. While such criteria may be intuitively
appealing, they are often inconsistent with theory. Scaling procedures that are made to be
theoretically consistent typically lead to the imposition of implausible behavioral
assumptions, such as zero substitution possibilities among goods (Deaton and
Muellbauer, 1980a).

Gorman (1976) proposed a general form that incorporates demographic
translating and scaling. Gorman’s speciﬁcation is obtained from the original demand
system by ﬁrst scaling and then translating. The “reverse Gorman” speciﬁcation is very
similar to Gorman’s speciﬁcation, except it is obtained ﬁrst by demographic translating
and then scaling. Given that this form proposed by Gorman and its “reverse” version nest
demographic scaling, it inherits the same weaknesses associated with scaling.

Proposed in its original form by Prais and Houthakker (1955), the modiﬁed Prais-
Houthakker procedure incorporates demographic variables into demand equations using a
single income scale and a speciﬁc scale for each good. The Prais-Houthakker procedure
replaces the original demand system by w, (p, m) = s,W, (p, m / so), where the s,~’s are
“speciﬁc scales” for commodities which depend on the demographic variables, and so is

an “income scale” implicitly deﬁned by the budget constraint 2:, p,s,W, (p,m/ s0 ) = m .

However, Prais and Houthakker never reconciled their technique with an overall budget
constraint (Pollak and Wales, 1981). The main limitation in applying the Prais-Houtkker
procedure is that it does not yield a theoretically consistent demand system. Pollak and
Wales (1981) show that this procedure yields theoretically plausible demand systems
only under the very special case where the original demand system corresponds to an

additive direct utility function. The limitation imposed by this additivity restriction is

20

quite severe. The implication of the additivity restriction is that no good (or group of
goods) occupies any special position in the utility function (Deaton and Muellbauer,
1980a). Since the function is additive, new groups can always be created by combining
any others, such that no particular relationship exists between pairs of goods.

Lewbel (1985) extended Gorman’s (1976) procedure by proposing a uniﬁed
approach which combined the ﬁve procedures explained above. Lewbel’s procedure
modiﬁes the expenditure function by ﬁrst replacing each price by a function that depends
on all prices and demographic variables and then subjecting the resulting expenditure
function to a further transformation that depends on all prices and demographic variables.
However, Lewbel’s contribution was mainly theoretical and too general to apply
empirically; hence it has rarely been used in empirical work.

A relatively recent study by Bollino et al. (2000) extends Gorman’s (1976)
procedure by following an approach similar to Lewbel’s. Unlike Lewbel, Bollino et al.
provide both a theoretical derivation of their technique and a procedure for empirical
estimation. Unfortunately, the estimation procedure proposed in Bollino et al. is
computationally complex, and it can accommodate the estimation of only a few
consumption categories. In their paper, Bollino et al. applied their procedure to only three
categories of goods.

An unambiguous ranking of these procedures is not possible (Pollak and Wales,
1981). One of the factors that make it difficult to rank these procedures is that not all of
them are nested. Their assessment also depends on the functional form used to estimate
the demand system. The theoretically more appealing technique of Bollino et al. (2000)

restricts the number of consumption categories that can be analyzed. However, the

21

number of goods estimated in empirical demand systems is large, so that its usefulness in
practice can at best be very limited. In this study, we are estimating demand for seven
food groups, which immediately rules out the use of Bollino et al.’s procedure. We
estimate the QUAIDS model in its most ﬂexible form, allowing for nonlinearity in the
price index used to deﬂate total expenditure and allowing the coefﬁcient of the quadratic
expenditure term to depend on prices. Given that we are estimating QUAIDS in this
highly nonlinear form, a preferred method to introduce demographic variables is one that
will not create further nonlinearities. It is for this reason that we choose to incorporate
demographic variables as intercept shifters through Pollak and Wales’s (1981) linear

demographic translation method.

2.5 Observed Zero Expenditures

The behavioral response of households to changes in their economic environment
takes place on either the intensive or extensive margin (Meyerhoefer, 2002). Households
respond along the intensive margin when they are consuming a non-zero amount of the
good, so that a change in the independent variable (such as a commodity’s price) leads
them to marginally increase or decrease the amount they presently consume. The
extensive margin refers to households that must make a decision whether or not to
consume any amount of the good when its price (or some other exogenous factor)
changes. These are households who are either not consuming the good initially, or those
that respond to the exogenous change by completely exiting the market for that good. The
response to changes in exogenous factors by households on the intensive margin entails a

continuous change in the dependent variable, and can be easily modeled by traditional

22

regression techniques. However, modeling scenarios with some households on the
extensive margin and others on the intensive margin requires statistical analyses based on
composite distributions. These are deﬁned to contain a discrete probability mass on the
boundary of the choice set, allowing for the positive probability of zero consumption, and
a continuous density corresponding to positive consumption levels (Meyerhoefer, 2002).
The early empirical work in demand modeling estimated demand functions on
aggregate time series data, or household level data with highly aggregated commodity
groupings. Demand estimation with these aggregate data allow the use of standard
econometric techniques that assume the dependent variables in the system of demand
equations follow a joint normal distribution, and hence, do not allow for the positive
probability of zero expenditure levels. When aggregate data are used, the number of
observations with zero expenditure share values is typically very small, such that deleting
these observations from the sample and carrying out estimations on only the positive
observations consistently identiﬁes the demand function (Meyerhoefer, 2002).
Subsequent work on demand modeling made increasing use of micro data on highly
disaggregate commodity groups. When micro data are used, it becomes increasingly
likely to observe non-consumption of some commodities by a large number of
households. This makes the strategy of deleting non-consuming households unattractive,
particularly given the large number of degrees of freedom that is lost. Also, the exclusion
of a large number of observations in this nonrandom manner may cause selection bias.
The ﬁrst attempts to develop estimation techniques that explicitly capture
consumer behavior on the extensive and intensive margins were done in a single equation I

context. In this context, several limited dependent variable models have been developed

23

to deal with zero expenditure values generated by different underlying processes. One of
the reasons for observed zero expenditures is that the market price for a given commodity
exceeds the household’s reservation price, leaving the household at a comer solution and
censoring the expenditure distribution at the point of non-consumption. This reasoning
has motivated the use of the Tobit model (Tobin, 195 8) to estimated censored
expenditure relationships. Under the Tobit formulation, the same variables are assumed
to determine both the value of the continuous observations and the discrete switch to non-
consumption at zero, making it only appropriate in cases where consumers are rationed
out of the market by prices higher than they are willing to pay.

Other models have been developed that are appropriate for situations where zero
expenditure values are a result of the inﬁ'equency of purchase, which occurs when the
purchase of some commodities is not observed due to the short span of the survey period
(Deaton and Irish, 1984; Blundell and Meghir, 1987). Popular among these is the “double
hurdle model” of Craig (1971).

The study by Wales and Woodland (1983) was among the ﬁrst attempts to derive
econometric techniques to estimate a theoretically plausible demand system in the
presence of zero expenditures. Wales and Woodland propose two alternative models to
estimate censored systems of equations, based on assumptions about preferences. The
ﬁrst model assumes that preferences are randomly distributed in the population, so that
each individual’s direct marginal utility function for each good can be additively
augmented with a normally distributed error term. These stochastic marginal utility
functions are then substituted into the Kuhn-Tucker conditions to determine the set of

goods with zero consumption and deﬁne the commodity demand functions. A

24

multivariate normal density function for the vector of commodity demands is derived
through a change of variables transformation, and used to assign a probability to each
possible combination of consumption and non-consumption. The number of integrations
to be performed on the density is equal to the number of non-consumption realizations.
Unfortunately, the derivation of the maximum likelihood estimates in this case involves
the evaluation of multiple integrals, which can be computationally infeasible for large
equation systems.

The second model proposed by Wales and Woodland assumes that commodity
demands are the result of individual nonrandom utility maximization subject to a budget
constraint. This second model essentially extends Am‘emiya’s (1974) Tobit estimator for
a system of simultaneous equations to account for the budget constraint during
estimation. An error term, assumed to follow a truncated multivariate normal distribution,
is added to the demand share equations. As is the case with the ﬁrst model, the truncated
density is obtained by integrating non-consumed goods out of the joint normal density,
and the likelihood function is constructed as the product of the individual truncated
density functions.

The main difference between the two approaches lies in the assumptions each
makes about the processes generating the zero consumption values. The ﬁrst model
assumes that zero consumption is determined by Kuhn-Tucker conditions, so that
stochasticity enters the model through random preferences, while the second model
incorporates stochasticity through additive disturbances on the share equations, so that
the possibility of zero consumption occurs because disturbances follow a truncated joint

normal density. The similarity between these models lies in the fact that both assume zero

25

expenditures represent comer solutions where consumers are rationed out of the market
by prices higher than they are willing to pay. The drawback in both models is that their
empirical implementation is virtually infeasible for larger systems of equations, given the
difficulty of performing multiple numerical integrations.

Building on Wales and Woodland’s ﬁrst model, Lee and Pitt (1986) develop a
method for estimating censored demand systems that is dual to the Kuhn-Tucker
approach. Lee and Pitt also assume that preferences are randomly distributed over the
population but, unlike Wales and Woodland, they use the indirect utility function
resulting from utility maximization without non-negativity constraints. Application of
Roy’s Identity to the indirect utility function deﬁnes what Lee and Pitt call unconstrained
“latent notional demands”, each of which is a ﬁrnction of market prices. They call the
demands notional because they result from utility maximization with respect to the
budget constraint only, allowing them to take on negative values, and latent in the sense
that only nonnegative realizations are observable (Meyerhoefer, 2002). The notional
demand ﬁmctions can be related to observed demands by ﬁnding positive shadow prices,
which are themselves functions of observable market prices, supporting the zero-valued
demand levels. Households compare shadow prices to market prices to select a demand
regime, so that if the shadow price of a good is less than its market price consumption is
zero. The likelihood function is constructed as the product of the conditional density of
disturbances for the consumed goods given the non-consumed disturbances with the
density of disturbances for the non-consumed goods. The likelihood must be integrated
over the domain of shadow price values. The drawback of Lee and Pitt’s approach is the

same as that of Wales and Woodland, namely that it can only be used where a small

26

number of commodities is involved. Hence, despite the theoretical attractiveness of the
Wales and Woodland and Lee and Pitt approaches, their computational infeasibility limit
their usefulness in practice.

Amdt (1999) proposed a methodology that attempts to overcome the above
limitation. Amdt follows Lee and Pitt’s formulation of estimating equations by solving
for the reservation prices and substituting them into the demand functions. But instead of
specifying a likelihood function to carry out the estimation, Amdt proposes maximizing
an entropy function subject to restrictions. These restrictions include prior distributions
imposed on elasticity estimates, symmetry restrictions, constraints that the reservation
prices are less than or equal to market prices, and the requirement that all outcome
probabilities sum to one. Since entropy maximization problems do not involve the
evaluation of numerical integrals, they can be solved using standard nonlinear
optimization packages. However, whether the maximum entropy estimator meets the
requirements of economic theory, particularly the curvature restrictions, has not been
fully investigated (Meyerhoefer, 2002).

Motivated by the work of Heckman (1976), other alternative two-step procedures
have been developed to reduce the computational burden of multiple integrals that
bedevils one-step procedures. Heien and Wessells (1990) proposed a two-step estimation
procedure for a system of demand equations with limited dependent variables. In the ﬁrst
step, a probit model is used to calculate the inverse Mills ratio (IMR) for each
commodity. The IMR is then used as a selectivity regressor in each equation during the
second stage. The system in the second stage is estimated with seemingly unrelated

regression (SUR). Heien and Wessells’s procedure has seen widespread use in empirical

27

food demand studies (see Yen et al. (2002) for examples). However, it was later shown
that Heien and Wessels’s procedure is inconsistent due to the presence of a mathematical
error in its derivation (Shonkwiler and Yen, 1999).

One feature to note about one—step estimation procedures, such as those due to
Wales and Woodland (1983) and Lee and Pitt (1986), is that they are only appropriate for
modeling comer solutions. This is because they assume that the same process that
governs the positive observed demand also governs the consumption decision itself. But
this is not the only explanation for the presence of zero expenditure levels. A natural
alternative would be a procedure that captures other phenomena such as infrequency of
purchases. Shonkwiler and Yen (1999) derive such as estimator as a multivariate
generalization of Amemiya’s (1985) type 2 Tobit model. Their model contains a separate
binary censor used to predict the probability of consumption for each good in the system.
This is then multiplied by the expectation of demand for the respective good conditional
on positive consumption to generate the unconditional censored demand equations.

The Shonkwiler and You procedure is carried out in two steps. In the ﬁrst step,
single equation probit models are used to forecast the probability of consumption and
construct the second stage demand system, which is subsequently estimated by either
maximum likelihood or seemingly unrelated regression. This procedure is particularly
suited to situations where large equation systems are involved, given the reduced
computational burden associated with it. In this study, we estimate a demand system
involving seven food groups. Given the suitability of Shonkwiler and Yen’s procedure

for large equation systems, and its consistency, it is our chosen approach to model the

28

zero-expenditure problem. A detailed discussion of this procedure follows in the

empirical model chapter.

2.6 Chapter Summary

This chapter reviewed literature on the relationship between utility maximization theory
and demand functional forms, and discussed alternative approaches to modeling
preferences. In empirical demand estimation, a large number of goods are involved, and
to reduce this large number of goods into a manageable few, the assumption of weak
separability is typically invoked. The developments in the literature on econometric tests
for separability have focused mainly on time series applications. The AIDS model. has
been the most widely used functional form for empirically estimating price and
expenditure elasticities. However, its assumptions that budget shares are linear in
expenditure, and that expenditure elasticities are constant regardless of the point in the
expenditure spectrum, are limiting. This study uses QUAIDS, which is a generalization
of AIDS that allows for nonlinearity in expenditure and allows the goods to be luxuries at
some expenditure levels and necessities at others. The effects of demographic variables
are incorporated into the demand model using demographic translation. The methods that
have been developed in the literature to model observed zero-expenditures are, for the
most part, not suitable for large equation systems due to their computational complexity.
Due to the large nmnber of equations estimated in this study, we use a two-step procedure

developed by Shonkwiler and Yen (1999).

29

CHAPTER THREE

EMPIRICAL MODEL

3.1 Introduction

This chapter discusses the speciﬁcation and estimation of the empirical model.
The general form of the model is discussed ﬁrst, followed by the estimation form. Section
3.3 discusses estimation issues, paying particular attention to implications of the
nonlinearity of the model, and deriving an LM test for nonlinearity. Econometric issues
associated with QUAIDS estimation are the focus of section 3.4. In this section, the
problems of expenditure endogeneity and non-consumption are discussed in more detail,
and the strategies to modeling them are provided. The ﬁnal section, section 3.5, is a

summary of the chapter.

3.2 Empirical Model

Popular functional forms such as the almost ideal demand system (AIDS) of
Deaton and Muellbauer (1980a) and the translog model of J orgenson et al. (1982) have
budget shares that are linear functions of log total expenditure. However, as discussed in
the previous chapter, further terms in total expenditure may be required for some, if not
all budget share equations. Banks et al. (1997) show that if some commodities require
these extra terms, then parsimony, coupled with utility theory, restricts the nonlinear term

to be quadratic in log income. Based on this restriction, they derive an extension of the

AIDS model—the quadratic almost ideal demand system (QUAIDS)—which has log

30

total expenditure as the leading term in budget share equations and higher order total

expenditure terms.

3.2.1 Quadratic Almost Ideal Demand System: The General Form
The QUAIDS model assumes that household preferences belong to the following

quadratic logarithmic family of expenditure functions:

_ ub(p)
lnc(u,p) — lna(p) + 1—2(p)b(p)u (3.1)

where u is utility, p is a vector of prices, a(p) is a function that is homogenous of degree
one in prices, b(p) and Mp) are functions that are homogeneous of degree zero in prices.

The corresponding indirect utility (V) function is:

 

1n V = ﬂ 1‘” ; (150(1)) T + l(p)}—l (3.2)

where x is total expenditure. The speciﬁc functional form for Mp) is:

K K
1(1)) = 22,111,)” where 2,1, = 0 (3.3)
i=1

(=1

and where i = 1, ..., K denote the number of goods entering the demand model. Deaton

and Muellbauer’s AIDS model has an indirect utility function given by equation (3.2),

31

but with 11(p) set to zero. The speciﬁcation Of the functional forms for a(p) and b(p) in
QUAIDS is similar to their speciﬁcation in AIDS, in which they are made to be
sufficiently ﬂexible to represent any arbitrary set of ﬁrst and second derivatives of the
cost function.

Application of Shepard’s lemma to the cost function (3.1) or Roy’s identity to the

indirect utility function (3.2) gives the QUAIDS model in budget shares form:

x

w, = a, +gy,1np, + ,6, ln[a(p)] + ﬁhnL—XQHZ (3.4)

where a, B, y, and A are parameters. As can be seen from the budget shares (3.4), the
QUAIDS model specializes to AIDS when all of the 2’s are zero across all equations.
Hence, the AIDS model is nested within QUAIDS, and the AIDS speciﬁcation can be
tested based on the statistical signiﬁcance of the 1’s.

As with the original AIDS model, the theoretical restrictions of adding-up,

homogeneity, and symmetry in the QUAIDS model are expressed in terms of its

parameters. Adding-up requires 21w, =1, and can be expressed in terms of model

parameters as:

Za,=l flaw £1130 Zy,=0 Vj. (3.5)

32

Since Marshallian demands are homogenous of degree zero in (p, x),

K
27,, =0 Vi. (3.6)

j=l
Slutsky symmetry implies that:
7,, = 7,, Vi,j. (3.7)

The parameter a,- in the QUAIDS model can be interpreted as the share of an item

in the budget of a subsistence household (i.e., the case of u = O) at the base year prices

(Meenkashi and Ray, 1999). The expression ,6, + 2(2, / b(P)Iln(x/ a(P))] measures the

impact of a 1% increase in real expenditure on the budget share of commodity i. Unlike

in the AIDS model where ,1,- = O V i, this expression is capable of changing signs

depending on the point in the expenditure spectrum. In other words, the QUAIDS model
allows the possibility of normal goods becoming inferior or inferior goods becoming
normal, as one moves along the expenditure spectrum of households. In contrast,
expenditure elasticities are all constant in the AIDS model.

Formulas for the QUAIDS expenditure and price elasticities are derived by
differentiating the budget share equations with respect to In x and In pj, respectively.
Following Banks et al. (1997), we simplify the expressions for the elasticity formulas by

using the intermediate results:

33

[1, a 5%? = ,3, + Z—&{ln[$]} (3.3)

._ 6W, _ _ K _ liﬂj l— 2
y” zalnp, 4" #{a’ +123,” In”) b(p){ln[a(P)]} ' (3'9)

 

 

In terms of the ,u, , the formula for expenditure elasticities can be written as:

e, =1+ﬂ. (3.10)

Using expression a, , the formula for the Marshallian or uncompensated price elasticities

can be written as:

e” =ﬁ_ _. (3.11)

where 6,115 the Kronecker delta taking the value 5,, =1 if i = j and 5,, = 0 if i ¢ j. The

Hicksian or compensated price elasticities are calculated by invoking the Slutsky

equation:

e; =e,',‘. +w,e, (3.12)

34

The QUAIDS model is used in this study to estimate price and expenditure elasticities
using panel data on households. The next subsection focuses on the empirical estimation

of the QUAIDS model.

3.2.2 Quadratic Almost Ideal Demand System: The Estimation Form

As before, denote commodities (and therefore, equations) by i, where i = 1,...,K ,

and let h = 1, ..., N denote households, and t = 1, ..., T index time periods. The empirical

speciﬁcation of the QUAIDS model is

2
K h A. xh S
w: = a, + E y, lnp", +,6, lnl: x, ]+ ’ lnl: ' ] + E 6323-1-85 (3.13)
Fl 1 1 06:) b6?) 06:) s=l ’

where Z, = (2,", ,..., 2:) is a set of demographic variables for household h at time t, In a(pf)

is the price index deﬁned as

K K
'= I:

K
lna(pf) = 01,, +2“) lnpj', +£22yjklnp21np£ (3.14)

j=l j 1

and b(pf) is the Cobb-Douglas price aggregator

b(pf’) = 1:103)“. (3.15)

35

The a’s, y’s, and ,B’s in the budget share equations (3.13) are restricted by theory to be the
same as those in equations (3.14) and (3.15).

In estimating the QUAIDS model, total expenditure, x, is deﬁned as expenditure
on all food items consumed by the household. Price data is at the cluster level, which in
most cases means at the village level for rural areas or at magisterially-deﬁned districts
for urban areas. So, households in different clusters face different prices, and this is the
reason commodity prices are indexed with the h (household) superscript.

To control for varying preference structures and heterogeneity across households,
demographic variables are incorporated in budget share equations through the linear
demographic translation method of Pollak and Wales (1978). This method speciﬁes

observed household heterogeneity as a linear combination of socio-demographic
variables observed in the data (sz '6, ). The socio-demographic variables considered here

are household size, rural-urban dummy, race, and education of the household head.
Dummy variables for the year of survey are included among the 2 variables to control for
structural change in consumers’ preferences and other aggregate time effects that may
inﬂuence expenditure patterns (such as those related to the overall macroeconomic
environment). The month of the survey is also included to control for the likely effects of
seasonality on consumption behavior.

Given that there are existing food demand studies in South Africa based on the
AIDS model, it is instructive to also estimate the AIDS model in this study, so that
elasticity estimates can be compared with those obtained from QUAIDS. After all, once

the unrestricted QUAIDS model has been estimated, the estimation of AIDS becomes a

36

trivial task because it only requires restricting the coefﬁcient on the quadratic expenditure

term to zero. The empirical speciﬁcation of AIDS is:

n h S
w" = a + ln ” + In x, + 52" +u” 3.16
I! l 27:} p}! ﬂ: JP?) é Is S! l! ( )

1=l

The ,6 parameters of the AIDS model determine whether goods are luxuries or necessities
(Deaton and Mueallbauer, 1980a). When ,8,- > 0, an increase in x leads to an increase in w,-
so that good i is a luxury. Similarly, ,6,- < O for necessities. The y), parameters measure the
change in the ith budget share following a unit proportional change in p,- with x/a(p) held

constant. The formula for the AIDS expenditure elasticity is given by3:

e =ﬁ+1. (3.17)

e; : 7—” _ EL[WJ _ ﬂ} 111(ij] (318)

where 6,, is the Kronecker delta taking a value of one if i = j, and zero if i 75 j. The

Hicksian price elasticities are obtained by invoking the Slutsky equation:

 

3 The household superscript and time subscripts are not included here because the elasticities are calculated
at time- and household-pooled sample means.

37

e; =e; +w,e, . (3.19)

The elasticities in both the QUAIDS and AIDS models are estimated at sample means of

prices, expenditures, and budget shares.

3.3 Estimation

For purposes of estimation, an error term, 5,? , is added to each of the commodity

. _ h . .
share equatrons. The errors a =[ 81'; , 5;, , ..., 5K, ] are assumed to have a multivariate normal

distribution with covariance matrix 2. However, due to the adding-up condition, direct
estimation of the hill equation system is not possible because 2‘. is singular. To get around
this problem, one of the K demand equations is dropped from the system during
estimation; the remaining (K-l) equations are estimated by maximum likelihood. The
question of which among the K equations to drop is irrelevant because, as Batten (1969)
shows, such a choice does not inﬂuence the demand parameter estimates. The full
covariance matrix, together with the parameters of the K ‘h equation, are recovered by
applying the delta method (Barten, 1969).

An interesting econometric feature of both the QUAIDS and AIDS models, is that
they are both conditionally linear in the price aggregators 1n a(pf) and b(pf ). This
conditional linearity has been used in the AIDS model (in which the only source of

nonlinearity is the ln a(pf’) price aggregator) to simplify empirical estimation. In

particular, most demand studies approximate the nonlinear price aggregator ln a(pf) by a

38

linear index, which leads to a speciﬁcation in which budget shares are linear in all

parameters and therefore, can be estimated in a straightforward way. The most commonly
used approximations for In a(pf) are the Laspeyres index, Stone index, or modiﬁed (by
Moschini (1995)) Stone index. Another reason for the linear approximation is that in
practical applications, prices are relatively collinear, so that In a(pf’) is approximately

proportional to any appropriately deﬁned price index (Deaton and Muellbauer, 1980a).
This latter reason is particularly relevant in demand studies that use time series data.

However, the imposition of a linear structure to variables whose true relationship
is nonlinear can have undesirable consequences on the reliability of parameter estimates.
Pashardes (1993) argues that the linearization of AIDS causes an omitted variables
problem. Based on analytical expressions and empirical results, Pashardes shows that
linearization of AIDS can understate own price elasticities and cross price elasticities of
goods that are either luxuries or necessities, and overstate the cross price elasticities of
the other goods. Buse (1994) also views linearization of AIDS as an omitted variable
problem, and shows through Monte Carlo analyses that linearization may lead to
inconsistency of the widely used seemingly unrelated regression (SUR) estimator. Both
Pashardes and Buse’s assessment of linearized AIDS are based on the original Stone
price index.

Moschini (1995) shows that the Stone index fails to satisfy the commensurability
property of index numbers; in other words, it is not invariant to changes in the units of
measurement. Using the Laspeyres price index as a starting point, Moschini develops a
price index—the modiﬁed Stone price index— which is invariant to units of

measurement and which, he argues, approximates the nonlinear AIDS model well. We

39

are not aware of studies that evaluate Moschini’s modiﬁed Stone price index in a manner

similar to those used by Buse and Pashardes to evaluate the original Stone index.

While approximating 1n a(pf') by a linear price index solves the nonlinearity
problem in the AIDS model, it does not solve the nonlinearity problem in the QUAIDS
model due to the division by the price aggregator b(pf’) in the coefﬁcient of the quadratic

expenditure term. The temptation to include a linear (in parameters) quadratic term in
expenditure may be natural. In fact, a number of demand studies force the coefﬁcient of
the quadratic expenditure term to be constant (included in these studies are Blundell et al.
(1993), Christensen (2004), Labeaga and Puig (2002), and Browing and Collado (2004).).
In the terminology of equation (2.1) of chapter 2, imposing a constant coefﬁcient on the

quadratic expenditure term is equivalent to assuming that C, (p) is independent of prices.

However, as Banks et al. (1997) show, no rank 3 exactly aggregable utility-derived
demand system exists that has both the coefﬁcients on the linear and the quadratic
expenditure terms independent of prices (Corollary 2 on p.533 of Banks et al. (1997)).
Some of these studies (speciﬁcally Christensen (2004)) acknowledge the fact that forcing
b(pf) to be constant is to give away the integrability property of the demand system.4

In this study, we build on Banks et al.’s (1997) study (particularly corollary 2)
and develop a formal test for the statistical signiﬁcance of prices in the coefﬁcient of the
quadratic expenditure term. The logic behind this test is that if this coefﬁcient does not

depend on prices, then there is no need to include a quadratic expenditure term in the

model once the linear term has been included, because the coefﬁcient of the quadratic

 

’ lntegrability as used here means that for a given system of demand functions (which have a symmetric,
negative semideﬁnite matrix), there should be a utility function from which these demand functions can be
derived.

4o

expenditure term must depend on prices. Higher order expenditure terms are also
unnecessary because utility theory restricts the nonlinear expenditure term to be
quadratic. So, a test of the statistical signiﬁcance of the quadratic expenditure term is in
effect, a speciﬁcation test of the AIDS versus QUAIDS model. But because AIDS can be
approximated linearly and QUAIDS cannot, a test for the statistical signiﬁcance of prices

can also be viewed as a test for nonlinearity of the demand model.

3.3.1 A Test for Nonlinearity of the Demand Model

To derive this test, it is necessary to relax the theoretical constraint in the
QUAIDS model that the ,8,- parameters in the Cobb-Douglas price aggregator b(pf') are
the same as the coefﬁcients on the linear expenditure terms (that is, the coefﬁcient on

h h . . . . . . . , . h
x, / a(p, )). This 13 because If we maintain the restrrctron that the ,6,- s In b(p, ) are the
same as the ,6,- coefﬁcients on the linear expenditure term, then the null hypothesis that

the A’s in b(pf) are all zero will make the second term, ln( x,"/ a(pf’ )), in budget share

equations to disappear. This will make the demand system to be a function only of the

quadratic expenditure term, which is inappropriate. To avoid this problem, deﬁne a new

K
price aggregator b(pf’)= n (193)” , where 19, and ,6, are allowed to differ from each

(=1
other. For ease of exposition, we suppress the household (h) and time (t) subscripts, and
absorb all the terms not involving the quadratic expenditure term into the vector q and

their associated parameters (i.e., parameters not involving the 6?, ’s) into the vector (p.

With this new notation, the expenditure share equations (3.13) can now be expressed as:

41

" a. '1 _x_ 2
W. — g.(q.¢)+)~,[l;[p.] {ln[a(p)]} +6, (3.20)

K —1
We want to test the null hypothesis that the vector of coefﬁcients 0 in [H [93' J is

i=1
identically zero (i.e., Ho: 0 = 0). The restricted model (with 0 = 0) is easier to estimate
than the unrestricted model, which makes the Lagrange Multiplier (LM) test an attractive
approach.

Consider maximization of the log-likelihood subject to a set of constraints

c(0) — r = 0. Let x be the Lagrange multiplier and deﬁne the Lagrangean function:
A = lnL+K(c(0)—r) (3.21)

where In L is the log-likelihood function for commodity i given by:

 

2

lnL = —%ln(27r)- glue2 — lip“ ‘:(W'» ]. (3.22)

i=1

The ﬁrst derivative of the log-likelihood function with respect to 6, is:

 

alnL _ K 9,4 .9” a, _x_ 2
66’, — l.[l;[p.~ J (mp. p. DP,- ]{1n[a(p):|} . (3.23)

42

Evaluated at the null, Ho: 0 = 0, the ﬁrst derivative (3.23) becomes:

6 ln L x 2
35-2., 1n p, {Int—d} . (324)

Based on equation (3.24), a test for statistical signiﬁcance of prices in b(p) reduces to

K
adding price times expenditure-squared interaction terms (Zln p, -{In [x/a(p)])2 ) to the

i=1
demand model that is linear in expenditure (i.e., equation (3.13) with A: = 0) — the
unrestricted model — and comparing it with the restricted model, which is just the
QUAIDS expenditure share equations (3.13). To carry out this test, we ﬁrst estimate the
restricted model and obtain the residuals. These residuals are then regressed on all

variables, including the price times expenditure-squared interaction terms. The R-

squared, R3 , from this regression is used to compute the LM statistic, LM = N - R: . This

LM statistic follows a Chi-squared distribution with degrees of freedom equal to the

number of restrictions being tested. For testing purposes, the translog price aggregator, 1n

a(pf ), is approximated by the modiﬁed Stone price index suggested by Moschini (1995),
In a(pf' )22 [:1 w,01n( ,,), where 75,0: Hz 1w: is the mean budget share across

households in the base period.
The LM test just discussed is useful for preliminary analysis of the data to determine
whether the demand model should be speciﬁed with a quadratic (QUAIDS) or a linear

(AIDS) expenditure variable. An obvious alternative would be to estimate the QUAIDS

43

model and test for the statistical signiﬁcance of the quadratic expenditure term.5

However, the QUAIDS model is highly nonlinear and difficult to estimate. This LM test
is a useﬁrl contribution because it allows one to test pararnetrically whether or not the
quadratic expenditure is necessary, without having to estimate the highly nonlinear

QUAIDS model.

3.3.2 Nonlinear Estimation

Given the speed and power of the nonlinear algorithms available today, maximum
likelihood estimation of more ﬂexible ﬁrnctional forms of the demand model is feasible.
This can improve the precision with which income and price elasticites are measured. For

this reason, we estimate the QUAIDS demand model (3.13)-(3.15) in its nonlinear form,
allowing ﬂexibility in the price aggregators 1n a(pf) and b(pf‘ ).

When modeling 1n a(pf) in the ﬂexible form (3. 14), one of the problems is that it
is virtually impossible to estimate a0 empirically. Deaton and Muellbauer (1980b)
suggest assigning a value to 01,, prior to estimation. In particular, they propose

interpreting do as the outlay required for a minimal standard of living when prices are

unity (see Deaton and Muellbauer (1980b, p. 316). However, as Moschini et al. (1994)

observe, the likelihood function is ﬂat in ac , so that the actual choice of a0 does not

matter for the approximation properties of the demand model. This implies that the

computed elasticities are not affected by the choice ofoto. Moschini et al. choose a value

of a0 = O, which proved useful in their context given that it simpliﬁed the formulas for

 

5 Also, one can use nonparametric methods to analyze the shape of the Engel curves (i.e., relationships
between a commodity’s budget share and total expenditure), as did Banks et al. (1997).

44

their separability tests. Our choice of (10 in this study is based on the suggestion by
Deaton and Muellbauer, primarily because choosing are in this way has relevance to

economic theory.

Apart from its inherent nonlinearity, the QUAIDS model has a very large number
of parameters. To reduce the total number of parameters to be estimated, cross-equation
restrictions are imposed during estimation. All the nonlinear AIDS and QUAIDS models
are estimated by maximum likelihood using Stata, extending the programs written by Poi
(2002) for estimating a four-equation demand system with no demographic variables to

those that allow for a seven-equation system with demographic variables.

3.4 Econometric Issues
3.4.1 Attrition

A typical concern when using household panel data involves the extent of sample
attrition and the degree to which attrition is nonrandom. While attrition is a common
concern in any longitudinal study, it is particularly serious for studies conducted in
developing countries, due to the generally poor communication infrastructures.
Furthermore, the high levels of mobility and long distance migration associated with
development are likely to complicate longitudinal survey work in developing countries.
Partly offsetting these concerns, however, are the much lower refusal rates typical in
developing countries, perhaps reﬂecting lower opportunity costs of time and possibly
different cultural attitudes toward the interviewing process (Deaton, 1997). While a large
literature exists in developed countries on the implications on nonrandom attrition, only a

few studies have considered this topic in developing countries, perhaps reﬂecting the

45

relative paucity of panel datasets in developing countries.These studies include those by
Alderman et al. (2000), Maluccio (2000), and Thomas et al. (2001)).

In theory, three factors underlie the level of attrition in a survey: (1) the mobility
of the target population, (2) the success with which those who move are followed and re-
interviewed, and (3) the number of refusals. Thus, attrition is often closely linked to
migration behavior (Maluccio, 2000). In the ﬁeld, poor effort by enumerators and
ﬁeldworkers can also exacerbate attrition.

Attrition in panel surveys can be viewed as a speciﬁc type of nonresponse and,
from a conceptual viewpoint, many of the insights regarding nonresponse in cross-
sectional surveys carry over to panels. Fitzgerald et al. (1998) provide a statistical
framework for the analysis of attrition bias. They distinguish between two types of
sample selections; selection of variables observed in the data, and selection on variables
that are unobserved. They develop tests for attrition using the two selection types. While
neither of the two attrition/selection types necessarily imposes a bias on estimates,
selection on observables is more amenable to statistical solutions. In particular, if one
ﬁnds that there is attrition in the data, then one can determine whether or not there is
selection on observables. Selection on observables basically means sample selection
based on variables that are observed prior to attrition (e. g., in the ﬁrst round of the
survey). Even if there is selection on observables, this does not necessarily bias the
estimates of interest. Thus, one needs to test for possible attrition bias in the estimates of
interest as well.

More formally, assume that what is of interest is a conditional population density

f(y|q) where y is a scalar dependent variable and q is a scalar independent variable (an

46

extension to make q a vector does not change to results of the discussion). The model

takes the form

y = no + 7r,q + s, y, observed if A = 0 (3.25)

where A is an attrition indicator equal to 1 if an observation is missing its value of y
because of attrition, and equal to zero if an observation is not missing its value of y. Since
(3.25) can be estimated only if A = 0 (that is, one can only determine g(qu, A = 0)), one
needs additional information or restrictions to infer f(.) from g(.). These can come from
the probability of attrition, Prob(A = 0L)», q, z), where z is an auxillary variable (or vector

of variables) that is observable for all units but not included in x. This implies estimations

ofthe form
A. =00 +0",q+0'22+u (3.26)
A, :1 if A,‘ 2 o
, (3.27)
=0 if A, <0

Selection on unobservables occurs if z is independent of e|q but v is not
independent of elq. Selection on observables is the reverse: it occurs if z is not
independent of elq but 0 is independent of elq. That is, selection on observables occurs if
Prob(A = Oly, q, z) = Prob(A = Olq, z); selection on unobservables occurs if this equality

fails to hold, so that the attrition function cannot be reduced from Prob(A = 0b», q, z).

47

Selection on unobservables is often presented as dependent on the estimation of
the attrition index equation. Identiﬁcation, however, usually relies on nonlinearities in the
index equation or an exclusion restriction, i.e., some 2 that is not in q. It is difﬁcult to
rationalize most such exclusion restrictions because, for example, personal characteristics
that affect attrition might also directly affect the outcome variable, i.e., they should be in
q (Alderman et al., 2000). There may be some such identifying variables that are external
to individuals and not under their control, such as characteristics of the interviewer in the
various rounds. However, identifying restrictions are generally not available, which
makes selection on unobservables an obstacle to accurate parameter estimation.

If there is selection on observables, the critical variable is z, a variable that affects
attrition probability and that is also related to the density of y conditional on q. Two
sufﬁcient conditions for the absence of attrition bias due to attrition on observables are
either (1)2 does not affect A or (2)2 is independent of y conditional on q. Attrition tests
can be based on either of these two conditions. One test is simply to determine whether
candidate variables for z signiﬁcantly affect A. Another test is based on Becketti, Gould,
Lillard, and Welch (BGLW) (1988). In the BGLW test, the value of y at the initial wave
of the survey (yo) is regressed on q and on A. The test for attrition is based on the
signiﬁcance of A in that equation.

The analysis of attrition in this study follows the approaches suggested by
Becketti et al. (1988) and Fitzgerald et al. (1998). In particular, we test for whether or not
attrition signiﬁcantly affects estimated multivariate relations. Our analysis of attrition
begins with a comparison of the means of a selected number of key household and

community variables. Besides being informative, the comparison of means is also

48

intuitively appealing, because the idea that attrition is likely to bias estimates is often
made on the basis of such univariate comparisons (Alderman et al., 2000). We then
estimate probits for the probability of attrition in order to investigate what variables
predict attrition and determine whether or not the probability of attrition can be explained
signiﬁcantly by observable variables. Finally, we test whether coefﬁcient estimates differ
for the two subsamples, one that attrits and one that is re-interviewed. The results from

these attrition tests will help us in deciding how to deal with it.

3.4.2 Expenditure Endogeneity

Most empirical demand analyses do not cover all products and services that
households purchase. Data limitations, ﬁnite computer memory, and the increased
complexity and time required for estimating large models make it necessary to abstract
from a completely speciﬁed demand system containing a different equation for each of
the myriad goods available in the market (LaFrance, 1991). The practice is typically to
assume that preferences are separable and estimate a set of conditional demands for the
goods of interest as functions of prices and total expenditure on these goods (Pollak,
1969). However, such a practice raises questions regarding the possibility of simultaneity
bias in the budget share equations. Total expenditure may be determined jointly with the
expenditure shares of the individual commodities being analyzed, making it endogenous
in the expenditure share equations. Also, expenditure endogeneity issues may arise
whenever the household expenditure allocation process is correlated with other
unobserved behavior not captured by the explanatory variables in the budget share

equations. In this case, these unobserved effects would be bundled in the error term.

49

Estimation ignoring expenditure endogeneity may lead to inconsistent demand parameter
estimates.

In cross-sectional demand studies, the common procedure to control for
expenditure endogeneity is instrumental variables. With panel data, a number of
possibilities to correct for unobserved heterogeneity are available, including linear
transformations of the original model, such as through ﬁxed effects and ﬁrst differencing
to remove the unobserved heterogeneity component of the error term. However, such
transformations are difficult to implement with nonlinear models such as QUAIDS
derived from consumer utility maximization theory. In this study, we follow Bundell and
Robin (1999) and control for endogeneity using an extension of the limited information
augmented regression technique suggested by Hausman (1978). This procedure is also
known as the control function approach.

To illustrate how the augmented regression technique works, consider the
regression of y), the dependent variable, on a set of exogenous explanatory variables, 2,
and an endogenous explanatory variable, y;, i.e., y) = z'p + 1922.6 Also, suppose an
instrumental variable, 22, exists for yz. Correction for the endogeneity of y; using the
control function approach proceeds in two steps. The ﬁrst step involves estimating a
reduced form regression of the endogenous variable on a set of instrumental variables,
where the set of instrumental variables include all the other exogenous explanatory
variables (i.e., regress y; on 1 and 22). The residuals, 17 , from this ﬁrst-stage regression are
then included as an additional explanatory variable in the original y) equation. The OLS

estimates of the parameters p and 1c in this augmented regression are identical to the Two-

 

6 For illustration purposes, we consider the case of one endogenous variable and one instrumental variable.
The case of multiple endogenous variables and multiple instruments can be handled in a straightforward
way using the basic framework explained here.

50

Stage Least Squares (ZSLS) estimator (Blundell and Robin, 1999). Moreover, testing for
the signiﬁcance of the coefﬁcient on 13 is a test for the exogeneity ofyz. Following Banks
et al. (1997), we use total household income and its square as instruments for expenditure

(and expenditure squared).

3.4.3 Observed Zero Expenditures

In each equation of the QUAIDS model, the dependent variable w,',’ is observed
with nonnegative values. In situations where micro data are used, it is very likely to
observe non-consumption of some commodities due to purchase infrequency and corner

solutions. If a nonnegligible proportion of the w,',' values are identically zero, then the w:

variable becomes partly continuous with a positive probability mass at zero. OLS

regression using the subsample for which w: > 0 estimates the demand parameters

inconsistently due to nonrandom sample selection problem, while OLS using all of the

data will not consistently estimate the demand parameters due to the nonlinearity in the
conditional mean of wf,’ (for a general discussion see Wooldridge (2002), pages 524-

525)

In the case of a single-equation demand model, censoring in the dependent
variable can be handled in a straightforward way by applying a maximum likelihood
(ML) Tobit model. However, when estimation is for systems of equations, and censoring
occurs in multiple equations, then direct estimation by ML becomes difﬁcult because of
the need to evaluate multiple integrals in the likelihood function. To a large extent, this
problem of having to evaluate multiple integrals explains why many of the theoretical

models discussed in chapter 2 have seen virtually no use in empirical demand studies.

51

The two-step procedure proposed by Heien and Wessells (1990) offered great promise as
a solution to the computational infeasibility of these models, but as was shown by
Shonkwiler and Yen (1999), it is inconsistent due to a mathematical error in its
derivation. In this study, we apply the consistent two-step procedure developed by
Shonkwiler and Yen, which corrects for the inconsistency associated with the Heien and
Wessells procedure.

To introduce the Shonkwiler and Yen procedure, consider a structure in which

censoring of each commodity i at time t is governed by a separate stochastic process
it h

2,, ' 1' , + V” such that
h h h h , h - h h

Wu =Wu t’mt a‘I’)+£u lfz,,'1', +v,, > 0

(3 .28)
= otherwise

where w,',' is observed expenditure share for hth household, \y is a vector containing all
parameters in a particular demand equation, 1: is a vector of exogenous variables, 1'; is a
conformable vector of parameters, and a: and v,’,' are random errors; p and m are
interpreted as before. Assume that the vector of disturbances a? = [8,}; , 6‘51”.” 62,] and

h

v, = [v3 , v; ,..., v2] are normally distributed. Correlation is allowed only between

h h h h h, .
z,,'r, + v,, and w,, , ,m, ,\|I) for each commodlty and among w,’,' (pf,m,” mt) and

52

wj’, f' ,m," ;\|l ), i #127 Using equation (3.28) and the bivariate normality of [8: ,v,’,' I , the

mean of w,’,’ conditional on a positive observation is

z’."'r

EIWIIIVL' > -ZZ'T.-)= w£(pf,m,";w)+ 5.- $13.1: (3.29)

where ¢ (.) and (I>(.) are the standard normal probability density and distribution
ﬁmctions, respectively. Based on the facts that Prob(vf,’ > —z,’; ’1', )= (b(zf; 'T,) and
E (w;l Iv;l < —z,';'t,)= O , the unconditional mean of w,’,’ is

E(w,’,’)= (b(zﬁ'r, )w: f,m,";w)+ 6,¢(z,'.;'r,). Based on E(W: ), the system of share

equations can be written as
w: = @(zixr. :(pi',m.";w)+ 6.¢(z$:'r.)+ 4‘: (3.30)

where 6,? = w: — E (w;I | pf , m,” , z 3 ). System (3.30) can be estimated in two steps: (i) ﬁrst,
obtain the maximum-likelihood probit estimates ‘9, of 1', using the binary outcomes
wf,‘ = O and w,',' > 0 , and then (ii) calculate ¢(zf;’r,) and <D(zf}’r,) for all i and estimate ‘1’ ,

6., 62, , 5,, in the augmented system

 

. . . . h . .
7 That Is, the binary censoring mechanism 1,, '1', + v: IS Independent of 2’}, '1' j + v7, and the level

equations r i for 1 as j.

53

w: = ¢(z:'%,)w.’:(pi',m.";w)+ 6.¢(z£:'r‘.)+ 5: (3.31)

by ML or SUR. Elasticities can be calculated as in equations (3.8) — (3.1 1), except the

intermediate derivatives p, 41,, are now replaced by ,1—1, , ii,

p, = 6E(w, )/alnm = <D(z,'i', )aw, mm»: (3.32)

p, = 6E(w, )/aln p, = (b(z,'i:,).6w,/61np, (3.33)

which are obtained by taking ﬁrst derivatives of equation (3.30). Shonkwiler and Yen’s
procedure has seen use in some recent food demand studies (Dong et al., 2004; Yen et

al., 2004; Aguero and Gould, 2003).

3.5 Chapter Summary

The chapter discussed how the empirical model will be estimated. The demand
parameters and price and expenditure elasticities will be estimated using the QUAIDS
functional form. For comparison with previous demand studies in South Africa, the
demand parameters will also be estimated using the AIDS functional form. The statistical
signiﬁcance of prices in the coefﬁcient of the quadratic expenditure term will be tested
using the LM test. Demographic translation will be used to incorporate demographic
variables into the demand model. The endogeneity of expenditure will be corrected for
using the augmented regression technique. The two-step procedure suggested by
Shonkwiler and Yen (1999) will be used as a corrective procedure for the zero-

expenditure problem.

54

CHAPTER FOUR

DATA SOURCES AND DESCRIPTION

4.1 Introduction

This chapter discusses the data sources used in this study, and presents summary
statistics of the variables entering the demand model. Section 4.2 describes the data and
methods used to collect them. Section 4.3 provides background information on KwaZulu-
Natal Province, focusing on the economic and social reforms that occurred between the
three panel waves. Section 4.4 provides a descriptive analysis of the expenditure patterns
of households, and presents summary statistics of their socioeconomic and demographic
characteristics. The extent of the zero-expenditure problem is discussed in section 4.5,

and a summary if the chapter provided in the ﬁnal section.

4.2 Surveys and Data Description

Data to be used in this study comes from the KwaZulu-Natal Income Dynamics
Study (KIDS). KIDS is a panel dataset comprising three surveys: the 1993 Project for
Statistics on Living Standards and Development (PSLSD) survey, and the 1998 and 2004
surveys which conducted further interviews on households from the 1993 PSLSD survey
who resided in KwaZulu-Natal Province.

The PSLSD is a nation-wide survey undertaken in the last half of 1993 by a
consortium of South Aﬁican groups and universities under the leadership of the South
African Labor and Development Research Unit at the University of Cape Town, with

technical expertise from the World Bank. The main instrument was a comprehensive

55

household survey collecting a broad array of information on the socio-economic
condition of households. The topics covered included household demographics,
education, food and non-food expenditures, remittances, employment and income,
agricultural activities, health and anthropometry.

In addition to the household questionnaire, a community questionnaire was
administered in each cluster to collect information common to households, such as the
availability of schools and health facilities. The community questionnaire also collected
data on prices for a detailed list of food products commonly purchased by households.
These prices were collected from at least two sources in or near each community. The
ﬁrst source was a formal retail store such as a supermarket, and the second source was a
less formal business such as a “corner café” (comer café’s are commonly referred to as
spaza shops in South Africa).8 In this study, we calculate the price for each food product
as the average of prices from the two sources.

The 1993 sample was selected using a two-stage, self-weighting design. In the
ﬁrst stage, clusters were chosen proportional to size from census enumerator districts.
The census enumerator districts were based on the 1991 population census. In the second
stage, all households in each chosen cluster were enumerated and then a random sample
selected. Nationwide, a total of 358 clusters were surveyed, and information on 8848
households was collected.

In 1998, households surveyed by the PSLSD in KwaZulu—Natal Province were

reinterviewed in the KIDS survey. The 1998 KIDS survey was undertaken by a

 

’ A spaza shop is a small store typically owned by an individual or a household, selling frequently
purchased consumer items such as food, body care products, and alcoholic beverages. These forms of
business are found in black townships and villages, and are operated from owners’ homes or in such places
as busy roads or intersections and taxi or bus stations.

56

consortium including the University of Natal, the University of Wisconsin-Madison, and
the International Food Policy Research Institute.9

The 1993 KwaZulu-Natal portion of the PSLSD sample was representative at the
province level (conditional on the accuracy of the 1991 census and other information
used in the sampling frame) and contained households of all races. In the 1998 KIDS
survey however, it was decided not to reinterview white and coloured households. The
reason was that the proportion of white and coloured households in the sample was small
(7% were whites and 3% coloureds), which precluded comparative ethnic analyses.
Another reason given was that white and coloured households were located in a small
number of clusters (due to the general lack of spatial integration of races in South Africa),
which appear to be non-representative at the ethnic group level.

The 1998 household questionnaire largely followed the 1993 version, except that
the former was appended to include aspects of asset ownership and economic shocks (as
was driven by the focus of the study, on “income dynamics”). The 1998 target sample
(i.e., the sample that would have resulted in the absence of attrition) was 1,354
households, of which 1,171 (86 percent) were successfully re-interviewed—success here
deﬁned as having re-interviewed at least one member from the 1993 household. The 1998
survey tracked and interviewed households that had moved or migrated to newer
locations. If a member split from the 1993 household (for example, to establish his/her
own household), this member was tracked for reinterviewing if he/she was regarded as

“core” in 1993. A core member is deﬁned as one who had inﬂuence in household

 

9 There were no speciﬁc reasons for choosing to focus only on KwaZulu-Natal (and not on other
provinces); “[t]he choice of KwaZulu-Natal was in part the result of practical considerations including a
conﬂuence of research interests, resources, and the feasibility of locating the households interviewed in
1993” (1998 KIDS Codebook)

57

decision-making in 1993, such as older and/or working children of the household head.
Of the 1,171 households that were reinterviewed, 1,058 were the original 1993
households. The interviews were undertaken during a three—month period, from March to
June.

The third wave of the KIDS survey was undertaken in 2004. The survey was
undertaken by a consortium including the Universities of waZulu-Natal and Wisconsin-
Madison, the International Food Policy Research Institute (IFPRI), the London School of
Hygiene and Tropical Medicine (LSHTM), and the Norwegian Institute of Urban and
Regional Studies (N IBR).

The structure of the 2004 questionnaire was very similar to 1998, except new
modules were introduced to collect information on children’s literacy rates and household
deaths. Similar to the 1998 survey, the 2004 survey tracked and interviewed core
members of the 1998 households. As a result, a total of 1428 households were
interviewed, 727 of which were interviewed in both the 1993 and 1998 surveys. Most of
the interviews were completed during the months of April and July. We restrict our
analysis to the households who were interviewed in all the three surveys, so that our
analysis is based on a total of 2,1 81 (3 X727) data points. This has the advantage of
ensuring greater variability in prices and income faced by each household, and hence,
enhances the identiﬁcation of demand behavioral parameters.

The next section provides a brief overview of the socioeconomic conditions of the
KwaZulu-Natal Province, as well as the economic and social reforms that occurred

between the three KIDS waves.

58

4.3 Background Information: KwaZulu-Natal Province

KwaZulu—Natal, the most populous province in South Africa, is home to
approximately 20% of South Africa’s population of 44 million and was formed in 1994
by combining the former Zulu homeland with the old Natal province. ’0 Although not the
poorest province in South Aﬁica, it arguably has the highest incidence of deprivation in
terms of access to services and perceived well-being (Carter and May, 2001; Leibbrandt
and Woolard, 1999). The province’s urbanization rate of 42 percent is relatively high
compared to poorer provinces such as the Eastern Cape (37 percent) and Limpopo
Province (11 percent). KwaZulu-Natal is also home to most of South Africa’s ethnically
Indian people who constitute 14% of the province’s population. Black Africans constitute
about 76% of the province’s population, with people of European descent (largely
British) and coloureds constituting 7% and 3%, respectively.11

The economic, social, and racial stratiﬁcation of KwaZulu-Natal mirrors that of
the country as a whole: the province includes a wealthy metropolitan area, Durban, poor
townships surrounding it, and a poor and largely rural former homeland, KwaZulu.
Poverty and inequality in the province are similar to those at the national level (Woolard
et al., 2002), so that reasonable generalizations can be made about the rest of the country
based on ﬁndings from this study.

The period covered by the KIDS data, coincides with the switch from minority to
democratic governance in South Africa. Since its inception in 1994, the democratic

government’s orientation toward addressing the problems of poverty and inequality

 

'0 During the racially segregationist apartheid government, homelands were created in South Africa as
reservation areas for black Africans. Infrastructural developments are usually low, and poverty rates high in
the homelands compared to the rest of the country.

” The population of South Africa has been historically categorized into ﬁve racial groups: blacks, whites,
Indians, coloureds, and Asians. Coloureds are deﬁned as people of “mixed” race.

59

underwent marked shifts. Aggressive programs were introduced to improve access to
shelter, sanitation, and education to the previously segregated black communities. In
1996, the government introduced a program known as Growth, Employment and
Redistribution (GEAR) which focused on macroeconomic stabilization and structural
adjustments. Under GEAR, many of South Africa’s sectors were reformed, agriculture
being among the most aggressively reformed. For instance, the Agricultural Marketing I
Act of 1996 called for closure of state supported commodity marketing boards and the
termination of all forms of subsidies to agriculture. Other major reforms were carried out
in the industrial, labor, and ﬁnance sectors.

Empirical evidence points to the deepening of inequality in post-apartheid South
Africa (Adato et al., 2004). In KwaZulu-Natal, the Gini coefﬁcient grew from 0.38 in
1993 to 0.42 in 1998. The poverty headcount in KwaZulu-Natal during the same period
increased from 27% to 42% (Carter and May, 2001).

In summary, the KIDS survey covers a period of signiﬁcant social and economic
changes in the South Africa. Hence, the KIDS dataset provides a unique opportunity to
learn about the household behavior in a period of rapidly changing economic and social

environment.

4.4 Descriptive Statistics

The questionnaires from each of the three survey waves contain two sections on
household expenditures. The ﬁrst section collected expenditure information on broad
consumption goods (such as food, housing and clothing), and the second collected

information on food expenditure and food prices.

60

Table 4.1 Average Budget Shares of Broad Consumption Goods

 

 

Year Budget Share % Change

Consumption Good 1993 1998 2004 Change 1993-2004
1993-2004

Food 0.52 0.40 0.37 -0.15 -29
Housing 0.11 0.18 0.16 0.05 45
Clothing 0.04 0.03 0.03 -0.01 25
Transportation 0.06 0.06 0.07 0.01 17
Health 0.01 0.01 0.01 0 0
Education 0.02 0.03 0.04 0.02 100
Utilities (energy, 0.10 0.10 0.10 0 0
water, etc.)
Personal Items 0.06 0.08 0.09 0.03 50
Insurance 0.02 0.02 0.03 0.01 50
Remittances 0.02 0.01 0.02 0 0
Other expenditure 0.04 0.06 0.07 0.03 75

 

Table 4.1 presents a list of the broad consumption goods and their expenditure
shares for each of the panel years. The budget share for food has consistently declined
across the panel years. This may be the result of a variety of factors, including the
possibility of structural change. We include year dummies to account for the possibility
of structural change. These dummies will, of course, capture the effects of other
aggregate time effects, not just structural change. The budget share on food is
consistently the highest category during each panel year. The decline in the share of food
in the households’ budgets may be reﬂection of Engel’s law, which holds that when a

family’s income increases, the proportion of money spent on food decreases.

61

The average household (nominal) income for 1993 was 1444.08 rands (R), and it
grew to R2757.66 and R3797.71 in 1998 and 2004, respectively.12 This represents
nominal income growth of over 150% during the 1993-2004 sample period. Expenditure
shares on education, housing and transportation experienced slight increases during the
sample period, while the share on clothing decreased.

The food expenditure information was collected by asking households if they had
eaten a particular food item in the month preceding the survey, and for the items eaten,
the amount spent on each item was requested. To maintain a reasonable number of
parameters, these food items are grouped into seven commodities: grains; meat and ﬁsh;
dairy products; fruits and vegetables; oils, butter, and fats; sugar and sugar products; and
other foods. In grouping these food items, an attempt was made to place goods that are
close substitutes in the same group whenever possible, in accordance with the commodity
grouping theories discussed in chapter 2. Table 4.2 lists the food groups and the
individual items in each group. ’3 The budget shares of each of these food groups and their
average prices at each Of the panel years are listed in Table 4.3.

Throughout the three panel years, grains constituted the largest share of
households’ total food expenditure. Maize, wheat ﬂour, and bread, all in the grains food

group, are staples in South Africa.

 

'2 Rand (R) is the South African currency; the exchange rate between South African Rand (SAR) and
United States Dollar (U SD) averaged 6.50 SAR = 1 USD between March 2005 and March 2006 (Statistics
South Africa).

’3 Alcohol products are not included among the list of food items in Table 4.2 because no data were
collected on alcohol consumption. Thus, we are effectively assuming that the direct utility function is
weakly separable between alcohol and other foods. Although this assumption may be reasonable in some
cases, its violation may lead to econometric problems of expenditure endogeneity. However, we explicitly
test for expenditure endogeneity in the next chapter, which may address this problem, at least in part.

62

Table 4.2 The Composition of Composite Food Commodity Groups

 

 

Food Group Food Items

Grains maize grain (samp), maize ﬂour, rice, white bread, brown bread, wheat
ﬂour, breakfast cereal

Meat and ﬁsh mutton, beef, pork, chicken, fresh ﬁsh, tinned ﬁsh

Fruits and vegetables dried peas, lentils, beans, potatoes, madumbes, sweet potatoes, pumpkin,

squash, carrots, cabbage, tomatoes, bananas, apples, citrus fruit
Dairy products fresh milk, sour milk, yoghurt, milk powder, cheese
Oils, butter, and fats cooking oil, margarine, butter
Sugar and sugar products Sugar, soft drinks

Other baby formula, salt

 

Table 4.3 Average Budget Shares and Prices of the Food Groups

 

 

Ave" 9 Bud 0‘ Shares Bud et Share-Wei hted Price
Indices

Commodity 1993 1998 2004 1993 1998 2004
Grains 0.35 0.32 0.31 0.38 1.09 7.18
Meat and ﬁsh 0.21 0.25 0.22 1.06 2.57 14.00
Fruits and vegetables 0.17 0.17 0.19 0.34 1.52 4.99
Dairy products 0.07 0.05 0.08 1.63 1.48 17.09
Oils, butter, and fats 0.06 0.05 0.05 1.09 2.31 4.80
Sugar and sugar 0.05 0.05 0.04 0.40 1.41 5.91
products
Other 0.09 0.11 0.11 0.55 2.14 15.12
Total food expenditure R 715.35 R 693.25 R 1013.27

 

 

 

I‘ With the exception of fresh milk, sour milk, cooking oil, and soft drinks, the prices for all the food items
are Rands per kilogram; prices for the former items are Rands per litre.

63

Meats and vegetables are typically consumed jointly with cooked maize meal, which
partly explain their relatively large share in households’ food budgets.

The share of grains in the households’ total food expenditure decreased slightly
between 1993 and 2004, which provides some evidence of Bennet’s law, which holds
that households switch from less to more expensive calorie consumption as their incomes
rise. The budget shares of meat products, a more expensive source of calories, rose
slightly during the same period. Total expenditure on food (last row in Table 4.3)
decreased between 1993 and 1998, but increased sharply between 1998 and 2004. This is
partly due to the unusually large increase in food prices between 2000 and 2002. In fact,
prices for many of major food products rose by over 100%. Concerns by consumer
groups and the government about possible price manipulation and unfair use of market
power even led to the establishment in 2002 of a commission of enquiry into food pricing

in South Africa (FPMC, 2003).

Income-groups and rural-urban differences

I As has been mentioned in chapter one, income distribution is South Africa is
highly uneven. Pooling incomes of all households (i.e., ignoring this income inequality)
may obscure important information on differences in the behavioral patterns of
households. An understanding of the differences in the food expenditure patterns of high
and low income households also has important implications for such policies as food
pricing reforms and safety nets. For these reasons, in this study, we divide households
into three income groups (low, middle, and high), and analyze the consumption behavior

of households in each group. Households are ranked from lowest to highest based on

64

their average (averaged over the three panel years) real incomes and divided into three
groups of equal sizes; the national consumer price index is used to convert incomes from

nominal to real. The average budget shares of the three income groups are reported in

 

 

 

 

Table 4.4.
Table 4.4 Income-groups and Rural-urban differences: Budget shares and prices
Average Budget Shares
Income Groups Regions Mean Prices

Commodity Low Middle High Rural Urban Rural Urban
Grains 0.37 0.35 0.26 0.37 0.24 4.15 4.68
Meat and ﬁsh 0.21 0.22 0.26 0.21 0.27 7.05 A 7.20
Fruits and vegetables 0.18 0.18 0.16 0.18 0.17 7.39 7.86
Dairy products 0.05 0.06 0.08 0.05 0.09 6.98 6.69
Oils, butter, and fats 0.05 0.05 0.05 0.05 0.05 8.18 7.87
Sugar and sugar products 0.06 0.05 0.03 0.05 0.04 8.87 8.74
Other 0.07 0.08 0.14 0.08 0.14 9.38 9.59
Mean household 584.97 746.51 1089.90 725.94 967.34
expenditure

774.34 1696.70 6064.22 1981.55 4553.35
Mean household income

 

 

 

 

1' With the exception of fresh milk, sour milk, cooking oil, and soft drinks, the prices for all the food items
are Rands per kilogram; prices for the former items are Rands per litre.

It is clear from Table 4.4 that expenditure patterns differ across households in
different income groups. Low-income households spend about 42% more of their total
food budgets on grains than high-income households. This is to be expected, given the
role of grains as a relatively inexpensive source of calories. On the other hand, high-
income households spent more on meats and dairy products, relatively expensive sources

of calories. The differences in incomes between high and low income households are also

65

very high; the average income of hi gh-income households is over seven times larger than
that of low-income households. Table 4.4 also reports the average budget shares of rural
and urban households, as well as rural-urban prices. On average, urban incomes are more
than two times rural incomes, and urban households have larger (over 30%) budgets for
food than rural households. This explains, in part, the low share of grains and the high
share of meat and dairy products in the food budgets of urban households. Part of the
reason urban households spend more on food than rural households is that prices of major
foods (namely, grains, meat/ﬁsh, and fruits/vegetables which constitute about 70% of the
food budget) are more expensive in urban than rural areas.

The socioeconomic and demographic characteristics of households play an
important role in determining their demand patterns. The demand model will be
estimated incorporating these variables to control for varying preference structures and
heterogeneity across households. The summary statistics of the socioeconomic and

demographic variables considered are reported in Table 4.5.

 

 

Table 4.5 Summary statistics of household composition variables

Income Groups Rural/Urban
Variable

Pooled Low Middle High Rural Urban

Household size 6.8 6.4 7.4 6.6 7.3 5.7
Education of head 5 3.1 3. 9 7.8 3.8 7.3
Age of household head 54.8 53.7 57.0 53.4 55.6 52.7
Proportion male headed 0.6 0.5 0.6 0.7 0.6 0.6
Proportion rural 0.7 0.9 0.7 0.4 - -
Proportion black (race) 0.8 1.0 0.9 0.6 1.0 0.6

 

 

 

 

66

On average, urban households are of smaller sizes and headed by younger males
with high levels of education. Most of these characteristics are shared by high-income
households, except the latter have larger family sizes. The rural and low-income groups
comprise mainly black households. Overall (i.e., in the pooled sample), black households
constitute 85% of the total sample. These statistics are in line with those for the entire
KwaZulu-Natal Province; the proportion of blacks in the province is 82 %, and 57 % of

the province’s population resides in rural areas.

4.5 Zero-Expenditure

When modeling demand using micro data, it is typical to observe a signiﬁcant
number of households that purchase zero quantity of some of items (or commodities)
during the survey period. A sample with a large number of non-purchasing households
poses a number of econometric challenges. One of the challenges arises when price data
are not available and unit values (calculated as purchase value divided by quantity) are
used in place of “prices”. In that case, the problem becomes one of missing price and
quantity data. In cases where price data are available, a large percentage of zero
consumptions requires estimation techniques that jointly capture the behavior of both
consuming and non-consuming households. Table 4.6 reports the percentages of
households with zero consumption in our sample. Clearly, the problem of zero
consumption is not severe in the food groups considered here. This is not surprising,

given that each of these food groups is an aggregate of several food items.

67

Table 4.6 Proportions of households with zero consumption for various food groups

 

Proportions of Zero Purchase

 

Groups Grains Meats/ﬁsh Fruits/Veg. Dairy Fats/Oils Sugar Other
Rural 0.00 0.02 0.00 0.18 0.03 0.01 0.01
(n = 1446)

Urban 0.00 0.01 0.00 0.05 0.01 0.01 0.00
(n = 735)

Low 0.00 0.03 0.00 0.24 0.04 0.02 0.02
(n = 729)

Middle 0.00 0.02 0.00 0.12 0.03 0.01 0.00
(n = 723)

High 0.00 0.01 0.00 0.05 0.00 0.00 0.00
(n = 729)

All @ooled) sample 0. 00 0.01 0. 00 0.14 0.02 0.0] 0.01
(n = 2181)

 

Typically, the seriousness of the zero-expenditure problem increases with the level of
disaggregation in the food groups. The dairy food group is the only one with a signiﬁcant
number of non-consuming households, particularly in the rural and lower-income
samples. Appropriate econometric techniques (explained in chapter three) will be applied

to the estimation of the budget share equation for dairy.

4.6 Chapter Summary

This chapter discussed the sources of the data to be used in estimating the demand
model. Descriptive statistics of the variables entering the model are presented. Food is
found to constitute the largest share of the households’ total expenditure. Within the food
commodity, the budget share of grains is the largest, although this share decreases at
higher income levels. Expenditure patterns differ among rural and urban households,

especially in the grains, meat and ﬁsh, and dairy commodities, with rural households

68

consuming more grains and less of the latter. Observed zero-expenditures are found to be

signiﬁcant only in the dairy food group.

69

CHAPTER FIVE

EMPIRICAL RESULTS

5.1 Introduction

This chapter presents results from estimating the demand model. The ﬁrst section
tests for the presence of nonrandom attrition. Section 5.3 presents the results of the LM
tests for quadratic expenditure speciﬁcation and expenditure endogeneity. The demand
estimation results are discussed in section 5.4, focusing mainly on the expenditure and
price elasticity estimates. Heterogeneity in the food expenditure patterns of rural versus
urban households, as well as across income groups, are analyzed in section 5.5. The
demand estimation results with correction for zero expenditures are presented in section
5.6. Section 5.7 presents estimates of the welfare effects of an indirect tax reform based
on different model speciﬁcations, and estimates the biases that result when due model
misspeciﬁcation. Section 5.8 summarizes and compares elasticity estimates from this
study with those from existing demand studies in South Aﬁica. The last section, section

5.11, summarizes the key ﬁndings from this chapter.

5.2 Attrition

This section analyzes and tests for attrition startig with a simple comparison of means
of selected key variables for two subsamples, one for households that were re-
interviewed in all the three panel rounds and the other for households that subsequently
drop from the sample. Although not a formal test for attrition, this univariate comparison

of means will give an idea of the extent to which the unconditional means of variables

70

differ among attritors and nonattritors. In order to determine the household and
community characteristics that explain which households attrit and which do not in a
conditional mean sense, a probit model for the probability of attrition will be estimated.
The results of the multivariate probit estimates and the univariate means-comparison tests
will be compared in terms of the signiﬁcance of the household and community
characteristics in explaining attrition, and the direction of these effects on attrition. To
determine whether or not attrition affects consistent estimation of the coefﬁcients of
interest, we estimate a reduced form for the household food expenditure function, and
test for whether there are signiﬁcant differences between the coefﬁcient estimates for
households that attrit and those that stay. The base sample for these analyses includes
black and Indian households that were interviewed in 1993, since these were the two
racial groups targeted for re-interview in the 1998 and 2004 surveys. The total number of
households in the 1993 sample is 1241, and 727 of these were re-interviewed in both the

1998 and 2004 surveys.

5.2.1 Difference-of-means tests for major outcomes and control variables

The means compared here are of household and community characteristics as well
as other control variables measured in the 1993 survey. The variables selected for this
purpose are either those that are most relevant to this study, in the sense that they are
related to household food expenditure allocation decisions, or those that are expected to
inﬂuence attrition. A list of these variables is presented in Table 5.1. The ﬁrst column of
Table 5.1 reports the means and standard deviations for households that are re-

interviewed and the second column for those that attrit. The third column lists the

71

differences in the means of the nonattritor and attritor samples, with the results of the t-

tests for equality of these means reported in parentheses.

 

 

 

 

Table 5.1 Differences-of-Means Tests between the Attritors and Nonattritors in KIDS 1993
Nonattritors Attritors Difference
(B) (A) (B - A)
Means (S.D.) Means (S.D.) In Means2 (t-test)’

Household Characteristics
Household size 6.956 (3.526) 5.066 (2.945) 1889‘" (10.25)
Race (1 if black) 0.855 (0.351) 0.794 (0.405) 0062*" (2.79)
Gender of head (1 if male) 0.673 (0.469) 0.687 (0.464) -0.014 (-0.53)
Education of head 3.645 (3.664) 4.196 (4.101) -0.551*"‘ (-2.43)
Age of head 52.35 (13.881) 49.25 (15.199) 3098*" (3.66)
Per capita monthly food 119.98 (72338)) 139.58 (90.517) -l9.598"* (-4.07)
expenditure
Per capita total monthly 274.81 (837.88) 334.33 (468.13) -59.52 (-l.59)
income

Community Characteristics
Rural (1 if rural) 0.663 (0.473) 0.632 (0.021) 0.031 (1.11)
Mean per capita food 126.19 (35.81) 130.78 (41.10) 4.59" (-2.04)
expenditure
Mean per capita income 264.37 (281.66) 349.19 (419.24) -84.72*"‘ (-3.99)
Number of schools 2.756 (2.131) 2.276 (1.766) 0480*“ (4.32)
Health facility 0.554 (0.497) 0.535 (0.022) 0.019 (0.67)
(1 if available)

Sample size 727 514

 

 

 

 

1' two-sample t-tests with unequal variances. 2' The asterisks *** indicate signiﬁcance at 1 percent level;
" and * indicate signiﬁcance at 5 % and 10 %, respectively.

Based on the signs of the differences in means, it can be seen that on average
households that were most likely to be re-interviewed are black, from rural areas, with
larger sizes, and an older head. Households headed by males, with lower levels of
education, and residing in communities with low mean per capita food expenditure and

income had a low likelihood of being re-interviewed.

72

 

These results conﬁrm a priori expectations. For instance, in the case where
attrition was due to migration, one would expect large-size households to be less mobile,
given the larger costs of relocating a family with many members. Higher income
facilitates mobility, and this effect is likely to be strengthened by factors such as
education and gender, because households headed by an educated male have higher
incomes on average.14 The number of schools in a community and the presence of a
health facility increased the likelihood of re-interview, partly due to the role they play as
primary sources of information for the survey teams. The means for household size,
education and age of household head, race, total monthly food expenditure, community
mean food expenditure and income differ signiﬁcantly (at the 5 percent level) between
the sample of households that are re-interviewed and those that attrit.

The problem with the foregoing univariate analysis is that it compares the
unconditional means of variables, and does not take account of the relationships among
variables. However, because interest in this study is in the relationships among variables,
it is more appropriate to examine the presence of non-random attrition in a multivariate
framework. The next section focuses on the question of whether or not attrition can be
predicted by the observable household and community variables, and on whether or not
the effects of each of these variables are attenuated when other socioeconomic variables

are conditioned-on in a regression framework.

 

’4 However, since the 1998 and 2004 KIDS surveys tracked households that moved, other factors may
offset this effect of income on migration; for instance, wealthier households are likely to be well known in
their communities, so that their departure from the community is likely not to be without trace.

73

5.2.2 A probit model for probability of attrition

In this subsection, we estimate a probit model for the probability of attrition in
order to determine whether attrition occurred in a nonrandom manner, and to determine
what variables predict attrition. The dependent variable in the probit model is a binary
variable of whether or not a household is re-interviewed in all the three surveys (=1 if the
household is re-interviewed; =0 if not). 15 The explanatory variables considered include
those that were in the univariate difference-of-means tests, as well as additional
household and community variables that are expected to affect re-contact and re-
interview. These additional variables are: a binary variable for whether or not a
household owned its place of residence in 1993, the month of the survey, a binary
variable for whether or not any member of the household has been a victim of crime in
the 12 months prior to the survey, and dummy variables for supervisor codes (there was
total of eight supervisors in the 1993 survey). The dummy variables for supervisor codes
control for the quality of the ﬁeldwork, since the ability to successfully track a
respondent in subsequent periods depends on the accuracy and detail of information on
the base period questionnaires.

The ﬁrst column of Table 5.2 reports coefﬁcient estimates of the probit model.
Household size, race, household income, and community income are signiﬁcantly
associated with attrition. The dummy variables for supervisor codes are not statistically
signiﬁcant individually, but they are jointly signiﬁcant as a group. Education and age of
the head, household food expenditure, community-mean food expenditures, and the

number of schools in the community are not signiﬁcant in the probit regression.

 

'5 Following Fitzgerald et al. (1998), we do not estimate a dynamic model of survey-by-survey (i.e.,
between-surveys) attrition. Hence, the estimates in this case can be viewed as coming from a model of
cumulative attrition, as opposed to survey-by-survey attrition.

74

Table 5.2 A Selection Probit Model for analyzing Attrition between KIDS Panel Waves

 

Household Characteristics

(Dep. Var. = 1 if attrited)’

Selection Probit

Household size -0.0795"* (0.0177)

Race (1 if black) 5.8547‘" (0.6755)

Gender of head (1 if male) 0.0789 (0.0864)

Education of head -0.0074 (0.0137)

Age of head 0.0011 (0.0031)

Food expenditure -0.0004 (0.0006) ‘
Monthly income 0.1162" (0.0569) "
Property ownership (1 if own) -0.3461*" (0.1183)

Community Characteristics ,_
Rural (1 if rural) 02469" (0.1287)

Mean food expenditure 0.0001 (0.0019)

Mean income 0.0004“ (0.0002)

Number of schools -0.0435 (0.0233)

Health facility( 1 if available) -0.1810" (0.1100)

Month of survey 0.0515 (0.0516)

Crime (1 if occurred) 0.1461 (0.1051)

Supervisor codes jointly signiﬁcant? Yes

Constant -6.2356

cm2 test: overall relation [p > Chiz] 164.08 [0.0000]

 

' Standard errors in parentheses? “" indicates signiﬁcance at 1 percent level; ” and "‘ indicate signiﬁcance at 5 %
and 10 %, respectively.

These variables are also not jointly signiﬁcant (p=0.4297). Households who
owned the dwellings they lived in 1993 were more likely to be re-interviewed, and those
who had been victims of crime 12 months prior to the 1993 survey were less likely to be
re-interviewed. The Chi2 statistic for the overall signiﬁcance of the relation is signiﬁcant,
which implies that attrition between 1993 and 2004 was not purely random. The issue of
whether or not attrition affects the consistent estimation of the parameters of interest in

this study is dealt with in the next section.

75

 

5.2.3 Difference-of-coefficient tests: attritors versus nonattritors

The question addressed in this section is whether or not the coefﬁcients for the
outcome variables that are relevant to this study are affected by attrition. In other words,
the task is to ﬁnd out whether or not the coefﬁcients of interest in this study can be
estimated consistently using only the sample of households that were re-interviewed. To
accomplish this task, we examine whether or not the households who subsequently leave
the sample differ in their initial behavioral relationships from those who stay. Following
Becketti et al. (1988) and Alderman et al. (2000), we regress an outcome variable at the
initial wave of the survey on predetermined variables and test whether the coefﬁcients of
the predetermined variables differ for those respondents who are subsequently lost due to
attrition versus those who are re-interviewed. The outcome variables chosen for this
analysis are the budget shares of the food groups that enter the demand model. We
estimate reduced forms for the budget share equations, and test for whether there are
signiﬁcant statistical differences in the estimated coefﬁcients of nonattitor and attritor
households. '6

To carry out the above difference-of-coefﬁcients test, we divide the 1993 sample
into two groups, group 1 comprising households who are interviewed in all the three
panel surveys, and group 2 comprising households who subsequently leave the sample.
Two indicator variables are then created, corresponding to each of the two groups. The
ﬁrst indicator variable, G1, takes on the value 1 if the household belongs to the ﬁrst group
and 0 otherwise, and the second indicator variable, G 2, takes on the value 1 if a household

belongs to the second group and 0 otherwise. The budget share equations are then

 

'6 In the next sections, we estimate two demand models separately, one using all households and another
using only households in the panel, to further determine the impact of attrition on coefﬁcient estimates.

76

 

 

regressed on a set of household and community variables and their interactions with the
G2 variable. The test for equality of coefficients involves testing whether the coefﬁcient
on each non-interacted variable is equal to the coefﬁcient of the corresponding variable
interacted with G 2.

To ﬁx ideas, let 2" represent the set of household and community variables

included as explanatory variables in the reduced-form food expenditure function, and let
z’,’ represent a full set of interaction terms involving G; and the 2" variables. The

following reduced form regressions are estimated

.11-

h h h
w, =a+z 'B+z,_'y+v

The test for equality of coefﬁcients between attritors and nonattritors is simply an F-test
of the null hypothesis that y = 0. The same household characteristics that enter the
selection probit model are used in the reduced form for household food expenditure,
except the property ownership variable is left out given that it is not expected to directly
affect food consumption decisions. Also, the aggregate food price index is replaced by
the individual commodity prices. The results of the F tests are reported in Table 5.3 (to
conserve space, the full set results are not reported). We report two F statistics at the
bottom of Table 5.3. The ﬁrst F statistic is for the joint equality of all coefﬁcient pairs
including the constant term, and the other for joint equality of all coefﬁcients excluding
the constant term. None of these F statistics is statistically signiﬁcantly different from
zero, implying that we cannot reject the null hypothesis of equality of coefficients for
attritors and nonattritors. In other words, it can be concluded that the coefﬁcients on the
variables in these budget share equations can be estimated consistently using the sample

of only nonattriting households.

77

Table 5.3 Testing Impact of Attrition on the Coefficients of the Budget Share Equations for
the Individual Food Groups

 

 

 

 

 

F tests for equality of coefﬁcients

Grains Meats/Fish FruitsNeg Dairy Oils/fats Sugar Other
Joint effect of 0.75 0.67 1.31 0.84 0.98 1.02 1.31
attrition on all (0.6816) (0.7494) (0.2172) (0.5867) (0.4611) (0.4238) (0.2172)
estimates including
the constant
Joint effect of 0.43 0.68 1.07 0.93 1.08 1.12 1.34
attrition on all (0.9209) (0.7249) (0.3790) (0.5008) (0.3764) (0.3422) (0.2092)
coefficients but not
the constant

 

 

 

 

 

 

 

 

p—values (for prob > F) in parentheses

Hence, based on these F -test tests, it can be concluded that, overall, attrition does not

have a signiﬁcant impact on the slope coefﬁcients of the budget share equations.17

5.3 Nonlinearity
5.3.1 LM test results: OLS and SUR estimations

Our test for nonlinearity, developed in chapter three, builds on the work by Banks et
al. (1997). In particular, the implication of corollary 2 in Banks et al. (p.533) is that a
utility-derived demand system that is rank 3 and exactly aggregable cannot have both the
coefficients on the linear and the quadratic expenditure terms that are independent of
prices. In other words, if such a demand model has a coefﬁcient on the linear expenditure
term that is independent of prices, then it must have a coefﬁcient on the quadratic

expenditure term that is price dependent. Hence, our test for nonlinearity involves testing

 

’7 Another way to check for the impact of attrition on coefficient estimates is to estimate the model of
interest without attrition correction and with attrition correction (using a procedure such as inverse
probability weighting), and then examine if there are large differences in the coefﬁcient estimates.
However, this is computationally burdensome when using nonlinear models that require difﬁcult user-
defrned programs.

78

 

 

for the statistical signiﬁcance of prices in the coefﬁcient on the quadratic expenditure
term. The top part of the table reports results of the LM tests for nonlinearity in each of
the budget share equations. The ﬁrst column of Table 5.4 reports the results of these tests

from pooled OLS estimation.

Table 5.4 Tests for Nonlinearity of the Demand System based on Statistical Signiﬁcance of
Prices of the Coefﬁcient on the Quadratic Expenditure Term

 

Nonlinearity tests in the individual budget share equations

 

Signiﬁcance of Prices:
LM Statistics (Heteroskedasticity-robust)

 

Commodity OLS (p-value) IV-ZSLS (p—value)

 

Grains

Meat and ﬁsh

Fruits and vegetables
Dairy

Oils, butter, and other fats
Sugar

Other

22.03 (0.0025)
5.23 (0.6314)
23.99 (0.0011)
23.77 (0.0012)
12.43 (0.0372)
19.63 (0.0064)

75.46 (0.0000)

24.64 (0.0009)
19.63 (0.0064)
21.59 (0.0030)
7.63 (0.3660)
6.98 (0.4310)
11.34 (0.1244)

41.87 (0.0000)

 

System-wide test for nonlinearity (all budget share equations)

 

SUR 3SLS

Chi-square (p-value) 158.63 (0.0000) 87.82 (0.0000)

 

Based on these results, the null hypothesis that the coefﬁcient on the quadratic
expenditure term is independent of prices is rejected (at the 10% signiﬁcance level) in all
individual budget share equations, except that for meat and ﬁsh. The implication of these

results is that the individual budget share equation for meat and ﬁsh only require a linear

79

expenditure term, so that the inclusion of the quadratic expenditure term is unnecessary in
this case.

To allow for cross equation correlations, we also estimate the equations jointly in a
systems framework and test the null hypothesis that the coefﬁcients on the expenditure
terms across all equations do not depend on prices. Results of the Chi2 test computed
from the SUR estimation of budget share equations are reported at the bottom part (ﬁrst
column) of Table 5.5. This test provides strong evidence against the null of price-

independence of the coefﬁcient on the quadratic expenditure term.

5.3.2 LM test results: IV-ZSLS and 3SLS estimations

As discussed in chapter three, total household food expenditure is likely to be
correlated with the error term, and this may affect the results of the LM tests. In this
subsection, we explicitly test for the endogeneity of expenditure to determine whether or
not the LM test needs to be adjusted. Total household income is used as an identifying
instrumental variable (IV) for total household food expenditure.18 For income to be a
good IV for expenditure, it must meet two conditions: the relevance condition, which
requires that income be sufﬁciently correlated with expenditure (the endogenous
variable), and the exogeneity condition, which requires that income must not be
correlated with the error term in the demand model. The former condition is testable, and
the latter cannot be tested (see Wooldridge, pages 118-122). A test for the relevance

condition involves determining whether income is partially correlated with expenditure.

 

'8 For brevity, the term expenditure will be used to refer to total household expenditure, and income will be
used to refer to total household income.

80

This test involves determining whether log total household income (In m) is statistically
signiﬁcant in the reduced form regression for log expenditure (In x).

The middle column of Table A1 in the appendix to this chapter reports parameter
estimates of the reduced form regression for In x. Based on simple t-tests, the coefﬁcient
on (In m)2 is signiﬁcantly different from zero, while the coefﬁcient on In m is not, mainly
due to the collinearity between 1n m and (In m)2. A formal test for the relevance condition

involves testing for the joint signiﬁcance of the coefﬁcients on both instrumental

’1

variables in the reduced form. The results of the F tests for the joint signiﬁcance of In m

and (In m)2 are presented in the bottom row of Table 5.4. These tests provide evidence of
a strong partial correlation between 1n m and (In m)2 and In x. Thus, based on the results
of this test, it can be concluded that income and income squared are relevant instruments
for expenditure, and hence, the former will be used as instrumental variables for the latter
in the analyses that follow (the exogeneity assumption is, of course, maintained).

Table 5.4 also reports the results of the tests for expenditure exogeneity. The
procedure for carrying out endogeneity tests is as discussed in chapter three; it involves
augmenting the budget share equation for each food group with residuals from the
reduced forms for expenditure (1?), then testing for their statistical signiﬁcance. Table A2
at the end of this chapter presents estimates of the reduced forms for each budget share
equation. The results of the tests for the signiﬁcance of r7 (and hence, for the test of the
null hypothesis that expenditure is exogeneous) are reported in the top portion of Table
5.5. As can be seen from these test results, there is limited statistical evidence against the
null hypothesis of expenditure exogeneity. The hypothesis is rejected (at the 10%

signiﬁcance level) only in the budget shares equations for grains, meat and ﬁsh, and

81

 

dairy. The strong statistical evidence supporting expenditure exogeneity in the grains
budget share is somewhat counterintuitive. One would have expected that, because grains
comprise food items that are major staples in South African diets, its relation with total
food expenditure would be somewhat ‘ﬁxed.’

The problem with testing for endogeneity in the individual budget share equations is
that it ignores correlations among the equations. To allow for these correlations, we
estimate the budget share equations as a system using the seemingly unrelated regressions

(SUR) and then test the null hypothesis that 1? is statistically signiﬁcant across all the

.f’T‘m'I

equations. Results of the 352 tests for the statistical signiﬁcance of 1? are reported in
middle part of Table 5.5 (to conserve space, not all the coefﬁcient estimates of the SUR
estimation are reported). The ﬁrst 12 statistic is computed from the unrestricted SUR
estimation, while the second one is calculated from the theory-restricted SUR estimation;
the demand theory restrictions imposed are homogeneity and symmetry. Both the
restricted and unrestricted SUR-based tests reject the null hypothesis that the coefﬁcients
on I? are jointly zero across all equations, providing evidence that expenditure is
endogenous in the system.

Since we are using two identifying instruments (In m and (In m)2) for In x, we have
one overidentifying restriction. Our test for overidentifying restriction follows
Wooldridge (2002), pp. 122-124. This test (also known as the Sargan test) involves
estimating each budget share equation by IV-ZSLS (using 1n m and (In m)2 as

instruments) and obtaining residuals, regressing these residuals on all exogenous

variables and obtaining the R-squared statistic (call this R: ), and then computing {(1) as

82

 

the product of the number of observations times R3. The results of these tests are also

presented in the top portion (second column) of Table 5.5.

Table 5.5 Results of the Test for the Endogeneity of Expenditure

 

Tests for endogeneity of expenditure in the individual budget share equations

 

 

Commodity Endogeneity tests Overidentiﬁcation tests
t stat (p-value) 12 (p-value)
Grains 3.59 (0.000) 0.01 (0.958)
Meat and ﬁsh -4.11 (0.000) 8.40 (0.004)
Fruits and vegetables 1.37 (0.171) 0.27 (0.600)
Dairy -1.85 (0.064)) 4.58 (0.032)
Oils, butter, and other fats -0.26 (0.796) 2.17 (0.141)
Sugar and sugar products 1.13 (0.258) 10.03 (0.001)
Other 0.22 (0.825) 1 1.12 (0.000)

 

Tests for endogeneity of expenditure across all budget share equations in the system

 

SUR (Unrestricted) 26.73 (0.0002)
SUR(Restricted)' 17.64 (0.0072)

 

Test for the relevance of income and income-squared as IVs for expenditure

 

F stat. (p-value) 1 16.90 (0.0000)

 

' The demand theory restrictions imposed during estimation are symmetry and homogeneity (additivity
is satisﬁed automatically by the data)

As with the ﬁndings from expenditure exogeneity tests, statistical evidence on the
validity of the instruments based on the overidentiﬁcation tests is mixed across budget
share equations. Statistical evidence in support of the exogeneity of In m and (In m)2 is
strong in the budget share equations for grains, fruits and vegetables, and oils and fats.
There is no clear relationship between ﬁndings from exogeneity tests and

overidentiﬁcation restrictions (i.e., the budget share equations that pass the

83

overidendiﬁcation tests are not the same as those that pass (or do not pass) expenditure
exogeneity tests). The ﬁnding that not all the budget share equations pass the
overidentiﬁcation tests indicates that one of the instruments, In m or (In m)2, may not be
completely exogenous in these equations.

In summary, the exogeneity tests indicate that expenditure is endogenous in the
budget share equations for grains, meat and ﬁsh, and dairy. However, the null hypothesis
that expenditure is exogenous across all budget share equations is rejected. Given these
ﬁndings, it is necessary to determine whether or not the LM tests results stay the same
when expenditure endogeneity is adjusted, particularly for the grains, meat and ﬁsh, and
dairy commodities.

The results in the second column of Table 5.4 are computed from budget share
equations estimated using instrumental variables two-stage least squares (IV-ZSLS), with
income used as an IV for expenditure. As can be seen from these results, after adjusting
for expenditure endogeneity, the null hypothesis that the budget share equation for meat
and ﬁsh is linear expenditure in expenditure is rejected. We consider these results (based
on IV-2SLS) to be more reliable in the case of meat and ﬁsh, given the ﬁnding from the
endogeneity tests which indicated that expenditure is endogenous in the budget share
equation for meat and ﬁsh. Contrary to the LM test results based on the equation-by-
equation OLS estimations, the null hypotheses that expenditure is linear in the budget
share equations for dairy and oils and fats are not rejected. The null hypothesis of
expenditure exogeneity was not rejected in the budget share equation for oils and fats,
which implies that if the individual budget share equations are considered, the OLS

results may be more reliable.

84

 

To account for cross equation correlations, we also estimated the equations as a
system, and tested the null hypothesis that the coefficient on the quadratic expenditure
term does not depend on prices. The results of this test are reported in the bottom part
(second column) of Table 5.4. The )8 statistic for this test is computed from three-stage
least squares (3 SLS) estimation with the expenditure instrumented by income. Similar to
the results of the SUR test, this test provides strong evidence against the null of price-
independence of the coefﬁcient on the quadratic expenditure term.

In summary, the null hypothesis that expenditure enters the demand model linearly is
rejected in six of the seven budget share equations based on the endogeneity-unadjusted
OLS estimations, and in four budget share equations when expenditure endogeneity is
corrected for using IV-ZSLS. When cross-equation correlations are allowed for using
SUR and 3SLS, we ﬁnd strong evidence in favor of the QUAIDS model speciﬁcation.

Given these results of the nonlinearity tests, and the ﬁnding in the previous subsection
that expenditure is endogenous in some budget share equations and that it is endogenous
in the equation system, we will proceed by estimating the demand models that include the
quadratic expenditure term (that is, the QUAIDS model) with expenditure endogeneity
endogeneity adjusted for. Results of the endogeneity-unadjusted models will also be
presented, so as to determine the extent to which ignoring endogeneity biases the

parameter estimates.

5.4 Demand Model Results
This section reports estimation results of the demand models. All of the demand
models are estimated using pooled maximum likelihood (ML), with convergence

occurring at 0.000001, the default tolerance level for MLE in Stata. Theoretical

85

restrictions of adding-up, homogeneity, and symmetry are maintained during estimation.
The budget equation for the ‘other’ food group was deleted during estimation to avoid
singularity of the variance-covariance matrix when all seven equations are included.
Parameters of the deleted equation are recovered through the adding-up restrictions.

Due to the large number of parameters estimated, not all estimation results will be
presented. Presentation will concentrate mainly on the elasticity estimates, and how these
change when different model speciﬁcations are considered.

This section starts by conducting model speciﬁcation tests. The LM tests for
QUAIDS versus AIDS model speciﬁcations based on the statistical signiﬁcance of prices
in the coefficient on the quadratic expenditure term (Table 5.5) supported the QUAIDS
speciﬁcation. In this section, we conduct the likelihood ratio (LR) tests for AIDS versus
QUAIDS speciﬁcations. The LR testing approach differs slightly from the LM-based
tests of the previous section in that the LR tests are based on the observation that the only
difference between the AIDS and QUAIDS models is that AIDS contains only the linear
expenditure term, while QUAIDS contains both the linear and quadratic expenditure
terms. In other words, QUAIDS nests AIDS, so that once QUAIDS has been estimated, a
test for whether or not AIDS is the appropriate model speciﬁcation involves simply

checking for the statistical signiﬁcance of the quadratic expenditure term. The coefficient

K
on the quadratic expenditure term is 2., / b(p) = 2, /1_[p”' so that testing for its

if ’
i=1

signiﬁcance involves simply testing for the statistical signiﬁcance of lambda (2,). The
main difference between this test and the LM tests is that this test requires the estimation
of the QUAIDS (unrestricted) model, as opposed to the LM test for which only the

estimation of the restricted model is needed. Also, the approaches followed in deriving

86

these tests are different in that the tests based on LM statistic tests for the statistical

signiﬁcance of prices in b(p), while the LR test checks for the signiﬁcance of 2 in the

coefﬁcient on the quadratic expenditure term.

The tests for signiﬁcance of 2,- are conducted in the endogeneity-uncorrected
QUAIDS model. The reason for using endogeneity-uncorrected model, as Opposed to the
model with endogeneity corrected for, is to avoid problems of inferential invalidity
caused by generated regressors (Wooldridge, 2002; pp. 115-118). This problem arises
here because the use of the control function procedure involves including the residuals
from the reduced form regressions as regressors in the demand model. But, because these
residuals are generated using the same data used for demand estimation, their inclusion as
regressors raises questions in terms of the asymptotic validity of the estimated standard
errors and test statistics on other regressors (parameters can still be estimated
consistently).

The ﬁrst column of Table 5.6 reports results of the tests of the null hypothesis that
lambda (2,) is zero in the budget share equation of each of the food groups. This
hypothesis is rejected in the budget share equations of four of the seven food groups, thus
providing some evidence in support of the QUAIDS model speciﬁcation. So, in addition
to the budget share equation for meat and ﬁsh, which was also found to require only the
linear expenditure term by the LM tests (Table 5.5), the LR tests indicate further that the
budget share equations for fruits and vegetables and oils and fats only require the linear
expenditure term. The ﬁndings in the case of oils and fats are the same as those from IV-
ZSLS. As explained above, the approaches followed in constructing the two tests differ,

so that their leading to different conclusions regarding which budget share equation is

87

linear in expenditure and which is not is not necessarily unexpected. However, what we
can conclude is that both provide evidence against the AIDS model as a system
speciﬁcation. A test of the null hypothesis that 2 is not different from zero in all the
budget share equations is strongly rejected (Chi2 = 72.56, p=0.0000).

Table 5.6 Tests Endogeneity of Expenditure, and for the Statistical Significance of Lambda

in the demographically-extended QUAIDS Model

 

Tests based on the budget share equations for each commodity

 

 

 

Expenditure Endogeneity Tests
Signiﬁcance of QUAIDS Nonlin. AIDS LA/AIDS
Commodity Lambda t-tests (p-val.) t-tests (p-val.) t-tests (p-val.)
11’ tests (p-val.)
Grains 12.42 (0.0004) -0.05 (0.964) -0.11 (0.911) 0.87 (0.385)
Meat and Fish 0.01 (0.9501) -1.53 (0.126) -1.75 (0.081) -2.60 (0.009)
Fruits and Vegetables 0.73 (0.3929) 1.17 (0.241) 1.06 (0.288) 1.81 (0.071)
Dairy 12.37 (0.0004) 0.31 (0.753) -0.02 (0.986) -0.67 (0.502)
Oils, butter, other fats 1.97 (0.1600) -0.99 (0.321) -1.12 (0.261) -0.68 (0.498)
Sugar 11.99 (0.0005) -O.24 (0.807) -0.83 (0.405) -0.09 (0.929)
Other 50.94 (0.0000) 1.07 (0.284) 1.93 (0.053) 1.12 (0.263)

 

 

 

System-wide (all equations) test

 

 

x2 (p-value)

 

72.56 (0.0000)

 

5.03 (0.5398)

8.22 (0.2226)

10.22 (0.1158)

 

The next step in the analysis in this section is to test for the exogeneity of total

household food expenditure in the QUAIDS model. As discussed in chapter three,

expenditure endogeneity is adjusted for using the control ﬁmction approach, which

88

 

involves augmenting each of the budget share equations in the demand system with the
residuals from the reduced form regression for expenditure. Once the reduced form
residuals have been augmented to the budget share equations, testing for exogeneity
becomes straightforward, as it involves simply testing for the statistical signiﬁcance of
the coefﬁcient on the residuals. We follow Blundell and Robin (1999) and include only
the residuals from the reduced form for In x, using income and income squared as
instruments for In x.

Results of the Chi2 tests for expenditure exogeneity in the QUAIDS-estimated budget
share equations of the individual food groups are reported in the second column of Table
5.6. As is clear from these results, statistical evidence against expenditure endogeneity in
the individual budget share equations is very weak, much weaker than was found with
OLS-based tests. The results of the test of the null hypothesis that expenditure is
exogenous across all budget share equations in the demand model are presented in the
last row of Table 5.6. This test gives a Chi2 statistic of 5.03 (p=0.5398), implying that in
the case of system estimation of the budget share equations, it may not be necessary to
control for the expenditure endogeneity. Thus, based on these results, if one were to test
the null hypothesis of expenditure exogeneity in the individual budget share equations
using tests based on OLS estimations, there would be a higher likelihood of rejecting the
null hypothesis than if one used tests based on the nonlinear QUAIDS estimation. The
third and fourth columns of Table 5.6 also report results of the tests for expenditure
endogeneity based on the AIDS and LA/AIDS models. These will be discussed in detail
in the latter sections. For now, it sufﬁces to mention that exogeneity tests in the nonlinear

AIDS model lead to the same conclusion as tests based on the QUAIDS model—that

89

expenditure is not endogeneous across all the budget share equations. Tests based on the
LA/AIDS model provide some evidence, although weaker (x2 = 10.22, p = 0.1158), Of
expenditure endogeneity.

To summarize the results in this section, we found that both the LM and LR
speciﬁcation tests support QUAIDS, as opposed to the AIDS, model. Tests for
expenditure exogeneity based on the QUAIDS estimation led to failure to reject the null
hypothesis of expenditure exogeneity. Hence, based on these test results, our preferred
estimates are the results of the QUAIDS model without adjustment for expenditure
endogeneity. However, given the ﬁndings from the OLS-based tests that expenditure is
endogenous, we also report the results of the endogeneity-adjusted QUAIDS model.

Maximum likelihood parameter estimates of the QUAIDS model are presented in
Table A3 at the end of this chapter. The third column reports parameter estimates of the
endogeneity-unadjusted QUAIDS model, while the ﬁfth column reports those for
estimated from QUAIDS controlling for expenditure endogeneity. Only 9 of the 28 price
effects are signiﬁcantly different from zero at the 10% signiﬁcance level, suggesting that
there is not much quantity response to movements in relative prices, possibly due to the
level of aggregation in the commodity groups. Most (34 out of 49) of the coefficient
estimates on the demographic variables are statistically different from zero. Households
with large sizes consume more grains and dairy products while their small-sized
counterparts consume more meat and ﬁsh and fruits and vegetables. These results are as
expected, given that grains provide a relatively cheap source of calories compared to such
foods as meat and ﬁsh, and given that large households are likely to have more children

who consume milk and other dairy products. Formal tests of the effects of household

90

demographic characteristics and time effects on expenditure patterns are presented in
Table 5.7. As is clear from these results, the null hypothesis of no demographic effects is
strongly rejected. The null hypothesis that preferences have remained stable over time
(i.e., that there was no structural change) is also rejected, as shown by highly signiﬁcant
year dummies. The month of the survey is also signiﬁcant across the budget share
equations, indicating the importance of seasonality in food purchase and consumption

patterns.

Table 5.7 Results of the Wald Tests for Demographic effects, Structural Change, and

 

 

Seasonality
12 Degrees of freedom p-value
Demographic effects 1244.97 24 0.0000
Structural change (aggregate time effects) 125.08 12 0.0000
Month/seasonality effects 45.24 6 0.0000

 

The interpretation Of price and income effects is best discussed in terms of elasticities.
Estimates of expenditure elasticities based on both the endogeneity-adj usted and
endogeneity-unadjusted QUAIDS models are reported in Table 5.8. We focus in this
section on the elasticity estimates from the endogeneity-unadjusted models. All
expenditure elasticity estimates are statistically signiﬁcant at less than 1% level. The
estimates are all positive, as would be expected for broadly deﬁned commodities like the

ones considered here. Hence, all of the seven food groups can be classiﬁed as normal,

91

which implies that their demand increases as total household expenditure increases. Meat

and ﬁsh are luxuries, with expenditure elasticities in excess of unity.

Table 5.8 Expenditure Elasticities estimated from QUAIDS Models with and without
Endogeneity Adjustments

 

 

Commodity Expenditure Elasticity
Endog. Adjusted
Grains 0.3881 0.3881
(0.1254) (0.1254)
Meat, ﬁsh 1.1363 1.1363
(0.1326) (0.1326)
Fruits, vegetables 0.9739 0.9739
(0.1095) (0.1095)
Dairy 0.6509 0.6509
(0.1518) (0.1518)
0115, butter, fats 0.5572 0.5572
(0.0989) (0.0989)
Sugar 0.2924 0.2924
(0.0886) (0.0886)
Other 2.9761 2.9761
(0.1818) (0.1818)

 

Standard errors in parentheses

Table 5.9 presents estimates of the own price elasticities. Estimates of all own and
cross price elasticities are reported in Table A4 at the end of this chapter. As can be seen
from Table 5.9, all estimates of the own price elasticities are highly signiﬁcant (at 1%
level). These estimates are negative, as expected. Apart from dairy, all food groups are
either (approximately) unitary elastic or price elastic based on the estimated Marshallian
price elasticities. This indicates the degree of responsiveness that households have to
changes in the prices of these foods. However, when only the substitution effects are
considered, grains and meat and ﬁsh become less price elastic, as shown by the inelastic

compensated own-price elasticities.

92

Table 5.9 Own-price elasticities estimated from QUAIDS models with and without

endogeneity adjustments

 

Marshallian/uncompensated own-price elasticities

 

Endog. Adjusted

 

 

Grains -1.0296 -1.0458
(0.0742) (0.0856)
Meat, ﬁsh -l.1077 -1.1058
(0.1586) (0.1943)
Fruits, vegetables -0.9803 -0.9739
(0.0957) (0.0967)
Dairy -0.8143 -0.8238
(0.0788) (0.0977)
Oils, butter, fats -l.0604 -l.0679
(0.0745) (0.0755)
Sugar -1 .0463 -l .0477
(0.0749) (0.0842)
Other -4.6426 -4.9186
(0.6605) (0.7423)
Hicksian/compensated own-price elasticities
Grains -0.9032 -0.9330
(0.0408) (0.0456)
Meat, ﬁsh -0.8455 -0.8312
(0.0306) (0.0342)
Fruits, vegetables -0.8087 -0.8082
(0.0193) (0.0217)
Dairy -0.7715 -0.7842
(0.0100) (0.0118)
0115, butter, fats -1.0307 -1.0334)
(0.0053) (0.0064)
Sugar -l.0320 -1.0333
(0.0043) (0.0053)
Other -4.3462 -4.6264
(0.0181) (0.0210)

 

Standard errors in parentheses

93

5.4.1. The effects of controlling for expenditure endogeneity

Given the ﬁndings from the OLS-based tests for expenditure endogeneity, we also
report results of the QUAIDS model with adjustment for expenditure endogeneity. The
ﬁfth column of Table A3 at end of this chapter reports the parameter estimates of the
endogeneity-corrected QUAIDS model. The estimates of most interest in comparing the
two QUAIDS speciﬁcations (one with, and the other without endogeneity adjustment) are
the expenditure elasticities. Expenditure elasticities estimated from endogeneity-adjusted
QUAIDS model are reported in the second column of Table 5.8. These estimates remain
virtually unchanged across all equations after controlling for expenditure endogeneity.
Their signs are the same, and their magnitudes and standard errors are very similar. The
own-price elasticity estimates computed from the endogeneity-adjusted QUAIDS model
are reported in the second column of Tables 5.9. As can be seen, controlling for
expenditure endogeneity does not change the estimates of the price elasticities
signiﬁcantly.

Given the ﬁnding that expenditure is not endogenous in the QUAIDS model, our

preferred estimates are those from QUAIDS without endogeneity adjustment.

5.4.2. The effects of home production

To determine the possible effects of home production on expenditure patterns, the
elasticities were also estimated excluding the households who reported engaging in home
production. The elasticity estimates are reported in Table A5 (Part I) at the end of the
chapter. We compare these elasticity estimates with those estimated from QUAIDS with

demographic variables. Apart for the meat and ﬁsh food group, the elasticity estimates

94

are similar to those obtained when all households are used. The exclusion of households
who report home production changes the classiﬁcation of meat and ﬁsh from luxuries to
necessities. However, these changes in magnitudes are also the result of the elimination
of a large number of observations from the main dataset. About 31% of the observations
have nonzero own production. The elimination of this large number of households is
expected to change results, so that these changes cannot all be attributed solely to own

production.

5.4.3. The effects of attrition

In addition to the attrition tests of section 5.2, we investigate the possible effect of
attrition on demand parameters by estimating the elasticities using data on all households,
including those who attrited. The elasticities are estimated using the QUAIDS model with
demographics. The results are reported in Table A5 (Part II) at the end of the chapter.
Compared these estimates with the panel data-based estimates, it can be seen that, apart
from dairy, the expenditure elasticities estimated using the two datasets are very similar.
The own-price elasticities, particularly the Hicksian elasticities, are also very similar.

These ﬁndings are consistent with those from the attrition tests in section 5.2.

5.4.4. The effects of excluding the quadratic expenditure term

This subsection examines the impact of excluding the quadratic expenditure term in
the demand model. As explained in chapter three, the exclusion of the quadratic
expenditure term from the QUAIDS model results in the AIDS model, so that the AIDS

is nested within QUAIDS. If no assumptions are made about the translog price

95

aggregator, 1n a(p) (equation (3.14), chapter 3), then the AIDS model is nonlinear in

parameters, which makes it hard to estimate empirically. However, once the QUAIDS

model has been estimated, estimation of the AIDS model is straightforward, because this

requires simply restricting the coefﬁcient on the quadratic expenditure term to zero. In

this subsection, we estimate the nonlinear AIDS model, and compare elasticities

computed from it with those computed from the QUAIDS model. Table A6 at the end of

this chapter presents the maximum likelihood parameter estimates of the AIDS model.

Estimates of the AIDS expenditure and own-price elasticities are reported in Table 5.10

and Table 5.1 1, respectively.

 

 

Table 5.10 Expenditure Elasticities estimated from LA/AIDS and AIDS models with and
without endogeneity adjustments
Nonlinear AIDS
Endog. Adjusted Endog. Adjusted
Grains 0.8237 0.7937 0.8288 0.8325
(0.0138) (0.0372) (0.0137) (0.0346)
Meat, ﬁsh 1.1482 1.2671 1.1434 1.2153
(0.0185) (0.0494) (0.0183) (0.0452)
Fruits, vegetables 0.8783 0.7993 0.8827 0.8408
(0.0176) (0.0471) (0.0174) (0.0432)
Dairy 1.1799 1.2438 1.1704 1.1720
(0.0378) (0.1024) (0.0374) (0.0940)
Oils, butter, fats 0.6846 0.7333 0.6899 0.7627
(0.0270) (0.0771) (0.0268) (0.0704)
Sugar 0.5800 0.5860 0.5874 0.6378
(0.0249) (0.0727) (0.0246) (0.0657)
Other 1.7038 1.5950 1.6900 1.5208
(0.0383) (0.1049) (0.0379) (0.0955)

 

 

 

Standard errors in parentheses

96

Estimated expenditure elasticities are all signiﬁcant at the 1% level. Given the ﬁnding
in the previous sections that the QUAIDS elasticity estimates are also signiﬁcant at the
1% level, the choice between QUAIDS and AIDS expenditure elasticity estimates cannot
be based on their statistical signiﬁcance. On average, the AIDS expenditure elasticity
estimates are larger than the QUAIDS estimates, which is consistent with the QUAIDS
model not allowing for adequate curvature in the expenditure response of households. On
average, the expenditure elasticity estimates differ by about 53% between the two
models, with most of the AIDS estimates being larger. The largest differences occur in
the elasticity estimates for grains, dairy, and sugar food groups, with expenditure
elasticity estimates from the AIDS model being about 113%, 80%, and 101%,
respectively, larger than those based on the QUAIDS model. Exclusion of the quadratic
expenditure term has a larger effect on the magnitudes of expenditure elasticities than
price elasticities. This is to be expected, given that the main difference between the AIDS
and QUAIDS models lies in the speciﬁcation of the expenditure term.

These are also the three food groups whose budget share equations were found to require
the quadratic expenditure term based on both the LM and LR tests. This partly explains
why exclusion of the quadratic expenditure term has the largest effect on elasticity
estimates of these food groups. Estimates of the own price elasticities are reported in
Table 5.11. The differences in the magnitudes of the estimated own price elasticities are
substantial also in the grains and sugar.

The expenditure and own-price elasticities do not change signiﬁcantly when
correction is made for endogeneity. This is to be expected because the null hypothesis of

expenditure exogeneity was rejected in the AIDS model (Table 5.6).

97

Table 5.11

Own-price elasticities estimated from LA/AIDS and AIDS models with and
without endogeneity adjustments

 

Marshallian/uncompensated own-price elasticities

 

Nonlinear AIDS

 

 

 

 

 

 

 

Endrg. Adjusted Endog. Adjusted
Grains -0.8828 -0.8451 -0.9279 -0.9274
(0.0384) (0.0593) (0.0356) (0.0395)
Meat, ﬁsh -1.0822 -1.0364 -1.0996 -l.1129
(0.0461) (0.0532) (0.0472) (0.0476)
Fruits, vegetables -0.8694 -0.8169 -0.9015 -0.8935
(0.0348) (0.0486) (0.0339) (0.0346)
Dairy -0.8545 -0.8441 -0.8797 -0.8775
(0.0784) (0.0810) (0.0774) (0.0778)
Oils, butter, fats -l.0293 -1.0522 -1.0668 -1.0845
(0.0747) (0.0828) (0.0733) (0.0761)
Sugar -0.8986 -0.8973 -0.9455 -0.9312
(0.0613) (0.0614) (0.0622) (0.0641)
Other -0.8830 -0.9873 -1.2065 -1.2240
(0.1094) (0.1387) (0.1029) (0.1037)
Hicksian/compensated own-price elasticities
LA/AIDS Nonlinear AIDS
Endog. Adjusted Endog Adjusted
Grains -0.6146 -0.5866 -0.6580 -0.6563
(0.0368) (0.0500) (0.0350) (0.0357)
Meat, fish -0.8172 -0.7440 -0.8357 -0.8325
(0.0466) (0.0600) (0.0471 ) (0.0470)
Fruits, vegetables -0.7146 -0.6761 -0.7459 -0.7454
(0.0340) (0.0429) (0.0338) (0.0338)
Dairy -0.7769 -0.7623 -0.8027 -0.8003
(0.0786) (0.0828) (0.0773) (0.0774)
Oils, butter, fats -0.9928 -1.0131 -1.0300 -1.0439
(0.0745) (0.0809) (0.0731) (0.0751)
Sugar -0.8704 -0.8688 -0.9169 ~0.9001
(0.0613) (0.0615) (0.0623) (0.0650)
Other -0.7133 -0.8284 -1 .03 82 -1.0726
(0.1108) (0.1459) (0.1031) (0.1051)

 

 

Standard errors in parentheses

98

5.4.5. The effect of imposing linearity

Nonlinearity in the AIDS model is caused by the translog price index, In a(p)
(equation (3.14), chapter 3). It is common in applied demand analysis to linearize the
AIDS model by replacing this translog price index with a share-weighted price index.
Moschini (1995) develops an index which enhances the approximation abilities of the
linear AIDS model compared to the commonly used indices (such as Stone’s, Laspeyres,
and Paasche indices). The replacement of the translog index with Moschini’s or any of
these linear indices leads to a model that is linear in parameters, which greatly simpliﬁes
empirical estimation. In fact, the only existing theory-based food demand study in South
Africa that considers an exhaustive list of food commodity groups similar to the one
considered in this study uses the linearized AIDS model (LA/AIDS model). This
subsection examines the effect on the price and expenditure elasticities, of imposing
linearity on the AIDS model. To accomplish this, an LA/AIDS model is estimated with
the translog index replaced by Moschini’s price index, and then the LA/AIDS elasticity
estimates are compared with those calculated from the nonlinear AIDS and QUAIDS
models. The estimates of the LA/AIDS expenditure and own-price elasticities are
reported in the ﬁrst two columns of Table 5.11.

The expenditure elasticities estimates and standard errors of the nonlinear AIDS and
LA/AIDS are very similar; on average, the elasticity estimates differ by less than 1% and
the standard errors by less than 2%. However, the differences in the magnitudes of the
elasticity estimates from the two models are larger (about 5%) when expenditure

endogeneity is corrected for. A possible explanation is the ﬁnding of some evidence of

99

expenditure endogeneity in the LA/AIDS model. The differences in the magnitudes of
own price elasticity estimates from the two models are also small. On average, the own
price elasticity estimates from LA/AIDS tend to be larger than those from the nonlinear
AIDS model.

There is an important difference between the elasticity estimates from the
endogeneity-corrected LA/AIDS and AIDS models: the estimates of the Marshallian and
Hicksian own-price elasticities calculated from the LA/AIDS model are larger in absolute
value than those computed from the nonlinear AIDS model for all food commodities.
Hence, at least for the current sample, the linearization of the AIDS model leads to a
downward bias in the estimates of own-price elasticities.

Similar to the ﬁndings in previous section when nonlinear AIDS was compared with
QUAIDS, the differences in the estimated expenditure elasticities between the LA/AIDS
and QUAIDS models are largest for grains (112%) and sugar (108%). The reason for
these large differences is that, in addition to excluding the quadratic expenditure term, the
LA/AIDS model further imposes linearity on the price index, In a(p). As will be shown
later, welfare measures that require estimates of expenditure elasticities will differ

substantially, depending on which model (QUAIDS or AIDS) is used.

5.5 Rural-Urban and Income-Groups Differences

This section examines whether or not there are any signiﬁcant disparities in food
expenditure patterns between rural and urban households, as well as among households in
different income groups. We estimate demand models separately for rural and urban
households, as well as for households in each of the three income groups. To create the

income groups, the CPI-deﬂated income of each household is averaged over the three

100

panel years, and then households are ranked from lowest to highest based on their
averaged incomes. Households are then divided into three income groups, with
households in each income group comprising about one-third of the total sample.

Although the inclusion of the quadratic expenditure term may be appropriate for the
pooled data (i.e., pooled across all households), it may not be necessary when speciﬁc
household groups are considered. For this reason, we start the analyses in this section by
testing for whether or not the quadratic expenditure term is signiﬁcant in the QUAIDS
model estimated for each of the sub-samples (i.e., in each of the rural, urban, and income
groups samples). As before, these tests are conducted in the endogeneity-unadjusted
models. Results Of these tests, based on the statistical signiﬁcance of lambda, are reported
in Table 5.12.

Similar to the ﬁndings with pooled data, evidence in support of the quadratic
expenditure speciﬁcation in the budget share equations for the individual commodities is
mixed. However, when all the budget share equations are considered jointly, the evidence
in favor of QUAIDS is robust across all the ﬁve sub-samples. An interesting observation
about these test results is that there is a clear rural-urban difference, with the statistical
evidence in support of QUAIDS stronger for the urban than for the rural sample. The
statistical evidence in favor of QUAIDS tends to also be weaker in the individual income
groups data than in the pooled data. A possible explanation is that because the role of the
quadratic expenditure term is to capture the curvature of the expenditure responses of
households, grouping households with similar incomes together homogenizes the sample,
thereby playing the role that is supposed to be played by the quadratic expenditure term.

Meenkashi and Ray (1999) found a similar result in India, where statistical evidence in

101

support of QUAIDS was weak when data on the individual Indian states were considered,

but strong in the data pooled across states.

Table 5.12 Tests for Quadratic Expenditure Speciﬁcation based on the Statistical

Signiﬁcance of Lambda in the QUAIDS model

 

Statistical Significance of Lambda: 1’ tests1

 

Commodity Rural Urban Low Middle High
Grains 26.28 4.23 1.10 9.08 0.25
(0.0000) (0.0397) (0.2951) (0.0026) (0.6165)
Meat, ﬁsh 11.30 32.75 1.34 1.73 6.78
(0.0008) (0.0000) (0.2473) (0.1886) (0.0092)
Fruits, vegetables 0.97 1.1 l 0.01 0.01 2.17
(0.3245) (0.2923) (0.9861) (0.9775) (0.1404)
Dairy 2.70 8.88 2.10 0.29 15.06
(0.1004) (0.0029) (0.1470) (0.5924) (0.0001)
Oils, butter, fats 0.19 3.89 2.02 2.76 0.15
(0.6661) (0.0486) (0.1556) (0.0964) (0.7018)
Sugar 12.52 3.11 6.53 8.84 4.08
(0.0004) (0.0777) (0.0106) (0.0029) (0.0433)
Other 17.37 25.35 5.53 15.70 7.78
(0.0000) (0.0000) (0.0187) (0.0002) 0.0053
All equations 49. 10 64. 93 I 4. 20 28.04 32. 82
(0.0000) (0.0000) JD. 02 75) (0.0001) (0.0000)

 

" p-values in parentheses

Another interesting observation about these test results is that the statistical evidence

in support of the inclusion of the quadratic expenditure term strengthens with income.

The main result derived from the tests in Table 5.12 is that it is appropriate to include the

quadratic expenditure term when estimating the demand model for each of the ﬁve sub-

samples, and hence, that all of the analyses in this section are based on QUAIDS.

Since it is possible that the results of the tests for expenditure endogeneity may

change depending on the speciﬁc sub-sample being considered, the next task in our

analysis is to F-tests for the endogeneity of expenditure in each of the ﬁve sub-samples.

102

Table 5.13

Samples

Tests for Expenditure Endogeneity in the Rural-Urban and Income Groups

 

Relevance of Instruments: F -tests

 

 

 

 

 

Rural Urban Low Middle High
Expenditure 59.94 77.68 14.40 14.81 16.71
(0.0000) (0.0000) (0.0000) (0.0000) (0.0000)
Expenditure Endogeneity: 12 tests based on QUAIDS estimationl
Commodity Rural Urban Low Middle High
Grains 0.06 30.86 1.36 0.27 1.07
(0.8121) (0.0000) (0.2443) (0.6012) (0.3012)
Meat, ﬁsh 3.57 0.45 0.28 1.87 0.58
(0.0590) (0.5010) (0.5990) (0.1711) (0.4473)
Fruits, vegetables 1.59 4.10 5.12 0.31 0.38
(0. 2075) (0. 0428) (0.0237) (0.5749) (0.5355)
Dairy 0.01 14.65 1.14 0.01 0.20
(0.9417) (0.0001) (0.2857) (0.9988) (0.6557)
Oils, butter, fats 3.19 3.19 0.61 0.38 0.01
(0.0740) (0.0740) (0.4364) (0.5366) (0.9873)
Sugar 2.09 7.58 2.52 0.66 1.62
(0.1479) (0.0059) (0.1 121) (0.4158) (0.2028)
Other 3.09 0.60 0.39 7.51 0.39
(0.0786) (0.4372) (0.5302) (0.0061) (0.5328)
All equations 9.89 51.06 10. 73 8.95 3.28
(0.1295) (0.0000) (0.0972) (0. I76 7) (0.7559)
Overidentiﬁcation: x2 tests
Grains 0.10 3.43 0.19 2.57 1.11
(0.7423) (0.0640) (0.661 1) (0.1089) (0.2919)
Meat, ﬁsh 0.05 14.72 1.41 1.30 1.71
(0.05) (0.0001) (0.2343) (0.2540) (0.1912)
Fruits, vegetables 0.95 11.23 0.37 32.46 0.43
(0.3290) (0.0008) (0.5439) (0.0000) (0.5106)
Dairy 2.75 1.83 2.46 3.33 1.18
(0.0971) (0.1759) (0.1 166) (0.0682) (0.2771)
Oils, butter, fats 0.12 2.28 0.16 3.99 0.04
(0.7299) (0.131 1) (0.6895) (0.0457) (0.8482)
Sugar 5.58 9.57 4.65 6.65 0.04
(0.0182) (0.0020) (0.0310) (0.0099) (0.8410)
Other 4.39 4.08 2.40 1.12 7.37
(0.03 84) (0.0433) (0.1215) (0.2904) 10.0066)

 

p-values in parentheses

103

The results of the tests for the relevance of income and income squared as instrumental
variables for expenditure are reported in the top part of Table 5.13. Consistent with the
previous ﬁndings based on the pooled sample, total household income explains a
signiﬁcant portion of the variation in total household food expenditure, so that assuming
the endogeneity condition is satisﬁed, income can be used as a valid instrument for
expenditure.

Since the QUAIDS model has already been estimated, testing for expenditure
endogeneity simply requires augmenting the residuals from the reduced form regressions
for expenditure to each of the budget share equations in the demand model, and testing
for their statistical signiﬁcance. The middle part of Table 5.13 reports results of these )8
tests, ﬁrst in the individual budget share equations, and then across all budget share
equations in the QUAIDS equation system.

Overall, statistical evidence against the null hypothesis of expenditure exogeneity is
very weak in the sub-samples. It is only in the urban sub-sarnple that statistical evidence
strongly supports the alternative of expenditure endogeneity. The null of expenditure
exogeneity is also rejected on the low income sub-sample, albeit weakly so (p = 0.0972).

Similar to the ﬁndings with pooled data, results of the overidentiﬁcation tests,
(reported in the bottom portion of Table 5.13) are mixed in the individual budget share
equations. There appears to be a problem with exogeneity of the instruments in the urban
sub-sample, which, unfortunately, happens to be the sub-sample that requires correction
for expenditure endogeneity. There does not appear to be problems with the exogeneity

of instruments in the budget share equations estimated using the low income sub-sample.

104

In accordance with the preceding model speciﬁcation and endogeneity test results,
the analyses that follow will be based on the QUAIDS model, with correction for
expenditure endogeneity in urban and low income sub-samples. The maximum likelihood
parameter estimates of the QUAIDS model for rural and urban samples are reported in
Table A8 at the end of this chapter. Given that the ﬁnding of expenditure endogeneity in
the urban sample, we report parameter estimates for both endogeneity-corrected and
uncorrected models for the urban samples in Table A8. From the parameter estimates, it
can be seen that in both rural and urban areas, larger-sized households consume more
grains and less meat and ﬁsh and fruits and vegetables.

The estimates of expenditure elasticities are presented in Table 5.14. For some food
groups, the difference in the estimated expenditure elasticities between rural and urban
samples is quite substantial. For urban households, a 1% increase in total food
expenditure leads to only 0.02% increase in the quantity consumed of meat and ﬁsh. It is
very different with the rural households, where the same 1% expenditure increase leads to
about 1.73% increase in consumption of meat and ﬁsh. This is one of the reasons why it
is necessary to examine expenditure patterns of rural households separately from urban
households. The ﬁnding that expenditure on grains is less responsive to increases in total
household expenditure in the rural areas than urban areas is counterintuitive. The reason
for the unresponsiveness of grain purchases to expenditure increases among rural
households could be due to their engagement in home production (90% of households
who reported nonzero home production reside in the rural areas). Endogeneity correction

does not signiﬁcantly impact the expenditure elasticity estimates of urban households.

105

Estimates Of all price and expenditure elasticities are reported in Table A9 at the end of

 

 

this chapter.
Table 5.14 Estimated Expenditure Elasticities: Rural-Urban and Income Group Differences
Rural Urban Low Middle High
Endog.Adjust Endog.Adjust

Grains 0.0662 0.9338 0.2122 0.1294 0.8626
(0.1524) (0.1937) (0.6568) (0.2370) (0.2566)

Meat, ﬁsh 1.7359 0.1164 1.8501 1.5624 0.3554
(0.1650) (0.1863) (0.6344) (0.2632) (0.2754)

Fruits, vegetables 1.0300 1.0548 0.7247 0.8229 1.2257
(0.1285) (0.1743) (0.5033) (0.2139) (0.2135)

Dairy 0.9512 0.7034 0.3841 1.0100 0.0249
(0.1991) (0.2277) (0.5209) (0.3445) (0.2626)

Oils, butter, fats 0.8042 0.3323 0.4615 0.4310 0.7425
(0.1 194) (0.1822) (0.3627) (0.1429) (0.2365)

Sugar 0.2423 0.1524 0.0332 0.1945 0.7116
(0.1051) (0.1664) (0.3796) (0.1425) (0.1448)

Other 2.6091 3.1482 3 .4620 3.2054 2.6957
(0.2251) (0.2942) (0.8175) (0.3584) (0.3541)

 

Standard errors in parentheses

We focus now on the income-group differences. The maximum likelihood estimates
of the QUAIDS model for each income group are presented in Table A10 at the end of
this chapter. As in the rural—urban samples, households with larger sizes consume more
grains and less meat and ﬁsh and fruits and vegetables in all the income groups.
Estimated expenditure elasticities for each of the income groups are also presented in
Table 5.14.

Grains are a necessity across income groups, while meat and ﬁsh are luxuries in
the low and middle income groups. High income households spend more of their total

expenditure increases on fruits and vegetables than middle and low income households.

106

Again, these differences in demand behavior reafﬁrm the need for disaggregated analysis
of expenditure patterns by income groups in a country with high income disparities like
South Africa. Nevertheless, the estimated expenditure elasticities are as one would expect
a priori. Given the budget share of oils and fats is about the same among all income
groups (approximately 6%), the ﬁnding that low income households respond to total
expenditure increases by consuming more 0118 and fats is of policy interest, given the
likely negative effects if the consumption levels of these products exceed levels
recommended for healthy diets. Correction for expenditure endogeneity in the low
income sub-sample has the largest impact on grains and dairy. Interestingly, expenditure
endogeneity was not found to be a problem in these commodities.

Table 5.15 reports estimates of the Marshallian and Hicksian price elasticities.
Own-price elasticities are all negative as expected. Rural households are less responsive
to increases in prices of grains and meat and ﬁsh, than rural households. This behavioral
pattern is also shared by high income households in comparison to low and middle
income households. The response to the price increase of meat and ﬁsh food group makes
the differences in the demand behavioral patterns among the rural~urban and income
group more vivid. High income households respond to a 1% increase in the price of meat
and ﬁsh by decreasing consumption by 0.59%. This is very different than low income
households, for whom the same 1% price increase leads to a decrease of about 2.48% in
the consumption of meat and ﬁsh. This further underscores the need to undertake

disaggregated analysis of demand behavior in a South Africa.

107

Table 5.15

Estimated Marshallian and Hicksian Own Price Elasticities

 

Marshallian Own Price Elasticities

 

 

 

 

Commodity Rural Urban Low Middle High
Endog.Adjust Endog.Adjust
Grains -1.0083 -0.7474 -0.8889 -1.1924 -0.8770
(0.1077) (0.0998) (0.1868) (0.1987) (0.0668)
Meat, ﬁsh -1.9868 -0.5248 -2.4796 -1.6434 -0.5898
(0.3020) (0.1889) (1.4364) (0.4451) (0.1550)
Fruits, vegetables -1.0614 -0.9598 -0.9468 -0.8690 -1.2072
(0.1287) (0.1568) (0.2343) (0.1374) (0.2764)
Dairy -0.9247 -0.7245 -0.9815 -0.7310 -1.1427
(0.0993) (0.1383) (0.3596) (0.1742) (0.3081)
Oils, butter, fats -1.1463 -0.8409 -0.9035 -1.2419 -0.9912
(0.0918) (0.1440) (0.1712) (0.0966) (0.1720)
Sugar -1.0731 -1.1547 -1.l357 -1.0992 -0.9203
(0.0905) (0.1502) (0.4463) (0.1241) (0.1075)
Other -2.8749 ~5.1792 -7.2 895 -5. 1092 -3 .9698
(0.5953) (1.1354) (3.6996) (1.3480) (1.2688)
Hicksian Own Price Elasticities
Grains -0.9840 -0.5 191 -0.8111 -1 . 1471 -0.6515
(0.0559) (0.0474) (0.2406) (0.0828) (0.0671)
Meat, ﬁsh -l.6203 -0.4934 -2.0963 -1.2967 -0.4964
(0.0348) (0.0502) (0.1314) (0.0584) (0.0724)
Fruits, vegetables -0.8751 -0.7835 -0.81 19 -0.7226 - l .0054
(0.0232) (0.0291) (0.0937) (0.0381) (0.0351)
Dairy -0.8719 -0.6640 -0.9617 -0.6669 -1.1407
(0.0110) (0.0196) (0.0268) (0.0219) (0.0215)
Oils, butter, fats -1.1040 -0.8227 -0.8781 -1.2191 -0.9524
(0.0063) (0.0100) (0.0200) (0.0076) (0.0123)
Sugar -1.0597 -1.1492 -1.1337 -l.0890 -0.8952
(0.0058) (0.0061) (0.0221) (0.0075) (0.0051)
Other -2.6709 -4.7331 -7.0282 -4.8478 -3.5879
(0.0176) (0.0417) (0.0617) (0.0292) (0.0502)

 

Standard errors in parentheses

108

5.6 The Problem of Observed Zero Expenditures

For reasons such as purchase infrequency and corner solution outcomes from agents’
optimization problems, it is common to observe zero budget shares for some
commodities in household expenditure data. Estimation of a demand system with a large
percentage of zero expenditure shares may lead to inconsistent parameter estimates
unless econometric techniques appropriate for such data structures are used.

As indicated in chapter four, the problem of zero expenditure shares is severe for the
dairy commodity (see Table 4.6). Apart from the dairy commodity, the percentage of
observations with zero expenditure shares is very low for the other six commodities (4%
at most). Hence, it would not be appropriate to model the budget shares for these
commodities using econometric techniques meant for data structures with large number
of zeros in the dependent variable. In the pooled sample, about 14% of the dairy budget
shares are zeros. Non-purchase of dairy products is higher among rural households (18%)
and among households in the lower income brackets (24% for low-income households
and 12% for middle-income households). Hence, adjustment for zero expenditure shares
is made in the estimation of the dairy budget share equations for these household groups.
In this study, the adjustment for zero expenditure shares follows the two-step procedure
proposed by Shonkwiler and Yen (1999).

The Shonkwiler and Yen procedure is carried out in two steps. In the ﬁrst step, a
single equation probit model is estimated to compute the probability and the cumulative
density values. The dependent variable in the probit models is a binary variable taking a
value of one if positive purchase occurs and zero otherwise. The independent variables

are the exogenous variables income and income-squared, household demographics that

109

enter the demand model (household size, urbanization, and education of household head),
year dummies and survey month variable. Four additional variables not included in the
demand model are included in the probit models, namely household size-squared, gender
and age of household head, and a dummy variable for household ownership of a
refrigerator. In the second step, equation (3.30) is re-speciﬁed with the following changes
made: (1) the budget shares of the dairy commodity are multiplied by the cumulative
density values (<D(.) ), and (2) the probability density values (¢(.)) are included as an
additional regressor in the budget share equation for the dairy commodity.19 The

discussion here focuses on the statistical signiﬁcance of 6—the coefﬁcient on ()3— and

on the impact on the elasticity estimates for the dairy commodity of controlling for the
zero expenditure problems. As before, the tests for the statistical signiﬁcance of 6 are
conducted in the endogeneity-unadjusted demand model. The results of these tests are
reported in the last row of Table 5.16. As can be seen from these results, the statistical
signiﬁcance of 6 is robust across the sample groups, indicating that the additional
information provided by the probability density values explains a signiﬁcant part of the
variation in the budget share of the dairy commodity.

Table 5.16 also reports estimates of the expenditure and own-price elasticities. For the
rural and middle income sub-samples, these elasticities are computed from the censored
QUAIDS model with no adjustment made for expenditure endogeneity, while for the low
income and pooled samples, they are estimated from the QUAIDS model with adjustment
for both expenditure endogeneity and censoring. Comparing these elasticity estimates

with those computed from QUAIDS without correcting for censoring (Table 5.10), it can

 

'9 For ease ofreference, we reproduce eq. (3.30) here: w: = (13(z' 1'. h hm,” ;\V)+ 5315(2: '1', )+ 5,?

ll 1 it

110

be seen that the correction for the zero-expenditure problem has the effect of decreasing

the magnitudes of the expenditure elasticity estimates for the dairy commodity.

Table 5.16 Expenditure and Own Price Elasticities for the Dairy Commodity with

adjustment for the Zero-Expenditure Problem

 

 

 

Household Group
Rural Low Middle All

Expenditure elasticity 0.8743 0.3397 0.6162 0.3881

(0.2028) (0.5450) (0.5579) (0.1865)
Marshallian own-price elasticity -1.3591 -0.8043 -0.2502 -0.5857

(0.2007) (0.2484) (0.5532) (0.1056)
Hicksian own-price elasticity -l. 3563 -0.7869 -0.2110 -0.5602

(0.0551) (0.0281) (0.0354) (0.0123)
t-ratio (5=0 vs. 5 #0) -3.87 -1.96 -2.74 -4. l 8
(p-value) (0.000) (0.050) (0.006) (0.000)

 

Standard errors in parentheses for the elasticity estimates

The magnitudes of decreases in the expenditure elasticities are large enough to change
the classiﬁcation of dairy from luxury to necessity in the case of middle income
households. Similar to the ﬁndings with regard to expenditure elasticities, on average,
adjustment for expenditure censoring has the effect of decreasing the absolute

magnitudes of the Marshallian and Hicksian own-price elasticities for dairy.

5.7 Implications of demand model selection for welfare measures

One of the main reasons for estimating demand systems is to facilitate welfare
analysis. Quantitative welfare measures are based on demand parameter estimates, and,
as the analyses in the previous sections showed, these parameter estimates differ
depending on the choice of the demand model. This raises the question: to what extent

does this sensitivity of demand parameter estimates to model selection affect welfare

111

measures and hence, policy advice? To answer this question, we use the estimated
demand models to estimate welfare effects of an indirect tax reform. In particular, we
compare these welfare measures using demand parameters from QUAIDS, nonlinear
AIDS, and LA/AIDS, all estimated on the pooled data from all households.

The tax reform evaluated is the zero-rating of the value-added tax (VAT) on meat
products. While most of the basic food commodities in South Africa such as grains, milk,
fruits and vegetables have zero VAT, meat is not zero-rated. That is, meat is taxed at the
standard VAT rate of 14%. The issue of whether or not meat should be zero-rated has
been contended for a long time by government and lobby groups, the Congress of South
African Trade Unions being most notable among the lobby groups (Watkinson and
Makgetla, 2002). In this section, we measure the consumer welfare impacts of adding
meat to the list of zero-rated commodities. We use the demand parameter estimates to
calculate the indirect utilities, both before and after the hypothesized tax reform. These
are then used to compute two money metric welfare measures, namely compensating

variation and equivalent variation.

Let p3 denote the price vector before the tax reform, and let us denote household h’s

utility given those prices. Let pf and u,” denote the price vector and utility level after the

tax reform has been implemented. Denote the expenditure function for price vector p"
and utility level uh by e(ph, uh). Compensating variation (CVh) is deﬁned as the amount

of money that a household would have to receive in order the remain at the level of utility
u: given the new price vector pf : CV” = e(pf , ug) - e( pg , u: ). Equivalent variation
(EVh), on the other hand, is based on the post-reform utility level u,” and asks how much

money a household would be indifferent about accepting in lieu of the price change; that

112

is, it is the change in the household’s wealth that would be equivalent to the price change
in terms of its welfare impact: EV” = e( pf , ul”) - e( p3 , u," ).
Because of the ﬁnding in the previous sections that expenditure endogeneity is not a

problem with the pooled data, we choose as our preferred model censored QUAIDS with
no adjustment for expenditure endogeneity. We calculate the new price vector, pf , and

the CV and EV using the ﬁnal year of the data (that is, 2004).

Figures 5.1 and 5.2 plot the CV and EV estimates based on the QUAIDS speciﬁcation
for each household. These are negative for every point in the data, indicating that each
household experiences a welfare gain as a result of the price decrease. The gains in
welfare increase with total expenditure, as would be expected.

To determine the sensitivity of welfare measures to demand model selection, Table
5.17 presents summary statistics of the CV and EV computed using the three model
speciﬁcations considered in this study, namely QUAIDS, nonlinear AIDS, and LA/AIDS.
Based on the QUAIDS model, the removal of a 14% VAT on meat would yield an
average compensating variation of R203.32, meaning that the average household would

gain R203.32 per month if this tax reform were in effect.20

 

2° The symbol R stands for Rand, the South African currency.

113

Figure 5.1 Welfare Gain due to Removal of 14% VAT on Meat: Compensated Variation

0 ‘0 I 0.0..

 

 

 

‘1 1

e4
‘1
on

6
Log of Real Expenditure

Figure 5.2 Welfare Gain due to Removal of 14% VAT on Meat: Equivalent Variation

0 —o e on...

0!
O
In

Rands per month

in
o
n
O

l

 

 

4500
d 1 l l I

6
Log of Real Expenditure

The equivalent variation is R110 higher, implying that the demand for meat exhibits

signiﬁcant income effects. The mean differences in the CV and EV estimates based on

114

the nonlinear AIDS and LA/AIDS models are small. However, compared to the QUAIDS
estimates, it is clear that the AIDS and the LA/AIDS models overstate the welfare

measures, presumably due to their exclusion of the quadratic expenditure term.

Table 5.17 Average Welfare Effects of Zero-Rating VAT on Meat

 

 

QUAIDS Nonlinear AIDS LA/AIDS
Compensating variation -203.32 -299.64 -306.62
Equivalent variation -313.93 -644.84 -676.46

 

Figure 5.3 shows the distribution of the welfare estimates across the sample using
the different models. The welfare effects from the three models are all skewed to the left,
with the AIDS and LA/AIDS welfare effects estimates being more variable than the
QUAIDS estimates. Figures 5.4 and 5.5 indicate the biases introduced when the AIDS
and LA/AIDS are used to estimate welfare measures. Based on the equivalent variation,
Figure 5.3 plots the difference between the AIDS welfare gain for each household as a
proportion of that household’s QUAIDS welfare gain. Figure 5.4 compares these biases
when the LA/AIDS model is used. It is clear from these ﬁgures that for the zero-rating of
meat, both AIDS and LA/AIDS models overstate the welfare gains of households, and
that this overstatrnent is larger for richer households. Again, this is consistent with both

AIDS and LA/AIDS models not allowing for adequate curvature in the Engel curves.

115

Figure 5.3 The Distribution of Welfare Gains

 

 

 

 

 

 

 

 

 

 

 

 

QUAIDS CV AIDS CV LA/AIDS CV
O O O
o « o - o -
N N N
O O O
.“3 ‘ :‘2 ‘ 4. 331
5‘ 5‘ I 6‘
8 O s O 0:) 0
g, o a 30 < .1 go -«
Ll. LL U.
o 4 o q o ,
LO I!)
o -i O -i " O -
I l I I I I If ﬁi I I I I I I I
-8000 -6000 4000 -2000 0 ~8000 -6000 4000 -2000 0 -8000 -6000 4000 -2000 0
Compensating Variation Compensating Variation Compensating Variation
QUAIDS EV AIDS EV LA/AIDS EV
0 O O
O .1 O -1 I O -*
N N l N
O O O
'0 '1 ID -1 1:2 -
S 6 6‘
C C 5
g8« g8‘ 38-
u. LI. u.
- o . o .
in It) I!)
o a 0 ~ ' ’— o -
I I I I I I T T I I I I I I ﬂ“
-8000 -6000 4000 -2000 0 -8000 -6000 4000 -2000 0 -8000 -6000 4000 ~2000 0
Equivalent Variation Equivalent Variation Equivalent Variation

To gain a further understanding of the distribution of welfare gains, Table 5.18
summarizes the estimates of compensating and equivalent variations for rural and urban
households, as well as for households in different income groups. Based on the
compensating variation, the welfare gains of a lower meat price accrue most to urban and
high—income households. As was indicated in chapter four, high-income households have
a higher share (0.26) of meat products in their budgets than low-income (0.21) and

middle-income (0.22) households.

116

Figure 5.4 Bias in Welfare Gain from Using the Nonlinear AIDS Model

In-
,_
e
e
o
0., e
”F
.‘2 o
n
or ’ o
8 .
. o
c
:3 .r " .
or .0 . 0
o. C
IO-i O ‘
o

 

 

 

6
Lot of Real Expenditure

Figure 5.5 Bias in Welfare Gain from Using the LA/AIDS Model

 

 

 

15-
0
0,10- '
8 .°.
0 e
g g"
8 ° 0
h .
a.) O r' .
5 r .0 . O
o 9 e
O .00”
o —i
l I 7 I I
4 5 6 8

7
Log of Real Expenditure

117

Table 5.18

Average Welfare Gains of Zero-Rating VAT on Meat: Rural-Urban and Income
Group Differences

 

 

 

Regions Income Groups
Rural Urban Low Middle High
Compensating -158.99 -275.00 -l38.23 -232.15 -328.85
variation
Equivalent -233.48 41 1.24 408.55 -7l7.75 -587.97
variation

 

Based on equivalent variation, middle-income households beneﬁt most from the tax

reform. As was shown in ﬁgures 5.3 - 5.4, the variability in gains is larger at higher levels

of expenditure, which makes the standard deviations of the welfare estimates to be larger

for middle and high income groups. On average, all households in rural and urban areas,

as well as the three income groups, beneﬁt from the zero-rating of VAT on meat.

118

5.8 Comparison with previous studies

The majority of food demand studies in South Africa are commodity-speciﬁc.
Virtually all of these studies are based on aggregate time series of price and expenditure
data, do not account for the effect of household demographics, and are not based on
theoretically consistent demand models. The exception is the study by Agbola (2003),
which estimates price and expenditure elasticities using the LA/AIDS model based on a
1993 cross-sectional survey. In this section, we compare elasticity estimates from this
study and those estimated by previous food demand studies in South Africa. Table 5.18
summarizes estimates of price and expenditure elasticities from these previous studies.
For ease of reference, we also summarize in Table 5.20 elasticity estimates from all
models based on pooled data (for reasons of space, standard errors are left out).

Elliot and van Zyl’s (1991) estimates of expenditure elasticities for maize and
potatoes, based on log-linear estimations of the budget share equations, are substantially
lower than the expenditure elasticity for grains and ﬁ'uits/vegetables estimated in this
study. Part of the reason for these differences is, of course, due to different levels of
aggregation. However, they ﬁtted log-linear models on the individual budget share
equations (as opposed to estimating these as a system), which implies that they did not
account for the interrelatedness of the commodities expenditure shares through, for
example, the adding-up constraint. This can lead to biases in the elasticity estimates. The
estimates by Niewuwoudt (1998) suffer from the same problem as those by Elliot and van
Zyl, in that they are based on individual budget share estimates. Taljaard (2003) used the
LA/AIDS to estimate price and expenditure elasticities for different meat types using

aggregate, national time series data. Taljaard’s estimates of the expenditure elasticities

119

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 5.19 Estimates of Elasticities in South Africa: Previous Studies
STUDY MODEL EXPENDITURE OWN-PRICE
ELASTICITY ELASTICITY
Rural Urban Marsh. Hick.
GRAINS Agbola (2003) LA/AIDS 1.250 -1.730 -1.394
Maize meal Elliot & van Zyl log-log 0.1961 0.0610
(1991)
Rice 0.1565 0.1567
Bread 0.2310 0.1111
MEAT/FISH Agbola (2003) LA/AIDS 1.027 -1 .266 -0.919
Nieuwoudt (1998) 1.34 0.95 (blacks)
(blacks)
Beef Hancock (1984) OLS 0.71 -0.96
Taljaard (2003) LA/AIDS 0.607 -0.544 1 -0.256
Cutts & Kirsten 1.265 -0.594
(2005)
Bowmaker & OLS 0.96 -l .72
Nieuwoudt (1990)

Chicken Taljaard LA/AIDS 0.053 -0.131 -0.1 16
Pork 0.015 -0.261 -0.260
Mutton 3.642 -0.923 -0.335

FRUITS
N EGETABLES
Fruits Agbola (2003) LA/AIDS 0.717 -0.263 -0.225
Vegetables 0.910 -1.312 -l.l95
Potatoes Elliot and van Zyl log-log 0.1597 0.1357
(1991)
DAIRY Agbola (2003) LA/AIDS 0.898 -1.237 -1 .160
Fresh Milk Nieuwoudt (1998) 0.60 0.50 (blacks)
(blacks) 0.74 (Asians)
Cheese 0.65 0.65 (blacks)
(blacks) 0.65 (Asians)

 

 

 

 

 

 

 

120

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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121

for the individual meat types differ substantially from our estimate for the meat and ﬁsh
composite, but their average of 1.07 falls below the range of estimates obtained in this
study. The main limitations with Taljaard’s study are that it is based on highly aggregate
data, and does not account for inﬂuence of demographic effects on demand behavior.

The results from Agbola (2003) are most comparable to the results in this study for
two reasons. First, Agbola’s is the only study that covers an exhaustive list of food
groups similar to the ones covered here, and second, the KwaZulu-Natal portion of the
1993 nationwide used by Agbola became the first wave of the KIDS panel data used in
this study. Agbola’s estimates of expenditure elasticities are higher for grains (1.250)
compared to this study’s estimates. Grains comprise mainly of items that are staple foods
in South Africa, so that one can consider an expenditure elasticity in excess of unity
(implying that grains are a luxury) to be too high. The Marshallian and Hicksian price
elasticity estimates reported by Agbola are also very high for a staple commodity.

The expenditure and price elasticities estimated in this study correct for many of the
problems associated with these previous estimates. The QUAIDS model used to estimate
expenditure and price elasticities in this study is derived from consumer utility
maximization problem (that is, it is theoretically consistent) and allows for more
curvature in the Engel curves. The system is estimated in its ﬂexible form, without
imposing linearity on the price aggregators, and corrections for econometric problems of
expenditure endogeneity and censoring are made. So, this study overcomes many of the
problems associated with the previous studies of demand behavior in South Africa, and
hence, the price and expenditure elasticity estimates obtained from this study are more

accurate and can be used more reliably for policy analysis.

122

5.9 Chapter summary

This chapter presented and discussed empirical results. Tests for attrition effects
showed that attrition does not affect consistent estimation of the coefﬁcients of the
demand model. In most of the models estimated, expenditure endogeneity was not found
to be problem. It was only in the urban and low income sub-samples that the null
hypothesis of expenditure exogeneity was rejected. Correction for expenditure
endogeneity was done using the control function approach. The LM tests and the tests for
the signiﬁcance of lambda in the QUAIDS model indicated that a quadratic expenditure
term needs to be included in the demand model (that is, these tests favored QUAIDS, as
opposed to AIDS, speciﬁcation). To determine the extent of the bias in parameter
estimates from excluding the quadratic expenditure term, the AIDS and LA/AIDS models
were also estimated. On average, the expenditure elasticity estimates based on the AIDS
and LA/AIDS models were found to be larger than the QUAIDS estimates, consistent
with the former models not allowing for adequate curvature in the Engel curves. Since
welfare measures depend on the demand parameter estimates, and demand parameter
estimates depend on the choice of the demand model, we examined how sensitive the
welfare measures are to demand model selection. For this purpose, we compared the
estimates of compensating variations and equivalent variations from the QUAIDS, AIDS,
and LA/AIDS models resulting from the removal of a 14% VAT on meat. AIDS and
LA/AIDS were found to overstate these welfare gains compared to QUAIDS.

Demand behavior was found to signiﬁcantly differ between rural and urban

households, as well as across income groups. Hence, to get a more accurate picture of

123

demand behavior, it is necessary to conduct a disaggregated analysis, as opposed to
aggregate analysis which masks these heterogeneous demand behavioral patterns.
Previous estimates of price and expenditure elasticities in South Africa are
commodity-speciﬁc, and most of them are also based on single equation estimations. The
existing theory-based study by Agbola (2003) that examines a range of food groups
similar to the ones examined in this study uses the restrictive LA/AIDS model. Our
estimates of expenditure and price elasticities correct for many of the problems associated
with Agbola’s and all other estimates from these previous studies. The QUAIDS model
used to estimate expenditure and price elasticities in this study is derived from consumer
utility maximization problem (that is, it is theoretically consistent) and allows for
curvature in the Engel curves. The system is estimated in its ﬂexible form, without
imposing linearity on the price aggregators, and corrections for econometric problems of
expenditure endogeneity and censoring are made. Hence, this study provides estimates of

price and expenditure elasticities that can be used reliably for policy analysis.

124

APPENDIX A

ADDITIONAL RESULTS FOR CHAPTER FIVE

 

 

 

 

 

 

Table A1 The estimated reduced forms for expenditure and expenditure-squared

Income included Income and Income— Income and Income-

Squared included Squared included
Variable
lnx lnx Qngf

Constant 6.3686 (0.2545) 7.0905 (0.3453) 52.0476 (4.4837)
Price of grains 0.1467 (0.0616) 0.1467 (0.0615) 2.0281 (0.7985)
Price of meat&ﬁsh 0.0668 (0.0557) 0.0707 (0.0555) 1.0588 (0.7213)
Price of fruits&vegetables 0.0441 (0.0419) 0.0461 (0.0418) 0.5116 (0.5434)
Price of dairy -0.0248 (0.0441) -0.0237 (0.0440) -0.1381 (0.5716)
Price of oils, butter&fats 0.1099 (0.0572) 0.1078 (0.0570) 1.3129 (0.7410)
Price of sugar -0.3062 (0.0508) -0.3050 (0.0506) 4.0938 (0.6577)
Price of other foods -0.2015 (0.0590) -0.2035 (0.0588) -2.5710 (0.7639)
Household size 0.0467 (0.0031) 0.0465 (0.0031) 0.6197 (0.0403)
Race -0.4110 (0.0425) -0.3944 (0.0427) -5.3974 (0.5554)
Rural 0.0110 (0.0308) 0.0129 (0.0308) 0.2539 (0.3994)
Education 0.0131 (0.0025) 0.0118 (0.0026) 0.1489 (0.0333)
Dummy for 1998 -0.4456 (0.0905) -0.4460 (0.0904) -5.8427 (1.1733)
Dummy for2004 -1.0470 (0.1413) -1.0427 (0.1411) 43.6487 (1.8316)
Survey month -0.0051 (0.0094) -0.0050 (0.0094) -0.0781 (0.1220)
Total household income 0.1743 (0.0117) -0.0409 (0.0706) -l.0062 (0.9167)
Total household income2 0.0152 (0.0049) 0.2302 (0.0640)
R2 0.4339 0.4364 0.4423
F (p-val) 223.38 (0.000) 116.90 (0.0000) 116.84 (0.0000)

 

 

 

 

1‘ Standard errors in parentheses

125

 

 

 

Table A2 The estimated reduced forms for individual commodity groups
Variable Grainsl Meat/ Fruits/ Dairy Oils/fats Sugar Other
Fish Veg.
Constant 0.5243 -0.5973 0.6058 -0.4770 0.0907 0.1 178 0.7358
(0.1964) (0.1873) (0.1369) (0.1093) (0.0631) (0.0528) (0.1659)
Price of grains -0.0037 0.0272 0.0157 -0.0121 0.0023 -0.0103 -0.0192
(0.0140) (0.0134) (0.0098) (0.0078) (0.0045) (0.0038) (0.01 18)
Price of meat/ﬁsh 0.0170 -0.0102 -0.0108 -0.0106 0.0043 0.0086 0.0017
(0.0125) (0.01 19) (0.0087) (0.0069) (0.0040) (0.0034) (0.0105)
Price of fruits/Veg. -0.0115 -0.0032 0.0172 -0.0021 0.0071 -0.0057 -0.0018
(0.0094) (0.0090) (0.0066) (0.0053) (0.0030) (0.0025) (0.0080)
Price of dairy -0.0014 0.0121 -0.0139 0.0103 -0.0038 0.0011 -0.0043
(0.0099) (0.0094) (0.0069) (0.0055) (0.0032) (0.0027) (0.0084)
Price of oils/fats 0.0423 -0.0129 -0.0080 -0.0015 -0.0048 0.0001 -0.0152
(0.0130) (0.0124) (0.0090) (0.0072) (0.0042) (0.0035) (0.01 10)
Price of sugar -0.0510 0.0239 0.0080 0.0161 -0.0005 0.0001 0.0033
(0.0124) (0.01 18) (0.0086) (0.0069) (0.0040) (0.0033) (0.0105)
Price of other foods -0.0167 0.0148 -0.0089 0.0154 -0.0012 0.0103 -0.0137
(0.0135) (0.0129) (0.0094) (0.0075) (0.0043) (0.0036) (0.01 14)
Expenditure 0.0545 0.1274 -0.0741 0.1 102 0.0120 0.0032 -0.2330
(0.0495) (0.0472) (0.0345) (0.0275) (0.0159) (0.0133) (0.0418)
Expenditure-squared -0.0128 -0.0028 0.003 1 -0.0064 -0.0022 -0.0022 0.0233
(0.0036) (0.0035) (0.0025) (0.0020) (0.0012) (0.0010) (0.0031)
Household size 0.0131 -0.0080 0.0001 -0.0004 0.0005 0.0016 -0.0070
(0.0011) (0.0010) (0.0008) (0.0006) (0.0004) (0.0003) (0.0009)
Race (1 if black) 0.0550 0.0495 -0.0240 -0.0189 -0.0093 0.0024 -0.0547
(0.0122) (0.0116) (0.0085) (0.0068) (0.0039) (0.0033) (0.0103)
Rural (1 if rural) 0.0379 -0.0381 0.0198 -0.0148 -0.0027 0.0050 -0.0071
(0.0069) (0.0066) (0.0048) (0.0038) (0.0022) (0.0019) (0.0058)
Education -0.0005 -0.0009 -0.0001 0.0006 0.0000 -0.0003 0.0012
(0.0006) (0.0006) (0.0005) (0.0004) (0.0002) (0.0002) (0.0005)
Dummy for 1998 -0.0660 0.0880 -0.0630 0.0342 -0.0291 -0.0215 0.0575
(0.0213) (0.0203) (0.0148) (0.0118) (0.0068) (0.0057) (0.0180)
Dummy for 2004 -0.2047 0.1045 -0.0003 0.0817 -0.0194 -0.0357 0.0740
(0.0355) (0.0338) (0.0247) (0.0197) (0.01 14) (0.0095) (0.03000
Survey month 0.0019 -0.0021 -0.0070 0.0060 -0.0008 -0.0006 0.0025
(0.0021) (0.0020) (0.0015) (0.0012) (0.0007) (0.0006) (0.0018)
13 0.0555 -0.0606 0.0147 -0.0159 -0.0013 0.0047 0.0029
(0.0154) (0.0147) (0.0108) (0.0086) (0.0050) (0.0042) (0.0130)

 

1. Standard errors in parentheses

126

 

 

 

 

 

 

Table A3 Parameter estimates for QUAIDS with and without endogeneity-adjustment
Eq.‘ QUAIDS Endogeneity-adjusted QUAIDS
Variable
Coeff. Std. Err. Coeff. Std. Err.
Constant a. 0.1185 (0.0250) 0.1 160 (0.0263)
(12 0.2965 (0.0234) 0.3093 (0.0248)
113 0.2328 (0.0167) 0.2265 (0.0176)
0.4 0.0404 (0.0141) 0.0380 (0.0149)
115 0.0571 (0.0084) 0.0590 (0.0087)
(16 0.0151 (0.0071) 0.0160 (0.0073)
(17 0.2395 (0.0214L 0.2351 (0.0224)
Expenditure B, -0.0950 (0.01 19) -0.0947 (0.0155)
[32 0.0327 (0.0113) 0.0465 (0.0146)
B; -0.0142 (0.0084) -0.0219 (0.0107)
[34 -0.01 l 1 (0.0068) -0.0128 (0.0088)
[35 -0.0215 (0.0038) -0.0180 (0.0051)
[36 -0.0304 (0.0032) -0.0297 (0.0043)
07 0.1395 (0.0104) 0.1308 (0.0135)
Prices y” 0.0220 (0.01 18) 0.0225 (0.0130)
“7'2. 0.0146 (0.0089) 0.0106 (0.0095)
731 -0.0015 (0.0061) 0.0006 (0.0064)
7.“ -0.0067 (0.0054) -0.0061 (0.005 7)
751 0.0076 (0.0039) 0.0065 (0.0040)
7’61 -0.0095 (0.0032) -0.0100 (0.0034)
771 -0.0265 (0.0083) -0.0241 (0.0091)
y22 -0.0172 (0.0112) -0.0147 (0.0115)
Y32 -0.0073 (0.0060) -0.0078 (0.0061)
742 -0.0028 (0.0052) -0.0032 (0.0053)
752 -0.0003 (0.0037) -0.0004 (0.003 8)
762 0.0044 (0.0031) 0.0044 (0.0032)
yn 0.0087 (0.0078) 0.01 11 (0.0081)
733 0.0111 (0.0060) 0.0110 (0.0061)
743 -0.0044 (0.0038) -0.0042 (0.0038)
753 0.0050 (0.0027) 0.0054 (0.0027)
763 -0.0077 (0.0023) -0.0077 (0.0023)
77, 0.0047 (0.0059) 0.0026 (0.0061)
y.“ 0.0081 (0.0050) 0.0083 (0.0050)
7,, -0.0026 (0.0027) 00027 (0.0027)
764 0.0033 (0.0023) 0.0032 (0.0024)
y74 0.0051 (0.0052) 0.0047 (0.0054)
‘7'” -0.0045 (0.0039) -0.0053 (0.0040)
765 0.0012 (0.0024) 0.0013 (0.0025)
775 -0.0063 (0.0037) -0.0049 (0.0039)
766 0.0013 (0.0030) 0.0015 (0.0031)
77., 0.0070 (0.0033) 0.0071 (0.0033)
777 0.0074 (0.0109) 0.0034 @0116)
Expenditure- 2.1 -0.0143 (0.0041) -0.0 144 (0.0041)
squared 7.2 -0.0002 (0.0038) -0.0004 (0.003 8)
7&3 0.0024 (0.0029) 0.0026 (0.0029)
3.4 -0.0081 (0.0023) -0.0081 (0.0023)
7.5 -0.0018 (0.0013) -0.0018 (0.0013)
2.6 -0.0037 (0.001 1) -0.0038 (0.001 1)
7.7 0.0258 (0.0036) 0.0259 (0.0036)

 

127

Table A3 (Cont’d)

 

 

 

 

 

 

 

Household size 2.. 0.0099 (0.0007) 0.0099 (0.0009)
22, -0.0044 (0.0007) -0.0053 (0.0009)
23] -0.0008 (0.0005) -0.0003 (0.0006)
241 0.0005 (0.0004) 0.0006 (0.0005)
251 0.0005 (0.0002) 0.0003 (0.0003)
261 0.0013 (0.0002) 0.0013 (0.0003)
271 -0.0071 (0.0006) -0.0066 (0.0008)
Race (1 if black) 2.2 0.0814 (0.0093) 0.0815 (0.0107)
222 0.0257 (0.0089) 0.0331 (0.0101)
232 -0.0189 (0.0065) -0.0229 (0.0074)
2.12 -0.0293 (0.0053) -0.0302 (0.0060)
252 -0.0096 (0.003 1) -0.0079 (0.0035)
262 0.0040 (0.0026) 0.0045 (0.0030)
272 -0.0534 (0.0080) -0.0580 (0.0092)
Rural/Urban (1 if 213 0.0499 (0.0066) 0.0502 (0.0066)
wral) 223 -0.0482 (0.0062) -0.0478 (0.0062)
233 0.0193 (0.0045) 0.0190 (0.0045)
243 -0.0159 (0.0036) -0.0160 (0.0036)
253 -0.0019 (0.0021) -0.0017 (0.0022)
263 0.0061 (0.0018) 0.0060 (0.0018)
273 -0.0093 (0.0055) -0.0098 (0.0055)
Education of head 2.4 -0.0018 (0.0006) —0.0018 (0.0006)
224 0.0005 (0.0005) 0.0002 (0.0006)
Z34 -0.0004 (0.0004) -0.0002 (0.0004)
2.14 0.0009 (0.0003) 0.0010 (0.0003)
254 -9.53e-06 (0.0002) -0.0001 (0.0002)
264 -0.0004 (0.0001) -0.0004 (0.0002)
Z74 0.001 1 (0.0005) 0.0013 (0.0005)
Survey year 115 -0.0426 (0.0159) -0.0411 (0.0165)
(=1 if 1998) 225 0.0498 (0.0156) 0.0549 (0.0160)
235 -0.0530 (0.0111) -0.0561 (0.0114)
Z45 0.0186 (0.0107) 0.0187 (0.0109)
Z55 -0.0256 (0.0061) -0.0243 (0.0062)
Z65 -0.0161 (0.0051) -0.0162 (0.0052)
275 0.0689 (0.0140) 0.0641 (0.0144)
Survey year 2.6 -0.0917 (0.0204) -0.0866 (0.0218)
(=1 if 2004) 226 0.0213 (0.0213) 0.0284 (0.0219)
236 -0.0192 (0.0157) -0.0247 (0.0164)
Z46 0.0410 (0.0144) 0.0409 (0.0149)
256 -0.0150 (0.0094) -0.01 19 (0.0098)
Z66 -0.0280 (0.0078) -0.0283 (0.0083)
276 0.0915 (0.0185) 0.0822 (0.0195)
Month of survey 2.7 0.0027 (0.0021) 0.0027 (0.0021)
227 -0.001 1 (0.0020) -0.0010 (0.0020)
Z37 -0.0076 (0.0014) -0.0077 (0.0014)
247 0.0047 (0.0012) 0.0047 (0.0012)
257 -0.0008 (0.0007) -0.0008 (0.0007)
2.37 -0.0007 (0.0006) -0.0007 (0.0006)
277 0.0028 (0.0018) 0.0027 (0.0018)

 

128

 

Table A3 (Cont’d)

Residuals v1 -0.0005 (0.0121)
v; 00173 (0.0113)
v3 0.0097 (0.0082)
v4 0.0021 (0.0067)
v5 -0.0040 (0.0040)
v6 -0.0008 (0.0034)
v7 0.0109 (0.0101)

 

1. GR = grains; MF = meat and ﬁsh; FV = fruits and vegetables; DAI = dairy; OBF = oils, butter,

and other fats; SUG = sugar; 0TH = other foods
2‘ Standard errors in parentheses

129

Own and Cross Price Elasticities estimated from the QUAIDS Mmodel with and
without Endogeneity Adjustment

Table A4

 

1. QUAIDS without adjusting for expenditure endogeneity

 

Marshallian/Uncompensated own-price elasticities"2

 

 

 

GR MF FV DA1 OBF SUG 0TH
GR -1.0296
(0.0742)
MF 0.4959 -l.1077
(0.1322) (0.1586)
FV 0.2624 -0.0604 -0.9803
(0.0773) (0.0891) (0.0957)
DA1 0.0126 -0.0181 -0.0272 -0.8143
(0.0309) (0.0242) (0.0248) (0.0788)
OBF 0.0416 -0.0090 0.0320 -0.0231 -1.0604
(0.0180) (0.0164) (0.0165) (0.0504) (0.0745)
SUG -0.0730 0.0152 -0.0263 -0.0231 -0.0081 -l.0463
(0.0193) (0.0220) (0.0218) (0.0504) (0.0548) (0.0749)
0TH 0.5649 0.0148 -0.1322 -0.0852 0.4248 1.0110 —4.6426
(0.1804) (0.2253) (0.2176) (0.0556) (0.3331) (0.2576) (0.6605)
Hicksian/Uncompensated own-price elasticities
GR MF FV DA1 OBF SUG 0TH
GR -0.9032
(0.0408)
MF 0.6222 -0.8455
(0.0947) (0.0306)
FV 0.3887 0.2018 -0.8087
(0.0441) (0.0606) (0.0193)
DA1 0.1390 0.2441 0.1444 -0.7715
(0.0401) (0.0300) (0.0251) (0.0100)
OBF 0.1680 0.2532 0.2036 0.0197 -1.0307
(0.0409) (0.0307) (0.0220) (0.0491) (0.0053)
SUG 0.0534 0.2774 0.1453 -0.0423 0.0216 -1.0320
(0.0552) (0.0498) (0.0386) (0.0623) (0.0576) (0.0043)
0TH 0.6912 0.2770 0.0394 1.7573 0.4546 1.3074 4.3462
(0.1412) (0.1954) (0.1989) (0.4879) (0.3282) (0.2633) (0.0181)

 

1. GR = grains; MF = meat and ﬁsh; FV = fruits and vegetables; DA1 = dairy; OBF = oils, butter,

and other fats; SUG = sugar; 0TH = other foods
2' Standard errors in parentheses

130

Table A4 (Cont’d)

ll. Endogeneity-adjusted QUAIDS model

 

Marshallian/Uncompensated own-price elasticities

 

 

 

GR MF FV DA1 OBF SUG 0TH
GR -1.0458
(0.0856)
MF 0.5888 —1.1058
(0.1651) (0.1943)
FV 0.2638 -0.0708 -0.9739
(0.0814) (0.0882) (0.0967)
DA1 0.0086 -0.0221 -0.0235 -0.8238
(0.0371) (0.0237) (0.0252) (0.0977)
OBF 0.0517 -0.0125 0.0327 0.0127 -1.0679
(0.0228) (0.0187) (0.0189) (0.0657) (0.0755)
SUG -0.0777 0.0125 -0.0232 -0.0941 -0.0081 -1.0477
(0.0222) (0.0230 (0.0231) (0.0645) (0.0563) (0.0842)
0TH 0.6149 0.0254 -0.1574 1.8302 0.4623 1.0634 -4.9186
(0.1965) (0.2414) (0.2333) (0.5426) (0.3570) (0.2785) (0.7422)
Hicksian/uncompensated own-price elasticities
GR MF FV DA1 OBF SUG 0TH
GR -0.9330
(0.0456)
MF 0.7017 -0.8312
(0.1232) (0.0342)
FV 0.3766 0.2038 -0.8082
(0.0484) (0.0572) (0.0217)
DA1 0.1215 0.2525 0.1422 -0.7842
(0.0485) (0.0337) (0.0278) (0.0118)
OBF 0.1645 0.2622 0.1984 0.0523 -1.0334)
(0.0430) (0.0293) (0.0205) (0.0624) (0.0064)
SUG 0.0351 0.2871 0.1424 -0.0545 0.0248 -1.0333
(0.0610) (0.0538) (0.0416) (0.0709) (0.0597) (0.0053)
OTl-I 0.7278 0.3000 0.0083 1.8698 0.4952 1.3587 -4.6264
(0.1540) (0.2093) (0.2134) (0.5328) (0.3519) (0.2861) (0.0210)

 

1. GR = grains; MF = meat and ﬁsh; F V = fruits and vegetables; DAI = dairy; OBF = oils, butter,

and other fats; SUG = sugar; 0TH = other foods
2‘ Standard errors in parentheses

131

Table A5 (Part 1)

Expenditure and Price Elasticities estimated using Data from only

Households who do not engage in Own-production

 

Expenditure elasticitiesl

 

GR MF FV

0.5201 0.8705 1.1284
(0.1670) (0.1686) (0.1207)

Expenditure elasticity

Marshallian/Uncompensated own-price elasticities

DAI

0.9217

OBF SUG 0TH

0.4113 0.1425 2.8063

(0.1863) (0.1133L(0.1138) (0.2318)

 

 

 

GR MF FV DA1 OBF SUG 0TH
GR -0.9315
(0.0646)
MF 0.3583 -0.8689
(0.1637) (0.1654)
FV 0.1872 0.1235 -1.1035
(0.0887) (0.1071) (0.1198)
DA1 0.0377 0.0267 -0.0944 -0.7855
(0.0449) (0.0518) (0.0514) (0.0942)
OBF 0.0307 -0.0038 0.0658 -0.0653 -1.2067
(0.0181) (0.0219) (0.0261) (0.0474) (0.0880)
SUG -0.0717 -0.0295 0.0153 -0.0717 -0.1134 -1.1248
(0.0272) (0.0329) (0.0337) (0.0737) (0.0715) (0.1130)
0TH 0.3962 0.4373 -0.5962 1.1016 1.0061 1.7515 -4.3722
(0.2350) (0.2827) (0.2458) (0.6089) (0.4066) (0.3708) (0.8207)
Hicksian/uncompensated own-price elasticities
GR MF FV DA1 OBF SUG 0TH
GR -0.7682
(0.0524)
MF 0.5217 -0.6601
(0.1 143) (0.0404)
FV 0.3506 0.3323 -0.9162
(0.0435) (0.0705) (0.0200)
DA1 0.2011 0.2355 0.0930 -0.7214
(0.0348) (0.0344) (0.0418) (0.0130)
OBF 0.1941 0.2050 0.2531 -0.0012 -1.1838
(0.0550) (0.0456) (0.0329) (0.0489) (0.0063)
SUG 0.0916 0.1793 0.2026 -0.0076 -0.0905 -1.1181
(0.0762) (0.0698) (0.0502) (0.0844) (0.0754) (0.0053)
0TH 0.5596 0.6461 -0.4089 1.1657 1.0290 2.0544 -4.0693
(0.1840) (0.2433) (0.2268) (0.5965) (0.4007) (0.3820) (0.0250)

 

1. GR = grains; MF = meat and ﬁsh; FV = fruits and vegetables; DA1 = dairy; OBF = oils, butter,
and other fats; SUG = sugar; 0TH = other foods
2' Standard errors in parentheses

132

Table A5 (Part II)

Households including those who Attrited

Expenditure and Price Elasticities estimated using Data on all

 

Expenditure elasticitiesl

 

GR MF FV DA1 OBF suo OTH
Expenditure elasticity 0.6048 1.0221 1.0191 1.0803 0.6479 0.4868 2.3860
(0.0793) (0.0794) (0.0597) (0.0694) (0.0413) (0.0400L(0.0958)

 

Marshallian/Uncompensated own-price elasticities

 

 

 

GR MF FV DA1 OBF SUG OTH
GR -0.9888
(0.0333)
MF 0.3560 -0.8343
(0.0854) (0.1079)
FV 0.1351 -0.0203 -1.0089
(0.0488) (0.0616) (0.0643)
DA1 0.0500 -0.0032 -0.0149 -1 . 1882
(0.0224) (0.0279) (0.0263) (0.0909))
OBF 0.0042 -0.0427 -0.0005 0.1972 -0.8863
(0.0122) (0.0158) (0.0150) (0.0422) (0.0551)
SUG -0.0168 0.0097 -0.0176 -0.0257 -0.0790 -0.8336
(0.0098) (0.0127) (0.0119) (0.0379) (0.0389) (0.0648)
OTH 0.1990 0.0752 -0.1776 0.4502 0.3779 0.5165 -2.5714
(0.0890) 40.1140) (0.1081) (0.2323) (0.1646) (0.1461) (0.3248)
Hicksian/uncompensated own-price elasticities
GR MF FV DA1 OBF SUG 0TH
GR -0.8008
(0.0246)
MF 0.5440 -0.5944
(0.0625) (0.0186)
FV 0.3230 0.2195 -0.8302
(0.0276) (0.0449) (0.0105)
DA1 0.2379 0.2366 0.1638 -1.1083
(0.022 8) (0.0240) (0.0229) (0.0051)
OBF 0.1922 0.1971 0.1782 0.2772 -0.8507
(0.0210) (0.0171) (0.0132) (0.0405) (0.0023)
SUG 0.1712 0.2495 0.1611 0.0543 -0.0434 -0.8104
(0.0276) (0.0237) (0.0168) (0.0385) (0.0390) (0.0019)
0TH 0.3870 0.3150 0.0012 0.5302 0.4134 0.7132 -2.3748
40.0659) (0.0964) (0.0983) (0.2278) (0.1627) (0.1477) (0.0079)

 

1. GR = grains; MF = meat and ﬁsh; FV = fruits and vegetables; DA1 = dairy; OBF = oils, butter,
and other fats; SUG = sugar; 0TH = other foods

2' Standard errors in parentheses

133

 

 

 

 

 

 

Table A6 Parameter Estimates from the AIDS Model with and without Endogeneity
Ajustment
Parameter/
Variable Equation #‘ AIDS Endogeneity-adjusted AIDS
Coeff. Std. Err. Coeff. Std. Err.
Constant 01. 0.1398 (0.0242) 0.1378 (0.0256)
012 0.3156 (0.0233) 0.3299 (0.0246)
013 0.2180 (0.0169) 0.2129 (0.0178)
014 0.0353 (0.0142) 0.0343 (0.0149)
015 0.0605 (0.0083) 0.0628 (0.0086)
016 0.0173 (0.0071) 0.0192 (0.0073)
017 0.2135 (0.0208) 0.2031 (0.0218)
Expenditure [31 -0.0557 (0.0045) -0.055 (0.01 1)
[32 0.0331 (0.0042) 0.050 (0.010)
[33 -0.0207 (0.003 1) -0.028 (0.008)
(3.. 0.0112 (0.0025) 0.01 1 (0.006)
[35 -0.0165 (0.0014) -0.013 (0.004)
06 -0.0201 (0.0012) -0.018 (0.003)
(37 0.0687 (0.0038) 0.052 (0.010)
Prices Yu 0.0167 (0.0117) 0.0171 (0.0126)
1’21 0.0144 (0.0088) 0.0104 (0.0094)
73, -0.0006 (0.0060) 0.0010 (0.0063)
7... -0.0083 (0.0054) -0.0083 (0.0056)
751 0.0066 (0.0039) 0.0055 (0.0040)
76. -0.0108 (0.0032) -0.01 19 (0.0033)
771 -0.0181 (0.0081) -0.0138 (0.0087)
722 -0.0126 (0.0112) -0.0097 (0.01 15)
732 -0.0101 (0.0060) -0.0105 (0.0061)
ya; -0.0052 (0.0052) -0.0053 (0.0053)
752 -0.0002 (0.0037) -0.0002 (0.0038)
762 0.0035 (0.003 1) 0.0038 (0.0032)
yn 0.0102 (0.0077) 0.01 14 (0.0080)
733 0.0128 (0.0061) 0.0128 (0.0061)
743 -0.0027 (0.0038) -0.0027 (0.0038)
y” 0.0051 (0.0027) 0.0054 (0.0027)
m -0.007 1 (0.0023) -0.0072 (0.0023)
773 0.0026 (0.005 9) 0.001 1 (0.0060)
744 0.0084 (0.0050) 0.0085 (0.0050)
y” -0.0030 (0.0027) -0.0032 (0.0027)
164 0.0034 (0.0023) 0.0033 (0.0024)
y“ 0.0074 (0.0052) 0.0076 (0.0053)
755 -0.0045 (0.0039) -0.0053 (0.0040)
765 0.0008 (0.0024) 0.0008 (0.0025)
775 -0.0048 (0.0037) -0.0030 (0.0038)
766 0.0022 (0.003 1) 0.0029 (0.0032)
We 0.0080 (0.0033) 0.0083 (0.0033)
177 -0.0053 (0.0107) -0.0116 (0.0111)
Household size 2.1 0.0096 (0.0007) 0.0096 (0.0009)
z2, -0.0045 (0.0007) -0.0055 (0.0009)
23. -0.0006 (0.0005) -0.0002 (0.0006)
2.“ 0.0004 (0.0004) 0.0004 (0.0005)
25. 0.0005 (0.0002) 0.0003 (0.0003)
26, 0.0013 (0.0002) 0.001 1 (0.0003)
Z71 -0.0067 (0.0006) -0.0057 (0.0008)

 

134

Table A6 (Cont’d)

 

 

 

 

 

 

 

Race (1 if black) 212 0.0852 (0.0093) 0.0858 (0.0107)
222 0.0254 (0.0088) 0.0338 (0.0101)
232 -0.0192 (0.0065) -0.0230 (0.0073)
Z42 -0.0266 (0.0052) -0.0265 (0.0060)
252 -0.0091 (0.0031) -0.0071 (0.0035)
Z62 0.0051 (0.0026) 0.0064 (0.0030)
272 -0.0607 (0.0080) -0.0694 (0.0092)
Rural/Urban 213 0.0489 (0.0066) 0.0492 (0.0066)
(1 ifrural) 223 -0.0483 (0.0062) -0.0478 (0.0062)
233 0.0196 (0.0045) 0.0193 (0.0045)
243 -0.0165 (0.0036) -0.0165 (0.0036)
253 -0.0020 (0.0021) -0.0019 (0.0022)
Z63 0.0059 (0.0018) 0.0059 (0.0018)
273 -0.0075 (0.0056) -0.0081 (0.0056)
Education of head 114 -0.0018 (0.0006) -0.0018 (0.0006)
224 0.0005 (0.0005) 0.0001 (0.0006)
234 -0.0004 (0.0004) -0.0002 (0.0004)
244 0.0010 (0.0003) 0.0010 (0.0003)
254 0.0000 (0.0002) -0.000 1 (0.0002)
2... -0.0004 (0.0001) -0.0004 (0.0002)
Z74 0.001 1 (0.0005) 0.0015 (0.0005)
Survey year 2.5 -0.0438 (0.0159) -0.0425 (0.0166)
(=1 if 1998) 225 0.0375 (0.0156) 0.0444 (0.0160)
235 -0.0453 (0.0112) -0.0487 (0.0116)
2.5 0.0280 (0.0107) 0.0287 (0.0109)
7.55 -0.0262 (0.0061) -0.0247 (0.0062)
265 -0.0143 (0.0052) -0.0138 (0.0052)
275 0.0641 (0.0141) 0.0566 (0.0146)
Survey year 2.6 -0.0945 (0.0204) -0.0901 (0.0221)
(=1 if 2004) 226 0.0038 (0.0213) 0.0140 (0.0220)
236 -0.0086 (0.0159) -0.0144 (0.0167)
Z46 0.0532 (0.0146) 0.0541 (0.0150)
256 -0.0166 (0.0094) -0.0136 (0.0099)
Z65 -0.0242 (0.0078) -0.0227 (0.0084)
276 0.0869 (0.0188) 0.0727 (0.0199)
Month of survey Zn 0.0025 (0.0021) 0.0026 (0.0021)
227 -0.0023 (0.0020) -0.0022 (0.0020)
237 -0.0069 (0.0015) -0.0069 (0.0015)
147 0.0058 (0.0012) 0.0059 (0.0012)
257 «0.0009 (0.0007) -0.0008 (0.0007)
267 -0.0006 (0.0006) -0.0006 (0.0006)
277 0.0023 (0.0018) 0.0021 (0.0018)
Residuals l: v“ -00014 (0.0123)
”Pend‘m’e V2: 00199 (0.01 14)
V31 0.0088 (0.0083)
V4: 00001 (0.0067)
V51 -0.0046 (0.0041)
v61 -0.0029 (0.0035)
V71 0.0200 (0.0104)

 

T. GR = grains; MF = meat and ﬁsh; FV = fruits and vegetables; DA1 = dairy; OBF = oils, butter,
and other fats; SUG = sugar; 0TH = other foods

2‘ Standard errors in parentheses

135

Table A7

Own and Cross Price Elasticities estimated from the AIDS Model with and
without Endogeneity-Adjustment

 

1. AIDS without adjusting for expenditure endogeneity

 

Marshallian/Uncompensated own-price elasticities‘

 

GR MF FV DA1 OBF SUG 0TH
GR 0.9279
(0.0356)
MF 0.0618 -1.0996
(0.0267) (0.0472)
FV 0.0103 0.0511 0.9015
(0.0184) (0.0258) (0.0339) .
DA1 0.0231 0.0239 0.0146 0.8797
(0.0164) (0.0223) (0.0218) (0.0774)
OBF 0.0235 0.0030 0.0303 0.0464 -1.0668
(0.0118) (0.0160) (0.0151) (0.0411) (0.0733)
SUG 0.0318 0.0142 0.0395 0.0518 0.0156 0.9455
(0.0097) (0.0135) (0.0130) (0.0357) (0.0459) (0.0622)
OTH 0.0432 0.0370 0.0191 0.1104 -0.0858 0.1537 -1.2065
(0.0246) (0.0333) (0.0332) (9.0787) (0.0694) (0.0612) (0.1029)

 

Hicksian/Uncompensated own-price elasticities

 

GR MF FV DA1 OBF SUG 0TH
GR 0.6580
(0.0350)
MF 0.2797 0.8357
(0.0268) (0.0471)
FV 0.1767 0.1310 0.7459
(0.0184) (0.0258) (0.0338)
DA1 0.0390 0.0440 0.0499 -O.8027
(0.0164) (0.0223) (0.0218) (0.0773)
OBF 0.0739 0.0522 0.0825 0.0075 -1.0300
(0.0118) (0.0160) (0.0150) (0.0411) (0.0731)
SUG 0.0142 0.0613 0.0082 0.1010 0.0635 0.9169
(0.0097) (0.0135) (0.0130) (0.0357) (0.0459) (0.0623)
0TH 0.0509 0.1399 0.1166 0.2111 0.0121 0.2513 -1.0382
(0.0246) (0.0333) @0332) (0.0787) (0.0694) (0.0612) (0.1031)

 

1. GR = grains; MF = meat and ﬁsh; F V = fruits and vegetables; DA1 = dairy; OBF = oils, butter,

2‘ Standard errors in parentheses

and other fats; SUG = sugar; 0TH = other foods

136

Table A7 (Cont’d)

 

lI. Endogeneity-adjusted AIDS model

 

Marshallian/Uncompensated own-price elasticities

 

 

 

GR MF FV DA1 OBF SUG 0TH
GR -0.9274
(0.0395)
MF 0.0498 -1 .1 129
(0.0278) (0.0476)
FV 0.0148 -0.0559 -0.8935
(0.0192) (0.0263) (0.0346)
DA1 -0.0231 -0.0250 -0.0142 -O.8775
(0.0172) (0.0226) (0.0218) (0.0778)
OBF 0.0201 -0.0039 0.0324 -0.0486 -1.0845
(0.0123) (0.0164) (0.0152) (0.0414) (0.0761)
SUG -0.0350 0.0153 -0.0399 0.0498 0.0144 -0.9312
(0.0101) (0.0135) (0.0130) (0.0359) (0.0474) (0.0641)
0TH -0.0310 0.0392 0.0120 0.1127 -0.0534 0.1586 -1.2240
(0.0258) (0.0338) (0.0335) (0.0803) (0.0715) (0.0619) (0.1037)
Hicksian/uncompensated own-price elasticities
GR MP FV DA1 OBF SUG 0TH
GR -0.6563
(0.0357)
MF 0.2680 -0.8325
(0.0282) (0.0470)
FV 0.1814 0.1290 -0.7454
(0.0191) (0.0261) (0.0338)
DA1 0.0391 0.0441 0.0498 -0.8003
(0.0172) (0.0225) (0.0218) (0.0774)
OBF 0.0705 0.0521 0.0842 0.0053 -1.0439
(0.0122) (0.0163) (0.0151) (0.0414) (0.0751)
SUG 0.0110 0.0616 0.0075 0.0990 0.0625 -0.9001
(0.0102) (0.0136) (0.0130) (0.0359) (0.0474) (0.0650)
OTH 0.0631 0.1437 0.1088 0.2134 0.0450 0.2565 -1.0726
(0.0261) (0.0339) (0.0337) (0.0804) (0.0716) (0.0620) (0.1051)

 

1. GR = grains; MF = meat and ﬁsh; FV = fruits and vegetables; DA1 = dairy; OBF = oils, butter,

and other fats; SUG = sugar; 0TH = other foods
2‘ Standard errors in parentheses

137

 

 

 

 

 

 

 

Table A8 Parameter Estimates for QUAIDS: Rural-Urban Differences
Eq.‘ RURAL URBAN URBAN
Variable Endgacorrected No enchorrec.
Coeff. Std. Err. Coeff. Std. Err. Coeff. Std. Err.
Constant a, 0.2480 (0.0346) 0.0322 (0.0372) 0.0505 (0.0352)
(12 0.2657 (0.0292) 0.3064 (0.0414) 0.2883 (0.0393)
(13 0.2538 (0.0220) 0.2196 (0.0263) 0.2184 (0.0251)
0.4 0.0056 (0.0181) 0.0715 (0.0248) 0.0598 (0.0240)
115 0.0497 (0.0108) 0.0751 (0.0146) 0.0744 (0.0141)
(16 0.0324 (0.0098) 0.0005 (0.0098) 0.0043 (0.0095)
(17 0.1449 (0.0250) 0.2947 40.0424) 0.3041 (0.0404)
Expenditure B, -0. 1282 (0.0149) -0.0701 (0.0223) -0.0509 (0.0191)
[32 0.0821 (0.0137) -0.0649 (0.0225) -0.0831 (0.0191)
03 -0.0080 (0.0101) -0.0061 (0.0164) -0.0070 (0.0141)
[34 0.0027 (0.0079) -0.0074 (0.0142) -0.0198 (0.0121)
135 -0.01 1 1 (0.0046) -0.0323 (0.0082) -0.0332 (0.0066)
56 -0.0356 (0.0042) -0.0292 (0.0053) -0.0243 (0.0043)
137 0.0980 (0.0112) 0.2100 (0.0248) 0.2181 @0214)
Prices 711 0.0073 (0.0170) 0.0260 (0.0171) 0.0156 (0.0157)
721 0.0262 (0.0121) -0.0063 (0.0139) -0.0003 (0.0131)
731 -0.0057 (0.0080) 0.0126 (0.0097) 0.0136 (0.0092)
y." -0.0002 (0.0070) 0.0067 (0.0089) 0.01 18 (0.0085)
751 0.0046 (0.0052) 0.0093 (0.0063) 0.0081 (0.0061)
761 -0.0144 (0.0047) 0.0022 (0.0041) 0.0005 (0.0041)
771 -0.0178 (0.0108) -0.0505 (0.0141) -0.0492 (0.0132)
722 -0.031 1 (0.0140) 0.0097 (0.0190) 0.0089 (0.0187)
732 -0.0016 (0.0073) -0.0132 (0.0105) -0.0142 (0.0104)
742 -0.0034 (0.0063) -0.0001 (0.0096) -0.003 1 (0.0096)
732 0.0024 (0.0048) 0.0010 (0.0066) 0.0001 (0.0063)
762 0.0071 (0.0044) 0.0010 (0.0043) 0.0029 (0.0042)
772 0.0004 (0.0093) 0.0099 (0.0144) 0.0058 (0.0142)
733 0.0046 (0.0073) 0.0239 (0.01 12) 0.0244 (0.01 1 1)
743 -0.0046 (0.0044) -0.0102 (0.0076) -0.01 13 (0.0076)
753 0.0056 (0.0031) 0.0008 (0.0054) 0.0002 (0.0052)
m 0.0075 (0.0029) 0.0046 (0.0037) 0.0038 (0.0036)
773 0.0092 (0.0067) -0.0093 (0.01 10) -0.0089 (0.0109)
744 0.0029 (0.0057) 0.01 19 (0.0102) 0.0085 (0.0101)
75. 0.0003 (0.0031) -0.0187 (0.0056) 0.0165 (0.0053)
764 0.0061 (0.0029) -0.0019 (0.003 9) 0.0001 (0.003 8)
774 -0.001 1 (0.0060) 0.0122 (0.0098) 0.0104 (0.0098)
755 -0.0079 (0.0047) 0.0067 (0.0079) 0.0077 (0.0070)
765 0.0012 (0.003 1) -0.0023 (0.0044) -0.0047 (0.0040)
775 -0.0061 (0.0046) 0.0052 (0.0068) 0.005 1 (0.0065)
766 -0.0007 (0.0041) -0.0024 (0.0053) -0.0042 (0.0052)
776 0.0081 (0.0043) 0.0081 (0.0052) 0.0092 (0.0050)
177 0.0072 (0.0126) 0.0243 (0.0214) 0.0276 (0.0209)
Expenditure- 3.. -0.0267 (0.0052) 0.0142 (0.0072) 0.0149 (0.0072)
squared 12 0.0158 (0.0047) 0.0415 (0.0073) 0.0417 (0.0073)
13 0.0034 (0.0034) 0.0059 (0.0054) 0.0057 (0.0054)
3.: -0.0045 (0.0027) -0.0136 (0.0047) -0.0139 (0.0047)
1.5 0.0007 (0.0016) -0.0050 (0.0025) -0.0050 (0.0025)
205, -0.0050 (0.0014) -0.0030 (0.0016) -0.0029 (0.0016)
1.7 0.0163 (0.0039) 0.0430 (0.0085) 0.0429 (0.0085)

 

 

138

Table A8 (Cont’d)

 

 

 

 

 

 

Household 2.1 0.0102 (0.0009) 0.0156 (0.0013) 0.0149 (0.0012)
size 221 -0.0051 (0.0008) -0.0032 (0.0014) -0.0025 (0.0013)
Z3] -0.0008 (0.0006) -0.0027 (0.0009) -0.0027 (0.0009)
2.“ 0.0002 (0.0005) -0.0016 (0.0008) -0.001 1 (0.0008)
25, 0.0003 (0.0003) 0.0002 (0.0005) 0.0002 (0.0004)
26. 0.0012 (0.0002) 0.0023 (0.0003) 0.0021 (0.0003)
27] -0.0062 (0.0006) -0.0105 (0.0014) -0.0108 (0.0013)
Education of 2,4 0.0016 (0.0007) -0.0024 (0.0009) 0.0031 (0.0008)
head 224 -0.0009 (0.0007) -0.0014 (0.0010) 0.0007 (0.0008)
234 -0.0002 (0.0005) -0.0008 (0.0006) 0.0008 (0.0006)
244 -0.0007 (0.0004) 0.0016 (0.0006) -0.0020 (0.0005)
254 0.0000 (0.0002) 0.0000 (0.0003) 0.0000 (0.0003)
7.64 0.0004 (0.0002) -0.0005 (0.0002) 0.0006 (0.0002)
Z74 -0.0001 (0.0005) 0.0035 @0010) -0.0032 (0.0009)
Survey year 2.5 -0.0681 (0.0209) 0.0319 (0.0240) 0.0414 (0.0236)
(=1 if 1998) 225 0.0906 (0.0192) 0.0172 (0.0260) 0.0077 (0.0261)
Z35 -0.0605 (0.0140) -0.0439 (0.0179) -0.0451 (0.0176)
Z45 0.0287 (0.0128) 0.0003 (0.0198) -0.0070 (0.0193)
255 -0.0188 (0.0074) -0.0539 (0.01 15) -0.0523 (0.0108)
265 -0.0208 (0.0068) -0.0106 (0.0076) -0.0068 (0.0072)
275 0.0489 (0.0163) 0.0591 (0.0262) 0.0621 (0.0261L
Survey year 216 -0. 1247 (0.0264) 0.0285 (0.0337) 0.0433 (0.0320)
(=1 if 2004) 226 0.0668 (0.0255) -0.0182 (0.0388) -0.0331 (0.0386)
236 -0.0320 (0.0190) -0.0022 (0.0291) -0.0014 (0.0278)
2.46 0.0439 (0.0167) 0.0294 (0.0297) 0.0183 (0.0282)
256 -0.0011 (0.0109) -0.0771 (0.0189) -0.0795 (0.0173)
266 -0.0336 (0.0099) -0.0250 (0.0127) -0.0195 (0.0122)
276 0.0806 (0.0213) 0.0647 (0.0359) 0.0718 (0.0347L
Month of 2.7 0.0024 (0.0027) 0.0061 (0.0031) 0.0063 (0.0031)
survey 227 0.0017 (0.0025) -0.0034 (0.0032) -0.0035 (0.0032)
Z37 -0.0091 (0.0019) -0.0050 (0.0021) -0.0049 (0.0021)
Z47 0.0052 (0.0015) 0.0026 (0.0019) 0.0025 (0.0019)
257 -0.0010 (0.0008) -0.0010 (0.001 1) -0.0010 (0.0011)
267 -0.0019 (0.0008) 0.0013 (0.0007) 0.0014 (0.0007)
277 0.0027 (0.0020) -0.0007 (0.0034) -0.0007 (0.0034)
Residuals v. 0.0237 (0.0150)
v2 -0.0239 (0.0157)
v3 -0.0004 (0.0108)
v4 -0.0153 (0.0096)
v5 -0.0016 (0.0059)
v6 0.0058 (0.0038)
v7 0.0117 (0.016(D

 

‘. The commodities represented by the different equation numbers are: 1 = grains; 2 = meat and ﬁsh;

3 = fruits and vegetables; 4 = dairy; 5 = oils, butter, and other fats; 6 = sugar; 7 = other foods

139

Table A9

Own and Cross Price Elasticities: Rural-Urban Differences

 

l. RURAL HOUSEHOLDS

 

Marshallian/Uncompensated own-price elasticitiesl

 

 

 

GR MF FV DA1 OBF SUG 0TH
GR -0.8399
(0.0815)
MF -0.0280 -0.6579
(0.1044) (0.1789)
F V 00944 0.5106 -0.9542
(0.1 168) (0.1844) (0.1577)
DA1 0.0498 0.0329 -0.0708 -0.8600
(0.0537) (0.1266) (0.0531) (0.1294)
OBF 0.0556 0.0031 0.0085 -0.1951 -0.8278
(0.0348) (0.0709) (0.0350) (0.0784) (0.1352)
SUG 0.0552 -0.1203 0.0064 -0.1353 -0.1607 -1.1789
(0.0327) (0.0498) (0.0349) (0.0685) (0.0880) (0.1463)
0TH -0.9685 2.2556 -0.5096 2.4149 1.5436 2.0453 -5.4848
(0.4150) (0.4872) (0.4592) (0.8329) (0.6892) (0.7210) (1.1737)
Hicksian/uncompensated own-price elasticities
GR MF FV DA1 OBF SUG 0TH
GR -0.5878
(0.0468)
MF 0.2242 -0.6526
(0.0906) (0.0499)
FV 0.1577 0.5159 -0.7788
(0.0808) (0.1536) (0.0282)
DA1 0.3019 0.0382 0.1046 -0.8129
(0.0709) (0.1216) (0.0545) (0.0182)
OBF 0.3077 0.0084 0.1840 -0.1480 -0.8106
(0.0575) (0.0835) (0.0423) (0.0781) (0.0087)
SUG 0.3073 -0.1149 0.1819 -0.0882 -0.1435 -l.1685
(0.0738) (0.0824) (0.0587) (0.0806) (0.0919) (0.0052)
OTH -0.7 164 2.2609 -0.3 341 2.4620 1.5608 2.5031 -5.0271
(0.3702) (0.4424) (0.4318) (0.8157) (0.6810) (0.7361) (0.0402)

 

140

Table A9 (Cont’d)

l. URBAN HOUSEHOLDS

 

Marshallian/Uncompensated own-price elasticitiesl

 

 

 

GR MF FV DA1 OBF SUG 0TH
GR -0.7474
(0.0998)
MF 0075] -0.5248
(0.1282) (0.1889)
FV -0.0686 0.4852 -0.9598
(0.1 185) (0.1942) (0.1568)
DA1 -0.0004 0.1449 -0.0876 -0.7245
(0.0631) (0.1441) (0.0625) (0.1383)
OBF 0.0631 0.0035 0.0097 -0.2214 -0.8409
(0.0370) (0.0811) (0.0368) (0.0951) (0.1440)
SUG 0.0715 -0.1611 0.0102 -0.1912 0.1396 -1.1547
(0.0386) (0.0580) (0.0406) (0.0835) (0.0945) (0.1502)
0TH -0.8574 2.0804 -0.4953 2.1835 1.4593 1.9692 -5.1792
(0.3894) (0.4748) (@280) (0.7891) (0.6475) (0.6798) (1.1354)
Hicksian/uncompensated own-price elasticities
GR MF FV DA1 OBF SUG OTH
GR -0.5191
(0.0474)
MF 0.1532 -0.4934
(0.1059) (0.0502)
FV 0.1597 0.5166 -0.7835
(0.0855) (0.1660) (0.0291)
DA1 0.2279 0.1762 0.0887 -0.6640
(0.0671) (0.1331) (0.0539) (0.0196)
OBF 0.2914 0.0349 0.1860 -0.1609 -0.8227
(0.0566) (0.0900) (0.0412) (0.0925) (0.0100)
SUG 0.2998 -0.1297 0.1864 -0.1306 -0.1214 -1.1492
(0.0802) (0.0904) (0.0652) (0.0954) (0.0986) (0.0061)
0TH 0629] 2.1118 -0.3191 2.2440 1.4774 2.4152 -4.7331
(0.3464) (0.4315) (0.4010) (0.7719) (0.6393) (0.6967) (0.0417)

 

'. GR = grains; MF = meat and ﬁsh; FV = fruits and vegetables; DAI = dairy; OBF = oils, butter,

and other fats; SUG = sugar; 0TH = other foods

141

 

 

 

 

 

 

Table A10 Parameter Estimates of the QUAIDS Model: Income-Groups Differences
lilq.f Low (End.Corrected) Middle High

Variable Coeff. Std. Err. Coeff. Std. Err. Coeff. Std. Err.

Constant a. 0.1616 (0.0632) 0.1 156 (0.0467) 0.1 166 (0.0339)

(12 0.3455 (0.0571) 0.3004 (0.0409) 0.2922 (0.0377)

(13 0.2041 (0.0417) 0.2333 (0.0297) 0.2292 (0.0248)

0.; 0.0427 (0.0278) 0.05 52 (0.0296) 0.0267 (0.0221)

115 0.0652 (0.0194) 0.0487 (0.0113) 0.0702 (0.0162)

6., 0.0206 (0.0200) 0.0172 (0.01 14) 0.0144 (0.0080)

(17 0.1603 (0.0480) 0.2297 (0.0362) 0.2507 (0.0367)

Expenditure [3, -0.0527 (0.0377) -0. 1207 (0.0230) -0.0609 (0.0180)

[32 0.0606 (0.0329) 0.0762 (0.0222) -0.0278 (0.0193)

03 -0.0465 (0.0254) -0.0321 (0.0166) 0.0034 (0.0130)

[34 -0.0136 (0.0162) 0.0044 (0.0151) -0.0398 (0.0117)

[35 -0.0173 (0.0118) -0.0265 (0.0055) -0.0152 (0.0081)

0; 0.0288 (0.0127) 0.0362 (0.0055) 0.0130 (0.0038)

[37 0.0982 (0.0299) 0.1349 (0.0183) 0.1534 (0.0201)

Prices 7” 0.0197 (0.0272) 0.0164 (0.0215) 0.0209 (0.0162)

721 0.0074 (0.0189) 0.0167 (0.0155) 0.0146 (0.0133)

731 0.0070 (0.0130) 0.0054 (0.0107) 0.0060 (0.0087)

741 0.0065 (0.0097) -0.0077 (0.0103) -0.0108 (0.0087)

751 0.0049 (0.0080) 0.0016 (0.0052) 0.01 17 (0.0073)

761 -0.0196 (0.0081) -0.0120 (0.0051) -0.0033 (0.0036)

771 0.0259 (0.0181) 0.0172 (0.0141) 0.0271 (0.0129)

722 0.0155 (0.0218) 0.0170 (0.0185) 0.0190 (0.0185)

732 0.0079 (0.0120) 0.0078 (0.0099) 0.0103 (0.0095)

742 0.0006 (0.0084) -0.0004 (0.0094) 0.0013 (0.0093)

752 -0.0064 (0.0073) 0.0027 (0.0048) 0.0045 (0.0073)

762 0.0081 (0.0074) 0.0037 (0.0048) -0.0012 (0.0037)

772 0.0138 (0.0150) 0.0021 (0.0125) 0.0100 (0.0137)

733 -0.0021 (0.0123) 0.0165 (0.0102) 0.0163 (0.0093)

743 -0.0085 (0.0063) -0.0062 (0.0070) -0.0017 (0.0066)

753 0.0056 (0.0052) 0.0054 (0.0035) 0.0079 (0.0052)

7.3 0.0082 (0.0053) 0.0087 (0.0035) 0.0030 (0.0027)

773 0.0141 (0.01 15) -0.0045 (0.0095) -0.0032 (0.0100)

744 -0.0024 (0.0069) 0.0132 (0.0095) 0.0199 (0.0102)

754 0.0042 (0.0044) -0.0003 (0.0035) -0.0148 (0.0062)

764 0.0023 (0.0046) 0.0019 (0.0036) -0.0006 (0.0035)

774 -0.0026 (0.0085) -0.0005 (0.0091) 0.0068 (0.0095)

755 -0.001 1 (0.0072) -0.0136 (0.0049) 0.0003 (0.0082)

765 0.0015 (0.0051) 0.0017 (0.0034) 0.0016 (0.0035)

775 -0.0086 (0.0074) 0.0057 (0.0049) -0.01 14 (0.0073)

766 0.0054 (0.0072) 0.0009 (0.0047) 0.0013 (0.0037)

776 0.0105 (0.0075) 0.0125 (0.0050) 0.0051 (0.0041)

(77 0.001 1 (0.0214) 0.0020 (0.0173) 0.0199 (0.0195)

Expenditure- 2.. -0.0090 (0.0081) -0.0249 (0.0083) 0.0042 (0.0085)

squared 3.2 0.0078 (0.0071) 0.0104 (0.0079) -0.0238 (0.0091 )

3.3 -0.0004 (0.0055) 0.0002 (0.0059) 0.0091 (0.0061)

3.4 -0.0049 (0.0034) -0.0028 (0.0053) -0.0216 (0.0056)

3.5 -0.0031 (0.0025) -0.0032 (0.0019) 0.0015 (0.003 8)

3.5 -0.0066 (0.0026) -0.0057 (0.0019) 0.0036 (0.0018)

17 0.0163 (0.0066) 0.0261 (0.0066) 0.0270 (0.0097)

 

 

 

 

142

Table A10 (Cont’d)

 

 

 

 

 

 

 

Household size 2.1 0.0097 (0.0022) 0.0091 (0.0012) 0.0102 (0.001 1)
22, 0.0061 (0.0019) 0.0042 (0.001 1) 0.0043 (0.0012)
23| 0.0007 (0.0015) 0.0010 (0.0008) 0.0000 (0.0008)
2..l 0.0014 (0.0009) 0.0002 (0.0007) 0.0003 (0.0007)
251 0.0000 (0.0007) 0.0000 (0.0003) 0.0012 (0.0005)
2.1 0.0009 (0.0007) 0.0013 (0.0003) 0.0014 (0.0002)
27. 0.0065 (0.0016) 0.0054 (0.0009) -0.0089 40.0012)
Race 2l2 0.0994 (0.0361) 0.0646 (0.0203) 0.0817 (0.0102)
(1 if black) 222 0.0335 (0.0324) 0.0096 (0.0188) 0.0338 (0.0110)
232 0.0253 (0.0246) 0.0308 (0.0140) 0.0289 (0.0074)
2.2 0.0342 (0.0159) 0.0291 (0.0131) 0.0323 (0.0065)
252 0.0232 (0.01 1 1) 0.0088 (0.0049) 0.0089 (0.0047)
262 0.0098 (0.01 16) 0.0044 (0.0050) 0.0047 (0.0023)
272 0.0435 (0.0274) 0.0100 (0.0158) 0.0503 (0.0112)
Rural/Urban (1 if 2.3 0.0242 (0.0176) 0.0596 (0.0112) 0.0402 (0.0090)
rural) 223 0.0159 (0.0157) -0.0480 (0.0104) 0.0425 (0.0095)
233 0.0041 (0.0119) 0.0138 (0.0077) 0.0265 (0.0064)
2.3 0.0241 (0.0077) 0.0093 (0.0071) 0.0130 (0.0054)
253 0.0054 (0.0054) 0.0061 (0.0027) 0.0023 (0.0040)
263 0.0095 (0.0056) 0.0031 (0.0027) 0.0035 (0.0019)
273 0.0031 (0.0132) 0.0130 (0.0086) 0.0170 (0.0095)
Education of head 2... 0.0005 (0.0015) 0.0024 (0.0010) 0.0015 (0.0007)
22. 0.0010 (0.0013) 0.0008 (0.0009) 0.0006 (0.0008)
234 0.0006 (0.0010) 0.0001 (0.0007) 0.0004 (0.0005)
2..., 0.0008 (0.0006) 0.0010 (0.0006) 0.001 1 (0.0004)
254 0.0007 (0.0005) 0.0003 (0.0002) 0.0001 (0.0003)
2.4 0.0009 (0.0005) 0.0001 (0.0002) 0.0004 (0.0001)
274 0.0002 (0.001 1) 0.0005 (0.0008) 0.0020 (0.0008L
Survey year 2,. -0.0226 (0.0349) 0.0477 (0.0281) 0.0291 (0.0232)
(=1 if 1998) 225 0.0561 (0.0321) 0.0932 (0.0265) 0.0284 (0.0260)
235 -0.0832 (0.0245) 0.0580 (0.0194) 0.0500 (0.0170)
2.5 0.0224 (0.0174) 0.0277 (0.0212) 0.0140 (0.0186)
255 0.0103 (0.01 18) 0.0289 (0.0080) 0.0408 (0.0126)
265 0.0210 (0.0122) 0.0234 (0.0080) 0.0097 (0.0065)
275 0.0587 (0.0271) 0.0371 (0.0229) 0.0872 (0.0248)
Survey year 2l6 0.0670 (0.0472) 0.0841 (0.0359) 0.0772 (0.0310)
(=1 112004) 226 0.0339 (0.0449) 0.0539 (0.0352) 0.0053 (0.0366)
23., 0.0715 (0.0359) 0.0226 (0.0262) 0.0087 (0.0255)
2.6 0.0121 (0.0246) 0.0440 (0.0275) 0.0548 (0.0270)
256 0.0123 (0.0193) 0.0096 (0.0122) 0.0431 (0.0197)
266 0.0251 (0.0204) 0.0383 (0.0119) -0.0181 (0.0100)
27., 0.1054 (0.0380) 0.0567 (0.0300) 0.0870 (0.032%
Month of survey 2.7 0.0036 (0.0045) 0.0030 (0.0036) 0.0018 (0.0029)
227 0.0027 (0.0041) 0.0023 (0.0033) 0.0019 (0.0030)
237 0.01 13 (0.0031) 0.0068 (0.0024) 0.0072 (0.0021)
2.7 0.0060 (0.0020) 0.0034 (0.0023) 0.0045 (0.0017)
257 0.0009 (0.0014) 0.0008 (0.0009) 0.0005 (0.0013)
267 0.001 1 (0.0014) 0.0008 (0.0009) 0.0001 (0.0006)
277 0.0064 (0.0034) 0.0003 (0.0027) 0.0032 (0.0031)

 

 

 

143

Table A10 (Cont’d)

 

Residuals v. -0.0296 (0.0275)
v; 00137 (0.0238)
v3 0.0403 (0.0182)
v4 0.0145 (0.0119)
V5 00090 (0.0086)
V6 00125 (0.0091)
v7 0.0101 (0.0204)

 

 

 

1. The commodities represented by the different equation numbers are: l = grains; 2 = meat and ﬁsh;
3 = fruits and vegetables; 4 = dairy; 5 = oils, butter, and other fats; 6 = sugar; 7 = other foods

144

Table All Own and Cross Price Elasticities: Income-Group Differences

 

I. LOW-IN COME (corrected for expenditure endogeneity)

 

Marshallian/Uncompensated own-price elasticities]

 

 

 

GR MF FV DA1 OBF SUG 0TH
GR -0.8889
(0.1868)
MF 0.921 1 -2.4796
(0.8679) (1.4364)
FV 0.2240 -0.3664 -0.9468
(0.2429) (0.3283) (0.2343)
DA1 0.0373 -0.0298 -0.0351 -0.9815
(0.0995) (0.1521) (0.0407) (0.3 596)
OBF 0.0645 -0.1135 0.0490 0.2605 -0.9035
(0.0841) (0.1289) (0.0650) (0.3146) (0.1712)
SUG -0.1019 0.1108 -0.0401 -0.1536 -0.0860 -1.1357
(0.0842) (0.1439) (0.0669) (0.3242) (0.2126) (0.4463)
OTH 0.6457 -1.0430 0.1735 2.6821 1.5030 2.5366 -7.2895
(0.6901) (1.0044) (0.84689 (2.0815) @3510) (1.1148) (3.6996)
Hicksian/uncompensated own-price elasticities
GR MF FV DA1 OBF SUG 0TH
GR -0.8111
(0.2406)
MF 0.9988 -2.0963
(0.6338) (0.1314)
FV 0.3018 0.0169 -0.8119
(0.1503) (0.2523) (0.0937)
DA1 0.1150 0.3535 0.0999 -0.9617
(0.2278) (0.1878) (0.0801) (0.0268)
OBF 0.1422 0.2698 0.1839 0.2803 -0.8781
(0.2019) (0.1281) (0.0447) (0.3036) (0.0200)
SUG -0.0242 0.4941 0.0948 -0.1338 -0.0606 -1.1337
(0.2931) (0.2456) (0.1559) (0.3348) (0.2213) (0.0221)
0TH 0.7234 -0.6597 0.3084 2.7019 1.5285 2.7980 -7.0282
(0.4609) (0.8818) (0.7552) (2.0583) (1.3337) (1.1491) (0.0617)

 

l. GR = grains; MF = meat and ﬁsh; FV = fruits and vegetables; DA1 = dairy; OBF = oils, butter,

and other fats; SUG = sugar; OTH = other foods

145

 

Table All (Cont’d)

 

ll. MIDDLE-INCOME

 

Marshallian/Uncompensated own-price elasticities]

 

 

 

GR MF FV DA1 OBF SUG 0TH
GR -1.l924
(0.1987)
MF 0.8583 -1.6434
(0.3035) (0.4451)
FV 0.3283 -0.2673 -0.8690
(0.1384) (0.1412) (0.1374)
DA1 0.1018 -0.0900 -0.0255 -0.7310
(0.0998) (0.0803) (0.0649) (0.1742)
OBF 0.0009 0.0026 0.0398 -0.0171 -1.2419
(0.0324) (0.0274) (0.0194) (0.0554) (0.0966)
SUG -0.1135 0.0658 -0.0434 -0.0265 -0.0297 -1.0992
(0.0409) (0.0497) (0.0423) (0.1104) (0.0865) (0.1241)
0TH 0.8653 -0.6195 0.0072 0.4973 0.9365 1.3480 -5.1092
(0.3258) (0.4322) (0.4018) (1.0297) (0.4669) (0.3776) (1.3480)
Hicksian/uncompensated own-price elasticities
GR MF FV DA1 OBF SUG 0TH
GR -0.8111
(0.2406)
MF 0.9988 -2.0963
(0.6338) (0.1314)
FV 0.3018 0.0169 -0.8119
(0.1503) (0.2523) (0.0937)
DA1 0.1150 0.3535 0.0999 -0.9617
(0.2278) (0.1878) (0.0801) (0.0268)
OBF 0.1422 0.2698 0.1839 0.2803 -0.8781
(0.2019) (0.1281) (0.0447) (0.3036) (0.0200)
SUG -0.0242 0.4941 0.0948 -0.1338 -0.0606 -1.1337
(0.2931) (0.2456) (0.1559) (0.3348) (0.2213) (0.0221)
0TH 0.7234 -0.6597 0.3084 2.7019 1.5285 2.7980 -7.0282
(0.4609) (0.8818) (0.7552) (2.0583) (1.3337) (1.1491) (0.0617)

 

1. GR = grains; MF = meat and ﬁsh; FV = fruits and vegetables; DAI = dairy; OBF = oils, butter,

and other fats; SUG = sugar; OTH = other foods

146

Table A1] (Cont’d)

 

ll. HIGH-INCOME

 

Marshallian/Uncompensated own-price elasticities]

 

 

 

GR MF FV DA1 OBF SUG OTH
GR -0.8770
(0.0668)
MF 0.0429 0.5898
(0.1826) (0.1550)
FV -0.0569 0.4815 -1 .2072
(0.1945) (0.2525) (0.2764)
DA1 -0.0092 -0. 1292 0.0725 -1 . 1427
(0.0595) (0.0980) (0.0833) (0.3081)
OBF 0.0501 0.0765 0.0149 0.0040 -0.9912
(0.0376) (0.0757) (0.0572) (0.1806) (0.1720)
SUG -0.0029 -0.0339 0.0004 -0.0901 0.0463 -0.9203
(0.0179) (0.0356) (0.0278) (0.0838) (0.0719) (0.1075)
0TH -0.2797 1.4025 -0.8377 4.1039 -0.5546 -0.7364 -3.9698
(0.4866) (0.5807) (0.5542) (1.1784) (1.1056) (1.0043) 41.2688)
Hicksian/uncompensated own-price elasticities
GR MF FV DA1 OBF SUG OTH
GR -0.6515
(0.0671)
MF 0.2685 -0.4964
(0.1212) (0.0724)
FV 0.1686 0.5749 -1.0054
(0.1296) (0.1895) (0.0351)
DA1 0.2163 -0.0358 0.2742 -1.1407
(0.1 196) (0.1366) (0.1080) (0.0215)
OBF 0.2756 0.1699 0.2167 0.0060 -0.9524
(0.0538) (0.0837) (0.0519) (0.1746) (0.0123)
SUG 0.2226 0.0595 0.2022 -0.0881 0.0851 -0.8952
(0.0785) (0.0888) (0.0527) (0.0905) (0.0768) (0.0051)
OTH -0.0542 1.4959 -0.6360 4.1060 -0.5159 -0.3545 -3.5879
(0.4205) (0.5115) (0.52049 (1.1586) (1.0938) (1.0100) (0.0502)

 

'. GR = grains; ME = meat and ﬁsh; FV = fruits and vegetables; DA1 = dairy; OBF = oils, butter,
and other fats; SUG = sugar; 0TH = other foods

147

CHAPTER SIX

SUMMARY AND CONCLUSIONS

6.] Summary

This study analyzed food expenditure patterns in South Africa, taking into
account differences in preferences across rural and urban households, as well as across
income groups. The study was motivated by the need to provide an accurate analysis of
food demand in South Africa, and to provide demand behavioral parameters that can be
used for welfare analyses. Analyses of the panel data indicated that there is a need to
allow for more curvature in the Engel curve relationships than is permitted by the
Working-Leser form, which allows for only a linear relationship between budget shares
and expenditure. The implication of this ﬁnding is that popular functional forms such as
AIDS do not provide an accurate picture of demand behavior in South Africa. Given this
ﬁnding, this study estimated the QUAIDS model developed by Banks et a1. (1997),
which is a generalization of the AIDS model that allows for a quadratic relationship
between budget shares and expenditure. The QUAIDS model was used to estimate
demand functions for seven food groups— grains, meat and ﬁsh, fruits and vegetables,
dairy, oils and fats, sugar, and all other foods. The demand functions were estimated
using panel data on household food consumption collected as part of the KwaZulu-Natal
Income Dynamics Study (KIDS), with surveys carried out in 1993, 1998, and 2004.

The QUAIDS model was estimated in its ﬂexible form, without imposing
linearity on the price aggregators, as is commonly done in empirical estimation of AIDS.

Expenditure endogeneity was explicitly tested, and corrected for using the control

148

function approach where necessary. Expenditure censoring, which was found to be a
problem in the dairy commodity, was corrected for using a two-step procedure suggested
by Shonkwiler and Yen (1999).

Because the existing food demand studies in South Africa are based on the
LA/AIDS model, the study also estimated the food demand system using AIDS and
LA/AIDS. The expenditure and price elasticity estimates from these models were
compared. It was found that the exclusion of the quadratic expenditure term has a larger
effect on the magnitudes of expenditure elasticities than price elasticities. On average, the
QUAIDS and AIDS expenditure elasticity estimates differed by about 53%, with most of
the AIDS estimates being larger. However, these differences were much larger in the case
of commodities that were found to require a quadratic expenditure term. The AIDS
expenditure elasticity estimates for grains, sugar, and dairy, which all required an a
quadratic expenditure term, were 113%, 101%, and 80%, respectively, larger than the
QUAIDS estimates. The standard errors of both the QUAIDS and AIDS expenditure
elasticity estimates were all signiﬁcant at the 1% level, so that the decision to choose
between QUAIDS and AIDS models could not be made based on the statistical
signiﬁcance of the estimated expenditure elasticities. The estimates of price and
expenditure elasticities from the AIDS and LA/AIDS models were found to be very
similar, and so were their standard errors.

In addition to comparing the elasticity estimates, the study also examined the bias
in welfare measures that can result if these are based on the restrictive AIDS and
LA/AIDS models. This was accomplished by measuring the welfare gains from the zero-

rating of the value-added tax (VAT) on meat products. Two common measures of welfare

149

were computed, namely, the compensating variation and equivalent variation. Similar to
the ﬁndings in the case of expenditure elasticities, it was found that AIDS and the
LA/AIDS models overstate the welfare gains from zero-rating meat. Consistent with both
AIDS and LA/AIDS models not allowing for adequate curvature in the Engel curves,
their overstating of welfare gains was found to be larger for richer households (that is, the
bias in welfare gains increases with total household expenditure).

Apart from the empirical contributions explained above, this study also makes
methodological contribution. The study build on the work of Bank et al. (1997) to
develop an LM test that can be used to determine whether or not a quadratic (QUAIDS)
or a linear (AIDS) demand model speciﬁcation is appropriate. In particular, the
implication of corollary 2 in Banks et al. (p.533) is that a utility-derived demand system
that is rank 3 and exactly aggregable cannot have coefﬁcients on both the linear and the
quadratic expenditure terms that are independent of prices. In other words, if a rank 3
exactly aggregable demand system that is derived from utility theory has a coefﬁcient on
the linear expenditure term that is independent of prices, then it must have a coefﬁcient
on the quadratic expenditure term that is price dependent. The study noted that since the
QUAIDS model, which is rank 3 and exactly aggregable, has a coefﬁcient on the linear
expenditure term that is independent of prices, then whether or not it is the appropriate
functional form can be tested for based on the statistical signiﬁcance of prices in the
coefﬁcient on the quadratic expenditure term. The test was developed and implemented
in this study, and provided statistical evidence in support of the QUAIDS functional
form. The overall conclusion from this test was consistent with that based on the

likelihood ratio test for signiﬁcance of lambda in the QUAIDS model, although the

150

results of the two tests sometimes differed in the individual budget share equations. These
differences in conclusions in the individual budget share equations (regarding which
equations are linear and which are not) was not necessarily unexpected, given the
differences in approach followed in constructing the two tests.

Given the highly unequal distribution of income in South Africa, and the large divide
in wealth distribution between urban and rural areas, it is expected that preferences will
differ signiﬁcantly among households in different socioeconomic and demographic
groups. Hence, pooling data across all households is likely to obscure important
information on variability in demand behavior. To determine the impact of this household
heterogeneity on demand, this study analyzed the demand behavior of rural and urban
households separately, as well as households in different income groups.

For some food groups, the difference in the estimated expenditure elasticities between
rural and urban samples was found to be substantial. For instance, a 1% increase in total
food expenditure for urban households leads to only about 0.02% increase in the budget
share of meat and ﬁsh, but to about 1.73% increase in the case of rural households. High
income households respond to a 1% increase in the price of meat and ﬁsh by decreasing
consumption by 0.59%, while low income households decrease consumption by about
2.48%. These results provide further evidence on the need to undertake disaggregated
analysis of demand behavior in a country with highly diverse socioeconomic and

demographic household groups like South Africa.

151

6.2 Conclusions

This study is the ﬁrst to apply the QUAIDS model to analyze food consumption
patterns in South Africa. The study implemented recent advances in econometric methods
designed to enhance demand estimation with micro-level data. Hence, the price and
expenditure elasticities estimated in this study are an improvement of the previous
estimates for South Africa, the majority of which are commodity-speciﬁc and based on
single equation estimation. Furthermore, most of these previous studies use aggregate
data, and therefore, do not allow for the impact of demographic effects on consumption.
The exception is a study Agbola (2003), that uses a 1993 cross-sectional dataset to
estimate demand functions for a broad range of food groups similar to the one estimated
in this study. However, Agbola uses the restrictive LA/AIDS model. As shown in chapter
ﬁve, the magnitudes of demand elasticities can vary widely depending on the functional
form used. For instance, the AIDS and LA/AIDS expenditure elasticities tend to be larger
than the QUAIDS expenditure elasticities; the standard errors of these elasticity estimates
were both signiﬁcant at the 1% level. This dependence of demand behavioral parameters
on model selection is particularly important because of its implication for policy advice.
We showed, through the example of a tax reform on meat products, that welfare measures
such as equivalent variation can differ signiﬁcantly between QUAIDS and AIDS. The
expenditure and price elasticities estimated in this study correct for many of the problems
associated with these previous estimates, and therefore, can be used more reliably in

calculating welfare measures.

152

The ﬁnding of substantial consumption differences between rural and urban
households, as well as among households in different income-groups has important
welfare implications. These results indicate that the design of anti-poverty and nutrient
enhancement policies needs to be region-speciﬁc and should be based on accurate and
comprehensive food poverty studies. No systematic differences in the absolute
magnitudes of the expenditure elasticities and own-price elasticities were found (for
instance, it could not be said that households are more responsive to expenditure changes
than price changes); this means that a combination of income and price policies may be
more effective in inﬂuencing consumption patterns than those based solely on one and
not the other. The usual challenge remains one of ﬁnding optimal policy designs that
make'food more affordable to vulnerable groups in the long run, while not adversely
affecting the deve10pment of a food marketing system that stimulates production
incentives and income growth. One of the keys to the design of such policies is that they
be based on thorough and robust statistical analyses.

As with all empirical models, there are some limitations to this study that should
form the basis for future research. The estimation of the QUAIDS model in this study
was based on pooled maximum likelihood estimation. One possibility is to extend the
QUAIDS model in ways that address the problem of unobserved heterogeneity taking

advantage of the panel structure of this dataset, such as random effects or ﬁxed effects.

153

REFERENCES

Aasnes, J ., E. Biom, and T. Skjerpen. “Engel Functions, Panel Data, and
Latent Variables.” Econometrica 61(6)(1993):1395-1422

Abdulai, A. “Household Demand for Food in Switzerland. A quadratic Almost Ideal
Demand System.” Swiss Journal of Economics and Statistics 138(1) (2002):1-18

Abdulai, A. “Economies of Scale and Demand for Food in Switzerland: Parametric and
Non-Parametric Analysis.” Journal of Agricultural Economics 54(2)(July
2003):247-267.

Abdulai, A. and D. Aubert “A cross-section analysis of household demand for food and
nutrients in Tanzania.” Agricultural Economics 31(2004):67-79

Adato, M., M.R. Carter, and J. May. “Sense in Sociability? Social Exclusion and
Persistent Poverty in South Africa.” Staff paper 477, University of Wisconsin,
Department of Agricultural and Applied Economics, Madison, WI, September
2004.

Agbola, F.W. “Estimation of Food Demand Patterns in South Africa Based on a Survey
of Households.” Journal of Agricultural and Applied Economics 35(3)(December
2003):662-670

Aguero, J .M. and B.W. Gould. “Household Composition and Brazilian Food Purchases:
An Expenditure System Approach.” Canadian Journal of Agricultural Economics
51(2003):323-345.

Anderson, G. and R.W. Blundell. “Estimation and Hypothesis Testing in Dynamic
Singular Equation Systems.” Econometrica 50(6)(1982): 1559-1579.

Amemiya, T. “Multivariate Regression and Simultaneous Equation Models When the
Dependent Variable Are Truncated Normal.” Econometrica 42(November
1974):999-1012.

Amemiya, T. Advanced Econometrics. Cambridge: Harvard University Press, 1985.

Amdt, C. “Demand for Herbicide Use in Corn: An Entropy Approach Using Micro-Level
Data.” Journal of Agricultural and Resource Economics 24(1)(1999):2004-221.

Amdt, C., S. Liu, and RV. Preckel. “On Dual Approaches to Demand Systems

Estimation in the Presence of Binding Quantity Constraints.” Applied Economics
31(1999):999-1008.

154

Banks, J .; Blundell, R., and A. Lewbel. “Tax Reform and Welfare Measurement: Do We
Need Demand System Estimates?” The Economic Journal 106(September
1996):]227-1241.

Banks, J .; Blundell, R., and A. Lewbel. “Quadratic Engel Curves and Consumer
Demand.” The Review of Economics and Statistics 79(4)(November 1997):527-
539.

Barten, A.P. “Family Composition, Price and Expenditure Patterns.” In Econometric
Analysis for National Planning, Hart, P.E., G. Mills, and J .K. Whittaker eds.,
Butterworth: London, 1964.

Barten, A.P. “Maximum Likelihood Estimation of Complete System of Demand
Equations.” European Economic Review 1(1969):7-73.

Becketti, S., W. Gould, L. Lillard, and F. Welch. “The Panel Study of Income Dynamics
aﬁer Fourteen Years: An Evaluation.” Journal of Labor Economics 6(4)(October
1988):472-492.

Belete, A., CD. Igodan, C. M’Marete, and W. van Averbeke. “Analysis of rural
household consumption expenditure in South Africa: the case of food plot holders

in the Tyefu irrigation scheme in the Eastern Cape Province.” Agrekon 38(2):]94-
201

Blundell, R.W., A. Duncan, and K. Pendakur. “Semiparametric Estimation and Consumer
Demand.” Journal of Applied Econometrics 13(5)(September-October 1998):435-
461.

Blundell, R.W. and C. Meghir. “Bivariate Alternatives to the Tobit Model.” Journal of
Econometrics 34(1987):179-200.

Blundell, R.W., P. Pashardes, and G. Weber. “What Do We Learn About Consumer
Demand Patterns from Micro Data.” American Economic Review 83(3)
(June1993):570-597.

Blundell, R.W. and J.L. Powell. “Endogeneity in Semiparametric Binary Response
Models.” Review of Economic Studies 71(2004):655-679.

Blundell, R.W. and J .M. Robin. “Estimation in Large and Disaggregated Demand
Systems: An Estimator for Conditionally Linear Systems.” Journal of Applied
Econometrics 14(1999):209-232.

Blundell, R.W. and J .M. Robin. “Latent Separability: Grouping Goods without Weak
Separability.” Econometrica 68(1)(2000):53-84.

155

Bollino, C.A., F. Perali, and N. Rossi. “Linear Household Technologies.” Journal of
Applied Econometrics 15(3)(May-June 2000): 275-87.

Bouis, H. “The Effect of Income on Demand for Food in Poor Countries: Are our Data

Bases giving us Reliable Estimates?” Journal of Development Economics
44(1994):199-226.

Bouis, H., and L. Haddad. “Are Our Estimates of calorie-income elasticities too high? A

recalibration of the plausible range.” Journal of Development Economics
39(2)(1992):333-364.

Bowmaker, RA, and W.L Nieuwoudt. “Demand equations for selected South African
agricultural commodities.” A grekon 29(1)(1 990):46—50.

Browning, R., and J .M. Collado. “The Response of Expenditures to Anticipated Income
Changes: Panel Data Estimates.” American Economic Review 91 (3)(June
2001):681-692.

Browning and Collado. “Habits and Heterogenity in Demands: A Panel Data Analysis.”
Centre for Applied Microeconometrics, Institute of Economics CAM working
Paper No. 2004-18, University of Copenhagen, Copenhagen, 2004.

Brownig, M.J., and C. Meghir. “The Effects of Male and Female Labour Supply on
Commodity Demands.” Econometrica 59 (1991):925-951.

Buse, A. “Evaluating the Linearized Almost Ideal Demand System.” American Journal of
Agricultural Economics 76(4)(November 1994):781-793.

Carpentier A. and H Guyomard. Unconditional Elasticities in Two-Stage Demand
Systems: An Approximate Solution.” American Journal of A gricultural
Economics 83(1)(February 2001):222-229

Carter, M.R., and J. May. “Poverty, Livelihood and Class in Rural South Africa.” World
Development 27(1)(January 1999): 1 -20.

Carter, M.R., and J. May. “One Kind of Freedom: Poverty Dynamics in Post-Apartheid
South Africa.” World Development 29(12)(December 2001): 1987-2006.

Christensen, M.L. “Heterogeneity in Consumer Demands and the Income Effect.”
Institute of Economics, University of Copenhagen, mimeo (2004).

Christensen, L.R., D.W. Jorgenson, and L.J. Lau. “Transcendental Logarithmic Utility
Functions.” American Economic Review 65 3(1975)(June): 367-3 83.

Chung, C.F. “Modelling Demand Systems with Demographic Effects Based on the
Modifying Function Approach.” Economics Letters (73)(2001):269-274.

156

Cox, T.L., and MK. Wohlgenant. “Prices and Quality Effects in Cross-Sectional Demand
Analysis.” American Journal of A gricultural Economics 68(4)(November
1986):908-19.

Craig, J .G. “Some Statistical Models for Limited Dependent Variables with Applications
to the Demand for Durable Goods.” Econometrica 39(1971):829-844.

Davis, G.C. “The Generalized Composite Commodity Theorem: Stronger Support in the
Presence of Data Limitations.” The Review of Economics and Statistics
85(2):476-480.

Deaton, A. “Quality, Quantity, And Spatial Variation of Price.” American Economic
Review 78(3)(June 1988):4l 8-430.

Deaton, A. The Analysis of Household Surveys: A Microeconomic Approach to
Development Policy. Baltimore, MD: John Hopkins University Press, 1997.

Deaton, A., and M. Irish. “A Statistical Model for Zero Expenditures in Household
Budgets.” Journal of Public Economics 23(1984):312-326.

Deaton, A., and J. Muellbauer. Economics and Consumer Behavior. Cambridge
University Press, 1980a.

Deaton, A., and J. Muellbauer. “An Almost Ideal Demand System.” American Economic
Review 70(3)(June 1980b):312-336.

Dhar, T., J .P. Chavas, and B.W. Gould. “An Empirical Assessment of Endogeneity Issues
in Demand Analysis for Differentiated Products.” American Journal of
Agricultural Economics 85(3)(August 2003):605-617.

Dockel, J .A., and J .A. Groenewald. “The demand for food in South Africa.” A grekon
9(4)(1970):15-20.

Dong, D., Shonkwiler, J .S., and O. Capps, Jr. “Estimation of Demand Functions Using
Cross-Sectional Household Data: The Problem Revisited.” American Journal of
Agricultural Economics 80(3)(August 1998):466-473.

Dynan, K.E. “Habit Formation in Consumer Preferences: Evidence from Panel Data.”
American Economic Review 90(3)(2000):391-406.

Eales, J .S. and L.J. Unnevehr. “Demand for Beef and Chicken Products: Separability and

Structural Change.” American Journal of Agricultural Economics 70(1988):521-
532.

157

Edgerton, D.L. “Weak Separability and the Estimation of Elasticities in Multistage
Demand Systems.” American Journal of Agricultural Economics 79(1997):62-79.

Elliot, M.B., and J. van Zyl. “The effect of income on the market for carbohydrates in
South Africa.” A grekon 30(4)(1991):269-71 .

Fitsgerald, J ., P. Gottschalk, and R. Mofﬁtt. “An Analysis of Sample Attrition in Panel
Data: The Michigan Panel Study of Income Dynamics.” Journal of Human
Resources 33(2)(Spring 1998):251-299.

Food Pricing Monitoring Committee. Report of the Food Pricing Monitoring Committee,
National Department of Agriculture, Pretoria, South Africa, 2003.

Gorman, W.M. “Tricks With Utility Functions.” In Essays in Economic Analysis, M.
Artis and R. Nobay eds. Cambridge: Cambridge University Press, 1976.

Gorman, W.M. “Some Engel Curves.” In The Theory and Measurement of Consumer
Behaviour, A. Deaton ed. Cambridge, UK: Cambridge University Press, 1981.

Gould, W., J. Pitblado, and W. Sribney. Maximum Likelihood Estimation with Stata.
College Station, Texas: Stata Corporation.

Gould, W. and H.J. Villarreal. “An Assessment of the Current Structure of Food Demand
in Urban China.” Agricultural Economics 34(2006):1-16.

Hancock, P.J., W. L Nieuwoudt, and MC. Lyne. “Demand analysis of meats in South
Africa.” Agrekon 23(3)(1984):26—29.

Heckman, J .J . “The Common Structure of Statistical Models of Truncation, Sample
Selection and Limited Dependent Variable Models Using Simulated ML and
GMM Estimation Methods.” Annals of Economic and Social Measurement
5(1976):475-492.

Heien, D., and CR. Wessells. “Demand System Estimation with Microdata: A Censored
Regression Approach.” Journal of Business and Statistics 8(3)(July l990):365-
371.

Hausman, J .A. “Speciﬁcation Tests in Econometrics.” Econometrica 46(1978):1251-
1271

Hausman, J .A., and W. E. Taylor. “Panel Data and Unobservable individual effects.”
Econometrica 31(1986):93-1 18.

Human Science Research Council (January 2004). Food Security in South Africa: Key
Policies Issues for the Medium Term (Online). Available from:
www.sarpn.org.za/documents/d0000685/Food_securitv SAjJanuarv2004mdf

158

Integrated Food Security Strategy (IF SS). National Department of Agriculture Policy
Document. Pretoria, South Africa, 2002.

J ooste, A. “Beef trade preferences and intensities in the Southern African Customs
Union.” Agrekon 35(3)(1996):l23—130.

J orgenson, D.W., L.J. Lau, and TM. Stoker. “The Transcendental Logarithmic Model of
Aggregate Consumer Behavior.” In R. Basman and G. Rhodes eds., Advances in
Econometrics, vol.1, Greenwich, Ct: JAI Press, 1982.

Koch, S.F. “South African Households: Are Expenditure Patterns Almost Ideal?” Paper
Presented at the 9th Annual Conference on Econometric Modelling for Africa,
June 30 — July 02, 2004, Cape Town, South Africa.

Labeaga, J .M., and A. Lopez. “A Study of Petro Consumption Using Spanish Panel
Data.” Applied Economics 29(6)(1997):795-802.

LaFrance, J .T. “When is Expenditure ‘Exogenous’ in Separable Demand Models?”
Western Journal of Agricultural Economics l6(1991):49-62

Laurent, C. and E. Comon. “Behavioral Heterogeneity and the Income Effect.” The
Review of Economics and Statistics 85(3)(2003):653-669.

Lecocq, S. and J. Robin. “Estimating Demand Response with Panel Data.” Empirical
Economics (2006). Forthcoming.

Lee, L., and M. M. Pitt. “Microeconometric Demand System with Binding Nonnegativity
Constraints: The Dual Approach.” Econometrica 54(5)(September 1986):]237-
1242.

Leibbrandt, M., and I. Woolard. “A comparison of poverty in South Africa’s nine
provinces.” Development Southern Africa 16(1)(March 1999):37-35.

Leibbrandt, M., G. Fields, and P. Cichello. “Earnings and Employment Dynamics for
Aﬁ'icans in Post-apartheid South Africa: A Panel Study of KwaZulu-Natal.”
Journal of Aﬁ'ican Economies (Forthcoming).

Lesser, C.E.V. “Forms of Engel Functions.” Econometrica 31(4)(October 1963): 694-703

Lewbel, A. “A Uniﬁed Approach to Incorporating Demographic or Other Effects into
Demand Systems.” Review of Economic Studies 52(1)(January l985):1-18.

Lewbel, A. “The Rank of Demand Systems: Theory and Nonparametric Estimation.”
Econometrica 59(1991):71 1-730.

159

Lewbel, A. “Aggregation Without Separability: A Generalized Composite Commodity
Theorem.” American Economic Review 86(3):524-542.

Lewbel, A. “Constructing instruments for regressions with measurement error when no
additional data are available, with an application to patents and R&D.”
Econometrica 65 (1997): 93-1 18.

Liu, K.E. “Food Demand in Urban China: An Empirical Analysis Using Micro
Household Data.” Unpublished Ph.D. Dissertation, Ohio State University,
Columbus, Ohio, 2003.

Loubser, M. (1990). “Income Elasticities of the demand for consumer goods and
services.” Bureau of Market Research No. 175, University of South Africa,
Pretoria.

Lubbe, W.F. “Decomposition of price time series components of the red meat industry for
efﬁcient policy and marketing strategies.” Agrekon 29(4)(1990): 296 - 304.

Maluccio, J. “Attrition in the KwaZulu Natal Income Dynamics Study, 1993-1998.” IFPRI
FCND Discussion Paper No. 95, October 2000.

May, J ., and I. Woolard. “Measurement and experience”. In J. May (Ed.), Poverty and
inequality in South Africa: report prepared for the office of the executive deputy
president and the inter-ministerial committee on poverty and inequality. Durban,
Praxis Publishing, 1998.

Meenakshi, J .V., and R. Ray. “Regional Differences in India’s Food and Expenditure
Pattern: A Complete Demand Systems Approach.” Journal of International
Development 11(Jan/Feb 1999): 47-74.

Meyerhoefer, CD. “The Econometrics of Non-Standard Structural Demand Modeling:
Applications to Transition Country Data.” Unpunblished Ph.D. Dissertation,
Cornell University, Ithaca, New York, 2002.

Meyerhoefer, C.D., C.K. Ranney, and DE. Sahn. “Consistent Estimation of Censored
Demand Systems using Panel Data.” American Journal of Agricultural
Economics 87(3)(August 2005):660-672.

Mofﬁt, R., J. Fitzgerald, and P. Gottschalk. “Sample Attrition in Panel Data: The Role of
Selection on Observables.” Annale d’Economie et de Statistique 55-56(1999)

Molina, J .S. and A. I. Gil. “The Demand Behavior of Consumers in Peru: A

Demographic Analysis using the QUAIDS.” Journal of Developing Areas
39(1)(Spring 2005): 191-206.

160

Moschini, G. “A Non-nested Test of Separability for Flexible Functional Forms.” The
Review of Economics and Statistics 74(2)(1992):365-369.

Moschini, G. “Units of Measurement and the Stone Index in Demand System
Estimation.” American Journal of Agricultural Economics 77(February 1995):63-
68.

Moschini, G., D. Moro, and RD. Green. “Maintaining and Testing Separability in
Demand Systems.” American Journal of Agricultural Economics 76(February
1994):61-73.

Moro, D. and P. Sckokai. “Heterogenous Preferences in Household Food Consumption in
Italy. European Review of Agricultural Economics 27(3)(2000):305-323.

Muellbauer, J. “Community Preferences and the Representative Consumer.”
Econometrica 44(1976): 525-543.

Muellbauer, J. “Testing the Barten Model of Household Composition Effects and the
Cost of Children.” Economic Journal 87(347)(September 1977):800-808.

Nayga, Jr., R. M. and O. Capps, Jr. "Tests of Weak Separability in Disaggregated Meat
Products." American Journal of A gricultural Economics. 76(4) (November
1994):800-808.

Nelson, J .A. “Quality Variation and Quantity Aggregation in Consumer Demand for
Food.” American Journal of A gricultural Economics 73(4)(November
1991):]204-12.

Nieuwoudt, W.L. “The demand for livestock products in South Africa for 2000, 2010 and
2020: Part 1." Agrekon 37(2)(1998).

Orcutt, G.H., H.W. Watts and J .B. Edwards (1968). “Data Aggregation and Information
Loss.” American Economic Review 58(4)(1968):773-787.

Park, J. and GO Davis. “The Theory and Econometrics of Health Information in Cross-
Sectional Nutrient Demand Analysis.” American Journal of Agricultural
Economics 83(4)(November 2001): 840-851.

Piggot, NE. “The Nested PIGLOG Model: An Application to US. Food Demand.”
American Journal of Agricultural Economics 85(1)(February 2003): 1-1 5.

Pitt, M.M.; M.R. Rosenzweig, and Md. N. Hassan. “Productivity, Health, and Inequality

in the Intrahousehold Distribution of Food in Low-Income Countries.” American
Economic Review 80(5)(December 1990): 1 139-1 156.

161

Poi, B. P. “From the Help Desk: Demand System Estimation.” Stata Journal
2(4)(2002):403-410.

Pollak, R. A., and T.J. Wales. “Estimation of the Linear Expenditure System.”
Econometrica 37(4)(October 1969): 611-627.

Pollak, RA, and T.J. Wales. “Estimation of Complete Demand Systems from Household
Budget Data: The Linear and Quadratic Expenditure Systems.” American
Economic Review 68(3)(June 1978):348-359.

Pollak, RA. and T.J. Wales. “Comparison of the Quadratic Expenditure System and
Translog Demand Systems with Alternative Speciﬁcations of Demographic
Effects.” Econometrica 48(3)(April l980):595-612.

Pollak, RA. and T.J. Wales. “Demographic Variables in Demand Analysis.”
Econometrica 49(6)(November 1981): 1533-1551 .

Pollak, RA. and T.J. Wales. Demand System Specification and Estimation. Oxford
University Press, 1992.

Poonyth, D., R. Hassan, and J .F. Kirsten. “Random Coefﬁcients Analysis of Changes in
Meat Consumption Preferences in South Africa.” Agrekon 4O (2001):426-437

Prais, S.J., and HS. Houthakker. The Analysis of Family Budgets. Cambridge University
Press, 1955.

Ravallion, M. “Income Effects of Malnutrition.” Economic Development and Cultural
Change 38(3):489-515.

Reed, A.J., J .W. Levendahl, and C. Hallahan. “The Generalized Composite Commodity
Theorem and Food Demand Estimation.” American Journal of Agricultural
Economics 87(1):28-37.

Shonkwiler, J .S., and ST. Yen. “Two-Step Estimation of a Censored System of
Equations.” American Journal of Agricultural Economics 81(4)(November
1999):972-982.

Skouﬁas, B. “Is the Calorie-Income Elasticity Sensitive to Price Changes? Evidence from
Indonesia.” World Development 31(7)(July 2003): 1291-1307.

Statistics South Africa (SSA). Bulletin of Statistics 33(1-2)(1999). Pretoria, South Africa.

Statistics South Africa (Stats SA) (2000). Website: www.statssa.gov.za

162

Stone, R. “Linear Expenditure Systems and Demand Analysis: An application to the
Pattern of British Demand.” The Economic Journal 64(225)(September
1954):511-27.

Subramanian, S., and A. Deaton. “The Demand for Food and Calories.” Journal of
Political Economy 104(1 )(1996): 133-162.

Taljaard, P.R., Z.G. Alemu, and H.D. van Schalkwyk. “The Demand for Meat in South
Aﬁica: An Almost Ideal Estimation.” Agrekon 43(4)(December 2004):430-443.

Theil, H. “The Information Approach to Demand Analysis.” Econometrica
(33)(1965):67-87.

Thomas, D., E. Frakenberg, and J .P. Smith. “Lost but not Forgotten: Attrition and
Follow-up in the Indonesia Family Health Survey.” Journal of Human Resources

36(4)(Autumn 2001):556-592.

Tobin, J. “Estimation of Relationships for Limited Dependent Variables.” Econometrica
26(1)(January 1958):24-36.

Trade and Industrial Policy Strategies (TIPS). Website: www.tips.org.za

Varian, H.R. Microeconomic Analysis. New York, N.Y.: W.W. Norton & Company, Inc.,
1992.

Wales, T.J., and AD. Woodland. “Estimation of Consumer Demand Systems with
Binding Non-Negativity Constraints.” Journal of Econometrics 21(3)(1983):263-
285.

Watkinson, E. and N. Makgetla. “COSATU looks at the Food Security Crisis.” South
African Labour Bulletin 6(2)(April 2002).

Woolard, 1., S. Klasen, and M. Leibbrandt. “Income mobility and household dynamics in
South Africa: The case of KwaZulu-Natal.” Labour Markets and Social Frontiers
2(2002):5-1 1.

Wooldridge, J .M. Introductory Econometrics: A Modern Approach. Cincinnati, OH:
South-Western, 2000.

Wooldridge, J .M. Econometric Analysis of Cross Section and Panel Data. Cambridge,
MA: MIT Press, 2002.

World Bank. GNI Per Capita 2004, Atlas Method and PPP. At: www.worldbank.org

World Development Report (2002), The World Bank.

163

World Health Organizations (1995). Website: www.who.int

 

van Zyl, J ., and J. Kirsten. “Food Security in South Africa.” Agrekon 31(4)(December
1992):]70-183.

Yen, S.T., K. Kan, and S. Su. “Household demand for fats and oils: two-step estimation
of censored demand system.” Applied Economics 34(14)(September 2002): 1799-
1806.

164

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