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dissertation entitled

A General Demand Framework For Goods And Money:
The Theoretical Model And Empirical Evidence In China

presented by

QIAO YU

has been accepted towards fulfillment
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A GENERAL DEMAND FRAMEWORK OF GOODS AND MONEY:
THE THEORETICAL MODEL AND EMPIRICAL EVIDENCE IN CHINA

BY

QIAO YU

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements

for the degree of

DOCTOR OF PHILOSOPHY

Department of Economics

1990

LC.” kg? t;

(0033

ABSTRACT
A GENERAL DEMAND FOR GOODS AND MONEY:
THE THEORY AND EMPIRICAL EVIDENCE IN CHINA
BY

QIAO YU

Since 1978 China has embarked on a complex and
historically unprecedented process of economic restructuring.
One of the difficult challenges facing the Chinese government
is to achieve the equilibrium in money market so as to tackle
the fundamental sources of inflation. Therefore, the monetary
authority has to understand fully the demand side of money.

The basic purpose of this thesis is to explain the
comprehensive demand structure of rural households in China,
especially the money demand.behavior. The main hypothesis is
thatmoney demand in LDC countries is not only determined by
the income level, general prices and interest rates explored
by the prevailing neoclassical theory, but it also is a
function of governmental pricing policies on specific goods
and socio-economic variables, such as the level of economic
development, demographic variables and fixed investment.

The neoclassical demand theory fails to explain the
interaction of goods demand and money demand. Also, it does
not explore the methodology for incorporating institutional

variables into the demand system. Further, as double

functional agents of both consumer and producer in a semi-
commercialized economy, rural households will retain a portion
of agri-products for consumption, while purchasing both
industrial consumer and producer goods in markets. The
conventional theory is difficult to describe these features.
Based upon the new home economics, this thesis constructs
a general demand framework for goods and money. It is so
general that in LDC countries, rural households' demand for
home-produced agricultural output, industrial consumer and
producer goods, as well as money assets can be simultaneously
analyzed within the framework. In addition, socio-economic
variables are explicitly incorporated into the general demand
system. The socio-economic variables defined are household
demographic factors, the indices characterizing rural economic
developmental level, and the indicator of fixed investment.
The major findings indicate that along with the process
of rural economic development, two contradictory effects exist
in the demand for'nl (cash and demand deposits): as the income
level of rural households rises, on the one hand, the demand
for M1 will increase; as the income becomes more monetized,
the level of rural production activities is more diversified
and the fixed investment is achieved, on the other hand, the
H1 demand tends to decline. Besides, governmental relative
pricing policies on specific goods may exert positive impacts

upon the demand for M1.

COPYRIGHT BY
QIAO YU

1990

ACKNOWLEDGEMENTS

I would thank professor Paul Strassmann, chairperson of
my dissertation committee, for his profound guidance and
delightful encouragement on this dissertation. I will express
my special thanks to Dr. Ching-Fan Chung, for his generous
contributions of lots of time and effort concerning the
theoretical and empirical portions of the thesis. Also, I
will thank professor Anthony Koo and Carl Liedholm, who
provide extreme help and. substantive suggestions for' my
dissertation.

I am grateful to the Institute of Development in China
co-sponsoring with the Ford Foundation, for providing funding
and data accessibility. I would thank all friends who work
in the Institute of Development and the Statistical Bureau for
the great help and assistance they offered.

I would like to dedicate this thesis to my parents for
their warm love and encouragement, which is one of the main

sources for me to complete my doctoral study.

iv

TABLE OF CONTENTS

Page
LIST OF TABLES vi
CHAPTER
I. INTRODUCTION 01
II. DATA DESCRIPTION 14
2.1 Introduction 14
2.2 Data Background 15
2.3 Data on Expenditures, Honey Assets,
and Prices . 23
2.4 Socio-economic Variables 32
2.5 Conclusion 41
III. NEW HOME ECONOMICS WITH RURAL HOUSEHOLD,
INSTITUTIONAL FACTORS AND MONEY ASSETS 45
3.1 Introduction 45
3.2 New Approach, Rural households, and
Institutional Factors 50
3.21 New approach of demand system 50
3.22 New approach and rural household 58

3.23 Methods of combining institutional factors 61
3.3 New Approach With Money Assets 66
3.31 Utility function and money asSets 69
3.32 Implication of new approach on money assets 75
3.4 Conclusion 82
IV. SPECIFICATIONS OF DEMAND SYSTEMS 84
4.1 Introduction 84
4.2 The Differential Modeling 85
4.3 AIDS Modeling 96
4.4 Methods Of Aggregation 102
V. RESULTS OF ESTIMATIONS 106
5.1 Introduction 106
5.2 Analysis Of Estimated Results 107
5.3 Income And Price Elasticities 121
5.4 Policy Implications 128
VI. CONCLUSION 132
APPENDIX 139
BIBLIOGRAPHY 150

vi

10:

11:

12:

LIST OF TABLES

Percent of Rural Population in 1987,
Selected Developing Countries

Percentage of Total Sales and Demand Deposits
in China's Rural Area

Population, Area and cities in China and
Sichuan Province.

Quantities and Values of Agricultural Products
in China and Sichuan Province

Quantities and Values of Industrial Products
in China and Sichuan Province

Detailed Items in the Catergries of "Clothes"
and "Agri-input"

Number of Households with Newly-built
Houses and Durable Equipment

1978-86 Commercial Percentages of Agricultural
Products and Non-agricultural Products in
China's Rural Households

1978-85 Commercial Percentage of Peasants'
Consumption in China's Rural Households

1978-86 Ratio of M1 to Net Income Per
Household in China

1978-86 Ratio of Non-agricultural Income to
Total Income in China's Rural Households

Log Likelihood Values for Alternative Model
Formations

vii

Page

02

03

17

18

19

26

29-31

34

35

36

37

108

13:

14:

15:

16:

17:

19:

20:

21:

Likelihood Ratio Test Statistics for
Estimations

Likelihood Ratio Test Statistics between
Linear and Quadratic Models

Maximum Likelihood Parameter Estimates

Significant Effects of Socio-economic
Variables upon a* Parameters

Significant Effects of Socio-economic
Variables upon Parameters 3* and 6*

Estimated Income Elasticities of Q8, QPI
and QDM Models

Estimated Price Elasticities of Q8, QPI
and QDM Models

Estimated Price Elasticities of LS, LPI and
DM Models

Estimated Income Elasticities of LS, LPI and
DM Models

viii

109

111

112-114

115

118

124

125

142

143

LIST OF MAPS

China's Administrative Division

Map of Sichuan Province

ix

Page
43

44

CHAPTER I
INTRODUCTION

In most developing countries, rural residents still
make up the major part of the population. In 1987, about 70
percent of the total population in low-income developing
countries resided in rural areas; while in lower-middle
income and upper-middle income developing countries, the
percentages of rural residents in the total population were
roughly 54 percent and 37 percent, respectively.1
Therefore, rural households in developing countries are
significant in the total demand for both goods_and monetary
assets. For example, in 1985, Chinese rural households'
demand for goods and money accounts for 58.5 percent and 60
percent of the whole country's demand for goods and money,

respectively.2

 

1 World Bank, "World Development Reports 1989", Oxford

University Press, 1989, Table 31, pp224.

2 The report of the Institute of Development under the
State Council of China, "Peasants, market and the
institutional innovation __ the reform in the depths facing
the rural development after eight years of fixing household
production quotas", Economic Research, Jan. 1987, Beijing,
PP7-

Table 1:

Percentage of Rural Population in 1987,
Selected Developing Countries.

 

Low-income Percent Lower-middle Percent Upper-middle Percent

 

 

 

economies income. income.

economies economies
China 62 Philippines 59 Brazil 25
Chad 70 Egypt 52 Hungary 41
Bangladesh 87 Thailand 79 Argentina 15
India 73 Turkey 53 Algeria 56
Sierra Leone 74 Peru 31 Venezuela 17
Pakistan 69 Malaysia 60 Panama 46
Haiti 71 Costa Rica 55 Gabon 57
Ghana 68 Morocco 53 Libya 33
Indonesia 73 Mexico 29 Iran 47
Zambia 77 Zimbabwe 74 Trinidad 33

& Tobago

Unweighted
Average 72.4 54.5 37.0
Sources: "World Development Report, 1989", World Bank,

Note:

Oxford University Press 1989, Table 31.

Low income economies: a GNP per capita of U.S.$480
or less in 1987; lower-middle income economies: a
GNP per capita between $480 and $1,940 in 1987;
upper-middle income economies: a GNP per capita
between $1,941 and $6,000 in 1987.

3

As a major part of total money demand in the economy,
rural households' money demand is extremely important for
the central bank's monetary policy in the money market, such
as money supply decisions and interest rate policy. In
addition, the general demand structure of rural households
also deeply reflects the government intervention such as
pricing policies, demographic policies, rural development
planning, and even direct investment in infrastructure and
projects: and it again impacts the non-rural economy through
demand linkages.

Consequently, it is important to understand and account

for rural households' general demand behavior for goods and

Table 2: Percentage of Total Sales and Demand.
Deposits in China's Rural Area.

 

 

Years Percent of total goods Percent of total demand
sales in rural areas deposits in rural areas

1984 59.2 36.1

1985 58.5 34.8

1986 57.7 34.2

1987 57.6 32.8

 

Sources: "Abstract of Chinese Statistics, 1988", the
National Bureau of Statistics, the Press of
Statistics, 1988, Beijing.

4
money assets. One of the main problems specifying and
predicting general demand systems of rural households in
developing countries, however, is that the demand framework
is often confounded by the complex characteristic of rural
households in LDC countries as a double functional agent in
semi-commercialized rural economies. Most rural households,
on the one hand, will purchase industrial consumer goods and
retain some agri-output for their own consumption; and on
the other hand, they will also buy industrial producer goods
(like fertilizer, pesticides and etc.) for the production of
agricultural output. Besides demand for both market and
non-market goods, rural households highly desire to obtain
monetary assets, especially cash-holdings and demand
deposits. Hence a general demand system must include
households' demand for money. Furthermore, households'
demand functions are not only determined by the income
level, market prices and interest rates, but also affected
by some socio-economic or institutional factors such as
demographic variables or rural income structures, which may
reflect some features of the development process.

In Chapter II, we will discuss the data. First of all,
we will describe the general economic and social conditions
of the areas from which the rural households data come.

Then we will explain the categories of the data set which
will be applied to our theoretical formulation for

estimation. The micro-economic data are Chinese rural

5
households in the province of Sichuan, surveyed annually by
the Sichuan Provincial Statistical Bureau. Two hundred and
forty households during the period of 1985 to 1987 are
available. They include many detailed variables: quantities
of goods items obtained by households, and expenditure upon
those goods, money assets required by households,
demographic information, and the sources of income. Besides
those micro-household data we will use exogenous macro-
aggregate data published by the People's Bank of China (the
central bank of China), the National Statistical Bureau and
the Provincial Statistical Bureau; for example, annual
interest rates, inflation rates, and others.

Obviously, the traditional theory is insufficient to
describe the general demand behavior of rural households in
developing countries. Again, it rarely considers the
methodology of combining socio-economic variables into the
demand system; and it also implicitly excludes the money
market while specifying demand framework for goods.

Hence, in Chapter III we will construct a model which
is capable of amending the conventional theory. First, we
will discuss the new approach proposed by Becker, G. (1965),
Lancaster, K. (1966), and adjusted by Pollak and Wachter
(1975). Following this approach, we will specify rural
households' optimizing problem. The new theory of home
economics which is characterized by the internal household

technology can be extended to depict rural households'

6
demand behavior. Essentially, in this model, households will
maximize the so-called "consumptive characteristics" which
cannot be directly purchased. Instead, households will
obtain economic goods to generate the censumptive
characteristics via their internal production function.
Thus the purchased goods are not arguments in household
preference orderings, they just act as inputs of producing
characteristics.

The extension of the new approach will show that, both
rural households' purchased industrial producer goods and
retained agricultural output will perform the role as inputs
to produce the consumptive characteristics via households'
internal technology, in which rural households' production
function is implicitly incorporated.

Under budget and technological constraints, households'
optimizing decision for consumptive characteristics is then
equivalent to maximize the "inputs of characteristics", or
the economic goods bundle. Therefore, an original household
utility function of characteristics is translated into a
modified utility function of goods, which obeys properties
of the conventional theory. The optimal space of so-called
"characteristics" is replaced by tangible goods space. This
transformation then distinguishes the difference of
household tastes and technology, which is often confounded
by traditional theory. Consequently, the socio-economic

variables can be explicitly expressed as parameters

7
affecting households' internal technology in the modified
utility function.

Since this theoretical treatment is compatible with
many analytical searches incorporating secio-economic
factors such as demographic variables into the demand
equations, we will briefly review some concise methods which
specify socio-economic factors as exogenous impacts on the
demand system of households. Barten (1964) proposed a
scaling method to incorporate exogenous variables into the
demand system. The method consists of a commodity specific
equivalent scales based upon the direct utility function.
After Barten, Pollak and Wales (1978, 1980, 1981)
contributed a translating procedure of combining demographic
effects into the demand system with basis of duality theory.
Also, German (1976) introduced a technique which was
employed by Pollak and Wales (1980, 1981), Barnes and
Gillingham (1983) to conduct the empirical studies.
Methodologically, Gorman's technique combines both
translating and scaling specifications, but essentially it
is more general than linear techniques due to its built-in
joint demographic effects across demand functions. Finally,
Lewbel (1985) proved that there exists the compatibility of
the new home economics with these procedures by unifying
them through a concise theoretical modeling.

Then we will discuss a general demand framework with

money assets included. Some neoclassical economists like

8
Hicks, Samuelson (1947), Morishima (1952), Patinkin (1965),
and Friedman (1969) have made attempts to incorporate money
assets into the general utility function, in order to deal
with demand for money. Recently many researchers have
revisited the utility approach to combine money demand,
among them were Chetty (1969), Bisgnano (1974), Diewert
(1974), Clements (1976), Barnett (1981), Ewis and Fisher
(1984). Also, the perfect foresight modeling with money in
utility functions has been formulated by Brock (1974), Clavo
(1979), Obstefeld (1983) and others. On the contrary, some
economists, such as Clower (1967), Nichans (1980), Kareken
and Wallace (1980) have questioned the attempts of treating
money as an argument in the general utility function. Their
arguments claim that the characteristics of money assets
were not revealed: instead they proposed the method of
including money into the budget constraint. Finally, these
two approaches have been synthesized and proved to be
functionally equivalent by Fischer (1974) and Feenstra
(1986).

However, the criticism from Clower, Nichans, or Kareken
and others has revealed the difference of "monetary
characteristics" and money assets itself. We will extend
the new approach of home economics to be a general framework
in which households will optimize their utility function
through both "consumptive and monetary characteristics"

arguments. This original utility function is equivalent to

9
maximize a modified utility function with goods and money
assets as arguments, where goods and money assets are inputs
to generate "characteristics" through household internal
technology. In other words, an intangible bundle of
"consumptive and monetary characteristics" derived from the
original utility function is transformed into a tangible
bundle of goods and money from a well modified utility
function. Therefore, with the extended unitary household
modeling, a general demand system for both goods and money
assets under the influence of socio-economic factors is then
obtainable.

In Chapter IV, based upon the modified utility
maximization structure which satisfies all properties of
traditional theory, we will investigate the specifications
of demand functions which we will employ to conduct our
empirical studies. Contemporary economic literature has
specified demand systems through two procedures: by deriving
demand systems from a process of utility maximization or by
expressing them directly with certain restrictions. All
demand systems obtained from these two procedures, however,
will correspond to an explicit or implicit utility
maximization problem.

The procedure of specifying a utility function or an
expenditure function has been explored by many authors.
Klein and Rubin (1947-48) suggested linear expenditure

system (LES) derived from a direct utility function, with

10
Stone (1954) making a more detailed discussion about this
model. Then Lluch (1973) generalized the extended linear
expenditure system (ELES) based on an intertemporal
maximization of the Klein-Rubin utility function. With a
rapid development of duality theory, Houthakker (1960)
derived a set of demand equations termed as the indirect
addilog demand system (IADS) based upon an indirect
function. Christenson, Jogenson and Lau (1975) explored a
flexible functional form of demand system which is obtained
from the quadratic approximation of the indirect translog
utility function. This specification can be useful to test
assumptions such as additivity of preferences. But the
major limitation for it is the number of structural
parameters required; thus, annual data series of usual
length and more refined commodity groups involve serious

problems of estimation.3

Deaton and Muellbauer (1980)
proposed an Almost Ideal Demand System (AIDS). They derived
AIDS model from a specific class of preferences represented
by a cost or expenditure function. This model is such a
flexible functional form that the demand functions derived

are first-order approximation to any set of demand functions

from utility-maximizing behavior.

 

3 Berndt, E. R., Darrough, M. N., and Diewert, W. E.,

"Flexible functional forms and expenditure distributions: an
application to Canadian consumer demand functions" , Discussion
paper pp77-100, Department of Economics, University of British
Columbia.

11

Alternative procedure, on the other hand, directly
expresses specifications of demand systems. Powell (1966)
introduced a demand system of additive preferences. Barten
(1964, 68, 69) and Theil (1967, 1971, 1975, 1976, 1980)
proposed the Rotterdam demand system, which is formulated
from first order differential forms. The Rotterdam model
under appropriate restrictions can be rationalized as
following from a utility maximization problem; for example,
the Rotterdam demand system can be derived from the Klein

4 This system of demand

and Rubin utility function.
functions implies that all income elasticities are one, all
own price elasticities are negative one, and all cross price
elasticities are zero.

In particular, Deatan and Muellbauer's AIDS model in
the first procedure and Rotterdam model in the alternative
procedure are interesting ones. Since our data are cross-
sectional, we will further explore adaption of Rotterdam and
AIDS models as the linear Slutsky model (LS), the linear
preference independence model (LPI), and the DM model: and
the quadratic versions as the quadratic Slutsky model (QPI),
quadratic independence model and quadratic AIDS model (QDM),
which are originated by Theil, Chung and Seals (1989). With

a modified utility maximization framework with goods and

 

4 Yoshihara, K.,"Demand functions: an application to the
Japanese expenditure pattern", Econometrica, vol.37, April
1969, pp257-74.

12
money assets as arguments, we will then extend all of the
six specifications to explicitly obtain a general demand
systems for goods and money: and also functionally
incorporating socio-economic factors as demographic
variables or income structural parameters into the demand
equations. Then we will discuss methods of aggregating our
detailed data, among which the Greary (1958)-Khamis (1967,
70, 72) procedure is required as part of the modeling.

In chapter V we will employ the specified demand
modeling to estimate rural households data in China. Based
upon the results of the estimations, we will test the
availability of demand specifications of the framework.
Then we will discuss the effects of economic variables such
as price, interest rate and income vectors on household
simultaneous demand equations for goods and money, and the
interactions among market goods and non-market goods,
consumer goods and agri-input goods, as well as goods and
money, for which we may tell whether the good and money are
correlated. Also, we will demonstrate the impacts of socio-
economic factors on demands for goods and money, which may
reveal some profound aspects for rural households in the
process of development.

With our empirical studies of general demand framework
for China's rural households, we can then investigate
government's interventions in the rural development. We can

discuss the central bank's equalibrium money supply decision

13

and interest rate policy; the effects of the government's
pricing policies toward agri—output and agri-input; and its
demographic policies. Also we can observe the impact of
structural change and rural growth upon demand pattern. For
example, the changes in household income structure may help
us to capture the effects of growth of small scale
industries in rural areas as well as the level of rural
households commercialization. Furthermore, this study can
indicate some indirect demand linkages to other sectors due
to change in rural households' expenditure pattern.

In the last Chapter, we will briefly review the
procedure of modeling, summarize our empirical results, and

then present some economic explanations for the results.

CHAPTER II

DATA DESCRIPTION

2.1 Introduction

The basic data employed in the empirical study are a
set of Chinese rural household data in the period of 1985-
1987, which we will describe in this chapter.

The rural household data include basic information such
as demographic formation, land, house condition, production
equipment and others; household income and the sources;
their expenditures and quantities of specific goods, and
financial assets held. In addition, we will employ some
macro-data such as interest rates, inflation rates, and
others. The household data were surveyed by the National
Statistical Bureau of China, and the macro-data were
published by the People's Bank of China ( the Central Bank )
and the National Statistical Bureau of China. We will
briefly introduce the regions where our rural household data
were collected: describe in detail the raw data: and finally
define the commodity categories and socio-economic variables

which are used in our model.

14

15

2 ta Back r und

Our household data are from rural households in Sichuan
province of the PeOple's Republic of China for the years of
1985-1987. Sichuan province is located at 26 01'-34
21'North Latitude and 97 60'-110 12'East Longitude on the
upper reaches of the Yangtze River in the southwest China.
It covers an area of 567,000 square kilometers. With its
population of more than one hundred million people, Sichuan
is the most populous province among the thirty in the
country. There are fifteen nationalities inhabited in
Sichuan such as Han, Yi, Tibetan, and others. The capital
is Chengdu.

The topography of Sichuan is highly diverse. In the
eastern part of the province is the Sichuan Basin, the most
fertile one of the four big basins in China. It is hemmed
in by high mountains with rolling hilly land sprawling
across the Chengdu Plain. The rainfall in this region is
plentiful, and the frostfree period is long. The Yangtze
River and its tributaries crisscross the basin, providing
favorable conditions for irrigation, navigation and
hydropower generation. The western part of the province
abuts on the eastern edge of the Qinghai-Tibet Plateau and
covers with 7.37 million hectare with virgin forests and
10.7 million hectare with grassland, making Sichuan to be

one of the country's three forest centers and one of the

16
China's five major livestock breeding bases. The total area
of the mountainous regions comprises 49.8 percent of the
province, the plateaus 29.02 percent, the hilly land and
plain 21.18 percent. A

There is much variation in the climate of the province.
The east Sichuan Basin has a sub-tropical climate with wet
southeast monsoons and characterized by warm winters, early
springs, hot and prolonged summers. Its average frost-free
period lasting more than three hundred days a year. The
plateau in the northwest has an intensely cold continental
climate with wintery cold all year around. The highland in
the southwest also has a sub-tropical climate with southwest
monsoon alternates of rainy and dry seasons, but no severe
summer and winter. The average annual precipitation of the
province is about 1,000 mm.

Traditionally, Sichuan province has been one of China's
most important agricultural regions. Rice, wheat, corn and
sweet potato are its main staple-food products. Among the
thirty provinces in China, Sichuan ranks first in the
productions of grain, silk, tung oil, oranges, tangerines,
and pigs: it also leads the country in the productions of
rapeseeds, tea, ramie, sugarcane, tobacco, honey and
medicinal herbs.

As one of two pioneering provinces, Sichuan led the
rural economic reform started in 1978: the People's Commune

system was disbanded and agricultural collective productions

17
were abandoned. All of the farming land, and the majority of
grassland and collective-owned woods and water areas were
contracted to rural households for a period of more than
fifteen years; big animals and production equipments were
sold to households; and properties of non-agricultural
production activities were partly distributed to households.
Because these practices highly stimulated peasants'
production incentive, agricultural products have greatly
increased and the rural economy has thrived since then.
Statistical data listed in Table 3-5 indicate the economic

role of Sichuan province in China.

Table 3: Population, Area, Cities and Counties (1987) of
China and Sichuan Province, Respectively.

 

 

Items China Sichuan Percent
Population (1,000) 1,045,320 101,880 9.75
(end of 1985)

Area (1,000 km ) 9,600 570 5.94
Cities 378 19 5.03
Counties 1,986 174 8.76

 

Sources: (1) "A statistical Survey of China, 1988", the
National Bureau of Statistics, Statistical
Press, Beijing, 1988.

(2) "the Year Book of China, 1985", the National
Bureau of Statistics, Beijing, 1985.

18

Table 4: Quantities and Values of Agricultural Products
(1987) of China and Sichuan Province, Respectively.

 

 

Items China Sichuan Percent
Grain (10,000 ton) 40,473.30 3,921.30 9.69
Cotton 424.50 10.20 0.24
Oil-bearing crops 1,527.80 161.50 10.60
Sugar-bearing crops 5,550.40 241.50 4.40
Red meats(pork, beef,

and mutton) 1,986.00 336.00 16.90
Dairy Products 330.10 24.30 7.36
Value of Agricultural

products(billion RMB) 467.57 38.894 8.32

 

Sources: "A Statistical Survey of China, 1988", the National
Bureau of Statistics,

1988.

Statistical Press, Beijing,

19

Table 5: Quantities and Value of Industrial Products (1987)
of China and Sichuan Province, Respectively.

 

 

Items China Sichuan Percent
Steel(10,000ton) 5,601.70 428.30 7.65
Iron 5,432.40 373.80 6.88
Coal 92,808.30 6,132.50 6.60
Petroleum 13,404.10 11.70 0.09
Electricity

(billion kW/hr) 497.27 26.29 5.29
Concrete 18,128.30 1,243.90 6.86
Chemical fertilizers 1,703.30 154.40 9.06
Chemical pesticides 26.00 0.80 3.08
Cotton clothes

(billion meter) 16.71 0.81 4.85
Chemical fabrics 115.70 2.40 2.07
Papers 1,008.20 70.20 6.96
Sugar 510.80 16.10 3.15

Industrial Products'
Value (billion RMB) 13,806.40 725.00 5.25

 

Sources: "A Statistical Survey of China, 1988" National
Bureau of Statistics, Statistical Press, Beijing,
1988.

20

Our rural household data came from three agriculture-
dominated counties: Beichuan, Mianzhu and Wulon in the
Sichuan Province during the period of 1985-87. They are
geographically different areas, representing different
levels of economic development. The survey was conducted by
the Statistical Bureau of China. In each county eighty
sampled rural households were surveyed quarterly by the
Statistics Bueau. These sampled households have book-kept
their all kinds of income sources and expenditure items. In
total there are two hundred and forty rural households'

information available over three consecutive years.

1) Beichuan County:

This county covers 2,952 square kilometers. It is
divided into thirty-four townships with the population of
144,000.

Located on northwest edge of Sichuan Basin, Beichuan county
is dominated by rugged area. There are four major rivers
providing the region's irrigation and hydropower resources.
The climate is quite various: generally it is warmer along
the riverside than in the mountain region. Annual
precipitation is 1377.2mm.

Beichuan is rich in forest resources and is the habitat
of many rare animals including giant pandas. The main
agricultural products include corn, wheat, potatoes, rice,

beans and rapeseeds: and animal husbandry is also important

21
in this area.

Mineral deposits consist of coal, iron and titanium.
There are some small scale industries like mineral
exploitation, hydro-power generation, concrete, food
processing, tea processing, and timber mill. The high way
system in the county facilitates transportation by
connecting externally Beichuan to major cities and
internally townships to one another. As far as per capita
income is concerned, Beichuan is ranked the intermediate

level in the province.

2) Mianzhu County:

The area is 1,233 square kilometers, and the population
is 462,600. Mianzhu is divided into twenty-five townships.
It lays in the Sichuan Basin. The plain dominates its
southeast part: and the hilly area is in the northwest part.
Two rivers flow through the county and provide reliable
irrigation networks. The climate is mild, and annual
rainfall is 1103mm.

The main agricultural products are rice, wheat, corn,
sweet potatoes, rapeseeds, peanuts, tobacco and sugarcane.
This county also supplies large quantity of pigs.

Many state—owned and province-owned large and medium
size factories are located in the county, among which are
machinery, fertilizer, and mineral exploitations. Small

scale industries are also booming, such as food processing,

22
paper-making, concrete, and printing. Since the Baoji-
Chengdu railway passes through Mianzhu and the highway
system is well developed, a convenient transportation is the
county's big advantage. The per capita income is one of the

highest in the province.

3) Wulon county:

It is located in the southeast side of the province,
and the population is 350,000 with an area of 3,008 square
kilometers. There are fifty-one townships. Wulon county
lays on the fringe of Sichuan Basin, which is dominated by
rugged region. There are some small size plains and hilly
areas scattered within mountains. The Wu River, one of
major contributories of Yangtze River, runs through the
county. Along with about fifty small rivers, it provides
the convenience of navigation, irrigation and electric
generation.

The climate in this area is also quite various: in the
mountain regions, there is a long period of snow covered
winter and a very short summer. While the riverside areas
are characterized by warm winters and prolonged summers.
Annual raindrop is about 900-1,200mm.

The county is rich in natural resources like wood,
coal, iron and aluminum. There are a few big state-owned
and province-owned factories engaging in coal and iron

exploitations, hydro-power generation, and others. The

23
small scale industries in coal exploitation, concrete, and
machinery repairs have taken shape.

The major agricultural products are corn, sweet
potatoes, potatoes, rice, wheat, paulownia oil, tea,
tangerines and oranges. Livestock breeding also constitutes
an important part of rural production activities. This

county's per capita income is placed in the low level in the

province.
2.; Expenditures, Money Assets and Prices

This portion of data contains rural households' annual
expenditures on goods and money assets held, two major
components of households annual income. Expenditures can be

divided into four categories:

I) Staple Food
II) Non-staple Food
III) Clothing & Footwares

IV) Non-fixed Industrial Agri-input

These four categories are based upon the fact that
rural households will retain part of their home-produced
agricultural products and buy marketable consumer goods for
the consumption, while also purchase industrial producer
goods for agricultural production. "Staple food" is the

aggregate of retained home-made goods: "non-staple food" and

24
"clothing & footware" are aggregates of major industrial
consumption goods: and "non-fixed industrial agri-input" is
the aggregate of purchased industrial producer goods. Since
the expenditure and quantity vectors of quite detailed
consumption items are available for each household, we can
then derive the price vectors of corresponding detailed
commodities. With the expenditure, quantity and price
vectors on all detailed commodities, we can aggregate price
vectors for these four categories through the weighted
average method. The detailed commodity items aggregated in

the categories are listed below:

I) Staple Food
1. Rice
2. Wheat
3. Corn
4. Others
II) Non-staple Food
1. Vegetables
2. Bean products
3. Meats
4. Sugar
5. Cookies & Candies
6. Cigarettes
7. Wine & Liquors

8. Tea

25
9. Fruits
III) Clothing & Footwares
1. Cotton clothes
2. Composed clothes
3. Woolen clothes
4. Silk
5. Leather shoes
6. Rubber shoes & Sport shoes
7. Blankets
8. Others
IV) Non-fixed Agricultural Input
1. Chemical fertilizer
2. Pesticides
3. Gas & Goal

4. Others

In category III, only commodity items (1), (2), and (6)
are included, because these items consist of more than 85
percent of the households' consumption on this category.
For the same reason only items (1) and (2) are included into
category IV: they make up more than 95 percent purchases on
"non-fixed industrial agri-input". Table 6 shows mean
percentages of included items in category III and IV for
each county in 1985-1987.

Besides expenditures on both market and non-market

goods, rural households hold "money assets" at the end of

26
the year that mainly consists of cash holdings and net
demand deposits. Because of relatively low income level,
most rural households do not have time deposits. Precisely,
cash holdings plus net demand deposits is the narrowly

defined money or M1. This category is equivalent to rural

Table 6: Percentages of the Included Items in "Clothes"
and "Agri-input".

 

County/Year Percent of included Percent of included

 

items in "clothes" items in "agri-input"
Beichuan 1985 85.49 98.00
Beichuan 1986 81.03 97.50
Beichuan 1987 81.04 95.61
Mianzhu 1985 90.92 97.72
Mianzhu 1986 87.00 97.88
Mianzhu 1987 86.74 98.36
Wulon 1985 85.92 99.10
Wulon 1986 89.01 98.31
Wulon 1987 88.44 94.77

 

Note: Caculated from the "Rural Household Survey" 1985-1987,
unpublished, Sichuan Provincial Bureau of tatistics.

27

households demand for money. It is the stock of money and
serves as the means of wealth transaction from one time
period to the next: it is also the principal financial
assets held by the rural households.1

The "price" or cost of cash holdings consists of both
opportunity cost and inflation cost, or internal and
external costs. It can be expressed as rc = (1 + R/(1+R)) +
I. Where rc stands the "price" of cash holdings, R is the
interest rate paid to the alternative financial assets, and
R/(1+R) states the so-called user's cost suggested by
Barnett;2 u is the annual inflation rates. The first part
of re is the opportunity cost of cash holdings, and second
part is the inflation cost. Thus, rc reflects the actual
cost of holding money balances. By the same token, the
"price" of net demand deposits also consists of_both
opportunity cost and inflation cost. It can be stated as:
rd = (1 + (R-r)/(1+R)) + n, where r is the interest rate
paid to demand deposits, and (R-r)/(1+R) states the user's
cost for demand deposit, and rd is the total costs of having
net demand deposit.

Other than above five goods and money categories, rural

households also invest in consumer durable goods, production

 

1 Niehans, J. "The theory of money", the Johns Hopkins

University Press, 1980, pp16-17.

2 Barnett, W. "Consumer demand and labor supply", North-
Holland Publishing Co. 1981, pp196-197.

28
equipment and construction of new houses. The detailed
items of those investments which are available in our

original data are listed as follows:

1) Durable goods

1. Bicycles

2. Sewing machines

3. Watches & Clock sets

4. Washing machines

5. Furniture

6. Television sets

7. Radios & Cassette recorders
2) Capital Production Equipments

1. Tractors

2. Water pumps

3. Draft & Big animals

4. Wood & Steel

5. Carts

6. Others

3) New Houses

All the above investment items are characterized by the
durability and not determined by current income level alone.
Hence we will not consider them as current consumptions.
Instead, we will regard the investment in durables and

houses as exogenous factor that may influence rural

29

Table 7.1: Number of Households with New—built Houses, and
Equipments Purchased In the period of 1985-1987.

Beichuan County:

 

 

Items 1985 1986 1987 Total Percent
Bicycles 2 2 3 7 2.9
Sewing machines 3 1 1 5 2.1
Watches/clocks 11 5 7 23 9.6
Washing machines 0 2 1 3 1.3
Furniture 2 1 0 3 1.3
Televisions 2 2 12 14 6.7
Radio/cassettes 2 4 5 11 4.6
Tractors 0 0 0 0 0.0
Carts 0 0 0 0 0.0
Water pumps 0 0 0 0 0.0
Draft animals 0 1 4 5 2.1
Steel/wood 3 3 3 3 3.8
New houses 7 3 3 13 5.4

 

Note: Caculated from the "Rural Household Survey" 1985-1987,
unpublished, Sichuan Provincial Bureau of Statistics.

30

Table 7.2: Number of Households
Equipments Purchased In the period of 1985-1987.

Mianzhu County:

with New-built Houses, and

 

 

Items 1985 1986 1987 Total Percent
Bicycles 13 12 6 31 12.9
Sewing machines 0 0 1 1 0.4
Watches/clocks 10 12 7 29 12.1
Washing machines 1 1 0 2 0.8
Furniture 5 5 7 17 7.1
Televisions 6 3 6 15 6.3
Radios/cassettes 0 2 2 4 1.7
Tractors 2 0 0 2 0.8
Carts 0 1 1 2 0.8
Water pumps 0 0 1 1 0.4
Draft animals 2 8 5 13 6.3
Steel/wood 11 14 5 30 12.5
New houses 15 14 8 37 15.4

 

Note: Caculated from the "Rural Household Survey" 1985-1987,
unpublished, Sichuan Provincial Bureau of Statistics.

31

Table 7.3: Number of Households with New-built Houses, and
Equipments Purchased In the period of 1985-1987.

 

 

Wulon:

Items 1985 1986 1987 Total percent
Bicycles 0 0 0 0 0.0
Sewing machines 1 2 3 6 2.5
Watches/clocks 14 13 9 36 15.0
Washing machines 0 0 0 0 0.0
Furniture 0 0 5 5 2.1
Televisions 0 1 2 3 1.3
Radio/cassettes 2 1 6 9 3.8
Tractors 0 0 0 0 0.0
Carts 0 0 0 0 0.0
Water pumps 0 0 0 0 0.0
Draft animals 8 5 8 21 8.8
Steel/wood 8 5 10 23 9.6
New houses 2 5 3 10 4.2

 

Note: Caculated from the "Rural household Survey" 1985-1987,
unpublished, Sichuan Provincial Bureau of Statistics.

32
households' current expenditure pattern.

Tables 7.1-7.3 indicate the number of households with
new-built houses, purchased durable and capital equipments,
and the percentage in the 240 sample households in each
county during the period of 1985-1987.

Since the investment on house construction and durable
goods does not occur in every households nor in every year,
it could be represented by a dummy variable and included in
our estimation model. If household investment on new house
construction or durables of either consumer or producer
goods occur, the dummy variable is 1, otherwise it is 0. We
will label this varible as "investment indicator". Through
this practice we could observe how the fixed investment in
houses and durables may affect the current expenditure

pattern of rural households.

2&1 §QQinE§QEQEiQ YQILQDLQS

There were many profound changes in China's rural
economy over the last ten years. The biggest changes were
to disband collective production system and to withdraw
strict state planning on agricultural production activities.
Therefore, rural households again became both productive and
consumptive units. Since then they have experienced a change
from the state of self-sufficiency to commercialized
economy, and the total sales and purchases on market have

significantly increased.

33

Of all agricultural and non-agricultural products the
percentage of agricultural products sold commercially
increased from 42.5 percent in 1978 to 58.0 percent in 1986;
and that of non-agricultural products sold commercially rose
from 53.7 percent to 68.1 percent. Both percentages
increased by 15.5 percent and 14.4 percent within ten years,
respectively. Table 8 below reveals these changes.

Such a change has great impacts upon the expenditure
pattern of rural households. Along with the increase in the
sales of rural products in the markets, the consumer goods
purchased on market or, in another words, the commercial
consumption of goods has also risen. Of the whole country's
purchased commodities, the peasants' purchases of goods
increased from 47.9 percent in 1978 to 65.0 percent in 1985:
that is, the percentage had a rise by 17.1 percent within
seven years. Table 9 states this fact.

The level of market involvement or commercialization of
rural households can be described in many ways. Along with
increases in rural households' sales and purchases, their
incomestructure has also changed. In 1985 the ratio of
rural households' net money income to total net income
reached 63.1 percent, rising by 12 percent since 1980;3 the

ratio of cash holdings plus deposits to total net income per

 

3 Lu, Mai and Dai, Xiaojing, "An analysis of the rural
households' economic behavior", the Journal of Economic
Research, July, 1987, Beijing, pp12.

34

Table 8: 1978-86 Commercial Ratios of Agricultural Products
and Non-agricultural Products in China.

 

 

Years Percent of Commercial Percent of Commercial
Agri-output in Total Nonagri-output in Total
Agri-output Nonagri-output

1978 45.2 53.7

1980 49.6 56.9

1981 49.9 57.1

1982 49.8 57.0

1983 52.0 59.2

1984 52.7 61.0

1985 53.9 63.9

1986 58.0 68.1

 

Sources: "The Statistical Year Book Of Chinese Rural
Econom ", 1985 and 1987; The National Bureau of
Statistics, The Statistical Press, Beijing.

35

Table 9: Percentage of Peasants' Commercial Consumption
of the All Consumption in China during 1978-85.

 

 

 

Year Percent of Peasants' Commercial
Consumption in the Total Amount

1978 47.9

1979 50.5

1980 55.8

1981 55.9

1982 56.4

1983 57.3

1984 60.3

1985 65.0

Sources: "the Collection of National Income Statistics:

1949-1985", the National Bureau of Statistics,
Statistical Press, Beijing, 1986.

36

Table 10: Ratio of Cash and Deposits to Net Income
Per Household in China during 1978-1986.

 

 

Years Percent
1978 13.7
1980 13.9
1981 16.0
1982 18.4
1983 19.4
1984 26.0
1985 28.3
1986 35.2

 

Sources: "the Statistical Year Book of Chinese Rural
Economy", 1985 and 1987, Statistical Press,
Beijing.

37

household rose from 13.7 percent in 1978 to 35.2 percent in
1986, increasing by 21.5 percent; and the ratio of non-
agricultural income to total income rose from 31.4 percent
to 46.9 percent, increasing by 15.5 percent. Table 10 and
Table 11 show those ratios.

The ratios of households' commercialization and income
diversification reflect the level of rural development which
may affect the households' expenditure pattern. Thus we

will choose two indices to describe change in rural

Table 11: 1978-1986 Ratio of Non-agricultural
Income to Total Income in China.

 

 

Year Percent
1978 31.4
1980 31.1
1983 33.3
1984 36.8
1986 46.9

 

Sources: "the Statistical Year Book of Chinese Rural
Economy", 1985 and 1987, Statistical Press,
Beijing.

38
households' income structure and the development level of

rural households.

(1) Monetized Index:

This is the ratio of a rural household's money income
to its total income, also called commercialized index, which
is based upon these facts: it is available in our data sets,
and it reveals the level of household's market involvement
or eonomic commercialization. Total income refers to the
value of products and services provided by a rural household
annually, while money income are the inflow of cash balances
through selling agricultural and non-agricultural products
or services in markets, the money borrowed, and interest
payment earned by lending and deposits.

Generally, this ratio lies between zero and one. The
higher the index, the higher the commercialized degree of a
rural household. In some cases, however, a household's
annual money income may surpass its total income so that the
index is bigger that one. This abnormal ratio may be due to
a mass money borrowing for new house construction.

Fortunately, this situation just occurs once in a while.

(2) Diversified Index:
This is the ratio of non-agricultural income to total
income indicating how a rural household diversifies its

sources of income, or in another words, its production

activities.

39

The sources of households' total income can be

divided into two parts: agricultural income and non-

agricultural income. The sources of both parts are listed

below:

1) Sources of Agricultural Income:

Farming
Animal husbandry
Forestry
Fishery

Collecting & hunting

2) Sources of Non-agricultural Income:

1.

2.

Handcrafts

Rural industries

Construction

Transportation

Exploitation of natural resources
Vending & catering services

Other services

Employment in small scale industries

Since rural households have more or less engaged in

some agricultural activities, this ratio also lies between

zero and one, just like the commercialized index. The

agricultural activities are not the only way to absorb rural

laborers nor the sole source to provide household income;

40
and there is a tendency of the growth of rural household's
non-agricultural activities.

Many less-developed countries' experiences have
revealed this fact.‘ In China, about 45,772,000 rural
laborers have switched from agricultural production
activities to non-agricultural production activities during
the period of 1979-1985: among which 6,000,000 rural
laborers have gone to cities to look for works: and one
fifth rural laborers left off agricultural activities. In
1985 there exist twelve principal kinds of rural non-
agricultural production activities, and non-season workers
in these productions accounts for 19 percent of total rural
employment.5 The switch of agricultural to non-
agricultural production activities can be directly reflected
in the rural household's income structure. Hence the
diversified index may help us to explain structural changes

and also the rural household expenditure pattern.

(3) Demographic Variables

The demographic variables are one of very important

 

‘ Liedholm, C. and Mead, D., "Small scale industries in

developing countries: empirical evidence and policy
implications", MSU International Development Paper No.9, 1987:
pp14-15, 18-20, 41-42.

5 The report of the Institute of Development, "Peasants,
market and the institutional innovation .__ the reform in the
depth facing the rural development.after eight years of fixing
household output quatos", the Journal of Economic Research,
Jan. 1987, Beijing.

41
factors to affect rural household expenditure pattern. The
size and age composition of a household, the combination of
its laborers, and even educational level may have some
impacts on the household's expenditure. For simplicity we
will choose two groups of demographic variables for our
model:

1) family size: it is the number of total family
members, including children, elders and adults who are
permanent residents of a household.

2) laborers: this is the number of total laborers
available in a household which include male people aged
between sixteen to sixty years old, female people between
sixteen to fifty-five years old, and those who are capable

to engage in manual work.

2.5 Conclusion

In this chapter we have introduced the data backgound
and described the data we will use. Besides the category of
money demand, we have also aggregated demands for detailed
commodities into four categories as staple food, non-staple
food, industrial consumer goods and industrial producer
goods. Furthermore, we have defined five socio-economic
variables: commercialized index, diversified index,
investment indicator, family size and labor size. These

variables characterize the features of rural households and

42
the level of economic development, which may have
significant impacts upon the general demand structure. In
the next two chapters we will construct the theoretical
general demand framework of rural households for goods and
money, and then investigate the specifications of demand

systems and discuss the methods of aggregation.

43

Map 1: Map of China

 

 

 

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.. . .. . 2:81.35
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as: jzfdzu;
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44

Map2: Map of Sichuan Province

‘ Beichuan
Mfizu .
A
O
CHENGDU “I

at"

      
   

CHAPTER THREE

THE NEW HOME ECONOMICS APPLIED TO RURAL HOUSEHOLD
WITH INSTITUTIONAL VARIABLES AND MONETARY ASSETS

3.1 Introduction
The traditional demand theory, originated by Slutsky

and completed by Allen and Hicks, specifies consumer's
behavior by introducing the concept of the utility function.
The utility function is the measurement of satisfaction
which a consumer derives as he consumes a particular bundle
of goods and services. Implicitly, goods and services are
consumed through a time dimension so that a flow of
consumption bundles has to be evaluated. A demand system
for goods and services can be obtained from a wel-behaved
utility function, given the expenditure constraint faced by
a specific consumer. In other words, the consumer can

maximize his utility function subject to the budget

constraint:
max U = U ( q ) (3-1)
st. y = p.q

45

46
where U denotes direct utility function; y, p and q denote
vectors of consumer's total expenditure, commodities' prices
and quantities, respectively.

The demand system, thereafter, is expressed as:

q=q(p.y) (3.2)

The consumer's demand expression for commodities is of
function of price and income vectors.

The utility function (3.1) is theoretically assumed to
be strictly increasing in q, twice continuously
differentiable, and strictly quasi-concave. These
assumptions ensure a behavioral consistent choice the
consumer makes. Then the demand function g = q( p, y ) is
characterized as homogeneous of degree zero in price and
income vectors, symmetricity of slutsky matrix, and negative
semidifinity.

Besides the conventional direct optimizing utility
framework, the equivalent demand system can be acquired by
an alternative and analytically convenient approach. That
is, the formulation of a consumer maximizing behavior can be
constructed by the duality theory initiated by Houthakker
(1952), Hotelling (1952), Shepherd (1953), and then Hicks
(1958). The alternative approach can be embodied in the

expression:

47

V ( P , Y ) = max U ( q ) (3-3)
st- pq = y

where V( p , y ) is defined as the indirect utility
function. If substituting demand function (3.2) into the

direct utility function (3.1), we can obtain an equivalent

expression:

U = U ( q ( P , Y ) ) = V ( P y Y ) (3-3)'

The indirect utility function takes price and income
vectors as arguments, and thus the demand system can be
derived simply through differentiating the indirect utility
function V( p, y ) with respect to both price and income

vectors and then applying Roy's identity:

qi( pi, y ) = - [ dV( p. y )/dpi]/[ dV( p. y )/dy]

i = 1, 2, ...n (3.4)

Also, a direct utility function U(q) can be obtained
from the indirect utility function, as to minimize the

indirect utility V(p, y) with respect to prices and income

48
and subject to the budget constraint. Thus, the
relationship between the indirect utility function and the
direct utility function is established via the concept of
duality (Houthakker 1952). The indirect utility function is
then characterized as continuously decreasing in prices,
increasing in income, strictly quasi-convex in P, and
homogeneous of degree zero.

However, the analytical powers of traditional theory
are effectively circumscribed by the presence of some
unidentified exogenous variables, for example, the
consumer's preferences structure. Assigning sources of
preferences over commodities contained into the utility
function, the conventional demand model fails to explore the
underlying structure. If some socio-economic factors such
as demographic variables and parameters of income structure
are considered within the demand system, the traditional
analysis may attribute consumer's preferences to be
functions of these variables. Unfortunately, this naive
approach only partially captures the impacts of
institutional factors on the demand system. If a rural
household as both consumptive and productive unit is
considered, the traditional theory becomes quite intricate
to demonstrate the demand system. It has to associate the
rural household's external production function into the

framework, as the agricutural model constructed by Singh,

49
I., Squire, L. and Strauss J. (1985).1 Furthermore, the
conventional theory tends to make such an abstract
assumption of a money-free society. In any exchange
economy, however, monetary assets always perform a very
important role to facilitate economic activities, and it is
quite necessary to incorporate money assets into the general
demand structure.

In this chapter we will present the concept of the new
home economics originally proposed by Becker, G. (1965) and
Lancaster K. (1966), and then we will discuss its extension
and implication on rural households incorporating socio-
economic factors and money assets. Specifically, in the
section 3.2, we will show how this new approach modifies the
conventional demand theory through the introduction of
internal household technology, then we will apply this
concept to a rural household model and review some practical
methods of incorporating socio-economic variables into the
household demand system. In the section 3.3 we will discuss
the new demand theory with the association of monetary
assets, which completes the rural households' general demand

framework.

 

1 Singh, Inderjit, Squire, Lyn and Strauss, John,
"Agricutural houeshold models", the Johns Hopkins University
Press, Baltimore, 1986, pp71-93.

50

3,2 The New Approach: Rural Households With Institutional
Vaziapies

The traditional theory is attacked by many writers such
as Becker (1965), Lancaster (1966), Simon (1966), Shubik
(1970), Furubotn (1974) and others. The new home economics
approach, based upon the unit of household instead of unit
of individual, is proposed to explore the structure of the
transformation between commodities and elementary
consumption characteristics, and it becomes the well-
received method of modeling the structure of household
preferences and internal household technology. As a
consequence, the implication of the internal household
structure has provided a sophisticated formulation for rural
household model, revealing profound effects of institutional

variables on the household demand system.

3.21 New approach of demand system

The new approach to consumer theory was proposed by
Gary Becker (1965), Kelvin Lancaster (1966) and among
others. This prOposition views consumption as an activity,

just as Lancaster wrote (1966):

”...in which goods, singly or in combination, are
inputs and in which the output in a collection of
characteristics. Utility or preference orderings are
assumed to rank collections of goods indirectly through the

51

characteristics they possess."2

The household is taken to be the decision unit in this
new approach of the "home economics", hence, the household

utility function may be defined in characteristics space:
U = U ( x ) (3-5)

where the vector X denotes consumption characteristics which
constitutes the direct ingredients of household preferences.
The household, however, cannot directly purchase
characteristics: instead it only confronts purchasable
economic goods and services on the market. Via the
household production process of combining market purchasing
goods and services, the household can generate consumption
characteristics. The market purchasing goods and services,
or commodities, are not arguments in the household
preference orderings, but they just act as inputs of
producing consumption characteristics. Therefore, the
implicit household production function is the key
proposition of the new approach, which transforms
characteristics vector (x) into a consumption bundle
involving market purchasable commodities (q).

The internal household technology or production

 

2 Lancaster, Kelvin "A new approach to consumer theory",
Journal of Political Economy, vol.74, April, 1966: pp133.

52

function is expressed as:
H ( x , q ) = 0 (3.6)

where q denotes market purchasable goods and services.
Since the combination of both the constraints of internal
household production technology and total expenditure
imposes limitations for household's consumption
opportunities, Pollak and Wachter (1975) have shown that a
cost function exists, such that c(p , x) is the least cost
of commodities which are capable of producing households'
consumption characteristics, and also equal to total

expenditure:3

C(X.P)=minpq , (3-7)
where p is the price vector of market goods q, pq is equal
to total expenditure. The implicit price or shadow price of
characteristics can be defined as follow:

h(p,x)=dc(p,x)/dx (3-8)

The vector of shadow price h( p , x ) depends on both price

 

3 Pollak, R. and Wachter, M., "The relevance of the
household production function and its implications for the
allocation of time", Journal of Political Economy, vol.83,
197s; pp257-61.

53
vector of market goods and the level of "characteristics".
If the shadow price becomes independent of x, so as to h* =
h ( p , x ) = h ( p ) to be exogenous, we can access to the
properties of the conventional demand theory and have no
restriction of applying its results.

Pollak and Wachter have then defined and proved two
necessary conditions for the employment of traditional
theory's properties: 1) household's technology exhibits a
constant return to scale, that is, c ( p , x ) = x c ( p ):
and 2) there is no joint production among characteristics,
i.e, the bundle of commodities (q) acts exclusively as the

input for producing characteristics space (x):

C(p,x)=2ici(p,x) (3'9)

so that the cost function becomes:

C(P7X)=Eici(P,1)X (3-10)

and shadow price is:
h. = c. ( p , 1 ) = h. ( p ) (3.11)
Thus, the shadow price vector h's only depends on the price

vector of commdities p and the internal technology H(x, q) =

0, and it becomes exogenous.

54

Pollak and Wachter believe that the joint production
among characteristics breaks the link between the existing
neoclassical demand theory and the implicit household
production function, so that it confounds the household
tastes and technology within the shadow prices. However,
Barnett (1981) does not agree with this point. He argues
that as the demand structure is overidentified, the joint
production just increases the number of overidentifying
restrictions. Furthermore, the joint production, in general
cases, tends to assist the identification of demand system
without introducing any non-neoclassical complication.
Thus, Barnett concluded that there exists no problem of
modeling a household structure while the joint production
appears.‘

Being exogenous variables, the shadow prices will
reflect the changes in the commodities' prices and
household's technology, but they are independent of the
household's tastes. Hence, the household decision problem

is:

max U ( x ) (3.12)

st. ( min p q st. H ( x , q ) = 0 )

II
'<

= max U ( x )

st. h ( p ) x = y

 

‘ Barnett, W. "Consumer demand and labor supply", North-
Holland Publishing Co., 1981: pp243.

55
This is the expression of obtaining the optimal bundle of
the characteristics x which generates utility for household.
By the duality theory, equation (3.12) can be rewritten as

follows:

V(h(p)IU) (3.13)

= max U( x ) st. h ( p ) X = Y

where the expression V( h (p) , U ) is the indirect utility
function. Correspondingly, the cost function can be

obtained by inverting indirect utility function:

C ( h ( P ) I U ) (3.14)

= min x h ( p ) st. U ( x ) = U

Thus the solution is:

x=f(h(p).y)=f(p.y) (3-15)

This is the household demand function for characteristics x.
If the above two assumptions hold, the vector x will exhibit
all of the properties of the traditional theory. Thus the
household maximizing decision process for characteristics
can be translated into the optimal process for purchasable

commodity bundle:

56

max u ( q ) (3.16)

= ( max ( x ) st. h ( q ) x = y ) .st. pq = y

Then the solution is the market goods demand function:

q=g(pIY) (3.17)

The new approach of home economics shows that under
both budget and technological constraints, the household
optimizing decision for the bundle of characteristics is
equivalent to the maximization of the inputs of
characteristics, or the bundle of tangible market goods.
That is, an original utility function is translated into a
modified utility function which obeys all properties of the
traditional theory. Thereafter, the optimal space of the
unobservable characteristics is replaced by the maximum
space of observable market goods.

The transformation has also distinguished both
household tastes and technology, while the traditional
demand theory just confounds both of them. Consequently,
the traditional analysis always tends to attribute changes

in household production function to changes in tastes.5

 

5 Pollak, Robert and Wachter, Michael "The relevence of

the household production function and its implications for the
allocation of time", Journal of Political Economy, vol.83,
1975; pp26o.

57

The new approach of a household structural form, if obeying
to restrictions given, will possess conventional theory's
properties, and explicitly tell the difference of household
tastes and technology. The causality of household demand
system can then be imputed by the exogenous variables of
household's total income and market goods price vector, and
be also explainable with respect to household tastes change.

The preferences over the consumptive characteristics is
usually assumed to be constant across households and over
time. This is a not too strict assumption for rational
decision makers, since the preferences are largely
cultivated by the nature of consumptions as well as cultural
background. Therefore, the differences across households
are embodied in household's technology which can be a
function of household's demographic parameters as household
age, number and composition, and other institutional factors
as different income structures.

If we assume that socio-economic variables are indexed
in the parameter cl,‘S the internal household technology will
explicitly contain the parameter d, i.e. H(x, q, d) = 0;

thus the equation (3.16) becomes:

 

6 Lewbel, Arthur "A unified approach to incorporating
demographic or other effects into demand systems", Review of
Economic Studies, vol.52, 1985: PP3.

58

max u ( q : d ) = ( max U ( x ) st. h ( p, d ) x = y

st. pq = y i (3.16)'

and the equation (3.17) becomes:

q = h ( pl Yr d ) (3.17)'

The result satisfies conventional theory's properties. The
parameter d, representing random variations across

households such as demographic variables or income

structures, explicitly exhibits the impact of institutional

factors on the household demand system.

3. ew a ro ch and rural household

When rural households in LDC countries are considered,
we will observe at least two features: first, rural
households will not only consume market goods and services,
but some agricultural output produced by themselves as well.
Second, rural households also purchase non-consumer goods as
inputs for their agricultural production. The new demand
theory characterized by the internal technology can be
extended for rural households. We let A and I denote agri-
output retained and agri-input purchased by a rural
household: then the internal production function for

households' consumptive characteristics is expressed as:

59

H ( x, q, A, I ) = o . (3.18)

We define characteristics' price vector as h = (h1,...hm),
which is the implicit or shadow price vector implied by
rural household internal technology. The shadow price
vector for each characteristics is equal to its unit cost

function:

hi = C1 ( 9. Pa: Pie 1 ) = hi ( p. pa. pi) (3.19)

where pa and pi are market prices for agricultural product
and industrial agri—input. The equations (3.18) and (3.19)
show that agricultural output A is taken as an input of
producing consumptive characteristics. Also, the rural
households' external production function is contained into
the internal technology, so that industrial agri-input I
performs as another kind of input of producing

7

characteristicsa Hence the equation (3.16)' can be

 

7'Pollak, R. and Wachter, M. have showed that labor input
is one of the important ingredients in the household internal
technology to produce consumptive characteristics, so that the
modified utility function is expressed as u(q, T), where q and
T are market goods and labor spent in the household internal
production function to produce characteristics. "The relevence
of the household production function and its implications for
the allocation of time", Journal of Political Economy, vol.83,
1975; pp266-69.

60

extended as follows:

max u ( q, A, I : d ) (3.16)"
= ( max U ( x ) st- h ( p. pa. pi. d ) x = y )

st. pq + paA + piI = y

The demand equations will be:

q = h ( pr pal pi' Y! d ) (3.176)"
A g ha( pr pal pi! Yr d ) (3'17b)"
I = h1( 9. pa. pi. y, d ) (3.17c)"

The demand equations (3.17)" satisfy all traditional
theory's properties. For simplicity, we let q denote all
purchased consumer and non-consumer goods, as well as
retained agri-output. Rural households will make their
optimal decision based upon an original utility function
U(x), which is equivalent to a modified utility function
u(q) under the constraints of both budget and technology.
These two constraints summarize the features of rural
households:

1). The internal technological constraint x = H'(q,d) is of
constant returns to scale and non-joint production and
contains rural household external production function. This
expression states that the households' characteristics is

the function of economic goods q and socio-economic

61
parameter d.
2). The budget constraint y = pq is for maximizing economic
goods q which households acquire to generate characteristics
x. q can be market purchased consumer and non-consumer

goods, or rural households retained agri-products.

W

The new approach of demand theory opens a way
theoretically accessible to encompass the household demand
system with some important socio-economic variables. Then
we will ask how can we specifically incorporate those
factors into the demand system. The most convenient method
is to make estimated parameters of the demand system either
implicit or explicit functions of the socio-economic factors
such as demographic variables and to assume demand
parameters vary freely across these factors.

Specifically, there are three main procedures
incorporating demographic factors: the scaling procedure
employed by Barten (1964); the translating procedure used by
Pollak and Wales (1978, 1980, 1981); and the Gorman
procedure proposed by Gorman (1976). Lewbel (1985)
demonstrates that it is theoretically possible to unify
these procedures, and he also provides a concise formation
to generalize them. We will briefly review these three
general techniques. They smoothly incorporate demographic

variables or other factors into the household demand system,

62
and they are concise specifications of demand functions with

demographic variables.8

1). Equivalent scaling technique:

An equivalent scaling method was proposed by Engel
(1893), which is a non-commodity specific scaling procedure.
Barten (1964) first proposed a demographic scaling method
systematically incorporating exogenous variables into the
demand system. Barten style is commodity specific

9 This procedure first introduces n

equivalent scales.
parameters, ( t1 ... tn ) into the original demand system

Q = g ( p , y ), where i = 1 ... n ; and vectors p, x, and
y denote prices, quantities and expenditures, respectively.
Furthermore, it assumes that only these parameters are
implicit functions of demographic variables, that is, ti =

Ti(D)' where D denotes vectors of demographic factors. Thus

the modified demand system is designated as :

q1(p1' Y)=tg(pl t1 I p2 t2 "° pntn I Y) (3'20)

 

8 The key concept of the Lewbel's model is to define two
modified functions, which permit socio-economic factors
interact with price and income vectors. Lewbel, Arthur "A
unified approach to incorporating demographic or other effects
into demand systems", Review of Economic Studies, vol.52,
1985.

9 Barten, A. P. "Family composition, prices and
expenditure patterns", in Econometric Analysis for National
Economic Planning: 16th symposium of the Colston Society; ed.
by Hart, P. Mills, G. and Whitaker, J. K.; London:
Butterworth, 1964.

63
The modified demand equations satisfy the first order

conditions corresponding to the indirect utility function:

V ( p I Y ) = V ( p1 t1 °°° pn tn I Y ) (3'21)

and the direct utility function is:

max U ( q1 /t1, q2 /t2 ,... qn /tn ) (3.22)

st. pq = y

where t measures the number of equivalent adults on a scale
appropriate to good i as commodity specific scaling
functions differ from one good to another. This procedure
can be either scaling prices or quantities. Specifically, t
can be designated as an exponential form for the ith scaling

function:

d. (3.23)

where dj is the jth demographyic factor and sij denotes its
estimated parameter. The value of t must be positive since
it scales price or quantity vector. When D is defined as a

vector of qualitative factors, the value of t does not need

64

to be positive.10

2). Demographic translating technique:

This procedure was employed by Pollak and Wales.11 It
assumes t1... tn as n translation paprameters which depend
on demographic variables ti = Ti ( d ). These parameters

are introduced into the original demand system [ Q = g ( p,

Y ) ] =

i i K
q(pIY)=ti+e(pIy-zk=1pktk) (3°24)
Then the corresponding indirect utility function is:

K
v < p . y ) = v* < p . y - 2k=1 pktk ) V (3.25)

and the direct utility function is:

 

1° Barnes, Roberta and Gillingham Robert "Demographic
effects. in. demand analysis: estimation of the quadratic
expenditure system using micodata", Review of Economics and
Statistics, 1984; pp 593.

11 Pollak, Robert and Wales, T. J. "Estimation of complete
demand systems for household budget data: the linear and
quadratic expenditure systems", American Economic Review,
vol.68, 1978: pp348-59. "Comparison of the quadratic
expenditure system and translog demand systems with
alternative specifications of demographic effects",
Econometrica, vol.48, April,1980: pp595-612. "Demographic
variables in demand analysis", Econometrica, vol.49, Nov.
1981, pp1533-51.

65

max U ( Q ) (3.26)

_ _ K
st. p Q — y 2k=1 pktk

This demographic translating procedure in practice specifies
an addictive linear form for the translation function of the

ith demand function:
t. = z. r..d. (3.27)

where dj is the jth demographic factor and Tij the unknown

parameter to be estimated.

3). Gorman technique:
Gorman introduces two kinds of parameters di and mi,
(1 = 1... n) into the demand system, where ony d and m depnd

12

on demographic variables. So that the demand function is:

i _ i _ K
q ( p e y ) — ti + m q* ( plm1--- ann' y 2k=1 pktk )
(3.28)

Correspondingly, indirect utility function is:

 

‘2 Gorman, W. M. "On a class of preference fields",

Metroeconomica, vol. 13, 1961, pp53-56. "Tricks with utility
functions" in Essays in Economic Analysis: Proceedings of the
1975 AUTE Conference, Sheffield, ed. by Artis, M. J. and
Nobay, A. R., Cambridge: Cambridge University Press, 1976.

66

K
V ( p . y ) = V ( plm1 .... ann' Y - 2k=1 pktk )
(3.29)
and direct utility function is:
max U ( q1 / m1 , q2 / m2 ... qn / mn ) (3.30)

_ _ K
st. p q — y 2k=1 tkpk

The Gorman's technique is obtained by translating and
then scaling specification, so that it is regarded as the
combination of the above two procedures. Rather, Gorman
presents a more general specification with a linear
household technologies, where not only demographic
translating and scaling are relevent, but also joint
demographically varying effects across commodities are

considered.

3.; New Apppoach With Money Assets

The conventional consumer theory has implicitly assumed
an abstract money-free society, in which consumers are
engaging in their economic activities. But in any exchange
economy consumers have to deal with money assets so that a
general utility theory must include monetary aspects and an

explanation of consumers' demand for money. Neoclassical

67
economists, like Hicks, Samuelson (1947), Morishima (1952),
Patinkin (1965), Sidrauski (1967), Friedman (1969) and
others, have made efforts to incorporate money assets into
the general equilibrium framework so as to enable to deal
with consumer's monetary behavior.

In spite of these endeavors, however, there still
remains some troublesome drawbacks within the extended
neoclassical model. Recently many researchers have
reformulated the utility approach to money demand, such as
Chetty (1969), Bisgnano (1974), Diewert (1974), Clements
(1976), Offenbacher (1979), Barnett (1981), Ewis and Fisher
(1984) and etc. Furthermore, the theoretical growth models
of perfect foresight with money in the utility function have
also been proposed by Brock (1974), Clavo (1979), Fisher
(1979), and Obstfeld (1983), among others. These
developments have added and revealed many profound aspects
of modeling money demand in accordance with the old utility
approach, which is again and again claimed to be a
convenient as well as eligible method to treat consumers'
money demand side.

On the other hand, some economists, such as Clower
(1967), Niehans (1978), Kareken and Wallace (1980),and
others criticized the approach that including money balances
within the utility function as an argument is not an

appropriate way to deal with consumers' demand for money

68

B They argued that the characteristics of money

balances.
is not revealed as a medium of exchange or as a store of
value; instead, money is euphemistically regarded as if it
were a consumer's goods or a producer's goods. What we need
rather is a theory that treats money assets not
metaphorically "as if" it were a common goods, but as
playing a special role in an exchange system. They also
questioned that the consistency of the utility approach with
money assets would be in doubt, and it might be difficult to
identify the properties of the utility function. Instead,
they proposed a solution through entering money assets into
the budget constraint. This approach, by their point of
view, will derive an appropriate demand function for money
demand by avoiding confounding money with common goods.

Some researchers, however, have discovered-that there
is a functional equivalence of including money assets in the
utility function as an argument and combining it into budget
constraint as a liquidity cost. This issue was first

explored by Fischer (1974) for money in the production

function and then currently extended and synthesized by

 

B Friedman, M. "The optimal quantity of money and other
essays", Chicago: Aldine, 1969, pp14. Levhari, D. and
Patinkin D. "The role of money in a simple growth model",
American Economic Review, vol.58, 1968, pp713-53. Niehans,
J. "The theory of money", the Johns hopkins University Press,
Baltimore, 1980, pp1-19.

69
Feenstra (1986).“

In this section we will demonstrate that the new
approach of home economics discussed in the section 3.2 can
amend drawbacks of the neoclassical approach, so as to
satisfy the criticism made by Clower, Niehans and others.
The characteristics of money is not confounded with common
goods, and it is valid to include money assets in an utility
function while properties of the utility function may be
checked through the duality of two approaches of dealing
with money assets. We will consider a general household
model with monetary aspects that investigates the occurrence
of rural households' demand for stock of money and the flow
of commodities under the impacts of some institutional

variables.

3. t lit unction and mone assets

When we discuss a micro-oriented household model with
money assets included, the basic question is, how can we
incorporate money in the households' optimal decisions?
The neoclassical approach is to extend the basic consumer's
maximizing model by including real money assets as an

argument in a utility function: the objection approach, on

 

M Fischer, Stanley "Money and the production function",

Economic Inquiry, vol.12, 1974, pp518-33. Feenstra, Robert
"Functional equivalence between liquidity costs and the
utility of money", Journal of Monetary Economics, vol.17,
1986, pp271-91.

70

the other hand, questions that it lacks integration and
fails to reveal the characteristics of money assets. An
alternative method is proposed to combine money assets in
the budget constraint as a liquidity coSt. Finally, the
Fischer (1974)-Feenstra (1986) model proves that both
approaches, by revealing different sides of the same
consumer's optimizing behavior, is in principle equivalent,
and also the properties of the utility function with money
assets included can be specified. The following
demonstration is based on Feenstra's synthesis.

The budget constraint approach to deal with money

balances can be formulated by the below intertemporal

expression:
T t
max Et=1 6 U ( ct ) (3.31)
-st. ct + ¢ ( ct , mt ) + mt = y t = 1,2,...T

where y = wt + mt ¢(Pt_1/Pt) denotes wealth 1n per1od t;

vector P is the general price level: 6t denotes discount

rate in period t; vecotr c denotes value of net consumption

t
in period t: vector mt is the real money balances in period

t, and ¢ ( ct , m is the liquidity cost in period t.

t )
We consider that a household makes an intertemporal

decision in period t , then the utility function is U(Ct)

with U'>0 and U"<0. Also, we assume that m is the only

71
financial assets. The liquidity cost is contained in the
household budget constraint which represnets the costs a
household has to pay for the value of net consumption ct .
Then we will propose a general set of hypotheses for the

liquidity cost function contained in the budget constraint:

THEOREM 1: for all ct > 0, and mt > 0, the liquidity cost
¢ ( ct , mt ) is twice continuously differentiable and
satisfies the following conditions:

(1) ¢ > 0, ¢ ( 0 , m ) = O:

(2) ¢C > 0, ¢m < 0;

(3) ¢cc > 0, ¢mm > 0, ¢mc < 0:

(4) ¢ is quasi-convex and thus ct + ¢( ct, mt ) is also
quasi-convex with non-negative slope for Engel expansion

path.

After discussing the budget constraint approach, we
will now turn to the utility approach of money assets. We
assume that a household will optimize its gross consumption
goods qt and money assets mt in the period of t through the
utility function U*t:

max 2 6t U* ( qt , mt ) (3.32)

st. qt + mt = y

72
where qt is the value of real gross consumption and equal to
the sum of both value of net consumption ct and liquidity

costs ¢(ct , mt):
qt: Ct + ¢ ( Ct I mt ) (3.33)

Now the utility approach of incorporating money assets
and the budget constraint approach of combining money assets
are in principle equivalent. The difference between them
appears to be the different functional notation. That is ,

we can write:

U < ct ) = U* ( qt . mt ) (3.34)

=U*[Ct+¢(ct ,mtlemt]

where the utility function U(ct) in the liquidity approach
is equivalent to the utility function U*(qt , mt) in the

utility approach, if above expressions hold for all c and

t

mt. This equivalence indicates that the household can solve
U(ct) to obtain the space (ct , mt) which is corresponding
to solve U*(qt, mt) with the demand space (qt, mt).

Moreover, this duality can be expressed by another way: let

us define:

W(q,m)=U [U*(qu)] (3-35)
t t t

73

Then we have the equation ( 3.34 ) as:
ct = W [ ct + ¢ ( ct , mt ) ] , (3.36)

If this expression holds for all ct and mt , then the
liquidity cost function ¢ will be equivalent to the utility
function W, and vice versa. Therefore, given the utility
function W, the utility function U* is simply obtained by

the concave transformation expressed as follows:
0* ( qt . mt ) = U [ w ( qt . mt ) 1 (3.37)

where the first and second derivatives are assumed as U' >
0, and U" <0.

Corresponding to the liquidity approach, we hence
define a set of hypotheses for the utility maximization

approach with money assets incorporated as an arguement.

THEOREM 2: for all qt > 0, mt > 0, the utility function

W(qt, mt) is twice continuously differentiable and satisfies

the following conditions:

(1) W > 0, W ( 0, mt ) = 0, W ( qt , Int )40 : as qt~0 and

fixed mt >0;

(2) Wh > 0, 0 < Wq < 1;

(3) W < 0, Wmm < 0, W > 0:

qq gm
(4) W is quasi-concave with Engel curves exhibiting a non-

74

negative slope.

COROLLARY: given the equation qt = ct + ¢( ct , mt ), if
the liquidity cost function ¢(ct , mt ) satisfies theorem 1,
then there exists an equivalent utility function W(qt , mt )

which satisfies theorem 2, and vice versa.

Given the liquidity cost function ¢( ct , mt ) with a
demand space ( ct , mt ), the utility function W ( qt , mt )
with space ( qt, mt ) can be obtained by inverting the gross
consumption qt = ¢t+ ct to get the net consumption function
ct = W ( qt , mt ), which depends on gross consumption and
money holdings. Essentially, the above duality theory will
attribute the liquidity cost function ¢t as an implicitly
indirect utility function which is equivalent to the direct
since

utility function Wt with the demand space (qt , m

t).
the space of (ct, mt ) can be easily transformed into the
space (qt, mt ). As the above two theorems are satisfied,
the duality theory works and therefore either approach would
provide an identical solution for the household optimizing
decision in an exchange system. Combining the both methods

we obtain an integrative utility theory with money assets

included, for which all properties of the utility function
are still valid.

75

3.32 Implicatipn of the new approach on money assets

The above demonstration based on the Fischer-Feenstra
model shows us that it is eligible to incorporate money
assets as an argument in a utility function, for which the
features of the integration and duality of demand theory
are still preserved. Due to the unobservable structure of
an utility function, the issue is not whether money assets
are in an utility function as an argument, but whether it is
helpful to analyze the actual household's demand system for
commodities and money assets as if they are arguments in the
household's utility function.

As for the utility of money assets there are two
aspects: a flow aspect of money and a stock aspect of money.
The first aspect has to do with the marginal utility of
money spent by households on commodities, reflecting the
market goods money can purchase. The stock aspect refers to
the utility of money balances held by households. It is the
direct motivation of households to demand for money balances
because the stock of money is regarded as the means of
transferring wealth from one time period to the next in any
exchange economy.15 We can employ a simple exhibition below

to explain this idea.

 

u Patinkin, D. "Money, interest and prices", 2nd ed. New
York, Harper & Row, 1965, pp580. Niehans J. "The theory of
money", the Johns Hopkins University Press, Baltimore, 1980,
pp14.

76
Let us suppose a household lives in two periods, with
its endowment q1 > 0 and q2 = 0. Then the household will
maximize a utility function u(ql, qz) subject to q1> 0, q2>
0 and p1q1= y; p and y are prices and income. The optimal
consumption bundle (q1, q2) cannot be achieved unless the

household holds some real money assets m < plq1 by the end

1
of the first period. Where m1= Ml/P2 denotes the ratio of
nominal money and the second period price vector; the second
period price vector is expected upon the first period price
vector p2 = E( pzlpl). With the above assumptions, then

the household's optimal decision over two periods can be

expressed as follows:

max u ( q1 , q2 ) = max v ( q1 , m1 ) (3.38)
st. q1, q2 > 0 st. q1 > 0
Y = P191 Y > P1q1+ m1

This analysis shows that money balances included in the
utility function are relevant to the stock of money, or,
equivalently, a household's money demand function is related
to the stock of money. In order to make things precise, we
assume that, in an exchange system there exists a large
number of households with low and middle levels of income,
so that they practically keep money balances as their needs
of transaction other than investment in interest-bearing

financial assets, which insures the assumption of money

77
assets being only financial assets meaningful.

So far we have considered money balances in the
conventional utility function other than postulating it by
the concept of new home economics approach. However, by the
study of the above sections of this chapter, we have shown
that the unobservable consumption characteristics space (x)
can be translated into the observable commodities space (q),
and we can acquire the demand functions from a modified
function system which exactly obey the properties of the
conventional demand theory.

The new home economics approach is relevant to the
modified functional framework containing a money market.

The new approach implicitly assumes that the household
internal production structure may experience changes in the
modeof transforming economic goods into consumption
characteristics, but the demand for comsuptive
characteristics may remain stable. As money market is
included, the households' demand for money balances
implicitly implies the demand for "monetary characteristics"
which is generated by money balances. The changes in demand
for money balances in various forms may just reflect how
efficiency changes in the household internal monetary
productive technology: while household's tastes for means of
transaction, store of value or other kinds of monetary
characteristics stay unchanged.

The new approach of demand theory distinguishes the

78
difference of "monetary characteristics" generated by money
balances and money balances itself, just like the similiar
statement that consumption characteristics is different from
its inputs as goods and services. Therefore, this new
treatment amends the neoclassical theory's drawbacks of
confounding money with common goods in the utility function,
failing to express the special characteristics of money
balances. In the new model, money balances, like other
economic goods, act as an input of producing household
consumption characteristics; as a consequence, it is valid
to list money balances as an argument in the modified
utility function.

When we add the money market into the analysis, the new
approach postulated by Becker and Lancaster becomes unitary
in an exchange economy. The consumption for monetary
characteristics can then be translated into the demand for
money balances. Therefore, we can transform the consumption
space of characteristics (x) in term of market demand space
(q , m) from a well modified function system with all
required properties. Hence let us turn back to equation

(3.16)':

max u ( q I d ) = max [ U ( x )

st. h ( p, d ) x = y ] St- Pq = Y

The parameter d stands for institutional index, which

79
will alter the household internal production technology as
H = H(x, q, d); via this internal technology, household can
transform goods q into consumption characteristics x. The
above expression should be adjusted or extended as a general
structure with money market is taken into consideration.
Specifically, the modified utility function U(q:d) and its
constraint pq = y need to be extended.

Since money holdings perform the means of transferring
wealth from one time period to the next, a household will
make the optimal decision intertemporally. In the current
period t, the household's optimal bundle of demand for goods
and money assets (qt , mt) can be obtained through the

maximization of a modified utility function:

T I
max Et=16tU ( qt , mt ,

st. pt qt + rt mt = yt + rt( 1 + T ) m

at) _ (3.39)

t-l

where m denotes vector of money holdings, 6 denotes discount
rate 0 < 6 < 1, and r =[1 + (R - r)/(1 + R)] + w. R and 7
denote interest rate of money assets and rate of a long
period deposit, respectively; (R-r)/(1+R) is the user's cost
derived by Barnett,16 which states the discounted interest

foregone by holding money assets. 7 is the annual inflation

 

m Barnett, W. "Consumer demand and labor supply", North-
Holland Publishing Co., New York, 1981; pp196.

80

rate. Thus, r expresses the total costs of having money
assets: the first part consists of the opportunity cost, and
the second part is the inflation cost of money holdings.

Further, we assume that the utility function is varying
over time and the household has to adjust its planning over
time so that the household behavior is only bounded by
decisions concerning the current demand (qt , mt), subject
to the current budget constraint. If household's current
demand functions are determined, then the following period
demand function system will be adjusted according to the
current demand functions and future budget, and so on. So
that we may regard household's utility function as separable

in T blocks:

T t ,
Et=1 6 U ( qt , mt I dt) . (3.40)

= U1( q , m l d ) + U2( q , m l d ) + ... +
1 1 1 2 2

UT(qT.mT:dT)

The first block contains current demand space (qt, mt) and
other blocks contain future demand spaces. Therefore, we
can take the household's current optimal decision as
independent of future's desisions, or it depends only on the
current condition and last period's left-over money

holdings. The household decision is then simplified as:

81

max u ( qt , m d (3.41)

t i t )
st. pt qt + rt mt = yt + rt( 1 + ft ) mt_1

In the current period, 6 = 1. The utility function is
assumed twice differentiable, monotonically increasing and
also strictly quasiconcave. According to the duality
theory, we have a corresponding indirect utility function
structure which can derive the equivalent demand system.
Some writers, as Dornbusch and Mussa (1975), for the purpose
of explaining the gap between real money holdings and
desired money holdings, assume a utility function U(qt, mt)
being homogenous of degree one;17 and in order to apply
the aggregate theory, Barnett (1981) assumes a utility
function U(qt, (mt- emt_1)) to be homogenous of degree
one.18 We do not adopt this assumption since it is too
restrictive which requires household's Engel curve being
identical linear line, though it exhibits some convenient
features.

The above extension of a modified functional system has

already implicitly assumed money assets incorporated in the

internal household production technology H = H( x, q, m, d)

 

17 Dornbusch, R. and Mussa, M. "Consumption, real balances
and hoarding function", International Economic Review, vol.16,
1975; pp415-20.

“ Barnett, W. "Consumer demand and labor supply", North-
Holland Publishing Co., New York, 1981; pp193-204.

82
which plays an important role of generating household's
consumption on monetary characteristics; so that the
equation (3.16)' could be rewritten as the current period

household's maximization problem:

max u( qt, mt,} dt) = { max U( xt) st. h( pt, rt, dt) xt

= yt) st. ptqt+ rtmt = yt - rt( 1 + rt) mt_1

If we consider m as the difference of period t and t-l,
we can eliminate the subscript t and result in a cross-
sectional model. Therefore, we obtain an unitary household
modeling with money market included, for which given desired
properties of traditional demand theory, we can employ the
modified utility function to acquire rural household demand
functions for both goods and money assets under the
influence of some socio-economic factors, such as and
demographic variables or income structures; the results will
be equivalent to household demand for consumption

characteristics produced by goods and money assets.

W
In this chapter, we have already demonstrated that it
is eligible to extend the new home economics to rural

households under the influence of some socio-economic

83

variables. We have also shown that it is valid to regard
money assets as an argument in the modified utility function
system which observes all required properties of the
traditional theory. A

The extension of new home economics introduces a new
regime: as arguments in the rural households' modified
utility function, the market purchased consumer goods,
producer goods and retained agri-output aa well as money
assets perform the role of inputs for producing household
consumptive characteristics; the socio-economic variables,
such as demographic variables or income structures, are
systematically combined into the demand system. Moreover,
the extension of new approach opens a way to investigate the
relationship of current demand of goods and demand of money
assets. Therefore, we have constructed a general demand
framework for economic goods and money assets, for which we
can investigate the rural households' simultaneous demand
decision upon goods and money. In the next chapter, based
upon this general demand structure, we will specify some

demand framework to engage in our empirical studies.

CHAPTER FOUR

SPECIFICATIONS OF DEMAND SYSTEMS

Med—um

In the last chapter we presented extensions of the new
home economics from which we constructed a general demand
structure. The framework of this new approach satisfies
features of rural household modeling with money assets and
institutional factors included, and it then amends drawbacks
of the conventional consumer theory. In this chapter, based
upon this theoretical structure, we will investigate some
specifications for demand system which are available for us
to conduct estimations with our cross-sectional and panel
rural household data.

Corresponding to a utility maximization problem, there
are two major approaches to specify functional forms of
demand system in contemporary economic literature. One
approach is to specify a direct or an indirect utility
function, and sometimes cost or expenditure function from

which demand system specifications can be developed. Many

84

85

authors attributed to this approach, such as Klein and Rubin
(1947-1948), Stone (1954), Frisch (1959), Houthakker (1960),
Parks (1969), Yoshihara (1969), Diewert (1971), Christensen,
Jogenson and Lau (1975), Berndt, Darrough and Diewert (1977)
or Deaton and Muellbauer (1980) and others. Alternatively,
demand system specifications can be expressed directly with
certain restrictions imposed. This is represented by Theil-
Barten procedure, Barten (1964, 1968, 1969, 1977), Theil
(1967, 1971, 1975, 1976) and Powell specification (1966).

We will follow these two approaches to obtain our
demand system framework. In the section 3.1, we will
discuss Rotterdam model and its extension; in the section
3.2, we will investigate Deaton and Muellbauer model and its
extension; and in the section 3.3, we will bring some
special aggregation methods of dealing with data as part of

the models.

4.; The Diggerential Modeling

The framework of demand system can be constructed from
differential approaches. One of examples is the Rotterdam
model.1 Corresponding to an implicit utility function
maximization which is assumed to be symmetric negative

definite, this approach specifies demand equations as the

 

1 Theil, H. "Theory and measurement of consumer demand",
Amsterdam: North-Holland Publishing Co., 1975-76, pp2. Theil, H.
"the system-wide approach to microeconomics", The University of
Chicago Press, 1980, pp12-15.

86
function of prices and real income in logarithmic

differential forms. The specification can be written as:

d (logqi) = E eijd (logpj) + nid (log Q) (4.1)

1.»: 1’2, ...n.

where eij is the cross price elasticity of the ith commodity
with respect to the jth price vector and n1 is the income
elasticity of the commodity i; vectors qi, pi and Qi are

the ith quantity demanded, the ith price and real income,
respectively. The individual commodity demand functions as
(4.1) are then multiplied by their corresponding expenditure

proportions or budget share wi = piqi/M:

_ n
Wid(logqi) — oid(logQ) + 2j=1 nijd(logpi) (4.2)

where coefficient oi= pi(dqi/dM), the marginal budget share
of the ith commodity; and the slutsky price coefficient fij

=(pipj/M)(qi/pj) is the cross price elasticity ei. weighted

J
by the ith budget share; with the assumption of utility

function being symmetric negative definite, the n x n matrix
[ Iij ] is then negative semidefinite with rank n-l; which

satisfies homogeneity and symmetry. If time series data are

employed to estimate the model, we can obtain the Rotterdam

87
model in relative prices through replacing infinite
logarithmic changes by finite log-changes from period t-l to
t, and also the budget share wi (where i = 1 ,..., n)
by the arithmetic average of wi in period t-l and t.2
If cross-sectional data are used, Theil, Chung and Seale
(1989) provided another solution:3 since the differential
of the budget constraint can be written as dMi= E qidpi+
E pidp , which is a decomposition of dM in terms of a price
component and a volume component; i = 1...n. Then dividing

both sides by M:
d(logM) = d(logP) + d(logQ) (4.3)

where d(logP) = Ewid(logpi) and d(logQ) = Ewid(logqi).
Also, the budget share wi= piqi/M in logarithmic form is
logwi= logpi + logqi- logM. if taking total differential
of this equation:

dwi= wid(logpi) + wid(1ogqi) - wid(logM) (4.4)

Then substitute (4.2) and (4.3) into (4.4), we can obtain

equation (4.5):

 

2 Theil, H. "Theory and measurement of consumer
demand",Amsterdam: North-Holland Publishing Co., 1975-76, pp3.

3 Theil, H., Chung, C. F. and Seale, J. K. "Advances in
econometrics, international evidence on consumption patterns",
Greenwich, Conn. JAI Press, 1989.

88

dGi= (”1' $1)d(1090) + wi[d(109pi) - d(logP)] +

2 2 wijd(logpj) (4.5)

Partially differentiating this equation with respect to the
log real income y a d(logQ), we can express expected budget
share 51 as:

d wi/ dy = oi - wi (4.6)

to reverse (4.6), there is:

wi = oi + f fi(y)dy z ai + Biy (4.7)
the expression $1 reflects the income effect on demand, the
difference of real budget share wi and 61 will be accounted
by the price effects, which are equal to the last two terms

in equation(4.5); hence there is:

_ - - _ n
wi - wi+ wi[ d(logpi) d(logP) ] + Ej=1nijd(logpj)

n
oi + Biy + ( oi + Biy )[ d(logpi) - 2j=l ( aj

n
+ Bjy ) + d(logpj) ] + Ej=lwijd(logpj) (4.8)

To define real income as an independent of variants of

89

the observed prices for each observation, it is necessary to
assume there is a set of central prices Bi, which are
constant across observations. The real income term can then
be obtained by the central prices, on which income effects
are based; while the price effects are expressed as the
difference of observed prices pic for each observation c

and central prices 51 , which are defined as 109(pic/ 51).

Therefore, the Linear Slutsky (LS) model is expressed:

_ - _ n
wic‘ “i + Biyc + ( “i + Biyc )[1°9(Pic/ Pi) 2j=1( “j

+ Bjy ) 109(pj C/ pj )] + 2 1°9(ch/ pj ) (4.9)

1:31 11

where i=1,...,n for goods, and c=1,...,N for observations;
a, B, and w are estimated parameters. The system satisfies
adding-up restr1ctions E ai= 1, E Bi= E Vij= 0; [ ”ij ] are
Slutsky coefficients. Due to the strong assumption of a
negative definite utility function, the Slutsky coefficients
meet negative semi-definity, as well as homogeneity E rij= 0
and symmetry 'ij= 'ji'
be estimated in this model.

There are 2n+(n'-n)/2 parameters to

Theil, Chung and Seale derived another model under the
assumption of preference independence, where "i = ¢0. l(1-0 1)

if i=j, and xij=-¢0.0 if i=/=j (Theil 1975); so that the

1 j
cross-price effects are eliminated and Slutsky coefficients

90

are reduced to be a single parameter ¢. Furthermore, by the
equation (4.6), oi= 81+ wi = ai + Bi(y + 1); let y* = (y +
1), the linear preference independence model (LPI) can be

expressed as:

_ - _ n
“1c ‘ “i + Biyc + ‘ “i I Biyc)[ 1°9‘Pic/ Pi) Zj=1( “j

+ Bjyc) log<pjc/ Bj) 1 + ¢ ( ai + Biyg).

[ loq(pjc/ Ej) - zj21( aj + Bjy; )log(pjc/ fij) 1
(4.10)

This model also satisfies adding-up restrictions, where
Edi = 1 and 281 = 0; since the utility function is assumed
to be negative definite, income flexibility ¢ is negative.
The LPI model emphasizes on the income effects on demand
system with assumption of no any direct price effects.

If in the equation (4.5) the term ffi(y)dy is specified
by a quadratic form of y, then 61 = ai + Biyc + 6iya, so
that in the LS and LPI models the term (ai+ Biyc) can be
replaced by ( ai+ Biyc+ 6iyé) and (a1 + Biyg ) by (01 + 81y;
+ 6iy3*'), where y$*=( yc+ 2yc). The new quadratic models

are referred as the Quadratic Slutsky (QS) model and the

Quadratic preference Independence (QPI) model.

Now we will extend the LS and LPI models to include

monetary assets. In the last chapter we have demonstrated

91
that it is legitimate to contain monetary assets in a
modified utility function, which is equivalent to the
original utility function of maximizing consumptive
characteristics space (x), and from which a general
household demand system for goods and monetary assets bundle
(q, m) can be derived. We recall that our rural household
would maximize its modified utility function subject to the

budget constraint:

I
max u ( qt, mt . dt )

= [ max U ( xt ) st. h ( pt, rt, dt) xt = yt]

st. yt + rt ( 1 + Tt ) mt_1= 2 pitqit + rt mt

The subscript t in the equation can be eliminated by
assuming m to be the difference of period t and t-l, so as
to result in a cross-sectional modeling. At this stage the
institutional factors d will not yet be specificied. With
the above underlining utility structure, the general demand
system for both goods and money can be obtained. Therefore,
the differential approach specified as the LS demand model
can be extended as households' general demand for both goods

and money:‘

 

‘ Clements, K. and Nguyen, P. "Money demand, consumer demand
and relative prices in Australia", The Economic Record, Dec. 1980,
pp339-40.

92

- n
wim — am + Bmyc + ( am + Bmyc)[ log(rmc/ rm) - 2j=1 (

aj + Bo jcy )log(p jc/ pj ) 1 + 2 1°9(ch/ pj ) -

j= 51 ii

[(am + Bmyc)(aj + Bjyc) ' 7mm11°g(rmc/ rm)
(4.11a)

_ - _ n
“1c ’ “i + Biyc + ( “i + Biyc)[ 1°9(Pic/ Pi) 3j=1 (

a. + 3 ch )1°9(Pj C/ Pj ) ] + 2

j log<pjc/ pj ) -

j: 31 ij

[(ai + Biyc)( am + Bmyc) - Wimllog(rmc/ Em)

(4.11b)

where rmc denotes the opportunity cost or actural price of

holding monetary assets for each household c, while Em is
the central price of holding monetary assets; wmc= mr/y is
the budget share for money holdings. The above general
household demand system explicitly reflects the interactions
of demands for goods and money; and it satisfies adding up
restrictions, homogeneity, symmetry and semi-negativity.

The Slutsky coefficients [ n ] can be expressed by Barten's

expression:S

 

5 Barten, A. P. "Consumer demand functions under conditions
of almost addictive preferences", Econometrica, vol. 39, J an.-April,
1969, pp2.

93

w = dq / dp = u U’1 — u/uy Q Q' q;

‘where U-1 is the inverse Hessian,
-1 d’u/d’m d'u/dmdq' -1
U = d'u/dqdm d'u/d'q

Since the sufficient condition for utility maximization
as symmetric negative definite Hessian U is assumed, the
inverse Hessian U"1 must exist, and it is negative semi-
ciefinite. Therefore, the existence of the Slutsky
<:oefficients are insured, and they express the relationship
(sf monetary assets and goods in the household demand system.
ZIf there is no relationship of goods' demand and monetary
iassets' demand, we must then have d'U/dqdm = diU/dmdq'= 0,
:i.e. off-diagonal terms are zeros, so that Hessian and its

iJrverse must be a block diagonal.‘

With the underlining modified utility maximization
Stzructure obtained in last chapter, we can also extend the
IJPI demand specification to be a general demand system which

irlcorporate both goods' demand and monetary assets' demand:

 

 

‘Clements, K. and Nguyen, P. "Money demand, consumer demand
Sgg4gelative prices in Australia", The Economic Record, Dec. 1980,
—41.

94

- n

wmc = am + Bmyc + ( am + BmYC)[1°9(rmc/ rm) ' 2:j=1( aj+
Bjyc)1°g(pjc/ fij)] + ¢( am + Bmyg)[log(rmc/ Em) _
zj:1( aj + Bjyg)log(pjc/ lel ‘ [( am + Bmyc)( am

+ Bmyc) + ¢< am + Bmyg)( am + amyg)ilog(rmc/ Em)
(4.12a)

n ( a.+

wic = “i + Biyc + ‘ “i + Biyc)[1°g(pic/ Pi) ‘ zj=1 3

Bch)1°9(ch/ Ej)] + ¢( 01 + BiY3)[1°9(Pic/ pi) -
zj:1( aj + Bjyg)log(ch/ Pj)] - [( a1 + Biyc)( am

+ amyc> + ¢< ai + siyg)( am + Bmygiilog(rmc/ Em)

(4.12b)

The above equations reveal the effect of cost of
holding monetary assets on the real income. Also, they
satisfy the restrictions on the original LPI model.

Again, when we replace the linear terms (a + B y ) and
(a + B y* ) by the quadratic terms (a + B y +6 y') and (a +
B y* + 6 y**'), respectively, we can obtain the general QS

and QPI demand systems with monetary assets included.

95

Now we will consider explicitly incorporating
demographic variables, rural development indecies and
investment indicator into the demand system of rural
households. In the last chapter we demonstrated that socio-
economic factors would be encompassed in the internal
household technology, and they would alter the parameters of
the demand system; hence the estimated parameters of the
demand system may be explicit or implicit functions of the
households' socio-economic variables. We also discussed
some specific procedures which express the functional
relationship between the estimated parameters and
demographic variables. These methods can be used in our
model. For convenience, we will explore the idea of the
translating procedure: the original demand framework as a
function of households' socio-economic variables, not merely
the demographic profile.7 Therefore, we assume the
estimated parameters in our extended LS and LPI models a*
and B* to be additive linear functions of all institutional

or socio-economic variables:

 

7 Pollak, R. and Wales, T. initiated the translating
procedure, which defined demand system. to be a function of
households' demographic factors. "Estimation of complete demand
systems from household budget data: the linear and quadratic
expenditure systems", American Economic Review, vol.68, 1978,
pp349-59. "Comparison of the quadratic expenditure system and
translog demand systems with alternative specifications of
demographic effects", Econometrica, vol.48, April, 1980, pp596-99.
"Demographic variables in demand analysis", vol.49, Nov., 1981,
pp1534-4o.

96
a. d (4.13a)

B*i = Bi + 2k£1 pikdk ’ (4.13b)

where k = 1...K, dk is the kth socio-economic variables, aik
and “ik are unknown parameters which need to be estimated.
This procedure will add 2(n x K) independent parameters to
the original models. For the quadratic models, we can also
make 6* to be an addictive linear function of all socio-

ecomonic variables d:

6*i = 61 + zk=1 rikdk (4.13C)
Again, where Tik is an unknown parameter. Then we will have
3(nxK) more independent estimated parameters comparing with

the original quadratic models.

4,; AIDS Mogeiing
The model of an almost ideal demand system is proposed

by Deaton and Muellbauer.8

This specification of demand
system is originated from a specific class of preferences,

represented by a cost or expenditure function that defines

 

8 Deaton, A. and Muellbauer, J. "An almost ideal demand
system", American Economic Review, 1980, pp312-325.

97
the minimum expenditure necessary to obtain a specific

utility level at given prices:

logc(u, p) = a, + 2k aklogpk+ 1/2 EkEj ’kj logpklogpj

Bk (4.13)

+ n B. Pk p k

where a, B and r are estimated parameters; according to
Sheperd's lemma, demand functions can be directly derived
from the cost function. The price derivatives of the cost
function are quantities demanded, qi= dlogc(u, pi)/dlogpi;
if multiplying it by the ratio pi/c(u, pi), we obtain budget
share of good 1. Thus the demand system is expressed as in

budget share form:

w. = ai + Bilog(M/P*) + 2.: (4.14)

1 j 1 rijlogp.

3

where M is total expenditure and P* is a price index which

is defined as:

P* = a. + 2k aklogpk + 1/2 EkEj rkjlogpklogp. (4.15)

J

The term (M/P*) is interpreted as "real expenditure".
The restrictions on parameters are 1) 2 ai= 1, E fij = 0,

E Bi= 0; 2) E 7ij= 0; and 3) fij= Tji' The demand system

98
can add up to total expenditure as restriction 1) meets; it
will satisfy the homogeneity and Slutsky symmetry as the
restrictions 2) and 3) hold. In the AIDS demand system, in
order to eliminate some parameters, we need an additional
restriction on cross price parameter 1.. . For some

13

pairs (i, j), r.. should be zero; that is, for such pairs of

1)
goods, one budget share is independent of another's price.

But Deaton (1978) rejected an extreme restriction of all fij

being equal to zero.9

The AIDS cost function is such a flexible functional
form that the demand functions obtained are so general as
first order approximations to any set of demand functions
derived from a utility maximizing behavior. Even if a
household maximizing behavior is not assumed, i.e. second
order condition can not be satisfied, and thereafter

homogeneity E Tij= 0 and slutsky symmetry Tij= Tji

can
not hold. This flexible specifications for demand system
derived from the cost function still have its meaning:
demand functions are still continuous in expenditure and
prices and then provide local first order approximation.

Due to this characteristic of flexible functional forms, the

property of negativity can not be guaranteed by the

 

9 Deaton, A. "Specification and testing in applied demand
analysis", Economic Journal, vol.88, Sept. 1978, pp524-36.

99
restrictions on parameters.10
Deaton and Muellballer estimated the system through
substituting the price index in the equation (4.15) into the

demand equations (4.14). Since there is'a problem of
practically identifying parameters a., they suggested to
assign a value to a. prior to the estimations. But this

practice, pointed by Chung (1989), can not guarantee to

obtain the right value.11

However, Theil, Chung & Seale (1989) indicated that, we
do not need to use equation (4.15) to implement the AIDS
model. The price index log P could be replaced by the

approximation equation without unknown parameters:

~ n
logP ~ 21:1 wilogpi . (4.16)
This price index approximation has some limitations.12
If the equation (4.16) is used, wi will appear on both sides
of the equation (4.14); this raises problems: if E wilogpi

on the right-hand side is treated as exogenous, then wi on

 

1° Deaton, A. and Muellbauer, J. "An almost ideal demand

system", Amerian Economic Review, 1980, pp316.

11 Chung, C. F. "A cross-sectional demand analysis with an
application to Spanish provincial food consumption", forthcoming
publication, pp4.

n: Theil, H., Chung, C. F. and Seale, J. "Advances in
econometrics, international evidence on consumptions",Greenwich,
Conn. JAI Press, 1989,pp184-186.

100
the left-hand side should also be regarded as exogenous.
Further, P is a price index in a limited sense, since it
fails to satisfy an identity test which requires price index
unchanged when all individual prices do no change, but P
may change due to change in wi. So they proposed another
more satisfactory approximation: the cross-sectional data
for the LS and LPI models provide a choice to replace (M/P)
in equation (4.14) by real income term Qc based on the
concept of central prices P in the LS and LPI models.
Again, it should subtract logpj from logpjc for j=1...n in
the price term. By making y=loch, we obtain an AIDS cross-
sectional demand model:

wic = ai + siyc + Ejglrijlog(pjc/ Ej) (4.17)

The AIDS demand form is an alternative for LS model,
but with these differences between them: AIDS model has just
one price term, and its matrix [ Tij ] does not satisfy the
negative semi-definity, though it satisfies the symmetry and
homogeneity.

In the last chapter we have demonstrated that it is
equivalent to contain monetary assets in a utility formation
or to include them in an expenditure function from which a
demand functions of goods and money can be simultaneously
derived. Hence, as we consider a general demand system with

monetary assets, the expenditure function should explicitly

101
contain cost for money demand. The extended cost equation

would then look like:

logc(u, p, r) = a. + arlogr + 2k aklogpk +1/2( er

Bk Br
logrrjlogpj + Ekzjrkjlogpklogpj ) + uB.Pkpk r

(4.18)

Thus the demand system in budget share form is expressed as:

- ' n ‘
wmc- am + BmyC + rmmlog(rmc/ rm) + Ej=11mjlog(pjc/ pj)

(4.19a)

n

w. = a. + Biyc + r.mlog(rmc/ rm) + 2]:

1c 1 i 1Tij1°g(pij/ pj)
(4.1913)

where the restrictions on parameters are the same: for the

21. = 21 .= 21.

adding-up restrictions, Edi + em = 1, EBi 1m m] ij

= 0; the AIDS coefficients [ r ] satisfy the homogeneity

T..=

Erim= Erm.= Erij= 0 and the symmetry Tim: ij’ 1] Tji'

3
They can not satisfy the slutsky negativity, since the AIDS
function is such a flexible form that there may not exist a
second order derivative required as the approximation of

utility maximization. That is, for this flexible formation,

102
we can not assume a negative definite utility function. The

parameters 1 represent effects of prices for money demand

1113'
on goods in budget share. If some pairs of rim or ’mj are
equal to zero, they will indicate that meney demand is
independent of goods' prices; or, goods demand independent
of the price of monetary assets.

Like the LS and LPI models, AIDS model can become a
quadratic form by replacing the term (ai + Biyc) with (a1 +
Biyc + 6iyé). Also, we can incorporate all institutional

variables into the demand functions by making estimated

parameters a., B

1 i' and 61 to be additive linear functions of

the institutional variables d.

4,4 Mptpods p; Aggregation

In our cross-section and panel data, we aggregate
detailed items of economic goods listed in the chapter II
into four categories: staple food, non-staple food,
clothing & footware, and agricultural input. Also, we
aggregate cash holdings and demand deposits into the
catergory of monetary assets. In order to obtain "prices"
of these five aggregate categories from detailed items for
each household, we employ the average weight procedure

expressed as follows:

_ M
Pic ‘ zj=1‘ch/Eic’P3-c (4.20)

103

We define the expenditure on ith category as:

_ M
Eic ' Ej=1ch

(4.21)
where j = 1...M stands for detailed items; i = 1...n for
five categories of aggregates; and c = 1...N for observed
households. pic denotes the aggregate price of ith group
for household c, p.

3
for c's household, and ch is the c's household expenditure

c denotes the price of jth detailed good

on jth good, where ch = pjcqjc‘

The ratio of jth good in
ith group (ch/Eic) for household c acts as the wight for
the contribution of jth good's price in the aggregate price
of ith group.

However, as price variants in aggregate price vectors
of each group across households exist, it is necessary to
construct central price vectors Si as a benchmark for every
observation; furthermore, central price vectors 51 are so
important as to obtain real income Q for each observation
required by the modelling.

The concept of central prices can obtained through

Geary (1958) - Khamis (1967, 70, 72) procedure.” This

 

n Geary, R. C. "A note on the comparison of exchange rates

and purchasing power between countries", Journal of the Royal
Statistical Society, Series A, 1958, pp97-99u Khamis, S. H. "Some
problems relating to the international comparability and
fluctuations of production volume indicators", Bulletin of the
International Statistical Institute, 1967, 42, Part1: pp213-30;
"Properties and conditions for the existance of a new type of index

104
procedure gives a set of parameters called household

purchasing power ratios 6c for household c: c=1,...N

n

 

 

2. p. q.
6C = l 1 1C 1C (4.22)
n -
Zi=1Pi qic
where central price Si is defined as:
N
_ 2 = P- (I- / 6
pi = c 1 1c 1c c (4.23)
N
2c=1qic

Simultaneously solving (4.21) and (4.22), we can obtain

the central price vector, which is linear homogeneous in

each household's price pic' Then we can get real income by

the expression:

— n -
Qc ‘ 21=1‘ Eic/ pic) Pi (4°24)

where the term (Eic/pic) is the cth household expenditure on
the ith aggregate group divided by its observed price, which
is regarded as "quantity demanded" for the ith aggregate by

c. Then multiplying this "quantity demanded" by the ith

 

numbers", Sankhya, 1970, Series. B. 32, pp81-98; "A new system of
index numbers for national and international purposes", Journal of
the Royal Statistical Society, 1972, Series A, 135: pp96-121.

105

central price vector 5i, we obtain the "real expenditure" on
the ith group. Thus, the aggregation of real expenditures
on all five groups makes up of cth household real income Qc'
As a consequence, the Geary—Khamis procedure renders central
prices 51 and real income Qc' which constitute an integral

part of the model discussed in last two sections.

CHAPTER FIVE

RESULTS OF ESTIMATIONS

5,1 Introdugtion

In this chapter we will present the results of empirical
estimations of the general demand systems based upon Chinese
rural household data.

We will discuss these questions: whether the socio-
economic variables we chose to represent features of rural
households and the process of rural development really
matter in the general demand system fo goods and money? Do
the money demand and goods demand interact with each other?

What is the relationship between home-produced agri-goods
and market-purchased goods? Moreover, what kinds of policy
implications can we derive from the empirical studies?

In Section 5.2 we will discuss the importance of the
socio-economic factors in the general demand framework and
the possible directions of their influences; in Section 5.3,

we will present income and price elasticities derived from

106

107
the models and the explanations; in Section 5.4, we will

briefly summarize some important policy implications.

5 n s’s Estim ed Results

In Chapter four we have specified six linear and
quadratic general demand systems as LS, LPI, DM, QS, QPI and
QDM. We can obtain stochastic specifications for these
demand systems by adding the vector of disturbances to each
equation. We will assume that the disturbance term ei is
independently and identically distributed across households
with a zero mean and a positive definite variance-covariance
matrix. Because the dependent variables and the non-
stochastic terms in the equations are in share forms which
can be added to one and the covariance is singular, we have
to drop any equation in order to estimate the general demand
system.

With above assumptions we can estimate general demand
systems by the maximum likelihood method. We use Gauss
program (version 2.0, 1988) to conduct the estimations.

We have made twelve estimations as two groups for the
six models. The first group of estimations does not
explicitly the associate socio-economic factors, that are
labeled as L80, LPIO, DMO, QSO, QPIO, and QDMO; the second
group systematically incorporates socio-economic factors in

the demand frameworks according to the method we have

described in Chapter four, and they are called as L81, LPIl,

108

Table 12: Log Likelihood Values for Alternative

Model Formations.

 

 

Estimated Socio-economic Log likeli— Number of
procedure variables affecting hood values parameter
estimated parameters:
a B 6

L30 ignore 4245.39 18
L31 d1,d2,d3,d4,d5 d1,d4,d5 - 4452.75 50
LPIO ignore 4172.07 9
LPIl d1,d2,d3,d4,d5 d1,d4,d5 - 4385.10 41
DEO ignore 4247.20 18
DMl dl,d2,d3,d4,d5 d1,d4,d5 - 4445.70 50
QSO ignore 4260.84 22
QSl d1,d2,d3,d4,d5 d1,d3,d5 - 4465.73 so
QPIO ignore 4184.62 13
QPIl d1,d2,d3,d4,d5 d1,d3,d5 d4 4403.97 49
QDMO ignore 4258.99 22
QDMl d1,d2,d3,d4,d5 d1,d3,d5 - 4461.70 54

 

Note: socio-economic variables: d1: family size; d2: labor
size; d3: monetized index; d4: diversified index; d5:

investment indicator.

109
DMl, QSl, QPIl, and QDMl.

Our results show that the socio-economic variables have
important impact upon rural households' general demand
system for goods and money. In Table 12, we present log
likelihood values for all twelve linear and quadratic
models. The six estimates belonging to the first group are
procedures without combining socio-economic variables, and
the second group estimates are best values of the models
incorporating socio-economic variables which are selected

from the likelihood ratio tests.

Table 13: Likelihood Ratio Test Statistics for Estimations.
(x-distribution at the .05 level in parentheses)

 

 

Null hypothesis Alternative
hypothesis

LSO VS. LSl 414.73 (41.94)
LPIO VS. LPIl 426.06 (41.94)
DMO vs. DMl 397.00 (41.04)
050 vs. QSl 409.78 (40.10)
QPIO VS.QPI1 438.7 (49.77)

QDMO VS. QDMl 405.42 (41.94)

 

110

The report exhibits that, the parameter a*, as the
constant terms in the models, are highly affected by all
five socio-economic variables, except in the Q8 model which
is not affected by the household investment indicator. The
parameters 8*, as the coefficients of real income, are
significantly affected by family size, labor size and
diversified index in the linear forms; in the quadratic
models, however, B* is affected by family size, monetized
index and investment indicator. The socio-economic
variables have almost no significant impacts on parameters
6*, which are the coefficients of squared real income,
except in the QPI model which is affected by diversified
index.

Now the question is whether the models of incorporating
the socio-economic variables significantly improve the
estimations? The likelihood ratio tests are reported.

In Table 13 the nested hypothesis tests are such that
the null hypothesis states no difference between the models
without incorporating socio-economic variables and the
corresponding models with those variables. The testing
results clearly indicate the latter very superior to the
former, so as to highly significantly reject the null
hypothesis. Therefore, we will only report the estimates
with the socio-economic factors incorporated.

Since the linear models are special cases of the

quadratic models, we will conduct the nested likelihood

111
ratio test with hypothesis of linear models against their
corresponding quadratic forms. The test statistics are
reported in Table 14. The numbers of estimated parameters
in the LS model are equal to those in the Q8 model, so that
the likelihood ratio statistics indicates the quadratic
model QS better than the linear model LS. Also, the
quadratic models QPI and QDM are superior to their
corresponding linear forms LPI and DM.

However, since the quadratic forms QS, QPI and QDM are
not nested specifications for each other, we cannot directly
conduct the significance tests of the differences in the
likelihood values. Then we will present estimates of all
quadratic specifications: QS, QPI and QDM. Tables 15.1-15.3
below will show all estimated parameters obtained from these

three quadratic forms.

Table 14: Likelihood Ratio Test Statistics between Linear
and Quadratic Models.
(x-distribution at the .05 level in parentheses)

 

 

Null Hypothesis Alternative Hypothesis
Ls vs. 08 25.96 ( - )
LPI vs. QPI 37.74 (15.51)

DM vs. QDM 32.00 (9.49)

 

112

Table 15.1: Maximum Likelihood Parameter Estimates QS
(t-statistic in parentheses)

 

 

Estimated Staple Non-staple Clothing& Agri- Money
parameters food food footware inputs assets
a*:
constant .2418 .1396 .0679 i .0444 .5063
(9.0309) (5.4617) (4.1850) (2.9745) (13.6893)
d1 01564 ”.0455 .0063 .0331 -01504
(9.3543) (—2.8107) (.6343) (3.6450) (—6.5144)
d2 -.0157 .0159 .0124 -.0091 -.0395
(-1.3046) (4.5500) (1.7575) (-1.4207) (-2.3947)
d3 -.0350 .0816 .0003 .0570 -.1040
(-1.7523) (4.2389) (.0232) (5.0264) (-3.7213)
d4 .1405 .1957 .0380 -.1100 .0167
(5.9367) (8.6794) (2.6618) (-8.4785) (.5109)
8*:
con -.3068 -.0965 —.0402 -.0420 .4856
(-6.3636) (-2.1217) (-1.4092) (-1.5882) (7.2724)
d1 .0222 .0373 .0328 .0222 -.1145
(.9201) (1.6273) (2.2855) (1.7022) (-3.4426)
d3 .1706 .0327 -.0373 -.0315 -.1345
(3.9051) (.7937) (-1.4418) (-1.3016) (-2.2216)
d5 .0588 -.0432 -.0027 .0041 -.0169
(3.1187) (-2.4714) (—.2573) (.4013) (-.6532)
6*:
con -.0777 -.0211 .0012 -.0101 .1077
(-5.2116) (-1.5200) (.1367) (-1.2076) (5.1837)
n: ----------------------------------------------------------
Staple -.2229
(-6.0889)
Nonstaple .1811 .0646
(5.7185) (1.2713)
Clothing .0110 -.0237 -.1117
(1.0961) (-1.1414) (-7.6286)
Agri-input -.0617 .0373 .0010 -.0357
(2.6336) (1.4547) (.7503) (-1.4867)
Money .0836 -.2593 .1054 .0501 .0202

(1.7505) (-4.5843) (3.7420) (1.1336) (.2042)

 

113

Maximum Likelihood Parameter Estimates QPI
(t-statistic in parentheses)

Table 15.2:

 

 

est.parameters Staple Non-staple Clothing Agri-input Money
0*:
con .02381 .1295 .0539 .0500 .5285
(8.9538) (5.1524) (3.2178) (3.5002) (14.2978)
d1 .1465 -.0655 .0214 .0307 -.1331
(8.9388) (-4.2134) (2.0430) (3.5008) (-5.8424)
d2 -.0127 .0545 .0103 -.0077 -.0441
(-1.0389) (4.7218) (1.3568) (-1.1974) (-2.6000)
d3 -.0162 .0990 -.0169 .0471 -.1130
(-.7773) (5.0884) (-1.3315) (4.2119) (-3.8978)
d4 -.1266 .2285 .0516 -.1155 -.0381
(-4.2938) (8.2261) (3.0113) (-7.617) (-.9381)
d5 .0003 .0046 .0056 .0123 -.0229
(.0417) (.5764) (1.0949) (2.7490) (-2.0025)
B*:
con -.2936 -.0307 -.0279 -.0409 .3931
(-5.7548) (-.6247) (-.8411) (-1.6671) (5.5361)
d1 .0190 .0123 .0318 .0118 -.0747
(.7583) (.5076) (1.8717) (.9739) (-2.1909)
d3 .1656 .0184 -.0515 -.0245 -.1079
(3.6647) (.4198) (-1.7329) (-l.0978) (-1.7299)
d5 .0574 -.0403 -.0113 .0026 -.0084
(3.0233) (-2.1462) (-.9055) (.2689) (-.3220)
6*:
con -.0812 .0121 .0442 -.0070 .0319
(3.6306) (.5634) (2.8642) (-.7258) (1.0429)
d4 -.0223 -.1230 -.1271 .0190 .0319
(-3.6306) (.5636) (2.8642) (-.7258) (1.0429)
6: —.9376 (-11.2019)

 

Note: Staple: staple food; Nonstaple: non-staple food;
Clothing: industrial consumer goods; Agri-input:
industrial agri-producer goods; Money: money assets.

Table 15.3:

114

Maximum Likelihood Parameter Estimates QDM

 

Staple Nonstaple

Clothing Agri-input Money

 

a*:
con .2427 .1435 .0680 .0483 .4974
(8.8539) (5.6386) (4.0984) (3.2706) (13.0108)
d1 .1549 -.0460 .0054 .0307 -.1450
(9.1047) (-2.8491) (.5248) (3.3309) (-6.0373)
d2 -.0138 .0520 .0125 -.0083 -.0425
(-1.1235) (4.5834) (1.6987) (-1.2716) (-2.4713)
d3 -.0345 .0790 -.0029 .0485 -.0901
(-1.6353) (4.0236) (-.2326) (4.3056) (-3.0376)
d4 -.1397 .1846 .0309 -.1055 .0296
(-5.7331) (8.1665) (2.1119) (-8.1006) (.8663)
d5 .00001 .0038 .0010 .0010 -.0237
(.0005) (.4831) (1.9879) (2.2232) (-2.0150)
B*:
con -.3072 -.0915 -.0403 -.0373 .4762
(-6.1947) (-1.9752) (-1.3470) (-1.4065) (6.7906)
d1 .0174 .0354 .0390 .01717 -.1090
(.7047) (1.5301) (2.6275) (1.2896) (-3.1130)
d3 .01771 .0296 -.0468 -.0283 -.1316
(3.9459) (.7118) (-1.453) (-1.1857) (-2.0955)
d5 .0622 -.0465 -.0095 .0016 -.0078
(3.1889) (-2.57l9) (-.8132) (.1545) (-2.0955)
6*:
con -.0753 -.0171 .0013 -.0053 .0974
(-4.9512) (-1.1894) (.1382) (-.6437) (4.4843)
1: ----------------------------------------------------------
Staple .0165
(.4464)
Nonstaple .1012 .2390
(3.2433) (4.5586)
Clothing -.0182 —.0480 -.0272
(-1.0077) (-2.3271) (-1.9452)
Ag-input -.0979 .0172 -.0004 .0571
(-4.2774) (.6740) (-.0333) (2.232)
Money -.0016 -.3093 .0938 .0240 .1930
(-.0336) (-5.4552) (3.2873) (.5354) (1.9801)

 

115

As the intercept of all quadratic models, parameter
vector 0* represents the basic demands for goods or money
which are free from changes in income vector. But the
parameter 0* can be divided into two parts, the first part
is the constant term which is independent of socio-economic
factors, and the second part is the portion of 0* which is
affected by socio-economic variables.

The constant terms of 0* express the independent or
constant demands which are not affected by income, price and
socio-economic vectors. They are positive and variant
across goods and money demand, the averages are .05, .07,

.14, .24 and .5 for the demands of industrial producer

Table 16: Significant Effects of Socio-economic
Variables upon 0* Parameters.

 

Staple Nonstaple Clothing Agri-input Money

 

0*:
d1 + - + + _
d2 + -
d3 + + -
d4 +,- + + -

d5 + + -

 

116
goods, industrial consumer goods, non-staple food, staple
food and money assets,respectively.

Another portion of intercepts 0*, however, is
influenced by the socio-economic variables. In order to
make things clear, we tabulate the positive and negative
influences of all socio-economic variables upon economic
goods and money assets which are significant in t-statistics
in Table 16.

Specifically, demographic variables have significant
impacts on the intercepts of all goods and money demand. As
family size (d1) becomes larger, constant demand for staple
food, industrial consumer and producer goods will rise,
while intercepts for non-staple food and money demand will
decline. When labor size (d2) rises, constant demand for
non-staple food will increase but the demand for money will
drop. This result indicates that, increase indemographic
variables will increase rural households' basic demand for
"necessary" goods, while decrease their base for relatively
"unnecessary" demand, especially basic demand for money
assets.

The indices of rural development level are important
factors influencing households' basic demand. On the one
hand, the monetized index (d3) will positively affect
intercepts for non-staple food and industrial consumer goods
while negatively affect money. The increase in the

monetized index reflects the fact that rural households have

117
higher purchasing power and potentiality of accessing money
assets, and hence they tend to expand their "constant
bundle" of market consumer goods and evaluate opportunity
cost of money holdings higher than before. On the other
hand, the diversified index (d4) will affect all constant
demand for goods but money. Along with the rise of this
index, the constant demand for market consumer goods (non-
staple food and clothing) will increase, the demand for
home-produced staple food can move in either direction, but
demand for agri-input will decline. The increase of
diversified index reveals the fact that rural households
engage in more other non-farming production activities than
agricultural activities, thus the constant demand for agri-
input naturally decreases, while the demand for market
consumer goods such as non-staple food and clothing goods
increase.

The investment indicator affects clothing and agri-
input positively, but affects money negatively. It may
express the relationship between non-durable goods, money
and household investment in this way: in order to invest in
new houses or durable goods, households have to restrict
their basic needs for market goods and claim money balances.
As the investment is achieved, however, this restriction is
lifted so that the constant demand for market goods rises
and the desire for money drops.

Also, the socio-economic factors have important impacts

118
upon 8*, the parameter vector of log real income. The
constant terms in B* are all negative for good demands,
arranged as -.3, -.09, -.04, -.04 for staple food, non-
staple food, clothing, and agri-input, respectively; but it
is positive and valued about .5 for money demand. This
phenomenon can be explained as follows: along with the
increase in income, a decreasing portion of income is
allocated to good demands while an increasing portion is

directed to money demand.

Table 17: Significant Effects of Socio-economic
Variables upon Parameters B* and 6*.

 

Staple Nonstaple Clothing Agri-input Money

 

 

B*:
d1 + -
d3 + -
d5 + - -
6*:

d4 - +

 

119

The 6* is the parameters of squared log real income.

In the Q8 and QDM models, the constant terms in 6* are
negative for staple food, non-staple food and agri-input
demand, with the values of -.08, -.02 and -.01; those for
clothing and money demand are positive, valued as .001 and
.1, respectively. In the QPI model, constant terms in 6*
for staple food and agri-input demand are negative with the
values of -.08 and -.007; but those are positive for non-
staple food, clothing and money demand, ranging .01, .04 and
.03, respectively. This fact may hint at an increasing
portion of real income being directed to market goods such
as clothing, which is relatively less "necessary".

In Table 17 above, we demonstrate the effects of the
socio-economic variables upon all quadratic forms'
parameters B* and 6* with significant t-statistics, which
are the direct coefficients of real income.

The parameters B* are significantly affected by family
size, monetized index and investment indicator, while the
parameters 6* are only affected by diversified index.
Specifically, as family size rises, a higher portion of the
increase in real income will be directed to the demand of
industrial consumer goods, and a lower portion to the demand
of money assets; the high monetized index will allocate more
of the increased real income to the demand of staple food
and less to money assets. When household investment has

been achieved, the increased income will be allocated to the

120
demand for staple food and less to money. It is interesting
to observe that, for parameters 6*, diversified index does
not significantly affect money demand, but does affect
staple food negatively and clothing positively.

The summerization is that the socio—economic variables
have significant influences upon the general demand
framework for goods and money. Specifically speaking,
demographic variables, rural economic development level and
fixed investment will not only affect constant portions of
the demand systems, but will also greatly influence the
allocation of change in real income as well. The very
important fact is that these socio-economic variables will
affect money demand only negatively, though their affects of
goods are in either the positive or negative direction. The
explanation may be stated as follows: more household members
or working people will require more goods and less money.
The upgrade of development level characterized by the
indices of income monetization and diversification of
production activities will decrease household demand for
money, since rural households have enlarged capacity and
sources to obtain money assets. The households' investment
are complements of money assets, as a certain satisfactory
level of households' investment is achieved, the motivation

of holding money declines.

121

5.; income and Price Elasticities

In the above section, we have tested that the quadratic
specifications of demand equations are better than the
linear forms, and we have also exhibited the impacts of
socio-economic factors upon general demand systems through
influencing parameters. In this section we will present
income elasticities and compensated price elasticities for
the quadratic forms ( in order to make comparisons, we will
report both income and price elasticities of the linear
equations in Appendix 2 ).

The income elasticities of demand equations are the

marginal share divided by the budget share. The marginal
share is:

= - = 3 4
Bi B; + wic a; + B: + nyc + 6; yC (5.1)

While budge share is:

_ = 2
wiC a: + BiyC + 6§yc (5.2)

Then the income elasticity is expressed:

e. = Bi / wic = 1 + ( B; + 261yc )/ wic (5.3)

where parameters 0*, B* and 6* are:

122

K

“*1 = “i 1 2k=1°ikdk '
_ K

3*1 ‘ Bi 1 2k=1"ikdk '
_ K

The compensated price elasticity eij is the ratio of
Slutsky price coefficients 'ij to the budge share of the ith
good wic' Since the QS model has Slutsky price coefficients
[ w ], its price elasticity can be directly derived:

(5.4)

Since the QPI and QDM models, however, do not directly
express the Slustky price coefficients, it is necessary to
derive them first, with which the corresponding price
elasticities are obtainable. In the QPI model the Slutsky

price coefficients are:1

nij= ¢ei( 1-ej) if i=\=j (5.5)

Fij= -¢eiej if 1 = j

where 81 = B: + 61c is the marginal share, and o is the

income flexibility. For the model GDM, the Slutsky price

 

1 Theil, H., Chung, C. F. and Seale, J. K. "International
evidence on consumption patterns", Greenwhich, Conn. JAI Press
1989, pp155.

123

coefficients [ w ] can be expressed as:2

Wij= Tij + Bifijyic + wiwj V if 1=\=j (5.6)
uij= 1ij + Bizyic+ ( wi- 1 )wi if i = j

where [ 1 ] are the AIDS price coefficients.

In Table 18, the mean income elasticities of the all
three quadratic forms will be reported. The term of
"income" indicates the total expenditure on goods and money
assets. The income elasticities of these three models are
quite similar, especially the models QS and QDM. They have
exhibited that all aggregate goods and money are normal
"goods". However, all the four aggregate goods are
"necessities", though the "necessary degrees" of these goods
are different. As income increases by 10 percent, demand
for staple food rises about 6.5 percent, non-staple food
rises about 8.4 percent, clothing around 7.8 percent and
agri-input by 6.1 percent. For rural households, industrial
agri-input is listed as the most "necessary" demand while
staple food as the second necessary demand, the values of
both elasticities are quite similar. Clothing and non-
staple food are listed as less "necessary" goods, or,

relatively more elastic ones with respect to income change.

 

2 Theil, H. "Theory and measurement of consumer demand",
Amsterdam: North-Holland Publishing Company. "The system-wide
approach to microeconomics", The University of Chicago Press, 1980.

124

It is very interesting to notice that the rural
households' demand for money (precisely, narrowly defined
money M1) is highly elastic comparing with aggregate goods.
When real income rises by 10 percent, the money demand will
increase by more than 22 percent. This observation is quite
important: there is a very high desire for Chinese rural
households to hold money assets as their income increases
while their demand for market and home-produced goods are
relatively constant.

In Table 19, the mean compensated price elasticities
are reported. The Theil model suggests that the utility
function is negatively definite, so that the matrix [ n J is
negatively semidefinite and own compensated price

elasticities are negative. The estimated results indicate

Table 18: Estimated Income Elasticities of Q8, QPI and QDM.

 

 

Food Non-staple Clothing & Agri- Money

food footware inputs assets

Q8 .6430 .7914 .8012 .6652 2.2031
QPI .6087 .9146 .7496 .5713 2.1247

QDM .6896 .7907 .7928 .6053 2.2967

 

125

Table 19: Estimated Price Elasticities of Q8, QPI and QDM.

 

 

 

 

Staple Nonstaple Clothing Agri-input Money
QS:
Staple -.5759 .9047 .2113 -.26801 .5634
Nonstaple .4678 .3226 -.2504 .4147 -1.7482
Clothing .0516 -.1182 -l.1827 .1108 .7110
Ag-input .1593 .1862 .1055 -.3823 .3378
Money .2159 -1.2954 1.1164 .5371 .1361
QPI:
Staple .4582 .2234 .1922 .1520 .5749
Nonstaple .1113 -.7014 .1207 .0890 .3588
Clothing .0478 .0651 -.6519 .0449 .1705
Ag-input .0394 .0509 .0451 -.4905 .1349
Money .2597 .3620 .2939 .2046 -1.2391
QDM:
Staple -.5688 .8948 .1984 -.7480 .4731
Nonstaple .4559 .3939 -.3026 .4169 -1.9590
Clothnig .0502 -.1413 -l.1952 .0928 .7632
Ag-input .1391 .1849 .0955 -.2288 .2803
Money .2016 -1.3322 1.2020 .4671 .4422

 

126
that the Q8 model does not satisfy this restriction, while
the QPI model does it since its all diagonal terms are
negative. As far as the QDM model is concerned, it is so
flexible that no restriction on the utility function and the
negativity does not apply.

We observe that in the models QS and QPI, the own price
responsiveness of clothing are elastic, valued about -1.2
for both models; own price responsiveness of staple food and
agri-input are inelastic, with values of -.57 and -.35,
respectively. But the own compensated price elasticities
for non-staple food and money in the two models are
positive, This is not unusual for money demand: a rise in
inflation rate indicates a higher general price level so
that the demand for money may increase given households'
inflation expectation constant; even though a high level of
general prices produces higher opportunity cost of holding
money than before. In the QPI model, own compensated price
responsiveness of money demand are elastic and those of all
goods are inelastic.

We are very interested in the cross price elasticities
of staple food with respect to market goods, elasticities of
agri-input to consumer goods, and elasticities of money to
all goods. The cross price elasticities of staple food with
respect to market goods and the elasticities of agri-input
to consumer goods are positive in the QPI model. In the

both QS and QDM models, the elasticities of staple food with

127

respect to agri-input are negative, but positive to other
goods; the elasticities of agri-input to staple food are
negative, but positive to other consumer goods. This fact
indicates that home-produced staple food and agri-input are
complements while staple food and market consumer goods,
agri-input and market consumer goods are substitutes. The
higher price of agri-input will increase the cost of
producing staple food so that the demand for staple food
tends to decline. As prices of market consumer goods
increase, rural households have to sell more home-produced
staple food to trade the same amount of market goods; and it
is relatively cheaper to retain more staple food. Also, a
rise in the prices of market consumer goods tends to drive
demand for agri-input upward because agri-input becomes
relatively cheaper and the demand for staple food higher.

The cross price responsiveness of money and goods are
all positive in the QPI model, and also positive in the Q8
and QDM models except price elasticity of money with respect
to non-staple food. This result is quite important,
indicating money and non-durable goods are substitutes for
each other. When market prices of goods increase, the
demand for money tends to rise since rural households may
regard this time as not right time for "spending" and decide

to hold money for the future expenditure.

128

5. ol' Im ic tions

Quite a few government policy issues can be discussed
within the general demand framework we have developed and
estimated. We can directly derive some important policy
implications from the empirical results.

Since money demand in the rural areas consists of a
major part of all society's money demand in developing
countries, it is very important to explain systematically
rural households' money demand. What we have discovered in
the estimations is that two groups of exogenous variables
may affect rural households' demand for money assets: socio-
economic variables positively influencing the money demand,
and all prices of non-durable goods negatively affecting the
demand for money. Specifically, on the one hand, along with
fewer family members, higher economic development levels, or
investment in durables and new houses, the momentum of rural
households' demand for money will decline. On the other
hand, if prices for agri-output, industrial agri-input and
market consumer goods increase, the money demand will move
upward.

If the People's Bank of China (the central bank) aims
to stabilize the money market by providing an adequate money
supply, it has to consider the contrary influences of these
two groups of exogenous variables upon the money demand of

rural households. Unfortunately, the monetary authorities

129
tend to emphasize only the income and interest rate effects
of money demand while ignoring the changes in the income
structure and effects of specific goods'prices. This result
has important monetary policy implications: the estimations
have exhibited that money demand is greatly influenced by
socio-economic factors and interacted with the demand for
goods, the equilibrium of the money market, therefore,
cannot be achieved without taking these exogenous variables
into consideration.

The Chinese government, as the main supplier of
industrial goods, determines the prices of most industrial
consumer and producer goods; and as the monopolistic
purchaser of major agricultural products through allocating
annual procurement quotas to rural households, it directly
controls or tightly intervenes over the prices of most
agricultural products. The pricing policy is regarded as a
very important policy instrument to adjust national income
distribution and is enforced by the Department of Commerce.
Because this maneuver will deeply affect the money demand
behavior of rural households, it appears quite necessary for
the People's Bank of China to coordinate the monetary policy
with the pricing policy which is enforced by the Department
of Commerce.

In most developing countries the government is always
involved in some way in determining the prices of agri-

output and agri-input. The goal of government intervention

130
focuses on how to promote rural development, to increase
rural households' welfare and to guarantee the supply of
agricultural output. If price of agricultural product
rises, though its own price elasticity indicates a declining
demand for staple food, the cross price elasticities may
suggest that it has positive impact upon households'
expenditures on market goods. Every 10 percent of a staple
food price increase will decrease consumption of it by 5
percent, with demand for non-staple food rising by 9 percent
and clothing by 2 percent. Hence it is likely to enhance
the welfare of rural households. An opposite effect occurs
when industrial agri-input price increases. In this case,
rural households have to sacrifice more home-produced output
to obtain the same quantities of industrial agri-input:
every 10 percent increase in the price of agri-input will
decrease the households' consumption of staple food by about
1.5 percent. And moreover, rural households will reallocate
their budget by purchasing less market agri-input good and
more market consumer goods. For every 10 percent increase
in the price of agri-input, its purchase will decrease by
more than 3.5 percent, while purchases on non-staple food
and clothing will increase about 1.8 and 1.0 percent. Of
course, the agricultural production and the supply of agri-
output will be hurt, and the welfare of rural households
will then inevitably decrease.

When monetary authorities change interest policies, the

131
demand for goods will also be affected. Generally, interest
rate is tightly controlled by the central bank and it is
quite stable for a long period. Any increase in interest
rates will hint a high inflation level for the public which
tends to encourage the expansion of rural households'
current expenditure on non-durable goods.

The government may have some specific plans to enhance
rural socio-economic development such as demographic
policies, rural small scale industry projects, rural non-
farming employment plans, rural infrastructural enforcement
or others. These policies and plans' effects upon the rural
households general demand for goods and money could also be

analyzed through our modeling.

CHAPTER SIX

SUMMARY

In order to explain the general demand structure of
rural households in developing countries, especially the
money demand behavior, this thesis has constructed a general
demand model for both goods and money and tested it with
Chinese rural household data. Our framework differs from
the prevailing neoclassical money demand model through
incorporating some quite important institutional impacts
upon money demand and also considering the interaction of
goods demand and money demand.

The traditional money demand model implicitly assumes
the total separability of money demand and goods demand, and
confines the determinants of money demand as income level,
interest rates and general price level. These hypotheses,
unfortunately, fail to describe rural money demand which is
the major portion of money demand in developing countries.
The striking facts in developing countries are that rural

households perform in a semi-commercialized economy, in

132

133
which their annual income is simultaneously allocated upon
home-produced agri-output, market industrial consumer and
producer goods, as well as money assets. Institutional
changes such as monetized level of rural economy and
diversification of rural production activities may have
strong impacts upon rural households' demand behavior; and
moreover, governmental pricing policies of specific
agricultural and industrial goods will heavily affect rural
demand structure.

The theoretical model we constructed is based upon the
new home economics. It is so general that in developing
countries rural households' demand for industrial consumer
and producer goods, and home-produced agricultural output as
well as money assets can be simultaneously analyzed within
this structure. The analytical power of the framework could
overcome drawbacks of the traditional procedure which
usually ignores the interaction of demand for goods and
demand for money assets.

In addition, we also explicitly incorporate socio-
economic variables into the general demand system. The
socio-economic variables we have specified are family size,
labor force, monetized index, diversified income index and
investment indicator. The first two variables are rural
household demographic factors, the third and fourth indices
characterize the economic development level of rural

households, and the last one indicates rural households'

134
investment in house construction and durable purchases.

The estimations are based upon the Chinese rural
household data. Our empirical results can lead to the
following results:

First, the rural household demand for non-durable goods
are highly influenced by socio-economic variables, although
these socio-economic factors affect different goods in
different directions depending upon the nature of the goods.
Specifically, demand for staple food is positively affected
by family size, the monetized index, and the investment
indicator, but negatively by the diversified index. Demand
for non-staple food is positively affected by labor force,
the monetized and the diversified indices, while negatively
affected by family size and the investment indicator.

Demand for industrial consumer goods is just positively
affected by family size and the diversified index. Finally,
demand for industrial producer goods is positively affected
by family size, the monetized index, and the investment
indicator, but negatively by the diversified index.

Second, the socio-economic variables will significantly
affect rural household demand for cash and demand deposits
(M1), but all demographic factors and the development
indices, as well as the investment indicator, will
negatively affect demand for M1.

Third, all non-durable goods belong to "necessary"

goods for rural households, although their degrees of

135
"necessity" are different. Industrial producer goods are
the most "necessary" good, staple food is listed as the
second "necessity" one, while industrial consumer goods and
non-staple food are placed as the least "necessary" good for
rural households.

Fourth, money assets (M1) are a "luxury" demand for
households: as rural households' income rises by 10 percent,
the demand for M1 will increase by more than 22 percent.
That is, there will be an increasing desire of rural
households to hold money.

Fifth, demand for money assets (M1) may rise even if
actual cost or price of holding cash balances or demand
deposits increase which can be originated from decreases in
interest rates or increases in inflation rate.

Sixth, demands for home-produced staple food and
industrial producer goods are highly correlated, they appear
as substitutes for each other. Demands for staple food and
industrial consumer goods are complements, and so are the
demand of industrial producer goods and other market goods.

Seventh, rural households' demands for non-durable
goods interact with their demand for money. Increases in
the prices of non-durable goods tend to enhance households'
demand for money.

The high income elasticity of M1 demand is an important
feature and agrees with the neoclassical theory of money

demand; also the fact that money demand is positively

136
related with inflation rate and negatively with interest
rates are explainable by the established theory. Except for
these, the new discoveries in the thesis which have not yet
been explored by the conventional monetary theory are: (1):
rural households' demand for M1 is positively affected by
relative prices of specific non-durable goods which are
usually manipulated by government policy; (2): M1 demand is
negatively influenced by the rural economic developmental
level, rural households' fixed investment and demographic
variables.

Therefore, the major conclusion can be stated that
along with the process of rural economic development, there
exist two contradictory effects upon demand for M1: As
rural households' income level increases, on the one hand,
they have a strong drive to obtain M1; on the other hand, as
an upgrading of the monetized income level, the diversified
level of rural production activities, and an achievement of
fixed investment, rural households tend to hold less M1.
Besides, governmental relative pricing policies on specific
goods may exert positive impacts upon demand for M1.

Our findings have direct policy implications. In order
to inject an adequate money supply and to reach money market
equilibrium, other than emphasizing income and interest
rates the People's Bank of China (the Central Bank) has to
consider those respects: First, since rural money demand

consists of over 60 percent of the whole society's demand

137
for M1, the Central Bank of China needs to systematically
distinguish the money demand in rural areas and in cities.
Second, it must pay attention to the two contradictory
trends along with the economic development. A rise of the
rural income level will stimulate rural households to
allocate an increasing proportion of income upon money
assets, but upgrading of the monetized level of income
structure, the diversified level of rural production
activities and the rural household investment will decrease
the incentive of holding money. Third, the Central Bank
needs to coordinate its monetary policy with the pricing
policies conducted by the Department of Commerce, because
changes in relative prices of specific industrial and
agricultural goods tend to positively influence rural
households' demand for M1. That is, the empirical results
highlight the important roles of analyzing the rural
development level, the rural households' fixed investment,
demographic factors and relative price changes of specific
goods in the process of the monetary authorities' decision
of money supply; and the results indicate the requirement of
coordination of monetary policy and pricing policy.

Also, the results suggest that the combination of
pricing policies upon staple food and industrial producer
goods is crucial for enhancing the rural welfare and
development. For example, on the one hand, if government

increases prices of agricultural products, rural households

138
will reallocate their income from home-made agri-products to
industrial consumer goods, their welfare tends to rise; on
the other hand, if prices of industrial producer goods rise,
there will be a negative effect on households' expenditure
of both home-made agri-products and industrial goods.
Again, the monetary authorities' interest policy may

have a quite significant effect upon demand for goods. Any

.—

rise in interest rates by the Central Bank's manipulation
will hint an increase in inflation, so that the public tends
to expand the expenditure on non-durable goods.

Moreover, these analyses could be further employed to
discuss government rural policies such as a small scale
industry policy, demographic policy, and non-farming

employment policy.

139

APPENDIX

140
AP ENDI : Proof of the Corolary in Chapter 3.3:

According to Feenstra, the proof can be stated as
follows: Assuming that ¢t satisfies the theorem 1, then
define qt = ct+ ¢(ct, mt), or ct = W(qt, mt), where 0 < q
< w, and m > 0. Then checking the conditions (1) and (2) in
the theorem 2, we have:

1) W ( 0 , m = 0:

t)
2)Wq=l/(l+¢c);

-¢m/(1+¢C).

3) Wm

So that 0 < Wq < 1 and Wm > 0.

Since ¢ is a non-decreasing and continuous function of
Ct’ if qt = ct + ¢t for fixed mt > 0, then ct = W - w. Then
assume W satisfies the theorem 2, so ¢(ct, mt)-= qt — ct =
q(ct, mt) - ct. To check the conditions (1) and (2) in the

theorem 1, we get

4)¢(0.mt)=q(0.mt)=0:

5)¢c=q -1=(1/w

c ) - l > 0;

q
- ( Wm / Wq ) < 0.

6) «em = <1m

Now consider the relations between the second derivatives of
W and ¢:

7) differentiate 2) with respect to qt ,

 

141

2

wqq = - wq 40c / < 1 + 4C ) .

8) differentiate 2) with respect to mt ,

wqm = - wq d[ ¢m / ( 1 + 40 > 1 / do.

9) differentiate 6) with respect to qt ,

 

d< - Wm / wq > / dq = ¢mc / ( 1 + 40 )-

10) differentiate 6) with respect to mt , holding qt fixed,

d(- Wm / wq )/ dm = ( 1 + 4C ) d[ 4m / < 1 + 4C ) 1 / am.

11) use 8) and 10),

d[ ¢m / < 1 + 4c ) J / dc - [ < 1 + 4c ) / ¢m 1
.dt ¢m / ( 1 + 4c ) 1 / dm = - wmm / "m .

12) differentiate 6) with respect to m with c fixed,

t t
¢mm = d( ' Wm / Wq ) / dm + ¢m d( - Wm / Wq ) / dQ~

Thus, if the theorem 1 holds, it implies that the theorem 2

holds; and vice versa.

142
AP :

Table 21: Estimated Price Elasticities for Linear Models.

 

 

 

 

Staple Nonstaple Clothing_ Ag-input Money
LSl:
Staple -.6342 .8249 .2439 .6893 .9824
Nonstaple .4425 .2931 -.2295 .2242 -1.9550
Clothing .0622 -.1091 -1.2027 .1272 .8902
Ag-input -.1702 .1032 .1232 -.4812 .6632
Money .2998 -1.1121 1.0651 .8196 -.5809
LPIl:
Staple -.4400 .2158 .1886 .1482 .5616
Nonstaple .1009 -.6923 .1198 .0917 .3625
Clothing .0462 .0646 -.6516 .0437 .1682
Ag-input .0385 .0531 .0464 -.5049 .1351
Money .2544 .3588 .2968 .2212 -.2274
DMl:
Staple -.5941 .8400 .2401 -.7970 1.6150
Nonstaple .4529 .3945 -.2902 .3240 -6.4760
Clothing .0580 -.1368 -1.2028 .1156 2.2200
Ag-input -.1684 .1463 .1140 -.3027 1.1612
Money .2545 -1.2398 1.1475 .6600 1.4802

 

Table 22:

143

Estimated Income Elasticities for Linear Models.

 

 

Nonstaple Clothing 'Ag-input Money
.7940 .6643 2.9955
.7596 .5801 2.2460
.8008 .6100 6.0437

 

144

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