Consumer behaviour in India

European Economic Revilmw14 (19801 221--235. 0 North-Holland

CONSUMER

BEHAVIOUR

Publishing Company

IN INDIA

An Application of the Rottertlam Demand System K.N. MURTY* Institut fiir Agrariikonomie, Unirersitiit Giittingen, FRG Received May 1979, final version received February 1980

The purpose of this paper is to analyse the extent to which the observed data support the postulates of neoclassical theory of consumer behaviour. The absolute price version of the Rotterdam model has been estimated for rural and urban areas of India separately. The results indicate a trade off between theoretical consistency and goodness of fit. The symmetry, but not homogeneity, conditions are found to be empirically valid in rural India. All the other hypotheses are rejected both in rural and urban areas of India. Frequent violation of convexity conditions is also observed. The estimated marginal budget shares, income and price elasticities show marked differences in consumption patterns of rural and urban consumers in India. The effect of foodgrains price rise on the demand for various items is also analysed.

1. Introduction Until recently, the studies on consumer behaviour in India were mostly confined to the analysis of Engel curves and the choice of functional forms therein. * One important assumption underlying such studies is that the consumer’s purchases are mostly influenced by his level of income, often total expenditure, and are independent of other socioeconomic factors. The use of Engel elasticities for demand projection further assumes the stability of income distribution. In reality, these assumptions are rarely met with, and more so, all the Engel functions or even the partial demand relations developed later put together, do not satisfy the consistency conditions and cannot be integrated with general equilibrium models. These considerations have led to the development of Complete Demand Systems which, not only *I am grateful to Professor R. Radhakrishna for his invaluable help and guidance in the preparatiion of this paper. I would like to thank Hartwig de Haen, Klaus Frohberg and J.M. Debois for their useful suggestions on an earlier version. The comments of an anonymous referee have also improved the paper. However, the errors, if any, are mine. The empirical content of this paper is based on the author’s Ph.D. dissertation - Econometrics of Consumer Behaviour in India: A Study on Complete Demand Systems, undertaken at Sardar Pate1 Institute. Ahmedabad, India. The financial assistance from ICSSR, Delhi. is gratefully acknowledged. Finally, I would like to thank Iutta Ihle for typing the manuscript., I A comprehensive review of the studies on consumer behaviour in India, is given in Bhattacharya (1975).

222

K.N. Murty, Conswner behaoiour in Irtiiitr

take care of the above limitations, but also bridge the gap between theory and empirics in applied demand analysis. Though there has been a large number of studies on complete demand systems for the developed countries, there are only relatively few for the developing countries. 2 However, in India, the availability of National Sample Survey (NSS) data on consumer exqpenditure has stimulated a number of studies on the linear expenditure system [Bhattacharya (1967), Joseph (1968), Radhakrishna and Murthy (,1973), Radhakrishtna and Murty (1978)], the indirect addilog system [Radhakrishna and hrlurty (1978)], the quadratic utility function [Radhakrishna (1969), Mahajan (1972), Radhakrishna and Murthy (1975), Radhakrishna (1977)-J,comparison of the above three models [Radhakrishna, Murthy and Shah (197911, and flexible functional forms Gke

the indirect translog and the Rotterdam model [Murty (1978)]. Among them, the studies using time series data have clearly brought out the influence of prices on household consumption and the income elasticities. In addition, the fm studies using time series of cross-section data have highlighted the inadequacy of a single demand system for forging a link between income distribution and consumption patterns in India. However, it may be mentioned that the time series models are useful for demand projection at the mean level. which do not envisage changes in the income distribution. In spite of the existence of a large number of studies on complete demand systems for the developed countries, there appears to be no concensus on the choice of the model. However, it is generally felt that the additive models often tend to oversimplify reality and allow too little flexibility for the crossprice eff&cts. the quantification of which is one of the main objectives of’ estimating complete demand systemns.3 Further, in a complete demand system, several hypotheses derived from the neoclassical theory of consumer behaviour like adding-up. homogeneity, symmetry and negativity of Slutsky matrix of price eff&zts,are either implied by the specification of the model or imposed as restrictions in the estimation procedure. It is often unknown whether these restrictions are likely to be valid in reality. The main stimulus to test the empirical validity of these hypotheses came from the works of Theil (1965, 1967) and Barten (1967, 1968) on the Rotterdam demand system.4 Since then, there has been a number of ‘For an e%cellent suney of the work on consumer demand models, see Brown atld lI$eaton (1972) and more recently. Barten (1977). Lluch, Fowell and Williams ( 1977) have made an =kn&e stdy of the household demand and saving patterns for a few of the devellopdng axmtries. “In addition, a comparison of the descriptive and the predictiv? performance of varit-us amptie syae~ns has kkated that the non-additive models as a class, are in general, r,ot inferii to the additive class [Klevmarken (1979)]. %JO Otbef models Ofier8 used for this pwpose are the Constant Elasticity Model [court

W67)1 Barten W68, 197Oa,b), Goldberger and Gamaletsos (1970), Lluch (1971)] and the Direct and the Indirect Translog demitnd systems [Christensen, Jorgensorn and Lau (1975). Christensen and bkmer (1977)]. The fomxr allows us to impose the restrictions only at the sample mean, while the fatter cannot be used for testing the homogeneity restrictions.

applications of this model’ to various developed countries [Barten ( 1969). Parks (1969), Yoshihara (1969), Lluch (1971), Deaton (1974). Theil (1975). Barten and Geyskens (1975)]. In spite of the many differences in sources of data, methods of estimation, and types of test procedures used, the results indicate considerable uniformity between the studies. In a majority of these studies, a more restrictive hypothesis like the symmetry passed the test while the homogeneity could not. Being inequalities, the negativity restrictions are often used to verify the empirical results rather than as a testable hypothesis. Many studies indicate their violation in the absence of the homogeneity and symmetry conditions. Given the homogeneity and symmetry, the study by Barten and Geyskens (1975) has shown their validity. Almost all studies tend to reject the additivity hypothesis as too restrictive, even at a broad level of commodity aggregation. The purpose of the present study is to see whether the experience of a less developed country like India, supports the above evidence from thle developed world. As an important byproduct. we shall also analyse the effect of various hypotheses on parameters like the marginal budget shares. the income and price elasticities, and the cross-price elasticities of foojdgrains price on other commodities. In what follows, we shal discuss, briefly. the formulation and the estimation of the Rotterdam demand system. Section 3 deals with the empirical results. In section 4, we summarise the results of the tests of hypotheses and section 5 contains the conclusions of our study. 2. Rotterdam demand system

The basic idea underlying the Rotterdam model is to view the demand theory as a budget sharing process for the consumer. Accordingly, budget shares and the changes in them are of interest rather than the actual quantities consumed. Changes in value shares consist of three components: changes in income, prices, and quantity consumed. Since changes in income and prices are assumed to be given in demand theory, the only component behaviourally determined is the change in quantity consumed. With this as “The criticism often levelled against the empirical use of this model rests on the resuh that the model implies a too simple preference structure. viz. Cobb- Douglas for the consumer, if it has to be t’leoretically consistent [McFadden (1964)3. The supporters of the model, for example Barten (19691, argue that the available data are often very aggregative in nature. at twt on a household, and hence it is of little interest to look for the rmderlying utility function. Accordingly, it is argued that the model might be considered a reasonable approximation to reality in narrow ranges of income. In this context. Barnett (1979) argues that the Rotterdam model approximates reality under far more weaker conditions than the other flexible functional forms, like the translog.

K.N. Mutty. Consumer

224

bekwiour k India

guiding principle, Theil (1975) has developed the Rotterdam model extensively. Following Barten (1969), a typical equation of the absolute price version of tk Rotterdam demand model can be written as the

I?i,d IOg qi# =hiC~~~,dlOe4mr+CSindlOE

pht +Lii tl’i,.

k

k

i-1,2, . . .. iz, t=l,2 ,..., T,

(1)

where d stands for the first difference operator over time, qir and Pit are pectively the quantity consumed of, and the price paid for the ith mmmodity in period t. and \Cil is the average budget &are of the ith commodity in period t and t - 1. ai, hi, su (i, k = 1,2,. . ., n) are the parameters interpreted as the intercept!<, the income and the prke coefficients respectively. t:iris the residual caf the ith equation in period t. Using matrix notation. we can rewrite (1) as Y,=WY,+SZ,+a+

I&

t=l,2,...J

(2)

where

a, b are the n vectors of intercepts and income coeffbents,

and S is the n x n

matrix of income compensated price coefficients respectively. T is the II vector of unities. The general restrictions implied by the neoclassical theory of consumer behatiiour6 have the following form for the above demand system:

r’b= 1

(adding-up property),

(3)

so=0

(homogeneity property),

(4)

s=s

(Slutsky symmetry property),

(5)

(negativity property)

(6)

X”SX For all X +z.

so

p_ x being a real scalar. Further the decomposition

VW a comprehcnwe treatment of these restrictions, see for example, Bridge (1971).

of

substitution

effect into the general and specific components

would result ill

the relation S = C --.&bb’,

(71

where C is the matrix of the specific substitution effects with Cik as a typical element and b)=zCL In addition, if we postulate the additivity hypothesis (also known as groupwise independence), then C, I=0 for all i # k (i, k =1,2 ,..., n). 2.2. Estitnutiors The usual procedure is to estimate the Rotterdam demand model subject to the general restrictions and the a priori hypothesis viz. additivity. Though the model in (2) is linear in parameters, it becomes non-linear when the additivity restrictions are imposed. The best and the well known method to deal with non-linearities is the maximum likelihood method.’ There are five stages in the estimation procedure. In the first stage. wg estimate the model without imposing any restrictions. However, in view of the identity relations in the model, we have (fr- 1 )(]I + 2) free parameters to be estimated. Then the homogeneity conditions are imposed. These pun one restriction on each equation of the system. The symmetry conditions are the ones to follow. These are n(n- 1)/2 in number, and affect all the equations. Next, we impose the homogeneity and symmetry restrictions together. There are (JI- 1 )(n -2)/2 of them. Finally, we impose the additivity conditions. These restrictions leave 2rg- I independent parameters (including the IZ- 1 intercepts). All these five stages are repeated for the model in (2) without the intercepts. Thus, altogether, there are ten alternative specifications to be estimated and compared empirically. 3. Empirical results 3.1.

hta

India is one among the few countries for which a reliable time series of cross-section data on consumer expenditure are available. Since the inception of the planning era in 195Os, the National Sample Survey organisation has been conducting repetitive surveys, called rounds, to collect. various types of ‘We follow the procedure indicated in Bartcn (1969). Under the symmetry and the additivity hypotheses, the covariance matrix of residuals obtained in the previous iteration was used to estimate a new set of parameters. The iterations are continued until convergence is obtained. This procedure is, thus, similar to Zellner’s iterative Aitken’s estimation for seemingly unrelated regressions. Mmenta and Gilbert (1968) have shown that such an estimator has the small sample properties as well. The computer programme for the estimation of the Rotter-dam model has been developed on an IBM,‘360 computer by the author himself.

216

K.N. Mzzrt_t-. Cfzfzszfzzz~r hehaziour irzlzzdili

tioeconomic information, including household consumption expenditure on a number of items. The data are usually published with rural-urban stratification, and according to 12 or 13 per capita monthly expenditure classes. In addition, the mean level data are also made available. Thus, two types of expenditure data - a time series, consisting of only the mean level expenditures, and a time series of cross-section - are distinguishable, separately for rural and urban areas of India. To reduce the computational burden, we have aggregated the published data to form the six commodity groups: (i) Foodgrains, (ii) Milk and milk products, (iii) Other food, (iv) Clothing, (I’) Fuel and light, (vi) Other non-food. We have limited our analysis to the years 1951-1966,

covering the rounds (2-20) in rural India and the rounds (3-20) in urban India.’ In order to utilise fully this expenditure data, we need a corresponding set of retail prices. In the (absence of a reliable retail price series collected by the

SS or any other source. uve are constrained to use‘ the wholesale price indicts.’ published by the office of the Economic Adviser.” The price indices have 19524953 as base, with the base year prices as unity. Though separate

prk

series are available for the rural and urban areas of India, we still have ta use the same set of prices for all expenditure classes, ignoring the price difces due to quality variation within a year. This permits us to use only the time series data for the Rotterdam demand system.’ 1

FQ~ judging the goodness of fit of the model estimated under specifications. we have used two measures - y2, defined as the correlation coefficient between the observed and the expected value and Theirs average information inaccuracy [Theil (1965)]. A

different squared shares,* 2

grouped distribution of r’ is presented in table 1. The table indicates that the overall goodness of Iit is satisfactory - of the total 120 equations estimated, 36 “Few u&the rounds pricerto 14th are of 3 !o 9 months duration. This has been made one year in subsequent rounds to avoid seasonal fluctuations in consumption. 9,4 comparison of the wholesale and the retail prices for a particular state, viz.. Gujarat has. Wewzr. shown strong collinearity between the two series. ‘% of5i of the Economic Adviser publishes monthly price indices for 112 commodities by cokctiog 555 price quotations scattered over 143 markets. These detailed price data are a~egated suitably by taking the NSS 13th rounds expenditure shares as weights. r“In Murty (197gk an attempt to use the fuller data base has been made by regrouping the SSS expenditure classc~ into three broader groups z-i=. lower, middle, and higher. The percentage population has been used as weight to aggregate the per capita expenditures. “?he reason for the choice of t2 instead of the usual multiple correlation coefficient, is that the latter can become negative for some commodities in a simultaneous system of equations, non-linear in parameters. However, in linear models, both the measures are identical. Even in the non-linear models, r instead of the 9, might be useful to judge the direction but not the kd of m - ment. between the observed and the expected value shares. I am thankful to K Frohbc+ ?‘orpointing out this to me.

K.N. Murty, Consumer

hehuriour

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227

(307;) equations have r2 greater than 0.70 and 55 (46 “/,/,)have r2 between 0.70 and 0.40. In the first category, the frequency decreases as we move from the unconstrained model to additive type. It can be seen that the explanatory power of the model suffers with the imposition of any restriction. Among the hypotheses, homogeneity seems to cause less reduction in r2 compared to symmetry and additivity. The average information inaccuracy also confirms this.’ 3 Table 1 Frequency distribution of the r2 under different model specifications.

Unconstrained Homogeneity Symmetry Homogeneity and symmetry Additivity Overall

r2 > 0.70

0.70 2 I’?2 0.40

13 10 6

9 12 12

2 2 6

24 24 24

4 3 36

14 8 55

6 13 29

24 24 120

0.40 > P2

Total -__

3.3. Mwgirxrl hudgvt shtrws Estimates of the marginal budget shares, also known as the income coefficients, under different model specifications are given in table 2. one broad feature of the estimates is their insensitivity to the model specification. The marginal budget shares of foodgrains, milk and milk products, and other non-food items in rural areas; foodgrains, milk and milk products, and other food items in urban areas, tend to increase with the imposition of the restrictions. The results also bring out the rural-urban differences in consumption patterns. More specifically, a rural consumer spends about 67”, of his marginal income on food and 33 7;; on non-food items; while an urban consumer spends only 477; and 537; on these two groups respectively. Tihe commoditywise differences are, however, more pronounced. For example. 29 y< of the marginal income of a rural conv\lmer is spent on foodgrains, whereas it is only 9 qd for an urban consumer.

The expenditure elasticities broadly reflect a pattern similar to that of the income coefficients. Since the model is estimated using time series data, the elasticity estimates reflect. mostly, the short-run effect and in general. are higher than the corresponding cross-section estimates for all food and sane 13The parameter estimates along with the goodness of fit measures are contained in an ear\iler version of this paper [Murty (197911.

K.N. Murty. Conswncr behwiour

228

in lttdia

Table 2 Estimates of the marginal budget shares.”

Unccnstrained

Homogeneity

Symmetry

Homogeneity and symmetry

Additivity

0.2314

0.2455

0.2857

0.2876

0.2448

(2) Milk and milk products

0.1103

0.1046

0.0854

0.0934

0.1228

(3) Other food

0.3342

0.3133

0.3046

0.2P 90

0.2528

(4) Clothing

0.1122

0.0888

0.1106

0.0984

0.1063

(5) Fuel and light

0.1131

0.1014

0.1017

0.0956

0.0774

(6) Other non-food

0.0988

0.1464

(11.062 1

0.1351

0.1959

0.0185

0.053 1

0.0911

0.0899

0.1165

(2) Milk and milk products

0.0691

0.0560

0.0938

0.0827

0.0868

(3) Other food

0.2253

0.2348

0.2946

0.2964

0.2838

(4) Clothing

0.1442

0.1602

0.0686

0.08 19

0.0733

(5) Fuel and light

0.0563

0.0527

0.0579

0.0593

0.0685

(6) Other non-food

0.4266

0.443 1

0.3720

0.3898

0.3711

Commodity

FO”P Rural lndia (1) Food-

grains

Crbun lndiu (1) Food-

grains

‘Estimates correspond to the w&h intercepts model.

non-food items. More specifically, in rural areas, the estimates of expenditure elasticities for other food and fuel and light are higher; while they are lower for clothing and other non-food. br urban areas, they are closer to the crosssection estimates for most of the items. One striking feature of the estimates is that the expenditure elasticities are remarkably insensitive to the model specification in both the areas (table 3). Howem, the symmetry and the additivity restrictions have some effect on these estimates. Under the additivity, the expenditure elasticities for other focHiand fuel and light in rural areas, clothing and other non-food in urban areas have declined; while they have increased for milk and milk products and other food in urban areas.

K.N. Murty, Covrsumcr bekariour

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229

‘Table 3 Estimates

of the total expenditure

elasticities.” -

Unconstrained

Homogeneity

metry

Homogeneity and symmetry

(1) Foodgrains

0.5662

0.6007

0.6990

0.7038

0.5990

(2) Milk and milk products

1.5313

1.4527

1.1855

1.3096

1.7053

(3) Other food

: .6683

1.5638

1.5205

1.4426

1.2618

(4) Clothing

Z.3529

1.0709

1.3329

1.1865

1.2808

(5) Fuel and light

!..8130

1.6254

1.6311

1.5324

1.2421

(6) Other non-food

4I.5692

0.8432

0.3575

0.7780

1.1282

( 1) Foodgrains

0.33 16

0.2242

0.3846

0.3797

0.4920

(2) Milk and milk products

0.7408

0.6006

1.0063

0.8873

0.9310

(3) Other

0.8814

0.9187

1.1523

1.8594

1.1103

(4) Clothing

2.0113

2.2346

0.9561

1.1417

lo’>29 . _

(5) Fuel and light

c.9309

0.8710

0.956 1

0.9806

1.1322

(6) Other non-food

1.5119

1.5706

1.3184

1.3815

1.3151

Commodity group

Sym-

Additivity

Rural lndiu

Urban Indiu

food

*‘Estimates correspond

to the with intercepts model.

can be expected from a flexible demand system like the Rotterdam model, the price elasticit’ s are more sensitive to the model specification. In both the areas. the range of variation for the own price elasticity of foodgrains is small compared to other items (table 4). It can also be observed that foodgrains, milk and milk products, and clothing in rural areas; fooAgrains, milk and milk products, and fuel and light in urban areas. have numerically smaller estimates under the additivity assumption. Foodgrains cross-price effects are dominant and are sensitive to the model specification in both the areas (table 5). In almost all specifications of the model, other items have negligible cross-price effects on the demand for foodgrains. The model under the additivity specification, tends to underestimate the foodgAs

EER

D

K.N. Murty, Consumer bekaviour in India

230

Table 4 Estimates of the own price elasticities. _

Unconst’rained

Homo- : geneity

Symmetry

Homogenei ty and symmetry

Additivity

-0.6063

-0.6130

-0.5012

- 0.4408

- 0.5375

(2) Milk and milk products

- 2.393 1

- 2.2822

- 2.3059

- 1.5567

- a.0905

(3) Other food

- 0.2545

- 0.3848

- 0.3570

- 0.4334

- 0.8627

(4) Clothing

- 1.5237

- 0.9998

- 1.4041

- 0.3634

- 0.8468

(5) Fuel and light

-0.3165

- 0.3839

- 0.5876

- 0.3562

-0.8188

0.2121

0.7161

2.9135

0.5099

- 0.7828

- 0.5251

- 0.5957

- 0.4230

- 0.3954

- 0.4041

(2) Milk and milk products

- 1.1631

- 0.9620

- 1.5590

- 1.2547

- 0.6494

(3) Other food

- 0.7276

- 0.6876

- 0.5696

- 0.5566

-0.8100

(4) Clothing

- 0.5944

- 1.3913

- 0.6277

- 0.7006

(5) Fuel and light

- 1.6173

- 1.6180

- 1.5693

- 1.5358

- 0.7664

(6y Other non-food

- 0.7198

- 0.9603

-0.8170

- 1.4334

-0.9184

Commodity SouP Rural’ lndia cl) Food-

grains

(6) Other non-food Urban India (1) Food-

grains

0.6579 -

“Estimates correspond to the with intercepts model.

rains cross-price effects, particularly on milk and milk products, clothing and fuel and light items in both the areas. 4. Tm

of hypohses

In the preoeding section, we have presented twenty different specifications

of the Rotterdam model - ten each for the rural and the urban areas of India. The five types of hypotheses - no constraints, homogeneity, symmetry, homogeneity and symmetry, and additivity, each with two variants, viz., with and without intercepts - constitute these ten specifications. It

K.N. Murty, Consumer behaoiour in India

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Table 5 Estimates of the cross-price elasticities.”

Commodity group

Unconstrained

Homogeneity

Symmetry

Homogenei ty and symmetry

Additivity

Rural Indiu (2) Milk and

1.5597

1.3298

0.3767

- 0.4898

- 0.4269

- 0.4428

-0.3159

-0.7916

- 0.3206

- 0.7077

-0.3109

milk products (3) Other food

-0.1849

- 0.0402

- 0.43 50

(4) Clothing

-2.1182

- 2.3051

0.1855

(5) Fuel and light

- 1.0308

- 0.8586

(6) Other non-food

0.5091

-0.0061

-0.1902 0.4473

0.0300

- 0.2824

Urban India (2) Milk and

0.9752

1.3741

-0.2215

- 0.2759

-0.1487

-0.0150

- 0.0085

- 0.0074

-0.1773

milk products (3) Other food

0.1259

(4) Clothing

- 2.1654

- 0.9783

- 1.0-55

- 0.7924

-0.1634

(5) Fuel and light

- 0.2007

-0.2167

-0.1366

-0.0191

-0.1808

(6) Other non-food

-0 8148

- 0.4847

-0.3134

0.2Ml

-0.2100

aPercentage change in the quantity demanded of different items corresponding rise in the price of foodgra$s. Estimates correspond to the with intercepts model.

to a 1 T,,

would be difficult to test all the alternatives pairwise. Therefore, we will attempt some important comparisons only. Table 6 shows the concentrated logarithmic likelihood values together with the degrees of freedom, separately for the rural and urban areas of India. The likelihood values show a declining trend as we move from a less restrictive model to a more restrictive type. The likelihood ratio test can be employed to verify the empirical validity of a more restrictive hypothesis against a less restriciive alternative. It is welil known that twice the difference between the maximum likelihood value for a less restrictive model and the corresponding value for a more restrictive one, is asymptoticaily distributed as a chi-square under the null hypothesis of the more restrictive model. The degrees of freedom of the chi-square statistic, is the difference in the number of unrestricted parameters. The chi-square values together with

K.N. Murty, Consumer behaciour in India

232

Table 6 Concentrated logarithmic likelihood values.”

Unconstrained

Homogeneity

Symmetry

Homogeneity and symmetry

Additivity

With inter-

347.220

cepls

(40)

340.282 (35)

340.137 (25)

328.0701 (20)

317.881 (111

Without intercepts

338.677 (35)

336.246 (30)

331.535 (201

325.2 19 (15)

314.116 (6)

With tnter-

345.103 (40)

339.919 (35)

325.222 125)

320.642 (20)

306.117 (11)

Without

341.286 (35)

332.757 (30)

322.708 (20)

3 18.975 (15)

303.468 (6)

Rural lndia

Urban Indict

intercepts

“The figures within parentheses are the degrees of freedom.

the degrees of freedom for five important pairs of hypotheses are given in table 7. To facilitate a quick reference, the chi-square table values for 5, 9, 10, 15, and 20 degrees of freedom at 5 ?A level of significance, are also provided at the bottom of the table. Broadly, the following conclusions emerge from the tests of hypotheses. In rural areas, the symmetry conditions passed the test, while the homogeneity could not. The only exception seems to be the model under the homogeneity specification without intercepts. In urban areas, all the hypotheses are rejected, except for one case of acceptance of the model under the homogeneity specification with intercepts. In both the rural and the urban areas of India, the additivity hypothesis appears to be empirically not valid at the sixcommodity aggregation level. Thus, the experience of a developing country like India, shows a pattern similar to that of the developed countries with regard to the empirical validity of various hypotheses implied by the neoclassical theory of consumer behaviour.

The following conclusions emerge from the application of the Rotterdam demand system for analysing the consumer behaviour in India. The results indicate that the overall goodness of lit as measured by the quasi-K2 and the average information inaccuracy, is satisfactory. However, it is clear that the explanatory power of the mcgdel decreases with the imposition of any theoretical restriction in gene.raf. symmetry and additivity in particular*. This

K.N. Murty, Conmtner

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in lmiicl

233

?‘a ble 7

Chi-squart c,tatistic values.”

Homogeneity us No con-

Symmetry ~7s No con-

Homogeneity and symmetry cs No con-

straints

straints

straints

Homogeneity

Homogeneity and symmetry

13.876

38.300 (20)

0.290 (10)

20.378 (9)

Symmetry cs Additivity t’s

Rural India With intercepts

(5)

14.166 (15)

Without intercepts

4.862 (5)

14.284 (15)

26.916 (20)

9.422 (10)

22.206 (9)

10.368 (5) 17.058 (5)

39.762 (15) 37.156 (15)

48.922 (20) 44.622 (20)

29.394 (10)

29.050 (9)

20.098

31.,014 (911

U rbm

In&u

With intercepts Without intercepts &O.OS) = 11.070,

j$O.OS)= 16.919. &(OOS)= 18.307,

&(0.05)=24.996,

&-,(0.05)=31.410.

--

“The figures within parentheses

(10) .-

are the degrees of freedom.

shows that these hypotheses are res:rrictive from both the statistical and the analytical considerations. The estimated marginal budget shares indicate that the expansion of demand for food items, comprising mostly the agricultural commodities, depends mainly on the income of ruit.4 households, whereas for the manufactured items, it depends on the income of urban consumers. Thus, the effect of any new income generating policy on the various sectors, would depend on to whom the additional income accrues. If the policy favours the rural rich or the urban middle and the higher income groups, then there would be an excess demand pressure on the sector producing. mostly the non-food items.” Among the price effects, the foodgrains cross-price effects are dominant in all the model specifications. This indicates that any change in the price of foodgrains would result in the expansion of demand in some sectors and shrinkage in others. This includes both the direct effect due to the changes in the real income and the relative prices, as well as an indirect $fect through changes in the ircome distribution.‘” This mig ht._possibly explain the often “For a detailed analysis of the consumption patterns over difl’erent expenditure groups. see Radhakrishna and Murty (1978). “The cross-price effects of foodgrains price on various items differ marhedly between the expenditure groups. The development implications of changes in *ti,odgrains price and tbtuations in the agricutural output, has been analysed in Radhakrishna (1978).

K.N. ;M~rrty,Consumer behatjiout iq lndia

2-34

observed phenomenon of inflation in some sectors and recession in others, due to fluctuations in the agricultural output, mostly foodgrains, caused by

the monsoon.

Barrett, W.A., 1979.. Theoretical foundations for the Rotterdam model. Review of Economic studies 46.109-130. Barten, A.P; 1967, Evidence on the Slutsky conditions *for dlemand equations, The Review of Economics and Statistics 49. 77-84. Barten, A.P., 1968, Estimating demand equations, Econometrica 36, 213-251. Barten, A.iP., 1969, ‘Maximum tikelihood estimation of a compjetc system of demand equations, European Econcrmic Review 1, 7-73. Barren. A.!f?, 1977, The syste-m of consume! demand function approach: A review, Econometrica 45, no. t. 23-51. Barten. A.P. and E. Geyskens. 1’975,The negativity conditior. in consumer demand, European Economic Review 6,227-260. Bhattacharya, N, 1967, Consumer behaviour in India - An application of linear expenditure system, Economic and Political Weekly 2. no. 47, 2093-2098. Bhattacharya. N, 1975, Studies on consumer behaviour in india, Mimeo. (Indian Statistical Institu& Calcutta). Bridge, AL., 1971, Applied economics (North-Holland, Amsterdam). Brown, J.A.C. and A. Deaton. 1972, Surveys in applied economics, models of consumer behaviour, The Economic Journal 82,1145- 1236. Byron. R-P.. 1%8, Methods for estimating demand equations using prior information: A series of experiments with Australian data, Australian Economic Papers 7, 227- 274. Byron. R.P., 197Oa, A simple method for estimating demand systems under separable utility assumptions, Review of Economic Studies 37,261-274. Byron, R-P, 197&, The restricted Aitken estimation of sets of demand relations, Econometrica 38,816830. Chm L.R.. D.W. Jorgenson and L.J. Lau, lb72; Transcendental logarithmic utility function., A-can Economic Review 65, 367-382. Christensen, L.R. and M.E. Manser, 1977, Estimating U.S. consumer preferences for meat with a ilexiMe utility function, Journal sf Econometrics 5, 37-54. Court, R-H, 1967, Utility maximisation and the demand for New Zealand meats, Econometrica 35,424-446. Deaton, A-S, 1974, The analysis of consumer demand in U.K. 1900-1970, Econometrica 42, 34 I-367. Goldberger, AS. and T. Gamaletsm, 1970, A cross-country comparison of consumer expenditure patEuropean Economic Review 1,357-400. Jose@, P, 1968, An application of linear expenditure system to NSS data -- Some further results+ Economic and Political Weekly 3. K&ken, N.A.. 1979, A comparative study of complete systems of demand functions, Journal of Econometrics 10,161-191. K-W J. and R-F. Gilbert, 1968, Smlall sample properties of seemingly unrelated regressions, Joumal of the American Statistical Association 63, 1180-1200. wuch, C, 1971, Consumer demand functions - Spain 1958-1964, European Economic Review 2,277--302. Liuch, C-, A.A- Powell and R-W. Williams, 1977, Patterns in household demand and saving (OxTord University Press, New York]. Mahajan, B-M.. 1972, Econometrics of consumer behaviour in Indii with articulation of methods for approximate determination of indifference surfaces, Ph.D: thesis (University of Poona, Poona). McFadden, D-C., 1964, Existence conditions for Theil-type preferences, Discussion paper (Depaftmt of Economics, University of California, Berkely, CA). l

K.N. Murty, Cortsumer behaoiour

in India

235

Murty, K.N., 1978, Econometrics of consumer behaviour in India -- A study on complete demand systems (Gujarat University, Ahmedabad). Murty, K.N., 1979, Consumer behaviour in India - An application of the Rotterdam demand system, Unpublished discussion paper (Institut fur Agrarijikonomie, Universitlt Giittingen). Parks, R.W., 1969, Systems of demand equations: An empirical comparison of alternative functional forms, Econometrica 37, 629--650. Radhakrishna, R., 1!)69, An analysis of consumption patterns in India with an application of Wald’s method o! determination of indifference surfaces, Doctoral dissertation (University of Poona, Poona). Radhakrishna. R., 1977, Approximate determination of indifference surface, Artha Vijnana 19. Radhakrishna, R., 1978, Demand functions and their development implications in a dual economy: India, The Developing Economics XVI, no. 2. Radhakrishna, R. and G.V.S.N. Murthy, 1973, Some results on the estimation of alternative demand systems for India, Paper presented at the 13th Indian Econometric Society meeting. Radhakrishna, R. and G.V.S.N. Murthy, 1975, Estimation of indifference surfaces under block independence specification, Paper presented at the 3rd World Congress of the Econometric Society. Radhakrishna, R., G.V.S.N. Murthy and N.C. Shah, 1979, Models of consumer behaviour for the Indian economy. Mimeo. (Satdar Pate1 Institute of Economic Br Social Research. Ahmedabad). Radhakrishna, R. and K.N. Murty, 1978, Food demand model for India, Mimeo. (Sardar Pate1 Institute of Economic & Social Research, Ahmedabad). Theil, H., 1965, The information approach to demand analysis, Econometrica 33. 67.-87. Theil, H., 1967, Economics and information theory (North-Holland. Amsterdam). Theil, I-I., 1975, Theory and measurement in consumer demand, Vols. 1 and 2 (North-Holland. Amsterdam). Yoshihara, K., 1969, Demand functions: An application to the Japanese expenditure pattern. Econometrica 37, 257 -274.