Conditional and unconditional food demand elasticities in a dynamic ...

Applied Economics, 2003, 35, 503–514

Conditional and unconditional food demand elasticities in a dynamic multistage demand system S T A T H I S KL O N A R I S * and DA V I D H A L L A M{ * Research Assistant, Agricultural University of Athens, Iera Odos 75, 118 55 Athens and { Chief – Raw Materials, Tropical and Horticultural Products Service Commodities and Trade Division, Food and Agriculture Organisation of the United Nations, Viale delle Terme di Caracalla, 00100 Rome, Italy

This paper estimates conditional and unconditional demand elasticities in a three stage analysis of consumer demand for food and non-food items in Greece. A dynamic version of the AIDS model is specified and estimated, and full system misspecification tests applied. Correction formulas for price and expenditure elasticities are used to calculate unconditional elasticities from conditional demand subsystems. All food items rank as price inelastic. Deviations between the calculated conditional and unconditional price and expenditure elasticities are found to be significant, demonstrating the importance of correcting conditional elasticities before they can be used for policy purposes or welfare analyses.

I. INTRODUCTION Demand analyses typically assume weak separability. This implies that commodities can be partitioned into groups, where the change in price of a commodity in one group affects the demand for all commodities in another group in the same manner. The partitioning will often also assume, at least implicitly, a multistage decision process. Separability leads to the specification of conditional demand systems providing the necessary and sufficient condition for conditional demand functions. However, while the number of estimated parameters is reduced, in empirical applications of multistage budgeting and conditional demand systems prior stages of expenditure allocation are typically unspecified or ad hoc, which limits the value of the resulting elasticity estimates. Studies of the demand for meat, for example (Cashin, 1991; Chalfant et al., 1991; Chen and Veeman, 1991; Burton and Young, 1996), have modelled demand for different types of meat under weak separability assumptions as a function of prices of these meat aggregates and of total meat expenditure, ignoring

prior stages of total budget allocations, and neglecting interrelationships with commodities in other sub-systems. However, from a multistage budgeting perspective, a change in the price of one meat will not only have a direct effect on the demands for each meat within the meats subsystem: it will also change the price index for meats and hence expenditure allocations to the meats and other groups in the previous budgeting stage, and cause further indirect changes within the meats sub-system. The total effect of the price change is the sum of direct and indirect effects at the various stages. Conditional elasticities estimated from conditional demand functions within a subsystem will therefore generally differ from unconditional elasticities calculated from a demand system that includes all goods. While the latter are arguably most relevant in welfare analyses and for policy purposes, most empirical studies focus on just one commodity group, which constitutes only one part of one stage of a multistage analysis, and fail to consider the implications of multistage budgeting for estimates of price and income elasticities. The relationships between conditional and unconditional

* Corresponding author. Applied Economics ISSN 0003–6846 print/ISSN 1466–4283 online # 2003 Taylor & Francis Ltd http://www.tandf.co.uk/journals DOI: 10.1080/00036840210148058

503

504

S. Klonaris and D. Hallam

elasticities in multistage demand systems have been explored by Edgerton (1997). For practical empirical work, two questions are of interest: first, whether differences between conditional and unconditional elasticities can be expected to be large; and second, how conditional elasticities might be corrected by the use of estimates from a multistage demand system. This study addresses these questions in the context of an analysis of food demand in Greece. Previous studies (Mergos and Donatos, 1989a and 1989b, for example) have focused on only one budgeting stage. Improved and more comprehensive estimates of Greek food demand elasticities are a further objective of this study. Unconditional price and expenditure elasticities for foods are estimated using a dynamic version of the AIDS model proposed by Alessie and Kapteyn (1991). In the next section the dynamic AIDS model is discussed, and formulae used for calculation of unconditional elasticities presented. The data set and the estimation method are discussed next. Finally, the empirical results of the application to a three-stage budget process for demand in Greece and the estimation of conditional and unconditional elasticities are discussed and some conclusions drawn.

II. MODEL SPECIFICATION AND ELASTICITY FORMULAE The ith equation of the Almost Ideal Demand System first proposed by Deaton and Muellbauer (1980) is written as: X wit ¼
i þ ij ln pjt þi ðln mt  ln Pt Þ ð1Þ j

where for observation t, wit is the budget share of the ith good, pjt is the price of commodity j, mt is total expenditure on the goods in the system, and Pt is a translog price index defined by n X n 1X  ln pjt ln pit ð2Þ 2 j¼1 i¼1 ji i¼1 P P The i
i ¼ 1, k i ¼ 0, P adding-up condition implies  ¼ 0, while the homogeneity and symmetry restrici ij P tions can be enforced by imposing j ij ¼ 0 and ij ¼ ji respectively. This static model assumes instantaneous adjustment to equilibrium which may be inappropriate where there is habit persistence or adjustment costs, or where expectations may be incorrect and real price changes misinterpreted. Dynamic adjustment to price and income changes is more plausible. The widespread incidence of serially correlated residuals in empirical demand studies may be evidence of dynamic misspecification in the basic AIDS model. Deaton and Muellbauer (1980) proposed using

ln Pt ¼
0 þ

n X


i ln pit þ

first differences to avoid these autocorrelation problems. A dynamic demand system consistent with cost minimization, requires the expenditure function to be adapted to allow for adjustment costs. Most commonly, this has been done by modifying the intercept term of the share equations
i (Blanciforti and Green, 1983; Blanciforti et al., 1986; Assarson, 1991; Alessie and Kapteyn, 1991; Edgerton et al., 1997), or the price index
0 (Ray, 1984). Blanciforti and Green’s (1983) approach, was used by Mergos and Donatos (1989b) and Karagiannis and Velentzas (1993) to incorporate linear habit formation in models of Greek consumption behaviour. Molina (1994) applied the habit persistence AIDS proposed by Blanciforti et al. (1986) to Spanish data. However, none of these models satisfy the adding up restriction. According to Alessie and Kapteyn (1991), the modification suggested by Blanciforti and Green (1983) (
i ¼
i þ
 i wit1 ) does not satisfy the theoretical requirements of utility theory, since imposition of the adding up restriction implies
 i ¼ 0, i ¼ 1; . . . ; N. Therefore, either there is habit formation and violation of the adding up restriction, or the adding up restriction is valid and there is no habit formation. The alternative formulation proposed by Blanciforti et al. (1986), also fails to satisfy the adding up restriction unless the additional restriction that the coefficient of the lagged budget share is the same for all the equations is imposed. Assarson (1991) related the
i parameters of Equation 1 to not only on its own past consumption level but also those of other items. Earlier, Ray (1984) developed a generalized dynamic AIDS model which allowed all the parameters in each equation to depend on the past aggregate consumption. The latter is not feasible in the current study with available data. Here, the intercept is specified as X
i ¼
i þ dij wjt1 ð3Þ j

After the substitution of the
i parameters in Equation 1 and Equation 3 the expenditure function is represented by X X wi ¼
i þ dij wjt1 þ ij log pjt þ i log fmt =Pt g ð4Þ j

j

P

where j dij wjt1 represents the aggregate consumption level laggedPone period. up condition is satisfied P ThePadding P  when i
P ¼ 1;  ¼  ¼ i i i i ij i dij ¼ 0. The additional restriction j dij ¼ 0 is imposed to enable identification of the system. The dynamic price index Pt is given by ln Pt ¼
0 þ

n X i¼1

þ


i ln pit þ

XX i

n X n 1X  ln pjt ln pit 2 j¼1 i¼1 ji

dij wjt1 ln pit

j

ð5Þ

505

Food demand elasticities

Fig. 1. Commodity partitioning

A linear version of the dynamic AIDS model in Equations 4 and 5P is obtained by using Stone’s price index ðln Pt ¼ ni¼1 wit ln pit Þ proposed by Deaton and Muellbauer (1980). However, the adequacy of this approximation depends on the degree of collinearity between Stone’s index and the exact price index Equation 5.1 The translating mechanism suggested above can be interpreted as the way subsistence expenditures vary according to the previous consumption patterns, since
i represents the budget share for the ithP good P when expenditures are at subsistence level. The term i j dij wjt1 ln pjt can be interpreted as the cost of habits. The short-run own-price, cross price and expenditure elasticities in period t are calculated according to expressions suggested by Goddard (1983) and by Chalfant (1987): eiit ¼

ij  i wi 1 wi

ð6Þ

eijt ¼

ij  i wi wi

ð7Þ

 Ei ¼ 1 þ i wi

ð8Þ

The deviations of the above formulae from the corrected ones proposed by Green and Alston (1990) when the linear approximation of the AIDS model is used, are minor for this data set (Klonaris, 1999). As noted above, where weak separability and multistage budgeting are assumed, unconditional and conditional elasticities for a particular commodity may be significantly different. However, Edgerton (1997) has derived general 1

formulae for the calculation of total expenditure and price elasticities under multistage budgeting. Under weak separability, total utility is a function of the sub-utility functions for each commodity sub-group U ¼ f fðuA ðqA Þ; uB ðqB Þ; . . . ; un ðqn Þg

ð9Þ

where f is an increasing function of the sub-utility functions un ðqn Þ and qn is a vector of quantities contained in the nth sub-group. Weak separability is a necessary condition for multistage budgeting where expenditure is allocated between groups using price indices, and within group allocation is performed independently. These allocations should be ‘perfect’ in the sense that the results of a multistage budgeting should be identical to what would occur if the allocation were made in one step. In the case of two groups, A and B, containing s and r goods respectively the unconditional demand function for good i in group A is qAi ¼ f ð pA1 ; pA2 ; . . . ; pAs ; pB1 ; pB2 ; . . . ; pBr ; mÞ

ð10Þ

where pAs and pBs are the prices of s and r in groups A and B, and m is the total expenditure. In two-stage budgeting, allocation of expenditure takes place in two independent steps. In the first, total expenditure is allocated between the two broad groups of commodities qA ¼ gA ðPA ; PB ; mÞ

ð11Þ

where qA is expressed in real expenditure (at base year prices) and the PA and PB are true cost of living indexes defined as PA ¼ cA ðuA ; pA1 ; pA2 ; . . . ; pAs Þ= cA ðuA ; p0A1 ; p0A2 ; . . . ; p0As Þ where cA denotes the cost function associated with group A, uA the corresponding utility and

In the authors’ case the degree of collinearity between actual and approximated price indices are high since the correlation coefficients for the five sub-systems under consideration are between 0.64 and 0.98.

506

S. Klonaris and D. Hallam

Table 1. Estimation Results: Stage 1 (standard errors in parentheses). 1st Stage

Food

Clothing and footwear

Housing

Durable household goods

Medical and personal care

Education and recreation

Transportation and communication

Other goods and services


i

1.5416 (0.6497)

71.8869 (0.6635)

1.0880 (0.2355)

70.3380 (0.3643)

70.3568 (0.1960)

70.2596 (0.3473)

0.7038 (0.5318)

70.4921 –

i1

0.1656 (0.0291)

70.0261 (0.0124)

70.0510 (0.0088)

70.0014 (0.0136)

0.0049 (0.0081)

70.0407 (0.0129)

70.0484 (0.0210)

70.0029 –

i2

70.0261 (0.0124)

0.0373 (0.0124)

70.0057 (0.0057)

70.0288 (0.0089)

0.0005 (0.0047)

70.0083 (0.0072)

0.0285 (0.0104)

0.0028 –

i3

70.0510 (0.0088)

70.0057 (0.0057)

0.0916 (0.0072)

0.0044 (0.0070)

70.0110 (0.0043)

70.0011 (0.0058)

70.0227 (0.0079)

70.0045 –

i4

70.0014 (0.0136)

70.0288 (0.0089)

0.0044 (0.0070)

0.0387 (0.0138)

0.0143 (0.0060)

70.0003 (0.0086)

70.0268 (0.0113)

70.0001 –

i5

0.0049 (0.0081)

0.0005 (0.0047)

70.0110 (0.0043)

0.0143 (0.0060)

70.0113 (0.0050)

0.0072 (0.0050)

70.0043 (0.0071)

70.0003 –

i6

70.0407 (0.0129)

70.0083 (0.0072)

70.0011 (0.0058)

70.0003 (0.0086)

0.0072 (0.0050)

0.0272 (0.0106)

0.0176 (0.0107)

70.0017 –

i7

70.0484 (0.0210)

0.0285 (0.0104)

70.0227 (0.0079)

70.0268 (0.0113)

70.0043 (0.0071)

0.0176 (0.0107)

0.0564 (0.0208)

70.0003 –

i8

70.0029 (0.0062)

0.0028 (0.0037)

70.0045 (0.0030)

70.0001 (0.0043)

70.0003 (0.0025)

70.0017 (0.0042)

70.0003 (0.0051)

0.0069 –

i

70.0753 (0.0106)

0.0210 (0.0099)

70.0066 (0.0037)

0.0086 (0.0058)

0.0086 (0.0031)

0.0129 (0.0054)

0.0338 (0.0083)

70.0029 –

w1ðt1Þ

0.0202 (0.6492)

1.6605 (0.6593)

70.9170 (0.2353)

0.2838 (0.3632)

0.2704 (0.1960)

0.1849 (0.3473)

71.0259 (0.5294)

70.4770 –

w2ðt1Þ

70.3203 (0.6236)

2.2611 (0.6335)

71.0317 (0.2252)

0.3400 (0.3480)

0.2416 (0.1877)

0.0784 (0.3315)

71.1510 (0.5077)

70.4180 –

w3ðt1Þ

70.1844 (0.6912)

1.8000 (0.6999)

70.7738 (0.2509)

0.1875 (0.3867)

0.5133 (0.2088)

0.0856 (0.3683)

71.1944 (0.5629)

70.4338 –

w4ðt1Þ

70.7013 (0.6349)

1.9141 (0.6319)

70.7343 (0.2378)

0.9417 (0.3604)

0.0250 (0.1965)

70.0804 (0.3521)

70.7457 (0.5184)

70.6190 –

w5ðt1Þ

70.6119 (0.7918)

1.6150 (0.7745)

70.7466 (0.2896)

0.3904 (0.4455)

0.9413 (0.2448)

0.2738 (0.4412)

71.4174 (0.6424)

70.4446 –

w6ðt1Þ

70.4160 (0.8199)

1.9667 (0.8296)

70.9703 (0.3002)

0.2728 (0.4605)

0.0586 (0.2496)

0.8371 (0.4420)

71.2851 (0.6716)

70.4638 –

w7ðt1Þ

70.2494 (0.6450)

1.2783 (0.6517)

70.6924 (0.2343)

0.1013 (0.3611)

0.3690 (0.1951)

0.1453 (0.3452)

70.5623 (0.5248)

70.3899 –

w8ðt1Þ

2.4631 –

R2 wi

0.99 0.434

712.4957 – 0.91 0.100

5.8661 –

72.5175 –

72.4191 –

71.5247 –

7.3818 –

3.2460 –

0.99 0.132

0.89 0.083

0.97 0.046

0.98 0.095

0.99 0.097

– 0.013

507

Food demand elasticities Estimation results: Stages 2-3 (standard errors in parentheses) 2nd Stage

3rd Stage

3rd Stage

Livestock products

Beverages and tobacco


i

70.54235 (0.1564)

0.0048 (0.1516)

0.5376 –

70.5184 (0.1192)

i1

0.1002 (0.0217)

0.0254 (0.0101)

70.1255 –

i2

0.0254 (0.0101)

0.0036 (0.0103)

i3

70.1255 (0.0227)

i

Dairy products

Nonalcoholic

Alcoholic

Tobacco

0.2951 (0.0919)

0.2233 –

70.2245 (0.0870)

0.8077 (0.1285)

70.5832 –

0.1502 (0.0296)

70.0247 (0.0135)

70.1255 –

0.0212 (0.0129)

0.0106 (0.0150)

70.0318 –

70.0290 –

70.0247 (0.0135)

0.0581 (0.0109)

70.0334 –

0.0106 (0.0150)

0.0669 (0.0226)

70.0775 –

70.0290 (0.0115)

0.1545 –

70.1255 (0.0260)

70.0334 (0.0106)

0.1589 –

70.0318 (0.0106)

70.0775 (0.0169)

0.1093 –

0.0706 (0.0175)

0.0009 (0.0168)

70.0715 –

0.0930 (0.0128)

70.0113 (0.0098)

70.0818 –

0.0272 (0.0094)

70.0390 (0.0139)

0.0118 –

w1ðt1Þ

0.5044 (0.0953)

0.0193 (0.0846)

70.5237 –

0.2635 (0.0459)

70.2284 (0.0319)

70.0351 –

0.4952 (0.1285)

0.0611 (0.1817)

70.5563 –

w2ðt1Þ

70.4211 (0.0970)

0.8933 (0.0877)

70.4722 –

70.5738 (0.0780)

0.4320 (0.0546)

0.1419 –

0.0101 (0.0306)

70.0997 (0.0441)

0.0896 –

w3ðt1Þ

70.0833 –

70.9126 –

0.9959 –

0.3104 –

70.2036 –

70.1067 –

70.5053 –

0.0386 –

0.4667 –

0.98 0.357

0.90 0.170

– 0.473

0.96 0.479

0.81 0.138

– 0.383

0.94 0.108

0.64 0.403

0.490

R2 wi

Various food

Fish

Meat

3rd Stage Bread and cereals

Oils and fats


i

1.2443 (0.4225)

0.40585 (0.2828)

i1

0.0338 (0.0229)

i2

Fruits and vegetables

Miscellaneous

71.2072 (0.4450)

0.8014 –

70.0084 (0.0137)

70.0687 (0.01560)

0.0771 –

70.0084 (0.0137)

0.1192 (0.0142)

70.0620 (0.01230)

70.0572 –

i3

70.0687 (0.0156)

70.0620 (0.0123)

0.1818 (0.02090)

70.1198 –

i4

0.0432 (0.0175)

70.0488 (0.0123)

70.0511 (0.01740)

0.0999 –

70.1207 (0.0333)

70.0258 (0.0222)

0.1413 (0.03510)

70.1155 –

w1ðt1Þ

0.6404 (0.1511)

70.0361 (0.0992)

0.1429 (0.15950)

70.1068 –

w2ðt1Þ

70.1055 (0.1796)

0.3126 (0.1280)

0.2240 (0.17500)

70.5366 7

w3ðt1Þ

0.2464 (0.1140)

70.0187 (0.0745)

0.2403 (0.12370)

70.2216 –

i

w4ðt1Þ R2 wi

70.7812 –

70.2577 –

70.6072 –

0.8649 –

0.99 0.197

0.89 0.134

0.98 0.483

– 0.186

508

S. Klonaris and D. Hallam

p0As

the price of good s in the base period. Unfortunately, it is not possible to replace the prices and quantities of all goods in a group with a single price and quantity index respectively. Edgerton (1997) proposes that in the second stage, each group expenditure function mA ¼ cA ðuA ; pA1 ; pA2 ; . . . ; pAs ) is minimized conditional on the utility level uA , implied by the first stage demand function (Equation 11). The resulting conditional or within group demand function for good i in group A is: qAi ¼ hA ð pA1 ; pA2 ; . . . ; pAs ; mA Þ

ð12Þ

If two stage budgeting is appropriate, then the unconditional (Equation 10) and conditional functions (Equations 11 and 12 for the first and second stage respectively) should yield the same results. However, the numerical values of the conditional and unconditional elasticities calculated using Equations 6–8 are different. Edgerton (1997) derived formulae which convert the calculated conditional to corresponding unconditional elasticities. Hence the total (unconditional) expenditure elasticity of an ith good within the A commodity group is Ei ¼

@ ln f @hA @ ln mA @hA @ ln gA ¼ ¼ ¼ EðAÞi  EðAÞ @ ln m @ ln m @ ln m @m @ ln m ð13Þ

I I I . D A T A A N D E ST I M A T I O N The dynamic AIDS model outlined in the previous section was applied in a three stage analysis of Greek consumption expenditures. Figure 1 shows the definition of the three stages and the subgroups within them. Annual time series data from the National Accounts of Greece for the period 1959–1995 on food and non-food consumption expenditures for each good, both in current and in constant prices (base year 1970) were used for the analysis. Dividing the current by constant expenditures provided the price index for each food and non-food item. The total expenditure of each sub-system was obtained by summing the expenditures on the individual items within each sub-system. As shown in Figure 1, five sub-systems were estimated with a total of 16 equations (n  1 equations for each sub-system due to singularity of variance–covariance matrix). Each sub-system of Equation 4 was estimated by the iterative seemingly unrelated regression (ISUR) method, to take into account the imposition of general restrictions, notably symmetry. ISUR and maximum likelihood (ML) lead to identical estimates, regardless of which equation is dropped (Greene, 1993).

IV. E MPI R IC AL R E SU LTS where EðAÞi is the conditional elasticity of the ith good in group A and EðAÞ is the group expenditure elasticity for the Ath group. For two goods, i and j, belonging to commodity groups A and B, Edgerton (1997) gives total price elasticities for goods i and j as eij ¼

@ ln fAi @ ln hAi @ ln hA @ ln gA ¼ þ @ ln pBj @ ln pBj @ ln gA @ ln pBj

@ ln gA @ ln PB ¼ ½AB þ eAB

@ ln pBj @ ln pBj

ð14Þ ð15Þ

where the expression outside the square brackets is equal to the budget share of the reference quantity bundle wBj . Substituting the last expression into Equation 14 yields the general expression eij ¼ AB  eðAÞij þ EðAÞi wðBÞ j ½AB ¼ eðAÞðBÞ

ð16Þ

where  is the Kronecker’s delta equal to one when A ¼ B and zero elsewhere. eðAÞij is the conditional cross price elasticity between i and j goods within group A and wðBÞ j is the budget share of the jth good within group B. These formulae for unconditional expenditure and price elasticities, can be generalized to any number of stages, and are used to calculate unconditional elasticities for the threestage utility tree in this study.

Estimates of the dynamic AIDS parameters for all subsystems are reported in Table 1. The theoretical restrictions of symmetry and homogeneity in prices were imposed. Coefficients of determination ðR2 Þ and budget shares are also reported. The three-stage system appears to have high explanatory power. R2 -values are above 0.90 for 12 of the 16 equations while three of the remaining four are above 0.80. However, these R2 -values can only be considered as broad indicators of the goodness of fit, since the measure is only truly applicable to single equation. Just over half of the estimated parameters are more than twice their standard errors. The results of single-equation and full-system misspecification tests are reported in Table 2. The misspecification testing strategy followed is broadly that suggested by McGuirk et al. (1995), to ensure that the statistical assumptions concerning autocorrelation, heteroscedasticity and functional form in individual equations and in the system as a whole are appropriate. The test for residual autocorrelation is a system equivalent of the Breusch–Godfrey test, while that for functional misspecification is a multivariate version of Ramsey’s RESET test. For static homoscedasticity, a multivariate Breusch–Pagan test is employed while the dynamic homoscedasticity test used is a system ARCH test. The p-values from the system tests for the five sub-systems, either for individual or joint tests are first order tests, using cross components from all

509

Food demand elasticities Table 2. P-values for full-system misspecification tests. Stage 1

Joint tests Overall mean tests Parameter stability Functional form Autocorrelation Overall variance tests Parameter stability Static heteroscedasticity Dynamic heteroscedasticity Individual tests Breusch–Godfrey test RESET Breusch–Pagan test ARCH

Stage 2

Stage 3

Total private consumption

Food

Livestock products

Beverages and tobacco

Various foods

0.40104 0.91755 0.10575 0.53681 0.32457 0.06695 0.10322 0.11411

0.00003 0.01703 0.00001 0.29205 0.94110 0.86901 0.80566 0.81568

0.00002 0.35764 0.00003 0.01340 0.16898 0.43478 0.11039 0.61070

0.04425 0.31458 0.03306 0.58277 0.75511 0.75444 0.84372 0.42207

0.05409 0.04161 0.21111 0.97671 0.05627 0.08257 0.12923 0.18819

0.03990 0.00000 0.11230 0.21148

0.05690 0.00002 0.63629 0.90743

0.02941 0.00010 0.01263 0.77036

0.10747 0.00291 0.63764 0.46500

0.69889 0.00637 0.20794 0.02072

Conclusion Rejected Rejected Rejected Rejected Rejected Rejected Rejected Rejected Rejected Accepted Accepted Rejected Accepted Accepted Rejected

Table 3. Test of restrictions.

1st stage

2nd stage

3rd stage MEAT 3rd stage BEV. and TOB 3rd stage VEG. and CER.

Null

Alternative

LRT

d.f.

5% critical value

Homogeneity Symmetry No dynamics Homogeneity Symmetry No dynamics Homogeneity Symmetry No dynamics Homogeneity Symmetry No dynamics Homogeneity Symmetry No dynamics

No-restrictions No-restrictions No-restrictions No-restrictions No-restrictions No-restrictions No-restrictions No-restrictions No-restrictions No-restrictions No-restrictions No-restrictions No-restrictions No-restrictions No-restrictions

64.69 111.90 150.28 60.53 61.82 23.47 10.42 11.44 41.93 1.01 1.06 56.32 7.08 11.32 17.13

7 28 49 2 3 4 2 3 4 2 3 4 3 6 9

14.07 41.34 66.05 5.99 7.82 9.49 5.99 7.82 9.49 5.99 7.82 9.49 7.82 12.59 16.92

equations within each sub-system. p-values are evaluated using the F-distribution associated with the appropriate likelihood ratio test adjusted for small samples (Bewley, 1986). Unfortunately none of the five sub-systems are free of misspecification. Specifically, the system tests of individual misspecification indicate possible problems with functional form for the five sub-systems, and existence of autocorrelation for the first (total private consumption) and third (livestock products) sub-systems (all p-values 4 0.05). There is also some indication of heteroscedasticity for the third and fifth sub-systems. The joint tests can help to

locate possible problems in the dynamic AIDS model. The full-system joint conditional-mean test suggests no system misspecification in the first and fifth sub-systems. However, the corresponding tests for the second sub-system suggest that misspecification problems may stem from inappropriate functional form and/or trending parameters rather than from autocorrelated residuals. For the third sub-system, inappropriate functional form and/or autocorrelated residuals are indicated. The relative magnitude of p-values on separate test components in the joint tests provides evidence that functional form may be the main problem since those values are lower than those of the

510

S. Klonaris and D. Hallam

Table 4. Conditional uncompensated cross-price and expenditure elasticities (at mean value) Stage 1

Fa

CL

H

DG

MD

ER

TC

OG

Expenditure

Food

70.543 (0.073) 70.354 (0.144) 70.364 (0.073) 70.061 (0.179) 0.026 (0.190) 70.488 (0.149) 70.648 (0.233) 70.124 (0.516)

70.043 (0.028) 70.647 (0.122) 70.038 (0.043) 70.357 (0.107) 70.008 (0.102) 70.101 (0.075) 0.258 (0.105) 0.235 (0.282)

70.095 (0.021) 70.085 (0.060) 70.300 (0.055) 0.039 (0.085) 70.263 (0.093) 70.029 (0.062) 70.279 (0.083) 70.312 (0.230)

0.011 (0.031) 70.307 (0.088) 0.037 (0.053) 70.544 (0.165) 0.293 (0.130) 70.014 (0.090) 70.304 (0.116) 0.014 (0.329)

0.019 (0.019) 70.005 (0.048) 70.081 (0.032) 0.167 (0.073) 71.253 (0.109) 0.070 (0.054) 70.060 (0.073) 70.013 (0.193)

70.077 (0.029) 70.103 (0.073) 70.003 (0.043) 70.013 (0.103) 0.138 (0.108) 70.726 (0.110) 0.148 (0.109) 70.108 (0.320)

70.095 (0.048) 0.265 (0.104) 70.167 (0.060) 70.332 (0.135) 70.110 (0.152) 0.173 (0.112) 70.455 (0.213) 70.001 (0.386)

70.004 (0.014) 0.025 (0.038) 70.033 (0.022) 70.001 (0.052) 70.009 (0.054) 70.020 (0.044) 70.060 (0.073) 70.466 (0.195)

0.826 (0.024) 1.211 (0.099) 0.950 (0.028) 1.104 (0.069) 1.186 (0.079) 1.136 (0.057) 1.348 (0.085) 0.776 (0.210)

Clothing and Footwear Housing Durable goods Medical and Personal Care Education and recreation Transportation and communication Other goods and services

Stage 2

LP

BT

VF

Expenditure

Livestock products

70.790 (0.062) 0.148 (0.075) 70.211 (0.046)

0.037 (0.024) 70.979 (0.050) 70.036 (0.020)

70.445 (0.075) 70.174 (0.099) 70.602 (0.071)

1.198 (0.049) 1.005 (0.099) 0.849 (0.041)

Stage 3: Livestock products

MT

F

DP

Expenditure

Meat

70.780 (0.056) 70.140 (0.093) 70.225 (0.065)

70.078 (0.031) 70.567 (0.087) 70.058 (0.030)

70.336 (0.057) 70.211 (0.079) 70.503 (0.072)

1.194 (0.027) 0.918 (0.071) 0.786 (0.025)

Stage 3: Beverages and tobacco

NA

A

TB

Expenditure

Non-alcoholoc

70.830 (0.119) 0.037 (0.037) 70.067 (0.022)

70.003 (0.141) 70.795 (0.056) 70.168 (0.035)

70.419 (0.116) 70.145 (0.049) 70.789 (0.051)

1.253 (0.877) 0.903 (0.035) 1.024 (0.037)

Beverages and tobacco Various food

Fish Dairy products

Alcoholic Tobacco

Stage 3: Various food

BC

OF

FV

M

Expenditure

Bread and cereals

70.708 (0.120) 70.025 (0.106) 70.292 (0.049) 0.227 (0.101)

0.039 (0.076) 70.082 (0.114) 70.230 (0.038) 70.266) (0.073)

70.052 (0.114) 70.371 (0.116) 70.765 (0.056) 70.288 (0.128)

0.333 (0.092) 70.330 (0.093) 70.160 (0.038) 70.701 (0.115)

0.388 (0.169) 0.807 (0.166) 1.292 (0.073) 1.028 (0.177)

Oils and fats Fruit and vegetables Miscellaneous

Note: Numbers in parentheses are standard errors. a: F: food, CL: Clothing and Footwear, H: Housing, DG: Durable goods, MD: Medical and Personal care, ER: Education and Recreation, TC: Transportation and Communication, OG: Other goods and services, LP: Livestock Products, BT: Beverages and Tobacco, VF: Various Foods, MT: Meat, F: Fish, DP: Dairy Products, NA: Non-alcoholic, A: Alcoholic, TB: Tobacco, BC: Bread and Cereals, OF: Oils and Fats, FV: Fruits and Vegetables, M: Miscellaneous.

511

Food demand elasticities Table 5. Conditional compensated cross-price elasticities (at sample means) Stage 1

F

CL

H

DG

MD

ER

TC

OG

Food

70.185 (0.067) 0.171 (0.125) 0.047 (0.067) 0.417 (0.163) 0.540 (0.174) 0.004 (0.136) 70.064 (0.216) 0.213 (0.471)

0.039 (0.029) 70.526 (0.124) 0.056 (0.043) 70.247 (0.107) 0.110 (0.102) 0.012 (0.076) 0.392 (0.107) 0.313 (0.284)

0.014 (0.020) 0.075 (0.057) 70.174 (0.055) 0.184 (0.084) 70.106 (0.092) 0.121 (0.061) 70.101 (0.081) 70.210 (0.227)

0.080 (0.031) 70.206 (0.089) 0.116 (0.053) 70.452 (0.166) 0..392 (0.130) 0.086 (0.091) 70.192 (0.116) 0.784 (0.331)

0.057 (0.018) 0.059 (0.047) 70.037 (0.032) 0.218 (0.072) 71.198 (0.109) 0.122 (0.053) 0.003 (0.073) 0.022 (0.192)

0.000 (0.030) 0.011 (0.072) 0.087 (0.044) 0.092 (0.103) 0.251 (0.109) 70.618 (0.112) 0.276 (0.110) 70.035 (0.322)

70.014 (0.048) 0.383 (0.104) 70.074 (0.060) 70.225 (0.136) 0.005 (0.153) 0.283 (0.113) 70.323 (0.214) 0.075 (0.388)

0.006 (0.014) 0.041 (0.037) 70.021 (0.022) 0.012 (0.052) 0.063 (0.054) 70.005 (0.045) 0.010 (0.052) 70.456 (0.195)

Clothing and Footwear Housing Durable goods Medical and Personal Care Education and recreation Transportation and communication Other goods and services

Stage 2

LP

BT

VF

Livestock products

70.362 (0.061) 0.507 (0.596) 0.092 (0.048)

0.241 (0.028) 70.809 (0.061) 0.108 (0.024)

0.122 (0.063) 0.302 (0.068) 70.200 (0.058)

Stage 3: Livestock products

MT

F

DP

Meat

70.207 (0.062) 0.300 (0.098) 0.152 (0.068)

0.086 (0.028) 70.441 (0.079) 0.505 (0.028)

0.121 (0.054) 0.140 (0.077) 70.202 (0.071)

Stage 3: Beverage and tobacco

NA

A

TB

Non-alcoholic

70.165 (0.120) 0.134 (0.037) 0.043 (0.022)

0.501 (0.140) 70.431 (0.056) 0.244 (0.035)

0.195 (0.093) 0.297 (0.042) 70.287 (0.043)

Beverages and tobacco Various food

Fish Dairy products

Alcoholic Tobacco

Stage 3: Various food

BC

OF

FV

Bread and cereals

70.631 (0.116) 0.134 (0.102) 0.055 (0.032) 0.430 (0.094)

0.091 (0.069) 70.026 (0.106) 0.005 (0.025) 70.129 (0.066)

0.135 (0.079) 0.019 (0.092) 70.141 (0.043) 0.208 (0.093)

Oils and fats Fruit and vegetables Miscellaneous

M 0.405 (0.088) 70.168 (0.092) 0.092 (0.636) 70.509 (0.114)

512

S. Klonaris and D. Hallam

Table 6. Unconditional uncompensated cross-price and expenditure elasticities (at sample means) Stage 1

F

CL

H

DG

MD

ER

TC

OG

Expenditure

Food Clothing and Footwear Housing Durable goods Medical and Personal Care Education and recreation Transportation and communication Other goods and services

70.543 70.354 70.364 70.061 0.026 70.488 70.648 70.124

70.043 70.647 70.038 70.357 70.008 70.101 0.258 0.235

70.095 70.085 70.300 0.039 70.263 70.029 70.279 70.312

0.011 70.307 0.037 70.544 0.293 70.014 70.304 0.014

0.019 70.005 70.081 0.167 71.253 0.070 70.060 70.013

70.077 70.103 70.003 70.013 0.138 70.726 0.148 70.108

70.095 0.265 70.167 70.332 70.110 0.173 70.455 70.001

70.004 0.025 70.033 70.001 70.009 70.020 70.060 70.466

0.826 1.211 0.950 1.104 1.186 1.136 1.348 0.776

Livestock products Beverages and tobacco Various food

Meat Fish Dairy products

Non-alcoholoc Alcoholic Tobacco

Bread and cereals Oils and fats Fruit and vegetables Miscellaneous

LP

BT

VF

Expenditure

70.595 0.312 70.073

0.130 70.902 0.030

70.186 0.044 70.418

0.990 0.831 0.701

MT

F

DP

Expenditure

70.548 0.039 70.073

70.012 70.516 70.014

70.151 70.069 70.381

1.182 0.909 0.778

NA

A

TB

Expenditure

70.817 0.046 70.057

0.046 70.759 70.127

70.359 70.101 70.739

1.041 0.750 0.851

BC

OF

FV

M

Expenditure

70.663 0.068 70.144 0.345

0.069 70.019 70.129 70.186

0.057 70.144 70.402 0.001

0.375 70.242 70.020 70.589

0.272 0.566 0.906 0.721

autocorrelation and parameter instability tests. The dynamic AIDS model might be tested against an alternative such as the Rotterdam model. However, the results of joint non-nested tests designed to test only the functional form of these two systems (Alston and Chalfant, 1993; Barten, 1993) and using the same data set but with a different aggregation, confirmed the superiority of the AIDS against the Rotterdam model (Klonaris, 1999). Restrictions implied by consumer theory were tested for all the sub-systems estimated. The results are reported in Table 3. The hypothesis of no-dynamics was also tested using a likelihood ratio test corrected for use with small samples. Homogeneity, and symmetry and homogeneity jointly were tested and were strongly rejected by the data for the first two stages. In the third budgeting stage, homogeneity and symmetry (given homogeneity) were rejected for the Meat sub-system but not for the sub-systems of Beverages and Tobacco and Vegetables and Cereals. The rejection of economic restrictions is not uncommon (for Greek food demand systems see, for example, Mergos

and Donatos 1989a and 1989b, and Klonaris 1999). The data are constructed using total disappearance of food and non-food items from national stocks and average retail prices. It is perhaps not surprising that such data may not be consistent with the theory of a representative utility-maximizing consumer. However, the acceptance of homogeneity and symmetry given homogeneity for two sub-systems, suggests that different commodity aggregation may lead to quite different results in tests of general restrictions in demand systems. Using the same data but a different commodity aggregation, Klonaris (1999) found homogeneity and symmetry rejected for all sub-systems of a fourth budgeting stage.

V . E S T I M A T E D E L A S T I C I T I ES The numerical values of the estimated short-run conditional uncompensated price and expenditure elasticities at means are shown in Table 4. The own-price elasticities are

513

Food demand elasticities Table 7. Differences between values of within and total elasticities Commodity

Own-price

Expenditure

Commodity

Own-price

Expenditure

Livestock products Beverages and tobacco Various food Meat Fish Dairy products

70.196 70.078 70.184 70.232 70.051 70.122

0.208 0.175 0.147 0.012 0.010 0.008

Non-alcoholoc Alcoholic Tobacco Bread and cereals Oils and fats Fruit and vegetables Miscellaneous

70.013 70.036 70.049 70.045 70.063 70.363 70.111

0.212 0.153 0.173 0.116 0.241 0.386 0.307

of the expected sign and plausible magnitudes. All the point estimates of the conditional own-price elasticities for all sub-systems are negative indicating the normality of all commodity groups, and that the Marshallian demand functions are downward sloping thus excluding the possibility of Giffen goods. Moreover, all commodities rank as price inelastic and in only one case (Medical and Personal Care) is demand apparently very price sensitive. According to the estimates of within group expenditure elasticities, Food is ranked as a necessity, which is in accordance with previous findings. Meat, Non-Alcoholic Beverages, Tobacco, Fruits and Vegetables and Miscellaneous foods are indicated as luxury goods, while the rest are income inelastic. The values of almost all the estimated own-price and expenditure elasticities are more than twice their standard errors. These conditional elasticities are broadly comparable with the results of previous studies (Mergos and Donatos, 1989b; Kariagiannis and Velentzas, 1993). The concavity of the underlying expenditure functions is implied by the negative corresponding compensated ownprice elasticities shown in Table 5. Tables 4 and 5 show conditional elasticities. Estimated total elasticities based on Equations 13 and 16, are reported in Table 6. The within and total elasticities for the first stage are identical. As in the case of the within group price elasticities, all the commodities rank as price inelastic except Medical and Personal Care for which demand appears to be sensitive to price. The estimates of total expenditure elasticities suggest that Food, Housing and Other Goods and Services are necessities, with the rest of stage 1 commodities being luxuries. The estimated unconditional elasticities for stage 2 deviate substantially from the corresponding conditional elasticities. The deviations between the two are shown in Table 7. The magnitudes of the deviations demonstrate the importance of correcting conditional elasticities. The deviations with respect to ownprice elasticities, are larger for Livestock Products and Various Foods than for Beverages and Tobacco, while the differences between income elasticities are relatively high for all the commodities in stage 2. Livestock Products and Beverages and Tobacco convert from within group luxury products to total necessities. The unconditional elasticities both with respect to price and expenditure

are inelastic at stage 3. Only Meat and Non-Alcoholic Beverages are classified as expenditure elastic. The rather low total own-price elasticities for most of the commodities in stage 3 reflect the strong habit persistence in Greek food consumption patterns. The deviations between total and within own-price elasticities are smaller than in the previous stage and are only noteworthy in the cases of Meat and Fruits and Vegetables. In contrast to own-price elasticities, there is in general less similarity between total and within expenditure elasticities for the commodities in the last sub-system of stage 3. Livestock products are the exception to this.

V I . SU M M A R Y A N D C O N C L U S I O N S This paper provides an empirical exploration of the relationship between conditional and unconditional elasticities of the demand for food. A dynamic version of the AIDS model was employed for the estimation of the parameters of a three-stage budget process for food demand in Greece using time series data for the period 1950–1995. Correction formulae were applied to calculate unconditional (total) price and expenditure elasticities from conditional demand systems. Full system misspecification tests were used for the statistical evaluation of the model. The hypothesis of nodynamics was strongly rejected for all sub-systems, and the theoretical restrictions of homogeneity and symmetry were accepted for two out of five sub-systems. All the commodities except Medical and Personal Care were found to have price inelastic demands. All commodities except Meat and Non-Alcoholic Beverages were classified as necessities. The deviation between conditional and unconditional elasticities shows the need for correction of unconditional elasticities where these are to be used for policy and welfare analyses.

REFERENCES Alessie, R. and Kapteyn, A. (1991) Habit formation, interdependent preferences and demographic effects in the almost ideal demand system, Economic Journal, 101, 404–19.

514 Alston, J. M. and Chalfant, J. (1993) The silence of the lambdas: a test of the Almost Ideal and Rotterdam models, American Journal of Agricultural Economics, 75, 304–13. Assarson, B. (1991) Alcoholic pricing policy and the demand for Alcohol in Sweden 1978–1988, Working Paper, Department of Economics, Uppsala University, Sweden. Barten, A. P. (1993) Consumer allocation models: choices of functional form, Empirical Economics, 18, 129–58. Bewley, R. (1986) Allocation Models: Specification, Estimation and Applications, Ballinger, Cambridge, Mass. Blanciforti, L. and Green, R. (1983) An Almost Ideal demand system incorporating habit effects, Review of Economics and Statistics, 65, 511–15. Blanciforti, L., Green, L. R. and King, G. (1986) US consumer behaviour over the postwar period: an Almost Ideal demand system analysis, University of California, Giannini Foundation Monograph No. 40. Burton, M. and Young, T. (1996) The impact of BSE on the demand for beef and other meats in Great Britain, Applied Economics, 28, 687–93. Cashin, P. (1991) A model of the desegregated demand for meat in Australia, Australian Journal of Agricultural Economics, 35, 263–84. Chalfant, J. A. (1987) A globally flexible Almost Ideal demand system, Journal of Business and Economic Statistics, 5, 312–26. Chalfant, J. A., Gray, R. S., and White, K. J. (1991) Evaluating prior beliefs in a demand system: the case of meat demand in Canada, American Journal of Agricultural Economics, 73, 476–90. Chen, P. Y. and Veeman, M. M. (1991) An Almost Ideal demand analysis for meats with habit formation and structural change, Canadian Journal of Agricultural Economics, 39, 223–35.

S. Klonaris and D. Hallam Deaton, A. and Muellbauer, J. (1980) An Almost Ideal demand system, American Economic Review, 70, 312–26. Edgerton, D. L. (1997) Weak separability and the estimation of elasticities in multistage demand systems, American Journal of Agricultural Economics, 79, 62–79. Goddard, D. (1983) An analysis of Canadian aggregate demand for food at home and away from home, Canadian Journal of Agricultural Economics, 31, 289–318. Greene, W. H. (1993) Econometric Analysis, 2nd edn., PrenticeHall, New York. Karagiannis, G. and Velentzas, K. (1993) Habit and empirical analysis of demand for six aggregate commodity groups in Greece, Spoudai, 43, 139–54. Klonaris, S. (1999) Applied Demand analysis for Food in Greece: Exploration of an alternative AIDS Model. Unpublished PhD Thesis, The University of Reading, Department of Agricultural and Food Economics. McGuirk, A. M., Driscoll, P., Alwang, J. and Huang, H. (1995) System misspecification testing and structural change in the demand for meats, Journal of Agricultural and Resource Economics, 20, 1–21. Mergos, G. J. and Donatos, G. S. (1989a) Demand for food in Greece. An Almost Ideal demand system analysis, Journal of Agricultural Economics, 40, 178–84. Mergos, G. J. and Donatos, G. S. (1989b) Consumer behaviour in Greece: an application of the Almost Ideal demand system, Applied Economics, 21, 983–93. Molina, J. A. (1994) Food demand in Spain: an application of the Almost Ideal demand system, Journal of Agricultural Economics, 45, 252–8. Ray, R. (1984) A dynamic generalisation of the Almost Ideal demand system, Economics Letters, 14, 235–9.