An Experimental Comparison between Demand Systems of Major Food Groups in Urban Economics

Problem statement: This study examined the eleven major food groups d emand for urban areas of Iran during1361-1386. Approach: AIDS, ROTTERDAM, CBS and NBR models was compare together and Sur method was applied for est imating of systems, too. Results: Results of study showed cream and fresh fruits have smallest and lar gest income elasticity, respectively. Also, cream, bread, dairy, egg, fresh vegetables, oils and fats and sugar and products, are necessary, meat, fresh fruits and dried fruit are luxury and grain is only inferior group, too. The exception meat, dried fru it and sugar and its products, other groups are inelas tic than own price changes. Also, among them, grain and dried fruit are most inelastic and most elastic , respectively. That means that demand for them has smallest and largest sensitivity than own price inf luences. Also, cross price elasticity’s represented that nor of the groups, are gross strictly substitute, t oge her and gross substitute among them is weak. About complement relation, should say fresh fruits and oils and fats are gross strictly complement for cereal and sugar and its products, respectively and gross complement relation among other groups is found weak. Conclusion: AIDS was better than other models and should be ap ply for analysis of major food group demand for urban areas of Iran, al ternatively.


INTRODUCTION
Always, the economists and makers policies, were have considered to selection of suitable functional form for demand that, it is capable to represent consumers rational behavior hypothesis, goodly and it is compatible to demand theory. That means its price and income elasticity's and coefficients, be rational and agreement to fact.
In the article, is studied the major food groups demand in urban areas of Iran for the period 1361-1386 and experimental are compared AIDS, ROTTERDAM, CBS, NBR models. Eleven major food groups are survey in the study, include: 1-creal 2-bread 3-grain 4dairy 5-egg 6-meat 7-fresh fruits 8-fresh vegetables 9dried fruit 10-oils and fats 11-sugar and its products. In the field of demand, is studied many. Fousekis and Revell (2000) analyze demand for meat in the UK and found Rotterdam and CBS better explain consumers' retail purchase allocation decisions for beef, lamb, pork, bacon and poultry compared with models NBR and differential AIDS. Erkan (2006) study three demand systems with their extensions for agricultural products in OECD countries, namely the Rotterdam, AIDS and CBS model by SUR method. He understood significant empirical regularities for agricultural products in OECD countries and the superiority of AIDS and CBS models over the Rotterdam model. Blanciforti et al. (1986) with data during 1978-1984 for USA estimate consumer demand by using AIDS and LES and showed AIDS have rational coefficient and estimation of it is simplest than AIDS, by applying linear techniques and comparing the linear and nonlinear AIDS to Rotterdam model and fond out the models relative supremacy depended to substitute elasticity's of commodities. For example, when substitute among all of commodities is very high, nonlinear AIDS is better than Rotterdam and otherwise, both of them are suitable. Zhang et al. (2006), in analyzing demand for commonly and organic vegetables in US. Were found AIDS is better than other functional forms.

MATERIALS AND METHODS
Earlier studies use single equation techniques to estimate commodity demand by consumers. But in the last several decades, consumer demand analysis has moved toward system-wide approaches (Lee et al., 1994). System-wide approaches ensure that the demand system is consistent with consumer theory. On the other hand, single equation specifications are primarily concerned with estimating elasticity and paid little attention to consumer theory. Because of existence of correlation among residuals of demand equations, Sur method (Zellner, 1962) was applied for estimating of systems.

Differential demand systems: The Almost Ideal
Demand System (Deaton and Muellbauer, 1980), the Rotterdam model (Barten, 1964;Zhang et al., 2006) and their variants are probably the most commonly used functional forms in empirical demand analysis. The Rotterdam model, developed by Barten (1964) and Theil (1965), takes the following differential form: The term d logQ is an index number (Divisia volume index) for the change in real income and can be written as: The demand parameters θ i and ij π are given by: and: Where: m = The total outlay or the budget s ij = The (i,j)th element of the Slutsky substitution matrix parameter θ i = The marginal budget share of commodity i π ij = A compensated price effect The constraints of demand theory can be directly applied to the Rotterdam parameters. In particular, we have adding-up: Slutsky symmetry: The Rotterdam model is a particular parameterization of a system of differential demand equations where demand parameters θ i and ij π are assumed to be constant. However, there is no strong a priori reason that the θ i and ij π should be held constant.
By relaxing the marginal budget share parameter to be variable, Keller and Van Driel (1985) further proposed the CBS (Central Bureau of Statistics) model: by substituting i i i w θ = β + and moving it to the left, in (7), we have CBS form: Different from the Rotterdam model, the original AIDS model, in its original formulation, is not a differential function. It is specified as: where, P is a price index defined by: A fourth alternative, the National Bureau of Research (NBR) model (Lee et al., 1994) can be derived by substituting θ i -w i for first differential AIDS that is fallowing: the NBR is obtained as: So that it has the Rotterdam income coefficients but the AIDS price coefficients. Specifically, the four models have the same left-hand side variable wide log q i and right-hand side variables d logQ and d log p i .

RESULTS
In this study AIDS, CBS, NBR and Rotterdam models were applied and compared. AIDS, on the reason of having the most the numbers of significant coefficients, highest R 2 for each equation of the system, was selected Table 2.
Also, own price elasticity's were negative under AIDS, the homogeneity, symmetry and negativity was rejected for all. CBS can't provide the adding up and Rotterdam's own price elasticity's was positive, except in two cases. Also, NBR had the lesser the numbers of significant coefficients and lower R 2 for each equation of the system, than AIDS. Hence, AIDS was select Table 3.

DISCUSSION
Results represent that creal and fresh fruits have smallest and largest income elasticity, respectively. Also creal, bread, dairy, egg, fresh vegetables, oils and fats and sugar and products, are necessary groups, meat, fresh fruits and dried fruit are luxury groups and grain is only inferior group, too. The exception meat, dried fruit and sugar and its products, other groups are inelastic than own price changes. Also, among them, grain and dried fruit are most inelastic and most elastic, respectively. That means that demand for them has smallest and largest sensitivity than own price influences. Also, Cross price elasticity's represented that nor of the groups, are gross strictly substitute, together and gross substitute among them is weak. About complement relation, should say fresh fruits and oils and fats are gross strictly complement for cereal and sugar and its products, respectively and gross complement relation among other groups is found weak.

CONCLUSION
This research, intended to find which system of demand, is fitter for explaining consumers demand for major food groups, in urban areas of Iran. On the basis of finding, AIDS model was better than other models and should be apply for analysis of major food groups' demand for urban areas of Iran.