Estimating Demand Elasticities for Aggregate Food Groups using QUAIDS and Pooled HIES Data

Over the time there have been many changes in world’s as well as Pakistan’s economy. Pakistan faces the pacing urbanization and despite being an agrarian country, it is a net importer of many agricultural products. There are many determinants of changing consumption patterns like income variation, price change, population change and urbanization. Prices especially have shown remarkable variation resulting in food inflation. The aim of this research is to estimate the demand elasticities of the selected food groups using a panel of four Household Integrated Economic Survey Data sets. Two stage budgeting framework has been adopted for estimating per capita food expenditures in Pakistan at the first stage over the analysis period. The second stage has utilized Quadratic Almost Ideal Demand System (QUAIDS) for the estimation of budget shares of each food group which is used further to calculate the elasticities. All the expenditure elasticities are almost equal to unity representing one to one relationship between the food groups’ demand and expenditures on them with the changing income. All own price Marshallian elasticities are negatively signed as per expectations. The demand for all the taken food groups is inelastic with respect to price. All the selected food groups behave to be normal goods as the expenditures’ elasticities for all is positive. Majority of the Hicksian cross price elasticities are positively signed representing food groups to be substitutes of each other. Hicksian elasticities just take price effect into account. Compensated own price elasticities for all of the selected food groups bear expected negative sign. As all the food groups, have proved to be inelastic with respect to the prices, government needs to carefully design its taxation and pricing policies so that the most vulnerable section of the society is not affected badly. Apart from income and price effects, certain structural factors are very crucial in determining the consumption basket of households of a country. Huang and Bouis (2001) suggested broader range of food available, diet westernization, time constraint for urban women, lower caloric requirement and absence of high opportunity cost of selling own production for high priced food from retailers (in urban areas), as the main factors altering the patterns of food demand as urbanization proceeds. Hence analyzing the consumption basket of households for a long term, examining the determinants that cause such changes, estimating demand elasticities which elucidate the demand level by individual consumers with the specified structure of relative prices in the economy, real income and individual attributes, is very crucial. (Mittal, 2006). Keeping all this in view, the objective of the current study is to estimate for the presence of such shifts in Pakistan and the associated price elasticities of demand. These shifts in food demand are experienced throughout the world (Huang and Bouis2001 and Mittal 2006). Though in limited quantum, but earlier studies also prove for the prevalence of such shifts in Pakistan as well (Burki 1997 and Aziz & Malik, 2006). This study has utilized a pooled data set of the four Household Integrated Economic Survey (HIES) data sets for the years, 1985-86, 1993-94, 2001-02 and 2007-08. The food commodities have been aggregated into the eight food groups. Which include Cereals, milk and milk products named Milks here, pulses, sugar and sugar products, here named together as Sugars, vegetables and fruits named Vegfruit here, cooking oils and ghee named Oils, meat fish and egg named MFE and other food items named Other foods here. The food commodities in each of the eight food groups are the same as given in HIES data sets of the respective years. Very important to mention is the fact that the HIES 1985-86 and HIES 1993-94 are much different from the HIES 2001-02 and HIES 2007-08. Many of the quantities for the commodities had not been given in the former data. The quantities were essentially needed for finding the prices with the HIES data. The price statistics for the respective years were taken from the Pakistan Bureau of Statistics. The missing quantities for the food items were with little approximation assigned to those items and households on the basis of those price statistics. Another issue was the difference in the units in which the quantities were reported in the earlier and the later data sets. For instance, the beverages’ and Vinegar’s quantity had been given in bottles in 1993-94 HIES. The internet, and a small survey from those consumers which consumed these in 1993-94 and in 2007-08 as well, were taken aid of to convert the bottles into litres. For fulfilling adding up restriction and budget constraint, the other food items’ group has been included. It has a wide range of goods from condiments and spices to readymade food items and bakery products etc. The results of this group are not reported here in the results as the interpretation for such a diverse and large group will not bear any real implication. The study employs Quadratic Almost Ideal Demand system (QUAIDS) for the estimation of budget shares and the elasticities finally. QUAIDS given by Banks et al. (1997) is derived from indirect utility function having the following form Where a(p) and b(p) are given by following equations and Using Roy’s identity, the QUAIDs’ expenditure shares are given by The resultant model is hence Quadratic in total expenditures. This is a rank three demand system (Banks et al. 1997). Where, “the RANK M of any demand system is the maximum dimension of the function space spanned by the Engel curves of the demand system” (Lewbel, 1991). Demand systems have been estimated by many systems throughout the world and in Pakistan. Deaton and Muellbauer (1980) gave Almost Ideal Demand system (AIDS). AIDS is a complete demand system which satisfies axiom of choice and aggregates over consumers perfectly. Many of AIDS’ properties were present in other models as well but none combined all (Deaton and Muellbauer, 1980). For estimation of food demand and its changes and responsiveness to various factors, numerous demand systems and numerous extensions of AIDS have been used in literature. Like in recent years, Cranfield et al. (1998) used An Implicitly Directly Additive Demand System (AIDADS), Huang and Bouis (2001) and Farooq and Ali (2002) estimated AIDS, Burki (1997), Aziz and Malik (2006) and Nazli et al. (2008) employed LA-AIDS. Problem with AIDS is this that the demand equations are unrelated as none of the endogenous quantities are on the right-hand side of equations. Since the budget constraints should be satisfied by the dependent variables, error terms are correlated across equations (Mittal, 2006). Zellner (1962) developed the method for Seemingly Unrelated Regressions (SUR) which can be used to Estimate AIDs and provides more efficient estimates (Aziz and Malik, 2006). Many adaptations for AIDS are being employed throughout world and this research has used Quadratic Almost Ideal Demand System (QUAIDS) given and used by Banks et al. (1997). QUAIDS was in fact developed by Blundell et al. (1993) but refinements were made by Banks et al. (1997). This model is an extension of AIDS. The model has been employed in several studies because of many of its features. Goods can be necessities as well as luxuries at different income levels which is not permitted by Translog and AIDS (Ibid). Is affords greater flexibility due to being rank three (Ibid). Cranfield et al. (2003), put forth that in general the results from in- and out-of sample evaluations prioritize a demand system of rank three over those containing ranks two. Macro-aggregates like tobacco and beverages, food, recreation, housing and transport depict the behaviour of consumption that is best explained by a demand system having rank-three (Soregaroli et al., 2002). Above all, it permits for the Engel curvature and the systems that do not account for it give misleading and misguiding estimates of welfare variations resultant upon tax modifications (Banks et al. 1997). Estimation is divided in two levels. Ordinary Least Square (OLS) estimation at the first level is carried out to estimate for the per capita food expenditures. At the Second stage, seemingly unrelated regressions are employed following Zellner (1962). As the main objective is the elasticities’ estimation and analysis based on those elasticities, the results of first two stages have been reported in the appendix. Those results also confirm for the changing food consumption preferences of the households in Pakistan over the selected period of analysis. The table 1 and table 2 reports the uncompensated and compensated elasticity estimates. Table.1 Expenditure and Uncompensated Price Elasticity of Demand With Respect to Prices Groups Expenditure Cereals Pulses MFE Milks Oils Sugars Vegfruit Cereals 0.99 -0.853 -0.006 -0.03 -0.02 0.01 -0.01 -0.03 Pulses 0.99 -0.05 -0.40 -0.14 -0.11 -0.11 -011 -0.08 MFE 1.00 -0.100 -0.05 -0.415 -0.12 -0.04 -0.09 -0.12 Milks 1.00 -0.05 -0.02 -0.062 -0.834 -0.03 0.002 -0.04 Oils 0.99 0.01 -0.04 -0.04 -0.05 -0.72 -0.072 -0.10 Sugars 0.99 -0.04 -0.05 -0.11 0.02 -0.10 -0.598 -0.06 Vegfruit 0.99 -0.07 -0.02 -0.10 -0.06 -0.09 -0.04 -0.588 Table. 2 Compensated price Elasticity of Demand Groups Cereals Pulses MFE Milks Oils Sugars Vegfruit Cereals -0.65 0.03 0.09 0.18 0.11 0.07 0.09 Pulses 0.16 -0.35 -0.03 0.12 0.02 0.05 0.04 MFE 0.11 -0.02 -0.29 0.04 0.04 -0.04 -0.02 Milks 0.19 0.02 0.05 -0.61 0.07 0.07 0.08 Oils 0.24 0.01 0.07 0.15 -0.70 0.01 0.02 Sugars 0.22 0.02 -0.02 0.23 0.02 -0.58 0.09 Vegfruit 0.17 0.01 0.01 0.14 0.01 0.05 -0.45 All own price Marshallian elasticities are negatively signed as per expectations. This result is same as obtained by the other prominent researchers on food demand in Pakistan (Aziz & Malik 2006 and Nazli et al. 2008). The magnitude of the Marshallian own price elasticity for the meat fish and egg group is almost the same as obtained for meat by Nazli et al. (2008). Some of the Marshallian cross price elasticities are positively signed but majority of these are negatively signed. The demand for all the taken food groups is inelastic with respect to price. All the selected food groups behave to be normal goods as the expenditures’ elasticities for all is positive.