An analysis of price effects in cross-section data

Abstract

Most analyses of food consumption from household budget data assume that prices are constant in cross-section. However, if cross-section data have sufficient temporal and spatial dimensions, there is no a priori theoretical justification for this assumption. Recent cross-section data sources such as the U.S.D.A's 1977-78 Nationwide Food Consumption Survey (NFCS) contain detailed information on expenditures as well as quantities of food commodities consumed. Thus, implicit price measures (expenditures divided by quantities consumed) can be derived and incorporated in cross-sectional demand functions. This research uses the implicit prices for selected vegetable commodities (fresh, canned/frozen, and dehydrated potatoes; fresh, canned and frozen vegetables) from the Western region of the 1977-78 NFCS to evaluate empirically the constancy of cross-sectional prices. The research addresses the question of whether the observed variability in these cross-section prices is sufficient to identify quantity demand functions. Procedures for estimation of cross-sectional quantity demand functions are proposed using the Houthakker-Theil model of quality/quantity choice. This conceptual framework indicates bias in the estimation of family size and income effects if prices are not adjusted for the influence of household characteristics. The results of maximum likelihood Tobit estimation of the quality-adjusted quantity demand functions indicate negative and significant own-price effects for all commodities as well as numerous significant and positive cross-price effects. These results suggest that the Houthakker-Theil model is a viable framework for estimating substitution relationships among disaggregated food commodities. Significant influence due to region and quarter is found across commodities suggesting that the procedures are capable of estimating regional and quarterly price effects. Price elasticities based on these estimates could improve the specification of regional demand in models of inter-regional competition. Thus, overall, this research supports the conclusion that demand functions can be identified and estimated with cross-section data. If cross-sectional price effects can be estimated, than a considerable body of data becomes available for testing economic theory at the household level. This implies that several maintained hypotheses in time-series analyses (e.g., aggregation over consumers and goods) can be relaxed and tested. Therefore, cross-sectional price effects appear to hold considerable analytical potential.