Engel's Law and Linear-in-Moments Aggregation

Aggregation of individual Engel curves is considered such that aggregate food demand depends on the moments of the distribution of income across individuals. Given that aggregate demand is the sum of individual demands, consistent aggregation imposes a structure called the Linear-in-Moments form. This form is used to test whether the mean and second moment of income must be used to capture aggregate food demand. Empirical analysis strongly supports the proposition that both the mean and variance of income are required. Hence, our results show that aggregate food demand under consistent aggregation is inherently sensitive to changes in the distribution of income. Key words: aggregation, Engel curves, food demand. Estimation of demand relationships is central to agricultural economics. Unfortunately, data are often limited. For example, time-series data typ-ically reflect aggregates well beyond the indi-vidual behavioral responses postulated by the-ory. And while these aggregate time-series data sets generally contain significant price varia-tion, they usually are not disaggregable in a consistent fashion. Cross-section data sets, on the other hand, are more representative of the individual behavioral response postulated by theory, but frequently lack significant price variation. Thus empirical agricultural demand analysis is often executed either at the very highest levels of aggregation (Blanciforti and Green 1983a, 1983b; George and King; Huang) or in the absence of price variation. The nexus between the cross-section and ag-gregate time-series approaches is the aggrega-tion problem: one seeks ways to aggregate con-sistently individual (cross-section) relationships to permit aggregate (time-series) variables to be used in econometric analysis based on micro-economic principles. Gorman (1953) early asked, under what condition does aggregate demand (defined as the sum of individual demands) de-pend only upon per capita income and price? This is tantamount to asking, when can the in-come distribution be safely ignored in analyzing aggregate demand? (Per capita income only measures the first moment of the income distri-The authors are professors at the University of Maryland and Brigha