This paper attempts to provide empirical evidence of the positive definiteness of the mean income effect matrix, a sufficient condition for market demand to satisfy the 'law of demand' derived by Härdle, Hildenbrand and Jerison [HHJ(1991)]. Increasing heterogeneity in spending of populations of households leads to this sufficient condition which is falsifiable from cross-section data. Based on this framework we use the National Sample Survey (NSS) 50-th round data (1993-1994) for the rural sector of Maharashtra > to examine the empirical viability of this condition. Due to a restrictive assumption on the density function and several other limitations of the indirect method we use the nonparametric direct average derivative estimation procedure [Stoker (1993)], unlike the indirect method used in the HHJ paper. It is shown that the income effect matrix is, indeed, positive definite. The required heterogeneity condition is also well supported in this data where one can not expect too much variation in spending patterns of population given the source of data, i.e., rural sector of a developing economy.
Aggregation Heterogeneity Income effect Law of Demand Average derivative estimator Nonparametric regression