Empirical Evidence on the Law of Demand - Hardle, Wolfgang; Hildenbrand, Werner; Jerison, Michael (Econometrica, 1991)
A sufficient condition for market demand to satisfy the Law of Demand is that the mean of all households' income effect matrices be positive definite. We show how this mean income effect matrix can be estimated from cross section data under metonymy, an assumption about the distribution of households' characteristics. The estimation procedure uses the nonparametric method of average derivatives. Income effect matrices estimated this way from U.K. family expenditure data are in fact positive definite. This result can be explained by a special form of heteroskedasticity in the data: households' demands are more dispersed at higher income levels.