Empirical Evidence on the Law of Demand
证明，当所有家庭收入效应矩阵的均值正定时，市场需求满足需求定律。利用英国家庭支出数据，通过非参数平均导数法估计收入效应矩阵，发现其确实正定，这可由数据中收入水平越高需求越分散的异方差性解释。
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.