Inspired by the recent literature on aggregation theory, this paper introduces HITS, a semiparametric model of consumer demand that allows for diversity in tastes. The strong variation of budget shares observed across income groups has two possible origins: the individual income effect, and taste differences between poor and rich households. Consumer surveys reporting repeated cross sections do not permit the direct measurement of these two effects. In HITS, linear heterogeneity allows the GMM estimation of structural coefficients on an aggregate series. The joint density of spending and tastes is then recovered from cross sections by a nonparametric procedure involving a deconvolution. We estimate the model on British data (1968–1998) and report that taste heterogeneity explains a large fraction of the variation of budget shares with income.