Bounding counterfactual demand with unobserved heterogeneity and endogenous expenditures

We propose a method to predict rational counterfactual demand responses from repeated cross-sections. We derive bounds on the distribution of counterfactual demands that are consistent with the Weak Axiom of Revealed Preferences, without putting any restriction on the preference heterogeneity across consumers. In contrast to existing methods, we also allow for endogeneity of total expenditures. In addition, the method can readily incorporate restrictions on the income elasticities of the consumption goods, which further enhances its identifying power (i.e. tighter bounds). We illustrate our approach through an application to data drawn from the U.S. Consumer Expenditure Survey.