Bounding Counterfactual Demand with Unobserved Heterogeneity and Endogenous Expenditures

We propose a novel method to predict rational counterfactual demand responses from an observed set of repeated cross-sections. Our method derives 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, our method also allows 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). The method is easy to implement and yields informative bounds on demand, which we illustrate through an application to data drawn from the U.S. Consumer Expenditure Survey (CEX).