The Revealed Preference Approach to Collective Consumption Behavior: Testing, Recovery, and Welfare Analysis

Abstract

We extend the nonparametric 'revealed preference' methodology for analyzing collective consumption behavior (with consumption externalities and public consumption), to ren- der it useful for empirical applications that deal with welfare-related questions. First, we provide a nonparametric necessary and su¢ cient condition for collectively rational group behavior that incorporates the possibility of assignable quantity information. This charac- terizes collective rationality in terms of feasible personalized prices, personalized quantities and income shares (representing the underlying sharing rule). Subsequently, we present nonparametric testing tools for data consistency with special cases of the collective model, which impose specific structure on the preferences of the group members (in terms of con- sumption externalities and public consumption); and we show that these testing tools in turn allow for nonparametrically recovering (bounds on) feasible personalized prices, per- sonalized quantities and income shares that underlie observed (collectively rational) group behavior. In addition, we present formally similar testing and recovery tools for the general collective consumption model, which imposes minimal a priori structure. Interestingly, the proposed testing and recovery methodology can be implemented through integer program- ming (IP and MILP), which is attractive for practical applications. Finally, while we argue that assignable quantity information generally entails more powerful recovery results, we also demonstrate that precise nonparametric recovery (i.e. tight bounds) can be obtained even if no assignable quantity information is available.