A Revealed Preference Approach to Identification and Inference in Producer-Consumer Models

This article provides a new identification result for a large class of models in which consumers participate in production. I show that consumer preferences are necessary and sufficient to identify production functions through cross-equation restrictions implied by first-order conditions. In addition, I derive a nonparametric revealed preference characterization of the class of models that exhausts its empirical implications. Finally, I use a novel and easy-to-apply inference method that is valid under partial identification. This method can be used to statistically test the model, can deal with any type of latent variables (e.g., measurement error), and can be combined with standard exclusion restrictions. Using data on shopping expenditures and shopping intensity from the NielsenIQ Homescan Dataset, I show that a doubling of shopping intensity decreases prices paid by about 15%. At the same time, I find that search costs are significant, hence, largely diminishing benefits of price search.