Nonparametric Identification of Risk Aversion in First-Price Auctions Under Exclusion Restrictions*

This paper studies the nonparametric identification of the first-price auction model with risk averse bidders within the private value paradigm. We show that the benchmark model is nonindentified in general from observed bids. We derive the restrictions imposed by the model on observables and show that these restrictions are quite weak. We then establish the nonparametric identification of the bidders’ utility function under exclusion restrictions. Our primary exclusion restriction takes the form of an exogenous bidders’ participation leading to a latent distribution of private values independent of the number of bidders. The key idea is to exploit that the bid distribution varies with the number of bidders while the private value distribution does not. We also characterize all the theoretical restrictions imposed by such an exclusion restriction on observables to rationalize the model. Though derived for a benchmark model, our results extend to more general cases such as a binding reserve price, affiliated private values and asymmetric bidders. Our theoretical results also extend to observed and unobserved heterogeneity. In particular, we consider endogenous bidders’ participation with exclusion restrictions and available instruments that do not affect the bidders’ private value distribution.