Identification and Inference in First-Price Auctions with Risk Averse Bidders and Selective Entry *

Abstract

We study identification and inference in first-price auctions with risk averse bidders and selective entry, building on a flexible framework we call the Affiliated Signal with Risk Aversion (AS-RA) model. Assuming exogenous variation in either the number of potential bidders (N) or a continuous instrument (z) shifting opportunity costs of entry, we provide a sharp characterization of the nonparametric restrictions implied by equilibrium bidding. This characterization implies that risk neutrality is nonparametrically testable. In addition, with sufficient variation in both N and z, the AS-RA model primitives are nonparametrically identified (up to a bounded constant) on their equilibrium domains. Finally, we explore new methods for inference in set-identified auction models based on Chen, Christensen, and Tamer (2018), as well as novel and fast computational strategies using Mathematical Programming with Equilibrium Constraints. Simulation studies reveal good finite-sample performance of our inference methods, which can readily be adapted to other set-identified flexible equilibrium models with parameter dependent support.

Keywords: Auctions, entry, risk aversion, boundary condition, identification, set inference, parameter-dependent support, MPEC, flexible parametric form, approximate profile likelihood-ratio, Bayes credible sets, frequentist confidence sets. JEL Classifications: D44

JEL Classification: D44, C57