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

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 et al. (2018, Econometrica, vol. 86, 1965-2018), as well as novel and fast computational strategies using Mathematical Programming with Equilibrium Constraints. Simulation studies reveal the good finite-sample performance of our inference methods, which can readily be adapted to other set-identified flexible equilibrium models with parameter-dependent support.