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.