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

We study identification and estimation in first-price auctions with risk averse bidders and selective entry, building on a flexible entry and bidding framework we call the Affiliated Signal with Risk Aversion (AS-RA) model. This framework extends the AS model of Gentry and Li (2014) to accommodate arbitrary bidder risk aversion, thereby nesting a variety of standard models as special cases. It poses, however, a unique methodological challenge – existing results on identification with risk aversion fail in the presence of selection, while the selection-robust bounds of Gentry and Li (2014) fail in the presence of risk aversion. Motivated by this problem, we translate excludable variation in potential competition into identified sets for AS-RA primitives under various classes of restrictions on the model. We show that a single parametric restriction – on the copula governing selection into entry – is typically sufficient to restore point identification of all primitives. In contrast, a parametric form for utility yields point identification of the utility function but only partial identification of remaining primitives. Finally, we outline a simple semiparametric estimator combining Constant Relative Risk Aversion utility with a parametric signal-value copula. Simulation evidence suggests that this estimator performs very well even in small samples, underscoring the practical value of our identification results.