Robust inference in first-price auctions: Overbidding as an identifying restriction

Laboratory experiments find consistently that bidding in first-price auctions tends to be more aggressive than predicted by the risk-neutral Bayesian Nash Equilibrium (RNBNE) — a finding known as the overbidding puzzle. Several alternative models can explain the overbidding puzzle, but no canonical alternative to RNBNE has emerged. Instead of estimating a particular model of overbidding, we use the overbidding restriction itself for identification, which allows us to bound the valuation distribution and the seller’s revenue under counterfactual reserve prices in the spirit of Haile and Tamer (2003). These bounds are consistent with RNBNE and all models of overbidding, and the bounds remain valid even if there is unobserved heterogeneity in bidding strategies. We evaluate the validity of the bounds numerically and in experimental data.