Identification in auctions with selective entry

This paper considers nonparametric identification of a two-stage entry and bidding model for auctions which we call the Affiliated-Signal (AS) model. This model assumes that potential bidders have private values, observe imperfect signals of their true values prior to entry, and choose whether to undertake a costly entry process. The AS model is a theoretically appealing candidate for the structural analysis of auctions with entry: it accommodates a wide range of entry processes, in particular nesting the Levin and Smith (1994) and Samuelson (1985) models as special cases. To date, however, the model's identification properties have not been well understood. We establish identifcation results for the general AS model, using variation in factors affecting entry behaviour (such as potential competition or entry costs) to construct identified bounds on model fundamentals. If available entry variation is continuous, the AS model may be point identified; otherwise, it will be partially identified. We derive constructive identification results in both cases, which can readily be refined to produce the sharp identified set. We also consider policy analysis in environments where only partial identifcation is possible, and derive identified bounds on expected seller revenue corresponding to a wide range of counterfactual policies while accounting for endogenous and arbitrarily selective entry. Finally we establish that our core results extend to environments with asymmetric bidders and nonseparable auction-level unobserved heterogeneity.