This paper considers nonparametric identification of a two-stage entry and bidding game we call the Affiliated-Signal (AS) model. This model assumes that potential bidders have private values, observe signals of their values prior to entry, and then choose whether to undertake a costly entry process, but imposes only minimal structure on the relationship between signals and values. It thereby nests a wide range of entry processes, including in particular the Samuelson (1985) and Levin and Smith (1994) models as special cases. Working within the AS model, we map variation in factors affecting entry behavior (potential competition or entry costs) into identified bounds on model fundamentals. These bounds are constructive, collapse to point identification when available entry variation is continuous, and can readily be refined to produce the pointwise sharp identified set. We then extend our core results to accommodate nonseparable unobserved auction-level heterogeneity and potential endogeneity of entry shifters, thereby establishing a formal identification framework for structural analysis of auctions with selective entry.
Centre for microdata methods and practice