Partial 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 formally nests the Levin and Smith (1994) model and approaches the Samuelson (1985) model as a limit. Unfortunately, since pre-entry signals are not observed, the AS model is nonparametrically non-identified. In this paper, we explore a partial identification approach to structural analysis using the AS model. In particular, we show how exogenous variation in entry behavior (induced by variation in factors such as potential competition or entry costs) can be used to construct nonparametric bounds on the fundamentals of the AS model under a general class of second-stage bidding mechanisms, and translate these bounds into bounds on counterfactual seller revenue corresponding to a wide variety of potential award rules. Finally, we state conditions under which the AS model is exactly identified. ∗Earlier versions of this paper have been presented at the EC Conference on Identification in Econometrics in Toulouse, December 2010, the North American Summer Meeting of the Econometric Society in St. Louis, June 2011, and the European Meeting of the Econometric Society in Oslo, August 2011. We thank participants of these conferences for comments and Yanqin Fan for helpful suggestions. Support from National Science Foundation (SES-0922109) is gratefully acknowledged. †Department of Economics, Vanderbilt University. Email: [email protected]. ‡Department of Economics, Vanderbilt University. Email: [email protected].