Bounds on the Counterfactual Distribution of Revenues in Auctions with Reserve Prices

In first-price auctions with interdependent bidder values, the distributions of private signals and values cannot be uniquely recovered from bids in Perfect Bayesian Nash equilibria. Non-identification invalidates structural

analyses that rely on exact identification of the model primitives. In this paper I introduce tight, informative bounds on the distribution of revenues in counterfactual first- and second-price auctions with binding reserve prices. These robust bounds are identified from distributions of equilibrium bids under minimal restrictions on first-price auctions with interdependent values and affiliated signals. The bounds can be used to compare auction formats and to select optimal reserve prices. I propose consistent nonparametric estimators of the bounds. I extend the approach to account for observed heterogeneity across auctions, as well as endogenous participation due to reserve prices. I analyze a recent dataset of 6,721 first-price auctions of U.S. municipal bonds. I estimate bounds on counterfactual revenue distributions, and use the estimates to bound optimal reserve prices for sellers with various risk attitudes.

For more information, contact Frank Schorfheide.