Bounds on Revenue Distributions in Counterfactual 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 Bayesian Nash equilibria. Non-identification invalidates structural analyses that rely on the exact knowledge of model primitives. In this paper I introduce tight, informative bounds on the distribution of revenues in counterfactual first-price and second-price auctions with binding reserve prices. These robust bounds are identified from distributions of equilibrium bids in first-price auctions under minimal restrictions where I allow for affiliated signals and both private and common-value paradigms. 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 binding reserve prices in the data. I use a recent data of 6,721 first-price auctions of U.S. municipal bonds to estimate bounds on counterfactual revenue distributions. I then bound optimal reserve prices for sellers with various risk attitudes.