How to Set Minimum Acceptable Bids, with an Application to Real Estate Auctions

In a general auction model with affiliated signals, common components to valuations and endogenous entry, we compute the equilibrium bidding strategies and outcomes, and derive a lower bound on the optimal reserve price. This lower bound can be computed using data on past auctions combined with information about the subsequent sales prices of unsold goods. We illustrate how to compute the lower bound using data from real estate auctions. * Department of Economics, University of Texas; Financial Management Dept., Cornell University; and Department of Economics, University of Maryland, respectively. We thank Susan Athey, Dennis Epple, Sridhar Moorthy, David Reiley and Richard Zeckhauser for useful comments. 1 The most important theoretical treatment is Paul Milgrom and Robert Weber (1982), which developed the mathematical tools used in the present study. The auction literature is surveyed in McAfee and John McMillan (1987a). More specialized surveys are provided by Milgrom (1988) and Robert Wilson (1991). Optimal auctions with correlated values were studied by Jacques Cremer and Richard McLean (1985), McAfee, McMillan, and Philip Reny (1989), and McAfee and Reny (1991). 2 Even if bidders know their own value for the item being sold, it would be rather surprising if these values weren't correlated through unobserved factors. For example, the desirability of a work of art purchased purely for private viewing is likely to be correlated across bidders. More generally, bidders only receive an estimate of the value, and the realized value will depend on unobserved factors correlated with all of the bidders' signals; e.g. the amount of oil in a tract is unobserved prior to drilling, but is presumably correlated with all the bidders' signals. In addition, the potential for resale at an uncertain future price induces correlation in the bidders' valuations. There are many situations in which a seller, often a government, auctions many similar items over a long period of time. For example, over the past several decades, the Federal Deposit Insurance Corporation (FDIC) and the Resolution Trust Corporation (RTC) have auctioned tens of thousands of houses for tens of billions of dollars. Over the past thirty years, the U.S. Department of the Interior has auctioned billions of dollars worth of timber cutting rights and offshore oil leases. Sales of treasury bills are in the trillions of dollars. This paper provides a procedure for increasing the seller's revenue over that obtained by ad hoc formulae used in practice by using historical data to improve on the minimum acceptable bid, or reserve price, imposed in the auction. Because the procedure is applicable to environments of considerable economic value, including not only real estate but also oil and other mineral rights, timber, radio spectrum and treasury bills, there is a potential for application of our theory to create a significant amount of increased revenue. In contrast to much of the literature, we study an environment which allows for affiliation in the signals and common components to value, and in which participation is endogenously determined. With some important exceptions, the empirical auction literature has concentrated on the independent private values environment in which bidders know their own valuations and these valuations are independently distributed. Such models cannot account for either correlation in valuations, as would occur if there are common factors that influence value and vary from auction to auction, or in unobserved factors affecting valuations that are common to the bidders. These factors are clearly important in any real world auction environment, as Paul