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How the U.S. Treasury Should Auction Its Debt (P Federal Reserve Bank of Minneapolis How the U.S. Treasury Should Auction Its Debt (p. 3) V. V. Chari Robert J. Weber No Relief in Sight for the U.S. Economy (p.13) David E. Runkle <C» Federal Reserve Bank of Minneapolis Quarterly Review vol. 16.no. 4 ISSN 0271-5287 This publication primarily presents economic research aimed at improving policymaking by the Federal Reserve System and other governmental authorities. Any views expressed herein are those of the authors and not necessarily those of the Federal Reserve Bank of Minneapolis or the Federal Reserve System. Editor: Arthur J. Rolnick Associate Editors: S. Rao Aiyagari, John H. Boyd, Warren E. Weber Economic Advisory Board: Bruce D. Smith, Richard M. Todd Managing Editor: Kathleen S. Rolfe Article Editor/Writers: Kathleen S. Rolfe, Martha L. Starr Designer: Phil Swenson Associate Designer: Beth Grorud Typesetters: Jody Fahland, Correan M. Hanover Circulation Assistant: Cheryl Vukelich The Quarterly Review is published by the Research Department Direct all comments and questions to of the Federal Reserve Bank of Minneapolis. Subscriptions are Quarterly Review available free of charge. Research Department Articles may be reprinted if the reprint fully credits the source— Federal Reserve Bank of Minneapolis the Minneapolis Federal Reserve Bank as well as the Quarterly P.O. Box 291 Review. Please include with the reprinted article some version of Minneapolis, Minnesota 55480-0291 the standard Federal Reserve disclaimer and send the Minneapo- (612-340-2341 / FAX 612-340-2366). lis Fed Research Department a copy of the reprint. Federal Reserve Bank of Minneapolis Quarterly Review Fall 1992 How the U.S. Treasury Should Auction Its Debt V. V. Chari Robert J. Weber Adviser Professor of Decision Sciences Research Department J. L. Kellogg Graduate School of Management Federal Reserve Bank of Minneapolis Northwestern University and Harold H. Hines Professor of Risk Management J. L. Kellogg Graduate School of Management Northwestern University Auctions have been around for more than 2,000 years. the total debt it plans to sell. Then, starting at the highest The Babylonians arranged marriages by auction. The Ro- price bid and moving down, the Treasury adds up the man legions sold booty at auction, and on one notable oc- competitive quantities bid until it hits its total. Each com- casion, the Praetorian Guard killed the emperor and put up petitive bidder who has won (or, in the Treasury's jargon, the whole empire for auction. Today, members of the gen- has been "awarded" the bid) pays the price stated in his or eral public sell at auction such diverse things as tobacco, her sealed bid; thus, each winning bidder may pay a dif- fish, cut flowers, works of art, thoroughbred horses, and ferent price. Noncompetitive bidders, again, pay the aver- used cars. The U.S. government sells natural resources by age of the awarded competitive bids. auction and may soon take bids on radio airwaves and This multiple-price, sealed-bid procedure, of course, is pollution rights. And in the largest auctions in recorded not the only way to design an auction. Indeed, most econ- human history, the U.S. Treasury each year sells roughly omists agree that it is not the best one for the Treasury. $2.5 trillion worth of debt. With such large amounts at We argue here, based on economic theory, that the Trea- stake, even small improvements in the Treasury's auction sury should switch to a uniform-price, sealed-bid auction. procedure can lead to large gains for taxpayers. In this pa- Under this procedure, with bids ordered by price, from the per, we review what economic theory tells us about ways highest to the lowest, the Treasury would still accept quan- to improve this procedure. tities up to the amount it planned to sell, but the price The Treasury's current procedure is what is known as winning bidders paid wouldn't vary. Instead, all bidders a multiple-price, sealed-bid auction. Roughly a week be- would pay the same price, that of the highest bid not ac- fore each of its more than 150 annual auctions, the Trea- cepted—the price that just clears the market. sury announces the amount of debt it plans to sell. Eligi- The main reason to make this change is that the current ble dealers and brokers submit competitive sealed bids auction procedure provides incentives for bidders to ac- which specify the price they are willing to pay for a par- quire more information than is socially desirable. In the ticular quantity of debt. Investors may also submit so- current procedure, again, bidders pay the amount of then- called noncompetitive bids up to a fairly low quantity ceil- bids if they win. Therefore, bidders have an incentive to ing without specifying a price if they are willing to accept shade their bids below the maximum amount they are whatever will turn out to be the average accepted-bid willing to pay in order to try to obtain the securities at a price. Once all bids are in, the Treasury first adds up the lower price. But bid-shading carries with it the risk that quantity of noncompetitive bids and subtracts that from the bid is so low that the bidder is not awarded any secu- 3 rities. In selecting a bid price, therefore, bidders want to The General Framework: Game Theory balance the gain from a lower winning bid against the risk Let's start by describing how economists generally think of not winning. Thus, they have incentives to learn what about bidder behavior under any type of auction proce- others plan to bid. dure. The framework we use is game theory. This is a In a uniform-price auction, by contrast, the price paid way to analyze how rational decisions are made by com- by a winning bidder does not depend on that bidder's bid. petitors in uncertain conditions. In auctions, of course, the Therefore, bid-shading is less extreme than in multiple- competitors are primarily the bidders. price auctions, and the incentives to acquire information A seller faced with the problem of choosing among about what others plan to bid is smaller. Information about auction procedures must predict how bidders will act. how bidders plan to bid is of no value to society as a Each bidder in a given auction, in turn, must predict how whole since such information merely ends up redistribut- other bidders will act. These actions depend both on how ing payments from uninformed to informed bidders. But much the bidder values the object being sold and on acquiring this information is costly. The loser from the re- guesses about how others will bid on it. Each bidder's val- sources expended in information acquisition is the Trea- uation of the object depends on his or her information sury (and, of course, ultimately, the taxpayers). A uniform- about the object. For example, a bidder on an oil tract price, sealed-bid auction will therefore yield more revenue may know something about oil or neighboring tracts. Ch- to the Treasury. in an art auction, bidders may know how valuable a paint- Uniform-price auctions are also likely to be less sus- ing will be to them. Successful bidding at an auction, ceptible to market manipulation. In 1990, Salomon Broth- therefore, involves successful guesses about other bidders' ers Inc. violated Treasury rules designed to protect against information and successful guesses about how these others market manipulation, and in 1991 the market was alleged- will guess about each other's information. ly manipulated twice more. We argue that episodes of this This is an apparently intractable problem, but the lan- kind are less likely under a uniform-price auction. guage of noncooperative game theory offers a neat way The Treasury did, in fact, experiment with such an auc- around it. The way is to shift attention from bids to bid- tion briefly in the 1970s, but abandoned the experiment as ding strategies. Formally, a (pure) strategy for a bidder is largely inconclusive. As will become obvious, we think a description of the relationship between what is known— the experiment was abandoned too hastily. In any event, the information of the bidder and the history of the auc- more recently, the Treasury embarked on a review of its tion—and what should occur—for each bidder's informa- auction procedures in collaboration with the Securities and tion and each stage of the auction, the appropriate decision Exchange Commission and the Board of Governors of the for the bidder to make. Of course, in practice, bidders sim- Federal Reserve System. (See U.S. Department of the ply choose their bids rather than their strategies. A strat- Treasury et al. 1992.) Therefore, a review of what eco- egy for a particular bidder is simply a way of describing nomic theory tells us about Treasury auctions seems par- how other bidders imagine the particular bidder will act ticularly desirable. (For recent reviews of auctions in gen- under various circumstances. A Nash equilibrium is a col- eral, see McAfee and McMillan 1987, Mester 1988, and lection of strategies, one for each bidder, such that given Milgrom 1989.) the strategies of the other bidders, no one prefers to change The plan for our review is as follows. We begin by his or her own strategy. laying out a general framework for analyzing bidder be- havior in auctions. We apply this framework to two mod- Single-Object Auctions els in which only one unit of an object is being sold at From this perspective, the nature of the information pos- auction: a simple model called the independent private- sessed by each bidder is critical in determining the out- values model and an extension called the correlated-val- come of a given auction procedure.
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