Lectu res on A uctions: A n Em p irical P erspectiv eKen Hend ricks, Univ e rsity of B ritish ColumbiaRobert H. Po rter, Northwe stern UniversityDecem ber, 19981IntroductionAuctions are an importan t market institution, and the subject of a lot of good theory.There has also been a lot of recent empirical work using auction data. Examples of auctionmarkets with available data sets inc lude:• government sales: timber and mineral rights, oil and gas rights, treasury bills, im portquotas, privatization such as spectrum auctions and SO2emission permits.• government procurement: defense, highway construction and repair, school milk• private sector: auction houses (Sotheb y’s, Christies) sell art, wine, memorabilia; agri-cultural (e.g., eggplants in Marmande, France); estate sales; real estate; used cars(wholesale); farm machinery (secondhand); railcar capacity (Burlington Northern).• newly created electricity markets in UK, Australia, California (Wolak, Wolfram, W il-son)• experimen tal: laboratory (see Kagel survey in Handbook of Experimental Econo mics);on line (Luc king-Reilly).Auction data sets are often better than the typical data set in industrial organization. Thegame is relatively simple , with well-specified rules. The actions of the participants areobserved directly. Pa yoffs can sometimes be inferred.Why use an auction rather than posting prices or bargaining or contracting? There isusually s ome uncertainty about the buyers’ willingness to pay, and heterogeneity among1potential buyers. Also some degree of product herterogeneity is often present, so past trans-actions are not a reliable guide to current market prices. In these circumstances, auctionscanbeanefficient price discovery process.There are many possible auction mechanisms. They can be characterized in terms of(1) a message space (i.e., what information does the bidder send to the seller) and (2) theseller’s rule for allocation (which, if any, bidders receive the item and the probability thathe receives it) and pa yment from (or transfers to) the bidders, as a function of the messagesreceived. For example, consider a seller who has one item to allocate, and where messagesare bids. Then one can roughly categorize common auction mechanisms into one of fourcells:Highest Bid Second HighestOpen Dutch EnglishClosed FPSB Vickrey (SPSB)Variations on these mechanisms include secret or fixed reserve price (minimum bid) andentry fee.These lectures describe the economics literature on auction markets, with an emphasison the connection between theory, empirical practice, and pulbic policy, and a discussionof outstanding issues. There are several excellen t surveys of theoretical work, by Milgromand by Wilson, and more recently, b y Klemperer. There is also an older but thoroughsurvey by McAfee and McMillan. These surveys describe a lot of research on auctions.Surveys by Hendricks and Paarsch and by Laffont describe some of the recen t empiricalwork done on auctions. Finally, Kagel surveys the considerable literature on experimentalauctions markets. We refer to this literature only occassionally, and interested readersshould consult Kagel for much more detail.Auctions offer the prospect of a close connection between theory and empirical wo rk.Moreover m uch of the theoretical work on auctions has specific positive or normative goalsin mind, and so empiricists are not usually required to re-cast the theory before testingtheoretical predictions. Given a specific auction mechanism, theory’s positive role is todescribe how to bid rationally, which usually in volv es characterizing the Bayesian Nashequilibrium (BNE) of the bidding game. Given the number of bidders, the join t distributionof their valuations and signals, and some behavioral assumption, its normative role is tocharacterize the optimal or efficient selling mechanism. These roles are reflected in the waytheoretical work has been employed to guide empirical work and policy advice. It helps to2shed light on how to interpret patterns in the data, suggests comparative static results thatcan be tested, and guide optimal mechanism design.Empirical work also has positive and normative goals. The positive goal is to answer suchquestions as how do agents behave and are their valuations correlated and if so, what is thesource of the correlation? Given the auction environment, a bidder’s strategy is a mappingfrom information to a bid. Hence, a realization of signals induces a distribution of bids.One can then ask whether the observed bid distribution is consistent with BNE and testfor such properties as independence. With experimental data, the researcher knows whatsignals we re received (but not the preferences of the bidders), and can compare predictedto actual bids. Thus, the consistency question is we ll-defined. However, with field data,the researcher does not know what signals were received and real modeling issues arise inexamining the consistency question. The positive analysis can be of more than academicinterest, since bid rigging or collusion may be distinguishable from non-cooperative behavior,if the two have different positive implications. One can also ask whether risk aversion is animportant feature.The normative goal of empirical work is to answ er such questions as what is the rev-enue maximizing or effecient auction? If one knows or can estimate the relevant featuresof the auction environment (especially the joint distribution of valuations and signals forpotential bidders), and one knows which behavioral model is appropriate, then optimalauction design is feasible. Alternatively, one can test whether the auction design is optimal,e.g. McAfee/Vincent (AER ’92): is reserve price chosen optimally in first-price, sealed bid(FPSB)?For want of a better description, there have been two kinds of approaches adoptedin the empirical literature, which we term reduced form and structural. Reduced formanalysis tests predictions of the theory to make inferences about behavior and the biddingenvironment. The goal of the structural approach is to estimate the data generating processdirectly, in particular, the joint distribution of valuations and signals (usually assume riskneutrality). The strategy is to characterize the Bayesian Nash equilibrium of the auctionto get a functional relationship bet ween signals and bids, and between the distributionsof signals and bids. Assuming such an equilibrium exists, one can use the relationship toconstruct a