Econometrics of auctions by least squares

I investigate using the method of ordinary least squares (OLS) on auction data. I find that for parameterizations of the valuation distribution that are common in empirical practice, an adaptation of OLS provides unbiased estimators of structural parameters. Under symmetric independent private values, adapted OLS is a specialization of the method of moments strategy of Laffont, Ossard and Vuong (1995). In contrast to their estimator, here simulation is not required, leading to a computationally simpler procedure. The paper also discusses using estimation results for inference on the shape of the valuation distribution, and applicability outside the symmetric independent private values framework. Copyright © 2008 John Wiley & Sons, Ltd.

[1]  Quang Vuong,et al.  Asymmetry in first-price auctions with affiliated private values , 2003 .

[2]  H. Harter.  Expected values of normal order statistics , 1961 .

[3]  Dan Levin,et al.  Some Evidence on the Winner's Curse: Comment , 1991 .

[4]  Otis W. Gilley,et al.  The Competitive Effect in Bonus Bidding: New Evidence , 1981 .

[5]  Susan Athey,et al.  Identification of Standard Auction Models , 2000 .

[6]  R. Parrish,et al.  Computing expected values of normal order statistics , 1992 .

[7]  Sushil Bikhchandani,et al.  Symmetric Separating Equilibria in English Auctions , 2000, Games Econ. Behav..

[8]  Harry J. Paarsch.  Deciding between the common and private value paradigms in empirical models of auctions , 1992 .

[9]  R. McAfee,et al.  Auctions with entry , 1987 .

[10]  Wassily Hoeffding,et al.  On the Distribution of the Expected Values of the Order Statistics , 1953 .

[11]  Lung-fei Lee,et al.  Estimation of Linear and Nonlinear Errors-in-Variables Models Using Validation Data , 1995 .

[12]  H. Godwin.  Some Low Moments of Order Statistics , 1949 .

[13]  Ali Hortaçsu,et al.  Winner's Curse, Reserve Prices and Endogenous Entry: Empirical Insights from Ebay Auctions , 2003 .

[14]  Yingyao Hu,et al.  Identification and estimation of nonlinear models with misclassification error using instrumental variables: A general solution , 2008 .

[15]  David H. Reiley,et al.  Pennies from Ebay: The Determinants of Price in Online Auctions , 2000 .

[16]  Whitney K. Newey.  Flexible Simulated Moment Estimation of Nonlinear Errors-in-Variables Models , 2001, Review of Economics and Statistics.

[17]  B. Lebrun.  Existence of an equilibrium in first price auctions , 1996 .

[18]  Harry J. Paarsch,et al.  Piecewise Pseudo-maximum Likelihood Estimation in Empirical Models of Auctions , 1993 .

[19]  E. Tamer,et al.  A simple estimator for nonlinear error in variable models , 2003 .

[20]  A. Pakes,et al.  The Dynamics of Productivity in the Telecommunications Equipment Industry , 1992 .

[21]  R. McAfee,et al.  Auctions with a stochastic number of bidders , 1987 .

[22]  Jean-Jacques Laffont,et al.  Structural Analysis of Auction Data , 1996 .

[23]  Han Hong,et al.  Nonparametric Tests for Common Values at First-Price Sealed-Bid Auctions , 2003 .

[24]  G. Ridder,et al.  Estimation of Nonlinear Models with Measurement Error Using Marginal Information1 , 2004 .

[25]  Paul R. Milgrom,et al.  A theory of auctions and competitive bidding , 1982 .

[26]  John Wooders,et al.  Auctions with a buy price , 2004 .

[27]  Harry J. Paarsch,et al.  An Introduction to the Structural Econometrics of Auction Data , 2006 .

[28]  M. Melnik,et al.  Does a Seller's Ecommerce Reputation Matter? Evidence from Ebay Auctions , 2003 .

[29]  Harry J. Paarsch.  Empirical Models of Auctions and an Application to British Columbian Timber Sales , 1992 .

[30]  J. Laffont,et al.  ECONOMETRICS OF FIRST-PRICE AUCTIONS , 1995 .

[31]  Harry J. Paarsch,et al.  Superconsistent estimation and inference in structural econometric models using extreme order statistics , 2002 .

[32]  L. K. Chan.  On a Characterization of Distributions by Expected Values of Extreme Order Statistics , 1967 .

[33]  Cynthia G. McDonald,et al.  Reputation in an Internet Auction Market , 2002 .

[34]  Q. Vuong,et al.  Optimal Nonparametric Estimation of First-price Auctions , 2000 .

[35]  M. Pollak.  On Equal Distributions , 1973 .

[36]  Elena Krasnokutskaya,et al.  Identification and Estimation in Highway Procurement Auctions Under Unobserved Auction Heterogeneity , 2004 .

[37]  Roger B. Myerson,et al.  Optimal Auction Design , 1981, Math. Oper. Res..

[38]  Harry J. Paarsch,et al.  Identification, Estimation, and Testing in Parametric Empirical Models of Auctions within the Independent Private Values Paradigm , 1996, Econometric Theory.

[39]  Stuart E. Thiel,et al.  Some Evidence of the Winner's Curse , 1988 .

[40]  Philip A. Haile,et al.  Inference with an Incomplete Model of English Auctions , 2000, Journal of Political Economy.

[41]  J. Wooders,et al.  Reputation in Auctions: Theory, and Evidence from Ebay , 2006 .

[42]  Susanne M. Schennach,et al.  Estimation of Nonlinear Models with Measurement Error , 2004 .

[43]  Yasuo Amemiya,et al.  Instrumental variable estimator for the nonlinear errors-in-variables model , 1985 .

[44]  William Vickrey,et al.  Counterspeculation, Auctions, And Competitive Sealed Tenders , 1961 .

[45]  Ziro Yamauti,et al.  Statistical Tables and Formulas with Computer Applications , 1975 .

[46]  William Samuelson.  Competitive bidding with entry costs , 1985 .

[47]  Howard L. Jones,et al.  Exact Lower Moments of Order Statistics in Small Samples from a Normal Distribution , 1948 .