Semiparametric Estimation of First-Price Auction Models

Aryal, Gaurab and Gabrielli, Maria F. and Vuong, Quang (2014): Semiparametric Estimation of First-Price Auction Models.

Abstract

We propose a semiparametric estimator within the class of indirect methods. Specifically, we model private valuations through a set of conditional moment restrictions. Our econometric model calls for a two step procedure. In the first step we recover a sample of pseudo private values while using a Local Polynomial Estimator. In the second step we use a GMM procedure to obtain an estimate for the parameter of interest. The proposed semiparametric estimator is shown to have desirable statistical properties namely, it is consistent and has an asymptotic normal distribution. Moreover, the estimator attains the parametric rate of convergence.

• Item Type: MPRA Paper
• Language: English
• Keywords: Auctions, Structural Approach, Semiparametric Estimator, Local Polynomial, GMM.
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C14 - Semiparametric and Nonparametric Methods: General; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games; D - Microeconomics > D4 - Market Structure, Pricing, and Design > D44 - Auctions

References

Ai, C. and X. Chen (2003): “Efficient Estimation of Models with Conditional Moment Restrictions Con- taining Unknown Functions,” Econometrica, 71, 1795-1843.

Campo, S., E. Guerre, I. Perrigne and Q. Vuong (2006): “Semiparametric Estimation of First-Price Auctions with Risk Averse Bidders,” Review of Economic Studies ,78, 1, 112-147.

Campo, S., I. Perrigne and Q. Vuong (1998): “Asymmetry and Joint Bidding in OCS Wildcat Auctions,” mimeo, University of Southern California.

Donald, S. and H. Paarsch (1993): “Piecewise Pseudo-Maximum Likelihood Estimation in Empirical Models of Auctions,” International Economic Review, 34, 121-148.

Elyakime, B., J.J Laffont, P. Loisel, and Q. Vuong (1994): “First-Price Sealed-Bid Auctions with Secret Reservation Prices,” Annales d’Economie et de Statistiques, 34, 115-141.

Fan, J. and I. Gijbels (1996): Local Polynomial Modelling and Its Applications, Chapman & Hall. Guerre, E., I. Perrigne and Q. Vuong (2000): “Optimal Nonparametric Estimation of First-Price Auctions,” Econometrica, 68, 525-574.

Hardle, W. (1991): Smoothing Techniques with Implementation in S, Springer Verlag.

Honoré, B.E. and E. Kryriazidou (2000): “Panel Data Discrete Choice Models with Lagged Dependent Variable,” Econometrica, 68, 839-874.

Horowitz, J.L. (2000): “A Smoothed Maximum Score Estimator for the Binary Response Model,” Econometrica, 60, 505-531.

Ibragimov, I.A. and R.Z. Hasminskii (1981): Statistical Estimation. Asymptotic Theory, Springer Verlag.

Korostelev, A.P. and A.B. Tsybakov (1993): “Minimax Theory of Image Reconstruction,” Lecture Notes in Statistics, 82.

Krishna, V. (2002): Auction Theory, Academic Press.

Kryriazidou, E. (1997): “Estimation of a Panel Data Sample Selection Model,” Econometrica, 65, 1335- 1364.

Laffont, J.J., T. Li and Q. Vuong (1999): “Identification of First-Price Auctions with a Large Trader,” mimeo, University of Southern California.

Laffont, J.J., H. Ossard and Q. Vuong (1995): “Econometrics of First-Price Auctions,” Econometrica, 63, 953-980.

Laffont, J.J. and Q. Vuong (1996): “Structural Analysis of Auction Data,” American Economic Review, Papers and Proceedings, 86, 414-420.

Lavergne, P. and Q. Vuong (1996): “Nonparametric Selection of Regressors: The Nonnested Case,” Econometrica, 64, 207-219.

Li, T. and I. Perrigne (2003): “Timber Sale Auctions with Random Reserve Prices,” Review of Economics and Statistics, 85, 189-200.

Li, T., I. Perrigne and Q. Vuong (1999): “Structural Estimation of Affiliated Private Values with an Application to OCS Auctions,” mimeo, University of Southern California.

Manski, C.F. (1985): “Semiparametric Analysis of Discrete Response: Asymptotic Properties of the Maximum Score Estimator,” Journal of Econometrics, 27, 205-228.

McAfee, R.P. and J. McMillan (1987): “Auction and Bidding,” Journal of Economic Literature, 25, 699-738.

Newey, W.K. and D.L. McFadden (1994): “Large Sample Estimation and Hypothesis Testing,” in R.F. Engle and D.L. McFadden, eds., Handbook of Econometrics, Volume IV, Amsterdam: North Holland.

Paarsch, H.J. (1992): “Deciding Between the Common and Private Value Paradigms in Empirical Models of Auctions,” Journal of Econometrics, 51, 191-215.

Paarsch, H.J. and H. Hong (2006): An Introduction to the Structural Econometrics of Auction Data, MIT Press.

Perrigne, I. and Q. Vuong (1999): “Structural Econometrics of First-Price Auctions: A Survey of Methods,” Canadian Journal of Agricultural Economics, 47, 203-223.

Perrigne, I. and Q. Vuong (2008): “Auctions: Empirics,” in The New Palgrave Dictionary of Economics, Second Edition, S. Durlauf and L. Blume, eds., Palgrave McMillan.

Powell, J.L. (1994): “Estimation of Semiparametric Models,” in R.F. Engle and D.L. McFadden, eds. Handbook of Econometrics, Volume IV, Amsterdam: North Holland.

Powell, J.L., J.H. Stock and T. M. Stoker (1989): “Semiparametric Estimation of Index Coefficients,” Econometrica, 57, 1403-1430.

Robinson, P.M. (1988): “Root-N-Consistent Semiparametric Regression,” Econometrica, 56, 931-954.

Riley, J.G. and W.F. Samuelson (1981): “Optimal Auctions,” American Economic Review, 71, 381-392.

Wilson, R. (1992): “Strategic analysis of auctions,” in R.J. Aumann and S. Hart, eds. Handbook of Game Theory with Economic Applications, Volume I, New York: North Holland.