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IDENTIFICATION AND ESTIMATION IN A THIRD-PRICE AUCTION MODEL

  • Andreea Enache (a1) and Jean-Pierre Florens (a2)
Abstract

The first novelty of this paper is that we show global identification of the private values distribution in a sealed-bid third-price auction model using a fully nonparametric methodology. The second novelty of the paper comes from the study of the identification and estimation of the model using a quantile approach. We consider an i.i.d. private values environment with risk-averse bidders. In the first place, we consider the case where the risk-aversion parameter is known. We show that the speed of convergence in process of our nonparametric estimator produces at the root-n parametric rate, and we explain the intuition behind this apparently surprising result. Next, we consider that the risk-aversion parameter is unknown, and we locally identify it using exogenous variation in the number of participants. We extend our procedure to the case where we observe only the bids corresponding to the transaction prices, and we generalize the model so as to account for the presence of exogenous variables. The methodological toolbox used to analyse identification of the third-price auction model can be employed in the study of other games of incomplete information. Our results are interesting, also from a policy perspective, as some authors recommend the use of the third-price auction format for certain Internet auctions. Moreover, we contribute to the econometric literature on auctions using a quantile approach.

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Corresponding author
*Address correspondence to Andreea Enache, Center for Data Analytics, Department of Economics, Stockholm School of Economics, Sveavägen 65, SE-113 83 Stockholm, Sweden; email: andreea.enache@hhs.se.
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We are indebted to Jérôme Adda, Stéphane Bonhomme, Christian Bontemps, Philippe Février, Xavier D’Haultfoeuille, Christophe Hurlin, Laurent Linnemer, David Martimort, Peter C.B. Phillips (the editor), Ingrid Van Keilegom, Andrew Rhodes, Quang Vuong, Dennis Kristensen (the co-editor), the three anonymous referees, and many seminar audiences for their insightful comments. We thank financial support from ANR-13BSH1-0004-03-IPANEMA. Andreea Enache gratefully acknowledges financial support from the Carlo Giannini Research Fellowship in Econometrics (2016–2018). All remaining errors are ours.

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Arnold, B., Balakrishnan, N., Nagaraja, H., & Nagaraja, H. (2008) A First Course in Order Statistics, vol. 54. Society for Industrial Mathematics.
Athey, S. & Haile, P. (2002) Identification of standard auction models. Econometrica 70(6), 21072140.
Carrasco, M., Florens, J.-P., & Renault, E. (2007) Linear inverse problems in structural econometrics estimation based on spectral decomposition and regularization. Handbook of Econometrics 6, 56335751.
Csörgö, M. (1983) Quantile Processes with Statistical Applications, vol. 42. Society for Industrial Mathematics.
Donald, S. & Paarsch, H. (1993) Piecewise pseudo-maximum likelihood estimation in empirical models of auctions. International Economic Review 34(1), 121148.
Donald, S. & Paarsch, H. (1996) Identification, estimation, and testing in parametric empirical models of auctions within the independent private values paradigm. Econometric Theory 12(3), 517567.
Dvoretzky, A., Kiefer, J., & Wolfowitz, J. (1956) Asymptotic minimax character of the sample distribution function and of the classical multinomial estimator. The Annals of Mathematical Statistics 27(3), 642669.
Enache, A. & Florens, J.-P. (2017) A quantile approach to the estimation of first-price private value auction. Working Paper.
Enache, A. & Florens, J.-P. (2018a) Nonparametric estimation for regulation models. Annals of Economics and Statistics/Annales d’Économie et de Statistique (131), 4558.
Enache, A. & Florens, J.-P. (2018b) Quantile analysis of hazard-rate game models, European University Institute Working Paper, MWP Red Number Series 2016/10, Max Weber Programme.
Florens, J.-P., Protopopescu, C., & Richard, J. (1998) Identification and estimation of a class of game theoretic models (Mimeo). University of Toulouse.
Florens, J.-P. & Sbaï, E. (2010) Local identification in empirical games of incomplete information. Econometric Theory 26(06), 16381662.
Gimenes, N. (2017) Econometrics of ascending auctions by quantile regression. Review of Economics and Statistics 99(5), 944953.
Gimenes, N., Guerre, E. et al. (2016) Quantile Methods for First-Price Auction: A Signal Approach. Working Papers, Department of Economics 2016_23, University of São Paulo (FEA-USP).
Goeree, J., Maasland, E., Onderstal, S., & Turner, J. (2005) How (not) to raise money. Journal of Political Economy 113(4), 897918.
Guerre, E., Perrigne, I., & Vuong, Q. (2000) Optimal nonparametric estimation of first-price auctions. Econometrica 68(3), 525574.
Guerre, E., Perrigne, I., & Vuong, Q. (2009) Nonparametric identification of risk aversion in first-price auctions under exclusion restrictions. Econometrica 77(4), 11931227.
Guerre, E. & Sabbah, C. (2012) Uniform bias study and Bahadur representation for local polynomial estimators of the conditional quantile function. Econometric Theory 28(1), 87129.
Haile, P. A., Hong, H., & Shum, M. (2003) Nonparametric Tests for Common Values at First-Price Sealed-Bid Auctions. Technical report, National Bureau of Economic Research.
Kagel, J. & Levin, D. (1993) Independent private value auctions: Bidder behaviour in first-, second-and third-price auctions with varying numbers of bidders. The Economic Journal 103(419), 868879.
Laffont, J., Ossard, H., & Vuong, Q. (1995) Econometrics of first-price auctions. Econometrica: Journal of the Econometric Society 63(4), 953980.
Laffont, J. & Tirole, J. (1993) A Theory of Incentives in Procurement and Regulation. MIT press.
Liu, N., Luo, Y. et al. (2014) A Nonparametric Test of Exogenous Participation in First-Price Auctions. Working Papers tecipa-519, University of Toronto, Department of Economics.
Mammen, E. (2012) When Does Bootstrap Work? Asymptotic Results and Simulations, vol. 77. Springer Science & Business Media.
Marmer, V. & Shneyerov, A. (2012) Quantile-based nonparametric inference for first-price auctions. Journal of Econometrics 167(2), 345357.
Marmer, V., Shneyerov, A., & Xu, P. (2013) What model for entry in first-price auctions? A nonparametric approach. Journal of Econometrics 176(1), 4658.
Matzkin, R. L. (2013) Nonparametric identification in structural economic models. Annual Review of Economics 5(1), 457486.
Monderer, D. & Tennenholtz, M. (1998) Internet Auctions-are they Gamblers’ Attraction. Technical report, Technion.
Monderer, D. & Tennenholtz, M. (2000a) K-price auctions. Games and Economic Behavior 31(2), 220244.
Monderer, D. & Tennenholtz, M. (2000b) Optimal auctions revisited. Artificial Intelligence 120(1), 2942.
Monderer, D. & Tennenholtz, M. (2004) K-price auctions: Revenue inequalities, utility equivalence, and competition in auction design. Economic Theory 24(2), 255270.
Nashed, M. (1971) Generalized inverses, normal solvability, and iteration for singular operator equations. In Rall, L. B. (ed.), Nonlinear Functional Analysis and Applications, 311–59. Academic Press.
Paarsch, H. (1992) Deciding between the common and private value paradigms in empirical models of auctions. Journal of Econometrics 51(1–2), 191215.
Serfling, R. (1980) Approximation Theorems of Mathematical Statistics. Wiley Online Library.
Stute, W. (1986) Conditional empirical processes. The Annals of Statistics 14(2), 638647.
Tauman, Y. (2002) A note on k-price auctions with complete information. Games and Economic Behavior 41(1), 161164.
Van der Vaart, A. (1998) Asymptotic Statistics. Cambridge University Press.
Van Keilegom, I. (1998) Nonparametric Estimation of the Conditional Distribution in Regression with Censored Data. Ph.D thesis, University of Hasselt, Belgium. Available at https://ibiostat.be/publications/phd/ingridvankeilegom.pdf
Wolfstetter, E. (1996) Auctions: An introduction. Journal of Economic Surveys 10(4), 367420.
Zincenko, F. (2018) Nonparametric estimation of first-price auctions with risk-averse bidders. Journal of Econometrics 205(2), 303335.
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Econometric Theory
  • ISSN: 0266-4666
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