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IDENTIFICATION AND ESTIMATION IN A THIRD-PRICE AUCTION MODEL

Published online by Cambridge University Press:  08 March 2019

Andreea Enache and
Jean-Pierre Florens
Andreea Enache*
Affiliation:
Stockholm School of Economics
Jean-Pierre Florens
Affiliation:
Toulouse School of Economics
*
*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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Abstract

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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.

Information

Type
ARTICLES
Information
Econometric Theory , Volume 36 , Issue 3 , June 2020, pp. 386 - 409
Copyright
Copyright © Cambridge University Press 2019 

Footnotes

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.

References

REFERENCES

Arnold, B., Balakrishnan, N., Nagaraja, H., & Nagaraja, H. (2008) A First Course in Order Statistics, vol. 54. Society for Industrial Mathematics.CrossRefGoogle Scholar
Athey, S. & Haile, P. (2002) Identification of standard auction models. Econometrica 70(6), 2107–2140.CrossRefGoogle Scholar
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, 5633–5751.CrossRefGoogle Scholar
Csörgö, M. (1983) Quantile Processes with Statistical Applications, vol. 42. Society for Industrial Mathematics.CrossRefGoogle Scholar
Donald, S. & Paarsch, H. (1993) Piecewise pseudo-maximum likelihood estimation in empirical models of auctions. International Economic Review 34(1), 121–148.CrossRefGoogle Scholar
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), 517–567.CrossRefGoogle Scholar
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), 642–669.CrossRefGoogle Scholar
Enache, A. & Florens, J.-P. (2017) A quantile approach to the estimation of first-price private value auction. Working Paper.CrossRefGoogle Scholar
Enache, A. & Florens, J.-P. (2018a) Nonparametric estimation for regulation models. Annals of Economics and Statistics/Annales d’Économie et de Statistique (131), 45–58.Google Scholar
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.Google Scholar
Florens, J.-P., Protopopescu, C., & Richard, J. (1998) Identification and estimation of a class of game theoretic models (Mimeo). University of Toulouse.Google Scholar
Florens, J.-P. & Sbaï, E. (2010) Local identification in empirical games of incomplete information. Econometric Theory 26(06), 1638–1662.CrossRefGoogle Scholar
Gimenes, N. (2017) Econometrics of ascending auctions by quantile regression. Review of Economics and Statistics 99(5), 944–953.CrossRefGoogle Scholar
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).Google Scholar
Goeree, J., Maasland, E., Onderstal, S., & Turner, J. (2005) How (not) to raise money. Journal of Political Economy 113(4), 897–918.CrossRefGoogle Scholar
Guerre, E., Perrigne, I., & Vuong, Q. (2000) Optimal nonparametric estimation of first-price auctions. Econometrica 68(3), 525–574.CrossRefGoogle Scholar
Guerre, E., Perrigne, I., & Vuong, Q. (2009) Nonparametric identification of risk aversion in first-price auctions under exclusion restrictions. Econometrica 77(4), 1193–1227.Google Scholar
Guerre, E. & Sabbah, C. (2012) Uniform bias study and Bahadur representation for local polynomial estimators of the conditional quantile function. Econometric Theory 28(1), 87–129.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
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), 868–879.CrossRefGoogle Scholar
Laffont, J., Ossard, H., & Vuong, Q. (1995) Econometrics of first-price auctions. Econometrica: Journal of the Econometric Society 63(4), 953–980.CrossRefGoogle Scholar
Laffont, J. & Tirole, J. (1993) A Theory of Incentives in Procurement and Regulation. MIT press.Google Scholar
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.Google Scholar
Mammen, E. (2012) When Does Bootstrap Work? Asymptotic Results and Simulations, vol. 77. Springer Science & Business Media.Google Scholar
Marmer, V. & Shneyerov, A. (2012) Quantile-based nonparametric inference for first-price auctions. Journal of Econometrics 167(2), 345–357.CrossRefGoogle Scholar
Marmer, V., Shneyerov, A., & Xu, P. (2013) What model for entry in first-price auctions? A nonparametric approach. Journal of Econometrics 176(1), 46–58.CrossRefGoogle Scholar
Matzkin, R. L. (2013) Nonparametric identification in structural economic models. Annual Review of Economics 5(1), 457–486.CrossRefGoogle Scholar
Monderer, D. & Tennenholtz, M. (1998) Internet Auctions-are they Gamblers’ Attraction. Technical report, Technion.Google Scholar
Monderer, D. & Tennenholtz, M. (2000a) K-price auctions. Games and Economic Behavior 31(2), 220–244.CrossRefGoogle Scholar
Monderer, D. & Tennenholtz, M. (2000b) Optimal auctions revisited. Artificial Intelligence 120(1), 29–42.CrossRefGoogle Scholar
Monderer, D. & Tennenholtz, M. (2004) K-price auctions: Revenue inequalities, utility equivalence, and competition in auction design. Economic Theory 24(2), 255–270.Google Scholar
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.CrossRefGoogle Scholar
Paarsch, H. (1992) Deciding between the common and private value paradigms in empirical models of auctions. Journal of Econometrics 51(1–2), 191–215.CrossRefGoogle Scholar
Serfling, R. (1980) Approximation Theorems of Mathematical Statistics. Wiley Online Library.CrossRefGoogle Scholar
Stute, W. (1986) Conditional empirical processes. The Annals of Statistics 14(2), 638–647.CrossRefGoogle Scholar
Tauman, Y. (2002) A note on k-price auctions with complete information. Games and Economic Behavior 41(1), 161–164.CrossRefGoogle Scholar
Van der Vaart, A. (1998) Asymptotic Statistics. Cambridge University Press.CrossRefGoogle Scholar
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.pdfGoogle Scholar
Wolfstetter, E. (1996) Auctions: An introduction. Journal of Economic Surveys 10(4), 367–420.CrossRefGoogle Scholar
Zincenko, F. (2018) Nonparametric estimation of first-price auctions with risk-averse bidders. Journal of Econometrics 205(2), 303–335.CrossRefGoogle Scholar