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Semiparametric estimation in models of first-price, sealed-bid auctions with affiliation

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  • Hubbard, Timothy P.
  • Li, Tong
  • Paarsch, Harry J.

Abstract

Within the affiliated private-values paradigm, we develop a tractable empirical model of equilibrium behaviour at first-price, sealed-bid auctions. The model is non-parametrically identified, but the rate of convergence in estimation is slow when the number of bidders is even moderately large, so we develop a semiparametric estimation strategy, focusing on the Archimedean family of copulae and implementing this framework using particular members—the Clayton, Frank, and Gumbel copulae. We apply our framework to data from low-price, sealed-bid auctions used by the Michigan Department of Transportation to procure road-resurfacing services, rejecting the hypothesis of independence and finding significant (and high) affiliation in cost signals.

Suggested Citation

  • Hubbard, Timothy P. & Li, Tong & Paarsch, Harry J., 2012. "Semiparametric estimation in models of first-price, sealed-bid auctions with affiliation," Journal of Econometrics, Elsevier, vol. 168(1), pages 4-16.
  • Handle: RePEc:eee:econom:v:168:y:2012:i:1:p:4-16
    DOI: 10.1016/j.jeconom.2011.09.006
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    References listed on IDEAS

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    1. Emmanuel Guerre & Isabelle Perrigne & Quang Vuong, 2000. "Optimal Nonparametric Estimation of First-Price Auctions," Econometrica, Econometric Society, vol. 68(3), pages 525-574, May.
    2. Chen, Xiaohong & Fan, Yanqin, 2006. "Estimation of copula-based semiparametric time series models," Journal of Econometrics, Elsevier, vol. 130(2), pages 307-335, February.
    3. Paarsch, Harry J., 1997. "Deriving an estimate of the optimal reserve price: An application to British Columbian timber sales," Journal of Econometrics, Elsevier, vol. 78(2), pages 333-357, June.
    4. Li, Tong & Perrigne, Isabelle & Vuong, Quang, 2000. "Conditionally independent private information in OCS wildcat auctions," Journal of Econometrics, Elsevier, vol. 98(1), pages 129-161, September.
    5. Krishna, Vijay, 2009. "Auction Theory," Elsevier Monographs, Elsevier, edition 2, number 9780123745071, August.
    6. Donald, Stephen G. & Paarsch, Harry J., 2002. "Superconsistent estimation and inference in structural econometric models using extreme order statistics," Journal of Econometrics, Elsevier, vol. 109(2), pages 305-340, August.
    7. Xiaohong Chen & Xiaotong Shen, 1998. "Sieve Extremum Estimates for Weakly Dependent Data," Econometrica, Econometric Society, vol. 66(2), pages 289-314, March.
    8. Donald, S.G. & Paarsch, H.J., 1992. "Maximum Likelihood Estimation in Empirical Models of Auctions," UWO Department of Economics Working Papers 9211, University of Western Ontario, Department of Economics.
    9. Laffont, Jean-Jacques & Ossard, Herve & Vuong, Quang, 1995. "Econometrics of First-Price Auctions," Econometrica, Econometric Society, vol. 63(4), pages 953-980, July.
    10. Harry J. Paarsch & Han Hong, 2006. "An Introduction to the Structural Econometrics of Auction Data," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262162350, November.
    11. Philip A. Haile & Elie Tamer, 2003. "Inference with an Incomplete Model of English Auctions," Journal of Political Economy, University of Chicago Press, vol. 111(1), pages 1-51, February.
    12. Fermanian, Jean-David, 2005. "Goodness-of-fit tests for copulas," Journal of Multivariate Analysis, Elsevier, vol. 95(1), pages 119-152, July.
    13. Jean-David FERMANIAN & Olivier SCAILLET, 2004. "Some Statistical Pitfalls In Copula Modeling For Financial Applications," FAME Research Paper Series rp108, International Center for Financial Asset Management and Engineering.
    14. Donald, Stephen G & Paarsch, Harry J, 1993. "Piecewise Pseudo-maximum Likelihood Estimation in Empirical Models of Auctions," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 34(1), pages 121-148, February.
    15. Paarsch, Harry J., 1992. "Deciding between the common and private value paradigms in empirical models of auctions," Journal of Econometrics, Elsevier, vol. 51(1-2), pages 191-215.
    16. Brendstrup, Bjarne & Paarsch, Harry J., 2007. "Semiparametric identification and estimation in multi-object, English auctions," Journal of Econometrics, Elsevier, vol. 141(1), pages 84-108, November.
    17. Müller, Alfred & Scarsini, Marco, 2005. "Archimedean copulæ and positive dependence," Journal of Multivariate Analysis, Elsevier, vol. 93(2), pages 434-445, April.
    18. Donald, Stephen G. & Paarsch, Harry J., 1996. "Identification, Estimation, and Testing in Parametric Empirical Models of Auctions within the Independent Private Values Paradigm," Econometric Theory, Cambridge University Press, vol. 12(03), pages 517-567, August.
    19. Laffont, Jean-Jacques & Vuong, Quang, 1996. "Structural Analysis of Auction Data," American Economic Review, American Economic Association, vol. 86(2), pages 414-420, May.
    20. Milgrom, Paul R & Weber, Robert J, 1982. "A Theory of Auctions and Competitive Bidding," Econometrica, Econometric Society, vol. 50(5), pages 1089-1122, September.
    21. Tong Li, 2005. "Econometrics of first-price auctions with entry and binding reservation prices," Journal of Econometrics, Elsevier, vol. 126(1), pages 173-200, May.
    22. Castro, Luciano I. de, 2007. "Affiliation, equilibrium existence and the revenue ranking of auctions," UC3M Working papers. Economics we074622, Universidad Carlos III de Madrid. Departamento de Economía.
    23. Guerre, E. & Perrigne, I. & Vuong, Q., 1995. "Nonparametric Estimation of First-Price Auctions," Papers 9504, Southern California - Department of Economics.
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    Citations

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    Cited by:

    1. repec:spr:annopr:v:258:y:2017:i:2:d:10.1007_s10479-016-2164-x is not listed on IDEAS
    2. Tong Li & Bingyu Zhang, 2015. "Affiliation and Entry in First-Price Auctions with Heterogeneous Bidders: An Analysis of Merger Effects," American Economic Journal: Microeconomics, American Economic Association, vol. 7(2), pages 188-214, May.
    3. Luciano De Castro, 2010. "Affiliation, Equilibrium Existence and Revenue Ranking of Auctions," Discussion Papers 1530, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    4. repec:eee:forpol:v:80:y:2017:i:c:p:107-115 is not listed on IDEAS
    5. Hickman Brent R. & Hubbard Timothy P. & Sağlam Yiğit, 2012. "Structural Econometric Methods in Auctions: A Guide to the Literature," Journal of Econometric Methods, De Gruyter, vol. 1(1), pages 67-106, August.
    6. Luciano I. de Castro, 2009. "Affiliation and Dependence in Economic Models," Discussion Papers 1479, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    7. Timothy P. Hubbard & Harry J. Paarsch, 2012. "On the Numerical Solution of Equilibria in Auction Models with Asymmetries within the Private-Values Paradigm," Carlo Alberto Notebooks 291, Collegio Carlo Alberto.
    8. Rosa, Benjamin, 2016. "Resident Bid Preference, Affiliation, and Procurement Competition: Evidence from New Mexico," MPRA Paper 68759, University Library of Munich, Germany.
    9. repec:eee:indorg:v:52:y:2017:i:c:p:282-306 is not listed on IDEAS
    10. Ma, Jun & Marmer, Vadim & Shneyerov, Artyom, 2016. "Inference for First-Price Auctions with Guerre, Perrigne, and Vuong's estimator," Microeconomics.ca working papers vadim_marmer-2016-4, Vancouver School of Economics, revised 17 Mar 2018.

    More about this item

    Keywords

    First-price; sealed-bid auctions; Copulae; Affiliation;

    JEL classification:

    • C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • L1 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance

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