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A new approach to identifying generalized competing risks models with application to second-price auctions

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  • Komarova, Tatiana

Abstract

This paper proposes an approach to proving nonparametric identification for distributions of bidders' values in asymmetric second-price auctions. I consider the case when bidders have independent private values and the only available data pertain to the winner's identity and the transaction price. My proof of identification is constructive and is based on establishing the existence and uniqueness of a solution to the system of nonlinear differential equations that describes relationships between unknown distribution functions and observable functions. The proof is conducted in two logical steps. First, I prove the existence and uniqueness of a local solution. Then I describe a method that extends this local solution to the whole support. This paper delivers other interesting results. I demonstrate how this approach can be applied to obtain identification in auctions with a stochastic number of bidders. Furthermore, I show that my results can be extended to generalized competing risks models.

Suggested Citation

  • Komarova, Tatiana, 2013. "A new approach to identifying generalized competing risks models with application to second-price auctions," LSE Research Online Documents on Economics 50245, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:50245
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    File URL: http://eprints.lse.ac.uk/50245/
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    References listed on IDEAS

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    1. A. Banerji & J.V. Meenakshi, 2004. "Buyer Collusion and Efficiency of Government Intervention in Wheat Markets in Northern India: An Asymmetric Structural Auctions Analysis," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 86(1), pages 236-253.
    2. Susan Athey & Jonathan Levin & Enrique Seira, 2011. "Comparing open and Sealed Bid Auctions: Evidence from Timber Auctions," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 126(1), pages 207-257.
    3. Athey, Susan & Haile, Philip A., 2007. "Nonparametric Approaches to Auctions," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 60, Elsevier.
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    Cited by:

    1. Yao Luo & Peijun Sang & Ruli Xiao, 2024. "Order Statistics Approaches to Unobserved Heterogeneity in Auctions," Working Papers tecipa-776, University of Toronto, Department of Economics.
    2. Federico A. Bugni & Yulong Wang, 2023. "Inference in Auctions with Many Bidders Using Transaction Prices," Papers 2311.09972, arXiv.org, revised Sep 2024.
    3. Fan Wu & Yi Xin, 2024. "Estimating Nonseparable Selection Models: A Functional Contraction Approach," Papers 2411.01799, arXiv.org.
    4. Komarova, Tatiana, 2017. "Extremum sieve estimation in k-out-of-n system," LSE Research Online Documents on Economics 79388, London School of Economics and Political Science, LSE Library.
    5. Kong, Yunmi, 2022. "Identification of English auctions when losing entrants are not observed," International Journal of Industrial Organization, Elsevier, vol. 85(C).
    6. Yao Luo & Ruli Xiao, 2019. "Identification of Auction Models Using Order Statistics," Working Papers tecipa-630, University of Toronto, Department of Economics.
    7. Luo, Yao & Xiao, Ruli, 2023. "Identification of auction models using order statistics," Journal of Econometrics, Elsevier, vol. 236(1).

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    More about this item

    Keywords

    Second-price auctions; ascending auctions; asymmetric bidders; private values; nonparametric identification; competing risks; coherent systems;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C41 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Duration Analysis; Optimal Timing Strategies
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions

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