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Identification and estimation in first-price auctions with risk-averse bidders and selective entry

Author

Listed:
  • Matthew Gentry

    () (Institute for Fiscal Studies and London School of Economics)

  • Tong Li

    () (Institute for Fiscal Studies and Vanderbilt University)

  • Jingfeng Lu

    (Institute for Fiscal Studies)

Abstract

We study identification and estimation in first-price auctions with risk-averse bidders and selective entry, building on a flexible entry and bidding framework we call the Affiliated Signal with Risk Aversion (AS- RA) model. This framework extends the AS model of Gentry and Li (2014) to accommodate arbitrary bidder risk aversion, thereby nesting a variety of standard models as special cases. It poses, however, a unique methodological challenge - existing results on identification with risk aversion fail in the presence of selection, while the selection-robust bounds of Gentry and Li (2014) fail in the presence of risk aversion. Motivated by this problem, we translate excludable variation in potential competition into identified sets for AS-RA primitives under various classes of restrictions on the model. We show that a single parametric restriction - on the copula governing selection into entry - is typically sufficient to restore point identification of all primitives. In contrast, a parametric form for utility yields point identification of the utility function but only partial identification of remaining primitives. Finally, we outline a simple semiparametric estimator combining Constant Relative Risk Aversion utility with a parametric signal-value copula. Simulation evidence suggests that this estimator performs very well even in small samples, underscoring the practical value of our identification results.

Suggested Citation

  • Matthew Gentry & Tong Li & Jingfeng Lu, 2015. "Identification and estimation in first-price auctions with risk-averse bidders and selective entry," CeMMAP working papers CWP16/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  • Handle: RePEc:ifs:cemmap:16/15
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    File URL: https://www.ifs.org.uk/uploads/cemmap/wps/cwp161515.pdf
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    References listed on IDEAS

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    1. James J. Heckman, 1976. "The Common Structure of Statistical Models of Truncation, Sample Selection and Limited Dependent Variables and a Simple Estimator for Such Models," NBER Chapters,in: Annals of Economic and Social Measurement, Volume 5, number 4, pages 475-492 National Bureau of Economic Research, Inc.
    2. Philip A. Haile & Han Hong & Matthew Shum, 2003. "Nonparametric Tests for Common Values in First-Price Sealed-Bid Auctions," Cowles Foundation Discussion Papers 1445, Cowles Foundation for Research in Economics, Yale University.
    3. Tong Li & Xiaoyong Zheng, 2009. "Entry and Competition Effects in First-Price Auctions: Theory and Evidence from Procurement Auctions," Review of Economic Studies, Oxford University Press, vol. 76(4), pages 1397-1429.
    4. Samuelson, William F., 1985. "Competitive bidding with entry costs," Economics Letters, Elsevier, vol. 17(1-2), pages 53-57.
    5. repec:eee:econom:v:205:y:2018:i:2:p:303-335 is not listed on IDEAS
    6. Susan Athey & Jonathan Levin & Enrique Seira, 2011. "Comparing open and Sealed Bid Auctions: Evidence from Timber Auctions," The Quarterly Journal of Economics, Oxford University Press, vol. 126(1), pages 207-257.
    7. Gentry, Matthew & Stroup, Caleb, 2019. "Entry and competition in takeover auctions," Journal of Financial Economics, Elsevier, vol. 132(2), pages 298-324.
    8. Bajari, Patrick & Hortacsu, Ali, 2003. " The Winner's Curse, Reserve Prices, and Endogenous Entry: Empirical Insights from eBay Auctions," RAND Journal of Economics, The RAND Corporation, vol. 34(2), pages 329-355, Summer.
    9. Marmer, Vadim & Shneyerov, Artyom & Xu, Pai, 2013. "What model for entry in first-price auctions? A nonparametric approach," Journal of Econometrics, Elsevier, vol. 176(1), pages 46-58.
    10. Fang, Hanming & Tang, Xun, 2014. "Inference of bidders’ risk attitudes in ascending auctions with endogenous entry," Journal of Econometrics, Elsevier, vol. 180(2), pages 198-216.
    11. Matt Shum & Phil Haile & Han Hong, 2003. "Nonparametric Tests for Common Values in First-Price Auctions," Economics Working Paper Archive 501, The Johns Hopkins University,Department of Economics.
    12. Jingfeng Lu & Isabelle Perrigne, 2008. "Estimating risk aversion from ascending and sealed-bid auctions: the case of timber auction data," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(7), pages 871-896.
    13. Zincenko, Federico, 2018. "Nonparametric estimation of first-price auctions with risk-averse bidders," Journal of Econometrics, Elsevier, vol. 205(2), pages 303-335.
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    Cited by:

    1. Tong Li & Jingfeng Lu & Li Zhao, 2015. "Auctions with selective entry and risk averse bidders: theory and evidence," RAND Journal of Economics, RAND Corporation, vol. 46(3), pages 524-545, September.
    2. Serafin J. Grundl & Yu Zhu, 2019. "Robust Inference in First-Price Auctions : Experimental Findings as Identifying Restrictions," Finance and Economics Discussion Series 2019-006, Board of Governors of the Federal Reserve System (US).
    3. repec:eee:econom:v:210:y:2019:i:2:p:363-378 is not listed on IDEAS
    4. repec:eee:econom:v:204:y:2018:i:2:p:189-206 is not listed on IDEAS

    More about this item

    Keywords

    Auctions; endogenous participation; risk aversion; identification;

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