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Inference on Auctions with Weak Assumptions on Information

Author

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  • Vasilis Syrgkanis
  • Elie Tamer
  • Juba Ziani

Abstract

Given a sample of bids from independent auctions, this paper examines the question of inference on auction fundamentals (e.g. valuation distributions, welfare measures) under weak assumptions on information structure. The question is important as it allows us to learn about the valuation distribution in a robust way, i.e., without assuming that a particular information structure holds across observations. We leverage the recent contributions of \cite{Bergemann2013} in the robust mechanism design literature that exploit the link between Bayesian Correlated Equilibria and Bayesian Nash Equilibria in incomplete information games to construct an econometrics framework for learning about auction fundamentals using observed data on bids. We showcase our construction of identified sets in private value and common value auctions. Our approach for constructing these sets inherits the computational simplicity of solving for correlated equilibria: checking whether a particular valuation distribution belongs to the identified set is as simple as determining whether a {\it linear} program is feasible. A similar linear program can be used to construct the identified set on various welfare measures and counterfactual objects. For inference and to summarize statistical uncertainty, we propose novel finite sample methods using tail inequalities that are used to construct confidence regions on sets. We also highlight methods based on Bayesian bootstrap and subsampling. A set of Monte Carlo experiments show adequate finite sample properties of our inference procedures. We illustrate our methods using data from OCS auctions.

Suggested Citation

  • Vasilis Syrgkanis & Elie Tamer & Juba Ziani, 2017. "Inference on Auctions with Weak Assumptions on Information," Papers 1710.03830, arXiv.org, revised Mar 2018.
  • Handle: RePEc:arx:papers:1710.03830
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    References listed on IDEAS

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    1. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
    2. Bergemann, Dirk & Morris, Stephen, 2016. "Bayes correlated equilibrium and the comparison of information structures in games," Theoretical Economics, Econometric Society, vol. 11(2), May.
    3. Dirk Bergemann & Stephen Morris, 2013. "Robust Predictions in Games With Incomplete Information," Econometrica, Econometric Society, vol. 81(4), pages 1251-1308, July.
    4. Dirk Bergemann & Benjamin Brooks & Stephen Morris, 2017. "First‐Price Auctions With General Information Structures: Implications for Bidding and Revenue," Econometrica, Econometric Society, vol. 85, pages 107-143, January.
    5. Victor Chernozhukov & Han Hong & Elie Tamer, 2007. "Estimation and Confidence Regions for Parameter Sets in Econometric Models," Econometrica, Econometric Society, vol. 75(5), pages 1243-1284, September.
    6. Dirk Bergemann & Stephen Morris, 2013. "Robust Predictions in Games With Incomplete Information," Econometrica, Econometric Society, vol. 81(4), pages 1251-1308, July.
    7. Chamberlain, Gary & Imbens, Guido W, 2003. "Nonparametric Applications of Bayesian Inference," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(1), pages 12-18, January.
    8. repec:hrv:faseco:30780157 is not listed on IDEAS
    9. repec:cwl:cwldpp:1821rrr is not listed on IDEAS
    10. Dirk Bergemann & Stephen Morris, 2013. "Robust Predictions in Games With Incomplete Information," Econometrica, Econometric Society, vol. 81(4), pages 1251-1308, July.
    11. Brendan Kline & Elie Tamer, 2016. "Bayesian inference in a class of partially identified models," Quantitative Economics, Econometric Society, vol. 7(2), pages 329-366, July.
    12. Dirk Bergemann & Stephen Morris, 2013. "Robust Predictions in Games With Incomplete Information," Econometrica, Econometric Society, vol. 81(4), pages 1251-1308, July.
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    Citations

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    Cited by:

    1. Dirk Bergemann & Stephen Morris, 2019. "Information Design: A Unified Perspective," Journal of Economic Literature, American Economic Association, vol. 57(1), pages 44-95, March.
    2. Gualdani, Cristina & Sinha, Shruti, 2019. "Identification and inference in discrete choice models with imperfect information," TSE Working Papers 19-1049, Toulouse School of Economics (TSE), revised Jun 2020.
    3. Cristina Gualdani & Shruti Sinha, 2019. "Identification and inference in discrete choice models with imperfect information," Papers 1911.04529, arXiv.org, revised Jul 2020.
    4. Dirk Bergemann & Benjamin Brooks & Stephen Morris, 2019. "Counterfactuals with Latent Information," Cowles Foundation Discussion Papers 2162R, Cowles Foundation for Research in Economics, Yale University, revised Feb 2019.
    5. Francesca Molinari, 2020. "Microeconometrics with Partial Identification," Papers 2004.11751, arXiv.org.
    6. Giovanni Compiani & Philip A. Haile & Marcelo Sant'Anna, 2018. "Common Values, Unobserved Heterogeneity, and Endogenous Entry in U.S. Offshore Oil Lease Auctions," Cowles Foundation Discussion Papers 2137R, Cowles Foundation for Research in Economics, Yale University, revised Jun 2019.
    7. Laura Doval & Jeffrey C. Ely, 2020. "Sequential Information Design," Econometrica, Econometric Society, vol. 88(6), pages 2575-2608, November.
    8. Thomas M. Russell, 2020. "Policy Transforms and Learning Optimal Policies," Papers 2012.11046, arXiv.org.
    9. Giovanni Compiani & Philip A. Haile & Marcelo Sant'Anna, 2018. "Common Values, Unobserved Heterogeneity, and Endogenous Entry in U.S. Offshore Oil Lease Auctions," Cowles Foundation Discussion Papers 2137, Cowles Foundation for Research in Economics, Yale University.
    10. Giovanni Compiani & Phil Haile & Marcelo Sant'Anna, 2018. "Common values, unobserved heterogeneity, and endogenous entry in U.S. offshore oil lease auctions," CeMMAP working papers CWP37/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    11. Bulat Gafarov, 2019. "Inference in high-dimensional set-identified affine models," Papers 1904.00111, arXiv.org.

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