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Counterfactual prediction in complete information games: Point prediction under partial identification

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  • Jun, Sung Jae
  • Pinkse, Joris
Abstract
We study the problem of counterfactual prediction in discrete decision games with complete information, pure strategies, and Nash equilibria: the presence of multiple equilibria poses unique challenges. We introduce multiple types of counterfactuals to establish sharp identified bounds for their prediction probabilities. We propose and compare various point prediction methods, namely midpoint prediction, an approach using a Dirichlet-based prior, a maximum entropy method, and minmax with an entropy constraint. On balance, we conclude that the maximum-entropy approach is the least of several evils. Our results have implications for counterfactual prediction in other models with partial identification.

Suggested Citation

  • Jun, Sung Jae & Pinkse, Joris, 2020. "Counterfactual prediction in complete information games: Point prediction under partial identification," Journal of Econometrics, Elsevier, vol. 216(2), pages 394-429.
    • Handle: RePEc:eee:econom:v:216:y:2020:i:2:p:394-429
    DOI: 10.1016/j.jeconom.2019.02.009
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    as
    1. Song, Kyungchul, 2014. "Point Decisions For Interval–Identified Parameters," Econometric Theory, Cambridge University Press, vol. 30(2), pages 334-356, April.
    2. Peter Kooreman & Adriaan R. Soetevent, 2007. "A discrete-choice model with social interactions: with an application to high school teen behavior," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 22(3), pages 599-624.
    3. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, April.
    4. Patrick Bajari & C. Lanier Benkard & Jonathan Levin, 2007. "Estimating Dynamic Models of Imperfect Competition," Econometrica, Econometric Society, vol. 75(5), pages 1331-1370, September.
    5. Federico Ciliberto & Elie Tamer, 2009. "Market Structure and Multiple Equilibria in Airline Markets," Econometrica, Econometric Society, vol. 77(6), pages 1791-1828, November.
    6. Aradillas-Lopez, Andres & Tamer, Elie, 2008. "The Identification Power of Equilibrium in Simple Games," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 261-310.
    7. Kline, Brendan, 2015. "Identification of complete information games," Journal of Econometrics, Elsevier, vol. 189(1), pages 117-131.
    8. Paul L. E. Grieco, 2014. "Discrete games with flexible information structures: an application to local grocery markets," RAND Journal of Economics, RAND Corporation, vol. 45(2), pages 303-340, June.
    9. Susan Athey & Guido W. Imbens, 2007. "Discrete Choice Models With Multiple Unobserved Choice Characteristics," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 48(4), pages 1159-1192, November.
    10. Susanne M. Schennach, 2014. "Entropic Latent Variable Integration via Simulation," Econometrica, Econometric Society, vol. 82(1), pages 345-385, January.
    11. repec:hal:spmain:info:hdl:2441/5rkqqmvrn4tl22s9mc4ao8ocg is not listed on IDEAS
    12. Bulow, Jeremy I & Geanakoplos, John D & Klemperer, Paul D, 1985. "Multimarket Oligopoly: Strategic Substitutes and Complements," Journal of Political Economy, University of Chicago Press, vol. 93(3), pages 488-511, June.
    13. Patrick Bajari & Han Hong & Stephen P. Ryan, 2010. "Identification and Estimation of a Discrete Game of Complete Information," Econometrica, Econometric Society, vol. 78(5), pages 1529-1568, September.
    14. Kline, Brendan & Tamer, Elie, 2012. "Bounds for best response functions in binary games," Journal of Econometrics, Elsevier, vol. 166(1), pages 92-105.
    15. Kooreman, Peter, 1994. "Estimation of Econometric Models of Some Discrete Games," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 9(3), pages 255-268, July-Sept.
    16. Alfred Galichon & Marc Henry, 2011. "Set Identification in Models with Multiple Equilibria," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 78(4), pages 1264-1298.
    17. Ariel Pakes & Michael Ostrovsky & Steven Berry, 2007. "Simple estimators for the parameters of discrete dynamic games (with entry/exit examples)," RAND Journal of Economics, RAND Corporation, vol. 38(2), pages 373-399, June.
    18. Golan, Amos & Judge, George G. & Miller, Douglas, 1996. "Maximum Entropy Econometrics," Staff General Research Papers Archive 1488, Iowa State University, Department of Economics.
    19. Kandori, Michihiro & Mailath, George J & Rob, Rafael, 1993. "Learning, Mutation, and Long Run Equilibria in Games," Econometrica, Econometric Society, vol. 61(1), pages 29-56, January.
    20. Cass, David & Shell, Karl, 1983. "Do Sunspots Matter?," Journal of Political Economy, University of Chicago Press, vol. 91(2), pages 193-227, April.
    21. Xiaohong Chen & Demian Pouzo, 2012. "Estimation of Nonparametric Conditional Moment Models With Possibly Nonsmooth Generalized Residuals," Econometrica, Econometric Society, vol. 80(1), pages 277-321, January.
    22. Haiqing Xu, 2014. "Estimation of discrete games with correlated types," Econometrics Journal, Royal Economic Society, vol. 17(3), pages 241-270, October.
    23. van Damme, E.E.C., 1995. "Equilibrium selection in team games," Discussion Paper 1995-125, Tilburg University, Center for Economic Research.
    24. repec:hal:wpspec:info:hdl:2441/5rkqqmvrn4tl22s9mc4ao8ocg is not listed on IDEAS
    25. Elie Tamer, 2003. "Incomplete Simultaneous Discrete Response Model with Multiple Equilibria," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 70(1), pages 147-165.
    26. Robert H. Porter & J. Douglas Zona, 1999. "Ohio School Milk Markets: An Analysis of Bidding," RAND Journal of Economics, The RAND Corporation, vol. 30(2), pages 263-288, Summer.
    27. Andres Aradillas‐Lopez, 2011. "Nonparametric probability bounds for Nash equilibrium actions in a simultaneous discrete game," Quantitative Economics, Econometric Society, vol. 2(2), pages 135-171, July.
    28. Bresnahan, Timothy F & Reiss, Peter C, 1991. "Entry and Competition in Concentrated Markets," Journal of Political Economy, University of Chicago Press, vol. 99(5), pages 977-1009, October.
    29. Mar Reguant, 2016. "Bounding Equilibria in Counterfactual Analysis," 2016 Meeting Papers 140, Society for Economic Dynamics.
    30. Panle Jia, 2008. "What Happens When Wal-Mart Comes to Town: An Empirical Analysis of the Discount Retailing Industry," Econometrica, Econometric Society, vol. 76(6), pages 1263-1316, November.
    31. Kasy, Maximilian, 2011. "Identification In Triangular Systems Using Control Functions," Econometric Theory, Cambridge University Press, vol. 27(3), pages 663-671, June.
    32. Victor Aguirregabiria & Pedro Mira, 2007. "Sequential Estimation of Dynamic Discrete Games," Econometrica, Econometric Society, vol. 75(1), pages 1-53, January.
    33. 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.
    34. Patrick Bajari & Jinyong Hahn & Han Hong & Geert Ridder, 2011. "A Note On Semiparametric Estimation Of Finite Mixtures Of Discrete Choice Models With Application To Game Theoretic Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 52(3), pages 807-824, August.
    35. Katja Seim, 2006. "An empirical model of firm entry with endogenous product‐type choices," RAND Journal of Economics, RAND Corporation, vol. 37(3), pages 619-640, September.
    36. Bresnahan, Timothy F. & Reiss, Peter C., 1991. "Empirical models of discrete games," Journal of Econometrics, Elsevier, vol. 48(1-2), pages 57-81.
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    Cited by:

    1. Hoshino, Tadao & Yanagi, Takahide, 2023. "Treatment effect models with strategic interaction in treatment decisions," Journal of Econometrics, Elsevier, vol. 236(2).
    2. Brendan Kline & Elie Tamer, 2024. "Counterfactual Analysis in Empirical Games," Papers 2410.12731, arXiv.org.
    3. Jun, Sung Jae & Pinkse, Joris, 2024. "An information–Theoretic approach to partially identified auction models," Journal of Econometrics, Elsevier, vol. 238(2).

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    More about this item

    Keywords

    Complete information games; Counterfactual prediction; Partial identification; Maximum entropy; Dirichlet process; Minmax decisions;
    All these keywords.

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C57 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Econometrics of Games and Auctions

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