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Identification and Estimation of Games with Incomplete Information Using Excluded Regressors, Second Version

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Author Info

  • Arthur Lewbel

    ()
    (Department of Economics, Boston College)

  • Xun Tang

    ()
    (Department of Economics, University of Pennsylvania)

Abstract

We show nonparametric point identification of static binary games with incomplete information, using excluded regressors. An excluded regressor for player ¡ is a state variable that does not affect other players’ utility and is additively separable from other components in ¡’s payoff. When excluded regressors are conditionally independent from private information, the interaction effects between players and the marginal effects of excluded regressors on payoff are identified. In addition, if excluded regressors vary sufficiently relative to the support of private information, then the full payoff functions and the distribution of private information are also nonparametrically identified. We illustrate how excluded regressors satisfying these conditions arise in contexts such as entry games between firms, as variation in observed components of fixed costs. We extend our approach to accommodate the existence of multiple Bayesian Nash equilibria in the data-generating process without assuming equilibrium selection rules. For a semiparametric model with linear payoff, we propose root-N consistent and asymptotically normal estimators for parameters in players’payoffs.

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Bibliographic Info

Paper provided by Penn Institute for Economic Research, Department of Economics, University of Pennsylvania in its series PIER Working Paper Archive with number 12-018.

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Length: 61 pages
Date of creation: 25 Nov 2010
Date of revision: 20 Mar 2012
Handle: RePEc:pen:papers:12-018

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Related research

Keywords: Games with Incomplete Information; Excluded Regressors; Nonparametric Identification; Semiparametric Estimation; Multiple Equilibria;

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References

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  1. Arthur Lewbel & Oliver Linton & D. L. McFadden, 2006. "Estimating features of a distribution from binomial data," LSE Research Online Documents on Economics 4418, London School of Economics and Political Science, LSE Library.
  2. Magnac, Thierry & Maurin, Eric, 2007. "Identification and information in monotone binary models," Journal of Econometrics, Elsevier, vol. 139(1), pages 76-104, July.
  3. Magnac, Thierry & Maurin, Eric, 2004. "Partial Identification in Monotone Binary Models: Discrete Regressors and Interval Data," IDEI Working Papers 280, Institut d'Économie Industrielle (IDEI), Toulouse, revised Jan 2005.
  4. Federico Ciliberto & Elie Tamer, 2009. "Market Structure and Multiple Equilibria in Airline Markets," Econometrica, Econometric Society, vol. 77(6), pages 1791-1828, November.
  5. Arie Beresteanu & Ilya Molchanov & Francesca Molinari, 2011. "Sharp Identification Regions in Models With Convex Moment Predictions," Econometrica, Econometric Society, vol. 79(6), pages 1785-1821, November.
  6. repec:bla:restud:v:75:y:2008:i:3:p:835-864 is not listed on IDEAS
  7. Bajari, Patrick & Hong, Han & Krainer, John & Nekipelov, Denis, 2010. "Estimating Static Models of Strategic Interactions," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(4), pages 469-482.
  8. 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, 09.
  9. Áureo de Paula & Xun Tang, 2012. "Inference of Signs of Interaction Effects in Simultaneous Games With Incomplete Information," Econometrica, Econometric Society, vol. 80(1), pages 143-172, 01.
  10. Victor Aguirregabiria & Pedro Mira, 2005. "A Hybrid Genetic Algorithm For The Maximum Likelihood Estimation Of Models With Multiple Equilibria: A First Report," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 1(02), pages 295-303.
  11. Brock, William A. & Durlauf, Steven N., 2007. "Identification of binary choice models with social interactions," Journal of Econometrics, Elsevier, vol. 140(1), pages 52-75, September.
  12. Aradillas-Lopez, Andres, 2010. "Semiparametric estimation of a simultaneous game with incomplete information," Journal of Econometrics, Elsevier, vol. 157(2), pages 409-431, August.
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