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

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

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References

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  1. Thierry Magnac & Eric Maurin, 2004. "Partial Identification in Monotone Binary Models : Discrete Regressors and Interval Data," Working Papers, Centre de Recherche en Economie et Statistique 2004-11, Centre de Recherche en Economie et Statistique.
  2. 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.
  3. Magnac, Thierry & Maurin, Eric, 2003. "Identification and Information in Monotone Binary Models," IDEI Working Papers 180, Institut d'Économie Industrielle (IDEI), Toulouse, revised Oct 2004.
  4. Ciliberto, Federico & Tamer, Elie, 2009. "Market structure and multiple equilibria in airline markets," MPRA Paper 38635, University Library of Munich, Germany.
  5. Patrick Bajari & Han Hong & Stephen P. Ryan, 2010. "Identification and Estimation of a Discrete Game of Complete Information," Econometrica, Econometric Society, Econometric Society, vol. 78(5), pages 1529-1568, 09.
  6. Brock,W.A. & Durlauf,S.N., 2004. "Identification of binary choice models with social interactions," Working papers, Wisconsin Madison - Social Systems 2, Wisconsin Madison - Social Systems.
  7. Aureo de Paula & Xun Tang, 2010. "Inference of Signs of Interaction Effects in Simultaneous Games with Incomplete Information," PIER Working Paper Archive 10-010, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  8. Aradillas-Lopez, Andres, 2010. "Semiparametric estimation of a simultaneous game with incomplete information," Journal of Econometrics, Elsevier, Elsevier, vol. 157(2), pages 409-431, August.
  9. repec:bla:restud:v:75:y:2008:i:3:p:835-864 is not listed on IDEAS
  10. Arie Beresteanu & Ilya Molchanov & Francesca Molinari, 2010. "Sharp identification regions in models with convex moment predictions," CeMMAP working papers, Centre for Microdata Methods and Practice, Institute for Fiscal Studies CWP25/10, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  11. Arthur Lewbel & Daniel McFadden & Oliver Linton, 1997. "Estimating Features of a Distribution from Binomial Data," Boston College Working Papers in Economics 442, Boston College Department of Economics, revised 01 Jul 2010.
  12. Patrick Bajari & Han Hong & John Krainer & Denis Nekipelov, 2006. "Estimating Static Models of Strategic Interaction," NBER Working Papers 12013, National Bureau of Economic Research, Inc.
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