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Bayesian Estimation of a Dynamic Game with Endogenous, Partially Observed, Serially Correlated State

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  • A. Ronald Gallant
  • Han Hong
  • Ahmed Khwaja

Abstract

We consider dynamic games that can have state variables that are partially observed, serially correlated, endogenous, and heterogeneous. We propose a Bayesian method that uses a particle filter to compute an unbiased estimate of the likelihood within a Metropolis chain. Unbiasedness guarantees that the stationary density of the chain is the exact posterior, not an approximation. The number of particles required is easily determined. The regularity conditions are weak. Results are verified by simulation from two dynamic oligopolistic games with endogenous state. One is an entry game with feedback to costs based on past entry and the other a model of an industry with a large number of heterogeneous firms that compete on product quality.

Suggested Citation

  • A. Ronald Gallant & Han Hong & Ahmed Khwaja, 2012. "Bayesian Estimation of a Dynamic Game with Endogenous, Partially Observed, Serially Correlated State," Working Papers 12-01, Duke University, Department of Economics.
    • Handle: RePEc:duk:dukeec:12-01
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    1. Patrick Bajari & C. Lanier Benkard & Jonathan Levin, 2007. "Estimating Dynamic Models of Imperfect Competition," Econometrica, Econometric Society, vol. 75(5), pages 1331-1370, September.
    2. Federico Ciliberto & Elie Tamer, 2009. "Market Structure and Multiple Equilibria in Airline Markets," Econometrica, Econometric Society, vol. 77(6), pages 1791-1828, November.
    3. Gabriel Y. Weintraub & C. Lanier Benkard & Benjamin Van Roy, 2008. "Markov Perfect Industry Dynamics With Many Firms," Econometrica, Econometric Society, vol. 76(6), pages 1375-1411, November.
    4. Thierry Magnac & David Thesmar, 2002. "Identifying Dynamic Discrete Decision Processes," Econometrica, Econometric Society, vol. 70(2), pages 801-816, March.
    5. V. Joseph Hotz & Robert A. Miller, 1993. "Conditional Choice Probabilities and the Estimation of Dynamic Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 60(3), pages 497-529.
    6. Philip A. Haile & Ali Hortaçsu & Grigory Kosenok, 2008. "On the Empirical Content of Quantal Response Equilibrium," American Economic Review, American Economic Association, vol. 98(1), pages 180-200, March.
    7. Juan F. Rubio-Ramirez & Jesus Fernández-Villaverde, 2005. "Estimating dynamic equilibrium economies: linear versus nonlinear likelihood," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(7), pages 891-910.
    8. Han Hong & Ahmed Khwaja & A. Ronald Gallant, 2010. "Dynamic Entry with Cross Product Spillovers: An Application to the Generic Drug Industry," Working Papers 10-59, Duke University, Department of Economics.
    9. Berry, Steven T, 1992. "Estimation of a Model of Entry in the Airline Industry," Econometrica, Econometric Society, vol. 60(4), pages 889-917, July.
    10. Richard Ericson & Ariel Pakes, 1995. "Markov-Perfect Industry Dynamics: A Framework for Empirical Work," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 62(1), pages 53-82.
    11. Christophe Andrieu & Arnaud Doucet & Roman Holenstein, 2010. "Particle Markov chain Monte Carlo methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(3), pages 269-342, June.
    12. 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.
    13. Katherine Ho, 2009. "Insurer-Provider Networks in the Medical Care Market," American Economic Review, American Economic Association, vol. 99(1), pages 393-430, March.
    14. William R. Gebhardt & Charles M. C. Lee & Bhaskaran Swaminathan, 2001. "Toward an Implied Cost of Capital," Journal of Accounting Research, Wiley Blackwell, vol. 39(1), pages 135-176, June.
    15. 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.
    16. Keane, Michael P & Wolpin, Kenneth I, 1997. "The Career Decisions of Young Men," Journal of Political Economy, University of Chicago Press, vol. 105(3), pages 473-522, June.
    17. Gabriel Y. Weintraub & C. Lanier Benkard & Benjamin Van Roy, 2010. "Computational Methods for Oblivious Equilibrium," Operations Research, INFORMS, vol. 58(4-part-2), pages 1247-1265, August.
    18. A. Ronald Gallant & George Tauchen, "undated". "Reproducing Partial Observed Systems with Application to Interest Rate Diffusions," Computing in Economics and Finance 1997 114, Society for Computational Economics.
    19. Susumu Imai & Neelam Jain & Andrew Ching, 2009. "Bayesian Estimation of Dynamic Discrete Choice Models," Econometrica, Econometric Society, vol. 77(6), pages 1865-1899, November.
    20. Flury, Thomas & Shephard, Neil, 2011. "Bayesian Inference Based Only On Simulated Likelihood: Particle Filter Analysis Of Dynamic Economic Models," Econometric Theory, Cambridge University Press, vol. 27(05), pages 933-956, October.
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    More about this item

    Keywords

    Dynamic Games; Partially Observed State; Endogenous State; Serially Correlated State; Particle Filter;
    All these keywords.

    JEL classification:

    • E00 - Macroeconomics and Monetary Economics - - General - - - General
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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