IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1912.10488.html
   My bibliography  Save this paper

Efficient and Convergent Sequential Pseudo-Likelihood Estimation of Dynamic Discrete Games

Author

Listed:
  • Adam Dearing
  • Jason R. Blevins

Abstract

We propose a new sequential Efficient Pseudo-Likelihood (EPL) estimator for structural economic models with an equality constraint, particularly dynamic discrete choice games of incomplete information. Each iteration in the EPL sequence is consistent and asymptotically efficient, and iterating to convergence improves finite sample performance. For dynamic single-agent models, we show that Aguirregabiria and Mira's (2002, 2007) Nested Pseudo-Likelihood (NPL) estimator arises as a special case of EPL. In dynamic games, EPL maintains its efficiency properties, although NPL does not. And a convenient change of variable in the equilibrium fixed point equation ensures EPL iterations have the same computational simplicity as NPL iterations. Furthermore, EPL iterations are stable and locally convergent to the finite-sample maximum likelihood estimator at a nearly-quadratic rate for all regular Markov perfect equilibria, including unstable equilibria where NPL encounters convergence problems. Monte Carlo simulations confirm the theoretical results and demonstrate EPL's good performance in finite samples.

Suggested Citation

  • Adam Dearing & Jason R. Blevins, 2019. "Efficient and Convergent Sequential Pseudo-Likelihood Estimation of Dynamic Discrete Games," Papers 1912.10488, arXiv.org.
  • Handle: RePEc:arx:papers:1912.10488
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1912.10488
    File Function: Latest version
    Download Restriction: no

    References listed on IDEAS

    as
    1. Doraszelski, Ulrich & Escobar, Juan, 2010. "A theory of regular Markov perfect equilibria in dynamic stochastic games: genericity, stability, and purification," Theoretical Economics, Econometric Society, vol. 5(3), September.
    2. 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.
    3. Rust, John, 1987. "Optimal Replacement of GMC Bus Engines: An Empirical Model of Harold Zurcher," Econometrica, Econometric Society, vol. 55(5), pages 999-1033, September.
    4. V. Joseph Hotz & Robert A. Miller, 1993. "Conditional Choice Probabilities and the Estimation of Dynamic Models," Review of Economic Studies, Oxford University Press, vol. 60(3), pages 497-529.
    5. Patrick Bajari & C. Lanier Benkard & Jonathan Levin, 2007. "Estimating Dynamic Models of Imperfect Competition," Econometrica, Econometric Society, vol. 75(5), pages 1331-1370, September.
    6. Michael Egesdal & Zhenyu Lai & Che‐Lin Su, 2015. "Estimating dynamic discrete‐choice games of incomplete information," Quantitative Economics, Econometric Society, vol. 6(3), pages 567-597, November.
    7. Gourieroux,Christian & Monfort,Alain, 1995. "Statistics and Econometric Models 2 volume set," Cambridge Books, Cambridge University Press, number 9780521478373, December.
    8. V. Joseph Hotz & Robert A. Miller & Seth Sanders & Jeffrey Smith, 1994. "A Simulation Estimator for Dynamic Models of Discrete Choice," Review of Economic Studies, Oxford University Press, vol. 61(2), pages 265-289.
    9. Victor Aguirregabiria & Pedro Mira, 2002. "Swapping the Nested Fixed Point Algorithm: A Class of Estimators for Discrete Markov Decision Models," Econometrica, Econometric Society, vol. 70(4), pages 1519-1543, July.
    10. Pakes, Ariel S, 1986. "Patents as Options: Some Estimates of the Value of Holding European Patent Stocks," Econometrica, Econometric Society, vol. 54(4), pages 755-784, July.
    11. Victor Aguirregabiria & Pedro Mira, 2007. "Sequential Estimation of Dynamic Discrete Games," Econometrica, Econometric Society, vol. 75(1), pages 1-53, January.
    12. Martin Pesendorfer & Philipp Schmidt-Dengler, 2010. "Sequential Estimation of Dynamic Discrete Games: A Comment," Econometrica, Econometric Society, vol. 78(2), pages 833-842, March.
    13. Ulrich Doraszelski & Kenneth L. Judd, 2012. "Avoiding the curse of dimensionality in dynamic stochastic games," Quantitative Economics, Econometric Society, vol. 3(1), pages 53-93, March.
    14. Peter Arcidiacono & Robert A. Miller, 2011. "Conditional Choice Probability Estimation of Dynamic Discrete Choice Models With Unobserved Heterogeneity," Econometrica, Econometric Society, vol. 79(6), pages 1823-1867, November.
    15. Che‐Lin Su & Kenneth L. Judd, 2012. "Constrained Optimization Approaches to Estimation of Structural Models," Econometrica, Econometric Society, vol. 80(5), pages 2213-2230, September.
    16. Victor Aguirregabiria & Mathieu Marcoux, 2019. "Imposing equilibrium restrictions in the estimation of dynamic discrete games," Working Papers tecipa-646, University of Toronto, Department of Economics.
    17. Kasahara, Hiroyuki & Shimotsu, Katsumi, 2008. "Pseudo-likelihood estimation and bootstrap inference for structural discrete Markov decision models," Journal of Econometrics, Elsevier, vol. 146(1), pages 92-106, September.
    18. Federico A. Bugni & Jackson Bunting, 2018. "On the iterated estimation of dynamic discrete choice games," Papers 1802.06665, arXiv.org, revised May 2020.
    19. Martin Pesendorfer & Philipp Schmidt-Dengler, 2008. "Asymptotic Least Squares Estimators for Dynamic Games -super-1," Review of Economic Studies, Oxford University Press, vol. 75(3), pages 901-928.
    20. Hiroyuki Kasahara & Katsumi Shimotsu, 2012. "Sequential Estimation of Structural Models With a Fixed Point Constraint," Econometrica, Econometric Society, vol. 80(5), pages 2303-2319, September.
    21. Peter Arcidiacono & Patrick Bayer & Jason R. Blevins & Paul B. Ellickson, 2016. "Estimation of Dynamic Discrete Choice Models in Continuous Time with an Application to Retail Competition," Review of Economic Studies, Oxford University Press, vol. 83(3), pages 889-931.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Victor Aguirregabiria & Mathieu Marcoux, 2019. "Imposing equilibrium restrictions in the estimation of dynamic discrete games," Working Papers tecipa-646, University of Toronto, Department of Economics.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:1912.10488. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators). General contact details of provider: http://arxiv.org/ .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.