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Imposing equilibrium restrictions in the estimation of dynamic discrete games

Author

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  • Victor Aguirregabiria

    (University of Toronto)

  • Mathieu Marcoux

    (Université de Montréal)

Abstract

Imposing equilibrium restrictions provides substantial gains in the estimation of dynamic discrete games. Estimation algorithms imposing these restrictions – MPEC, NFXP, NPL, and variations – have different merits and limitations. MPEC guarantees local convergence, but requires the computation of high-dimensional Jacobians. The NPL algorithm avoids the computation of these matrices, but – in games – may fail to converge to the consistent NPL estimator. We study the asymptotic properties of the NPL algorithm treating the iterative procedure as performed in finite samples. We find that there are always samples for which the algorithm fails to converge, and this introduces a selection bias. We also propose a spectral algorithm to compute the NPL estimator. This algorithm satisfies local convergence and avoids the computation of Jacobian matrices. We present simulation evidence illustrating our theoretical results and the good properties of the spectral algorithm.

Suggested Citation

  • Victor Aguirregabiria & Mathieu Marcoux, 2019. "Imposing equilibrium restrictions in the estimation of dynamic discrete games," Cahiers de recherche 2019-08, Universite de Montreal, Departement de sciences economiques.
    • Handle: RePEc:mtl:montde:2019-08
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    File URL: http://hdl.handle.net/1866/22366
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    Cited by:

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    2. Victor Aguirregabiria & Allan Collard-Wexler & Stephen P. Ryan, 2021. "Dynamic Games in Empirical Industrial Organization," Papers 2109.01725, arXiv.org, revised Sep 2021.
    3. Takeshi Fukasawa, 2025. "When do firms sell high durability products? The case of light bulb industry," Papers 2503.23792, arXiv.org, revised May 2025.
    4. Blevins, Jason R. & Kim, Minhae, 2024. "Nested Pseudo likelihood estimation of continuous-time dynamic discrete games," Journal of Econometrics, Elsevier, vol. 238(2).
    5. Takeshi Fukasawa, 2024. "Fast and simple inner-loop algorithms of static / dynamic BLP estimations," Papers 2404.04494, arXiv.org, revised Apr 2025.
    6. Takeshi Fukasawa, 2024. "Computationally Efficient Methods for Solving Discrete-time Dynamic models with Continuous Actions," Papers 2407.04227, arXiv.org, revised Feb 2025.
    7. Pál, László & Sándor, Zsolt, 2023. "Comparing procedures for estimating random coefficient logit demand models with a special focus on obtaining global optima," International Journal of Industrial Organization, Elsevier, vol. 88(C).
    8. Takeshi FUKASAWA & Hiroshi OHASHI, 2023. "Long-run Effect of a Horizontal Merger and Its Remedial Standards," Discussion papers 23001, Research Institute of Economy, Trade and Industry (RIETI).

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    More about this item

    Keywords

    Dynamic discrete game; Nested pseudo-likelihood; Fixed point algorithms; Convergence; Convergence selection bias;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C57 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Econometrics of Games and Auctions
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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