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Faster estimation of dynamic discrete choice models using index invertibility

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  • Jackson Bunting
  • Takuya Ura
Abstract
Many estimators of dynamic discrete choice models with persistent unobserved heterogeneity have desirable statistical properties but are computationally intensive. In this paper we propose a method to quicken estimation for a broad class of dynamic discrete choice problems by exploiting semiparametric index restrictions. Specifically, we propose an estimator for models whose reduced form parameters are invertible functions of one or more linear indices (Ahn, Ichimura, Powell and Ruud 2018), a property we term index invertibility. We establish that index invertibility implies a set of equality constraints on the model parameters. Our proposed estimator uses the equality constraints to decrease the dimension of the optimization problem, thereby generating computational gains. Our main result shows that the proposed estimator is asymptotically equivalent to the unconstrained, computationally heavy estimator. In addition, we provide a series of results on the number of independent index restrictions on the model parameters, providing theoretical guidance on the extent of computational gains. Finally, we demonstrate the advantages of our approach via Monte Carlo simulations.

Suggested Citation

  • Jackson Bunting & Takuya Ura, 2023. "Faster estimation of dynamic discrete choice models using index invertibility," Papers 2304.02171, arXiv.org, revised Jul 2024.
    • Handle: RePEc:arx:papers:2304.02171
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    References listed on IDEAS

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    1. V. Joseph Hotz & Robert A. Miller & Seth Sanders & Jeffrey Smith, 1994. "A Simulation Estimator for Dynamic Models of Discrete Choice," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(2), pages 265-289.
    2. Victor Aguirregabiria & Arvind Magesan, 2020. "Identification and Estimation of Dynamic Games When Players’ Beliefs Are Not in Equilibrium," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 87(2), pages 582-625.
    3. Martin Pesendorfer & Philipp Schmidt-Dengler, 2008. "Asymptotic Least Squares Estimators for Dynamic Games -super-1," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 75(3), pages 901-928.
    4. 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.
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