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Solving Dynamic Discrete Choice Models Using Smoothing and Sieve Methods

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Listed:
  • Dennis Kristensen
  • Patrick K. Mogensen
  • Jong Myun Moon
  • Bertel Schjerning

Abstract

We propose to combine smoothing, simulations and sieve approximations to solve for either the integrated or expected value function in a general class of dynamic discrete choice (DDC) models. We use importance sampling to approximate the Bellman operators defining the two functions. The random Bellman operators, and therefore also the corresponding solutions, are generally non-smooth which is undesirable. To circumvent this issue, we introduce a smoothed version of the random Bellman operator and solve for the corresponding smoothed value function using sieve methods. We show that one can avoid using sieves by generalizing and adapting the `self-approximating' method of Rust (1997) to our setting. We provide an asymptotic theory for the approximate solutions and show that they converge with root-N-rate, where $N$ is number of Monte Carlo draws, towards Gaussian processes. We examine their performance in practice through a set of numerical experiments and find that both methods perform well with the sieve method being particularly attractive in terms of computational speed and accuracy.

Suggested Citation

  • Dennis Kristensen & Patrick K. Mogensen & Jong Myun Moon & Bertel Schjerning, 2019. "Solving Dynamic Discrete Choice Models Using Smoothing and Sieve Methods," Papers 1904.05232, arXiv.org.
  • Handle: RePEc:arx:papers:1904.05232
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    File URL: http://arxiv.org/pdf/1904.05232
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    References listed on IDEAS

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    1. Andriy Norets, 2010. "Continuity and differentiability of expected value functions in dynamic discrete choice models," Quantitative Economics, Econometric Society, vol. 1(2), pages 305-322, November.
    2. repec:wly:quante:v:8:y:2017:i:2:p:317-365 is not listed on IDEAS
    3. Judd, Kenneth L. & Maliar, Lilia & Maliar, Serguei & Valero, Rafael, 2014. "Smolyak method for solving dynamic economic models: Lagrange interpolation, anisotropic grid and adaptive domain," Journal of Economic Dynamics and Control, Elsevier, vol. 44(C), pages 92-123.
    4. Robin L. Lumsdaine & James H. Stock & David A. Wise, 1992. "Three Models of Retirement: Computational Complexity versus Predictive Validity," NBER Chapters,in: Topics in the Economics of Aging, pages 21-60 National Bureau of Economic Research, Inc.
    5. John Rust, 1997. "Using Randomization to Break the Curse of Dimensionality," Econometrica, Econometric Society, vol. 65(3), pages 487-516, May.
    6. Pál, Jenő & Stachurski, John, 2013. "Fitted value function iteration with probability one contractions," Journal of Economic Dynamics and Control, Elsevier, vol. 37(1), pages 251-264.
    7. McFadden, Daniel, 1989. "A Method of Simulated Moments for Estimation of Discrete Response Models without Numerical Integration," Econometrica, Econometric Society, vol. 57(5), pages 995-1026, September.
    8. John Rust, 1997. "A Comparison of Policy Iteration Methods for Solving Continuous-State, Infinite-Horizon Markovian Decision Problems Using Random, Quasi-random, and Deterministic Discretizations," Computational Economics 9704001, University Library of Munich, Germany.
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