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Approximating High-dimensional Dynamic Models: Sieve Value Function Iteration

In: Structural Econometric Models

Author

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  • Peter Arcidiacono
  • Patrick Bayer
  • Federico A. Bugni
  • Jonathan James

Abstract

Many dynamic problems in economics are characterized by large state spaces which make both computing and estimating the model infeasible. We introduce a method for approximating the value function of high-dimensional dynamic models based on sieves and establish results for the (a) consistency, (b) rates of convergence, and (c) bounds on the error of approximation. We embed this method for approximating the solution to the dynamic problem within an estimation routine and prove that it provides consistent estimates of the modelik’s parameters. We provide Monte Carlo evidence that our method can successfully be used to approximate models that would otherwise be infeasible to compute, suggesting that these techniques may substantially broaden the class of models that can be solved and estimated.

Suggested Citation

  • Peter Arcidiacono & Patrick Bayer & Federico A. Bugni & Jonathan James, 2013. "Approximating High-dimensional Dynamic Models: Sieve Value Function Iteration," Advances in Econometrics, in: Structural Econometric Models, volume 31, pages 45-95, Emerald Group Publishing Limited.
    • Handle: RePEc:eme:aecozz:s0731-9053(2013)0000032002
    DOI: 10.1108/S0731-9053(2013)0000032002
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    More about this item

    Keywords

    Large state space; dynamic decision problem; sieve approximation; value function; value function iteration; C02; C44; C60; C63;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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