Solving dynamic discrete choice models using smoothing and sieve methods

Dennis Kristensen*, Patrick K. Mogensen, Jong Myun Moon, Bertel Schjerning

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

3 Citations (Scopus)

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 smoothed versions of the random Bellman operators and solve for the corresponding smoothed value functions using sieve methods. We also show that one can avoid using sieves by generalizing and adapting the “self-approximating” method of Rust (1997b) to our setting. We provide an asymptotic theory for both approximate solution methods and show that they converge with 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.

Original languageEnglish
JournalJournal of Econometrics
Volume223
Issue number2
Pages (from-to)328-360
ISSN0304-4076
DOIs
Publication statusPublished - 2021

Bibliographical note

Publisher Copyright:
© 2020 Elsevier B.V.

Keywords

  • Dynamic discrete choice
  • Monte Carlo
  • Numerical solution
  • Sieves

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