Solving dynamic discrete choice models using smoothing and sieve methods

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 Bellm...

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Bibliographic Details
Published in:Journal of econometrics 2021-08, Vol.223 (2), p.328-360
Main Authors: Kristensen, Dennis, Mogensen, Patrick K., Moon, Jong Myun, Schjerning, Bertel
Format: Article
Language:English
Subjects:
Approximation
Decision making models
Discrete choice
Discrete element method
Dynamic discrete choice
Expected values
Monte Carlo
Monte Carlo simulation
Numerical solution
Operators
Random variables
Sieves
Simulation
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Summary: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.
ISSN:0304-4076
1872-6895
DOI:10.1016/j.jeconom.2020.02.007