Solving dynamic discrete choice models using smoothing and sieve methods
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Solving dynamic discrete choice models using smoothing and sieve methods. / Kristensen, Dennis; Mogensen, Patrick K.; Moon, Jong Myun; Schjerning, Bertel.
I: Journal of Econometrics, Bind 223, Nr. 2, 2021, s. 328-360.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Solving dynamic discrete choice models using smoothing and sieve methods
AU - Kristensen, Dennis
AU - Mogensen, Patrick K.
AU - Moon, Jong Myun
AU - Schjerning, Bertel
N1 - Publisher Copyright: © 2020 Elsevier B.V.
PY - 2021
Y1 - 2021
N2 - 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.
AB - 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.
KW - Dynamic discrete choice
KW - Monte Carlo
KW - Numerical solution
KW - Sieves
U2 - 10.1016/j.jeconom.2020.02.007
DO - 10.1016/j.jeconom.2020.02.007
M3 - Journal article
AN - SCOPUS:85094628639
VL - 223
SP - 328
EP - 360
JO - Journal of Econometrics
JF - Journal of Econometrics
SN - 0304-4076
IS - 2
ER -
ID: 270622185