Estimation of Discrete Choice Dynamic Programming Models

Kasahara, Hiroyuki; Shimotsu, Katsumi

doi:10.1111/jere.12169

Cited by 5 publications

(2 citation statements)

References 49 publications

(60 reference statements)

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“…Since I first proposed this technique, Chen (2017) and Kasahara and Shimotsu (2018) have independently validated it. Kasahara and Shimotsu (2018, p. 46) reported that my refinement "leads to substantial computational gains, reducing the average computational time and the average number of iterations by factors of 17 and 9, respectively."…”

Section: Nested Fixed Pointmentioning

confidence: 99%

Strong convergence and dynamic economic models

Bray¹

2019

Quantitative Economics

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Morton and Wecker (1977) stated that the value iteration algorithm solves a dynamic program's policy function faster than its value function when the limiting Markov chain is ergodic. I show that their proof is incomplete, and provide a new proof of this classic result. I use this result to accelerate the estimation of Markov decision processes and the solution of Markov perfect equilibria.Keywords. Markov decision process, Markov perfect equilibrium, strong convergence, relative value iteration, dynamic discrete choice, nested fixed point, nested pseudo-likelihood.JEL classification. C01, C13, C15, C61, C63, C65.1. The empirical likelihood of a dynamic model depends only on the dynamic program's policy function, not its value function.2. The policy function depends only on the value function's relative differences, not its absolute level.3. The value function's relative differences converge faster than its level under repeated Bellman contractions when the underlying stochastic process is ergodic. This is called strong convergence. Morton and Wecker (1977) discovered this strong convergence property, but their proof is wanting. At one point, they implicitly replace a close-to-optimal policy with the optimal policy, which is unwarranted. I provide a new proof, based on a straightforward envelope theorem argument. Markov decision processI consider a dynamic program with discrete time periods, an infinite planning horizon, a finite state space, and an uncountable, compact action space. Taking a specific action in a specific state yields a specific utility. The goal is to determine the actions that yield the Robert L. Bray: r-bray@kellogg.northwestern.edu I would like to thank Victor Aguirregabiria, Achal Bassamboo, Thomas Bray, Seyed Emadi, Soheil Ghili, Arvind Magesan, John Rust, Dennis Zhang, and three anonymous referees for their helpful comments.

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Section: Nested Fixed Pointmentioning

confidence: 99%

Strong convergence and dynamic economic models

Bray¹

2019

Quantitative Economics

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“…This framework may be applied to many areas involving local interactions and categorical outcomes such as criminal activities, modes of transport, or technology adoption. The structural parameters are estimated using a Recursive Pseudo Maximum Likelihood with an equilibrium fixed point subroutine following the Relaxation Method proposed by Kasahara and Shimotsu (2012) and Kasahara and Shimotsu (2018).…”

Section: Introductionmentioning

confidence: 99%

Multinomial Choice with Social Interactions: Occupations in Victorian London

Guerra

Mohnen

2022

The Review of Economics and Statistics

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We study the importance of social interactions on the occupational choice in Victorian London using a multinomial choice model within an incomplete social network. Individuals form heterogeneous rational expectations about their peers' behaviors taking into account their characteristics and the strength of their ties. We show the conditions under which the endogenous, exogenous and correlated effects can be identified and a unique equilibrium can be established. Using a novel dataset, we proxy social groups by parish boundaries and strength of ties by geographic distances. Our results show the importance of the endogenous effects and reveal distinct effects by occupation.

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