Publication: Pseudo-likelihood Estimation and Bootstrap Inference for Structural Discrete Markov Decision Models

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Title	Pseudo-likelihood Estimation and Bootstrap Inference for Structural Discrete Markov Decision Models
Authors/Editors*	Hiroyuki Kasahara and Katsumi Shimotsu
Where published*	Journal of Econometrics
How published*	Journal
Year*	2008
Volume	146
Number	1
Pages	92-106
Publisher	elsevier
Keywords	Edgeworth expansion, finite mixture, k-step bootstrap, maximum
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Abstract	This paper analyzes the higher-order properties of the estimators based on the nested pseudo-likelihood (NPL) algorithm and the practical implementation of such estimators for parametric discrete Markov decision models. We derive the rate at which the NPL algorithm converges to the MLE and provide a theoretical explanation for the simulation results in Hotz et al. (1994) and Aguirregabiria and Mira (2002), in which iterating the NPL algorithm improves the accuracy of the estimator. We then propose a new NPL algorithm that can achieve quadratic convergence without fully solving the fixed point problem in every iteration and apply our estimation procedure to a finite mixture model. We also develop one-step NPL bootstrap procedures for discrete Markov decision models. The Monte Carlo simulation evidence based on a machine replacement model of Rust (1987) shows that the proposed one-step bootstrap test statistics and confidence intervals improve upon the first order asymptotics even with a relatively small number of iterations.