Nested Pseudo-likelihood Estimation And Bootstrap-based Inference For Structural Discrete Markov Decision Models

QED Working Paper Number
1063

This paper analyzes the higher-order properties of nested pseudo-likelihood (NPL) estimators and their practical implementation for parametric discrete Markov decision models in which the probability distribution is defined as a fixed point. We propose a new NPL estimator that can achieve quadratic convergence without fully solving the fixed point problem in every iteration. We then extend the NPL estimators to develop one-step NPL bootstrap procedures for discrete Markov decision models and provide some Monte Carlo evidence based on a machine replacement model of Rust (1987). The proposed one-step bootstrap test statistics and confidence intervals improve upon the first order asymptotics even with a relatively small number of iterations. Improvements are particularly noticeable when analyzing the dynamic impacts of counterfactual policies.

Author(s)

Hiroyuki Kasahara
Katsumi Shimotsu

JEL Codes

Keywords

Edgeworth expansion
k-step bootstrap
maximum pseudo-likelihood estimators
nested fixed point algorithm
Newton-Raphson method
policy iteration

Working Paper

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