Abstract - Economics Research Reports
Nested Pseudo-likelihood Estimation and Bootstrap-based Inference for Structural Discrete Markov Decision Models
By Hiroyuko Kasahara (University of Western Ontario) and Katsumi Shimotsu (Queen's University)
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.
JEL Classification: C12; C13; C15; C44; C63
Keywords: k-step bootstrap; maximum pseudo-likelihood estimators; nested fixed point algorithm; Newton-Raphson method; policy iteration