Nested Pseudo-likelihood Estimation and Bootstrap-based Inference for Structural Discrete Markov Decision Models - Hiroyuki Kasahara; Katsumi Shimotsu (Queen's University, Department of Economics, 2006)
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.
Keywords: C12; C13; C14; C15; C44; C63; 330; Edgeworth expansion; k-step bootstrap; maximum pseudo-likelihood estimators; nested fixed point algorithm; Newton-Raphson method; policy iteration