Sequential Monte Carlo Methods for Estimating Dynamic Microeconomic Models

Jason R. Blevins
Duke University

Abstract. This paper develops methods for estimating a general class of dynamic structural microeconomic models with serially correlated unobserved state variables. These methods are based on sequential Monte Carlo methods, or particle filters, which simultaneously estimate both the structural parameters and the trajectory of the unobserved state variables. We focus two important special cases: single agent dynamic discrete choice models and dynamic games of incomplete information. The methods are applicable to discrete- and continuous-state-space models. We first develop a broad nonlinear state space framework which includes as special cases many dynamic structural models commonly used in applied microeconomics. Next, we discuss the nonlinear filtering problem that arises due to the presence of a latent state variable and show how it can be solved using sequential Monte Carlo methods which can approximate the posterior distribution of the latent state. We then turn to estimation of the structural parameters and consider two approaches, based on modifications of the standard methods of full-solution maximum likelihood estimation and two-step estimation in a revealed preference framework. Finally, we introduce an extension of the classic bus engine replacement model of Rust (1987) and use it both to carry out a series of Monte Carlo experiments and to provide empirical results using the original data.

Keywords: dynamic games, dynamic discrete choice, unobserved heterogeneity, serial correlation, identification, sequential Monte Carlo, particle filtering.

JEL Classification: C13, C15.

BibTeX Record:

@TechReport{blevins09sequential,
  author       = {Jason R. Blevins},
  title        = {Sequential Monte Carlo Methods for Estimating Dynamic
                  Microeconomic Models},
  institution  = {Duke University},
  year         = 2009,
  type         = {Unpublished manuscript}
}