Nested Pseudo Likelihood Estimation of Continuous-Time Dynamic Discrete Games

TL;DR

This paper develops a continuous-time nested pseudo likelihood estimator for dynamic discrete choice models and games, establishing its theoretical properties and demonstrating its effectiveness through Monte Carlo simulations.

Contribution

It adapts the NPL estimator from discrete to continuous time, providing consistency, asymptotic normality, and bias reduction insights for continuous-time models.

Findings

Estimator performs well in large samples

Finite-sample bias can be reduced with iteration

Mis-specification leads to significant bias in key parameters

Abstract

We introduce a sequential estimator for continuous time dynamic discrete choice models (single-agent models and games) by adapting the nested pseudo likelihood (NPL) estimator of Aguirregabiria and Mira (2002, 2007), developed for discrete time models with discrete time data, to the continuous time case with data sampled either discretely (i.e., uniformly-spaced snapshot data) or continuously. We establish conditions for consistency and asymptotic normality of the estimator, a local convergence condition, and, for single agent models, a zero Jacobian property assuring local convergence. We carry out a series of Monte Carlo experiments using an entry-exit game with five heterogeneous firms to confirm the large-sample properties and demonstrate finite-sample bias reduction via iteration. In our simulations we show that the convergence issues documented for the NPL estimator in discrete time models are less likely to affect comparable continuous-time models. We also show that there can be large bias in economically-relevant parameters, such as the competitive effect and entry cost, from estimating a misspecified discrete time model when in fact the data generating process is a continuous time model.