Nested Pseudo Likelihood Estimation of Continuous-Time Dynamic Discrete Games

• Main Authors: Blevins, Jason R, Kim, Minhae
• Format: Journal Article
• Language: English
• Published: 10-01-2023
• DOI: 10.48550/arxiv.2108.02182

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.