Leveraging Uniformization and Sparsity for Estimation and Computation of Continuous Time Dynamic Discrete Choice Games

TL;DR

This paper introduces novel computational and econometric methods for continuous-time dynamic discrete choice games, improving estimation accuracy and efficiency through uniformization, sparsity exploitation, and analytical derivatives.

Contribution

It develops convergence rates, Newton-Kantorovich algorithms, and a new value function representation, enhancing solution and estimation in continuous-time dynamic discrete choice models.

Findings

Significant improvements in estimation accuracy and computational speed.

Effective handling of discrete-time snapshot data.

Extension of methods to related models like Markov jump processes.

Abstract

Continuous-time empirical dynamic discrete choice games offer notable computational advantages over discrete-time models. This paper addresses remaining computational and econometric challenges to further improve both model solution and estimation. We establish convergence rates for value iteration and policy evaluation with fixed beliefs, and develop Newton-Kantorovich methods that exploit analytical Jacobians and sparse matrix structure. We apply uniformization both to derive a new representation of the value function that draws direct analogies to discrete-time models and to enable stable computation of the matrix exponential and its parameter derivatives for estimation with discrete-time snapshot data, a common but challenging data scenario. These methods provide a complete chain of analytical derivatives from the value function for a given equilibrium through the log-likelihood function, eliminating the need for numerical differentiation and improving finite-sample estimation accuracy and computational efficiency. Monte Carlo experiments demonstrate substantial gains in both statistical performance and computational efficiency, enabling researchers to estimate richer models of strategic interaction. While we focus on games, our methods extend to single-agent dynamic discrete choice and continuous-time Markov jump processes.