Identification and Estimation of Continuous-Time Dynamic Discrete Choice Games

TL;DR

This paper explores the identification, equilibrium existence, and estimation of continuous-time dynamic discrete choice games, analyzing their properties with Monte Carlo simulations and empirical data, especially considering variable move rates and discrete sampling.

Contribution

It extends previous models by allowing unknown move arrival rates, heterogeneous move rates, and discrete sampling, providing new conditions for equilibrium and estimation methods.

Findings

Establishment of conditions for equilibrium existence in generalized models.

Analysis of estimator behavior with varying data sampling frequencies.

Empirical demonstration of decision rate effects on model estimates.

Abstract

This paper considers the theoretical, computational, and econometric properties of continuous time dynamic discrete choice games with stochastically sequential moves, introduced by Arcidiacono, Bayer, Blevins, and Ellickson (2016). We consider identification of the rate of move arrivals, which was assumed to be known in previous work, as well as a generalized version with heterogeneous move arrival rates. We re-establish conditions for existence of a Markov perfect equilibrium in the generalized model and consider identification of the model primitives with only discrete time data sampled at fixed intervals. Three foundational example models are considered: a single agent renewal model, a dynamic entry and exit model, and a quality ladder model. Through these examples we examine the computational and statistical properties of estimators via Monte Carlo experiments and an empirical example using data from Rust (1987). The experiments show how parameter estimates behave when moving from continuous time data to discrete time data of decreasing frequency and the computational feasibility as the number of firms grows. The empirical example highlights the impact of allowing decision rates to vary.