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Identification and Estimation of Continuous Time Dynamic Discrete Choice Games

Jason R. Blevins.
The Ohio State University, Department of Economics
Working Paper.

2x2 Continuous Time Entry Model
2x2 Continuous Time Entry Model

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Abstract.

This paper considers the theoretical, computational, and econometric properties of a class of continuous time dynamic discrete choice games with stochastically sequential moves, introduced by Arcidiacono, Bayer, Blevins, and Ellickson (2016, Review of Economic Studies). In particular, we consider identification of the rate of move arrivals in the model, which was assumed to be known in previous work, as well as a generalized version of the model with heterogeneous move arrival rates. We first re-establish conditions for existence of a Markov perfect equilibrium in the generalized model and then consider identification of the model primitives with only discrete time data sampled at a fixed time interval. Three canonical models are considered: a single agent renewal model, a dynamic model of entry and exit, and a quality ladder model of oligopoly dynamics. These models are foundational for many applications in applied microeconomics. Through these examples we examine the computational properties of the model and statistical properties of estimators via a series of small- and large-scale Monte Carlo experiments and an empirical example using data from Rust (1987, Econometrica). The experiments shed light on how the parameter estimates behave as one moves from continuous time data to discrete time data of decreasing frequency and on the computational feasibility of the model as the number of firms grows. The empirical example highlights the impact of allowing decision rates to vary.

Keywords: Continuous time, Markov decision processes, dynamic discrete choice, dynamic games, identification.

JEL Classification: C13, C35, C62, C73.