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

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

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Abstract. Continuous-time empirical dynamic discrete choice games offer notable computational advantages over discrete-time models. This paper addresses remaining computational challenges to further improve both model solution and maximum likelihood 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 likelihood-based estimation with snapshot data only, a common but challenging data scenario. These methods provide a complete chain of analytical derivatives from the equilibrium value function through the log likelihood function, eliminating the need for numerical differentiation and improving estimation accuracy and computational efficiency. Monte Carlo experiments demonstrate substantial gains in computational time and estimator accuracy, enabling estimation of richer models of strategic interaction.

Keywords: Continuous time, Markov decision processes, dynamic discrete choice, dynamic stochastic games, uniformization, matrix exponential, sparse matrices, computational methods, numerical methods.

JEL Classification: C63, C73, L13.