arXiv 20 Jul 2024 · Econometrics
arXiv:2407.14914 · PDF · DOI · OpenAlex · Extracted main text
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. Critically, these methods provide a complete chain of analytical derivatives from the equilibrium value function through the log likelihood function, eliminating numerical approximations in both model solution and estimation and improving finite-sample statistical properties. Monte Carlo experiments demonstrate substantial gains in computational time and estimator accuracy, enabling estimation of richer models of strategic interaction.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Blevins, J. R (2025) Identification and estimation of continuous time dynamic discrete choice games self | 1.000 | 8 | 4 | 100% |
| 2 | Arcidiacono, P., P. Bayer, J. R. Blevins, and P. B. Ellickson (2016) Estimation of dynamic discrete choice models in continuous time with an application to retail competition | 0.961 | 9 | 5 | 89% |
| 3 | Rust, J (1987) Optimal replacement of GMC bus engines: An empirical model of Harold Zurcher | 0.737 | 3 | 2 | 100% |
| 4 | Sherlock, C (2022) Direct statistical inference for finite Markov jump processes via the matrix exponential | 0.737 | 3 | 2 | 100% |
| 5 | Aguirregabiria, V. and P. Mira (2007) Sequential estimation of dynamic discrete games | 0.644 | 3 | 2 | 67% |
| 6 | Billingsley, P (1961) Statistical Inference for Markov Processes | 0.644 | 2 | 2 | 100% |
| 7 | Blevins, J. R. and M. Kim (2024) Nested pseudo likelihood estimation of continuous-time dynamic discrete games self | 0.644 | 2 | 2 | 100% |
| 8 | Hotz, V. J. and R. A. Miller (1993) Conditional choice probabilities and the estimation of dynamic models | 0.644 | 2 | 2 | 100% |
| 9 | Jensen, A (1953) Markoff chains as an aid in the study of Markoff processes | 0.644 | 2 | 2 | 100% |
| 10 | Pesendorfer, M. and P. Schmidt-Dengler (2008) Asymptotic least squares estimators for dynamic games | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 44 scored citations.