Computational Advances in Dynamic Discrete Choice

Dynamic models with discrete choice are widely used in economics, but empirical applications remain challenging because discrete actions generate non-convexities and non-smooth policy rules, and rich state vectors make grid-based dynamic programming computationally costly. This survey reviews recent computational advances for solving and estimating dynamic discrete choice and dynamic discrete–continuous choice models. We organize the survey around three common computational bottlenecks: high-dimensional state spaces, non-smooth decision boundaries, and fixed-point problems in Bellman equations and equilibrium conditions. On the solution side, we discuss scalable benchmarks and neural-network-based methods that approximate policy functions and choice probabilities. On the estimation side, we summarize full-solution and two-step conditional choice-probability approaches, and we emphasize developments that mitigate the nested fixed-point problem, including mathematical programming with equilibrium constraints, Euler-type formulations, continuous-time reformulations, sieve approximation, and machine-learning procedures.