Estimation of Dynamic Discrete Choice Models in Continuous Time

This paper provides a method for estimating large-scale dynamic discrete choice models (in both single- and multi-agent settings) within a continuous time framework. The advantage of working in continuous time is that state changes occur sequentially, rather than simultaneously, avoiding a substantial curse of dimensionality that arises in multi-agent settings. Eliminating this computational bottleneck is the key to providing a seamless link between estimating the model and performing post-estimation counterfactuals. While recently developed two-step estimation techniques have made it possible to estimate large-scale problems, solving for equilibria remains computationally challenging. In many cases, the models that applied researchers estimate do not match the models that are then used to perform counterfactuals. By modeling decisions in continuous time, we are able to take advantage of the recent advances in estimation while preserving a tight link between estimation and policy experiments. We also consider estimation in situations with imperfectly sampled data, such as when we do not observe the decision not to move, or when data is aggregated over time, such as when only discrete-time data are available at regularly spaced intervals. We illustrate the speed and scope of our framework using several large-scale Monte Carlo experiments.