CCP Estimation of Dynamic Discrete Choice Models with Unobserved Heterogeneity

Abstract

We adapt the Expectation-Maximization (EM) algorithm to incorporate unobserved hetero- geneity into conditional choice probability (CCP) estimators of dynamic discrete choice problems. The unobserved heterogeneity can be time-invariant, fully transitory, or follow a Markov chain. By exploiting finite dependence, we extend the class of dynamic optimization problems where CCP estimators provide a computationally cheap alternative to full solution methods. We also develop CCP estimators for mixed discrete/continuous problems with unobserved heterogeneity. Further, when the unobservables affect both dynamic discrete choices and some other outcome, we show that the probability distribution of the unobserved heterogeneity can be estimated in a first stage, while simultaneously accounting for dynamic selection. The probabilities of being in each of the unobserved states from the first stage are then taken as given and used as weights in the second stage estimation of the dynamic discrete choice parameters. Monte Carlo results for the three experimental designs we develop confirm that our algorithms perform quite well, both in terms of computational time and in the precision of the parameter estimates.