Nonparametric identification and estimation of finite mixture models of dynamic discrete choices

In dynamic discrete choice analysis, controlling for unobserved heterogeneity is an important issue, and finite mixture models provide flexible ways to account for unobserved heterogeneity. This paper studies nonparametric identifiability of type probabilities and type-specific component distributions in finite mixture models of dynamic discrete choices. We derive sufficient conditions for nonparametric identification for various finite mixture models of dynamic discrete choices used in applied work. Three elements emerge as the important determinants of identification; the time-dimension of panel data, the number of values the covariates can take, and the heterogeneity of the response of different types to changes in the covariates. For example, in a simple case, a time-dimension of T=3 is sufficient for identification, provided that the number of values the covariates can take is no smaller than the number of types, and that the changes in the covariates induce sufficiently heterogeneous variations in the choice probabilities across types. Type-specific components are identifiable even when state dependence is present as long as the panel has a moderate time-dimension (T>=6). We also develop a series logit estimator for finite mixture models of dynamic discrete choices and derive its convergence rate.