Nonparametric Identification and Estimation of Finite Mixture Models of Dynamic Discrete Choices
Research, Preprint
OPEN
Hiroyuki Kasahara
;
Katsumi Shimotsu
(2006)
 Publisher: London (Ontario): The University of Western Ontario, Department of Economics

Subject:
C13  C23  panel data  C14  C25  sieve estimator  nonparametric identification  dynamic discrete choice models; finite mixture; nonparametric identification; panel data; sieve estimator; unobserved heterogeneity  finite mixture  dynamic discrete choice models  unobserved heterogeneity  dynamic discrete choice models, finite mixture, nonparametric identification, panel data, sieve estimator, unobserved heterogeneity
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 typespecific 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 timedimension 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 timedimension 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. Typespecific components are identifiable even when state dependence is present as long as the panel has a moderate timedimension (T = 6). We also develop a series logit estimator for finite mixture models of dynamic discrete choices and derive its convergence rate.