A Duration Model with Dynamic Unobserved Heterogeneity

The paper considers a new class of duration models in which unobserved heterogeneity changes with time. The class addresses two main questions: How does the exit probability from a state vary when unobserved heterogeneity evolves through time? And do changes in unobserved heterogeneity have a timing effect? We show the non- and semi-parametric identification of the new class by solving a nonlinear integral equation with unknown kernel. Both the function of observed covariates and the mean of the distribution of unobserved heterogeneity are nonparametrically identified. Identifying timing effects and the distribution of unobserved heterogeneity requires stronger assumptions on either one of the two. An extension to the case when unobserved heterogeneity is a function of observed covariates is also identified. We show that sieve maximum likelihood estimators are consistent and present Monte Carlo simulations for both correct specification and misspecification. The paper also presents an empirical model of unemployment duration in which individuals exit unemployment when total accumulated losses due to unemployment cross over a self-imposed spending limit.