Botosaru, Irene (2011) A Duration Model with Dynamic Unobserved Heterogeneity. TSE Working Paper, n. 11-262

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Abstract

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.