Duration Dependence and Nonparametric Heterogeneity: A Monte Carlo Study

We examine the behaviour of the nonparametric maximum likelihood estimator (NPMLE) for a discrete duration model with unobserved heterogeneity and unknown duration dependence. We find that a nonparametric specification of either the duration dependence or unobserved heterogeneity, when the other feature of the hazard is known to be absent, leads to estimators that are well behaved even in modestly sized samples. In contrast, there is a large and systematic bias in the parameters of these components when both are specified nonparametrically, as well as a complementary bias in the coefficients on observed heterogeneity. Furthermore, these biases diminish very gradually as sample size increases. We find that a minor modification of the quasilikelihood that penalizes specifications with many points of support leads to a dramatic improvement.