A Bayesian Semiparametric Competing Risk Model with Unobserved Heterogeneity

This paper generalizes existing econometric models for censored competing risks by introducing a new flexible specification based on a piecewise linear baseline hazard, time-varying regressors, and unobserved individual heterogeneity distributed as an infinite mixture of Generalized Inverse Gaussian (GIG) densities, nesting the gamma kernel as a special case. A common correlated latent time effect induces dependence among risks. Our model is based on underlying latent exit decisions in continuous time while only a time interval containing the exit time is observed, as is common in economic data. We do not make the simplifying assumption of discretizing exit decisions – our competing risk model setup allows for latent exit times of different risk types to be realized within the same time period. In this setting, we derive a tractable likelihood based on scaled GIG Laplace transforms and their higher-order derivatives. We apply our approach to analyzing the determinants of unemployment duration with exits to jobs in the same industry or a different industry among unemployment insurance recipients on nationally representative individual-level survey data from the U.S. Department of Labor. Our approach allows us to conduct a counterfactual policy experiment by changing the replacement rate: we find that the impact of its change on the probability of exit from unemployment is inelastic. JEL: C11, C13, C14, C41, J64