Nonparametric Analysis of a Duration Model with Stochastic Unobserved Heterogeneity

This paper develops nonparametric identification and estimation results for a single-spell hazard model, where the unobserved heterogeneity is specified as a LÈvy subordinator. The identification approach solves a nonlinear Volterra integral equation of the first kind with anunknown kernel function defined on a non-compact support. Both the kernel of the integral operator, which models the distribution of the unobserved heterogeneity, and the functions that enter it nonlinearly are identified given regularity conditions and minimal variation in the observed covariates. The paper proposes a shape-constrained nonparametric two-step sieve minimum distance estimator. The second step estimates the kernel of the integral operator, exploiting a monotonicity property. Rates of convergence are derived and Monte Carlo experiments show the finite sample performance of the estimator.