Semiparametric Efficiency Bounds and Efficient Estimation of Discrete Duration Models with Unspecified HazardRate

We consider semiparametric estimation of discrete duration models whose hazard rate can be characterized as an unknown transformation of a parametric index of the observable covariates and elapsed spell length. The information matrix is derived. In the case of separable duration dependence the information matrix for the parameters of the index is singular. In that situation, the information matrix for the regression component of the hazard function is derived. The information matrix is also singular when individual specific/time invariant unobserved errors are introduced. We develop root N- consistent estimators for those instances when the information matrix is nonsingular. Less than -root N-consistent estimators of the duration dependence component of the hazard rate of the separable model are developed. Simulations and an application to strike durations illustrate the viability of the approach.