Semiparametric identification in duration models

This paper explores the identifiability of ratios of derivatives of the index function in a model of a duration process in which the impact of covariates on the hazard function passes through a single index. The model allows duration and the index to appear in a nonseparable form in the hazard function and includes a latent heterogeneity term which acts multiplicatively on the hazard function. The model allows covariates to be endogenous, that is to be correlated with the heterogeneity term. Quantile invariance, local order and local rank conditions are shown to be sufficient to permit identification of ratios of derivatives of the index function. The framework constructed in this paper is suitable for the analysis of identification in panel duration models with heterogeneity.