Estimating the Derivative Function and Counterfactuals in Duration Models with Heterogeneity

This paper presents a new estimator for counterfactuals in duration models. The counterfactual in a duration model is the length of the spell in case the regressor would have been different. We introduce the structural duration function, which gives these counterfactuals. The advantage of focusing on counterfactuals is that one does not need to identify the mixed proportional hazard model. In particular, we present examples in which the mixed proportional hazard model is unidentified or has a singular information matrix but our estimator for counterfactuals still converges at rate <italic>N</italic> -super-1/2, where <italic>N</italic> is the number of observations. We apply the structural duration function to simulate important policy effects, including a change in welfare benefits.