Estimation of a nonparametric censored regression model with an application to unemployment insurance spells

In this paper we consider identification and estimation of a censored nonparametric location scale model. We first show that in the case where the location function is strictly less than the (fixed) censoring point for all values in the support of the explanatory variables, then the location function is not identified anywhere. In contrast, if the location function is greater or equal to the censoring point with positive probability, then the location function is identified on the entire support, including the region where the location function is below the censoring point. In the latter case we propose a simple estimation procedure based on combining conditional quantile estimators for three distinct quantiles. The new estimator is shown to converge at the optimal nonparametric rate with a limiting normal distribution. A small scale simulation study indicates that the proposed estimation procedure performs well in finite samples. We also present an empirical application to unemployment insurance duration using administrative level data from New Jersey.