Comparison between Tobit and Interval Censored Regression Model in STIFIN Test and GPA Prediction

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 on STIFIN Test and GPA prediction using example data test. The survival curve for benefit receipt based on our new estimator closely matches the Kaplan-Meier estimate in the non-censored region and is relatively flat past the censoring point. We find that incorrect distributional assumptions can significantly bias the results for estimates past the censoring point.