Three-step censored quantile regression and extramarital affairs

This article suggests very simple three-step estimators for censored quantile regression models with a separation restriction on the censoring probability. The estimators are theoretically attractive (i.e.. asymptotically as efficient as the celebrated Powell's censored least absolute deviation estimator). At the same time, they are conceptually simple and have trivial computational expenses. They are especially useful in samples of small size or models with many regressors. with desirable finite-sample properties and small bias. The separation restriction costs a small reduction of generality relative to the canonical censored regression quantile model, yet its main plausible features remain intact. The estimator can also be used to estimate a large class of traditional models. including the normal Amemiya-Tobin model and many accelerated failure and proportional hazard models. We illustrate the approach with an extramarital affairs example and contrast our findings with those of Fair.