Simple 3-step censored quantile regression and extramartial affairs

Victor Chernozhukov

This paper suggests simple 3- and 4-step estimators for censored quantile regression models with an envelope or a separation restriction on the censoring probability. The estimators are theoretically attractive (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 envelope 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 normal Amemiya-Tobin model and many accelerated failure and proportional hazard models. The...