Truncated quantile regression

Abstract

This paper deals with the estimation of conditional quantiles of linear truncated regression models with known truncation point. The truncated quantile model is shown to posses an important property related to or 2 (0, 1), a set of quantiles of the original latent model: truncation-invariance. Truncation-invariance means that there is a one-to-one function F : or ! tr, tr 2 (0, 1) and where tr is a set of quantiles of the truncated variable. That property turns out to be fundamental to identification of the model, as well as estimation and inference. In fact, simplicity is a major appeal of our semi-parametric approach compared to alternatives estimator of truncated models, as it does not require any modification of available software.