Quantile Regression

The quantile regression is a semiparametric technique that has been gaining considerable popularity in economics (for example, Buchinsky, 1994). It was introduced by Koenker and Bassett (1978b) as an extension to ordinary quantiles in a location model. In this model, the conditional quantiles have linear forms. A well-known special case of quantile regression is the least absolute deviation (LAD) estimator of Koenker and Bassett (1978a), which fits medians to a linear function of covariates. In an important generalization of the quantile regression model, Powell (1984; 1986) introduced the censored quantile regression model. This model is an extension of the ‘Tobit’ model and is designed to handle situations in which some of the observations on the dependent variable are censored.