Quantile Regression Methods

Quantile regression is emerging as a popular statistical approach, which complements the estimation of conditional mean models. While the latter only focuses on one aspect of the conditional distribution of the dependent variable, the mean, quantile regression provides more detailed insights by modeling conditional quantiles. Quantile regression can therefore detect whether the partial effect of a regressor on the conditional quantiles is the same for all quantiles or differs across quantiles. Quantile regression can provide evidence for a statistical relationship between two variables even if the mean regression model does not.
We provide a short informal introduction into the principle of quantile regression which includes an illustrative application from empirical labor market research. This is followed by briefly sketching the underlying statistical model for linear quantile regression based on a cross-section sample. We summarize various important extensions of the model including the nonlinear quantile regression model, censored quantile regression, and quantile regression for time-series data. We also discuss a number of more recent extensions of the quantile regression model to censored data, duration data, and endogeneity, and we describe how quantile regression can be used for decomposition analysis. Finally, we identify several key issues, which should be addressed by future research, and we provide an overview of quantile regression implementations in major statistics software. Our treatment of the topic is based on the perspective of applied researchers using quantile regression in their empirical work.