Quantile Regression Methods

Bernd Fitzenberger, Ralf Andreas Wilke

Research output: Chapter in Book/Report/Conference proceedingBook chapterResearchpeer-review


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.
Original languageEnglish
Title of host publicationEmerging Trends in the Social and Behavioral Sciences : An Interdisciplinary, Searchable, and Linkable Resource
EditorsRobert A. Scott , Stephen M. Kosslyn
Number of pages18
Place of PublicationHoboken, N.J.
Publication date2015
ISBN (Print)9781452216454
ISBN (Electronic)9781118900772
Publication statusPublished - 2015

Bibliographical note

Published online: 15 May 2015

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