Unconditional Quantile Regressions

Authors

  • Sergio Firpo,

    1. Escola de Economia de São Paulo, Fundação Getúlio Vargas, Rua Itapeva 474, São Paulo, SP 01332-000, Brazil; sergio.firpo@fgv.br
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  • Nicole M. Fortin,

    1. Dept. of Economics, University of British Columbia, 997-1873 East Mall, Vancouver, BC V6T 1Z1, Canada and Canadian Institute for Advanced Research, Toronto, Canada nifortin@interchange.ubc.ca
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  • Thomas Lemieux

    1. Dept. of Economics, University of British Columbia, 997-1873 East Mall, Vancouver, BC V6T 1Z1, Canada; tlemieux@interchange.ubc.ca
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    • We thank the co-editor and three referees for helpful suggestions. We are also indebted to Joe Altonji, Richard Blundell, David Card, Vinicius Carrasco, Marcelo Fernandes, Chuan Goh, Jinyong Hahn, Joel Horowitz, Guido Imbens, Shakeeb Khan, Roger Koenker, Thierry Magnac, Ulrich Müller, Geert Ridder, Jean-Marc Robin, Hal White, and seminar participants at CESG2005, UCL, CAEN–UFC, UFMG, Econometrics in Rio 2006, PUC-Rio, IPEA-RJ, SBE Meetings 2006, Tilburg University, Tinbergen Institute, KU Leuven, ESTE-2007, Harvard–MIT Econometrics Seminar, Yale, Princeton, Vanderbilt, and Boston University for useful comments on earlier versions of the manuscript. Fortin and Lemieux thank SSHRC for financial support. Firpo thanks CNPq for financial support. Usual disclaimers apply.


Abstract

We propose a new regression method to evaluate the impact of changes in the distribution of the explanatory variables on quantiles of the unconditional (marginal) distribution of an outcome variable. The proposed method consists of running a regression of the (recentered) influence function (RIF) of the unconditional quantile on the explanatory variables. The influence function, a widely used tool in robust estimation, is easily computed for quantiles, as well as for other distributional statistics. Our approach, thus, can be readily generalized to other distributional statistics.

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