UNCONDITIONAL QUANTILE REGRESSIONS* Sergio Firpo Nicole M. Fortin Departamento de Economia Department of Economics Catholic University of Rio de Janeiro (PUC-Rio) University of British Columbia R. Marques de S. Vicente, 225/210F #997-1873 East Mall Rio de Janeiro, RJ, Brasil, 22453-900 Vancouver, BC, Canada V6T 1Z1
[email protected] [email protected] Thomas Lemieux Department of Economics University of British Columbia #997-1873 East Mall Vancouver, Canada, BC V6T 1Z1
[email protected] July 2007 ABSTRACT We propose a new regression method to estimate the impact of 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 is a widely used tool in robust estimation that can easily be computed for each quantile of interest. We show how standard partial effects, as well as policy effects, can be estimated using our regression approach. We propose three different regression estimators based on a standard OLS regression (RIF-OLS), a logit regression (RIF-Logit), and a nonparametric logit regression (RIF-OLS). We also discuss how our approach can be generalized to other distributional statistics besides quantiles. * We are indebted to Joe Altonji, Richard Blundell, David Card, Vinicius Carrasco, Marcelo Fernandes, Chuan Goh, Joel Horowitz, Shakeeb Khan, Roger Koenker, Thierry Magnac, Whitney Newey, Geert Ridder, Jean-Marc Robin, Hal White and seminar participants at Yale University, CAEN-UFC, CEDEPLARUFMG, PUC-Rio, IPEA-RJ and Econometrics in Rio 2006 for useful comments on this and earlier versions of the manuscript.