NATIONAL BUREAU OF ECONOMIC RESEARCH
NATIONAL BUREAU OF ECONOMIC RESEARCH

Unconditional Quantile Regressions

Sergio Firpo, Nicole M. Fortin, Thomas Lemieux

NBER Technical Working Paper No. 339
Issued in July 2007
NBER Program(s):   LS   TWP

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.

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Document Object Identifier (DOI): 10.3386/t0339

Published: Econometrica Volume 77, Issue 3, pages 953–973, May 2009

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