Unconditional Quantile Regressions

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.

Universal Child Care, Maternal Employment, and Children’s Long-Run Outcomes: Evidence from the US Lanham Act of 1940

“…The method proposed by Firpo et al (2009) provides estimates of the effect of changes in a given right-hand-side variable on the unconditional quantiles of the left-hand-side variable. "Unconditional" in this context means the integration of the conditional outcome distribution, given a set of explanatory variables, over the distribution of those explanatory variables.…”

“…The approach I take here is to examine whether the Lanham Act influenced the adult outcome distribution for treated relative to comparison cohorts. In particular, I rely on quantile regression methods developed by Firpo, Fortin, and Lemieux (2009) to assess whether the childcare program differentially influenced adult earnings at different points in the distribution.…”

Growing Apart: The Changing Firm-Size Wage Premium and Its Inequality Consequences

“…We used re-centered influence function (RIF regressions (see Firpo, Fortin, and Lemieux 2009;Fortin et al 2011; for more discussion) to detect how the FSWE may vary across wage distribution. That is, we compared the logged wage differences among workers of different firm sizes who were otherwise similar in observed characteristics and location in the wage distribution.…”

Are there Long-Term Earnings Scars from Youth Unemployment in Germany?

“…To explore this possibility, we now investigate whether the scarring effect of early-career unemployment varies across the unconditional distribution of prime-age earnings. For this purpose, we run regressions of the recentered influence function (RIF) of each unconditional decile of cumulative prime-age earnings, see Firpo et al (2009). The models' specification is identical to the one in column (2) of Table 3.…”