Quantile Treatment Effects in the Presence of Covariates

Abstract

This paper proposes a method to estimate unconditional quantile treatment effects (QTEs) given one or more treatment variables, which may be discrete or continuous, even when it is necessary to condition on covariates. The estimator, Generalized Quantile Regression (GQR), is developed in an instrumental variable framework for generality to permit estimation of unconditional QTEs for endogenous policy variables, but is also applicable in the conditionally exogenous case. The framework includes simultaneous equations models with nonadditive disturbances which are functions of both unobserved and observed factors. Quantile regression and instrumental variable quantile regression are special cases of GQR and available in this framework.

What Quantile Regression Does and Doesn't Do: A Commentary on Petscher and Logan (2014)

“…Porter () and Killewald and Bearak (), for instance, provide accessible discussions of one of these approaches—the Unconditional Quantile Regression Model (Firpo et al., ). More advanced contributions that also cover other unconditional QR estimators include Frölich and Melly (, ), Melly and Wüthrich (), and Powell (, ). Furthermore, the QRM is not suited particularly well to model nonlinear relations but indeed for detecting and describing heteroscedasticity.…”

“…Only under rank-invariance or rank-similarity the QRM may allow statements about observations. Also, to examine effects on the unconditional distribution of y, more recent approaches (e.g., Chernozhukov et al, 2013;Firpo, 2007;Firpo et al, 2009;Powell, 2016) need to be applied. Porter (2015) and Killewald and Bearak (2014), for instance, provide accessible discussions of one of these approaches-the Unconditional Quantile Regression Model (Firpo et al, 2009).…”

“…This is because the QR estimator (Koenker & Bassett, ) assesses changes in the conditional distribution, , and because—in contrast to the mean—in case of quantiles it depends on the distribution of the covariates, , how these changes affect . , of course, is affected by the distribution of both and (Powell, , ).…”

“…18-22, 453). Methods for investigating effects on quantiles of the unconditional distribution of y have been developed more recently (e.g., Chernozhukov, Fern andez-Val, & Melly, 2013;Firpo, 2007;Firpo, Fortin, & Lemieux, 2009;Fr€ olich & Melly, 2013;Gosling, Machin, & Meghir, 2000;Machado & Mata, 2005;Powell, 2016). While a detailed discussion of these methods is beyond the scope of this commentary, I will return to this issue in the next section.…”

International corruption and its impacts across entrepreneurship types

“…Furthermore, this estimation procedure, in particular, is conducive to panel data and allows for unconditional quantile treatment effects in the presence of other control variables and thus solves the traditional problem with interpretations of the treatment effects in quantile regression when other control variables are included (Powell, ). An additional benefit is that quantile estimates are robust to outliers.…”