Flexible and fast estimation of quantile treatment effects: The rqr and rqrplot commands

Using quantile regression models to estimate quantile treatment effects is becoming increasingly popular. This paper introduces the rqr command that can be used to estimate residualized quantile regression (RQR) coefficients and the rqrplot postestimation command that can be used to effortless plot the coefficients. The main advantages of the rqr command compared to other Stata commands that estimate (unconditional) quantile treatment effects are that it can include high-dimensional fixed effects and that it is considerably faster than the other commands.

Bootstrap Inference for Quantile Treatment Effects in Randomized Experiments with Matched Pairs

This paper examines methods of inference concerning quantile treatment effects (QTEs) in randomized experiments with matched-pairs designs (MPDs). Standard multiplier bootstrap inference fails to capture the negative dependence of observations within each pair and is therefore conservative. Analytical inference involves estimating multiple functional quantities that require several tuning parameters. Instead, this paper proposes two bootstrap methods that can consistently approximate the limit distribution of the original QTE estimator and lessen the burden of tuning parameter choice. Most especially, the inverse propensity score weighted multiplier bootstrap can be implemented without knowledge of pair identities.

A New Framework for Estimation of Unconditional Quantile Treatment Effects: The Residualized Quantile Regression (RQR) Model

The identification of unconditional quantile treatment effects (QTE) has become increasingly popular within social sciences. However, current methods to identify unconditional QTEs of continuous treatment variables are incomplete. Contrary to popular belief, the unconditional quantile regression model introduced by Firpo, Fortin, and Lemieux (2009) does not identify QTE, while the propensity score framework of Firpo (2007) allows for only a binary treatment variable, and the generalized quantile regression model of Powell (2020) is unfeasible with high-dimensional fixed effects. This paper introduces a two-step approach to estimate unconditional QTEs where the treatment variable is first regressed on the control variables followed by a quantile regression of the outcome on the residualized treatment variable. Unlike much of the literature on quantile regression, this two-step residualized quantile regression framework is easy to understand, computationally fast, and can include high-dimensional fixed effects.

Quantile Regression Models and the Crucial Difference Between Individual-Level Effects and Population-Level Effects

The unconditional quantile regression (UQR) model – which has gained increasing popularity in the 2010s and is regularly applied in top-rated academic journals within sociology and other disciplines – is poorly understood and frequently misinterpreted. The main reason for its increased popularity is that the UQR model seemingly tackles an issue with the traditional conditional quantile regression (CQR) model: the interpretation of coefficients as quantile treatment effects changes whenever control variables are included. However, the UQR model was not developed to solve this issue but to study influences on quantile values of the overall outcome distribution. This paper clarifies the crucial conceptual distinction between influences on overall distributions, which we term population-level influences, and individual-level quantile treatment effects. Further, we use data simulations to illustrate that various classes of quantile regression models may, in some instances, give entirely different conclusions (to different questions). The conceptual and empirical distinctions between various quantile regression models underline the need to match the correct quantile regression model to the specific research questions. We conclude the paper with some practical guidelines for researchers.

Quantile Treatment Effects in the Presence of Covariates

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 it 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.

The worse the better? Quantile treatment effects of a conditional cash transfer programme on mental health

Poor mental health is a pressing global health problem, with high prevalence among poor populations from low-income countries. Existing studies of conditional cash transfer (CCT) effects on mental health have found positive effects. However, there is a gap in the literature on population-wide effects of cash transfers on mental health and if and how these vary by the severity of mental illness. We use the Malawian Longitudinal Study of Family and Health containing 790 adult participants in the Malawi Incentive Programme, a year-long randomized controlled trial. We estimate average and distributional quantile treatment effects and we examine how these effects vary by gender, HIV status and usage of the cash transfer. We find that the cash transfer improves mental health on average by 0.1 of a standard deviation. The effect varies strongly along the mental health distribution, with a positive effect for individuals with worst mental health of about four times the size of the average effect. These improvements in mental health are associated with increases in consumption expenditures and expenditures related to economic productivity. Our results show that CCTs can improve adult mental health for the poor living in low-income countries, particularly those with the worst mental health.