Quantile Treatment Effects in the Presence of Covariates

2020 ◽  
Vol 102 (5) ◽  
pp. 994-1005 ◽  
Author(s):  
David Powell
Keyword(s):  
Quantile Regression ◽  
Instrumental Variable ◽  
Treatment Effects ◽  
Simultaneous Equations ◽  
Quantile Treatment Effects ◽  
Simultaneous Equations Models ◽  
Special Cases ◽  
Instrumental Variable Quantile Regression

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.

scholarly journals INSTRUMENTAL VARIABLE QUANTILE REGRESSION WITH MISCLASSIFICATION

2020 ◽  
pp. 1-36
Author(s):  
Takuya Ura
Keyword(s):  
Quantile Regression ◽  
Instrumental Variable ◽  
Reduced Form ◽  
Outcome Variable ◽  
Annual Review ◽  
Monotonicity Condition ◽  
Treatment Variable ◽  
Treatment Status ◽  
Instrumental Variable Quantile Regression ◽  
Quantile Treatment Effect

This article investigates the instrumental variable quantile regression model (Chernozhukov and Hansen, 2005, Econometrica 73, 245–261; 2013, Annual Review of Economics, 5, 57–81) with a binary endogenous treatment. It offers two identification results when the treatment status is not directly observed. The first result is that, remarkably, the reduced-form quantile regression of the outcome variable on the instrumental variable provides a lower bound on the structural quantile treatment effect under the stochastic monotonicity condition. This result is relevant, not only when the treatment variable is subject to misclassification, but also when any measurement of the treatment variable is not available. The second result is for the structural quantile function when the treatment status is measured with error; the sharp identified set is characterized by a set of moment conditions under widely used assumptions on the measurement error. Furthermore, an inference method is provided in the presence of other covariates.

Factor instrumental variable quantile regression

2015 ◽  
Vol 19 (1) ◽  
Author(s):  
Jau-er Chen
Keyword(s):  
Quantile Regression ◽  
Factor Structure ◽  
Instrumental Variable ◽  
Asymptotic Properties ◽  
Principal Component ◽  
Firm Level ◽  
Data Set ◽  
Monte Carlo Studies ◽  
Instrumental Variable Quantile Regression ◽  
Unobservable Factors

AbstractThis paper proposes a factor instrumental variable quantile regression (FIVQR) estimator and studies its asymptotic properties. The proposed estimators share with quantile regression the advantage of exploring the shape of the conditional distribution of the dependent variable. When there are a factor structure and co-movement for economic variables, the underlying unobservable factors (or common components) are more efficient instruments. The proposed estimators achieve the optimality in the following sense: The method of principal component consistently estimates the space spanned by the ideal instruments which are utilized to control the endogeneity in the quantile regression analysis. Analyzing the asymptotic properties of the estimator, we assume that a panel of observable instruments follows a factor structure and the endogenous variables also share the same unobservable factors. Using the estimated factors as instruments, we show that the FIVQR estimator is consistent and asymptotically normal. Furthermore, when compared in the GMM framework, the proposed estimator is more efficient than the GMM estimator using many observable instruments directly. Monte Carlo studies demonstrate that the proposed estimators perform well. For an empirical application, we use a firm-level panel data set consisting of trading volumes and returns on DJIA to explore the asymmetric return–volume relation, controlling the endogeneity problem with the estimated factor instruments.

Local Average and Quantile Treatment Effects Under Endogeneity: A Review

2018 ◽  
Vol 8 (1) ◽  
Author(s):  
Martin Huber ◽  
Kaspar Wüthrich
Keyword(s):  
Instrumental Variable ◽  
Treatment Effects ◽  
Randomized Experiments ◽  
Quantile Treatment Effects ◽  
Indirect Treatment ◽  
Treatment Effect Models ◽  
Multiple Treatments ◽  
The Relationship ◽  
Local Average ◽  
Heterogeneous Treatment Effect

Abstract This paper provides a review of methodological advancements in the evaluation of heterogeneous treatment effect models based on instrumental variable (IV) methods. We focus on models that achieve identification by assuming monotonicity of the treatment in the IV and analyze local average and quantile treatment effects for the subpopulation of compliers. We start with a comprehensive discussion of the binary treatment and binary IV case as for instance relevant in randomized experiments with imperfect compliance. We then review extensions to identification and estimation with covariates, multi-valued and multiple treatments and instruments, outcome attrition and measurement error, and the identification of direct and indirect treatment effects, among others. We also discuss testable implications and possible relaxations of the IV assumptions, approaches to extrapolate from local to global treatment effects, and the relationship to other IV approaches.

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

2021 ◽  
Author(s):  
Nicolai T. Borgen ◽  
Andreas Haupt ◽  
Øyvind N. Wiborg
Keyword(s):  
Quantile Regression ◽  
Fixed Effects ◽  
Regression Models ◽  
Treatment Effects ◽  
The Other ◽  
High Dimensional ◽  
Fast Estimation ◽  
Quantile Treatment Effects

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.

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

2020 ◽  
Author(s):  
Nicolai T. Borgen ◽  
Andreas Haupt ◽  
Øyvind N. Wiborg
Keyword(s):  
Quantile Regression ◽  
Regression Models ◽  
Treatment Effects ◽  
Population Level ◽  
Conditional Quantile ◽  
Individual Level ◽  
Quantile Treatment Effects ◽  
Crucial Difference ◽  
Practical Guidelines ◽  
Conceptual Distinction

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.

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