Instrumental Variables Estimation of Quantile Treatment Effects - Technical Working Paper 229

Sep 4, 2026

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This paper introduces an instrumental variables estimator to measure how a binary treatment shifts the quantiles of potential outcomes. The quantile treatment effects (QTE) estimator handles exogenous covariates and nests quantile regression when treatment is exogenous. The work develops asymptotic distribution theory and practical computation. It proposes a piecewise linear objective whose local minimum can be found with a modified Barrodale-Roberts algorithm. The estimator is illustrated using the effect of childbearing on family income distribution.

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ABSTRACT

1. INTRODUCTION

# INSTRUMENTAL VARIABLES ESTIMATIONOF QUANTILE TREATMENT EFFECTS Alberto Abadie Joshua D.Angrist Guido W.Imbens Technical Working Paper 229 TECHNICAL WORKING PAPER SERIES INSTRUMENTAL VARIABLES ESTIMATIONOF QUANTILE TREATMENT EFFECTS Alberto Abadie Joshua D.Angrist Guido W.Imbens Technical Working Paper 229http://www.nber.org/papers/T0229 NATIONAL BUREAU OF ECONOMIC RESEARCH1050 Massachusetts AvenueCambridge,MA 02138March 1998 We thank Gary Chamberlain,Jerry Hausman,Whitney Newey,James Orlin and seminar participantsat Berkeley,MIT-Harvard and Penn for helpful comments and discussions.Thanks also go toMoshe Buchinsky and Gary Chamberlain for providing us with their MATLAB code for quantileregression.Abadie acknowledges financial support from the Bank of Spain.Any opinionsexpressed are those of the authors and not those of the National Bureau of Economic Research. ◎1998 by Alberto Abadie,Joshua D.Angrist and Guido W.Imbens.All rights reserved.Shortsections of text,not to exceed two paragraphs,may be quoted without explicit permission providedthat full credit,including C notice,is given to the source. Instrumental Variables Estimationof Quantile Treatment EffectsAlberto Abadie,Joshua D.Angristand Guido W.Imbens NBER Technical Working Paper No.229March 1998JEL Nos.C13,C14,C31,J13 Alberto Abadie Department of Economics,E52-391Massachusetts Institute of Technology50 Memorial DriveCambridge,MA 02139aabadie@mit.edu Guido W.ImbensDepartment of Economics University of California,Los AngelesLos Angeles,CA 90094and NBERimbens@econ.ucla.edu ## ABSTRACT This paper introduces an instrumental variables estimator for the effect of a binary treatmenton the quantiles of potential outcomes.The quantile treatment effects(QTE)estimatoraccommodates exogenous covariates and reduces to quantile regression as a special case whentreatment status is exogenous.Asymptotic distribution theory and computational methods arederived.QTE minimizes a piecewise linear objective function for which a local minimum can beobtained using a modified Barrodale-Roberts algorithm.The QTE estimator is illustrated byestimating the effect of childbearing on the distribution of family income. Joshua D.Angrist Department of Economics,E52-353Massachusetts Institute of Technology50 Memorial DriveCambridge,MA 02139and NBERangrist@mit.edu ## 1. INTRODUCTION Understanding the effect of an event or intervention on distributions of outcomes is offundamental importance in many areas of empirical economic research.A leading examplein labor economics is the impact of union status on the distribution of earnings.Oneof the earliest studies of the distributional consequences of unionism is Freeman(1980),while more recent studies include Card(1996),and DiNardo,Fortin,and Lemieux(1996),who have asked whether changes in union status can account for a significant fraction ofincreasing wage inequality in the 1980s.Another application where distribution effects areimportant is the range of government training programs funded under the Job TrainingPartnership Act(JTPA).Policy makers hope that subsidized training programs will workto reduce earnings inequality by raising the lower deciles of the earnings distribution andreducing poverty(Lalonde(1995),US Department of Labor(1995)). Although the importance of distribution effects is widely acknowledged,most evaluationresearch focuses on mean outcomes,probably because the statistical techniques requiredto estimate effects on means are easy to use.Many econometric models also implicitlyrestrict treatment effects to operate in the form of a simple “location shift”,in whichcase the mean effect captures the impact of treatment at all quantiles.Of course,theimpact of treatment on a distribution is easy to assess when treatment status is assignedin controlled randomized trials and there is perfect compliance with treatment assignment.Because randomization guarantees that individual outcomes in the treatment

FAQs

What does the paper estimate?

The paper estimates quantile treatment effects (QTE), describing how a binary treatment changes the quantiles of potential outcomes.

How does the QTE estimator relate to quantile regression?

When treatment status is exogenous, the QTE estimator reduces to quantile regression as a special case.

How are causal effects identified in observational or imperfectly compliant settings?

The paper uses an instrumental variable to estimate treatment effects for the subpopulation of compliers, leveraging exogenous variation in treatment status.

Sep 4, 2026

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