The Oaxaca–Blinder Unexplained Component as a Treatment Effects Estimator
| Author | Tymon Słoczyński |
| DOI | http://doi.org/10.1111/obes.12075 |
| Date | 01 August 2015 |
| Published date | 01 August 2015 |
588
©2014 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd.
OXFORD BULLETIN OF ECONOMICSAND STATISTICS, 77, 4 (2015) 0305–9049
doi: 10.1111/obes.12075
The Oaxaca–Blinder Unexplained Component as a
Treatment Effects Estimator*
Tymon Słoczy ´
nski†,‡
†Department of Economics I, Warsaw School of Economics, ul. Madali´nskiego 6/8 p. 228,
02-513 Warszawa, Poland
‡Institute for the Study of Labor (IZA), Bonn, Germany
(e-mail: tymon.sloczynski@gmail.com)
Abstract
In this paper I use the National Supported Work (NSW) data to examine the finite-sample
performance of the Oaxaca–Blinder unexplained component as an estimator of the popula-
tion average treatment effect on the treated (PATT). Precisely, I followsample and variable
selections from Dehejia and Wahba (1999), and conclude that Oaxaca–Blinder performs
better than any of the estimators in this influential paper, providedthat overlap is imposed.
As a robustness check, I consider alternative sample (Smith and Todd, 2005) and variable
(Abadie and Imbens, 2011) selections, and present a simulation study which is also based
on the NSW data.
I. Introduction
Recent papers by Barsky et al. (2002), Black et al. (2006), Melly (2006) and Fortin,
Lemieux and Firpo (2011) have noted that the Oaxaca–Blinder decomposition, a pop-
ular method used in empirical labour economics to study differentials in mean wages,1
provides a consistent estimator of the population average treatment effect on the treated
(PATT). Precisely, applied researchers in labour economics have often used the Oaxaca–
Blinder decomposition to estimate two components of a wage differential: a component
attributable to differences in group composition (the explained component) and a compo-
nent attributable to net effects of group membership (the unexplained component). It is the
*I am grateful to two anonymous referees,Ar unAdvani, Joshua Angrist, Thomas Crossley, Patrick Kline, Michał
Myck, Paweł Strawi´nski and seminar and conference participants in Dublin, Krak´ow,Odense and Warsaw for useful
comments and discussions. I would like to acknowledge financial support for this research from the Foundationfor
Polish Science (a START scholarship), the National Science Centre (grant DEC-2012/05/N/HS4/00395), theWarsaw
School of Economics (grant 03/BMN/25/11), and the ‘We´z stypendium - dla rozwoju’ scholarship programme. I
would also like to thank the Clifford and Mary Corbridge Trust, the Cambridge EuropeanTrust and the Faculty of
Economics at the University of Cambridge for financial support which allowed me to undertake graduate studies at
the University of Cambridge where this project was started.
JEL Classification numbers: C21, J24.
1See Blinder (1973) and Oaxaca (1973) for seminal contributions and Fortin et al. (2011) for a comprehensive
survey. Over the last two decades, the decomposition framework has also been extended to distributional statistics
other than the mean (see, e.g. Juhn, Murphy and Pierce, 1993; DiNardo, Fortin and Lemieux, 1996; Melly, 2005).
Oaxaca-Blinder and treatment effects 589
unexplained component in the most basic version of the Oaxaca–Blinder decomposition
which constitutes a consistent estimator of the PATT. In an important contribution, Kline
(2011) has recently shown that this method is equivalent to a propensity score reweight-
ing estimator based on a linear model for the treatment odds, and satisfies therefore the
‘double robustness’ property (Robins, Rotnitzky and Zhao, 1994). He has also used the
well-known NSW data2to provide a seminal assessment of the finite-sample performance
of the Oaxaca–Blinder decomposition, though he has only used a single non-experimental
comparison data set and a single selection of control variables, and he has compared his
result to a relatively small number of alternative estimates.
In this paper, I provide a much broader picture of the finite-sample performance of the
Oaxaca–Blinder unexplained component as an estimator of the PATT. I also use the NSW
data, but I closely follow Dehejia andWahba (1999) in their sample and variable selections,
so that I can reassess their influential claim that methods based on the propensity score
compare favourably with other estimators. When overlap is imposed, the Oaxaca–Blinder
decomposition is shown to perform superior compared to any of the estimators in Dehejia
and Wahba(1999) and to additional methods such as inverse probability weighting, kernel
matching, matching on covariates,and bias-cor rected matching.To assess the robustness of
this result, I consider alternative sample and variable selections, and present an ‘empirical
Monte Carlo study’ (Huber, Lechner and Wunsch, 2013) which is also based on the NSW
data.3Generally, the Oaxaca–Blinder decomposition always performs very well, and never
significantly worse than any other method.At first, this might be seen as sur prising, given
the simplicity of this estimator. Note, however, that at least tworecent papers, Khwaja et al.
(2011) and Huber et al. (2013), have presented simulation studies which are suggestive
of very good finite-sample performance of flexible OLS.4In both cases, the authors have
actually applied an estimator which is either equivalentor ver y similar to Oaxaca–Blinder,
although they have referred to this method in a different way.5In this paper, I complement
these previous analyses by exploringthe connection with the decomposition literature, and
focus on the NSW data.
II. The treatment effects framework
Consider a population of Nindividuals, indexed by i=1,…, N, who are divided into two
disjoint groups, 0 and 1.6Individuals in group 1 are exposed to regime that is called
treatment, while individuals in group 0 are exposed to regime that is called control.To
indicate group membership, a binary variable Wiis used, and Wi=0(Wi=1) if individual
2These data were analysed originallyby LaLonde (1986) and subsequently by Heckman and Hotz (1989), Dehejia
and Wahba(1999, 2002), Smith and Todd (2001, 2005), Becker and Ichino (2002),Angrist and Pischke (2009), Porro
and Iacus (2009), Abadie and Imbens (2011), Diamond and Sekhon (2013), and others.
3Since Advani and Słoczy´nski (2013) have recently demonstrated that the internal validity of empirical Monte
Carlo studies might be quite low, this simulation study is only intended to provide a comparison with the previous
literature. The choice of simulation design is quite limited anyway,as it is widely accepted that stylized Monte Carlo
studies do not have much external validity (Busso, DiNardo and McCrary, 2013; Huber et al., 2013).
4A related point has also been made by Kang and Schafer (2007) in the context of incomplete data estimation.
5Generally, various versions of the Oaxaca–Blinder decomposition are equivalent to variousversions of flexible
OLS in Imbens and Wooldridge(2009). See also Słoczy ´nski (2013) for a discussion.
6The exposition here is standard and borrows notation from Imbens and Wooldridge (2009). Other surveys of the
treatment effects literature include Cobb-Clark and Crossley (2003) and Angrist and Pischke (2009).
©2014 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd
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