German Blanco is a PhD candidate in the Department of Economics at the State University of New York at Binghamton. Carlos A. Flores is an assistant professor in the Department of Economics at the University of
Miami. Alfonso Flores- Lagunes is an associate professor in the Department of Economics at the State Uni- versity of New York at Binghamton and a research fellow at IZA. The authors wish to thank Xianghong Li,
Oscar Mitnik, and participants at Binghamton University’s labor group for detailed comments. They also thank participants at the 2011 Institute for Research in Poverty Summer Workshop, the 2011 Agricultural
and Applied Economics Association Meetings, the 2011 Midwest Econometrics Group Meeting, the 2012 Society of Labor Economists Meeting, and seminar participants at Syracuse, York Canada, and Kent
State Universities for useful comments. A supplemental Internet Appendix is available at http: jhr.uwpress .org . The data used in this article can be obtained beginning January 2014 through December 2016 from
Alfonso Flores- Lagunes, Department of Economics at the State University of New York, PO Box 6000, Binghamton, NY 13902–6000, email: afl oresbinghamton.edu.
[Submitted October 2011; accepted July 2012] SSN 022 166X E ISSN 1548 8004 8 2013 2 by the Board of Regents of the University of Wisconsin System
T H E J O U R N A L O F H U M A N R E S O U R C E S • 48 • 3
Bounds on Average and Quantile Treatment Effects of Job Corps
Training on Wages
German Blanco Carlos A. Flores
Alfonso Flores- Lagunes
A B S T R A C T
We review and extend nonparametric partial identifi cation results for average and quantile treatment effects in the presence of sample selection.
These methods are applied to assessing the wage effects of Job Corps, United States’ largest job- training program targeting disadvantaged youth.
Excluding Hispanics, our estimates suggest positive program effects on wages both at the mean and throughout the wage distribution. Across the
demographic groups analyzed, the statistically signifi cant estimated average and quantile treatment effects are bounded between 4.6 and 12 percent, and
2.7 and 14 percent, respectively. We also document that the program’s wage effects vary across quantiles and demographic groups.
I. Introduction
Sample selection is a well- known and commonly found problem in applied econometrics that arises when there are factors simultaneously affecting both
the outcome and whether or not the outcome is observed. Sample selection arises, for
example, when analyzing the effects of a given policy on the performance of fi rms, as there are common factors affecting both the performance of the fi rm and the fi rm’s
decision to exit or remain in the market or when evaluating the effects of an interven- tion on students’ test scores if students can self- select into taking the test. Even in a
controlled or natural experiment in which the intervention is randomized, outcome comparisons between treatment and control groups yield biased estimates of causal
effects if the probability of observing the outcome is affected by the intervention. For instance, Sexton and Hebel 1984 employ data from a controlled experiment to
analyze the effect of an antismoking assistance program for pregnant women on birth weight. Sample selection arises in this context if the program has an effect on fetal
death rates. An example of a natural experiment where sample selection bias may arise is on the study of the effects of the Vietnam- era draft status on future health,
as draft- eligible men may experience higher mortality rates Hearst, Newman, and Hulley 1986; Angrist, Chen, and Frandsen 2010; Dobkin and Shabani 2009; Eisen-
berg and Rowe 2009. In this paper, we review and extend recent nonparametric par- tial identifi cation results for average and quantile treatment effects in the presence
of sample selection. We do this in the context of assessing the wage effects of Job Corps, which is the largest job training program targeting disadvantaged youth in the
United Sates.
The vast majority of both empirical and methodological econometric literature on the evaluation of labor market programs focuses on estimating their causal effects
on total earnings for example, Heckman, LaLonde, and Smith 1999; Imbens and Wooldridge 2009. Evaluating the impact on total earnings, however, leaves open a
relevant question about whether these programs have a positive effect on the wages of participants through the accumulation of human capital, which is an important goal
of active labor market programs. Earnings have two components: price and quantity supplied of labor. By focusing on estimating the impact of program participation on
earnings, one cannot distinguish how much of the effect is due to human capital im- provements. Assessing the labor market effect of program participation on human cap-
ital requires focusing on the price component of earnings—that is, wages— because wage increases are directly related to the improvement of participants’ human capital
through the program. Unfortunately, estimation of the program’s effect on wages is not straightforward due to sample selection: Wages are observed only for those individuals
who are employed Heckman 1979. As in the previous examples, randomization of program participation does not solve this problem because the individual’s decision to
become employed is endogenous and occurs after randomization.
Recently, new partial identifi cation results have been introduced that allow the construction of nonparametric bounds for average and quantile treatment effects that
account for sample selection. These bounds typically require weaker assumptions than those conventionally employed for point identifi cation of these effects.
1
We review
1. Many of the methods employed for point identifi cation of treatment effects under sample selection require strong distributional assumptions that may not be satisfi ed in practice, such as bivariate normality Heckman
1979. One may relax this distributional assumption by relying on exclusion restrictions Heckman 1990; Imbens and Angrist 1994; Abadie, Angrist, and Imbens 2002, which require variables that determine selec-
tion into the sample employment but do not affect the outcome wages. It is well known, however, that in the case of employment and wages it is diffi cult to fi nd plausible exclusion restrictions Angrist and Krueger
1999; Angrist and Krueger 2001.
these techniques and extend them by presenting a method to use covariates to narrow the bounds for quantile treatment effects. Subsequently, we use data from the National
Job Corps Study NJCS, a randomized evaluation of the Job Corps JC program, to empirically assess the effect of JC training on wages. We analyze effects both at the
mean and at different quantiles of the wage distribution of participants, as well as for different demographic groups. We focus on estimating bounds for the subpopulation
of individuals who would be employed regardless of participation in JC, as previously done in Lee 2009 and Zhang, Rubin, and Mealli 2008, among others. Wages are
nonmissing under both treatment arms for this group of individuals, thus requiring fewer assumptions to construct bounds on their effect. This is also an important group
of participants: It is estimated to be the largest group among eligible JC participants, accounting for close to 60 percent of them.
We start by considering the Horowitz and Manski 2000 bounds, which exploit the randomization in the NJCS and use the empirical support of the outcome. How-
ever, they are wide in our application. Subsequently, we proceed to tighten these bounds through the use of two monotonicity assumptions within a principal stratifi ca-
tion framework Frangakis and Rubin 2002. The fi rst states individual- level weak monotonicity of the effect of the program on employment. This assumption was also
employed by Lee 2009 to partially identify average wage effects of JC. The second assumption not considered by Lee 2009 is on mean potential outcomes across strata,
which are subpopulations defi ned by the potential values of the employment status variable under both treatment arms. These assumptions result in informative bounds
for our parameters.
We contribute to the literature in two ways. First, we review, extend, and apply recent partial identifi cation results to deal with sample selection. In particular, we
illustrate a way to analyze treatment effects on different unconditional quantiles of the outcome distribution in the presence of sample selection by employing the set of
monotonicity assumptions described above.
2
Thus, our focus is on treatment effects on quantiles of the unconditional or marginal distribution of the outcome for example,
Firpo, Fortin, and Lemieux 2009 rather than on conditional quantiles for example, Koenker and Bassett 1978. In addition, we propose a method to employ a covariate
to narrow trimming bounds for unconditional quantile treatment effects. Second, we add to the literature analyzing the JC training program by evaluating its effect on
wages with these methods. With a yearly cost of about 1.5 billion, JC is America’s largest job training program. As such, this federally funded program is under constant
examination and, given legislation seeking to cut federal spending, the program’s op- erational budget is currently under scrutiny see, for example, Korte 2011. Our results
suggest that the program is effective in increasing wages. Moreover, they contribute to a policy- relevant question regarding the potential heterogeneity of the wage impacts
of JC at different points of the wage distribution, and across different demographic groups. In this way, we add to a growing literature analyzing the effectiveness of ac-
tive labor market programs across different demographic groups Heckman and Smith 1999; Abadie, Angrist, and Imbens 2002; Flores- Lagunes, Gonzalez, and Neumann
2010; Flores et al. 2012.
2. Other recent work to be discussed below that employs bounds on quantile treatment effects under differ- ent monotonicity assumptions are Blundell et al. 2007 and Lechner and Melly 2010.
Our empirical results characterize the heterogeneous impact of JC training at differ- ent points of the wage distribution. The estimated bounds for a sample that excludes
the group of Hispanics suggest positive effects of JC on wages, both at the mean and throughout the wage distribution. For the various non- Hispanic demographic groups
analyzed, the statistically signifi cant estimated average effects are bounded between 4.6 and 12 percent, while the statistically signifi cant quantile treatment effects are
bounded between 2.7 and 14 percent. Our analysis by race and gender reveals that the positive effects for blacks appear larger in the lower half of their wage distribution,
while for whites the effects appear larger in the upper half of their wage distribution. Non- Hispanic females in the lower part of their wage distribution do not show statisti-
cally signifi cant positive effects of JC on their wages, while those in the upper part do. Lastly, our set of estimated bounds for Hispanics are wide and include zero.
3
The paper is organized as follows. Section II presents the sample selection problem and the Horowitz and Manski 2000 bounds. Sections III and IV discuss, respectively,
bounds on average and quantile treatment effects, as well as the additional assump- tions we consider. Section V describes the JC program and the NJCS, and Section VI
presents the empirical results from our application. Section VII concludes.
II. Sample Selection and the Horowitz- Manski Bounds
