# Heterogeneous earnings effects of the Job Corps by gender: A translated
quantile approach

Anthony Strittmatter111 Previous versions of this manuscript were circulated
under different titles. The manuscript was presented at the SSES 2012 in
Zurich, at the NOeG 2012 in Vienna, at the EALE 2013 in Torino, at the ESEM
2013 in Goteborg, at the IAAE 2014 in London, at the Humboldt University
Berlin 2015, and at the ZEW 2017. I thank the participants for their useful
comments. In particular, I am grateful for helpful suggestions made by Simone
Balestra, Xuan Chen, Annabelle Dörr, Alfonso Flores-Lagunes, Bernd
Fitzenberger, Michael Lechner, Jan Nimczik, Stefan Sperlich, and Andreas
Steinmayr. I thank Ozkan Eren and Serkan Ozbeklik, who kindly shared their
data and programmes with me. The usual disclaimer applies. E-mail:
<EMAIL_ADDRESS>
University of St. Gallen

( August 27, 2024)

###### Abstract

Several studies of the Job Corps tend to find more positive earnings effects
for males than for females. This effect heterogeneity favouring males
contrasts with the results of the majority of other training programmes’
evaluations. Applying the translated quantile approach of Bitler, Hoynes, and
Domina (2014), I investigate a potential mechanism behind the surprising
findings for the Job Corps. My results provide suggestive evidence that the
effect of heterogeneity by gender operates through existing gender earnings
inequality rather than Job Corps trainability differences.

JEL-Classification: J38, C21
Keywords: Gender Inequality, Decomposition, Quantile Regression, Programme
Evaluation

##  1 Introduction

In this study, I investigate the heterogeneous earnings effects of the Job
Corps by gender. In particular, I show that gender differences in labour
market opportunities contribute to the overall effect heterogeneity. To this
end, I apply the translated quantile decomposition of Bitler, Hoynes, and
Domina (2014). Furthermore, I extend this approach to incorporate average
translated effects.

The Job Corps is the largest U.S. labour market programme targeting
disadvantaged youth. It provides academic, vocational, and social training, as
well as health care counselling and job search assistance, for an average
duration of eight to nine months. Blanco, Flores, and Flores-Lagunes (2013),
Chen and Flores (2015), and Lee (2009) show that the Job Corps has positive
wage effects for both genders. This effect is expected to increase earnings
through higher hourly wages and greater labour supply.222Chen, Flores, and
Flores-Lagunes (2017) report positive employment effects of the Job Corps four
years after assignment. The female labour supply is expected to be more
elastic to wage changes than is the male labour supply (see, e.g., the
discussion in Bargain, Orsini, and Peichl, 2013, Killingsworth and Heckman,
1986). However, several studies observe a tendency that the Job Corps
increases the gender earnings inequality. In a large-scale experimental
evaluation, Schochet, Burghardt, and McConnell (2008) show evidence of higher
average earnings gain from the Job Corps for males than for females. Moreover,
Eren and Ozbeklik (2014) report more positive quantile earnings effects for
males than for females. These findings contrast with the empirical evaluations
of many other active labour market programmes (ALMPs). Meta studies performed
by Bergemann and van den Berg (2008) and Card, Kluve, and Weber (2018) report
evidence of higher ALMP returns for females than for males. In this study, I
highlight one potential mechanism behind the unexpected findings for the Job
Corps.

Frumento, Mealli, Pacini, and Rubin (2012) investigate the effect
heterogeneity for various socio-economic groups using a principal
stratification approach with strong functional form assumptions. They observe
that individuals with worse initial conditions (in terms of education, labour
market experience, race, and gender) profit less from the Job Corps than do
those with good labour market opportunities.333This is another peculiarity of
the Job Corps because for many other ALMPs, the returns do not increase with
labour market opportunities (see, e.g., Card, Kluve, and Weber, 2018, Rinne,
Schneider, and Uhlendorff, 2011). Expected earnings can be viewed as an
aggregate measure of labour market opportunities. Quantile regressions can
identify (distributional) heterogeneity by expected earnings. Eren and
Ozbeklik (2014) report larger earnings differences for the Job Corps at higher
quantiles than at lower quantiles. Such a pattern can be expected if the Job
Corps is more effective for groups with better labour market opportunities,
that is, those with high earnings even without training. Higher opportunity
costs for participants with better earnings opportunities can explain this
positive relationship between earnings opportunities and Job Corps returns. It
is well documented that a larger share of females is located in the lower part
than in the upper part of the earnings distribution. Thus, unexpected effect
heterogeneity can arise in favour of males from structural gender earnings
inequality rather than from gender differences in Job Corps trainability. The
latter could arise from programme content that is, for example, more aligned
to the needs of one gender. In this study, I decompose those potential
channels using the translated quantile approach of Bitler, Hoynes, and Domina
(2014).

For an example of the relevance of the translated quantile approach, assume
the need to determine assignment criteria for offering participation in the
Job Corps that do not increase gender inequality. If structural gender
earnings inequality leads to heterogeneity, a non-discriminatory assignment
rule offers participation to males and females with balanced labour market
opportunities. If Job Corps trainability differs by gender, then other
dimensions of the Job Corps programmes need to be better aligned with the
specific training demands of males and females. For example, vocational
training offered during the programme could meet the needs of males better
than the needs of females.

My findings, consistent with the existing literature, provide suggestive
evidence for larger quantile treatment effects for males than for females.
Structural gender earnings inequality possibly accounts for 82% of the average
effect heterogeneity by gender. Trainability differences by gender appear to
play only a minor role. Even though the effects are statistically
insignificant, these findings suggest that the offer to participate in the Job
Corps does not disfavour females with earnings opportunities that are equal to
those of males. However, it seems that the Job Corps amplifies the existing
structural earnings inequality in favour of males. Randomly offering
participation in the Job Corps to eligible individuals increases the average
earnings opportunities by 8% after four years but could possibly also increase
the average gender earnings gap by 8% within the eligible group. An allocation
scheme that balances the earnings structures of the selected programme
participants by gender could yield similar average returns but tends to have a
lower impact on gender earnings inequality.

Furthermore, I report effect heterogeneity by gender and parenthood. While
mothers tend to profit more from Job Corps than do fathers, the results
suggest the opposite for women and men without children. I document that
differences in the earnings structure by gender and parenthood can account for
a large proportion of this heterogeneity (on average, 71%). This suggests the
within-group earnings structure is an important factor for between-group
effect heterogeneity. Accordingly, the within-group earnings structures should
receive more attention when rules used to award Job Corps offers are designed.

The remainder of the paper is structured as follows. Section 2 reviews the
institutional background of the Job Corps and the related literature. Section
3 describes the experimental data. Section 4 explains the quantile
transformation approach. Section 5 presents the main empirical results.
Section 6 describes effect heterogeneity by gender and parenthood, and the
final section concludes the paper. Online Appendix A contains supplementary
descriptive statistics. Online Appendix B provides the details on the
estimation approach. Online Appendix C presents robustness checks. Online
Appendix D documents distributional effect heterogeneity by gender and
parenthood.

##  2 Job Corps

The Job Corps was established in the United States in 1964 under the Economic
Opportunity Act. The aim of the Job Corps is to provide counselling and to
develop individualized programmes that enhance participants’ job
opportunities. In particular, completing a vocational degree and earning
General Educational Development (GED) credentials are two major goals of the
Job Corps. Job Corps programmes follow a holistic approach. They can include
physical and mental healthcare counselling, various vocational and social
education schemes, and job search assistance. Courses have theoretical and
practical content, and training can be partly on the job. Participants are
trained in one of approximately 125 Job Corps centres and typically live on
Job Corps campuses during the programme. Candidates must pass a screening and
recruitment process administered by certain admission agencies. Eligible
participants are disadvantaged youth (aged 16–24 years) in need of additional
education and training. Candidates must have low incomes to meet the
eligibility criteria. Approximately 60,000 eligible youth enrol in the Job
Corps each year. In 2008, total programme expenditures exceeded 1.58 billion
U.S. dollars (Job Corps Annual Report, 2008).444Of the total expenditures,
training costs account for 40%, support services (e.g., meals, lodging, and
medical care) account for 33%, and administration and infrastructure
investment costs account for 26%. In 2008, expenditures per participant were
approximately 26,000 U.S. dollars, or approximately ten times the cost of a
typical programme under the Workforce Investment Act (Eren and Ozbeklik,
2014).

Numerous studies investigate the effectiveness of Job Corps programs in
improving participants’ post-programme earnings. Early studies using data from
the 1970s observe that males benefited more from the Job Corps than did
females. Mallar, Kerachsky, Thornton, and Long (1982) observe that
participation in the Job Corps increases annual earnings by 2,000 U.S. dollars
for males and 1,000 U.S. dollars for females. Gay and Borus (1980) report
negative earnings impacts for black female participants and positive effects
for black male participants. Between 1994 and 1996, Mathematica Policy
Research performed a randomized National Job Corps Study (NJCS). That study
had an experimental design and hence became the benchmark for evaluating the
Job Corps. Using survey data collected from NJCS participants in 1998,
Schochet, Burghardt, and McConnell (2008) observe a yearly earnings gain of
1,530 U.S. dollars for males, but only 1,134 U.S. dollars for females. These
earnings differences are not statistically significant. However, Schochet,
Burghardt, and McConnell (2008) report a significantly higher yearly earnings
gain of 540 U.S. dollars for male than for female participants when using the
administrative data of NJCS participants collected from the 1998 Summary
Earnings Records (SER). Flores, Flores-Lagunes, Gonzalez, and Neuman (2012)
explore the marginal returns of additional exposure to academic and vocational
training and instruction by gender. The average marginal returns of additional
exposure are twice as large for males than for females.

Furthermore, Schochet, Burghardt, and McConnell (2008) report the effects of
receiving an offer to participate in the Job Corps, which could include actual
participation in the programme. Using the survey data collected from NJCS
participants four years after randomization, the authors observe an average
yearly earnings gain of 828 U.S. dollars, equivalent to an average weekly
earnings gain of 16 U.S. dollars. Using the same data, Eren and Ozbeklik
(2014) report weekly earnings gains of 18 U.S. dollars for male and 11 U.S.
dollars for female recipients of an offer to join the Job Corps. Quantile
differences suggest almost zero effects on the earnings distribution of males
below the 4th decile. Above the 4th decile, the quantile earnings differences
increase to approximately 30 U.S. dollars and remain at this positive level.
For females, the quantile earnings differences reach approximately 20 U.S.
dollars at the 15th percentile. Above this percentile, the positive quantile
earnings differences remain almost stable. Thus, offers to join the Job Corps
tend to increase gender earnings inequality.

##  3 Experimental data

As previously mentioned, Mathematica Policy Research performed a randomized
experiment with the Job Corps. Of 80,833 eligible individuals who first
applied for participation in the programme between November 1994 and February
1996, 15,386 were randomly selected for the experiment’s research sample. From
this group, 9,409 were randomly selected to receive an offer to participate in
the Job Corps. Of these, 73% joined the Job Corps programme and actually
started to participate after an average duration of 1.4 months. The remaining
5,977 individuals were assigned to the control group. Control group members
were not eligible for the Job Corps programs for three years following
randomization (approximately 1% participated anyway). Nevertheless, most
control group members received some sort of alternative training in the form
of GED preparation (27%), high school (23%), or vocational, technical, or
trade school (21%) (Burghardt et al., 2001). The intensity of training was
higher among treatment group members than among those in the control group.
During the four years following the randomization, 47% of the treatment group
members and 27% of those in the control group obtained GED credentials. During
the same period, 38% of the treatment group members and 15% of those in the
control group obtained a vocational degree. Approximately 5–8% of eligible
individuals in both groups received a high school diploma (Burghardt et al.,
2001). To improve the accuracy of the research sample, some subgroups were
oversampled (see description in Schochet, 2001). To account for this, I use
sampling weights throughout the analyses.555Eren and Ozbeklik (2014) condition
on key features of the sample design in a regression framework instead of
using sampling weights. Unreported robustness checks find that the results are
not sensitive to various ways of constructing sampling weights.

Interviews were conducted with members of the research sample 12, 30, and 48
months after randomization. This study considers publicly released interviews
of the sample of individuals conducted 48 months after randomization,
eliminating observations with missing information (3,951 observations are
dropped).6663,650 observations are dropped because earnings in year 4 are
unobserved, and 301 observations are dropped because of missing data of
covariates. The share of attrition is 6.5% among males and 6.1% among females.
Lee (2009) proposes an indirect test for potential attrition bias in the NJCS
data. His analysis reveals no strong evidence of attrition bias (see Remark 2
in Lee, 2009). Throughout the study, I use the non-response adjusted sampling
weights (wgt48b) provided in the NJCS data to account for sample attrition.
The final sample includes 10,595 observations, of which 6,372 are in the
treatment sample and 4,223 are in the control sample.

The outcome of interest is average weekly earnings (in nominal U.S. dollars)
in year 4 after random assignment, which is more than two years after 92% of
the participants completed the program. I investigate the effects of the
randomized offer to participate in the Job Corps programme. This intention-to-
treat effect (ITT) differs from the effect of actual participation. The ITT
effect is relevant to investigating the optimal selection rules for awarding
offers to join the Job Corps programme. The award of such offers is under the
control of the decision makers; however, enrolment and actual participation
are not under their control. An alternative approach is to investigate the
local average treatment effects of actual participation. This approach
identifies the effects for those individuals who only enrol in Job Corps if
they receive the offer to participate instead of considering all eligible
individuals (the latter group is called compliers). Chen, Flores, and Flores-
Lagunes (2017) address this limitation with an interesting bound analysis
designed to identify the effects for individuals rejecting the offer to
participate. I focus only on the ITT effects in this study.

Table 1: Share of compliers.

|  |  | Share of | Share of | Share of | Share of
---|---|---|---|---|---|---
| Share of | Share of | female | male | female | male
| female | male | compliers | compliers | compliers | compliers
| compliers | compliers | with | with | without | without
|  |  | children | children | children | children
| (1) | (2) | (3) | (4) | ( 5) | (6)
Full sample | 69% | 75% | 64% | 67% | 71% | 76%
$Y(0)<1^{st}$ quartile | 69% | 75% | 64% | 62% | 71% | 76%
$1^{st}$ quartile $\leq Y(0)<2^{nd}$ quartile | 69% | 76% | 64% | 67% | 71% | 77%
$2^{nd}$ quartile $\leq Y(0)<3^{rd}$ quartile | 69% | 74% | 64% | 66% | 71% | 76%
$Y(0)\geq 3^{rd}$ quartile | 67% | 73% | 62% | 65% | 69% | 74%

Note: See Angrist and Fernández-Val (2013) for a description of the
calculation of complier shares. The potential outcome $Y(0)$ denotes earnings
under non-treatment.

Table 1 documents the share of compliers by gender and by different quartiles
of the earnings distribution. Females comply 6 percentage points less
frequently with the offer to participate in the Job Corps than do males. The
difference is statistically significant at all conventional levels.
Accordingly, compliance with the offer to join the Job Corps can explain some
amount of effect heterogeneity by gender, but the effects of actual
participation are also more beneficial for males than for females (see the
results in, e.g., Schochet, Burghardt, and McConnell, 2008, Flores, Flores-
Lagunes, Gonzalez, and Neuman, 2012). This suggests that non-compliance cannot
explain why participation in Job Corps tends to increase gender inequality of
earnings. The share of compliers does not vary significantly across the
earnings distribution. Furthermore, parenthood is a strong predictor of
compliance for both males and females.

Table 2: Means and standard deviations conditional on receiving (or not) an
offer to join Job Corps (JC).

| Offer to join JC | Not invited to JC | Standardized
---|---|---|---
| Mean | Std. Dev. | Mean | Std. Dev. | Difference
| (1) | (2) | (3) | (4) | (5)
Earnings per week in Year 4 | 210.854 | 200.359 | 195.846 | 187.475 | 7.740
Ever enrolled in a Job Corps centre | 0.733 | 0.442 | 0.011 | 0.106 | 224.320
Socioeconomic characteristics
Female | 0.412 | 0.492 | 0.406 | 0.491 | 1.200
Aged 16-17 years | 0.414 | 0.493 | 0.417 | 0.493 | 0.590
Aged 18-19 years | 0.317 | 0.465 | 0.317 | 0.465 | 0.070
Aged 20-24 years | 0.269 | 0.443 | 0.266 | 0.442 | 0.580
White | 0.277 | 0.447 | 0.266 | 0.442 | 2.470
Black | 0.479 | 0.500 | 0.478 | 0.500 | 0.120
Hispanic | 0.171 | 0.377 | 0.180 | 0.384 | 2.420
Native American | 0.074 | 0.261 | 0.076 | 0.265 | 0.900
Lives with a spouse or a partner | 0.061 | 0.239 | 0.063 | 0.243 | 0.980
Dummy for bad health | 0.127 | 0.333 | 0.137 | 0.344 | 3.090
0-6 month education programme in the preceding year | 0.268 | 0.442 | 0.254 | 0.435 | 2.990
6-12 month education programme in the preceding year | 0.352 | 0.477 | 0.368 | 0.482 | 3.360
High school credential | 0.228 | 0.420 | 0.238 | 0.426 | 2.380
Lives in PMSA | 0.319 | 0.466 | 0.327 | 0.469 | 1.610
Lives in MSA | 0.459 | 0.498 | 0.454 | 0.498 | 1.110
Past employment and earnings history
Ever had job for two or more weeks | 0.803 | 0.398 | 0.792 | 0.406 | 2.750
Worked during the year prior to random assignment | 0.653 | 0.476 | 0.645 | 0.478 | 1.750
Had a job at the time of random assignment | 0.211 | 0.408 | 0.206 | 0.404 | 1.300
Employed less than 3 months during the preceding year | 0.190 | 0.380 | 0.189 | 0.379 | 0.270
Employed 3-9 months during the preceding year | 0.282 | 0.437 | 0.276 | 0.433 | 1.510
Employed 9-12 months during the preceding year | 0.181 | 0.373 | 0.180 | 0.372 | 0.230
Yearly earnings less than $1,000 | 0.107 | 0.309 | 0.111 | 0.314 | 1.470
Yearly earnings $1,000 to $5,000 | 0.273 | 0.446 | 0.264 | 0.441 | 2.060
Yearly earnings $5,000 to $10,000 | 0.138 | 0.345 | 0.133 | 0.339 | 1.530
Yearly earnings above $10,000 | 0.067 | 0.250 | 0.067 | 0.250 | 0.060
Past welfare history
Family on welfare when growing up | 0.200 | 0.400 | 0.193 | 0.395 | 1.530
Received food stamps during the preceding year | 0.435 | 0.496 | 0.435 | 0.496 | 0.090
Public or rent-subsidized housing | 0.204 | 0.400 | 0.193 | 0.392 | 2.940
Received AFDC in last year | 0.300 | 0.458 | 0.297 | 0.457 | 0.620
Drugs and crime
Used hard drugs during the preceding year | 0.068 | 0.251 | 0.063 | 0.243 | 1.970
Smoked marijuana during the preceding year | 0.249 | 0.432 | 0.243 | 0.429 | 1.380
“Ever arrested” dummy | 0.250 | 0.433 | 0.253 | 0.434 | 0.700
No. of Observations | 6,372 | 4,223 |

Note: Time-varying control variables are measured at the time of random
assignment. Weights ($wgt48b$) accounting for the sampling design and non-
response of the 48-month interview are used. JC denotes for Job Corps. PMSA
stands for Primary Metropolitan Statistical Area. MSA denotes Metropolitan
Statistical Area. AFDC stands for Aid to Families with Dependent Children.

Table 2 reports the means and standard deviations of the observed variables.
In year four after a randomized assignment, individuals with an offer to join
the Job Corps earn on average 15 U.S. dollars per week more than do
individuals without an offer. Furthermore, I report the descriptive statistics
for socioeconomic characteristics, employment, earnings, and welfare
histories, as well as drug use and arrests. For all of these observed control
variables, I observe little difference between individuals with and without an
offer to join the Job Corps. The standardized differences are always below
3.5.777The standardized difference of variable $X$ between samples $A$ and $B$
is defined as
$SD=\frac{|\bar{X}_{A}-\bar{X}_{B}|}{\sqrt{\frac{1}{2}\left(Var(X_{A})+Var(X_{B})\right)}}\cdot
100,$ where $\bar{X}_{A}$ denotes the mean of sample $A$, and $\bar{X}_{B}$
denotes the mean of sample $B$. Rosenbaum and Rubin (1983) consider an
absolute standardized difference exceeding 20 to be “large.” This confirms
that the offer to join the Job Corps was randomized appropriately.

Table A.1 in Online Appendix A documents the descriptive statistics of
observed variables by gender without conditioning on an offer to join the Job
Corps. On average, males earn 66 U.S. dollars per week more than do females
four years after the randomized offer. Relative to males, females in the
sample were less likely to be white, more likely to have high school
credentials, less likely have used drugs during the previous year, and
arrested less often. Females received food stamps and aid to families with
dependent children (AFDC) more often than did males. The families of females
in the sample were on welfare during their childhood more often than were the
families of males. These differences in socioeconomic characteristics may
explain effect heterogeneity by gender but cannot explain why the findings for
Job Corps differ from those of the previous literature (e.g., Card, Kluve, and
Weber, 2018).888Furthermore, Huber (2015) points at causal pitfalls in
controlling for post-birth covariates in gender decompositions.

##  4 Empirical approach

###  4.1 Econometric Intuition

The earnings are a function of a Job Corps offer $D$, gender $G$, and an error
term $U$ that incorporates labour market opportunities. The structural
earnings function is $\varphi_{1}(G,U)$ if there is an offer to join the Job
Corps and $\varphi_{0}(G,U)$ if there is no offer. The error term possibly
interacts non-separably with gender. The quantile earnings function is
$Q_{\varphi_{d}(G,U)}(\tau)$ for $d\in\\{0,1\\}$.999$Q_{A}(\tau)$ represents
the $\tau$th quantile of $A$. For an insight, assume that $\varphi_{d}(\cdot)$
is strictly increasing in its second argument. Then, the conditional quantile
function $Q_{\varphi_{d}(G,U)|G}(\tau|g)$ equals
$\varphi_{d}(g,Q_{U|G}(\tau|g))$, where $Q_{U|G}(\tau|g)$ is the quantile of
the error term distribution for those with gender $g\in\\{m,f\\}$. The
conditional quantile treatment effects (CQTEs) for males ($g=m$) and females
($g=f$) are, respectively,

$\displaystyle\delta_{CQTE}(\tau,m)=$
$\displaystyle\varphi_{1}(m,Q_{U|G}(\tau|m))-\varphi_{0}(m,Q_{U|G}(\tau|m))\mbox{
and }$ $\displaystyle\delta_{CQTE}(\tau,f)=$
$\displaystyle\varphi_{1}(f,Q_{U|G}(\tau|f))-\varphi_{0}(f,Q_{U|G}(\tau|f)).$

Thus, even if the earnings functions are homogeneous by gender (i.e.,
$\varphi_{d}(m,U)=\varphi_{d}(f,U)$), the CQTEs can be heterogeneous if
$Q_{U|G}(\tau|m)\neq Q_{U|G}(\tau|f)$ (this is noted in Abadie, Angrist, and
Imbens, 2002 and Bitler, Hoynes, and Domina, 2014, among others). The direct
effect operates through heterogeneity caused by the first argument of the
earnings functions. The structural effect operates through heterogeneity
caused by the second argument. The direct and structural channels cannot be
distinguished simply by comparing $\delta_{CQTE}(\tau,m)$ and
$\delta_{CQTE}(\tau,f)$.

Bitler, Hoynes, and Domina (2014) use unique reference quantiles for their
translated quantile treatment effect (TQTE) approach that I denote by
$Q_{U_{r}}(\tau)$. They use the same reference quantile to transform CQTE of
different groups:101010Powell (2016) proposes a generalized quantile
regression (GQR) that also uses a transformation of conditional quantiles. The
main purpose of GQR is to estimate unconditional quantiles under unrestrictive
assumptions.

$\displaystyle\delta_{TQTE}(\tau,m)=$
$\displaystyle\varphi_{1}(m,Q_{U_{r}}(\tau))-\varphi_{0}(m,Q_{U_{r}}(\tau))\mbox{
and }$ $\displaystyle\delta_{TQTE}(\tau,f)=$
$\displaystyle\varphi_{1}(f,Q_{U_{r}}(\tau))-\varphi_{0}(f,Q_{U_{r}}(\tau)).$

Heterogeneity arises between $\delta_{TQTE}(\tau,m)$ and
$\delta_{TQTE}(\tau,f)$ solely from the first argument of the earnings
function. Accordingly, this approach enables us to isolate effect
heterogeneity by gender, but the size of the effect will depend on the
reference quantile. I propose using the reference quantiles from the potential
earnings distribution under non-treatment. I show that TQTE equals CQTE when
no structural earnings inequality exists. Furthermore, I show that TQTE equals
the (unconditional) quantile treatment effect (QTE) when structural inequality
is solely responsible for the effect heterogeneity by gender.

The conditional average treatment effects (CATE) are defined as

$\delta_{CATE}(m)=\int_{0}^{1}\delta_{CQTE}(\tau,m)d\tau\mbox{ and
}\delta_{CATE}(f)=\int_{0}^{1}\delta_{CQTE}(\tau,f)d\tau.$

This definition implies that inequalities in the earnings structure can be
carried through to average effects. Therefore, I extend the approach in
Bitler, Hoynes, and Domina (2014) to incorporate average effects.

###  4.2 Treatment effect framework

In the programme evaluation literature, it is common to use the potential
outcomes instead of the earnings functions. The potential earnings under
assignment to and possible participation in the Job Corps are
$Y_{i}(1)=\varphi_{1}(G_{i},U_{i})$ (for $i=1,...,N$). The potential earnings
when individual $i$ does not receive an offer to participate in the Job Corps
are $Y_{i}(0)=\varphi_{0}(G_{i},U_{i})$. For each individual, only the
realized earnings,

$Y_{i}=Y_{i}(1)\cdot D_{i}+Y_{i}(0)\cdot(1-D_{i}),$

are observed, implying that either $Y_{i}(1)$ or $Y_{i}(0)$ is
counterfactual.111111The observational rule holds only under the stable unit
treatment value assumption (e.g., Rubin, 2005). The individual-specific causal
effects are

$\delta_{i}=Y_{i}(1)-Y_{i}(0)=\varphi_{1}(G_{i},U_{i})-\varphi_{0}(G_{i},U_{i}).$

In the remainder of the paper, I use the potential outcome notation. We cannot
identify individual-specific causal effects using cross-sectional data without
making strong assumptions, such as rank preservation. The latter implies that
individuals do not change their rank because of their treatment status (see
discussion in Firpo, 2007).121212Chernozhukov and Hansen (2005) use the term
rank invariance to refer to this assumption. The authors also introduce rank
similarity, which is a weaker assumption than rank preservation because it
allows for random deviations in ranks.

Nevertheless, quantile differences can be identified without assuming rank
preservation. The potential quantile $Q_{Y(d)}(\tau)$ is the minimum value of
$Y_{i}(d)$ such that at least the share $\tau$ of the potential earnings
distribution lies below this value.131313$F_{Y(d)}(y)=Pr(Y_{i}(d)\leq
y)=Pr(Y_{i}\leq y|D_{i}=d)$ is identified from observable data because of the
random treatment assignment. It denotes the cumulative distribution function
of $Y_{i}(d)$. The $\tau$th quantile of $Y_{i}(d)$ is
$Q_{Y(d)}(\tau)=\operatornamewithlimits{inf\vphantom{p}}\\{y:F_{Y(d)}(y)\geq\tau\\},$
for the real $\tau\in(0,1)$. Quantile treatment effects (QTEs) are defined as

$\delta_{QTE}(\tau)=Q_{Y(1)}(\tau)-Q_{Y(0)}(\tau),$

the difference between the potential quantiles. QTEs identify the horizontal
differences in potential earnings distributions at specific ranks.

Furthermore, the potential conditional quantile $Q_{Y(d)|G}(\tau|g)$ is the
minimum value of $Y_{i}(d)$ such that at least the share $\tau$ of the
conditional potential earnings distribution lies below this
value.141414$F_{Y(d)|G}(y|g)=Pr(Y_{i}(d)\leq y|G_{i}=g)=Pr(Y_{i}\leq
y|D_{i}=d,G_{i}=g)$ is identified from observable data because of the random
treatment assignment. It denotes the potential earnings distribution of
$Y_{i}(d)$ conditional on gender $g$ for $g\in\\{m,f\\}$. The $\tau$th
quantile of $Y_{i}(d)$ conditional on gender is
$Q_{Y(d)|G}(\tau|g)=\operatornamewithlimits{inf\vphantom{p}}\\{y:F_{Y(d)|G}(y|g)\geq\tau\\}.$
The CQTEs are defined as

$\delta_{CQTE}(\tau,g)=Q_{Y(1)|G}(\tau|g)-Q_{Y(0)|G}(\tau|g),$

the difference between the conditional potential quantiles.

Finally, the average treatment effect (ATE) is the expected value of
$\delta_{i}$,

$\delta_{ATE}=\int_{0}^{1}\delta_{QTE}(\tau)d\tau=E[Y_{i}(1)-Y_{i}(0)],$

and the CATE is

$\delta_{CATE}(g)=\int_{0}^{1}\delta_{CQTE}(\tau,g)d\tau=E[Y_{i}(1)-Y_{i}(0)|G_{i}=g].$

Both average effects can be identified without assuming rank preservation.

###  4.3 Quantile transformations

One non-separable method of incorporating the earnings structure is to fix the
value of the non-treated outcome at which CQTEs are measured. This requires a
unique reference distribution, the quantiles of which are used as fixed anchor
points. The CQTEs of various groups are transformed to these reference
quantiles to place each CQTE on the same absolute scale. The required quantile
transformations can be conceptualized through a relative rank (see Morris,
Bernhardt, and Handcock, 1994). Although the choice of reference distribution
is obviously crucial, generally, there is no best choice. I propose using the
potential earnings distribution under non-treatment as a reference
distribution and define the relative rank as

$\tau_{g}^{r}=F_{Y(0)|G}(Q_{Y(0)}(\tau)|g).$

This relative rank can be interpreted as the proportion of the conditional
population with potential earnings below the $\tau^{th}$ potential earnings
quantile of the population under non-treatment. Subsequently, I demonstrate
why this relative rank allows a meaningful decomposition of CQTE.
Nevertheless, many alternative measures are available for the relative rank,
and these can also be meaningful. Currently, Bitler, Hoynes, and Domina (2014)
is the only other study that uses the translated quantile approach. They use
the observed outcome distribution under non-treatment as reference
distribution in their instrumental variable approach.

The translated quantile treatment effect (TQTE) is defined as

$\delta_{TQTE}(\tau,g)=Q_{Y(1)|G}(\tau_{g}^{r}|g)-Q_{Y(0)|G}(\tau_{g}^{r}|g),$
(1)

implying that TQTE measures the horizontal distance between two conditional
potential outcome distributions at $\tau_{g}^{r}$. The only difference between
CQTE and TQTE is that the location has shifted from $\tau$ to $\tau_{g}^{r}$.
TQTEs establish a mapping between the conditional and reference distributions.

If $F_{Y(0)|G}(y|g)$ is strictly increasing in the interval $(0,1)$, such that
$Q_{Y(0)|G}(F_{Y(0)|G}(y|g)|g)=y$, then TQTE can be rearranged as151515For
example, suppose that the median potential earnings under non-treatment are
200 U.S. dollars for females. For further simplification, assume that
$F_{Y(0)|G}(200|f)=0.5$ (i.e., the outcome is continuous). If
$F_{Y(0)|G}(200|f)$ is strictly increasing, then $Q_{Y(0)|G}(0.5|f)=200$ is an
equality. Otherwise, $Q_{Y(0)|G}(0.5|f)\leq 200$ is not a strict inequality.
Both results hold also when the outcome is not continuous, i.e., if
$F_{Y(0)|G}(200|f)\leq 0.5$.

$\delta_{TQTE}(\tau,g)=Q_{Y(1)|G}(\tau_{g}^{r}|g)-Q_{Y(0)}(\tau).$ (2)

This quantity is related to the changes-in-changes estimator proposed by Athey
and Imbens (2006). The structural conditional quantile treatment effect (SQTE)
can be defined as

$\delta_{SQTE}(\tau,g)=\delta_{CQTE}(\tau,g)-\delta_{TQTE}(\tau,g).\\\ $

This describes the difference between CQTE and TQTE.

For an explicit example, assume that the median potential outcome under non-
treatment is 300 U.S. dollars, i.e., $Q_{Y(0)}(0.5)=300$. However, females
earning 300 U.S. dollars would already be at the 75% rank in the conditional
potential earnings distribution of females under non-treatment, i.e.,
$F_{Y(0)|G}(300|f)=0.75$. Then, the relative rank for females would be
$\tau_{f}^{r}=0.75$. The median TQTE would measure the difference between the
conditional potential quantiles under treatment and non-treatment of females
at rank $\tau_{f}^{r}=0.75$. In contrast, the median CQTE would measure the
difference between the conditional potential quantiles under treatment and
non-treatment of females at rank $\tau=0.5$. The median SQTE would measure the
difference between the conditional potential quantiles under treatment of
females at ranks $\tau=0.5$ and $\tau_{f}^{r}=0.75$. Accordingly, TQTE and
CQTE would be similar, and SQTE would be zero if the relative rank were 0.5,
which is not the case in the presented example.

In the following, I illustrate the interpretation of TQTE and SQTE in two
important special cases. First, assume that the structural inequality between
males and females is zero. This implies that $F_{Y(0)|G}(y|g)=F_{Y(0)}(y)$ for
all $y$, and $Q_{Y(0)|G}(\tau|g)=Q_{Y(0)}(\tau)$ for all $\tau$. Further,
assume that $Y_{i}(0)$ is continuously distributed such that
$F_{Y(0)|G}(Q_{Y(0)|G}(\tau|g)|g)=\tau$. Now, we can show that
$\delta_{TQTE}(\tau,g)=\delta_{CQTE}(\tau,g)$ and $\delta_{SQTE}(\tau,g)=0$
because $\tau_{g}^{r}=\tau$.161616The continuity assumption can be relaxed.
Without assuming continuity, Athey and Imbens (2006) show that
$Q_{Y(0)|G}(F_{Y(0)|G}(Q_{Y(0)|G}(\tau|g)|g)|g)=Q_{Y(0)|G}(\tau|g)$ (see Lemma
A.1 in Athey and Imbens, 2006). Furthermore, the condition
$Q_{Y(1)|G}(F_{Y(0)|G}(Q_{Y(0)|G}(\tau|g)|g)|g)=Q_{Y(1)|G}(\tau|g)$ will hold
if $F_{Y(0)|G}(y|g)$ is at least as smooth as $F_{Y(1)|G}(y|g)$. This means
that the step size to the next higher rank must satisfy the condition
$F_{Y(0)|G}(Q_{Y(0)|G}(\tau|g)|g)\leq F_{Y(1)|G}(Q_{Y(1)|G}(\tau|g)|g)$ for
all $\tau$. However, the assumption of continuity is more intuitive and
appears reasonable in many applications. Thus, CQTEs have no structural
component, and the entire effect heterogeneity can be directly associated with
gender; that is,
$\delta_{TQTE}(\tau,f)-\delta_{TQTE}(\tau,m)=\delta_{CQTE}(\tau,f)-\delta_{CQTE}(\tau,m)$
and $\delta_{SQTE}(\tau,f)-\delta_{SQTE}(\tau,m)=0$.

Second, assume that the entire effect heterogeneity by gender can be explained
by structural earnings differences. This implies that the transformed
quantiles are equal for females and males,

$Q_{Y(1)|G}(\tau_{f}^{r}|f)=Q_{Y(1)|G}(\tau_{m}^{r}|m),$ (3)

because conditional potential quantiles would not be heterogeneous by gender
after rank adjustment. If $Y_{i}(d)$ is continuously distributed such that
$F_{Y(d)|G}(Q_{Y(d)|G}(\tau|g)|g)=\tau$, equation (3) can be rearranged as

$\tau_{f}^{r}=F_{Y(1)|G}(Q_{Y(1)|G}(\tau_{m}^{r}|m)|f).$ (4)

The law of iterative expectations for a distribution implies that
$F_{Y(1)}(y)=Pr(G_{i}=f)F_{Y(1)|G}(y|f)+Pr(G_{i}=m)F_{Y(1)|G}(y|m)$. Thus,

$Pr(G_{i}=f)\cdot\tau_{f}^{r}=F_{Y(1)}(Q_{Y(1)|G}(\tau_{m}^{r}|m))-Pr(G_{i}=m)\cdot
F_{Y(1)|G}(Q_{Y(1)|G}(\tau_{m}^{r}|m)|m).$

Further rearrangements using the abovementioned continuity assumption lead to

$Pr(G_{i}=f)\cdot\tau_{f}^{r}+Pr(G_{i}=m)\cdot\tau_{m}^{r}=F_{Y(1)}(Q_{Y(1)|G}(\tau_{m}^{r}|m)).$

The left side of this equation is exactly the marginal distribution
$F_{Y(0)}(y)=Pr(G_{i}=f)F_{Y(0)|G}(y|f)+Pr(G_{i}=m)F_{Y(0)|G}(y|m)$ evaluated
at $Q_{Y(0)}(y)$. This leads to the equality
$\tau=F_{Y(1)}(Q_{Y(1)|G}(\tau_{m}^{r}|m))$ under the above continuity
assumption. If $F_{Y(1)}(y)$ is strictly increasing in the interval $(0,1)$ so
that $Q_{Y(1)}(F_{Y(1)}(y))=y$, this result implies that

$Q_{Y(1)}(\tau)=Q_{Y(1)|G}(\tau_{g}^{r}|g)$

under condition (3).171717This quantile-quantile stability condition is
strongly related to the rank stability condition
$F_{Y(1)|G}(Q_{Y(1)}(\tau)|g)=F_{Y(0)|G}(Q_{Y(0)}(\tau)|g)$, which is used in
Bitler, Gelbach, and Hoynes (2008) and Frandsen and Lefgren (2018) as a
falsification test for rank preservation. Essentially, the researchers’
findings imply that the assumption of rank preservation must be rejected if
the quantile-quantile stability condition does not hold. TQTEs implicitly test
this condition. Although the results of Section 5 cannot reject this
condition, it is possible that variables other than gender are associated with
rank reorganization. When this finding is substituted into equation (2), the
results are $\delta_{TQTE}(\tau,g)=\delta_{QTE}(\tau)$ and
$\delta_{TQTE}(\tau,f)-\delta_{TQTE}(\tau,m)=0$. Furthermore,
$\delta_{SQTE}(\tau,g)=\delta_{CQTE}(\tau,g)-\delta_{QTE}(\tau)$, implying
that the entire inter-gender CQTE difference is attributed to the structural
effect
$\delta_{SQTE}(\tau,f)-\delta_{SQTE}(\tau,m)=\delta_{CQTE}(\tau,f)-\delta_{CQTE}(\tau,m)$.

In summary, TQTE equals CQTE if the structural earnings difference is zero. In
contrast, TQTE equals QTE if the heterogeneity between CQTE for males and
females can be fully explained by structural earnings inequality. This is a
meaningful interpretation for TQTE because QTE represents the unconditional
quantile effects.

Finally, the translated conditional average treatment effect (TATE) can be
shown to be

$\delta_{TATE}(g)=\int_{0}^{1}\delta_{TQTE}(\tau,g)d\tau=E[Q_{Y(1)|G}(F_{Y(0)|G}(Y_{i}(0)|g)|g)]-E[Y_{i}(0)],$

as an analogy to equation (2), whereas the structural conditional average
treatment effect (SATE) can be shown to be

$\delta_{SATE}(g)=\int_{0}^{1}\delta_{SQTE}(\tau,g)d\tau=\delta_{CATE}(g)-\delta_{TATE}(g).$

These parameters enable the average decomposition to account for differences
in outcome structures. The interpretations of TATE and SATE are analogous to
those of TQTE and SQTE, respectively. If structural earnings inequality equals
zero, then TATE equals CATE and SATE equals zero. If the difference between
the CATE for males and females can be fully explained by structural earnings
inequality, TATE equals ATE, and SATE is the difference between CATE and ATE.

###  4.4 Estimation

For an extensive study on estimating counterfactual distributions under
various identification strategies and model specifications, see, e.g.,
Chernozhukov, Fernández-Val, and Melly (2013) and Fortin, Lemieux, and Firpo
(2010). In this study, I compute quantiles of earnings by treatment status,
which identifies the potential earnings quantiles because of the randomized
research design. The most challenging estimation steps are the quantile
transformations. The first application of quantile transformation in labour
economics dates back to at least Juhn, Murphy, and Pierce (1991). I follow the
estimation approach proposed by Athey and Imbens (2006). They replace the
potential outcome distributions by empirical distribution functions.
Transformed quantiles can be obtained using a plug-in approach applied to the
empirical quantiles and ranks of the empirical distribution functions. The
average effects are estimated by replacing the expected values with the
transformed sample averages that incorporate quantile transformation.

In particular, I use the quantile regression estimator

$\operatornamewithlimits{argmin\vphantom{p}}_{\hat{\beta}_{\tau,0},\hat{\beta}_{\tau,1}}\sum_{i=1}^{N}\omega_{i}\cdot\rho_{\tau}(Y_{i}-\hat{\beta}_{\tau,0}-\hat{\beta}_{\tau,1}D_{i}),$

where $\rho_{\tau}(a)=a(\tau-1\\{a\leq 0\\})$ is the check function, and
$\omega_{i}$ represents the sampling and non-response weights ($wgt48b$)
provided in the NJCS data. This estimator minimizes the weighted absolute
deviations. The hats indicate the estimated parameters. Parameters are
$\hat{\beta}_{\tau,0}=\hat{Q}_{Y(0)}(\tau)$ and
$\hat{\beta}_{\tau,1}=\hat{\delta}_{QTE}(\tau)$.

For the CQTE estimation, I use the model

$\operatornamewithlimits{argmin\vphantom{p}}_{\hat{\alpha}_{\tau,g,0},\hat{\alpha}_{\tau,g,1}}\sum_{i=1}^{N}1\\{G_{i}=g\\}\cdot\omega_{i}\cdot\rho_{\tau}(Y_{i}-\hat{\alpha}_{\tau,g,0}-\hat{\alpha}_{\tau,g,1}D_{i}),$
(5)

where $1\\{\cdot\\}$ is the indicator function. Under the randomized research
design, parameter $\hat{\alpha}_{\tau,g,1}=\hat{\delta}_{CQTE}(\tau,g)$.
Subsequently, I estimate $\hat{Q}_{Y(1|G)}(\tau|g)$ by
$\hat{Q}_{Y(1|G)}(\tau|g)=\hat{\alpha}_{\tau,g,0}+\hat{\alpha}_{\tau,g,1}$.

The conditional cumulative distribution functions under non-treatment are
estimated using the empirical distribution functions

$\hat{F}_{Y(0)|G}(y|g)=\displaystyle\frac{1}{\sum_{i=1}^{N}1\\{D_{i}=0,G_{i}=g\\}\cdot\omega_{i}}\sum_{i=1}^{N}1\\{Y_{i}\leq
y,D_{i}=0,G_{i}=g\\}\cdot\omega_{i}.$

Following Athey and Imbens (2006), the relative ranks are estimated using the
plug-in approach
$\hat{\tau}_{g}^{r}=\hat{F}_{Y(0)|G}(\hat{Q}_{Y(0)}(\tau)|g)$. Now, I can
obtain TQTE by replacing the rank $\tau$ with the estimated relative rank
$\hat{\tau}_{g}^{r}$ in (5),

$\operatornamewithlimits{argmin\vphantom{p}}_{\hat{\gamma}_{\tau,g,0},\hat{\gamma}_{\tau,g,1}}\sum_{i=1}^{N}1\\{G_{i}=g\\}\cdot\omega_{i}\cdot\rho_{\hat{\tau}_{g}^{r}}(Y_{i}-\hat{\gamma}_{\tau,g,0}-\hat{\gamma}_{\tau,g,1}D_{i}).$

Parameter $\hat{\gamma}_{\tau,g,1}=\hat{\delta}_{TQTE}(\tau,g)$. The SQTEs are
estimated by
$\hat{\delta}_{SQTE}(\tau,g)=\hat{\delta}_{CQTE}(\tau,g)-\hat{\delta}_{TQTE}(\tau,g)$.
I consider only $\hat{\tau}_{g}^{r}\in[0.01,0.99]$ to avoid estimating extreme
quantiles. Furthermore, I exclude all ranks below $\hat{F}_{Y(0)}(0)$ because
the continuity assumption is violated at the mass point with zero earnings.
This excludes quantiles below the 21st percentile.

Athey and Imbens (2006) show that the resulting estimates are $\sqrt{n}$
pointwise consistent and asymptotically normal.181818The inference is
pointwise and not uniformly valid. Accordingly, the empirical results could be
affected by the multiple testing problem. This could The standard deviations
of all parameters are estimated using a nonparametric bootstrap procedure
(sampling individual observations with replacement). Chaisemartin and
D’Haultfeuille (2017) show the validity of the bootstrap approach for this
estimation. Melly and Santangelo (2015) extend the quantile transformation
approach to incorporate exogenous control variables, but I do not need to
include additional controls because of the randomized research design. I
discuss the estimation of average effects as well as the computation of the
Kolmogorov–Smirnov test statistic in Online Appendix B.

##  5 Empirical results

###  5.1 QTE and CQTE

Figure 1 shows the QTE of the Job Corps on average weekly earnings four years
after the randomized assignment for all percentiles.191919Figure A.1 in Online
Appendix A shows the potential earnings distributions. Additionally, column 1
of Table 3 documents the deciles of the QTE, including standard errors. The
empirical results suggest that quantile differences increase with rank. The
QTEs below the 2nd decile do not differ from zero because of participants who
are unemployed with no earnings. Between the 2nd and 5th deciles, the earnings
gain is approximately 10 U.S. dollars. The earnings gain further increases to
approximately 20 U.S. dollars between the 5th and 9th deciles. Beyond the 9th
decile, the quantile earnings differences reach values exceeding 100 U.S.
dollars. The Kolmogorov–Smirnov test results at the bottom of Table 3 support
the findings that the Job Corps has a significant positive effect on earnings
distribution.

Figure 1: QTEs of the Job Corps on average weekly earnings (in U.S. dollars)
in year four after a randomized assignment.

Note: The lines report the point estimates calculated separately for all
percentiles. Crosses on the lines indicate significant effects at 10% level.
Hollow circles on the lines indicate significant effects at 5% level. Full
diamonds on the lines indicate significant effects at 1% level.

Table 3: QTE and CQTE of the Job Corps programme by gender on average weekly
earnings (in U.S. dollars) in year four after a randomized assignment.

Quantile | QTE | CQTE | Difference between
---|---|---|---
|  | Females | Males | (2) and (3)
| (1) | (2) | (3) | (4)
0.2 | 13.01*** | 4.425 | 8.011 | -3.585
| (4.166) | (3.326) | (8.133) | (8.730)
0.3 | 7.555 | 16.68*** | 2.743 | 13.94
| (5.943) | (6.134) | (8.735) | (10.79)
0.4 | 8.414 | 19.12** | 7.055 | 12.06
| (6.356) | (8.163) | (9.690) | (12.84)
0.5 | 16.21*** | 9.059 | 25.08*** | -16.03
| (4.490) | (9.225) | (7.387) | (11.70)
0.6 | 17.93*** | 11.99** | 17.25*** | -5.261
| (4.833) | (6.218) | (7.749) | (9.929)
0.7 | 17.14*** | 22.36*** | 23.43*** | -1.070
| (4.950) | (6.536) | (3.966) | (7.605)
0.8 | 23.28*** | 12.08* | 22.64*** | -10.56
| (6.424) | (8.259) | (8.334) | (11.70)
0.9 | 16.51 | 22.38* | 10.03 | 12.35
| (11.01) | (12.38) | (11.47) | (16.70)
KS statistic | 11,231*** | 3,610 | 16,029*** | 12,419*
| [0.002] | [0.508] | [0.004] | [0.086]
PSD statistic | 11,231*** | 3,610 | 16,029*** | 1,507
| [0.002] | [0.259] | [0.001] | [0.811]
NSD statistic | 0 | 0 | 0 | -12,419**
| [0.983] | [0.978] | [0.991] | [0.033]

Note: *** indicates significance at 1% level, ** indicates significance at 5%
level, and * indicates significance at 10% level. Bootstrapped standard errors
are in parentheses and are obtained from 1,999 bootstrap replications. “KS
statistic” denotes the Kolmogorov–Smirnov statistic. “PSD statistic”
represents the Kolmogorov–Smirnov-type test statistic for positive stochastic
dominance. “NSD statistic” represents the Kolmogorov–Smirnov-type test
statistic for negative stochastic dominance. Bootstrapped p-values (obtained
using 1,999 replications) are in square brackets.

Figure 2: CQTE of the Job Corps programme by gender on average weekly earnings
(in U.S. dollars) in year four after a randomized assignment.

Note: The lines represent point estimates calculated separately for all
percentiles. Crosses on the lines indicate significant effects at 10% level.
Hollow circles on the lines indicate significant effects at 5% level. Full
diamonds on the lines indicate significant effects at 1% level.

Figure 3: Difference between the Job Corps CQTEs for females and males.

Note: The outcome is average weekly earnings (in U.S. dollars) in year four
after a randomized assignment. The lines represent the point estimates
calculated separately for all percentiles. Crosses on the lines indicate
significant effects at 10% level. Hollow circles on the lines indicate
significant effects at 5% level. Full diamonds on the lines indicate
significant effects at 1% level.

The patterns of CQTE for each gender are somewhat different and are reported
in Figure 2 and columns 2 and 3 of Table 3 (the scale of the y-axis differs
between Figures 1 and 2). For males, the CQTEs are close to zero until the 4th
decile. CQTEs jump to a positive impact on earnings of approximately 25 U.S.
dollars above the 4th decile. Beyond the 9th decile, the quantile earnings
differences exceed 150 U.S. dollars. For females, the CQTEs are zero until the
2nd decile. At the 2nd decile, the quantile earnings differences are
approximately 13 U.S. dollars and increase with rank to approximately 25 U.S.
dollars. These results are consistent with the findings of Eren and Ozbeklik
(2014). The Kolmogorov–Smirnov test results in Table 3 suggest that the Job
Corps programme has significant positive effects on the potential earnings
distribution of males, but no significant effects on that of females.

Figure 3 and column 4 of Table 3 show the differences between the CQTEs for
females and males. The negative differences at the 56th and 57th percentiles
are significant at 1% level. The negative differences at the 58th percentile
are significant at 5% level. The negative differences at the 18th, 46th, and
99th percentiles are significant at 10% level. Furthermore, the
Kolmogorov–Smirnov statistics in Table 3 represent the differences between the
CQTEs for females and males, which are significant at 10% level. The test of
negative stochastic dominance suggests that the CQTEs for females are always
equal to or smaller than the CQTEs for males (at 5% level). This suggests that
the returns of the offer to participate in the Job Corps are larger for males
than for females. Accordingly, the Job Corps offers tend to increase gender
earnings inequality at some quantiles.

###  5.2 TQTE and SQTE

Figure 4 shows the potential earnings distributions by gender. Females earn
less than males at all quantiles. It is possible that the differences between
the CQTEs for females and males can be explained by structural differences
between females’ and males’ earnings distributions.

Figure 5 shows the transformed relative ranks on the ordinate and the
untransformed ranks on the abscissa. The relative ranks would be on the
$45^{\circ}$ line in the absence of structural earnings inequality. The
average rank difference between females and males is 12.1 percentage points
(the minimum is 2.5, and the maximum is 18.4 percentage points). The relative
rank of females is always lower than the $45^{\circ}$ line. The relative rank
of males is always higher than the $45^{\circ}$ line. For example, males
(females) at the 40th percentile of the conditional potential earnings
distribution would have rank 48 (rank 34) in the population distribution.
Accordingly, the relative rank shifts the ranks of males upward and the ranks
of females downward. This implies that TQTE shifts the CQTE for males to the
right and that for females to the left.

Figure 4: Potential earnings distributions by gender.

Note: The treatment is an offer to join the Job Corps program. The outcome is
average weekly earnings (in U.S. dollars) four years after a randomized
assignment. The figure is truncated by 600 U.S. dollars in earnings per week.

Figure 5: Rank transformation.

Note: I consider the relative ranks only in the interval $[0.01,0.99]$ and
exclude all ranks below $\hat{F}_{Y(0)}(0)$ (for explanation, see Online
Appendix B).

Figure 6: TQTEs of the Job Corps by gender on average weekly earnings (in U.S.
dollars) in year four after a randomized assignment.

Note: The lines represent point estimates calculated separately for all
percentiles. Crosses on the lines indicate significant effects at 10% level.
Hollow circles on the lines indicate significant effects at 5% level. Full
diamonds on the lines indicate significant effects at 1% level. I consider
only the relative ranks in the interval $[0.01,0.99]$ and exclude all ranks
below $\hat{F}_{Y(0)}(0)$ (for explanation, see Online Appendix B).

Table 4: TQTEs and SQTEs of the Job Corps by gender on average weekly earnings
(in U.S. dollars) in year four after a randomized assignment.

Quantile | TQTE | Difference between |  | SQTE | Difference between
---|---|---|---|---|---
| Females | Males | (1) and (2) |  | Females | Males | (4) and (5)
| (1) | (2) | (3) |  | (4) | (5) | (6)
0.3 | 14.83* | 0.650 | 14.13 |  | 1.853 | 2.093 | -0.240
| (8.499) | (8.289) | (12.107) |  | (4.431) | (4.024) | (6.208)
0.4 | 14.18* | 4.863 | 9.314 |  | 4.940 | 2.192 | 2.748
| (7.994) | (9.096) | (12.11) |  | (4.614) | (4.865) | (6.795)
0.5 | 7.461 | 23.25*** | -15.79 |  | 1.598 | 1.830 | -0.232
| (6.829) | (7.846) | (10.92) |  | (6.060) | (6.628) | (7.034)
0.6 | 19.13*** | 17.20*** | 1.928 |  | -7.133 | 0.056 | -7.189
| (7.391) | (5.886) | (8.863) |  | (5.299) | (4.425) | (6.587)
0.7 | 13.45* | 25.92*** | -12.47 |  | 8.913* | -2.485 | 11.40
| (7.649) | (7.326) | (11.17) |  | (5.201) | (5.290) | (7.737)
0.8 | 16.56 | 24.31*** | -7.747 |  | -4.479 | -1.669 | -2.810
| (10.30) | (7.734) | (13.11) |  | (6.720) | (4.268) | (7.741)
0.9 | 20.30 | 14.79 | 5.501 |  | 2.082 | -4.767 | 6.850
| (17.26) | (12.86) | (20.56) |  | (12.10) | (7.161) | (13.57)
KS statistic | 2,659 | 11,490** | 2,455 |  | 1,417 | 4,539 | 2,056
| [0.741] | [0.011] | [0.909] |  | [0.988] | [0.310] | [0.973]
PSD statistic | 2,659 | 11,490*** | 1,610 |  | 1,417 | 4,539 | 1,258
| [0.378] | [0.010] | [0.727] |  | [0.844] | [0.112] | [0.982]
NSD statistic | 430 | 67 | -2,455 |  | -1,361 | -1,369 | -2,056
| [0.993] | [0.993] | [0.551] |  | [0.833] | [0.904] | [0.743]

Note: *** indicates significance at 1% level, ** indicates significance at 5%
level, and * indicates significance at 10% level. Bootstrapped standard errors
are in parentheses and are obtained from 1,999 bootstrap replications. “KS
statistic” denotes the Kolmogorov–Smirnov statistic. “PSD statistic”
represents the Kolmogorov–Smirnov-type test statistic for positive stochastic
dominance. “NSD statistic” represents the Kolmogorov–Smirnov-type test
statistic for negative stochastic dominance. Bootstrapped p-values (obtained
from 1,999 replications) are in square brackets.

Figure 6 and columns 1 and 2 of Table 4 document the findings for TQTEs by
gender (the scale of the y-axis differs between Figures 2 and 6). The
reference distribution is the potential earnings distribution of all eligible
Job Corps candidates under non-treatment. This distribution is documented in
Figure A.1 in Online Appendix A. I do not consider the parts of the potential
earnings distribution with zero earnings for quantile transformation because
the continuity assumptions—described in Section 4.3—are violated at the mass
point with zero earnings. This excludes all ranks lower than the 21st
percentile. Furthermore, I exclude the relative ranks higher than the 99th
percentile, which avoids estimating extreme quantiles.

Figure 6 shows patterns of TQTE that are more consistent between males and
females. The TQTE for males is fairly close to zero below the median. Above
the median, the quantile earnings differences remain at approximately 25 U.S.
dollars. The large difference between the TQTE and CQTE for males at the 99th
percentile decreases by approximately 30% (from 156 to 112 U.S. dollars). The
CQTE and TQTE for females are overall quite similar. Below the median, TQTE
values are approximately 15 U.S. dollars. The increase to 25 U.S. dollars
occurs earlier for TQTE than for CQTE. The Kolmogorov–Smirnov-type test
results at the bottom of Table 4 show that the Job Corps influences the
potential earnings distribution of males, but not that of females. These
findings are consistent with the Kolmogorov–Smirnov-type tests applied to
CQTE.

Figure 7: Difference between Job Corps TQTEs for females and males.

Note: The outcome is average weekly earnings (in U.S. dollars) in year four
after a randomized assignment. The lines represent the point estimates
calculated separately for all percentiles. All point estimates are not
statistically different from zero. I consider the relative ranks only in the
interval $[0.01,0.99]$ and exclude all ranks below $\hat{F}_{Y(0)}(0)$ (for
explanation, see Online Appendix B).

Figure 7 and column 3 of Table 4 show the quantile differences between the
TQTEs for females and males. The differences oscillate around zero. The highly
significant negative differences at the 56th and 57th percentiles, which are
documented for CQTEs, decline for TQTEs by 45% (from approximately –22 to –12
U.S. dollars). For TQTEs, I do not observe statistically significant
differences between females and males. Tables 3 and 4 also report standard
errors. The standard errors of TQTE are not systematically higher than those
of CQTE. Therefore, the insignificant findings are not caused by a
comparatively imprecise estimation of TQTE relative to that of CQTE.
Furthermore, the bottom rows of Table 4 present the Kolmogorov–Smirnov-type
statistics. I observe no evidence of difference between the TQTEs of females
and males. I also observe no evidence that the TQTEs for females dominate the
effects for males or vice versa. Overall, these results imply that the direct
effects of the Job Corps are not highly heterogeneous by gender.

Figure 8: SQTEs of the Job Corps by gender on average weekly earnings (in U.S.
dollars) in year four after a randomized assignment.

Note: The lines represent the point estimates calculated separately for all
percentiles. Crosses on the lines indicate significant effects at 10% level.
Hollow circles on the lines indicate significant effects at 5% level. Full
diamonds on the lines indicate significant effects at 1% level. I consider the
relative ranks only in the interval $[0.01,0.99]$ and exclude all ranks below
$\hat{F}_{Y(0)}(0)$ (for an explanation, see Online Appendix B).

Figure 9: Difference between SQTEs of the Job Corps for females and males.

Note: The outcome is weekly earnings (in U.S. dollars) in year four after a
randomized assignment. The lines represent point estimates calculated
separately for all percentiles. Crosses on the lines indicate significant
effects at 10% level. Hollow circles on the lines indicate significant effects
at 5% level. Full diamonds on the lines indicate significant effects at 1%
level. I consider the relative ranks only in the interval $[0.01,0.99]$ and
exclude all ranks below $\hat{F}_{Y(0)}(0)$ (for an explanation, see Online
Appendix B).

Finally, Figure 8 reports the SQTEs by gender, and Figure 9 reports the
heterogeneity between SQTEs by gender. SQTE is the difference between CQTE and
TQTE. Figure 8 reports highly significant SQTEs. For males, CQTEs are larger
than TQTEs between the 4th and 5th deciles. For females, the positive and
negative differences are mixed. Overall, large differences are observed
between CQTEs and TQTEs in Figure 8. The differences between SQTEs for males
and females are significantly different from zero at some quantiles. Figure 9
reports the negative effects at the 46th and 58th percentiles, which are
significant at 1% level, and those at the 45th and 59th percentiles, which are
significant at 5% level. Further, positive effects are reported at the 71st
and 74th percentiles, which are significant at 10% level. Thus, the earnings
structure tends to affect CQTE heterogeneity by gender. However, the
Kolmogorov–Smirnov-type statistics at the bottom of Table 4 do not indicate
significant effects.

In summary, the quantile earnings differences increase with rank. This could
favour males because they typically have higher earnings distribution ranks
than do females. Accordingly, the Job Corps programme tends to increase the
existing inequality in structural earnings. After accounting for expected
earnings opportunities, I observe no strong evidence that the Job Corps is
more aligned with the training needs of males than those of females.

###  5.3 Average effects

Table 5: ATE, CATE, TATE, and SATE of the Job Corps on average weekly earnings
(in U.S. dollars) in year four after a randomized assignment.

Gender | Potential Outcome | Average | Average Differences
---|---|---|---
| Levels | Effects | between Females
| Y(1) | Y(0) |  | and Males
| (1) | (2) | (3) | (4)
ATE
Both Genders | 210.9 | 195.8 | 15.01*** | -
|  |  | (3.85) |
CATE
Females | 170.4 | 158.1 | 12.31** | -5.22
|  |  | (5.26) | (7.55)
Males | 239.2 | 221.6 | 17.54*** | -
|  |  | (5.32) |
TATE
Females | 212.3 | 195.8 | 16.39** | -0.95
|  |  | (6.98) | (9.22)
Males | 213.6 | 195.8 | 17.34*** | -
|  |  | (5.88) |
SATE
Females | - | - | -4.08* | -4.28
|  |  | (2.26) | (2.96)
Males | - | - | 0.19 | -
|  |  | (1.70) |

Note: *** indicates significance at 1% level, ** indicates significance at 5%
level, and * indicates significance at 10% level. Bootstrapped standard errors
are in parentheses and are obtained from 499 bootstrap replications.

Table 5 shows that individuals awarded offers to participate in the Job Corps
experience an average earnings gain of 15 U.S. dollars, or 8%. Females with no
award earn 63 U.S. dollars or 29% less than males with no award of an offer.
In the following discussion, I call this the average gender earnings gap. The
offer to participate in the Job Corps increases the earnings of females by 12
U.S. dollars and the earnings of males by 18 U.S. dollars. The average effect
is approximately 5 U.S. dollars lower for females than for males,
corresponding to approximately 42% ($=5/12\cdot 100\%$) higher earnings gain
for males than for females. These higher earnings increase the average gender
earnings gap by 8% ($=5/63\cdot 100\%$). Eren and Ozbeklik (2014) and
Schochet, Burghardt, and McConnell (2008) report results of a similar
magnitude. In the experimental survey data, the average effect heterogeneity
is not significantly different from zero.

TATE accounts for 1 U.S. dollar of the earnings difference between females and
males. SATE accounts for 4 U.S. dollars of that difference. Accordingly, the
structural earnings inequality could account for up to 82% and the direct
gender effects for only 18% of the increase in the average gender earnings
gap. Despite the insignificant average effects, a large structural earnings
inequality can cause the effect heterogeneity by gender. Job Corps
trainability differences by gender do not seem to be an important channel of
effect heterogeneity. If the offers to participate in the Job Corps are
awarded to males and females so that the unconditional potential earnings
distributions are aligned under non-treatment, then the average effects are
larger for females (average TATE is larger than average CATE), but do not
hamper the effects for males. At the same time, gender earnings inequality
increases by only 2% ($=1/63\cdot 100\%$).

###  5.4 Alternative reference distributions and relative ranks

Online Appendix C.1 reports TQTE and SQTE when the reference quantiles are
from the potential outcome distribution under treatment ($Q_{Y(1)}(\tau)$),
the observed outcome distribution ($Q_{Y}(\tau)$), the potential outcome
distribution of males under non-treatment ($Q_{Y(0)|G}(\tau|m)$), and the
potential outcome distribution of females under non-treatment
($Q_{Y(0)|G}(\tau|f)$). The results do not change qualitatively when a
different reference distribution is used (see Figures C.3-C.4).

Online Appendix C.2 reports TQTE and SQTE when the relative rank is defined
under treatment $\tau_{g}^{r}=F_{Y(1)|G}(Q_{Y_{r}}(\tau)|g)$. Again, I
consider many possible reference distributions (see Figures C.1–C.4). The
results do not change qualitatively when the relative rank is defined under
treatment. Accordingly, the results are not sensitive to the choice of the
reference distributions and relative ranks.

##  6 Effect heterogeneity by gender and parenthood

Figure 10: Rank transformation.

Note: I consider the relative ranks only in the interval $[0.01,0.99]$ and
exclude all ranks below $\hat{F}_{Y(0)}(0)$ (for explanation, see Online
Appendix B).

Having children greatly influences the decision to accept an offer to
participate in the Job Corps (see Table 1). Therefore, I investigate effect
heterogeneity with respect to gender and children. Among the sample’s
individuals, 33% are mothers, and 10% are fathers.202020For 1% of the sample,
the data on children is missing. Figure 10 shows the relative ranks by gender
and parenthood.212121Figure A.2 in Online Appendix A documents the potential
earnings distributions under non-treatment by gender and parenthood. For low
percentiles, the relative ranks of mothers and fathers are close to the
$45^{\circ}$ line, which indicates little structural gender earnings
inequality. However, for high percentiles the relative ranks of mothers are
more disperse than for females without children, indicating more structural
earnings inequality.

Table 6: CATE, TATE, and SATE of the Job Corps by parenthood on average weekly
earnings (in U.S. dollars) in year four after a randomized assignment.

Gender | With Children | Without Children | Difference between
---|---|---|---
| Level | Difference | Level | Difference | (2) and (4)
| (1) | (2) | (3) | (4) | (5)
CATE
Females | 20.46*** | 5.40 | 9.12 | -9.01 | 14.42
| (7.25) | (17.00) | (6.04) | (8.52) | (21.95)
Males | 15.05 |  | 18.13*** |  |
| (15.79) |  | (5.57) |  |
TATE
Females | 4.17 | 0.70 | -2.49 | -3.43 | 4.14
| (5.31) | (7.43) | (2.83) | (2.81) | (7.86)
Males | 3.47 |  | 0.95 |  |
| (6.29) |  | (0.65) |  |
SATE
Females | 16.29*** | 4.70 | 11.61* | -5.58 | 10.28
| (5.92) | (14.6) | (6.12) | (8.16) | (22.13)
Males | 11.58 |  | 17.19*** |  |
| (15.12) |  | (5.66) |  |

Note: *** indicates significance at 1% level, ** indicates significance at 5%
level, and * indicates significance at 10% level. Bootstrapped standard errors
are in parentheses and are obtained from 499 bootstrap replications.

Table 6 reports suggestive evidence for effect heterogeneity in CATEs by
gender and parenthood. On average, mothers benefit more from an offer to join
the Job Corps than do fathers. In contrast, childless males profit more from
an offer to join the Job Corps than do childless females. Strikingly, the
effect of an offer to join the Job Corps is twice as large for mothers as for
childless women.222222The average earnings of mothers with an offer to join
the Job Corps are 175 U.S. Dollars, and the respective amount is 154 U.S.
Dollars for those without an offer. The average earnings of childless women
with an offer to join the Job Corps is 169 U.S. Dollars, and the respective
amount is 160 U.S. Dollars for those without an offer. The SATE accounts for
87% ($=4.7/5.4\cdot 100\%$) of the CATE heterogeneity by gender for those with
children and for 62% ($=5.58/9.01\cdot 100\%$) in the absence of children.
Even though the effect heterogeneity is insignificant, there is a tendency for
the structural earnings inequality to have an economically meaningful
influence. Overall, the TATE accounts for 29% ($=4.14/14.42\cdot 100\%$) and
the SATE for 71% ($=10.28/14.42\cdot 100\%$) of the CATE effect heterogeneity
by gender and parenthood. These results suggest that within-group
heterogeneity in the earnings structures contribute substantially to the
between-groups effect heterogeneity. This is consistent with the findings of
Bitler, Gelbach, and Hoynes (2017), who document that average effects by group
miss important within-group heterogeneity. The results for quantiles are
qualitatively similar and are reported in Online Appendix D.

##  7 Conclusions

The existing studies tend to conclude that the Job Corps increases gender
earnings inequality. These findings are surprising because most other ALMP
evaluations show more positive effects for females than for males (see, e.g.,
Bergemann and van den Berg, 2008). I estimate the TQTEs, initially proposed by
Bitler, Hoynes, and Domina (2014), to reveal the potential mechanism behind
these unexpected findings. Frumento, Mealli, Pacini, and Rubin (2012) identify
labour market opportunities as the main reason for effect heterogeneity. I
approximate such opportunities using expected earnings. Because the earnings
distributions differ by gender, the existing structural gender earnings
inequality can be a mechanism for effect heterogeneity by gender.

The results suggest that the award of an offer to participate in the Job Corps
increases the average weekly earnings of eligible individuals by approximately
15 U.S. dollars. The absolute earnings gain is approximately 5 U.S. dollars
lower for females than for males. The Job Corps offer is least beneficial for
childless women. Randomly awarding offers to participate in the Job Corps
could increase the gender earnings gap by up to 8%. My findings suggest that
the average structural earnings inequality accounts for 82% of the effect
heterogeneity by gender, whereas only 18% of the effect heterogeneity can be
explained by Job Corps trainability differences by gender. Even though the
effect heterogeneity is mostly not significant, this suggests structural
earnings differences between groups are important for explaining the overall
effect heterogeneity.

These results suggest that programme administrators should pay more attention
to heterogeneous gender earnings structure when designing assignment rules for
Job Corps (and potentially also for other ALMPs). An assignment rule that
balances the earnings structure of male and female participants would lead to
similar effects for both genders. However, several factors have to be
considered before implementing such an assignment rule. First, such a rule
would crowd-out some males that would significantly benefit from the
programme. It is unclear if this is in the interest of the programme
administrators. Second, an assignment rule that increases the overall
effectiveness of Job Corps would target males and females at the higher end of
the earnings distribution. However, such a rule would mainly support those
participants who are already well-off. Third, it is unclear how such
assignment rules would be implemented in practice. The assignment decision
would be based on the potential earnings under non-treatment four years after
the programme assignment, which is obviously unobservable at the time the
assignment decision is made. Accordingly, the potential earnings under non-
treatment would have to be predicted using variables that are observed in the
baseline period (e.g., previous earnings, education, etc.), and the assignment
rule would have to be based on the predicted potential earnings under non-
treatment.232323To illustrate the approach, I predict earnings in the NJCS
subsample without an offer to participate in Job Corps with a Tobit model for
each gender separately. Table A.2 in Online Appendix A documents quite
heterogeneous earning prediction models for males and females eligible for Job
Corps. Ethnic origin, drug experience, and past arrests are good earnings
predictors for males eligible for Job Corps. Education and welfare history are
good earnings predictors for females eligible for Job Corps. Employment
history and living in a PMSA are good earnings predictors for both genders.
The correlation between the predicted and observed earnings is above 30% for
both genders, even though the NJCS contains only relatively few covariates.

There are three potential explanations why many other ALMPs have more positive
effects for females than for males. First, other ALMPs could have trainability
differences by gender that are in favour of females. Second, many other ALMPs
entail non-random selection into treatment, which could also favour females
(following the arguments of the preceding paragraph). Third, other ALMPs might
mainly support participants with low labour market opportunities, (e.g., Card,
Kluve, and Weber, 2018, provide evidence supporting this argument), which too
could favour females. In the latter case, the structural earnings inequality
would also be responsible for effect heterogeneity, but in this case it would
support females. However, the influence of structural earnings inequality on
the effectiveness of other ALMPs is beyond the scope of this study and is a
topic for future research.

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– The following appendices will be made available online. –

##  A Descriptive statistics by gender

Figure A.1: Potential earnings distribution of all eligible Job Corps
candidates.

Note: The treatment is a offer to join the Job Corps program. The outcome is
average weekly earnings (in U.S. dollars) in year four after randomized
assignment. The figure is truncated by earnings of 600 U.S. dollars per week.

Figure A.2: Potential earnings distributions by gender and existence of
children.

Note: The treatment is a offer to join the Job Corps program. The outcome is
average weekly earnings (in U.S. dollars) four years after the randomized
assignment. The figure is truncated by 600 U.S. dollars in earnings per week.

Table A.1: Means and standard errors by gender.

| Males | Females | Standardized
---|---|---|---
| Mean | Std. Err. | Mean | Std. Err. | Difference
| (1) | (2) | (3) | (4) | (5)
Earnings per week in Year 4 | 230.310 | 206.581 | 164.308 | 167.071 | 35.130
Offer to join Job Corps | 0.495 | 0.500 | 0.502 | 0.500 | 1.220
Ever enrolled in a Job Corps center | 0.380 | 0.485 | 0.351 | 0.477 | 6.140
Socio-economic characteristics
Aged between 16-17 years | 0.435 | 0.496 | 0.386 | 0.487 | 9.960
Aged between 18-19 years | 0.310 | 0.463 | 0.327 | 0.469 | 3.620
Aged between 20-24 years | 0.254 | 0.436 | 0.287 | 0.452 | 7.220
White | 0.305 | 0.460 | 0.222 | 0.415 | 19.010
Black | 0.450 | 0.497 | 0.519 | 0.500 | 13.950
Hispanic | 0.169 | 0.375 | 0.185 | 0.388 | 4.180
Indian | 0.076 | 0.265 | 0.074 | 0.261 | 0.820
Lives with spouse or partner | 0.051 | 0.219 | 0.078 | 0.268 | 11.170
Dummy for bad health | 0.121 | 0.326 | 0.147 | 0.355 | 7.720
0-6 months education program in last year | 0.243 | 0.429 | 0.287 | 0.452 | 9.900
6-12 months education program in last year | 0.385 | 0.486 | 0.324 | 0.468 | 12.660
High school credential | 0.198 | 0.398 | 0.285 | 0.451 | 20.500
Lives in PMSA | 0.316 | 0.465 | 0.334 | 0.471 | 3.770
Lives in MSA | 0.440 | 0.496 | 0.480 | 0.500 | 7.910
Past employment and earnings history
Ever had job for two weeks or more | 0.809 | 0.393 | 0.779 | 0.415 | 7.490
Worked in year prior to random assignment | 0.664 | 0.472 | 0.628 | 0.483 | 7.430
Has job at random assignment | 0.212 | 0.409 | 0.203 | 0.402 | 2.240
Below 3 months employed in last year | 0.190 | 0.378 | 0.190 | 0.382 | 0.080
3-9 months employed in last year | 0.287 | 0.437 | 0.268 | 0.432 | 4.380
9-12 months employed in last year | 0.187 | 0.377 | 0.171 | 0.366 | 4.360
Yearly earnings less than $1,000 | 0.099 | 0.299 | 0.123 | 0.328 | 7.590
Yearly earnings $1,000 to $5,000 | 0.269 | 0.444 | 0.268 | 0.443 | 0.340
Yearly earnings $5,000 to $10,000 | 0.143 | 0.350 | 0.124 | 0.330 | 5.600
Yearly earnings above $10,000 | 0.079 | 0.269 | 0.050 | 0.219 | 11.530
Past welfare history
Family on welfare when growing up | 0.174 | 0.379 | 0.229 | 0.420 | 13.850
Received food stamps in last year | 0.366 | 0.482 | 0.534 | 0.499 | 34.290
Public or rent-subsidized housing | 0.183 | 0.384 | 0.222 | 0.413 | 9.790
Received AFDC in last year | 0.222 | 0.416 | 0.408 | 0.491 | 40.860
Drugs and crime
Used hard drugs in last year | 0.076 | 0.265 | 0.050 | 0.218 | 10.620
Smoked marijuana in last year | 0.277 | 0.448 | 0.200 | 0.400 | 18.250
Ever arrested dummy | 0.311 | 0.463 | 0.164 | 0.370 | 35.180
Observations | 6,104 | 4,491 |

Note: Time-varying control variables are measured at the time of random
assignment. Weights accounting for the sampling design and non-response of the
48-month interview are used ($wgt48b$). PMSA stand for Primary Metropolitan
Statistical Area. MSA stand for Metropolitan Statistical Area. AFDC stands for
Aid to Families with Dependent Children.

Table A.2: Tobit model to predict earnings.

| Males | Females
---|---|---
| Coef. | Std. Err. | Coef. | Std. Err.
| (1) | (2) | (3) | (4)
Socio-economic characteristics
Aged between 18-19 years | 17.8 | (11.9) | -5.96 | (12.9)
Aged between 20-24 years | 2.26 | (15.1) | -16.9 | (16.1)
White | 106*** | (11.4) | -5.54 | (14.5)
Hispanic | 78.4*** | (13.4) | 17.7 | (15.1)
Indian | 78.6*** | (18.1) | 3.84 | (19.7)
Lives with spouse or partner | -9.57 | (23.0) | -19.8 | (21.5)
Dummy for bad health | -12.7 | (14.4) | -11.8 | (14.8)
0-6 months education program in last year | 13.0 | (12.5) | 32.2** | (13.0)
6-12 months education program in last year | 11.6 | (11.8) | 15.4 | (13.4)
High school credential | 21.4 | (13.3) | 51.8*** | (13.4)
Lives in PMSA | 43.6*** | (13.1) | 42.4*** | (15.8)
Lives in MSA | 8.73 | (11.7) | 33.9** | (13.3)
Past employment and earnings history
Ever had job for two weeks or more | 16.1 | (15.4) | 45.5*** | (17.0)
Worked in year prior to random assignment | 65.8** | (25.5) | 10.0 | (29.5)
Has job at random assignment | 8.88 | (11.9) | 28.4* | (14.5)
3-9 months employed in last year | -7.12 | (16.4) | 19.6 | (18.0)
9-12 months employed in last year | 30.4 | (21.1) | 42.7 | (28.4)
Yearly earnings less than $1,000 | -21.5 | (25.1) | -8.27 | (29.0)
Yearly earnings $1,000 to $5,000 | -15.4 | (21.7) | 27.9 | (25.9)
Yearly earnings $5,000 to $10,000 | -1.96 | (23.2) | 22.3 | (29.1)
Yearly earnings above $10,000 | 37.0 | (29.7) | 82.8** | (35.6)
Past welfare history
Family on welfare when growing up | -3.59 | (13.1) | -30.9*** | (11.9)
Received food stamps in last year | -5.48 | (11.4) | -7.47 | (12.0)
Public or rent-subsidized housing | 0.079 | (13.1) | -16.8 | (11.9)
Received AFDC in last year | -16.6 | (12.4) | 3.42 | (11.9)
Drugs and crime
Used hard drugs in last year | -48.7*** | (18.6) | 20.1 | (29.1)
Smoked marijuana in last year | -11.8 | (10.6) | 3.98 | (12.1)
Ever arrested dummy | -19.4* | (10.4) | -7.24 | (12.9)
Observations | 2,620 | 1,603

Note: We predict the weekly earnings (in U.S. dollars) 48 months after
randomized assignment. *** indicates significance at the 1% level, **
indicates significance at the 5% level, and * indicates significance at the
10% level. Heteroskedastie robust standard errors are in parentheses.

##  B Estimation

###  B.1 Average effects

The ATEs are simply estimated using a univariate weighted ordinary least
squares (OLS) earnings regression on the treatment dummy. To estimate CATE, I
proceed in a similar manner but restrict the sample by gender. The TATEs are
computationally very intensive to estimate. Again, I follow the approach of
at06 and replace the expectations by their sample average. In particular,

$\hat{\delta}_{TATE}(g)=\displaystyle\frac{1}{\sum_{1=1}^{N}(1-D_{i})\cdot\omega_{i}}\sum_{1=1}^{N}(1-D_{i})\cdot\omega_{i}\cdot\left(\hat{Q}_{Y(1)|G}(\hat{F}_{Y(0)|G}(Y_{i}|g)|g)-Y_{i}\right).$

Finally, I estimate SATE by
$\hat{\delta}_{SATE}(g)=\hat{\delta}_{CATE}(g)-\hat{\delta}_{TATE}(g)$.

###  B.2 Kolmogorov–Smirnov test

Additionally, I report the rank invariant Kolmogorov–Smirnov test statistics
for all effects. The test statistics are

$T_{KS}=\sqrt{n}\cdot\operatornamewithlimits{sup\vphantom{p}}_{\tau}(|\hat{\delta}(\tau)|),$

where $\hat{\delta}(\tau)$ indicates the estimate of some quantile difference
$\delta(\tau)$. The null hypothesis is $\delta(\tau)=0$ for all $\tau$. Thus,
this is a test for significant effects at some quantile or, in other words,
for the inequality between some potential earning distributions. Further, I
report signed versions of the Kolmogorov–Smirnov statistics, which enable
testing for positive or negative first-order stochastic dominance. Positive
stochastic dominance is defined as $\delta(\tau)\geq 0$ for all $\tau$.
Accordingly, under (positive) stochastic dominance, $\delta(\tau)$ is never
negative regardless of the quantile at which the effect is measured. In
contrast, negative stochastic dominance is defined as $\delta(\tau)\leq 0$ for
all $\tau$. Accordingly, under negative stochastic dominance, $\delta(\tau)$
is never positive, regardless of the quantile at which the effect is
measured.242424In particular, I use the test statistics for positive
stochastic dominance
$T_{PSD}=\sqrt{n}\cdot\operatornamewithlimits{sup\vphantom{p}}_{\tau}(\hat{\delta}(\tau))$
and negative stochastic dominance
$T_{NSD}=\sqrt{n}\cdot\operatornamewithlimits{inf\vphantom{p}}_{\tau}(\hat{\delta}(\tau))$.
For all Kolmogorov–Smirnov-type test statistics, I estimate p-values using the
recentered bootstrapping approach proposed by chern05. This non-pivotal method
computes p-values by avoiding restrictive assumptions. chern05 show that
recentering can substantially improve the finite-sample power of the
Kolmogorov–Smirnov test relative to its uncentered counterpart.

##  C Alternative relative ranks

###  C.1 Relative rank is defined under non-treatment

####  C.1.1 Reference distribution is the potential outcome distribution under
treatment

Figure C.3: TQTEs of the Job Corps by gender on average weekly earnings (in
U.S. dollars) in year four after randomized assignment.

Note: The lines report the point estimates separately calculated for all
percentiles. Crosses on the lines indicate significant effects at the 10%
level. Hollow circles on the lines indicate significant effects at the 5%
level. Full diamonds on the lines indicate significant effects at the 1%
level. The reference quantiles are from the potential outcome distribution
under treatment, $Q_{Y(1)}(\tau)$. The relative rank is defined by
$\tau_{g}^{r}=F_{Y(0)|G}(Q_{Y(1)}(\tau)|g)$. I consider only the relative
ranks in the interval $[0.01,0.99]$ and exclude all ranks below
$\hat{F}_{Y(1)}(0)$ (for explanations, see Online Appendix B).

Figure C.4: Difference between Job Corps TQTEs for females and males.

Note: The lines report the point estimates calculated separately for all
percentiles. All point estimates are not statistically different from zero.
The reference quantiles are from the potential outcome distribution under
treatment, $Q_{Y(1)}(\tau)$. The relative rank is defined by
$\tau_{g}^{r}=F_{Y(0)|G}(Q_{Y(1)}(\tau)|g)$. I consider only the relative
ranks in the interval $[0.01,0.99]$ and exclude all ranks below
$\hat{F}_{Y(1)}(0)$ (for explanations, see Online Appendix B).

Figure C.5: SQTEs of the Job Corps by gender on average weekly earnings (in
U.S. dollars) in year four after randomized assignment.

Note: The lines report the point estimates separately calculated for all
percentiles. Crosses on the lines indicate significant effects at the 10%
level. Hollow circles on the lines indicate significant effects at the 5%
level. Full diamonds on the lines indicate significant effects at the 1%
level. The reference quantiles are from the potential outcome distribution
under treatment, $Q_{Y(1)}(\tau)$. The relative rank is defined by
$\tau_{g}^{r}=F_{Y(0)|G}(Q_{Y(1)}(\tau)|g)$. I consider only the relative
ranks in the interval $[0.01,0.99]$ and exclude all ranks below
$\hat{F}_{Y(1)}(0)$ (for explanations, see Online Appendix B).

Figure C.6: Difference between SQTEs of the Job Corps for females and males.

Note: The lines report the point estimates calculated separately for all
percentiles. Crosses on the lines indicate significant effects at the 10%
level. Hollow circles on the lines indicate significant effects at the 5%
level. Full diamonds on the lines indicate significant effects at the 1%
level. The reference quantiles are from the potential outcome distribution
under treatment, $Q_{Y(1)}(\tau)$. The relative rank is defined by
$\tau_{g}^{r}=F_{Y(0)|G}(Q_{Y(1)}(\tau)|g)$. I consider only the relative
ranks in the interval $[0.01,0.99]$ and exclude all ranks below
$\hat{F}_{Y(1)}(0)$ (for explanations, see Online Appendix B).

####  C.1.2 Reference distribution is the observed outcome distribution

Figure C.1: TQTEs of the Job Corps by gender on average weekly earnings (in
U.S. dollars) in year four after randomized assignment.

Note: The lines report the point estimates calculated separately for all
percentiles. Crosses on the lines indicate significant effects at the 10%
level. Hollow circles on the lines indicate significant effects at the 5%
level. Full diamonds on the lines indicate significant effects at the 1%
level. The reference quantiles are from the observed outcome distribution,
$Q_{Y}(\tau)$. The relative rank is defined by
$\tau_{g}^{r}=F_{Y(0)|G}(Q_{Y}(\tau)|g)$. I consider only the relative ranks
in the interval $[0.01,0.99]$ and exclude all ranks below $\hat{F}_{Y}(0)$
(for explanations, see Online Appendix B).

Figure C.2: Difference between Job Corps TQTEs for females and males.

Note: The lines report the point estimates calculated separately for all
percentiles. Crosses on the lines indicate significant effects at the 10%
level. The reference quantiles are from the observed outcome distribution,
$Q_{Y}(\tau)$. The relative rank is defined by
$\tau_{g}^{r}=F_{Y(0)|G}(Q_{Y}(\tau)|g)$. I consider only the relative ranks
in the interval $[0.01,0.99]$ and exclude all ranks below $\hat{F}_{Y}(0)$
(for explanations, see Online Appendix B).

Figure C.3: SQTEs of the Job Corps by gender on average weekly earnings (in
U.S. dollars) in year four after randomized assignment.

Note: The lines report the point estimates calculated separately for all
percentiles. Crosses on the lines indicate significant effects at the 10%
level. Hollow circles on the lines indicate significant effects at the 5%
level. Full diamonds on the lines indicate significant effects at the 1%
level. The reference quantiles are from the observed outcome distribution,
$Q_{Y}(\tau)$. The relative rank is defined by
$\tau_{g}^{r}=F_{Y(0)|G}(Q_{Y}(\tau)|g)$. I consider only the relative ranks
in the interval $[0.01,0.99]$ and exclude all ranks below $\hat{F}_{Y}(0)$
(for explanations, see Online Appendix B).

Figure C.4: Difference between SQTEs of the Job Corps for females and males.

Note: The lines report the point estimates calculated separately for all
percentiles. Crosses on the lines indicate significant effects at the 10%
level. Hollow circles on the lines indicate significant effects at the 5%
level. Full diamonds on the lines indicate significant effects at the 1%
level. The reference quantiles are from the observed outcome distribution,
$Q_{Y}(\tau)$. The relative rank is defined by
$\tau_{g}^{r}=F_{Y(0)|G}(Q_{Y}(\tau)|g)$. I consider only the relative ranks
in the interval $[0.01,0.99]$ and exclude all ranks below $\hat{F}_{Y}(0)$
(for explanations, see Online Appendix B).

####  C.1.3 Reference distribution is the potential outcome distribution of
males under non-treatment

Figure C.1: TQTEs of the Job Corps by gender on average weekly earnings (in
U.S. dollars) in year four after randomized assignment.

Note: The lines report the point estimates calculated separately for all
percentiles. Crosses on the lines indicate significant effects at the 10%
level. Hollow circles on the lines indicate significant effects at the 5%
level. Full diamonds on the lines indicate significant effects at the 1%
level. The reference quantiles are from the potential outcome distribution of
males under treatment, $Q_{Y(1)|G}(\tau|m)$. The relative rank is defined by
$\tau_{g}^{r}=F_{Y(0)|G}(Q_{Y(1)|G}(\tau|m)|g)$. I consider only the relative
ranks in the interval $[0.01,0.99]$ and exclude all ranks below
$\hat{F}_{Y(1)|G}(0|m)$ (for explanations, see Online Appendix B).

Figure C.2: Difference between Job Corps TQTEs for females and males.

Note: The lines report the point estimates calculated separately for all
percentiles. Crosses on the lines indicate significant effects at the 10%
level. The reference quantiles are from the potential outcome distribution of
males under treatment, $Q_{Y(1)|G}(\tau|m)$. The relative rank is defined by
$\tau_{g}^{r}=F_{Y(0)|G}(Q_{Y(1)|G}(\tau|m)|g)$. I consider only the relative
ranks in the interval $[0.01,0.99]$ and exclude all ranks below
$\hat{F}_{Y(1)|G}(0|m)$ (for explanations, see Online Appendix B).

Figure C.3: SQTEs of the Job Corps by gender on average weekly earnings (in
U.S. dollars) in year four after randomized assignment.

Note: The lines report the point estimates calculated separately for all
percentiles. Crosses on the lines indicate significant effects at the 10%
level. Hollow circles on the lines indicate significant effects at the 5%
level. Full diamonds on the lines indicate significant effects at the 1%
level. The reference quantiles are from the potential outcome distribution of
males under treatment, $Q_{Y(1)|G}(\tau|m)$. The relative rank is defined by
$\tau_{g}^{r}=F_{Y(0)|G}(Q_{Y(1)|G}(\tau|m)|g)$. I consider only the relative
ranks in the interval $[0.01,0.99]$ and exclude all ranks below
$\hat{F}_{Y(1)|G}(0|m)$ (for explanations, see Online Appendix B).

Figure C.4: Difference between SQTEs of the Job Corps for females and males.

Note: The lines report the point estimates calculated separately for all
percentiles. Crosses on the lines indicate significant effects at the 10%
level. Hollow circles on the lines indicate significant effects at the 5%
level. Full diamonds on the lines indicate significant effects at the 1%
level. The reference quantiles are from the potential outcome distribution of
males under treatment, $Q_{Y(1)|G}(\tau|m)$. The relative rank is defined by
$\tau_{g}^{r}=F_{Y(0)|G}(Q_{Y(1)|G}(\tau|m)|g)$. I consider only the relative
ranks in the interval $[0.01,0.99]$ and exclude all ranks below
$\hat{F}_{Y(1)|G}(0|m)$ (for explanations, see Online Appendix B).

####  C.1.4 Reference distribution is the potential outcome distribution of
females under non-treatment

Figure C.1: TQTEs of the Job Corps by gender on average weekly earnings (in
U.S. dollars) in year four after randomized assignment.

Note: The lines report the point estimates calculated separately for all
percentiles. Crosses on the lines indicate significant effects at the 10%
level. Hollow circles on the lines indicate significant effects at the 5%
level. Full diamonds on the lines indicate significant effects at the 1%
level. The reference quantiles are from the potential outcome distribution of
females under treatment, $Q_{Y(1)|G}(\tau|f)$. The relative rank is defined by
$\tau_{g}^{r}=F_{Y(0)|G}(Q_{Y(1)|G}(\tau|f)|g)$. I consider only the relative
ranks in the interval $[0.01,0.99]$ and exclude all ranks below
$\hat{F}_{Y(1)|G}(0|f)$ (for explanations, see Online Appendix B).

Figure C.2: Difference between Job Corps TQTEs for females and males.

Note: The lines report the point estimates calculated separately for all
percentiles. Crosses on the lines indicate significant effects at the 10%
level. The reference quantiles are from the potential outcome distribution of
females under treatment, $Q_{Y(1)|G}(\tau|f)$. The relative rank is defined by
$\tau_{g}^{r}=F_{Y(0)|G}(Q_{Y(1)|G}(\tau|f)|g)$. I consider only the relative
ranks in the interval $[0.01,0.99]$ and exclude all ranks below
$\hat{F}_{Y(1)|G}(0|f)$ (for explanations, see Online Appendix B).

Figure C.3: SQTEs of the Job Corps by gender on average weekly earnings (in
U.S. dollars) in year four after randomized assignment.

Note: The lines report the point estimates calculated separately for all
percentiles. Crosses on the lines indicate significant effects at the 10%
level. Hollow circles on the lines indicate significant effects at the 5%
level. Full diamonds on the lines indicate significant effects at the 1%
level. The reference quantiles are from the potential outcome distribution of
females under treatment, $Q_{Y(1)|G}(\tau|f)$. The relative rank is defined by
$\tau_{g}^{r}=F_{Y(0)|G}(Q_{Y(1)|G}(\tau|f)|g)$. I consider only the relative
ranks in the interval $[0.01,0.99]$ and exclude all ranks below
$\hat{F}_{Y(1)|G}(0|f)$ (for explanations, see Online Appendix B).

Figure C.4: Difference between the SQTEs of the Job Corps for females and
males.

Note: The lines report the point estimates calculated separately for all
percentiles. Crosses on the lines indicate significant effects at the 10%
level. Hollow circles on the lines indicate significant effects at the 5%
level. Full diamonds on the lines indicate significant effects at the 1%
level. The reference quantiles are from the potential outcome distribution of
females under treatment, $Q_{Y(1)|G}(\tau|f)$. The relative rank is defined by
$\tau_{g}^{r}=F_{Y(0)|G}(Q_{Y(1)|G}(\tau|f)|g)$. I consider only the relative
ranks in the interval $[0.01,0.99]$ and exclude all ranks below
$\hat{F}_{Y(1)|G}(0|f)$ (for explanations, see Online Appendix B).

###  C.2 Relative rank is defined under treatment

####  C.2.1 Reference distribution is the potential outcome distribution under
non-treatment

Figure C.1: TQTEs of the Job Corps by gender on average weekly earnings (in
U.S. dollars) in year four after randomized assignment.

Note: The lines report the point estimates calculated separately for all
percentiles. Crosses on the lines indicate significant effects at the 10%
level. Hollow circles on the lines indicate significant effects at the 5%
level. Full diamonds on the lines indicate significant effects at the 1%
level. The reference quantiles are from the potential outcome distribution
under non-treatment, $Q_{Y(0)}(\tau)$. The relative rank is defined by
$\tau_{g}^{r}=F_{Y(1)|G}(Q_{Y(0)}(\tau)|g)$. The rank transformation uses the
conditional potential outcome distribution under treatment. I consider only
the relative ranks in the interval $[0.01,0.99]$ and exclude all ranks below
$\hat{F}_{Y(1)}(0)$ (for explanations, see Online Appendix B).

Figure C.2: Difference between Job Corps TQTEs for females and males.

Note: The lines report the point estimates calculated separately for all
percentiles. All point estimates are not statistically different from zero.
The reference quantiles are from the potential outcome distribution under non-
treatment, $Q_{Y(0)}(\tau)$. The relative rank is defined by
$\tau_{g}^{r}=F_{Y(1)|G}(Q_{Y(0)}(\tau)|g)$. The rank transformation uses the
conditional potential outcome distribution under treatment. I consider only
the relative ranks in the interval $[0.01,0.99]$ and exclude all ranks below
$\hat{F}_{Y(1)}(0)$ (for explanations, see Online Appendix B).

Figure C.3: SQTEs of the Job Corps by gender on average weekly earnings (in
U.S. dollars) in year four after randomized assignment.

Note: The lines report the point estimates calculated separately for all
percentiles. Crosses on the lines indicate significant effects at the 10%
level. Hollow circles on the lines indicate significant effects at the 5%
level. Full diamonds on the lines indicate significant effects at the 1%
level. The reference quantiles are from the potential outcome distribution
under non-treatment, $Q_{Y(0)}(\tau)$. The relative rank is defined by
$\tau_{g}^{r}=F_{Y(1)|G}(Q_{Y(0)}(\tau)|g)$. The rank transformation uses the
conditional potential outcome distribution under treatment. I consider only
the relative ranks in the interval $[0.01,0.99]$ and exclude all ranks below
$\hat{F}_{Y(1)}(0)$ (for explanations, see Online Appendix B).

Figure C.4: Difference between SQTEs of the Job Corps for females and males.

Note: The lines report the point estimates calculated separately for all
percentiles. Crosses on the lines indicate significant effects at the 10%
level. Hollow circles on the lines indicate significant effects at the 5%
level. Full diamonds on the lines indicate significant effects at the 1%
level. The reference quantiles are from the potential outcome distribution
under non-treatment, $Q_{Y(0)}(\tau)$. The relative rank is defined by
$\tau_{g}^{r}=F_{Y(1)|G}(Q_{Y(0)}(\tau)|g)$. The rank transformation uses the
conditional potential outcome distribution under treatment. I consider only
the relative ranks in the interval $[0.01,0.99]$ and exclude all ranks below
$\hat{F}_{Y(1)}(0)$ (for explanations, see Online Appendix B).

####  C.2.2 Reference distribution is the potential outcome distribution under
treatment

Figure C.1: TQTEs of the Job Corps by gender on average weekly earnings (in
U.S. dollars) in year four after randomized assignment.

Note: The lines report the point estimates calculated separately for all
percentiles. Crosses on the lines indicate significant effects at the 10%
level. Hollow circles on the lines indicate significant effects at the 5%
level. Full diamonds on the lines indicate significant effects at the 1%
level. The reference quantiles are from the potential outcome distribution
under treatment, $Q_{Y(1)}(\tau)$. The relative rank is defined by
$\tau_{g}^{r}=F_{Y(1)|G}(Q_{Y(1)}(\tau)|g)$. The rank transformation uses the
conditional potential outcome distribution under treatment. I consider only
the relative ranks in the interval $[0.01,0.99]$ and exclude all ranks below
$\hat{F}_{Y(1)}(0)$ (for explanations, see Online Appendix B).

Figure C.2: Difference between Job Corps TQTEs for females and males.

Note: The lines report the point estimates calculated separately for all
percentiles. Crosses on the lines indicate significant effects at the 10%
level. The reference quantiles are from the potential outcome distribution
under treatment, $Q_{Y(1)}(\tau)$. The relative rank is defined by
$\tau_{g}^{r}=F_{Y(1)|G}(Q_{Y(1)}(\tau)|g)$. The rank transformation uses the
conditional potential outcome distribution under treatment. I consider only
the relative ranks in the interval $[0.01,0.99]$ and exclude all ranks below
$\hat{F}_{Y(1)}(0)$ (for explanations, see Online Appendix B).

Figure C.3: SQTEs of the Job Corps by gender on average weekly earnings (in
U.S. dollars) in year four after randomized assignment.

Note: The lines report the point estimates calculated separately for all
percentiles. Crosses on the lines indicate significant effects at the 10%
level. Hollow circles on the lines indicate significant effects at the 5%
level. Full diamonds on the lines indicate significant effects at the 1%
level. The reference quantiles are from the potential outcome distribution
under treatment, $Q_{Y(1)}(\tau)$. The relative rank is defined by
$\tau_{g}^{r}=F_{Y(1)|G}(Q_{Y(1)}(\tau)|g)$. The rank transformation uses the
conditional potential outcome distribution under treatment. I consider only
the relative ranks in the interval $[0.01,0.99]$ and exclude all ranks below
$\hat{F}_{Y(1)}(0)$ (for explanations, see Online Appendix B).

Figure C.4: Difference between SQTEs of the Job Corps for females and males.

Note: The lines report the point estimates calculated separately for all
percentiles. Crosses on the lines indicate significant effects at the 10%
level. Hollow circles on the lines indicate significant effects at the 5%
level. Full diamonds on the lines indicate significant effects at the 1%
level. The reference quantiles are from the potential outcome distribution
under treatment, $Q_{Y(1)}(\tau)$. The relative rank is defined by
$\tau_{g}^{r}=F_{Y(1)|G}(Q_{Y(1)}(\tau)|g)$. The rank transformation uses the
conditional potential outcome distribution under treatment. I consider only
the relative ranks in the interval $[0.01,0.99]$ and exclude all ranks below
$\hat{F}_{Y(1)}(0)$ (for explanations, see Online Appendix B).

####  C.2.3 Reference distribution is the observed outcome distribution

Figure C.1: TQTEs of the Job Corps by gender on average weekly earnings (in
U.S. dollars) in year four after randomized assignment.

Note: The lines report the point estimates calculated separately for all
percentiles. Crosses on the lines indicate significant effects at the 10%
level. Hollow circles on the lines indicate significant effects at the 5%
level. Full diamonds on the lines indicate significant effects at the 1%
level. The reference quantiles are from the observed outcome distribution,
$Q_{Y}(\tau)$. The relative rank is defined by
$\tau_{g}^{r}=F_{Y(1)|G}(Q_{Y}(\tau)|g)$. The rank transformation uses the
conditional potential outcome distribution under treatment. I consider only
the relative ranks in the interval $[0.01,0.99]$ and exclude all ranks below
$\hat{F}_{Y}(0)$ (for explanations, see Online Appendix B).

Figure C.2: Difference between Job Corps TQTEs for females and males.

Note: The lines report the point estimates calculated separately for all
percentiles. All point estimates are not statistically different from zero.
The reference quantiles are from the observed outcome distribution,
$Q_{Y}(\tau)$. The relative rank is defined by
$\tau_{g}^{r}=F_{Y(1)|G}(Q_{Y}(\tau)|g)$. The rank transformation uses the
conditional potential outcome distribution under treatment. I consider only
the relative ranks in the interval $[0.01,0.99]$ and exclude all ranks below
$\hat{F}_{Y}(0)$ (for explanations, see Online Appendix B).

Figure C.3: SQTEs of the Job Corps by gender on average weekly earnings (in
U.S. dollars) in year four after randomized assignment.

Note: The lines report the point estimates calculated separately for all
percentiles. Crosses on the lines indicate significant effects at the 10%
level. Hollow circles on the lines indicate significant effects at the 5%
level. Full diamonds on the lines indicate significant effects at the 1%
level. The reference quantiles are from the observed outcome distribution,
$Q_{Y}(\tau)$. The relative rank is defined by
$\tau_{g}^{r}=F_{Y(1)|G}(Q_{Y}(\tau)|g)$. The rank transformation uses the
conditional potential outcome distribution under treatment. I consider only
the relative ranks in the interval $[0.01,0.99]$ and exclude all ranks below
$\hat{F}_{Y}(0)$ (for explanations, see Online Appendix B).

Figure C.4: Difference between SQTEs of the Job Corps for females and males.

Note: The lines report the point estimates calculated separately for all
percentiles. Crosses on the lines indicate significant effects at the 10%
level. Hollow circles on the lines indicate significant effects at the 5%
level. Full diamonds on the lines indicate significant effects at the 1%
level. The reference quantiles are from the observed outcome distribution,
$Q_{Y}(\tau)$. The relative rank is defined by
$\tau_{g}^{r}=F_{Y(1)|G}(Q_{Y}(\tau)|g)$. The rank transformation uses the
conditional potential outcome distribution under treatment. I consider only
the relative ranks in the interval $[0.01,0.99]$ and exclude all ranks below
$\hat{F}_{Y}(0)$ (for explanations, see Online Appendix B).

####  C.2.4 Reference distribution is the potential outcome distribution of
males under non-treatment

Figure C.1: TQTEs of the Job Corps by gender on average weekly earnings (in
U.S. dollars) in year four after randomized assignment.

Note: The lines report the point estimates calculated separately for all
percentiles. Crosses on the lines indicate significant effects at the 10%
level. Hollow circles on the lines indicate significant effects at the 5%
level. Full diamonds on the lines indicate significant effects at the 1%
level. The reference quantiles are from the potential outcome distribution of
males under treatment, $Q_{Y(0)|G}(\tau|m)$. The relative rank is defined by
$\tau_{g}^{r}=F_{Y(1)|G}(Q_{Y(0)|G}(\tau|m)|g)$. The rank transformation uses
the conditional potential outcome distribution under treatment. I consider
only the relative ranks in the interval $[0.01,0.99]$ and exclude all ranks
below $\hat{F}_{Y(0)|G}(0|m)$ (for explanations, see Online Appendix B).

Figure C.2: Difference between Job Corps TQTEs for females and males.

Note: The lines report the point estimates calculated separately for all
percentiles. Crosses on the lines indicate significant effects at the 10%
level. The reference quantiles are from the potential outcome distribution of
males under treatment, $Q_{Y(0)|G}(\tau|m)$. The relative rank is defined by
$\tau_{g}^{r}=F_{Y(1)|G}(Q_{Y(0)|G}(\tau|m)|g)$. The rank transformation uses
the conditional potential outcome distribution under treatment. I consider
only the relative ranks in the interval $[0.01,0.99]$ and exclude all ranks
below $\hat{F}_{Y(0)|G}(0|m)$ (for explanations, see Online Appendix B).

Figure C.3: SQTEs of the Job Corps by gender on average weekly earnings (in
U.S. dollars) in year four after randomized assignment.

Note: The lines report the point estimates calculated separately for all
percentiles. Crosses on the lines indicate significant effects at the 10%
level. Hollow circles on the lines indicate significant effects at the 5%
level. Full diamonds on the lines indicate significant effects at the 1%
level. The reference quantiles are from the potential outcome distribution of
males under treatment, $Q_{Y(0)|G}(\tau|m)$. The relative rank is defined by
$\tau_{g}^{r}=F_{Y(1)|G}(Q_{Y(0)|G}(\tau|m)|g)$. The rank transformation uses
the conditional potential outcome distribution under treatment. I consider
only the relative ranks in the interval $[0.01,0.99]$ and exclude all ranks
below $\hat{F}_{Y(0)|G}(0|m)$ (for explanations, see Online Appendix B).

Figure C.4: Difference between SQTEs of the Job Corps for females and males.

Note: The lines report the point estimates calculated separately for all
percentiles. Crosses on the lines indicate significant effects at the 10%
level. Hollow circles on the lines indicate significant effects at the 5%
level. Full diamonds on the lines indicate significant effects at the 1%
level. The reference quantiles are from the potential outcome distribution of
males under treatment, $Q_{Y(0)|G}(\tau|m)$. The relative rank is defined by
$\tau_{g}^{r}=F_{Y(1)|G}(Q_{Y(0)|G}(\tau|m)|g)$. The rank transformation uses
the conditional potential outcome distribution under treatment. I consider
only the relative ranks in the interval $[0.01,0.99]$ and exclude all ranks
below $\hat{F}_{Y(0)|G}(0|m)$ (for explanations, see Online Appendix B).

####  C.2.5 Reference distribution is the potential outcome distribution of
females under non-treatment

Figure C.1: TQTEs of the Job Corps by gender on average weekly earnings (in
U.S. dollars) in year four after randomized assignment.

Note: The lines report the point estimates calculated separately for all
percentiles. Crosses on the lines indicate significant effects at the 10%
level. Hollow circles on the lines indicate significant effects at the 5%
level. Full diamonds on the lines indicate significant effects at the 1%
level. The reference quantiles are from the potential outcome distribution of
females under treatment, $Q_{Y(0)|G}(\tau|f)$. The relative rank is defined by
$\tau_{g}^{r}=F_{Y(1)|G}(Q_{Y(0)|G}(\tau|f)|g)$. The rank transformation uses
the conditional potential outcome distribution under treatment. I consider
only the relative ranks in the interval $[0.01,0.99]$ and exclude all ranks
below $\hat{F}_{Y(0)|G}(0|f)$ (for explanations, see Online Appendix B).

Figure C.2: Difference between Job Corps TQTEs for females and males.

Note: The lines report the point estimates calculated separately for all
percentiles. All point estimates are not statistically different from zero.
The reference quantiles are from the potential outcome distribution of females
under treatment, $Q_{Y(0)|G}(\tau|f)$. The relative rank is defined by
$\tau_{g}^{r}=F_{Y(1)|G}(Q_{Y(0)|G}(\tau|f)|g)$. The rank transformation uses
the conditional potential outcome distribution under treatment. I consider
only the relative ranks in the interval $[0.01,0.99]$ and exclude all ranks
below $\hat{F}_{Y(0)|G}(0|f)$ (for explanations, see Online Appendix B).

Figure C.3: SQTEs of the Job Corps by gender on average weekly earnings (in
U.S. dollars) in year four after randomized assignment.

Note: The lines report the point estimates calculated separately for all
percentiles. Crosses on the lines indicate significant effects at the 10%
level. Hollow circles on the lines indicate significant effects at the 5%
level. Full diamonds on the lines indicate significant effects at the 1%
level. The reference quantiles are from the potential outcome distribution of
females under treatment, $Q_{Y(0)|G}(\tau|f)$. The relative rank is defined by
$\tau_{g}^{r}=F_{Y(1)|G}(Q_{Y(0)|G}(\tau|f)|g)$. The rank transformation uses
the conditional potential outcome distribution under treatment. I consider
only the relative ranks in the interval $[0.01,0.99]$ and exclude all ranks
below $\hat{F}_{Y(0)|G}(0|f)$ (for explanations, see Online Appendix B).

Figure C.4: Difference between SQTEs of the Job Corps for females and males.

Note: The lines report the point estimates calculated separately for all
percentiles. Crosses on the lines indicate significant effects at the 10%
level. Hollow circles on the lines indicate significant effects at the 5%
level. Full diamonds on the lines indicate significant effects at the 1%
level. The reference quantiles are from the potential outcome distribution of
females under treatment, $Q_{Y(0)|G}(\tau|f)$. The relative rank is defined by
$\tau_{g}^{r}=F_{Y(1)|G}(Q_{Y(0)|G}(\tau|f)|g)$. The rank transformation uses
the conditional potential outcome distribution under treatment. I consider
only the relative ranks in the interval $[0.01,0.99]$ and exclude all ranks
below $\hat{F}_{Y(0)|G}(0|f)$ (for explanations, see Online Appendix B).

##  D Distributional heterogeneity by gender and parenthood

Table D.1 and Figures D.1-D.5 in Online Appendix D report CQTE by gender and
parenthood. Mainly parents and childless men profit from a Job Corps offer.
Offering participation in the Job Corps to childless women has the smallest
earnings impact of all four groups. The effect heterogeneity by gender is not
strongly significant for parents, but significant for childless women and men.
Considering heterogeneity between all four groups, the effect heterogeneity by
gender and parenthood is large, but the effects are only significant at some
quantiles (see Figure D.5).

Table D.2 and Figures D.6-D.10 in Online Appendix D report TQTE by gender and
parenthood. The TQTE show large effect heterogeneity by gender of parents, but
the differences are not significant (see Figure D.7). The effect heterogeneity
is significant between childless women and men (see Figure D.9). Their is a
tendency that TQTE can explain heterogeneity between the two groups, because
the Kolmogorov–Smirnov test is weakly significant (see Table D.2 and Figure
D.10). The results for SQTE are ambiguous (see Table D.3 and Figures D.11-D.15
in Online Appendix D). We find significant SQTE for all groups, but the signs
of the effects are mixed. At some quantile the SQTE have a large magnitude.
Accordingly, the TQTE and SQTE contribute both to the effect heterogeneity in
the CQTE by gender and parenthood.

###  D.1 CQTE by gender and parenthood

Table D.1: CQTE of the Job Corps program by gender and parenthood on average
weekly earnings (in U.S. dollars) in year four after randomized assignment.

Quantile | With children | Without children | Difference between
---|---|---|---
| Females | Males | Difference | Females | Males | Difference | (3) and (6)
| (1) | (2) | (3) | (4) | (5) | (6) | (7)
0.2 | -3.41 | 27.8 | -31.21 | 5.56 | 7.29 | -1.74 | -29.48
| 8.16 | 22.09 | 23.3 | 3.64 | 8.57 | 9.21 | 25.28
0.3 | 5.71 | 39.49 | -33.78 | 20,5*** | -2.09 | 22,59* | -56,38*
| 10.91 | 28.09 | 30.17 | 7.19 | 10.02 | 12.36 | 32.59
0.4 | 11.24 | 58,09* | -46.85 | 23,95** | 2.49 | 21.46 | -68,31*
| 11.27 | 30.45 | 32.71 | 10.89 | 9.79 | 14.87 | 36.04
0.5 | 14.97 | 47.02 | -32.05 | 5.85 | 23,28*** | -17.43 | -14.63
| 14.77 | 22.88 | 27.55 | 11.8 | 7.86 | 14.19 | 31.19
0.6 | 25,49** | 32.4 | -6.91 | 5.66 | 17,48** | -11.82 | 4.9
| 9.97 | 19.44 | 21.95 | 7.11 | 7.67 | 10.6 | 24.7
0.7 | 28,57*** | 28.53 | 0.04 | 13.18 | 23,43*** | -10.26 | 10.29
| 9.17 | 18.38 | 20.3 | 9.2 | 4.3 | 10.18 | 22.95
0.8 | 28,01* | 16.88 | 11.13 | 5.81 | 23,21*** | -17.41 | 28.54
| 15.66 | 26.84 | 31.08 | 10.19 | 8.75 | 13.39 | 34.09
0.9 | 60,82*** | 5.41 | 55.41 | 7.73 | 13.04 | -5.31 | 60.73
| 18.87 | 35.96 | 40 | 15.47 | 12.87 | 20.01 | 45.06
KS statistic | 12,318 | 8,261 | 13,598 | 2,466 | 16,041*** | 14,295* | 25,861
| 0.175 | 0.955 | 0.837 | 0.899 | 0.009 | 0.059 | 0.534
PSD statistic | 12,318*** | 7,995 | 13,598 | 2,466 | 16,041*** | 2,513 | 25,861
| 0.008 | 0.552 | 0.522 | 0.584 | 0.009 | 0.713 | 0.338
NSD statistic | -351 | -8,261 | -6,595 | -814 | -265 | -14,295** | -8,921
| 0.97 | 0.621 | 0.674 | 0.856 | 0.966 | 0.025 | 0.587

Note: *** indicates significance at the 1% level, ** indicates significance at
the 5% level, and * indicates significance at the 10% level. Bootstrapped
standard errors are in parentheses and are obtained from 1,999 bootstrap
replications. ”KS statistic” indicates the Kolmogorov–Smirnov statistic. ”PSD
statistic” indicates the Kolmogorov–Smirnov-type test statistic for positive
stochastic dominance. ”NSD statistic” indicates the Kolmogorov–Smirnov-type
test statistic for negative stochastic dominance. Bootstrapped p-values (1,999
replications) are in squared brackets.

Figure D.1: CQTE of the Job Corps program with children by gender on average
weekly earnings (in U.S. dollars) in year four after randomized assignment.

Note: The lines report the point estimates calculated separately for all
percentiles. Crosses on the lines indicate significant effects at the 10%
level. Hollow circles on the lines indicate significant effects at the 5%
level. Full diamonds on the lines indicate significant effects at the 1%
level.

Figure D.2: Difference between the Job Corps CQTEs for females and males with
children.

Note: The outcome is average weekly earnings (in U.S. dollars) in year four
after randomized assignment. The lines report the point estimates calculated
separately for all percentiles. Crosses on the lines indicate significant
effects at the 10% level. Hollow circles on the lines indicate significant
effects at the 5% level. Full diamonds on the lines indicate significant
effects at the 1% level.

Figure D.3: CQTE of the Job Corps program without children by gender on
average weekly earnings (in U.S. dollars) in year four after randomized
assignment.

Note: The lines report the point estimates calculated separately for all
percentiles. Crosses on the lines indicate significant effects at the 10%
level. Hollow circles on the lines indicate significant effects at the 5%
level. Full diamonds on the lines indicate significant effects at the 1%
level.

Figure D.4: Difference between the Job Corps CQTEs for females and males
without children.

Note: The outcome is average weekly earnings (in U.S. dollars) in year four
after randomized assignment. The lines report the point estimates calculated
separately for all percentiles. Crosses on the lines indicate significant
effects at the 10% level. Hollow circles on the lines indicate significant
effects at the 5% level. Full diamonds on the lines indicate significant
effects at the 1% level.

Figure D.5: Difference between the Job Corps CQTEs for females and males, with
and without children.

Note: The outcome is average weekly earnings (in U.S. dollars) in year four
after randomized assignment. The lines report the point estimates calculated
separately for all percentiles. Crosses on the lines indicate significant
effects at the 10% level. Hollow circles on the lines indicate significant
effects at the 5% level. Full diamonds on the lines indicate significant
effects at the 1% level.

###  D.2 TQTE by gender and parenthood

Table D.2: TQTEs of the Job Corps by gender and parenthood on average weekly
earnings (in U.S. dollars) in year four after randomized assignment.

Quantile | With children | Without children | Difference between
---|---|---|---
| Females | Males | Difference | Females | Males | Difference | (3) and (6)
| (1) | (2) | (3) | (4) | (5) | (6) | (7)
0.3 | 6.93 | 35.81 | -28.88 | 19.29 | -2.04 | 21.33 | -50.21
| 13.54 | 30.88 | 34.02 | 10,74* | 8.22 | 13.67 | 36.69
0.4 | 18.82 | 77,98** | -59.17 | 14.01 | -2.07 | 16.08 | -75.25
| 15.25 | 32.93 | 36.7 | 9.44 | 9.63 | 13.48 | 39.46
0.5 | 27,16** | 49,6** | -22.44 | 2.95 | 19.04 | -16.09 | -6.35
| 12.89 | 19.03 | 23.42 | 7.32 | 8,89** | 12.06 | 26.7
0.6 | 37,34*** | 42,13** | -4.79 | 12.39 | 15,02*** | -2.63 | -2.16
| 11.87 | 20.26 | 23.39 | 10.1 | 5.92 | 11.03 | 25.96
0.7 | 34,97** | 36,52** | -1.55 | 7.06 | 24,43*** | -17.37 | 15.82
| 15.67 | 14.12 | 20.9 | 8.99 | 8.24 | 12.77 | 24.59
0.8 | 53,62** | 17.61 | 36.01 | 9.26 | 25,17*** | -15.91 | 51.92
| 21.96 | 18.82 | 28.73 | 12.08 | 8.24 | 14.72 | 32.44
0.9 | 57,41* | 1.35 | 56.06 | 4.54 | 15.76 | -11.22 | 67.28
| 30.69 | 29.02 | 42.63 | 21.52 | 14.42 | 24.31 | 49.71
KS statistic | 9160 | 8027 | 9693 | 2412 | 12488** | 6416 | 13605
| 0.16 | 0.779 | 0.334 | 0.884 | 0.013 | 0.302 | 0.185
PSD statistic | 9160 | 8027 | 9693 | 2412 | 12488** | 2458 | 13605*
| 0.125 | 0.384 | 0.172 | 0.474 | 0.013 | 0.599 | 0.094
NSD statistic | -84 | -4374 | -6090 | -1578 | -303 | -6416 | -7745
| 0.967 | 0.676 | 0.47 | 0.721 | 0.973 | 0.126 | 0.374

Note: *** indicates significance at the 1% level, ** indicates significance at
the 5% level, and * indicates significance at the 10% level. Bootstrapped
standard errors are in parentheses and are obtained from 1,999 bootstrap
replications. ”KS statistic” indicates the Kolmogorov–Smirnov statistic. ”PSD
statistic” indicates the Kolmogorov–Smirnov-type test statistic for positive
stochastic dominance. ”NSD statistic” indicates the Kolmogorov–Smirnov-type
test statistic for negative stochastic dominance. Bootstrapped p-values (1,999
replications) are in squared brackets.

Figure D.6: TQTEs of the Job Corps with children by gender on average weekly
earnings (in U.S. dollars) in year four after randomized assignment.

Note: The lines report the point estimates separately calculated for all
percentiles. Crosses on the lines indicate significant effects at the 10%
level. Hollow circles on the lines indicate significant effects at the 5%
level. Full diamonds on the lines indicate significant effects at the 1%
level. I consider only the relative ranks in the interval $[0.01,0.99]$ and
exclude all ranks below $\hat{F}_{Y(0)}(0)$ (for explanations, see Online
Appendix B).

Figure D.7: Difference between Job Corps TQTEs for females and males with
children.

Note: The outcome is average weekly earnings (in U.S. dollars) in year four
after randomized assignment. The lines report the point estimates separately
calculated for all percentiles. All point estimates are not statistically
different from zero. I consider the relative ranks only in the interval
$[0.01,0.99]$ and exclude all ranks below $\hat{F}_{Y(0)}(0)$ (for
explanations, see Online Appendix B).

Figure D.8: TQTEs of the Job Corps without children by gender on average
weekly earnings (in U.S. dollars) in year four after randomized assignment.

Note: The lines report the point estimates separately calculated for all
percentiles. Crosses on the lines indicate significant effects at the 10%
level. Hollow circles on the lines indicate significant effects at the 5%
level. Full diamonds on the lines indicate significant effects at the 1%
level. I consider only the relative ranks in the interval $[0.01,0.99]$ and
exclude all ranks below $\hat{F}_{Y(0)}(0)$ (for explanations, see Online
Appendix B).