Heterogeneous Earnings Effects of the Job Corps by Gender Earnings: A Translated Quantile Approach
HHeterogeneous earnings effects of the Job Corps bygender: A translated quantile approach
Anthony Strittmatter ∗ University of St. Gallen
August 26, 2019
Abstract
Several studies of the Job Corps tend to find more positive earnings effects for malesthan for females. This effect heterogeneity favouring males contrasts with the results ofthe majority of other training programmes’ evaluations. Applying the translated quantileapproach of Bitler, Hoynes, and Domina (2014), I investigate a potential mechanism behindthe surprising findings for the Job Corps. My results provide suggestive evidence that theeffect of heterogeneity by gender operates through existing gender earnings inequalityrather than Job Corps trainability differences.JEL-Classification: J38, C21Keywords: Gender Inequality, Decomposition, Quantile Regression, Programme Evaluation ∗ Previous versions of this manuscript were circulated under different titles. The manuscript was presentedat the SSES 2012 in Zurich, at the NOeG 2012 in Vienna, at the EALE 2013 in Torino, at the ESEM 2013 inGoteborg, at the IAAE 2014 in London, at the Humboldt University Berlin 2015, and at the ZEW 2017. I thankthe participants for their useful comments. In particular, I am grateful for helpful suggestions made by SimoneBalestra, Xuan Chen, Annabelle Dörr, Alfonso Flores-Lagunes, Bernd Fitzenberger, Michael Lechner, JanNimczik, Stefan Sperlich, and Andreas Steinmayr. I thank Ozkan Eren and Serkan Ozbeklik, who kindly sharedtheir data and programmes with me. The usual disclaimer applies. E-mail: [email protected]. a r X i v : . [ ec on . E M ] A ug Introduction
In this study, I investigate the heterogeneous earnings effects of the Job Corps by gender. Inparticular, I show that gender differences in labour market opportunities contribute to theoverall effect heterogeneity. To this end, I apply the translated quantile decomposition ofBitler, Hoynes, and Domina (2014). Furthermore, I extend this approach to incorporate averagetranslated 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 andjob search assistance, for an average duration of eight to nine months. Blanco, Flores, andFlores-Lagunes (2013), Chen and Flores (2015), and Lee (2009) show that the Job Corps haspositive wage effects for both genders. This effect is expected to increase earnings throughhigher hourly wages and greater labour supply. The female labour supply is expected tobe more elastic to wage changes than is the male labour supply (see, e.g., the discussion inBargain, Orsini, and Peichl, 2013, Killingsworth and Heckman, 1986). However, several studiesobserve a tendency that the Job Corps increases the gender earnings inequality. In a large-scale experimental evaluation, Schochet, Burghardt, and McConnell (2008) show evidence ofhigher average earnings gain from the Job Corps for males than for females. Moreover, Erenand 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 marketprogrammes (ALMPs). Meta studies performed by Bergemann and van den Berg (2008) andCard, Kluve, and Weber (2018) report evidence of higher ALMP returns for females than formales. In this study, I highlight one potential mechanism behind the unexpected findings forthe Job Corps.Frumento, Mealli, Pacini, and Rubin (2012) investigate the effect heterogeneity for varioussocio-economic groups using a principal stratification approach with strong functional formassumptions. 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 Chen, Flores, and Flores-Lagunes (2017) report positive employment effects of the Job Corps four years afterassignment. Expected earnings can be viewed as an aggregate measureof labour market opportunities. Quantile regressions can identify (distributional) heterogeneityby expected earnings. Eren and Ozbeklik (2014) report larger earnings differences for theJob Corps at higher quantiles than at lower quantiles. Such a pattern can be expected if theJob Corps is more effective for groups with better labour market opportunities, that is, thosewith high earnings even without training. Higher opportunity costs for participants with betterearnings opportunities can explain this positive relationship between earnings opportunities andJob Corps returns. It is well documented that a larger share of females is located in the lowerpart than in the upper part of the earnings distribution. Thus, unexpected effect heterogeneitycan arise in favour of males from structural gender earnings inequality rather than from genderdifferences in Job Corps trainability. The latter could arise from programme content that is, forexample, more aligned to the needs of one gender. In this study, I decompose those potentialchannels using the translated quantile approach of Bitler, Hoynes, and Domina (2014).For an example of the relevance of the translated quantile approach, assume the needto determine assignment criteria for offering participation in the Job Corps that do not in-crease gender inequality. If structural gender earnings inequality leads to heterogeneity, anon-discriminatory assignment rule offers participation to males and females with balancedlabour market opportunities. If Job Corps trainability differs by gender, then other dimensionsof the Job Corps programmes need to be better aligned with the specific training demands ofmales and females. For example, vocational training offered during the programme could meetthe needs of males better than the needs of females.My findings, consistent with the existing literature, provide suggestive evidence for largerquantile treatment effects for males than for females. Structural gender earnings inequality pos-sibly accounts for 82% of the average effect heterogeneity by gender. Trainability differencesby gender appear to play only a minor role. Even though the effects are statistically insignif-icant, these findings suggest that the offer to participate in the Job Corps does not disfavourfemales with earnings opportunities that are equal to those of males. However, it seems that the This is another peculiarity of the Job Corps because for many other ALMPs, the returns do not increase withlabour market opportunities (see, e.g., Card, Kluve, and Weber, 2018, Rinne, Schneider, and Uhlendorff, 2011).
The Job Corps was established in the United States in 1964 under the Economic OpportunityAct. The aim of the Job Corps is to provide counselling and to develop individualized pro-grammes that enhance participants’ job opportunities. In particular, completing a vocationaldegree and earning General Educational Development (GED) credentials are two major goalsof the Job Corps. Job Corps programmes follow a holistic approach. They can include physical4nd mental healthcare counselling, various vocational and social education schemes, and jobsearch assistance. Courses have theoretical and practical content, and training can be partly onthe job. Participants are trained in one of approximately 125 Job Corps centres and typicallylive on Job Corps campuses during the programme. Candidates must pass a screening andrecruitment process administered by certain admission agencies. Eligible participants are dis-advantaged youth (aged 16–24 years) in need of additional education and training. Candidatesmust have low incomes to meet the eligibility criteria. Approximately 60,000 eligible youthenrol in the Job Corps each year. In 2008, total programme expenditures exceeded 1.58 billionU.S. dollars (Job Corps Annual Report, 2008). In 2008, expenditures per participant wereapproximately 26,000 U.S. dollars, or approximately ten times the cost of a typical programmeunder the Workforce Investment Act (Eren and Ozbeklik, 2014).Numerous studies investigate the effectiveness of Job Corps programs in improving partic-ipants’ post-programme earnings. Early studies using data from the 1970s observe that malesbenefited 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 negativeearnings impacts for black female participants and positive effects for black male participants.Between 1994 and 1996, Mathematica Policy Research performed a randomized National JobCorps Study (NJCS). That study had an experimental design and hence became the bench-mark for evaluating the Job Corps. Using survey data collected from NJCS participants in1998, 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 notstatistically significant. However, Schochet, Burghardt, and McConnell (2008) report a signif-icantly higher yearly earnings gain of 540 U.S. dollars for male than for female participantswhen using the administrative data of NJCS participants collected from the 1998 SummaryEarnings Records (SER). Flores, Flores-Lagunes, Gonzalez, and Neuman (2012) explore themarginal returns of additional exposure to academic and vocational training and instruction by Of the total expenditures, training costs account for 40%, support services (e.g., meals, lodging, and medicalcare) account for 33%, and administration and infrastructure investment costs account for 26%.
As previously mentioned, Mathematica Policy Research performed a randomized experimentwith the Job Corps. Of 80,833 eligible individuals who first applied for participation in theprogramme between November 1994 and February 1996, 15,386 were randomly selected for theexperiment’s research sample. From this group, 9,409 were randomly selected to receive anoffer to participate in the Job Corps. Of these, 73% joined the Job Corps programme andactually started to participate after an average duration of 1.4 months. The remaining 5,977individuals were assigned to the control group. Control group members were not eligible for theJob Corps programs for three years following randomization (approximately 1% participatedanyway). Nevertheless, most control group members received some sort of alternative trainingin the form of GED preparation (27%), high school (23%), or vocational, technical, or tradeschool (21%) (Burghardt et al., 2001). The intensity of training was higher among treatmentgroup members than among those in the control group. During the four years following the6andomization, 47% of the treatment group members and 27% of those in the control groupobtained GED credentials. During the same period, 38% of the treatment group membersand 15% of those in the control group obtained a vocational degree. Approximately 5–8% ofeligible individuals in both groups received a high school diploma (Burghardt et al., 2001). Toimprove the accuracy of the research sample, some subgroups were oversampled (see descriptionin Schochet, 2001). To account for this, I use sampling weights throughout the analyses. Interviews were conducted with members of the research sample 12, 30, and 48 months afterrandomization. This study considers publicly released interviews of the sample of individualsconducted 48 months after randomization, eliminating observations with missing information(3,951 observations are dropped). The share of attrition is 6.5% among males and 6.1% amongfemales. Lee (2009) proposes an indirect test for potential attrition bias in the NJCS data. Hisanalysis reveals no strong evidence of attrition bias (see Remark 2 in Lee, 2009). Throughoutthe study, I use the non-response adjusted sampling weights ( wgt48b ) provided in the NJCSdata to account for sample attrition. The final sample includes 10,595 observations, of which6,372 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 afterrandom assignment, which is more than two years after 92% of the participants completedthe program. I investigate the effects of the randomized offer to participate in the Job Corpsprogramme. 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 tojoin the Job Corps programme. The award of such offers is under the control of the decisionmakers; however, enrolment and actual participation are not under their control. An alternativeapproach is to investigate the local average treatment effects of actual participation. Thisapproach identifies the effects for those individuals who only enrol in Job Corps if they receivethe offer to participate instead of considering all eligible individuals (the latter group is calledcompliers). Chen, Flores, and Flores-Lagunes (2017) address this limitation with an interesting Eren and Ozbeklik (2014) condition on key features of the sample design in a regression framework instead ofusing sampling weights. Unreported robustness checks find that the results are not sensitive to various ways ofconstructing sampling weights. Share of Share of Share of Share ofShare of Share of female male female malefemale male compliers compliers compliers complierscompliers compliers with with without withoutchildren children children children(1) (2) (3) (4) ( 5) (6)Full sample 69% 75% 64% 67% 71% 76% Y (0) < st quartile 69% 75% 64% 62% 71% 76% st quartile ≤ Y (0) < nd quartile 69% 76% 64% 67% 71% 77% nd quartile ≤ Y (0) < rd quartile 69% 74% 64% 66% 71% 76% Y (0) ≥ 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 potentialoutcome Y (0) denotes earnings under non-treatment. 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 documents the share of compliers by gender and by different quartiles of the earningsdistribution. Females comply 6 percentage points less frequently with the offer to participate inthe 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 effectheterogeneity by gender, but the effects of actual participation are also more beneficial for malesthan 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 cannotexplain why participation in Job Corps tends to increase gender inequality of earnings. Theshare 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 reports the means and standard deviations of the observed variables. In year fourafter a randomized assignment, individuals with an offer to join the Job Corps earn on average15 U.S. dollars per week more than do individuals without an offer. Furthermore, I reportthe descriptive statistics for socioeconomic characteristics, employment, earnings, and welfarehistories, as well as drug use and arrests. For all of these observed control variables, I observelittle difference between individuals with and without an offer to join the Job Corps. The8able 2: Means and standard deviations conditional on receiving (or not) an offer to join JobCorps (JC). Offer to join JC Not invited to JC StandardizedMean 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 7.740Ever 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 1.200Aged 16-17 years 0.414 0.493 0.417 0.493 0.590Aged 18-19 years 0.317 0.465 0.317 0.465 0.070Aged 20-24 years 0.269 0.443 0.266 0.442 0.580White 0.277 0.447 0.266 0.442 2.470Black 0.479 0.500 0.478 0.500 0.120Hispanic 0.171 0.377 0.180 0.384 2.420Native American 0.074 0.261 0.076 0.265 0.900Lives with a spouse or a partner 0.061 0.239 0.063 0.243 0.980Dummy for bad health 0.127 0.333 0.137 0.344 3.0900-6 month education programme in the preced-ing year 0.268 0.442 0.254 0.435 2.9906-12 month education programme in the pre-ceding year 0.352 0.477 0.368 0.482 3.360High school credential 0.228 0.420 0.238 0.426 2.380Lives in PMSA 0.319 0.466 0.327 0.469 1.610Lives 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 2.750Worked during the year prior to random assign-ment 0.653 0.476 0.645 0.478 1.750Had a job at the time of random assignment 0.211 0.408 0.206 0.404 1.300Employed less than 3 months during the pre-ceding year 0.190 0.380 0.189 0.379 0.270Employed 3-9 months during the preceding year 0.282 0.437 0.276 0.433 1.510Employed 9-12 months during the precedingyear 0.181 0.373 0.180 0.372 0.230Yearly earnings less than $1,000 0.107 0.309 0.111 0.314 1.470Yearly earnings $1,000 to $5,000 0.273 0.446 0.264 0.441 2.060Yearly earnings $5,000 to $10,000 0.138 0.345 0.133 0.339 1.530Yearly 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 1.530Received food stamps during the preceding year 0.435 0.496 0.435 0.496 0.090Public or rent-subsidized housing 0.204 0.400 0.193 0.392 2.940Received 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 1.970Smoked 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 0.700No. of Observations 6,372 4,223Note: Time-varying control variables are measured at the time of random assignment. Weights ( wgt b )accounting for the sampling design and non-response of the 48-month interview are used. JC denotes for JobCorps. PMSA stands for Primary Metropolitan Statistical Area. MSA denotes Metropolitan Statistical Area.AFDC stands for Aid to Families with Dependent Children. This confirms that the offer to join the JobCorps was randomized appropriately.Table A.1 in Online Appendix A documents the descriptive statistics of observed variablesby gender without conditioning on an offer to join the Job Corps. On average, males earn 66U.S. dollars per week more than do females four years after the randomized offer. Relativeto males, females in the sample were less likely to be white, more likely to have high schoolcredentials, less likely have used drugs during the previous year, and arrested less often. Femalesreceived food stamps and aid to families with dependent children (AFDC) more often than didmales. The families of females in the sample were on welfare during their childhood more oftenthan were the families of males. These differences in socioeconomic characteristics may explaineffect heterogeneity by gender but cannot explain why the findings for Job Corps differ fromthose of the previous literature (e.g., Card, Kluve, and Weber, 2018). The earnings are a function of a Job Corps offer D , gender G , and an error term U thatincorporates labour market opportunities. The structural earnings function is ϕ ( G, U ) if thereis an offer to join the Job Corps and ϕ ( G, U ) if there is no offer. The error term possiblyinteracts non-separably with gender. The quantile earnings function is Q ϕ d ( G,U ) ( τ ) for d ∈{ , } . For an insight, assume that ϕ d ( · ) is strictly increasing in its second argument. Then,the conditional quantile function Q ϕ d ( G,U ) | G ( τ | g ) equals ϕ d ( g, Q U | G ( τ | g )) , where Q U | G ( τ | g ) isthe quantile of the error term distribution for those with gender g ∈ { m, f } . The conditional The standardized difference of variable X between samples A and B is defined as SD = | ¯ X A − ¯ X B | (cid:113) ( V ar ( X A ) + V ar ( X B )) · , where ¯ X A denotes the mean of sample A , and ¯ X B denotes the mean of sample B . Rosenbaum and Rubin (1983)consider an absolute standardized difference exceeding 20 to be “large.” Furthermore, Huber (2015) points at causal pitfalls in controlling for post-birth covariates in gender decompo-sitions. Q A ( τ ) represents the τ th quantile of A . g = m ) and females ( g = f ) are, respectively, δ CQT E ( τ, m ) = ϕ ( m, Q U | G ( τ | m )) − ϕ ( m, Q U | G ( τ | m )) and δ CQT E ( τ, f ) = ϕ ( f, Q U | G ( τ | f )) − ϕ ( f, Q U | G ( τ | f )) . Thus, even if the earnings functions are homogeneous by gender (i.e., ϕ d ( m, U ) = ϕ d ( f, U ) ), theCQTEs can be heterogeneous if Q U | G ( τ | m ) (cid:54) = Q U | G ( τ | f ) (this is noted in Abadie, Angrist, andImbens, 2002 and Bitler, Hoynes, and Domina, 2014, among others). The direct effect operatesthrough heterogeneity caused by the first argument of the earnings functions. The structuraleffect operates through heterogeneity caused by the second argument. The direct and structuralchannels cannot be distinguished simply by comparing δ CQT E ( τ, m ) and δ CQT E ( τ, f ) .Bitler, Hoynes, and Domina (2014) use unique reference quantiles for their translated quan-tile treatment effect (TQTE) approach that I denote by Q U r ( τ ) . They use the same referencequantile to transform CQTE of different groups: δ T QT E ( τ, m ) = ϕ ( m, Q U r ( τ )) − ϕ ( m, Q U r ( τ )) and δ T QT E ( τ, f ) = ϕ ( f, Q U r ( τ )) − ϕ ( f, Q U r ( τ )) . Heterogeneity arises between δ T QT E ( τ, m ) and δ T QT E ( τ, f ) solely from the first argument ofthe earnings function. Accordingly, this approach enables us to isolate effect heterogeneity bygender, but the size of the effect will depend on the reference quantile. I propose using thereference quantiles from the potential earnings distribution under non-treatment. I show thatTQTE equals CQTE when no structural earnings inequality exists. Furthermore, I show thatTQTE equals the (unconditional) quantile treatment effect (QTE) when structural inequalityis solely responsible for the effect heterogeneity by gender. Powell (2016) proposes a generalized quantile regression (GQR) that also uses a transformation of conditionalquantiles. The main purpose of GQR is to estimate unconditional quantiles under unrestrictive assumptions. δ CAT E ( m ) = (cid:90) δ CQT E ( τ, m ) dτ and δ CAT E ( f ) = (cid:90) δ CQT E ( τ, f ) dτ. This definition implies that inequalities in the earnings structure can be carried through toaverage effects. Therefore, I extend the approach in Bitler, Hoynes, and Domina (2014) toincorporate average effects.
In the programme evaluation literature, it is common to use the potential outcomes instead ofthe earnings functions. The potential earnings under assignment to and possible participation inthe Job Corps are Y i (1) = ϕ ( 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) = ϕ ( G i , U i ) . For eachindividual, only the realized earnings, Y i = Y i (1) · D i + Y i (0) · (1 − D i ) , are observed, implying that either Y i (1) or Y i (0) is counterfactual. The individual-specificcausal effects are δ i = Y i (1) − Y i (0) = ϕ ( G i , U i ) − ϕ ( G i , U i ) . In the remainder of the paper, I use the potential outcome notation. We cannot identifyindividual-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 becauseof their treatment status (see discussion in Firpo, 2007). Nevertheless, quantile differences can be identified without assuming rank preservation. Thepotential quantile Q Y ( d ) ( τ ) is the minimum value of Y i ( d ) such that at least the share τ of the The observational rule holds only under the stable unit treatment value assumption (e.g., Rubin, 2005). Chernozhukov and Hansen (2005) use the term rank invariance to refer to this assumption. The authors alsointroduce rank similarity, which is a weaker assumption than rank preservation because it allows for randomdeviations in ranks. Quantile treatment effects (QTEs) aredefined as δ QT E ( τ ) = Q Y (1) ( τ ) − Q Y (0) ( τ ) , the difference between the potential quantiles. QTEs identify the horizontal differences inpotential earnings distributions at specific ranks.Furthermore, the potential conditional quantile Q Y ( d ) | G ( τ | g ) is the minimum value of Y i ( d ) such that at least the share τ of the conditional potential earnings distribution lies below thisvalue. The CQTEs are defined as δ CQT E ( τ, g ) = Q Y (1) | G ( τ | g ) − Q Y (0) | G ( τ | g ) , the difference between the conditional potential quantiles.Finally, the average treatment effect (ATE) is the expected value of δ i , δ AT E = (cid:90) δ QT E ( τ ) dτ = E [ Y i (1) − Y i (0)] , and the CATE is δ CAT E ( g ) = (cid:90) δ CQT E ( τ, g ) dτ = E [ Y i (1) − Y i (0) | G i = g ] . Both average effects can be identified without assuming rank preservation. F Y ( d ) ( y ) = P r ( Y i ( d ) ≤ y ) = P r ( Y i ≤ y | D i = d ) is identified from observable data because of the randomtreatment assignment. It denotes the cumulative distribution function of Y i ( d ) . The τ th quantile of Y i ( d ) is Q Y ( d ) ( τ ) = inf { y : F Y ( d ) ( y ) ≥ τ } , for the real τ ∈ (0 , . F Y ( d ) | G ( y | g ) = P r ( Y i ( d ) ≤ y | G i = g ) = P r ( Y i ≤ y | D i = d, G i = g ) is identified from observable data because ofthe random treatment assignment. It denotes the potential earnings distribution of Y i ( d ) conditional on gender g for g ∈ { m, f } . The τ th quantile of Y i ( d ) conditional on gender is Q Y ( d ) | G ( τ | g ) = inf { y : F Y ( d ) | G ( y | g ) ≥ τ } . .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 aretransformed to these reference quantiles to place each CQTE on the same absolute scale. Therequired quantile transformations can be conceptualized through a relative rank (see Morris,Bernhardt, and Handcock, 1994). Although the choice of reference distribution is obviouslycrucial, generally, there is no best choice. I propose using the potential earnings distributionunder non-treatment as a reference distribution and define the relative rank as τ rg = F Y (0) | G ( Q Y (0) ( τ ) | g ) . This relative rank can be interpreted as the proportion of the conditional population with poten-tial earnings below the τ 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 alsobe meaningful. Currently, Bitler, Hoynes, and Domina (2014) is the only other study thatuses the translated quantile approach. They use the observed outcome distribution undernon-treatment as reference distribution in their instrumental variable approach.The translated quantile treatment effect (TQTE) is defined as δ T QT E ( τ, g ) = Q Y (1) | G ( τ rg | g ) − Q Y (0) | G ( τ rg | g ) , (1)implying that TQTE measures the horizontal distance between two conditional potential out-come distributions at τ rg . The only difference between CQTE and TQTE is that the locationhas shifted from τ to τ rg . TQTEs establish a mapping between the conditional and referencedistributions.If F Y (0) | G ( y | g ) is strictly increasing in the interval (0 , , such that Q Y (0) | G ( F Y (0) | G ( y | g ) | g ) = , then TQTE can be rearranged as δ T QT E ( τ, g ) = Q Y (1) | G ( τ rg | g ) − Q Y (0) ( τ ) . (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 δ SQT E ( τ, g ) = δ CQT E ( τ, g ) − δ T QT E ( τ, g ) . This describes the difference between CQTE and TQTE.For an explicit example, assume that the median potential outcome under non-treatment is300 U.S. dollars, i.e., Q Y (0) (0 .
5) = 300 . However, females earning 300 U.S. dollars would alreadybe at the 75% rank in the conditional potential earnings distribution of females under non-treatment, i.e., F Y (0) | G (300 | f ) = 0 . . Then, the relative rank for females would be τ rf = 0 . .The median TQTE would measure the difference between the conditional potential quantilesunder treatment and non-treatment of females at rank τ rf = 0 . . In contrast, the median CQTEwould measure the difference between the conditional potential quantiles under treatment andnon-treatment of females at rank τ = 0 . . The median SQTE would measure the differencebetween the conditional potential quantiles under treatment of females at ranks τ = 0 . and τ rf = 0 . . Accordingly, TQTE and CQTE would be similar, and SQTE would be zero if therelative 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 specialcases. First, assume that the structural inequality between males and females is zero. Thisimplies that F Y (0) | G ( y | g ) = F Y (0) ( y ) for all y , and Q Y (0) | G ( τ | g ) = Q Y (0) ( τ ) for all τ . Further,assume that Y i (0) is continuously distributed such that F Y (0) | G ( Q Y (0) | G ( τ | g ) | g ) = τ . Now, wecan show that δ T QT E ( τ, g ) = δ CQT E ( τ, g ) and δ SQT E ( τ, g ) = 0 because τ rg = τ . Thus, CQTEs For 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 . (i.e., the outcome is continuous). If F Y (0) | G (200 | f ) is strictly increasing, then Q Y (0) | G (0 . | f ) = 200 is an equality. Otherwise, Q Y (0) | G (0 . | f ) ≤ is not a strictinequality. Both results hold also when the outcome is not continuous, i.e., if F Y (0) | G (200 | f ) ≤ . . The 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 ( τ | g ) | g ) | g ) = Q Y (0) | G ( τ | g ) (see Lemma A.1 in Athey and Imbens, 2006). Further- δ T QT E ( τ, f ) − δ T QT E ( τ, m ) = δ CQT E ( τ, f ) − δ CQT E ( τ, m ) and δ SQT E ( τ, f ) − δ SQT E ( τ, m ) = 0 .Second, assume that the entire effect heterogeneity by gender can be explained by structuralearnings differences. This implies that the transformed quantiles are equal for females andmales, Q Y (1) | G ( τ rf | f ) = Q Y (1) | G ( τ rm | m ) , (3)because conditional potential quantiles would not be heterogeneous by gender after rank ad-justment. If Y i ( d ) is continuously distributed such that F Y ( d ) | G ( Q Y ( d ) | G ( τ | g ) | g ) = τ , equation(3) can be rearranged as τ rf = F Y (1) | G ( Q Y (1) | G ( τ rm | m ) | f ) . (4)The law of iterative expectations for a distribution implies that F Y (1) ( y ) = P r ( G i = f ) F Y (1) | G ( y | f )+ P r ( G i = m ) F Y (1) | G ( y | m ) . Thus, P r ( G i = f ) · τ rf = F Y (1) ( Q Y (1) | G ( τ rm | m )) − P r ( G i = m ) · F Y (1) | G ( Q Y (1) | G ( τ rm | m ) | m ) . Further rearrangements using the abovementioned continuity assumption lead to
P r ( G i = f ) · τ rf + P r ( G i = m ) · τ rm = F Y (1) ( Q Y (1) | G ( τ rm | m )) . The left side of this equation is exactly the marginal distribution F Y (0) ( y ) = P r ( G i = f ) F Y (0) | G ( y | f )+ P r ( G i = m ) F Y (0) | G ( y | m ) evaluated at Q Y (0) ( y ) . This leads to the equality τ = F Y (1) ( Q Y (1) | G ( τ rm | m )) under the above continuity assumption. If F Y (1) ( y ) is strictly increasing in the interval (0 , so that Q Y (1) ( F Y (1) ( y )) = y , this result implies that Q Y (1) ( τ ) = Q Y (1) | G ( τ rg | g ) more, the condition Q Y (1) | G ( F Y (0) | G ( Q Y (0) | G ( τ | g ) | g ) | g ) = Q Y (1) | G ( τ | g ) will hold if F Y (0) | G ( y | g ) is at least assmooth 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 ( τ | g ) | g ) ≤ F Y (1) | G ( Q Y (1) | G ( τ | g ) | g ) for all τ . However, the assumption of continuity is moreintuitive and appears reasonable in many applications. When this finding is substituted into equation (2), the results are δ T QT E ( τ, g ) = δ QT E ( τ ) and δ T QT E ( τ, f ) − δ T QT E ( τ, m ) = 0 . Furthermore, δ SQT E ( τ, g ) = δ CQT E ( τ, g ) − δ QT E ( τ ) , implying that the entire inter-gender CQTE difference is attributedto the structural effect δ SQT E ( τ, f ) − δ SQT E ( τ, m ) = δ CQT E ( τ, f ) − δ CQT E ( τ, 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 fullyexplained by structural earnings inequality. This is a meaningful interpretation for TQTEbecause QTE represents the unconditional quantile effects.Finally, the translated conditional average treatment effect (TATE) can be shown to be δ T AT E ( g ) = (cid:90) δ T QT E ( τ, g ) dτ = 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 δ SAT E ( g ) = (cid:90) δ SQT E ( τ, g ) dτ = δ CAT E ( g ) − δ T AT E ( g ) . These parameters enable the average decomposition to account for differences in outcome struc-tures. 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 SATEequals zero. If the difference between the CATE for males and females can be fully explained bystructural earnings inequality, TATE equals ATE, and SATE is the difference between CATEand ATE. This quantile-quantile stability condition is strongly related to the rank stability condition F Y (1) | G ( Q Y (1) ( τ ) | g ) = F Y (0) | G ( Q Y (0) ( τ ) | g ) , which is used in Bitler, Gelbach, and Hoynes (2008) and Frandsen and Lefgren (2018) as afalsification test for rank preservation. Essentially, the researchers’ findings imply that the assumption of rankpreservation must be rejected if the quantile-quantile stability condition does not hold. TQTEs implicitly testthis condition. Although the results of Section 5 cannot reject this condition, it is possible that variables otherthan gender are associated with rank reorganization. .4 Estimation For an extensive study on estimating counterfactual distributions under various identificationstrategies 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 bytreatment status, which identifies the potential earnings quantiles because of the randomizedresearch design. The most challenging estimation steps are the quantile transformations. Thefirst 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 quan-tiles and ranks of the empirical distribution functions. The average effects are estimated byreplacing the expected values with the transformed sample averages that incorporate quantiletransformation.In particular, I use the quantile regression estimator argmin ˆ β τ, , ˆ β τ, N (cid:88) i =1 ω i · ρ τ ( Y i − ˆ β τ, − ˆ β τ, D i ) , where ρ τ ( a ) = a ( τ − { a ≤ } ) is the check function, and ω i represents the sampling andnon-response weights ( wgt b ) provided in the NJCS data. This estimator minimizes theweighted absolute deviations. The hats indicate the estimated parameters. Parameters are ˆ β τ, = ˆ Q Y (0) ( τ ) and ˆ β τ, = ˆ δ QT E ( τ ) .For the CQTE estimation, I use the model argmin ˆ α τ,g, , ˆ α τ,g, N (cid:88) i =1 { G i = g } · ω i · ρ τ ( Y i − ˆ α τ,g, − ˆ α τ,g, D i ) , (5)where {·} is the indicator function. Under the randomized research design, parameter ˆ α τ,g, =ˆ δ CQT E ( τ, g ) . Subsequently, I estimate ˆ Q Y (1 | G ) ( τ | g ) by ˆ Q Y (1 | G ) ( τ | g ) = ˆ α τ,g, + ˆ α τ,g, .The conditional cumulative distribution functions under non-treatment are estimated using18he empirical distribution functions ˆ F Y (0) | G ( y | g ) = 1 (cid:80) Ni =1 { D i = 0 , G i = g } · ω i N (cid:88) i =1 { Y i ≤ y, D i = 0 , G i = g } · ω i . Following Athey and Imbens (2006), the relative ranks are estimated using the plug-in approach ˆ τ rg = ˆ F Y (0) | G ( ˆ Q Y (0) ( τ ) | g ) . Now, I can obtain TQTE by replacing the rank τ with the estimatedrelative rank ˆ τ rg in (5), argmin ˆ γ τ,g, , ˆ γ τ,g, N (cid:88) i =1 { G i = g } · ω i · ρ ˆ τ rg ( Y i − ˆ γ τ,g, − ˆ γ τ,g, D i ) . Parameter ˆ γ τ,g, = ˆ δ T QT E ( τ, g ) . The SQTEs are estimated by ˆ δ SQT E ( τ, g ) = ˆ δ CQT E ( τ, g ) − ˆ δ T QT E ( τ, g ) . I consider only ˆ τ rg ∈ [0 . , . to avoid estimating extreme quantiles. Further-more, I exclude all ranks below ˆ F Y (0) (0) because the continuity assumption is violated at themass point with zero earnings. This excludes quantiles below the 21st percentile.Athey and Imbens (2006) show that the resulting estimates are √ n pointwise consistent andasymptotically normal. This could The standard deviations of all parameters are estimatedusing a nonparametric bootstrap procedure (sampling individual observations with replace-ment). Chaisemartin and D’Haultfeuille (2017) show the validity of the bootstrap approachfor this estimation. Melly and Santangelo (2015) extend the quantile transformation approachto incorporate exogenous control variables, but I do not need to include additional controlsbecause of the randomized research design. I discuss the estimation of average effects as wellas the computation of the Kolmogorov–Smirnov test statistic in Online Appendix B. The inference is pointwise and not uniformly valid. Accordingly, the empirical results could be affected by themultiple testing problem. Empirical results
Figure 1 shows the QTE of the Job Corps on average weekly earnings four years after therandomized assignment for all percentiles. Additionally, column 1 of Table 3 documents thedeciles of the QTE, including standard errors. The empirical results suggest that quantile dif-ferences increase with rank. The QTEs below the 2nd decile do not differ from zero because ofparticipants who are unemployed with no earnings. Between the 2nd and 5th deciles, the earn-ings gain is approximately 10 U.S. dollars. The earnings gain further increases to approximately20 U.S. dollars between the 5th and 9th deciles. Beyond the 9th decile, the quantile earningsdifferences reach values exceeding 100 U.S. dollars. The Kolmogorov–Smirnov test results atthe bottom of Table 3 support the findings that the Job Corps has a significant positive effecton earnings distribution.The patterns of CQTE for each gender are somewhat different and are reported in Figure2 and columns 2 and 3 of Table 3 (the scale of the y-axis differs between Figures 1 and 2). Formales, the CQTEs are close to zero until the 4th decile. CQTEs jump to a positive impacton earnings of approximately 25 U.S. dollars above the 4th decile. Beyond the 9th decile, thequantile earnings differences exceed 150 U.S. dollars. For females, the CQTEs are zero untilthe 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 consistentwith the findings of Eren and Ozbeklik (2014). The Kolmogorov–Smirnov test results in Table 3suggest that the Job Corps programme has significant positive effects on the potential earningsdistribution 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 femalesand 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 negativedifferences 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 Figure A.1 in Online Appendix A shows the potential earnings distributions.
Note: The lines report the point estimates calculated separately for all percentiles. Crosses on the lines indicatesignificant effects at 10% level. Hollow circles on the lines indicate significant effects at 5% level. Full diamondson the lines indicate significant effects at 1% level. females and males, which are significant at 10% level. The test of negative stochastic dominancesuggests 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 arelarger for males than for females. Accordingly, the Job Corps offers tend to increase genderearnings inequality at some quantiles.
Figure 4 shows the potential earnings distributions by gender. Females earn less than males atall quantiles. It is possible that the differences between the CQTEs for females and males canbe explained by structural differences between females’ and males’ earnings distributions.Figure 5 shows the transformed relative ranks on the ordinate and the untransformed rankson the abscissa. The relative ranks would be on the ◦ line in the absence of structuralearnings inequality. The average rank difference between females and males is 12.1 percentage21igure 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 indicatesignificant effects at 10% level. Hollow circles on the lines indicate significant effects at 5% level. Full diamondson 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 indicatesignificant effects at 10% level. Hollow circles on the lines indicate significant effects at 5% level. Full diamondson the lines indicate significant effects at 1% level.
Quantile QTE CQTE Difference betweenFemales 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 at10% 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-typetest statistic for negative stochastic dominance. Bootstrapped p-values (obtained using 1,999 replications) arein square brackets. points (the minimum is 2.5, and the maximum is 18.4 percentage points). The relative rankof females is always lower than the ◦ line. The relative rank of males is always higher thanthe ◦ line. For example, males (females) at the 40th percentile of the conditional potentialearnings 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. Thisimplies that TQTE shifts the CQTE for males to the right and that for females to the left.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 thepotential earnings distribution of all eligible Job Corps candidates under non-treatment. This23igure 4: Potential earnings distributions by gender. Note: The treatment is an offer to join the Job Corps program. The outcome is average weekly earnings (inU.S. dollars) four years after a randomized assignment. The figure is truncated by 600 U.S. dollars in earningsper week.
Figure 5: Rank transformation.
Note: I consider the relative ranks only in the interval [0 . , . and exclude all ranks below ˆ F Y (0) (0) (forexplanation, see Online Appendix B). Note: The lines represent point estimates calculated separately for all percentiles. Crosses on the lines indicatesignificant effects at 10% level. Hollow circles on the lines indicate significant effects at 5% level. Full diamondson the lines indicate significant effects at 1% level. I consider only the relative ranks in the interval [0 . , . and exclude all ranks below ˆ F Y (0) (0) (for explanation, see Online Appendix B). distribution is documented in Figure A.1 in Online Appendix A. I do not consider the partsof the potential earnings distribution with zero earnings for quantile transformation becausethe continuity assumptions—described in Section 4.3—are violated at the mass point with zeroearnings. This excludes all ranks lower than the 21st percentile. Furthermore, I exclude therelative 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 quantileearnings differences remain at approximately 25 U.S. dollars. The large difference between theTQTE and CQTE for males at the 99th percentile decreases by approximately 30% (from 156to 112 U.S. dollars). The CQTE and TQTE for females are overall quite similar. Below themedian, TQTE values are approximately 15 U.S. dollars. The increase to 25 U.S. dollars occursearlier for TQTE than for CQTE. The Kolmogorov–Smirnov-type test results at the bottomof Table 4 show that the Job Corps influences the potential earnings distribution of males, but25able 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 betweenFemales 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 at10% 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-typetest statistic for negative stochastic dominance. Bootstrapped p-values (obtained from 1,999 replications) arein square brackets. not that of females. These findings are consistent with the Kolmogorov–Smirnov-type testsapplied to CQTE.Figure 7 and column 3 of Table 4 show the quantile differences between the TQTEs forfemales and males. The differences oscillate around zero. The highly significant negative differ-ences at the 56th and 57th percentiles, which are documented for CQTEs, decline for TQTEsby 45% (from approximately –22 to –12 U.S. dollars). For TQTEs, I do not observe statisticallysignificant 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 TQTErelative to that of CQTE. Furthermore, the bottom rows of Table 4 present the Kolmogorov–26igure 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 notstatistically different from zero. I consider the relative ranks only in the interval [0 . , . and exclude allranks below ˆ F Y (0) (0) (for explanation, see Online Appendix B). Smirnov-type statistics. I observe no evidence of difference between the TQTEs of females andmales. 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 highlyheterogeneous by gender.Finally, Figure 8 reports the SQTEs by gender, and Figure 9 reports the heterogeneitybetween SQTEs by gender. SQTE is the difference between CQTE and TQTE. Figure 8reports highly significant SQTEs. For males, CQTEs are larger than TQTEs between the 4thand 5th deciles. For females, the positive and negative differences are mixed. Overall, largedifferences are observed between CQTEs and TQTEs in Figure 8. The differences betweenSQTEs for males and females are significantly different from zero at some quantiles. Figure9 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,27igure 8: SQTEs of the Job Corps by gender on average weekly earnings (in U.S. dollars) inyear four after a randomized assignment.
Note: The lines represent the point estimates calculated separately for all percentiles. Crosses on the linesindicate significant effects at 10% level. Hollow circles on the lines indicate significant effects at 5% level. Fulldiamonds on the lines indicate significant effects at 1% level. I consider the relative ranks only in the interval [0 . , . and exclude all ranks below ˆ F Y (0) (0) (for an explanation, see Online Appendix B). the Kolmogorov–Smirnov-type statistics at the bottom of Table 4 do not indicate significanteffects.In summary, the quantile earnings differences increase with rank. This could favour malesbecause they typically have higher earnings distribution ranks than do females. Accordingly,the Job Corps programme tends to increase the existing inequality in structural earnings. Afteraccounting for expected earnings opportunities, I observe no strong evidence that the Job Corpsis more aligned with the training needs of males than those of females. Table 5 shows that individuals awarded offers to participate in the Job Corps experience anaverage earnings gain of 15 U.S. dollars, or 8%. Females with no award earn 63 U.S. dollarsor 29% less than males with no award of an offer. In the following discussion, I call this theaverage gender earnings gap. The offer to participate in the Job Corps increases the earnings28igure 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. Thelines represent point estimates calculated separately for all percentiles. Crosses on the lines indicate significanteffects at 10% level. Hollow circles on the lines indicate significant effects at 5% level. Full diamonds on thelines indicate significant effects at 1% level. I consider the relative ranks only in the interval [0 . , . andexclude all ranks below ˆ F Y (0) (0) (for an explanation, see Online Appendix B). of females by 12 U.S. dollars and the earnings of males by 18 U.S. dollars. The average effect isapproximately 5 U.S. dollars lower for females than for males, corresponding to approximately42% ( = 5 / · ) higher earnings gain for males than for females. These higher earningsincrease the average gender earnings gap by 8% ( = 5 / · ). Eren and Ozbeklik (2014)and Schochet, Burghardt, and McConnell (2008) report results of a similar magnitude. In theexperimental survey data, the average effect heterogeneity is not significantly different fromzero.TATE accounts for 1 U.S. dollar of the earnings difference between females and males. SATEaccounts for 4 U.S. dollars of that difference. Accordingly, the structural earnings inequalitycould account for up to 82% and the direct gender effects for only 18% of the increase in theaverage gender earnings gap. Despite the insignificant average effects, a large structural earningsinequality can cause the effect heterogeneity by gender. Job Corps trainability differences bygender do not seem to be an important channel of effect heterogeneity. If the offers to participate29able 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 DifferencesLevels Effects between FemalesY(1) Y(0) and Males(1) (2) (3) (4)ATEBoth Genders 210.9 195.8 15.01*** -(3.85)CATEFemales 170.4 158.1 12.31** -5.22(5.26) (7.55)Males 239.2 221.6 17.54*** -(5.32)TATEFemales 212.3 195.8 16.39** -0.95(6.98) (9.22)Males 213.6 195.8 17.34*** -(5.88)SATEFemales - - -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 at10% level. Bootstrapped standard errors are in parentheses and are obtained from 499 bootstrap replications. in the Job Corps are awarded to males and females so that the unconditional potential earningsdistributions 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 thesame time, gender earnings inequality increases by only 2% ( = 1 / · ). Online Appendix C.1 reports TQTE and SQTE when the reference quantiles are from thepotential outcome distribution under treatment ( Q Y (1) ( τ ) ), the observed outcome distribution( Q Y ( τ ) ), the potential outcome distribution of males under non-treatment ( Q Y (0) | G ( τ | m ) ), andthe potential outcome distribution of females under non-treatment ( Q Y (0) | G ( τ | f ) ). The resultsdo 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 under30igure 10: Rank transformation. Note: I consider the relative ranks only in the interval [0 . , . and exclude all ranks below ˆ F Y (0) (0) (forexplanation, see Online Appendix B). treatment τ rg = F Y (1) | G ( Q Y r ( τ ) | g ) . Again, I consider many possible reference distributions (seeFigures C.1–C.4). The results do not change qualitatively when the relative rank is definedunder treatment. Accordingly, the results are not sensitive to the choice of the reference distri-butions and relative ranks. 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. Figure 10 shows therelative ranks by gender and parenthood. For low percentiles, the relative ranks of mothersand fathers are close to the ◦ line, which indicates little structural gender earnings inequality.However, for high percentiles the relative ranks of mothers are more disperse than for females For 1% of the sample, the data on children is missing. Figure A.2 in Online Appendix A documents the potential earnings distributions under non-treatment by genderand parenthood.
Gender With Children Without Children Difference betweenLevel Difference Level Difference (2) and (4)(1) (2) (3) (4) (5)CATEFemales 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)TATEFemales 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)SATEFemales 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 at10% level. Bootstrapped standard errors are in parentheses and are obtained from 499 bootstrap replications. without children, indicating more structural earnings inequality.Table 6 reports suggestive evidence for effect heterogeneity in CATEs by gender and parent-hood. 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 childlessfemales. Strikingly, the effect of an offer to join the Job Corps is twice as large for mothersas for childless women. The SATE accounts for 87% ( = 4 . / . · ) of the CATE het-erogeneity by gender for those with children and for 62% ( = 5 . / . · ) in the absenceof children. Even though the effect heterogeneity is insignificant, there is a tendency for thestructural earnings inequality to have an economically meaningful influence. Overall, the TATEaccounts for 29% ( = 4 . / . · ) and the SATE for 71% ( = 10 . / . · ) of theCATE effect heterogeneity by gender and parenthood. These results suggest that within-groupheterogeneity in the earnings structures contribute substantially to the between-groups effectheterogeneity. This is consistent with the findings of Bitler, Gelbach, and Hoynes (2017), who The average earnings of mothers with an offer to join the Job Corps are 175 U.S. Dollars, and the respectiveamount is 154 U.S. Dollars for those without an offer. The average earnings of childless women with an offer tojoin the Job Corps is 169 U.S. Dollars, and the respective amount is 160 U.S. Dollars for those without an offer.
The existing studies tend to conclude that the Job Corps increases gender earnings inequal-ity. These findings are surprising because most other ALMP evaluations show more positiveeffects for females than for males (see, e.g., Bergemann and van den Berg, 2008). I estimate theTQTEs, initially proposed by Bitler, Hoynes, and Domina (2014), to reveal the potential mech-anism behind these unexpected findings. Frumento, Mealli, Pacini, and Rubin (2012) identifylabour market opportunities as the main reason for effect heterogeneity. I approximate suchopportunities using expected earnings. Because the earnings distributions differ by gender, theexisting structural gender earnings inequality can be a mechanism for effect heterogeneity bygender.The results suggest that the award of an offer to participate in the Job Corps increases theaverage weekly earnings of eligible individuals by approximately 15 U.S. dollars. The absoluteearnings gain is approximately 5 U.S. dollars lower for females than for males. The Job Corpsoffer is least beneficial for childless women. Randomly awarding offers to participate in the JobCorps could increase the gender earnings gap by up to 8%. My findings suggest that the averagestructural earnings inequality accounts for 82% of the effect heterogeneity by gender, whereasonly 18% of the effect heterogeneity can be explained by Job Corps trainability differences bygender. Even though the effect heterogeneity is mostly not significant, this suggests structuralearnings differences between groups are important for explaining the overall effect heterogeneity.These results suggest that programme administrators should pay more attention to heteroge-neous gender earnings structure when designing assignment rules for Job Corps (and potentiallyalso for other ALMPs). An assignment rule that balances the earnings structure of male andfemale participants would lead to similar effects for both genders. However, several factorshave to be considered before implementing such an assignment rule. First, such a rule wouldcrowd-out some males that would significantly benefit from the programme. It is unclear if this33s in the interest of the programme administrators. Second, an assignment rule that increasesthe overall effectiveness of Job Corps would target males and females at the higher end of theearnings distribution. However, such a rule would mainly support those participants who arealready well-off. Third, it is unclear how such assignment rules would be implemented in prac-tice. The assignment decision would be based on the potential earnings under non-treatmentfour years after the programme assignment, which is obviously unobservable at the time theassignment decision is made. Accordingly, the potential earnings under non-treatment wouldhave to be predicted using variables that are observed in the baseline period (e.g., previousearnings, education, etc.), and the assignment rule would have to be based on the predictedpotential earnings under non-treatment. There are three potential explanations why many other ALMPs have more positive effects forfemales than for males. First, other ALMPs could have trainability differences by gender thatare in favour of females. Second, many other ALMPs entail non-random selection into treat-ment, which could also favour females (following the arguments of the preceding paragraph).Third, other ALMPs might mainly support participants with low labour market opportuni-ties, (e.g., Card, Kluve, and Weber, 2018, provide evidence supporting this argument), whichtoo could favour females. In the latter case, the structural earnings inequality would also beresponsible for effect heterogeneity, but in this case it would support females. However, theinfluence of structural earnings inequality on the effectiveness of other ALMPs is beyond thescope 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 perweek.
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 perweek.
Males Females StandardizedMean 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 35.130Offer to join Job Corps 0.495 0.500 0.502 0.500 1.220Ever 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 9.960Aged between 18-19 years 0.310 0.463 0.327 0.469 3.620Aged between 20-24 years 0.254 0.436 0.287 0.452 7.220White 0.305 0.460 0.222 0.415 19.010Black 0.450 0.497 0.519 0.500 13.950Hispanic 0.169 0.375 0.185 0.388 4.180Indian 0.076 0.265 0.074 0.261 0.820Lives with spouse or partner 0.051 0.219 0.078 0.268 11.170Dummy for bad health 0.121 0.326 0.147 0.355 7.7200-6 months education program in last year 0.243 0.429 0.287 0.452 9.9006-12 months education program in last year 0.385 0.486 0.324 0.468 12.660High school credential 0.198 0.398 0.285 0.451 20.500Lives in PMSA 0.316 0.465 0.334 0.471 3.770Lives 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 7.490Worked in year prior to random assignment 0.664 0.472 0.628 0.483 7.430Has job at random assignment 0.212 0.409 0.203 0.402 2.240Below 3 months employed in last year 0.190 0.378 0.190 0.382 0.0803-9 months employed in last year 0.287 0.437 0.268 0.432 4.3809-12 months employed in last year 0.187 0.377 0.171 0.366 4.360Yearly earnings less than $1,000 0.099 0.299 0.123 0.328 7.590Yearly earnings $1,000 to $5,000 0.269 0.444 0.268 0.443 0.340Yearly earnings $5,000 to $10,000 0.143 0.350 0.124 0.330 5.600Yearly 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 13.850Received food stamps in last year 0.366 0.482 0.534 0.499 34.290Public or rent-subsidized housing 0.183 0.384 0.222 0.413 9.790Received 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 10.620Smoked marijuana in last year 0.277 0.448 0.200 0.400 18.250Ever arrested dummy 0.311 0.463 0.164 0.370 35.180Observations 6,104 4,491Note: Time-varying control variables are measured at the time of random assignment. Weights accounting forthe sampling design and non-response of the 48-month interview are used ( wgt b ). PMSA stand for PrimaryMetropolitan Statistical Area. MSA stand for Metropolitan Statistical Area. AFDC stands for Aid to Familieswith Dependent Children. Males FemalesCoef. 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 1,603Note: We predict the weekly earnings (in U.S. dollars) 48 months after randomized assignment. *** indicatessignificance at the 1% level, ** indicates significance at the 5% level, and * indicates significance at the 10%level. Heteroskedastie robust standard errors are in parentheses. 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 mannerbut 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. Inparticular, ˆ δ T AT E ( g ) = 1 (cid:80) N (1 − D i ) · ω i N (cid:88) (1 − D i ) · ω i · (cid:16) ˆ Q Y (1) | G ( ˆ F Y (0) | G ( Y i | g ) | g ) − Y i (cid:17) . Finally, I estimate SATE by ˆ δ SAT E ( g ) = ˆ δ CAT E ( g ) − ˆ δ T AT E ( g ) . B.2 Kolmogorov–Smirnov test
Additionally, I report the rank invariant Kolmogorov–Smirnov test statistics for all effects. Thetest statistics are T KS = √ n · sup τ ( | ˆ δ ( τ ) | ) , where ˆ δ ( τ ) indicates the estimate of some quantile difference δ ( τ ) . The null hypothesis is δ ( τ ) = 0 for all τ . Thus, this is a test for significant effects at some quantile or, in otherwords, for the inequality between some potential earning distributions. Further, I report signedversions of the Kolmogorov–Smirnov statistics, which enable testing for positive or negativefirst-order stochastic dominance. Positive stochastic dominance is defined as δ ( τ ) ≥ for all τ . Accordingly, under (positive) stochastic dominance, δ ( τ ) is never negative regardless ofthe quantile at which the effect is measured. In contrast, negative stochastic dominance isdefined as δ ( τ ) ≤ for all τ . Accordingly, under negative stochastic dominance, δ ( τ ) is neverpositive, regardless of the quantile at which the effect is measured. For all Kolmogorov– In particular, I use the test statistics for positive stochastic dominance T P SD = √ n · sup τ (ˆ δ ( τ )) and negativestochastic dominance T NSD = √ n · inf τ (ˆ δ ( τ )) . chern05 . This non-pivotal method computes p-values by avoiding restrictiveassumptions. chern05 show that recentering can substantially improve the finite-sample powerof the Kolmogorov–Smirnov test relative to its uncentered counterpart.44 Alternative relative ranks
C.1 Relative rank is defined under non-treatment
C.1.1 Reference distribution is the potential outcome distribution under treat-ment
Figure C.3: TQTEs of the Job Corps by gender on average weekly earnings (in U.S. dollars) inyear four after randomized assignment.
Note: The lines report the point estimates separately calculated for all percentiles. Crosses on the lines indicatesignificant effects at the 10% level. Hollow circles on the lines indicate significant effects at the 5% level. Fulldiamonds on the lines indicate significant effects at the 1% level. The reference quantiles are from the potentialoutcome distribution under treatment, Q Y (1) ( τ ) . The relative rank is defined by τ rg = F Y (0) | G ( Q Y (1) ( τ ) | g ) . Iconsider only the relative ranks in the interval [0 . , . and exclude all ranks below ˆ F Y (1) (0) (for explanations,see Online Appendix B). Note: The lines report the point estimates calculated separately for all percentiles. All point estimates arenot statistically different from zero. The reference quantiles are from the potential outcome distribution undertreatment, Q Y (1) ( τ ) . The relative rank is defined by τ rg = F Y (0) | G ( Q Y (1) ( τ ) | g ) . I consider only the relativeranks in the interval [0 . , . and exclude all ranks below ˆ F Y (1) (0) (for explanations, see Online AppendixB). Note: The lines report the point estimates separately calculated for all percentiles. Crosses on the lines indicatesignificant effects at the 10% level. Hollow circles on the lines indicate significant effects at the 5% level. Fulldiamonds on the lines indicate significant effects at the 1% level. The reference quantiles are from the potentialoutcome distribution under treatment, Q Y (1) ( τ ) . The relative rank is defined by τ rg = F Y (0) | G ( Q Y (1) ( τ ) | g ) . Iconsider only the relative ranks in the interval [0 . , . and exclude all ranks below ˆ F Y (1) (0) (for explanations,see Online Appendix B). Note: The lines report the point estimates calculated separately for all percentiles. Crosses on the lines indicatesignificant effects at the 10% level. Hollow circles on the lines indicate significant effects at the 5% level. Fulldiamonds on the lines indicate significant effects at the 1% level. The reference quantiles are from the potentialoutcome distribution under treatment, Q Y (1) ( τ ) . The relative rank is defined by τ rg = F Y (0) | G ( Q Y (1) ( τ ) | g ) . Iconsider only the relative ranks in the interval [0 . , . and exclude all ranks below ˆ F Y (1) (0) (for explanations,see Online Appendix B). .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) inyear four after randomized assignment.
Note: The lines report the point estimates calculated separately for all percentiles. Crosses on the lines indicatesignificant effects at the 10% level. Hollow circles on the lines indicate significant effects at the 5% level. Fulldiamonds on the lines indicate significant effects at the 1% level. The reference quantiles are from the observedoutcome distribution, Q Y ( τ ) . The relative rank is defined by τ rg = F Y (0) | G ( Q Y ( τ ) | g ) . I consider only the relativeranks in the interval [0 . , . and exclude all ranks below ˆ F Y (0) (for explanations, see Online Appendix B). Note: The lines report the point estimates calculated separately for all percentiles. Crosses on the lines indicatesignificant effects at the 10% level. The reference quantiles are from the observed outcome distribution, Q Y ( τ ) .The relative rank is defined by τ rg = F Y (0) | G ( Q Y ( τ ) | g ) . I consider only the relative ranks in the interval [0 . , . and exclude all ranks below ˆ F Y (0) (for explanations, see Online Appendix B). Note: The lines report the point estimates calculated separately for all percentiles. Crosses on the lines indicatesignificant effects at the 10% level. Hollow circles on the lines indicate significant effects at the 5% level. Fulldiamonds on the lines indicate significant effects at the 1% level. The reference quantiles are from the observedoutcome distribution, Q Y ( τ ) . The relative rank is defined by τ rg = F Y (0) | G ( Q Y ( τ ) | g ) . I consider only the relativeranks in the interval [0 . , . and exclude all ranks below ˆ F Y (0) (for explanations, see Online Appendix B). Note: The lines report the point estimates calculated separately for all percentiles. Crosses on the lines indicatesignificant effects at the 10% level. Hollow circles on the lines indicate significant effects at the 5% level. Fulldiamonds on the lines indicate significant effects at the 1% level. The reference quantiles are from the observedoutcome distribution, Q Y ( τ ) . The relative rank is defined by τ rg = F Y (0) | G ( Q Y ( τ ) | g ) . I consider only the relativeranks in the interval [0 . , . and exclude all ranks below ˆ F Y (0) (for explanations, see Online Appendix B). .1.3 Reference distribution is the potential outcome distribution of males undernon-treatment Figure C.1: TQTEs of the Job Corps by gender on average weekly earnings (in U.S. dollars) inyear four after randomized assignment.
Note: The lines report the point estimates calculated separately for all percentiles. Crosses on the lines indicatesignificant 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 thepotential outcome distribution of males under treatment, Q Y (1) | G ( τ | m ) . The relative rank is defined by τ rg = F Y (0) | G ( Q Y (1) | G ( τ | m ) | g ) . I consider only the relative ranks in the interval [0 . , . and exclude all ranksbelow ˆ F Y (1) | G (0 | m ) (for explanations, see Online Appendix B). Note: The lines report the point estimates calculated separately for all percentiles. Crosses on the lines indicatesignificant effects at the 10% level. The reference quantiles are from the potential outcome distribution of malesunder treatment, Q Y (1) | G ( τ | m ) . The relative rank is defined by τ rg = F Y (0) | G ( Q Y (1) | G ( τ | m ) | g ) . I consider onlythe relative ranks in the interval [0 . , . and exclude all ranks below ˆ F Y (1) | G (0 | m ) (for explanations, seeOnline Appendix B). Note: The lines report the point estimates calculated separately for all percentiles. Crosses on the lines indicatesignificant 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 thepotential outcome distribution of males under treatment, Q Y (1) | G ( τ | m ) . The relative rank is defined by τ rg = F Y (0) | G ( Q Y (1) | G ( τ | m ) | g ) . I consider only the relative ranks in the interval [0 . , . and exclude all ranksbelow ˆ F Y (1) | G (0 | m ) (for explanations, see Online Appendix B). Note: The lines report the point estimates calculated separately for all percentiles. Crosses on the lines indicatesignificant 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 thepotential outcome distribution of males under treatment, Q Y (1) | G ( τ | m ) . The relative rank is defined by τ rg = F Y (0) | G ( Q Y (1) | G ( τ | m ) | g ) . I consider only the relative ranks in the interval [0 . , . and exclude all ranksbelow ˆ F Y (1) | G (0 | m ) (for explanations, see Online Appendix B). .1.4 Reference distribution is the potential outcome distribution of females un-der non-treatment Figure C.1: TQTEs of the Job Corps by gender on average weekly earnings (in U.S. dollars) inyear four after randomized assignment.
Note: The lines report the point estimates calculated separately for all percentiles. Crosses on the lines indicatesignificant 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 thepotential outcome distribution of females under treatment, Q Y (1) | G ( τ | f ) . The relative rank is defined by τ rg = F Y (0) | G ( Q Y (1) | G ( τ | f ) | g ) . I consider only the relative ranks in the interval [0 . , . and exclude all ranks below ˆ F Y (1) | G (0 | f ) (for explanations, see Online Appendix B). Note: The lines report the point estimates calculated separately for all percentiles. Crosses on the lines indicatesignificant effects at the 10% level. The reference quantiles are from the potential outcome distribution of femalesunder treatment, Q Y (1) | G ( τ | f ) . The relative rank is defined by τ rg = F Y (0) | G ( Q Y (1) | G ( τ | f ) | g ) . I consider onlythe relative ranks in the interval [0 . , . and exclude all ranks below ˆ F Y (1) | G (0 | f ) (for explanations, seeOnline Appendix B). Note: The lines report the point estimates calculated separately for all percentiles. Crosses on the lines indicatesignificant 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 thepotential outcome distribution of females under treatment, Q Y (1) | G ( τ | f ) . The relative rank is defined by τ rg = F Y (0) | G ( Q Y (1) | G ( τ | f ) | g ) . I consider only the relative ranks in the interval [0 . , . and exclude all ranks below ˆ F Y (1) | G (0 | f ) (for explanations, see Online Appendix B). Note: The lines report the point estimates calculated separately for all percentiles. Crosses on the lines indicatesignificant 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 thepotential outcome distribution of females under treatment, Q Y (1) | G ( τ | f ) . The relative rank is defined by τ rg = F Y (0) | G ( Q Y (1) | G ( τ | f ) | g ) . I consider only the relative ranks in the interval [0 . , . and exclude all ranks below ˆ F Y (1) | G (0 | f ) (for explanations, see Online Appendix B). .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) inyear four after randomized assignment.
Note: The lines report the point estimates calculated separately for all percentiles. Crosses on the lines indicatesignificant effects at the 10% level. Hollow circles on the lines indicate significant effects at the 5% level. Fulldiamonds on the lines indicate significant effects at the 1% level. The reference quantiles are from the potentialoutcome distribution under non-treatment, Q Y (0) ( τ ) . The relative rank is defined by τ rg = F Y (1) | G ( Q Y (0) ( τ ) | g ) .The rank transformation uses the conditional potential outcome distribution under treatment. I consider onlythe relative ranks in the interval [0 . , . and exclude all ranks below ˆ F Y (1) (0) (for explanations, see OnlineAppendix B). Note: The lines report the point estimates calculated separately for all percentiles. All point estimates arenot statistically different from zero. The reference quantiles are from the potential outcome distribution undernon-treatment, Q Y (0) ( τ ) . The relative rank is defined by τ rg = F Y (1) | G ( Q Y (0) ( τ ) | g ) . The rank transformationuses the conditional potential outcome distribution under treatment. I consider only the relative ranks in theinterval [0 . , . and exclude all ranks below ˆ F Y (1) (0) (for explanations, see Online Appendix B). Note: The lines report the point estimates calculated separately for all percentiles. Crosses on the lines indicatesignificant effects at the 10% level. Hollow circles on the lines indicate significant effects at the 5% level. Fulldiamonds on the lines indicate significant effects at the 1% level. The reference quantiles are from the potentialoutcome distribution under non-treatment, Q Y (0) ( τ ) . The relative rank is defined by τ rg = F Y (1) | G ( Q Y (0) ( τ ) | g ) .The rank transformation uses the conditional potential outcome distribution under treatment. I consider onlythe relative ranks in the interval [0 . , . and exclude all ranks below ˆ F Y (1) (0) (for explanations, see OnlineAppendix B). Note: The lines report the point estimates calculated separately for all percentiles. Crosses on the lines indicatesignificant effects at the 10% level. Hollow circles on the lines indicate significant effects at the 5% level. Fulldiamonds on the lines indicate significant effects at the 1% level. The reference quantiles are from the potentialoutcome distribution under non-treatment, Q Y (0) ( τ ) . The relative rank is defined by τ rg = F Y (1) | G ( Q Y (0) ( τ ) | g ) .The rank transformation uses the conditional potential outcome distribution under treatment. I consider onlythe relative ranks in the interval [0 . , . and exclude all ranks below ˆ F Y (1) (0) (for explanations, see OnlineAppendix B). .2.2 Reference distribution is the potential outcome distribution under treat-ment Figure C.1: TQTEs of the Job Corps by gender on average weekly earnings (in U.S. dollars) inyear four after randomized assignment.
Note: The lines report the point estimates calculated separately for all percentiles. Crosses on the lines indicatesignificant effects at the 10% level. Hollow circles on the lines indicate significant effects at the 5% level. Fulldiamonds on the lines indicate significant effects at the 1% level. The reference quantiles are from the potentialoutcome distribution under treatment, Q Y (1) ( τ ) . The relative rank is defined by τ rg = F Y (1) | G ( Q Y (1) ( τ ) | g ) .The rank transformation uses the conditional potential outcome distribution under treatment. I consider onlythe relative ranks in the interval [0 . , . and exclude all ranks below ˆ F Y (1) (0) (for explanations, see OnlineAppendix B). Note: The lines report the point estimates calculated separately for all percentiles. Crosses on the lines indicatesignificant effects at the 10% level. The reference quantiles are from the potential outcome distribution undertreatment, Q Y (1) ( τ ) . The relative rank is defined by τ rg = F Y (1) | G ( Q Y (1) ( τ ) | g ) . The rank transformation usesthe conditional potential outcome distribution under treatment. I consider only the relative ranks in the interval [0 . , . and exclude all ranks below ˆ F Y (1) (0) (for explanations, see Online Appendix B). Note: The lines report the point estimates calculated separately for all percentiles. Crosses on the lines indicatesignificant effects at the 10% level. Hollow circles on the lines indicate significant effects at the 5% level. Fulldiamonds on the lines indicate significant effects at the 1% level. The reference quantiles are from the potentialoutcome distribution under treatment, Q Y (1) ( τ ) . The relative rank is defined by τ rg = F Y (1) | G ( Q Y (1) ( τ ) | g ) .The rank transformation uses the conditional potential outcome distribution under treatment. I consider onlythe relative ranks in the interval [0 . , . and exclude all ranks below ˆ F Y (1) (0) (for explanations, see OnlineAppendix B). Note: The lines report the point estimates calculated separately for all percentiles. Crosses on the lines indicatesignificant effects at the 10% level. Hollow circles on the lines indicate significant effects at the 5% level. Fulldiamonds on the lines indicate significant effects at the 1% level. The reference quantiles are from the potentialoutcome distribution under treatment, Q Y (1) ( τ ) . The relative rank is defined by τ rg = F Y (1) | G ( Q Y (1) ( τ ) | g ) .The rank transformation uses the conditional potential outcome distribution under treatment. I consider onlythe relative ranks in the interval [0 . , . and exclude all ranks below ˆ F Y (1) (0) (for explanations, see OnlineAppendix B). .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) inyear four after randomized assignment.
Note: The lines report the point estimates calculated separately for all percentiles. Crosses on the lines indicatesignificant effects at the 10% level. Hollow circles on the lines indicate significant effects at the 5% level. Fulldiamonds on the lines indicate significant effects at the 1% level. The reference quantiles are from the observedoutcome distribution, Q Y ( τ ) . The relative rank is defined by τ rg = F Y (1) | G ( Q Y ( τ ) | g ) . The rank transformationuses the conditional potential outcome distribution under treatment. I consider only the relative ranks in theinterval [0 . , . and exclude all ranks below ˆ F Y (0) (for explanations, see Online Appendix B). Note: The lines report the point estimates calculated separately for all percentiles. All point estimates are notstatistically different from zero. The reference quantiles are from the observed outcome distribution, Q Y ( τ ) .The relative rank is defined by τ rg = F Y (1) | G ( Q Y ( τ ) | g ) . The rank transformation uses the conditional potentialoutcome distribution under treatment. I consider only the relative ranks in the interval [0 . , . and excludeall ranks below ˆ F Y (0) (for explanations, see Online Appendix B). Note: The lines report the point estimates calculated separately for all percentiles. Crosses on the lines indicatesignificant effects at the 10% level. Hollow circles on the lines indicate significant effects at the 5% level. Fulldiamonds on the lines indicate significant effects at the 1% level. The reference quantiles are from the observedoutcome distribution, Q Y ( τ ) . The relative rank is defined by τ rg = F Y (1) | G ( Q Y ( τ ) | g ) . The rank transformationuses the conditional potential outcome distribution under treatment. I consider only the relative ranks in theinterval [0 . , . and exclude all ranks below ˆ F Y (0) (for explanations, see Online Appendix B). Note: The lines report the point estimates calculated separately for all percentiles. Crosses on the lines indicatesignificant effects at the 10% level. Hollow circles on the lines indicate significant effects at the 5% level. Fulldiamonds on the lines indicate significant effects at the 1% level. The reference quantiles are from the observedoutcome distribution, Q Y ( τ ) . The relative rank is defined by τ rg = F Y (1) | G ( Q Y ( τ ) | g ) . The rank transformationuses the conditional potential outcome distribution under treatment. I consider only the relative ranks in theinterval [0 . , . and exclude all ranks below ˆ F Y (0) (for explanations, see Online Appendix B). .2.4 Reference distribution is the potential outcome distribution of males undernon-treatment Figure C.1: TQTEs of the Job Corps by gender on average weekly earnings (in U.S. dollars) inyear four after randomized assignment.
Note: The lines report the point estimates calculated separately for all percentiles. Crosses on the lines indicatesignificant 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 thepotential outcome distribution of males under treatment, Q Y (0) | G ( τ | m ) . The relative rank is defined by τ rg = F Y (1) | G ( Q Y (0) | G ( τ | m ) | g ) . The rank transformation uses the conditional potential outcome distribution undertreatment. I consider only the relative ranks in the interval [0 . , . and exclude all ranks below ˆ F Y (0) | G (0 | m ) (for explanations, see Online Appendix B). Note: The lines report the point estimates calculated separately for all percentiles. Crosses on the lines indicatesignificant effects at the 10% level. The reference quantiles are from the potential outcome distribution ofmales under treatment, Q Y (0) | G ( τ | m ) . The relative rank is defined by τ rg = F Y (1) | G ( Q Y (0) | G ( τ | m ) | g ) . Therank transformation uses the conditional potential outcome distribution under treatment. I consider only therelative ranks in the interval [0 . , . and exclude all ranks below ˆ F Y (0) | G (0 | m ) (for explanations, see OnlineAppendix B). Note: The lines report the point estimates calculated separately for all percentiles. Crosses on the lines indicatesignificant 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 thepotential outcome distribution of males under treatment, Q Y (0) | G ( τ | m ) . The relative rank is defined by τ rg = F Y (1) | G ( Q Y (0) | G ( τ | m ) | g ) . The rank transformation uses the conditional potential outcome distribution undertreatment. I consider only the relative ranks in the interval [0 . , . and exclude all ranks below ˆ F Y (0) | G (0 | m ) (for explanations, see Online Appendix B). Note: The lines report the point estimates calculated separately for all percentiles. Crosses on the lines indicatesignificant 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 thepotential outcome distribution of males under treatment, Q Y (0) | G ( τ | m ) . The relative rank is defined by τ rg = F Y (1) | G ( Q Y (0) | G ( τ | m ) | g ) . The rank transformation uses the conditional potential outcome distribution undertreatment. I consider only the relative ranks in the interval [0 . , . and exclude all ranks below ˆ F Y (0) | G (0 | m ) (for explanations, see Online Appendix B). .2.5 Reference distribution is the potential outcome distribution of females un-der non-treatment Figure C.1: TQTEs of the Job Corps by gender on average weekly earnings (in U.S. dollars) inyear four after randomized assignment.
Note: The lines report the point estimates calculated separately for all percentiles. Crosses on the lines indicatesignificant 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 thepotential outcome distribution of females under treatment, Q Y (0) | G ( τ | f ) . The relative rank is defined by τ rg = F Y (1) | G ( Q Y (0) | G ( τ | f ) | g ) . The rank transformation uses the conditional potential outcome distribution undertreatment. I consider only the relative ranks in the interval [0 . , . and exclude all ranks below ˆ F Y (0) | G (0 | f ) (for explanations, see Online Appendix B). Note: The lines report the point estimates calculated separately for all percentiles. All point estimates arenot statistically different from zero. The reference quantiles are from the potential outcome distribution offemales under treatment, Q Y (0) | G ( τ | f ) . The relative rank is defined by τ rg = F Y (1) | G ( Q Y (0) | G ( τ | f ) | g ) . Therank transformation uses the conditional potential outcome distribution under treatment. I consider only therelative ranks in the interval [0 . , . and exclude all ranks below ˆ F Y (0) | G (0 | f ) (for explanations, see OnlineAppendix B). Note: The lines report the point estimates calculated separately for all percentiles. Crosses on the lines indicatesignificant 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 thepotential outcome distribution of females under treatment, Q Y (0) | G ( τ | f ) . The relative rank is defined by τ rg = F Y (1) | G ( Q Y (0) | G ( τ | f ) | g ) . The rank transformation uses the conditional potential outcome distribution undertreatment. I consider only the relative ranks in the interval [0 . , . and exclude all ranks below ˆ F Y (0) | G (0 | f ) (for explanations, see Online Appendix B). Note: The lines report the point estimates calculated separately for all percentiles. Crosses on the lines indicatesignificant 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 thepotential outcome distribution of females under treatment, Q Y (0) | G ( τ | f ) . The relative rank is defined by τ rg = F Y (1) | G ( Q Y (0) | G ( τ | f ) | g ) . The rank transformation uses the conditional potential outcome distribution undertreatment. I consider only the relative ranks in the interval [0 . , . and exclude all ranks below ˆ F Y (0) | G (0 | f ) (for explanations, see Online Appendix B). 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 theJob Corps to childless women has the smallest earnings impact of all four groups. The effectheterogeneity by gender is not strongly significant for parents, but significant for childlesswomen and men. Considering heterogeneity between all four groups, the effect heterogeneityby gender and parenthood is large, but the effects are only significant at some quantiles (seeFigure D.5).Table D.2 and Figures D.6-D.10 in Online Appendix D report TQTE by gender and parent-hood. The TQTE show large effect heterogeneity by gender of parents, but the differences arenot significant (see Figure D.7). The effect heterogeneity is significant between childless womenand men (see Figure D.9). Their is a tendency that TQTE can explain heterogeneity betweenthe two groups, because the Kolmogorov–Smirnov test is weakly significant (see Table D.2 andFigure D.10). The results for SQTE are ambiguous (see Table D.3 and Figures D.11-D.15 inOnline Appendix D). We find significant SQTE for all groups, but the signs of the effects aremixed. At some quantile the SQTE have a large magnitude. Accordingly, the TQTE andSQTE contribute both to the effect heterogeneity in the CQTE by gender and parenthood.81 .1 CQTE by gender and parenthood
Table D.1: CQTE of the Job Corps program by gender and parenthood on average weeklyearnings (in U.S. dollars) in year four after randomized assignment.
Quantile With children Without children Difference betweenFemales 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 -29.488.16 22.09 23.3 3.64 8.57 9.21 25.280.3 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 32.590.4 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 36.040.5 14.97 47.02 -32.05 5.85 23,28*** -17.43 -14.6314.77 22.88 27.55 11.8 7.86 14.19 31.190.6 25,49** 32.4 -6.91 5.66 17,48** -11.82 4.99.97 19.44 21.95 7.11 7.67 10.6 24.70.7 28,57*** 28.53 0.04 13.18 23,43*** -10.26 10.299.17 18.38 20.3 9.2 4.3 10.18 22.950.8 28,01* 16.88 11.13 5.81 23,21*** -17.41 28.5415.66 26.84 31.08 10.19 8.75 13.39 34.090.9 60,82*** 5.41 55.41 7.73 13.04 -5.31 60.7318.87 35.96 40 15.47 12.87 20.01 45.06KS statistic 12,318 8,261 13,598 2,466 16,041*** 14,295* 25,8610.175 0.955 0.837 0.899 0.009 0.059 0.534PSD statistic 12,318*** 7,995 13,598 2,466 16,041*** 2,513 25,8610.008 0.552 0.522 0.584 0.009 0.713 0.338NSD statistic -351 -8,261 -6,595 -814 -265 -14,295** -8,9210.97 0.621 0.674 0.856 0.966 0.025 0.587Note: *** indicates significance at the 1% level, ** indicates significance at the 5% level, and * indicatessignificance at the 10% level. Bootstrapped standard errors are in parentheses and are obtained from 1,999bootstrap replications. ”KS statistic” indicates the Kolmogorov–Smirnov statistic. ”PSD statistic” indicatesthe Kolmogorov–Smirnov-type test statistic for positive stochastic dominance. ”NSD statistic” indicates theKolmogorov–Smirnov-type test statistic for negative stochastic dominance. Bootstrapped p-values (1,999 repli-cations) are in squared brackets.
Note: The lines report the point estimates calculated separately for all percentiles. Crosses on the lines indicatesignificant effects at the 10% level. Hollow circles on the lines indicate significant effects at the 5% level. Fulldiamonds 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. Thelines report the point estimates calculated separately for all percentiles. Crosses on the lines indicate significanteffects at the 10% level. Hollow circles on the lines indicate significant effects at the 5% level. Full diamondson the lines indicate significant effects at the 1% level.
Note: The lines report the point estimates calculated separately for all percentiles. Crosses on the lines indicatesignificant effects at the 10% level. Hollow circles on the lines indicate significant effects at the 5% level. Fulldiamonds on the lines indicate significant effects at the 1% level.
Note: The outcome is average weekly earnings (in U.S. dollars) in year four after randomized assignment. Thelines report the point estimates calculated separately for all percentiles. Crosses on the lines indicate significanteffects at the 10% level. Hollow circles on the lines indicate significant effects at the 5% level. Full diamondson the lines indicate significant effects at the 1% level.
Note: The outcome is average weekly earnings (in U.S. dollars) in year four after randomized assignment. Thelines report the point estimates calculated separately for all percentiles. Crosses on the lines indicate significanteffects at the 10% level. Hollow circles on the lines indicate significant effects at the 5% level. Full diamondson the lines indicate significant effects at the 1% level. .2 TQTE by gender and parenthood Table D.2: TQTEs of the Job Corps by gender and parenthood on average weekly earnings (inU.S. dollars) in year four after randomized assignment.
Quantile With children Without children Difference betweenFemales 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 -50.2113.54 30.88 34.02 10,74* 8.22 13.67 36.690.4 18.82 77,98** -59.17 14.01 -2.07 16.08 -75.2515.25 32.93 36.7 9.44 9.63 13.48 39.460.5 27,16** 49,6** -22.44 2.95 19.04 -16.09 -6.3512.89 19.03 23.42 7.32 8,89** 12.06 26.70.6 37,34*** 42,13** -4.79 12.39 15,02*** -2.63 -2.1611.87 20.26 23.39 10.1 5.92 11.03 25.960.7 34,97** 36,52** -1.55 7.06 24,43*** -17.37 15.8215.67 14.12 20.9 8.99 8.24 12.77 24.590.8 53,62** 17.61 36.01 9.26 25,17*** -15.91 51.9221.96 18.82 28.73 12.08 8.24 14.72 32.440.9 57,41* 1.35 56.06 4.54 15.76 -11.22 67.2830.69 29.02 42.63 21.52 14.42 24.31 49.71KS statistic 9160 8027 9693 2412 12488** 6416 136050.16 0.779 0.334 0.884 0.013 0.302 0.185PSD statistic 9160 8027 9693 2412 12488** 2458 13605*0.125 0.384 0.172 0.474 0.013 0.599 0.094NSD statistic -84 -4374 -6090 -1578 -303 -6416 -77450.967 0.676 0.47 0.721 0.973 0.126 0.374Note: *** indicates significance at the 1% level, ** indicates significance at the 5% level, and * indicatessignificance at the 10% level. Bootstrapped standard errors are in parentheses and are obtained from 1,999bootstrap replications. ”KS statistic” indicates the Kolmogorov–Smirnov statistic. ”PSD statistic” indicatesthe Kolmogorov–Smirnov-type test statistic for positive stochastic dominance. ”NSD statistic” indicates theKolmogorov–Smirnov-type test statistic for negative stochastic dominance. Bootstrapped p-values (1,999 repli-cations) are in squared brackets.
Note: The lines report the point estimates separately calculated for all percentiles. Crosses on the lines indicatesignificant effects at the 10% level. Hollow circles on the lines indicate significant effects at the 5% level. Fulldiamonds on the lines indicate significant effects at the 1% level. I consider only the relative ranks in the interval [0 . , . and exclude all ranks below ˆ F Y (0) (0) (for explanations, see Online Appendix B). Note: The outcome is average weekly earnings (in U.S. dollars) in year four after randomized assignment. Thelines report the point estimates separately calculated for all percentiles. All point estimates are not statisticallydifferent from zero. I consider the relative ranks only in the interval [0 . , . and exclude all ranks below ˆ F Y (0) (0) (for explanations, see Online Appendix B). Note: The lines report the point estimates separately calculated for all percentiles. Crosses on the lines indicatesignificant effects at the 10% level. Hollow circles on the lines indicate significant effects at the 5% level. Fulldiamonds on the lines indicate significant effects at the 1% level. I consider only the relative ranks in the interval [0 . , . and exclude all ranks below ˆ F Y (0) (0) (for explanations, see Online Appendix B). Note: The outcome is average weekly earnings (in U.S. dollars) in year four after randomized assignment. Thelines report the point estimates separately calculated for all percentiles. All point estimates are not statisticallydifferent from zero. I consider the relative ranks only in the interval [0 . , . and exclude all ranks below ˆ F Y (0) (0) (for explanations, see Online Appendix B). Note: The outcome is average weekly earnings (in U.S. dollars) in year four after randomized assignment. Thelines report the point estimates separately calculated for all percentiles. All point estimates are not statisticallydifferent from zero. I consider the relative ranks only in the interval [0 . , . and exclude all ranks below ˆ F Y (0) (0) (for explanations, see Online Appendix B). .3 SQTE by gender and parenthood Table D.3: SQTEs of the Job Corps by gender and parenthood on average weekly earnings (inU.S. dollars) in year four after randomized assignment.
Quantile With children Without children Difference betweenFemales Males Difference Females Males Difference (3) and (6)(1) (2) (3) (4) (5) (6) (7)0.3 -1.22 3.68 -4.9 1.21 -0.05 1.26 -6.165.71 14.32 15.51 6.13 4.72 7.66 16.760.4 -7.57 -19.9 12.32 9,95* 4.56 5.39 6.938.57 16.16 18.25 6.04 5.17 7.94 19.690.5 -12.2 -2.58 -9.62 2.9 4.24 -1.34 -8.289.48 14.08 16.38 7.59 6.86 8.77 18.650.6 -11.85 -9.73 -2.12 -6.73 2.46 -9.18 7.069.09 12.85 15.54 6.67 4.53 7.4 17.640.7 -6.4 -7.98 1.58 6.12 -1,0 7.12 -5.5311.68 10.32 15.87 6.05 5.99 8.64 17.580.8 -25.61 -0.73 -24.88 -3.45 -1.95 -1.5 -23.3815.93 16.07 22.67 7.55 4.42 8.74 24.650.9 3.41 4.06 -0.65 3.19 -2.72 5.91 -6.5622.83 21.3 30.49 14.85 8.32 15.94 34.73KS statistic 3432 7058 4446 2181 5916* 3522 79680.89 0.918 0.973 0.905 0.096 0.738 0.679PSD statistic 1102 3730 4446 2169 5916** 2047 79680.993 0.88 0.742 0.726 0.046 0.88 0.369NSD statistic -3432 -7058 -2561 -2181 -1263 -3522 -44040.638 0.789 0.991 0.589 0.961 0.451 0.891Note: *** indicates significance at the 1% level, ** indicates significance at the 5% level, and * indicatessignificance at the 10% level. Bootstrapped standard errors are in parentheses and are obtained from 1,999bootstrap replications. ”KS statistic” indicates the Kolmogorov–Smirnov statistic. ”PSD statistic” indicatesthe Kolmogorov–Smirnov-type test statistic for positive stochastic dominance. ”NSD statistic” indicates theKolmogorov–Smirnov-type test statistic for negative stochastic dominance. Bootstrapped p-values (1,999 repli-cations) are in squared brackets.
Note: The lines report the point estimates separately calculated for all percentiles. Crosses on the lines indicatesignificant effects at the 10% level. Hollow circles on the lines indicate significant effects at the 5% level. Fulldiamonds on the lines indicate significant effects at the 1% level. I consider the relative ranks only in the interval [0 . , . and exclude all ranks below ˆ F Y (0) (0) (for explanations, see Online Appendix B). Note: The outcome is average weekly earnings (in U.S. dollars) in year four after randomized assignment. Thelines report the point estimates separately calculated for all percentiles. Crosses on the lines indicate significanteffects at the 10% level. Hollow circles on the lines indicate significant effects at the 5% level. Full diamonds onthe lines indicate significant effects at the 1% level. I consider the relative ranks only in the interval [0 . , . and exclude all ranks below ˆ F Y (0) (0) (for explanations, see Online Appendix B).(for explanations, see Online Appendix B).
Note: The lines report the point estimates separately calculated for all percentiles. Crosses on the lines indicatesignificant effects at the 10% level. Hollow circles on the lines indicate significant effects at the 5% level. Fulldiamonds on the lines indicate significant effects at the 1% level. I consider the relative ranks only in the interval [0 . , . and exclude all ranks below ˆ F Y (0) (0) (for explanations, see Online Appendix B). Note: The outcome is average weekly earnings (in U.S. dollars) in year four after randomized assignment. Thelines report the point estimates separately calculated for all percentiles. Crosses on the lines indicate significanteffects at the 10% level. Hollow circles on the lines indicate significant effects at the 5% level. Full diamonds onthe lines indicate significant effects at the 1% level. I consider the relative ranks only in the interval [0 . , . and exclude all ranks below ˆ F Y (0) (0) (for explanations, see Online Appendix B).(for explanations, see Online Appendix B). Note: The lines report the point estimates separately calculated for all percentiles. Crosses on the lines indicatesignificant effects at the 10% level. Hollow circles on the lines indicate significant effects at the 5% level. Fulldiamonds on the lines indicate significant effects at the 1% level. I consider the relative ranks only in the interval [0 . , . and exclude all ranks below ˆ F Y (0) (0) (for explanations, see Online Appendix B). Note: The outcome is average weekly earnings (in U.S. dollars) in year four after randomized assignment. Thelines report the point estimates separately calculated for all percentiles. Crosses on the lines indicate significanteffects at the 10% level. Hollow circles on the lines indicate significant effects at the 5% level. Full diamonds onthe lines indicate significant effects at the 1% level. I consider the relative ranks only in the interval [0 . , . and exclude all ranks below ˆ F Y (0) (0) (for explanations, see Online Appendix B).(for explanations, see Online Appendix B).
Note: The lines report the point estimates separately calculated for all percentiles. Crosses on the lines indicatesignificant effects at the 10% level. Hollow circles on the lines indicate significant effects at the 5% level. Fulldiamonds on the lines indicate significant effects at the 1% level. I consider the relative ranks only in the interval [0 . , . and exclude all ranks below ˆ F Y (0) (0) (for explanations, see Online Appendix B). Note: The outcome is average weekly earnings (in U.S. dollars) in year four after randomized assignment. Thelines report the point estimates separately calculated for all percentiles. Crosses on the lines indicate significanteffects at the 10% level. Hollow circles on the lines indicate significant effects at the 5% level. Full diamonds onthe lines indicate significant effects at the 1% level. I consider the relative ranks only in the interval [0 . , . and exclude all ranks below ˆ F Y (0) (0) (for explanations, see Online Appendix B).(for explanations, see Online Appendix B). Note: The lines report the point estimates separately calculated for all percentiles. Crosses on the lines indicatesignificant effects at the 10% level. Hollow circles on the lines indicate significant effects at the 5% level. Fulldiamonds on the lines indicate significant effects at the 1% level. I consider the relative ranks only in the interval [0 . , . and exclude all ranks below ˆ F Y (0) (0) (for explanations, see Online Appendix B). Note: The outcome is average weekly earnings (in U.S. dollars) in year four after randomized assignment. Thelines report the point estimates separately calculated for all percentiles. Crosses on the lines indicate significanteffects at the 10% level. Hollow circles on the lines indicate significant effects at the 5% level. Full diamonds onthe lines indicate significant effects at the 1% level. I consider the relative ranks only in the interval [0 . , . and exclude all ranks below ˆ F Y (0) (0) (for explanations, see Online Appendix B).(for explanations, see Online Appendix B). Note: The outcome is average weekly earnings (in U.S. dollars) in year four after randomized assignment. Thelines report the point estimates separately calculated for all percentiles. Crosses on the lines indicate significanteffects at the 10% level. Hollow circles on the lines indicate significant effects at the 5% level. Full diamonds onthe lines indicate significant effects at the 1% level. I consider the relative ranks only in the interval [0 . , . and exclude all ranks below ˆ F Y (0) (0) (for explanations, see Online Appendix B).(for explanations, see Online Appendix B).