Appendix

40

A NFP Randomization Protocol

Pregnant women were enrolled as they visited the Medical Center during pregnancy. The randomization

protocol was sequential, that is to say that each participant was randomized according to the order of

enrollment. Pregnant women who accepted to enroll were classified in strata defined by 5 characteristics:

1. Maternal race (African American vs non-African American);

2. Maternal age (< 17, 17− 18, > 18 years );

3. Gestational age at enrollment (< 20, ≥ 20 weeks);

4. Employment status of the head of household and

5. 4 geographic regions of residence.17

Within strata, randomization was perform following the Soares and Wu (1983) method as follows:

1. If the participant had a sibling already enrolled in the program, the participant was assigned to the

same treatment status of the elder sibling.

2. Else, the participant was randomized according in to control (C) or treatment group (T). However, if the

sample size difference between treatment and control group is larger that a threshold, the participant

is deterministically assigned to the treatment status that has fewer participants.

3. Next the participant was randomized again into her final treatment status. If in step 2 the participant

was assigned to the control, she is next randomized in to:

• Group 1 : control women that received free transportation to and from their prenatal appointments

(sample size: 166).

• Group 2 : control women that received developmental screening and referral services at ages 6, 12

and 24 months in addition to the benefits of Group 1 (sample size: 514).

If she was assigned to the treatment group previously, she is next randomized into

• Group 3 : treated women that had home visits by nurses during pregnancy, one visit in the hospital

and one visit at home after childbirth in addition to the benefits of Group 2 (sample size: 230).

• Group 4 : treated women that received home visits by nurses during pregnancy until the child’s

2nd birthday in addition to the benefits of Group 2 (sample size: 228)

17The regions are: Inner City, Bisson, Cawthon and Hollywood.

41

As in the previous step, if the absolute difference in group size exceed some threshold then the partic-

ipant was deterministically assigned to the group with the lowest number of participants. Otherwise,

the pregnant woman was randomly assigned.

Importantly, the randomization method incorporated a trigger mechanism that deterministically assigned

a treatment status to participants if the sequence of assignments became too imbalanced due to sampling

variation. In this context, imbalance was measured by the difference of persons assigned to T and the persons

assigned to C. In practice less than 1% of the women were assigned according to the trigger mechanism.

Thus, the NFP Memphis trial can be treated as a non-sequential protocol.

B Instruments

B.1 HOME

The Home Observation for Measurement of the Environment (HOME) was first developed in the 1960s by

Caldwell. It measures the quality and quantity of stimulation and support available to a child at home

(Bradley and Caldwell (1984)). The test is based on the child and is carried on during a visit of 45 to 90

minutes. A more in depth explanation of the HOME inventory is in Bradley and Caldwell (1984).

There are several versions of the inventory. The initial version, Infant/Toddler HOME, is for kids aged 0

to 3 years old. It consists of 45 binary-choice items grouped into 6 subscales. The Early Childhood HOME

is for kids aged 3 to 6 years old. It consists of 55 binary-choice items clustered into 8 subscales. Finally, the

Middle Childhood HOME is used for kids aged 6 to 10 years old. It consists of 59 items in 8 subscales. The

NFP uses the first version of the Inventory, the Infant/Toddler HOME.

The 45 items of the HOME inventory contain the six following subscales:

1. Emotional and Verbal Responsiveness of the Mother (11 items): measures the mother’s ability to communicate with the

child.

2. Avoidance of Restriction and Punishment (8 items): measures the mother’s ability to discipline the child.

3. Organization of the Environment (6 items): measures the daily changes in the child’s environments.

4. Provision of Appropriate Play Material (9 items): measures the types of toys and their contributions to the child’s motor

skills.

5. Maternal Involvement with Child (6 items): measures the aspects in which the mother is involved in the child’s daily

life.

6. Opportunities for Variety in Daily Stimulation (5 items): measures the levels of interaction the mother and other family

members have with the child.

42

The NFP measured the HOME Inventory when the child was 12 and 24 months old.

B.2 KABC

The Kafuman Assessment Battery for Children (KABC) was developed by Alan S. Kaufman and Nadeen L.

Kaufman in 1983 with a later revision in 2004. The KABC focuses on processes required to solve problems

compared to intelligence. The KABC contains 16 subtests (10 mental processing and 6 achievement), which

can be grouped into 3 scales. Due to the nature of the subtests, 13 subtests can be taken at once, with the

mandatory age range to be between 7 to 12.5 years old. The NFP used the following 11 subtests:

1. Sequential Processing Scale (Hand Movements, Number Recall, Word Order): measures short-term memory and problem-

solving skills. It emphasizes how children are able to follow ordered sequenced.

2. Simultaneous Processing Scale (Gestalt Closure, Triangles, Matrix Analogies, Spatial Memory, Photo Series): measures

problem-solving skills. It involves several processes at once such as scenes in a partially completed picture.

3. Achievement Scale (Arithmetic, Riddles, Reading/Decoding): measures achievement and focus on applied skills and

facts learned through the home/school environment.

The NFP Program used these three scales when the child was 6 years old.

B.3 PPVT

The Peabody Picture Vocabulary Test (PPVT) is an individual verbal intelligence test that measures re-

ceptive vocabulary, developed by Llyod M. Dunn and Leota M. Dunn in 1959. It is a verbal test that lasts

between 20 and 30 minutes. The child is presented a series of pictures. There are four pictures in a page.

The examiner states a word and asks the child to associate it with a picture. The diffusion of the figures

increases over time. The exam stops when the child answers six out of eight questions incorrectly. After

completion, a raw score is given, normalized to a mean of 100 and standard deviation of 15. The NFP

Program used PPVT when the child was 6 years old.

B.4 WISC-III

The Wechsler Intelligence Scale for Children — Third Edition (WISC-III) was created in 1949. The third

edition was published in 1991 (Wechsler, 1991). WISC is an intelligence test for children between the ages

6 and 16 years old. It can be completed without reading or writing. The exam takes between 65 and 80

minutes. There are two subscales: verbal and performance, which provide a Verbal IQ (VIQ), a Performance

IQ (PIQ), and a Full Scale IQ (FSIQ). The NFP only used the coding, part of the Processing Speed Index.

43

1. Coding: the child marks rows of shapes with different lines to transcribe a digit-symbol code. It measures visual or motor

integration and visual scanning.

The NFP Program used WISC-III when the child was 6 years old.

B.5 CBCL

The Child Behavior Checklist (CBCL) is a parent-report questionnaire developed by Thomas M. Achenbach.

In it, the child is rated on several behavioral and emotional problems. The goal of the inventory is to assess

internalizing and externalizing behaviors. The responses are recorded using a Likert scale: 0 = Not True, 1

= Sometimes True, 2 = Very True. The preschool checklist (18 months to 5 years) contains 100 questions

and the school-age checklist (6 to 18 years) contains 120 questions. The preschool checklist questions can

be broken down into the following subscales: anxious/depressed, withdrawn, sleeping problems, somatic

problems, aggressive behavior, and destructive behavior. The school-age checklist questions can be broken

down into the following subscales: withdrawn, somatic complaints, anxious/depressed, social problems,

thought problems, attention problems, delinquent behavior, aggressive behavior, and other problems. The

NFP Program used the CBCL when the child was 2 and 6 years old.

B.6 C-DISC

The Computerized Diagnostic Interview Schedule for Children (C-DISC) is a comprehensive and structured

interview that studies mental health disorders such as general anxiety, panic, eating, elimination, depression,

ADHD, and conduct. The majority of the questions are “yes and no”. Some questions have additional

options such as “sometimes”. The C-DISC has about 3, 000 questions with 358 core questions that the child

must answer. About 1300 questions are asked depending on the answer to the core questions. There are 732

questions that ask about age of onset and treatment for reported symptoms. Lastly, there are about 700

questions from the optional whole-life module. The NFP Program used C-DISC when the child was 9 years

old.

B.7 MacArthur

The MacArthur Story Stem Battery (MSSB) was created by the MacArthur Narrative Working Group that

included Bretherton, Buchsbaum, and several other collaborators. The story stem method is where the

examiner presents a story to the child that culminates at a high point, at which the child is then asked

to complete the story; this type of method allows insight into the child’s inner workings of the mind. The

44

MSSB uses 15 stories and measures: dysregulated aggression, empathy/warmth, emotional integration, and

performance anxiety.

1. Dysregulated Aggression Dimension: aggression, injury, danger, destruction, dishonesty, escalation of conflict, negative

story endings, inappropriate child power, controlling toward examiner.

2. Empathy/Warmth Dimension: empathy-helping, affiliation, affection, reparation or guilt, parental warmth.

3. Emotional Integration Construct: ability to maintain story coherence with the inclusion of emotional expression. The

affects included are joy, anger, distress, concern, sadness.

4. Avoidance or Withdrawal Dimension: characters leaving the scene repetition of previous story fragments, denial of

central conflict or challenge, family characters leave, avoiding separation from parents, dissociative behaviors.

5. Performance Anxiety Dimension: unwillingness to verbalize, unresponsiveness to examiner, anxious behaviors.

The NFP Program used the MSSB when the child was 6 years old.

C Method for Permutation-based Inference

As mentioned, the standard model of program evaluation describes the observed outcome Yi of participant

i ∈ J by

Yi = DiYi,1 + (1−Di)Yi,0, (15)

where J = 1, . . . , N denotes the sample space indexing set, Di denotes the treatment assignment for

participant i ∈ J, (Di = 1 if treatment occurs, Di = 0 otherwise) and (Yi,0, Yi,1) are potential outcomes for

participant i when treatment is fixed at control and treatment status respectively.

Randomized experiments solve potential problems of selection bias by inducing independence between

counterfactual outcomes (Yi,0, Yi,1) and treatment status Di when conditioned on the pre-program variables

X used in the randomization protocol. All variables are defined in the common probability space (Ω,F ,P).

In our notation, a randomized experiment must satisfy the following assumption:

Assumption A-1. Y (d) ⊥⊥ D | X; d ∈ supp(D),

where variables X = (Xi; i ∈ J), D = (Di; i ∈ J) are N -dimensional vectors of treatment assignments

and pre-program variables, and Y (d) = (Yi,di ; i ∈ J, di ∈ 0, 1) and d ∈ supp(D) = 0, 1|J| denotes the

vector of counterfactual outcomes. In the same fashion, we represent the vector of observed outcomes of

Equation (15) by Y = (Yi; i ∈ I). The no treatment hypothesis is equivalent to the statement that the

conditional counterfactual outcome vectors share the same distribution:

45

Hypothesis H-1. Y (d)d= Y (d′) | X ; d,d′ ∈ supp(D),

Hypothesis H-1 can be restated in more tractable form:

Hypothesis H-1′. Under Assumption A-1 and Hypothesis H-1, we have that Y ⊥⊥ D | X.

Testing Hypothesis H-1′ poses some statistical challenges. First, small sample sizes cast doubt on

inference that rely on the asymptotic behavior of test statistics. We address the problem of small sample size

by generating the exact of a test statistic conditioned on data. Second, the presence of multiple outcomes

allows for the arbitrary selection of statistically significant outcomes. The selectively reporting statistically

significant outcomes is often termed cherry picking and generates a downward biased inference with smaller

p-values. We solve the problem of cherry picking by implementing a multiple-hypothesis testing based on

the stepdown procedure of (Romano and Wolf, 2005a). They explain that the stepdown procedure strongly

controls for Family-wise error rate (FWER), while classical tests do not. Also, Romano and Wolf (2005a)

shows that the strong FWER control can be obtained by ensuring a certain monotonicity condition on the

test statistics. This requirement is weaker than the assumption of subset pivotality, used in various methods

of resampling outcomes presented in Westfall and Young (1993).

In summary, our method is based on three steps. First, we seek to characterise the exact conditional

distribution of D|X. Specifically we characterize the a multiset Dx(d), defined by:

Dx(d) = d′ ∈ 0, 1|J| ; P(D = d|X = x) = P(D = d′|X = x),

such that the distribution of D conditioned on realised data is uniform among elements of Dx(d). Next we

use the assumption of null hypothesis of no treatment effects, i.e. H0 : Y ⊥⊥ D|X, to generate the exact

conditional distribution of a test statistic T (Y,D)|X. Upon it, we can construct an inference that controls

for the probability of falsely rejecting the null hypothesis. We control for this probability in two ways: (1) in

the case of single (joint) null hypothesis, we control for the standard Type-I error; (2) in the case of multiple

hypothesis inference, we control for the Family-wise error rate.

More notation is necessary to describe the method. Let K represent the indexing set for all available

outcomes Yk; k ∈ K. We represent the single (joint) null hypothesis that a set L ⊂ K of outcomes Yk; k ∈ L

are jointly independent of treatment status D conditional on pre-program variables X by

HL : YL ⊥⊥ D|X, where YL = (Yk : k ∈ L). (16)

When L is a singleton, say L = k, then the null hypothesis is given by Hk : Yk ⊥⊥ D|X. In this notation,

we can write the joint Hypothesis HL as HL = ∩k∈LHk.

46

Our goal is to tests a single (joint) null hypothesis controlling for the probability of a Type I error at

level α, that is, P( reject HL|HL is true ) ≤ α. To do so, we rely on the fact that, under Hypothesis (16),

(YL, D)|X d= (YL, gD)|X ∀ g ∈ GX , (17)

where GX comprises all the permutations within strata of X, that is,

GX = g ; g : J → J is a bijection and g(j) = j′ ⇒ (Xj) = (Xj′),

and gD is a vector defined by:

gD = (Di ∈ supp(D); i ∈ J and Di = Dg(i)).

We use Relation (17) to generate a statistical test whose exact distribution the test statistic TL(YL, gD) is

obtained by re-evaluating TL(YL, gD) as g varies in GX . Note that the inference on Hypothesis 16 is depend

on the choice of statistics. That is to say that even though any statistics TL(YL, D) whose value provide

evidence against the null hypothesis can be used, the inference is dependent on this choice of statistic. An

example of such statistic is the maximum of the t-statistic associated with the difference in means between

treated and control groups over outcomes Yk such that k ∈ L. Formally,

TL(YL, D) = maxk∈L

Tk(Yk, D), (18)

where Tk(Yk, D) is the t-statistics for outcome Yk. Relation (17) implies that TL(YL, D)|X d= TL(YL, gD)|X

for any g ∈ GX . Moreover, let d ∈ 0, 1|J| such that P(D = d|X = x) > 0, then the distribution of D

conditioned on X = x is uniform across elements of Dx(d) (see Lehmann and Romano (2005), Chapter 15).

Thus, a critical value cL,x(YL,d, α) such that P(TL(YL, D) > cL,x(YL,d, α)|X = x,HL is true) ≤ α can be

computed as:

cL,x(YL,d, α) = inft∈R

∑d′∈Dx(d)

ITL(YL,d′) ≤ t ≥ (1− α)|Dx|

,

where I· is the indicator function. The following notation is useful to further characterize cL,x(YL,d, α).

Let T(1)L,x, . . . , T

(|Dx(d)|)L,x be the sequence of increasing ordered statistics TL(YL,d

′) as d′ varies in Dx(d). In

this notation we can write the critical value as

cL,x(YL,d, α) = T(d(1−α)|Dx|e)L,x (19)

47

where dae stands for the smallest integer bigger or equal than a.

Under the null hypothesis HL, the probability of a test statistic be bigger or equal than the statistic

TL(YL,d) actually observed, i.e. the p-value, is given by:

pL,x(d) = infα∈[0,1]

cL,x(YL,d, α) ≤ TL(YL,d)

. (20)

Now let rL,x ∈ 1, . . . , |Dx(d)| be the lowest rank that the value of the observed test statistic TL(YL,d)

takes in the sequence T(1)L,x, . . . , T

(|Dx(d)|)L,x , that is to say:

rL,x = 1 +∑

d′∈Dx(d)

ITL(YL,d′) < TL(YL, d).

Thus:

T(rL,x)L,x = TL(YL,d). (21)

Then, by the ordered property of T(r)L,x; r ∈ 1, . . . , |Dx(d)| and the definition of rL,x, we have that:

pL,x(d) = 1− rL,x|Dx(d)|

. (22)

Moreover, p-value pL,x(d) complies with the following property:

P(pL,x(d) ≤ φ|X = x) ≤ φ ∀φ ∈ [0, 1].

We implemented a inference method that tests for the multiple null hypothesis that each outcome Yk; k ∈

L is independent of treatment status D conditional on pre-program variables X. The representation of these

multiple hypothesis in the same fashion as the single (joint) null hypothesis, namely:

HL = ∩k∈LHk ; Hk : Yk ⊥⊥ D|(Z,U).

The multiple hypothesis testing differs from the single (joint) hypothesis testing in the way it controls for

the probability of false rejection. Specifically, let the subset L0 be the set of true Hypothesis Hk such that

k ∈ L0 ⊂ L. Our multiple hypothesis testing controls for the familywise error rate (FWER), that is, the

probability of even one false rejection among the set of true hypothesis L0. Formally, we control for:

P( reject at least one Hk; k ∈ L0|HL0is true ) ≤ α,

48

while single (joint) hypothesis testing controls for P( reject HL|HL is true ) ≤ α.

Bonferroni or Holm are examples of inference methods that test multiple hypothesis controlling for

FWER. These methods rely upon a “least favorable” dependence structure among the p-values. The step-

down procedure of Romano and Wolf (2005a) is less conservative as it accounts for the information about

the dependence structure of p-values. The method is based on the monotonicity assumption, which, in our

case, can be stated as:

cK,x(YK ,d, α) ≥ cL0,x(YL0 ,d, α) for any subset K of L containing L0 i.e. L0 ⊂ K ⊂ L. (23)

Assumption (23) is satisfied by our choice of test statistic (18) and the fact that L0 ⊂ K.

The stepdown procedure given in Romano and Wolf (2005a) is a stepwise method summarized in the

following algorithm:

Algorithm 1.

Step 1: Set L1 = L. If

maxk∈L1

Tk(Yk,d) ≤ cL,x(YL1 ,d, α) , (24)

then stop and reject no null hypotheses; otherwise, reject any Hk with

Tk(Yk,d) > cL,x(YL1,d, α)

and go to Step 2.

...

Step j: Let Lj denote the indices of remaining null hypotheses. If

maxk∈Lj

Tk(Yk,d) ≤ cL,x(YLj ,d, α), (25)

then stop and reject no further null hypotheses; otherwise, reject any Hk with

Tk(Yk,d) > cL,x(YLj ,d, α)

and go to Step j + 1.

...

49

We can compute the multiplicity-adjusted p-values of Equations(24)–(25) in the same fashion described

by Equations (20)–(22).

C.1 Conditioning and Linearity

A typical problem in small sample randomized trials is sampling variation, where pre-program variables differ

across treatment groups by chance. One can increase the power of a statistical inference by conditioning on

those pre-program variables. Let Z be the pre-program variables that were not used in the randomization

protocol and we ought to control for.

Variables Z precede the treatment intervention and therefore Z ⊥⊥ D | X holds due to randomization.

Under the hypothesis of no-treatment, Y ⊥⊥ D | X also holds. These two relations imply that Y ⊥⊥

D | (X,Z). Likewise Section 4.1, we can use this relation to to generate a permutation test that consider

the strata formed by values of covariates X and Z. This way we can generates an inference method that

non-parametrically condition on variables X and Z.

Non-parametric conditioning through block permutation comes at a cost. A fine conditioning set decreases

the share of available data that can be permuted and a sufficiently large conditioning set prohibits the

implementation of a permutation-based test. We solve this problem by evoking linearity. That is to say, we

condition variables through a linear regression instead of a non-parametric block permutation. Anderson and

Legendre (1999) tested a range of permutation methods for linear models. They found that Freedman and

Lane (1983) generated the most consistent and reliable results among the available models in this literature.

We non-parametrically condition on variables used in the randomization protocol to achieve valid ex-

changeable properties (i.e. we use permutations in GX); We linearly condition on additional pre-program

variables Z not used in the randomization protocol. According to Freedman and Lane (1983) method,

our approach can be summarized by the following steps: (1) compute the residuals Y − Zβ such that

β = (Z ′Z)−1Z ′Y ; (2) permute these residuals according to permutations g ∈ GX . (3) add these permuted

residuals to Zβ, call it Y ; (4) regress Y on Z and the treatment statuses D. (5) we then use the t-statistic

associated with covariate D of the last regression as test statistic.

As mentioned, Beaton (1978) and Freedman and Lane (1983) suggested a permutation inference based

on Shuffle Residuals. Buy this I mean regressing Y on X, shuffling the residuals from this regression, and

adding them to the predicted Y, say Y , to form a new variable, say Y , which is then regressed on Z and D.

Formally, let the regression:

Y = Zβ +Dδ + ε,

where Z stands for the pre-program variables we wish to control for and includes a vector of elements ones

50

that play the role of a contant term for the regression. Error term ε is a mean-zero exogenous random

variable independent of Z and D.

Now let Bg; g ∈ GX be a permutation matrix associated with a permutation g in GX . Let also the operator

that projects a vector in the orthogonal space generated by columns of Z be MZ = I−Z(Z ′Z)−1Z ′, where I

denotes the identity matrix. As properties of Matrix MZ , we can say that MZ is symmetric and idempotent,

that is:

MZ = M ′Z = MZMZ = M ′ZMZ . (26)

The estimated residuals of Y generated by the the regression

Y = Zβ + ε

is given by e = MZY. The predicted outcome based on this regression is given by: Y = Z(Z ′Z)−1X ′Y.

We define the new outcome based on the sum of the predicted outcome Y with permuted errors e

according to permutation g ∈ GX as

Y = Y +Bg e. (27)

We then use the newly computed outcome in the following regression:

Y = Zβ +Dδ + ε. (28)

We now examine the δ estimate on Equation (28). This estimate ia actually the same as the one computed

by the following regression:

MZ Y = MZDδ + ε. (29)

Thus. by applying the Ordinary Least Square formula, we obtain:

δg = (D′M ′ZMZD)−1D′M ′ZMZ Y . (30)

51

We now use previous equations to transform Equation (30) into a more general formula:

δg = (D′M ′ZMZD)−1D′M ′ZMZ Y by (30),

= (D′MZDMZD′MZ Y by (26),

= (D′MZDMZD′MZ(Y +Bg e) by (27) ,

= (D′MZDMZD′MZ((I −MZ)Y +Bg e) because MZ = I − Z(Z ′Z)−1Z ′,

= (D′MZDMZD′((MZ −MZ)Y +MZBg e),

= (D′MZDMZD′(MZBg e),

= (D′MZDMZD′(MZBgMZY ) because e = MZY . (31)

Kennedy (1995) pointed out that Freedman and Lane (1983) algorithm is summarized by Equation 31.

Notationally, we can use TZ(Y, gD); g ∈ GX (instead of T (Y, gD); g ∈ GX) to represent the distribution of

the test statistic associated with the t-statsitic of the D covariate in the Freedman and Lane (1983) regression

just described. Using this notation, the analysis of the previous sections holds unaltered.

D Additional Baseline Tables

These tables explore differences in pre-program variables between treatment and control groups at each

follow up wave. These results are presented in order to highlight that there were no differential patterns of

attrition across waves.

52

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80.

420

0.20

50.

405

0.51

50.

219

0.41

40.

222

0.41

80.

945

0.23

70.

426

0.18

80.

393

0.31

7G

reat

er th

an $

1100

00.

161

0.36

80.

125

0.33

20.

222

0.18

80.

391

0.08

10.

274

0.00

50.

134

0.34

10.

168

0.37

60.

434

Inco

me,

No

Resp

onse

0.09

20.

289

0.08

00.

272

0.62

50.

085

0.27

90.

111

0.31

60.

476

0.09

80.

298

0.05

00.

218

0.09

9

Regio

n of

Resid

ence

Inne

r City

0.29

50.

456

0.29

00.

455

0.90

50.

286

0.45

30.

303

0.46

20.

755

0.30

40.

461

0.27

70.

450

0.62

8Bi

sson

0.19

20.

394

0.21

50.

412

0.50

60.

179

0.38

40.

232

0.42

40.

282

0.20

50.

405

0.19

80.

400

0.87

9Ca

wth

on0.

194

0.39

60.

190

0.39

30.

900

0.21

00.

408

0.16

20.

370

0.29

70.

179

0.38

40.

218

0.41

50.

420

Hol

lywoo

d0.

319

0.46

70.

305

0.46

20.

719

0.32

60.

470

0.30

30.

462

0.68

40.

313

0.46

50.

307

0.46

40.

920

Mat

ernal

Men

tal H

ealth M

ater

nal I

Q (S

hipl

ey)

96.2

7010

.287

96.4

4010

.360

0.84

796

.223

10.2

7996

.061

10.6

180.

898

96.3

1710

.317

96.8

1210

.140

0.68

6M

ater

nal B

avol

ek S

core

99.7

947.

657

101.

133

8.50

20.

057

100.

091

7.41

110

1.43

18.

727

0.18

699

.499

7.89

910

0.84

28.

309

0.17

3M

ater

nal M

enta

l Hea

lth10

0.18

49.

979

99.4

4710

.352

0.39

899

.717

9.77

799

.741

10.1

720.

984

100.

649

10.1

7899

.158

10.5

680.

235

Self-

Effi

cacy

100.

083

10.0

1799

.788

9.86

60.

727

100.

862

9.77

810

0.58

39.

253

0.80

699

.307

10.2

1299

.008

10.4

190.

810

Mat

erna

l Mas

tery

100.

065

10.2

1399

.535

9.99

20.

537

99.8

7910

.155

99.1

7310

.246

0.56

810

0.25

010

.290

99.8

919.

774

0.76

4M

ater

nal P

sych

olog

ical R

esou

rces

100.

060

10.0

4599

.533

10.6

490.

554

100.

030

9.71

199

.619

10.6

340.

743

100.

090

10.3

9099

.448

10.7

150.

615

Mat

ernal

Hea

lth C

hara

cteris

tics

Mat

erna

l Heig

ht16

4.55

77.

253

164.

064

6.56

90.

397

164.

331

7.40

416

4.47

26.

546

0.86

516

4.78

17.

108

163.

651

6.60

10.

170

Pre-

Preg

nanc

y W

eight

62.0

9714

.866

62.3

3913

.588

0.83

962

.828

13.7

7561

.394

12.3

750.

355

61.3

6215

.885

63.2

6414

.683

0.29

4G

esta

tiona

l Age

(Int

ake)

16.5

605.

794

16.6

305.

728

0.88

716

.402

5.74

616

.364

5.59

60.

955

16.7

195.

850

16.8

915.

870

0.80

7

Mat

ernal

Socia

l Sup

port

Gra

ndm

othe

r Soc

ial S

uppo

rt10

0.19

79.

474

101.

517

8.56

60.

081

99.3

5710

.486

101.

434

9.10

00.

073

101.

034

8.28

510

1.59

98.

054

0.56

3H

usba

nd/B

oyfr

iend

Socia

l Sup

port

100.

030

9.99

410

0.70

49.

754

0.42

199

.892

10.0

5799

.907

9.52

40.

990

100.

169

9.95

210

1.48

49.

960

0.27

2

Mat

ernal

Risk

y Beh

avior

sA

lcoho

l Con

sum

ptio

n (P

ast 2

wks

)0.

043

0.20

20.

050

0.21

80.

680

0.03

60.

186

0.07

10.

258

0.22

80.

049

0.21

70.

030

0.17

10.

385

Smok

ing

(Pas

t 3 d

ays)

0.08

50.

279

0.11

00.

314

0.33

40.

081

0.27

30.

121

0.32

80.

284

0.08

90.

286

0.09

90.

300

0.78

4U

sed

Miar

juan

a (P

ast 2

wks

)0.

034

0.30

90.

070

0.86

00.

560

0.02

70.

283

0.02

00.

201

0.80

90.

040

0.33

20.

119

1.19

40.

517

Use

d Co

cain

e (P

ast 2

wks

)0.

007

0.14

20.

000

0.00

00.

318

0.00

00.

000

0.00

00.

000

.0.

013

0.20

00.

000

0.00

00.

318

Sexu

ally

Tran

smitt

ed D

iseas

es0.

333

0.47

20.

375

0.48

50.

301

0.33

00.

471

0.35

40.

480

0.68

80.

335

0.47

30.

396

0.49

20.

294

Wh

ole

Sam

ple

Fem

ale

Sam

ple

Mal

e Sa

mp

le

Notes:

This

table

pre

sents

the

stati

stic

al

desc

ripti

on

of

sele

cte

dpre

-pro

gra

mvari

able

saft

er

6years

of

the

pro

gra

m.

The

firs

tcolu

mn

of

the

table

giv

es

the

vari

able

desc

ripti

on.

Vari

able

sare

div

ided

into

gro

ups

that

share

sim

ilar

meanin

gs.

The

rem

ain

der

of

the

table

consi

sts

of

the

desc

ripti

on

of

the

blo

cks

of

vari

able

sass

ocia

ted

wit

hth

ew

hole

sam

ple

,th

efe

male

sam

ple

and

the

male

sam

ple

.E

ach

blo

ckhas

6colu

mns:

(1)

Contr

ol

mean

(CM

ean),

(2)

Contr

ol

standard

devia

tion

(CSD

),(3

)T

reatm

ent

mean

(TM

ean),

(4)

Tre

atm

ent

standard

devia

tion

(TSD

),and

(5)

Asy

mpto

ticp-v

alu

eass

ocia

ted

wit

hth

ediff

ere

nce

inm

eans.

Boldp-v

alu

es

indic

ate

that

the

t-st

ati

stic

betw

een

the

contr

ol

and

the

treatm

ent

means

issi

gnifi

cant

at

the

10%

level.

53

Tab

leD

.2:

Des

crip

tive

Sta

tist

icof

Base

lin

eC

hara

cter

isti

cs(Y

ear

12)

C M

ean

C SD

T M

ean

T SD

Pval

C M

ean

C SD

T M

ean

T SD

Pval

C M

ean

C SD

T M

ean

T SD

Pval

Back

groun

d Ch

arac

terist

icsM

ater

nal R

ace

(Blac

k)0.

057

0.23

20.

084

0.27

80.

244

0.05

60.

231

0.06

50.

248

0.77

00.

057

0.23

30.

101

0.30

30.

208

Mar

ital S

tatu

s (M

arrie

d)0.

014

0.11

90.

010

0.10

20.

690

0.00

50.

069

0.01

10.

104

0.60

30.

024

0.15

30.

010

0.10

10.

346

Mat

erna

l Age

18.0

523.

215

18.0

473.

268

0.98

618

.258

3.32

418

.174

3.58

10.

847

17.8

423.

093

17.9

292.

960

0.81

2Y

ears

of E

duca

tion

10.2

541.

860

10.0

732.

025

0.29

610

.324

1.82

810

.043

2.08

00.

265

10.1

821.

893

10.1

011.

982

0.73

5M

othe

r in

Scho

ol0.

599

0.49

10.

565

0.49

70.

444

0.55

70.

498

0.59

80.

493

0.50

50.

641

0.48

10.

535

0.50

10.

081

Hea

d of

Hou

seho

ld is

Em

ploy

ed0.

556

0.49

70.

495

0.50

10.

163

0.58

50.

494

0.47

80.

502

0.08

90.

526

0.50

10.

510

0.50

20.

793

% o

f Cen

sus T

ract

Belo

w P

over

ty34

.800

21.3

8035

.727

20.1

850.

606

33.6

3220

.150

37.2

0822

.390

0.18

935

.990

22.5

5034

.351

17.9

000.

492

Hou

seho

ld D

ensit

y0.

940

0.48

61.

023

0.55

90.

081

0.96

90.

483

1.04

90.

662

0.29

90.

911

0.48

80.

998

0.44

50.

123

Tota

l Hou

sehold

Incom

e (Pa

st 6

Mon

ths)

Less

than

$30

000.

280

0.44

90.

361

0.48

20.

048

0.27

70.

449

0.33

70.

475

0.30

50.

282

0.45

10.

384

0.48

90.

083

$300

0 - $

6999

0.24

20.

429

0.23

60.

425

0.87

00.

239

0.42

80.

239

0.42

90.

995

0.24

40.

431

0.23

20.

424

0.82

2$7

000

- $10

999

0.23

00.

421

0.18

80.

392

0.23

80.

230

0.42

20.

217

0.41

50.

808

0.23

00.

422

0.16

20.

370

0.15

1G

reat

er th

an $

1100

00.

159

0.36

60.

126

0.33

20.

269

0.17

80.

384

0.08

70.

283

0.02

20.

139

0.34

70.

162

0.37

00.

606

Inco

me,

No

Resp

onse

0.09

00.

287

0.08

90.

285

0.96

70.

075

0.26

40.

120

0.32

60.

251

0.10

50.

308

0.06

10.

240

0.16

6

Regio

n of

Resid

ence

Inne

r City

0.29

10.

455

0.28

30.

452

0.82

50.

282

0.45

10.

293

0.45

80.

836

0.30

10.

460

0.27

30.

448

0.60

3Bi

sson

0.19

40.

396

0.22

50.

419

0.39

10.

169

0.37

60.

239

0.42

90.

176

0.22

00.

415

0.21

20.

411

0.87

4Ca

wth

on0.

204

0.40

30.

188

0.39

20.

657

0.22

10.

416

0.15

20.

361

0.14

80.

187

0.39

10.

222

0.41

80.

477

Hol

lywoo

d0.

310

0.46

30.

304

0.46

10.

867

0.32

90.

471

0.31

50.

467

0.81

90.

292

0.45

60.

293

0.45

70.

985

Mat

ernal

Men

tal H

ealth M

ater

nal I

Q (S

hipl

ey)

96.0

669.

987

96.7

5910

.181

0.43

396

.075

10.0

0296

.011

10.7

890.

961

96.0

579.

997

97.4

559.

585

0.24

0M

ater

nal B

avol

ek S

core

99.9

477.

604

101.

078

8.56

80.

118

100.

190

7.48

910

1.42

78.

718

0.23

899

.701

7.72

910

0.75

48.

459

0.29

6M

ater

nal M

enta

l Hea

lth10

0.10

69.

744

99.5

5010

.612

0.53

899

.766

9.52

999

.909

10.4

290.

911

100.

451

9.96

899

.216

10.8

210.

339

Self-

Effi

cacy

99.8

139.

995

99.6

719.

912

0.87

010

0.64

09.

746

100.

192

9.33

90.

705

98.9

7310

.197

99.1

8610

.440

0.86

6M

ater

nal M

aste

ry10

0.05

910

.236

99.4

4610

.098

0.48

999

.954

10.3

0199

.085

10.5

330.

507

100.

165

10.1

9399

.781

9.71

80.

751

Mat

erna

l Psy

chol

ogica

l Res

ourc

es99

.857

9.65

299

.664

10.9

140.

834

99.9

479.

401

99.5

3710

.896

0.75

499

.765

9.92

399

.782

10.9

840.

990

Mat

ernal

Hea

lth C

hara

cteris

tics

Mat

erna

l Heig

ht16

4.59

57.

349

164.

303

6.68

00.

630

164.

297

7.48

316

4.90

46.

664

0.48

516

4.89

67.

217

163.

732

6.68

00.

170

Pre-

Preg

nanc

y W

eight

62.3

9815

.149

62.7

3513

.786

0.78

663

.078

14.0

7661

.880

12.3

690.

458

61.7

0116

.178

63.5

3015

.003

0.33

2G

esta

tiona

l Age

(Int

ake)

16.4

745.

830

16.6

075.

639

0.78

916

.235

5.79

116

.228

5.48

90.

993

16.7

185.

873

16.9

605.

780

0.73

3

Mat

ernal

Socia

l Sup

port

Gra

ndm

othe

r Soc

ial S

uppo

rt10

0.40

79.

331

101.

623

8.40

60.

110

99.6

2410

.361

101.

370

9.30

60.

148

101.

200

8.10

210

1.85

87.

514

0.48

5H

usba

nd/B

oyfr

iend

Socia

l Sup

port

100.

266

9.95

110

0.29

99.

986

0.96

910

0.02

39.

949

99.8

339.

700

0.87

710

0.51

19.

971

100.

731

10.2

750.

859

Mat

ernal

Risk

y Beh

avior

sA

lcoho

l Con

sum

ptio

n (P

ast 2

wks

)0.

040

0.19

70.

047

0.21

20.

710

0.03

80.

191

0.06

50.

248

0.34

50.

043

0.20

30.

030

0.17

20.

568

Smok

ing

(Pas

t 3 d

ays)

0.08

10.

273

0.10

50.

307

0.35

60.

075

0.26

50.

120

0.32

60.

255

0.08

60.

281

0.09

10.

289

0.89

1U

sed

Miar

juan

a (P

ast 2

wks

)0.

036

0.31

80.

073

0.88

00.

566

0.02

80.

291

0.02

20.

209

0.82

40.

043

0.34

40.

121

1.20

60.

528

Use

d Co

cain

e (P

ast 2

wks

)0.

007

0.14

60.

000

0.00

00.

318

0.00

00.

000

0.00

00.

000

.0.

014

0.20

80.

000

0.00

00.

318

Sexu

ally

Tran

smitt

ed D

iseas

es0.

347

0.47

70.

372

0.48

50.

554

0.33

50.

473

0.33

70.

475

0.97

20.

359

0.48

10.

404

0.49

30.

450

Wh

ole

Sam

ple

Fem

ale

Sam

ple

Mal

e Sa

mp

le

Notes:

This

table

pre

sents

the

stati

stic

al

desc

ripti

on

of

sele

cte

dpre

-pro

gra

mvari

able

saft

er

6years

of

the

pro

gra

m.

The

firs

tcolu

mn

of

the

table

giv

es

the

vari

able

desc

ripti

on.

Vari

able

sare

div

ided

into

gro

ups

that

share

sim

ilar

meanin

gs.

The

rem

ain

der

of

the

table

consi

sts

of

the

desc

ripti

on

of

the

blo

cks

of

vari

able

sass

ocia

ted

wit

hth

ew

hole

sam

ple

,th

efe

male

sam

ple

and

the

male

sam

ple

.E

ach

blo

ckhas

6colu

mns:

(1)

Contr

ol

mean

(CM

ean),

(2)

Contr

ol

standard

devia

tion

(CSD

),(3

)T

reatm

ent

mean

(TM

ean),

(4)

Tre

atm

ent

standard

devia

tion

(TSD

),and

(5)

Asy

mpto

ticp-v

alu

eass

ocia

ted

wit

hth

ediff

ere

nce

inm

eans.

Boldp-v

alu

es

indic

ate

that

the

t-st

ati

stic

betw

een

the

contr

ol

and

the

treatm

ent

means

issi

gnifi

cant

at

the

10%

level.

54

E Additional Inference Results: Addressing Attrition using In-

verse Propensity Weights

One aspect of the NFP that may cause concern is attrition. In order to address this we proceed as follows. We

estimate by OLS a linear regression model which dependent variable is binary and equal to one if the mother

represents an attrition case. We choose the model as to maximize the R2 and incorporate pre-program

variables with very few missing values. This permits us to establish the set of variables that provides the

maximum amount of information when it comes to estimate the probability of attrition. Then, we predict

the probability of attrition through a Logit model and apply an inverse probability weighting scheme to our

estimations. The results do not change much after this correction. Tables E.4–10 show these results. The

tables can be read in the same way as Tables 7–10 in the paper.

55

Tab

leE

.3:

Usi

ng

Logit

toO

bta

inP

rob

ab

ilit

ies

Sam

ple

Psy. Res.Pct. Pov.SmokerDrinkerEduc.Mom SupportHus./BF SupportRaceHH Emp.AgeAge SquaredSTDs# STDsMental HealthMasteryBavolekIncome (5 Cat.)Gest. Wks.HeightPre. Preg. Wt.Schooling

LR C

hi2

Prob

. > C

hi2

AIC

BIC

Trea

tmen

t Fem

ales

Yea

r 12

xx

xx

xx

xx

xx

xx

x25

.79

0.06

45.2

690

.70

Yea

r 9x

xx

xx

xx

xx

x22

.53

0.05

51.3

988

.81

Yea

r 6x

xx

xx

xx

xx

17.6

20.

0230

.361

54.4

17Y

ear 4

.5x

xx

xx

xx

xx

16.6

70.

0521

.291

48.0

19Y

ear 2

xx

xx

xx

xx

xx

24.1

80.

01-2

0.92

8.79

Cont

rol F

emale

s Yea

r 12

xx

xx

xx

xx

20.3

10.

0120

5.54

237.

16Y

ear 9

xx

xx

xx

xx

19.2

90.

0112

2.33

153.

81Y

ear 6

xx

xx

xx

x17

.84

0.01

103.

7213

1.73

Yea

r 4.5

xx

xx

xx

x14

.68

0.02

114.

5413

9.16

Yea

r 2x

xx

xx

xx

10.0

00.

12-1

9.62

5.01

Trea

tmen

t Male

s Yea

r 12

xx

xx

xx

xx

xx

22.9

70.

0410

6.90

144.

96Y

ear 9

xx

xx

9.38

0.05

82.5

596

.14

Yea

r 6x

xx

xx

xx

x17

.66

0.02

62.9

187

.37

Yea

r 4.5

xx

xx

xx

xx

xx

x14

.03

0.23

46.0

478

.66

Yea

r 2x

xx

xx

x15

.73

0.02

-3.5

415

.49

Cont

rol M

ales Y

ear 1

2x

xx

xx

xx

xx

32.0

70.

0015

5.12

200.

37Y

ear 9

xx

xx

xx

x37

.02

0.00

95.7

213

4.01

Yea

r 6x

xx

xx

xx

x34

.24

0.00

68.2

010

9.91

Yea

r 4.5

xx

xx

xx

xx

xx

22.0

30.

0212

1.86

160.

14Y

ear 2

xx

xx

12.3

80.

01-2

4.20

-6.6

3

Notes:

The

table

desc

rib

es

the

pre

-pro

gra

mvari

able

suse

dto

calc

ula

teth

ein

vers

epro

babilit

yw

eig

hts

.T

he

firs

tcolu

mn

pro

vid

es

the

four

div

isio

ngro

ups:

treatm

ent

fem

ale

s,contr

ol

fem

ale

s,tr

eatm

ent

male

s,and

contr

ol

male

s.A

ddit

ionally,

there

isa

corr

esp

ondin

gti

me

peri

od

for

each

row

.T

he

next

23

colu

mns

repre

sents

the

set

of

pre

-pro

gra

mch

ara

cte

rist

ics

that

were

use

dfo

rlo

git

.A

“x”

repre

sents

that

that

vari

able

was

use

dfo

rth

esp

ecifi

csa

mple

and

tim

ep

eri

od.

The

colu

mn

lab

ele

d“L

RC

hi2

”is

the

chi-

square

dcalc

ula

ted

usi

ng

the

logit

regre

ssio

nand

the

next

colu

mn,

“P

rob.>

Chi2

,”pro

vid

es

the

corr

esp

ondin

gp-v

alu

es.

The

last

two

colu

mns,

AIC

and

BIC

,pro

vid

es

the

Akaik

ein

form

ati

on

cri

teri

on

and

Bayesi

an

info

rmati

on

cri

teri

on

resp

ecti

vely

.

56

Tab

leE

.4:

Ch

ild

Hea

lth

Ou

tcom

es

Out

com

e D

escr

iptio

nC

ntr.

Mea

nC

d. D

iff. M

n.C

d. E

ff. S

ize

Asy

P-v

alSi

ngle

P-v

alSt

epdo

wn

Cnt

r. M

ean

Cd.

Diff

. Mn.

Cd.

Eff

. Siz

eA

sy P

-val

Sing

le P

-val

Step

dow

nBi

rth O

utco

mes

for C

hild

Plac

enta

Wei

ght

683.

488

-11.

638

-0.0

730.

707

0.46

70.

717

662.

401

27.9

650.

157

0.11

20.014

0.036

Birt

h W

eigh

t30

50.5

65-1

28.4

56-0

.235

0.96

60.

903

0.90

329

93.7

2620

4.97

70.

292

0.006

0.000

0.001

Hea

d C

ircum

fere

nce

33.2

570.

038

0.02

30.

425

0.20

30.

459

33.5

060.

327

0.14

60.

107

0.060

0.060

Leng

th49

.652

0.23

40.

087

0.23

60.

202

0.51

349

.908

0.71

10.

196

0.042

0.018

0.033

Ges

tatio

nal A

ge a

t Del

iver

y39

.092

-0.5

45-0

.242

0.94

00.

854

0.91

938

.526

0.74

50.

214

0.028

0.001

0.005

Chi

ld H

ealth

Out

com

es (Y

ear 1

2)A

ny I

njur

ies

sinc

e La

st I

nter

view

0.17

5-0

.043

-0.1

220.

171

0.21

60.

386

0.23

2-0

.059

-0.1

490.

132

0.12

00.

474

# H

ospi

taliz

atio

ns fo

r Inj

urie

s si

nce

Last

Int

ervi

ew0.

009

-0.0

11-0

.116

0.13

80.

185

0.45

10.

011

-0.0

13-0

.134

0.13

20.

170

0.58

2To

tal #

Inj

urie

s si

nce

Last

Int

ervi

ew0.

200

-0.0

68-0

.156

0.10

20.074

0.22

40.

278

-0.0

57-0

.110

0.21

20.

268

0.68

5H

ospi

taliz

ed s

ince

Las

t Int

ervi

ew0.

059

-0.0

44-0

.226

0.033

0.035

0.14

00.

040

0.05

40.

299

0.97

50.

890

0.89

0H

ave

Chr

onic

Con

ditio

n/H

ealth

Pro

blem

0.20

3-0

.003

-0.0

090.

473

0.63

90.

639

0.36

00.

077

0.16

30.

885

0.84

90.

965

Stan

dard

ized

Chi

ld B

MI

1.09

0-0

.240

-0.2

770.019

0.012

0.060

0.77

80.

224

0.25

70.

968

0.83

30.

988

Bas

ic S

tatis

tics

Blo

ck P

erm

. FL

Bas

ic S

tatis

tics

Blo

ck P

erm

. FL

Fem

ales

Mal

es

Notes:

The

firs

tcolu

mn

pro

vid

es

the

outc

om

edesc

ripti

on.

Our

resu

lts

are

pre

sente

din

six

colu

mns

for

each

gender.

The

firs

tcolu

mn

(Cntr

.M

ean)

of

each

resu

ltse

tsh

ow

sth

em

ean

for

the

contr

ol

gro

up.

When

facto

rsc

ore

sw

ere

com

pute

d,

we

set

the

mean

inth

econtr

ol

gro

up

tozero

.T

he

second

colu

mn

(Cd.

Diff

.M

n.)

giv

es

the

condit

ional

diff

ere

nce

inm

eans

betw

een

the

treatm

ent

gro

up

and

the

contr

ol

gro

up.

The

thir

dcolu

mn

(Cd.

Eff

.Siz

e)

calc

ula

tes

the

condit

ional

eff

ect

size

for

the

resp

ecti

ve

gro

up.

The

fourt

hcolu

mn

(Asy

.P

-val.)

pro

vid

es

the

asy

mpto

ticp-v

alu

efo

rth

eone-s

ided

single

hyp

oth

esi

ste

stass

ocia

ted

wit

hth

et-

stati

stic

for

the

diff

ere

nce

inm

eans

betw

een

treatm

ent

and

contr

ol

gro

ups.

As

menti

oned

inSecti

on

2,

the

contr

ol

gro

up

stands

for

the

ori

gin

al

treatm

ent

gro

up

2of

the

NF

Pexp

eri

ment

and

the

treatm

ent

gro

up

stands

for

the

ori

gin

al

gro

up

4.

The

fift

hcolu

mn

(Blo

ckP

erm

.F

L/Sin

gle

P-v

al.)

pre

sents

the

one-s

ided

rest

ricte

dp

erm

uta

tionp-v

alu

es

for

the

single

-hyp

oth

esi

ste

stin

gbase

don

thet-

stati

stic

ass

ocia

ted

wit

hth

etr

eatm

ent

indic

ato

rin

the

Fre

edm

an

and

Lane

(1983)

regre

ssio

nas

desc

rib

ed

inSecti

on

4.

By

rest

ricte

dp

erm

uta

tion

we

mean

that

perm

uta

tions

are

done

wit

hin

stra

tadefined

by

the

base

line

vari

able

suse

din

the

random

izati

on

pro

tocol:

mate

rnal

age

and

race,

gest

ati

onal

age

at

enro

llm

ent,

em

plo

ym

ent

statu

sof

the

head

of

the

house

hold

,and

geogra

phic

regio

n.

The

covari

ate

suse

din

the

Fre

edm

an

and

Lane

(1983)

regre

ssio

nare

:m

ate

rnal

heig

ht,

house

hold

incom

e,

gra

ndm

oth

er

supp

ort

,m

ate

rnal

pare

nti

ng

att

itudes

and

moth

er

curr

entl

yin

school.

Fin

ally,

the

last

colu

mn

(Blo

ckP

erm

.F

L/Ste

pdow

n)

pro

vid

esp-v

alu

es

that

account

for

mult

iple

-hyp

oth

esi

ste

stin

gbase

don

the

Ste

pdow

nalg

ori

thm

of

Rom

ano

and

Wolf

(2005a).

Blo

cks

of

outc

om

es

that

are

test

ed

join

tly

are

separa

ted

by

lines.

The

sele

cti

on

of

blo

cks

of

outc

om

es

isdone

on

the

basi

sof

their

meanin

g.

Outc

om

es

that

share

sim

ilar

meanin

gare

gro

up

ed

togeth

er.

Fem

ale

mate

rnal

outc

om

es

all

ude

tom

oth

ers

whose

firs

tch

ild

isa

gir

l.L

ikew

ise,

male

mate

rnal

outc

om

es

alludes

tom

oth

ers

whose

firs

tch

ild

isa

boy.

The

resu

lts

inth

ista

ble

use

an

invers

epro

babilit

yw

eig

hti

ng

schem

eto

addre

ssatt

riti

on.

The

weig

hts

are

base

don

the

pre

dic

ted

pro

babilit

yto

dro

pth

esa

mple

.T

he

pre

dic

tion

isbase

don

aL

ogit

model

that

isdesc

rib

ed

at

the

begin

nin

gof

this

secti

on.

57

Tab

leE

.5:

Fam

ily

Envir

on

men

t

Out

com

e D

escr

iptio

nC

ntr.

Mea

nC

d. D

iff. M

n.C

d. E

ff. S

ize

Asy

P-v

alSi

ngle

P-v

alSt

epdo

wn

Cnt

r. M

ean

Cd.

Diff

. Mn.

Cd.

Eff

. Siz

eA

sy P

-val

Sing

le P

-val

Step

dow

nH

ome E

nviro

nmen

t, Pa

rent

ing (

Year

1) -

Fac

tor S

core

sH

ome

Obs

erva

tion

Mea

sure

men

t of

the

Env

ironm

ent (

HO

ME

)0.

000

0.33

80.

338

0.004

0.004

0.004

-0.0

050.

154

0.15

40.

114

0.079

0.079

Non

-Abu

ssiv

e Pa

rent

ing

Atti

tude

s (B

avol

ek)

0.00

70.

294

0.29

30.010

0.003

0.006

-0.0

020.

364

0.36

40.002

0.001

0.002

Hom

e Env

ironm

ent,

Pare

ntin

g (Ye

ar 2

)- Fa

ctor S

core

sH

ome

Obs

erva

tion

Mea

sure

men

t of

the

Env

ironm

ent (

HO

ME

)0.

001

0.29

80.

297

0.010

0.004

0.007

-0.0

080.

116

0.11

60.

186

0.11

10.

111

Non

-Abu

ssiv

e Pa

rent

ing

Atti

tude

s (B

avol

ek)

0.01

20.

374

0.37

20.003

0.005

0.005

-0.0

050.

481

0.48

10.000

0.001

0.001

Mat

erna

l Men

tal H

ealth

(Yea

r 2)

Anx

iety

-0.0

01-0

.226

-0.2

260.042

0.038

0.086

0.01

2-0

.052

-0.0

520.

340

0.34

80.

633

Dep

ress

ion

0.00

0-0

.115

-0.1

150.

180

0.10

20.

169

0.01

0-0

.011

-0.0

110.

465

0.52

40.

692

Posi

tive

Wel

l-Bei

ng-0

.002

0.09

60.

096

0.22

20.

413

0.41

3-0

.006

-0.2

13-0

.214

0.95

00.

947

0.94

7E

mot

iona

l Sta

bilit

y0.

001

0.18

50.

185

0.076

0.056

0.11

3-0

.012

0.04

20.

042

0.36

70.

427

0.68

9O

vera

ll M

enta

l Hea

lth0.

000

0.19

30.

193

0.066

0.066

0.12

2-0

.011

-0.0

47-0

.047

0.64

40.

666

0.77

2Se

lf-E

stee

m0.

011

0.28

30.

283

0.014

0.003

0.014

-0.0

110.

045

0.04

50.

367

0.46

70.

707

Mas

tery

0.00

90.

251

0.25

00.030

0.018

0.057

-0.0

100.

253

0.25

20.026

0.040

0.13

7

Tota

l Cos

t of

Gov

t. Pr

ogra

ms (

Chi

ld A

ges 1

- 12

Yea

rs)

AFD

C/T

AN

F25

85.2

86-1

77.2

26-0

.070

0.28

00.

627

0.62

726

57.0

84-4

26.4

34-0

.165

0.073

0.087

0.15

6Fo

od S

tam

p29

00.6

13-3

74.6

02-0

.229

0.026

0.24

10.

362

3191

.672

-288

.782

-0.1

870.061

0.11

80.

155

Med

icai

d34

62.0

64-3

67.1

66-0

.221

0.035

0.27

50.

377

3747

.045

-271

.420

-0.1

830.068

0.15

30.

153

Fem

ales

Mal

esB

asic

Sta

tistic

sB

lock

Per

m. F

LB

asic

Sta

tistic

sB

lock

Per

m. F

L

Notes:

The

firs

tcolu

mn

pro

vid

es

the

outc

om

edesc

ripti

on.

Our

resu

lts

are

pre

sente

din

six

colu

mns

for

each

gender.

The

firs

tcolu

mn

(Cntr

.M

ean)

of

each

resu

ltse

tsh

ow

sth

em

ean

for

the

contr

ol

gro

up.

When

facto

rsc

ore

sw

ere

com

pute

d,

we

set

the

mean

inth

econtr

ol

gro

up

tozero

.T

he

second

colu

mn

(Cd.

Diff

.M

n.)

giv

es

the

condit

ional

diff

ere

nce

inm

eans

betw

een

the

treatm

ent

gro

up

and

the

contr

ol

gro

up.

The

thir

dcolu

mn

(Cd.

Eff

.Siz

e)

calc

ula

tes

the

condit

ional

eff

ect

size

for

the

resp

ecti

ve

gro

up.

The

fourt

hcolu

mn

(Asy

.P

-val.)

pro

vid

es

the

asy

mpto

ticp-v

alu

efo

rth

eone-s

ided

single

hyp

oth

esi

ste

stass

ocia

ted

wit

hth

et-

stati

stic

for

the

diff

ere

nce

inm

eans

betw

een

treatm

ent

and

contr

ol

gro

ups.

As

menti

oned

inSecti

on

2,

the

contr

ol

gro

up

stands

for

the

ori

gin

al

treatm

ent

gro

up

2of

the

NF

Pexp

eri

ment

and

the

treatm

ent

gro

up

stands

for

the

ori

gin

al

gro

up

4.

The

fift

hcolu

mn

(Blo

ckP

erm

.F

L/Sin

gle

P-v

al.)

pre

sents

the

one-s

ided

rest

ricte

dp

erm

uta

tionp-v

alu

es

for

the

single

-hyp

oth

esi

ste

stin

gbase

don

thet-

stati

stic

ass

ocia

ted

wit

hth

etr

eatm

ent

indic

ato

rin

the

Fre

edm

an

and

Lane

(1983)

regre

ssio

nas

desc

rib

ed

inSecti

on

4.

By

rest

ricte

dp

erm

uta

tion

we

mean

that

perm

uta

tions

are

done

wit

hin

stra

tadefined

by

the

base

line

vari

able

suse

din

the

random

izati

on

pro

tocol:

mate

rnal

age

and

race,

gest

ati

onal

age

at

enro

llm

ent,

em

plo

ym

ent

statu

sof

the

head

of

the

house

hold

,and

geogra

phic

regio

n.

The

covari

ate

suse

din

the

Fre

edm

an

and

Lane

(1983)

regre

ssio

nare

:m

ate

rnal

heig

ht,

house

hold

incom

e,

gra

ndm

oth

er

supp

ort

,m

ate

rnal

pare

nti

ng

att

itudes

and

moth

er

curr

entl

yin

school.

Fin

ally,

the

last

colu

mn

(Blo

ckP

erm

.F

L/Ste

pdow

n)

pro

vid

esp-v

alu

es

that

account

for

mult

iple

-hyp

oth

esi

ste

stin

gbase

don

the

Ste

pdow

nalg

ori

thm

of

Rom

ano

and

Wolf

(2005a).

Blo

cks

of

outc

om

es

that

are

test

ed

join

tly

are

separa

ted

by

lines.

The

sele

cti

on

of

blo

cks

of

outc

om

es

isdone

on

the

basi

sof

their

meanin

g.

Outc

om

es

that

share

sim

ilar

meanin

gare

gro

up

ed

togeth

er.

Fem

ale

mate

rnal

outc

om

es

all

ude

tom

oth

ers

whose

firs

tch

ild

isa

gir

l.L

ikew

ise,

male

mate

rnal

outc

om

es

alludes

tom

oth

ers

whose

firs

tch

ild

isa

boy.

The

resu

lts

inth

ista

ble

use

an

invers

epro

babilit

yw

eig

hti

ng

schem

eto

addre

ssatt

riti

on.

The

weig

hts

are

base

don

the

pre

dic

ted

pro

babilit

yto

dro

pth

esa

mple

.T

he

pre

dic

tion

isbase

don

aL

ogit

model

that

isdesc

rib

ed

at

the

begin

nin

gof

this

secti

on.

58

Tab

leE

.6:

Cogn

itiv

eA

bil

itie

san

dA

chie

vem

ent

Ou

tcom

es

Out

com

e D

escr

iptio

nC

ntr.

Mea

nC

d. D

iff. M

n.C

d. E

ff. S

ize

Asy

P-v

alSi

ngle

P-v

alSt

epdo

wn

Cnt

r. M

ean

Cd.

Diff

. Mn.

Cd.

Eff

. Siz

eA

sy P

-val

Sing

le P

-val

Step

dow

nK

aufm

an A

ssessm

ent B

atter

y for

Chi

ldre

n (Y

ear 6

)G

esta

lt C

losu

re9.

026

0.24

40.

081

0.26

60.

193

0.48

79.

787

-0.3

88-0

.134

0.83

70.

636

0.63

6H

and

Mov

emen

ts9.

267

0.43

80.

203

0.065

0.025

0.15

09.

319

0.12

70.

060

0.33

20.

398

0.71

1M

atrix

Ana

logi

es8.

636

0.13

60.

080

0.27

30.

300

0.57

98.

480

0.28

50.

180

0.092

0.12

40.

434

Num

ber R

ecal

l9.

390

0.43

70.

152

0.12

00.086

0.32

78.

886

1.00

40.

421

0.002

0.004

0.029

Phot

o Se

ries

7.04

00.

424

0.21

20.055

0.064

0.28

46.

791

0.03

00.

014

0.45

80.

496

0.70

0Sp

atia

l Mem

ory

8.44

10.

204

0.08

40.

264

0.34

10.

516

8.56

80.

218

0.09

00.

258

0.19

40.

531

Tria

ngle

s8.

845

0.43

50.

188

0.070

0.12

90.

402

9.20

10.

094

0.04

10.

382

0.21

30.

522

Wor

d O

rder

9.73

7-0

.079

-0.0

300.

591

0.38

60.

386

9.14

80.

763

0.29

80.016

0.006

0.039

Kau

fman

Asse

ssmen

t Bat

tery f

or C

hild

ren

(Yea

r 6)

Non

verb

al89

.267

2.11

80.

239

0.041

0.051

0.10

489

.466

1.10

40.

118

0.19

60.

187

0.23

5Se

quen

tial P

roce

ssin

g96

.587

1.68

50.

131

0.16

00.071

0.12

494

.353

3.67

60.

312

0.013

0.011

0.023

Sim

ulta

neou

s Pr

oces

sing

88.9

811.

980

0.19

60.072

0.094

0.094

90.1

280.

498

0.05

00.

359

0.23

10.

231

WIS

C-II

I, PP

VT-

III f

or C

hild

ren

(Yea

r 6)

Wec

hsle

r Int

ellig

ence

Sca

le fo

r Chi

ldre

n (W

ISC

-III

)96

.518

0.90

00.

050

0.34

80.

352

0.35

290

.692

1.74

60.

102

0.22

70.

298

0.29

8Pe

abod

y Pi

ctur

e V

ocab

ular

y Te

st (P

PVT-

III)

83.6

821.

685

0.15

40.

119

0.16

40.

286

82.6

952.

325

0.22

10.062

0.013

0.024

Chi

ld C

ogni

tion

(Yea

r 6)

- Fac

tor S

core

sC

ogni

tion

+ a

chie

vmen

t (K

AB

C, P

PVT,

WIS

C)

0.00

50.

118

0.11

80.

188

0.067

0.092

-0.0

100.

182

0.18

20.092

0.063

0.063

Cog

nitiv

e sk

ills

(Men

tal P

roce

ssin

g C

ompo

site

-KA

BC

)0.

000

0.13

70.

137

0.15

00.073

0.073

-0.0

070.

277

0.27

70.023

0.015

0.021

Rea

ding

Ach

ievem

ent f

or th

e Chi

ld (Y

ear 1

2)A

vera

ge R

eadi

ng G

rade

(Gra

des

1 - 5

)2.

694

0.07

60.

101

0.22

80.

107

0.27

12.

348

0.05

80.

078

0.29

60.100

0.16

4T

CA

P %

Lan

guag

e (S

choo

l Yea

rs 1

- 5,

Grd

3+

)51

.600

0.37

20.

016

0.45

60.

180

0.30

737

.918

5.07

60.

233

0.067

0.005

0.021

TC

AP

% R

eadi

ng (S

choo

l Yea

rs 1

- 5,

Grd

3+

)42

.374

0.19

70.

010

0.47

30.

164

0.31

035

.020

1.75

00.

088

0.28

00.043

0.11

7PI

AT

Tot

al R

eadi

ng (D

eriv

ed S

core

)90

.420

0.66

20.

069

0.30

70.

344

0.40

489

.350

1.38

10.

103

0.22

10.063

0.12

9PI

AT

Rea

ding

Com

preh

ensi

on (D

eriv

ed S

core

)88

.458

-0.2

32-0

.026

0.57

60.

546

0.54

687

.641

2.36

90.

203

0.072

0.022

0.070

PIA

T R

eadi

ng R

ecog

nitio

n (D

eriv

ed S

core

)94

.486

2.17

50.

180

0.10

20.

156

0.32

592

.620

0.26

60.

018

0.44

70.

136

0.13

6

Mat

h A

chiev

emen

t for

the C

hild

(Yea

r 12)

Ave

rage

Mat

h G

rade

(Gra

des

1 - 5

)2.

622

0.09

30.

113

0.19

60.

146

0.27

02.

391

0.09

90.

130

0.18

30.072

0.072

TC

AP

% M

ath

(Sch

ool Y

ears

1 -

5, G

rd 3

+)

47.6

101.

896

0.08

00.

291

0.18

80.

279

40.1

763.

086

0.13

90.

185

0.033

0.082

PIA

T M

athe

mat

ics

(Der

ived

Sco

re)

87.4

13-0

.080

-0.0

080.

525

0.72

70.

727

86.5

381.

947

0.19

30.086

0.048

0.085

Fem

ales

Mal

esB

asic

Sta

tistic

sB

lock

Per

m. F

LB

asic

Sta

tistic

sB

lock

Per

m. F

L

Notes:

The

firs

tcolu

mn

pro

vid

es

the

outc

om

edesc

ripti

on.

Our

resu

lts

are

pre

sente

din

six

colu

mns

for

each

gender.

The

firs

tcolu

mn

(Cntr

.M

ean)

of

each

resu

ltse

tsh

ow

sth

em

ean

for

the

contr

ol

gro

up.

When

facto

rsc

ore

sw

ere

com

pute

d,

we

set

the

mean

inth

econtr

ol

gro

up

tozero

.T

he

second

colu

mn

(Cd.

Diff

.M

n.)

giv

es

the

condit

ional

diff

ere

nce

inm

eans

betw

een

the

treatm

ent

gro

up

and

the

contr

ol

gro

up.

The

thir

dcolu

mn

(Cd.

Eff

.Siz

e)

calc

ula

tes

the

condit

ional

eff

ect

size

for

the

resp

ecti

ve

gro

up.

The

fourt

hcolu

mn

(Asy

.P

-val.)

pro

vid

es

the

asy

mpto

ticp-v

alu

efo

rth

eone-s

ided

single

hyp

oth

esi

ste

stass

ocia

ted

wit

hth

et-

stati

stic

for

the

diff

ere

nce

inm

eans

betw

een

treatm

ent

and

contr

ol

gro

ups.

As

menti

oned

inSecti

on

2,

the

contr

ol

gro

up

stands

for

the

ori

gin

al

treatm

ent

gro

up

2of

the

NF

Pexp

eri

ment

and

the

treatm

ent

gro

up

stands

for

the

ori

gin

al

gro

up

4.

The

fift

hcolu

mn

(Blo

ckP

erm

.F

L/Sin

gle

P-v

al.)

pre

sents

the

one-s

ided

rest

ricte

dp

erm

uta

tionp-v

alu

es

for

the

single

-hyp

oth

esi

ste

stin

gbase

don

thet-

stati

stic

ass

ocia

ted

wit

hth

etr

eatm

ent

indic

ato

rin

the

Fre

edm

an

and

Lane

(1983)

regre

ssio

nas

desc

rib

ed

inSecti

on

4.

By

rest

ricte

dp

erm

uta

tion

we

mean

that

perm

uta

tions

are

done

wit

hin

stra

tadefined

by

the

base

line

vari

able

suse

din

the

random

izati

on

pro

tocol:

mate

rnal

age

and

race,

gest

ati

onal

age

at

enro

llm

ent,

em

plo

ym

ent

statu

sof

the

head

of

the

house

hold

,and

geogra

phic

regio

n.

The

covari

ate

suse

din

the

Fre

edm

an

and

Lane

(1983)

regre

ssio

nare

:m

ate

rnal

heig

ht,

house

hold

incom

e,

gra

ndm

oth

er

supp

ort

,m

ate

rnal

pare

nti

ng

att

itudes

and

moth

er

curr

entl

yin

school.

Fin

ally,

the

last

colu

mn

(Blo

ckP

erm

.F

L/Ste

pdow

n)

pro

vid

esp-v

alu

es

that

account

for

mult

iple

-hyp

oth

esi

ste

stin

gbase

don

the

Ste

pdow

nalg

ori

thm

of

Rom

ano

and

Wolf

(2005a).

Blo

cks

of

outc

om

es

that

are

test

ed

join

tly

are

separa

ted

by

lines.

The

sele

cti

on

of

blo

cks

of

outc

om

es

isdone

on

the

basi

sof

their

meanin

g.

Outc

om

es

that

share

sim

ilar

meanin

gare

gro

up

ed

togeth

er.

Fem

ale

mate

rnal

outc

om

es

all

ude

tom

oth

ers

whose

firs

tch

ild

isa

gir

l.L

ikew

ise,

male

mate

rnal

outc

om

es

alludes

tom

oth

ers

whose

firs

tch

ild

isa

boy.

The

resu

lts

inth

ista

ble

use

an

invers

epro

babilit

yw

eig

hti

ng

schem

eto

addre

ssatt

riti

on.

The

weig

hts

are

base

don

the

pre

dic

ted

pro

babilit

yto

dro

pth

esa

mple

.T

he

pre

dic

tion

isbase

don

aL

ogit

model

that

isdesc

rib

ed

at

the

begin

nin

gof

this

secti

on.

59

Tab

leE

.7:

Soci

o-

Em

oti

on

al

Ab

ilit

ies

Out

com

e D

escr

iptio

nC

ntr.

Mea

nC

d. D

iff. M

n.C

d. E

ff. S

ize

Asy

P-v

alSi

ngle

P-v

alSt

epdo

wn

Cnt

r. M

ean

Cd.

Diff

. Mn.

Cd.

Eff

. Siz

eA

sy P

-val

Sing

le P

-val

Step

dow

nC

hild

Beh

avior

Che

cklis

t (Ye

ar 2

) - F

acto

r Sco

res

Aff

ectiv

e Pr

oble

ms

-0.0

01-0

.337

-0.3

370.002

0.003

0.015

0.00

40.

287

0.28

70.

985

0.95

50.

955

Anx

iety

Pro

blem

s-0

.002

-0.1

81-0

.181

0.066

0.24

90.

249

0.00

70.

016

0.01

60.

550

0.63

60.

907

Perv

asio

n D

evel

opm

enta

l Pro

blem

s-0

.005

-0.2

61-0

.261

0.013

0.060

0.100

0.00

50.

185

0.18

50.

925

0.81

70.

950

Atte

ntio

n D

efic

it H

yper

activ

ity D

isor

der

-0.0

01-0

.243

-0.2

420.025

0.019

0.060

0.00

30.

056

0.05

60.

670

0.70

60.

923

Opp

ositi

onal

Def

iant

Pro

blem

s-0

.001

-0.2

17-0

.217

0.040

0.053

0.12

00.

005

0.12

60.

126

0.85

30.

880

0.96

2

Chi

ld B

ehav

ior C

heck

list (

Year

6) -

Fac

tor S

core

sA

ffec

tive

Prob

lem

s-0

.010

-0.0

07-0

.007

0.47

90.

612

0.79

6-0

.004

-0.1

03-0

.103

0.20

30.

151

0.48

1A

nxie

ty P

robl

ems

-0.0

08-0

.061

-0.0

610.

306

0.49

20.

759

0.00

90.

083

0.08

20.

729

0.81

30.

813

Som

atic

Pro

blem

s-0

.003

0.13

00.

130

0.83

20.

884

0.88

40.

007

0.06

30.

063

0.67

80.

442

0.75

7A

ttent

ion

Def

icit

Hyp

erac

tivity

Pro

blem

s-0

.012

-0.2

30-0

.230

0.035

0.096

0.30

7-0

.006

-0.0

40-0

.040

0.37

90.

310

0.71

3O

ppos

ition

al D

efia

nt P

robl

ems

0.00

0-0

.027

-0.0

270.

415

0.28

60.

608

-0.0

13-0

.083

-0.0

830.

270

0.31

70.

672

Con

duct

Pro

blem

s-0

.002

-0.2

67-0

.266

0.013

0.003

0.015

-0.0

09-0

.011

-0.0

110.

467

0.48

50.

665

Mac

Arth

ur S

tory

Stem

Bat

tery (

MSS

B) (Y

ear 6

) - F

acto

r Sco

res

Dys

regu

late

d A

ggre

ssio

n-0

.006

-0.0

27-0

.027

0.41

30.

135

0.26

9-0

.009

-0.1

30-0

.130

0.18

90.

137

0.49

6W

arm

th a

nd E

mpa

thy

-0.0

110.

388

0.38

80.002

0.005

0.019

-0.0

11-0

.099

-0.0

990.

770

0.53

50.

832

Em

otio

nal I

nteg

ratio

n-0

.005

-0.0

28-0

.028

0.58

50.

765

0.76

5-0

.015

0.05

50.

055

0.34

90.

429

0.84

9Pe

rfor

man

ce A

nxie

ty0.

010

-0.0

38-0

.038

0.37

30.093

0.25

9-0

.009

0.07

70.

077

0.70

10.

843

0.84

3A

ggre

ssio

n-0

.005

-0.1

64-0

.164

0.084

0.003

0.012

-0.0

10-0

.095

-0.0

950.

260

0.17

70.

570

Inter

naliz

ing,

Ext

erna

lizin

g, A

bsen

ces (Y

ear 1

2) Inte

rnal

izin

g D

isor

ders

0.24

0-0

.028

-0.0

660.

309

0.45

30.

813

0.39

7-0

.087

-0.1

830.090

0.082

0.15

4E

xter

naliz

ing

Dis

orde

rs0.

183

-0.0

13-0

.032

0.40

20.

641

0.86

60.

183

0.08

90.

239

0.95

10.

859

0.85

9A

vera

ge #

of

Abs

ence

s (S

choo

l Yea

rs 1

- 5)

10.1

440.

263

0.03

50.

605

0.66

60.

666

11.5

48-1

.838

-0.2

460.029

0.027

0.077

Fem

ales

Mal

esB

asic

Sta

tistic

sB

lock

Per

m. F

LB

asic

Sta

tistic

sB

lock

Per

m. F

L

Notes:

The

firs

tcolu

mn

pro

vid

es

the

outc

om

edesc

ripti

on.

Our

resu

lts

are

pre

sente

din

six

colu

mns

for

each

gender.

The

firs

tcolu

mn

(Cntr

.M

ean)

of

each

resu

ltse

tsh

ow

sth

em

ean

for

the

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on.

60

F Theoretical Framework for Mediation Analysis

This section develops a theoretical framework that helps to interpret the estimates of a standard mediation

model for early childhood interventions. Our model is based on a technology of skill formation according

to (Cunha and Heckman, 2007b). In it, later skills build on previous ones to generate human capital.

Notationally, let θi,t be the vector of skills during childhood for individual i at period t and t ∈ 0, 1, . . . , T,

where T is the number of periods of childhood. Let Ii,t represent investments at the same period. We use

Xi for family background characteristics and υi,t for an exogenous error term independent of θi,t, Ii,t and

Xi. The structural equation that governs the evolution of skills is given by:

θi,t+1 = qt+1(θi,t, Ii,t+1, Xi, υi,t+1); t ∈ 0, 1, . . . , T − 1. (32)

By structural equation, we mean autonomous functions in the language of Frisch (1938), i.e. deterministic

functions whose functional form do not change as its arguments vary. We also allow for skills to affect

investments, that is:

Ii,t+1 = ht+1(θi,t, Xi, εi,t+1); t ∈ 0, 1, . . . , T − 1, (33)

where εi,t+1 is an exogenous error term independent of θi,t and Xi. Our model is completed by the following

structural outcome equation at period T :

Yi = gT (θi,T , Xi, ξi,T ). (34)

where ξi,T is an exogenous error term independent of θi,T and Xi.

We can use a recursive substitution of investments and skills of Equations (32)–(33) into (34) to generate

the following equation:

Yi = ft′(θi,t′ , Xi, υi,tTt=t′ , εi,tTt=t′ , ξi,T ), (35)

where υi,tTt=t′ = υi,t′ , υi,t′+1, . . . , υi,T and εi,tTt=t′ = εi,t′ , εi,t′+1, . . . , εi,T .

Suppose that an intervention occurs at period t′ where t′ ∈ 1, . . . , T. Let Di ∈ 0, 1 be the treatment

indicator of this intervention which takes value 1 if participant i is treated and 0 otherwise. The intervention

enters our technology of skill formation model as a form of skill investment. Thus we append the investment

Equation (33) at period t′ by:

Ii,t′ = ht′(θi,t′−1, Di, Xi, εi,t′); for some t′ ∈ 0, 1, . . . , T − 1, (36)

61

The counterfactual values investment Ii,t′ are defined by the value Ii,t′ takes when the intervention Di is

fixed at a level d ∈ 0, 1. By fixing, I mean the causal operation defined in Haavelmo (1944) where Di is

set to d ∈ 0, 1 as argument in the structural equation (36). That is:

Ii,t′,d = ht′(θi,t′−1, d,Xi, εi,t′); d ∈ 0, 1 for some t′ ∈ 0, 1, . . . , T − 1. (37)

Let the counterfactual skills be defined in a symmetric fashion by:

θi,t′,d = qt′(θi,t′−1, Ii,t′,d, Xi, υi,t′).

We also define the counterfactual skills and investments for periods t > t′ by:

Ii,t+1,d = ht+1(θi,t,d, Xi, εi,t+1), and

θi,t+1,d = qt+1(θi,t,d, Ii,t+1,d, Xi, υi,t+1); t > t′.

We can also define the counterfactual outcomes by:

Yi,d = ft′(θi,t′,d, Xi, εi,tTt=t′ , εi,tTt=t′ , ξi,T ), (38)

If the intervention assignment uses the method of randomization, then we have that:

(Yi,d,θi,t′,d) ⊥⊥ Di|Xi; d ∈ 0, 1.

We can also write the realized values of skills and outcomes as:

Yi = Yi,1Di + Yi,0(1−Di), and

θi,t = θi,t,1Di + θi,t,0(1−Di); t ≥ t′.

We now cast on Equation (38) to generate a tractable equation to examine mediation effects. Note that

Equation (38) holds ont onlt for t′ but for any t ≥ t′.

Yi,d = ft(θi,t,d, Xi, υi,tTt=t, εi,tTt=t, ξi,T ), for any t ∈ t′, t′ + 1, . . . , T. (39)

Error terms (υi,tTt=t, εi,tTt=t, ξi,T ) are independent of θi,t,d and Xi. For sake of notational simplicity, we

62

can substitute those error terms by ζt without loss of generality. Equation (39) then becomes:

Yi,d = ft(θi,t,d, Xi, ζi,t). (40)

We achieve a linear form of Equation (40) by approximating it through a Maclaurin expansion. This generates

the following equation:

Yi,d = κt +αt,dθi,t,d + βt,dXi + εi,t,d, d ∈ 0, 1. (41)

where εt,d accounts for the approximation error. Equations (40)–(41) are used in our mediation analysis in

Section 5.

G Mediation Methodology

G.1 Three Step Procedure

This part of the appendix explains in detail the three step procedure that we use in order to decompose the

NFP treatment effects. As highlighted in the paper, we perform two sets of analysis. First, we study if the

treatment effects on child skills at age 6 were mediated by program enhancement of birth weight, parenting

attitudes and investments, and maternal socio-emotional skills at age 2. Second, we study if the program

impact on outcomes at age 12 was mediated by the NFP enhancement of skills at age 6. The results from

these analysis shed light on the complementarity of investments and skills in explaining the NFP treatment

effects.

Step One The idea is to develop a measurement system that links the observed items and the latent

skills. In order to do that, we assume that our measurements are dedicated. This means that each observed

measurement is linked to a unique skill. Specifically, let Mj be the index set of measures associated with

trait j, where j ∈ J = P,C, SE. P,C, SE denote, respectively, parenting skills, child cognitive skills, and

child socio-emotional abilities.18 Thus, our linear measurement system looks as follows:19

M jmj ,d = νjmj + ϕjmjθ

jd + ηjmj ,d, (42)

where νjmj is the intercept term and ϕjmj represents the loading factor of trait j. We cannot reject the

null hypothesis that the intercepts and loading factors depend on treatment status. ηmj ,d is a mean zero

18This follows the same notation as Heckman et al. (2013)19We control for pre-program variables X but we keep it implicit to shorten notation.

63

idiosyncratic error term which, by assumption, is independent of θjd ∀j ∈ J . We normalize the loading factor

associated with the first measure of each factor to 1 to set a scale, otherwise the scale is arbitrary.20 Finally,

we allow for factor correlation.

The parameters that identify the measurement system are the factor means, the factor covariances, the

intercepts, the factor loadings, and the variances of the error terms: E[θj(d)] = µjd, V ar[θd] = Σθd , νjmj ,

ϕjmj , V ar[ηjmj ]). Heckman et al. (2013) show that the existence of at least three measures for each latent

skill guarantees identification.21 Broadly, means, variances, and covariances across the measures identify the

parameters of the system.

We estimate the parameters of the measurement system that links skills with measures both at ages 2

and 6. Variables become potential mediators if we estimate an effect of the NFP on it, so that they are

potential meaningful channels. For age 2, non-abusive parenting attitudes are approximated by the Adult-

Adolescent Parenting Inventory (Bavolek), which comprises 32 items, and home investments are measured

by the Bradley and Caldwell Home Observation for measurement of the Environment (HOME) inventory,

which is composed by 45 items.

The maternal skills selected correspond to anxiety, assessed by the Rand Mental Health Inventory, self-

esteem, measured by the Rosemberg scale, and mastery, approximated by the Pearlin scale. Similarly, for age

6, we select as plausible mediators children’s skills influenced by the NFP. Children cognition is measured by

8 subtests from the K-ABC mental processing composite. For children’s socio-emotional skills, we identify

as potential mediators the treatment reduction in conduct, attention and aggression problems, as well as

the enhancement of children’s pro-social skills. Attention and conduct problems are approximated by items

from the Child Behavior Checklist. Pro-social skills (warmth or empathy) and aggression problems are

approximated by items from the MacArthur Story Stem Battery. Section B of the Appendix explains in

more detail these tests, as well as the instruments they use.

We estimate the parameters of the measurement system by maximum likelihood. In order to do this, we

assume that the latent skills and the error terms, , θj , ηjmj , are normal and i.i.d. We use full-information

maximum likelihood to deal with the missing values in the measures for some individuals. Recent work by

citation shows that FIML yields unbiased estimates that are more efficient than ad hoc methods like list-wise

and pair-wise deletion, which work under the implicit assumption of random missing data.22

For the case of the measurement system at age 2, we have 146 items. Although it is ideal to estimate

the complete set of items (skills) jointly, it is not feasible. Thus, we estimate them in two blocks: one for

20Given that the first measure sets the scale, we choose it to be the most correlated with the skill. The results are robust toalterations of this.

21 Carneiro et al. (2003) and Cunha et al. (2010) also discuss identification of factor models.22Missing at random means that the probability of missing data in a variable x can depend on other observed variables but

not on the values of x itself

64

parenting and home investments and other for maternal characteristics. This allows us to account for the

correlation between the skills that are in the same block. For the case of the measurement system at age 6,

the set of items is smaller and we do a joint estimation.

Step Two In the second step we use the parameter estimates from the first step to construct factor

scores for each children. The objective of this is to construct approximations for the latent skills. The two

most common linear scoring methods are the regression method (Bartlett, 1937; Thomson, 1934) and the

Bartlett method, which resembles GLS. We use the Bartlett (1937) method because it estimates unbiased

approximations of the unobserved skills. Actually, this guarantees that the difference in means between the

factor scores for children in the treatment and the control groups equals the difference in means in the true

scores. The derivation of the Bartlett estimator begins with the measurement system summarized as:

Mi︸︷︷︸|M|×1

= ϕ︸︷︷︸|M|×|J |

θi︸︷︷︸|J |×1

+ ηi︸︷︷︸|M|×1

where the dimension of each term is below the braces (recall that J and M are the indexing sets for skills

and measures respectively). Assume that the (θi,ηi), i ∈ 1, . . . , I, are independent across i. For simplicity,

we assume that they are i.i.d.23 Let Cov(Mi,Mi) = Σ, Cov(θi,θi) = Φ and Cov(ηi,ηi) = Ω. The linear

relation between the factor scores and the measures is the following:

θS,i = L′Mi (43)

In order to obtain unbiased estimates, Barlett imposes the restriction that L′ϕ = I|J |. The Bartlett

estimator for the vector of approximated skills (θi) is:

θS,i = (ϕ′Ω−1ϕ)−1ϕ′Ω−1Mi, (44)

where the matrix of loading factors, ϕ, and Ω = Cov(ηi,ηi) are both estimated in the first step. Bartlett’s

estimator is a Generalized Least Squares, GLS, procedure where measures are used as dependent variables

and loading factors are treated as regressors. By the Gauss-Markov theorem, the Bartlett GLS estimator is

optimal and hence leads to the best linear unbiased predictor (BLUE).

There are individuals that have missing data in some of the items that compose the measurement system.

In order to take advantage of the information that they have (instead of list-wise delete them), we predict

factor scores for them. We use the covariance between the measures and the factors from the sample with

23This is not strictly required but simplifies the notation.

65

complete measurement system to predict scores for these people. Additionally, for the cases were individuals

are missing a factor score because they did not have any item in that measurement system, we impute factor

scores with the regression method.24 This procedure recovers around 10% of the randomized sample.

Step 3 In this step, we use factor scores as approximations of the true skills to estimate the models that

link the later outcomes with the intermediate skills. The factor scores are measured with error, which

produces downward biased estimates of the parameters of the outcome equations. This bias corresponds to

the traditional attenuation that results from classical measurement error. In factor scored regressions, Bolck

et al. (2008) prove this. We adopt the bias correction strategy proposed by Croon (2002). In summary, this

approach takes advantage of the fact that we have estimates of all the components of the bias. This strategy,

also used by Heckman et al. (2013), can be summarized as follows:

Consider the model following model. To simplify notation, we use W to denote pre-program variables

X, treatment indicator and the intercept of equation 8:

Yi = αθi + γWi + εi, i = 1, . . . , N. (45)

The covariance matrix of (θi,Wi) is

Cov(θ,θ) Cov(θ,W )

Cov(W ,θ) Cov(W ,W )

.

We measure θi with error. Thus,

θS,i = θi + Vi, i = 1, . . . , N

(Wi,θi) ⊥⊥ Vi, E(Vi) = 0, Cov(V ,V ) = ΣV V

Denote Cov(θS,i,θS,i) = ΣθS,θS . We assume that the (θi,Wi, εi) are i.i,d, but much weaker conditions

suffice. Note that we do not assume that θi ⊥⊥ Wi as in traditional factor analysis. We do assume that

(θi,Wi) ⊥⊥ εi and E(εi) = 0.

If we use θS,i in place of Yi, it follows that:

Yi = αθS,i + γWi + εi − αVi. (46)

24We impute factor scores for individuals that have at least two other factor scores.

66

The estimation of equation 46 using OLS produces estimates that are biased:

plim

α

γ

=

Cov(θS ,θS) Cov(θS ,W )

Cov(W ,θS) Cov(W ,W )

−1 Cov(θ,θ) Cov(θ,W )

Cov(W ,θ) Cov(W ,W )

α

γ

.

Let ΣB,C be Cov(B,C). Observe that Σθ,W = ΣθS ,W as a consequence of our assumptions. In this

notation

plim

α

γ

=

Σθ,θ + ΣV ,V Σθ,W

ΣW ,θ ΣW ,W

−1 Σθ,θ Σθ,W

ΣW ,θ ΣW ,W

︸ ︷︷ ︸

A

α

γ

(47)

which is the usual attenuation formula.

From the estimation of the measurement system, we can identify Σθ,θ, Σθ,W , ΣV ,V , and we have all

the components of A. Hence if we pre-multiply the least squares estimator by A−1, we obtain:

plimA−1

α

γ

=

α

γ

.

This is called “Croon’s method” in psychometrics (Croon, 2002). In our application, there are two groups

corresponding to D = 0 and D = 1 (control and treatment, respectively). We allow θi to vary by treatment

status. Indeed, our method assumes that treatment only operates through shifting the distribution of θ. We

do not normalize the means of θ (or W ) to be zero.

In the third step of our estimation procedure we compute bootstrapped p-values for each decomposition

channel of the treatment effects. We take 100,000 resamples with replacement. The bootstrapped p-value

for the null hypothesis H0 : αj = 0 is calculated as follows:

p-value =1

B

B∑b=1

1(tj,∗b > tj) with tj =αj

σ(αj)and tj,∗b =

(αjb − αj)σ(αjb)

(48)

whereˆαjb is bootstrapped estimated in the bth resample and αj is estimated from the original data. Given

the estimates of the outcome equation and of the factor scores, we construct the bootstrapped p-value for

the contribution of skill k under the null hypothesis H0 : αjE(θj1 − θj0) = 0 as follows:

p-value =1

B

B∑b=1

1(T j,∗b > T j) with T j =αj ∗ E( θj(1)− θj(0))

σ(αj ∗ E( θj(1)− θj(0)))(49)

67

where T j,∗b is the statistic T j computed with the parameters obtained in the bth resample. Notice that the

p-value combines the variation in two population parameters: 1) the coefficient of the outcome equation;

2) the experimentally induced difference in means in the skills. It could be the case that each of these

parameters are, separately, statistically significant. However, the p-value may increase due to a loss in power

when they are combined.

Tables G.8 - G.11 shows the parameters of the outcome equations as wells as the decompositions com-

ponents.

68

Tab

leG

.8:

Fem

ale

Dec

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posi

tion

(Yea

r6)

Coef

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0.71

0.06

0-0

.03

0.16

90.

210.

007

0.11

0.01

8-0

.01

0.43

4-0

.29

0.07

30.

290.

093

304

Agg

ress

ion

0.74

0.10

3-0

.03

0.17

30.

160.

090

0.02

0.40

1-0

.12

0.12

70.

130.

263

0.10

0.35

130

4

Hom

e y2

Pare

ntin

g y2

Mas

tery

y2

Anx

iety

y2Se

lf-E

stee

m y

2Sa

mpl

e Si

zeTr

eatm

ent

Birth

Weig

ht

Notes:

The

firs

tcolu

mn

pro

vid

es

the

outc

om

edesc

ripti

on

and

the

top

row

pro

vid

es

info

rmati

on

on

the

media

tors

.For

Year

6,

the

media

tors

are

treatm

ent,

bir

thw

eig

ht,

hom

eenvir

onm

ent,

pare

nti

ng,

anxie

ty,

self

-est

eem

and

mast

ery

.T

he

last

colu

mn

pro

vid

es

the

sam

ple

size

for

the

corr

esp

ondin

goutc

om

ein

the

firs

tcolu

mn.

The

row

sare

div

ided

into

3gro

ups:

Outc

om

eC

oeffi

cie

nts

,T

reatm

ent

Eff

ect

and

Tre

atm

ent

Eff

ect

Fra

cti

on.

The

last

of

these

gro

ups

isals

osh

ow

vis

ually

inF

igure

3.

Each

media

tor

has

two

sub

colu

mns

of

info

rmati

on:

the

coeffi

cie

nt

and

thep-v

alu

e.

Boldp-v

alu

es

are

signifi

cant

at

the

10%

level.

We

use

dth

efo

llow

ing

contr

ols

:m

ate

rnal

race,

mate

rnal

age,

mate

rnal

heig

ht,

gest

ati

onal

age,

house

hold

densi

ty,

regio

n,

em

plo

ym

ent

statu

sof

house

hold

head,

gra

ndm

oth

er

supp

ort

,ra

ndom

izati

on

wave,

incom

ecate

gory

,m

oth

er

curr

entl

yin

school,

and

mate

rnal

pare

nti

ng

att

itudes.

69

Tab

leG

.9:

Male

Dec

om

posi

tion

(Yea

r6)

Coef

ficien

tp-

valu

eCo

effic

ient

p-va

lue

Coef

ficien

tp-

valu

eCo

effic

ient

p-va

lue

Coef

ficien

tp-

valu

eCo

effic

ient

p-va

lue

Coef

ficien

tp-

valu

eO

utcom

e Coef

ficien

tsCo

gniti

ve0.

080.

240

0.08

0.09

30.

350.

004

0.11

0.01

40.

060.

327

-0.0

40.

447

0.02

0.46

430

5A

ggre

ssio

n-0

.08

0.18

6-0

.02

0.33

10.

070.

241

-0.0

50.

091

-0.2

30.

014

0.37

0.05

8-0

.11

0.31

030

5

Trea

tmen

t Effe

ctCo

gniti

ve0.

080.

240

0.02

0.06

40.

040.

054

0.02

0.04

70.

000.

281

-0.0

00.

362

0.00

0.42

230

5A

ggre

ssio

n-0

.08

0.18

6-0

.01

0.29

60.

010.

165

-0.0

10.

091

-0.0

10.

252

0.02

0.17

3-0

.02

0.23

030

5

Trea

tmen

t Effe

ct Fr

actio

nCo

gniti

ve0.

500.

240

0.14

0.06

40.

220.

054

0.11

0.04

70.

020.

281

-0.0

20.

362

0.02

0.42

230

5A

ggre

ssio

n0.

840.

186

0.05

0.29

6-0

.07

0.16

50.

080.

091

0.12

0.25

2-0

.23

0.17

30.

200.

230

305

Mas

tery

y2

Sam

ple

Size

Trea

tmen

tBi

rth W

eight

Hom

e y2

Pare

ntin

g y2

Anx

iety

y2Se

lf-E

stee

m y

2

Notes:

The

firs

tcolu

mn

pro

vid

es

the

outc

om

edesc

ripti

on

and

the

top

row

pro

vid

es

info

rmati

on

on

the

media

tors

.For

Year

6,

the

media

tors

are

treatm

ent,

bir

thw

eig

ht,

hom

eenvir

onm

ent,

pare

nti

ng,

anxie

ty,

self

-est

eem

and

mast

ery

.T

he

last

colu

mn

pro

vid

es

the

sam

ple

size

for

the

corr

esp

ondin

goutc

om

ein

the

firs

tcolu

mn.

The

row

sare

div

ided

into

3gro

ups:

Outc

om

eC

oeffi

cie

nts

,T

reatm

ent

Eff

ect

and

Tre

atm

ent

Eff

ect

Fra

cti

on.

The

last

of

these

gro

ups

isals

osh

ow

vis

ually

inF

igure

4.

Each

media

tor

has

two

sub

colu

mns

of

info

rmati

on:

the

coeffi

cie

nt

and

thep-v

alu

e.

Boldp-v

alu

es

are

signifi

cant

at

the

10%

level.

We

use

dth

efo

llow

ing

contr

ols

:m

ate

rnal

race,

mate

rnal

age,

mate

rnal

heig

ht,

gest

ati

onal

age,

house

hold

densi

ty,

regio

n,

em

plo

ym

ent

statu

sof

house

hold

head,

gra

ndm

oth

er

supp

ort

,ra

ndom

izati

on

wave,

incom

ecate

gory

,m

oth

er

curr

entl

yin

school,

and

mate

rnal

pare

nti

ng

att

itudes.

70

Tab

leG

.10:

Fem

ale

Dec

om

posi

tion

(Yea

r12)

Coef

ficien

tp-

valu

eCo

effic

ient

p-va

lue

Coef

ficien

tp-

valu

eCo

effic

ient

p-va

lue

Coef

ficien

tp-

valu

eCo

effic

ient

p-va

lue

Out

come C

oeffic

ients

Tota

l # D

ays C

hild

Use

d M

ariju

ana

-0.1

50.

060

-0.1

20.

086

0.03

0.37

30.

000.

515

0.12

0.15

80.

040.

192

271

Child

Use

d A

lcoho

l, M

ari ju

ana,

or T

obac

co in

Las

t 30

Day

s-0

.02

0.19

8-0

.02

0.04

80.

000.

467

0.02

0.33

8-0

.00

0.47

70.

000.

457

268

Stan

dard

ized

Chi

ld B

MI (

Yea

r 12)

-0.3

00.

016

-0.1

10.

100

-0.2

20.

115

0.37

0.03

00.

080.

206

-0.1

10.

197

272

Trea

tmen

t Effe

ctCh

ild E

ver U

sed

Mar

i juan

a-0

.15

0.06

0-0

.01

0.21

8-0

.00

0.31

8-0

.00

0.48

40.

040.

111

-0.0

10.

155

271

Child

Use

d A

lcoho

l, M

ari ju

ana,

or T

obac

co in

Las

t 30

Day

s-0

.02

0.19

8-0

.00

0.21

7-0

.00

0.43

1-0

.00

0.27

3-0

.00

0.46

9-0

.00

0.42

426

8St

anda

rdiz

ed C

hild

BM

I (Y

ear 1

2)-0

.30

0.01

6-0

.01

0.20

90.

030.

109

-0.0

50.

060

0.02

0.16

20.

020.

145

272

Trea

tmen

t Effe

ct Fr

actio

nCh

ild E

ver U

sed

Mar

i juan

a1.

120.

060

0.05

0.21

80.

030.

318

0.00

0.48

4-0

.26

0.11

10.

060.

155

271

Child

Use

d A

lcoho

l, M

ari ju

ana,

or T

obac

co in

Las

t 30

Day

s0.

830.

198

0.05

0.21

70.

020.

431

0.07

0.27

30.

010.

469

0.01

0.42

426

8St

anda

rdiz

ed C

hild

BM

I (Y

ear 1

2)1.

060.

016

0.02

0.20

9-0

.11

0.10

90.

190.

060

-0.0

80.

162

-0.0

80.

145

272

War

mth

/Em

path

yA

ggre

ssio

nSa

mpl

e Si

zeTr

eatm

ent

Cogn

ition

Atte

ntio

n pr

oblem

sCo

nduc

t Pro

blem

s

Notes:

The

firs

tcolu

mn

pro

vid

es

the

outc

om

edesc

ripti

on

and

the

top

row

pro

vid

es

info

rmati

on

on

the

media

tors

.For

Year

12,

the

media

tors

are

treatm

ent,

cognit

ion,

att

enti

on

pro

ble

ms,

Conduct

Pro

ble

ms,

Warm

th/E

mpath

yand

Aggre

ssio

n.

The

last

colu

mn

pro

vid

es

the

sam

ple

size

for

the

corr

esp

ondin

goutc

om

ein

the

firs

tcolu

mn.

The

row

sare

div

ided

into

3gro

ups:

Outc

om

eC

oeffi

cie

nts

,T

reatm

ent

Eff

ect

and

Tre

atm

ent

Eff

ect

Fra

cti

on.

The

last

of

these

gro

ups

isals

osh

ow

vis

ually

inF

igure

7.

Each

media

tor

has

two

sub

colu

mns

of

info

rmati

on:

the

coeffi

cie

nt

and

thep-v

alu

e.

Bold

edp-v

alu

es

are

signifi

cant

at

the

10%

level.

Boldp-v

alu

es

are

signifi

cant

at

the

10%

level.

We

use

dth

efo

llow

ing

contr

ols

:m

ate

rnal

race,

mate

rnal

age,

mate

rnal

heig

ht,

gest

ati

onal

age,

house

hold

densi

ty,

regio

n,

em

plo

ym

ent

statu

sof

house

hold

head,

gra

ndm

oth

er

supp

ort

,ra

ndom

izati

on

wave,

incom

ecate

gory

,m

oth

er

curr

entl

yin

school,

and

mate

rnal

pare

nti

ng

att

itudes.

71

Tab

leG

.11:

Male

Dec

om

posi

tion

(Yea

r12)

Coef

ficien

tp-

valu

eCo

effic

ient

p-va

lue

Coef

ficien

tp-

valu

eCo

effic

ient

p-va

lue

Coef

ficien

tp-

valu

eCo

effic

ient

p-va

lue

Out

come C

oeffic

ients

Ave

rage

TCA

P pe

rcen

tile,

y1-5

: lan

guag

e co

mpo

site

2.88

0.18

811

.93

0.00

02.

210.

379

-0.9

40.

442

2.40

0.17

8-3

.88

0.17

022

2PI

AT

read

ing

com

preh

ensio

n de

rived

scor

e1.

690.

134

7.44

0.00

0-1

.41

0.32

60.

450.

480

0.31

0.39

10.

570.

371

272

Ave

rage

mat

h gr

ade

grad

es 1

-50.

030.

368

0.50

0.00

0-0

.21

0.14

50.

220.

137

0.05

0.28

8-0

.13

0.11

824

3A

vera

ge m

ath

grad

e. Y

ears

1-5

afte

r KG

-0.0

00.

538

0.50

0.00

0-0

.15

0.20

50.

160.

198

0.03

0.32

4-0

.14

0.09

624

6av

erag

e tc

ap p

erce

ntile

y1-

5: m

ath

0.81

0.34

815

.29

0.00

05.

320.

231

-2.8

60.

336

-0.9

80.

380

-3.4

70.

204

223

PIA

T m

ath

deriv

ed sc

ore

1.64

0.10

67.

860.

000

-1.3

60.

324

0.20

0.51

50.

710.

232

1.53

0.14

627

0SC

eve

r trie

d sm

okin

g: 1

=ye

s-0

.05

0.07

90.

020.

254

0.04

0.27

90.

020.

341

-0.0

20.

192

0.01

0.40

427

4SC

use

alc,

mar

, tob

last

30

days

-0.0

50.

04-0

.00

0.40

-0.0

10.

410.

040.

25-0

.02

0.07

0.03

0.20

272

Inte

rnali

zing

diso

rder

s - Y

outh

repo

rt-0

.05

0.21

3-0

.07

0.04

70.

020.

421

0.03

0.40

60.

030.

295

0.10

0.07

227

4A

nxio

us/d

epre

ssed

- cli

nica

l or b

orde

rline

diso

rder

, you

th re

port

-0.0

50.

082

-0.0

50.

016

-0.0

50.

167

0.06

0.10

10.

010.

332

0.07

0.08

327

3A

vera

ge n

umbe

r of a

bsen

ces,

scho

ol y

ears

1-5

-1.0

50.

146

-2.2

50.

001

4.36

0.01

0-3

.87

0.00

90.

220.

372

-1.1

00.

156

267

Trea

tmen

t Effe

ctA

vera

ge T

CAP

perc

entil

e, y1

-5: l

angu

age

com

posit

e2.

880.

188

2.09

0.06

4-0

.02

0.43

20.

030.

361

-0.3

90.

135

0.45

0.16

122

2PI

AT

read

ing

com

preh

ensio

n de

rived

scor

e1.

690.

134

1.44

0.04

10.

110.

255

-0.0

30.

364

-0.0

40.

313

-0.0

70.

270

272

Ave

rage

mat

h gr

ade

grad

es 1

-50.

030.

368

0.08

0.08

0-0

.00

0.36

60.

000.

449

-0.0

10.

200

0.02

0.10

724

3A

vera

ge m

ath

grad

e. Y

ears

1-5

afte

r KG

-0.0

00.

538

0.08

0.06

10.

000.

451

-0.0

00.

335

-0.0

00.

230

0.02

0.12

124

6av

erag

e tc

ap p

erce

ntile

y1-

5: m

ath

0.81

0.34

82.

680.

070

-0.0

90.

367

0.09

0.31

30.

160.

303

0.41

0.20

322

3PI

AT

mat

h de

rived

scor

e1.

640.

106

1.55

0.04

20.

110.

242

-0.0

10.

420

-0.0

80.

169

-0.1

80.

102

270

SC e

ver t

ried

smok

ing:

1=

yes

-0.0

50.

079

0.00

0.19

8-0

.00

0.23

4-0

.00

0.33

40.

000.

194

-0.0

00.

324

274

SC u

se a

lc, m

ar, t

ob la

st 3

0 da

ys-0

.05

0.04

3-0

.00

0.34

20.

000.

328

-0.0

00.

262

0.00

0.14

4-0

.00

0.17

027

2In

tern

alizi

ng d

isord

ers -

You

th re

port

-0.0

50.

213

-0.0

10.

058

-0.0

00.

342

-0.0

00.

303

-0.0

00.

245

-0.0

10.

116

274

Anx

ious

/dep

ress

ed -

clini

cal o

r bor

derli

ne d

isord

er, y

outh

repo

rt-0

.05

0.08

2-0

.01

0.02

80.

000.

213

-0.0

00.

219

-0.0

00.

251

-0.0

10.

085

273

Ave

rage

num

ber o

f abs

ence

s, sc

hool

yea

rs 1

-5-1

.05

0.14

6-0

.36

0.06

3-0

.27

0.25

80.

070.

424

-0.0

30.

272

0.14

0.12

726

7

Trea

tmen

t Effe

ct Fr

actio

nA

vera

ge T

CAP

perc

entil

e, y1

-5: l

angu

age

com

posit

e0.

570.

188

0.41

0.06

4-0

.00

0.43

20.

010.

361

-0.0

80.

135

0.09

0.16

122

2PI

AT

read

ing

com

preh

ensio

n de

rived

scor

e0.

540.

134

0.46

0.04

10.

030.

255

-0.0

10.

364

-0.0

10.

313

-0.0

20.

270

272

Ave

rage

mat

h gr

ade.

Yea

rs 1

-5 a

fter K

G0.

230.

368

0.68

0.08

0-0

.03

0.36

60.

010.

449

-0.0

50.

200

0.16

0.10

724

3av

erag

e tc

ap p

erce

ntile

y1-

5: m

ath

0.20

0.34

80.

660.

070

-0.0

20.

367

0.02

0.31

30.

040.

303

0.10

0.20

322

3PI

AT

mat

h de

rived

scor

e0.

540.

106

0.51

0.04

20.

040.

242

-0.0

00.

420

-0.0

30.

169

-0.0

60.

102

270

SC u

se a

lc, m

ar, t

ob la

st 3

0 da

ys0.

920.

043

0.02

0.34

2-0

.02

0.32

80.

040.

262

-0.0

40.

144

0.08

0.17

027

2In

tern

alizi

ng d

isord

ers -

You

th re

port

0.63

0.21

30.

170.

058

0.01

0.34

20.

020.

303

0.03

0.24

50.

140.

116

274

Anx

ious

/dep

ress

ed -

clini

cal o

r bor

derli

ne d

isord

er, y

outh

repo

rt0.

710.

082

0.14

0.02

8-0

.05

0.21

30.

050.

219

0.02

0.25

10.

120.

085

273

Ave

rage

num

ber o

f abs

ence

s, sc

hool

yea

rs 1

-50.

700.

146

0.24

0.06

30.

180.

258

-0.0

50.

424

0.02

0.27

2-0

.09

0.12

726

7

Trea

tmen

tCo

gniti

onA

ttent

ion

prob

lems

Cond

uct P

robl

ems

War

mth

/Em

path

yA

ggre

ssio

nSa

mpl

e Si

ze

Notes:

The

firs

tcolu

mn

pro

vid

es

the

outc

om

edesc

ripti

on

and

the

top

row

pro

vid

es

info

rmati

on

on

the

media

tors

.For

Year

12,

the

media

tors

are

treatm

ent,

cognit

ion,

att

enti

on

pro

ble

ms,

Conduct

Pro

ble

ms,

Warm

th/E

mpath

yand

Aggre

ssio

n.

The

last

colu

mn

pro

vid

es

the

sam

ple

size

for

the

corr

esp

ondin

goutc

om

ein

the

firs

tcolu

mn.

The

row

sare

div

ided

into

3gro

ups:

Outc

om

eC

oeffi

cie

nts

,T

reatm

ent

Eff

ect

and

Tre

atm

ent

Eff

ect

Fra

cti

on.

The

last

of

these

gro

ups

isals

osh

ow

vis

ually

inF

igure

s5

-6.

Each

media

tor

has

two

sub

colu

mns

of

info

rmati

on:

the

coeffi

cie

nt

and

thep-v

alu

e.

Boldp-v

alu

es

are

signifi

cant

at

the

10%

level.

We

use

dth

efo

llow

ing

contr

ols

:m

ate

rnal

race,

mate

rnal

age,

mate

rnal

heig

ht,

gest

ati

onal

age,

house

hold

densi

ty,

regio

n,

em

plo

ym

ent

statu

sof

house

hold

head,

gra

ndm

oth

er

supp

ort

,ra

ndom

izati

on

wave,

incom

ecate

gory

,m

oth

er

curr

entl

yin

school,

and

mate

rnal

pare

nti

ng

att

itudes.

72

H Mediation Specification Test

In this section we specify how do we empirically test the effect that the mediators have on the final outcomes.

We use J for an indexing set of skills. We use Jp ⊆ J for the subset of measured skills. Our model for the

outcome equation is:

Yd = κd +∑j∈J

αjdθjd + βdX + εd, d ∈ 0, 1,

where κd is an intercept, (αjd; j ∈ J ) are loading factors and βd are |X|-dimensional vectors of parameters.

The error term εd is a zero-mean i.i.d. random variable assumed to be independent of regressors (θjd; j ∈ J )

and X.

The NFP analysts collected a rich array of measures of cognitive and personality skills. However, it

is likely that there are skills that they did not measure. As noted before, we use Jp ⊆ J be the index

set of measured skills. Namely, skills for which we have enough psychological instruments that allows for

estimation. We rewrite the equation for potential outcome Yd as:

Yd = κd +∑j∈J

αjdθjd + βdX + εd

= κd +∑j∈Jp

αjdθjd︸ ︷︷ ︸

skills thatwe measure

+∑

j∈J\Jp

αjθjd︸ ︷︷ ︸skills that we

do not measure

+βdX + εd

= κd +∑

j∈J\Jp

αjd E(θjd)︸ ︷︷ ︸new intercept

+∑j∈Jp

αjdθjd︸ ︷︷ ︸

skills thatwe measure

+∑

j∈J\Jp

αjd(θjd − E(θjd))︸ ︷︷ ︸

skills that wedo not measure

+βdX + εd,

= τd︸︷︷︸new intercept

+∑j∈Jp

αjdθjd︸ ︷︷ ︸

skills thatwe measure

+βdX +∑

j∈J\Jp

αjd(θjd − E(θjd)) + εd︸ ︷︷ ︸

new error term

(50)

where d ∈ 0, 1, τd = κd +∑j∈J\Jp α

jd E(θjd).Any differences in the error terms between treatment and

control groups can be attributed to differences in unmeasured skills. Thus, we assume, without loss of

generality, that ε1d= ε0, where

d= means equality in distribution.

The goal of this section is to examine the statistical assumptions needed to estimate unbiased parameters

(αjd : j ∈ Jp, d ∈ 0, 1). These parameters are used to perform the decomposition of outcome treatment

effects into parts associated with skills enhancement (θj1 − θj0 : j ∈ Jp). Parameters α may suffer from

confounding effects if measured and unmeasured skills are not independent. We can solve this confounding

73

problem by assuming that unmeasured skills are independent of measures skills. Namely,

(θjd; j ∈ J \ Jp) ⊥⊥ (θjd; j ∈ Jp)|X; d ∈ 0, 1,

then the regression:

Yd = τd +∑j∈Jp

αjdθjd + βdX + εd, (51)

produces unbiased estimates of parameter (αjd; j ∈ Jp); d ∈ 0, 1. Indeed error terms εd in equation (51)

are given by

εd = εd +∑

j∈J\Jp

αjd(θjd − E(θjd))

which are independent of (θjd; j ∈ Jp) conditional on X under the assumption that skills are independent.

Now suppose that instead of the skills independence assumption for both groups, we focus only on the

control group, thus,

(θj0; j ∈ J \ Jp) ⊥⊥ (θj0; j ∈ Jp)|X.

Moreover, suppose we also assume that αj1 = αj0; j ∈ J . Equivalently, the outcome loading factors for

both treatment and control groups are the same. In this new setup, the regression

Y0 = τ0 +∑j∈Jp

αjθj0 + β0X + ε0, (52)

also produces unbised estimates of (αj ; j ∈ Jp). Now consider the regression

Y1 = τ1 +∑j∈Jp

αjθj1 + β1X + ε1.

According to our rationale, this regression only produces unbiased estimates of (αj ; j ∈ Jp) if:

(θj1; j ∈ J \ Jp) ⊥⊥ (θj1; j ∈ Jp)|X, (53)

or, alternatively,

(θj1 − θj0; j ∈ J \ Jp) ⊥⊥ (θj1 − θ

j0; j ∈ Jp)|X. (54)

Thus, under this new set of assumptions, testing H0 : α1 = α0 is translated into testing the independence

relations of equations (53)–(54).

While the skill independence assumption in equation (53) may appear strong, the rich settlement of

74

information on NFP surveys makes this assumption more plausible. NFP data has a huge selection of

psychological questionnaires that aims to measure both cognitive and non-cognitive skills though childhood.

We examine all the available data and only a subset of these measures turns out to be statistically relevant

for mediation analysis. We use these measures to estimate factors that are able to explain the majority of

the treatment effects. Thus, it seems unlikely that some unobserved skills overlooked by psychologists could

have a major impact on mediating treatment effects.

H.1 Skills and the Measurement System

The assumption that the loading factors in the measurement system (equation 42) are the same for treatment

and control is not necessary to identify the model. It is useful for clarity in the interpretation because the

treatment operates by the shift of the latent skills and not by the map between measures and skills.

Ultimately, we need the decomposition of the treatment effects, (12), to be invariant to the choice of the

measurement system we used. Thus, for each skill’s contribution to treatment effect on each outcome, we

want to test the null hypothesis that:

H0 : α0(E(θ1 − θ0)) = α1(E(θ1 − θ0)) (55)

where αd = (αjd : j ∈ Jp) and θd = (θjd : j ∈ Jp) such that d ∈ 0, 1 denotes treatment status.

Let θi be the estimated factor score for individual i, assigned to treatment status Di ∈ 0, 1, using the

estimated loading factors from the subsample of individuals with the same treatment status, i.e. for each

individual factor score:

θi = (ϕDi′(ΩDi)

−1ϕDi)−1ϕDi

′(ΩDi)−1Mi.

We would like to test if the contributions to the treatment effects is independent if we use the parameters’

from different measurement system (i.e if we estimate a different set of loading factors for the treatment and

control group).

Hence, an appropriate single hypothesis test statistic for each skill j ∈ Jp becomes:

αj0(θj1 − θj0)− αj1(θj1 − θ

j0)

where we use a hat subscript to denote estimated parameters. α are Croon corrected estimates of α. We can

use a summary statistic to test the joint hypothesis stated in (55).

75

Independence between αd and θd − θd yields:

Var(αd(θ1 − θ0)) = (αd)2 Var(θ1 − θ0) + Var(αd)(θ1 − θ0)2 + Var(α) Var(θ1 − θ0)

Independence between the quantities estimated for each of the d’s yields:

Var(α0(θ1 − θ0)− α1(θ1 − θ0)) = Var(α0(θ1 − θ0)) + Var(α1(¯θ1 − ¯

θ0))

This variance helps us to get the z-statistic:

z =α0(θ1 − θ0)− α1(θ1 − θ0)√

Var(α0(θ1 − θ0)− α1(θ1 − θ0))

A two-sided z-test gives a p-value associated with the skill and outcome null hypothesis of invariance to

the choice of the measurement system.

These (outcome, skill) paired p-values are shown in Tables H.12 and H.13. We find that we can not

reject the null hypothesis for any skill-outcome pair which suggests that our decompositions of the NFP

treatment effects are not driven by the choice of the measurement system.

H.1.1 Additional Specification Test for the Outcome Equation

In order to clearly interpret the channels through which the NFP affects later outcomes, (5) assumes that the

parameters that map skills and pre-program variables with the outcomes are not affected by the programs.

Put another way, the mediated channels operate exclusively on the program effect on the skills. This

assumption is not necessary to identify the model.

For each outcome decomposed, we test the hypothesis that αj1 = αj0,∀j ∈ J and β1 = β0 with a

Wald test. Tables H.14 and H.15 show the results of this test. We cannot reject the null hypothesis of

equality of the coefficients for the treatment and control groups. This evidence strengthens the validity of

our interpretation of the decomposition of the NFP treatment effect into interpretable channels.

I Oaxaca-Blinder Decomposition Results

Oaxaca-Blinder decompositions are often used to examine sources of treatment effects. This method de-

composes the difference in means between two groups (treatment and control) into the part that is due to

the group differences in the channels and into the part that is due to group differences in the parameters

that capture the relationship between the channels and the outcomes. In our context, the Oaxaca-Blinder

76

decomposition is summarized as follows:25

E(Y |D = 1)− E(Y |D = 0)︸ ︷︷ ︸Treatment Effects

= (α1 − α0)θ0︸ ︷︷ ︸Differences unexplained by the skills

+ (θ1 − θ0)α︸ ︷︷ ︸Explained: differences in skills

. (56)

The decomposition that we propose summarizes the unexplained part in the above equation through

the difference in the intercepts between the treatment and the control groups. In order to assess if our

decomposition is a plausible specification, we estimate an Oaxaca-Blinder decomposition. The results in

Tables I.16 - I.20 evidence that the Oaxaca-Blinder unexplained part that accounts for differences in the

mapping of the skills on outcomes is not statistically significant for any outcome. Therefore, the results from

the decomposition of the NFP treatment effects presented in the paper seem to be correctly specified.

25We implicitly control for pre-program variables.

77

Tab

leH

.12:

Sp

ecifi

cati

onT

est

-In

vari

an

ceof

the

Contr

ibu

tion

of

Skil

lsto

the

Ch

oic

eof

the

Mea

sure

men

tS

yst

em(F

emale

s)

Age

6 o

utco

mes

Hom

eP

aren

ting

Mat

erna

l an

xiet

ySe

lf-es

teem

mas

tery

Cog

nitio

n0.

263

0.90

70.

859

0.69

80.

672

Atte

ntio

n pr

oble

ms

0.36

30.

709

0.70

20.

667

0.74

8C

ondu

ct p

robl

ems

0.42

10.

694

0.92

20.

721

0.67

7W

arm

th-e

mpa

thy

(pro

-soc

ial

skill

s)0.

267

0.90

70.

644

0.83

30.

973

Agr

essi

on P

robl

ems

0.69

20.

819

0.86

20.

821

0.78

6

Age

12

outc

omes

Cog

niti

onA

tten

tion

pr

obs

Con

duct

pr

obs

Em

path

yA

gres

sion

SC # days e

ver u

sed marijuana

0.86

70.

878

0.59

20.

885

0.28

0SC use alc, m

ar, tob

last 30 days

0.87

60.

695

0.90

70.

893

0.81

2St

anda

rized

Chi

ld B

MI

0.88

90.

822

0.57

40.

953

0.32

4

Fact

or T

estin

g R

esul

ts -

Fem

ales

Mat

erna

l ski

lls-

age

2

Chi

ldre

n's

skill

s. A

ge 6

Notes:

The

table

show

sp-v

alu

es

for

the

Wald

test

:z

=α

0(¯ θ0 1−

¯ θ0 0)−α

1(¯ θ1 1−

¯ θ1 0)

√ Var(α

0(¯ θ0 1−

¯ θ0 0)−α

1(¯ θ1 1−

¯ θ1 0))

78

Tab

leH

.13:

Sp

ecifi

cati

onT

est

-In

vari

ance

of

the

Contr

ibu

tion

of

Skil

lsto

the

Ch

oic

eof

the

Mea

sure

men

tS

yst

em(M

ale

s)

Age

6 o

utco

mes

Hom

eP

aren

ting

Mat

erna

l an

xiet

ySe

lf-es

teem

mas

tery

Cog

nitio

n0.

349

0.39

40.

971

0.92

70.

946

Agr

essi

on P

robl

ems

0.92

80.

959

0.95

00.

843

0.53

7

Age

12

outc

omes

Cog

niti

onA

tten

tion

pr

obs

cond

uct

prob

sE

mpa

thy

Agr

essi

on

Ave

rage

TC

AP

perc

etile

. Yea

rs 1

-5

afte

r KG

: Lan

guag

e0.

529

0.97

50.

993

0.63

60.

882

PIA

T re

adin

g co

mpr

ehen

sion

de

rived

sco

re0.

420

0.79

40.

941

0.86

70.

812

Ave

rage

mat

h gr

ades

. Yea

rs 1

-5

afte

r KG

0.42

50.

953

0.83

00.

871

0.79

2

Ave

rage

TC

AP

perc

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rs 1

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afte

r KG

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h0.

571

0.94

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951

0.94

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875

PIA

T m

athe

mat

ics

deriv

ed s

core

0.43

30.

503

0.81

70.

976

0.65

2SC

use

of

alc,

mar

, tob

. Lat

30

days

0.84

50.

970

0.75

10.

791

0.53

8

Inte

rnal

izin

g di

sord

ers

- you

th

repo

rt0.

582

0.93

40.

911

0.90

50.

509

Clin

ical

or b

orde

rline

an

xiou

s/de

pres

sed

diso

rder

0.

537

0.93

60.

771

0.91

60.

687

Ave

rage

num

ber o

f ab

senc

es,

scho

ol y

ears

1-5

aft

er K

G0.

379

0.90

80.

706

0.83

30.

735

Mat

erna

l ski

lls-

age

2

Chi

ldre

n's

skill

s. A

ge 6

Notes:

The

table

show

sp-v

alu

es

for

the

Wald

test

:z

=α

0(¯ θ0 1−

¯ θ0 0)−α

1(¯ θ1 1−

¯ θ1 0)

√ Var(α

0(¯ θ0 1−

¯ θ0 0)−α

1(¯ θ1 1−

¯ θ1 0))

79

Tab

leH

.14:

Sp

ecifi

cati

on

Tes

t-

Ou

tcom

eE

qu

ati

on

(Fem

ale

s)

Out

com

eTe

st S

tat

P-V

al6

Year

sCo

gniti

on0.

982

0.49

0A

ttent

ion

prob

.1.

753

0.01

8Co

nduc

t Pro

b.0.

846

0.67

5Pr

o-so

cial

1.26

40.

189

Agg

ress

ion

0.55

80.

955

12 Y

ears

SC u

se a

lc, m

ar, t

ob la

st 3

0 da

ys1.

266

0.18

9SC

# d

ays u

se o

f alc,

mar

, tob

last

30

days

1.27

10.

186

Stan

dard

ized

Chi

ld B

MI (

Yea

r 12)

1.17

20.

270

Notes:

The

table

show

sp-v

alu

es

for

Wald

test

sfo

rth

eequality

of

slop

es

betw

een

treatm

ent

and

contr

ol

gro

up

inth

eoutc

om

eequati

on.

80

Tab

leH

.15:

Sp

ecifi

cati

on

Tes

t-

Ou

tcom

eE

qu

ati

on

(Male

s)

Out

com

eTe

st S

tat

P-V

al6

Year

sCo

gniti

on0.

609

0.92

6A

ggre

ssio

n0.

881

0.62

8

12 Y

ears

aver

age

tcap

per

cent

ile, y

1-5:

lang

uage

com

posit

e1.

162

0.28

3PI

AT

read

ing

com

preh

ensio

n de

rived

scor

e1.

286

0.17

5A

vera

ge m

ath

grad

e gr

ades

1-5

1.65

50.

034

Ave

rage

mat

h gr

ade.

Yea

rs 1

-5 a

fter K

G1.

493

0.07

3av

erag

e tc

ap p

erce

ntile

y1-

5: m

ath

1.24

20.

213

PIA

T m

ath

deriv

ed sc

ore

1.10

20.

343

SC u

se a

lc, m

ar, t

ob la

st 3

0 da

ys1.

208

0.23

7In

tern

alizi

ng d

isord

ers -

You

th re

port

0.99

30.

477

Anx

ious

/dep

ress

ed -

clini

cal o

r bor

derli

ne d

isord

er0.

682

0.86

7A

vera

ge n

umbe

r of a

bsen

ces,

scho

ol y

ears

1-5

0.79

80.

738

Notes:

The

table

show

sp-v

alu

es

for

Wald

test

sfo

rth

eequality

of

slop

es

betw

een

treatm

ent

and

contr

ol

gro

up

inth

eoutc

om

eequati

on.

81

Tab

leI.

16:

Oaxaca

-Blin

der

Dec

om

posi

tion

,ou

tcom

esat

age

6(F

emale

s)

Effe

ctSE

P-V

alFr

actio

nE

ffect

SEP

-Val

Frac

tion

Effe

ctSE

P-V

alFr

actio

nE

ffect

SEP

-Val

Frac

tion

Effe

ctSE

P-V

alFr

actio

nO

verall

Tota

l Diff

. in

Mea

ns0.

114

0.11

20.

311

--0

.189

0.09

20.

039

--0

.197

0.07

20.

006

-0.

235

0.10

20.

021

--0

.187

0.09

40.

046

-E

xplai

ned

0.08

30.

041

0.04

40.

706

-0.0

800.

037

0.03

30.

271

-0.0

510.

030

0.08

60.

213

0.06

90.

035

0.05

00.

291

-0.0

240.

030

0.42

10.

260

Une

xplai

ned

0.03

10.

112

0.78

40.

294

-0.1

100.

093

0.23

70.

729

-0.1

460.

072

0.04

50.

787

0.16

60.

099

0.09

30.

709

-0.1

630.

090

0.07

10.

740

Exp

laine

d Po

rtion

Hom

e In

dex

0.03

20.

020

0.11

30.

355

-0.0

160.

015

0.27

90.

096

-0.0

100.

013

0.42

00.

063

0.03

40.

019

0.07

10.

214

-0.0

150.

015

0.34

40.

160

Pare

ntin

g In

dex

0.02

80.

026

0.28

40.

137

-0.0

480.

024

0.04

60.

093

-0.0

180.

018

0.31

40.

046

0.04

00.

023

0.07

40.

106

0.00

20.

019

0.93

50.

015

Mat

erna

l Anx

iety

Inde

x0.

024

0.02

00.

217

0.25

4-0

.018

0.01

60.

271

0.10

0-0

.019

0.01

40.

181

0.13

70.

006

0.01

40.

671

-0.0

080.

009

0.01

40.

536

-0.1

16M

ater

nal S

elf-E

stee

m In

dex

0.00

70.

021

0.75

10.

238

0.00

90.

020

0.64

2-0

.204

-0.0

320.

022

0.14

50.

187

-0.0

430.

028

0.12

2-0

.290

-0.0

220.

021

0.28

30.

131

Mat

erna

l Mas

tery

Inde

x0.

002

0.02

10.

913

-0.1

92-0

.019

0.02

30.

409

0.25

60.

017

0.01

90.

375

-0.1

570.

039

0.02

80.

158

0.29

5-0

.003

0.02

30.

893

0.09

6Bi

rthw

eight

-0.0

110.

012

0.39

3-0

.086

0.01

20.

013

0.35

3-0

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0.01

10.

012

0.36

1-0

.063

-0.0

060.

009

0.48

1-0

.027

0.00

50.

007

0.48

3-0

.027

Une

xplai

ned

Porti

onH

ome

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008

0.02

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746

0.06

8-0

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80.

842

0.01

90.

000

0.01

40.

994

0.00

10.

028

0.02

30.

222

0.11

8-0

.009

0.01

90.

624

0.05

1Pa

rent

ing

Inde

x0.

020

0.02

80.

461

0.17

90.

033

0.02

20.

130

-0.1

76-0

.001

0.01

60.

965

0.00

40.

007

0.02

10.

741

0.03

00.

010

0.01

90.

615

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51M

ater

nal A

nxiet

y In

dex

-0.0

170.

021

0.43

4-0

.145

0.03

40.

024

0.16

1-0

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0.03

20.

020

0.11

1-0

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017

0.69

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0.00

50.

016

0.75

7-0

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Mat

erna

l Self

-Est

eem

Inde

x-0

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0.02

90.

757

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800.

041

0.02

90.

164

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160.

022

0.02

20.

306

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13-0

.018

0.03

50.

599

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770.

006

0.02

40.

802

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33M

ater

nal M

aste

ry In

dex

0.01

70.

034

0.62

80.

147

-0.0

460.

036

0.20

00.

244

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380.

026

0.14

80.

193

0.01

80.

037

0.62

50.

077

0.00

10.

029

0.97

4-0

.005

Birth

weig

ht-0

.002

0.00

70.

719

-0.0

220.

000

0.00

30.

915

-0.0

020.

002

0.00

60.

695

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11-0

.002

0.00

70.

758

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090.

002

0.00

50.

749

-0.0

09Re

sidua

l0.

014

0.11

70.

904

0.12

4-0

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0.09

40.

074

0.89

1-0

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0.07

40.

028

0.82

80.

140

0.09

90.

156

0.59

5-0

.176

0.09

10.

052

0.94

3

Cogn

ition

Atte

ntio

n Pr

oblem

sCo

nduc

t Pro

blem

sW

arm

th/E

mpa

thy

Agg

ress

ion

Notes:

The

indic

es

are

means

of

the

non-m

issi

ng

item

s.T

he

fracti

ons

are

pro

port

ions

of

the

tota

lcondit

ional

diff

ere

nce

inm

eans.

82

Tab

leI.

17:

Oaxaca

-Blin

der

Dec

om

posi

tion

,ou

tcom

esat

age

6(M

ale

s)

Effe

ctSE

P-V

alFr

actio

nE

ffect

SEP

-Val

Frac

tion

Effe

ctSE

P-V

alFr

actio

nE

ffect

SEP

-Val

Frac

tion

Effe

ctSE

P-V

alFr

actio

nO

verall

Tota

l Diff

. in

Mea

ns0.

173

0.10

50.

100

--0

.025

0.09

50.

797

--0

.012

0.08

80.

891

--0

.080

0.10

40.

442

--0

.099

0.08

60.

250

-E

xplai

ned

0.09

20.

037

0.01

20.

496

-0.0

640.

033

0.05

1-5

.856

-0.0

560.

035

0.11

1-1

.130

0.02

20.

025

0.38

7-0

.254

-0.0

250.

025

0.32

20.

158

Une

xplai

ned

0.08

10.

101

0.42

20.

504

0.03

90.

092

0.67

06.

856

0.04

40.

090

0.62

82.

130

-0.1

020.

105

0.33

21.

254

-0.0

740.

085

0.38

30.

842

Exp

laine

d Po

rtion

Hom

e In

dex

0.02

10.

022

0.34

40.

220

-0.0

030.

006

0.62

7-0

.303

-0.0

090.

010

0.39

5-0

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0.00

60.

009

0.51

3-0

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0.00

20.

005

0.72

8-0

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Pare

ntin

g In

dex

0.04

40.

022

0.04

20.

112

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210.

019

0.25

8-0

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110.

018

0.54

0-0

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0.00

80.

017

0.64

0-0

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013

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00.

085

Mat

erna

l Anx

iety

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001

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847

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561

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546

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970.

003

0.00

70.

629

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46-0

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0.01

80.

538

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5M

ater

nal S

elf-E

stee

m In

dex

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050.

009

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0.59

21.

536

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015

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009

0.69

00.

034

0.01

20.

014

0.39

9-0

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Mat

erna

l Mas

tery

Inde

x0.

009

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80.

598

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0.01

80.

385

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78-0

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40.

964

0.55

30.

004

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80.

831

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0.01

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833

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7Bi

rthw

eight

0.02

20.

017

0.19

20.

140

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230.

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0.21

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160.

015

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010

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055

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xplai

ned

Porti

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ome

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834

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002

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90.

846

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008

0.01

20.

529

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96-0

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0.00

90.

836

0.01

9Pa

rent

ing

Inde

x-0

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0.02

40.

760

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430.

012

0.02

40.

627

-0.4

710.

016

0.02

20.

467

-1.3

140.

010

0.02

70.

698

-0.1

290.

034

0.02

10.

110

-0.3

40M

ater

nal A

nxiet

y In

dex

0.00

60.

012

0.62

20.

035

0.00

00.

006

0.94

50.

016

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011

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50.

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8-0

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0.62

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040

Mat

erna

l Self

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eem

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004

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00.

665

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771

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004

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688

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005

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00.

642

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590.

000

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60.

970

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ater

nal M

aste

ry In

dex

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0.78

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230.

029

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10.

288

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90.

026

0.26

8-0

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Birth

weig

ht0.

020

0.02

40.

418

0.11

3-0

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80.

034

2.42

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0.02

80.

022

5.33

5-0

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525

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sidua

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090

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70.

400

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100

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072

0.09

80.

462

-5.9

70-0

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0.11

60.

436

1.12

1-0

.128

0.07

60.

091

1.29

3

Cogn

ition

Atte

ntio

n Pr

oblem

sCo

nduc

t Pro

blem

sW

arm

th/E

mpa

thy

Agg

ress

ion

Notes:

The

indic

es

are

means

of

the

non-m

issi

ng

item

s.T

he

fracti

ons

are

pro

port

ions

of

the

tota

lcondit

ional

diff

ere

nce

inm

eans.

83

Tab

leI.

18:

Oaxaca

-Blin

der

Dec

om

posi

tion

,ou

tcom

esat

age

12

(Fem

ale

s)

Effe

ctSE

P-V

alFr

actio

nE

ffect

SEP

-Val

Frac

tion

Effe

ctSE

P-V

alFr

actio

nTo

tal D

iff. i

n M

eans

-0.1

410.

085

0.09

8-

-0.0

210.

020

0.28

1-

-0.1

970.

110

0.07

2-

Exp

laine

d0.

026

0.03

80.

488

-0.1

84-0

.005

0.00

70.

460

0.24

20.

020

0.03

80.

601

-0.1

02U

nexp

laine

d-0

.167

0.11

10.

133

1.18

4-0

.016

0.02

10.

429

0.75

8-0

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0.11

40.

056

1.10

2

Exp

laine

dCo

gniti

ve-0

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0.01

80.

723

0.04

6-0

.001

0.00

30.

708

0.05

8-0

.004

0.01

30.

777

0.01

9A

ttent

ion

Prob

lems

0.00

00.

013

0.99

10.

001

-0.0

010.

005

0.82

70.

051

0.01

60.

017

0.35

4-0

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Cond

uct P

robl

ems

-0.0

030.

010

0.77

50.

019

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030.

004

0.46

80.

149

-0.0

270.

022

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50.

138

War

mth

/Em

path

y0.

038

0.03

80.

318

-0.2

680.

000

0.00

40.

934

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150.

023

0.02

30.

331

-0.1

15A

ggre

ssio

n-0

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0.00

50.

644

0.01

80.

000

0.00

20.

988

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010.

013

0.02

10.

554

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64

Une

xplai

ned

Cogn

itive

0.01

20.

018

0.52

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0.00

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004

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6-0

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40.

015

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ntio

n Pr

oblem

s0.

002

0.01

50.

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150.

008

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70.

288

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64-0

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40.

293

0.18

1Co

nduc

t Pro

blem

s0.

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91-0

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0.01

20.

522

0.36

40.

095

0.04

70.

043

-0.4

81W

arm

th/E

mpa

thy

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290.

032

0.37

40.

202

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050.

004

0.25

40.

228

-0.0

260.

023

0.26

00.

132

Agg

ress

ion

-0.0

020.

009

0.80

30.

016

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010.

003

0.69

70.

062

0.01

30.

037

0.72

4-0

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Resid

ual

-0.1

630.

096

0.08

91.

155

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130.

027

0.62

90.

603

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680.

122

0.02

81.

358

SC #

day

s eve

r use

d m

ariju

ana

SC u

se a

lc, m

ar, t

ob la

st 3

0 da

ysSt

anda

rdiz

ed C

hild

BM

I (12

Y)

Notes:

The

indic

es

are

means

of

the

non-m

issi

ng

item

s.T

he

fracti

ons

are

pro

port

ions

of

the

tota

lcondit

ional

diff

ere

nce

inm

eans.

84

Tab

leI.

19:

Oaxaca

-Bli

nd

erou

tcom

esat

age

12,

Dec

om

posi

tion

Part

1(M

ale

s)

Effe

ctSE

P-V

alFr

actio

nE

ffect

SEP

-Val

Frac

tion

Effe

ctSE

P-V

alFr

actio

nE

ffect

SEP

-Val

Frac

tion

Effe

ctSE

P-V

alFr

actio

nE

ffect

SEP

-Val

Frac

tion

Tota

l Diff

. in

Mea

ns4.

403

3.28

90.

181

-2.

022

1.58

40.

202

-0.

117

0.10

70.

275

-0.

083

0.10

30.

422

-2.

818

3.42

90.

411

-2.

447

1.32

40.

065

-E

xplai

ned

1.56

41.

520

0.30

40.

355

0.94

10.

808

0.24

40.

466

0.07

70.

063

0.21

90.

660

0.06

70.

058

0.24

20.

814

2.22

61.

820

0.22

10.

790

0.94

60.

817

0.24

70.

387

Une

xplai

ned

2.83

93.

105

0.36

10.

645

1.08

01.

454

0.45

70.

534

0.04

00.

090

0.65

80.

340

0.01

50.

087

0.86

00.

186

0.59

23.

111

0.84

90.

210

1.50

11.

103

0.17

40.

613

Exp

laine

dCo

gniti

ve1.

831

1.33

70.

171

0.41

60.

910

0.70

50.

197

0.45

00.

057

0.05

40.

285

0.49

20.

057

0.05

10.

266

0.68

22.

146

1.66

40.

197

0.76

20.

939

0.75

00.

211

0.38

4A

ttent

ion

Prob

lems

0.07

50.

275

0.78

70.

017

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00.

131

0.64

70.

030

0.00

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016

0.57

00.

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0.00

70.

012

0.54

80.

087

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570.

312

0.85

5-0

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0.06

70.

123

0.58

90.

027

Cond

uct P

robl

ems

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030.

273

0.99

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0.03

70.

122

0.76

50.

018

0.00

00.

010

0.96

4-0

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010.

008

0.93

3-0

.008

0.02

00.

281

0.94

50.

007

0.03

50.

110

0.75

10.

014

War

mth

/Em

path

y-0

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0.46

80.

253

-0.1

22-0

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0.15

60.

611

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39-0

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0.01

30.

475

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79-0

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0.01

40.

362

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49-0

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0.38

50.

870

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22-0

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0.12

20.

441

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38A

ggre

ssio

n0.

197

0.41

90.

639

0.04

50.

014

0.16

10.

930

0.00

70.

020

0.01

80.

267

0.17

10.

017

0.01

70.

328

0.20

30.

181

0.43

90.

681

0.06

4-0

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0.14

20.

995

0.00

0

Une

xplai

ned Co

gniti

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540

0.98

00.

582

0.12

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80.

958

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005

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787

0.04

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0.01

90.

652

0.10

50.

563

0.78

00.

470

0.20

0-0

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0.22

80.

943

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ttent

ion

Prob

lems

0.69

90.

769

0.36

30.

159

0.44

90.

342

0.18

90.

222

0.00

90.

020

0.65

90.

077

0.00

60.

020

0.75

20.

075

0.51

80.

663

0.43

50.

184

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292

0.57

9-0

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Cond

uct P

robl

ems

0.00

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427

0.99

50.

001

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920.

242

0.70

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0.85

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015

0.86

4-0

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0.00

20.

402

0.99

50.

001

0.00

40.

183

0.98

30.

002

War

mth

/Em

path

y0.

373

0.69

10.

590

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50.

134

0.27

10.

622

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60.

011

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00.

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0-0

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0.65

00.

907

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070

0.22

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752

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n-0

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740

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933

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664

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468

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69Re

sidua

l1.

302

3.44

70.

706

0.29

60.

675

1.61

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676

0.33

40.

023

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927

-0.0

99-0

.150

3.28

90.

964

-0.0

531.

773

1.19

10.

137

0.72

4

PIA

T m

ath

deriv

ed sc

ore

langu

age

com

posit

ede

rived

scor

eA

vera

ge m

ath

grad

e gr

ades

1-5

afte

r KG

aver

age

tcap

per

cent

ile y

1-5:

mat

h

Notes:

The

indic

es

are

means

of

the

non-m

issi

ng

item

s.T

he

fracti

ons

are

pro

port

ions

of

the

tota

lcondit

ional

diff

ere

nce

inm

eans.

85

Tab

leI.

20:

Oaxaca

-Bli

nd

erou

tcom

esat

age

12,

Dec

om

posi

tion

Part

2(M

ale

s)

Effe

ctSE

P-V

alFr

actio

nE

ffect

SEP

-Val

Frac

tion

Effe

ctSE

P-V

alFr

actio

nE

ffect

SEP

-Val

Frac

tion

Effe

ctSE

P-V

alFr

actio

nTo

tal D

iff. i

n M

eans

-0.0

630.

034

0.06

5-

-0.0

340.

025

0.17

6-

-0.0

680.

063

0.28

1-

-0.0

530.

030

0.08

1-

-1.0

170.

931

0.27

5-

Exp

laine

d-0

.005

0.01

00.

644

0.07

6-0

.003

0.01

00.

741

0.09

9-0

.030

0.02

20.

163

0.44

5-0

.014

0.01

20.

248

0.26

2-0

.524

0.34

60.

130

0.51

5U

nexp

laine

d-0

.058

0.03

60.

103

0.92

4-0

.031

0.02

50.

231

0.90

1-0

.038

0.06

20.

546

0.55

5-0

.039

0.03

00.

192

0.73

8-0

.493

0.91

80.

591

0.48

5

Exp

laine

dCo

gniti

ve0.

001

0.00

40.

727

-0.0

210.

000

0.00

30.

886

0.01

3-0

.006

0.00

90.

477

0.09

0-0

.006

0.00

60.

330

0.10

8-0

.237

0.22

80.

298

0.23

3A

ttent

ion

Prob

lems

-0.0

040.

005

0.50

50.

057

0.00

10.

003

0.78

9-0

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-0.0

040.

008

0.58

80.

062

0.00

00.

002

0.89

00.

006

-0.2

120.

237

0.37

00.

209

Cond

uct P

robl

ems

-0.0

010.

005

0.77

70.

022

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010.

004

0.74

00.

042

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020.

007

0.81

10.

024

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010.

004

0.74

20.

026

0.05

60.

180

0.75

8-0

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War

mth

/Em

path

y0.

002

0.00

40.

569

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340.

004

0.00

40.

296

-0.1

17-0

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0.00

70.

762

0.03

00.

001

0.00

40.

811

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18-0

.125

0.13

10.

339

0.12

3A

ggre

ssio

n-0

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0.00

60.

556

0.05

4-0

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0.00

80.

459

0.18

4-0

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0.01

50.

267

0.23

9-0

.007

0.00

70.

313

0.14

0-0

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0.11

90.

970

0.00

4

Une

xplai

ned

Cogn

itive

-0.0

010.

005

0.90

60.

010

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060.

007

0.38

20.

187

-0.0

030.

012

0.79

90.

046

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010.

007

0.87

90.

020

0.10

30.

135

0.44

4-0

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Atte

ntio

n Pr

oblem

s-0

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00.

650

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90.

000

0.00

50.

980

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0.01

60.

657

0.10

7-0

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0.00

50.

907

0.01

0-0

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0.19

90.

612

0.09

9Co

nduc

t Pro

blem

s0.

002

0.00

60.

783

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250.

002

0.00

50.

734

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470.

001

0.01

00.

960

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070.

002

0.00

60.

765

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340.

003

0.09

60.

977

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03W

arm

th/E

mpa

thy

-0.0

070.

007

0.33

50.

105

0.00

00.

004

0.91

30.

012

0.01

40.

014

0.33

8-0

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0.00

30.

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0.67

8-0

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510.

205

0.80

30.

050

Agg

ress

ion

0.00

10.

006

0.87

2-0

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0.00

60.

009

0.52

0-0

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0.00

40.

014

0.74

2-0

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0.00

10.

008

0.93

2-0

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0.05

40.

169

0.74

9-0

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Resid

ual

-0.0

490.

042

0.23

90.

780

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310.

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0.23

50.

923

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460.

069

0.50

30.

679

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440.

035

0.21

10.

818

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011.

072

0.64

00.

493

SC e

ver t

ried

smok

ing:

1=

yes

SC u

se a

lc, m

ar, t

ob la

st 3

0 da

ysIn

tern

alizi

ng d

isord

ers -

You

th

Anx

ious

/dep

ress

ed -

clini

cal o

r A

vera

ge n

umbe

r of a

bsen

ces,

Notes:

The

indic

es

are

means

of

the

non-m

issi

ng

item

s.T

he

fracti

ons

are

pro

port

ions

of

the

tota

lcondit

ional

diff

ere

nce

inm

eans.

86