The Economics and Econometrics of Human Development

The Economics and the Econometrics
of Human Development
James J. Heckman
University of Chicago
March 31, 2014
Institute of Economic Growth
New Delhi
Econ and Ecom of Hum Dev

Intergenerational Mobility and Inequality:
The “Great Gatsby Curve”
IGE: ln Y1
Income in current
generation
= α + βln Y0
Income of
parents
+ ε
India
Source: Corak 2011, Inequality from generation to generation: the United States in Comparison.
Notes: Inequality is measured post-taxes and transfers. Gini index deﬁned on household income. IGE measured by pre-tax
and transfer income of individual fathers and sons. The IGE estimate for India is taken from Hnatkovska et al. (2013).

Link to Appendix I

(a) Should there be policies that attempt to lower the IGE?
(b) If so, what form should they take?

Becker-Tomes-Solon
Heritability ↑ β ↑
Eﬃciency of parental investment ↑ β ↑
Inequality in wages ↑ β ↑
Inequality of public provision of investment ↑ β ↑

• As a purely statistical matter, the more heterogeneity across
units within an area the greater the estimated β.

• Main ﬁndings of the empirical literature

Hart & Risley, 1995
Children enter school with “meaningful differences” in vocabulary knowledge.
1. Emergence of the Problem
In a typical hour, the average child hears:
Family Actual Differences in Quantity Actual Differences in Quality
Status of Words Heard of Words Heard
Welfare 616 words 5 affirmatives, 11 prohibitions
Working Class 1,251 words 12 affirmatives, 7 prohibitions
Professional 2,153 words 32 affirmatives, 5 prohibitions

Hart & Risley, 1995
Children enter school with “meaningful differences” in vocabulary knowledge.
1. Emergence of the Problem
In a typical hour, the average child hears:
Family Actual Differences in Quantity Actual Differences in Quality
Status of Words Heard of Words Heard
Welfare 616 words 5 affirmatives, 11 prohibitions
Working Class 1,251 words 12 affirmatives, 7 prohibitions
Professional 2,153 words 32 affirmatives, 5 prohibitions
2. Cumulative Vocabulary at Age 3
Cumulative Vocabulary at Age 3
Children from welfare families: 500 words
Children from working class families: 700 words
Children from professional families: 1,100 words

Understanding Mechanisms

Capabilities, the Technology of Capability Formation, and
the Essential Ingredients of a Life Cycle Model of Human
Development

• Capabilities are multiple in nature.
• They encompass cognition, noncognitive and social preferences
and personality and preference traits, as well as health.
• Vector of capabilities at age t: θt.
• Capacities to act.
• Capabilities aﬀect (a) resource constraints, (b) agent
information sets and expectations, (c) parental information and
expectations and (d) preferences.
• They are stable across situations but evolve over time.

Deﬁne relationships Mt mapping θt to outcomes Yt at stage t of
the life cycle as:
Mt : θt → Yt. (1)
A core low-dimensional set of capacities generates a variety of
diverse outcomes.

Technology of Capability Formation
Cunha and Heckman (2007), Cunha (2007)
θt: a vector
θt+1 = ft( θt
self productivity
and cross eﬀects
, It
investment
broadly deﬁned
(parents, environment)
, θP ,t
parental
capabilities
) (2)

Complementarity Increases with Age
∂2
θt+1
∂θt∂It
↑ t ↑ .

Positive at later stages (t > t∗
) of childhood
∂2
θt+1
∂θt∂It
> 0, t > t∗
.
Some evidence suggesting
∂2
θt+1
∂θt∂It
≤ 0, t < t∗
,
But even if positive, still smaller than at t > t∗
.

Complementarity coupled with self-productivity ⇒
Dynamic Complementarity
It ↑ θt+1 ↑
θt+1 ↑ ⇒ θt+s ↑ s > 1
∴
∂2
θt+s+1
∂It∂It+s
> 0

Family Preferences for Child Outcomes
Diﬀerent versions of altruism, paternalism and beliefs about
“proper” child rearing

Family Resources Broadly Deﬁned:
Parental and Child Interactions
with Financial Markets and Access to Support from External
Institutions
(a) Restrictions on transfers across generations
(b) Restrictions on transfers within generations (parental lifetime
liquidity constraints)
(c) Public provision of investment; public policy towards children

Other Constraints on The Family Actively Being Investigated
(a) Information on parenting and other aspects of life across
generations
(b) Genes
(c) Structure of household and assortative matching patterns
(marriage markets)

The Empirical and Theoretical Challenge
A Life Cycle Framework for Organizing Studies and Integrating Evidence
θt: Capacities at t; It: investment at t; θP ,t: Parental environmental variables
θt+1 = ft(θt, It, θP ,t): Technology of Skill Formation
θ−1
θ0
θ1
θ2
θT
θT +1
I−1
I0
I1
I2
IT
θP ,−1
θP ,0
θP ,1
θP ,2
θP ,T
Prenatal
Birth
Early
Childhood, 0–3
Later
Childhood, 3–6
Adulthood
and Beyond

A Bare-Bones Model of Parental Investment

The Problem of the Parent
Link to Appendix II

Life lasts four periods:
• Two periods as a passive child who makes no economic
decisions (and whose consumption is ignored) but who receives
investment in the form of goods.
• Two periods as a parent.

Denote by θ1 the initial capability level of a child drawn from the
distribution J(θ1).
(For notational simplicity, denote θP,t = θP = h.)
Denoting by h the human capital of the child when child reaches
adulthood

Simpliﬁed parameterization of technology:
θt+1 = δt



γ1,tθφt
t + γ2,tIφt
t
investment
+ γ3,thφt
parental
human
capital



ρt
φt
with 0 < γ1,t, γ2,t, γ3,t, ρt ≤ 1, φt ≤ 1, k γk,nt = 1.

Final Form Representation
If T = 2, ρ1 = ρ2 = 1, δ1 = 1, and φ1 = φ2 = φ ≤ 1, skills at
adulthood, h = θ3 = θT+1 can be written as
h = δ2


γ1,2γ1,1θφ
1 + γ1,2γ2,1
“Multiplier”
Iφ
1 + γ2,2Iφ
2 + (γ3,2 + γ1,2γ3,1) hφ



1
φ
.

• If φ = 1, then investments at diﬀerent periods are (almost)
perfect substitutes.

• Polar example arises in the Leontief case where φ → −∞:
h = m2 h, θ0, min(I1, I2) (3)

• u(·): parental utility function
• β: discount factor
• r: real interest rate
• υ: parental altruism
• c1, c2 are consumption in parental life cycle periods 1 and 2

The goal of the parent is to optimize:
V (h, b, θ1) = max
c1,c2,I1,I2
u (c1) + βu (c2) + β2
υE [V (h , b , θ1)]
(4)
subject to technology and budget constraints.

Budget constraint is:
c1 + I1 +
c2 + I2
(1 + r)
+
b
(1 + r)2 = wh +
wh
(1 + r)
+ b. (5)

• Tractable ﬁnal form technology:
h = m2






h, θ0,





γ
investment
multiplier
(I1)φ
+ (1 − γ) (I2)φ





ρ
φ






, (6)
for φ ≤ 1 and 0 ≤ γ ≤ 1, ρ ≤ 1.

I1
I2
=
γ
(1 − γ) (1 + r)
ρ
1−φ
. (7)
I1
I2
↑ as γ ↑, φ ↑, ρ ↑ and r ↓.

• Important policy question: How easy (costly) is it to remediate
low I1 with high I2?

Implications of the Model

Borrowing Limits

Liquidity Constraints Within the Life Cycles of Parents
• The parent, within his/her lifetime, faces a sequence of
constraints at each stage of the life of the child.

Denoting parental ﬁnancial assets by a and allowing parental labor
market productivity to grow at exogenous rate g, these budget
constraints can be represented by a sequence of constraints:
c1 + I1 +
a
(1 + r)
= wh + b (8)
and
c2 + I2 +
b
(1 + r)
= w (1 + g) h + a (9)
and the borrowing constraints a ≥ a and b ≥ 0.
Assume that a ≥ 0: parents cannot borrow against their own future
income.
Child investments at diﬀerent ages are not perfect substitutes
(φ < 1).

Parental utility: u (c) = cλ
− 1 /λ.
I1
I2
=
γ
(1 − γ) (1 + r)
1
1−φ
unconstrained ratio
[β(1 + r)]
1
1−φ
c1
c2
1−λ
1−φ
=1 if unconstrained,
<1 if constrained
.
(10)
λ ≤ 1

• Cunha, Heckman, and Schennach (2010):
1/(1 − φ) = .¯3 (φ
.
= −2).
• Attanasio and Browning (1995): λ ∈ [−3, −1.5]
• (1 − λ)/(1 − φ) ∈ [0.8¯3, 1.¯3]. Family resource inﬂuence on
relative investment.
• Dynamic complementarity coupled with borrowing constraints
in the early years raises a potentially serious market
imperfection.

Introducing income uncertainty

Empirical Estimates of Credit Constraints and the Eﬀects of
Family Income on Child Outcomes

Recent Evidence on the Importance of Credit Constraints
and Family Income

College attendance by AFQT and Family Income Quartiles (1979)
Source: Belley and Lochner (2007).

College attendance by AFQT and Family Income Quartiles (1997)

College attendance by AFQT and Family Income Quartiles (1979 and
1997 placed on one graph)
Lochner 1979
Lochner 1997

• More people going to college at virtually all quartiles of
ability and income.
• Increases in college going is strongest for the lowest ability
group, especially less able children with richer parents.

• This provides no ﬁrm evidence for or against credit constraints.

Studies on the role of income on children’s outcomes and on
credit constraints
Link to Appendix III

Summary of the Evidence on Family Income, Credit
Constraints, and Child Development
• The literature on credit constraints and family income shows that higher
levels of parental resources, broadly defined, promote child outcomes.
• However, a clear separation of parental resources into pure income flows,
parental environmental variables and parental investment has not yet been
done.
• It is premature to advocate pure income transfer policies as effective ways
for promoting child welfare and promoting social mobility.
• What studies exist suggest very weak effects of income transfers on
childhood test scores.
• The evidence from the structural models supports this conclusion.
• Many of the studies show effects of prices, not constraints or pure income.

Structural Models of Parental Investment
Link to Appendix IV

Recent Extensions
(a) Parental time (mother and father) (Del Boca et al., 2013; Gayle
et al., 2013)
(b) Role of multiple parents (Del Boca et al., 2013; Gayle et al.,
2013)
(c) Multiple children (Del Boca et al., 2013; Gayle et al., 2013)
(d) Parental learning about technology (Badev and Cunha, 2012;
Cunha, 2012; Cunha et al., 2013)
(e) Fertility (Gayle et al., 2013)
(f) Marriage market (Gayle et al., 2013)
(g) Multiple capabilities (Cunha and Heckman, 2008; Cunha,
Heckman, and Schennach, 2010)

Estimates of the Technology of Capability Formation in the
Literature
(a) Most of literature focuses on cognitive skill technology
(b) Noncognitive skills recently introduced (Cunha and Heckman)
(c) Noncognitive skills foster production of cognitive skills
(d) Most analysts use linear technologies
(e) Nonlinearity essential to capture dynamic complementarity
(f) When estimated complementarity increases with the stage of
the life cycle (dynamic complementarity)
(g) Measurement error empirically important

Table 1: Capability Production Functions
Skill Output Functional
Cognitivea
Non-cognitivea
Health Form Anchoring
Todd and Wolpin (2003) X X Linear X
Bernal and Keane (2010) X X Linear X
Cunha and Heckman (2008) X Linear b
Cunha et al. (2010) X CES
Todd and Wolpin (2007) X X Linear X
Cunha (2007) X X CES
Del Boca et al. (2013) X X Log-Linear X
Caucutt and Lochner (2012) X X CES j
Bernal (2008) X X Linear X
Gayle et al. (2013) Xg
Xg
X N/S X
Bernal and Keane (2011) X X Linear X

Table 1 (continued): Capability Production Functions
Self Productivitya
Cross Productivitya
Increasing Investments / Skill
Cognitive Non-cognitive Cognitive Non-cognitive Complementarity over Timeh
Todd and Wolpin (2003) - N/A X X U
Bernal and Keane (2010) - N/A X X U
Cunha and Heckman (2008) 0.977 0.884 0.003 0.028 U
Cunha et al. (2010) 0.487/0.902c
0.649/0.868c
0.000/0.008c
0.083/0.011c
Todd and Wolpin (2007) 0.21 - 0.34d
X X U
Cunha (2007) 0.735/0.799 /0.872f
X X
Del Boca et al. (2013) (0.14, 0.503)/(0.172, 0.922)f
X X N/A
Caucutt and Lochner (2012) - N/A X X N/A
Bernal (2008) - N/A N/A X U
Gayle et al. (2013) N/S N/S X N/S
Bernal and Keane (2011) - N/A X X U

Investment with Multiple Children

Representation for the utility parents receive from N children:
V c
=
N
k=1
ωkV σ
k
1
σ
(11)
where Vk represents the relevant outcome for each child which is
valued by parents Behrman et al. (1982).

Targeting Relatively More Investment Toward Disadvantaged
Children Can Be Socially Eﬃcient
Link to Appendix V

In a one period of childhood problem where parents (or social
planners) seek to maximize the aggregate of adult skills (θ2):
θA
2 + θB
2
subject to E = p1(IA
1 + IB
1 ),
the ﬁrst order condition is
F.O.C.: f
(1)
2 γθB
1 , IA
1 = f
(1)
2 θB
1 , IB
1 .

sign
∂IA
1
∂γ
= sign f
(1)
12 (·)
γ=1
.
Parents (social planners) invest more in the disadvantaged if inputs
are substitutes with initial endowments and they invest less if they
are complements.

Suppose that parents (or social planners) seek to maximize
θA
3 + θB
3
subject to
E = p1(IA
1 + IB
1 ) + p2(IA
2 + IB
2 ).

Consider the following two-stage model of childhood investment.
θ3 = f (2)
(θ2, I2) (12)
θ2 = f (1)
(θ1, I1) (13)
where θ3 represents the level of skill at the beginning of adulthood.

Even if (f
(1)
12 > 0), greater first period investment in the initially
disadvantaged child may be optimal. This is more likely (ceteris
paribus)
(a) the more steeply diminishing is the productivity of second period
skills (f
(2)
22 );
(b) the greater the self productivity of the stock of skills in the first
period (f
(1)
1 = ∂θ2
∂θ1
);
(c) the smaller first period complementarity (f
(1)
21 ) relative to second
period complementarity and absolutely

(d) the more rapidly diminishing the marginal productivity of
θ1(f
(1)
11 );
(e) the greater the second period complementarity (f
(2)
12 );
(f) the greater the ﬁrst period productivity of investment (f
(1)
2 ) and
(g) the more rapidly diminishing the productivity of second period
investment (f
(2)
22 ).

An Example
Suppose that, for each child k, the outcome of interest for parents
are children’s earnings Ek and that they are function of children’s
adult human capital determined by genes (θ1,k) and early (I1,k) and
late (I2,k) parental investments.
Ek = wf 2
(θ2,k, I2,k) = τ2
γ2θφ2
2,k + (1 − γ2)Iφ2
2,k
ρ2
φ2
(14)
with θ2,k = f 1
(θ1,k, I1,k) = τ1
γ1θφ1
1,k + (1 − γ1)Iφ1
1,k
ρ1
φ1
(15)

w is common across families and siblings. Human capital is chosen
so that w = 1. The budget constraint faced by the parents with
total resources Re
is:
p1
n
k=1
I1 + p2
n
k=1
I2 = Re
. (16)

Measure of parental compensation with respect to initial inequality.
Define the parameter τ as:
τ ≡
Ei
Ej
θ1,i
θ1,j
. (17)
If τ = 1, the parents perfectly translate initial differences into
earnings differences.

Figure 1: Earnings Equalization
τ
ρ1
Notes: The parental preference parameters used in the simulation are σ = 1 and ωi = ωj = 0.5. Total resources are Re
= 4.
The technology of skill formation parameters, capturing increasing complementarity between skills and investments over time,
are: γ1 = γ2 = 0.5, φ1 = 0.6, φ2 = −0.5, ρ2 = 1. The parameter ρ1 deﬁnes the degree of homogeneity of the ﬁrst period
technology. We vary the value of ρ1 over the range [0.1, 1]. Child i has a skill endowment of 5 while child j of 1.

Figure 2a: Parental Investments
Ratio Early to Late Investments
More endowed child
Less endowed child
1
Notes: The solid line refers to the most endowed child, the dashed line to the least endowed child. The parameters used are
as in Figure 1.

Figure 2b: Parental Investments
Levels of Early Investments
More endowed child
Less endowed child
1
as in Figure 1.

Figure 2c: Parental Investments
Levels of Late Investments
More endowed child
Less endowed child
1
as in Figure 1.

Testing and Operationalizing the Theory

Capabilities as Determinants of Functionings

Decompose the θt vector into three subvectors:
θt = (θC,t, θN,t, θH,t) (18)
where θC,t is a vector of cognitive abilities (e.g., IQ) at age t, θN,t
is a vector of noncognitive abilities (e.g., patience, self-control,
temperament, risk aversion, discipline, and neuroticism) at age t,
and θH,t is a vector of health stocks for mental and physical health
at age t.

• Capabilities, combined with eﬀort, incentives and purchased
inputs determine functionings.

• Functionings (task j) at age t:
Yj,t = ψj,t(θt, ej,t, Xj,t), j ∈ {1, . . . , Jt} and t ∈ {1, . . . , 2T}
(19)
• Yj,t: outcome from activity j at time t
• θt is the vector of capabilities at age t
• Xj,t is a vector of purchased inputs that aﬀect the functionings
• ej,t is eﬀort in task
• T is the length of childhood
• T is the length of adulthood
• 2T is total lifetime

Eﬀort: ej,t
ej,t = δj (θt, At, Xj,t, Ra
j,t(It−1) | u). (20)
• At: environment
• Ra
j,t: incentives

Estimating and Interpreting the Distribution of Capabilities,
the Maps Between Capabilities and Functionings and the
Technology of Capability Formation

Nonparametric Factor Models Are Natural Frameworks for
Estimating Capabilities and Determining Frontier Capability
Sets

• Low dimensional capabilities (“factors”) generate a high
dimensional set of functionings.
• Dimension and factor structures selected through a variety of
methods.
• Exploratory factor analysis.
• Novel Bayesian procedures—avoid arbitrary methods in
Exploratory Factor Analysis.

Technology of Skill Formation
•
θk,t+1 = fs,k (θt, Ik,t, θP,t) (21)
for k ∈ {C, N, H}, t ∈ {1, 2, . . . , T}.

Identiﬁcation of the Technology of Skill Formation
• To estimate the technology of skill formation: Have to solve
three problems.

Identiﬁcation of the Technology of Skill Formation
• To estimate the technology of skill formation: Have to solve
three problems.
1 Don’t observe (θt, Ik,t, θP,t) directly, but have many
measurements on it. Measurement error in nonlinear
systems.
2 Don’t know which scale to use to measure components of θt.
Anchor test scores on adult outcomes.
3 Investment Ik,t may be chosen by parents based on information
that may be unobserved by the econometrician (ηk,t).
Endogeneity of investment.

Estimating Functionings and Extracting Factors:
Multiple Capabilities Shape Human Achievement Across a
Variety of Dimensions

• The relationship between capabilities estimated in the recent
literature and traditional preference parameters (time
preference, leisure, risk aversion, etc.) is weak. Dohmen, Falk,
et al. (2012)
• Suggests that a richer set of preference and constraint
descriptions may characterize choice behavior.

Decile of Cognitive
1 2 3 4 5 6 7 8 9 10
Decile of Socio-Emotional
1
2
34
5
67
8
9
10
Probability
0
0.2
0.4
0.6
0.8
1
Decile of Cognitive
1 2 3 4 5 6 7 8 9 10
Probability
0
0.2
0.4
0.6
0.8
1
Fraction
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
Probability
Decile of Socio-Emotional
1 2 3 4 5 6 7 8 9 10
Probability
0
0.2
0.4
0.6
0.8
1
Fraction
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
Probability
Figure 3: The Probability of Educational Decisions, by Endowment
Levels, Dropping from Secondary School vs. Graduating
(Source: Heckman et al., 2011)

The same low-dimensional vector of capabilities predicts a wide
variety of outcomes for:
• Crime
• Wages
• Health
• Healthy behaviors (smoking, drug use)
• Trust
• Voting behavior
• Employment
• Participation in welfare

Estimates of Technologies of Capability Formation and Some
Implications

• Capabilities evolve over the life cycle
• Parental investments explain 34% of variance of educational
attainment
• Self-productivity becomes stronger as children become older,
for both cognitive and noncognitive skill formation
(i.e., ∂θt+1
∂θt
↑ t).
• Strong cross eﬀects (noncognitive skills foster cognitive
investment)
• Complementarity between cognitive skills and investment
becomes stronger as children become older. The elasticity of
substitution for cognitive production is smaller in second stage
production

• Emerging dynamic complementarity.
• It is more difficult to compensate for the effects of adverse
environments on cognitive endowments at later ages than it is
at earlier ages. This pattern of the estimates helps to explain
the evidence on ineffective cognitive remediation strategies for
disadvantaged adolescents reported in Cunha et al. (2006),
Cunha (2007), and later papers.
• Complementarity between noncognitive skills and investments
stays roughly constant over the life cycle.
• Suggests that later life investments should be more focused on
promoting noncognitive—personality—skills.
• The evidence on which adolescent interventions are successful
is consistent with this evidence.

The Implications of the Estimates for Design of Policy
• Targeted strategies
• Consider a policy for a social planner to optimize the stock of
education in society.
• Assume (for simplicity) full control of investment (ignores
parental responses)
• The bulk of the evidence in the child development literature
shows reinforcement of investment by parents.
• No consideration of social fairness, equality of opportunity or
equality of final outcomes—just efficiency.
• Yet with these estimates the optimal policy invests the most in
the disadvantaged.
• As an empirical matter, social justice is enhanced by what is
productively efficient.

Socially Optimal Early and Late Levels of Investment by Initial
Capabilities
Child Initial
Cognitive Skill
Child Initial
Noncognitive Skill
Child Initial
Noncognitive Skill
Child Initial
Cognitive Skill
Source: Cunha et al. (2010). Optimal investments to maximize aggregate education in society.

0.5 1 1.5 2 2.5
0
0.5
1
1.5
2
2.5
3
3.5
Figure 5
Densities of Ratio of Early to Late Investments
Maximizing Aggregate Education Versus Minimizing Aggregate Crime
Ratio Early to Late Investment
Education
Crime

Using Economics to Go Behind Estimated Program
Treatment Effects and Beyond Meta-Analyses of Treatment
Effects:
Linking the Program Evaluation Literature with
the Economics of the Family
• Widely used “metanalyses” on early childhood do not recognize
that various interventions in early childhood previously
implemented differ.
1 The populations targeted differ.
2 The objectives and curricula of the programs differ.
3 The measurement systems for backgrounds and outcomes
differ among each other and also with observational studies.
4 The methods of evaluation differ.
5 Need to integrate the studies of family influence with the
intervention studies to understand how interventions affect
family life.
6 Need to compare alternative policies in comparable metrics;
i.e., rates of return to policies or cost-benefit analyses.

Lessons From and Lessons For the Intervention Literature
Link to Appendix VI

The Mechanisms Producing the Treatment Eﬀects:
A Case Study

Cognitive Evolution by Age, Perry Males
Male Cognitive Dynamics
79.2 94.9 95.4 91.5 91.1 88.3 88.4 83.7
77.8 83.1 84.8 85.8 87.7 89.1 89.0 86.0
75
80
85
90
95
100
105
Treatment
Control
IQ
4 5 6 7 8 9 10Entry
Age
Treatment
Control

Personal Behavior Index by Treatment Group
Control Treatment
0.2.4.6.81
density
2 2.5 3 3.5 4 4.5 5
®
0.2.4.6.81
density
2 2.5 3 3.5 4 4.5 5
®

Socio-Emotional Index by Treatment Group
Control Treatment
0.2.4.6.8
density
1 2 3 4 5 0.2.4.6.8
density
1 2 3 4 5

Decomposition of Treatment Effects, Males
32THEAMERICANECONOMICREVIEWMONTHYEAR
0.056
0.149
0.077
0.013
0.130
0.085
0.136
0.046
0.089
0.062
0.071
0.071 0.557
0.499
0.403
0.086
0.161
0.032
0.018
0.204
0.088
0.141
0.027
0.144
0.246
0.114
0% 20% 40% 60% 80% 100%
Use heroin, age 40(-0.143*)
Employed, age 40 (0.200**)
# of lifetime arrests, age 40 (-4.20*)
# of adult arrests (misd.+fel.), age 40 (-4.26**)
# of felony arrests, age 40 (-1.14*)
# of misdemeanor arrests, age 40 (-3.13**)
Use tobacco, age 27 (-0.119*)
Monthly income, age 27 (0.876**)
# of adult arrests (misd.+fel.), age 27 (-2.33**)
# of felony arrests, age 27 (-1.12)
# of misdemeanor arrests, age 27 (-1.21**)
CAT total at age 14, end of grade 8 (0.566*)
Cognitive Factor Externalizing Behavior Academic Motivation Other Factors
Figure 6. Decompositions of Treatment Effects on Outcomes, Males
Note: The total treatment effects are shown in parentheses. Each bar represents the total treatment effect normalized to 100 percent. One-sided p-values
are shown above each component of the decomposition. The figure is a slightly simplified visualization of Tables L.10 and L.14: small and statistically
insignificant contributions of the opposite sign are set to zero. See Web Appendix L for detailed information about the simplifications made to produce
the figure. “CAT total” denotes California Achievement Test total score normalized to control mean zero and variance of one. Asterisks denote statistical
significance: * – 10 percent level; ** – 5 percent level; *** – 1 percent level. Monthly income is adjusted to thousands of year-2006 dollars using annual
national CPI.

Health Outcomes
Link to Appendix VII

Attachment, Engagement
Toward a Deeper Understanding of Parenting and Learning
• In both Perry and ABC (and many other interventions) a main
channel of inﬂuence is on the parent-child interactions.
• Enhanced attachment and engagement of parents.
• This has important implications for how we model family
inﬂuence.

Mechanisms—producing eﬀects
(a) Information
(b) Changing preferences of parents
(c) Parental response to child’s curiosity and interest induced by
participation in the program

Parental response to Perry Preschool Program
102030405060
Proportion
−.015 −.01 −.005 0 .005 .01 .015
Belief in Importance of Parenting
Control Treatment

Table 2: Models of Parent-Child Interaction
(“ ” means present; “X” means absent)
Parental
Monetary
Investments
Discordance in
Preferences
between Parent
and Child
Multiple
Children
Parental
Incentives for
Child Effort
Cosconati (2013) X a,b
X c
Akabayashi (2006) a
X d,e
Hao et al. (2008) b e
Lizzeri and Siniscalchi (2008) X d
X X
a
Difference in discount factors. b
Differences in utility functions. c
Restrictions on leisure. d
Differences in knowledge about
proper task execution. e
Time investments in the child. f
Monetary investments in the child. g
The authors analyze the
effects of time investments. h
Implications from the model are empirically tested.

Table 2 (continued): Models of Parent-Child Interaction
Eﬀort Produces
Greater Capability
Parental
Learning about
Child Quality
Parental Actions
Facilitate
Acquisition of
Information
Parental
Beliefs Can
Diverge
from Truth
Cosconati (2013) X X X
Akabayashi (2006) f
Hao et al. (2008) X X X X
Lizzeri and Siniscalchi (2008) X X X
a

Table 2 (continued): Models of Parent-Child Interaction
Child’s Eﬀort
Observable
Child’s
Human Capital
Observable
Model Is
Estimated
Cosconati (2013) X
Akabayashi (2006) X X
Hao et al. (2008) X X g
Lizzeri and Siniscalchi (2008) X X
a

An Economic Model of Mentoring and Scaﬀolding
(Garc´ıa, Heckman, Mosso, and Wang, 2013)

Mentor’s Problem
Yt: Measured output of child at age t
θt: Capabilities at outset
θt: Parental targets
It: Parental investment at age t
at: Child eﬀort at age t
The mentor’s problem is to minimize
Vt(Yt) = min
It ,...IN−1
E
N−1
τ=t
βτ
θτ Qθτ + Iτ RIτ + θN Qf θN |Yt
where Q, Qf , R ≥ 0.

Technology: θt+1 = Aθt + BIt + Fat + wt
θt+1 = Ψ(θt, It, at)
θt+1 = Ψ(θt, It, at)
Yt = Cθt + Dat + vt
θt = θt − θt
It = It − It
at = at − at.

Child’s Problem
(with development of agency of the child)
• The child chooses a sequence of eﬀort (a1, . . . , aN−1) to
maximize her utility in each period.
• Her value function at time t is:
Jt(Yt) = max
at ,...,aN−1
λt(θt)J1
t (Yt) + (1 − λt(θt))J2
t (Yt)

J1
t (Yt) = max
at ,...,aN−1
E
N−1
τ=t
βτ
−
(h It)
η
2γ
(at − a) (at − a + α It) |Yt
J2
t (Yt) = max
at ,...,aN−1
E
N−1
τ=t
βτ
−
h RP
t (at)
η
2γ
(at − a) (at − a) + α It |Yt
• RP
t (·) is the best response function of the mentor

Integrating Experimental Studies with Family Inﬂuence
Studies

• IGt : government investment
• IPt : private (family) investment
• Government technology: f G
(θt, θPt , IGt , IPt )
• Private technology: f P
• Mixed technology: f M

• Studies under way doing this (Fan, Hai, Heckman, Wei, and
Zhang, 2013)

What about promoting education?

Early development is as important as education in promoting
wages, employment, and health.

Disparities by Education (Post-compulsory Education)
• Education, Wages, Employment, and Health
Note: Conti and Heckman (2010). Author’s calculations using British Cohort Study, 1970.

Summary

Predistribution Not Simply Redistribution

(a) Should there be policies that attempt to lower the IGE?
(b) If so, what form should interventions take?

Appendix I

USA
Canada
Denmark
Finland
France
Germany
Norway
Sweden
UKItaly
Japan
0.1.2.3.4.5
Intergen.ElasticityofEarnings(IGE)
.2 .25 .3 .35
Gini Coefﬁcient, After Taxes and Transfers
Corak's Chosen IGE OLS Slope=2.19, p-value=.003
• In Corak (2013), the Great Gatsby Curve has signiﬁcant,
positive slope in OLS regression.

USA
Canada
Denmark
Finland
France
Germany
Norway
Sweden
UKItaly
Japan
0.1.2.3.4.5
.34 .38 .42 .46
Gini Coefficient, Before Taxes and Transfers
Corak's Chosen IGE OLS Slope=1.82, p-value=.059
• However, there is a methodological mistake in Corak (2013):
after tax-and-transfer Gini coefficients are compared to before
tax-and-transfer IGE.
• Correcting this mistake makes the Great Gatsby Curve
insignificantly sloped.

USA
Canada
DenmarkFinland
France
Germany
Norway
Sweden
UKItaly
Japan
0.1.2.3.4.5
.2 .25 .3 .35
Corak's Chosen IGE except USA OLS Slope=0.70, p-value=.003
• Due to the anchoring scheme employed by Corak (2013), the
slope of the Great Gatsby Curve is arbitrarily controlled by the
partly subjective choice of USA IGE estimate.

USACanada
Denmark
Finland
France
Germany
Norway
Sweden
UK
Italy
Japan
0.1.2.3.4.5
.34 .38 .42 .46
Gini Coefﬁcient, Before Taxes and Transfers
Alternate IGE Choice OLS: Slope=-0.16, p-value=.869
• By replacing only three of the countries’ IGE estimates with
plausible alternates from the literature, we arrive at a
negatively-sloped Great Gatsby Curve.
• Conclusion: Corak’s Great Gatsby Curve is not robust. This
does not disprove the hypothesis that inequality and IGE are
positively related.

USA
Canada
Denmark
Finland
France
Germany
Norway
Sweden
UK
0.1.2.3.4.5
IntergenerationalElasticity(FathertoSonEarnings)
.2 .25 .3 .35
Corak's Preferred Data OLS (Slope=2.05, p-value=.008)
Corak's Great Gatsby Curve
Source: Corak, JEP(2013)

USA
Canada
Denmark
Finland
France
Germany
Norway
Sweden
UK
0.1.2.3.4.5
IntergenerationalElasticity
.2 .25 .3 .35
Corak's Preferred Data OLS (Slope=2.64, p-value=.016)
Great Gatsby Curve without Corak's Adjustments
Source: Bradley Setzler 2013

USACanada
Denmark
Finland
France
Germany
Norway
Sweden
UK
0.1.2.3.4.5
.2 .25 .3 .35
Alternate Data Choice OLS (Slope=-0.02, p-value=.980)
Great Gatsby Curve using Alternate Elasticities

USA
Canada
Denmark
Finland
France
Germany
Norway
Sweden
UK
0.1.2.3.4.5
.2 .25 .3 .35
Corak's Preferred Data except USA OLS (Slope=0.65, p-value=.008)
Great Gatsby Curve with Lower USA Choice

Return to main text

Appendix II

Dynastic Model of Parental Investment that Emphasizes the
Interaction of Dynamic Complementarity and Credit Markets

• Parents face diﬀerent constraints
i Inability of the family to borrow against future income of child
(Already in the Becker–Tomes–Solon model: BTS)
ii Inability of parents to borrow against their own future
income (new to literature)

Capability Formation in an Economy with
Idiosyncratic Uncertainty and Liquidity Constraints
(New to Literature)

Generational Structure
• Each agent lives for 2T periods (T = 1 in BTS).
• During the ﬁrst T years of life, the agent is a child and by
assumption makes no economic decisions.
• Upon reaching age T + 1, the agent becomes an adult and
gives birth to a child. (Exogenous fertility.)
• The agent dies at the end of the calendar year in which she
completes 2T years of age and is replaced in the beginning of
the next calendar year by the generation of her grandchild.

The Technology of Skill Formation

• It is investment; θt stock of child skills; h stock of
parental skills (h ≡ θP).
• T distinct stages of development.
• The technology for capability formation:
θt+1 = ft (θt, It, h) (22)
• f : increasing in each of its arguments, strictly concave, and
twice-continuously diﬀerentiable.

• To develop some intuition about the skill formation process
implied by the production function (22), consider the following
parameterization:
θt+1 = δt γ1tθφt
t + γ2tIφt
t + γ3thφt
ρt
φt
with 0 < γ1,t, γ2,t, γ3,t, ρt < 1, φt ≤ 1, k γk,nt = 1.

• If T = 2, ρ1 = ρ2 = 1, δ1 = 1, and φ1 = φ2 = φ ≤ 1.
• Skills at adulthood, h = θ3 = θT+1:
h = δ2


γ1,2γ1,1θφ
1 + γ1,2γ2,1
“Multiplier eﬀect”
Iφ
1 + γ2,2Iφ
2 + (γ3,2 + γ1,2γ3,1) hφ



1
φ
.

• An extreme example arises in the Leontief case where
φ → −∞, in which case we would write:
θ3 = δ2 min {θ1, I1, I2, h} (23)

The Problem of the Parent

The Problem When the Child Is between 1 and T − 1 Years
Old
• Parental labor supply is perfectly inelastic.
• At each age t of the child, the parent is subject to productivity
innovations εt. Corresponding to labor market uncertainty.
• The shocks εt are independently and identically distributed
across parents.
• The shocks follow a ﬁrst-order Markov process:
ln εt+1 = ρε ln εt + σηηε
t . (24)
• Parents are assumed to have positive earnings.
• Restrict productivity innovations such that there exists εmin with
the property that εt ≥ εmin > 0 for any t = T + 1, . . . , 2T.
• Labor income of the parent: whεt
• w is the eﬃciency wage
• r is risk-free discount rate

• Given the state variables, the parent chooses household
consumption Ct, savings st+1, and investments It in the
cognitive skill of the child.
• The savings of the parents are in a risk-free asset which pays a
rate of interest r.
• p denotes the price of the investment goods in cognitive skill.
• Following Laitner (1992), the parents cannot leave debts to
their children and have negative net worth, so savings are
subject to the lower bound equal to −whεmin
(1+r)
.

• V (t, h, θt, st, εt): the value function of the parent of a child at
age t, 1 ≤ t ≤ T − 1.
• The problem of the parent:
V (t, h, θt, st, εt)
= max
Ct ,It ,st+1
{u (Ct) + βE [V (t + 1, h, θt+1, st+1, εt+1)| εt]}
subject to:
Ct + pIt + st+1 = whεt + (1 + r) st (25)
st+1 ≥ − (whεmin) , It, Ct ≥ 0 (26)
and the technology for capability formation (22).

The Problem When the Child Is T Years Old:
Go to College or Not?

Steady State GE
• Firms producing ﬁnal output (CRS)
• Also child investment good (Produced)
• Can establish stochastic GE for steady state, extending Aiyagari
and Laitner to include human capital

Appendix III

Table 3a: Studies on the Role of Income on Children’s Outcomes
Dataset Outcome
Studied: Test
Scores (T),
Schooling (S)
Timing of Income
(Developmental Stage
of the Child at Which
Income Eﬀects are
Studied)
Separate the
Eﬀect of Income
from Changes in
Labor Supply or
Family
Environment
Carneiro and Heckman
(2002)
NLSY79∗ S Early (E) and Late
(L)
College Enrollment
X
Belley and Lochner
(2007)
NLSY79∗,
NLSY97∗
S L
High school
completion and
College Enrollment
X
Dahl and Lochner
(2012)
NLSY79∗,
C-
NLSY79∗
T E
Preadolescence
(ages 8 to 14)
Xa
Duncan et al. (1998) PSID∗ Sd E and L
Childhood and
Preadolescence
(ages 0 to 15)
X

Table 3a (cont.): Studies on the Role of Income on Children’s Outcomes
Dataset Outcome Studied:
Test Scores (T),
Schooling (S)
Timing of Income
(Developmental Stage of the
Child at Which Income
Eﬀects are Studied)
Separate the Eﬀect of
Income from Changes in
Labor Supply or Family
Environment
Duncan et al. (2011) Randomized
Interventions
on Welfare
Support
T E
Early Childhood
(ages 2 to 5)
X
Loken (2010) Norwegian
Administrative
Data
S E
Childhood
(ages 1 to 11)
c
Loken et al. (2012) Norwegian
Administrative
Data
S E
Childhood
(ages 1 to 11)
X
Milligan and Stabile
(2011)
CCTB∗∗
,
NCBS∗∗∗
T E
Childhood
(ages 0 to 10)
X
Carneiro et al. (2013) Norwegian
Registry
Se
E and L
Childhood to Adolescence
(ages 0 to 17)
X

Table 3b: Studies on the Role of Income on Children’s Outcomes
Distinguishes the
Eﬀects of
Contemporaneous vs.
Permanent Income
Sources of Income
Whose Eﬀects are
Studied
Instrument Used
Carneiro and Heckman (2002) Total family income None
Belley and Lochner (2007) X Total family income None
Dahl and Lochner (2012) Xb
Total family income Policy variation in EITC
eligibility
Duncan et al. (1998) Total family income None

Table 3b (continued): Studies on the Role of Income on Children’s
Outcomes
Distinguishes the
Effects of
Contemporaneous vs.
Permanent Income
Sources of Income
Whose Effects are
Studied
Instrument Used
Duncan et al. (2011) X Total family income Random assignment to programs
offering welfare transfers conditional
on employment or education related
activities, or full time work
Loken (2010) X Total family income Oil discovery (inducing regional
increase in wages)
Loken et al. (2012) X Total family income Oil discovery (inducing regional
increase in wages)
Milligan and Stabile (2011) X Child related tax benefits
and income transfers
Variation in benefits eligibility
Carneiro et al. (2013) Total family income None

Table 3c: Studies on the Role of Income on Children’s Outcomes
Effect of Income on Human Capital Investments
Carneiro and Heckman (2002) Percentage of people constrained = weighted gap in educational outcome to highest
income group: 5.1% are constrained in college enrollment (1.2% among low income, low
ability, 0.2% low income high ability), 9% in completion of 2-year college (5.3% among
low income, low ability, 0.3% low income high ability). No effect of timing of receipt of
family income on child outcomes.
Belley and Lochner (2007) High school completion: +8.4% for highest income quartile compared to lowest in 79,
+6.7 in 97 cannot reject equal effect of income; college enrollment: +9.3% for highest
income quartile compared to lowest in 79, +16 in 97, cannot reject equal effect of income.
Dahl and Lochner (2012) $1,000 extra per year for 2 years: +6% of a standard deviation in math and reading
combined PIAT score.
Duncan et al. (1998) $10,000 increase in average (age 0-15) family income: +1.3 years of schooling in low
income (¡$20,000) families, +0.13 in high income ones. Relevance of income is stronger
in the early years (age 0-5): $10,000 increase in average (age 0-5) family income leads to
extra 0.8 years of schooling in low income families, 0.1 in high income ones. Income at
age 6-10 and 11-15: no significant effect. Similar results in a sibling differences model.

Table 3c (continued): Studies on the Role of Income on Children’s
Outcomes
Effect of Income on Human Capital Investments
Duncan et al. (2011) $1,000 extra per year for 2 to 5 years: +6% of a standard deviation in child’s achievement
score.
Loken (2010) OLS: positive relationship of average (age 1-13) family income on children’s education,
IV: no causal effect. Results are robust to different specification and splitting the sample
by parental education.
Loken et al. (2012) Non-linear IV (quadratic model): increase of $17,414, +0.74 years of education for chil-
dren in poor families, +0.05 for children in rich families.
Milligan and Stabile (2011) Low education mothers: positive effects of child benefits on cognitive outcomes for boys,
on emotional outcomes for girls, weak on health. Results are non robust to the exclusion
of Quebec.
Carneiro et al. (2013) All outcomes: monotone and concave relationship with permanent income. £100,000
increase in permanent father’s earnings: +0.5 years of schooling. Timing of income: a
balanced profile between early (age 0-5) and late childhood (age 6-11) is associated with
the best outcomes; shifting income to adolescence is associated with better outcomes in
dropping out of school, college attendance, earnings, IQ and teen pregnancy. Early and
late childhood income are complements in determining schooling attainment, early and
adolescent income are substitutes.

Table 4a: Studies on Tests of Credit Constraints
Dataset Outcome
Studied:
School-
ing
(S)
Timing of Income
(Developmental
Stage of the Child
at Which
Constraints are
Studied)
Explicit
Dynamic
Model
Who is Aﬀected
by Constraints:
Parent of the
Agent (P), Agent
/ Child (C)
Keane and
Wolpin
(2001)
NLSY79∗ S L
College
Enrollment
C
Carneiro and
Heckman
(2002)
NLSY79∗,
C-
NLSY79∗
S E and L
College
Enrollment,
Comple-
tion,
Delayed
Entry
X P

Table 4a (continued): Studies on Tests of Credit Constraints
Dataset Outcome
Studied:
School-
ing
(S)
Timing of Income
(Developmental
Stage of the Child
at Which
Constraints are
Studied)
Explicit
Dynamic
Model
Who is Aﬀected
by Constraints:
Parent of the
Agent (P), Agent
/ Child (C)
Cameron and
Taber (2004)
NLSY79∗ S L
Adolescence and
College Enrollment
X C
Caucutt and
Lochner
(2012)
NLSY79∗,
C-NLSY79∗
Ta E and L
Childhood and
Adolescence
P

Table 4b: Studies on Tests of Credit Constraints
Method to Test for
Credit Constraints
Find Presence of Credit
Constraints
Effect of Income or Constraints on Human
Capital Investments
Keane and Wolpin
(2001)
Structural estimation of
the lower bound on asset
level
YES
But irrelevant for
schooling decisions
Increase borrowing limit to $3,000 (3× max es-
timated): no change in mean highest grade com-
pleted; +0.2% in college enrollment; -0.2$ on mean
hourly wage rate; increase in consumption and re-
duction in market hours; moderate reduction in
parental transfers especially for the least educated
parents.
Carneiro and
Heckman (2002)
(1) Gap to students from
highest income quartile.
(2) Timing of income.
(3) Difference in IV and
OLS estimates of Mincer
coefficient
YES
But affecting at most
8% of students
(1) Conditioning on ability and family background
factors, the role of income in determining school-
ing decisions is minimal. The strongest evidence is
in the low ability group. The test is not robust to
accounting for parental preferences and paternal-
ism. Observed differences in attendance might be
due to a consumption value of child’s schooling for
parents.
(2) There is no evidence of a independent effect
on college enrollment of early or late income once
permanent income is accounted for.
(3) The claim that higher IV than OLS estimates of
the Mincer coefficient implies credit constraints are
incorrect: instruments used are invalid, the quality
margin is ignored and self selection and compara-
tive advantage can produce the result also in ab-
sence of financial constraints.

Table 4b (continued): Studies on Tests of Credit Constraints
Method to Test for
Credit Constraints
Find Presence of Credit
Constraints
Effect of Income or Constraints on Human
Capital Investments
Cameron and
Taber (2004)
IV estimation of
“returns” to schooling
using costs of schooling
or foregone earnings as
instruments
NO Theoretical prediction: if borrowing constraints,
IV estimates using direct costs of schooling higher
than using opportunity costs. Data: IV estimates
using the presence of a local college are smaller
than the ones using foregone earnings. Regressions
which interact college costs and characteristics po-
tentially related to credit availability: no evidence
of excess sensitivity to costs for potentially con-
strained sample. Structural model: almost 0% of
the population is found to borrow at a rate higher
than the market one.
Caucutt and
Lochner (2012)
Structural estimation of
the lower bound on asset
level
YES
Stronger effect on high
skilled parents
50% of young parents are constrained: high school
dropouts (50%), high school graduates (38%), col-
lege dropouts (60%), college graduates (68%); and
12% of old parents are constrained. Families with
college graduate parents benefit the most from a
reduction in credit constraints.

Appendix IV

Table 5: Structural Models of Parental Investments
OLG Model Dynastic Links Explicit
Models of
Parental
Preferences,
Altruism (A)
or Paternalism
(P)
Model
Estimated
Cunha and Heckman (2007) A,B,C, i
(A) X
Cunha (2007) A,B,C i
(A)
Caucutt and Lochner (2012) B,C i
(A)
Del Boca et al. (2013) X X j
(P)
Gayle et al. (2013) A,C j
(P)
Cunha et al. (2013) X X j
(P)
Bernal (2008) X X j
(P)
AThrough parental skills, BThrough asset transfers, COnly through genes (initial
conditions), DNatural borrowing limit, ELimits can be more stringent than natural
limit.

Parental
Goods
Investment
Parental Time
Investment
Technology
Depends on
Parental Skill
Self-
productivity
Cunha and Heckman (2007) X
Cunha (2007) X
Caucutt and Lochner (2012) X X
Del Boca et al. (2013) X
Gayle et al. (2013) X
Cunha et al. (2013) X
Bernal (2008)
limit.

Parental
Learning
About
Technology
Bequests Intragenerational
Borrowing
Multiple Skills
of Children
Cunha and Heckman (2007) X E
X
Cunha (2007) X D
X
Caucutt and Lochner (2012) X X E
X
Del Boca et al. (2013) X X X X
Gayle et al. (2013) X X X X
Cunha et al. (2013) X X X
Bernal (2008) X X X X
AThrough parental skills, BThrough asset transfers, COnly through genes (ini-
tial conditions), DNatural borrowing limit, ELimits can be more stringent than
natural limit.

Table 5: Structural Models of Parental Investment
Multichild
Families
(Preferences for
Equity vs.
Eﬃciency)
Endogenous
Fertility
Decisions
Multiple
Parents
Endogenous
Mating
Decisions
Cunha and Heckman (2007) X X X X
Cunha (2007) X X X X
Caucutt and Lochner (2012) X X X X
Del Boca et al. (2013) X X
Gayle et al. (2013)
Cunha et al. (2013) X X X X
Bernal (2008) X X X X
limit.

Appendix V

Targeting Relatively More Investment Toward Disadvantaged
Children Can Be Socially Eﬃcient

Notice that
sign
∂IA
1
∂γ
= sign f
(1)
12 (·)
γ=1
,
where f
(1)
12 (·) is the value of f (12)
in the neighborhood of (·).
Parents (social planners) invest more in the disadvantaged if inputs
are substitutes with initial endowments and they invest less if they
are complements.

Roughly speaking, the more concave are the technologies in terms of
stocks of skills, the more favorable is the case for investing relatively
more in the disadvantaged child. The greater the second period
complementarity (f
(2)
12 ), the greater the case for investing more in
the initially disadvantaged child to allow the child to benefit from
greater second period complementarity of the stock of skills with
second period investment. In general, even when investment is
greater in the first period for the disadvantaged child, second period
investment is greater for the initially advantaged child. It is
generally not efficient to make the initially disadvantaged child
whole as it enters the second period when the effect of greater
second period complementarity kicks in.

Appendix VI

Table 6a: Summary of Eﬀects for Main Interventions
Participant/Evaluation Characteristics
Program
Age
Duration
Target
Selection
Follow-Up
Sample
RCTEval
Elementary
LA’s Best 5–6 6Y SES Schl 12Y 19,320 No
CSP 5–13 5Y Behav Refer 35Y 510 Yes
SSDP 6–7 6Y Crime Prgrm 21Y 610 Yes
Adolescence
BBBS 10-16 1Y SES Self 1Y 960 Yes
IHAD 11–12 7Y SES Prgrm 8Y 180 Yes
EPIS 13–15 3Y Schl Schl 2Y 45,070 No
xl club 14 2Y Schl Schl 2Y 261,420 No
SAS 14–15 5Y Schl, SES Schl 6Y 430 No
STEP 14–15 2Y Schl, SES Self 4Y 4,800 Yes
QOP 14–15 5Y Schl Prgrm 10Y 1,070 Yes
Academies 13–16 4Y Schl, SES Self 12Y 1,460 Yes
ChalleNGe 16–18 1Y Dropout Self 3Y 1,200 Yes
Job Corps 16–24 1Y SES Self 9Y 15,300 Yes
Year-Up 18–24 1Y SES Self 2Y 200 Yes

Table 6b: Summary of Eﬀects for Main Interventions
Components
Program
Home
Health
Parental
OnSite
Group
Elementary
LA’s Best
CSP
SSDP
Adolescence
BBBS
IHAD
EPIS
xl club
SAS
STEP
QOP
Academies
ChalleNGe
Job Corps
Year-Up

Table 6c: Summary of Effects for Main Interventions
Effects on Outcomes Return/Benefits
Program
IQ
School
Character
Education
Health
Crime
Earnings
Return
BenefitCost
Elementary
LA’s Best 0.9
CSP
SSDP 3.1
Adolescence
BBBS 1.0
IHAD
EPIS 0.9–3.0
xl club
SAS
STEP
QOP 0.42
Academies
ChalleNGe 6.4 2.66
Job Corps 0.22
Year-Up

Table 6d: Summary of Eﬀects for Main Interventions
Participant/Evaluation Characteristics
Program Age
Duration
Target
Selection
Follow-Up
Sample
RCTEval
Early
NFP < 0 2Y SES Prgrm 19Y 640 Yes
ABC 0 5Y SES Refer 30Y 90 Yes
IHDP 0 3Y Health Prgrm 18Y 640 Yes
FDRP 0 5Y SES Prgrm 15Y 110 No
PCDC 1 2Y SES Prgrm 15Y 170 Yes
JSS 1–2 2Y Health Prgrm 22Y 160 Yes
Perry 3 2Y SES, IQ Prgrm 37Y 120 Yes
Head Start 3 2Y SES Prnt 23Y 4,170 Yes
CPC 3–4 2Y SES Prnt 25Y 1,290 No
TEEP 3,5 2Y SES Prgrm 22Y 260 Yes
STAR 5–6 4Y SES Prgrm 22Y 11,000 Yes

Table 6e: Summary of Eﬀects for Main Interventions
Components
Program
Home
Health
Parental
OnSite
Group
Early
NFP
ABC
IHDP
FDRP
PCDC
JSS
Perry
Head Start
CPC
TEEP
STAR

Table 6f: Summary of Effects for Main Interventions
Effects on Outcomes Return/Benefits
Program IQ
School
Character
Education
Health
Crime
Earnings
Return
BenefitCost
Early
NFP 2.9
ABC 3.8
IHDP
FDRP
PCDC
JSS
Perry 7–10 7.1–12.2
Head Start
CPC 18 10.8
TEEP
STAR 6.2
Return to main text

Appendix VII

Appendix VIII

Closing the Gap: Perry Program Applied to Disadvantaged Black
Population: Males

Closing the Gap: Perry Program Applied to Disadvantaged Black
Population: Females
Return to main text

Appendix IX

Simulation

Results

Setup 1: Fixed Target Between Disadvantaged and
Advantaged Children

Scenario 1: Constant Complementarity

Scenario 2: Increasing Complementarity

Scenario 3: Complementarity and Substitutability

Table 1, Setup 1: Fixed Targets between Advantaged and Disadvantaged Children
Initial Endowment Investment in each Period Total Investment Target Level of Skill in the Last Period
Scenario 1: Fixed Complementarity
t=1 t=2 t=3 t=4
0.01 1.51 2.18 3.14 4.52 11.36 10 2.63
0.05 1.55 2.23 3.21 4.63 11.62 10 2.86
0.01 1.33 2.17 3.24 4.66 11.41 10 2.94
0.05 1.30 2.16 3.26 4.69 11.41 10 3.01
Scenario 3: First Substitutes and Then Complements
0.01 0.69 1.58 3.25 4.68 10.19 10 2.97
0.05 0.67 1.57 3.25 4.68 10.16 10 2.98

Setup 2: Higher Skill Target for Advantaged Child

Table 2, Setup 2: Higher Target for the Advantaged Child
t=1 t=2 t=3 t=4
0.01 1.36 1.97 2.83 4.08 10.24 9 2.38
0.05 1.70 2.45 3.53 5.09 12.77 11 3.13
0.01 1.20 1.96 2.92 4.21 10.29 9 2.67
0.05 1.43 2.37 3.57 5.15 12.52 11 3.28
0.01 0.64 1.42 2.94 4.23 9.23 9 2.73
0.05 0.72 1.73 3.56 5.12 11.12 11 3.22

Setup 3: Greater Target for Disadvantaged Kid

Table3, Setup 3: Higher Target for the Disadvantaged Child
t=1 t=2 t=3 t=4
0.01 1.66 2.40 3.45 4.97 12.48 11 2.88
0.05 1.40 2.01 2.90 4.17 10.48 9 2.59
0.01 1.46 2.39 3.55 5.12 12.52 11 3.21
0.05 1.18 1.95 2.94 4.23 10.30 9 2.74
0.01 0.75 1.74 3.55 5.12 11.16 11 3.21
0.05 0.61 1.41 2.94 4.23 9.19 9 2.74

Appendix X

Comparing Perry Intervention to Eﬀect of Changing Family
Environments

Disadvantaged Children: First Decile in the Distribution of
Cognitive and Non-Cognitive Skills at Age 6
Mothers are in First Decile in the Distribution
of Cognitive and Non-Cognitive Skills at Ages 14–21
Changing initial Adolescent Changing
conditions: moving intervention: Moving initial conditions
children to the 4th investments at last and performing
decile of distribution transition from 1st a balanced
of skills only through to 9th decile intervention
Baseline early investments
High School Graduation 0.4109 0.6579 0.6391 0.9135
Enrollment in College 0.0448 0.1264 0.1165 0.3755
Conviction 0.2276 0.1710 0.1733 0.1083
Probation 0.2152 0.1487 0.1562 0.0815
Welfare 0.1767 0.0905
Perry Treatment Eﬀects
0.0968 0.0259
The adolescent-only and balanced intervention programs
cost 35% more than the Perry program.
Source: Cunha and Heckman (2007)
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