The Economics and Econometrics of Human Development
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Transcript of The Economics and Econometrics of Human Development
The Economics and the Econometrics
of Human Development
James J. HeckmanUniversity of Chicago
March 31, 2014Institute of Economic Growth
New Delhi
Econ and Ecom of Hum Dev
Intergenerational Mobility and Inequality:The “Great Gatsby Curve”IGE: lnY1︸︷︷︸
Income in currentgeneration
= α + βlnY0︸︷︷︸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-taxand transfer income of individual fathers and sons. The IGE estimate for India is taken from Hnatkovska et al. (2013).
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Link to Appendix I
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(a) Should there be policies that attempt to lower the IGE?
(b) If so, what form should they take?
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Becker-Tomes-Solon
Heritability ↑ β ↑
Efficiency of parental investment ↑ β ↑
Inequality in wages ↑ β ↑
Inequality of public provision of investment ↑ β ↑
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• As a purely statistical matter, the more heterogeneity acrossunits within an area the greater the estimated β.
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• Main findings of the empirical literature
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Hart & Risley, 1995
Children enter school with “meaningful differences” in vocabulary knowledge.1. Emergence of the ProblemIn a typical hour, the average child hears:
Family Actual Differences in Quantity Actual Differences in QualityStatus of Words Heard of Words HeardWelfare 616 words 5 affirmatives, 11 prohibitions
Working Class 1,251 words 12 affirmatives, 7 prohibitionsProfessional 2,153 words 32 affirmatives, 5 prohibitions
2. Cumulative Vocabulary at Age 3
Cumulative Vocabulary at Age 3Children from welfare families: 500 wordsChildren from working class families: 700 wordsChildren from professional families: 1,100 words
Econ and Ecom of Hum Dev
Hart & Risley, 1995
Children enter school with “meaningful differences” in vocabulary knowledge.1. Emergence of the ProblemIn a typical hour, the average child hears:
Family Actual Differences in Quantity Actual Differences in QualityStatus of Words Heard of Words HeardWelfare 616 words 5 affirmatives, 11 prohibitions
Working Class 1,251 words 12 affirmatives, 7 prohibitionsProfessional 2,153 words 32 affirmatives, 5 prohibitions
2. Cumulative Vocabulary at Age 3
Cumulative Vocabulary at Age 3Children from welfare families: 500 wordsChildren from working class families: 700 wordsChildren from professional families: 1,100 words
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Understanding Mechanisms
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Capabilities, the Technology of Capability Formation, andthe Essential Ingredients of a Life Cycle Model of Human
Development
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• Capabilities are multiple in nature.
• They encompass cognition, noncognitive and social preferencesand personality and preference traits, as well as health.
• Vector of capabilities at age t: θt.
• Capacities to act.
• Capabilities affect (a) resource constraints, (b) agentinformation sets and expectations, (c) parental information andexpectations and (d) preferences.
• They are stable across situations but evolve over time.
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Define relationships Mt mapping θt to outcomes Yt at stage t ofthe life cycle as:
Mt : θt → Yt. (1)
A core low-dimensional set of capacities generates a variety ofdiverse outcomes.
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Technology of Capability FormationCunha and Heckman (2007), Cunha (2007)
θt: a vector
θt+1 = ft( θt︸︷︷︸self productivityand cross effects
, It︸︷︷︸investment
broadly defined(parents, environment)
, θP ,t︸︷︷︸parental
capabilities
) (2)
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Complementarity Increases with Age
∂2θt+1
∂θt∂I ′t↑ t ↑ .
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Positive at later stages (t > t∗) of childhood
∂2θt+1
∂θt∂I ′t> 0, t > t∗.
Some evidence suggesting
∂2θt+1
∂θt∂I ′t≤ 0, t < t∗,
But even if positive, still smaller than at t > t∗.
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Complementarity coupled with self-productivity ⇒Dynamic Complementarity
It ↑ θt+1 ↑θt+1 ↑ ⇒ θt+s ↑ s > 1
∴∂2θt+s+1
∂It∂I ′t+s
> 0
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Family Preferences for Child Outcomes
Different versions of altruism, paternalism and beliefs about“proper” child rearing
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Family Resources Broadly Defined:Parental and Child Interactions
with Financial Markets and Access to Support from ExternalInstitutions
(a) Restrictions on transfers across generations
(b) Restrictions on transfers within generations (parental lifetimeliquidity constraints)
(c) Public provision of investment; public policy towards children
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Other Constraints on The Family Actively Being Investigated
(a) Information on parenting and other aspects of life acrossgenerations
(b) Genes
(c) Structure of household and assortative matching patterns(marriage markets)
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The Empirical and Theoretical ChallengeA Life Cycle Framework for Organizing Studies and Integrating Evidence
θt : Capacities at t; It: investment at t; θP ,t: Parental environmental variablesθt+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
EarlyChildhood, 0–3
LaterChildhood, 3–6
Adulthoodand Beyond
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A Bare-Bones Model of Parental Investment
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The Problem of the Parent
Link to Appendix II
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Life lasts four periods:
• Two periods as a passive child who makes no economicdecisions (and whose consumption is ignored) but who receivesinvestment in the form of goods.
• Two periods as a parent.
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Denote by θ1 the initial capability level of a child drawn from thedistribution J(θ1).(For notational simplicity, denote θP,t = θP = h.)Denoting by h′ the human capital of the child when child reachesadulthood
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Simplified parameterization of technology:
θt+1 = δt
γ1,tθ
φtt + γ2,t I
φtt︸ ︷︷ ︸
investment
+ γ3,thφt︸ ︷︷ ︸
parentalhumancapital
ρtφt
with 0 < γ1,t , γ2,t , γ3,t , ρt ≤ 1, φt ≤ 1,∑
k γk,nt = 1.
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Final Form Representation
If T = 2, ρ1 = ρ2 = 1, δ1 = 1, and φ1 = φ2 = φ ≤ 1, skills atadulthood, h′ = θ3 = θT+1 can be written as
h′ = δ2
γ1,2γ1,1θφ1 + γ1,2γ2,1︸ ︷︷ ︸
“Multiplier”
I φ1 + γ2,2Iφ2 + (γ3,2 + γ1,2γ3,1) hφ
1φ
.
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• If φ = 1, then investments at different periods are (almost)perfect substitutes.
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• Polar example arises in the Leontief case where φ→ −∞:
h′ = m2
(h, θ0,min(I1, I2)
)(3)
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• 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
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The goal of the parent is to optimize:
V (h, b, θ1) = maxc1,c2,I1,I2
{u (c1) + βu (c2) + β2υE [V (h′, b′, θ′1)]
}(4)
subject to technology and budget constraints.
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Budget constraint is:
c1 + I1 +c2 + I2(1 + r)
+b′
(1 + r)2 = wh +wh
(1 + r)+ b. (5)
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• Tractable final form technology:
h′ = m2
h, θ0,
γ︸︷︷︸investmentmultiplier
(I1)φ + (1− γ) (I2)φ
ρφ
, (6)
for φ ≤ 1 and 0 ≤ γ ≤ 1, ρ ≤ 1.
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I1I2
=
[γ
(1− γ) (1 + r)
] ρ1−φ
. (7)
I1I2↑ as γ ↑, φ ↑, ρ ↑ and r ↓.
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• Important policy question: How easy (costly) is it to remediatelow I1 with high I2?
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Implications of the Model
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Borrowing Limits
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Liquidity Constraints Within the Life Cycles of Parents
• The parent, within his/her lifetime, faces a sequence ofconstraints at each stage of the life of the child.
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Denoting parental financial assets by a and allowing parental labormarket productivity to grow at exogenous rate g , these budgetconstraints 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 futureincome.Child investments at different ages are not perfect substitutes(φ < 1).
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Parental utility: u (c) =(cλ − 1
)/λ.
I1I2
=
(γ
(1− γ) (1 + r)
) 11−φ
︸ ︷︷ ︸unconstrained ratio
[β(1 + r)]1
1−φ
(c1
c2
) 1−λ1−φ
︸ ︷︷ ︸=1 if unconstrained,<1 if constrained
.(10)
λ ≤ 1
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• Cunha, Heckman, and Schennach (2010):1/(1− φ) = .3 (φ
.= −2).
• Attanasio and Browning (1995): λ ∈ [−3,−1.5]
• (1− λ)/(1− φ) ∈ [0.83, 1.3]. Family resource influence onrelative investment.
• Dynamic complementarity coupled with borrowing constraintsin the early years raises a potentially serious marketimperfection.
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Introducing income uncertainty
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Empirical Estimates of Credit Constraints and the Effects ofFamily Income on Child Outcomes
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Recent Evidence on the Importance of Credit Constraintsand Family Income
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College attendance by AFQT and Family Income Quartiles (1979)
Source: Belley and Lochner (2007).
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College attendance by AFQT and Family Income Quartiles (1997)
Source: Belley and Lochner (2007).
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College attendance by AFQT and Family Income Quartiles (1979 and1997 placed on one graph)
Lochner 1979
Lochner 1997
Source: Belley and Lochner (2007).
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• More people going to college at virtually all quartiles ofability and income.
• Increases in college going is strongest for the lowest abilitygroup, especially less able children with richer parents.
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• This provides no firm evidence for or against credit constraints.
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Studies on the role of income on children’s outcomes and oncredit constraints
Link to Appendix III
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Summary of the Evidence on Family Income, CreditConstraints, and Child Development
• The literature on credit constraints and family income shows that higherlevels 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 beendone.
• It is premature to advocate pure income transfer policies as effective waysfor promoting child welfare and promoting social mobility.
• What studies exist suggest very weak effects of income transfers onchildhood test scores.
• The evidence from the structural models supports this conclusion.
• Many of the studies show effects of prices, not constraints or pure income.
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Structural Models of Parental Investment
Link to Appendix IV
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Recent Extensions
(a) Parental time (mother and father) (Del Boca et al., 2013; Gayleet 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)
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Estimates of the Technology of Capability Formation in theLiterature
(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 ofthe life cycle (dynamic complementarity)
(g) Measurement error empirically important
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Table 1: Capability Production Functions
Skill Output FunctionalCognitivea Non-cognitivea Health Form Anchoring
Todd and Wolpin (2003) X X X Linear XBernal and Keane (2010) X X X Linear X
Cunha and Heckman (2008) X X X Linear Xb
Cunha et al. (2010) X X X CES XTodd and Wolpin (2007) X X X Linear XCunha (2007) X X X CES XDel Boca et al. (2013) X X X Log-Linear X
Caucutt and Lochner (2012) X X X CES Xj
Bernal (2008) X X X Linear XGayle et al. (2013) Xg Xg X N/S XBernal and Keane (2011) X X X Linear X
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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) X- N/A X X UBernal and Keane (2010) X- N/A X X UCunha and Heckman (2008) 0.977 0.884 0.003 0.028 UCunha et al. (2010) 0.487/0.902c 0.649/0.868c 0.000/0.008c 0.083/0.011c XTodd and Wolpin (2007) 0.21 - 0.34d X X U
Cunha (2007) 0.735/0.799 /0.872f X X XDel Boca et al. (2013) (0.14, 0.503)/(0.172, 0.922)f X X N/ACaucutt and Lochner (2012) X- N/A X X N/ABernal (2008) X- N/A N/A X UGayle et al. (2013) N/S N/S X N/SBernal and Keane (2011) X- N/A X X U
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Investment with Multiple Children
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Representation for the utility parents receive from N children:
V c =
(N∑
k=1
ωkVσk
) 1σ
(11)
where Vk represents the relevant outcome for each child which isvalued by parents Behrman et al. (1982).
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Targeting Relatively More Investment Toward DisadvantagedChildren Can Be Socially Efficient
Link to Appendix V
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In a one period of childhood problem where parents (or socialplanners) seek to maximize the aggregate of adult skills (θ2):
θA2 + θB2
subject to E = p1(IA1 + IB1 ),
the first order condition is
F.O.C.: f(1)
2
(γθB1 , I
A1
)= f
(1)2
(θB1 , I
B1
).
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sign
(∂IA1∂γ
)= sign
(f
(1)12 (·)
)γ=1
.
Parents (social planners) invest more in the disadvantaged if inputsare substitutes with initial endowments and they invest less if theyare complements.
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Suppose that parents (or social planners) seek to maximize
θA3 + θB3
subject toE = p1(IA1 + IB1 ) + p2(IA2 + IB2 ).
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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.
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Even if (f(1)
12 > 0), greater first period investment in the initiallydisadvantaged child may be optimal. This is more likely (ceterisparibus)
(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 secondperiod complementarity and absolutely
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(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 ).
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An Example
Suppose that, for each child k , the outcome of interest for parentsare children’s earnings Ek and that they are function of children’sadult human capital determined by genes (θ1,k) and early (I1,k) andlate (I2,k) parental investments.
Ek = wf 2(θ2,k , I2,k) = τ 2(γ2θ
φ2
2,k + (1− γ2)I φ2
2,k
) ρ2φ2 (14)
with θ2,k = f 1(θ1,k , I1,k) = τ 1(γ1θ
φ1
1,k + (1− γ1)I φ1
1,k
) ρ1φ1 (15)
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w is common across families and siblings. Human capital is chosenso that w = 1. The budget constraint faced by the parents withtotal resources Re is:
p1
n∑k=1
I1 + p2
n∑k=1
I2 = Re . (16)
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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 intoearnings differences.
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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 periodtechnology. 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.
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Figure 2a: Parental Investments
Ratio Early to Late Investments
More endowed child
Less endowed child
1Notes: The solid line refers to the most endowed child, the dashed line to the least endowed child. The parameters used areas in Figure 1.
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Figure 2b: Parental Investments
Levels of Early 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 areas in Figure 1.
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Figure 2c: Parental Investments
Levels of Late Investments
More endowed child
Less endowed child
1Notes: The solid line refers to the most endowed child, the dashed line to the least endowed child. The parameters used areas in Figure 1.
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Testing and Operationalizing the Theory
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Capabilities as Determinants of Functionings
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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 healthat age t.
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• Capabilities, combined with effort, incentives and purchasedinputs determine functionings.
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• 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
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Effort: ej ,t
ej ,t = δj(θt,At,Xj,t,Raj,t(It−1) | u). (20)
• At : environment
• Raj,t : incentives
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Estimating and Interpreting the Distribution of Capabilities,the Maps Between Capabilities and Functionings and the
Technology of Capability Formation
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Nonparametric Factor Models Are Natural Frameworks forEstimating Capabilities and Determining Frontier Capability
Sets
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• Low dimensional capabilities (“factors”) generate a highdimensional set of functionings.
• Dimension and factor structures selected through a variety ofmethods.
• Exploratory factor analysis.
• Novel Bayesian procedures—avoid arbitrary methods inExploratory Factor Analysis.
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Technology of Skill Formation
•θk,t+1 = fs,k (θt , Ik,t , θP,t) (21)
for k ∈ {C ,N ,H}, t ∈ {1, 2, . . . ,T}.
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Identification of the Technology of Skill Formation
• To estimate the technology of skill formation: Have to solvethree problems.
1 Don’t observe (θt , Ik,t , θP,t) directly, but have manymeasurements on it. Measurement error in nonlinearsystems.
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 informationthat may be unobserved by the econometrician (ηk,t).Endogeneity of investment.
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Identification of the Technology of Skill Formation
• To estimate the technology of skill formation: Have to solvethree problems.
1 Don’t observe (θt , Ik,t , θP,t) directly, but have manymeasurements on it. Measurement error in nonlinearsystems.
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 informationthat may be unobserved by the econometrician (ηk,t).Endogeneity of investment.
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Estimating Functionings and Extracting Factors:Multiple Capabilities Shape Human Achievement Across a
Variety of Dimensions
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• The relationship between capabilities estimated in the recentliterature and traditional preference parameters (timepreference, leisure, risk aversion, etc.) is weak. Dohmen, Falk,et al. (2012)
• Suggests that a richer set of preference and constraintdescriptions may characterize choice behavior.
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Decile of Cognitive
1 2 3 4 5 6 7 8 9 10
Decile of Socio-Emotional12
34567
8910
Pro
bab
ility
0
0.2
0.4
0.6
0.8
1
Decile of Cognitive
1 2 3 4 5 6 7 8 9 10
Pro
bab
ility
0
0.2
0.4
0.6
0.8
1
Fra
ctio
n0
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
Pro
bab
ility
0
0.2
0.4
0.6
0.8
1
Fra
ctio
n
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 EndowmentLevels, Dropping from Secondary School vs. Graduating(Source: Heckman et al., 2011)
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The same low-dimensional vector of capabilities predicts a widevariety of outcomes for:
• Crime
• Wages
• Health
• Healthy behaviors (smoking, drug use)
• Trust
• Voting behavior
• Employment
• Participation in welfare
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Estimates of Technologies of Capability Formation and SomeImplications
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• Capabilities evolve over the life cycle
• Parental investments explain 34% of variance of educationalattainment
• 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 cognitiveinvestment)
• Complementarity between cognitive skills and investmentbecomes stronger as children become older. The elasticity ofsubstitution for cognitive production is smaller in second stageproduction
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• Emerging dynamic complementarity.
• It is more difficult to compensate for the effects of adverseenvironments on cognitive endowments at later ages than it isat earlier ages. This pattern of the estimates helps to explainthe evidence on ineffective cognitive remediation strategies fordisadvantaged adolescents reported in Cunha et al. (2006),Cunha (2007), and later papers.
• Complementarity between noncognitive skills and investmentsstays roughly constant over the life cycle.
• Suggests that later life investments should be more focused onpromoting noncognitive—personality—skills.
• The evidence on which adolescent interventions are successfulis consistent with this evidence.
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The Implications of the Estimates for Design of Policy
• Targeted strategies
• Consider a policy for a social planner to optimize the stock ofeducation in society.
• Assume (for simplicity) full control of investment (ignoresparental responses)
• The bulk of the evidence in the child development literatureshows reinforcement of investment by parents.
• No consideration of social fairness, equality of opportunity orequality of final outcomes—just efficiency.
• Yet with these estimates the optimal policy invests the most inthe disadvantaged.
• As an empirical matter, social justice is enhanced by what isproductively efficient.
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Socially Optimal Early and Late Levels of Investment by InitialCapabilities
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.
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0.5 1 1.5 2 2.50
0.5
1
1.5
2
2.5
3
3.5
Figure 5Densities of Ratio of Early to Late Investments
Maximizing Aggregate Education Versus Minimizing Aggregate Crime
Ratio Early to Late Investment
EducationCrime
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Using Economics to Go Behind Estimated ProgramTreatment 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 recognizethat various interventions in early childhood previouslyimplemented 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 affectfamily life.
6 Need to compare alternative policies in comparable metrics;i.e., rates of return to policies or cost-benefit analyses.
Econ and Ecom of Hum Dev
Lessons From and Lessons For the Intervention Literature
Link to Appendix VI
Econ and Ecom of Hum Dev
The Mechanisms Producing the Treatment Effects:A Case Study
Econ and Ecom of Hum Dev
Cognitive Evolution by Age, Perry MalesMale 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 10EntryAge
Treatment
Control
Econ and Ecom of Hum Dev
Personal Behavior Index by Treatment Group
Control Treatment
0.2
.4.6
.81
dens
ity
2 2.5 3 3.5 4 4.5 5
®
0.2
.4.6
.81
dens
ity
2 2.5 3 3.5 4 4.5 5
®
Econ and Ecom of Hum Dev
Socio-Emotional Index by Treatment Group
Control Treatment
0.2
.4.6
.8
dens
ity
1 2 3 4 5
0
.2.4
.6.8
dens
ity1 2 3 4 5
Econ and Ecom of Hum Dev
Decomposition of Treatment Effects, Males
32
THE
AMERIC
AN
ECONOMIC
REVIE
WMONTH
YEAR
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-valuesare shown above each component of the decomposition. The figure is a slightly simplified visualization of Tables L.10 and L.14: small and statisticallyinsignificant contributions of the opposite sign are set to zero. See Web Appendix L for detailed information about the simplifications made to producethe figure. “CAT total” denotes California Achievement Test total score normalized to control mean zero and variance of one. Asterisks denote statisticalsignificance: * – 10 percent level; ** – 5 percent level; *** – 1 percent level. Monthly income is adjusted to thousands of year-2006 dollars using annualnational CPI. Econ and Ecom of Hum Dev
Health OutcomesLink to Appendix VII
Econ and Ecom of Hum Dev
Attachment, EngagementToward a Deeper Understanding of Parenting and Learning
• In both Perry and ABC (and many other interventions) a mainchannel of influence is on the parent-child interactions.
• Enhanced attachment and engagement of parents.
• This has important implications for how we model familyinfluence.
Econ and Ecom of Hum Dev
Mechanisms—producing effects
(a) Information
(b) Changing preferences of parents
(c) Parental response to child’s curiosity and interest induced byparticipation in the program
Econ and Ecom of Hum Dev
Parental response to Perry Preschool Program
1020
3040
5060
Pro
port
ion
−.015 −.01 −.005 0 .005 .01 .015Belief in Importance of Parenting
Control Treatment
Econ and Ecom of Hum Dev
Table 2: Models of Parent-Child Interaction(“X” means present; “X” means absent)
ParentalMonetary
Investments
Discordance inPreferences
between Parentand Child
MultipleChildren
ParentalIncentives forChild Effort
Cosconati (2013) X Xa,b X Xc
Akabayashi (2006) X Xa X Xd,e
Hao et al. (2008) X Xb X Xe
Lizzeri and Siniscalchi (2008) X Xd 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.
Econ and Ecom of Hum Dev
Table 2 (continued): Models of Parent-Child Interaction(“X” means present; “X” means absent)
Effort ProducesGreater Capability
ParentalLearning aboutChild Quality
Parental ActionsFacilitate
Acquisition ofInformation
ParentalBeliefs CanDivergefrom Truth
Cosconati (2013) X X X X
Akabayashi (2006) X X X Xf
Hao et al. (2008) X X X X
Lizzeri and Siniscalchi (2008) X X 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.
Econ and Ecom of Hum Dev
Table 2 (continued): Models of Parent-Child Interaction(“X” means present; “X” means absent)
Child’s EffortObservable
Child’sHuman Capital
Observable
Model IsEstimated
Cosconati (2013) X X X
Akabayashi (2006) X X X
Hao et al. (2008) X X Xg
Lizzeri and Siniscalchi (2008) X 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.
Econ and Ecom of Hum Dev
An Economic Model of Mentoring and Scaffolding(Garcıa, Heckman, Mosso, and Wang, 2013)
Econ and Ecom of Hum Dev
Mentor’s Problem
Yt : Measured output of child at age tθt : Capabilities at outsetθt : Parental targetsIt : Parental investment at age tat : Child effort at age tThe mentor’s problem is to minimize
Vt(Yt) = minIt ,...IN−1
E
[N−1∑τ=t
βτ(θτ′Q θτ + Iτ
′RIτ)
+ θN′Qf θN |Yt
]
where Q,Qf ,R ≥ 0.
Econ and Ecom of Hum Dev
Technology: θt+1 = Aθt + BIt + F at + wt
θt+1 = Ψ(θt , It , at)
θt+1 = Ψ(θt , It , at)
Yt = C θt + Dat + vt
θt = θt − θtIt = It − It
at = at − at .
Econ and Ecom of Hum Dev
Child’s Problem(with development of agency of the child)
• The child chooses a sequence of effort (a1, . . . , aN−1) tomaximize her utility in each period.
• Her value function at time t is:
Jt(Yt) = maxat ,...,aN−1
(λt(θt)J
1t (Yt) + (1− λt(θt))J2
t (Yt))
Econ and Ecom of Hum Dev
J1t (Yt) = max
at ,...,aN−1
E
[N−1∑τ=t
βτ(− (h′It)
η
2γ(at − a)′ (at − a + α′It)
)|Yt
]
J2t (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
Econ and Ecom of Hum Dev
Integrating Experimental Studies with Family InfluenceStudies
Econ and Ecom of Hum Dev
• IGt : government investment
• IPt : private (family) investment
• Government technology: f G (θt , θPt , IGt , IPt )
• Private technology: f P(θt , θPt , IGt , IPt )
• Mixed technology: f M(θt , θPt , IGt , IPt )
Econ and Ecom of Hum Dev
• Studies under way doing this (Fan, Hai, Heckman, Wei, andZhang, 2013)
Econ and Ecom of Hum Dev
What about promoting education?
Econ and Ecom of Hum Dev
Early development is as important as education in promotingwages, employment, and health.
Econ and Ecom of Hum Dev
Disparities by Education (Post-compulsory Education)
• Education, Wages, Employment, and Health
Note: Conti and Heckman (2010). Author’s calculations using British Cohort Study, 1970.
Econ and Ecom of Hum Dev
Disparities by Education (Post-compulsory Education)
• Education, Wages, Employment, and Health
Note: Conti and Heckman (2010). Author’s calculations using British Cohort Study, 1970.
Econ and Ecom of Hum Dev
Disparities by Education (Post-compulsory Education)
• Education, Wages, Employment, and Health
Note: Conti and Heckman (2010). Author’s calculations using British Cohort Study, 1970.
Econ and Ecom of Hum Dev
Summary
Econ and Ecom of Hum Dev
The Empirical and Theoretical ChallengeA Life Cycle Framework for Organizing Studies and Integrating Evidence
θt : Capacities at t; It: investment at t; θP ,t: Parental environmental variablesθt+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
EarlyChildhood, 0–3
LaterChildhood, 3–6
Adulthoodand Beyond
Econ and Ecom of Hum Dev
Predistribution Not Simply Redistribution
Econ and Ecom of Hum Dev
(a) Should there be policies that attempt to lower the IGE?
(b) If so, what form should interventions take?
Econ and Ecom of Hum Dev
Appendix I
Econ and Ecom of Hum Dev
USA
Canada
DenmarkFinland
France
Germany
Norway
Sweden
UKItaly
Japan0
.1.2
.3.4
.5In
terg
en. E
last
icity
of E
arni
ngs
(IGE)
.2 .25 .3 .35Gini 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.
Econ and Ecom of Hum Dev
USA
Canada
Denmark
Finland
France
Germany
Norway
Sweden
UKItaly
Japan
0.1
.2.3
.4.5
Inte
rgen
. Ela
stici
ty o
f Ear
ning
s (IG
E)
.34 .38 .42 .46Gini 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 beforetax-and-transfer IGE.
• Correcting this mistake makes the Great Gatsby Curveinsignificantly sloped.
Econ and Ecom of Hum Dev
USA
Canada
DenmarkFinland
FranceGermany
NorwaySweden
UKItaly
Japan
0.1
.2.3
.4.5
Inte
rgen
. Ela
stici
ty o
f Ear
ning
s (IG
E)
.2 .25 .3 .35Gini Coefficient, After Taxes and Transfers
Corak's Chosen IGE except USA OLS Slope=0.70, p-value=.003
• Due to the anchoring scheme employed by Corak (2013), theslope of the Great Gatsby Curve is arbitrarily controlled by thepartly subjective choice of USA IGE estimate.
Econ and Ecom of Hum Dev
USACanada
Denmark
Finland
France
Germany
NorwaySweden
UK
Italy
Japan
0.1
.2.3
.4.5
Inte
rgen
. Ela
stici
ty o
f Ear
ning
s (IG
E)
.34 .38 .42 .46Gini Coefficient, Before Taxes and Transfers
Alternate IGE Choice OLS: Slope=-0.16, p-value=.869
• By replacing only three of the countries’ IGE estimates withplausible alternates from the literature, we arrive at anegatively-sloped Great Gatsby Curve.
• Conclusion: Corak’s Great Gatsby Curve is not robust. Thisdoes not disprove the hypothesis that inequality and IGE arepositively related.
Econ and Ecom of Hum Dev
USA
Canada
Denmark
Finland
France
Germany
Norway
Sweden
UK
0.1
.2.3
.4.5
Inte
rgen
erat
iona
l Ela
stic
ity (F
athe
r to
Son
Earn
ings
)
.2 .25 .3 .35
Corak's Preferred Data OLS (Slope=2.05, p-value=.008)
Corak's Great Gatsby Curve
Source: Corak, JEP(2013)
Econ and Ecom of Hum Dev
USA
Canada
Denmark
Finland
France
GermanyNorway
Sweden
UK
0.1
.2.3
.4.5
Inte
rgen
erat
iona
l Ela
stici
ty
.2 .25 .3 .35Gini Coefficient, After Taxes and Transfers
Corak's Preferred Data OLS (Slope=2.64, p-value=.016)
Great Gatsby Curve without Corak's Adjustments
Source: Bradley Setzler 2013
Econ and Ecom of Hum Dev
USACanada
Denmark
Finland
France
Germany
NorwaySweden
UK
0.1
.2.3
.4.5
Inte
rgen
erat
iona
l Ela
stici
ty
.2 .25 .3 .35Gini Coefficient, After Taxes and Transfers
Alternate Data Choice OLS (Slope=-0.02, p-value=.980)
Great Gatsby Curve using Alternate Elasticities
Source: Bradley Setzler 2013
Econ and Ecom of Hum Dev
USA
Canada
Denmark
Finland
France
Germany
Norway
Sweden
UK
0.1
.2.3
.4.5
Inte
rgen
erat
iona
l Ela
stic
ity (F
athe
r to
Son
Earn
ings
)
.2 .25 .3 .35
Corak's Preferred Data OLS (Slope=2.05, p-value=.008)
Corak's Great Gatsby Curve
Source: Corak, JEP(2013)
Econ and Ecom of Hum Dev
USA
Canada
Denmark
Finland
FranceGermany
Norway
Sweden
UK
0.1
.2.3
.4.5
Inte
rgen
erat
iona
l Ela
stici
ty
.2 .25 .3 .35Gini Coefficient, After Taxes and Transfers
Corak's Preferred Data except USA OLS (Slope=0.65, p-value=.008)
Great Gatsby Curve with Lower USA Choice
Source: Bradley Setzler 2013
Econ and Ecom of Hum Dev
USACanada
Denmark
Finland
France
Germany
NorwaySweden
UK
0.1
.2.3
.4.5
Inte
rgen
erat
iona
l Ela
stici
ty
.2 .25 .3 .35Gini Coefficient, After Taxes and Transfers
Alternate Data Choice OLS (Slope=-0.02, p-value=.980)
Great Gatsby Curve using Alternate Elasticities
Source: Bradley Setzler 2013
Econ and Ecom of Hum Dev
Return to main text
Econ and Ecom of Hum Dev
Appendix II
Econ and Ecom of Hum Dev
Dynastic Model of Parental Investment that Emphasizes theInteraction of Dynamic Complementarity and Credit Markets
Econ and Ecom of Hum Dev
• 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 futureincome (new to literature)
Econ and Ecom of Hum Dev
Capability Formation in an Economy withIdiosyncratic Uncertainty and Liquidity Constraints
(New to Literature)
Econ and Ecom of Hum Dev
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 byassumption makes no economic decisions.
• Upon reaching age T + 1, the agent becomes an adult andgives birth to a child. (Exogenous fertility.)
• The agent dies at the end of the calendar year in which shecompletes 2T years of age and is replaced in the beginning ofthe next calendar year by the generation of her grandchild.
Econ and Ecom of Hum Dev
The Technology of Skill Formation
Econ and Ecom of Hum Dev
• It is investment; θt stock of child skills; h stock ofparental 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, andtwice-continuously differentiable.
Econ and Ecom of Hum Dev
• To develop some intuition about the skill formation processimplied by the production function (22), consider the followingparameterization:
θt+1 = δt
{γ1tθ
φtt + γ2t I
φtt + γ3th
φt} ρtφt
with 0 < γ1,t , γ2,t , γ3,t , ρt < 1, φt ≤ 1,∑
k γk,nt = 1.
Econ and Ecom of Hum Dev
• If T = 2, ρ1 = ρ2 = 1, δ1 = 1, and φ1 = φ2 = φ ≤ 1.
• Skills at adulthood, h′ = θ3 = θT+1:
h′ = δ2
γ1,2γ1,1θφ1 + γ1,2γ2,1︸ ︷︷ ︸
“Multiplier effect”
I φ1 + γ2,2Iφ2 + (γ3,2 + γ1,2γ3,1) hφ
1φ
.
Econ and Ecom of Hum Dev
• An extreme example arises in the Leontief case whereφ→ −∞, in which case we would write:
θ3 = δ2 min {θ1, I1, I2, h} (23)
Econ and Ecom of Hum Dev
The Problem of the Parent
Econ and Ecom of Hum Dev
The Problem When the Child Is between 1 and T − 1 YearsOld
• 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 + σηηεt . (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
Econ and Ecom of Hum Dev
• Given the state variables, the parent chooses householdconsumption Ct , savings st+1, and investments It in thecognitive skill of the child.
• The savings of the parents are in a risk-free asset which pays arate of interest r .
• p denotes the price of the investment goods in cognitive skill.
• Following Laitner (1992), the parents cannot leave debts totheir children and have negative net worth, so savings aresubject to the lower bound equal to −whεmin
(1+r).
Econ and Ecom of Hum Dev
• V (t, h, θt , st , εt): the value function of the parent of a child atage t, 1 ≤ t ≤ T − 1.
• The problem of the parent:
V (t, h, θt , st , εt)
= maxCt ,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).
Econ and Ecom of Hum Dev
The Problem When the Child Is T Years Old:Go to College or Not?
Econ and Ecom of Hum Dev
Steady State GE
• Firms producing final output (CRS)
• Also child investment good (Produced)
• Can establish stochastic GE for steady state, extending Aiyagariand Laitner to include human capital
Econ and Ecom of Hum Dev
Return to main text
Econ and Ecom of Hum Dev
Appendix III
Econ and Ecom of Hum Dev
Table 3a: Studies on the Role of Income on Children’s Outcomes
Dataset OutcomeStudied: Test
Scores (T),Schooling (S)
Timing of Income(Developmental Stageof the Child at Which
Income Effects areStudied)
Separate theEffect of Incomefrom Changes inLabor Supply or
FamilyEnvironment
Carneiro and Heckman(2002)
NLSY79∗ S Early (E) and Late(L)
College Enrollment
X
Belley and Lochner(2007)
NLSY79∗,NLSY97∗
S LHigh school
completion andCollege Enrollment
X
Dahl and Lochner(2012)
NLSY79∗,C-
NLSY79∗
T EPreadolescence(ages 8 to 14)
Xa
Duncan et al. (1998) PSID∗ Sd E and LChildhood andPreadolescence(ages 0 to 15)
X
Econ and Ecom of Hum Dev
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 IncomeEffects are Studied)
Separate the Effect ofIncome from Changes inLabor Supply or Family
Environment
Duncan et al. (2011) RandomizedInterventionson Welfare
Support
T EEarly Childhood
(ages 2 to 5)
X
Loken (2010) NorwegianAdministrative
Data
S EChildhood
(ages 1 to 11)
Xc
Loken et al. (2012) NorwegianAdministrative
Data
S EChildhood
(ages 1 to 11)
X
Milligan and Stabile(2011)
CCTB∗∗,NCBS∗∗∗
T EChildhood
(ages 0 to 10)
X
Carneiro et al. (2013) NorwegianRegistry
Se E and LChildhood to Adolescence
(ages 0 to 17)
X
Econ and Ecom of Hum Dev
Table 3b: Studies on the Role of Income on Children’s Outcomes
Distinguishes theEffects of
Contemporaneous vs.Permanent Income
Sources of IncomeWhose Effects are
Studied
Instrument Used
Carneiro and Heckman (2002) X Total family income None
Belley and Lochner (2007) X Total family income None
Dahl and Lochner (2012) Xb Total family income Policy variation in EITCeligibility
Duncan et al. (1998) X Total family income None
Econ and Ecom of Hum Dev
Table 3b (continued): Studies on the Role of Income on Children’sOutcomes
Distinguishes theEffects of
Contemporaneous vs.Permanent Income
Sources of IncomeWhose Effects are
Studied
Instrument Used
Duncan et al. (2011) X Total family income Random assignment to programsoffering welfare transfers conditionalon employment or education related
activities, or full time work
Loken (2010) X Total family income Oil discovery (inducing regionalincrease in wages)
Loken et al. (2012) X Total family income Oil discovery (inducing regionalincrease in wages)
Milligan and Stabile (2011) X Child related tax benefitsand income transfers
Variation in benefits eligibility
Carneiro et al. (2013) X Total family income None
Econ and Ecom of Hum Dev
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 highestincome group: 5.1% are constrained in college enrollment (1.2% among low income, lowability, 0.2% low income high ability), 9% in completion of 2-year college (5.3% amonglow income, low ability, 0.3% low income high ability). No effect of timing of receipt offamily 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 highestincome 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 readingcombined PIAT score.
Duncan et al. (1998) $10,000 increase in average (age 0-15) family income: +1.3 years of schooling in lowincome (¡$20,000) families, +0.13 in high income ones. Relevance of income is strongerin the early years (age 0-5): $10,000 increase in average (age 0-5) family income leads toextra 0.8 years of schooling in low income families, 0.1 in high income ones. Income atage 6-10 and 11-15: no significant effect. Similar results in a sibling differences model.
Econ and Ecom of Hum Dev
Table 3c (continued): Studies on the Role of Income on Children’sOutcomes
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 achievementscore.
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 sampleby 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 exclusionof Quebec.
Carneiro et al. (2013) All outcomes: monotone and concave relationship with permanent income. £100,000increase in permanent father’s earnings: +0.5 years of schooling. Timing of income: abalanced profile between early (age 0-5) and late childhood (age 6-11) is associated withthe best outcomes; shifting income to adolescence is associated with better outcomes indropping out of school, college attendance, earnings, IQ and teen pregnancy. Early andlate childhood income are complements in determining schooling attainment, early andadolescent income are substitutes.
Econ and Ecom of Hum Dev
Table 4a: Studies on Tests of Credit Constraints
Dataset OutcomeStudied:School-
ing(S)
Timing of Income(Developmental
Stage of the Childat Which
Constraints areStudied)
ExplicitDynamic
Model
Who is Affectedby Constraints:Parent of the
Agent (P), Agent/ Child (C)
Keane andWolpin(2001)
NLSY79∗ S LCollege
Enrollment
X C
Carneiro andHeckman(2002)
NLSY79∗,C-
NLSY79∗
S E and LCollege
Enrollment,Comple-
tion,Delayed
Entry
X P
Econ and Ecom of Hum Dev
Table 4a (continued): Studies on Tests of Credit Constraints
Dataset OutcomeStudied:School-
ing(S)
Timing of Income(Developmental
Stage of the Childat Which
Constraints areStudied)
ExplicitDynamic
Model
Who is Affectedby Constraints:Parent of the
Agent (P), Agent/ Child (C)
Cameron andTaber (2004)
NLSY79∗ S LAdolescence and
College Enrollment
X C
Caucutt andLochner(2012)
NLSY79∗,C-NLSY79∗
Ta E and LChildhood and
Adolescence
X P
Econ and Ecom of Hum Dev
Table 4b: Studies on Tests of Credit Constraints
Method to Test forCredit Constraints
Find Presence of CreditConstraints
Effect of Income or Constraints on HumanCapital Investments
Keane and Wolpin(2001)
Structural estimation ofthe lower bound on asset
level
YESBut 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 meanhourly wage rate; increase in consumption and re-duction in market hours; moderate reduction inparental transfers especially for the least educatedparents.
Carneiro andHeckman (2002)
(1) Gap to students fromhighest income quartile.(2) Timing of income.
(3) Difference in IV andOLS estimates of Mincer
coefficient
YESBut affecting at most
8% of students
(1) Conditioning on ability and family backgroundfactors, the role of income in determining school-ing decisions is minimal. The strongest evidence isin the low ability group. The test is not robust toaccounting for parental preferences and paternal-ism. Observed differences in attendance might bedue to a consumption value of child’s schooling forparents.(2) There is no evidence of a independent effecton college enrollment of early or late income oncepermanent income is accounted for.(3) The claim that higher IV than OLS estimates ofthe Mincer coefficient implies credit constraints areincorrect: instruments used are invalid, the qualitymargin is ignored and self selection and compara-tive advantage can produce the result also in ab-sence of financial constraints.
Econ and Ecom of Hum Dev
Table 4b (continued): Studies on Tests of Credit Constraints
Method to Test forCredit Constraints
Find Presence of CreditConstraints
Effect of Income or Constraints on HumanCapital Investments
Cameron andTaber (2004)
IV estimation of“returns” to schooling
using costs of schoolingor foregone earnings as
instruments
NO Theoretical prediction: if borrowing constraints,IV estimates using direct costs of schooling higherthan using opportunity costs. Data: IV estimatesusing the presence of a local college are smallerthan the ones using foregone earnings. Regressionswhich interact college costs and characteristics po-tentially related to credit availability: no evidenceof excess sensitivity to costs for potentially con-strained sample. Structural model: almost 0% ofthe population is found to borrow at a rate higherthan the market one.
Caucutt andLochner (2012)
Structural estimation ofthe lower bound on asset
level
YESStronger effect on high
skilled parents
50% of young parents are constrained: high schooldropouts (50%), high school graduates (38%), col-lege dropouts (60%), college graduates (68%); and12% of old parents are constrained. Families withcollege graduate parents benefit the most from areduction in credit constraints.
Econ and Ecom of Hum Dev
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Econ and Ecom of Hum Dev
Appendix IV
Econ and Ecom of Hum Dev
Table 5: Structural Models of Parental Investments(“X” means present; “X” means absent)
OLG Model Dynastic Links ExplicitModels ofParental
Preferences,Altruism (A)
or Paternalism(P)
ModelEstimated
Cunha and Heckman (2007) X A,B,C, Xi (A) X
Cunha (2007) X A,B,C Xi (A) XCaucutt and Lochner (2012) X B,C Xi (A) XDel Boca et al. (2013) X X Xj(P) XGayle et al. (2013) X A,C Xj(P) XCunha et al. (2013) X X Xj(P) XBernal (2008) X X Xj(P) X
AThrough parental skills, BThrough asset transfers, COnly through genes (initialconditions), DNatural borrowing limit, ELimits can be more stringent than naturallimit.
Econ and Ecom of Hum Dev
Table 5: Structural Models of Parental Investments(“X” means present; “X” means absent)
ParentalGoods
Investment
Parental TimeInvestment
TechnologyDepends on
Parental Skill
Self-productivity
Cunha and Heckman (2007) X X X XCunha (2007) X X X XCaucutt and Lochner (2012) X X X XDel Boca et al. (2013) X X X XGayle et al. (2013) X X X XCunha et al. (2013) X X X XBernal (2008) X X X X
AThrough parental skills, BThrough asset transfers, COnly through genes (initialconditions), DNatural borrowing limit, ELimits can be more stringent than naturallimit.
Econ and Ecom of Hum Dev
Table 5: Structural Models of Parental Investments(“X” means present; “X” means absent)
ParentalLearning
AboutTechnology
Bequests IntragenerationalBorrowing
Multiple Skillsof Children
Cunha and Heckman (2007) X X XE X
Cunha (2007) X X XD X
Caucutt and Lochner (2012) X X XE XDel Boca et al. (2013) X X X XGayle et al. (2013) X X X XCunha et al. (2013) X X X XBernal (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 thannatural limit.
Econ and Ecom of Hum Dev
Table 5: Structural Models of Parental Investment(“X” means present; “X” means absent)
MultichildFamilies
(Preferences forEquity vs.Efficiency)
EndogenousFertility
Decisions
MultipleParents
EndogenousMating
Decisions
Cunha and Heckman (2007) X X X XCunha (2007) X X X XCaucutt and Lochner (2012) X X X XDel Boca et al. (2013) X X X XGayle et al. (2013) X X X XCunha et al. (2013) X X X XBernal (2008) X X X X
AThrough parental skills, BThrough asset transfers, COnly through genes (initialconditions), DNatural borrowing limit, ELimits can be more stringent than naturallimit.
Econ and Ecom of Hum Dev
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Econ and Ecom of Hum Dev
Appendix V
Econ and Ecom of Hum Dev
Targeting Relatively More Investment Toward DisadvantagedChildren Can Be Socially Efficient
Econ and Ecom of Hum Dev
In a one period of childhood problem where parents (or socialplanners) seek to maximize the aggregate of adult skills (θ2):
θA2 + θB2
subject to E = p1(IA1 + IB1 ),
the first order condition is
F.O.C.: f(1)
2
(γθB1 , I
A1
)= f
(1)2
(θB1 , I
B1
).
Econ and Ecom of Hum Dev
Notice that
sign
(∂IA1∂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 inputsare substitutes with initial endowments and they invest less if theyare complements.
Econ and Ecom of Hum Dev
Suppose that parents (or social planners) seek to maximize
θA3 + θB3
subject toE = p1(IA1 + IB1 ) + p2(IA2 + IB2 ).
Econ and Ecom of Hum Dev
Even if (f(1)
12 > 0), greater first period investment in the initiallydisadvantaged child may be optimal. This is more likely (ceterisparibus)
(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 secondperiod complementarity and absolutely
Econ and Ecom of Hum Dev
(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 ).
Econ and Ecom of Hum Dev
Roughly speaking, the more concave are the technologies in terms ofstocks of skills, the more favorable is the case for investing relativelymore in the disadvantaged child. The greater the second periodcomplementarity (f
(2)12 ), the greater the case for investing more in
the initially disadvantaged child to allow the child to benefit fromgreater second period complementarity of the stock of skills withsecond period investment. In general, even when investment isgreater in the first period for the disadvantaged child, second periodinvestment is greater for the initially advantaged child. It isgenerally not efficient to make the initially disadvantaged childwhole as it enters the second period when the effect of greatersecond period complementarity kicks in.
Econ and Ecom of Hum Dev
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Econ and Ecom of Hum Dev
Appendix VI
Econ and Ecom of Hum Dev
Table 6a: Summary of Effects for Main Interventions
Participant/Evaluation Characteristics
Program Age
Dur
atio
n
Tar
get
Sel
ecti
on
Fol
low
-Up
Sam
ple
RC
TE
val
Elementary
LA’s Best 5–6 6Y SES Schl 12Y 19,320 NoCSP 5–13 5Y Behav Refer 35Y 510 YesSSDP 6–7 6Y Crime Prgrm 21Y 610 Yes
Adolescence
BBBS 10-16 1Y SES Self 1Y 960 YesIHAD 11–12 7Y SES Prgrm 8Y 180 YesEPIS 13–15 3Y Schl Schl 2Y 45,070 Noxl club 14 2Y Schl Schl 2Y 261,420 No
SAS 14–15 5Y Schl, SES Schl 6Y 430 NoSTEP 14–15 2Y Schl, SES Self 4Y 4,800 YesQOP 14–15 5Y Schl Prgrm 10Y 1,070 YesAcademies 13–16 4Y Schl, SES Self 12Y 1,460 Yes
ChalleNGe 16–18 1Y Dropout Self 3Y 1,200 YesJob Corps 16–24 1Y SES Self 9Y 15,300 YesYear-Up 18–24 1Y SES Self 2Y 200 Yes
Econ and Ecom of Hum Dev
Table 6b: Summary of Effects for Main Interventions
Components
Program Hom
e
Hea
lth
Par
enta
l
On
Sit
e
Gro
up
Elementary
LA’s BestCSPSSDP
Adolescence
BBBSIHADEPISxl club
SASSTEPQOPAcademies
ChalleNGeJob CorpsYear-Up
Econ and Ecom of Hum Dev
Table 6c: Summary of Effects for Main Interventions
Effects on Outcomes Return/Benefits
Program IQ Sch
ool
Cha
ract
er
Edu
cati
on
Hea
lth
Cri
me
Ear
ning
s
Ret
urn
Ben
efit
Cos
t
Elementary
LA’s Best 0.9CSPSSDP 3.1
Adolescence
BBBS 1.0IHADEPIS 0.9–3.0xl club
SASSTEPQOP 0.42Academies
ChalleNGe 6.4 2.66Job Corps 0.22Year-Up
Econ and Ecom of Hum Dev
Table 6d: Summary of Effects for Main Interventions
Participant/Evaluation Characteristics
Program Age
Dur
atio
n
Tar
get
Sel
ecti
on
Fol
low
-Up
Sam
ple
RC
TE
val
Early
NFP < 0 2Y SES Prgrm 19Y 640 YesABC 0 5Y SES Refer 30Y 90 YesIHDP 0 3Y Health Prgrm 18Y 640 YesFDRP 0 5Y SES Prgrm 15Y 110 No
PCDC 1 2Y SES Prgrm 15Y 170 YesJSS 1–2 2Y Health Prgrm 22Y 160 YesPerry 3 2Y SES, IQ Prgrm 37Y 120 YesHead Start 3 2Y SES Prnt 23Y 4,170 Yes
CPC 3–4 2Y SES Prnt 25Y 1,290 NoTEEP 3,5 2Y SES Prgrm 22Y 260 YesSTAR 5–6 4Y SES Prgrm 22Y 11,000 Yes
Econ and Ecom of Hum Dev
Table 6e: Summary of Effects for Main Interventions
Components
Program
Hom
e
Hea
lth
Par
enta
l
On
Sit
e
Gro
up
Early
NFPABCIHDPFDRP
PCDCJSS
PerryHead Start
CPCTEEPSTAR
Econ and Ecom of Hum Dev
Table 6f: Summary of Effects for Main Interventions
Effects on Outcomes Return/Benefits
Program IQ Sch
ool
Cha
ract
er
Edu
cati
on
Hea
lth
Cri
me
Ear
ning
s
Ret
urn
Ben
efit
Cos
t
Early
NFP 2.9ABC 3.8IHDPFDRP
PCDCJSSPerry 7–10 7.1–12.2Head Start
CPC 18 10.8TEEPSTAR 6.2
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Econ and Ecom of Hum Dev
Appendix VII
Econ and Ecom of Hum Dev
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Econ and Ecom of Hum Dev
Appendix VIII
Econ and Ecom of Hum Dev
Closing the Gap: Perry Program Applied to Disadvantaged BlackPopulation: Males
Econ and Ecom of Hum Dev
Closing the Gap: Perry Program Applied to Disadvantaged BlackPopulation: Females
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Econ and Ecom of Hum Dev
Appendix IX
Econ and Ecom of Hum Dev
Simulation
Econ and Ecom of Hum Dev
Results
Econ and Ecom of Hum Dev
Setup 1: Fixed Target Between Disadvantaged andAdvantaged Children
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Scenario 1: Constant Complementarity
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Scenario 2: Increasing Complementarity
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Scenario 3: Complementarity and Substitutability
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Table 1, Setup 1: Fixed Targets between Advantaged and Disadvantaged ChildrenInitial Endowment Investment in each Period Total Investment Target Level of Skill in the Last Period
Scenario 1: Fixed Complementarityt=1 t=2 t=3 t=4
0.01 1.51 2.18 3.14 4.52 11.36 10 2.630.05 1.55 2.23 3.21 4.63 11.62 10 2.86
Scenario 2: Increasing Complementarity0.01 1.33 2.17 3.24 4.66 11.41 10 2.940.05 1.30 2.16 3.26 4.69 11.41 10 3.01
Scenario 3: First Substitutes and Then Complements0.01 0.69 1.58 3.25 4.68 10.19 10 2.970.05 0.67 1.57 3.25 4.68 10.16 10 2.98
Econ and Ecom of Hum Dev
Setup 2: Higher Skill Target for Advantaged Child
Econ and Ecom of Hum Dev
Scenario 1: Constant Complementarity
Econ and Ecom of Hum Dev
Scenario 2: Increasing Complementarity
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Scenario 3: Complementarity and Substitutability
Econ and Ecom of Hum Dev
Table 2, Setup 2: Higher Target for the Advantaged ChildInitial Endowment Investment in each Period Total Investment Target Level of Skill in the Last Period
Scenario 1: Fixed Complementarityt=1 t=2 t=3 t=4
0.01 1.36 1.97 2.83 4.08 10.24 9 2.380.05 1.70 2.45 3.53 5.09 12.77 11 3.13
Scenario 2: Increasing Complementarity0.01 1.20 1.96 2.92 4.21 10.29 9 2.670.05 1.43 2.37 3.57 5.15 12.52 11 3.28
Scenario 3: First Substitutes and Then Complements0.01 0.64 1.42 2.94 4.23 9.23 9 2.730.05 0.72 1.73 3.56 5.12 11.12 11 3.22
Econ and Ecom of Hum Dev
Setup 3: Greater Target for Disadvantaged Kid
Econ and Ecom of Hum Dev
Scenario 1: Constant Complementarity
Econ and Ecom of Hum Dev
Scenario 2: Increasing Complementarity
Econ and Ecom of Hum Dev
Scenario 3: Complementarity and Substitutability
Econ and Ecom of Hum Dev
Table3, Setup 3: Higher Target for the Disadvantaged ChildInitial Endowment Investment in each Period Total Investment Target Level of Skill in the Last Period
Scenario 1: Fixed Complementarityt=1 t=2 t=3 t=4
0.01 1.66 2.40 3.45 4.97 12.48 11 2.880.05 1.40 2.01 2.90 4.17 10.48 9 2.59
Scenario 2: Increasing Complementarity0.01 1.46 2.39 3.55 5.12 12.52 11 3.210.05 1.18 1.95 2.94 4.23 10.30 9 2.74
Scenario 3: First Substitutes and Then Complements0.01 0.75 1.74 3.55 5.12 11.16 11 3.210.05 0.61 1.41 2.94 4.23 9.19 9 2.74
Econ and Ecom of Hum Dev
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Econ and Ecom of Hum Dev
Appendix X
Econ and Ecom of Hum Dev
Comparing Perry Intervention to Effect of Changing FamilyEnvironments
Econ and Ecom of Hum Dev
Disadvantaged Children: First Decile in the Distribution ofCognitive and Non-Cognitive Skills at Age 6
Mothers are in First Decile in the Distributionof Cognitive and Non-Cognitive Skills at Ages 14–21
Changing initial Adolescent Changingconditions: moving intervention: Moving initial conditionschildren to the 4th investments at last and performing
decile of distribution transition from 1st a balancedof skills only through to 9th decile intervention
Baseline early investments
High School Graduation 0.4109 0.6579 0.6391 0.9135Enrollment in College 0.0448 0.1264 0.1165 0.3755Conviction 0.2276 0.1710 0.1733 0.1083Probation 0.2152 0.1487 0.1562 0.0815Welfare 0.1767 0.0905︸ ︷︷ ︸
Perry Treatment Effects
0.0968 0.0259
The adolescent-only and balanced intervention programscost 35% more than the Perry program.Source: Cunha and Heckman (2007)
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Econ and Ecom of Hum Dev