T HE TECHNOLOGY OF SKILL FORMATION F LAVIO C UNHA AND J AMES H ECKMAN

AER papers and proceedings, 2007

()

1 / 18

Motivation

People have diverse abilities: cognitive, noncognitive. Abilities account for a substantial portion of the variation across people in socioeconomic success. Persistent and substantial ability gaps across children of various socioeconomic groups emerge before they start school.

()

2 / 18

Motivation

()

3 / 18

Motivation

Levels of child’s skills are highly correlated with family background factors. ()

4 / 18

Motivation

The family plays a powerful role in shaping these abilities: Genetics Parental investments Environment

Policy designed to reduce inequalities ⇒ early vs late remediation investments.

()

5 / 18

Goal of the paper Provide a theoretical framework for interpreting the evidence from a vast empirical literature on skill formation and child development. Present economic models of child development: Childhood has more than one stage Abilities are both inherited and created Skill begets skill through a multiplier process Skill attainment at one stage of the life cycle raises skill attainment at later stages of the life cycle (self-productivity) Early investment facilitates the productivity of later investment (complementarity)

Provide a framework for designing policies to reduce inequality.

()

6 / 18

Simple model Individual lives for 2T periods: Childhood: 1 to T Adulthood: T+1 to 2T Household: child +parent; altruism. During adulthood the individual works. Supplies labor inelastically. There are two kind of skills: Cognitive (θtC ) and non-cognitive(θtN ) Each agent is born with initial conditions (θ1C , θ1N ) Itk : parental investments in child skill k at period t. h0 : level of human capital as the child starts adulthood. h0 = g(θTC+1 , θTN+1 ) ()

7 / 18

Technology The technology of production of skill k at period t is

k θt+1 = ftk (h, θt , Itk ),

for k = C, N, t = 1, T ; θt = (θtC , θtN ).

(1)

Self-productivity: skills attained at one stage augment skills attained at later stages.

∂ftk (h, θt , Itk ) j

> 0,

j = C, N

(2)

∂θt Dynamic complementarity: Skills produced at one stage raise productivity of investment at subsequent stages. ∂ 2 ftk (h, θt , Itk ) j

∂Itk ∂θt

()

> 0,

k, j = C, N

(3)

8 / 18

Technology: Example T=2

First period technology: θ2k = ftk (θ1 , I1k ) = I1k . Second period technology (CES):  1/α θ3C = f2C (θ2 , I2C ) = γ1 (θ2C )α + γ2 (θ2N )α + (1 − γ1 − γ2 )(I2C )α  1/v θ3N = f2C (θ2 , I2C ) = η1 (θ2C )v + η2 (θ2N )v + (1 − η1 − η2 )(I2C )v Third period. Adult human capital:  1/φ h0 = τ (θ3C )φ + (1 − τ )(θ3N )φ

()

9 / 18

Technology: Example Assumtpions: ItC = ItN = It α=v =φ Adult human capital stock: n o1/φ h0 = γI1φ + (1 − γ)I2φ γ = τ (γ1 + γ2 ) + (1 − τ )(η1 + η2 ) ⇒ Skill multiplier Self productivity Direct complementarity

φ: Degree of complementarity(sustitutability) between early and late investments ⇒ how easy is to compensate for low levels of stage 1 skills in producting late skills.

()

10 / 18

Technology: CES complementarity/sustitutability 1) Perfect CES Substitutes: φ = 1 h0 = {γI1 + (1 − γ)I2 } it is possible in a physical productivity sense, to compensate for early investment deficits by later investments. Special case γ = 1/2 ⇒ only matters the total amount of human capital investments, regardless of how it is distributed across childhood periods.

2) Perfect CES Complements (leontief case): φ → −∞ h0 = min {I1 , I2 } Early investments are a bottleneck for later investments. Later investments are needed to harvest early investments. Compensation for adverse early environments through late environments is impossible.

()

11 / 18

Optimal timming of investments

Parent chooses I1 , I2 and level of risk free assets b that maximizes the present value of net wealth of their children.   0  1 qh (I , I ) + b 1 2 I1 ,I2 ,b (1 + r )2 I2 b s.t. I1 + + =M 1+r (1 + r )2 b≥0 

max

where q =

(4) (5) (6)

P4

t−3 1 wt t=3 ( (1+r ) )

()

12 / 18

Optimal timming of investments

1) Perfect CES substitutes(φ=1):

Invest early if γ > (1 − γ)(1 + r ) ⇒ γ >

1+r 2+r

2) Perfect CES complements(φ → −∞):

I1 = I2

()

13 / 18

Optimal timming of investments 3) −∞ < φ < 1 I1 I2

()

=



γ (1−γ)(1+r )



1 1−φ

14 / 18

Consequences of credit constraints

Assume: M A > M B ⇒ family A unconstrained; family B is constrained I1A > I1B ; I2A > I2B Facts: Ability gaps between individuals and across socioeconomic groups open up at early ages (Blau & Currie, 2006).

()

15 / 18

Late remediations for disadvantaged children Optimal policy ⇒ critically depend on the technology of skill production: Lower returns if early and late investments are not perfect substitutes. Late investment is more productive the higher the level of early investments.

⇒ Equity-efficiency trade-off in late remediation policies. Facts: Returns to secondary schooling and post-secondary schooling are higher for high-ability people than for low-ability people Higher returns to the most able in job training programs. College enrollment response to unanticipated increases in returns to college were initially strong for adolescents from advantaged families.

()

16 / 18

Early remediations for disadvantaged children

⇒ There is no trade-off between equity and efficiency in early childhood investments. The marginal return to one dollar invested in the poor child from family B is above the marginal return to the same dollar invested in the rich child from family A Facts: High economic returns to interventions targeted toward young disadvantaged children (Barbnet 2004). If early investments in disadvantaged is not followed up by later investments, its effects at later ages is lessened (Currie & Thomas 1995)

()

17 / 18

Conclusions

Considering different stages during childhood + special features of technology of skill formation is important: To undestand empirical evidence on child development. To guide further research on optimal policy interventions to reduce inequalities.

()

18 / 18