ages than it is at earlier ages.46 This pattern of the estimates helps to explain the evidence on
ineffective cognitive remediation strategies for disadvantaged adolescents reported in Cunha,
Heckman, Lochner, and Masterov (2006). (c) Complementarity between noncognitive skills
and investments becomes slightly weaker as children become older, but the estimated effects
are not that different across stages of the life cycle. The elasticity of substitution between
investment and current endowments increases slightly between the first stage and the sec-
ond stage in the production of noncognitive skills. It is somewhat easier at later stages of
childhood to remediate early disadvantage using investments in noncognitive skills.
Using the estimates present in Table 4, we find that 34% of the variation in educational
attainment in the sample is explained by the measures of cognitive and noncognitive capa-
bilities that we use. 16% is due to adolescent cognitive capabilities. 12% is due to adolescent
noncognitive capabilities.47 Measured parental investments account for 15% of the varia-
tion in educational attainment. These estimates suggest that the measures of cognitive and
noncognitive capabilities that we use are powerful, but not exclusive, determinants of edu-
cational attainment and that other factors, besides the measures of family investment that
we use, are at work in explaining variation in educational attainment.
To examine the implications of these estimates, we analyze a standard social planning
problem that can be solved solely from knowledge of the technology of skill formation and
without knowledge of parental preferences and parental access to lending markets. We
determine optimal allocations of investments from a fixed budget to maximize aggregate
schooling for a cohort of children. We also consider a second social planning problem that
minimizes aggregate crime. Our analysis assumes that the state has full control over family
investment decisions. We do not model parental investment responses to the policy. These
simulations produce a measure of the investment that is needed from whatever source to
achieve the specified target.
Suppose that there are H children indexed by h ∈ {1, . . . , H}. Let (θC,1,h, θN,1,h) de-
note the initial cognitive and noncognitive skills of child h. She has parents with cognitive
and noncognitive skills denoted by θC,P,h and θN,P,h , respectively. Let πh denote additional
unobserved determinants of outcomes. Denote θ1,h = (θC,1,h, θN,1,h, θC,P,h, θN,P,h, πh) and let
F (θ1,h) denote its distribution. We draw H people from the estimated initial distribution
F (θ1,h). We use the estimates reported in Table 4 in this simulation. The key substitution
parameters are basically the same in this model and the more general model with estimates
reported in Table 5.48 The price of investment is assumed to be the same in each period.
46This is true even in a model that omits noncognitive skills.
47The skills are correlated so the marginal contributions of each skill do not add up to 34%. The decom-
position used to produce these estimates is discussed in Web Appendix 12.
48Simulation from the model of Section 3.6.2 (with estimates reported in Section 4.2.5) that has time-
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