Estimating the Technology of Cognitive and Noncognitive Skill Formation

Comparing the estimates in Table 3 with those in Table 1, the estimated first stage investment
effects are much less precisely estimated in a model that ignores measurement errors than
in a model that corrects for them. In the second stage, the estimated investment effects are
generally stronger. Unlike all of the specifications that control for measurement error, we
estimate strong cross productivity effects of cognitive skills on noncognitive skill production.
As in Table 1, there are cross productivity effects of noncognitive skills on cognitive skills
at both stages although the estimated productivity parameters are somewhat smaller. The
estimated elasticities of substitution for cognitive skills at both stages are comparable across
the two specifications. The elasticities of substitution for noncognitive skills are substantially
lower at both stages in the specification that does not control for measurement error. The
error variances of the shocks are substantially larger. Parental cognitive skills are estimated
to have substantial effects on childhood cognitive skills but not their noncognitive skills.
This contrasts with the estimates reported in Table 1 that show strong effects of parental
noncognitive skills on childhood cognitive skills in both stages, and on noncognitive skills in
the first stage.

4.2.4 Controlling for Time-Invariant Unobserved Heterogeneity in the Esti-
mated Technology

We next consider the effect of controlling for unobserved heterogeneity in the model, with
estimates reported in Table 1. We follow the method discussed in Section 3.6.1. Doing so
allows for endogeneity of the inputs. We break the error term for the technology into two
parts: a time-invariant unobserved heterogeneity factor π that is correlated with the vector
(θ_t, I_t, θ_P) and an i.i.d. error term ν_k,t that is assumed to be uncorrelated with all other
variables.

Table 4 shows that correcting for heterogeneity, the estimated coefficients for parental
investments have a greater impact on cognitive skills at the first stage. The coefficient on
parental investment in the first stage is γ₁,C,₃ = 0.16, while in the second stage γ₂,C,₃ = 0.04.
The elasticity of substitution in the first stage is well above one, σ₁,C = _1-0 ₃₁ = 1.45,
and in the second stage it is well below one, σ₂,C = ₁+1 ₂₄ = 0.44. These estimates are
statistically significantly different from each other and from the estimates of the elasticities
of substitution σ1,N and σ2,N .³⁸ These results suggest that early investments are important
in producing cognitive skills. Consistent with the estimates reported in Table 1, noncognitive
skills increase cognitive skills in the first stage, but not in the second stage. Parental cognitive
and noncognitive skills affect the accumulation of childhood cognitive skills.

³⁸See Table 10-5 in Web Appendix 10.

28

<<   26   27   28   29   30   31   32   >>

More intriguing information