Panel B of Table 4 presents estimates of the technology of noncognitive skills. Note that,
contrary to the estimates reported for the technology for cognitive skills, the elasticity of
substitution increases slightly from the first stage to the second stage. For the early stage,
σ1,N = 0.62 while for the late stage, σ2,N = 0.65. The elasticity is about 50% higher for
investments in noncognitive skills for the late stage in comparison to the elasticity for invest-
ments in cognitive skills. The estimates of σ1,N and σ2,N are not statistically significantly
different from each other, however.39 The impact of parental investments is about the same
at early and late stages (γ1,N,3 = 0.06 vs. γ2,N,3 = 0.05). Parental noncognitive skills affect
the accumulation of a child’s noncognitive skills both in early and late periods, but parental
cognitive skills have no effect on noncognitive skills at either stage. The estimates in Ta-
ble 4 show a strong effect of parental cognitive skills at both stages of the production of
noncognitive skills.
4.2.5 A More General Approach to Solving the Problem of the Endogeneity of
Inputs
This section relaxes the invariant heterogeneity assumption and reports empirical results
from a more general model of time-varying heterogeneity. Our approach to estimation is
motivated by the general analysis of Section 3.6.2, but, in the interest of computational
tractability, we make parametric and distributional assumptions.
We augment the measurement system (3.1)-(3.3) by investment equation (3.11), which
is motivated by economic theory. Our investment equation is
It = kC θC,t + kN θN,t + kC,P θC,P + kN,P θN,P + kyyt + πt.40 (4.2)
We substitute (4.2) into equations (3.2) and (3.10). We specify the income process as
lnyt = ρy ln yt-1 + νy,t, (4.3)
and the equation of motion for πt as
πt = ρππt-1 + νπ,t. (4.4)
We assume that νy,t ⊥⊥ (θt0 , νy,t0 ) for all t0 6= t and νy,t ⊥⊥ (yt0 , νk,t, θP ), t > t0, k ∈ {C, N},
where “_LL” means independence. We further assume that νπ,t _LL (θto,θp,νk,to) and that
39See Table 10-5 in Web Appendix 10.
40 The intercept of the equation is absorbed into the intercept of the measurement equation.
29