(θ1,y1) _LL π.41 In addition, νy,t = N (θ, σ^) and νπ,t = N (θ,σ∏). In Web Appendix 8, we
report favorable results from a Monte Carlo study of the estimator based on these assump-
tions.
Table 5 reports estimates of this model.42 Allowing for time-varying heterogeneity does
not greatly affect the estimates from the model that assumes fixed heterogeneity reported
in Table 4. In the results that we describe below, we allow the innovation πt to follow
an AR(1) process and estimate the investment equation qk,t along with all of the other
parameters estimated in the model reported in Table 4.43 Estimates of the parameters of
equation (4.2) are presented in Web Appendix 1θ. We also report estimates of the anchoring
equation and other outcome equations in that appendix.44 When we introduce an equation
for investment, the impact of early investments on the production of cognitive skill increases
from γι,c,3 = θ.17 (see Table 4, Panel A) to γ1,C,3 = θ.26 (see Table 5, Panel A). At the
same time, the estimated first stage elasticity of substitution for cognitive skills increases
from σ1,C = 1-1 c = 1.5 to σ1,C = 1-φι c = 2.4. Note that for this specification the
impact of late investments in producing cognitive skills remains largely unchanged at γ2,C,3
== θ.θ45 (compare Table 4, Panel A with Table 5, Panel A). The estimate of the elasticity of
substitution for cognitive skill technology is about the same as σ2,C = 1-φ c = θ.44 (Table
4, Panel A) and σ2,C = 1-φ c = θ.45 (see Table 5, Panel A).
We obtain comparable changes in our estimates of the technology for producing noncog-
nitive skills. The estimated impact of early investments increases from γ1,N,3 == θ.θ65 (see
Table 4, Panel B) to γ1,N,3 == θ.2θ9 (in Table 5, Panel B). The elasticity of substitution
for noncognitive skills in the early period rises, changing from σ1,N = 1-J = θ.62 to
σ1,N = 1-,111 jv = θ.68 (in Table 5, Panel B). The estimated share parameter for late invest-
ments in producing noncognitive skills increases from γ2,N,3 == θ.θ5 to γ2,N,3 == θ.1θ. Compare
Table 4, Panel B with Table 5, Panel B. When we include an equation for investments, the
estimated elasticity of substitution for noncognitive skills slightly increases at the later stage,
from σ2 N = -j—1— = θ.645 (in Table 4, Panel B) to σ2 N = 1—1— = θ.66 (in Table 5, Panel
2,N 1-φ2,N 2,N 1-φ2,N
B), but this difference is not statistically significant. Thus, the estimated elasticities of sub-
stitution from the more general procedure show roughly the same pattern as those obtained
from the procedure that assumes time-invariant heterogeneity.45
41This assumption enables us to identify the parameters of equation (4.2).
42Table 10-6 in Web Appendix 10 reports estimates of the parameters of the investment equation (4.2).
43We model q as time invariant, linear and separable in its arguments, although this is not a necessary
assumption in our identification, but certainly helps to save on computation time and to obtain tighter
standard errors for the policy function and the production function parameters. Notice that under our
assumption IC,t = IN,t = It , and time invariance of the investment function, it follows that qk,t = qt = q for
all t.
44We also report the covariance matrix for the initial conditions of the model in the appendix.
45We cannot reject the null hypothesis that σ1,N = σ2,N but we reject the null hypothesis that σ1,C = σ2,C
3θ