The following empirical regularities emerge across all models that account for measure-
ment error.33 Self productivity of skills is greater in the second stage than in the first stage.
Noncognitive skills are cross productive for cognitive skills in the first stage of production.
The cross productivity effect is weaker and less precisely determined in the second stage.
There is no evidence for a cross productivity effect of cognitive skills on noncognitive skills at
either stage. The estimated elasticity of substitution for inputs in cognitive skill is substan-
tially lower in the second stage of a child’s life cycle than in the first stage. For noncognitive
skills, the elasticity in the second period is slightly higher for models that control for un-
observed heterogeneity (π). These estimates suggest that it is easier to redress endowment
deficits that determine cognition in the first stage of a child’s life cycle than in the second
stage. For socioemotional (noncognitive) skills, the opposite is true. For cognitive skills,
the productivity parameter associated with parental investment (γ1,C,3) is greater in the first
stage than in the second stage (γ2,C,3). For noncognitive skills, the pattern of estimates
for the productivity parameter across models is less clear cut, but there are not dramatic
differences across the stages. For both outputs, the parameter associated with the effect of
parental noncognitive skills on output is smaller at the second stage than the first stage.
Web Appendix 11 discusses the sensitivity of estimates of a one-stage two-skill model
to alternative anchors and to allowing for nonnormality of the factors. For these and other
estimated models which are not reported, allowing for nonnormality has only minor effects
on the estimates. However, anchoring affects the estimates.34 To facilitate computation, we
use years of schooling attained as the anchor in all of the models reported in this section of
the paper.35
4.2.1 The Baseline Specification
Table 1 presents evidence on our baseline two stage model of skill formation. Outcomes are
anchored in years of schooling attained. Factors are assumed to be normally distributed
and we ignore heterogeneity (π). The estimates show that for both skills, self productivity
increases in the second stage. Noncognitive skills foster cognitive skills in the first stage but
not in the second stage. Cognitive skills have no cross-productivity effect on noncognitive
skills at either stage.36 The productivity parameter for investment is greater in the first
period than the second period for either skill. The difference across stages in the estimated
33Estimated parameters are reported in Web Appendix 10.
34Cunha and Heckman (2008) show the sensitivity of the estimates to alternative anchors for a linear
model specification.
35The normalizations for the factors are presented in Web Appendix 10.
36Zero values of coefficients in this and other tables arise from the optimizer attaining a boundary of zero
in the parameter space.
25