Estimating the Technology of Cognitive and Noncognitive Skill Formation

The general pattern of decreasing substitution possibilities across stages for cognitive
skills and roughly constant or slightly increasing substitution possibilities for noncognitive
skills is consistent with the literature on the evolution of cognitive and personality traits
(see Borghans et al., 2008; Shiner, 1998; Shiner and Caspi, 2003). Cognitive skills stabilize
early in the life cycle and are difficult to change later on. Noncognitive traits flourish, i.e.,
more traits are exhibited at later ages of childhood, and there are more possibilities (more
margins to invest in) for compensation of disadvantage. For a more extensive discussion, see
Web Appendix 1.2.

4.2.6 A Model Based Only on Cognitive Skills

Most of the empirical literature on skill production focuses on cognitive skills as the output
of family investment (see, e.g., Todd and Wolpin, 2005, 2007, and the references they cite).
It is of interest to estimate a more traditional model that ignores noncognitive skills and the
synergism between cognitive and noncognitive skills and between investment and noncog-
nitive skills in production. Web Appendix Table 14.1 reports estimates of a version of the
model in Table 4, based on a model with time-invariant heterogeneity, where noncognitive
skills are excluded from the analysis.

The estimated self-productivity effect increases from the first stage to the second stage, as
occurs with the estimates found for all other specifications estimated in this paper. However,
the estimated first period elasticity of substitution is much smaller than the corresponding
parameter in Table 4. The estimated second period elasticity is slightly higher. The es-
timated productivity parameters for investment are substantially higher in both stages of
the model reported in Web Appendix Table 14.1, as are the productivity parameters for
parental cognitive skills. We note in the next section that the policy implications from a
cognitive-skill-only model are very different from the policy implications for a model with
cognitive and noncognitive skills.

4.3 Interpreting the Estimates

The major findings from our analysis of models with two skills that control for measure-
ment error and endogeneity of inputs are: (a) Self-productivity becomes stronger as children
become older, for both cognitive and noncognitive skill formation. (b) Complementarity
between cognitive skills and investment becomes stronger as children become older. The
elasticity of substitution for cognition is smaller in second stage production. It is more diffi-
cult to compensate for the effects of adverse environments on cognitive endowments at later

and that the elasticities of different skills are equal. See Table 10-7 in Web Appendix 10.

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