Estimating the Technology of Cognitive and Noncognitive Skill Formation

4.4 Implications of a One Cognitive Skill Model

Web Appendix 14.1 considers the policy implications of the social planner’s problem from
our estimates of a model formulated solely in terms of cognitive skills. This is the traditional
focus in the analysis of educational production functions. (See, e.g., Todd and Wolpin, 2003,
2007 and Hanushek and Woessmann, 2008.) The optimal policy is to invest relatively more
in the early years of the initially advantaged. Our estimates of two-stage and one-stage
models based solely on cognitive skills would indicate that it is optimal to perpetuate initial
inequality, and not to invest relatively more in disadvantaged young children.

5 Conclusion

This paper formulates and estimates a multistage model of the evolution of children’s cog-
nitive and noncognitive skills as determined by parental investments at different stages of
the life cycle of children. We estimate the elasticity of substitution between contempora-
neous investment and stocks of skills inherited from previous periods and determine the
substitutability between early and late investments. We also determine the quantitative im-
portance of early endowments and later investments in determining schooling attainment.
We account for the proxy nature of the measures of parental inputs and of outputs and
find evidence for substantial measurement error which, if not accounted for, leads to badly
distorted characterizations of the technology of skill formation. We establish nonparametric
identification of a wide class of nonlinear factor models which enables us to determine the
technology of skill formation. We present an analysis of the identification of production tech-
nologies with endogenous missing inputs that is more general than the replacement function
analysis of Olley and Pakes (1996) and allows for measurement error in the proxy variables.⁵¹
A by-product of our approach is a framework for the evaluation of childhood interventions
that avoids reliance on arbitrarily scaled test scores. We develop a nonparametric approach
to this problem by anchoring test scores in adult outcomes with interpretable scales.

Using measures of parental investment and children’s outcomes from the Children of the
National Longitudinal Survey of Youth, we estimate the parameters governing the substi-
tutability between early and late investments in cognitive and noncognitive skills. In our
preferred empirical specification, we find much less evidence of malleability and substitutabil-
ity for cognitive skills in later stages of a child’s life cycle, while malleability for noncognitive
skills is about the same at both stages. These estimates are consistent with the evidence
reported in Cunha, Heckman, Lochner, and Masterov (2006).

⁵¹See Heckman and Robb (1985), Heckman and Vytlacil (2007) and Matzkin (2007) for a discussion of
replacement functions.

36

<<   34   35   36   37   38   39   40   >>

More intriguing information