Estimating the Technology of Cognitive and Noncognitive Skill Formation

parameters is dramatic for cognitive skills. The variability in the shocks is greater in the
second period than in the first period. The elasticity of substitution for cognitive skills is
much greater in the first period than in the second period. However, the estimated elasticity
of substitution is about the same in both stages of production.

For cognitive skill production, the parental cognitive skill parameter is about the same in
both stages. The opposite is true for parental noncognitive skills. In producing noncognitive
skills, parental cognitive skills play no role in the second stage. Parental noncognitive skills
play a strong role in stage 1 and a weaker role in stage 2.

4.2.2 The Empirical Importance of Measurement Error

Using our estimated factor model, we can investigate the extent of measurement error on
each measure of skill and investment in our data. To simplify the notation, we keep the
conditioning on the regressors implicit and, without loss of generality, consider the measure-
ments on cognitive skills in period t. For linear measurement systems, the variance can be
decomposed as follows:

V ar (Z1,C,t,j) = α₁²_,C,t,jV ar (ln θC,t) + V ar (ε1,C,t,j) .

The fractions of the variance of Z_1,C,t,j due to measurement error, s^ε_1,C,t,j , and true signal,
s^θ_1,C,t,j are, respectively,

_____________V (^ει^,c^,tj)_____________ (noise)
α‰,tj '■ (ln θc,t) + '■    (ε_tc,tj) ⁽      )

and

^αLc_jjV^ar !∣n^θc,H

^α2C,tjV^{ar (ln} θC,t) + V^ar (^ε1,C,tj)

For each measure of skill and investment used in the estimation, we construct s^ε_1,C,t,j and
s^θ_1,C,t,j which are reported in Table 2A. Note that the early proxies tend to have a higher
fraction of observed variance due to measurement error. For example, the measure that
contains the lowest true signal ratio is the MSD (Motor and Social Developments Score) at
year of birth, in which less than 5% of the observed variance is signal. The proxy with the
highest signal ratio is the PIAT Reading Recognition Scores at ages 5-6, for which almost
96% of the observed variance is due to the variance of the true signal. Overall, about 54%
of the observed variance is associated with the cognitive skill factors θ_C,t .

Table 2A also shows the same ratios for measures of childhood noncognitive skills. The

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