4 Estimating the Technology of Skill Formation
Technology (2.1) and the associated measurement systems are nonparametrically identified.
However, we use parametric maximum likelihood to estimate the model and do not estimate
it under the most general conditions. We do this for two reasons. First, a fully nonparametric
approach is too data hungry to apply to samples of the size that we have at our disposal,
because the convergence rates of nonparametric estimators are quite slow. Second, solving a
high-dimensional dynamic factor model is a computationally demanding task that can only
be made manageable by invoking parametric assumptions. Nonetheless, the analysis of this
paper shows that in principle the parametric structure used to secure the estimates reported
below is not strictly required to identify the technology. The likelihood function for the
model is presented in Web Appendix 5. Web Appendix 6 describes the nonlinear filtering
algorithm we use to estimate the technology. Web Appendix 7 discusses how we implement
anchoring. Section 8 of the Web Appendix reports a limited Monte Carlo study of a version
of the general estimation strategy discussed in Section 4.2.5 below.
We estimate the technology on a sample of 2207 firstborn white children from the Children
of the NLSY/79 (CNLSY/79) sample (see Center for Human Resource Research, 2004).
Starting in 1986, the children of the NLSY/1979 female respondents, ages 0-14, have been
assessed every two years. The assessments measure cognitive ability, temperament, motor
and social development, behavior problems, and self-competence of the children as well as
their home environments. Data are collected via direct assessment and maternal report
during home visits at every biannual wave. Section 9 of the Web Appendix discusses the
measurements used to proxy investment and output. Web Appendix Tables 9-1-9-3 present
summary statistics on the sample we use.28 We estimate a model for a single child and ignore
interactions among children and the allocation decisions of multiple child families.
To match the biennial data collection plan, in our empirical analysis, a period is equivalent
to two years. We have eight periods distributed over two stages of development.29 We report
estimates for a variety of specifications.
Dynamic factor models allow us to exploit the wealth of measures on investment and
28While we have rich data on home inputs, the information on schooling inputs is not so rich. Consistent
with results reported in Todd and Wolpin (2005), we find that the poorly measured schooling inputs in the
CNLSY are estimated to have only weak and statistically insignificant effects on outputs. Even correcting
for measurement error, we find no evidence for important effects of schooling inputs on child outcomes. This
finding is consistent with the Coleman Report (1966) that finds weak effects of schooling inputs on child
outcomes once family characteristics are entered into an analysis. We do not report estimates of the model
which include schooling inputs.
29The first period is age 0, the second period is ages 1-2, the third period covers ages 3-4, and so on until
the eighth period in which children are 13-14 years-old. The first stage of development starts at age 0 and
finishes at ages 5-6, while the second stage of development starts at ages 5-6 and finishes at ages 13-14.
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