measures of noncognitive skills tend to be lower in informational content than their cognitive
counterparts. Overall, less than 40% of the observed variance is due to the variance associated
with the factors for noncognitive skills. The poorest measure for noncognitive skills is the
“Sociability” measure at ages 3-4, in which less than 1% of the observed variance is signal.
The richest is the “BPI Headstrong” score, in which almost 62% of the observed variance is
due to the variance of the signal.
Table 2A also presents the signal-noise ratio of measures of parental cognitive and noncog-
nitive skills. Overall, measures of maternal cognitive skills tend to have a higher information
content than measures of noncognitive skills. While the poorest measurement on cognitive
skills has a signal ratio of almost 35%, the richest measurements on noncognitive skills are
slightly above 40%.
Analogous estimates of signal and noise for our investment measures are reported in
Table 2B. Investment measures are much noisier than either measure of skill. The measures
for investments at earlier stages tend to be noisier than the measures at later stages. It is
interesting to note that the measure “Number of Books” has a high signal-noise ratio at
early years, but not in later years. At earlier years, the measure “How Often Mom Reads to
the Child” has about the same informational content as “Number of Books.” In later years,
measures such as “How Often Child Goes to the Museum” and “How Often Child Goes to
Musical Shows” have higher signal-noise ratios.
These estimates suggest that it is likely to be empirically important to control for mea-
surement error in estimating technologies of skill formation. A general pattern is that at early
ages compared to later ages, measures of skill tend to be riddled with measurement error,
while the reverse pattern is true for the measurement errors for the proxies for investment.
4.2.3 The Effect of Ignoring Measurement Error on the Estimated Technology
We now demonstrate the impact of neglecting measurement error on estimates of the tech-
nology. To make the most convincing case for the importance of measurement error, we use
the least error prone proxies as determined in our estimates of Table 2.37 We continue to
assume no heterogeneity.
Not accounting for measurement error has substantial effects on the estimated technology.
37At birth we use Cognitive Skill: weight at birth, Noncognitive Skill: Temperament/Difficulty Scale,
Parental Investment: Number of books. At ages 1-2 we use Cognitive Skill: Body Parts, Noncognitive Skill:
Temperament/Difficulty Scale, Parental Investment: Number of books. At ages 3-4 we use Cognitive Skill:
PPVT, Noncognitive Skill: BPI Headstrong, Parental Investment: How often mother reads to the child. At
ages 5-6 to ages 13-14 we use Cognitive Skill: Reading Recognition, Noncognitive Skill: BPI Headstrong,
Parental Investment: How often child is taken to musical performances. Maternal Skills are time invariant:
For Maternal Cognitive Skill: ASVAB Arithmetic Reasoning, For Maternal Noncognitive Skill: Self-Esteem
Item: I am a failure.
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