876 vIII. EMERGING ISSuES AND NEW DIRECTIONS
where T′a–1 might represent a fundamentally 
different task that measures the same set 
of skills. For example, T ′a–1 could represent 
the number of course credits that a student 
earns, and Ta could represent graduating 
from high school. Both are valid measures 
of skills. As suggested by Jackson (2018) and 
Kautz and Zanoni (2019), credits earned is 
a valid measure of noncognitive skills, be-
cause successfully completing courses de-
pends on noncognitive skills. Similarly, as 
argued by Heckman, Humphries, and Kautz 
(2014), graduating from high school is a task 
that depends in part on noncognitive skills. 
A complication arises because students who 
earn more credits in ninth grade might be 
more likely to graduate from high school 
in part, not only because they have higher 
levels of skills, but also because high school 
graduation is a direct function of credits 
earned. More generally, task T ′a–1 captures 
something other than the underlying skills 
of students that can affect performance on 
Ta. Econometric methods can separate the 
direct effect of past measures from the ef-
fect of skills (Athans & Falb, 2013; Grang-
er, 1969; Heckman, 1981a, 1991b, 1991c; Harvey, 1989; Torgovitsky, 2015; Williams, 
2020). Models of this type are also common 
in the economics literature and are infor-
mative, because they capture learning (G. 
Becker & Murphy, 1988; Hai & Heckman, 
2019; Pollak, 1976).
This framework recognizes that differ-
ent skills might be relatively easy to shape 
at different stages of the life cycle. Sensitive 
periods  for a given skill are periods when 
investments are relatively more productive. 
Critical periods  for a particular skill are 
periods when investment during any other 
period is not productive.
Figure 42.12 illustrates why understand-
ing the effects attributable to specific inter-
ventions is such a challenging task. Most 
empirical studies only investigate the inter-
ventions aimed at one slice of the life cycle. 
They do not connect the links in Figure 
42.12 or correct for the effects of later in-
vestment in producing the outcomes attrib-
uted to early investments. One important 
area for future research on skills formation 
is to better document how early interven-
tions influence the efficacy of later interven-
tions.Prenatal
InvestmentsInherited
TraitsPrenatal
Skills Birth
Parenting,
Self Investments,
Environment, School
Parenting,
Self Investments,
Environment, SchoolSkillsSkills
SkillsChildhood
Adulthood
Higher Education Earnings Crime Health
FIGURE 42.12. Framework for understanding skills development.