B. Period 0: The “Shaping” of Teenagers
We assume that a child is endowed with an ability vector, θ , at birth. The vector has
two elements, corresponding to cognitive and noncognitive ability, and is determined by,
1
= f
1
F
, where
f
1
.,. is a possibly nonlinear function, θ
F
is a 2 × 1 vector of hereditary cognitive and noncognitive abilities characterizing a family and ι is a vector of
individual- specifi c traits that are randomly assigned. Ideally, we would like to separately account for the impact of youth’s ability and
observable parental characteristics, such as education, on the dropout decision. How- ever, this is complicated by:
1. The fact that parental education is likely a function of θ
F
. Indeed, we will assume that parental education PE is determined as,
2 PE = f
2
F
,
p
, where ν
p
corresponds to parental valuations of education and η summarizes all fac- tors contributing to PE, which are orthogonal to θ
F
and ν
p
. To be more specifi c, we interpret ν
p
as refl ecting parents’ beliefs about returns to education, with parents who believe that returns are higher having higher values for ν
p
. One could, alternatively, interpret ν
p
as a preference parameter refl ecting parental taste for education. There is nothing in the data that would allow us to delineate these interpretations and changing
the interpretation does not affect the nature of our estimator. 2. The ability we observe in the data—ability at the start of the teenage period,
denoted as θ
1
—will itself be a function of parental inputs. In particular, we assume it is a function of θ
, of parental education either because it refl ects family income effects or because hours of parental time from educated parents are more effective in
generating children’s ability, and of parental valuation of education because it helps determine how much effort parents invest in improving their child’s ability. That is,
3
1
= f
3
, PE,
p
where, following CH07 and CHS, it is possible that cognitive ability at age 15 is a function of both endowed cognitive and noncognitive abilities, and the same is true
for age 15 noncognitive ability.
C. Periods 1 and 2: The Dropout Decision and After
Kategori