Does Money in Schools Matter? Evaluating the Effects ... - EPGE/FGV

This means that the teachers’ wages in both private and public schools in 1997 and 1999
can be written as:
w
it
= β + γ + δF
+ ε
(3)
t
s
i
it
where F
i
is a dummy variable equal to 1 if school i was directly affected by FUNDEF, that
is, it was a public school observed in 1999. Differentiating the wages across schools and
years, we have:
{ E[
wi
/ s =
{ E[
w / s =
i
pub,
t = 99] − E[
w / s = priv,
t = 99]} −
i
pub / t = 97] − E[
w / s = priv,
t = 97]} = δ
i
(4)
As many school and students’ characteristics may have changed between 1997 and
1999, and in public schools differently from in the private ones, we will stack the micro
data for all schools and years and estimate an equation like:
w
it
= β + γ + δF
+ θX
+ λS
+ ε
(5)
t
s
i
it
it
it
where X is a vector of school characteristics and S is a vector of the teachers
characteristics.
The main identification assumption we need is that:
{ E[
ε / X , S,
s =
i
{ E[
ε / X , S,
s =
i
pub,
t = 99] − E[
ε / X , S,
s = priv,
t = 99]} −
i
pub / t = 97] − E[
ε / X , S,
s = priv,
t = 97]} = 0
i
(6)
that is, there could be no changes in the unobserved characteristics of the public schools or
of their teachers, relative to the private ones, between 1997 and 1999. Since we have no
idea about the plausibility of this assumption, we will include as many observable
characteristics as possible given our data set, and compare their means between 1997 and
1999.