Versión de HTML Básico
Andrea Molina Vera
Analítika, Revista de análisis estadístico, (2015), Vol. 9
10
x
i
is the endogenous fertility measure of interest. In this case it is the third child variable
or number of children variable. It is replaced in (1) by the predicted value of the following
regression to obtain 2SLS estimates.
x
i
=
ρ
+
w λ
+
γ
(
Samesex
) +
η
i
(2)
Where
Samesex
is a dummy for whether the sex of the second child matches the sex of
the first child.
2.2 Theoretical Model
In a simple static model, women or families choose the levels of consumption (
C
), time of
leisure
t
l
and number of children (N) that solves the maximization of a utility function
2
U
=
u
(
C, t
l
, N
)
U
=
u
(
C, t
l
, N
)
(3)
Equation 3 is subject to following time and money constraints:
T
=
t
m
+
t
h
+
t
l
(4)
I
+
wt
m
=
p
c
C
+
p
n
n
(5)
Where: the time restriction has a total time(
T
) distributable for market (
t
m
), work at
home (including housework and childcare(
t
h
)) and leisure (
t
l
); the money restriction has a
non-labor income(
I
), hour-paid wage (
w
), price of goods (
p
c
) and cost of child rearing (
p
n
).
Here the female labor supply (
L
) is a function of number of children (
N
) and other variables
(
Y
)
vector
, namely
L
=
f
(
Y, N
).
The effect of interest is the labor supply response to changes in fertility. But as fertility
can be correlated with omitted variables related with labor supply (as professional ambition,
etc.), to identify the direct effect of fertility is necessary to use an instrument (
Z
) that takes
into account the exogenous variation of fertility but is not related with labor supply. Thus,
the effect of interest can be identified as follows:
∂L/∂Z
=
f
y
∂Y/∂Z
+
f
N
∂N/∂Z
(6)
Since
Z
is exogenous with respect to
Y
, then
∂/∂Z
= 0. Therefore, the response of labor
supply to changes in fertility is identified as:
f
N
= (
∂L/∂Z
)
/
(
∂N/∂Z
)
(7)
2
This Utility is increasing in all this arguments
4