Page 47 - IJPS-3-2

Do young children prohibit mothers from working in Ethiopia?

Appendix A

Model specification
First, the structural form for the probit regression model (Y 1i) can be given as:
Y    x   Y   U i (1)
1
2i
1i
1i
0
th
where, Y is the probability of mother’s work participation for the i household (1=If she works, 0=Otherwise)
i 1
 is parameter coefficient of the vector of an exogenous variable, x
i 1
1
 is parameter coefficient of the vector of the number of children, Y i 2
U is an error term assumed to be normally distributed with mean zero.
i
However, the literature tells us that the number of children (Y 2i) is endogenous. That is,
Cov Y 2i , i   (2)
0U
If the equation is estimated by OLS, the estimate will be biased. Therefore, Y 2i should be itself predicted first in a
reduced form as a function of sibling sex composition, Z i, and other covariates.
Y    x   Z   e i (3)
0
2
2i
i
3i
where, Y is the predicted number of children for the i household,
th

3i
 is parameter coefficient of the vector of exogenous variables, x , for the i household,
th

2
i 2
 is parameter coefficient of the vector of the instrumental variable, Z ,

i
e is an error term associated to household i.

i
The instrumental variable, Z , is assumed to be uncorrelated with the error term, but partially correlated with the number
i
of children. That is,

0U
Cov Z i , i   (4) and,
Cov Z i 2i   0. (5)
 ,Y
The instrument is also assumed to be uncorrelated with other exogenous covariates. That is,

,
Cov Z X 1i   0. (6)
i
Because U is unobservable, Cov Z   ,Y  which can be readily tested using the data.
 ,U is untestable, unlike Cov Z
i i i i 2i
Once the number of children is exogenously predicted in (3), the final equation which estimates the mother’s work
participation can be specified by inserting the predicted number of children, Y , in place of Y as:
3i 2i
Y    x   Y   i (7)

3
0
3i
1i
3i
where, Y is defined as in (1) above.
1i
 is parameter coefficient of the vector of exogenous variables, x
3
3i
 is parameter coefficient of the estimated number of children, Y

3i
 is an error term associated to household i.

i
The estimated maternal work participation, Y , is now assumed to be unbiased.
i 1

International Journal of Population Studies | 2017, Volume 3, Issue 2 41