Question

1. Suppose that you are interested how education effects fertility decisions of women.

a. Carefully describe the simple linear regression model relating fertility to education. You will have to define variables denoting the number of children ever born to a woman, and denoting years of education for the woman. [3 points]
b. What are some of the other determinants of fertility decisions? Are these likely to be correlated with the education? Explain how. [3 points]
c. Will your linear model in part a recover the causal effect of education on fertility decisions of a woman? [3 points]

Answer 1

1. Simple linear regression model:

logY=β0- β1X+e

where y= number of children ever born to a woman

X= years of education that women have completed.

E= error term includes all other variables which could affect the fertility rate of women.

This regression function tells that for every additional increase in years of education for a woman leads to a lower number of children ever born to a woman.

2. Other determinants of fertility decision are Income level, the literacy rate among females, female labor force participation rate, number of contraceptive use,pro-family government programs.

Yes, there are likely to be correlated with education. Higher-income level leads to higher education. If a woman is educated well, she is more likely to use a contraceptive .highly educated women are more likely to participate in the labor /Job market.

c.Yes, if we define some other variable in our model which could affect our dependent variable.Multilinear regression model

logY=β0- β1X1+-β1X2+-β1X3+e

Here, x1= years of education that women have completed.

X2=number of women participating in the labor force

X3= Income level

The problem of endogeneity is solved by IV (Instrumental variable ). We choose some variable in a model so that it only affects( y) dependental variable through independent variable(x).