The data in FERTIL2.RAW includes, for women in Botswana during 1988, information on number of children, years of education, age, and religious and economic status variables. (i) Estimate the model children = β0 + β1educ + β2age + β3age2 + u by OLS, and interpret the estimates. In particular, holding age fixed, what is the estimated effect of another year of education on fertility? If 100 women receive another year of education, how many fewer children are they expected to have?
(ii) The variable frsthalf is a dummy variable equal to one if the woman was born during the first six months of the year. Assuming that frsthalf is uncorrelated with the error term from part (i), show that frsthalf is a reasonable IV candidate for educ. (Hint: You need to do a regression.)
(iii) Estimate the model from part (i) by using frsthalf as an IV for educ. Compare the estimated effect of education with the OLS estimate from part (i).
(iv) Add the binary variables electric, tv, and bicycle to the model and assume these are exogenous. Estimate the equation by OLS and 2SLS and compare the estimated coefficients on educ. Interpret the coefficient on tv and explain why television ownership has a negative effect on fertility.