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The data in FERTIL2 include, 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$$children=\beta_{0}+\beta_{1} \text { educ }+\beta_{22} a g e+\beta_{3} a g e^{2}+u$$by OLS and interpret the estimates. In particular, holding age fixed, what is the estimated effectof another year of education on fertility? If 100 women receive another year of education, howmany 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 firstsix months of the year. Assuming that frsthalf is uncorrelated with the error term from part (i),show that $f r$thalf 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, $t v$ , and bicycle to the model and assume these are exogenous. Estimate the equation by OLS and 2 $\mathrm{SLS}$ and compare the estimated coefficients on educ. Interpret the coefficient on $t v$ and explain why television ownership has a negative effect on fertility.

(i) The coefficient of educ is $-0.091$ indicating that an additional one year of education, holding the age fixed would reduce the number of living children by 0.091. If 100 women receive another year of education, they are expected to have 9.1 fewer children. (ii) frsthalf is shown to be a reasonable IV candidate for educ (iii) The estimated effects of education from IV model is $-0.1715$ as oppose to $-0.091$ from OLS model (iv) See video

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Chapter 15

Instrumental Variables Estimation and Two Stage Least Squares

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part one. This is the equation estimated by L s. Look at the estimate on education. Another year of education holding age fixed results in about 0.91 fewer Children. In other words, for a group of 100 women, if each gets another year of education, they collectively are predicted to have about nine fewer Children. Part two, this is reduced form for education. Mm hmm. We need by three to be non zero. When we run the regression, we obtain Pi three hat to be minus 0.852 with a standard barrel of 0.113 Yeah, it okay? Therefore, women born in the first half of the year are predicted to have almost one year less education holding age fixed. The T statistic on first half is over 7.5. So we reject the non hypothesis that by three equals zero. And that means the identification assumption. Home, part three. This is the structural equation. Estimates by instrumental variable. The estimated effect of education on fertility is now much larger. The standard bearer for the Ivy estimate is also bigger, about nine times bigger. This produces is fairly white. 95% confidence. Interval four beat her one. But in part four, we will add electric TV and bicycle to the equation and estimated by old L S N i v for education we have minus point oh seven for L s estimate and minus 70.164 for ivy, estimate each 0.34 versus 0.3 to 8 h square. They are roughly equal. Electric minus 0.303 and minus point 17 for TV ownership minus point to 53 vs minus point oh 26 And for bicycle, we have 0.318 versus 0.332 Our square. It's a little bit different between two estimates. All right, What we observe here is that adding electric TV and bicycle to the model reduces the estimated effect of education in both cases, but not by too much mhm in the equation estimated by old ls the coefficient on TV implies other factors fixed for families that oh, a television will have about one fewer child than four families without a TV. Television ownership can be a proxy for different things, including income and perhaps geographic location. A council interpretation is that TV provides an alternative form of recreation. You may notice a big difference in the estimate on TV between LS and Ivy. The effect of TV ownership is practically and statistically insignificant in the equation estimated by Ivy, even though we are not using an I V for T. V. Okay, the coefficient on electric is also greatly reduced in magnitude in the I V estimation. The drops in the magnitude of these coefficients suggests that a linear model might not be the best functional form, which is not surprising because Children the dependent variable is a count variable.

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