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Use the data in HTV for this exercise.(i) Run a simple OLS regression on educ. Without controlling for other factors, whatis the 95$\%$ confidence interval for the return to another year of education?(ii) The variable ctuit, in thousands of dollars, is the change in college tuition facing students fromage 17 to age $18 .$ Show that $e d u c$ and ctuit are essentially uncorrelated. What does this sayabout ctuit as a possible IV for educ in a simple regression analysis?(iii) Now, add to the simple regression model in part (i) a quadratic in experience and a full set ofregional dummy variables for current residence and residence at age $18 .$ Also include the urbanindicators for current and age 18 residences. What is the estimated return to a year of education?(iv) Again using ctuit as a potential IV for educ, estimate the reduced form for educ. [Naturally, thereduced form for educ now includes the explanatory variables in part (iii).] Show that ctuit isnow statistically significant in the reduced form for educ.(v) Estimate the model from part (ii) by IV, using ctuit as an IV for educ. How does the confidenceinterval for the return to education compare with the OLS CI from part (iii)?(vi) Do you think the IV procedure from part (v) is convincing?

(i) ii) See video (iii) The estimated return to a year of education is given by the coefficient of educ which is 0.137 (iv) The coefficient of ctuit is $-0.165$ with p-value 0.0057, indicating that ctuit is statistically significant at 5$\%$ level (v) (vi) 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 result of the simple regression equation. The estimate on education is 0.1 oh one with a standard barrel of 10.7 This variable is highly significant, and you can calculate the 95% confidence interval of the return to education as a range of from 8.7% to 11.5%. Recall that the 95% confidence interval is calculated as the estimate plus or minus the margin of error and the margin of error is the standard error times a critical value. We need to look at the alpha level of 5% because we need the 95% confidence. Yeah, you should have the alpha level because this is a two sided interval. The degree of freedom is the number of observations minus two. We need to degree of freedom or two pieces of information to estimate the slope. And there, uh, the to intercept the intercept and the slope coefficient. So this is what you get. Part two. The simple regression of education on C two. It gives the variable see to it is not significant. The T statistic, which is the ratio of the estimate over the standard error is minus 0.59 And so we cannot use see to it as an instrument for education. Part three. The multiple regression equation estimated by L s is as follows. The coefficient on education is 1.137 experience 0.11 to experience square point oh three. And we have other factors which are not our main focus in this problem. Mhm, even the estimate on education. You can see that the estimated return to education is now higher 13.7%. We convert the estimate on education 2% because our dependent variable, the left hand side variable is in log and education is in level Part four in the multiple regression above. In part two. Mm hmm. No. The one with other explanatory variables. In part three, the coefficient on C two. It is minus point 165 Yeah, and the T statistic is minus 2.8. So an increase of $1000? Yeah. In institution reduces years of education by about Hong 165 Remember that the Tunisian variables are measured in thousands. Part five. Now we estimate the multiple regression model by Ivy using See to it as an I V for education. The I V estimate of beta education is point 25 with a standard error of 250.1 to 2. The point estimate seems large, but the 95% confidence interval is very white from 1.1% to 48.9%. We could reject the value zero for beta education, but this confidence interval is too white to be useful. Lastly, part six very large standard error of the Ivy Estimate in Part five shows that the ivy analysis is not very useful. Yeah, and see to it is not convincing as an I V, as we can see also from part two mhm.

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