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Use the data in ECONMATH to answer this question. The population model isscore $=\beta_{0}+\beta_{1} a c t+u .$(i) For how many students is the ACT score missing? What is the fraction of the sample?Define a new variable, actmiss, which equals one if act is missing, and zero otherwise.(ii) Create a new variable, say $a c t 0,$ which is the $a c t$ score when $a c t$ is reported and zero when act is missing. Find the average of $a c t 0$ and compare it with the average for act.(iii) Run the simple regression of score on act using only the complete cases. What do you obtainfor the slope coefficient and its heteroskedasticity-robust standard error?(iv) Run the simple regression of score on $a c t 0$ using all of the cases. Compare the slope coefficient with that in part (iii) and comment.(v) Now use all of the cases and run the regressionscore$_{i}$ on $a c t 0_{i},$ actmiss.What is the slope estimate on $a c t 0 ?$ How does it compare with the answers in parts (iii)and (iv)?(vi) Comparing regressions (iii) and (v), does using all cases and adding the missing data estimatorimprove estimation of $\beta_{1} ?$(vii) If you add the variable colgpa to the regressions in parts (ii) and (v), does this change youranswer to part (vi)?

(i) see video, coefficient on female is particularly large (ii) jointly significant (iii) jointly insignificant

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Chapter 8

Heteroskedasticity

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part one. The regression result is on the panel on the left. Yeah. All right. There are two observations coming from this uh result for variable above average. The coefficient is negative and insignificant. The second observation, the coefficient on variable female is especially large and significant. Okay, it's negative sign implies that controlling for experience and education, a woman with an average look earns 41% less than a man with an average look are too. The result is in the right panel we add to the right hand side. The interaction term of female dummy and above below average and female dummy with education, experience and experience square based on the P value. We conclude that the interaction terms are individually insignificant except for the interaction of female and experience. However, these variables are jointly significant. The f statistic of five and 12 48 degrees of freedom yields 3.43 We have a P value of 0.5 Changing to robust version, doesn't change the result. The p value is even smaller and two get the robust version of the F. Test in our you will do function linear hypothesis with a capital H. The name of the regression and the name of the variables to be test. The robust option will come at the end. The robust argument is written as V C O. V. This is for variance variance matrix. You set, it equals H C C. M. Or three. R three is based on the regression in part two. Yeah. Now we test the joint significance of the interaction terms of female with below or above average. Look dummies, the two interaction terms are jointly insignificant. Have statistic has two and 12 48 degrees of freedom. Yeah, it's very small 0.38 and the p value is 0.42 The coefficients of these variables are not particularly small. They equal to an average of 4 to 8% change in wage

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