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# Assignment III Due at 5: You can use any formula taught in class without proof.cation. Note: (i) You need to print out and turn in your STATA code...

Assignment III Due at 5:30pm of April 24 (Monday) This assignment is related to Chapter 6 (problems 1, 2 and 3), 7 (problems 4 and 5) and 8 (problems 6, 7 and 8). You can use any formula taught in class without proof. If you want to use any result from other courses, please provide proof or justi&cation. Note : (i) You need to print out and turn in your STATA code for all empirical exercises. (ii) All STATA outputs are reported in the standard format as required in Assignment II, Problem 5(i). 1. (10 points) Read "Beta Coe¢ cients" of Section 6-1a before answering this question. For a random variable X , de&ne the z -score of X as X & X b & X , where X is the sample mean and b & X is the sample deviation of X . In the simple linear regression, y = ± 0 + ± 1 x + u; E [ u j x ] = 0 ; we &rst calculate the z -scores of y and x , denoted as e y and e x , and then run the regression of e y on 1 and e x . Show that the resulting slope estimator is the sample correlation of x and y . 2. (10 points) Problem 2 of Chapter 6 in the textbook. Note: Use the method suggested in the hint, which is di/erent from what was taught in class. 3. (10 points) Computer Exercise C2 of Chapter 6 in the textbook. 4. (10 points) Problem 5 of Chapter 7 in the textbook. 5. (20 points) Use the data in SLEEP75.dta for this exercise. The equation of interest is sleep = ± 0 + ± 1 totwrk + ± 2 educ + ± 3 age + ± 4 age 2 + ± 5 yngkid + u; where sleep and totwrk (total work) are measured in minutes per week, educ and age are measured in years, and yngkid is a dummy variable for the presence of children less than 3 years old. (i) Estimate this equation separately for men and women and report the results in the stan- dard format. Are there notable di/erences in the two estimated equations? (ii) Compute the Chow test for equality of the parameters in the sleep equation for men and women. Use the form of the test that adds male and the interaction terms male & totwrk , . . . , male & yngkid and uses the full set of observations. What are the relevant df for the test? Should you reject the null at the 5% level? 1
(iii) Now, allow for a di/erent intercept for males and females and determine whether the interaction terms involving male are jointly signi&cant. (iv) Given the results from parts (ii) and (iii), what would be your &nal model? 6. (5 points) In the simple linear regression, suppose y i = & 0 + & 1 x i + u i ; E [ u i j x i ] = 0 ; V ar ( u i j x i ) = ± 2 i ; where ± 2 i is known. Derive the formulae of the WLS estimator of ( & 0 ; & 1 ) . 7. (15 points) Suppose \ lbwght = 7 : 96 & : 0023 ± cigs + : 0121 ± npvis & : 00024 ± npvis 2 (0 : 05)( : 0012) ( : 0037) ( : 00012) [0 : 05] [ : 0012] [ : 0051] [ : 00014] & : 00098 ± mage + : 0022 ± fage & : 0014 ± meduc + : 0027 ± feduc ( : 0015) ( : 0012) ( : 0030) ( : 0027) [ : 0016] [ : 0012] [ : 0028] [ : 0027] n = 1624 ; R 2 = : 0194 where lbwght is the log of the birth weight, cigs is the number of cigarettes, npvis is the number of prenatal visits, mage is mother±s age, fagem is father±s age, meduc is mother±s education, and feduc is father±s education. The usual standard errors are in parentheses and the heteroskedasticity-robust standard errors are in brackets. (i) Interpret the coe¢ cient on cigs . Does the 95% con&dence interval for & cigs depend on which standard error you use? (ii) Comment on the statistical signi&cance of npvis 2 , using both the usual and heteroskedasticity- robust standard errors. (iii) If the four age and education terms are dropped from the regression (and the same set of observations is used), the R 2 becomes : 0162 . Develop the homoskedasticity-only test of H 0 : & mage = 0 , & fage = 0 , & meduc = 0 , & feduc = 0 . 8. (20 points) Use the data in R²D_Sales_Pro&ts.dta for this exercise. We want to explain the research and development (R²D) expenditures incurred by 18 industries. All data are in million of US dollars. Consider the following regressions: Model (1): R & D i = ² 0 + ² 1 ± Profits i + u i 2
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Zoya Zaheer 3035146449 Assignment 3 1.
2. 3. i) Estimated equation is
^
log ( wage) = 0.128 +0.0904educ + 0.0410exper – 0.000714exper2
(0.106) (0.0075)
(0.0052)
(0.000116)
´ 2 =0.296
n=526,...

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