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1 Monday October 3 10:11: Page 1 (R) / / / / / / / / / / / / Statistics/Data Analysis Education Box and save these files in a local folder. name: <unnamed log: M:\pc\Dokumenter\ECON4135\Extra_sem\Extraseminar.smcl log type: smcl opened on: 3 Oct 2011, 10:06:48 1. /* ECON4135 Applied Statistics and Econometrics Autumn 2011 STATA course UiO Problem set for the extra seminar on week 39 Exercise 1 Consider the Education Box, on page 202 in the textbook (Chapter 5). It is claimed that earnings of workers with high education are more spread than those w ith lower education. And this will result in heteroskedastic error terms when we regress hourly earnings on education. In this exercise, we will provide more explicit justification for some of the claims in the Education Box. First of all, save the excel dataset and the file that describes the data by following these instructions: 1. Go to the course homepage: Econ4135 Autumn Click on the Lecture and seminar plan link. 3. When the pdf file opens, click on the Student resource link and allow the connection. 4. On the textbook website that opens up, click on Datasets for Replicating Empirical on the left column. 5. Choose Data Description and Excel Data Set, under Economic value of a Year of Education Box and save these files in a local folder. NOTE: The above dataset comes also in Stata format, which is simpler to save and load on Stat a directly. For the sake of practicing how to upload a dataset in excel format onto Stata, let us u se the excel version /* a) Open the dataset in an Excel sheet. Save the dataset as a tab delimited text file: name _of_file.txt. The txt ending is important here. Upload this txt file on Stata by using the command insheet. Remember that you need to include the directory path with the name of the txt file when you use the insheet command, so that Stata will be able to find the file. 4. insheet using "M:\pc\Dokumenter\ECON4135\Extra_sem\ch5_cps_box.txt" (4 vars, 2989 obs) /* b) Use the information on the file that describes the dataset to label the variables. (HINT: Stata command label var ) 8. label var a_age "age"

2 Monday October 3 10:11: Page 2 9. label var a_sex "1 if male; 2 if female" 10. label var ahe "Average Hourly Earnings in 2004" 11. label var yrseduc "Years of Education" /* c) What are the types (i.e. string or numeric) of variables in this dataset? Transform all the variables in numeric format. (HINT: Stata command destring; pay particular attention to the option dpcomma; you may also want to use the replace option) 14. describe Contains data obs: 2,989 vars: 4 size: 65,758 (99.9% of memory free) storage display value variable name type format label variable label a_age byte %8.0g age a_sex byte %8.0g 1 if male; 2 if female ahe str11 %11s Average Hourly Earnings in 2004 yrseduc byte %8.0g Years of Education Sorted by: Note: dataset has changed since last saved 15. destring ahe, replace dpcomma ahe has all characters numeric; replaced as double /* d) Are there any missing values in this dataset? If yes, from which variable(s)? 18. gen x=1 if missing( a_age) missing( a_sex) missing(ahe) missing( yrseduc) (2989 missing values generated) 19. tab x, missing 20. drop x x Freq. Percent Cum.. 2, Total 2, /* e) Consider the variable a_sex. Create a dummy variable called male that takes the value 1 if a_sex refers to a male an d 0 otherwise. Label the values of the variable male by using the Stata command label.

3 Monday October 3 10:11: Page gen male=1 if a_sex==1 (1331 missing values generated) 24. replace male=0 if missing(male) (1331 real changes made) 25. label define male_label 1 "male" 0 "female" 26. label values male male_label 27. tab male, missing male Freq. Percent Cum. female 1, male 1, Total 2, /* f) Replicate the regression results (5.23) and figure (5.3) in the Education Box on page regress ahe yrseduc Source SS df MS Number of obs = 2989 F( 1, 2987) = Model Prob F = Residual R-squared = Adj R-squared = Total Root MSE = ahe Coef. Std. Err. t P t [95% Conf. Interval] yrseduc _cons twoway (scatter ahe yrseduc) (lfit ahe yrseduc) /* g) Calculate the predicted values from the above regression by using the Stata command pre dict with the option xb. (e.g. predict ahe_hat, xb). Notice that this command will work only if you have already run the regression. Now generate the residuals of the regression (e.g. gen resid= ahe ahe_hat). 34. predict ahe_hat, xb 35. gen resid=ahe-ahe_hat /* h) To verify that the claims on the last paragraph in the Education Box, find the standard deviation of the residuals for the following subgroups: -those with 10 years of education -those with a high school diploma (i.e. 12 years of education) -those with a college degree (i.e. 16 years of education)

4 Monday October 3 10:11: Page sum resid if yrseduc==10 resid sum resid if yrseduc==12 resid sum resid if yrseduc==16 resid /* i) Run a regression of earnings on years of education (just like (5.23) in the Education B ox) only for men. Does the distribution of earnings for men spread out as education inc reases? 44. regress ahe yrseduc if male==1 Source SS df MS Number of obs = 1658 F( 1, 1656) = Model Prob F = Residual R-squared = Adj R-squared = Total Root MSE = ahe Coef. Std. Err. t P t [95% Conf. Interval] yrseduc _cons *if condition is important 46. predict ahe_hat_men if male==1, xb (1331 missing values generated) 47. *if condition is VERY important 48. gen resid_men=ahe-ahe_hat_men if male==1 (1331 missing values generated) sum resid_men if yrseduc==10 & male==1 resid_men sum resid_men if yrseduc==12 & male==1 resid_men

5 Monday October 3 10:11: Page sum resid_men if yrseduc==16 & male==1 resid_men /* Exercise 2 There is a typing mistake in the book. Two exercises are numbered E5.2 on page 215. Do both! In order to have access to the data that these exercises refer, follow these instructio ns: 1. Go to the course homepage: Econ4135 Autumn Click on the Lecture and seminar plan link. 3. When the pdf file opens, click on the Student resource link and allow the connection. 4. On the textbook website that opens up, click on Data for Empirical Exercises a nd Test on the left column. 5. Choose College Distance and Teacher Ratings Data from the list of data. Save th e Stata version of the datasets on a local folder so that you can open them with Stata. Use the PDF files that provide a description of the datasets in order to become acquainted with the datasets. Here is the command that loads a datasets (of Stata type) on Stata: use filename.dta, clear The dta ending of the filename is important. filename should include also the directory path that tells Stata where to find the saved filename. 55. *E5.2 (the first) 56. use "M:\pc\Dokumenter\ECON4135\Extra_sem\TeachingRatings.dta", clear 57. reg course_eval beauty Source SS df MS Number of obs = 463 F( 1, 461) = Model Prob F = Residual R-squared = Adj R-squared = Total Root MSE = course_eval Coef. Std. Err. t P t [95% Conf. Interval] beauty _cons *E5.2 (the second) 61. use "M:\pc\Dokumenter\ECON4135\Extra_sem\CollegeDistance.dta", clear 62. *doing the calculations 63. regress ed dist Source SS df MS Number of obs = 3796 F( 1, 3794) = Model Prob F = Residual R-squared = Adj R-squared = Total Root MSE = ed Coef. Std. Err. t P t [95% Conf. Interval] dist _cons

6 Monday October 3 10:11: Page tab female, missing female Freq. Percent Cum. 0 1, , Total 3, bysort female: regress ed dist - female = 0 Source SS df MS Number of obs = 1726 F( 1, 1724) = Model Prob F = Residual R-squared = Adj R-squared = Total Root MSE = ed Coef. Std. Err. t P t [95% Conf. Interval] dist _cons female = 1 Source SS df MS Number of obs = 2070 F( 1, 2068) = Model Prob F = Residual R-squared = Adj R-squared = Total Root MSE = ed Coef. Std. Err. t P t [95% Conf. Interval] dist _cons *Coefficient of interest 67. display (-0.064) *Variance of the coefficient 69. display * * *St. error 71. display sqrt( ) *t statisitc 73. display -0.02/

7 Monday October 3 10:11: Page *Letting Stata do the calculations 76. *females 77. regress ed dist if female==1 Source SS df MS Number of obs = 2070 F( 1, 2068) = Model Prob F = Residual R-squared = Adj R-squared = Total Root MSE = ed Coef. Std. Err. t P t [95% Conf. Interval] dist _cons matrix b=e(b) 79. matrix V=e(V) matrix list b b[1,2] dist _cons y matrix list V symmetric V[2,2] dist _cons dist _cons scalar coef_female=b[1, 1] 85. scalar var_female=v[1,1] display coef_female display var_female *males 91. regress ed dist if female==0 Source SS df MS Number of obs = 1726 F( 1, 1724) = Model Prob F = Residual R-squared = Adj R-squared = Total Root MSE = ed Coef. Std. Err. t P t [95% Conf. Interval] dist _cons

8 Monday October 3 10:11: Page matrix b=e(b) 93. matrix V=e(V) 94. scalar coef_male=b[1, 1] 95. scalar var_male=v[1,1] 96. display coef_male display var_male scalar t_stat=(coef_male-coef_female)/sqrt(var_male+var_female) 100. display t_stat /* Exercise 3 Repeat the exercise from the last seminar. Use the nlsw88.dta data. (Remember that to upload this dataset you need to type: sysuse nslw88.dta) 105. sysuse nlsw88.dta (NLSW, 1988 extract) 106. *1. What is mean of schooling grade in the sample? 107. sum grade, detail current grade completed Percentiles Smallest 1% 7 0 5% % 11 4 Obs % 12 4 Sum of Wgt % 12 Mean Largest Std. Dev % % Variance % Skewness % Kurtosis *2. Are there any missing values? 110. tab grade, missing current grade completed Freq. Percent Cum

9 Monday October 3 10:11: Page Total 2, *3. What is the age of those with missing values in education? 113. tab age if missing(grade) age in current year Freq. Percent Cum Total *4. Are they union workers? 116. tab union if missing(grade) union worker Freq. Percent Cum. nonunion union Total *5. Do they live in the south? 119. sum south if missing(grade) south *6. Do they live in smsa? 122. sum smsa if missing(grade) smsa *7. What is the relationship between wages and grades (education)? 125. *Create a scatter and a best linear fit with confidence intervals twoway (scatter wage grade) (lfit wage grade) *8. Regress wages on grades reg wage grade Source SS df MS Number of obs = 2244 F( 1, 2242) = Model Prob F = Residual R-squared = Adj R-squared = Total Root MSE = wage Coef. Std. Err. t P t [95% Conf. Interval] grade _cons

10 Monday October 3 10:11: Page *9. Test whether the slope is equal to test grade=1 ( 1) grade = 1 F( 1, 2242) = Prob F = *10. Regress wages on grades separately for union and non-union members bysort union: reg wage grade - union = nonunion Source SS df MS Number of obs = 1416 F( 1, 1414) = Model Prob F = Residual R-squared = Adj R-squared = Total Root MSE = wage Coef. Std. Err. t P t [95% Conf. Interval] grade _cons union = union Source SS df MS Number of obs = 460 F( 1, 458) = Model Prob F = Residual R-squared = Adj R-squared = Total Root MSE = wage Coef. Std. Err. t P t [95% Conf. Interval] grade _cons union =. Source SS df MS Number of obs = 368 F( 1, 366) = Model Prob F = Residual R-squared = Adj R-squared = Total Root MSE = wage Coef. Std. Err. t P t [95% Conf. Interval] grade _cons

11 Monday October 3 10:11: Page *11. Predict wages from the regression of wages on grades reg wage grade Source SS df MS Number of obs = 2244 F( 1, 2242) = Model Prob F = Residual R-squared = Adj R-squared = Total Root MSE = wage Coef. Std. Err. t P t [95% Conf. Interval] grade _cons predict wage_hat, xb (2 missing values generated) *12. Add the predicted wages to the graph above twoway (scatter wage grade) (lfit wage grade) (scatter wage_hat grade) log close name: <unnamed log: M:\pc\Dokumenter\ECON4135\Extra_sem\Extraseminar.smcl log type: smcl closed on: 3 Oct 2011, 10:06:57