Problem 4. Empirical exercise - private college wage premium and selectivity Download STATA dataset College Admissions_PSET1B.dta Variables: Applicant_group: Applicant group based on selectivity of colleges admitting them Private: Chose to attend private college Earnings: Earnings in 1996 Group A were admitted to highly selective public and private universities. Group B were admitted to less selective public and private universities. Group C were admitted to only highly selective private universities. Group D were admitted to only less selective public universities. a) Calculate the mean earnings for students attending private and public colleges separately. b) Regress earnings on private. Show the regression output, and interpret the coefficient. How does this compare to group mean earnings difference between public and private from part (a)? How do you interpret the standard error and statistical significance?/nb) Regress earnings on private. Show the regression output, and interpret the coefficient. How does this compare to group mean earnings difference between public and private from part (a)? How do you interpret the standard error and statistical significance? c) Create a new variable with a natural log of earnings and call it log_earnings. Regress log_earnings on private. Interpret the coefficient. d) Now create dummies for different applicant_group values. Regress log_earnings On private and include the applicant group dummies. a. comment on the private coefficient with the new controls b. what does this suggest about omitted variables bias? e) Create a new variable that is the average earnings by each of the 4 groups (A, B, C and D), and take the log of this value (log_earnings_group).(Hint: use The egen command to create the average earnings by group.) Regress Log_earnings on private and also include log_earnings_group

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