1. What the properties necessary for OLStobethe Best Linear Unbiase...

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1. What the properties necessary for OLStobethe Best Linear Unbiased Estimator? (List and describe) 2. Table shows summary statistics for subsample of the 2014 CPS Useto answer the following questions: (a) What percent of the sample Female? (b) What percent of the sample lists race as American Indian? (c) How many people the sample list noed to round it off.) 3. Table shows regression results from an equation where trage, the dependent variable. Each column has slightly different independent variables. Use the table to answer the following questions (a) Interpret the coefficient on years of schooling in column 4. (b) Interpret the coefficient on fornale in column (c) Whv the coefficient on female different column? (d) Write out the estimated equation in column (Write the numbers in for the B's.) (e) Use the estimated equation in column predict the wages for man with 12 years education and a woman with years education (f) What racial group the reference (or omitted group) in columns 3and 43 (g) Interpret the coefficient on race in column 3. 4. Use the attached data set to complete the following tasks: (a) Write down an equation for estimating income function of age, high- est grade completed gender. race. and parent's income during adolescents (b) Which coefficient describes the difference in wages by gender? What sign do ou expect find? (c) Estimate equation and report the results in table similar to table 2 (Include the n° your table. The STATA help section shows how to make the table.) (d) Interpret the coefficient on highest grade completed (e) What the R² and what does tell us about the regression? (f) Give prediction of wage for 30 year old Hispanic worman with 14 grades completed whose household income was $40,000 whenshe was an adolescent 1 Stata Help The command torun an OLS in stata "regress" or "reg" for short. Fol lowing command should be list with the dependent variable Soif want estimate Stata will return something like figure 2 that example. 947394. We will learn what the other numbers mean later point. 1.1 Making Regression Table 1. Make sure the estout package installed 2. Run regressions: "reg: xl x2x3" 3. store results estato rl 4. Make table: esttab using tl.rtf. replace label star(* 0.10 ** 0.05 *** 0.01) se r2 ar2 Table Summary Stats 2014 CPS Data (1) Earnings hour 22.65 (13.90) Number own children 18 0.749 (1.140) Fernale 0.503 (0.500) Male 0.497 (0.500) Years Schooling 13.83 (2.828) Enrolled School 0.0578 (0.234) Age 41.60 (10.76) race: White 0.811 (0.392) Black 0.107 (0.309) American Indian 0.0100 (0.0996) Asian Pacific Islands 0.0584 (0.235) Other 0.0142 (0.118) Observations 1199 mean coeflicients; sd it parentheses Table Wage Regressions on 2014 CPS Data (2) (3) (4) Wage Wage Wage Wage Fernale -1.691° -2.745*** -2.328** -2.238*** (0.976) (0.882) (0.862) (0.863) Years Schooling 2.197*** 2.222*** 2.198*** (0.160) (0.157) (0.157) Age 0.249*** 0.229*** (0.0405) (0.0420) race: White -6.560* -6.857** (3.417) (3.417) e==Black 10.45*** 10,51*** (3.645) (3.640) American Indian -14.41** -14.16** (6.017) (6.010) Asian/Pacific Islands -7,099* 7,636** (3.768) (3.775) Other 1.604* (0.906) Constant 23.45*** -6.923** -10.77** -10.26** (0.671) (2.294) (4.309) (4.313) 812 812 812 812

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1. What are the properties necessary for OLS to be the Best Linear Unbiased Estimator? (List and describe)

If all Gauss-Markov assumptions are met than the OLS estimators alpha and beta are BLUE – best linear unbiased estimators:

best: variance of the OLS estimator is minimal, smaller than the variance of any other estimator
linear: if the relationship is not linear – OLS is not applicable.
unbiased: the expected values of the estimated beta and alpha equal the true values describing the relationship between x and y.

2. Table 1 shows summary statistics for a subsample of the 2014 CPS. Use to answer the following questions:
(a) What percent of the sample is Female? 50.3%
(b) What percent of the sample lists race as American Indian? %1
(c) How many people in the sample list race as other? (You may need to round it off. ) 0.0142*1199=17.03

It shows 17 people list race as other....

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