Please answer the questions.

Using R. The data file: cps4_small.dta

*DO NOT COPY AND PASTE ANSWERS FROM OTHERS!!

Background You are interested in estimating the effect of education on earnings. The data file cps4_small.dta contains 1,000 observations on hourly wage rates, education, and other variables from the 2008 Current Population Survey (CPS): - wage: earnings per hour - educ: years of education - exper: post education years experience - hrswk: working hours per week - married: dummy for married - female: dummy for female - metro, midwest, south, west: location dummies - black: dummy for black - asian: dummy for Asian 2. (25 points) Estimate the linear regression ln(wagei)=1+2educi+ei. where ei is the error and 1 and 2 are the unknown population coefficients. (c) (4 points) Assuming that E[e educ ]=0, interpret the estimated coefficient on educ ( 2 points) and test whether or not the population coefficient is zero at the 1% significance level (2 points). (d) (6 point) You suspect that the hourly wage could depend on working hours per week. Discuss under what condition(s) the estimated coefficients in (a) would be biased due to the omission of the weekly working hours ( 2 points). Give a reasonable and intuitive story on why omission of the weekly working hours would cause omitted variable bias in the regression in (a) (2 points). Under your story, explain whether the estimated coefficient on educ in (a) would be overestimated or underestimated ( 2 points). See pages 4 and 5 of Lecture note 4 . (e) (5 point) The variable hrswk is the average weekly working hours for each individual in the data. Regress ln (wage) on educ and hrswk. Discuss the estimation results. In particular, how would you revise your answer in (c)? Are the estimates are statistically significant? Background You are interested in estimating the effect of education on earnings. The data file cps4_small.dta contains 1,000 observations on hourly wage rates, education, and other variables from the 2008 Current Population Survey (CPS): - wage: earnings per hour - educ: years of education - exper: post education years experience - hrswk: working hours per week - married: dummy for married - female: dummy for female - metro, midwest, south, west: location dummies - black: dummy for black - asian: dummy for Asian 2. (25 points) Estimate the linear regression ln(wagei)=1+2educi+ei. where ei is the error and 1 and 2 are the unknown population coefficients. (c) (4 points) Assuming that E[e educ ]=0, interpret the estimated coefficient on educ ( 2 points) and test whether or not the population coefficient is zero at the 1% significance level (2 points). (d) (6 point) You suspect that the hourly wage could depend on working hours per week. Discuss under what condition(s) the estimated coefficients in (a) would be biased due to the omission of the weekly working hours ( 2 points). Give a reasonable and intuitive story on why omission of the weekly working hours would cause omitted variable bias in the regression in (a) (2 points). Under your story, explain whether the estimated coefficient on educ in (a) would be overestimated or underestimated ( 2 points). See pages 4 and 5 of Lecture note 4 . (e) (5 point) The variable hrswk is the average weekly working hours for each individual in the data. Regress ln (wage) on educ and hrswk. Discuss the estimation results. In particular, how would you revise your answer in (c)? Are the estimates are statistically significant