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Economics 420 (sections 2 and 3) Professor Woodbury Fall Semester 2019 Problem Set #3 (Due: Thursday, October 17) Instructions • Use Stata and a word processor for this assignment. • Read the question and answer what is asked. • For each question that asks you to use Stata, copy and paste the Stata output into a wordprocessing document, then type your answer. Staple all pages together at the upper-left corner before you turn in your homework. • Assignments turned in unstapled will be returned with a grade of zero. • Only stapling is acceptable—paper clips and other methods of binding are not acceptable. • If we cannot discern the meaning of your work, your response will be scored as incorrect. This problem set introduces you to multiple regression in Stata, hypotheses tests about regression parameters, and omitted variable bias. The problem set uses the Stata dataset HTV.dta that can be downloaded from the D2L website. This dataset includes data on 1,230 men aged 26–34 who were interviewed in 1991 for the National Longitudinal Survey of Youth. You will be using the the following variables: lwage natural logarithm of the person’s hourly wage rate in 1991 educ highest grade level completed by 1991 abil score from an ability test administered in 1979 ne = 1 if the person lived in one of the northeastern states Part 1: Multiple regression basics (30 points total) 1. (5 points) What are the mean and standard deviation of lwage in the data? What are the mean and standard deviation of abil in the data? 2. (5 points) Suppose the correct population model for the log of the wage rate (lwage) is given by: lwage = β0 + β1 educ + β2 abil + u Estimate the above model and paste in your Stata output. Hint: type reg lwage educ abil. 3. (5 points) What is the R2 of the regression and how do you interpret it? What does it tell you about the extent to which wages are causally affected by education? 4. (5 points) What is the OLS estimate of β1 from this regression and how do you interpret it? 5. (10 points) Use the output from your regression to test the hypothesis that education is unrelated to log-earnings. State the null and the alternative hypotheses in terms of the notation used in class, then state the test statistic you use. Using a significance level of 5%, what do you conclude and why? Be sure to explain your reasoning.

Part 2: Omitted variable bias in estimating the return to education (35 points total) Suppose you cannot observe a person’s ability, so you estimate the following simple linear regression model: lwage = β0 + β1 educ + v where ability ends up in the error term u. 1. (5 points) What is the OLS estimate of the slope coefficient on education from the above simple regression? (Paste in your Stata output.) How do you interpret the coefficient? 2. (5 points) Write down the OVB formula. 3. (10 points) Use the formula you just wrote down to explain the two conditions that need to be satisfied in order for omitting ability from the lwage regression to result in a biased estimator of β1 (the return to education)? Do you think these conditions hold? Why or why not? 4. (5 points) In light of your answer to the last question, why does it makes sense that the estimated slope coefficient on education in the simple regression above is smaller than the estimate from the the multiple regression of lwage on educ and abil? 5. (5 points) Estimate the regression of abil on educ and paste in your Stata output. Interpret coefficient on educ in the regression. 6. (5 points) Again write down the OVB formula, and plug in the estimates from the equations you have estimated to show that it “works.” Is the estimated bias from the OVB equation positive or negative? Is it consistent with your answer to question 4 above? Extra Credit (5 points) Are lwage and abil approximately normally distributed? How do you know? Hint: type sum lwage abil, detail, then then check to see whether approximately 90% of the lwage observations lie within 1.64 standard deviations of the mean lwage. Do the same for abil....