Econ 3210: Assignment 3 Winter 2024 Due Date: Friday March 29, 2024 at 5pm. General Instructions You may work and submit assignments in groups no larger than four (4). Please submit answers to each question in the field available for that question on Crowdmark. Please submit all Stata code in the field assigned to the very last question on Crowdmark ("Submit your Stata code here"). It is sufficient for one group member to submit on behalf of the entire group. The deadline to submit the assignment and the associated Stata code on Crowdmark is 5pm on Friday March 29, 2024. Mandatory Questions The following questions are mandatory and must be submitted as part of this assignment. Chapters 3 and 4 1. Wooldridge Textbook, Chapter 3, Computer Question C6. [Small Note/Point of clari- fication: log(wage) is equivalent to In(wage) for Wooldridge, despite these two things technically being different mathematical objects. Therefore, when you see log(wage), just use In(wage)-] 2. Use the WAGE2 data again. (a) Regress In(wage) on educ and IQ. Report and interpret both the coefficient on educ and the coefficient on IQ. (b) Now do the following:1. Regress edue on 1Q and save the residuals from this regression (hint: use the predict' command after the regression with the appropriate option after the comma, just like we did in class). Let's label the residuals educ". [Remember: if you estimate the model educ = of + a1/Q, + n and obtain fitted values (or model predictions) as educ, = do + 61/Q, then the estimated residual is educ = educ, - educ = edun - 60 - a,IQ.] 2. Regress In(wage) on educ . Report and interpret the coefficient on educt. How does it compare to the coefficient on educ from part (a)? Given the relationship between the coefficient here and that in part (a), what can you say about how to interpret the estimated coefficients in a multiple regression? (Hint: we talked about the 'partialling out' interpretation in class. There is also a great discussion in Chapter 3.) (c) Now regress In(wage) on IQ only and save the residuals from this regression. Let's call these residuals In(wage)". Now regress In(wage)" on educ (from above) and report the coefficient. How does it compare to the estimated coefficient from part (a) and estimated coefficient from part (b)? In(wage) is the part of In(wage) that is independent of IQ and eduer is the part of educ that is independent of IQ. Given this knowledge, expand here on your explanation in part (b) about how to interpret estimated coefficients in a multiple regression. 3. Load the Stata dataset CRIMEL.dta from the Assignment 3 folder on our class website. (a) Regress nair86 on penu, ptime86, and gemp86. How does employment in 1986 affect arrests?' Is it statistically significant at the 5% level on a two-sided test. (b) Is the estimated coefficient on gemp56 statistically different from 0.1 at the 5% level using a two-sided test? (c) The data contains information on demographic characteristics. Add to the model the variables black, hispan, born60, which are indicator variables for Black and Hispanic ethnicity, and being born after 1960. Interpret the estimated coefficients for each of these variables. Are they individually significant? (d) The R" increases from the first to the second specification, which is not surprising. Does this indicate that the demographic variables are jointly statistically significant? Conduct a formal statistical test of this hypothesis by estimating both the restricted and unrestricted models and using the relevant information to calculate the test statistic and then conduct the test. Verify that you get the same answer using Stata's test command. 24. Computer question C9 in Chapter 4 of Wooldridge Textbook. Optional Questions These questions are not to be submitted, but they do provide extra practice and you are expected to know the content they test. 5. Wooldridge Textbook, Chapter 3, Question 3. 6. Wooldridge Textbook, Chapter 3, Question 9. 7. Wooldridge Textbook, Chapter 4, Question 1.C6 Use the data set in WAGE2 for this problem. As usual, be sure all of the following regressions contain an intercept. i. Run a simple regression of IQ on educ to obtain the slope coefficient, say, 4; . ii. Run the simple regression of log(wage) on educ, and obtain the slope coefficient, 3; . iii. Run the multiple regression of log(wage) on educ and IQ, and obtain the slope coefficients, f;?] and f-fg , respectively. iv. Verify that B, = By + Bad; . C9 Use the data in DISCRIM to answer this question. (See also Computer Exercise C8 in Chapter 3.) i. Use OLS to estimate the model log(psoda) = By + Biprpblck + folog(income) + Byprppov + u, and report the results in the usual form. Is 3, statistically different from zero at the 5% level against a two-sided alternative? What about at the 1% level? ii. What is the correlation between log(income) and prppov? Is each variable statistically significant in any case? Report the two-sided p-values. iii. To the regression in part (i), add the variable log(hseval). Interpret its coefficient and report the two-sided p-value for Hy: Big(sevary = 0 iv. In the regression in part (iii), what happens to the individual statistical significance of log(income) and prppov? Are these variables jointly significant? (Compute a p-value.) What do you make of your answers? v. Given the results of the previous regressions, which one would you report as most reliable in determining whether the racial makeup of a zip code influences local fast- food prices