Econ 184b Professor Brainerd Fall 2023 Problem Set 4 Due Wednesday, October 25:11 by 11:00pm Important: please follow these instructions to submit your problem set: 0 Please use a separate page for each question 0 Submit a single PDF le on Latte as your solution to the entire problem set. You can either type your solution and save it as it as a PDF file, or write your solution on paper, scan it and make it into a legible PDF file. Please make sure your handwriting is legible. 0 Please write the name(s) of any students you worked with on the first page of your problem set. 0 Attach your R code and output to your problem set. No credit will be given if the R code and output are missing. 0 No credit will be given if you report only the final answers without showing formulas and calculations where appropriate. 0 Make sure to use the Empirical exercise from the 4th edition to do the problem set. The scanned exercise is posted on our Latte page with the PS 4 materials. TAs will not grade answers to questions from other editions and no credit will be given for this work. 0 You will need the packages tidyverse, stats, sandwich, lmtesi and car for this problem set. 1. From problem set 3 we have data on GPA, demographic characteristics and drinking behavior of college students from 119 US. colleges in 2015. For this question you will again use the college data set on Latte. This question will explore the impact of drinking behavior on GPA. The main alcohol consumption variable is called drinks. This variable reects student responses to the question: \"In the past 30 days, on those occasions when you drank alcohol, how many drinks did you usually have?\" Answers are coded as follows: 0 : did not drink in the past 30 days; 1 = 1 drink, 2:2 drinks, up to 9 = 9 or more drinks. a. Write an equation that allows you to estimate the effects of alcohol consumption on GPA, while controlling for the other factors in the survey. What should be the functional form of this regression? (In other words, should GPA and/0r drinks be in logs? Why or why not? Should a polynomial in drinks be considered?) Explain your reasoning. b. Write an equation that would allow you to test whether alcohol consumption has different effects on GPA for men and women (use the linear version of drinks). How would you test that there are no differences in the effects of alcohol consumption on GPA for men and women? Explain. c. Estimate the equation in (b) and run the test. Is there a difference in how alcohol consumption affects GPA for men and women? Is the difference statistically significant? d. Suppose you think it is better to measure alcohol consumption by putting students into one of four categories: abstainer, light drinker, moderate drinker and heavy drinker. Now, write a model that allows you to estimate the effects of alcohol consumption on GPA. (Assume there is no interaction effect with gender.) Using this model, explain clearly how to test the null hypothesis that alcohol consumption has no effect on GPA (write down your null and alternative hypotheses, and the number of restrictions). e. Estimate the regression in (d) and run the test. What do you conclude about the impact of alcohol consumption on GPA based on these results? 2. What is the rate of return to an additional year of education? Does this rate of return differ for men and women? What is the gender wage gap? You will answer these and related questions by analyzing a large household survey called the Current Population Survey (CPS) conducted in March 2016. The survey is described in the document ch87cps.docx and the data set is called cps22764.csv (where the original CPS data set has been limited to individuals age 22 to 64). a. Run a regression of average hourly earnings (ahe) on female, age and years of education (yrseduc). If age increases from 34 to 35, how are earnings expected to change? Ifage increases from 54 to 55, how are earnings expected to change? (Clearly state the units.) b. Create a new variable for the log of average hourly earnings (lnahe), and repeat question (a) using [make as the dependent variable. Why do your answers to (a) and (b) differ? c. Do you prefer the specification of the regression model in part (a) or part (b)? Explain your reasoning briey. d. Create a new variable for potential work experience (pexp), which is a proxy for the years of work experience an individual may have (the CPS does not ask about work experience): pexp : age - (yrseduc + 6). Also create a variable for the square of potential work experience (pexp2). Estimate the regression of [make on female, years of education, potential experience and its square. Should age be included as a control variable in this regression? Why or why not? e. What do the estimated coefcients in the regression in (d) imply about the rate of return to an additional year of (potential) work experience? Explain. At what potential work experience level are log hourly earnings maximized? f. Interpret the coefficients onFemale and Y rseduc. (In other words, what is the gender wage gap, according to these regression results? What is the rate of return to an additional year of education?) g. Suppose you want to test the null hypothesis that the rate of return to education differs for men and women. How would you modify the regression in part (d) to test this? Estimate this modied regression. Based on your results, what is the estimated rate of return to an additional year of education for men? For women? Is the difference in the rate of return to education for men and women statistically significant? h. The regression in part (g) produces two regression lines, one for female : 0 and one for female I 1. Write out the estimated regression lines (in equation form) for the two groups. Is the difference between the two intercepts statistically signicantly different from zero at the 5% significance level? Explain. i. According to the regression results in part (g), does the gender wage gap differ by level of education? Compute the gender wage gap for (i) twelve years of education and (ii) 16 years of education (assume zero years of work experience). j. For all of the above regressions, the coefficient on female is negative, large and statistically signicant. Do these results indicate that there is gender discrimination in the labor market? Explain. 3. S & W Chapter 9: 9.2. For part (b), you only need to show E( v. | X) = 0. For parts (0), (d), and (e), assume that all of the assumptions in Key Concept 4.3 are satisfied