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Instructions: Please submit one self-contained Word or PDF document that includes all of your calculations, written explanations, R scripts, and R output. It is due on Sunday, July 3 in Canvas before 10 p.m. as attachments in Assignments. You may also attach supplementary files, such as the actual R script files, etc. All of your work must be typed and well-formatted. No handwritten scans will be accepted, nor will late work. Submit what you have prior to 10 p.m. The data for this problem set are in gendergap1100.csv and the data set consists of 1,100 observations from a random sample of individuals, and it includes the following dependent and explanatory variables: 1nwage looks union goodhealth black married south bigcity csv name smallcity service education female experience female: experience Description The natural logarithm of hourly wages A measure of physical attractiveness on a 1 to 5 scale (5=best) 1 if a member of a labor union, and 0 otherwise. 1 if person says they are in good health, and 0 otherwise. 1 if person is black, and 0 otherwise. 1 if person is married, and 0 otherwise. 1 if person lives in South, and 0 otherwise. 1 if person lives in a large city, and 0 otherwise. 1 if person lives in a small city, and 0 otherwise. 1 if person works in a service sector occupation, and 0 otherwise. The number of years of formal education. 1 if a person is female, and 0. otherwise. The number of years of work experience. Interactive dummy variable Stargazer table label Natural Log of Wages Physical Attractiveness Member of Labor Union Good Health Black Married Lives in Southern U.S. Lives in a Big City Lives in a Small City Works in Service Sector Occupation Years of Education Female Years of Work Experience Female:Years of Work
service education female experience female: experience 1. 2. 3. 1 if person works in a service sector occupation, and 0 otherwise. The number of years of formal education. 1 if a person is female, and 0 otherwise. The number of years of work experience. Interactive dummy variable (see Part 1 below) Estimate the Unrestricted Model with OLS A. B. Works in Service Sector Occupation Interpreting Coefficients Years of Education Assume initially that the data-generating process (DGP) or true population regression function (PRF) is: Female Inwage; = B₁ + B₂looks; + P3union; + P4goodhealth; + ß5black; + ßomarried; + B7south; + Bębigcity; + Basmallcity; + ₁0service; + P₁1education; + B₁2expierience; + P13 female; + B14 (female; experience;) + &₁ Years of Work Experience Female:Years of Work Experience Estimate the model using the 1m () command in R and report the results with the summary() command. Note that all of the variables are in the data frame, except the interactive dummy variable multiplying female and experience. You can use female: experience or female*experience inside your lm () function to create this interactive variable. Name the unrestricted model in R as olsu. 2 Precisely interpret the estimated coefficient on "smallcity". Precisely interpret the estimated coefficient on "looks". Testing a Linear Restriction Suppose you want to test for whether females have a different intercept and/or partial slope coefficient with regard to experience. As is standard, the null hypothesis is the "no effect" or "no difference" hypothesis. So, in this case, the null hypothesis is:
4. 5. Ho: B13 B14 = 0 First, do this test the "long way" by saving the unrestricted residual sum of squares from Part 1. Then, impose the restriction above and re-estimate the model to get the restricted residual sum of squares. Third, compute the F- statistic using the unrestricted and restricted sum of squares from the unrestricted model (Part 1) and the restricted model (Part 3). Compare this F- statistic to the appropriate F critical value or use R to get the p-value. Can you reject the null hypothesis above and accept the alternative hypothesis of a different intercept and/or partial slope for females at conventional significance levels? Briefly explain. Finally, use anova () to let R do the entire test with this one line of code to check your work. Jarque-Bera Normality Test Use the results from Part 3 above to determine the "preferred" model at this point. If you cannot reject the null hypothesis of the restriction, then use the restricted model in the tests below. If you reject the null hypothesis of the restriction, then use the unrestricted model in the tests below. Using R to conduct and interpret a Jarque-Bera (JB) normality test and graph the histogram of the residuals. What are your overall conclusions from this test? Explain. Estimate the Model and Report the Results with stargazer () Report the results in a well-labeled and formatted regression table using stargazer (). Your stargazer command should begin with: stargazer (olsu, no.space=TRUE, style="ajps", ....) The "...." above are meant to show that you need to include other arguments within this stargazer function besides what I've shown above. The style is from the American Journal of Political Science and it seems to format things well in this case. Use the labels for the dependent and explanatory variables given in the third column of the table of the variable descriptions on pp. 1-2 on this problem set, and add the title: "Table 1: Multiple Regression Results". Finally, report all digits in your regression table to the 4th decimal place with digits=4. 3