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:
csv name Description Stargazer table label
lnwage The natural logarithm of
hourly wages Natural Log of Wages
looks A measure of physical attractiveness on a 1 to 5
scale (5=best) Physical Attractiveness
union 1 if a member of a labor
union, and 0 otherwise. Member of Labor Union
goodhealth 1 if person says they are in
good health, and 0 otherwise. Good Health
black 1 if person is black, and 0
otherwise. Black
married 1 if person is married, and 0
otherwise. Married
south 1 if person lives in South, and
0 otherwise. Lives in Southern U.S.
bigcity 1 if person lives in a large
city, and 0 otherwise. Lives in a Big City
smallcity 1 if person lives in a small
city, and 0 otherwise. Lives in a Small City
service 1 if person works in a service sector occupation, and 0
otherwise. Works in Service Sector Occupation
education The number of years of
formal education. Years of Education
female 1 if a person is female, and 0
otherwise. Female
experience The number of years of work
experience. Years of Work Experience
female:experience Interactive dummy variable
(see Part 1 below) Female:Years of Work
Experience
1. Estimate the Unrestricted Model with OLS
Assume initially that the data-generating process (DGP) or true population regression function (PRF) is:
lnwagei = β1 + β2looksi + β3unioni + β4goodhealthi + β5blacki + β6marriedi
+ β7southi + β8bigcityi + β9smallcityi + β10servicei
+ β11educationi + β12expieriencei + β13femalei
+ β14(femalei • experiencei) + si
Estimate the model using the lm() 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. Interpreting Coefficients
A. Precisely interpret the estimated coefficient on “smallcity”.
B. Precisely interpret the estimated coefficient on “looks”.
3. 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:
H0: β13 = β14 = 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.
4. 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.
5. 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.
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