Two Small Stata Homework Problems

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My version of Stata only allows for 1200 data entries. The presented short problems have 1900 data entries and i dont want to buy the larger version just to use once.

Problem #1
You have been hired by the Labor and Employment Relations Association to explore if African-American women are being discriminated against, relative to white women, and whether possible discrimination is alleviated by union membership. The data set you manage to obtain contains 2012 data on wage, race, union affiliation, and job tenure (in years) for 1878 working women. Since wages represent possibly non-normally distributed dollar values, you choose to work with the log of wages instead of the original dollar amounts
a) You begin with regressing the log of wages on being black, being “other” race and union affiliation. Why you should not include all three dummy variables for race in your regression. (2pts)
gen lwage=log(wage)—creates the log of wages
tabulate race, generate(R)—creates dummy variables for the different races
reg lwage R2 R3 union

b) Why do you choose to omit in particular the race category “white”? (8pts)

c) What is the percentage difference in wages between African-American and white women. (5pts)

d) You want to test if everything else constant African-American women are paid less than white women. Write down the null and alternative hypotheses that would allow you to test for possible discrimination against African-American women. (3pts)

e) What is the precise interpretation of the null and the alternative? (7pts)

f) Do you reject at 10% level of significance or not? Explain. (7pts)

g) Write down the equation that would allow you to test if union affiliation affects discrimination against African-American women. (3pts)

h) Regress the equation you created in part g. What is the percentage difference in mean wages between African-American women that belong to a union and African-American women who do not belong to a union? (5pts)

i) Write down the null and alternative hypotheses that would allow you to test if union membership alleviates any possible discrimination. (3pts)

j) Does union membership alleviate discrimination at 1% level of significance? Explain (7pts)

Problem #2
Let Bwght denote infant birth weights in ounces, Cigs denote the average number of cigarettes the mother smoked per day during pregnancy, and Alch denote the average number of drinks the mother had per day during pregnancy.
a) In order to account for the effects of Alch and Cigs on Bwght, as well as their possible interaction, you estimate the following equation:
Bwght =β0+ β1 Cigs+ β2 Alch+ β3 CigsAlch +u
What is the economic interpretation of β3 . (10 pts)

b) You decide that since cigarettes and alcohol appear in the interaction term, you do not need separate terms for each variable. Thus the equation you would estimate becomes

Bwght =β0+ β3 CigsAlch +u

Why such a specification may not be correct? (10pts)

c) Next, you decide to estimate the following equation:
Bwght =β0+ β1 Cigs+ β2 Alch + β3 CigsAlch +β4 CigsAlchD +u
D represents a binary variable equal to 1 if the infant is male and 0 otherwise. Why would you add the term β4 CigsAlchD? (10pts)
d) It the average number of drinks increases from 6 to 5, using the model you created in part c), by how much would the effect of the number of cigarettes change for male and female infants? (10pts)

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