1. Use the attached data set for the following questions (laborEcon.dta) . Feel free to resample the data set if you think it is appropriate. Consider the earning function in the form of a linear regression equation we discussed before:
ln(w) = α0 + α1schooling + α2age + α3age2 (1)
whereln(w) is the natural log of earnings, α is the constant of the regression and αi , ∀i = 1, 2, 3 are the parameters associated with schooling, age and age squared, respectively.
Or in a more compact way,
ln(w) = α + βX (2)
where α is the constant of the linear regression and X the vector of observable characteristics (schooling, age, age2 ), and β, the vector of parameters associated with those characteristics.
(a) Summarize the mean and standard deviation of these variables. Describe in few words what you observe.
(b) Report the average earnings (the variable for earnings in this data set is 'incwage')by marital status (married==1, single==6 and divorced ==4) , level of education(post-graduate, college graduates and high-school graduates), sex (male ==1,female==2), and race (focus on white==100 and black==200). Describe in few words what you observe.
(c) What are the signs do you anticipate for α1, α2, and α3? Explain
(d) Why it is common to include the variable age2 ? Explain
(e) What is the interpretation of each coefficient, i.e αi ∀i = 0, 1, 2, 3 (translate these coefficients into a sentence that people outside of our field would understand).
(f) Estimate equation (1) using our data file "laborEcon.dta". Verify your claim in part 1c.
(g) Now estimate equation (1) only for the white group. Describe your findings 1
(h) Estimate equation (1) only for the black group. How do the estimates differ from the white group's estimates?