This problem set covers regression with dummy variables (including dummy variables for multiple categories and interaction terms) and models with a quadratic specification. Use the Stata dataset CPS_ASEC_420.dta to answer all the questions. CPS_ASEC_420.dta contains a sample of 53,066 workers aged 25-54 from the March 2018 CPS Annual Social and Economic supplement. All workers in the sample had at least $1,000 in earnings during the previous year (2017). Self-employed and family workers have been dropped. The variables in the extract include the following

lnearn log of the worker's 2017 earnings

educyrs worker's years of schooling

exper worker's maximum possible years of workforce experience

(age - years of education - 6)

expersq maximum possible years of workforce experience squared

female = 1 if the worker was female, 0 otherwise

pubsector = 1 if the worker was employed in local, state, or federal government,

0 otherwise

wkswork1 weeks worked last year

uhrsworkly usual hours worked per week last year

The dataset CPS_ASEC_420.dta also includes a set of six mutually exclusive and exhaustive dummy variables indicating a worker's highest level of schooling achieved.

lthsch = 1 if the worker did not have a high school diploma, 0 otherwise

highsch = 1 if the worker had a high school diploma but no further education, 0

otherwise

somecoll = 1 if the worker had some college but no degree, 0 otherwise

assoc = 1 if the worker had an associate's degree but no further education, 0

otherwise

bachdeg = 1 if the worker had a bachelor's degree, but no further education, 0

otherwise

maprofdoc = 1 if the worker had a master's, professional, or doctoral degree, 0

otherwise

This set of education indicators gives you an alternative way of specifying education, rather than specifying education as a number of years (educyrs), which you have been doing to this point.

1. (10 points) Estimate the following model for lnearn and report the estimates:

lnearn = ₀ + ₁lthsch + ₂somecoll + ₃assoc + ₄bachdeg + ₅maprofdoc +

₁exper + ₂expersq + ₃female + ₄pubsector + ₆wkswork1 + ₇uhrsworkly + u

Interpret the estimated coefficients on assoc (₃) and bachdeg (₄).

Hint: The omitted category is workers with a high school diploma but no further education (highsch), so the coefficient on assoc indicates the difference in expected log earnings between workers with an associate's degree and workers with a high school diploma.

The value of ₃ is 0.1494863 so difference in expected log earnings between workers with an associate's degree and workers with a high school diploma 16.12%

the value of ₄ is 0.3885562 so difference in expected log earnings between workers with a bachelor's degree and workers with a high school diploma 47.48%

2. (10 points) Assuming it takes two years to earn an associate's degree, and four years to earn a bachelor's degree, is the expected return to a year of education at a two-year college that leads to an associate's degree the same as the expected return to a year of education at a four-year college that leads to a bachelor's degree?

Hint: From your answer to question 1, what is the average return to one year of education devoted to earning an associate's degree? What is the average return to one year of education devoted to earning a bachelor's degree?

I need question 2