Advanced Econometrics

Problem Set 7

(Due Optional)

Empirical Problems

Use the dataset, CENSUS90, to answer the following questions.

1. We are interested in examining how immigrants and native-born Americans differ in what determines their levels of earnings.

a) Using the regression of log earnings on a constant, female, age, education (HIGRADE), married, and children, formulate and test the hypothesis that the two groups have the same earnings functions.

b) We now want to test whether immigrants and natives differ in only their return to education. Assuming that the effects of the other independent variables on earnings are the same, formulate and test the hypothesis.

2. Using PROC MEANS. fill in the following table:

Average Log Earnings

ImmigrantNative

Men

Women

(a) Report the estimates of your table.

(b) Fill in the table with the coefficients (not the coefficient estimates) from the following regression equation:

LOG EARNINGS = β1+β2*FEMALE+β3*IMMIGRANT+β4*FEMALE*IMMIGRANT,

where IMMIGRANT is a dummy variable indicating whether the individual is an immigrant. Report this table. Run the regression and check to make sure that your expression is correct.

3. In a previous empirical problem, it was hinted that the relationship between log earnings and education may not be linear. One method of partially correcting for this while remaining in the class of linear models is to use dummy variables. Create the following dummy variables: high school graduate, some college, and college graduate (high school dropouts will be the left out category). Do not allow individuals to be in more than one category, i.e. a person who has 1 year of college should have a 1 for the some college dummy variable and a 0 for the high school and college graduate dummy variables.

(a) What percent of the sample graduated from college?

(b) Estimate two regressions. One that includes higrade and another that includes the set of dummy variables created above. Include age, female, married, and number of children as additional regressors in both regressions. Report the results.

(c) Do earnings increase with education levels? What is the extra gain in log earnings from receiving a college degree relative to attending college for only 3 years? What is the extra gain in log earnings from increasing education from 2 years of college to 3 years of college? Answer these questions using your results from both regressions.

(d) Based on your answer to (c), which measure of education do you prefer?

4. We now want to use a spline to estimate the relationship between log earnings and education. The break points for the spline should be at 12 and 16 years of school.

(a) Report estimates for this regression.

(b) Using Excel and your coefficient estimates graph the relationship between log earnings and education.