Text: show your working
Question four
a. Clearly stating the null and alternative hypotheses, discuss how the researcher can perform the Breusch-Pagan test of heteroskedasticity. [You DO NOT need to carry out the actual test] [6 MARKS]
b. A researcher is investigating the returns to education for women, and they are specifically interested in how having children can affect the wage offer mothers receive at different ages. Using data from the CPS, the researcher estimates the following model using Ordinary Least Squares:
lwage = β0 + β1*educ + β2*age + β3*kidlt6 + β4*(age*kidlt6) + ε
where lwage is the log of hourly wage, educ is the years of education, age is the woman's age, and kidlt6 is a dummy variable taking the value 1 if the woman has young children (under the age of 6) and 0 otherwise. Stata output for summary statistics for these variables and the OLS results are on page 9.
i. Consider two women, Anne and Wilma, both are 35 years old and have 13 years of education, but Anne has two young children (under 6 yrs old) and Wilma has no children. Calculate the predicted logwage for these two women. [2 MARKS]
ii. In light of the answer to the previous question, how do you interpret the coefficients on kidlt6 and age*kidlt6? [4 MARKS]
iii. The researcher wants to know whether having children has any effect on wages, so they propose to test that the coefficients β3 and β4 are jointly zero. Explain clearly how they could test this hypothesis. Your answer should detail what additional regression(s) would need to be run, the null and alternative hypotheses, the form of the test statistic, and the required distribution. State the rejection rule and how the result of the test would be interpreted. [8 MARKS]
