A bit of practice with dummy variables and heterosiredast'icity: Consider the following model for

the logarithm of wage given years of university education and gender of person i : log (wagegr) = ﬁg + dofemalei + ﬁltotanig + 61 female; x totem,- + “a; (1) where log is the natural logarithm, female, is a dummy variable that is equal to 1 if person 3'

is female is 0 otherwise, and totem},- is the number of years of university education that person

i has. Based on a random sample of 6763 individuals, we have estimated this model using OLS

and obtained the following estimated equation: (a) (b)

(8) _--"'_"'-~-_ log('wage,r) = 31.3%}; — 31,333 f emal e,- + (filigggtotunti + 31351;; female,- x totunii, it = 1,2,...,6763, 122:0.202. Explain how you would test the hypothesis that the conditional expectation of log (wage)

conditional on years of university education is exactly the same for men and women. You

need to specify the null and the alternative, the test statistic and its distribution under the

null, the regression that you should run so that you can compute the test statistic, and the rule for rejection or non-rejection of the null hypothesis. Explain what insights the estimated model reported above provide about the conditional

expectation of log (wage) given years of university education for men and women. Using the estimated equation, ﬁnd the value of totnmi (total number of years in university)

such that the predicted values of log(1uage) are the same for men and women. Can women

realistically get enough years of university education so that their earnings catch up to

those of men? Explain. Suppose we snapect that the variation of log (wage) around its conditional mean is larger

for women than it is for men. That means that in the population regression model, we

believe that Var (n | Eternal, female = 1) > Var (a | totum', female = 0) . Explain the con-

sequences of this for the OLS estimator and for the t—tests based on OLS estimates and

their OLS standard errors.