Question 1

Final Term Exam Part 2

MSDA3055 Linear Regression and Time Series

True or False. Five points per question: 2 pts for a correct T/F and 3 pts for the explanation

a) When the disturbance term is subject to autocorrelation, the ordinary least squares estimators, are biased.

b) The OLS slope estimator is biased when X2 and X3 are correlated.

c) Ordinary least squares (OLS) is a special case of generalized least squares.

d) Heteroskedasticity occurs when the disturbance term in a regression model is correlated with one of the explanatory variables.

Question 2

In a study of returns to education, a researcher estimates log-lin regressions of the form logYi =+Xi +i,

where Y is weekly earnings and X is years of schooling. The researcher begins by estimating the regression using the complete sample of n = 1000 people:

full sample: log Yi = 7.60 + 0.075 Xi + ei SSE = 2.175. (0.906) (0.00110)

She then estimates separate subsample regressions for males and females, based on n1 = 600 and n2 = 400 observations respectively:

Answer the following questions.

males: females:

Yi = 7.26 + 0.072 Xi + ei (0.944) (0.00102)

Yi = 7.02 + 0.076 Xi + ei (0.891) (0.00104)

SSE = 0.922 SSE = 1.013.

(a) According to the coefficient point estimates, which group earns the highest return to education, males or females? Cite the estimates that are the basis for your conclusion.

(b) Perform a test of whether the data support imposing a common model on both males and females. State carefully all parts of your test procedure.

(c) An alternative means of distinguishing between males and females would be to define a dummy variable

like

0 ifmale

Di = 1 iffemale

and introduce this into the full-sample regression as follows:

dummy variable regression: log Yi = + Xi + Di + DiXi + i. Under this approach, what would be the least squares estimates of these coefficients?