Econometrics I

Econometrics I
Problem Set 3
1. (Wooldridge 3.8) Which of the following can cause OLS estimators to be biased
(a) Heteroskedasticity.
(b) Omitting an important variable.
(c) A sample correlation coefficient of .95 between two independent variables both included
in the model.
2. (Wooldridge 3.9) Suppose that you are interested in estimating the ceteris paribus relationship
between y and x 1 . For this purpose, you can collect data on two control variables, x 2
and x 3 . (For concreteness, you might think of y as final exam score, x 1 as class attendance,
x 2 as GPA up through the previous semester, and x 1 as SAT or ACT score.) Let ˜β 1 be the
simple regression estimate from y on x 1 and let ˆβ 1 be the multiple regression estimate from
y on x 1 , x 2 , x 3 .
(a) If x 1 is highly correlated with x 2 and x 3 in the sample, and x 2 and x 3 have large partial
effects on y, would you expect ˜β 1 and ˆβ 1 to be similar or very different Explain.
(b) If x 1 is almost uncorrelated with x 2 and x 3 , but x 2 and x 3 are highly correlated, will
˜β 1 and ˆβ 1 tend to be similar or very different Explain.
(c) If x 1 is highly correlated with x 2 and x 3 , and x 2 and x 3 have small partial effects on
y, would you expect se( ˜β 1 ) or se( ˆβ 1 ) to be smaller Explain.
(d) If x 1 is almost uncorrelated with x 2 and x 3 , x 2 and x 3 have large partial effects on y,
and x 2 and x 3 are highly correlated, would you expect se( ˜β 1 ) or se( ˆβ 1 ) to be smaller
Explain.
3. (Wooldridge 4.1) Consider an equation to explain salaries of CEOs in terms of annual firm
sales, return on equity (roe, in percent form), and return on the firms stock (ros, in percent
1

form):
log(salary) = β 0 + β 1 log(sales) + β 2 roe + β 3 ros + u
(a) In terms of the model parameters, state the null hypothesis that, after controlling for
sales and roe, ros has no effect on CEO salary. State the alternative that better stock
market performance increases a CEOs salary.
(b) Using the data in CEOSAL1.RAW, the following equation was obtained by OLS:
̂ log(salary) = 4.32 + .280 log(sales) + .0174roe + .00024ros
(.32) (.035) (.0041) (.00054)
n = 209, R 2 = 0.283.
By what percentage is salary predicted to increase if ros increases by 50 points Does
ros have a practically large effect on salary
(c) Test the null hypothesis that ros has no effect on salary against the alternative that
ros has a positive effect. Carry out the test at the 10% significance level.
(d) Would you include ros in a final model explaining CEO compensation in terms of firm
performance Explain.
4. Wooldridge C3.6
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