Consider an equation to explain salaries of CEOs in terms of annual firm sales, return on equity ( roe in percentage form), and return on the firm’s stock ( ros, in percentage form): log (salary) = β...

Consider an equation to explain salaries of CEOs in terms of annual firm sales, return on equity (roe in percentage form), and return on the firm’s stock (ros, in percentage form):

log (salary) = β


0


+ β


1


 log(sales) + β


2


roe


+ β


3


ros – u


.

1. In terms of the model parameters, state the null hypothesis that, after controlling forsales androe, ros has no effect on CEO salary. State the alternative that better stock market performance increases a CEO’s salary.

1. Using the data in CEOSAL1, the following equation was obtained by OLS:

log(salary) ˆ

=

4.32 + .280

 log(sales) +

 .0174

 roe +

 .00024

 ros

                           (.32)    (.035)                  (.0041)        (.00054)

                   n = 209,R
2
= .283

By what percentage is salary predicted to increase ifros increases by 50 points? Doesroshave a practically large effect onsalary?

1. Test the null hypothesis thatros has no effect onsalary against the alternative thatros has a positive effect. Carry out the test at the 10% significance level.

1. Would you includeros in a final model explaining CEO compensation in terms of firm performance? Explain.