Problem
Consider an equation to explain salaries of CEO's in terms 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
In terms of the model parameters, state the null hypothesis, after controlling for sales and roe, ros has no effect on CEO's salary. State the alternative that better stock market performance increases a CEO's salary.
Using data on CEO's salaries, sales, roe and ros of 209 companies, the following equation was obtained by OLS:
log?((salary) ^ )=4.32+0.280 log?(sales)+0.0174roe+0.00024ros
se (0.32) (0.035) (0.0041) (0.00054)
R2=0.283
Interpret the preceding regression taking into account any prior expectations that you may have about the expected signs of the various coefficients.
By what percentage is salary predicted to increase if ros increases by 50 points? Does ros have practically large effect on salary?
Test the null hypothesis that ros has no effect on salary against the alternative that ros has a positive effect (Hint; use one-tailed t-statistic at the 5% significance level).
Would you include ros in a final model explaining CEO compensation in terms of firm performance? Explain
What the overall significance of the regression? Which test do you use and why?
Can you interpret the coefficients of roe and ros as elasticity coefficients? Why or why not?