Math Solutions

(Step-by-Step) Consider an equation to explain salaries of CEOs in terms of annual firm sales, return equity (roe, in percent form), and return on the firm's

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

\[\log (\text { salary })=\beta_{0}+\beta_{1} \log (\text { sales })+\beta_{2} r o e+\beta_{3} r o s+u\]
  1. 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 CEO's salary.
  2. Using the data in CEOSAL1.RAW, the following equation was obtained by OLS:
    By what percentage is salary predicted to increase if ros increases by 50 points? Does ros have a practically large effect on salary?
  3. 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.
  4. Would you include ros in a final model explaining CEO compensation in terms of firm performance? Explain.

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