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 firm's stock (ROS, in percent form):
Log(salary) = β_{0} + β_{1 }log (sales) + β_{2 }ROE + β_{3 }ROS +u
a) In terms of 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 (higher ROS) increases a CEO's salary.
Assume the following was estimated based on this model from a sample of 209 firms where the standard errors are given in parentheses:
Log(salary) = 4.32+0.280* log(sales) +0.0174*ROE +0.00024*ROS
(0.32) (0.035) (0.0041) (0.00054)
b) By what percent is salary predicted to increase, if ROS increases by 50 points?
c) Test the hypothesis that ROS has a positive effect. Carry out the test at the 10% significance level.
d) Test the hypothesis that a 1% increase in sales implies a less than 1% increase in CEO salary at the 5% significance level.