1 /3 Problems Consider an equation to explain salaries of CEOs in terms of annua

Question

1 /3 Problems 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): 1. log(salary)-A + A log(sales) + Aroe + 3ros+ u (i) In terms of the model parameters, state the null hypothesis that, after controlling for sales and roe, ros has no effect on CEO salary. Also, state the alternative that ros does affect a CEO's salary (ii) Using the data in CEOSALI DTA, the following equation was obtained by OLS: log salary) 4.32+280 log(sales) +0174roe +00024ros (.32) (035) n=209, R2 = .283 (0041) (.00054) By what percentage is salary predicted to increase if ros increases by 50? Does ros have a practically large effect on salary? (ii) Test the null hypothesis that ros has no effect on salary against the alter- native that ros does have an effect. Garry ont the test at the 10% significance level. iv) Would vou include ros in a final model explaining CEO compensa tion in

Explanation / Answer

Solution:-

1)

Null hypothesis: none of the variables are sifgnificant for the model such that the model is useless ie H0 : 1 = 2 = 0. We need to use the F-test for this test and it is available in the output, F = 26.93 and p = 0.0000. Hence we should reject the null and conclude that there is statistically significant evidence that atleast some of the variables in this model are significant and that the model is useful since  p = 0.0000 < = 10%. Also note that the  F = 26.93 > F(3, 205) = 2.08 at 10% significance and again, we should reject the null.

2)

Since log(salary)/ ros = 0.0002417= ˆ 3, then plugging in ros = 50, and multiplying we get log(salary) = 50 0.0002417 = 0.012085 = 1.2085% increase in salary.

3)

Since log(salary)/ log(sales) = 0.2803149 = ˆ 1, then plugging in log(sales) = 10% and multiplying we get log(salary) = 10% 0.2803149 = 0.02803149 = 2.803% increase in salary.

4)

All of the estimated coefficients are positive and intuitive. these are all relevant for measuring the performance of the CEO and should raise the compensation/salary paid to them.

Adj. R2 = 0.2722 = 27.22%. it measures that 27.22% of variation in log(salary) explained by the regression model includes these 3 variables sales, roe and ros.

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