2. Consider an equation to explain salaries of CEOs (Chief Economic Of- ficer) i
ID: 1109190 • Letter: 2
Question
2. Consider an equation to explain salaries of CEOs (Chief Economic Of- ficer) 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) = 0 + 1 log(sales) + Aroe + Aros + u. Estimating the model from a sample of n 209 firms yielded the following OLS estimation results Estimate Std. Error t value Pr(>Itl) (Intercept) 4.3117124 0.3154329 13.669 2e-16 log(sales) 0.2803149 0.0353200 7.936 1.34e-13 0.0174167 0.0040923 4.256 3.17e-05 0.0002417 0.0005418 0.446 0.656 roe ros Residual standard error 0.4832 on 205 degrees of freedom Multiple R-squared: 0.2827,Adjusted R-squared: 0.2722 F-statistic: 26.93 on 3 and 205 DF, p-value: 1.001e-14 a) 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 (again in terms of the model param- eters) that better market performance increases CEO's salary. b) Carry out the hypothesis testing in a), report the t-value and p- value alongside with your conc lusion c) How much salary is predicted to change if roe increases by 10 points?Explanation / Answer
a) So here we are testing the significance of B3 as a coefficient. Thus the null hypothesis will be H0:B3 =0 as against H1:B3 not equal to 0. If we reject the null hypothesis here we mean that return on firm's stock has an impact on CEO salary.
b) The t value is given by the ratio of the coefficient to the standard error of the coefficient. Thus we have the t stat as 0.446 and the p value as 0.656. Thus here we accept the null hypothesis that B3 has no impact at 10% level of significance as the p value is greater than 0.05.
c) If roe increases by 10%, then the CEO salary will increase by (10*0.0174167)=0.174167%.
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