Question

  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

Answer 1

(i) \(H_{0}: \beta_{3}=0 H_{1}: \beta_{3}>0\).

(ii) The proportionate effect on salary is \(0.00024 \cdot(50)=0.012\). To obtain the percentage effect, we multiply this by \(100: 1.2 \%\). Therefore, a 50 ppoint ceteris paribus increase in ros is predicted to increase salary by only \(1.2 \%\). Practically speaking this is a very small effect for such a large change in ros.

(iii) The \(10 \%\) critical value for a one-tailed test is obtained from Table G.2 (WO, p. 827) as 1.282. The t-statistic on \(\operatorname{ros}\) is \(0.00024 / 0.00054 \approx 0.44\), which is well below the critical value. Therefore, we fail to reject \(H_{0}\) at the \(10 \%\) significance level.

(iv) Based on this sample, the estimated ros coefficient appears to be different from zero only because of sampling variation. On the other hand, including ros may not be causing any harm; it depends on how correlated it is with the other independent variables (although these are very significant even with ros in the equation).