Question

Suppose we are interested in modeling the factors that affect salaries of CEO’s of companies. Let salaryi denote CEO compensation in 1990 measured in $1000 increments. Let salesi denote the 1990 sales of a firm in millions of dollars. Let mktvali denote the market value of the firm at the end of 1990 in millions of dollars. Let profitsi denote 1990 profits in millions of dollars. Finally, let the dummy variable collegei = 1 if a CEO attended college and 0 otherwise and let the dummy variable gradi = 1 ,if a CEO attended graduate school and 0 otherwise.
First consider a simpler model where log denotes the natural logarithm (log base e):
log(salaryi) = β1 + β2 log(salesi) + β3 log(mktvali) + εi.
Assume that Classical Assumptions for MLR hold. This regression was estimated using a random sample of 177 firms. Standard errors are in parentheses:
log(sal?aryi) = 4.62 (0.25)
R2 = 0.299
(a) Test the joint significance of β2 and β3 at the 1% significance level.
Suppose an undergraduate RA student majoring in economics was working on this empirical question. Given the lack of training, this student could only think to estimate the simple regression model
log(salaryi) = β1 + β2 log(salesi) + εi. and he only reported that RSS from this regression was 46.51.
(b) Would the R2 from this simple regression be larger or smaller than 0.299? Give an explanation for your answer.
One might think that the profits of a firm would affect CEO pay (the more a firm makes, the more it can pay its CEO). Consider the following fitted model
log(sal?aryi) = 4.69 +0.161 log(salesi) +0.098 log(mktvali) +0.000036profitsi
(0.38) (0.04)
(0.064) (0.00015)
+0.162 log(salesi) +0.170 log(mktvali) (0.04) (0.05)
RSS = 45.31 TSS = 64.65 RSS = 43.295
(c) Test for the joint significance of the two slope parameters for log(mktval) and profits at the 1% signif-
icance level.
A more complete model of CEO salaries would take into effect the education of the CEOs:
log(salaryi) = β1 + β2 log(salesi) + β3 log(mktvali) + β4collegei + β5gradi + εi. (1)
This model was estimated by OLS yielding
log(sal?aryi) = 4.68 +0.160 log(salesi) +0.112 log(mktvali) −0.056collegei −0.057gradi
(0.35) (0.04)
(0.05) (0.237) (0.080)
RSS = 43.137

Answer 1