. Consider the following estimated regression equation relating CEO compensation to firm performance:
logsalary=4.36.275logsales.0179roe (0.29) (.033) (.0040)
where salary denotes annual salary, sales denotes annual sales, and roe denotes average return on equity for the CEO’s firm for the previous three years expressed as percentages. (Return on equity is defined in terms of net income as a percentage of common equity.) The R2 is .282 (measured between 0 and 1) and the sample has 209 observations.
a) Compute the t-ratios for the three estimates. What do you conclude about the likelihood that the true, unobserved parameter values are all equal to zero?
b) Can you reconcile your answer to part (a) with the fact that the R2 is fairly low (much closer to zero than to one)?
c) Based on the estimates, what is the predicted percentage change in CEO salary if return on equity increases by 30 percentage points (that is, roe=30 ), holding everything else constant?
d) Note that, holding all else constant, in the above model logsalary=.275logsales and we learned in class that 100× log y≈% y so if we multiply both sides of the equation by 100 we obtain approximately % salary=.275 % sales. Thus, the estimates reveal that, ceteris paribus, a, say, 1 percent increase in sales generates a 0.275 percent increase in CEO salary, and a 10 percent increase in sales generates a 2.75 percent increase in salary. If we now divide both sides of the equation by % sales we obtain:
% salary =.275
% sales In the lexicon of economics, what is the name given to a number like .275? That is, what do we call the percent response in one variable to a percent change in another variable?
logsalary=4.36.275logsales.0179roe (0.29) (.033) (.0040)
where salary denotes annual salary, sales denotes annual sales, and roe denotes average return on equity for the CEO’s firm for the previous three years expressed as percentages. (Return on equity is defined in terms of net income as a percentage of common equity.) The R2 is .282 (measured between 0 and 1) and the sample has 209 observations.
a) Compute the t-ratios for the three estimates. What do you conclude about the likelihood that the true, unobserved parameter values are all equal to zero?
b) Can you reconcile your answer to part (a) with the fact that the R2 is fairly low (much closer to zero than to one)?
c) Based on the estimates, what is the predicted percentage change in CEO salary if return on equity increases by 30 percentage points (that is, roe=30 ), holding everything else constant?
d) Note that, holding all else constant, in the above model logsalary=.275logsales and we learned in class that 100× log y≈% y so if we multiply both sides of the equation by 100 we obtain approximately % salary=.275 % sales. Thus, the estimates reveal that, ceteris paribus, a, say, 1 percent increase in sales generates a 0.275 percent increase in CEO salary, and a 10 percent increase in sales generates a 2.75 percent increase in salary. If we now divide both sides of the equation by % sales we obtain:
% salary =.275
% sales In the lexicon of economics, what is the name given to a number like .275? That is, what do we call the percent response in one variable to a percent change in another variable?
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