Question

1. Suppose you are interested in investigating the determinants of CEO salary in a given industry. You suspect that CEO's salary depends on the profitability of the company as well as its size. To that end, you contemplate running the following regression. CEO salary β0 + β1 revenue + β2profit + u, where CEO salary is the CEO's salary, revenue is the firm's revenue (used as a measure of its size), and profit is the firm's profit. (a) Suppose you could not obtain data on firm's profit level. Therefore, you are thinking about regressing CEO salary on revenue only. Explain whether you would overstate or understate the true effect of firm's revenue on CEO's salary. (b) Suppose you were able to obtain data on profit, and you regress CEO salary on both revenue and profit. However, you find that the R2 is too low. There- fore, you consider adding firm's cost as an explanatory variable since CEOs that can keep the cost down relative to the industry average should be re- warded. What would be the effect of including cost in the regression?

Answer 1

a) If we choose to leave out the profit level from the regression model, we will only be predicting the CEO salary on the basis of the revenue. This would lead to overstatement of true effect of firm's revenue on the salary, since we will be trying to explain the salary variations based on revenue alone while there could be other relevant factors.

b) If we include firm's cost as well in the regression model, the R-squared increases making it seem as if the new predictor actually improved the model. However, in reality, even a non-relevant predictor could make the R-squared increase. To get around this, we should use the adjusted R-squared, which increases only if the addition of the new predictor variable improves the model, and decreases otherwise. Hence, adjusted R-squared will actually help to ensure that newly added variables are relevant and considered only if they improve the model.