# solution

You are examining the relationship between bonus paid to the CEO and its firmâ€™s future performance. Your alternative hypothesis is that the higher the bonus paid, the higher the performance of the firm.

For a bonus paid in year t, future performance (PERF) is measured as the firmâ€™s average monthly return in the 3 years following t (that is, t+1 through t+3). To measure bonus, the study defines LBONUS as the natural logarithm of the bonus paid (US\$ thousands) to the CEO in year t. The other variables of the study are:

• ? LSIZE: the logarithm of market value of equity (US\$ millions) for the firm measured at year t.

• ? BEME: the ratio of book value of equity to market value of equity, both measured at the end of year t

• ? CHAIR: dummy equal to 1 if the CEO is also the Chairman of the Board in year t

• ? TENURE: the number of years since the person started in the CEO position

Summary statistics for the data as of t=2006 is shown in Figure 1. For our sample, the 3- year average performance of firms is 2.63%, firmâ€™s average size is \$8.4 billion, average book-to-market is 0.52, and average CEO bonus is \$738,000. Finally, 18% of the firms in our sample have CEO cumulating the role of Chairman of the Board, and the average CEO tenure is 3.43 years.

• Figure 1: Summary statistics

The results of a SAS execution of the regression explaining future performance, PERFi=ÃŸ0+ ÃŸ1*LBONUSi + ÃŸ2*LSIZEi + ÃŸ3*BEMEi + ÃŸ4*CHAIR+ ÃŸ5*TENURE + ei

appear in Figure 2.

• Figure 2: Regression results

• a) Examine the effect of bonus payments on companyâ€™s future performance. Please formulate your hypothesis clearly and how it is being tested in the model above. Do bonus payments matter? How so?

• b) Define a 95% two-tailed confidence interval for the coefficient on tenure (TENURE). Then conclude whether and how tenure affects the future performance of the firms.

• c) Interpret the coefficient ÃŸ0 in the model above. Is it meaningful in this regression

• d) Your colleague argues that, since you are interested in the relationship between BONUS and future performance, you should be running a simple regression model, as in

PERFi=ÃŸ0+ ÃŸ1*LBONUSi + ei

Your colleague believes that this would give a cleaner measure of association between these measures, and that the introduction of other right-hand side variable can confound the true association between bonus and performance. Please argue which modelâ€”your colleagueâ€™s model or the extended version used to produce the results in Figure C.2â€” is more suited to the analysis of the relationship between bonus and performance, and why.

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