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 booktomarket 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% twotailed 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 righthand 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.