Question1 A researcher is interested in how different factors relating to firm p

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Question1 A researcher is interested in how different factors relating to firm performance impact on the salaries of Chief Executive Officers (CEO's) of the firm. Two alternative models are considered: (MI) log(salary),-B + 2log(sales), + 3roei + .ros, + ui (M2) log(salary)i-ci+,log(sales), +,roe, ta,rosneg, tui where variable definitions are given below together with variable means provided in brackets salary -1990 CEO salary, thousands $ [1,281] sales-annual firm sales in 1990, millions $ [6,924] roe- average percent return on equity 1988-1990 [17.21 ros = average percent return on stock 1988-1990 [61.8] rosneg= 1 if percent return on stock is negative and-0 otherwise [0.11] (i)Carefully outline your expectations about each of the parameters in both of these models including their expected signs. In particular, explain the differences between M1 and M2 in terms of how the impact of return on stock on CEO salary s being modelled. Table 1 provides OLS estimates for both models using a sample of 209 US-based firms. Using the M1 results discuss the economic and statistical significance of the impact of ros on CEO salaries. On the basis of these results only, would you include ros in a model of CEO salaries? Explain you reasoning Now using the M2 results discuss the economic and statistical significance of the impact of ros on CEO salaries Briefly discuss and explain any substantive differences between M1 and M2 i terms of the inferences associated with all of the explanatory variables. (ii) (iii) (iv) Table 1: OLS estimates of models CEO salaries Variable Intercept M1 4.32 (0.32) 0.280 (0.035) 0.0174 (0.0041) 0.00024 (0.00054) M2 4.30 (0.29) 0.288 (0.034) 0.0167 (0.0040) log(sales) roe ros 0.226 0.109 rosneg Observations 209 209 0.283 0.297 Note: Numbers in brackets below coefficient estimates are standard errors

Explanation / Answer

Considering two equations given above M1 & M2 we have independant variables as roe ros rosnev & salary.

In M1 if 1% change in either ways in return on stock would give b% change in salary assuming other variables constant.

In M2 we have used resneg that is a dummy variable as if return on stock is negative we have intercept term "alpha1 - alpha4" in an hypothesis of alpha 2 =alpha3 = 0 which we cannot reject it states that in negative returns on stock % change in salary is "alpha1 -alpha4". ROS has no direct impact on salary in M2.

Sign of alpha 4 should be negative as bad performance of stock could impact salary of Director adversely.

Signs of alpha 2 alpha 3 beta 2 beta 3 are postiive as all the varialbes are positively linked.

Sign of Beta 4 should be positive as per the logic of alpha 4.

Assuming the obtained OLS estimates for parametersof ros are effiecient and unbiased we can say 0.02% increasein salary for 1% increase in ros.

Lets to find statistical significance of beta 4 we run a hypothesis as below

h0: beta 4 =0

We have more than 200 samples iin this data hence using t test for statistical significance hence critical t value for beta 4 is 0.00024/0.00054 = 8/18 =4/9 =0.444 which is less than 2 hence we can not  reject the hypothesis for 0.05 percent of p value

therefor with this data we may have b4 which is not significantly different than 0 hence cahave no real impact on the salary.

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