FILE The issues regarding executive compensation have received extensive media attention. The government is even considering a cap on high-flying salaries for executives

(New York Times, February 9 , 2009). Consider a regression model that links executive compensation w ith the total assets of the firm and the firm's industry. Dummy variables are used to represent four industries: Manufacturing Technology d 1 M anufacturing O ther d2, Financial Services d3, and Nonfinancial Services d4. A portion of th e data for 455 highest-paid CEOs in 2006 is given in th e accom panying table; th e com plete data, labeled Industry C om pensation, are available on th e text website.

Compensation

(in $ million)

Assets

(in $ millions) d1 d2 d3 d 4 16.58 20,917.5 1 0 0 0 26.92 32,659.5 1 0 0 0

⋮ ⋮ ⋮ ⋮ ⋮ ⋮

2.30 44,875.0 0 0 1 0 S o u r c e : SEC w e b site a n d C o m p u sta t.

a. Estimate th e model: ln(y ) = β 0 + β1 ln(x ) + β 2d 1+

β 3d 2 + β 4d3 + ε , w here ln(y ) and ln(x ) d en o te th e log of com pensation and th e log of total assets, respectively.

The nonfinancial services industry dum m y d4 is used for reference.

b. Interpret th e estim ated coefficients.

c. Use a 5% level of significance to determ ine which industries, relative to th e nonfinancial services industry, have a different executive com pensation.

d. Use th e partial F test to determ ine if th e th ree industry d um m y variables used in th e m odel are jointly significant at th e 5% level.