BLS WORKING PAPERS

U.S. DEPARTMENT OF LABOR

Bureau of Labor Statistics

 

OFFICE OF EMPLOYMENT RESEARCH

AND PROGRAM DEVELOPMENT

Principal-Agent Models of CEO Pay-For-Performance Relationships

David S. Kaplan

Working Paper 318

December 1998

 

I would like to thank Felipe Balmaceda, Fran Blau, Ken Chay, Todd Keister, Kevin Murphy, Rob Olsen, Andy Schneider,

Ramsey Shehadeh, Tim Vogelsang, and seminar participants at the Bureau of Labor Statistics, Cornell University, the University of

Illinois, and the University of Texas at Dallas. I especially thank John Abowd and Bob Gibbons for their help on earlier drafts. All

remaining errors are mine. The opinions expressed in this paper reflect the views of the author, and do not necessarily reflect the

policies of the Bureau of Labor Statistics or the views of other staff members.
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Table 1: Descriptive Statistics for Execucomp Data (1992-1996)

Variable Mean Std. Dev.

sigmm = Estimated standard deviation of the error term from

the firm's market model

tenure = years as CEO prior to current year 8.460 8.140

ret = stock market rate of return 0.157 0.387

sret = (residual from market model)/sigmm -0.101 0.846

Log(Sales) = Log of Sales in millions 6.819 1.554

Log(Assets) = Log of Current Assets in millions 7.051 1.752

Log(Compensation)=Log of Total CEO Compensation in thousands 6.971 0.910

Observations 3,325

CEOs 1,014

Firms 821

0.384 0.250
Table 2: Cross-Sectional Estimate of Standardized Log-Linear 

Pay Schedules

for Low, Middle, and High Variability Firms

Variable Estimate Standard Error

medium variability firm 0.055 0.028

high variability firm 0.228 0.034

sret for low variability firms 0.078 0.026

sret for medium variability firms 0.078 0.024

sret for high variability firms 0.112 0.027

Tenure 0.004 0.002

Log(Sales) 0.184 0.016

Log(Assets) 0.211 0.013

year effects included, but not shown

Observations 3,325

CEOs 1,014

Firms 821

R2 0.444

Standard Errors are Calculated Under the Assumption of Arbitrary 

Heteroscedasticity
Table 3: Effect of Performance Variability on Compensation 

Across

Standardized Quartiles of the Performance Distribution

Variable Estimate Standard Error

Performance in 2nd quartile of firm

distribution of returns

Performance in 3rd quartile of firm

distribution of returns

Performance in highest quartile of firm

distribution of returns

sigmm in lowest quartile 0.317 0.126

sigmm in 2nd quartile 0.271 0.100

sigmm in 3rd quartile 0.515 0.119

sigmm in highest quartile 0.397 0.119

Tenure 0.004 0.002

Log(Sales) 0.191 0.015

Log(Assets) 0.204 0.013

year effects included, but not shown

Observations 3,325

CEOs 1,014

Firms 821

R2 0.444

Standard Errors are Calculated Under the Assumption of Arbitrary 

Heteroscedasticity

0.115 0.067

0.200 0.071

0.097 0.069
Table 4: Cross-Sectional Estimate of CEO Pay-Performance

Relationships (ignoring performance variability, nonstandardized performance)

Variable Estimate Standard Error

Performance in 2nd quartile of market 0.068 0.033

distribution of returns

Performance in 3rd quartile of market 0.167 0.034

distribution of returns

Performance in highest quartile of market 0.299 0.036

distribution of returns

Tenure 0.004 0.002

Log(Sales) 0.179 0.015

Log(Assets) 0.189 0.013

year effects included, but not shown

Observations 3,325

CEOs 1,014

Firms 821

R2 0.444

Standard Errors are Calculated Under the Assumption of Arbitrary 

Heteroscedasticity
Table 5: Correlations Between Estimated 

Performance Variability and Quartile

of Market Distribution

sigmm

Performance in lowest quartile of market

distribution of returns

Performance in 2nd quartile of market

distribution of returns

Performance in 3rd quartile of market

distribution of returns

Performance in highest quartile of market

distribution of returns

0.162

All correlations are significant at the 0.01 level.

0.142

-0.155

-0.149
Table 6: Cross-Sectional Estimate of CEO Pay-Performance

Relationships (accounting for performance variability, nonstandardized performance)

Variable Estimate Standard Error

Performance in 2nd quartile of market

distribution of returns

Performance in 3rd quartile of market

distribution of returns

Performance in highest quartile of market

distribution of returns

sigmm 0.371 0.064

Tenure 0.004 0.002

Log(Sales) 0.192 0.015

Log(Assets) 0.199 0.013

year effects included, but not shown

Observations 3,325

CEOs 1,014

Firms 821

R2 0.452

Standard Errors are Calculated Under the Assumption of Arbitrary 

Heteroscedasticity

0.101 0.033

0.034

0.295 0.035

0.198
Table 7: Cross-Sectional Estimate of Standardized LogLinear Pay Schedules

for Low, Middle, and High Variability Firms (RestrictedStock Grants

Excluded for CEOs of High Variability Firms)

Variable Estimate Standard Error

medium variability firm 0.051 0.028

high variability firm 0.183 0.034

sret for low variability firms 0.079 0.026

sret for medium variability firms 0.078 0.024

sret for high variability firms 0.104 0.026

Tenure 0.004 0.002

Log(Sales) 0.182 0.015

Log(Assets) 0.209 0.013

year effects included, but not shown

Observations 3,325

CEOs 1,014

Firms 821

R2 0.446

Standard Errors are Calculated Under the Assumption of Arbitrary 

Heteroscedasticity
Table 8: Effect of Performance Variability on Compensation 

Across

Standardized Quartiles of the Performance Distribution 

(Restricted-Stock Grants

Excluded for CEOs of High Variability Firms)

Variable Estimate Standard Error

Performance in 2nd quartile of firm

distribution of returns

Performance in 3rd quartile of firm

distribution of returns

Performance in highest quartile of firm

distribution of returns

sigmm in lowest quartile 0.256 0.122

sigmm in 2nd quartile 0.239 0.099

sigmm in 3rd quartile 0.482 0.116

sigmm in highest quartile 0.334 0.115

Tenure 0.004 0.002

Log(Sales) 0.188 0.015

Log(Assets) 0.204 0.013

year effects included, but not shown

Observations 3,325

CEOs 1,014

Firms 821

R2 0.449

Standard Errors are Calculated Under the Assumption of Arbitrary 

Heteroscedasticity

0.070

0.066

0.068

0.102

0.196

0.086
Table 9: Hazard Model of CEO Tenure Duration

Variable Estimate Standard Error Risk Ratio

sigmm -0.729 0.360 0.482

sret -0.206 0.084 0.814

Log(Sales) 0.221 0.084 1.247

Log(Assets) -0.147 0.076 0.863

year effects included, but not shown

CEO Spells 1,014

-2(Log Liklihood) 2,030.45