Page info: *Author:Mathiesen, H. *Document version:2.0. *Copyright 1997-2017, ViamInvest.Legal notice. 

 

Statistical model: Determinants of executive compensation in listed US firms

 

Introduction: The equation below is a cross-sectional statistical regression model of the determinants of executive compensation. It shows the variables that are important in explaining the variation in executive compensation from firm to firm. The applied variable abbreviations are explained briefly below followed by a link with more detailed information about definition and theoretical justification for the inclusion of the variable in the model. This particular model has been estimated on the entire population of all listed firms in the US or about 8000 firms and 22000 top level executives for year 2002 and 2001. These analyses are described in Mathiesen [2005, section 6].

 

where,

Dependent variable:

          ExeComp is executive compensation measured by either the highest paid executive or by the sum of compensation by all high level executives. More info.

Mechanical variables:

          ROA is return on assets measured by earnings before interest and taxes (EBIT) to total assets. More info.

          ROS is return on stocks measured by % change in capitalization plus dividends. More info.

          NoExe is the number of executives used to calculate executive compensation by sum of all top-level executives. Only included if team compensation is used. More info.

Common sense variables:

          Labor is measured by the number of employees in the firm. More info.

          MarkCap is the firmís market capitalization. More info.

          Ow is the aggregated executive and director ownership in percentage of common shares outstanding at time t in firm i. More info.

          ExeCoRisk is executive compensation risk measured by the variance of executive compensation divided by the average compensation. More info.

Political variables:

          ExeAge is executive age. More info.

          StockR is the consensus stock recommendation. More info.

          SelfMan is self management measured by the number of executives that are also directors divided by the total number of directors. More info.

Dummy variables:

         dIndust1 are SIC industry dummies. More info.

         dIncorp are dummies for US state of incorporation. More info.

         dSub are dummy variables that are used to control for substituted observations. More info.

and finally,

         ax,yare model parameters to be estimated by regression techniques.

         e2,iare the residual errors for equation 2 and each firm i.

Dependent variable:

Variable name

Elaborated variable definitions and theoretical justifications

ExeCompi,t

Executive compensation

A generic abbreviation for the level of executive compensation measured at time t for firm i. One of the following two specific measures is applied: 1) top executive compensation by the highest paid executive, and 2) executive team compensation by the sum of compensation for all top level managers. Executive team compensation is preferred, because the firmís management is being executed by a team of managers rather than a single person. Moreover, evidence from regressions of executive compensation also favors executive team compensation because this measure produces more significant parameter estimates and higher adjusted R squares than similar regressions on top executive compensation. All executive data are obtained from proxy statements pursuant to Section 14(a) of the US Securities Exchange Act of 1934. The compensation data include all types of base salary, bonuses, perquisites, restricted stock awards, and long-term incentive plans (LTIP) except option based compensation and pensions. The exclusion of stock options is important because as reported by Jensen, Murphy and Wruck [2004] stock options represent about 50% of all CEO compensation for the S&P500 companies in the years 2000, 2001 and 2002.

Source: Thomson, One Banker. The SEC database. Proxy statements.

Mechanical variables:

The variables listed below are called mechanical, because managers are paid according to compensation contracts that increase their compensation if the stock return or the accounting return increases whether or not the managers are responsible for the increase in return or not.

Variable name

Elaborated variable definitions and theoretical justifications

ROAi,t

Return on assets

Return on assets for firm i measured at time t. The preferred and applied return measure is EBIT (earnings before interest and taxes) to total assets. Earning on equity is not suited for regressions because equity very often is negative making such earnings measures meaningless. Total assets are never negative; however, it is an ultimo measure so the relevant timing is total assets the previous year. In other words ROAi,t = EBITi,t / Assetsi,t-1. EBIT is preferred for three reasons. The first is that earnings need to be measured before interest expenses because the numerator, total assets, represents investments by both debt holders and equity holders. It should therefore include return for both kinds of constituencies. The other reason is that taxes should be excluded from earnings because they often involve industry subsidies and accumulated tax benefits that would distort the true company performance if they where included. The third reason is that EBIT is such a common and well known earnings measure. There may therefore be more consensus about how to measure EBIT making it a more reliable earnings measure.

One argument in particular can explain why ROA should determine executive compensation. The reason is that bonuses in the managerial compensation contract depend on ROA or other variables that are correlated with ROA such as profit margins or sales growth. The intention of correlating compensation with ROA is to create additional incentives for the manager to maximize profit. However, it should be noted that even in the case where the managers exercise no effort or have no ability to improve ROA their compensation will still be positively correlated with ROA because ROA varies for other reasons than managerial effort and prudence. This is why ROA is categorized as a mechanical variable; it varies positively with managerial compensation whether or not the managers are excellent or not.

Source: Thomson, One Banker. The SEC, CS, WS and EX databases.

ROSi,t

Return on stocks

Return on common stocks for firm i measured at time t. Stock return is measured as the percentage gain or fall in the firmís market capitalization plus dividend yield. The use of market capitalization means that the measure is fully adjusted for capital changes.

Managerial compensation is hypothesized to be an increasing function of the return on stocks (ROS). The explanation is that an important part of the managersí compensation consists of awards of stocks and stock options and the value of these awards will tend to be higher the higher the stock return. This is so because many firms award a fixed quantity of stocks to the management, not a fixed dollar amount of stocks. It is also possible that the compensation contract specifies that more stocks are awarded the higher the realized market return. This would further intensify the positive correlation between stock return and managerial compensation. It should be noted that even if the managers exercise no effort or have no ability to improve ROS their compensation will still be positively correlated with ROS, because ROS varies for other reasons than managerial effort and prudence. This is why ROS is categorized as a mechanical variable in the compensation function.

Source: Thomson, One Banker. The SEC, DS, CS, WS and EX databases.

NoExei,t

Number of executives in team

This is a simple count of the number of executive salaries that have been used to calculate the dependent variable executive team compensation. The variable is used to control for the fact that different firms report executive compensation for a different number of top managers in their proxy reports. The variable is not included in regressions using top executive compensation.

It should be needless to say that the more executive compensations that are added, the higher is the executive team compensation. This is also why NoExe is characterized as a mechanical variable.

Source: Thomson, One Banker. The SEC database. Proxy statements.

Common sense variables:

The variables below are called common sense variables, because the theory behind the inclusion of these variables is predominantly based on classic efficiency arguments.

Variable name

Elaborated variable definitions and theoretical justifications

Labori,t

Number of employees

Labor is the number of employees in the firm. This number normally includes part time employees. Only one database supplier, namely, Extel has specific numbers on full time and part time employment. The measurement error from pooling part and full time employment is unevenly distributed throughout the sample because some industries relies more on part time employment than others. Retail stores may for example have many part time employees so the 1.4 million employees of Wal Mart Stores Inc in 2002 may be inflated. Another source of measurement error in this variable is that some firms report average number of employees during the year and others report ultimo numbers.

The number of employees is a classic determinant of executive compensation. It should be positively correlated and there are several explanations for this. 1) The marginal productivity theory: According to this theory it is efficient for firms to pay their managers (indeed any employee) a salary that is equal to their marginal productivity. Furthermore, managers should be expected to have a much higher productivity than other workers because their decisions affect the productivity of all who work below the managers. In larger firms there are more people who work below the top management and as a result the managerial productivity is much higher in large firms. In larger firms it is therefore more important to attract the most competent managers in the market for managerial labor, and consequently larger firms need to pay higher executive compensations (for a detailed presentation of this theory see Rosen [1982, 1992, Section 2]). 2) The budget argument: Managers are paid more in firms with more employees because it is economically possible to do so. After all, the cost of management must be born by revenues generated from lover level employees. In other words, more employees mean higher revenues and this makes it more possible to pay higher compensations for the management whether or not they are worth it.

Source: Thomson, One Banker. The CS, WS and EX databases.

MarkCapi,t

Market capitalization

The firmís market capitalization is the market value of all outstanding shares measured at year end (Market price year end * Common shares outstanding). The most difficult measurement aspect of this variable is to determine the correct number of common shares outstanding. This may change during the year and the databases may not be up to date on this information and it could be further complicated by the presence of several types of common shares.

Market capitalization determines executive compensation for the same reasons as those mentioned for size measured by number of employees. However, market capitalization captures a different dimension of company size than labor does. Market capitalization says something about the expected potential future size of the company from the ownersí point of view, whereas labor captures a dimension of size that is present in nature and that is known to be considered when setting the level of executive compensation. Both of these dimensions should have a positive impact on managerial compensation.

Source: Thomson, One Banker. The SEC, DS, CS, WS and EX databases.

Owi,t

Executive & director ownership in %

Ownership is measured by total percentage ownership by all executives and directors. This is calculated as total shares held by executives and directors as a group divided by common shares outstanding. A difficult measurement aspect of this variable is to determine the correct number of common shares outstanding. This may change during the year and the databases may not be up to date on this information and it could be further complicated by the presence of several types of common shares.

Manager ownership is hypothesized to be negatively related to executive compensation for at least two reasons. 1) The substitution argument: The more a manager owns of the company the more income does the manager have from dividends and capital gains and the less important is the income from management compensation. Furthermore, managerial ownership includes all the important incentive properties that can be found in managerial compensation. Indeed, at 100% managerial ownership the managerial compensation become completely redundant since any dollar that are paid as managerial compensation simply reduces the managerís gains from ownership with the same dollar amount. This is ceteris paribus because there may be specific tax benefits from doing it one way or another. 2) The indirect size argument: It is a stylized fact that managerial ownership is strongly and negatively correlated with company size and it is also a stylized fact that managerial compensation is strongly and positively correlated with company size. It is therefore possible that the hypothesized negative relation between managerial ownership and managerial compensation is an indirect result of size correlations. That is, high managerial ownership means small size which again means low managerial compensation. To minimize this kind of omitted variable error the compensation regression should be controlled for size.

Source: Thomson, One Banker. The SEC database. Proxy statements.

ExeCoRiski,t

Executive compensation risk

Executive compensation risk is measured slightly different depending on whether compensation is defined as the highest paid executive or the sum of compensation for all top level executives. When executive compensation is defined as the highest paid executive then executive compensation risk has been calculated as the two-year standard deviation of top executive compensation divided by the two-year average of top executive compensation. When executive compensation is measured by the sum of all executive compensation, then the executive compensation risk has been calculated as follows: Only the three highest paid executives are considered. For each of these the executive compensation risk is calculated in the same way as it was calculated for the highest paid executive. Then the average of these three numbers is used as the final executive compensation risk.

It is hypothesized that executive compensation risk is positively correlated with executive compensation. The argument is the classic risk aversion argument. According to this argument a risk adverse person need to be paid a higher average compensation the riskier his compensation in order to get the same utility from his compensation package (Copeland and Weston [1988, pages 96-102]).

Source: Thomson, One Banker. The SEC database. Proxy statements.

Political variables:

These variables are called political because the theory used to explain their inclusion in the compensation model mainly supports a political theory of managerial rent-seeking.

Variable name

Elaborated variable definitions and theoretical justifications

ExeAgei,t

Average top level executive age

Executive age is defined as the average top level executive age. This measure is preferred to other measures, such as the age of the CEO, because the management of the firm is being executed by a team of executives rather than a single person. It is therefore also more relevant to consider the average age of that team rather than the age of a single person. This argument is furthermore supported by the fact that the executive team compensation measure produces the regressions with the most significant parameter estimates and the highest adjusted R square when compared to regressions that use compensation by the highest paid executive.

Average executive age is expected to be positively correlated with executive compensation for at least two reasons. 1) The influence argument: The argument is that older executives have more time to build up trust and influence at the board of directors and at key shareholders that need to approve their compensation contracts. Older teams of executives are therefore more able to increase their compensation than younger executive teams. 2) The experience argument: In addition, it could be argued that older executives are more capable and have more experience in securing a profitable compensation contract. Both of these arguments are to some degree based on an assumption that executive age is a proxy for executive tenure, i.e. the length of executive service. However, it should be noted that the kind of experience that secures high levels of compensation could also be gained outside the company in other companies. In other words, tenure could be low and management compensation high, as long as age is high.

Source: Thomson, One Banker. The SEC database. The companyís 10-K or 20-F filings.

StockRi,t

Consensus stock recommendation

The consensus stock recommendation is calculated as the mean of several similarly scaled grades of common stock delivered by stock analysts from various investment banks to First Call previously called I/B/E/S. In particular, common stock is graded on a discrete scale from 1 to 5, where mark 1 is a strong buy, 2 is a buy, 3 is a hold, 4 is a sell and 5 is a strong sell.

The consensus stock recommendation is hypothesized to be negatively correlated with executive compensation for at least one reason. The expectations argument: The explanation is that managers are more able to succeed in getting high compensation packages when their company looks good in the stock market. After all, if you ask the board and the shareholders to approve a huge increase in compensation it should be more likely to go through when the firm is rated a strong buy rather than a strong sell (Mathiesen [2005, Section 6.2]).

Source: Thomson, One Banker. The FC database (previously called I/B/E/S).

SelfMani,t

Self-management by fraction of directors that are also executives

Self-management is defined as the fraction of directors that are executives as well. For example, if self-management is equal to 0.75 it implies that 75% of the directors also functions as executives.

There are at least two arguments that can explain why self-management is correlated with executive compensation. 1) The self-dealing argument: According to this argument executive compensation is a positive function of self-management. The idea is that the more the executives are in direct control of the board of directors the more able are they to award themselves high compensation packages. 2) The alibi argument: If you want to commit an offense without getting captured you need an alibi. The alibi argument claims that the self-dealing argument is not working in practice because it would be too easy for unhappy shareholders to sue a self-dealing management and win. Instead, it is claimed that management compensation is a negative function of self-management. The argument is that if you really want to increase managerial compensation, much beyond what is reasonable given the size and the economic performance of the firm, then you need an alibi to avoid being sued afterwards. The perfect alibi is low self-management. The claim is that the board can be controlled indirectly just as well as if the executives had the board positions themselves, but it is practically impossible to sue the management if the board is controlled indirectly because it is very difficult to prove indirect control (Mathiesen [2005, Section 6.2]).

Source: Thomson, One Banker. The SEC database. The companyís 10-K or 20-F filings.

Dummy variables:

Variable name

Elaborated variable definitions and theoretical justifications

dIndust1i,t,j

SIC industry dummies

This is industry dummies created from the primary four-digit SIC code. The classification contains 213 dummies including 26 financial industry dummies. It should be noted that the industry is the primary industry among several industries that the firm operates in. This is sometimes misleading if the primary industry is not the majority industry of the firm. For example, the primary industry of the General Electric Company is 6159 a financial industry. It is well known that General Electric is foremost an industrial conglomerate and for that reason it is more appropriate to reassign the SIC to 9997. The distinction between financials and non-financials is important because in most circumstances it would be wrong to make a regression on a sample including both financials and non-financials because they are too different to be treated alike. The point is, that in order to produce better industry dummies it is necessary to use an error correcting procedure that corrects the most obvious SIC classification errors.

It is hypothesized that compensation is determined by the type of industries because different industries over time may have created a tradition for certain compensation levels.

Source: Thomson, One Banker. The SEC, CS, WS and EX databases.

dIncorpi,t,h

Dummies for US state of incorporation

Dummies for incorporation in the US. The incorporation dummies include fifty US states, one district (District of Columbia) and one dependent area (Puerto Rico).

These dummies are hypothesized to be determinants of executive compensation because of differences in the legal environment from state to state both with regard to disclosure requirements and with regard to taxes.

Source: Thomson, One Banker. The SEC, CS, WS and EX databases.

dSubi,t,l

Substitution dummies

Substitution dummies are dummy variables that are included to control for the effect of substituting missing observations in a variable with a constant so that a single missing observation does not lead to the deletion of the entire observation set from the regression sample. To be sure, if for example advertising expense to sales is missing the trick is to substitute a constant, such as 0%, and include a new regression dummy with the value one each time a missing value is substituted and zero otherwise. It should be emphasized that the choice of constant has no effect on the regression estimates of the model with the exception of the estimator of the substitution dummy. There is therefore no need to worry much about the choice of constant (however, a sensible choice is to pick a value (such as the median) that has minimal impact on the descriptive statistics of the substituted sample). The substitution technique may be very important for maintaining a large sample size available for regression. For example, advertising intensity is missing for about 73% of all publicly listed US companies in 2002. In other words, unless the substitution technique is used 73% of the sample will be lost and it will therefore most certainly be biased. This problem of losing data and getting biased samples because of missing observations increases when other variables are considered. To be sure, the research and development intensity is missing for about 66% of all publicly listed US companies in 2002 and when it is combined with missing values from advertising and if we assume that missing observations are randomly distributed we will loose about 91% of the sample (1-[1-0.73]*[1-0.66] = 0.9082)!

The substitution technique does a fine job of preserving sample size and avoiding sample biases and for that reason it has been applied on all variables apart from the dependent variable, incorporation, industry, total assets and market capitalization.

-Copyright 1997-2017, ViamInvest. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.Legal notice.