Managerial Compensation: Luck, Skill or Labor Markets?

Transcription

1 Managerial Compensation: Luck, Skill or Labor Markets? Jeff Brookman a and Paul D. Thistle b March 2013 ABSTRACT Luck, skill and labor markets all have empirical support as determinants of managerial compensation. We examine the relative importance of pay for luck, managerial skill and labor market opportunities in determining compensation. We measure luck as the predictable component of firm performance, measure skill using managerial fixed effects and measure labor market opportunities as the compensation of executives at matched firms. Our results imply that managerial skill is the most important determinant of managers compensation, followed by firm size and labor market opportunities, and that luck is not an important determinant of managerial compensation. Keywords: executive compensation, human capital, managerial ability JEL Codes: G20, G34, J24, J 33 a Brookman: Department of Finance, Idaho State University, 921 S. 8th Ave, Pocatello, ID phone , broojeff@isu.edu b Thistle (corresponding author): Department of Finance, Lee Business School, University of Nevada, Las Vegas, 4505 Maryland Parkway, Box , Las Vegas, Nevada, , phone: , fax: , paul.thistle@unlv.edu

2 Managerial Compensation: Luck, Skill or Labor Markets? 1. Introduction Recent literature has concluded that CEO compensation represents a failure of the underlying principal-agent models and a failure of corporate governance (e.g, Bebchuck and Fried 2004; Bebchuk, Grinstein and Peyer, 2009; Goergen and Renneboog, 2011) and has led to calls for the reform of managerial compensation (e.g, Kandel, 2009). Consistent with this view, one strand of research provides evidence that CEO compensation is related to overall market performance when the market performs well but not when the market performs poorly. Bertrand and Mullainathan (2001) provide evidence that CEOs are rewarded as much for luck as for general performance, where "luck" is the portion of firm performance predictable from exogenous market factors beyond the CEO's control. In particular, they find that CEO cash compensation and total compensation are as sensitive to average industry performance as to firm performance. They interpret this result as supporting the "skimming" view of CEO compensation - that CEOs effectively control their own compensation. Garvey and Milbourn (2006) argue that, if the skimming view is correct, then CEOs remuneration will reflect market performance when market performance is good but not when market performance is poor. They report that, while CEOs are rewarded for both luck and skill, pay for luck is asymmetric, so that CEOs are rewarded for good luck, but not penalized for bad luck. Gopalan, Milbourn and Song (2010) report additional evidence of asymmetric pay for luck. However, they interpret this as consistent with incentivizing CEOs to optimally choose the firm s exposure to industry performance.

3 A second strand of literature suggests that managerial remuneration is related to labor markets or to a manager s outside employment opportunities. Himmelberg and Hubbard (2000) and Oyer (2004) argue that adjusting compensation for industry performance is optimal if CEOs' outside employment opportunities vary directly with industry or overall market performance. If CEO talent is scarce, then allowing compensation to increase with overall market levels may enable firms to retain talented managers. Bizjak, Lemmon and Naveen (2008) document the use of compensation consultants and point out that companies commonly compare CEO pay to compensation at a peer group of companies. They report that, controlling for performance and for other factors known to affect compensation, CEOs who are paid below the median of their peer group are more likely to receive raises and receive larger raises. Bizjak, Lemmon and Naveen interpret their results as evidence that peer group benchmarking of CEO compensation is used as a retention device. Bizjak, Lemmon and Nguyen (2011) analyze compensation peer groups reported in They find that, while there is some evidence of opportunism, firms choose peers based on industry, size, and other economic characteristics that reflect the labor market for managerial talent. Firms are aware of labor markets or outside opportunities and adjust compensation accordingly. A third strand of literature relates managerial compensation to managerial skill. Rajgopal, Shevlin and Zamora (2006) argue that more talented CEOs should have better outside opportunities. They proxy talent by the number of articles about the CEO in the business press and by past firm performance. Garvey and Milbourn (2006) and Bizjak, Lemmon and Naveen (2008) proxy skill by the part of firm performance that is not explained by industry performance. Graham, Li and Qiu (2012) and Coles and Li (2013b) find that compensation is related to skill, 2

4 where more highly skilled managers receive higher levels of compensation. They measure skill using a three way fixed effects model developed by Abowd, Kramerz and Margolis (1999). In this paper we study the explanatory power of luck, labor markets and skill on managerial compensation. In essence, we conduct a horse race between luck, labor markets and skill to see which has the most explanatory power. While prior studies have shown that luck, labor markets and skill are all important determinants of managerial compensation, we are unaware of research showing the degree to which each variable explains compensation. We also extend the existing literature in other important ways. First, we extend the analysis of compensation from CEOs to the top management team. While there are some studies of the determinants of non-ceo compensation (Core and Guay, 2001; Sapp, 2008; Kale, Reis and Venkateswaran, 2009), the existing literature has focused largely on CEO compensation. But if compensation contracts are determined optimally or if the compensation process is captured by corporate insiders, it should be evident in the determinants of the pay of top managers beside the CEO. 1 Second, we measure managerial skill using a three way fixed effects model (Abowd, Kramerz and Margolis, 1999) that allows us to separately identify the effects of individual managers, firms and time. Graham, Li and Qiu (2012) and Coles and Li (2013b) show that manager fixed effects are an important determinant of managerial compensation. Applying this same approach, Coles and Li (2013a) find that managerial skill and unobservable firm characteristics account for almost all of the explained variation in executives incentives measured by delta and vega of managerial wealth. More broadly, Coles and Li (2013b) use this 1 Our view is that if the firm has good corporate governance, then it should contract efficiently with all of the top management team. Conversely, if the firm has poor corporate governance, then it will contract inefficiently with all of the top management team. The alternative view, that firms contract efficiently with some members of the top management team but not others, seems less reasonable. 3

5 same approach to show that unobservable managerial and firm characteristics are important determinants of a range of corporate policies. Following Bertrand and Mullainathan (2001) and Garvey and Milbourn (2006), we take luck to be the part of firm performance that can be predicted from industry performance. While the interpretation of the empirical result is still being debated, these papers provide evidence of asymmetric application in CEO compensation. However, there is no research on whether this phenomenon extends to non-ceo members of the top management team. We know there are important differences in CEO and non-ceo compensation (e.g., Kale, Reis and Venkateswaran, 2009). We provide evidence on the extent to which non-ceo compensation is sensitive to luck, and on whether the sensitivity of compensation to luck depends on whether luck is good or bad. The managerial labor market determines managers outside opportunities. To control for managers outside opportunities, we employ a procedure similar to Bizjak, Lemmon and Naveen (2008). For each firm we construct a comparison group of size and industry matched firms. We classify top managers according to their position into twelve job categories. We take compensation for the manager's job category at peer firms as a proxy for the manager s outside opportunities. We measure managerial skill using a three way fixed effects model (Abowd, Kramerz and Margolis, 1999); our approach is essentially the same as that of Graham, Li and Qiu (2012). This approach has a number of characteristics that make it useful for our purposes. First, this approach allows us to identify individual effects for managers who moved, for all individuals who worked at a firm where the mover worked and the firm effects for firms where the mover was employed. A relatively small amount of mobility in the data set lets us identify individual effects for a large number of individuals and firms. Another useful characteristic of the three- 4

6 way fixed effect approach is that it can be applied to large data sets. The least squares dummy variable approach widely used to estimate fixed effect models is computationally infeasible for three way fixed effects except in relatively small data sets. The manager fixed effects capture unobservable time-invariant managerial characteristics, such as psychological and personality traits, in addition to managerial ability. As Abowd, et. al. (2005) point out, the individual manager fixed effects can be interpreted as the portable time-invariant component of the managers' compensation; it captures the influence of unobservable components of managers' characteristics. When we estimate the models of managers compensation by OLS, we find results that weakly support pay for luck. We also find that labor market opportunities and firm size are important determinants of managers compensation. The results for pay for luck do not survive the inclusion of labor market opportunities or firm fixed effects. When we include labor market opportunities or firm fixed effects, we find that the pay for luck variables are not significant, nor do they provide much explanatory power. We then estimate the models using three-way fixed effects. We find that labor market opportunities are significant, but pay for luck is not. Managerial skill explains about 40 percent of the variation in managers compensation. Firm size, firm effects, the CEO effect and labor market opportunities are also important in explaining managers compensation. We find that there is a CEO premium of about 40 percent and a small CFO premium. We discuss the empirical methodology in more detail in Section 2. Section 3 describes the data. Section 4 reports the empirical results and Section 5 provides a brief conclusion. 5

7 2. Empirical Methodology 2.1 Three-way fixed effects model We begin with a Becker (1962, 1964) Mincer (1974) model of human capital. The manager's annual compensation is Y it = ν t H it, (1) where Y it is compensation, ν t is the rental rate of human capital at time t and H it is manager i's stock of human capital at time t. Assuming an exponential form for the production function and that manager i works at firm j, the manager's human capital can be written as H it = exp{x it β + w jt γ + θ i + φ j }, (2) where x it and w jt are the observable time-varying manager and firm characteristics and θ i and φ j are the latent manager specific and firm specific characteristics. Combining equations (1) and (2), taking logarithms and adding a random error term yields the empirically estimable compensation equation: y it = x it β + w jt γ + θ i + φ j + µ t + it, (3) where y it = ln{y it } and µ t = ln{ν t }. This model implies that the manager's expected compensation consists of the market valuation of his observable and unobservable personal characteristics, x it β + θ i, the firm's observable and unobservable characteristics, w jt γ + φ j, and a time effect, µ t. The model implies that manager i's latent characteristics, i, do not vary over time and do not vary over employers. That is, i captures the value of managers general skills that are transferable across employers. 2 2 The manager fixed effects capture unobservable time-invariant managerial traits, which, in addition to innate ability, could include characteristics such as psychological and personality traits, (Chatterjee and Hambrick, 2007; Hackbarth, 2008; Malmandier and Tate, 2005, 2008), socio-economic background, (Hambrick and Mason, 1984), functional backgroung (Hambrick and Mason, 1984; Hambrick, 2007) or risk aversion (Coles and Li, 2013a) which are known to influence firm policies and performance and thus would influence compensation. 6

8 Managers may also possess firm-specific skills which, while valued by firm j, are not transferable to different employers; these are captured by the firm effect φ j. 2.2 Identification of manager and firm effects The potential problem in identifying individual manager and firm effects is easy to see intuitively. If manager i works only at firm j, then the manager and firm effects, i and φ j, are perfectly correlated and, without further information, cannot be separated. Mobility of managers across firms provides the additional information needed to identify individual manager and firm effects. The identification of manager and firm effects works through group connection. When a group of managers and firms is connected, the group contains all of the managers who ever worked at any of the firms in the group and all of the firms that ever employed any manager in the group. There is no connection between different groups. That is, no manager in group 1 has ever worked for any firm in group 2, nor ever worked with any manager in group 2, and vice versa. The economic interpretation of group connection is that it shows the empirical mobility network within the managerial labor market. Group connection is illustrated in Figure 1, which shows five firms and six managers divided into 2 groups. Managers A and B work at firm 1, so both managers and firm 1 are in group 1. Manager A then changes jobs and works for firm 2 with manager C. As a result, manager C and firm 2 are added to group 1. Manager C has also worked at firm 3 with manager D, so manager D and firm 3 are also included in the group. Note that manager B and manager D are connected, even though they have never worked at the same firm and have never changed jobs. Manager E has worked at firms 4 and 5, so manager E and firms 4 and 5 are in group 2. 7

9 Manager F works at firm 5, so manager F is also in group 2. Observe that there is no overlap between groups 1 and 2. Within each group, all manager and firm effects are identified up to a normalization. If that there are N g managers and J g firms in group g, then N g + J g - 1 effects are identified. One of the manager or firm effects must be taken as the benchmark and the remaining effects are measured as differences from the benchmark. If there are N managers, J firms and G groups in the data, then a total of N + J - G manager and firm effects are identified. In terms of Figure 1, six manager and firm effects are identified for group 1 (4 managers + 3 firms - 1) and three manager and firm effects are identified for group 2. To see how mobility and group connection permits the identification of individual manager and firm effects, consider the following example. Managers X, Y and Z are identical in all observable characteristics, likewise, firms 1 and 2 are identical in all observable characteristics. Suppose managers X and Y work at firm 1 and earn $1 million and $2 million respectively, while manager Z works at firm 2 and earns $3 million. Now manager Y moves to firm 2 for compensation of $2.5 million. Since all else is equal, including manager Y's latent characteristics, this implies that firm 2 has a $0.5 million higher fixed effect than firm 1 (φ 2 - φ 1 = 0.5). Take firm 1's fixed effect as the benchmark and set it equal to zero (φ 1 = 0). The manager fixed effects are found by subtracting the firm fixed effects. Thus, manager X's fixed effect is $1 million ( X = 1-0). Manager Y's fixed effect is $2 million ( Y = 2-0 from firm 1 or Y = from firm 2) and manager Z's fixed effect is $2.5 million ( Z = 3 -.5). 8

10 2.3 Estimation In principal, the three way fixed effect model can be estimated by least squares by including dummy variables for each manager, firm and time period. But if there are N managers, J firms and T time periods along with K time varying regressors, then the cross-product matrix (X'X) has dimension (N + J + T + K). In practice, the memory required to invert the crossproduct matrix renders the least squares dummy variable approach computationally infeasible except for small data sets. We utilize the fixed effect least squares dummy variable (FELSDV) approach developed in Abowd, Kramerz and Margolis (1999). This approach first differences out the manager fixed effects, then uses the least squares dummy variable approach to estimate firm and time effects. The individual manager fixed effects are then recovered. As discussed, group connection allows the identification of individual manager and firm effects. Group connection also implies a block diagonal structure for the cross-product matrix, and Abowd, Creecy and Kramarz (2002) show that this fact can be used to solve the least squares normal equations exactly. Cornelissen (2006) recognizes that, because most workers are only employed at one firm during the sample period, the cross-product matrix is sparse. This implies that further computational efficiencies can be achieved. Taken together, these developments imply that the three way fixed effect model can be applied to analyze large data sets. 3 3 Gruetter and Lalive (2009) provide an alternative, iterative algorithm to estimate the three-way fixed effects model. We do not implement their algorithm. 9

11 3. Data 3.1 Sample The initial sample consists of all managers in Standard and Poor s ExecuComp database from 1993 to While most firms report manager-level data for five executives, ExecuComp can have data for up to nine executives; we collect data on all managers for whom information is available. We exclude financial firms (SIC codes ) and utility firms (SIC codes ). We combine the ExecuComp data on manager characteristics with data on firms financial characteristics from Compustat and stock return data from CRSP. We eliminate observations for which the firm's sales or assets are missing. The resulting data set contains 107,137 observations on 28,855 managers at 2,784 firms. The identification of individual manager and firm fixed effects depends on the mobility of managers across firms. Table 1 presents information on the movers and non-movers in the sample. Panel A shows the number and proportion of managers classified by the number of sample firms for which the managers worked. Over the sample period, percent of managers were employed at only one sample firm, 5.26 percent were employed at two firms while just over one-half percent were employed at three or more sample firms. Altogether, 1,674 managers moved and were employed at more than one sample firm. Panel B of Table 1 classifies firms by the number of movers. Managers did not move in about 44 percent of firms. About 31 percent of the firms have had between one and five managers that are movers, about 15 percent of firms have between 6 and 10 movers and 9 percent of firms have between 11 and 20 movers. Just under two percent of firms have between 21 and 30 movers, while about one-half of a percent have had more than 30 managers that have moved during the sample period. These proportions are similar to Graham, Li and Qiu (2012). 10

12 Altogether, 57 percent of firms (1,573 firms) have had at least one manager move between sample firms. Our analysis requires that we separately identify manager and firm fixed effects. We can identify the manager fixed effects and firm fixed effect for all 18,328 managers who worked at the 1,573 firms where at least one manager moved between sample firms. Even though only 5.80 percent of managers move among sample firms, group connection allows us to include 64 (18,328/28,855) percent of all managers and 57 (1,573/2,784) percent of all firms. There are a total of 167 groups. We carry out our main analysis on the connected sample, that is, the subsample of firms where at least one manager moved. The sample contains 69,387 observations Variable Description and Measurement Compensation Our primary measure of compensation is total compensation. This measure includes compensation from all sources, including salary and bonuses, restricted stock, long-term incentive plans and stock and option grants. Options are valued at their Black-Sholes value. Compensation amounts are measured in thousands of dollars. Consistent with our empirical model in (3) and since the distributions of the compensation variables are highly skewed, we use the log of the compensation variables in our regression analyses. We add one to all variables where we use logs to remove the problem of taking the log of a zero value. Summary statistics for compensation are reported in Table 2. 4 Median total compensation is $972 thousand (mean $2.0 million). 4 Throughout the paper, all dollar amounts are measured in constant 1993 dollars. 11

13 Labor Market Opportunities To control for managers' labor market opportunities, we use a procedure similar to that of Bizjak, Lemmon and Naveen (2008). For each firm, we select comparison firms having the same industry (2 digit SIC) and sales between 50% and 200% of the sample firm. We classify managers into twelve categories according to their job titles as listed in ExecuComp. The classification is selected based on recurrent observations, using the most common job titles in ExecuComp. We use the median compensation of executives with the same job title at peer firms as our measure of outside labor market opportunities. Panel A of Table 2 reports median and mean compensation for each job category used in the analysis. Not surprisingly, individuals with the title Chairman and CEO have the highest median compensation at $2.5 million (mean $4.9 million), with Chairman, President and CEO's earning nearly as much (median $2.3 million, mean $4.3 million). The lowest paid category in our sample is Vice-President, with median compensation $686 thousand (mean $1.2 million). For all of the job categories, compensation is highly variable and highly skewed. The median industry total compensation is $896 thousand (mean $1.5 million) Luck As in Bertrand and Mullainathan (2001) and Garvey and Milbourn (2006), we take luck to be the component of firm performance that is predictable from market factors beyond managers' control. We regress each firm s unadjusted stock return on year indicator variables and on equal weighted and value weighted average industry returns using all ExecuComp firms in the primary two-digit SIC industry. That is, we estimate the regression R jt = + EWI t + VWI t + D t + jt (4) 12

14 where R jt is the raw return for firm j in year t, EWI t and VWI t are the equally weighted and value weighted industry indices and D t is the year dummy variable; the equation is estimated for the full sample. Similar to Garvey and Milbourn (2006) we do not include market returns because our estimates include time indicator variables. Luck is measured as the predicted value from this regression. We do not multiply this value by beginning of year market capitalization because we use log compensation as the dependent variable. The median and mean values of luck are 14 percent and 16 percent, respectively. The R 2 for the equation is (adjusted R 2 = ). To test for asymmetric pay for luck, we use the indicator variable, BadLuck, which takes a value of one when luck is negative and is zero if luck is nonnegative. Luck is bad 40 percent of the time. If executives can influence how their pay is set, then compensation should not be adjusted for luck when luck is good, but should be indexed to luck when luck is bad. If so, the coefficient on luck should be positive, and the coefficient on the interaction between luck and the indicator for bad luck should be negative. Following Aggarwal and Samwick (1999) and Garvey and Milbourn (2006), we do not require the sensitivity of pay to luck to be the same for all firms. We estimate the volatility of luck for each firm-year as the standard error of the predicted value from the regression in (4). Using the estimated volatility of luck, we construct the empirical cumulative distribution function (cdf) for the volatility of luck. The cfd is the normalized ranking, from smallest to largest, of the volatility of luck. We include the interaction between luck and the cdf of volatility to allow the effect of luck to vary across firms. 13

15 Returns The stock return is measured as the twelve-month holding period return for the firm s fiscal year. Stock return volatility is measured as the standard deviation of the monthly return for the thirty-six months prior to the end of the firm s fiscal year. Return on assets (ROA) is earnings before interest and taxes divided by total assets. The median (mean) stock return is 0.08 (0.14) and the median (mean) volatility is 0.34 (0.40). The median ROA is 0.13 and the mean is Our specification allows us to test for relative performance evaluation (RPE) as well as pay for luck. 5 RPE implies that firm performance should be adjusted for industry performance in determining compensation. The adjustment for industry performance should be attenuated as it becomes more variable (Holmstrom and Milgrom, 1987). If so, the coefficient for luck should be negative and the coefficient on the interaction between luck and the cdf of the variance of luck should be positive. The coefficient for the interaction between luck and bad luck should be zero Manager Characteristics In Panel E of Table 2 we report descriptive statistics for age as a proxy for the time varying component of managers human capital. Median and mean age are 53 years. Since there may be differences in CEO and non-ceo compensation, we include an indicator variable if the manager is the CEO during the fiscal year. Approximately 18 percent (12,682/69,387) of the sample consists of observations on CEOs. We also include an indicator variable if the manager 5 Albuquerque (2009) points out that tests for relative performance evaluation are necessarily joint tests of the incentive design and the peer group. Since the test for relative performance evaluation is a by-product of our analysis of pay for luck and labor market opportunities and not the focus of our study, we use industry (SIC code) as the peer group. 14

16 is female. Approximately five percent (3,560/69,387) of the observations consist of female managers. We also include an indicator for CFOs. Approximately 14 percent (10,021/69,387) of the sample consists of observations on CFOs Firm Characteristics In Panel F of Table 2 we report statistics for several firm specific variables. We measure firm size as book value of total assets. The median value of assets is $1.4 billion (mean $8.6 billion). The market-to-book ratio is measured as the book value of asset less the book value of equity plus the market value of equity divided by the book value of assets. The market value of equity is the share price times the number of shares outstanding. The median market-to-book ratio is 1.7 and the mean market-to-book ratio is 2.2. Leverage is measured as the book value of liabilities divided by the book value of assets. Median leverage is 0.58 and mean leverage is Managerial Compensation In this section, we analyze the effect of luck, managerial skill and outside labor market opportunities on managerial compensation. The basic specification is the model of compensation used in Graham, Li and Qiu (2012), with the addition of the luck and labor market variables: y it = + x it + w jt + r jt 1 + LM jt 2 + L it 3 + it. (5) In eq. (5), the dependent variable, y it, is the log of compensation, x it is the vector of manager characteristics including the log of age, the indicator for gender and the indicators for the CEO and CFO, w jt is the vector of firm characteristics including size, the market-to-book ratio and 15

17 leverage, and r jt is the vector of returns including the stock return and its lag, the volatility of the stock return and ROA and its lag. The labor market variable is LM it, and L jt is the vector of pay for luck variables including luck, the interaction between luck and the bad luck indicator and interaction between luck and the cdf of the volatility of luck. Table 3 reports OLS estimates of the compensation equation. All of the models in Table 3 include year fixed effects, but do not include manager or firm effects. Model 1 is the most basic specification with observed manager and firm characteristics and year fixed effects. Consistent with results in the literature, compensation is increasing in firm size and market-tobook, age, current and lagged stock return and ROA and in the volatility of the stock return and decreasing in leverage. The coefficient for the CEO indicator is 0.82, which implies being the CEO increases compensation by 127%. The coefficient on the CFO indicator variable is not significantly different from zero. The coefficient for the female indicator is -0.07, which implies that female executives earn about 6.8% less than male executives. Forty-seven percent of the variation in compensation is explained by Model 1. We also estimate the variance decomposition for several of the explanatory variables to determine which has the greatest effect on compensation. The model R 2 is K K Cov(y, ŷ )/var(y) = cov( y, ˆ z ) / var( y) cov( y, ˆ z ) / var( y), i 1 k k i 1 where the z k are the right-hand side variables (including the fixed effects). Since they must sum to the R 2 for the model, the components of the variance decomposition can be interpreted as the relative contribution of the variable or combination of variables to the variation in the log of total compensation. The variance decomposition of Model 1 indicates that 10% of the variation in compensation is explained by the CEO indicator variable. Less than one percent of the variation is explained by stock performance or the CFO indicator variable and one percent is explained by k k 16

18 accounting performance. Thirty percent is explained by firm size. This is consistent with Murphy (1999), who states that firm size is an important determinant of managerial compensation. Year effects explain five percent of the variation of compensation. Model 2 adds outside opportunities. Compensation is increasing in labor market opportunities, consistent with the argument that labor market opportunities are an important determinant of compensation (Rajgopal, Shevlin and Zamora, 2006; and Bizjak, Lemmon and Naveen, 2008). The coefficient for labor market opportunities can be interpreted as the elasticity, so the results imply a one percent increase in the value of outside opportunities increases compensation by about one-third percent. The inclusion of labor market opportunities decreases the estimated CEO premium to approximately 103 percent. The CFO indicator variable is different from zero but a coefficient of 0.02 implies that the premium for CFOs is only two percent. There is very little change in the effects of the other control variables on total compensation. Including labor market opportunities reduces the explanatory power of CEO, firm size and year effects. Labor market opportunities explains fifteen percent of managerial compensation. Model 3 examines whether managers are paid for luck. The coefficient on the luck variable is positive, implying that managers' compensation rises with industry performance. The coefficient for the interaction between luck and the bad luck indicator is not significant. This implies that the effect of luck on compensation is symmetric. The interaction between luck and the cdf of the variance of luck is not significant. The result that luck affects compensation is consistent with the results in Bertrand and Mullanathian (2001) and Garvey and Milbourn (2006). The variance decomposition is similar to those in Model 1 for the CEO and CFO 17

19 indicators, stock return, accounting performance and firm size variables. Luck provides almost no explanatory power for managerial compensation. Model 4 includes both labor market opportunities and pay for luck variables. The coefficient for labor market opportunities is similar to the estimated coefficient in Model (2), the estimated elasticity is about one-third. Model 4 also examines whether compensation contracts are determined differently for CEOs and non-ceo managers; we interact the CEO indicator with labor market opportunities and the pay for luck variables. These interaction terms have a small effect for labor market opportunities and are not significant at conventional levels for the luck variables. This implies that the effect of labor market opportunities is nearly equally important for all managers. Including labor market opportunities again reduces the CEO premium to about 105 percent. None of the pay for luck variables are significant. Luck is not significant when labor market opportunities are included, suggesting luck may proxy for outside opportunities (Himmelberg and Hubbard, 2000, Oyer, 2004) The results in Model 4 also indicate that the majority of explanatory power for managerial compensation comes from the firm size (22%), labor market opportunities (15%) and whether the manager is a CEO (9%). Luck has practically no explanatory power (0.0%). Stock and accounting performance have small explanatory power (1.0% or less). While the models in Table 3 have included labor market opportunities, luck and control variables, they have not included skill, nor have they controlled for firm fixed effects. In Table 4 we add firm fixed effects and managerial effects to understand compensation. Table 4 analyzes the effects of pay for luck, managerial skill and labor market opportunities on managerial compensation. 18

20 Models 1, 2 and 3 in Table 4 include firm fixed effects and year fixed effects. In Model 1, we see the labor market opportunities variable is positive and significant but smaller than the OLS estimate. The inclusion of firm fixed effects reduces the effects of most of the control variables including firm size, the market-to-book ratio and leverage on compensation. The effect of stock return volatility becomes much smaller with the inclusion of the firm fixed effects. The coefficient for the CEO indicator is 0.64, which implies that CEOs earn approximately 90 percent more than non-ceos. The CFO indicator is not significant. The variance decomposition indicates that the variables that provide the most explanatory power include firm size (18%), labor market opportunities (9%) and the CEO indicator variable (8%). Model 2 excludes labor market opportunities and investigates pay for luck. When labor market opportunities are omitted, the estimated CEO premium increases. The coefficients on the other control variables are similar to Model 1. We find that, with the inclusion of firm fixed effects, only the interaction of luck and the cdf of the variance of luck is significant. The variance decomposition value for luck is zero. Firm size (22%), the CEO effect (10%) and year effects (6%) provide the most explanatory power. Model 3 incorporates both labor market opportunities and luck. The results are similar to the prior two models. The labor market opportunities variable is positive and significant and explains 9% of compensation. None of the pay for luck variables are significant nor do they provide any explanatory power. The CEO indicator variable is 0.65 suggesting that CEO receive 92% more compensation than non-ceos; it explains 8.0% of compensation. Firm size, also significant, remains the most important explanatory variable, explaining 18% of compensation. Model 4 is estimated using FELSDV and does not include luck or labor market opportunity variables. This model includes both manager and firm effects. Compared to the 19

21 OLS estimates in Table 3, the effect of most of the control variables is smaller. The coefficient for firm size is nearly one-half of the OLS estimate. In particular, the estimated coefficient for the CEO indicator is 0.41, which implies the CEO premium is about 51 percent. The CFO indicator is small but significant, the estimated CFO premium is four percent. The variance decomposition shows that managerial skill is the most important determinant of compensation, accounting for about 40 percent of the variation in executive compensation. Firm size, year and the CEO indicator are also important determinants of compensation, accounting for 15, seven and five percent. These results are similar to those of Graham, Li and Qiu (2012) and Coles and Li (2013b). In Model 5 we extend the model to include labor market opportunities and pay for luck in addition to skill. The coefficient on the labor market opportunities variable is positive and significant with an estimated elasticity of 0.09; this is smaller than estimates that do not include manager effects. This variable also explains five percent of the variation in compensation. The pay for luck variables are not significant with the exceptions of the interaction of luck with the cdf variable and with the CEO indicator. These variables again have no explanatory power in explaining compensation. Managerial skill is captured by the individual fixed-effects and explains 39% of compensation. The managerial skill is the single most important component in explaining the variation in compensation. The coefficients for the control variables in Models 4 and 5 are similar. Of the control variables, firm size provides the most explanatory power, explaining 14% of compensation. The CEO effect and year effects each explain about five percent of manager compensation, while stock and accounting performance each explain one percent of compensation. 20

22 These results indicate that managerial skill is the most important factor in explaining variation in managerial compensation. It is worth repeating that the manager fixed effects capture unobservable time-invariant managerial traits, such as psychological and personality traits or functional background or risk preferences, in addition to managerial ability. The results also indicate that the effect of firm size and the CEO indicator are reduced by about one-half in the fixed effect model compared to the OLS model. These results are consistent with those of Graham, Li and Qiu (2012) and Coles and Li (2013b). We also find that the effects of the market-to-book ratio and leverage on compensation are reduced by about one-half when managerial skill is included. Labor market opportunities are also a significant factor in explaining managerial compensation. While luck has explanatory power when labor market opportunities or firm fixed effects are not included, when they are included its explanatory power disappears. Firm size provides the most explanatory power of all of the control variables, explaining more of managerial compensation than labor market opportunities. 5. Robustness tests 5.1 Luck To investigate why our results concerning pay for luck are different from Garvey and Milbourn (2006) and the previous literature we replicated their model (Table 4, Model 1) using our dataset. We use our sample period, , all fiscal year ends (not just December), winzorize the data at 1%, and do not drop years in which the CEO changed. We measure luck and skill as the predicted and residual portions of returns, multiplied by market capitalization. We estimate the model using the change in total CEO compensation as the dependent variable. Our results are qualitatively the same as in Garvey and Milbourn (2006). We find that the 21

23 change in compensation increases with both luck and skill, but the effect is attenuated as luck or skill becomes more variable. We repeat the analysis using all managers, and again find qualitatively similar results. We also repeat the analysis for CEOs only and for the top management team using the sample period. Again, the results are qualitatively similar. This implies that the fact that we use a different sample period and the fact that we analyze the top management team are not driving our results. A second issue is that, since we measure luck as the predicted part of the return, luck may be correlated with the return. We re-estimate the models in Tables 3 and 4 omitting the current and lagged stock return. This has no effect on the results. In addition, our results for the OLS estimates (Table 3) are similar to the results in Bertrand/Mullainathan and Garvey/Milbourn. We find that managers compensation depends on luck. This suggests that estimating the model in levels rather than differences is not driving our results. Taken together, these results suggest that the difference between our results and the previous literature are primarily due to the inclusion of labor market opportunities and the firm and manager effects. 5.2 Skill Studies have used several other measures of skill. The most notable practice is to estimate skill as the residual from the regression of firm performance on industry performance, scaled by the market value of equity (Garvey and Milbourn, 2006; Bizjak, Lemmon and Naveen, 2008). This proxy has some logical limitations, most notably, since it is the residual of the regression it can be either positive or negative, suggesting that CEOs randomly forget and remember how to reason analytically or negotiate contracts from year to year. Even more 22

24 importantly, FELSDV creates an effect for each manager, allowing each manager s skill to be estimated. The residual based method is computed from a firm-level regression, and requires us to assume that all members of the top management team have the same level of skill. In Table 5 we re-estimate the regressions using the residual based measure of skill instead of manager fixed effects. We find that the residual based measure of skill is significant. We find that labor market opportunities are positive and significant. Luck is significant, but none of the other pay for luck variables are significant in any of the specifications in Table 5. These results are consistent with Bertrand and Mullainathan; there is no evidence of asymmetric pay for luck. The variance decomposition for the pay for luck variables and for the residual based measure of skill are both negligible, indicating that neither has explanatory power for managerial compensation. Firm size, labor market opportunities and the CEO indicator are the most important explanatory variables. The R 2 for the models in Table 5 is substantially lower than for the models that include managerial fixed effects. On both conceptual and empirical bases, managerial fixed effects provide a better measure of managerial skill than the residual based measure. 5.3 Sample size If our goal is to estimate the effect of managerial skill then we can only look at firms for at least one manager moved using the FELSDV procedure. Our sample size using this methodology is 69,387 observations. The complete sample is 107,137 observations. If we are not interested in estimating the managerial fixed effects but simply wish to control for them, we can do so by using spell fixed effects, that is, by including a dummy variable for each unique manager/firm combination (Graham, Li and Qiu, 2012). In Figure 1, since managers A, C and E 23

25 each work for two firms, there are a total of nine spells; this is comparable to the nine identified manager and firms effects under the three-way fixed effects approach. In Table 6 we estimate our regressions using a spell fixed effects rather than using FELSDV. In Model 1 we estimate the regression for the connected sample used in the main analysis and in Model 2 we estimate the regression for the full sample. The number of unique manager-firm combinations in Model 1 is 20,176 and the number of unique manager-firm combinations in Model 2 is 30,703. Because Model 1 uses the connected sample, it has the same number of spells as the models in Tables 3 and 4. The results are similar for both samples. Similar to the prior results we find labor market opportunities positive, significant and explaining approximately five percent of managerial compensation. The luck variable is not significant in either model. The estimated coefficients for the control variables are qualitatively similar to the models in Table 4. The variance decompositions indicates that, as in previous models, firm size, year, labor market opportunities and the CEO indicator variables contribute the most to the explained variation in managerial compensation, while the pay for luck variables contribute little. The R 2 for the models in Table 6 are lower that the R 2 for the comparable model estimated by FELSDV. This implies that being able to separately identify managerial skill makes an important contribution to explaining managerial compensation. 5.4 Compensation Measurement The methodology for reporting option grants in ExecuComp changed in 2006 (Coles, Daniel and Naveen, 2010). Before fiscal 2006, ExecuComp estimated the value of option grants using their estimates of the risk-free rate, dividend yield, volatility, time to maturity and grant date. Beginning with 2006, ExecuComp reported grant values given by the company. This 24

26 change in reporting increases the noise in the data because even if firms use the Black-Scholes model, they may use different underlying assumptions. Consequently, it is possible values are not comparable across firms and not consistent within the same firm over multiple years. Similarly, Coles, Daniel and Naveen (2010) report changes in stock awards and long-term incentive plan (LTIP) remuneration. Coles et al. estimate total compensation values, including option and stock awards, using ExecuComp s pre-fiscal 2006 methodology for remuneration given post 2006 and find a correlation coefficient of 0.90 with ExecuComp reported values. It appears that while new reporting techniques increase noise, total compensation is highly correlated with the prior ExecuComp approach. Accordingly, we re-estimated the regressions in Table 4 using the subsample 1993 through The results of the variance decomposition are reported in Panel A of Table 7. The results are qualitatively similar to full sample regressions. Skill accounts for about 48 percent of the variation in compensation, firm size explains about 12 percent, and labor market opportunities, the CEO effect and year effects also contribute to the explanatory power of the regressions. The pay for luck variables do not contribute to the explanatory power of the regressions. 5.5 Managers Taking More Than $1 in Salary and Bonus A number of CEOs have taken either zero or $1 in salary, often when their firms encounter financial difficulty. For example, in 1997 James Barksdale of Netscape took $1 in salary and bonus, compared to $100,000 the prior year. Barksdale s total 1997 compensation was $5.4 million. Following the loss of patent protection on its blockbuster drug Prozac, Sidney Taurel of Eli Lilly took $1 in salary and bonus in Even with this sacrifice, Taurel s total 2002 compensation was $10.3 million. Steve Jobs of Apple took $1 in salary in However, 25

27 Jobs also received $93.5 million in total compensation including a $43.2 Gulfstream jet (Chaffin, 2004). Altogether, 69 CEOs and 34 non-ceos took either $0 or $1 in salary and bonus at some point in our sample period. The median total compensation for these executives was $176 thousand (mean $6.3 million). We re-estimated the regressions omitting the 180 observations where managers took $0 or $1 salary and bonus. The results of the variance decomposition are reported in Panel B of Table 7. Again, skill is the most important contributor to the explanatory power of the regression, accounting for about 40 percent of the variation in compensation. Firm size explains at least 15 percent of the variation in managers compensation. Labor market opportunities, the CEO effect and the year effects also contribute to explaining the variation in compensation. The pay for luck variables do not contribute to the explanatory power of the regressions. 5.6 CEOs An issue that remains is whether our results are driven by the fact that we have examined compensation for the top management team rather than CEO compensation. To address this issue, we repeat the analysis for CEOs. We collected information on all individuals with CEO in their title from the original full sample of 107,131 observations; this yields a sample of 12,682 observations. We then determined which CEOs have moved and constructed the connected sample of CEOs following the same procedure used to develop the connected sample of managers. The connected-ceo sample has 2,121 observations on 463 CEOs at 269 firms in 120 groups. We re-estimated the regressions in Table 4 using the connected-ceo sample. The results of the variance decomposition are reported in Panel C of Table 7. The results are qualitatively similar to the full 26

28 connected sample results. CEO skill is the most important determinant of compensation. Firm size, labor market opportunities and year effects each provide some explanatory power, although the effects are smaller than for the full connected sample. The pay for luck variables again do not contribute to explaining CEO compensation. 6. Conclusion We examine the relative importance of luck, skill and labor markets in determining top managers' compensation. Previous research (Bertand and Mullainathan 2001; Garvey and Milbourn, 2006; Bizjak, Lemmon and Naveen, 2008) has examined how each of these factors affect CEO compensation. We extend this research and analyze compensation for the top management team, not just the CEO. We compare the relative explanatory power of luck, skill and labor markets for managerial compensation. We find that managerial skill is the most important determinant of managers compensation, followed by firm size and labor market opportunities, and that luck is not an important determinant of managerial compensation. Our results suggest that it is better to be good than lucky. We find evidence that pay for luck is not important compared to other factors. The OLS estimates are consistent with symmetric pay for luck. However, in models which include labor market opportunities or firm fixed effects, either with or without manager fixed effects, the coefficients for the pay for luck variables are not significant. The pay for luck variables may be proxying for the effect of labor market opportunities on compensation. The firm fixed effects capture firm characteristics that are time invariant or that evolve very slowly over time. Such characteristics could include features of firm governance, such as board size and the proportion of independent board members as well as less easily quantified firm characteristics including 27