Managerial Attributes, Incentives, and Performance

Transcription

1 Managerial Attributes, Incentives, and Performance Jeffrey L. Coles ** David Eccles School of Business University of Utah Tel: (801) Zhichuan (Frank) Li Richard Ivey School of Business University of Western Ontario Tel: (519) Abstract This paper examines the relative importance of observed and unobserved firm- and manager-specific heterogeneities in determining the primary aspects of contract design and the implications of thee associated incentives for firm policy, risk, and performance. We focus on the sensitivity of managerial wealth to stock price (delta) and the sensitivity of expected managerial wealth to stock volatility (vega) for named executive officers. First, following Graham, Li, and Qiu (2010), who apply the econometric approach of Abowd, Karmarz, and Margolis (1999) to executive pay level, we decompose the variation in executive incentives into time variant and invariant firm and manager components. We find that manager fixed effects and observable firm attributes combined supply 80-90% of explained variation in managerial delta and vega. Second, accommodating unobserved firm and manager heterogeneity and controlling for matching of executives to firms alters parameter estimates and corresponding inference on observed firm and manager characteristics, most notably board independence, firm risk, and market-to-book. Third, we explore the economic content of the estimated executive delta and vega fixed effects. There is a strong empirical association between the executive delta and vega fixed effects and attributes of managers and firms that are seen to proxy for manager human capital and risk aversion and firm marginal revenue product in application of manager skill. Moreover, larger CEO delta fixed effects are associated with higher Tobin s Q and ROA. Larger CEO vega fixed effects are associated with riskier corporate policies, including higher R&D, lower capital expenditures, and lower fixed assets, as well as higher aggregate firm risk. JEL Classifications: G3, G32, G34, J24, J31, J33, C23 Keywords: Executive compensation; Managerial incentives; Managerial ability; Human capital; Risk aversion; Investment policy; Financing policy; Firm fixed effects; Manager fixed effects; Delta; Vega **We thank seminar participants at ASU and Sreedhar Bharath, John Graham, Mike Hertzel, Si Li, Laura Lindsey, and Jiaping Qiu for helpful comments.

2 Managerial Attributes, Incentives, and Performance 1. Motivation, Literature, Framework for Analysis, and Overview Researchers continue to work to identify the economic causes and consequences of contract design. This paper uses the approach of Abowd, Karmarz, and Margolis (1999) to identify the relative importance of firm- and manager-specific characteristics in determining primary attributes of executive incentives, firm policy, firm risk, and firm performance. In our examination of contract design, we focus on the sensitivity of managerial wealth to stock price (delta) and the sensitivity of expected managerial wealth to stock volatility (vega) for named executive officers (NEOs) of U. S. corporations. For managerial compensation contracts, the intuition from the standard principalagent problem (e.g., Holmstrom (1979), Mirrlees (1976)) often is the framework for analysis and empirical design. In the model the manager can affect firm performance by application of human capital in the production function to generate cash flow. In this regard, however, managerial input is not observable, so managerial compensation depends instead on observable firm performance. The optimal sensitivity of managerial compensation or wealth to performance, delta, will be higher when the manager is better able on the margin to improve the distribution of firm payoffs. Think of the manager as providing input (such as effort) that is more effective when the manager is skilled or talented, so that effective managerial input might be represented as the product of effort and quality of effort. Absent considerations outside the model, compensation delta should be higher when the manager is less effort averse and more capable and also when the marginal revenue product of application of effective managerial input through the - 2 -

3 production function is high. 1 On the other hand, delta exposes managers to risk. Accordingly, all else equal, delta will be lower the higher is firm risk and the more risk averse is the manager in relation to the shareholders. In this last respect, the tendency for managers to forgo risky projects that have positive net present value (NPV) can be offset by compensation that is convex in payoffs while still maintaining incentive provision through delta (e.g., Myers (1977), Guay (1999)). Despite the intuitive appeal of this argument, its validity depends on the extent to which equity-based instruments, such as stock options or option-like vesting provisions, impose enough convexity in compensation to offset concavity of the risk-averse manager s utility function (Guay (1999), Ross (2004)). The effect of vega on investment and financial policy and, thus, on firm risk becomes an empirical question. There have been numerous empirical attempts to explain delta, vega, and total compensation. While the essential characteristics of firms and managers identified in the agency model are not directly observable, prior studies employ a logical set of proxies. For the marginal value of effective managerial input or human capital on firm performance, firm size, the ratio of market value to book value of assets, and R&D intensity are commonly employed. These firm characteristics are seen to represent the marginal productivity of managerial human capital in the production function. Beyond manager education (e.g., Custodio, Ferreira, and Matos (2010)), tenure, age, and board seats there are few agreed-upon proxies for managerial effort aversion and for the ability the manager applies to firm assets. Likewise, measures of managerial risk aversion have been elusive. Proxies used prior to gauge managerial risk aversion include age, gender, 1 See Holmstrom (1979) for the original logic and Coles, Lemmon, and Meschke (2007) for an illustration of specific functional forms for utility and production that would accommodate the statement

4 and tenure. Otherwise, holding managerial risk aversion constant, the relevance of managerial risk aversion at the firm level has been measured using volatility of firm stock returns, firm-specific risk, and firm size. To be more specific, focusing first on just a few of the many papers on delta, Bizjak, Brickley, and Coles (1993) find a negative relation between delta and each of total assets, market-to-book, and R&D intensity, and no relation to firm risk. Gaver and Gaver (1993) find a positive relation between the incidence of stock and option grants and ln(assets). Core and Guay (1999) find a positive relation between delta and ln(assets), ln(firm-specific risk), and ln(ceo tenure) and a negative relation to book-to-market. Himmelberg, Hubbard, and Palia (1999) find that average managerial equity ownership is positively related to ln(sales) and the ratio of PP&E to sales, unrelated to R&D intensity, and negatively related to firm-specific risk. Coles, Daniel and Naveen (2006) find a positive relation between delta and ln(sales), CEO tenure, and market-to-book, and a relation to firm risk that varies in the form of the regression specification. There is much less literature on the determinants of vega. Core and Guay (1999) find a positive relation between vega and ln(market value of assets) and R&D intensity and a negative relation with book-to-market assets. Coles et al. (2006) find a positive relation between vega and ln(sales), market-to-book assets, R&D intensity, and firm risk. Unlike vega, the level of managerial pay has been a lightning rod for attention. 2 It seems that managerial talent and performance would increase the level of pay. Higher firm risk and managerial risk aversion also would lead to higher expected pay as compensation for risk bearing. Nonetheless, Graham, Li, and Qiu (2010, p. 2) affirm that 2 With the accumulated literature being too large to describe here, see Murphy (1999) for an excellent survey of early empirical work and Graham, Li, and Qiu (2010) for description of recent contributions

5 (I)t is well known that labor market outcomes are extremely heterogeneous and that observationally equivalent individuals sometimes earn markedly different compensation. As our discussion suggests, in some ways the accumulated evidence is disappointing. Though the literature employs logical proxies for managerial and firm productivity, firm risk, and managerial risk aversion, there is substantial variation in results and explanatory power is low. Graham, Li, and Qiu (2010), as above, are quite clear on fit for pay level. For determinants of delta, the estimated coefficient of a proxy can vary in sign and significance across specifications and sample periods that vary slightly. Moreover, fit is poor, with adjusted R-squared less than 10% in specifications for delta without firm fixed effects (Gaver and Gaver (1993), Bizjak et al. (1993)). The few contributions on the determinants of vega tend to yield similar results across studies, but fit is poor with adjusted R-squared generally at best slightly better than 20%. In this context, our paper assesses the role of unobserved (to the econometrician) versus conventional observed firm and managerial characteristics as determinants of executive delta and vega. Following Graham, Li, and Qiu (GLQ, 2010), who examine the level of executive pay, we use the method of Abowd, Karmarz, and Margolis (AKM, 1999) to construct a sample of connected groups. This allows us to identify both firm and manager fixed effects and thereby decompose the variation in executive incentives into observable and unobservable time variant and invariant firm and manager components and a residual component. Our analysis yields four classes of results that comprise two contributions to the literature. First, we separate and estimate both firm and manager fixed effects while controlling for observable manager and firm attributes and time fixed effects. We find that manager fixed effects and observable firm attributes combined provide almost all of - 5 -

6 the explained variation in managerial delta and vega. For example, of the variation of delta explained by all model components together, 75.3% arises from unobserved managerial characteristics, 14.8% from observed firm characteristics, only 6.2% from observable managerial variables, 2.5% from unobserved firm features, and 1.2% from year dummies. The analysis of vega yields a similar composition of explanatory power. Second, it is widely known that when unobservable manager or firm heterogeneity is correlated with observable characteristics, regression specifications that do not explicitly account for such heterogeneity can produce biased coefficient estimates (see Kennedy (1997) on omitted variables). Our analysis indicates that this is a concern for empirical models of contract design. Including one or both of unobservable firm and manager characteristics significantly alters inference. For example, in regressions of delta and vega on firm risk, adding firm and manager fixed effects changes the signs of the estimated coefficients on firm risk from positive to negative, a result consistent with the standard agency model (Holmstrom (1979)). So as to further address endogeneity concerns, we augment fixed effects with estimated equations that represent two-sided matching of firms and executives (per Ackerberg and Botticini (2002)). This further refinement also alters inference. For example, including matching reduces substantially the strength of the association between market-to-book and executive delta. Third, in an empirical attempt to attach economic meaning to the estimated manager delta and vega fixed effects, we find a strong association between the fixed effects and manager and firm attributes that are perceived to proxy for human capital, marginal revenue product of application of that human capital, risk tolerance, and risk exposure. For example, the manager delta fixed effect is positively related to manager tenure, holding the CEO position, and directorship of the executive. The manager vega - 6 -

7 fixed effect is negatively related to age, tenure, and firm risk, but positively related to market-to-book. Finally, in further assessing economic content of the estimated fixed effects, we find that managerial fixed effects are related to firm performance, investment policy, and risk. Tobin s Q and ROA increase in the CEO delta fixed effect, which is consistent with the CEO fixed-effect component of delta capturing some element of managerial ability or human capital. Similarly, the volatility of stock returns and riskiness of investment policy increase in the CEO vega fixed effect. This is consistent with the notion that less risk-averse managers sort to high-vega contracts (Goel and Thakor (2008)) and/or higher vega induces riskier policy choices (Coles, Daniel, and Naveen (2006)). These results contribute to two dimensions of the literature. First, the paper enlarges the literature on contract design by providing the first comprehensive empirical examination of the role of unobserved firm and managerial heterogeneities in determining executive incentives. Observable characteristics of firms and particularly managers at best have modest explanatory power. Either the underlying theoretical models, such as the principal-agent problem, do not include the economic forces that determine the structure of executive incentives, or the empirical proxies for those forces are inadequate. While this conclusion seems pessimistic, we believe it represents opportunity for both empiricists to develop better proxies for primary variables in existing models and theorists to develop models that identify other economic determinants of contract design. In particular, the high relative explanatory power of unobserved managerial heterogeneity suggests that both theoretical and empirical work focusing on the attributes, role, and incentives of managers in decision making, policy selection, and performance would be relatively fruitful. Our empirical results, analysis of - 7 -

8 relative explanatory power, and suggestions for future research complement and extend the prior contributions of Bizjak et al. (1993), Guay (1999), Core and Guay (1999), Aggarwal and Samwick (1999), Himmelberg et al. (1999), Coles et al. (2006), GLQ (2010), and others on the determinants of managerial pay and incentives. Second, our empirical exploration of the economic content of the estimated manager fixed effects contributes to the growing literature on how unobservable versus observable managerial attributes affect corporate policy and performance. Insofar as the manager delta fixed effect is positively related to firm performance, our evidence extends prior work on the relation between managerial ownership and firm performance (e.g., Morck, Shleifer, and Vishny (1988), McConnell and Servaes (1990), Himmelberg et al. (1999), and Coles, Lemmon, and Meschke (2007)). Likewise, vega fixed effects are associated with riskier investment policy and higher volatility of firm stock returns. Thus, our results illuminate prior work on the relation between vega and policy choices and firm risk (Rogers (2002), Nam, Ottoo, and Thornton (2003), and Coles et al. (2006)). Our results also relate to contributions that show that managerial fixed effects affect return on assets, investment, leverage, and cash holdings (Bertrand and Schoar (2003)) and leverage (Frank and Goyal (2007)). Beyond managerial skill and risk aversion, our analysis accommodates the literature that asserts that psychological traits (Chatterje and Hambrick (2007), Malmendier and Tate (2005, 2008), Hackbarth (2008), Graham, Harvey, and Puri (2009), Grable (2000)), personalities (Kaplan, Klebanov, and Sorensen (2008)), and functional background (e.g. Hambrick (2007)) influence firm policies and performance. The paper proceeds as follows. Section 2 discusses the empirical methodology. Section 3 describes the data, variables, and summary statistics. Section 4 examines the - 8 -

9 role of firm and manager attributes not observed by the econometrician in determining executive incentives. Section 5 presents evidence on the empirical association between the manager delta and vega fixed effects and manager and firm attributes that proxy for human capital, productivity of managerial input, risk tolerance, and risk exposure. Sections 6 and 7 examine the effect of manager delta and vega fixed effects on firm performance and policy, respectively. Section 8 concludes. 2. Estimation Methodology Our objectives require that we quantify how much of variation in executive incentives is attributable to observable time variant firm effects, observable time variant manager effects, time invariant firm fixed effects, time invariant manager fixed effects, and year effects. Towards this end, we employ the group connection method of AKM (1999). Because this approach is relatively new, we provide a brief description herein. For illustration and more detail see GLQ (2010), who apply AKM to executive pay level. The simplest way to include fixed effects is to create a dummy variable for each unique combination of manager and firm (i.e. for each employment spell). In Execucomp data, each employment spell has a unique firm-executive ID: CO_PER_ROL. This approach has been used in the economics literature by AKM (1999), Schank, Schnable, and Wagner (2007), and Munch and Skaksen (2008). The spell method uses the full sample and addresses possible omitted variable bias, but it can only estimate the joint firm and manager effects and does not disentangle the two. Note that simply using firm dummies and manager dummies is insufficient for separating the effects. If a firm has no managerial turnover, the two effects are perfectly collinear. This does suggest one way forward, which is to restrict the sample to cases in - 9 -

10 which the firm has at least one manager who has moved from one company to another. Bertrand and Schoar (2003) use this approach to examine whether unobserved managerial heterogeneity has power to explain return on assets, investment, leverage, and cash holdings. One potential difficulty with the mover dummy variables (MDV) approach is that movers may be significantly different from the non-movers, resulting in selection bias and limiting the generalizability of results. Furthermore, the sample that can be studied is usually quite small due to infrequent managerial turnover. Or, in case of a large sample, this method may be computationally infeasible because it requires inverting a covariate matrix with many dummy variables. Relative to the MDV and spell approaches, the method of Abowd, Karmarz, and Margolis (1999) achieves separate identification of the firm and manager fixed effects. First, begin with an arbitrary manager and include all the firms for which he or she has ever worked. Then include all the managers who have ever worked for those companies. Next, continue adding all other firms for which any of these managers has ever worked. Repeatedly add all the managers in those firms until no more managers or firms can be added to the current group. Repeat the above steps for the next group and continue until all data are exhausted. The final sample will contain not only all the movers but also non-movers as long as they work in firms that have hired at least one mover. In this way, for example, the firm fixed effect for a non-moving manager can be estimated if any executive of that firm moved, which in turn allows estimation of the fixed effect for any non-moving manager at that same firm. AKM (1999) prove that such connectedness is necessary and sufficient to separately identify firm and individual fixed effects in a group-connected sample. This approach restricts sample attrition to executive-years in which a firm employs the same group of executives for the entire sample period. GLQ

11 (2010) use the AKM method to good effect in their analysis of the explanatory power of firm and manager fixed effects for total compensation levels for top executives. To reduce concerns about selection bias and to increase sample size, we report results using the AKM method. In the Appendix (Robustness) we estimate primary specifications using the MDV and spell methods to check robustness of our results based on AKM. 3. Assembling the Sample We begin with all executive-year observations from Execucomp for firms with fiscal years ending from 1993 to For a firm-year this includes up to five NEOs. We exclude any observations without matching CRSP and Compustat North America data and, consistent with prior literature, we eliminate financial services and utility firms from the sample. The full sample consists of 109,995 executive-year observations. Of course, the usable sample will be smaller for the AKM and MDV methods and some specifications use fewer observations due to one or more missing data values. We follow Guay (1999) and Core and Guay (2002) to calculate accumulated delta and vega for each executive on an annual basis. 3 Delta is defined as the change in the dollar value of the executive s wealth for a one percentage point change in stock price. 4 Vega is the change in the dollar value of the executive s wealth for a 0.01 change in the annualized standard deviation of stock returns. Guay (1999) shows that option vega is 3 This generally is consistent with numerous recent papers, including Yermack (1995), Hall and Liebman (1998), Aggarwal and Samwick (1999), Cohen, Hall, and Viceira (2000), Datta, Iskandar-Datta, and Raman (2001), Rajgopal and Shevlin (2002), and Coles et al. (2006). 4 We repeat our analysis using the Jensen and Murphy (1990) measure of executive wealth change per $1000 change in shareholder wealth. The estimated coefficients and composition of fit generally are similar to those reported in the tables. One exception is that the sign on ln(net assets), which is positive in Panel A of Table 2, becomes negative when using the alternative construction of delta

12 many times higher than stock vega. Therefore we use vega of the option portfolio to measure the total vega of the stock and option portfolio. 5 Please refer to the Appendix (Variable Definitions) and tables for detailed definitions of these and other variables. Maximal sample size varies by estimation method. After eliminating observations with one or more missing primary data items (delta, vega, and market-tobook of assets), the spell method can employ up to 104,260 observations, including 2,233 unique firms and 24,631 unique executives. Using MDV reduces the maximal sample to 9,816 executive-year observations, represented by 1,284 firms and 1,454 movers. In contrast, the AKM approach generates connected subsamples that aggregate to 64,245 executive-year observations arising from 1,302 firms and 15,590 managers. 6 Table 1 presents summary statistics on the incentives of the top executives, executive characteristics, firm characteristics, and investment and financing measures. Consistent with previous literature (Guay (1999), Core and Guay (1999), Coles et al. (2006)), we winsorize delta, vega, and the market-to-book ratio at the 1 st and 99 th percentiles. Mean (median) delta is $206,674 ($38,896) and mean (median) vega is $39,851 ($7,969) in the full sample. The full (spell) sample and MDV sample differ in that movers have shorter tenure and higher incentives than the non-movers. 7 Otherwise, the observable characteristics of the MDV and spell samples are similar. Such similarity, however, may not extend to the unobservable firm and manager features. For example, 5 Knopf, Nam, and Thornton (2002), Rajgopal and Shevlin (2002), and Coles et al. (2006), among others, adopt the same approximation. 6 Some of the secondary variables, such as age and tenure, are often missing. To maximize sample size we define indicator variables that indicate whether the variable is missing (= 1, otherwise = 0), and set the variable itself equal to zero when the indicator equals 1. This procedure follows a number of recent papers, including Himmelberg et al. (1999) and Byoun (2008). 7 The differences in delta and vega are likely to arise because movers in the Execucomp data are usually higher-ranked executives, such as CEOs, in larger firms. When managers of lower rank or in smaller firms switch companies, they are less likely to show up in the data again (i.e. the top-five executives in the new company). These managers are not identified as movers in the sample and thus are the reason for some of the sample attrition in the MDV and AKM samples

13 unobservable managerial talent and risk aversion, of central interest in this paper, may differ significantly between movers and non-movers even if their observable characteristics appear similar. Based on the figures in Table 1, this appears to be less of a potential issue for the sample of connected groups. To avoid selection bias, our primary approach is to employ the AKM method to include all listed named executives, both movers and non-movers, in each firm. Again, we use the MDV and spell methods as a robustness check. We use the estimated manager fixed effects to examine firm performance and various other corporate outcomes. We measure performance with Tobin s Q and return on assets (ROA). The policy variables we consider are: (1) R&D, defined as research and development expenditures scaled by net assets; (2) CAPEX, defined as net capital expenditures (capital expenditures less sales of property, plant, and equipment) scaled by net asset; (3) Leverage, defined as total book debt divided by market value of assets (i.e. market leverage); and (4) PPE is investment in property, plant, and equipment scaled by net asset. The effect of these policy variables should be captured in stock return volatility (Firm Risk), which we define as the ranking (CDF) of the standard deviation of one-year daily stock returns. 4. Executive Incentives and Unobservable Firm and Manager Heterogeneity The literature on the determinants of executive incentives and pay level suffers from substantial variation in results and low explanatory power. Summarizing the literature on executive pay level, GLQ (2010) note that pay level varies widely for executives who appear equally-qualified and work in similar firms. Based on this premise, GLQ (2010) assess the importance of such unobserved attributes by

14 decomposing the variation in executive pay level into various components. They find that time-variant firm variables and especially manager fixed effects capture more than half of the explained variation in the logarithm of the level of executive pay. Like compensation levels, for delta and vega as dependent variables the estimated regression coefficients on observable characteristics of firms and managers vary in sign and significance across studies. Moreover, aggregate explanatory power for the righthand-side variables tends to be poor. For contract design, given the importance of delta and vega in determining managerial incentives, we perform a similar analysis for these two aspects of managerial incentives. Firm and manager fixed effects represent characteristics that are potentially observable to the contracting parties but are unobservable to the econometrician. Note that, for the unobserved factor to affect the contract, one or both contracting parties must have at least some information on that attribute. Write delta or vega for manager j at time t, y jt jt or jt, as: y F ˆ M ˆ ˆ ˆ ˆ (1) jt it jt i j t jt where the right-hand side is comprised of observable time-variant firm characteristics ( F ˆ it ), observable time-variant manager characteristics ( M ˆ jt ), firm fixed effects ( ˆi ), manager fixed effects ( ˆj ), year fixed effects ( ˆ t ), and residuals ( ˆ jt ). Hat denotes an estimate of a parameter or a vector of parameters. 4.1 Observable Firm/ Manager Characteristics as Determinants of Delta and Vega We follow existing literature in selecting the observable characteristics that determine managerial incentives (e.g., Bizjak et al. (1993), Core and Guay (1999), Guay (1999), Aggarwal and Samwick (1999), Coles et al. (2006)). Specifically, firm characteristics from these studies include market-to-book (assets), board independence,

15 surplus cash, leverage, R&D intensity, firm risk, capital and equipment expenditures, and firm size. Manager characteristics include tenure in the company, age, gender, whether the manager is the CEO, and whether the manager is a member of the board. 4.2 Determinants of Delta and Vega: Estimates Based on the AKM (1999) Method Our primary approach to quantifying the absolute and relative importance of different factors in determining delta and vega is to apply the AKM regression approach to the connectedness sample. In addition to various combinations of manager and firm fixed effects, all specifications include year fixed effects to capture systemic effects, such as regulatory changes and macro shocks, which potentially affect delta and vega of all executives. Table 2 contains the regression results. Consider wealth-performance sensitivity first. Specification (1) in Panel A is a pooled OLS regression without firm or manager fixed effects. The adjusted R-squared for this regression is 25%, which is similar to the higher adjusted R-squareds found in previous studies, such as Himmelberg et al. (1999). We include firm fixed effects in specification (2) to control for unobservable differences across firms, such as unobserved core competencies, firm culture, or other unobserved aspects of the contracting environment. The adjusted R-squared increases to 37%, suggesting unobservable firm heterogeneity is a significant component in explaining delta. Specification (3) uses manager fixed effects instead. 8 The adjusted R-squared is 73%, a 48% absolute increase over pooled OLS, and a 36% increase compared with the incremental improvement in adjusted R-squared from firm fixed effects. When we include both unobservable firm- 8 Time-invariant or slow changing manager heterogeneity, such as latent managerial ability and risk aversion, will be captured by manager fixed effects. For example, Iranzo, Schivardi, and Tosetti (2008), Abowd et al. (1999) and Abowd, Lengermann, and McKinney (2003) use person fixed effects to proxy for employee human capital. It is also possible that the ability may change over time. We model time-variant ability by including job tenure and age

16 level and manager-level heterogeneities the adjusted R-squared increases very slightly to 74%. Unobservable managerial attributes have substantial explanatory power in determining managerial wealth-performance-sensitivity. In Panel B, with vega as the dependent variable, the adjusted R-squared increases from 28% in pooled OLS to 40% and 45% after including firm and manager fixed effects, respectively. Including both manager and firm fixed effects in the regression improves the adjusted R-squared by a small amount to 47%. This first pass indicates that for executive delta and vega both unobserved manager and firm characteristics provide large additional explanatory power. Of the two, it appears that the former provides a larger enhancement to fit than the latter. To provide a quantitative comparison of the relative economic significance of the classes of variables, we follow GLQ (2010) to decompose variation of the dependent variable (delta or vega) into five estimated components and the unexplained remainder. Based on equation (1), model R-squared can be decomposed as: R 2 cov( yˆ, ) cov( ˆ ˆ ˆ ˆ ˆ jt y jt Fit M jt i j t, y jt ) var( y ) var( y ) jt cov( F ˆ, ) cov( ˆ, ) cov( ˆ, ) cov( ˆ, ) cov( ˆ it y jt M jt y jt i y jt j y jt t, y jt ) var( y ) var( y ) var( y ) var( y ) var( y ) jt jt jt jt jt jt Panels C and D in Table 2 present the covariances between dependent variables (delta and vega, respectively) and each of the components, normalized by the variance of dependent variable. These percentages are the fractions of the model sum of squares attributable to particular components. For example, applying the AKM method to delta with both manager and firm fixed effects (specification (4) of Panel A), manager fixed effects, firm fixed effects, observable manager characteristics, firm characteristics, and

17 year effects account for proportions 0.61, 0.02, 0.05, 0.12, and 0.01 of total variation of delta, with proportional residual unexplained variation of 0.19 (Table 2, Panel C). Normalized by variation of delta explained by the model (0.81 = ), the five classes of variables contribute 75.31% (0.61/(1-0.19)), 2.47% (0.02/(1-0.19)), 6.17%, 14.81%, and 1.23% of model R-squared, respectively. Panel D of Table 2 provides similar calculations for vega and the five variable classes. Based on specification (4) in Panel B of Table 3, proportions of explained variation of vega attributable to these five components separately are 60.66% (0.37/(1-0.39), 4.92%, 9.84%, 19.67%, and 4.92%, respectively. Overall, among the candidate classes of explanatory variables, unobserved timeinvariant manager characteristics (i.e., manager fixed effects) play far and away the most important role in providing explained variation in delta (75.31%) and vega (60.66%). Unobserved manager attributes and observed firm characteristics combined provide more than 90% of explained variation in delta and more than 80% of explained variation in vega. 4.3 Two-Sided Matching of Executives and Firms Empirical designs to explain contract formation typically regress contract choice on observed principal, agent, and firm (or task) characteristics. If some of these characteristics are unobserved, then estimated coefficients on the observed characteristics may be misleading. When omitted relevant variables or unobserved factors that cause endogeneity are time constant or slow moving, then fixed effects provide a simple solution. On the other hand, should the unobserved factors vary through time, fixed effects is not a solution for endogeneity or bias from omitted variables. Other methods to extract causation, such as instrumental variables, are required

18 In our empirical context, one likely source of time-variation is endogenous matching or sorting (of agents to firms, for example). Following Ackerberg and Botticini (2002), if one agent contracts with multiple firms or one firm contracts with multiple agents, and unobserved characteristics are constant across these contracts, panel techniques can address the endogeneity problem. In particular, the use of firm and manager fixed effects with explicit consideration of two-sided matching, can ameliorate concerns about omitted variables and various sources of endogeneity. In terms of wealth-performance sensitivity, one selection effect would be for high-ability workers to co-locate with high incentives (Lazear (1996)). It seems natural to match high managerial talent with exceptional professional opportunity and then maximize the value of that match with high delta. 9 Likewise, risk tolerant managers are likely to select firms with high risk and be subjected to higher risk through high delta. In the first stage of our procedure, we estimate firm risk as a function of proxies for risk aversion, specifically executive gender and age, and market-to-book as a function of proxies for managerial talent, specifically tenure, age, and whether the executive serves as a director of the firm. (We discuss these proxies in more detail in Section 5 below.) In matching firms and executives, we obtain: MTB xTenure xAge 0.100xDirector xDage xDtenure noise it ( 22.90) jt jt jt jt jt ijt xFemale xAge xDage noise it j jt jt ijt with t-statistics in parentheses and R 2 = 0.02 in both equations. 9 Lazear (1996) studies the impact of piece rates on the performance of workers who install auto windshields. He documents that productivity rose by 35% through adopting piece rates (incentives), with wages increasing by 12%. By using the turnover data which documents that the less able left the plant and more talented workers replaced them, the paper concludes that one third of the improved performance can be attributed to selection effects in this case. Note that Lazear (1996) and similar studies such as Ferrall and Shearer (1999) and Paarsch and Shearer (2000) essentially use worker-fixed-effects methodology to isolate worker selection. Our analysis is similar in spirit

19 In the second stage, we insert the fitted values in place of the actual values on the right-hand side of the equations that explain delta and vega. On the right-hand side we continue to include firm and manager fixed effects. We also exclude some missing data dummies (e.g., Dtenure) so as to achieve identification and thus inclusion of some of the explanatory variables (e.g., Tenure) used in the matching equations. Panels A (delta) and B (vega) of Table 2 report the results in column (5). For both delta and vega, fit is quite similar to the specifications that use fixed effects and do not control for two-sided matching (model (4) in each case). Thus, it is not surprising that attribution of explained variation to the five components, though not reported here, is very similar to that for model (4) (in Panels A and B) as reported in Panels C and D. Once again, manager fixed effects provide much of the explained variation, with observable firm characteristics coming in a distant second. 4.4 Statistical and Economic Inference for Observable Attributes To this point, we have used fixed effects and instruments for matching to assess whether standard empirical designs using observed firm and manager attributes do well in explaining contract design. The significant improvement in the explanatory power in the fixed effect regressions suggests that unobservable differences in firms and managers play an important role in determining executive incentives. While increasing explanatory power is a worthy goal, we now assess whether inferences about the economic implications of observable attributes are altered when we control for unobserved firm and managerial heterogeneity and sorting effects. We find that in several prominent instances, including fixed effects and matching changes the magnitude, sign, and significance of coefficients

20 For example, in specification (1) in Panel A of Table 2, cross-sectional analysis provides a positive and significant estimate of the relation between delta and firm risk. This result on the correlates of delta is consistent with numerous previous findings (e.g., Core and Guay (1999) and Coles et al. (2006)). If the standard agency problem is the primary explanation for compensation structure and suitable controls are included, lower delta will impose less risk on the manager, which is particularly important in a firm with high risk, so the sign would be negative. Note that the sign on risk (or fitted risk) does indeed become negative and significant as soon as firm and/or manager fixed effects are included (specifications (2), (3), (4), and (5) in Panel A). This is a result that is quite different from the pooled OLS result without fixed effects but is consistent with Aggarwal and Samwick (1999, 2003) and Himmelberg et al. (1999), who report a negative coefficient on risk in some specifications. A second example is the coefficient on board independence. Experiments that regress structure on structure arise naturally from the notion that the firm is an incentive system (Holmstrom and Milgrom (1991)). Are two different mechanisms, managerial compensation and board independence, for example, substitutes or complements in production? Restated, if a relatively independent board fulfills the monitoring function, is it necessary to expose the management team to high pay-performance sensitivity? Again, the empirical evidence is mixed. Denis and Sarin (1999), Shivdasani and Yermack (1999), and Coles, Daniel, and Naveen (2008) estimate a negative relation between managerial ownership and the proportion of outsiders on the board. In contrast, Ryan and Wiggins (2004) and Davila and Penalva (2006) find a positive relation. Model (1) (Panel A, Table 2), which has no fixed effects, delivers a significantly negative coefficient on board independence. In contrast, including one or both of firm and

21 manager fixed effects changes the sign to positive (Models (2) (5)), and the coefficient is at least marginally significant in two specifications ((2) and (5)). Including fixed effects and matching has other implications. In Panel A of Table 2, a comparison of models (1)-(3) versus (4) and (5) shows a reduction in the absolute magnitude and significance of the coefficients on market-to-book, executive tenure, and R&D intensity. Also, comparing (4) with (5), accounting for sorting of managers to firms reduces the size and significance of the coefficients on R&D and market-to-book. In specifications with vega as the dependent variable, Panel B of Table 2 indicates that adding firm and manager fixed effects and including matching most often implies attenuation of the coefficient estimate towards zero and a reduction in statistical significance of the estimate. For example, models (2) (4) yield a significantly negative coefficient on firm risk. Including matching of executives to firms, as in model (5), yields a coefficient on risk that is insignificant. Panel B also indicates that fixed effects and matching attenuate and reduce the significance of the coefficients on executive age, R&D, and market-to-book. Regardless of specification, for both delta and vega the coefficient on logarithm of net assets is positive and significant, as in Coles et al. (2006). Overall, including manager and firm fixed effects and matching affects regression coefficients on primary explanatory variables. In estimating the marginal effects of observable determinants of contract design and in assessing causation it is likely to be important both to control for unobserved heterogeneity of firms and managers, with fixed effects, for example, and to account for two-sided matching of firms and executives. 4.5 Robustness: Estimates Based on the Spell and MDV Methods To test the robustness of the AKM results in Table 2, we perform our analysis using both the spell and MDV methods. Keep in mind that MDV is based on a small

22 sample and may suffer from selection bias. On the other hand, using the full sample prohibits identification of both firm and manager fixed effects, so we employ spell fixed effects instead. The results are contained in the Appendix (Robustness) in Tables A1 (MDV) and A2 (spell). The overall conclusions about the sources of explained variation are similar, though at least one specific difference is noteworthy. Moving first to the MDV estimates, which are based on 9,816 observations for executives that switch companies, consider the explanatory share figures for delta in Panel C of Table A1 (based on specification (4) in Panel A). Coming in first in the explanatory horse race once again is the manager fixed effects with a 54.32% share of explained variation in delta. Unlike the AKM results, however, second place belongs now to the firm fixed effects (17.28%), which just edge out observable firm characteristics (16.05%) in third place. Observed managerial attributes come in fourth at 9.88%. MDV suggests that the explanatory power of observable firm characteristics for executive delta is lower than indicated by AKM. For vega, the results for share of explained variation across classes of independent variables are similar for MDV versus AKM. Panels A (delta) and B (vega) of Table A2 report the results for spell fixed effects in the full sample. The adjusted R-squared for the pooled OLS regression without firm, manager, or firm-manager spell fixed effects (specification (1) in Panel A) is 23%. Including firm fixed effects only (specification (2)) increases adjusted R-squared to 36%. Specification (3) uses only manager fixed effects instead. The adjusted R-squared is 74%, a 51% absolute increase over the pooled OLS, and a 38% increase over the increment from the firm fixed effects alone. Spell fixed effects deliver adjusted R-squared of 75%. In Panel B of Table A2, with vega as the dependent variable, the adjusted R-squared

23 increases from 26% in pooled OLS to 38% and 43% after including firm and manager fixed effects, respectively, and to 45% for spell fixed effects. 4.6 Determinants of Executive Pay Level: AKM (1999) Method To frame and further check our results on delta and vega using the AKM method, we estimate executive pay level as a function of our variables and compare our results to those in GLQ (2010). These calculations also allow us to employ the estimated manager pay-level fixed effects in our analysis of firm performance. Table A3 in the Appendix (Robustness) contains the results for the AKM method applied in our data to executive pay level. Moving from specifications that use no fixed effects to those that include one or both of manager and firm fixed effects, several coefficient estimates change in magnitude (Panel A) and fit improves substantially (Panel B). The coefficient estimates on R&D intensity, the CEO indicator, and firm risk differ across specifications. Unlike GLQ (2010), however, our estimates on firm size do not decline markedly as additional fixed effects are included. In terms of explained variation in executive pay level, as in GLQ (2010) manager fixed effects and observable firm characteristics come first and second Summary and Directions for Future Research Using any of our three estimation approaches, we consistently find that manager fixed effects, first and foremost, and then observable firm characteristics account for the bulk of explained variation in executive incentives. In terms of the important economic determinants of delta and vega, it appears that the standard proxies for managerial skill and risk aversion are inadequate and that perhaps some of these characteristics are 10 The specifications in Table A3 are similar to those in GLQ (2010). The primary differences are that as independent variables GLQ (2010) also include ROA, lagged ROA, and lagged market-to-book and we include board independence and institutional ownership. Excluding our additional variables and including the GLQ variables in our regression model generates results that differ little from those in Table A

24 captured instead by manager fixed effects. Moreover, our analysis indicates that omitted variable bias is likely to be a concern for empirical models of managerial incentives. These results suggest limitations to conventional empirical approaches to managerial compensation but, at the same time, evoke at least three corresponding potential opportunities for improvement. First, supposing that the standard Holmstrom (1979) agency problem is a primary determinant of the structure of managerial compensation, it appears that our current empirical proxies for managerial risk aversion and talent and the marginal revenue product of managerial effort and skill in production are inadequate. Recent work towards improved measures includes Custodio, Ferreira, and Matos (2010) who, based on detailed information on CEOs past industry background, past experience as top executive, and educational training, construct an index of general managerial ability. Second, based again on the supposition that the agency model captures essential economic aspects of the organization design problem, progress may be possible using a structural model (containing the agency problem) to provide more appropriate specifications that researchers can estimate or calibrate with data. Coles, Lemmon, and Meschke (2007) and Coles, Lemmon, and Wang (2008) do this with some success. Third, it is likely that other forces aside from those in the agency problem are germane. Attributes of managers that are likely to be relevant include social capital, personality, other psychological traits, religion, functional experience, education, and genetic makeup. Developing new models of how managerial attributes affect firm policy and performance and the contractual structure of managerial compensation is likely add to our understanding of the determinants and implications of organization form

25 5. The Association between Manager Delta and Vega Fixed Effects and Manager and Firm Attributes We now empirically assess the economic content of the estimated manager delta and vega fixed effects. In this section we explore the extent to which the estimated manager delta and vega fixed effects are empirically associated with manager and firm attributes. In Section 6 we examine the relation between the estimated fixed effects and firm policy and performance. Figures 1 and 2 present the distributions of executive delta and vega fixed effects as estimated by the AKM method in the connectedness sample (Table 2, Model (4), Panel A for delta and Panel B for vega). Note that, under the AKM method, the means of the fixed effects in each connected group are adjusted to zero so that they can be compared across groups. Figures 1 and 2 indicate that managers exhibit substantial heterogeneity in attributes that affect contract design but which are unobserved by us as the econometricians. The manager delta fixed effect for manager delta has a standard deviation of 0.56 ($millions for a one percent change in stock price), the standard deviation of manager vega fixed effects is 0.14 ($millions per 0.01 change in standard deviation of stock return), and both are approximately normally distributed. What are the correlates of the manager delta and vega fixed effects? In Table 3 we provide both univariate (Panel A) and multivariate (Panel B) results. We include firm dummies in the regression specifications to control for any selection effects not captured in the matching equations. We use tenure in the firm, whether the executive is CEO, and serving on the board as indicators of ability. Presumably increased tenure in the firm is associated with accumulation of both general and firm-specific human capital. An executive who serves as CEO, being the winner of the succession tournament, is more