Accounting and stock price performance in dynamic CEO compensation arrangements.
I. INTRODUCTION
Prior research on the role that accounting measures of performance play in determining chief executive officer (CEO) compensation has yielded two primary conclusions. First, increases in accounting performance positively and significantly affect current CEO compensation,
We examine whether these conclusions continue to hold in the long run. Theory suggests that firms can mitigate agency problems by tying CEO pay to multiple periods of performance (Fama 1980; Lambert 1983; Rogerson 1985; Murphy 1986; Gibbons and Murphy 1992), and empirical evidence shows that CEOs do engage in long-term relationships with their firms (Warner et al. 1988; Weisbach 1988; Murphy and Zimmerman 1993; DeFond and Park 1999). Boschen and Smith (1995) show that the long-run effects of unexpected stock price performance on CEO compensation are substantially larger than the current-period effects. However, we currently know very little about how unexpected accounting performance affects CEO compensation in the long run.
Our results show that accounting performance and stock price performance have different long-run effects on CEO compensation. Like prior research, we find that unexpectedly good accounting performance is initially associated with higher CEO compensation. Surprisingly, however, we find that this initial increase is offset by lower pay in the future. Our results suggest that, over the long run, the CEO receives essentially no reward for an unexpected increase in accounting performance. In contrast, the CEO receives a substantial reward over the long run for an unexpected increase in stock price performance. Our evidence that the two main performance measures in compensation arrangements both have important multiperiod dynamics--particularly the puzzling result that better accounting performance is associated with lower future CEO compensation--suggests that future research on CEO incentives must address the multiperiod effects of performance on CEO pay arrangements.
Our analysis reveals that the traditional pay-performance model, based on first-differenced compensation, does not adequately capture the long-run effects of firm performance on CEO compensation. We show how researchers can adapt the vector autoregression (VAR) model that is widely used in the analysis of time series data (Hamilton 1994) to effectively capture these long-run relations. Finally, we conclude from our robustness tests that compensation models should allow for at least three lags of compensation and firm performance in order to fully capture the dynamics.
The paper proceeds as follows. In the next section, we review the findings of the prior literature. Section III describes the sample of firms we use, defines the variables, and presents descriptive statistics for the major variables. Section IV presents the empirical results that we obtain from estimating several versions of the dynamic pay-performance model. Section V summarizes and offers some concluding comments.
II. BACKGROUND AND PRIOR RESEARCH
Implied Dynamics of Traditional Compensation Models
Multiperiod agency models suggest that firms can mitigate both the moral hazard problem (Lambert 1983; Rogerson 1985; Murphy 1986) and the adverse selection problem (Fama 1980; Gibbons and Murphy 1992) by tying employee compensation to multiple years of performance. Relatively low turnover rates among chief executive officers (Warner et al. 1988; Weisbach 1988; Murphy and Zimmerman 1993; DeFond and Park 1999) indicate that chief executives do, in fact, have long-term relationships with their firms. However, empirical compensation researchers traditionally model changes in CEO compensation as a function of unexpected firm performance in the current period only (e.g., Lambert and Larcker 1987; Jensen and Murphy 1990; Sloan 1993). (1)
We present a simplified version of this traditional model (Lambert and Larcker 1987), with one performance measure, to show how compensation responds to unexpected firm performance in both the short run and the long run:
(1) [DELTA][C.sub.t] = [[beta].sub.X][[X.sub.t] - E([X.sub.t])] + [z.sup.C.sub.t],
where [C.sub.t] and [X.sub.t], are compensation and firm performance in period t, E is the expectation operator, and [Z.sup.C.sub.t] is the unexpected change in compensation. The response of compensation in period t to unexpected firm performance in period t (i.e., the contemporaneous response) is [[beta].sub.X]. (2) Previous research has focused on this single parameter, [[beta].sub.X], as the measure of the pay-performance relation and has ignored the effects of unexpected firm performance on compensation over the long run. Although the model in Equation (1) does not explicitly estimate the long-run response of compensation to unexpected firm performance, the structure of the model implies that pay raises from unexpected firm performance remain permanently in the level of compensation. For example, if a CEO receives an extra $100 in period t as a reward for his performance in period t, the model in Equation (1) predicts that he will also receive $100 in period t + 1, another $100 in period t + 2, and so on. Over a ten-year period, the CEO would receive a total of $1,000 for his performance in period t.
To show why the model above implies that pay raises remain permanently in compensation, we rewrite Equation (1) in levels, with unexpected firm performance denoted as [Z.sup.X.sub.t] (i.e., [[X.sub.t] - E([X.sub.t])] = [Z.sup.X.sub.t]):
(2) [C.sub.t] = [C.sub.t-1] + [[beta].sub.X][Z.sup.X.sub.t] + [Z.sup.C.sub.t].
Then we write similar expressions for compensation in later periods, written in moving-average form, to illustrate the pattern that develops over time:
[C.sub.t] = [C.sub.t-1] + [[beta].sub.X][Z.sup.X.sub.t] + [Z.sup.C.sub.t]
[C.sub.t+1] = ([C.sub.t-1] + [[beta].sub.X][Z.sup.X.sub.t] + [z.sup.C.sub.t]) + [[beta].sub.X][Z.sup.X.sub.t+1] + [[z.sup.C.sub.t+1]
[C.sub.t+2] = ([C.sub.t-1] + [[beta].sub.X][Z.sup.X.sub.t] + [Z.sup.C.sub.t] + [[beta].sub.X][Z.sup.X.sub.t+1] + [Z.sup.C.sub.t+1]) + [[beta].sub.X][Z.sup.X.sub.t+2] + [Z.sup.C.sub.t+2]
[C.sub.t+k] = ([C.sub.t-1] + [[beta].sub.X][Z.sup.X.sub.t] + [Z.sup.C.sub.t] + [[beta].sub.X][Z.sup.X.sub.t+1] + [Z.sup.C.sub.t+1] + [[beta].sub.X][Z.sup.X.sub.t+2] + [Z.sup.C.sub.t+2] + ... + [[beta].sub.X][Z.sup.X.sub.t+k-1] + [Z.sup.X.sub.t+k-1])
The response of compensation in any period t + k, to unexpected firm performance in period t, is simply the partial derivative of [C.sub.t+k] with respect to [Z.sup.X.sub.t]. We say that the effect of unexpected firm performance on compensation is permanent when these derivatives are non-zero and identical for all periods. For the model above, this is clearly the case, since:
[??][C.sub.t]/[??][Z.sup.X.sub.t] = [??][C.sub.t+1]/[??][Z.sup.X.sub.t] = [??][C.sub.t+2]/[??][Z.sup.X.sub.t] = ... = [??][C.sub.t+k]/[??][Z.sup.X.sub.t] = ... = [[beta.sub.X].
The traditional compensation model in Equation (1) constrains the coefficient on prior compensation, [C.sub.t-1], to equal 1.0, as shown in Equation (2). However, if we relax this constraint, and allow the coefficient on [C.sub.t-1] to be positive, but less than 1, then compensation responds to unexpected firm performance quite differently. We denote the coefficient on [C.sub.t-1] as [rho] and rewrite Equation (2) as;
(2') [C.sub.t] = [rho][C.sub.t-1] + [[beta].sub.X][Z.sup.X.sub.t] + [Z.sup.C.sub.t].
We then follow the same process as above (i.e., we write the moving-average form for each [C.sub.t+k] and take partial derivatives). However, now the responses of compensation to unexpected firm performance are no longer constant across periods. In fact, the derivatives showing the effects of unexpected firm performance on future CEO compensation (i.e., [??][C.sub.t+k]/[??][Z.sup.X.sub.t] = [[rho].sup.k][[beta].sub.X] for any k) approach zero as k becomes large. In this case, we say the effects of unexpected firm performance remain in compensation levels only temporarily. For example, if [rho]= 0.5, then a CEO receiving an extra $100 in period t as a reward for his performance in period t would receive only $50 in period t + 1, $25 in period t + 2, and so on, for a total of only $200 over a ten-year period.
Boschen and Smith (1995) is the first study to model the long-run effects of firm performance (in their case, stock price performance) on CEO compensation. They show that, although the long-run response of CEO compensation to unexpected stock price performance is not permanent, it is long-lived, and the contemporaneous portion of the response is small relative to the long-run response. Thus, Boschen and Smith (1995) conclude that modeling only the contemporaneous portion of the compensation response misrepresents the long-run relation between CEO compensation and stock price performance. Their findings raise an important question about whether the contemporaneous relation between CEO compensation and accounting performance is also a misleading indicator of the long-run relation.
The Role of Accounting Performance in CEO Compensation
There are three non-mutually exclusive hypotheses as to why CEO compensation contracts include accounting performance in addition to stock price performance (Bushman and Smith 2001). These are: (1) the direct incentive hypothesis, in which accounting performance directly encourages work effort, (2) the filtering hypothesis, in which accounting performance filters out common noise in stock price performance, and (3) the effort allocation hypothesis, in which accounting performance shifts the CEO's work effort toward, or away from, a specific subset of actions. Below we discuss the implications of each of these hypotheses for the empirical relation between CEO pay and accounting performance.
The direct incentive hypothesis is based on the assumption that accounting performance provides another noisy signal about the CEO's effort, in addition to stock price performance. In this case, linking compensation to accounting performance allows the firm's owners to more closely tie the CEO's compensation to his work effort. Thus, this hypothesis implies a positive relation between accounting performance and CEO compensation. This positive relation does not require that accounting performance be less noisy than stock price performance. The essential requirement is that accounting performance contains independent information on CEO work effort. (3)
The filtering hypothesis is based on the assumption that the noise component in accounting performance is correlated with the noise component in stock price performance. In this case, linking compensation to accounting performance allows the firm's owners to partially or fully filter the noise from stock price performance. As with the direct incentive hypothesis, the goal is to more closely tie the CEO's compensation to his work effort (Banker and Datar 1989; Sloan 1993). This hypothesis predicts that the relation between CEO pay and accounting performance depends on the sign of the correlation between the noise components of accounting and stock price performance. For example, if the noise component in accounting performance is positively correlated with the noise component in stock price performance, then the filtering hypothesis implies a negative relation between accounting performance and CEO compensation.
The effort allocation hypothesis is based on the assumption that accounting performance only captures a subset of the CEO's actions, but stock price performance captures the effects of all CEO actions. In this case, linking compensation to accounting performance allows the firm's owners to provide the CEO with incentive to emphasize particular types of work effort (Bushman and Indjejikian 1993; Lambert 1993; Feltham and Xie 1994; Lambert 2001). For example, the firm's owners can provide an additional incentive for the subset of actions captured by accounting performance (above and beyond the incentive provided from their impact on stock price performance) by imposing a positive relation between accounting performance and CEO compensation. Alternatively, a negative relation between accounting performance and CEO compensation reduces the incentive for the subset of actions captured by accounting performance, by counteracting the incentive provided from the impact of these actions on stock price performance.
III. DATA
We use compensation and performance data for 30 firms over the 1959-1995 period, for a total of 1,110 firm-years. Appendix A lists the sample firms and their industries. Masson (1971) first presents a data set of compensation and performance data for 50 firms over the 1948-1966 period. Antle and Smith (1985, 1986) extend Masson's (1971) data set for the 39 firms still operating in 1977, and Boschen and Smith (1995) further extend it for the 16 firms remaining as of 1990. We extend Boschen and Smith's (1995) data set for the 15 firms still operating in 1995, and we also add data on 15 new firms, for which we are able to obtain full sets of proxy statements for the years 1959-1995. However, increasing the number of firms constrains our time period because we can obtain data on the new firms extending only back to 1959.
We use two measures of CEO compensation: (1) cash compensation, measured as the log of compensation paid in cash, and (2) total compensation, measured as the log of the sum of cash compensation, stock grants, stock option grants (valued using the Black and Scholes [1973] method), and any other noncash compensation. We use two measures of firm performance, accounting performance and stock price performance. We measure accounting performance as the annual rate of return on assets, calculated as earnings before extraordinary items divided by average total assets. We measure stock price performance as the ex post annual rate of return to shareholders, including dividends. We adjust both performance measures for inflation and then standardize them (i.e., subtracting the mean and dividing by the standard deviation) to facilitate comparison of the pay-performance responses for stock price and accounting measures of performance.
Table 1 presents descriptive statistics for our major variables. Panel A presents measures of central tendency and variation in the variables. The mean firm-specific average annual CEO cash and total compensation, expressed in 1982 dollars, are $830,000 and $1,150,000, respectively. We benchmark our compensation data for the last year of the sample period, 1995, by comparing our compensation data with compensation data for the Standard & Poor's (S&P) 500. Untabulated results show that our sample firms' average total CEO compensation does not differ significantly from the average total CEO compensation for the S&P 500. Furthermore, none of the main components of average compensation (i.e., salary, cash bonus, long-term incentive plans, restricted stock, or stock option grants) differs significantly between our sample firms and the S&P 500.
Our accounting and stock price performance variables, accounting returns and stock returns, average 2.5 percent and 10.2 percent, respectively. The standard deviations of accounting returns and stock returns are 5.4 percent and 30.3 percent, respectively. Means and standard deviations are similar to those of the S&P 500 over the years 1959-1995. In addition, the (unreported) cross-sectional average firm beta, which we calculate using annual data over the 37 years, does not significantly differ from 1.
Panel B of Table 1 presents the simple correlations among our major variables. As expected, cash and total compensation are positively correlated, and both measures of compensation are positively correlated with stock price performance. Surprisingly, both measures of compensation are negatively contemporaneously correlated with accounting performance. (4) Finally, as expected, accounting performance is positively correlated with stock price performance.
Table 2 presents evidence on the time-series behavior of the compensation, accounting performance, and stock price performance data. Panel A shows that the autocorrelations for stock price performance are insignificant at all lags. In contrast, both measures of compensation and accounting performance are autocorrelated. The autocorrelations for cash compensation and accounting performance slowly damp out by lag four, although the autocorrelation for total compensation is still significant at lag four. Thus, both compensation and accounting performance have important dynamic components.
Panel B of Table 2 presents the results of unit root tests (Dickey and Fuller 1981). The null hypothesis of a unit root is rejected for all four series. This means that, over the sample period, these variables have not been subjected to changes that remain permanently in the level of the variables. These results suggest that it would be inappropriate to fit these compensation and performance data to a model that implicitly assumes unexpected performance leads to permanent changes in CEO compensation.
The 30 firms in our sample have a total of 128 different CEOs during the 1959-1995 period, resulting in an average of 4.27 different CEOs per firm, with a minimum of 2 and a maximum of 8. The average CEO tenure is 8.67 years, similar to the Hall and Liebman (1998) sample. Finally, almost all of the CEOs in our sample are promoted from within, similar to Gibbons and Murphy's (1992) sample.
IV. EMPIRICAL ANALYSIS
Long-Run Estimates from the Traditional Compensation Model
We begin by estimating a version of the traditional compensation model presented in Equation (2'). We denote CEO compensation for firm i in period t as [C.sub.it]. Next, we introduce our measures of firm performance for firm i in period t: unexpected accounting performance, denoted as [Z.sup.A.sub.it], and unexpected stock price performance, denoted as [Z.sup.S.sub.it]. We also add exogenous variables to control for broader industry-level events and trends: firm size, as measured by net sales (SIZE), and an indicator variable that takes on a value of 1 during the year of a CEO turnover, and 0 otherwise ([DELTA]CEO). These two variables allow the level of pay to shift when the size of the firm changes or a new CEO starts on the job. Our empirical version of the traditional compensation model can then be written as:
(3) [C.sub.it] = [[beta.sub.i0] + [rho][C.sub.it-1] + [[beta].sub.S][Z.sup.S.sub.it] + [[beta].sub.A][Z.sup.A.sub.it] + [[beta].sub.i1][DELTA][CEO.sub.it] + [[beta].sub.i2][SIZE.sub.it-1] + [Z.sup.C.sub.it].
In this model, [[beta].sub.S], and [[beta].sub.A] are estimated across firms, but the remaining [beta] coefficients are estimated as firm specific parameters. [[beta].sub.S] and [[beta].sub.A] are of particular interest because they measure the current-period response of CEO compensation to unexpected stock and accounting price performance. We estimate one version of the model with [rho] = 1, and a second version of the model with [rho] freely estimated.
[Z.sup.S.sub.it] and [Z.sup.A.sub.it] represent the effects of unexpected actions or events on stock price performance and accounting performance, respectively. An example of a [Z.sup.S.sub.it] is a CEO action that increases expected future earnings, but has little or no effect on current earnings. Examples would include a CEO's unanticipated decision to increase future research and development efforts on new product lines, or to dramatically change the firm's strategic focus over the next few years. A simple example of a [Z.sup.A.sub.it] is unobserved earnings management that inflates accounting performance in the current period. Another, more complicated example, would be an unanticipated increase in current earnings as a result of the CEO's unobserved decision to engage in a marketing plan that works better than anyone expected. In this latter case, although the action primarily affects current earnings, it may also affect expected future earnings and therefore stock prices. As we will show below, our model handles this complication by allowing unexpected accounting performance to affect stock prices contemporaneously.
Before we can estimate Equation (3), we must first obtain estimates of [Z.sup.A.sub.it] and [Z.sup.S.sub.it]. We model unexpected accounting performance as the residual from the following regression model:
(4) [A.sub.it] = [[phi].sub.i0] + [[phi].sub.1][A.sub.it-1] + [Z.sup.A.sub.it],
where we denote accounting performance for firm i in period t as [A.sub.it]. We estimate the [[phi].sub.i0]] as firm-specific constants, and we estimate [[phi].sub.1]] across firms. The parameter [[phi].sub.1]] describes the relation between accounting performance in periods t and t-1. For example, if [[phi].sub.1]] = 1, accounting performance follows a random walk. (5) Otherwise, if 0<[[phi].sub.1]]<1, the effects of past accounting performance on current accounting performance damp out over time.
After obtaining the [Z.sup.A.sub.it] estimated from Equation (4), we model unexpected stock price performance as the residual from the following regression:
(5) [S.sub.it] = [[upsilon].sub.i0] + [[upsilon].sub.i1][MKT.sub.t] + [[upsilon].sub.2][Z.sup.A.sub.it] + [Z.sup.S.sub.it],
where we denote stock price performance for firm i in period t as [S.sub.it], and the value-weighted market return with dividends as [MKT.sub.t]. We estimate the [[upsilon].sub.i0] as firm-specific constants, and we estimate the [[upsilon].sub.i1] as firm-specific parameters corresponding to firm-specific annual betas from the capital asset pricing model. The parameter [[upsilon].sub.2] is the estimate across all firms of the effect of unexpected accounting performance on stock price performance.
After obtaining the [Z.sup.S.sub.it] estimated from Equation (5), we use the [Z.sup.A.sub.it] and [Z.sup.S.sub.it] to estimate Equation (3). We denote Equations (3), (4), and (5), with [rho] and [phi] restricted to be 1, as the restricted traditional model. We estimate these three equations as seemingly unrelated regressions (SURs).
As we note in Section I, prior research has concluded that: (1) increases in accounting performance positively and significantly affect current CEO compensation, and (2) accounting performance often appears to have more impact on CEO compensation than does stock price performance. Panel A of Table 3 shows that when we use the traditional model that restricts [rho] and [[phi].sub.1], to be 1, our data confirm these conclusions: (1) the coefficient on unexpected accounting performance, [[beta].sub.A], is positive and significant, and (2) the coefficient on unexpected accounting performance, [[beta].sub.A], is two to three times larger than the coefficient on unexpected stock price performance, [[beta].sub.S]. A Wald test of the hypothesis that [[beta].sub.A] = [[beta].sub.S] is rejected for both cash and total compensation. Thus, our data are representative in that, when we use the traditional form of the compensation model, we obtain results similar to those found in previous research.
Figure 1 graphs the long-run response of CEO compensation to unexpected accounting and stock price performance, under the restricted traditional model in Equations (3), (4), and (5), with [rho] = 1 and [[phi].sub.1] = 1. The horizontal axis measures time. The vertical axis measures the percent increase in compensation from a one-standard-deviation increase in unexpected performance (i.e., the [??][C.sub.t+k]/[??][Z.sup.A.sub.t] and [??][C.sub.t+k]/[??][Z.sup.S.sub.t] for k = 0, ...,9. (6) As discussed in Section II, the restricted traditional model implies that compensation responses are permanent. Thus, the current-period coefficients reported in Table 3 determine the long-run effect. For example, Panel A of Table 3 shows that a one-standard-deviation increase in unexpected accounting performance leads to a 6.8 percent increase in current-period total CEO compensation. As shown in Panel B of Figure 1, the restricted traditional model assumes that this 6.8 percent raise remains permanently in the CEO's total pay. Similarly, Panel A of Table 3 shows that a one-standard-deviation increase in unexpected stock price performance leads to a 3.3 percent increase in current-period total CEO compensation. Again, the traditional model implies that this 3.3 percent raise remains permanently in the CEO's pay, as shown in Panel B of Figure 1.
[FIGURE 1 OMITTED]
In Table 4, we test how relaxing the restrictions that [rho] = 1 in Equation (3) and [[phi].sub.1] = 1 in Equation (4) affects the long-run implications of the traditional model. That is, we estimate all three equations without placing any restrictions on [rho] and [[phi].sub.1]. Table 4, Panel A, shows that our estimates of [rho] (the coefficient on [C.sub.t-1] in Equation (3)) are well below 1.
For total compensation the estimated value of [rho] is only 0.513. A Wald test of the hypothesis that [rho] = 1 is rejected in both the cash and total compensation models. Panel B shows that the estimate of [[phi].sub.1] (the coefficient on [A.sub.t-1] in Equation (4)) is 0.705, and the hypothesis that [[phi].sub.1] = 1 is rejected. Overall, the traditional model restrictions of [rho] = 1 and [[phi].sub.1] = 1 are not consistent with the data. This finding implies that models of the pay-performance relation that use first-differenced compensation and first-differenced accounting performance are misspecified.
In Figure 2 we show that relaxing the restrictions that [rho] = 1 and [[phi].sub.1] = 1 has substantial implications for the long-run response of CEO compensation to unexpected firm performance. Because Table 4 shows that [rho] < 1 and [[phi].sub.1] < 1, the CEO's raise for unexpectedly good firm performance no longer remains in his compensation permanently. Instead, the CEO's raise dissipates over time. For example, although Panel A of Table 4 shows that the CEO receives an initial raise in total compensation of 7.1 percent for an unexpected increase in accounting performance in the current period, only about 1 percent (i.e., [[rho].sup.3] X [[beta].sub.A] = [(0.513).sup.3] X 0.071) remains in his pay by year t+3.
[FIGURE 2 OMITTED]]
As explained above, the model in Equation (3) uses the single parameter, [rho], to describe the dynamics of the compensation responses. For values of [rho] greater than zero but less than 1, the effect of unexpected performance on CEO compensation decays over time, at a constant rate of 1 - [rho]. However, a model that assumes a constant decay rate will not uncover a more complicated pattern of responses, such as a cyclical response or the hump-shaped response found in Boschen and Smith (1995). In the next section we use a more flexible VAR approach to fully examine the current and long-run effects of performance on pay.
Long-Run Estimates from the Vector Autoregression Model
We present a vector autoregression (VAR) model of CEO compensation and firm performance that extends Boschen and Smith's (1995) model by adding accounting performance, in addition to stock price performance. This model allows for more complicated dynamics in three ways. First, we include three lags of CEO compensation, accounting performance, and stock price performance. Second, (unreported) Granger (1969) causality tests show that stock price performance and accounting performance Granger-cause one another, so we allow accounting and stock price performance to be jointly determined. Third, we allow for feedback from compensation to performance (Abowd 1990; Anderson et al. 2000; Hayes and Schaefer 2000).
The VAR model we present below contains the same set of three variables, [C.sub.it], [A.sub.it], and [S.sub.it], as do Equations (3), (4), and (5). (7) We continue to include the exogenous variables [SIZE.sub.t-1], [DELTA][CEO.sub.t], and [MKT.sub.t]. In addition to these variables, we enter the lagged market return ([MKT.sub.t-1]) in the compensation equation and the levels of current and lagged real Gross Domestic Product ([GDP.sub.t] and [GDP.sub.t-1]) in the equation for [A.sub.it]. (8,9) The model, which is similar to Boschen and Smith's (1995) model (1) extended to include accounting performance, is:
(6) [C.sub.it] = [[gamma].sub.i10] + 3[summation over (l=1)] [[gamma].sup.l.sub.11[C.sub.it-l] + 3[summation over (l=0)] [[gamma].sup.l.sub.12][S.sub.it-l] + 3[summation over (l=0)] [[gamma].sup.l.sub.13][A.sub.it-l] + [[gamma].sup.1.sub.iM][MKT.sub.t-1] + [[gamma.sup.0.sub.i[DELTA]][DELTA][CEO.sub.it] + [[gamma].sup.1.sub.iZ][SIZE.sub.it-1] + [Z.sup.C.sub.it]
[S.sub.it] = [[gamma].sub.i20] + 3[summation over (l=0)] [[gamma].sup.l.sub.21[C.sub.it-l] + 3[summation over (l=1)] [[gamma].sup.l.sub.22][S.sub.it-l] + 3[summation over (l=0)] [[gamma].sup.l.sub.23][A.sub.it-l] + [[gamma].sup.0.sub.iM][MKT.sub.t] + [Z.sup.S.sub.it]
[A.sub.it] = [[gamma].sub.i30] + 3[summation over (l=0)] [[gamma].sup.l.sub.31][C.sub.it-l] + 3[summation over (l=0)] [[gamma].sup.l.sub.32][S.sub.it-l] + 3[summation over (l=1)] [[gamma].sup.l.sub.33][A.sub.it-l] + [[gamma].sup.0.sub.iGDP][GDP.sub.t] + [[gamma.sup.l.sub.iGDP][GDP.sub.t-1] + [Z.sup.A.sub.it].
We continue to interpret the [Z.sup.A.sub.it] and [Z.sup.S.sub.it] as unexpected accounting performance and unexpected stock price performance, respectively. As before, the partial derivatives from the system in (6) (i.e., [??][C.sub.t+k/[??][Z.sup.A.sub.it] and [??][C.sub.t+k/[??][Z.sup.S.sub.it], for k = 0, 1, 2, ...) are the responses of compensation in period t+k to unexpected performance in t. The model looks different because [Z.sup.A.sub.it] and [Z.sup.S.sub.it] are not substituted directly into the compensation equation, as we did in Equation (3). Instead, they enter the equation for [C.sub.it] through [A.sub.it] and [S.sub.it]. Thus, in the VAR we calculate the compensation responses (i.e., the partial derivatives) using a two-step process, as Appendix B explains in more detail. First, we estimate the VAR equations for the system in (6) and obtain the regression coefficients. Then we invert the estimated model to obtain its moving-average form (i.e., [C.sub.it], [S.sub.it], and [A.sub.it] written as a function of the current and past value of [Z.sup.A.sub.it], [Z.sup.S.sub.it], [Z.sup.C.sub.it] and the exogenous variables) and calculate the partial derivatives from the moving-average form of the model.
We use the 2SLS approach (Hamilton 1994, 238-241) to obtain consistent estimates of the regression coefficients in (6). In this approach, we use the lagged values of compensation, stock price performance, accounting performance, and the exogenous variables as instruments to obtain fitted values for the endogenous variables. (10) Then, we substitute these fitted values for the endogenous variables (i.e., compensation, stock price performance, and accounting performance) and estimate each equation as an SUR. The confidence intervals for the compensation responses cannot be easily obtained analytically because the long-run responses are nonlinear combinations of the regression coefficients in Model (6). Thus, we obtain confidence intervals for the long-run responses using Monte Carlo simulations in which we calculate empirical distributions of the response functions based on 1,000 draws from the estimated distributions of the underlying VAR parameters (Hamilton 1994, 337).
Table 5 presents the estimation results for the model in (6). Panel A shows the results for cash compensation and Panel B shows the results for total compensation. The compensation regressions show that nearly all lags of compensation, all lags of stock price performance, and nearly all lags of accounting performance are significantly related to current compensation. The stock price performance regressions show that all lags of stock price performance, at least one lag of accounting performance, and most lags of compensation are significantly related to current stock price performance. Finally, the accounting performance regressions show that all lags of accounting performance, all lags of stock price performance, and all lags of compensation are significantly related to current accounting performance. Overall, the significance of these lags demonstrates that there are, in fact, substantial and important dynamics associated with each variable.
We use the coefficients in Table 5 to calculate the long-run responses of compensation to unexpected accounting and stock price performance that are presented in Figure 3. Specifically, we invert the system and then calculate the partial derivatives [??][C.sub.t+k]/[??][Z.sup.A.sub.t] and [??][C.sub.t+k]/ [[??]z.sup.s.sub.t], for k = 0,..., 9. Panel A of Figure 3 shows the compensation responses for cash compensation and Panel B of Figure 3 shows the responses for total compensation. The compensation responses to unexpected stock price performance exhibit a "hump-shaped" pattern, consistent with Boschen and Smith's (1995) results. The hump-shaped pattern means that the partial derivatives are increasing in value for the first several years, but decline toward zero in later years. In contrast, the response of CEO compensation to accounting performance is positive and statistically significant in the first period (as shown in Table 5 and in Figure 3), but the response falls off very quickly. In fact, by the year t+3, the compensation response is negative (although not statistically significant). That is, the CEO seems to reap rewards for good accounting performance for one or two periods, but then these rewards are taken back in years t+3 through t+9.
[FIGURE 3 OMITTED]
Table 6 summarizes the current-period and long-run responses of CEO compensation to unexpected accounting and stock price performance. We use this summary of the compensation responses to illustrate the rewards accruing to a hypothetical CEO in our sample who earns the sample average of $1 million in total compensation. Panel A summarizes the compensation responses indicated by the traditional restricted model, as shown in Panel A of Table 3 and in Figure 1. This traditional restricted model suggests that our hypothetical CEO would receive a reward of $68,000 in the current year's total compensation and a total of $680,000 over ten years for a one-standard-deviation increase in accounting performance. However, the traditional restricted model suggests that the CEO's total compensation reward for a one-standard-deviation increase in stock price performance is only $33,000 in the current period and $330,000 over ten years.
Panel B of Table 6 summarizes the compensation responses calculated from the VAR model (i.e., by estimating the coefficients for the model in (6) as shown in Table 5, inverting the system, and calculating the partial derivatives shown in Figure 3). Our hypothetical CEO receives an increase in total compensation of $60,000 in the current year for a one-standard deviation increase in accounting performance, but the VAR model suggests that this reward is followed by future pay cuts. The net loss to our CEO over the ten-year period is $49,000 (a value not significantly different from zero). In contrast, the VAR model suggests that our CEO's reward for a one-standard-deviation increase in stock price performance is $97,000 in the current period and $529,000 over ten years.
We now consider whether this puzzling dynamic effect of unexpected accounting performance on CEO compensation can be explained by the three major hypotheses about why firms use accounting performance data in setting CEO compensation. As discussed in Section II, the incentive, filtering, and effort allocation hypotheses can be consistent with either positive or negative relations between CEO compensation and accounting performance. However, it is difficult to see how using accounting performance in compensation contracts to provide incentives and/or to filter noise could explain a response of compensation to accounting performance that shifts from positive to negative. Use of accounting performance as a straightforward effort incentive cannot explain this pattern because the dynamics imply that rewards for actions that raise current accounting performance will be followed by (future) penalties for these same actions. These dynamics also appear inconsistent with the use of accounting performance to filter noise, because such a pattern would require that the correlations between current unexpected accounting performance and future realizations of unexpected stock price performance reverse sign over time.
One possible explanation is that incentive effects dominate in the short run (consistent with the positive compensation responses to accounting performance) and filtering effects dominate in the long run (consistent with the negative responses). However, to play a filtering role over the long run, accounting data lagged two or more years must convey substantial information about the current noise in stock prices. Although this is possible, accounting data are not usually considered strongly predictive of variation in future stock price performance.
Turning to the effort allocation hypothesis, one possible explanation is that firms use accounting performance to direct CEOs away from certain types of actions (Bushman and Indjejikian 1993; Lambert 2001). For example, consider a firm that ratchets performance standards (Indjejikian and Nanda 1999; Murphy 2000). In such a firm, a CEO who takes an action resulting in an earnings increase that is not sustainable is rewarded in the short run, but penalized in the long run. As another example, consider a CEO who chooses to manage earnings upward by aggressively accelerating the recognition of revenues or deferring the recognition of expenses. Such a choice may have no cash flow consequences overall, but the acceleration of earnings into the current period will, by definition, result in future earnings that are lower than they would otherwise be. Thus, a positive initial compensation response is followed by a later adverse response. Both of these examples suggest compensation responses to unexpected accounting performance that are initially positive, but decrease and become negative over time, consistent with our findings.
Robustness
We conduct a variety of robustness tests on the VAR model in (6) to evaluate whether a more parsimonious model can adequately capture the full dynamic responses of CEO compensation to firm performance. For brevity, we summarize our findings but do not report tabulated results. We begin by testing the sensitivity of the compensation responses shown in Table 5 to simplifications of the performance equations in (6). First, we eliminate the feedback from compensation back to both performance equations (i.e., we set [[gamma].sup.l.sub.21] = [[gamma].sup.l.sub.31] = 0 for all l). Second, we eliminate the feedback from stock price performance in the accounting performance equation (i.e., we set [[gamma].sup.l.sub.32] = 0 for all l). These restrictions reduce the model to a recursive form, which eliminates the need for 2SLS estimation. Third, we limit the performance equations to a maximum of one lag of any variable (i.e., [[gamma].sup.2.sub.22] = [[gamma].sup.3.sub.22] = [[gamma].sup.2.sub.23] = [[gamma].sup.3.sub.23] = [[gamma].sup.2.sub.33] = [[gamma].sup.3.sub.33] = 0). In each case, despite the increasing restrictions placed on these equations, the shape and the magnitude of the compensation responses remain virtually identical to the main VAR results in Figure 3. Thus, we can model firm performance with fewer parameters and still capture the essential compensation dynamics.
In contrast, when we restrict the compensation equation, we find substantial changes in the magnitude of the compensation responses. Specifically, when we eliminate all but one lag of compensation in the compensation equation, the cumulative response to unexpected stock price performance drops by about half. When we further restrict the compensation equation to include only one lag of all the variables, much of the long-run compensation response is eliminated altogether. These results suggest that it is necessary to include multiple lags of compensation, accounting performance, and stock price performance in the compensation equation, in order to fully capture the dynamic compensation responses.
Changing Dynamics over Three Decades
Figure 4 shows how the responses of compensation to unexpected accounting performance and unexpected stock price performance have changed over time. To obtain these estimates, we use a version of the system in (6) that includes time-period dummy variables interacted with the firm-specific constants and interacted with each performance variable. We use two dummies, one to indicate the 1972-1983 period, and the other to indicate the 1984-1995 period. Because of the large number of parameters involved, we take advantage of the findings from our robustness testing above. Specifically, we simplify the performance equations in Equation (6) so that (1) stock price performance is only affected by one lag of stock price performance and current and one lag of accounting performance, and (2) accounting performance is only affected by one lag of accounting performance. Panels A, B, and C of Figure 4 show the responses of CEO compensation to unexpected accounting performance and unexpected stock price performance for the 1960-1971, 1972-1983, and 1984-1995 periods, respectively.
[FIGURE 4 OMITTED]
Panels A, B, and C of Figure 4 show that the current-period effect of unexpected accounting performance is stable over the three decades. In contrast, the current-period effect of unexpected stock price performance rises considerably in the 1984-1995 period. These latter findings are consistent with those reported in Murphy (1999) and Bushman et al. (2000). The long-run effects of unexpected stock price performance have also increased over time. However, the long-run effects of unexpected accounting performance have declined sharply in the last decade and, in fact, have shifted from positive to significantly negative. These results are consistent with the idea that firms have implicitly shifted their CEO compensation arrangements to reward stock price performance and de-emphasize accounting performance. Future research on how firms use accounting performance to provide incentives for specific types of actions seems a promising avenue in explaining these shifts.
V. CONCLUSION
Prior empirical research using restricted models of the pay-performance relation finds that CEO compensation often responds more strongly to accounting performance than to stock price performance (Antle and Smith 1986; Lambert and Larcker 1987; Rosen 1992; Sloan 1993). However, we show that this finding does not hold when the empirical model is extended to allow unrestricted estimation of the long-run response of CEO compensation to unexpected accounting performance. We find that the compensation response to unexpected stock price performance is positive and persistent over time, but the compensation response to unexpected accounting performance is positive in the early years, and negative in later years. Overall, the cumulative long-run response of CEO compensation to unexpected accounting performance is not significantly different from zero.
From a methodological viewpoint, we conclude that pay-performance models should include at least three lags of all compensation and performance variables in order to fully capture the dynamics of the pay-performance relation. The traditional compensation model based on first-differences of compensation and accounting performance is, therefore, mis-specified. A limitation of our study is that it is based on only 30 firms (even though there are 1,110 firm-years of data). Also, requiring that firms have 37 years of data introduces survivorship bias, so the dynamic pay-performance relation we describe generalizes only to large, mature, surviving firms.
Finally, it is tempting to interpret our findings as diminishing the empirical importance of accounting performance in executive compensation arrangements. However, we have argued above that CEOs who take actions that increase accounting performance only temporarily, may face future penalties. These penalties may arise because firms ratchet performance standards, or because earnings management that accelerates earnings into the current period necessarily trades off current against future earnings. We conclude that understanding the long-run relation between accounting performance and compensation will require a complex set of theoretical considerations and more empirical work.
APPENDIX A Sample Firms and Industry Firm Industry 1. Allied Signal Manufacturing (Diversified) 2. Boeing Aerospace/Defense 3. Coming Manufacturing (Diversified) 4. Dow Chemical Chemicals 5. Eastman Kodak Photography/Imaging 6. Eaton Manufacturing (Diversified) 7. Federal Mogul Auto Parts and Equipment 8. FMC Chemicals (Diversified) 9. Ford Motor Automobiles 10. Goodrich (B. F.) Chemicals (Diversified) 11. Grace (W. R.) Chemicals (Specialty) 12. Harsco Manufacturing (Diversified) 13. Hercules Foods 14. Hershey Foods 15. Kellogg Foods 16. Kerr McGee Oil and Gas (Exploration/Production) 17. Kimberly Clark Household Products (Nondurable) 18. Minnesota Mining Manufacturing (Diversified) 19. Mobil Oil (Internationally Integrated) 20. Monsanto Chemicals (Diversified) 21. NL Industries Industrial Inorganic Chemicals 22. Northrop Grumman Aerospace/Defense 23. Pfizer Health Care (Drugs/Pharmaceuticals) 24. PPG Industries Chemicals (Diversified) 25. Raytheon Electronics/Defense 26. Rockwell International Electrical Equipment 27. Rohm & Haas Chemicals 28. Tenneco Manufacturing (Diversified) 29. TRW Auto Parts and Equipment 30. Union Carbide Chemicals
APPENDIX B
Calculation of Dynamic Responses for Vector Autoregression Model of CEO Compensation, Accounting Performance, and Stock Price Performance
In this appendix, we detail the calculation of the dynamic responses for the vector autoregression model in (6). We can write this model, with constants, exogenous variables, and firm indicators suppressed, as:
(B1) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
and condense it into vector form as:
(B2) [[GAMMA].sub.0][[Y.sub.t] = 3[summation over (l=1)] [[GAMMA].sub.l][Y.sub.t-l] + [Z.sub.T],
where [Y.sup.'.sub.t] = [[C.sub.t] [S.sub.t] [A.sub.t]], [[ZETA].sup.'.sub.t] = [[z.sup.c.sub.t] [z.sup.s.sub.t] [z.sup.A.sub.t], and the [[GAMMA].sub.l] are the coefficient matrices on the endogenous vectors at lag [??].
One standard version of the vector autoregression assumes that [[GAMMA].sub.0] = I and imposes a matrix of restrictions on the [[ZETA].sub.t] (which imposes an ordering on the estimation of the vector autoregression). Unlike the standard vector autoregression, the model we estimate does not restrict [[GAMMA.sub.0] to identity. Instead, we allow for simultaneity to accommodate the endogenous relations among compensation, stock price performance, and accounting performance. Our model also differs from the standard vector autoregression by recognizing that the three dependent variables do not exist as a fully closed system. Thus, our model allows exogenous variables to affect the system. However, since the exogenous variables do not affect the calculation of the dynamic responses, we suppress them in this appendix.
To calculate the dynamic responses, we invert Equation (B2) to obtain the moving-average form shown in Equation (B3):
(B3) [Y.sub.t] = t[summation over (k=o)] [[beta].sub.k], [[ZETA].sub.t-k],
where the [[beta].sub.k] are complex functions of the [[GAMMA].sub.t] matrices. The dynamic response of compensation through period t+k to unexpected stock price performance in period t is the sequence of derivatives [??][C.sub.t+k]/[??][[ZETA].sup.s.sub.t] that correspond to the elements [[beta].sub.k](1,2), for k = 0, ...,K. Analogously, the dynamic response of compensation through period t+k to unexpected accounting performance in period t is the sequence of derivatives [??][C.sub.t+k]/[??][[ZETA].sup.A.sub.t] that correspond to the elements [[beta].sub.k](1,3) for k = 0, ...,K.
As described in the body of the paper, we use a two-step procedure to obtain the dynamic responses of compensation to unexpected firm performance. In the first step, we use SUR to obtain the structural coefficients (i.e., the [[GAMMA].sub.l] matrices). In the second step, we invert the estimated structural system to obtain the moving-average form (i.e., the [[beta]k matrices). We calculate these [[beta]k matrices as follows:
[[beta].sub.0] = [[GAMMA].sup.-1.sub.0]
[[beta.sub.1] = ([[GAMMA.sup.-1.sub.0][[GAMMA].sub.1])[[GAMMA.sup.-1.sub.0]
[[beta].sub.2] = [([[GAMMA.sup.-1.sub.0][[GAMMA.sub.1]) ([[GAMMA].sup.-1.sub.0][[GAMMA.sub.1]) + ([[GAMMA.sup.-1.sub.0][[GAMMA].sub.2])][GAMMA.sup.-1.sub.0]
[[beta].sub.3] = [{([[GAMMA].sup.-1.sub.0][[GAMMA].sub.1] ([[GAMMA].sup.-1.sub.0][[GAMMA.sub.1]) + ([[GAMMA.sup.-1.sub.0][[GAMMA].sub.2]} ([[GAMMA.sup.-1.sub.0][[GAMMA.sub.1]) + ([[GAMMA.sup.-1.sub.0][[GAMMA.sub.1]) ([[GAMMA.sup.-1.sub.0][[GAMMA.sub.2]) + ([[GAMMA].sup.-1.sub.0][[GAMMA.sub.3])] [[GAMMA].sup.-1.sub.0]
The matrices of dynamic response follow [[beta].sub.k] = [Q.sub.k] [[GAMMA].sup.-1.sub.0], where [Q.sub.k] = 0 for k < 0, [Q.sub.0] = I, and [Q.sub.k] = [Q.sub.k-1]([[GAMMA].sup.-1.sub.0][[GAMMA].sub.-1] + [Q.sub.k-1] ([[[GAMMA].sup.-1.sub.0][[GAMMA].sub.2) + [Q.sub.k-3][[GAMMA].sup.-1.sub.0][[GAMMA].sub.3]) for k > 0.
TABLE 1
Descriptive Statistics for CEO Compensation,
Accounting Performance, and Stock Price Performance (a,b)
(1,110 firm-years--30 firms for the 1959-1995 period)
Panel A: Central Tendency and Variation
Mean
Cash Compensation (in $1,000s) (c) 830
Total Compensation (in $1,000s) (c) 1,150
Accounting Performance 0.025
Stock Price Performance 0.102
Panel B: Simple Correlations (d)
Cash Total
Compensation Compensation
Cash Compensation 1.000 0.884
Total Compensation 1.000
Accounting Performance
Stock Price Performance
Panel A: Central Tendency and Variation
Standard
Median Deviation
Cash Compensation (in $1,000s) (c) 703 572
Total Compensation (in $1,000s) (c) 813 1,346
Accounting Performance 0.023 0.054
Stock Price Performance 0.077 0.303
Panel B: Simple Correlations (d)
Accounting Stock Price
Performance Performance
Cash Compensation -0.097 0.073
Total Compensation -0.120 0.100
Accounting Performance 1.000 0.095
Stock Price Performance 1.000
(a) We measure cash compensation as the sum of all
compensation paid in cash. We measure total compensation as
the sum of cash compensation, stock grants, stock option
grants, and any other noncash compensation. We measure
accounting performance as earnings before extraordinary
items, scaled by average total assets. We measure stock
price performance as the ex post annual rate of return
to shareholders, including dividends. We adjust all variables
for inflation.
(b) We calculate the descriptive statistics in Panel A and
simple correlations in Panel B with the data arranged in
columns. The data for each firm is vertically stacked for
firms 1 through 30.
(c) Cash and total compensation are expressed in 1982
dollars in Panel A.
(d) We use the natural log of cash and total compensation
to calculate the correlations in Panel B.
TABLE 2
Time-Series Behavior of CEO Compensation, Accounting
Performance, and Stock Price Performance (a)
(1,110 firm-years--30 firms for the 1959-1995 period)
Panel A: Autocorrelations (b)
Lag 1 Lag 2
Cash Mean: 0.703 0.549
Compensation Std. Deviation 0.172 0.207
Minimum 0.229 0.066
Maximum 0.882 0.799
Total Mean: 0.643 0.553
Compensation Std. Deviation 0.201 0.208
Minimum -0.108 -0.247
Maximum 0.865 0.808
Accounting Mean: 0.696 0.446
Performance Std. Deviation 0.114 0.164
Minimum 0.435 0.138
Maximum 0.849 0.713
Stock Mean: -0.048 -0.137
Performance Std. Deviation 0.128 0.153
Minimum -0.322 -0.616
Maximum 0.159 0.179
Panel B: Unit Root Tests (c)
[eta]
Cash Compensation 0.610
Total Compensation 0.578
Accounting Performance 0.632
Stock Performance -0.281
Panel A: Autocorrelations (b)
Lag 3 Lag 4
Cash Mean: 0.409 0.347
Compensation Std. Deviation 0.230 0.201
Minimum -0.079 -0.009
Maximum 0.737 0.690
Total Mean: 0.498 0.403
Compensation Std. Deviation 0.124 0.163
Minimum 0.253 -0.097
Maximum 0.673 0.611
Accounting Mean: 0.288 0.235
Performance Std. Deviation 0.191 0.179
Minimum -0.173 -0.202
Maximum 0.642 0.602
Stock Mean: -0.028 0.118
Performance Std. Deviation 0.100 0.162
Minimum -0.201 -0.291
Maximum 0.169 0.444
Panel B: Unit Root Tests (c)
p-value
Cash Compensation 0.000
Total Compensation 0.000
Accounting Performance 0.000
Stock Performance 0.000
(a) We measure cash compensation as the log of the sum
of all compensation paid in cash. We measure total
compensation as the log of the sum of cash compensation,
stock grants, stock option grants, and any other noncash
compensation. We measure accounting performance as earnings
before extraordinary items, scaled by average total assets
and then standardized. We measure stock price performance
as the ex post annual rate of return to shareholders,
including dividends. We adjust all variables for inflation.
(b) The autocorrelations in Panel A are cross-sectional
averages of firm-by-firm autocorrelations.
(c) We test the null hypothesis of the unit root (i.e.,
[eta] = 1) via augmented Dickey and Fuller (1981) tests (ADF).
The test equation for the ADF test is [DELTA][y.sub.it]
= [a.sub.0i] + [a.sub.1]t + ([eta] - 1)[y.sub.it - 1] +
[a.sub.2] [DELTA] [y.sub.it - 1] + [a.sub.3][DELTA][y.sub.it
- 2] + [[epsilon].sub.it] where [y.sub.it] is each individual
series in turn. We perform these tests using a standard
fixed-effect model (i.e., firm-specific intercepts, all other
parameters equated across firms) for each series.
TABLE 3
Restricted Regressions of CEO Compensation on
Unexpected Accounting Performance and
Unexpected Stock Price Performance Based
on the Traditional Model (a) (1,110 firm
-years--30 firms for the 1959-1995 period)
Panel A: Results from Compensation Regressions
Coefficients on
[C.sub.t - 1] [z.sup.S.sub.t]
Cash Compensation 1.00 * 0.021 ([dagger])
Total Compensation 1.00 * 0.033 ([dagger])
Panel B: Results from
Supporting Regressions
Coefficient on [z.sup.A.sub.t] in Stock
Price Performance Regression
Coefficient on [A.sub.t - 1] in
Accounting Performance Regression
Panel A: Results from Compensation Regressions
Coefficients on
[z.sup.A.sub.t]
Cash Compensation 0.066 ([dagger])
Total Compensation 0.068 ([dagger])
Panel B: Results from
Supporting Regressions
Coefficient on [z.sup.A.sub.t] in Stock 0.071 ([dagger])
Price Performance Regression
Coefficient on [A.sub.t - 1] in 1.00 *
Accounting Performance Regression
([dagger]) Indicates a p-value less than 0.05.
* Indicates the parameter is restricted
to the reported value.
(a) We estimate the traditional compensation model
in Equation (3) with p = 1:
[C.sub.it] = [[beta].sub.i0] + [C.sub.it - 1]
+ [[beta].sub.s][z.sup.S.sub.it] + [[beta].sub.A][z.sup.A.sub.it]
+ [[beta].sub.i1][DELTA][CEO.sub.it] + [[beta].sub.i2]
[SIZE.sub.it - 1] + [z.sup.C.sub.it],
where [C.sub.it], is the log of cash or total CEO compensation
for firm i in year t. Cash compensation is the sum of all
compensation paid in cash. Total compensation is the sum of
cash compensation, stock grants, stock option grants, and any other
noncash compensation. [z.sup.A.sub.it] is unexpected accounting
performance for firm i in year t, estimated as the residual from
a restricted version of the accounting performance regression
model in Equation (4): [A.sub.it] = [A.sub.it - 1] + [z.sup.A.sub.it],
where [A.sub.it], is accounting performance for firm i in year t,
measured as earnings before extraordinary items scaled by average
total assets and then standardized to have a mean of zero and
standard deviation of 1. [z.sup.S.sub.it] is unexpected stock
price performance for firm i in year t, estimated as the residual
from the stock price performance regression model in Equation
(5): [S.sub.it] = [v.sub.i0] + [v.sub.i1] [MKT.sub.t] + [v.sub.2]
[z.sup.A.sub.it] + [z.sup.S.sub.it], where [S.sub.it] is stock
price performance for firm i in year t, measured as the ex post
annual rate of return to shareholders, including dividends,
standardized to have a mean of zero and standard deviation
of 1. We adjust all variables for inflation. We do not report
the firm-specific coefficients on the constants and exogenous
variables. These results are available from the authors upon request.
TABLE 4
Unrestricted Regressions of CEO Compensation
on Unexpected Accounting Performance and
Unexpected Stock Price Performance Based
on the Traditional Model (a) (1,110
firm-years--30 firms for the 1959-1995 period)
Panel A: Relevant Results from Compensation Regressions
Coefficients on
[C.sub.t - 1] [z.sup.S.sub.t]
Cash Compensation 0.662 ([dagger]) 0.022 ([dagger)]
Total Compensation 0.513 ([dagger]) 0.029 ([dagger])
Panel B: Relevant Results from
Supporting Regressions
Coefficient on [z.sup.A.sub.t] in Stock
Price Performance Regression
Coefficient on [A.sub.t - 1] in
Accounting Performance Regression
Panel A: Relevant Results from Compensation Regressions
Coefficients on
[z.sup.A.sub.t]
Cash Compensation 0.065 ([dagger])
Total Compensation 0.071 ([dagger])
Panel B: Relevant Results from
Supporting Regressions
Coefficient on [z.sup.A.sub.t] in Stock 0.060 ([dagger])
Price Performance Regression
Coefficient on [A.sub.t - 1] in 0.705 ([dagger])
Accounting Performance Regression
([dagger]) Indicates a p-value less than 0.05.
(a) We estimate the unrestricted version of the
traditional compensation model in Equation (3):
[C.sub.it] = [[beta].sub.i0] + [rho][C.sub.it - 1]
+ [[beta].sub.s][z.sup.S.sub.it] + [[beta].sub.A]
[z.sup.A.sub.it] + [[beta].sub.i1][DELTA][CEO.sub.it]
+ [[beta].sub.i2] [SIZE.sub.it - 1] + [z.sup.C.sub.it],
where [C.sub.it] is the log of cash or total CEO
compensation for firm i in year t. Cash
compensation is the sum of all compensation
paid in cash. Total compensation is the sum of
cash compensation, stock grants, stock option grants,
and any other noncash compensation. [z.sup.A.sub.t]
is unexpected accounting performance for firm i in
year t, estimated as the residual from an unrestricted
version of the accounting performance model in Equation
(4): [A.sub.it], = [[phi].sub.i0] + [[phi].sub.1] [A.sub.it - 1]
+ [z.sup.A.sub.it], where [A.sub.it] is accounting performance
for firm i in year t, measured as earnings before extraordinary
items scaled by average total assets and then standardized to
have a mean of zero and standard deviation of 1. [z.sup.S.sub.it]
is unexpected stock price performance for firm i in year t,
estimated as the residual from the stock price performance model
in Equation (5): [S.sub.it] = [v.sub.i0] + [v.sub.i1] [MKT.sub.t]
+ [v.sub.2][Z.sup.A.sub.it] + [z.sup.S.sub.it], where [S.sub.it]
is stock price performance for firm i in year t, measured as the
ex post annual rate of return to shareholders, including dividends,
standardized to have a mean of zero and standard deviation of 1.
We adjust all variables for inflation. We do not report the
firm-specific coefficients on the constants and exogenous variables.
These results are available from the authors upon request.
TABLE 5
Vector Autoregression Model of CEO Compensation, Accounting
Performance, and Stock Price Performance (a,b)
(1,110 firm-years--30 firms for the 1959-1995 period)
Panel A: Cash Compensation
Dependent Variable
Stock Price
Coefficients on Compensation Performance
[C.sub.t] -- 0.464 ([dagger])
[C.sub.t-1] 0.570 ([dagger]) -0.226 ([dagger])
[C.sub.t-2] 0.156 ([dagger]) -0.048
[C.sub.t-3] -0.049 -0.173 ([dagger])
S[R.sub.t] 0.013 ([dagger]) --
S[R.sub.t-1] 0.026 ([dagger]) -0.063 ([dagger])
S[R.sub.t-2] 0.018 ([dagger]) -0.040 ([dagger])
S[R.sub.t-3] 0.008 ([dagger]) -0.045 ([dagger])
A[R.sub.t] 0.077 ([dagger]) 0.210 ([dagger])
A[R.sub.t-1] -0.062 ([dagger]) -0.233 ([dagger])
A[R.sub.t-2] 0.019 ([dagger]) -0.000
A[R.sub.t-3] -0.027 ([dagger]) -0.016
Panel B: Total Compensation
Dependent Variable
Stock Price
Coefficients on Compensation Performance
[C.sub.t] -- 0.395 ([dagger])
[C.sub.t-1] 0.389 ([dagger]) -0.140 ([dagger])
[C.sub.t-2] 0.210 ([dagger]) -0.086 ([dagger])
[C.sub.t-3] 0.212 ([dagger]) -0.161 ([dagger])
S[R.sub.t] 0.082 ([dagger]) --
S[R.sub.t-1] 0.040 ([dagger]) -0.067 ([dagger])
S[R.sub.t-2] 0.055 ([dagger]) -0.048 ([dagger])
S[R.sub.t-3] 0.018 ([dagger]) -0.059 ([dagger])
A[R.sub.t] 0.038 ([dagger]) 0.208 ([dagger])
A[R.sub.t-1] -0.029 ([dagger]) -0.219 ([dagger])
A[R.sub.t-2] 0.005 0.004
A[R.sub.t-3] -0.024 ([dagger]) -0.031 ([dagger])
Panel A: Cash Compensation
Dependent Variable
Accounting
Coefficients on Performance
[C.sub.t] 0.432 ([dagger])
[C.sub.t-1] -0.120 ([dagger])
[C.sub.t-2] 0.081 ([dagger])
[C.sub.t-3] 0.097 ([dagger])
S[R.sub.t] 0.197 ([dagger])
S[R.sub.t-1] 0.123 ([dagger])
S[R.sub.t-2] 0.073 ([dagger])
S[R.sub.t-3] 0.029 ([dagger])
A[R.sub.t] --
A[R.sub.t-1] 0.525 ([dagger])
A[R.sub.t-2] -0.114 ([dagger])
A[R.sub.t-3] 0.122 ([dagger])
Panel B: Total Compensation
Dependent Variable
Coefficients on Accounting
Performance
[C.sub.t]
[C.sub.t-1] 0.264 ([dagger])
[C.sub.t-2] 0.099 ([dagger])
[C.sub.t-3] 0.139 ([dagger])
S[R.sub.t] 0.084 ([dagger])
S[R.sub.t-1] 0.175 ([dagger])
S[R.sub.t-2] 0.129 ([dagger])
S[R.sub.t-3] 0.065 ([dagger])
A[R.sub.t] 0.022 ([dagger])
A[R.sub.t-1] --
A[R.sub.t-2] 0.473 ([dagger])
A[R.sub.t-3] -0.086 ([dagger])
0.091 ([dagger])
([dagger]) Indicates a p-value less than 0.05.
(a) We measure cash compensation as the log of the sum of all
compensation paid in cash. We measure total compensation as the log of
the sum of cash compensation, stock grants, stock option grants, and
any other noncash compensation. We measure accounting performance as
earnings before extraordinary items, scaled by average total assets,
and then standardized. We measure stock price performance as the ex
post annual rate of return to shareholders, including dividends, and
then standardized. We adjust all variables for inflation.
(b) We estimate the model from a set of pooled time-series seemingly
unrelated regressions based on the system in (6). We do not report
the coefficients on the constants and exogenous variables. These
results are available from the authors upon request.
TABLE 6
Current-Period and Long-Run Cumulative Responses of CEO Compensation to
Unexpected Accounting Performance and Unexpected Stock Price
Performance (a) (1,110 firm-years--30 firms for the 1959-1995 period)
Panel A: Traditional Compensation Model (b)
Cash Compensation
Current- Long-Run
Period (d) Cumulative (e)
Response to [z.sup.A.sub.t] 0.066 ([dagger]) 0.660 ([dagger])
Response to [z.sup.S.sub.t] 0.021 ([dagger]) 0.210 ([dagger])
Panel B: Vector Autoregression Model (c)
Cash Compensation
Current- Long-Run
Period (d) Cumulative (e)
Response to [z.sup.A.sub.t] 0.088 ([dagger]) 0.054
Response to [z.sup.S.sub.t] 0.031 ([dagger]) 0.199 ([dagger])
Panel A: Traditional Compensation Model (b)
Total Compensation
Current- Long-Run
Period (d) Cumulative (e)
Response to [z.sup.A.sub.t] 0.068 ([dagger]) 0.680 ([dagger])
Response to [z.sup.S.sub.t] 0.033 ([dagger]) 0.333 ([dagger])
Panel B: Vector Autoregression Model (c)
Total Compensation
Current- Long-Run
Period (d) Cumulative (e)
Response to [z.sup.A.sub.t] 0.060 ([dagger]) -0.049
Response to [z.sup.S.sub.t] 0.097 ([dagger]) 0.529 ([dagger])
([dagger]) Indicates a p-value less than 0.05.
(a) We measure cash compensation as the log of the sum of all
compensation paid in cash. We measure total compensation as the log of
the sum of cash compensation, stock grants, stock option grants, and
any other noncash compensation. We adjust all variables for inflation.
We measure accounting performance as earnings before extraordinary
items, scaled by average total assets, and then standardized. We
measure stock price performance as the ex post annual rate of return
to shareholders, including dividends, and then standardized. We adjust
all variables for inflation.
(b) In Panel A, we obtain the responses of cash and total CEO
compensation to unexpected accounting performance and unexpected stock
price performance by estimating the restricted traditional compensation
model in Equation (3), using the estimates calculated from Equations
(4) and (5). We calculate the long-run compensation responses
to unexpected stock price performance and unexpected accounting
performance as the sequences of derivatives [??][C.sub.t+k]/[??]
[z.sup.S.sub.t] and [??][C.sub.t+k]/[??][z.sup.A.sub.t] for
k = 0, ..., 9.
(c) In Panel B, we obtain the responses of cash and total CEO
compensation to unexpected accounting performance and unexpected stock
price performance via a two-step process. First, we estimate a vector
autoregression based on the system in (6). In the second step, we
invert the system and calculate the long-run compensation responses
to unexpected stock price performance and unexpected accounting
performance as the sequences of derivatives [??][C.sub.t+k]/[??]
[z.sup.S.sub.t] and [??][C.sub.t+k]/[??][z.sup.A.sub.t] k = 0, ..., 9.
(d) For both models, we calculate the current-period responses of cash
and total CEO compensation to unexpected stock price performance and
unexpected accounting performance as [??][C.sub.t]/[??][z.sup.S.sub.t]
and [??][C.sub.t]/[??][z.sup.A.sub.t].
(e) For both models, we calculate the cumulative responses of cash and
total CEO compensation to unexpected stock price performance and
unexpected accounting performance as the sums of the derivatives above,
that is, [[summation].sup.9.sub.k=0] [??][C.sub.t+k]/[??]
[z.sup.S.sub.t] and [[summation].sup.9.sub.k=0]
[??][C.sub.t+k]/[??][z.sup.A.sub.t],
respectively.
We thank Bill Baber, John Core, Martin Loeb, Denise Jones, Larry Pulley, David Reeb, Aamer Sheikh, and Bob Thompson for useful suggestions. William Compton, Meredith Hines, Asif Dhala, Tom Pappalardo, Tracy Morse, and Melissa Smith provided excellent research assistance. We are particularly grateful to Linda Bamber (the editor), Raffi Indjejikian (the associate editor) and an anonymous reviewer for their substantial contributions to this paper.
Submitted November 1999 Accepted September 2002
(1) Both Jensen and Murphy (1990) and Anderson et al. (2000) incorporate one lag of firm performance in their compensation equations, but they do not model the dynamic responses over time.
(2) As noted in Bushman and Smith (2001), early literature used the term pay-performance sensitivity to refer to the weight on a performance measure in a regression of compensation on performance--that is, the partial derivativeof compensation with respect to firm performance (Murphy 1985). However, Banker and Datar (1989) use the term sensitivity to refer to the partial derivative of a performance measure with respect to an agent's action. To avoid ambiguity, and to be consistent with the time-series literature, we will use the term response, in the time-series sense, to denote the partial derivative of current (and future) compensation with respect to current unexpected firm performance.
(3) The amount of noise in accounting and stock price performance does affect the relative size of the coefficients on each measure in a compensation regression. Lambert and Larcker (1987) and Sloan (1993) show that when accounting performance has less noise (i.e., more precision) than stock performance, it has a larger impact on CEO compensation.
(4) Antic and Smith (1986) show a negative coefficient on accounting performance in their compensation regressions for a subset of their sample firms.
(5) Although most prior compensation research uses a random walk to model the time-series behavior of annual accounting performance, Baber et al. (1998, 1999) adopt an IMA (1,1) characterization of accounting performance.
(6) These partial derivatives are actually taken with respect to the [Z.sup.A.sub.t] and [Z.sup.S.sub.t], but for notational simplicity, we suppress the hats.
(7) We modify the standard VAR by entering exogenous variables in the system. In addition, most VARs do not estimate the parameters on the current values of the endogenous variables.
(8) Adut et al. (2003) include a time-trend variable in a model of CEO compensation. They find that a deterministic trend alters the relation between CEO compensation and restructuring charges. However, including trend variables (time and time-squared) in our compensation equation does not affect our inferences.
(9) CDP plays a dual role. First, this variable controls for variations in real spending that would likely affect current and near-future accounting performance. Second, GDP, as an exogenous variable, is an additional instrument for use in the Two-Stage Least Squares (2SLS) approach we use to deal with the simultaneity in the VAR model.
(10) The average [R.sup.2] of the regressions that yield these fitted values are: 0.71 for the cash compensation equation, 0.69 for the total compensation equation, 0.35 for the stock price performance equation, and 0.73 for the accounting performance equation.
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John F. Boschen College of William & Mary Augustine Duru American University Lawrence A. Gordon University of Maryland at College Park Kimberly J. Smith College of William & Mary
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