the optimal and actual use of economic value added in
TRANSCRIPT
The Optimal and Actual Use of Economic Value Added in
Incentive Compensation�
Gerald T. Garveyy Todd T. Milbournz
November 15, 2005
�Acknowledgments: Helpful comments were received from Gilles Chemla, Peter Christiansen, Jerry Feltham, KinLo, Alex Stomper, Anjan Thakor, Martin Wu, Josef Zechner, and seminar participants at UBC and the Universityof Vienna. We wish to thank Xifeng Diao for research assistance and the Bureau of Asset Management and theHampton Fund at UBC for �nancial support.
yBarclays Global Investors, 45 Fremont St., San Francisco, CA 94105, Tel: 415-597-2133, Fax: 415-597-2292,e-mail: [email protected]
zWashington University in St. Louis, John M. Olin School of Business, Campus Box 1133, 1 BrookingsDrive, St. Louis, MO 63130-4899 Tel: 314-935-6392 Fax 314-935-6359 e-mail: [email protected] website:http://www.olin.wustl.edu/faculty/milbourn/
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The Optimal and Actual Use of Economic Value Added inIncentive Compensation
Abstract
Executive compensation is increasingly sensitive to stock returns. However, even abnormal stock
returns are highly volatile, and an optimal contract shields the agent from as much variability as
possible. It is not surprising then that non-stock performance measures, such as earnings and
other accounting measures, are explicitly used for short-term bonus payments. Accounting perfor-
mance also a¤ects the decision to grant new stock options. In this paper, we use a formal method
for ascertaining the value of accounting earnings relative to that of its most popular competitor,
Economic Value Added (EVA), for incentive contracting purposes. We apply the method �rst by
estimating the optimal relative weight on these two measures for a large sample of �rms. We then
demonstrate that actual compensation practice in these �rms is consistent with our estimates of
optimal compensation arrangements.
2
1 Introduction
Executive compensation has become increasingly sensitive to stock prices, primarily through the
increased use of options (see Hall and Liebman (1998)). While such compensation seems the natural
and obvious way to align managers�and shareholders�interests, it is far from a perfect tool. For
example, Warren Bu¤et argues that stock option plans are �wildly capricious in their distribution
of rewards, ine¢ cient as motivators, and inordinately expensive for shareholders�.1 The formal
agency literature also recognizes that linking managers� pay to volatile stock prices inevitably
makes their rewards somewhat capricious, and the cost of imposing this risk on executives has been
estimated to be as much as half the market value of the executive�s stock or option compensation
(see Murphy (1999) and Muelbroek (2000)).2 Multi-task, multi-signal agency models, such as Paul
(1992), also show how informationally-e¢ cient stock prices which re�ect the value-relevance of
alternative signals, will not generally re�ect their value in incentive contracting.
Given the problems above, it is not particularly surprising that actual compensation plans
often use accounting-based measures of performance to supplement stock prices. Many companies
use earnings to determine bonus payments, and the decision to grant new stock options is also
linked to recent accounting performance.3 However, earnings have many well-known �aws as a
performance measure, particularly the lack of an explicit charge for the cost of equity capital (see
Rogerson (1997)). Recognizing this problem, some �rms supplement earnings with measures such
as Economic Value Added (EVA),4 and others either ration capital or impose a charge for use of
capital.5
Conceptually, EVA is closely related to earnings. It di¤ers mainly by adding back depreciation
to earnings, capitalizing some expenses, and subtracting an equity cost of capital. Empirically, the
1The Economist (1999) �Survey: Pay: Who Wants to Be a Billionaire�May 8, S14-S17.2Aggarwal and Samwick (1999) document that �rms with more volatile stock returns o¤er less powerful stock-based
incentives.3While the link between cash compensation (salary plus bonus) and accounting earnings has been shown in many
papers, the recent ExecuComp data allows us to investigate the e¤ects on total compensation, including restrictedstock and the Black-Scholes value of option grants. If we regress total compensation on lagged compensation, rawstock returns, and earnings innovations scaled by the lagged market value of equity, we obtain: ln(total comp) =2.21 + 0.73*ln(total comp, lagged) + 0.40*raw stock returns + 0.57*Earnings innovations scaled by lagged marketvalue of equity. All coe¢ cients are signi�cant at 5% or better. Observe that this speci�cation overstates the case forearnings relative to prices because it neglects the stock price sensitivity of existing options and shares. However, thesigni�cance of the ceo¢ cient shows that earnings are important in determining executive pay.
4EVA is a periodic measure calculated as after-tax operating pro�ts less a charge for capital, where the charge isbased on the cost of capital (or WACC) times the level of capital employed.
5For example, OM Scott imposes a charge against earnings for working capital employed (see Baker and Wruck(1989)). Other �rms design their own measures, such as Clorox, that closely resemble EVA by charging all capitalagainst earnings. Many other �rms use basic capital budgeting principles in performance evaluation and since EVAis consistent with such principles, these �rms may also pay according to EVA at least implicitly. Support for thesedecisions to adopt EVA can be found in the theoretical work of Rogerson (1997). He shows that a performancemeasure akin to EVA is part of an optimal compensation contract when agents have control over both their e¤ortsand capital investments. See Garvey and Milbourn (2000) for an analysis of the decision to adopt EVA.
3
two are also positively related. In our sample of large US �rms from 1986 to 1997, the correlation
between earnings and EVA growth is over 60%.6 Important to our work, however, is that this
correlation di¤ers widely across �rms. For some the correlation is over 95%, while for others, it is
either zero or negative. Obviously EVA adds little value when it is highly correlated with earnings.
But how do we know when the di¤erences introduced by EVA are signal or noise?
Formal agency models provide a straightforward answer to the above issues: weight accounting
measures according to the incremental information each conveys about the manager�s value-added.
But an empiricist, or a practitioner, must still address the basic question of how exactly to mea-
sure such information content. Existing empirical research (e.g., Lambert and Larcker (1987) and
Yermack (1995)) assumes that low volatility is a reliable indicator of information content, which is
only true if all measures are equally sensitive to changes in underlying value-added. Some propo-
nents of newer performance measures have argued that their measure is superior because it shows
a stronger statistical relationship to stock returns than do alternative measures. This is plausible
in that a measure that captures value should also be re�ected in stock returns, but seems to throw
out the baby with the bathwater in that a measure that is perfectly correlated with stock returns
also shares all of its weaknesses as a performance measure.
In this paper, we present and test a simple model that deals with all of the above issues:
1. The agency problem is multidimensional and stock prices are a noisy, imperfect performance
measure despite our assumption of capital market e¢ ciency.
2. The �rm has access to multiple accounting measures to supplement stock prices. Such mea-
sures are allowed to have insu¢ cient, as well as excess, volatility. Speci�cally, while all
accounting measures contain noise, they may also miss some portion of the manager�s con-
tribution, and this underlying �signal content�may vary across the measures.
3. The information content of the accounting numbers is imperfectly revealed through the stock
price. Thus, while each signal�s signal content is not empirically observable, it can be inferred
by their relationship to stock returns.
The model generates an expression for the optimal relative weight that a �rm should place on
alternative measures of performance that contains only observable quantities. We implement the
model by �rst estimating the optimal weights that �rms should place on EVA versus earnings
(according to our model). We then test the model by making the additional assumption that �rms
6The correlation in levels is closer to 0.8, but this is because both are dollar measures.
4
are aware of these optimal weights. We compare the actual weights they place on each measure in
determining executive compensation to the optimal weights suggested by the model.
Because our technique relies on associations between the measures and with stock prices, it
could apply to any non-stock performance measure including those that are not based in accounting
data. We use EVA because it is the most prominent alternative measure and because data is readily
available for a relatively long time-series. An alternative approach which could prove fruitful in
future research would be to identify a priori which kinds of �rms are more likely to bene�t from
including an explicit capital charge in their compensation schemes. This is challenging because
capital costs are important for all �rms and �rms from a wide variety of industries have adopted
some version of EVA. Consultants such as Stern Stewart claim that a measure like EVA is thereby
relevant for all �rms, and it is di¢ cult a priori to identify �rms, or even industries, where EVA is
most important.7 Seemingly obvious candidates would include �rms engaged in capital-intensive
endeavors. However, if both the type of �xed assets and the scale thereof are standardized,
managers have little discretion over their usage. Thus, EVA�s incremental value to earnings would
be diminished. The O.M. Scott example provided by Baker and Wruck (1989) documents that
retailers (often considered capital-nonintensive businesses) found value in an EVA-related measure
that charged earnings for the use of working capital.
Given the above problems, we rely on the empirically-observed association of EVA with stock
prices and with earnings to help identify its incremental contracting value. Garvey and Milbourn
(2000) successfully apply this technique to help predict which �rms formally adopt EVA. A weakness
of that study is that it ignores the many �rms such as OM Scott that use EVA-like performance
measures without formal adoption.8 Here we use actual compensation outcomes for a large sample
of �rms and �nd that almost half make a signi�cant use of EVA in compensation. The theory
helps us predict which �rms will do so. Another advantage of our approach is that we can identify
whether �rms in practice use EVA for compensation even when they claim to the contrary. This
speaks directly to the work of Ittner and Larcker (1998),who document that many �rms who have
formally adopted EVA claim to not use it for incentive compensation.
Data on �rm level earnings and EVA are collected for the time period 1978-1997. These data
are then merged with the Compustat ExecuComp database, which provides detailed compensation
data for the top �ve executives named in the proxy statements over 1992-1997. We �rst estimate the
7See Wallace (1997), Hogan and Lewis (1999), and Kleiman (1999) for lists of �rms that have adopted EVA or arelated measure of economic pro�t. As shown there, adopters span numerous industries.
8As an additional example, Clorox has used the �Clorox Value Measure� equal to operating pro�ts less 12% oftotal capital since the early 1990�s (see Davis (1996)).
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optimal relative weights that should be placed on EVA and earnings in the compensation contract.
In order to compare our results to others in the compensation literature, we also calculate the
relative weights that would be placed on EVA and earnings by simply comparing the ratio of
variances of these two measures. Our estimates of the optimal weights show a correlation of only
20% with the ratio of variances.
We then assess whether our optimal weights approximate actual compensation practice. Our
�rst test distinguishes between subsets of �rms that our theory predicts should and should not use
EVA. For the latter sample, earnings are signi�cantly related to total compensation, while EVA
is insigni�cant. For those �rms for which we expect EVA to have value, earnings are insigni�cant
in explaining total compensation, while EVA is positively related to total compensation. As a
means of comparison, the simple ratio of variances is insigni�cant in both subsamples. In a more
re�ned test of the model, we allow the coe¢ cients on EVA and Earnings to vary continuously by
incorporating interaction terms between our estimates of the optimal weights and each of these
measures. The results again support the theory while the simple ratio of variances performs badly.
The rest of the paper is organized as follows. Section 2 develops the model and characterizes
the problem we explore. Section 3 provides our empirical results. Section 4 concludes.
2 The Model
We begin with the compensation design problem between a �rm�s risk-neutral shareholders and
its risk-averse manager. Our purpose is to characterize the optimal incentive contract that re-
sults when various managerial actions are imperfectly revealed through accounting measures and
the �rm�s stock price. Important to our formulation is the assumption that various accounting
measures are di¤erentially informative of the manager�s e¤ort choice in equilibrium. Therefore,
our �rst task is to solve for the optimal weighting scheme that these accounting measures and
the stock price should receive in an incentive scheme when the �rm�s shares are traded in an
informationally-e¢ cient market. The economic approach that we employ is positive, rather than
normative. Thus, we derive the optimal contract in light of the assumption that the �rm is in-
formed of the di¤erential signal content of its accounting measures. More important, in comparing
the theoretically-optimal wage contract to observed compensation practices, we express our results
in terms of empirically-observable quantities. We rely on Garvey and Milbourn�s (2000) method
for inferring the di¤erential signal content of accounting measures using the �rm�s stock price.
In this section, we derive the optimal contract, show that it is optimally tied to both accounting
6
measures and stock price, and summarize the empirical method that allows us to confront the
model with compensation data.
2.1 Basic Setup
The underlying value of the �rm is determined by the manager�s e¤ort choices and random error
terms. We assume that there are two dimensions of managerial e¤ort, denoted ac and af . The
e¤ort ac can be captured by accounting measures, while the e¤ort af cannot. This e¤ort choice
is noisily revealed through stock prices. Garvey and Milbourn (2000) uses only one dimension of
e¤ort and does not consider the value of stock prices in compensation.
The �rm�s terminal value is given by
Xc +Xf = (ac + �c) + (af + �f ),
where ai 2 [0;1), for i 2 fc; fg, are the manager�s unobservable e¤ort choices across ac and af ,
and �i is noise, with �i s N(0; �2i ) for i 2 fc; fg. The terms �c and �f are independent shocks to
the manager�s e¤orts, with means normalized to zero and variances of �2c and �2f , respectively. The
marginal and average productivity of the manager�s two e¤ort choices are normalized to one, but
we allow the costs and hence the value marginal products of these e¤ort choices to vary arbitrarily.
The manager�s utility is separable in wealth and e¤ort, and his reservation utility is normalized
to zero. We assume that the manager has negative exponential utility over wealth, with a coe¢ -
cient of risk-aversion given by r. The manager�s cost of e¤ort is given by the general functional
form C(ac; af ), where@C()@ac
> 0, @C()@af> 0, and @2C()
@ac@af= 0. Risk-neutral shareholders design
the manager�s compensation contract to maximize their wealth, subject to the participation and
incentive compatibility constraints.
Given the unobservability of both e¤ort decisions, shareholders must rely on performance-based
compensation arrangements to motivate the e¤ort-averse manager to provide e¤orts in equilibrium.
However, the underlying value of the �rm (Xc + Xf ) is not directly contractible. Instead, the
compensation contract must be written on a set of imperfectly informative performance measures.
We assume that there are two observable and veri�able measures of the �rst component of �rm
value, Xc. These are given by Y1 and Y2 and are referred to as accounting measures. The �rm
can use these measures directly in incentive contracts if it so chooses. There is also one measure of
the second component of �rm value (Xf ) given by Yf , which is de�ned below. The two accounting
7
performance measures are de�ned as
Y1 = �1Xc + "1
Y2 = �2Xc + "2;
where "1 � N(0; �21), "2 � N(0; �22) and Cov("1; "2) = �"1"2�1�2. Naturally, the volatility of Y1
and Y2 could di¤er. Moreover, our framework allows for the fact that these accounting measures
may also have di¤erential signal content with respect to the manager�s choice of ac. The signal
content of these two measures is captured by the parameters �1 and �2. These are positive and
deterministic scalars that represent the proportion of the manager�s contribution to �rm value
through ac that is successfully captured by the performance measure.
In the empirical section, we will operationalize the two accounting performance measures as
EVA and earnings. It is well-known that earnings are an imperfect measure of current contribution
to the �rm�s market value (see, e.g., Sloan (1993)). Since stock value can be expressed as the sum
of book value and the present value of future EVAs (see, e.g., Ohlson (1990)) it may appear that
current period EVA should have a � value of one and no noise. While this is true of perfectly
measured EVA, actual EVA is subject to a long list of potential errors. First and most obviously,
the cost of equity capital is merely an estimate. Second, EVA involves a host of decisions regarding
the capitalization or expensing of items such as advertising and R&D, and even outlays such as
labor costs can involve a signi�cant investment component.
In addition to the accounting measures, there is a measure of the manager�s equilibrium choice
of af given by
Yf = Xf + "f ;
where "f � N(0; �2f ). We assume that Yf is only observed by capital market investors and
hence, revealed through the stock price alone. The measure Yf could represent information that is
privately observed by some capital market investors, but this could also be observed by the �rm�s
shareholders who design the manager�s wage contract. What is important for our model is that
Yf is noncontractible.
In equilibrium, the stock price (P ) is set by competitive, risk-neutral traders who observe Y1,
Y2 and Yf , and observe the informational properties of each measure. The stock price is
P = E(Xc +Xf j Y1; Y2; Yf ).
Observe that expected stock returns are zero, and therefore any non-zero return represents an ab-
8
normal return re�ecting innovations in the performance measures (Y1, Y2 or Yf ).9 We characterize
the stock price more fully in a later subsection when we summarize Garvey and Milbourn�s (2000)
empirical method for extracting the critical contracting information from the price. We focus now
on solving for optimal compensation contracts, as the contribution of this paper is to explicitly test
whether �rms pay their managers according to the model.
2.2 Optimal Contracts
For incentive contracting purposes, the �rm�s shareholders are interested in the manager�s contri-
butions to �rm value through ac and af . As delineated above, the accounting measures of Y1
and Y2 provide information related to ac, and the stock price provides information on af via the
noncontractible signal of Yf . We proceed with the analysis in three major steps. First, we derive
the optimal weighting scheme that the measures Y1 and Y2 should receive to elicit the desired choice
of ac. Second, we show that the market-derived stock price also places the right relative weights
on these two measures from both an informational and incentive perspective. Our third step is to
show that while the stock price e¢ ciently balances the information contained in Y1 and Y2, it does
not e¤ectively weight the information in these two measures with respect to the measure of the
managerial choice of af . As a consequence, it is endogenous to our model that shareholders will
optimally contract with the manager on both the accounting measures and the �rm�s stock price
as in Paul (1992). Unlike previous work, we characterize the optimal relative weights on the two
accounting measures entirely in terms of observables.
Optimal relative weights on the accounting measures
We turn �rst to the derivation of the weighting scheme on Y1 and Y2, and ignore for now the
contractual problem of motivating managerial choices of af . Restricting the set of feasible wage
contracts to be linear in Y1 and Y2, we posit that shareholders would o¤er the manager the following
wage contract:
W (Y1; Y2) = w + 1Y1 + 2Y2,
where w represents the �xed wage.10
9We ignore the fact that the manager�s wage comes out of the stock price, but this assumption is made solely forsimplicity and does not qualitatively a¤ect our results.10For our purposes, we will only consider linear compensation contracts. See Holmstrom and Milgrom (1987) for
a general examination of the limits of this approach.
9
Since all of the random variables are assumed to have zero mean and shareholders are risk-
neutral, their problem is given by
Max 1; 2
a�c �W (Y1; Y2)
subject to the manager�s individual rationality constraint:24 w + 1Y1 + 2Y2 � C(a�c)
� r2
� 21V ar(Y1) +
22V ar(Y2) + 2 1 2Cov(Y1; Y2)
�35 � 0
and the constraint that the e¤ort choice a�c is implicitly determined by the �rst-order condition:
1�1 + 2�2 �@C(ac)
@ac= 0. (1)
Given that the manager�s reservation utility is assumed to be zero, we can solve for w in the
individual rationality constraint and substitute this into the shareholders�objective function. This
yields
Max 1; 2
a�c � C(a�c)�r
2
� 21V ar(Y1) +
22V ar(Y2) + 2 1 2Cov(Y1; Y2)
�,
subject to (1). The necessary �rst-order conditions for the optimal contracting weights 1 and 2
are then given by:
@a�c@ 1
(1� Cac)� r[ �1V ar(Y1)� �2Cov(Y1; Y2)] = 0
@a�c@ 2
(1� Cac)� r[ �2V ar(Y2)� �1Cov(Y1; Y2)] = 0, (2)
where Cac �@C(ac)@ac
. From the manager�s �rst order condition in (1) and the fact that Yj =
�jXc + "j = �j(ac + �c) + "j for all j 2 f1; 2g, we observe that
@a�c@ 1
=�1Cacac
@a�c@ 2
=�2Cacac
; (3)
where Cacac �@2C(ac)@a2c
.
Upon substituting (3) into (2) and dividing through by r, we see that the two �rst-order
conditions for the optimal choices of 1 and 2 require that
[ �1V ar(Y1) + �2Cov(Y1; Y2)]
�1=[ �2V ar(Y2) +
�1Cov(Y1; Y2)]
�2.
Consequently, the ratio of optimal weights can be expressed as
�1 �2=�1V ar(Y2)� �2Cov(Y1; Y2)�2V ar(Y1)� �1Cov(Y1; Y2)
. (4)
10
The absolute weights 1 and 2 in this wage contract naturally depend on the manager�s cost of
e¤ort function. However, as Banker and Datar (1989) show, in a single-e¤ort decision problem,
the optimal relative weights on the two accounting measures depends only on their signal-to-noise
ratios. This is su¢ cient for our purposes as well since both Y1 and Y2 are noisy measures of the same
action ac.11 For our purposes, it is convenient to characterize the ratio result in (4) as an optimal
relative weighting �� on the two measures. That is, the wage contract o¤ered to the manager by
shareholders can be written as ��Y1 + (1� ��)Y2, where
�� = �1
�1 + �2
=�1V ar(Y2)� �2Cov(Y1; Y2)
�1V ar(Y2) + �2V ar(Y1)� �1Cov(Y1; Y2)� �2Cov(Y1; Y2). (5)
With the optimal ratio of contracting weights from (4) in hand, we next show that an e¢ cient
stock price places the same relative weights on the measures Y1 and Y2. Again, suppressing the
e¤ort choice af and its nonveri�able signal Yf , the stock price can be written as
P = E(Xc j Y1; Y2)
P = K + b1Y1 + b2Y2,
where the constant K and the weights b1 and b2 are set to minimize the sum of squared errors.
These are given by
MinK;b1;b2
X(Xc �K � b1Y1 � b2Y2)2: (6)
Proposition 1
The relative weights on Y1 and Y2 in the equilibrium stock price, given by b1b2, are identical to
the relative weights derived in the shareholders�compensation design problem, 1 2 , given by (4).
Optimal contracts based on accounting information and the stock price
The implication of Proposition 1 is that stock prices incorporate the relevant information in Y1 and
Y2 in a manner that is e¢ cient for incentive-based compensation. However, as stressed by Paul
(1992), this does not imply that the �rm should use only the stock price in a multi-task agency
setting. The problem is that the stock price takes no account of the relative cost-e¤ectiveness of
the two aspects of e¤ort, ac and af . As we now show, in our multi-task setting the shareholders
will generally use both the accounting measures Y1 and Y2, and the stock price.
11Feltham and Xie (1994) provide a characterization of the case where performance measures capture multipleaspects of e¤ort.
11
We begin by de�ning an optimally-weighted combination of Y1 and Y2, using (5), as
Yc = ��Y1 + (1� ��)Y2
= 1
1 + 2Y1 +
2 1 + 2
Y2 =b1
b1 + b2Y1 +
b2b1 + b2
Y2,
where the last equality follows from Proposition 1. We can now write the optimal linear incentive
contract as
W (Yc; P ) = w + cYc + �P , (7)
where P is the stock price and c and � are weights to be determined. For convenience, we can
express the stock price as
P = E(Xc +Xf j Y1; Y2; Yf )
= E(Xc j Y1; Y2) + E(Xf j Yf )
= k + bcYc + bfYf ,
where bc and bf represent the capital market�s weights on the two measures.12
The optimal contracting weights in (7) maximize shareholder wealth which can be written:
Max c;�
a�c + a�f � C(ac; af )�
r
2[( c + �bc)
2V ar(Yc) + �2b2fV ar(Yf )],
subject to the constraints that the manager�s e¤ort choices a�c and a�f maximize his own utility
according to the �rst-order conditions:
@Yc@ac
( c + �bc)� Cac =
� 1
1 + 2�1 +
2 1 + 2
�2
�( c + �bc)� Cac = 0
@Yf@af
(�bf )� Caf = �bf � Caf = 0. (8)
Similar to the contracting problem above, the necessary �rst-order conditions for the optimal con-
tracting weights c and � are:
@a�c@ c
(1� Cac)� r( c + �Bc)V ar(Yc) = 0 (9)�@a�c@�(1� Cac)� rbc( c + �bc)V ar(Yc)
�+
�@a�f@�
(1� Caf )� r�b2fV ar(Yf )�= 0 (10)
Further, from the manager�s �rst-order conditions in (8), we see that @a�c
@ cbc =
@a�c@� . Thus, if we
substitute for @a�c
@� in (10), we obtain
bc
�@a�c@ c
(1� Cac)� r( c + �bc)V ar(Yc)�+
�@a�f@�
(1� Caf )� r�b2fV ar(Yf )�= 0.
12We use a lower-case k as a constant rather than the upper-case one used earlier because the upper-case K also
included e¤ects of the measure Y2.
12
Observe that the �rst set of curly brackets is identical to (9), and therefore must equal zero. The
immediate implication is that the contracting weight on the stock price (�) is set solely to elicit
the desired managerial choice of af , as (10) reduces ton@a�f@� (1� Caf )� r�b
2fV ar(Yf )
o= 0. Thus,
in equilibrium, the shareholders will design a contract that optimally uses both the accounting
measures and the stock price. To solidify this point, the following result highlights the contracting
distortion that obtains if shareholders attempt to pay the manager based solely on the stock price.
Proposition 2
If shareholders o¤er the manager a wage contract of the form W (P ) = w + �P , instead of
W (Yc; P ) = w + cYc + �P , both the ac and af e¤ort choices are distorted by the manager in
equilibrium.
The immediate implication of Proposition 2 is that shareholders will optimally contract on both
accounting measures and the stock price. Not to do so needlessly distorts e¤ort choices and reduces
�rm value.
2.3 Empirically Estimating the Information Content of Accounting Measures
The expression for �� (see (4)) is intuitive in that it weights the two accounting measures according
to their signal-to-noise ratio. However, this expression cannot be directly taken to the data as the
informational content of each measure (captured by �1 and �2) are not directly observable. In
this last subsection, we summarize the empirical framework for using the information contained in
stock prices to infer the relative informativeness of each measures.13
As before, we can write the price as a linear regression of terminal �rm value on the available
signals:
P = E(Xc +Xf j Y1; Y2; Yf ) = K + b1Y1 + b2Y2 + bfYf ,
where we now separate the market weight bc on the joint accounting measure into the weights b1
and b2 individually attached to Y1 and Y2. Ideally, a direct estimate of the �1 and �2 values could
be obtained by regressing Y1 and Y2 individually on the price in order to reveal each measure�s
sensitivity to fundamental value. The problem is that the observable measures Y1 and Y2 are
13Our signal structure has similarities to Sloan (1993) in that the accounting measures are related to �rm valueby a multiplicative constant. However, Sloan (1993) assumes that abnormal stock returns are a noiseless measureof Xc, whereas we do not. The implication of Sloan�s (1993) more extreme assumption is that accounting variablesshould be ignored in the optimal contract since abnormal returns are a su¢ cient statistic. In our setting in whichall measures are noisy, including abnormal stock returns, the optimal contract is written on both the accountingmeasures and the �rm�s stock price.
13
correlated through both the common component Xc and their individual �noise� components "1
and "2. To solve these problems, we need to analyze the stock price weights more thoroughly than
we have in Proposition One. Speci�cally, we need to express the weights in terms of the underlying
parameters of the contracting and production environment. Minimizing the sum of squared errors
(Xc +Xf � P )2 and solving for the coe¢ cients of interest yields:
b1 =Cov(Y1; X)V ar(Y2)� Cov(Y1; Y2)Cov(Y2; X)
V ar(Y1)V ar(Y2)� (Cov(Y1; Y2))2=
�1�2c!22 � �2�2cCov("1; "2)
V ar(Y1)V ar(Y2)� (Cov(Y1; Y2))2
b2 =Cov(Y2; X)V ar(Y1)� Cov(Y1; Y2)Cov(Y1; X)
V ar(Y1)V ar(Y2)� (Cov(Y1; Y2))2=
�2�2c!21 � �1�2cCov("1; "2)
V ar(Y1)V ar(Y2)� (Cov(Y1; Y2))2.
Suppose we now use the simple regression Yj = kj + �jP + �j , which yields
�j =Cov(Yj ; P )
V ar(P )(11)
as a �raw�estimate of �j . Given our expression for P and the fact that Yf is orthogonal to both
Y1 and Y2, we can write
Cov(Y1; P ) = b1V ar(Y1) + b2Cov(Y1; Y2).
Using our expressions for b1 and b2, we can express the two terms on the right-hand side as:
b1V ar(Y1) =V ar(Y1)[Cov(Y1; X)V ar(Y2)� Cov(Y1; Y2)Cov(Y2; X)]
V ar(Y1)V ar(Y2)� (Cov(Y1; Y2))2
b2Cov(Y1; Y2) =Cov(Y1; Y2)[Cov(Y2; X)V ar(Y1)� Cov(Y1; Y2)Cov(Y1; X)]
V ar(Y1)V ar(Y2)� (Cov(Y1; Y2))2.
Noting that the second term in b1V ar(Y1) and the �rst term in b2Cov(Y1; Y2) sum to zero and
taking out the common term Cov(Y1; X) from the remaining two terms in the denominator, we can
write:
Cov(Y1; P ) = b1V ar(Y1) + b2Cov(Y1; Y2)
=Cov(Y1; X)
�V ar(Y1)V ar(Y2)� [Cov(Y1; Y2)]2
�V ar(Y1)V ar(Y2)� (Cov(Y1; Y2))2
= Cov(Y1; X) = �1�2c .
With this, we can express the coe¢ cient from the simple regression of Yj on P as:
�j =Cov(Yj ; P )
V ar(P )=
�j�2c
V ar(P ). (12)
While the non-zero covariance between the accounting measures Yj no longer appears, �j still
understates the true �j since V ar(P ) > �2c . This is apparent given that the stock price depends
14
not just on Xc (as captured by Y1 and Y2), but also on Xf (revealed through Yf ). However, we do
not need to completely solve this problem to obtain an unbiased measure of the relative optimal
weights on our accounting performance measures because the severity of the underestimation is
equivalent across both performance measures. De�ning g � V ar(P )�2c
, our estimate of �j is
b�j = g�j = g�Yj ;P SD(Yj)SD(P ), (13)
for j 2 f1; 2g, which conveniently carries the same constant g in both b�1 and b�2.This estimation procedure allows us to express the optimal relative weights (given by (4))
completely in terms of observable magnitudes. We start with the expression from (4),
�� =�1V ar(Y2)� �2Cov(Y1; Y2)
�1V ar(Y2) + �2V ar(Y1)� �1Cov(Y1; Y2)� �2Cov(Y1; Y2),
and substitute for b�j from (13), yielding
b�� = SD(Y2)��Y1P � �Y1Y2�Y2P
�SD(Y2)(�Y1P � �Y1Y2�Y2P ) + SD(Y1)
��Y2P � �Y1Y2�Y1P
� . (14)
The optimal weight b�� can be computed empirically from the variance-covariance matrix of
innovations in earnings, EVA, and stock values. These weights can then be compared to those
obtained by regressing compensation on these same measures. It is important to recognize that
the theory only restricts the relative sensitivity of compensation to EVA and to earnings. Without
information on the manager�s risk-aversion and the marginal value product of ac versus af , the
model is silent on either the absolute weight placed on accounting measures, or the weight of
earnings or EVA relative to stock returns. To gauge the importance of di¤erential value-relevance,
we also use a crude measure of this weighting scheme, b�naive = SD(Y2)=[SD(Y1) + SD(Y2)]. Thiscorresponds to the common practice of empirical researchers of using only the raw volatility of the
competing performance measures (e.g., Yermack (1995) and Garen (1994)) in order to weight their
value in a compensation contract.
3 Empirical Results
3.1 Raw data and derived measures
To derive our theoretical expectation of the weight that �rms will place on alternative performance
measures, we use standard accounting and stock price data from Standard and Poors�Compustat
and CRSP, respectively. These data are augmented with estimates of Economic Value Added
15
secured from the Stern Stewart Performance 1000 spanning the years 1978-1997. Our compensation
data are drawn from Standard and Poors�ExecuComp, beginning in 1992 and running through 1997.
Table 1 provides basic descriptive statistics of our sample. We have 6,251 observations to compute
the optimal compensation weights, representing the universe of �rms which appear in the Stern
Stewart Performance 1000 list, as well as CRSP and COMPUSTAT, for at least six years of our
sample period. We require six years of data to produce �ve years per �rm of innovations in both
stock values and accounting performance measures to compute our optimal weights. Thus, given
that our compensation data begin in 1992, our primary sample covers the years 1986-1997.14
As is common with panel data on large companies, the �rst seven rows of Table 1 indicate some
large outliers in accounting performance measures, stock returns, and �rm size.15 To reduce the
e¤ects of such extreme observations, we winsorize all values at the 1% tails before performing our
statistical analyses. That is, if an observation falls outside the 1% con�dence interval at either
tail, we set it equal to the upper or lower bound of that interval.
The next six rows of Table 1 summarize our estimates of the optimal weight on EVA for each
�rm and the �ve data items necessary for their estimation. To compute the correlations that yield
this calculation, we use abnormal stock returns and innovations in EVA and earnings. We scale the
accounting measures by lagged market value of equity as this provides consistent scaling with stock
returns. Finally, we use an AR1 speci�cation to identify innovations in the accounting numbers.
Our results are highly similar if we use simple �rst di¤erences to proxy for unexpected changes in
EVA or earnings.
Standard contract theory requires that performance measures be tailored to each �rm�s speci�c
circumstances. Thus, the weight on EVA, b��, (see (14)) is computed using �rm-speci�c statisticalcorrelations. With at most 12 years of data on each �rm, we will inevitably have noisy measures
of the relevant correlations and variances.16
As documented by Biddle et al (1997), earnings innovations tend to be more highly correlated
with abnormal returns (average correlation is 0.336) than are innovations in EVA (average corre-
lation with abnormal returns is 0.123). The two measures also tend to be highly correlated with
one another (average correlation is 0.403), but such multicollinearity is explicitly accounted for in
the theory. Moreover, the range of correlations documented in our universe of �rms spans -0.896
14Our EVA sample begins as early as 1978 for many �rm, and extending our analysis to this longer time perioddoes not change our results.15Abnormal stock returns are estimated assuming a beta of one and using the NYSE value-weighted index as the
market portfolio as in Biddle et al (1997). Results are essentially identical using �rm-speci�c betas from CRSP.16We extend the series to 19 years for a subsample of �rms, and our results are similar.
16
to 0.981. Both accounting measures have approximately the same amount of volatility and are in
turn approximately �ve times less volatile than either raw or abnormal stock returns. The next
row of Table 1 summarizes our �rm-speci�c estimates of the optimal weight placed on EVA relative
to earnings, b��, using data from 1986-97. To compute these values we follow the theory exactly
in all but the following cases. If EVA innovations are negatively related to abnormal returns, this
implies that �EV A is actually negative and we set its optimal weight at zero. There are 186 such
cases. If on the other hand earnings innovations are negatively related to abnormal returns and
EVA innovations are positively related to abnormal returns, we set the weight on EVA at one.
There are 36 such cases. Even when both measures are positively related to abnormal returns,
it is possible for the optimal weight on EVA to be below zero or greater than one if the two are
su¢ ciently highly correlated. For example, if EVA is highly positively related to earnings but has
little correlation with stock returns, then according to optimal compensation theory EVA should
be e¤ectively used as an index and receive a negative weight. While strictly consistent with the
theory, for most of our tests we do not permit either measure to receive negative weight because
both are intended to be measures of performance rather than indices.17 For completeness, we also
report some sensitivity analyses using unrestricted weights, and results are qualitatively similar.
Consequently, the empirical estimations, in conjunction with these three decision rules, results
in a sample with just over half of our optimal weights on EVA given by zero, and with the upper
quartile beginning with �rms that put approximately a 44% weight on EVA. Consistent with the
pattern of �rms that have explicitly adopted EVA examined in Garvey and Milbourn (2000), EVA is
highly valuable in many cases, but not by any means in all cases. At the upper extreme, 11% of our
sample are predicted by the theory to place a weight of one on EVA and a weight of zero on earnings.
There is some industry pattern to the optimal weights, but there is so much heterogeneity within
industries that no one or two-digit SIC code has optimal weights that are signi�cantly di¤erent
from the global mean or median. Doubtless there are important aspects of �rms�productive and
market environment that makes EVA more or less valuable for compensation purposes, but they
are not captured well by SIC codes.
The last three rows of Table 1 summarize our compensation measures from Standard and Poors
ExecuComp. Both Salary and Bonus average just above $750,000, with bonuses being far more
variable than salary. Total compensation is computed by ExecuComp using the Black-Scholes
value of options granted plus any grants of stock and other annual compensation. Not surprisingly,
17 It is di¢ cult to imagine EVA being marketed as an index. The story would have to be that high earnings are theprimary indication of good performance, but if the manager also had a high value of EVA this would indicate thathe just �got lucky�and should receive less of a reward. Such a story seems to have little practical validity.
17
given the importance of stock options in executive compensation documented by Hall and Liebman
(1998), salary plus bonus represents just over a third of total compensation, and accounts for less
than one-sixth of the variability in total compensation. We therefore focus on total compensation
as our primary measure of incentives. In using the value of such compensation as a measure of
managers�rewards, we do not account for the fact that options and shares continue to be sensitive to
stock price performance in years after the grant date (that is, until the manager sells the security).
This is appropriate as our focus is on how �rms make use of the unique information conveyed by
earnings and shareholder value measures exempli�ed by EVA in their choice of executive awards.
Moreover, an option granted in 1993 will contain some sensitivity to earnings in 1994, but only
insofar as earnings are correlated with stock returns.
3.2 Simple Correlations
Table 2.1 gives a preliminary indication of how compensation is related to our alternative perfor-
mance measures. We use simple �rst di¤erences of EVA and earnings, scaled by lagged market value
of equity as our accounting performance measures, and percent changes in pay and compensation
for our incentive rewards. Consistent with past studies, we �nd that cash compensation is more
strongly related to accounting performance measures than is total compensation. In the univariate
setting, accounting performance measured as either EVA or earnings are a stronger determinant of
salary and bonus payouts than they are of stock and option grants. Such grants are more strongly
related to past stock performance, and overall they are harder to predict than salary and bonus
payments. One reason may simply be measurement error in valuing options with Black-Scholes (see
Huddart (1994)). We nonetheless focus on total compensation because incentives are not re�ected
in any single component of managerial pay packages and ignoring options would introduce even
more error.
Table 2.2 provides background evidence on our estimates of the optimal weights accounting
measures should receive under the wage contract ���EV A+[1� ��]�Earnings. It is reassuring
to see that they are relatively stable over time in that there is a high correlation between weights
using shorter (1986-97) and longer (1978-97) windows. In part, this is simply because we only have
more than 12 years of data available for a subsample of our �rms. Not surprisingly, according to
our theory, the correlation between the naive ratio of variances and the optimally-derived measure
is quite low. The last rows and columns of Table 2.2 establish that our weights are not simply
picking up size, leverage, or Tobin�s q e¤ects. Industry e¤ects may be present in our weights, but
18
we have experimented with industry controls in the regressions and our results are robust to this.
This is to be expected since even if industry e¤ects are present, our model allows us to identify
which industries should rely relatively more on EVA, and which �rms within each industry should
do so.
3.3 Tests of the theory
Before we present our formal parametric tests of the theory, Table 3 exploits the fact that we
estimate an optimal weight of zero on EVA for over half the �rms in our sample by simply splitting
the sample into those that should and should not use EVA. In all our regressions, the dependent
variable is the log of total compensation. To isolate unexpected payments, we use the log of
the previous year�s total compensation as an explanatory variable. This is similar to using �rst
di¤erences except that we do not restrict expected compensation to equal last year�s compensation
(which would involve setting the coe¢ cient on lag ln(total compensation) to 1). As observed by
Anderson et al (1999), the coe¢ cient turns out to be signi�cantly di¤erent from one.
The �rst column restricts all �rms to make the same use of EVA relative to earnings. Consistent
with past research, we �nd that the stock returns are positively related to total compensation. Our
results are virtually identical if we use abnormal returns and we use raw returns to be consistent
with the past literature, including Jensen and Murphy (1990) and Aggarwal and Samwick (1999).
In the full-sample, neither earnings innovations nor EVA innovations are signi�cantly di¤erent from
zero. In part, this is because the two are signi�cantly correlated. However, as the next two columns
demonstrate, the primary reason is that we have restricted the coe¢ cients to be equal across �rms.
The second column of results in Table 3 uses only those �rms for which the theory says all weight
on the accounting measures should be placed on earnings. Consistent with the theory, earnings
have a positive e¤ect on compensation which is signi�cant at the 5% level, while EVA becomes more
negative but still insigni�cant. The last column of results restricts attention to those �rms which
in theory should use EVA. Earnings are no longer signi�cant for this subsample while EVA has a
positive, rather than a negative sign as in previous regressions. Unfortunately, the large standard
errors on the coe¢ cient of EVA in the b�� = 0 subsample and on earnings in the b�� > 0 subsamplemean that the estimated coe¢ cients for EVA or earnings are not signi�cantly di¤erent from one
another across subsamples. Nonetheless, our theoretically optimal measures perform much better
than the alternatives. For example, if we split the sample according to the median of the naive
variance weights, the coe¢ cients change in the wrong direction (EVA is less important and earnings
19
are more important when b�naive is greater than its median), although none of these are signi�cant.Table 4 presents a more re�ned test of our model. To produce a directly testable prediction we
re-express the theoretically optimal compensation contract as
W (Yc; P ) = w + cYc + �P
= w + c
hb��Y1 � h1� b��iY2i+ �P= w + cY2 + cb�� [Y1 � Y2] + �P ,
where we let Y1 � EV A Innovations and Y2 � Earnings Innovations. Analogous to the work
of Janakiriman et al (1992) on relative performance evaluation, we can distinguish between a weak
and a strong-form implication of our theory. The weak-form implication of the theory is that the
estimated coe¢ cient on the interaction term between the theoretically optimal weights and the
di¤erence between EVA and earnings, b�� [Y1 � Y2] ; is positive, and the strong-form implication
is that the estimated coe¢ cient on the interaction term is equal to the coe¢ cient on earnings
innovations alone, c.
The �rst column presents our basic test. We �nd support for both implications of the theory.
The interaction term with the optimal weights is signi�cantly greater than zero at the 5% level. It
is also clear that it is not signi�cantly di¤erent from the weight on earnings alone; even the point
estimate of the earnings weight is not signi�cantly less than the coe¢ cient on the interaction term.
The second column in Table 4 does not restrict our estimates of the optimal weights (b��) tofall between zero and one. Because of the greater variance of the dependent variable, coe¢ cient
estimates are now smaller but still signi�cantly di¤erent from zero. We also �nd support for
the strong-form implication of the theory in that we are unable to reject the hypothesis that the
interaction term with the optimal weights is di¤erent from the earnings coe¢ cient.18 In the third
column, we highlight the importance of controlling for stock returns in our tests. If we combine
Proposition 1 with the empirical observation that stock prices are important for compensation, it
becomes clear that if we leave out the stock price, we will bias our tests towards accepting our
theory since the stock price places the exact same relative weights on EVA and earnings that we
predict in the theory. Consistent with this observation, when we drop raw stock returns from
the empirical speci�cation, we �nd overwhelming evidence for the theory in that the earnings and
interaction terms are almost identical. This is for illustrative purposes only as the test is biassed
towards the theory. The two prior columns are the more relevant tests of the theory.18The primary reason is the relatively large standard error on the earnings coe¢ cient. It is di¤erent from zero at
the 5% level but insigni�cantly di¤erent from the point estimate on the interaction term. A t-test that incorporatesthe errors in estimates of both coe¢ cients takes only the value 0.85.
20
The fourth column provides some perspective on our results relative to previous studies. Here
we use the naive variance weights b�naive in place of the theoretically optimal weights b��. Theseweights have no ability to identify �rms where EVA is relatively more important than earnings.
It is also noteworthy, analogous to Aggarwal and Samwick�s (1999) �ndings on the use of stock
returns, that earnings innovations have a statistically signi�cant e¤ect on compensation only when
we use our optimal weights to allow the e¤ect to di¤er across �rms.
In the empirical speci�cations found in Table 4, we only allow a single estimate of c cross-
sectionally. Although by design we allow the relative weight on EVA and earnings to vary contin-
uously across �rms, the restriction on the coe¢ cient c might a¤ect our conclusions. Speci�cally,
our results could be biased in support of our theory if the di¤erences of unanticipated innovations
in EVA and earnings were positively correlated with the true underlying c of each �rm. By
de�nition, such unanticipated di¤erences should not be correlated with c. In the next section we
allow for some cross-sectional variation in this weight.
A comparison of the coe¢ cients on earnings and the interaction of our optimal weights with
di¤erences in EVA and earnings to raw stock returns seems to indicate that accounting numbers
are a more important determinant of compensation than are stock returns. Such a conclusion
is unwarranted. As highlighted by Hall and Liebman (1998), much of executives� stock-based
incentives stem from their accumulated portfolio of options and shares. We have neglected these
e¤ects in our study of annual compensation awards. The reason we have done so is that existing
stock or option grants will be sensitive to accounting measures only to the extent that these measures
drive stock prices. In this dimension, there is no scope for placing weights that di¤er from those
placed by the stock market.
3.4 Additional evidence
Table 5 is included for completeness and comparability to some of the past literature. Here we
restrict attention to �rst di¤erences in cash and total compensation, thereby restricting the co-
e¢ cient on lagged compensation to one. We also use �rst di¤erences rather than innovations in
the EVA and earnings measures. As can be seen, we document very similar �ndings and further
support for our theory.
In Table 6, we control for �rms that have been identi�ed as formally adopting EVA. We rely
on the lists of �rms that have explicitly adopted EVA or a related �economic pro�t� measure
for incentive purposes from Wallace (1997), Hogan and Lewis (1999), and Kleiman (1999). We
21
create an indicator variable, Adopter, that takes the value of one if the �rm is an adopter of EVA,
and zero otherwise. The �rst and second columns replicate the estimation of Table 4 for the
set of adopting and non-adopting �rms, respectively. As seen in the second column, our results
are virtually unchanged when adopting �rms are removed. Moreover, the �rst column provides
suggestive evidence of the fact that EVA adopters do use EVA more. While the small sample
size of adopters (159 �rm-years) reduces our statistical power, the estimated coe¢ cient (although
statistically insigni�cant) on the interaction term is 3.144 in the sample of adopters, versus 1.150 in
the sample of non-adopters. Further evidence that EVA-adopting �rms rely on EVA more relative
earnings can be found in the third column. Here, we include both the Adopter indicator variable
and the interaction of Adopter and EVA innovations into the empirical speci�cation. Again, while
the small sample size of adopters reduces power, the estimated coe¢ cient on the interaction of
Adopter and EVA innovations is positive (0.222).
Our last set of empirical tests seeks to shed light on the reliance on accounting measures relative
to stock price in annual compensation awards, that is, c relative to �. While our model is
silent on this issue without empirical proxies for the cost of various types of managerial e¤ort, the
compensation literature suggests that the portion of �rm value attributable to growth opportunities
should be positively related to the reliance on stock price. Consequently, we estimate our empirical
speci�cation for �rms below and above the median value of Tobin�s q. The �rst two columns of
Table 7 summarize our �ndings. While our estimates on the accounting measures are noisier,
we see that the estimated coe¢ cient on stock returns is signi�cantly higher in the sample of high
Tobin�s q �rms (0.332) than in the sample of low Tobin�s q �rms (0.214). As a further check, we
also split our sample according to �rm size, measured as the market capitalization of the �rm�s
equity. Here, smaller �rms tend to rely on stock returns more (0.300) than larger �rms do (0.259).
4 Concluding Remarks
Given the prominence of shareholder value principles at public corporations, performance measure-
ment and managerial compensation have become of paramount concern. While stock prices are
obviously informative, they are an imperfect tool for performance measurement even at the execu-
tive level we are examining. As a consequence, less noisy accounting measures may be useful, but
their individual usefulness cannot be directly observed. We have used a formal empirical method
for ascertaining the relative value of two accounting measures, EVA and earnings, which allows us
to construct an optimal compensation contract. Using executive pay data, we �nd evidence that
22
�rms pay according to principal-agent theory. These �ndings are important in light of recent work
that suggests that �rms adopting EVA claim to not use it often for compensation purposes. In
contrast, while �rms may claim not to be using it, in reality, compensation awards based on EVA
are positively related to the informativeness of EVA. Importantly, this result holds for a very large
sample of �rms that is overwhelmingly larger than the sample of �rms claiming to have adopted
measures such as EVA.
23
5 Appendix
5.1 Proof of Proposition 1
The two �rst order conditions with respect to b1 and b2 in the minimization program of (6) are,
respectively
�2X
Y1(Xc � b1Y1 � b2Y2) = �2[Cov(Y1; Xc)� b1V ar(Y1)� b2Cov(Y1; Y2)] = 0
�2X
Y2(Xc � b1Y1 � b2Y2) = �2[Cov(Y2; Xc)� b2V ar(Y2)� b1Cov(Y1; Y2)] = 0.
These can be simpli�ed by observing that Cov(Yj ; Xc) = Cov(�jXc + �c) = �jV ar(Xc) for all
j 2 f1; 2g. Therefore, we �rst substitute for Cov(Yj ; Xc) = �jV ar(Xc), and then divide the �rst
and second �rst-order conditions by �1 and �2, respectively. Setting them equal to one another,
yields
b1V ar(Y1) + b2Cov(Y2; Y2)
�1=b2V ar(Y2) + b1Cov(Y2; Y2)
�2.
Rearranging, we see that
b1b2=�1V ar(Y2)� �2Cov(Y1; Y2)�2V ar(Y1)� �1Cov(Y1; Y2)
= �1 �2. �
5.2 Proof of Proposition 2
In light of the wage contract W (P ) = w + �P , shareholders solve the following maximization
program:
Max c;�
a�c + a�f � C(ac; af )�
r
2[�2bc
2V ar(Yc) + �2b2fV ar(Yf )],
subject to the constraints that the e¤ort choices a�c and a�f are implicitly determined by the man-
ager�s �rst-order conditions:
@Yc@ac
(�bc)� Cac =
� 1
1 + 2�1 +
2 1 + 2
�2
�(�bc)� Cac = 0
@Yf@af
(�bf )� Caf = �bf � Caf = 0. (15)
The necessary �rst-order condition for the optimal contracting weight � is:�@a�c@�(1� Cac)� r�b2cV ar(Yc)
�+
�@a�f@�
(1� Caf )� r�b2fV ar(Yf )�= 0 (16)
24
From the manager�s �rst-order conditions in (15), we see that @a�c
@� =bc
Cacac
� 1
1+ 2�1 +
2 1+ 2
�2
�and
@a�f@� =
bfCaf af
. Solving for the ��� when the accounting information is ignored (as posited by
the wage contract W (P ) = w + �P ), we obtain
��� =bc
� 1
1+ 2�1 +
2 1+ 2
�2
�(1� Cac)
rCacac
�b2cV ar(Yc) + b
2fV ar(Yf )
� + bf (1� Caf )
rCafaf
�b2cV ar(Yc) + b
2fV ar(Yf )
� .The stock price, while e¢ ciently aggregating the information relevant to ac contained in Y1 and Y2,
does not e¢ ciently weight the di¤erential costs of e¤ort. In contrast, if shareholders optimally con-
tract on both the accounting measures and stock price, the equilibrium contract weights according
to (9) and (10) are:
�c =
� 1
1+ 2�1 +
2 1+ 2
�2
�(1� Cac)
rCacacV ar(Yc)� �bc
and
�� =(1� Caf )
rCafaf bfV ar(Yf ).
Thus, conditioning on both the accounting numbers and the stock price in the wage contract
e¢ ciently weights the di¤erential costs of information, whereas the expression for ��� does not. �
25
6 References1. Aggarwal, Rajesh and Andrew Samwick, 1999, �The Other Side of the Trade-o¤: The Impactof Risk on Executive Compensation�, Journal of Political Economy 107-1, 65-105.
2. Anderson, Mark, Rajiv Banker, and Sury Ravindran, 1999, �Interactions Between Compo-nents of Executives�Compensation and Market and Accounting Based Performance Mea-sures�, working paper AIM-98-2, School of Management, University of Texas at Dallas.
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26
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Table 1: Descriptive Statistics
Variable Obs. Mean Median SD Min Max
MV of Equity 6,251 7,806 3,143 15,211 120 339,539
Book Assets 6,251 11,646 3,229 21,762 147 304,142
Long-Term Debt 6,251 1,755 514 4,578 0 80,923
Earnings 6,251 385.7 156.0 829.2 -7,987 8,203
EVA 6,251 -37.42 0.783 534.8 -6,604 4,821
Raw Returns 6,251 0.239 0.184 0.364 -0.703 5.44
Abnormal Returns 6,251 0.177 0.266 0.255 -0.986 1.04
Corr(uearn, ab. Ret.) 549 0.336 0.400 0.355 -0.927 0.982
Corr (ueva, ab. Ret.) 549 0.123 0.125 0.354 -0.863 0.861
Corr (uearn, ueva) 549 0.403 0.495 0.432 -0.896 0.991
SD (uearn) 549 0.0405 0.0307 0.300 0.0051 0.225
SD (ueva) 549 0.0470 0.0348 0.391 0.0041 0.256b�� (optimal weight ueva) 549 0.241 0.0 0.355 0.0 1.0
Salary 2,996 0.707 0.660 0.326 0 3.649
Bonus 2,996 0.758 0.506 1.022 0 11.79
Total Compensation 2,996 3.980 2.413 6.786 0.0032 202.2
Notes: All dollar �gures are in millions. Ueva and Uearn are residuals from regressing EVA andearnings, respectively, on last year�s value, all scaled by market value of equity. Abnormal returns arecomputed as raw returns less the return on the value-weighted S&P 500 Index. b�� is the optimal weight onEVA versus earnings.
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Table 2.1: Simple Correlations Between Compensation,Performance Measures and Returns
D CashCompensation
D TotalCompensation
D earn D EVARaw StockReturn
AbnormalStock Return
D CashCompensation
1
D TotalCompensation
0.292 1
D earn0.346 0.0918 1
D EVA0.276 0.0841 0.625 1
Raw StockReturn
0.303 0.164 0.197 0.147 1
AbnormalStock Return
0.342 0.176 0.252 0.155 0.897 1
Notes: Percentage changes in various measures of compensation and performance, pre�xed by �D�.2,087 observations remain after dropping all �rms with only one observation per executive. Changes in EVAand Earnings are scaled by lagged market value of equity rather than their own lagged levels.
Table 2.2: Simple Correlations Between Weighting Schemes andFirm Characteristics
b�� b��L b�naive b�naiveL MV of Equity Assets Leverage Tobin�s qb�� 1b��L 0.585 1b�naive 0.202 0.122 1b�naiveL 0.173 0.166 0.789 1MV of Equity 0.024 -0.010 0.048 0.038 1Assets 0.021 0.046 0.026 0.012 0.496 1Leverage 0.010 0.054 -0.020 -0.024 0.033 0.378 1Tobin�s q 0.042 0.023 0.132 0.137 0.294 -0.170 -0.454 1
Notes: Simple correlations with di¤erent weighting schemes for EVA versus Earnings (b��). b�� isthe optimal weight computed with innovations from 1986-1997, b��L is the optimal weight computed withinnovations from 1978-1997, b�naive is the naive volatility-based weight equal to V ar(uearn)
V ar(ueanr)+V ar(ueva) using
innovations from 1987-1997, b�naiveL is identical except that it uses innovations from 1978-1997. Leverageis the average ratio of long-term debt to total book assets averaged from 1986-1997 and Tobin�s q is the ratioof the book value of debt plus the market value of equity to total book assets, also averaged over 1986-1997.549 observations (one per �rm).
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Table 3: Determinants of Log Total Compensation for Firms thatTheoretically Should and Should Not Use EVA
Explanatory variables Full-sample Firms with b�� = 0 Firms with b�� > 0Constant 2.53� 2.41� 2.75�
(12.23) (8.73) (8.79)Lagged Ln(Total Comp) 0.664� 0.664� 0.653�
(23.92) (17.81) (16.00)Uearn 0.553 1.014�� -0.114
(1.151) (2.11) (0.202)Ueva -0.0234 -0.403 0.715
(-0.071) (-0.915) (1.437)Raw Stock Return 0.301� 0.338� 0.261�
(4.76) (3.37) (2.89)Tobin�s q 0.0971 0.227 -0.0105
(0.543) (1.00) (0.400)Market Value of equity 5.523� 4.022�� 7.06�
(millionths) (4.14) (2.12) (4.17)Leverage 0.143 0.303� -0.0448
(1.524) (2.355) (0.337)Total Assets 1.174��� 1.311 1.44(millionths) (1.793) (1.672) (1.39)Observations 2,090 1,180 910Adjusted R2 0.501 0.490 0.519
Notes: Ueva and Uearn are residuals from regressing EVA and earnings, respectively, on last year�s value,all scaled by market value of equity. b�� is the optimal weight on EVA versus earnings. T-statistics basedon robust standard errors allowing for heteroskedasticity in parantheses. * denotes statitistical signi�canceat the 1% level, ** at the 5% level, and *** at the 10% level.
30
Table 4: The E¤ect of our Optimal Weights on the use of EVAand Earnings in Ln(Total Compensation)
Dependent Variable Ln(Total Compensation)
Explanatory variables b��weights b�� weights(no negativityrestrictions)
b��weights(No StockReturns)
b�naiveweightsConstant 2.543� 2.550� 2.519� 2.532�
(12.254) (12.348) (12.051) (12.202)Lagged Ln (Tot. Comp) 0.663� 0.663� 0.662� 0.664�
(23.927) (23.932) (23.689) (23.907)Uearn 0.718�� 0.636�� 1.289� 0.536
(2.173) (2.007) (4.101) (1.537)b�� � [Ueva� Uearn] 1.231�� 0.166� 1.320(1.989) (3.665) (2.118)b�Naive � [Ueva� Uearn] -0.198
(-0.301)Raw Stock Return 0.297� 0.293� 0.299�
(4.669) (4.609) (4.725)Tobin�s q 0.005 0.10 0.027 0.012
(0.280) (0.623) (1.643) (0.658)Market value of equity 5.53� 5.39� 5.71� 5.52�
(millionths) (4.180) (4.049) (4.273) (4.135)Leverage 0.147 0.135 0.216�� 0.142
(1.567) (1.439) (2.314) (1.521)Total Assets 1.18��� 1.23��� 1.12��� 1.16���
(millionths) (1.823) (1.896) (1.751) (1.785)Adjusted R2 0.50 0.50 0.50 0.63
Notes: Sample includes 2,090 observations, weighted by the square root of the number of observationsfor each �rm. Ueva and Uearn are residuals from regressing EVA and earnings, respectively, on last year�svalue, all scaled by market value of equity. b�� is the optimal weight on EVA versus earnings. b�naive is thenaive volatility-based compensation weights. T-stats based on robust standard errors in parentheses. *denotes statitistical signi�cance at the 1% level, ** at the 5% level, and *** at the 10% level.
31
Table 5: Regressions Using First Di¤erences in Cash and TotalCompensation
Dependent Variable 4(Cash Compensation) 4(Total Compensation)Explanatory variablesConstant 0.070� 0.066
(2.585) (0.870)D earn 1.714� 0.998�
(8.194) (2.841)b�� � [Deva�Dearn] 0.898� 1.227���
(2.978) (1.908)Raw Stock Return 0.251� 0.317�
(9.189) (4.692)Tobin�s q -0.015� -0.001
(-3.015) (-0.073)Market value of equity 0.326 0.835(millionths) (0.965) (0.703)Leverage -0.006 0.020
(-0.158) (0.209)Total Assets -0.066 -0.075(millionths) (-0.234) (-0.111)Observations 2,128 2,090Adjusted R2 0.18 0.025
Notes: D earn and D EV A are the percentage changes in Earnings and EVA, respectively, scaled bylagged market value of equity rather than their own lagged levels. b�� is the optimal weight on EVA versusearnings. T-stats based on robust standard errors in parentheses. * denotes statitistical signi�cance atthe 1% level, ** at the 5% level, and *** at the 10% level.
32
Table 6: The E¤ect of Controlling for EVA Adopters
Explanatory variables Adopters Non-Adopters Adoption Interaction TermConstant 3.780� 2.458� 2.544�
(6.085) (11.333) (12.261)Lagged Ln (Tot. Comp) 0.493� 0.673� 0.663�
(5.893) (23.150) (23.911)Uearn 1.311��� 0.702��� 0.701��
(1.894) (1.916) (1.983)b�� � [Ueva� Uearn] 3.144 1.150��� 1.241��
(0.657) (1.834) (1.979)Adopter Indicator Variable 0.044
(0.846)Adopter �EV A 0.222
(0.421)Raw Stock Return 0.193 0.300� 0.299�
(0.660) (4.565) (4.657)Tobin�s q 0.019 0.009 0.005
(0.259) (0.508) (0.273)Market value of equity 2.64 5.76� 5.44�
(millionths) (0.609) (3.883) (4.105)Leverage 0.296 0.146 0.142
(0.889) (1.486) (1.521)Total Assets 8.88 1.05 1.24���
(millionths) (1.370) (1.598) (1.908)Observations 159 1931 2,090Adjusted R2 0.44 0.51 0.50
Notes: Ueva and Uearn are residuals from regressing EVA and earnings, respectively, on last year�s value,all scaled by market value of equity. b�� is the optimal weight on EVA versus earnings. Adopter takes thevalue of 1 if the �rm is an EVA-adopter, and zero otherwise. T-statistics based on robust standard errorsallowing for heteroskedasticity in parantheses. * denotes statitistical signi�cance at the 1% level, ** at the5% level, and *** at the 10% level.
33
Table 7: Reliance on Accounting Measures versus Stock Price:Do Firm Size and Growth Opportunities Matter?
Dependent Variable Ln(Total Compensation)Explanatory variables Low Tobin�s q High Tobin�s q Large Firms Small FirmsConstant 2.424� 2.458� 3.268� 2.786�
(7.719) (8.404) (9.285) (8.098)Lagged Ln (Tot. Comp) 0.646� 0.663� 0.580� 0.635�
(17.422) (16.540) (12.887) (15.331)Uearn 0.857�� 0.856 0.262 0.771��
(2.348) (1.175) (0.397) (2.074)b�� � [Ueva� Uearn] 0.732 1.336 0.785 1.351(0.770) (1.491) (0.878) (1.413)
Raw Stock Return 0.215�� 0.332� 0.259�� 0.300�
(2.446) (3.430) (2.330) (3.929)Tobin�s q 0.214��� 0.004 -0.004 -0.053
(1.702) (0.198) (-0.218) (-1.205)Market value of equity 8.03� 4.75��� 4.90� 76.0�
(millionths) (2.704) (1.946) (3.828) (2.947)Leverage 0.102 0.332�� 0.276��� -0.99
(0.686) (2.341) (1.705) (-0.776)Total Assets 1.33 1.11 0.517 3.02(millionths) (1.475) (0.246) (0.755) (0.959)Observations 1,040 1,050 1,046 1,044Adjusted R2 0.53 0.48 0.39 0.42
Notes: Ueva and Uearn are residuals from regressing EVA and earnings, respectively, on last year�s value,all scaled by market value of equity. b�� is the optimal weight on EVA versus earnings. T-statistics basedon robust standard errors allowing for heteroskedasticity in parantheses. * denotes statitistical signi�canceat the 1% level, ** at the 5% level, and *** at the 10% level.
34