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SMOOTHING, CONSERVATIVE SMOOTHING,
AND TRUTH-TELLING:
THE EFFECT OF THE PRESSURE TO REPORT TARGET
EARNINGS ON THE EARNINGS MANAGEMENT STRATEGY AND
THE LIKELIHOOD OF A RESTATEMENT
Hila Bracha Yaari
Tel-Aviv University
And
Varda (Lewinstein) Yaari*
Morgan State University
Tel: 443-885-3967
July 2007
.
We grateful to Pete Dadalt, Masako Darrough, and Hila Yaari for valuable comments and
discussions. The paper has benefited from the comments of the participants of the
CAAA, Quebec, June 3, 2005, and especially those of the discussant, Alfred Wagenhofer,
and the moderator, Mary McNally, and to the participants of AAA meeting, SanFrancisco, August 2005, and especially those of the discussant, Bjorn Jorgensen.
Key words: earnings management, smoothing, repeated principal-agent contract,
restatement
Department of Accounting and Finance, Earl G. Graves School of Business and Management, 1700 E. Cold
Spring Lane, Baltimore, MD, 21251. Tel: 001-443-8853445, Fax 001-301-6544670. E-mail:
alexgum21@hotmail.com
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Smoothing, Conservative Smoothing, and truth-telling:
The effect of the pressure to report target earnings on the
earnings management strategy and the likelihood of a
restatement
ABSTRACT
This analytical study offers an insight into why the largest accounting scandals
and meltdowns occur in the United States, which is renowned for having the most
developed financial accounting system and firms with the lowest level of managed
earnings. We postulate that the answer lies in the demand for beating targets, where
targets are set for a variety of reasons, such as public debt (since debt covenants specify a
minimum accounting performance) and market expectations. We show that without the
demand to meet targets, the optimal reporting strategy is smoothing: the report overstates
(understates) low (high) outcomes. When there is demand to beat a target report, the
earnings management strategy is conservative: instead of overstating low earnings, the
firm either "takes a bath" or subtracts a downward bias from a truth-telling report. We
also show that the firm combines a low level of discretionary accruals with a restatement,
because a restatement de facto allows the firm to report the same dollar performance
twice: in the past, when it overstated performance, and then again when the past is
corrected and earnings are boosted at present.
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1. INTRODUCTION
The largest accounting scandals and meltdowns have happened in the United States. In a
study of 919 restatements between 1997 and 2002, the U.S. General Accounting Office (GAO)
stated: "[W]e found that the unadjusted and market-adjusted immediate losses in the market
capitalization of restating companies approximated $100 billion and $96 billion, respectively”
(GAO 2003 release GAO-03-395R). Coffee 2003, p. 5, reports that "approximately 10% of all
publicly listed U.S. companies restated their financial statements at least once between 1997 and
June 2002 and the annual rate of financial restatements soared during the latter half of the
1990s."
On the one hand, these facts come as no surprise, because public U.S. firms manage earnings
away from the truth. Over 97% of the respondents in a survey of financial officers by Graham,
Harvey, and Rajgopal 2005 admit to preferring "smoothing."1 If a firm overstates earnings long
enough, accruals will reverse and the truth will catch up with it, making the firm restate previous
reports.
On the other hand, these facts are a puzzle, since the U.S. system is known for its welldeveloped financial system, with checks on pernicious earnings management. Dechow and
Schrand 2004, p.62 comment: "A question that naturally arises in a discussion of earnings
management is how companies are able to get away with it. Citations of the U.S. securities
markets as the best regulated, most liquid, most efficient markets in the world are too numerous
to mention" (emphasis added). Furthermore, on the global level, Leuz, Nanda, and Wysocki
2003 find that U.S. firms have the lowest earnings management score (the aggregate of (1)
smoothness of earnings relative to volatility of cash flows, (2) the correlation between cash flows
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and accruals, (3) a discretionary accruals measure, and (4) loss avoidance). In sum, what is
unique to earnings management by U.S. firms such that they exhibit the lowest level of earnings
management concurrently with some of the largest accounting scandals?
Our explanation is based on the demand to beat target earnings numbers. The firm has to
deliver a target accounting earnings performance, and when it does not, an accounting scandal in
the wake of restatement might take place. Targets can arise for a variety of reasons: Firms do not
wish to disappoint analysts, so about 40% of public firms meet or beat the consensus analysts'
forecast (e.g., Bartov, Givoly, and Hayn 2002). Firms also may wish to show stable growth
relative to the same quarter of the previous year (e.g., DeGeorge, Patel, and Zeckhauser 1999;
Graham, Harvey, and Rajgopal 2005), avoid losses or earnings decreases (e.g., Burgstahler and
Dichev 1997; DeGeorge, Patel, and Zeckhauser 1999), and report a string of earnings increases,
because they are aware that when the string “breaks,” the price plummets—the “torpedo effect”
(e.g., DeAngelo, DeAngelo, and Skinner 1996; Barth, Elliott, and Finn 1999; Kim 2002). Firms
that issue bonds are concerned with reporting earnings that exceed minimum levels, since debt
covenants are based on accounting earnings (Smith and Warner 1979), and unlike private debt,
debt covenants in public debts are not renegotiated (Dichev and Skinner 2002). Firms preparing
for an IPO (Initial Public Offering) whose owners have a long-run perspective may set public
targets for earnings (e.g., Hellman 1999; Hochberg 2003; Wan-Hussin, Nordin, and Ripain
2003).
We examine the reporting strategy of firms that face the challenge of beating a target in
their forthcoming reports, modeling it as a principal-agent game between owners and the
manager. As a benchmark case, we show that in repeated principal-agent relationships, the
optimal strategy without targets is smoothing. That is, the reported earnings overstate low
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outcomes and understates high ones. When, however, a firm anticipates beating a target, its
reporting strategy is more conservative, as the firm takes a bath or reports the truth less a bias
when smoothing would prescribe an overstatement. This strategy creates a reserve of reported
earnings in order to beat future targets. To distinguish between this strategy and smoothing, we
refer to it henceforth as conservative smoothing. We show that conservative smoothing is the
equilibrium reporting strategy when the future outcome is uncertain. We next examine
restatements. When a restatement reveals the truth, it can be used as an earnings management
vehicle. Aggressive reporting de facto borrows reported earnings from the future. Restatement
undoes the previous borrowing by correcting the past report and shifting the borrowed reported
earnings to the period in which a restatement is made. That is, suppose that the true earnings in
2003 were $1.80 per share, and the firm increased them through aggressive reporting to $2.00.
Then, in 2004 the firm announces that its 2004 earnings are $1.90 before restatement, but
because it has to restate its 2003 earnings, its post-restatement earnings are actually $2.10 per
share. The firm thus achieves its target of reporting $2.00 and $2.10 in 2003 and 2004,
respectively. Examples of this feature of a restatement abound. Even Enron, in its 8-K filing on
November 8, 2001, announced that it "planned to restate its financial statements for 1997 to 2000
and the first two quarters of 2001 …the expected effects would 'include a reduction to reported
net income of $96 million in 1997, $113 million in 1998, $250 million in 1999, and $132 million
in 2000, increase of $17 million for the first quarter of 2001 and $5 million for the second
quarter…” (Jenkins 2003, p. 8; emphasis added).
Employing the “trembling-hand-perfection” concept of Selten, we show that restate
earnings when they mistakenly were too aggressive, so that on the average, a firm may both
reports conservatively and restate earnings. This result is robust to the case when the firm must
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beat targets repeatedly and the present target is not too ambitious. At the same time, meeting
targets repeatedly reduces the scope of hoarding reported earnings to beat future targets.
Our results explain the phenomenon of huge restatements by some U.S. firms when all
firms are characterized by a low level of earnings management. Others attempt to explain the
accounting scandals as the result of misbehavior by a few "bad apples" (Demski 2002). 2
Alternatively, Coffee 2003 claims that euphoria in the capital market drove firms to meet
expectations by inflating earnings:
Despite this earlier preference for income-smoothing, by the end of the 1990s,
these same firms were robbing future periods for earnings that could be
recognized immediately. In short, “income smoothing” gave way to more
predatory behavior. Interestingly, restatements involving revenue recognition
produced disproportionately large losses. (Coffee 2003, p. 23)
Yet when all firms manage earnings, all apples are rotten, and if all firms rob future
earnings, why do just 10% restate earnings? Our study identifies conditions under which the
same reporting strategy can yield low accruals for some firms and restatements for others.
In addition, although researchers are aware that firms "take a bath" and establish “cookiejar reserves" (Levitt 1998), empirical research tends to associate earnings management with high
levels of accruals (Beneish 1997). For example, Hochberg 2003 contends that IPO firms that are
supervised by venture capitalists engage less in earnings management because their discretionary
accruals are lower. We, however, offer a different interpretation. These firms, which are
characterized by long-term relationships between venture capitalists and the firm, engage in
conservative smoothing in anticipation of the need to deliver performance in the future.3
Finally, we analyze restatement as an earnings management strategy. To a large extent, a
restatement is viewed as "a moment of truth," as it exposes prior unobservable earnings
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management activity (see, e.g., Marquardt and Wiedman 2002, and the citations therein). Yet it
is also an earnings management vehicle, because the firm knows that if worst comes to worst, it
can admit to previous aggressive reporting and therefore can report performance twice, once
when it is "borrowed" to manage earnings and then again upon a restatement.
The paper proceeds as follows: Section 2 presents the model. Sections 3 and 4 analyze
the optimal reporting strategy and the probability of a restatement, respectively. A summary and
conclusions are given in Section 5. Proofs are available upon request.
2. THE MODEL
We study the firm as a two-period, principal-agent contract between the owners—the
principal—and the manager—the agent.4 In each period, the firm generates economic earnings,
xt, which are observed by the manager alone, xt Xt=[xt, xt ] t=1,2. The economic earnings,
referred to also as the outcome, are determined jointly by the unobservable periodic effort of the
manager, at, at  [ a, a ] , which is chosen at the beginning of each period, and nature.
The assumption that the manager alone observes the outcome implies that at the end of
the first period he alone knows x1, and at the end of period 2 he alone knows x1 and x2. The
owners only observe the yearly accounting reports, m1 and m2. We assume that at the end of the
second period, the total outcome, y, is observable. Hence, the total accumulated accounting
earnings, m1+m2, must equal the total economic earnings, y, y≡ x1+x2.5 Therefore, m2 is uniquely
determined by the accumulated outcome, y, and the previous report, m1, as follows:
m2 ≡ y  m1.6
(1)
Equation (1) implies that the owners infer the accumulated outcome, y, by the end of
period 2. The first-period report thus is a vehicle to divide the report of firm's value, y¸ between
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the two periods. This feature is supported by our assumption, similar to that of Demski and
Frimor (1999), that the manager commits to stay with the firm for the full duration of the
contract, and that the owners commit to the manager's employment for the two periods.7
Because the contract must be based on mutually observable variables, the manager's
incentives contract is based on the reports, m1 and m2. At the beginning of the first period, the
owners contract with the manager and design his payment schedules, S,
S  {S1(m1), S2(m1,m2)}, and the accounting policy, M. The accounting policy determines the set
of admissible reports, m1, {m1}  M. Both the owners and the manager know that the firm can
manage earnings by either inflating or deflating them.8
We assume that the reporting technology allows the manager the flexibility to overstate
or understate the first-period outcome. Hence, designing both compensation and the reporting
policy might yield a plethora of contract/reporting policies, all yielding the same payoff. To
illustrate, if the contract is S=0.2m when the manager reports the truth, the contract S=0.1m with
100% overstatement (m=2x) is equivalent. The common remedy to this multiplicity problem is
to invoke the revelation principle, which would let us restrict the analysis to incentivecompatible truth-telling equilibria (Ronen and Ronen 2003). In our setting, however, the
revelation principle does not apply, because target beating renders truth-elicitation prohibitively
costly.
The owners derive utility over the series of earnings, xtSt. Their payoff in the second
period is conditional on whether the firm's report exceeds a target report, L. The target report
represents a potentially traumatic event, since reporting less than L has value-decreasing
consequences. We assume that the target exceeds the minimum second-period outcome, L > x1,
so that if the second-period outcome is too low and insufficient reported earnings are reserved
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from period 1, the firm may fail to meet the target. We treat L as an exogenous variable that is
determined by the relationships between the firm and its constituency; its determination is
beyond the scope of this paper. Endogenous determination of L requires admitting a third player,
but this added complexity does not affect results qualitatively so long as L exceeds the minimum
second-period outcome. Since a lower target has no teeth, this requirement seems quite mild.
Denote the owners' piecewise von Neumann-Morgenstern utility function over the series
of reported earnings by V. The owners derive ex post piecewise utility of
tV(xtSt) – g(L– m2)
if m2  L,
tV(xtSt)
if m2 > L.
If the firm beats the target, the owners' payoff is a strictly increasing function of their
residual share of earnings, but if the firm does not, the owners lose utility, g, which is a function
of the gap between the target and the second-period report, Lm2. We make the standard
assumption that V is a strictly increasing concave function, V > 0, V > 0. We make the
following assumptions on g: (i) g is a positive function; i.e.,  m2  L, g>0. This assumption
guarantees that not beating a target is value-decreasing for the owners. (ii) The loss function is
increasing in the gap between the target and the second-period report; i.e., g=
g
>0.
 (L  m2 )
This assumption implies that the greater the gap between report and the target, the higher the
loss.9 (iii) Just missing the target is traumatic; i.e., g + (0)  . This mathematical assumption
reflects the psychological reality of counterfactual reasoning (Roese and Olson [1995]),
whereby, for example, people are known to experience much more pain when they miss an
airplane by two minutes than when they miss it by six hours.10 (iv) To ensure that the utility loss
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from missing a target does not overwhelm the owners' utility, we assume that
G(0)  0, where G=  g(z )dz . An example of a function that fulfils the four conditions is g(Lm2)
=
1
.
L  m2
The manager’s objective function is to maximize the expected indirect utility over the
stream of future incomes, E[U(St)|a1,a2], net of disutility over effort, W(at), t=1,2, where
U > 0, U < 0, W > 0, W > 0. The manager is risk-averse, effort-averse with an increasing
marginal disutility over effort. We also assume that W(a )  0 and W(a )  . This assumption
guarantees that the first-order conditions of the manager’s objective function with respect to
effort hold as strict equalities; i.e., the solution is interior. As is common in the principal-agent
literature, we assume that if the manager is indifferent between different effort levels, he chooses
the highest one to please the owners. The manager is willing to participate in the contract when it
guarantees him his reservation utility, U0, obtainable at an alternative job.
We assume that x1 and x2 are independent random variables with prior distribution
functions of f(x1|a1) and f(x2|a1,a2)
and corresponding CDF,
F(x1|a1) and F(x2|a1,a2),
respectively. That is, f(x1,x2|a1,a2)= f(x1|a1)*f(x2|a1,a2). To reflect the fact that some decisions
are investment decisions with repercussions that extend beyond the period in which they are
made, we let the second-period outcome depend on first- and second-period actions.11 These
functions are common knowledge between the owners and the manager. We also make the
standard technical assumptions:
(i)
All functions are twice continuously differentiable (expect for g at zero).
(ii)
The supports of the distribution functions are independent of effort.
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(iii)
The Maximum Likelihood Ratio Condition (MLRC) holds in each period:
f a ( x1 a1 )
1
f ( x1 a1 )
(iv)
ISBN : 978-0-9742114-9-7
and
f a ( x2 a1 , a2 )
t
f ( x1 a1 , a2 )
increase in x1 and x2, respectively.
The manager's utility is concave in the report.
Condition (i) is a regularity condition. Condition (ii) states that effort cannot be inferred
from the observed reports (Holmstrom 1979). Hence, the contract must provide the manager
with incentives to exert effort. By condition (iii), the greater the effort, the higher the expected
outcome. This condition is well-established in the principal-agent literature, because it is crucial
to the conflict of interests between the principal and the agent. The work-averse agent prefers to
work less, and the principal prefers him to work more, because, by the MLRC, higher effort
increases the expected value of the firm. Condition (iv) guarantees that the first-order conditions
used to characterize the equilibrium below are necessary and sufficient to derive the optimal
reporting strategy, the contract, and the probability of a restatement. Without this condition, if the
concavity assumption is not met, the Kuhn-Tucker conditions with respect to the report, m1, are
neither necessary nor sufficient (Chiang 1984), nor do the owners have a well-behaved program
in convex programming (Luenberger 1969). Note, however, that because the manager's utility is
a strictly concave function, this condition does not rule out a convex compensation schedule.
The only condition is that technology and the preferences of the owners and the manager do not
yield contracts that are too convex.
3. THE EQUILIBRIUM
3.1. The Derivation of the Equilibrium
We solve the Nash equilibrium of this setting backwards. We analyze the manager’s
decisions first and then substitute them into the owners' program.
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3.1. The Manager
The manager makes three decisions: two on actions, a1 and a2, and one on the first-period
report, m1. Since there is no new information between the choice of the first-period message and
the choice of the second-period effort, we assume that he chooses both simultaneously.
At the end of the first period, after observing the first-period outcome, the manager
makes his choices by solving the following program:
x1 , max U( S1 (m1 ))   U(S2 ( y  m1 ) f ( x2 a1 , a2 )dx2  W(a2 )
m1 , a2
s.t. {m1}  M, and a2  [ a, a ].
We specify the reporting policy of the owner as indicating a report mˆ 1 ( x1 ) . M and  are
the Lagrange multiplier of the constraint that is dictated by the accounting policy and the
Lagrangian of this program, respectively. The first-order-conditions are
 0
 M 
m1:
 0
m1 
 0
if m1  x1
if x1  m1  x1
if m1  x1


,


(3)
 M
where
= U( S1 (m1 )) S1   U(S2 ( y  m1 ) S2 f ( x2 a1 , a2 )dx2   M .
m1
 M : mˆ 1 ( x1 ) m1 =0.
(4)
a2:  U( S2 ( y  m1 )) f a2 ( x2 a1 , a2 )dx2  W(a2 )  0.
(5)
Unless the manager’s choice coincides with the message dictated by the owners, the
optimal report equates the marginal benefit over compensation of both periods with respect to the
message. The optimal message satisfies two demands: the demand for consumption smoothing,
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U1  EU 2 , where "E" denotes an expectations operator, and the demand for an increase in
wealth, S1  ES2 . To see the difference between the two, suppose that S1=0.7m1 and S2=0.8m2.
Then, without the demand for consumption smoothing, the manager is better off reporting
everything in period 2, m1=x1, m2=y. (More examples are given below.)
The second-period effort is chosen for its effect on the second-period report. The
manager chooses effort by equating the marginal benefit due to increased monetary payment
with the marginal disutility over effort. Recall that our assumptions on disutility over effort
imply an interior solution (Eq. (5) holds as a strict equality).
Definition 1:
(a) "Truth-telling" occurs if the first-period report coincides with the first-period outcome.
That is, m1=x1, and therefore m2=x2.
(b) "Smoothing" occurs if the first-period report overstates low outcomes and understates
high outcomes.
That is, there is a critical value of x1, x1c , such that if
x1 < (>) x1c , then m1 > (<) x1.
(c) "Aggressive reporting" occurs if the first-period report overstates all outcome. That is,
m1 > x1 for all x1.
(d) "Taking a bath" occurs if the firm reports the minimum first-period outcome, x1 ,
m1= x1 , even when the actual outcome is higher, x1 > m1= x1.
Definition 1 is consistent with the standard definitions of earnings management strategies
(Scott 1997).
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Proposition 1:
If M = 0, then the manager's reporting strategy is smoothing. If M >0, the manager reports
the message that is dictated by the owners; i.e., m1 ( x1 ) = mˆ 1 ( x1 ).
The smoothing result has already been established in the smoothing literature (see Dye
1988; Yaari 1991; Meth 1996; Boylan, and Villadsen 1997; Demski 1998; Sankar and
Subramanyam 2001; Srinidhi, Ronen, and Maindiratta 2001; and others). The fact that m1
allocates the report of aggregate outcome y between the two periods implies that the reporting
strategy can either report all in one period or divide the outcome between the two periods.
Smoothing obtains because the manager prefers to split the reported y between the two periods.
The manager maximizes expected utility by overstating (understating) the first-period message
when the first-period outcome is low (high) and the expected second-period compensation is
higher (lower), borrowing (hoarding) reported outcome from (for) the second period. Such a
reporting strategy maximizes the manager’s utility because the marginal utility over the firstperiod report is a deceasing function of this report. An optimal allocation of a dollar report
between two periods when the marginal payoff is a decreasing function is to split it to even out
the marginal payoff between the two periods.12
If, however, the owners' reporting policy does not enable the manager to smooth
optimally, he will make the report that the owners prefer, because the owners can enforce their
policy by penalizing the manger when the second-period cumulative outcome is inconsistent
with their design.
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Denote the equilibrium first-period report and second-period effort by *. At the beginning
of the first period, the manager chooses the first-period effort, a1, by solving the following
program:
max
m1 , a2
 U(S (m )) f ( x
*
1
1
1
a1 )dx1   U(S2 ( y  m1* ) f ( x1 a1 ) f ( x2 a1 , a2* )dx1dx2  W(a1 )  W(a2* )
s.t. a1  [ a, a ].
By our assumption on the disutility over effort, the first-order condition yields
a1:
 U(S (m )) fa ( x
1
*
1
1
1
a1 )dx1   U(S 2 ( y  m1* )) f a1 ( x1 a1 ) f ( x2 a1 , a2* )dx1dx2  W (a1 ) =0. (6)
The manager chooses effort by equating the marginal benefit due to increased monetary
payment with the marginal disutility over effort.
3.2. The Owners
With “E” denoting the expectations operator, the owners solve the following program
when they design the manager’s compensation:
x1
max
S1 , S2 , m1 , a1 , a2 , m1
x1 x2
  V( x
2
EV(S , m1 , m2 L,a1 , a2 )=  V( x1  S1 (m1 )) f ( x1 a1 )dx1 
x1
 S 2 (m2 )) f ( x1 a1 ) f ( x2 a1 , a2 )dx1dx2 
x1 x 2
x1 min{L+(m1  x1 ), x 2 }

x1

G(L  m2 ) f ( x1 a1 ) f ( x2 a1 , a2 )dx1dx2
x2
s.t.
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x1
EU(S a1 , a2 )  W(a1 )  EW( a2 )   U( S1 ( m1 )) f ( x1 a1 ) dx1  W( a1 ) 
x1
x1

x1
 x2

  U(S2 ( y  m1 ))( x2 a1 , a2 )dx2  W(a2 )  f ( x1 a1 )dx1  U 0 .
 x2

(IR)
{a1,a2,m1} = argmax EU(S a1 , a2 )  W(a1 )  EW( a2 ) .
(IC)
x1  m1  m1 ,
at [ a , a ], t 1,2
The contract must guarantee the manager his reservation utility level—the (IR)
constraint—and take into account the effect of the compensation schedules on the manager's
choices. That is, the owners are the Stackelberg leader in this principal-agent game, because the
compensation schedules and the reporting policy determine what the manager chooses for effort
in both periods and as the first-period report—the (IC) constraints. Note that the Lagrange
multiplier for a1 (Eq. (7)) is a scalar, but the Lagrange multipliers for the first-period message
and second-period effort are functionals of x1. In our working paper version, we set the Euler
equation of this program (see Gelfand and Fomin 1963) and solve it for the two compensation
schedules. Since this characterization is useful only to establish that the incentives contract is a
pointwise function of performance, a result that is already well-established in the principal-agent
literature, it is omitted here.
Proposition 2:
The owner design an increasing incentive contract.
Proposition 2 conveys the intuitive result that the owners design an incentive contract
that increases in the reported outcome. While this result is quite common in the principal-agent
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literature, still it does not extend here because the fact that the manager can manipulate the report
implies that the maximum likelihood ratio that drive this result in the standard game may not
hold in our scenario.
3.2. The Firm’s Reporting Strategy
Proposition 3 presents the equilibrium reporting strategy.
Proposition 3:
Divide the range of outcomes into three regions:


I: x1  X x1  L  x2  x1 ;


II: x1  X L  x 2  x1  x1  L  x 2  m1* ( x1 ) ; and


III: x1  X x1 >L  x 2  m1* ( x1 ) .
(a) In equilibrium, the reporting strategy is as follows:

ˆ 1 ( x1 )  x1 . .
In Region I, the firm "takes a bath," m

ˆ 1 ( x1 )  x1  (L  x2 ) .
In Region II, the firm reports the truth less a negative bias, m

In Region III, the firm smoothes (as per the manager's preferences).
(b) In regions II and III, the manager and the owners obtain the same payoff as under smoothing
(given the global effect of a piecewise contract on the incentives contract), and the manager is
penalized if the firm fails to beat the target in the second period.
Proposition 3 characterizes the firm’s reporting strategy as a function of L. We divide the
set of outcomes into three regions, depending on the availability of reserved reported first-period
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earnings, m1x1, that can be reported in the second period. In Region I this reserve is too low,
because it falls short of Lx2. In regions II and III, x1 is large enough, but in Region II the firstperiod message is too high.
Since the manager prefers smoothing (see Proposition 1), the issue is when to let him do so.
The answer depends on the target. If the first-period outcome is low, the first-period report that
minimizes the likelihood of failing to beat the target is the minimum first-period message; i.e.,
the firm "takes a bath." When, however, the first-period outcome is sufficient to guarantee
beating the target, but a smoothed report might prevent the firm from beating the second-period
target if it overstates the first-period outcome, the owners induce the manager to report the truth
less just enough to guarantee that the firm will beat its targets. For example, suppose that the
target report is 50 and the minimum second-period outcome is 0, the true first-period outcome is
60, and the desirable smoothed report is 120. The maximum report that guarantees beating the
target of 50 is 10, 60-50=10. A higher report might still allow the firm to beat the target, but the
result is not certain. The manager is paid the same as under smoothing (as per Proposition 1),
given the piecewise contract, because the owners can undo the report and pay him the same as
under a smoothed report. The manager follows suit, because if he reports more, the secondperiod outcome might fall short of the target, and he would be penalized. If he reports less, he
deviates from the optimal payment schedule specified under smoothing as per Eq. (3), which is a
utility-decreasing event.
Empirically, smoothing is a well-documented phenomenon (see, e.g., Ronen, and Sadan
1981; Belkaoui and Picur 1984; Bartov 1993; Brown, Ewers, Manson, and Turner 1994; Bhat
1996; Bitner and Dolan 1996; Moyer, Shevlin, and Hunt 1996; Carlson and Bathala 1997;
Defond and Park 1997; Chaney and Lewis 1998; Oyer 1998; Beattie, Anctil, and Chamberlain
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1999; Elgers, Pfeiffer, and Porter 2000; Buckmaster 2001; Wan-Hussin and Ripain 2003). As
Levitt 1998 and Turner 2001 have noted, however, firms also engage in creating "cookie jar
reserves" and "taking a bath." Proposition 3 characterizes a smoothing strategy that never
overstates earnings. We label this strategy “conservative smoothing.”
Kirschenheiter and Melumad 2000 identify a reporting strategy of "taking a bath" when
earnings are low and smoothing when earnings are higher, but their explanation differs from
ours. They study a model in which the firm's price is based on expected future performance and
the variability of the outcome. When earnings are low, the motivation to increase the price by
enhancing the report of future earnings dominates the reporting strategy, and the firm forgoes
smoothing and creates instead a "bank" of reported performance by taking a bath. When true
earnings are good news, the firm can afford to increase the price by smoothing out the variability
of earnings. Thus, their smoothing is a means to reduce the information asymmetry between the
firm and the market. The similarity between our studies is that the target creates the demand for
"taking a bath." In our study, however, the demand for smoothing follows from the favorable
effect of letting the manager smooth on the cost of the contract. In addition, we find that there is
demand for an understated report that equals a truth-telling message less a downward bias.
We summarize the analysis with a graph that compares truth-telling, smoothing
(Proposition 1), and smoothing with hoarding of reported earnings (Proposition 3). The distance
between the truth-telling line and the managed earnings measures the earnings management
intensity locally, so that the area between the two measures the intensity of earnings management
as defined in Definition 2 below. The graph is based on L1=40, L2=50, and the slope of
smoothing is 1/2.
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FIGURE 1: REPORTING STRATEGIES
400
350
Truth-telling (45 degress line)
Smoothing (Proposition 1)
Conservative smoothing (Proposition 3)
FIRST-PERIOD REPORT
300
250
200
150
100
50
0
0
50
100
150
200
250
300
350
-50
OUTCOME
We next present the implications of Proposition 3 for earnings management.
Definition 2
The magnitude of earnings management (EM) is the expected deviation of the reported
earnings from the true earnings, EM = ∫(m1x1)dx1.
Our definition captures the intuition behind empirical studies that examine earnings
management by total accruals (e.g., Healy 1985) and the magnitude of discretionary accruals
(e.g., Kline 2000).
If the firm reports the truth for all first-period outcomes, EM=0. Such a
measure allows us to compare the magnitude of earnings management under the different
reporting strategies.
Proposition 4: Control for the effect of target-beating on expected earnings:13
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(a)
ISBN : 978-0-9742114-9-7
The smoothed message of a target-beating firm is lower for each level of
outcome.
(b)
Targets reduce the magnitude of earnings management.
Proposition 4 is a corollary to Propositions 1 and 3.
Conservative reporting reduces the
level of earnings management.
Proposition 4 implies that a low level of discretionary accruals is an indication of earnings
management to beat future targets. Our result contrasts with that of Dutta and Gigler 2002, who
find that the magnitude of earnings management increases in the target, where targets are set by
earnings forecasts (disclosed by the privately informed manager). If earnings are insufficient to
beat the target, the manager resorts to an aggressive earnings management strategy. In our study,
earnings anticipate the target. Hence, targets create demand for building a reserve of reported
earnings.
4. THE PROBABILITY OF A RESTATEMENT
In this section we analyze the connection between targets, a target-beating reporting
strategy, and the probability of a restatement.
Definition 3:
A restatement of earnings occurs when the firm announces at the end of the second
period that the reported first-period earnings were misstated, m1 ≠x1.
This definition captures the essence of restatement, whereby firms rewrite history (Wu
2002). Some restatements are initiated by auditors (WorldCom), some by the company (Enron),
and some by an investigation by the SEC (Fannie Mae, AIG). The correction of previous reports
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usually has a favorable effect on earnings in the period of restatement, because, for example,
revenues were prematurely recognized and current earnings should be boosted.
We make the following assumption that the restatement reveals the truth.
Assumptions:
(A1)
When a firm restates earnings, the firm augments earnings in period 2 by the
difference between the reported and the actual first-period earnings, m1x1.
(A2)
Restatement is costly.
This assumption indicates that a restatement can "undo" previous earnings management,
so that the total true historical earnings effectively set a limit on the size of the restatement. In
our two-period example, this assumption implies that the firm reports the truth in the second
period, because by Eq. (1), m2 without a restatement is x1+x2m1, so that with a restatement, m2=
x2. We are unaware of any study that has clarified the connection between a restatement and the
truth. Because we observe examples of repeated restatements, it seems that firms are reluctant to
reduce past earnings, and they are forced to restate that much because the truth is discovered.
Thus, a restatement has limited usefulness as an earnings management vehicle, since a firm that
inflates earnings in period 1 cannot, through restatement, "take a bath" ex post, beyond the
obvious disadvantage of the costliness of a restatement.
We are aware that in large samples the latter assumption is not innocuous. (see Jones and
Weingram 1997; Coffee 2002; and Marquardt and Wiedman 2002). Wu 2002 and Richardson,
Tuna, and Wu 2004, for example, find abnormal returns of -11% over a three-day window
surrounding the restatement event, and Wu 2002 notes that when restatement involves revenues,
the abnormal return is even lower, -14.4% or less. Restatements reduce the credibility of the
firm's accounting earnings (Wu 2002; Anderson and Yohn 2002) and increase the cost of capital
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immediately after restatement (Hribar and Jenkins 2004). We expect that if the cost of a
restatement were considered, then the difference between Proposition 3 and Proposition 4 would
disappear and the firm would choose conservative reporting over smoothing with a restatement.
As we show in the next subsection, however, this conclusion changes when the firm endeavors to
beat targets repeatedly.
4.1. The Firm Beats One Target
Proposition 5
Consider the trembling-hand-perfect equilibrium reporting strategy.
(a)
The level of earnings management (Definition 2) of a target-beating firm is lower
than that of a firm that does not beat targets.
(b)
If a firm trembled in period 1 and reported aggressively, it restates earnings in
period 2 if it allows it to beat the target.
Proposition 5 indicates that the firm now has arsenal of means to beat the target. First by
reporting conservatively, and then, if a mistake was made, by restating earnings. The reason that
a restatement is not desirable as managing earnings is that it is costly.
Proposition 5 also indicates that the finding of low earnings management globally, with big
but a few restatements is a large sample phenomenon, since any single firm that did not tremble
and reported conservatively will not restate earnings. To sharpen this point, observe that there
will be two types of firms: conservative reporters and aggressive reporters who may restate
earnings.
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4.2. The Firm Beats Targets Repeatedly
In this section, we assume that the firm has to beat a target in both periods. Since
allocating a dollar of reported outcome might involve a trade-off between competing targets, we
make the following assumption:
Assumption: Not beating a target in period 1 entails the same utility loss as not beating a
target in period 2.
This assumption implies that the owners’ utility, when the target in period t is denoted by
Lt, is
t[V(xtSt) – gt(Lt– mt)1t,
where 1t is an indicator function that takes the value of one if mt  Lt, and zero otherwise.
Proposition 6:
(a) The reporting strategy when the firm has to beat targets repeatedly varies. If
x1 L1+L2+x2, the firm reports the target. If x1>L1+L2+x2, the firm smoothes. A
restatement is likely if the smoothed message falls in Region II.
(b)
There is a critical level of a target, denoted Lc, such that if L < Lc, the earnings
management level of a firm that beats targets repeatedly is lower than that of a
firm that does not beat targets.
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Proposition 6 indicates that when a firm has to beat targets repeatedly, the scope of
conservative reporting declines, and we are likely to witness restatements concurrently with a
low level of earnings management. This proposition is interesting because it shows that when the
firm has to choose between beating two targets, beating the earlier target takes precedence over
beating the later one. Since the firm cannot eliminate missing the target in the second period
with some positive probability, it prefers beating the first-period target with certainty and risking
not beating the target in period 2 to missing the target in period 1 for sure but missing the target
in period 2 with a lower probability.
5. SUMMARY
Our study explains why the level of earnings management as measured by the bias
between earnings and report is low in the United States, although the US also sees an avalanche
of restatements and large accounting scandals. We explain this puzzle by the practice of letting
financial reports beat targets that are determined by the interaction of the firm with its
stakeholders. We find that when targets are not in danger of being missed, firms smooth and
thus reduce the variability of earnings. When the target may not be reached, firms either adopt
truth-telling with a downward bias or take a bath. The result then is a reduction in the
magnitude of earnings management. The advantage of biased smoothing is that owners can
replicate the same payoffs as under the desirable equilibrium with smoothing without
compromising beating the target. We find that a restatement can be used as an earnings
management vehicle to eliminate mistakenly aggressive smoothing, which yields a profile of an
average firm reporting conservatively with the occurrence of restatement.
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Notes:
1
Furthermore, the respondents indicate a willingness to sacrifice long-term value in order to
pursue short-run earnings management objectives, by taking actions such as postponing
investment in value-enhancing projects.
2
We do not mention the “poor governance” explanation, because the evidence at hand suggests
that the United States has a better governance structure than other economies (see, e.g., Shleifer
and Vishny 1997).
3
Degeorge et al. 2005 provide international evidence of the effect of the pressure to beat targets
on earnings management.
4
In this study, we analyze finite-horizon games. One of the basic premises in accounting is the
"going concern" assumption, which some researchers translate to mean that the firm has infinite
life. Yet because all transactions tend to have finite life and accruals management is a matter of
allocating the recognition of transactions intertemporally (Dechow and Dichev 2002), it seems
that a repeated, finite-horizon model is better suited to study issues of earnings management with
reversal of accruals.
5
This feature of the model is common in the income-smoothing literature (see, e.g., Truman and
Titman 1988; Boylan and Villadsen 1997) and is based on the accounting principle that prohibits
double counting.
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6
As discussed in the introduction, note that the condition that a dollar performance cannot be
reported twice is a basic assumption in double-entry accounting. This assumption is prevalent in
the earnings management literature. There are a couple exceptions: Evans and Sridhar 1996
study the choice of control mechanism when there is an internal demand for earnings
management; they demonstrate that in the absence of resettling, the equilibrium of a repeated
game collapses to the equilibrium of a one-shot game. Sankar and Subramanyam 2000 examine
the value of endowing the manager with discretion over the choice of accounting treatment.
They assume that GAAP reverses discretionary accruals partially. They show that for some
threshold level of reversal, the manager overstates income boundlessly.
7
We assume away renegotiation of the original contract at the end of the first period. The
principal has incentives to ensure that renegotiation does not take place (as proved by
Dewatripont, Rey, and Aghion 1994, since renegotiation tends to reduce the principal’s welfare
(see, e.g., Fudenberg and Tirole 1990; Demski and Frimor 1999;Yim 2001; Christensen, Demski,
and Frimor 2002; Gigler and Hemmer 2004). To the best of our knowledge, only two studies find
that renegotiation is Pareto improvement: Hermalin and Katz 1990 assume that the principal and
the agent obtain non-contractible information after contracting that can yield the first-best
allocation, and Ronen and Yaari 2001 assume that renegotiation has no effect on incentives
because they study a one-shot game wherein the renegotiation takes place after effort has already
been exerted. Neither case is relevant to our framework.
8
It is reasonable that overstatement is different from understatement in terms of costs and
benefits. If a firm understates m1, m1 < x1, the firm accumulates hidden reserves that are
reinvested at an internal rate of return, r, which increases the second-period income by (1+r)(x1m1). If it overstates m1, m1 > x1, the firm either makes cash-increasing accounting changes or
engages in unobservable transactions that reduce the second-period outcome by (1+i)(m1 x1).
Without loss of generality, in what follows, we let r=i=0, which does not affect our results
qualitatively.
9
This assumption is a convenient technicality that allows us to use the generalized mean value
theorem in the proofs below. It can be relaxed without affecting the results.
10
We draw attention to the fact that this assumption represents the fact that the owners have
incentives to take measures that prevent the firm from not beating the target. We personally
sympathize with (iii) because it represents how we felt when less than a point was needed to earn
an A in a course as opposed to how we felt when the gap was larger.
11
For a study that explicitly models effort as investment decisions that affect earnings growth,
consult Gavious, Ronen, and Yaari 2001.
12
To illustrate, suppose that the contract is a linear function with the same marginal reward,
St=a+bmt, t=1,2. Then, if the manager's utility function is U(z)= z , a=0, b=0.01, allocation of
$10,000 between the two periods exceeds the payoff from reporting all in a single period:
2* 50 = 2*7> 100  10 . See also the valuable discussions in Dye 1988 and Yaari 1993.
13
Proposition 4 does not address the incentive effects of target beating. This can be addressed
by adapting the definition of earnings management to control for size effect the way it is done in
empirical research, which usually deflates all variables by lagged assets.
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