Product Market Competition and Real Activities
Manipulation: Theory and Implications
Cheng-Few Lee and Hao-Chang Sungy

Abstract
We investigate how a …rm manipulates its real activities in production to meet theearnings target in product market competition rather than provides a rational response
triggered by product market considerations. We show that the equilibratory way to reachthe earnings target is to set a higher …rst-period output, as this can reach a higher shortterm pro…t level. This also re‡ects the myopic concern for a …rm engaging in real activities
manipulation and may undermine its long-term competitiveness. Moreover, the tendency
for …rms to meet the earnings target is motivated by marketwide demand conditions, whereonce the expected level of demand uncertainty is high, a …rm will exploit the e¤ect of highlevel of expected demand uncertainty on its output choice by taking mixed strategy andraising its short-term output level. Thus, we show that abnormal output may occur inequilibrium even when opportunistic real activities manipulation is absent. This suggeststhat one should take into account longer-horizon paths of variables in attempting to detect
opportunistic real activities manipulation.

Keywords: Earnings Target; Real Activities Manipulation; Cournot Competition; Onesided Incomplete Information.
JEL: D82; L13; M41

Rutgers Business School, Rutgers –The State University of New Jersey, Room 5188, 100 Rockefeller Road
Piscataway, NJ 08854, USA. E-mail: c‡ee@business.rutgers.edu.
yCorresponding author. Department of Finance, College of Economics, Jinan University, No. 601 Huangpu
Avenue West, Guanzhou, Guandong 510632, People’s Republic of China. E-mail: songhaozhan0205@jnu.edu.cn

1Product Market Competition and Real Activities
Manipulation: Theory and Implications

Abstract
We investigate how a …rm manipulates its real activities in production to meet theearnings target in product market competition rather than provides a rational response
triggered by product market considerations. We show that the equilibratory way to reachthe earnings target is to set a higher …rst-period output, as this can reach a higher shortterm pro…t level. This also re‡ects the myopic concern for a …rm engaging in real activities
manipulation and may undermine its long-term competitiveness. Moreover, the tendency
for …rms to meet the earnings target is motivated by marketwide demand conditions, whereonce the expected level of demand uncertainty is high, a …rm will exploit the e¤ect of highlevel of expected demand uncertainty on its output choice by taking mixed strategy andraising its short-term output level. Thus, we show that abnormal output may occur inequilibrium even when opportunistic real activities manipulation is absent. This suggeststhat one should take into account longer-horizon paths of variables in attempting to detect
opportunistic real activities manipulation.

Keywords: Earnings Target; Real Activities Manipulation; Cournot Competition; Onesided Incomplete Information.
JEL: D82; L13; M41

1

1

Introduction

It is well-acknowledged that accounting earnings play an important role in the …nancial markets. Recent literature incorporates the role that the …nancial market plays in non-…nancial
market settings such as …rm internal compensation1 and investment2 . This paper, among
others, incorporates the desire to meet earnings target, a particular …nancial market phenomenon, into …rms’operating decision making vis-a-vis product market competition against its
product-market rivals. We investigate how a …rm manipulates its real activities in production
to meet the earnings target in product market competition rather than provides a rational response triggered by product market considerations. Economic shocks have an e¤ect on a …rm’s
performance and its real decision, which may create an uncertainty. When a …rm respondsby engaging in abnormal real activities, it could mask the e¤ect of the shocks on reported
earnings in an attempt to continue reporting high earnings3 or alter its real decisions as partof a rational response to the shocks so that the …rm’s reported earnings will re‡ect the shocks’e¤ect on …rm value. The former (opportunistic real activities manipulation) can be mixed
with the latter (rational real activities) and, hence, is di¢ cult for an auditor, regulator or1

For example, Andergassen (2016) considered an agency model in which managers can exert unobservablecost-cutting e¤orts and have private information about …rm pro…ts in which they may use fraudulent reporting
to in‡ate their stock and stock option-based compensation packages.
2

For example, Yang et al. (2016) showed that in order to satisfy its investment demands, …nanciallyconstrained …rms overstate their earnings around seasoned equity o¤erings (SEOs) and perform well after
SEOs.
3

Recent studies provide evidence that management may use real earnings manipulation for meeting or

beating some earnings target. Graham et al. (2005) indicated that 80 percent of respondents (chief …nancialo¢ cers and …nancial executives) would decrease discretionary spending on research and development (R&D),
advertising, or maintenance to meet an earnings target, and 60 percent would avoid initiating a positive netpresent value project if it meant falling short of analysts’ consensual earnings forecasts. If earnings targets
remain high, but accounting standards become increasingly stringent, there is a negative consequence formanagers seeking to meet short-term earnings goals, which may increasingly substitute accounting earnings
management with more substantive and potentially damaging changes in strategic decisions (Roychowdhury
2006; Mizik and Jacobson 2007; Cohen and Zarowin 2010; Badertscher 2011; Zang 2012; Chan et al. 2015;
Kothari et al. 2016).

2

even product market competitors to detect.
Opportunistic real activities manipulation will not only have competitive, but also informational impacts in product market competition. For product market competitors, the suspicion
that a …rm might manipulate its real activities for a higher pro…t will create additional uncertainty. For example, the …rm might engage in abnormal real activities on either a myopic
intention or a pro…t-maximization intention. This uncertainty can in‡uence competitors’real
activities. If opportunistic real activities manipulation is fully anticipated by its competitors,
it can induce competitive interaction and retaliation from the competitors in the long-termand can have an impact on the …rm’s long-term competitiveness as well.
Zhang and Gimeno (2010) examined the e¤ect of earnings pressure felt by management tomeet an earnings target on a …rm’s behavior in oligopolistic output competition in which the
production decisions serve as the vehicle through which the …rm carries out its real activities
manipulation. Zhang and Gimeno (2010) found that …rms facing an earnings target tended
to restrict output in markets in which market structure and competitor characteristics werefavorable for the exercise of market power, while their competitors tended to increase output
in those markets. However, if a …rm has a myopic incentive, how does this change the …rm
intertemporal operating activities for higher short-term earnings in equilibrium? Moreover,when opportunistic real activities manipulation creates an uncertainty such that abnormal
real activities may result from diverse objectives, how does the …rm take advantage of thisuncertainty to meet an earnings target and boost short-term earnings? Could the rival …rm
identify the informed …rm’s identity e¤ectively (i.e., identifying opportunistic real activities
manipulation or not)? How does this uncertainty in‡uence the rival …rm’s response?
We examine the competitive and informational impact of one …rm’s abnormal output levels(either opportunistically use abnormal output to mask the …rm’s reported earnings or rationally respond to competition pressure) on its rival’s responses within a Cournot game between
two …rms operating in the same product market. Output decisions in oligopolistic competition
are highly interactive, since …rms’output decisions a¤ect market-clearing prices and competitors’output decisions. This mutual adjustment of output decisions and equilibrium outcomes3

are captured in a simpli…ed form in the Cournot oligopoly model (Cournot, 1838), whereby…rms make simultaneous interdependent output decisions that determine market-clearings
prices and pro…ts. We consider a two-period Cournot competition model with one-sided incomplete information and demand shocks. The one-sided incomplete information refers to
one of two competing …rms that has private information on its identity, for example whether
it prefers to maximize pro…ts or attempts to meet two-period earnings target. The other(rival) …rm maximizes pro…ts and does not know the …rst …rm’s type (i.e., whether it is pro…tmaximization-type or earnings-target-type). The pro…t-maximization-type …rm pursues profits maximization within two periods, while the earnings-target-type …rm attempts to meetearnings target within two periods and smooth over the annual earnings, but pursues increasing short-term pro…t, which re‡ects this type of …rm’s myopic objective. Moreover, the demand
shock re‡ects that the informed …rm (either pro…t-maximization-type or earnings-target-type)may mask the e¤ect of demand shock on its …rst-period pro…t with an expectation on demand
shock and thus boost its …rst-period output level in an attempt to increase short-term pro…t.
By this setting, the rival (uninformed) …rm can revise its assessments of the informed …rm’s
identity depending on the informed …rm’s …rst-period output decisions and the realization ofdemand shock at the end of the …rst period, i.e., the informed …rm’s output level could be
used for both competitive and informational intentions in the product market competition.
In addition, the rival’s …rst-period responses a¤ect the informed …rm’s …rst-period output
decisions in two ways. First, the informed …rm may engage in real activities manipulation
by opportunistically altering its …rst-period output decisions to take advantage of the rival’s
uncertainty about the informed …rm’s identity and obtain higher short-term earnings (i.e., theinformed …rm is the earnings-target-type). Alternatively, the informed …rm may alter its …rstperiod decisions as a rational response to the rival’s …rst-period decision (i.e., the informed…rm is the pro…t-maximization-type). One informed …rm may mimick another’s behavior andthus create its rival uncertainty about the informed …rm’s objective, in which the informed…rm can take advantage of this uncertainty and change its intertemporal operating activities
for a higher short-term pro…t level. Speci…cally, the informed …rm could change its …rst-period4

output decisions before the realization of demand uncertainty in order to maintain its rival’s
uncertainty about the informed …rm’s objective.
In what follows, we brie‡y summarize the major results. For a higher …rst-period pro…tlevel, the earnings-target …rm raises its …rst-period output level to achieve a higher short-term
pro…t and lowers the second-period output to reach the earnings target, even though such
behaviors may undermine its competitiveness; the pro…t-maximization type …rm makes an
output decision as a rational response to the rival’s output decision in each period. This isa separating equilibrium because the equilibrium strategy separates the pro…t-maximization
type from the earnings-target type. Although the informed …rm can enhance its …rst-period
pro…t through boosting its output levels, this will induce the rival …rm to respond aggressively
in the second period. However, this does not violate the empirical results that a …rm distorts
its abnormal real decision intertemporally in order to meet earnings target, even though such
behavior may undermine its long-term competitiveness.
Moreover, we show that the tendency for …rms to meet earnings target is motivated bymarketwide demand conditions. Speci…cally, once the expected level of demand uncertainty in
the …rst period is high, the pro…t-maximization-type …rm is motivated to conceal its identity
by taking advantage of the e¤ect of the high level of expected demand shock on its …rst-period
output choice and then taking a mixed strategy. This type of …rm raises its …rst-period output
level in an attempt to enhance its pro…t level. This is a hybrid equilibrium in which with someprobability the pro…t-maximization-type …rm pretends to be the earnings-target-type …rm by
mimicking its aggressiveness in product market competition, and the rival …rm cannot perfectly
identify the opportunistic abnormal output activities. We further illustrates that the tendency
for …rms to meet earnings target is positively related to the marketwide business condition.
As the expected level of demand shock further increases, there will be a higher likelihoodthat the pro…t-maximization-type …rm pools with the earnings-target-type …rm. This further
confounds the rival …rm’s ability to identify opportunistic abnormal output activities andthus the pro…t-maximization-type …rm’s absolute amount of real activities manipulation gain
is higher. Accordingly, the rival …rm will respond less aggressively in the second period.
5The main contribution of this paper is to show that observing abnormal production is notsu¢ cient for identifying opportunistic real activities manipulation. The analysis suggests thatreversals in production may indicate that opportunistic real activities manipulation happens
previously. Speci…cally, a reversal of an abnormal decision in the second period after thedecision takes place could be indicative of the degree to which the decision is opportunistic or
rational and predicts that both current abnormal operating activity with a higher pro…t leveland future sub-optimal operating activity with a lower operating performance are relevant to
identify opportunistic real activities manipulation. In addition, our paper implies that thee¤ect of economic shocks on a …rm’s performance also confounds a rival’s ability to accurately
identify opportunistic real activities manipulation through observing only the realization ofshort-term output activity and economic shocks. This is consistent with Cohen et al. (2019)
who argued that economic shocks to a …rm’s performance could confound a researcher’s ability
to accurately estimate abnormal real activities. Owens et al. (2017) also analyzed how shocks
to …rms’business models confound estimation of discretionary accrual.
Our paper also suggests that a market-leader …rm facing earnings targets may exploit its
available market power to generate a higher short-term pro…t level through real distortionsin production and will induce a rival to respond aggressively later, thus reducing the marketleader …rm’s long-term product market competitiveness. This is consistent with Zhang and
Gimeno (2010), who provided evidence of the negative impact of short-term earnings pressure
on long-term product market competition, where a …rm will restrict output so as to increaseprices and current earnings, even though such behavior may encourage output expansion bycompetitors and undermine competitiveness. Chapman (2011) also presented evidence that…rms use quarter-end price promotions to accelerate pro…t intertemporally in order to meetearnings targets they otherwise would have missed. Chapman showed that price promotion
to boost short-term earnings at the end of the …scal quarter may persuade competitors within
an industry to follow.
Finally, our paper is related to recent studies which have examined the relation between
the kinky earnings phenomenon and (accruals) earnings manipulation and proposed di¤erent
6conclusions. On the one hand, some studies raise doubts about whether earnings manipulation explains the observed discontinuities in the distribution. Dechow et al. (2003) showedthat small pro…t …rms have high discretionary accruals relative to other …rms. However, theearnings kink does not disappear or decline when they focus on the distribution of …rms withincome decreasing discretionary accruals. They point out that the boosting of discretionary
accruals partially explains earnings kinky. Durtschi et al. (2005) found that earnings kinky
may be driven by other factors including: scaling, sample selection, and the e¤ects of special
items and taxes. Beaver et al. (2007) showed that the asymmetric e¤ects of income taxes
and special items rather than discretionary accrual behavior on the earnings of pro…t andloss …rms contribute to the discontinuity at zero in the earnings distribution. Other studies
present evidence that …rms engage in earnings management only to meet or beat earnings
target. Gore et al. (2007), for the U.K., and Daske et al. (2006), for the EU, presented
evidence that discretionary accruals have the e¤ect of increasing the frequency of achieving
positive earnings levels, earnings changes, and earnings surprises. Our analysis shows thatwhen a market is less transparent (on the producer side), there is a higher probability that thepro…t-maximization-type …rm pools with the earnings-target-type …rm and then this further
confounds a rival …rm’s ability to identify opportunistic real activities manipulation. Thisfurther creates a chance for the market-leader …rm to distort its production quantities andhave kinky earnings surrounding the current earnings threshold. Thus, this kinky earnings
phenomenon can re‡ect either opportunistic real activities manipulation or prudent businessdecisions (non-opportunistic real activities manipulation).
The remainder of this paper is organized as follows. Section 2 summarizes the related
literature and discusses the contribution of this paper relative to the existing literature. Section
3 describes a two-period Cournot competition model with one-sided incomplete information.
The objective function of each …rm is also provided. Section 4 characterizes the equilibrium
properties in a two-period Cournot competition with one-sided incomplete information anddiscusses our equilibrium results as well. Section 5 presents the conclusion. For ease ofpresentation, long proofs are relegated to the appendix.
7

2

Related Literature

Bagnoli and Watts (2010) investigated how misreporting in production cost a¤ects productmarket competition and how rivalry impacts both production decisions and misreporting decisions. They showed that Cournot competitors bias their reports to create the impression that
their costs are lower than they actually are. This bias leads to lower total production and ahigher product price, even though each …rm fully understands its rival’s incentives to bias its…nancial reports. Our study addresses the impact of real distortion in production on productmarket competition. Speci…cally„ in our model, opportunistic real activities manipulationin production emerges in equilibrium even though each …rm’s production cost information isnonproprietary in which …rms will not engage in accounting-based earnings manipulation in
product market competition. Thus, opportunistic real activities manipulation in production
is distinct from accounting-based earnings manipulation. Moreover, in our model, a rival…rm’s uncertainty about a signaling …rm’s real type provides another rationale of withholdingof information (preventing full disclosure in equilibrium). We show that real activities manipulation in production will provide a noisy signal about the signaling …rm’s strategic andinformational incentives. Such complexity will further impact the rival …rm’s response laterand the signaling …rm’s long-term product market competitiveness. Markarian and Santalo(2014) examined the impact of product market competition on a …rm’s incentive to engage
in real (accruals) earnings manipulation for capital market valuation. Our study investigates
the trade-o¤ between the informational and strategic impact of real activities manipulationin production and the long-term consequences of this, which makes our paper di¤erent fromMarkarian and Santalo (2014).
Our study is also related to the literature on real smoothing. Acharya and Lambrecht(2015) considered an environment where a manager fears intervention by investors, when theirearnings expectations are not met and as a result manages earnings downward and underproduces so as to lower investors’expectation about future income. Acharya and Lambrecht(2015) showed that based on sales information, the capital market may or may not infer

8the correct value of the …rm’s income, and the manager will reduce the production level todownplay the …rm’s fundamentals and lower outsiders’income expectation. Thus, the earnings
expectation is not raised in the future. Moreover, the …rm may smooth and adjust output
and payout process over time in response to economic shocks. In our paper, to motivate
the earnings-target-type …rm myopia, we focus on the case in which this type of …rm prefersa higher …rst-period pro…t and a lower second-period pro…t in which real smoothing is real
activities manipulation in production for a higher short-term pro…t in terms of expansion ofshort-term output at the risk of reducing long-term product market position for a myopic…rm. Due to this type of …rm myopic concern, it will not further beat the earnings target
and attempting to achieve a mark at least as large as the target. It will attempt to hit theearnings target.
One study examines the economic consequences of earnings management and fraudulent
accounting on aggregate economic activity. Kedia and Philippon (2009) studied a problem ofmanagers who privately observe the true productivity of their …rms and who make employment and investment decisions. They show that …rms with low true productivity boost theirreporting earnings (in terms of discretionary accruals earnings management) and mimick e¢ cient …rms’investment and employment to maintain consistency between reporting earnings
and actions. These will distort the allocation of resources in the economy, and hiring and investment are lower after the misreporting period. Our study varies from Kedia and Philippon(2009) because we examine the long-term consequence of real activities manipulation in anintertemporal Cournot competition setting. In particular, we investigate how opportunistic
real activities manipulation distorts a …rm’s intertemporal output decisions by taking advantage of its rivals’uncertainty about its truthfulness in its identity and the consequences of real
distortions in intertemporal productions on long-term product market competition.

9

3

The Model

To examine the impact of opportunistic real activities manipulation to meet earnings targets
on a …rm’s intertemporal real decisions and how this a¤ects real operating decisions of other…rms in the same industry, we consider a two-period Cournot competition model with onesided incomplete information in which one …rm is uncertain about the other …rm’s type. The
uncertainty about the informed …rm type re‡ects doubts concerning its operating activity
and its related strategic intentions. To give a conjecture on the plausibility of this setting, we
consider the U.S. electricity generation industry. A few large generators dominate this industry
and there are more for-pro…t competitors and few not-for-pro…t competitors. Moreover, someof the dominant …rms are pro…t-maximizers or face earnings benchmark felt by management
to avoid reporting losses and focus around the zero earnings level4 .
As argued in the introduction, the informed …rm’s real activities manipulation in production can be mixed with a rational response to a rival’s output decision in Cournot competition
and is di¢ cult for the rival to detect. With this uncertainty, the uninformed …rm (the rival) will not fully anticipate the real intention in an abnormal production level, which canre‡ect either opportunistic real activities manipulation or prudent business decisions (nonopportunistic real activities manipulation). We will investigate whether the informed …rm cantake advantage of its rival’s uncertainties regarding its truthfulness in its identity and thenarrange its outputs level for a higher …rst-period earnings level.
The Environment
We consider two …rms which provide di¤erentiated products in the industry with demand
uncertainty. Following Dixit (1979) and Singh and Vives (1984), we assume the following
inverse demand function for each period:pi (qi ; qj ; ") = a4qibqj + ";In addition, Carvajal et al. (2017) provided empirical evidence to suggest that Australian managers attempt

to avoid making losses and earnings decreases, which implies that managers consider these earnings benchmarks
as important.

10where market demand is determined by a constant term (a) and a random shock term (").
The random term " represents the demand shock, which is assumed to be an uniformed
distribution over [ "; "] and identical independent distribution for each period. Moreover, two…rms determine industry output (qi + qj ) where qi and qj , for i; j = 1; 2, denote …rm i and…rm j 0 s arbitrary output, respectively. b represents the extent of di¤erentiation between thetwo …rms’ products, 0 < b < 1. When b approaches 1, the two …rms’ products are perfect
substitutes, and when b approaches 0, the two …rms’ products are isolated. This inverse
demand function implies that high outputs (qi + qj ) could reduce market price, and highdemand (a + ") could induce a high market price. We assume a linear cost function for thetwo …rms: ci qi ; i = 1; 2, within two periods.
The Timeline
At the beginning of period 1, …rm 1 is privately informed of its type, which can be either
pro…t-maximization-type (m) or earnings-target-type (r). The pro…t-maximization-type …rm
maximizes the sum of pro…ts within two periods, while the earnings-target-type …rm attempts
to reach earnings targets within two periods and smooth over the annual earnings, but prefersa higher short-term earnings level. Firm 1 could be a market-leader …rm and may likely engage
in real activities manipulation strategy, because the erosion to its competitive advantage isrelatively small (e.g., Zhang and Gimeno, 2010; Zang, 2012). Firm 1 and …rm 2 engage in
Cournot competition in the …rst period with demand uncertainty. We investigate how …rm
1 engages in real activities manipulation through production in the …rst period and transfers
part of its pro…t from one period to the other period.
At the end of the …rst period, both …rms’…rst-period payo¤s and …rst-period random shock
are realized and …rm 2 updates its belief about …rm 1’s type after observing these. Based on
the realized pro…ts of the …rst period, the earnings-target-type of …rm 1 will determine therequired extent of pro…t for meeting the earnings target in the second period. Then, the two…rms compete in Cournot again, and the second-period pro…ts are realized in the end. We
assume that there is no demand shock in the second period and that this avoids failure toreach the earnings target for the earnings-target-type …rm.
11

Information
We use the following settings to describe the uncertainty about …rm 1’s type.

t , t = 1; 2,

represents …rm 2’s belief (ex-ante and ex-post) that …rm 1 is a pro…t-maximization-type, while1

t represents the belief that it is an earnings-target-type.
1 with 0 <Before competition, the …rst-period belief

1 < 1 is exogenously given as a

2 will be endogenously determined by the prior belief

prior belief. The second-period belief1;…rm 1’s …rst-period output levels, and the realization of …rst-period demand uncertainty. We
will discuss the on- and o¤-equilibrium path beliefs in a subsequent section on characterizing
the equilibrium.
To distinguish the output choices for each type of …rm 1, let q1t (k) denote the quantity set
by type k (k = m; r) of …rm 1 in period t. Let

t
i and

i represent …rm i0s pro…t in period t

and total pro…t, respectively, where
q11 (k)1 = (a=bq21 + "1 1
1
1 (q1 (k); q2 ; ") +c1 )q11 (k) + (aq12 (k)qp22

c1 )q12 (k)1

q21

qp11 (r) + "2 2
2
1 (q1 (k); q2 );

2 =

1

(a

q21

bq11 (m) + "

(a

q22

bq12 (m)c2 )q21 + (1

+

2

=

1 1 1 112 ( ; q2 ; q1 (m); q1 (r); ") +c2 )q22 + (1

2

)(a

)(a

q22

bq12 (r)c2 )q21c2 )q222 2 2 222 ( ; q2 ; q1 (m); q1 (r)):

Next, the objective function for each type of …rm 1 and …rm 2 is described.

Objective Function If …rm 1 is a pro…t-maximizer, the two …rms’ objective function
at the …rst period is
1
i +

maxE
qi1

2
i

; for i = 1; 2;(1)where E( ) denotes the expectation over the demand uncertainty. Notice that throughout thispaper, we have assumed that the discount factor is 1 for simpli…cation. Given the equilibrium
during the …rst period, the objective function during the second period is
max i2 ; for i = 1; 2;
qi2

12

(2)

Alternatively, if …rm 1 is of earnings-target-type, the …rst-period objective function of …rm 2
remains the same as equation (1), but the …rst-period objective function of …rm 1 is to …nd a
q11 to meet some earnings target. That isE

In this objective function,

1
i +

2
i

(3)

represents some earnings target for full-year earnings which con-sists of two half-year earnings. The earning target describes the …rm who wishes to avoid
reporting losses and focuses on …rms around the zero earnings level. Moreover, the earnings
targetcan be used to link …rm 1’s intertemporal output decisions such that …rm 1’s in-tertemporal pro…ts exactly hit the target and be taken as pre-commitment to pursue a higher…rst-period pro…t (thus a higher …rst-period earnings target) and bring forward a part of thesecond-period pro…t to the …rst period (thus a lower second-period target). Thus, under output competition this type of …rm prefers a higher output in the …rst period that allows it topursue a higher …rst-period pro…t. With this setting, if the earnings target is met, the output
will be di¤erent from the pro…t-maximizer’s output. To motivate the earnings-target-type…rm myopia, we focus on the case in which this type of …rm will prefer a higher …rst-period
pro…t and a lower second-period pro…t.
Two interpretations of the role of earnings target for a myopic …rm are provided. Fromthe view of strategic competition, earnings targets a¤ect …rms’ strategic behavior: marketleader …rms facing earnings targets exercise their available market power to generate a highshort-term pro…t. Thus, earnings targets tip the balance toward milking market position andcould contribute to the decline of market-leader …rms. This provides a view of the long-term
consequences of meeting earnings targets. From the view of agency theory, earnings target
could curtails managers’ empire-building tendencies for an excessive taste for running large…rms, as opposed to simply pro…table ones (Stein, 2003, p. 119). This may lead to excessive
investment and excessive focus on revenues and market share. Earnings target could be used to
discipline managers to generate current pro…t by de-escalating the pursuit of market position.
Both interpretations illustrate that earnings target induce the earnings-target type …rm to13

have a higher preference on short-term pro…t than on long-term pro…t. This does not violate
the empirical results that earnings target encourages dominant …rms to exercise their available
market power to generate current earnings, even though such behavior may encourage output
expansion by competitors and undermine competitiveness.
In our model, some …rms might not know whether their competitors are maximizing pro…ts
or trying to meet an earnings target. Thus, the informed …rm’s short-term output strategy canbe interpreted as a result of opportunistic real activities manipulation or of a purely strategic
concern. Under Cournot competition where …rms are strategic substitutes, if boosting shortterm output is recognized as an opportunistic real activities manipulation, this can induce
retaliation from the rival and thus encourage the rival’s output expansion in the long-term.
Based on this argument, the earnings-target-type …rm will not beat the earnings target andearn more than the earnings target. It will just meet the earnings target.
In the second period, the …rst period demand uncertainty has realized, the earnings-targettype of …rm 1 will calculate the extent of pro…t manipulation in the second period. Let
1 1 1
1
1
1 ( ; q1 (m); q1 (r); q2 ; ") represent the …rst-period realized pro…t of …rm 1.

pro…t manipulation is b ( 1 ; q11 (m); q11 (r); q21 ; ") =The extent of

1 1 1
1
1
1 ( ; q1 (m); q1 (r); q2 ; "): Firm 1 will

pursue to reach this pro…t level b ( 1 ; q11 (m); q11 (r); q21 ; ") by manipulating the output level inthe oligopoly market and choosing a q12 such that21b ( 1 ; q11 (m); q11 (r); q21 ; "):(4)

where b ( 1 ; q11 (m); q11 (r); q21 ; ") could be considered an earnings target in the second period

for the earnings-target-type …rm. Notice that for a myopic …rm, it will not further pursue ahigher possible pro…t. Thus, any production plan that delivers a pro…t at least as high as thetarget b ( 1 ; q11 (m); q11 (r); q21 ; ") is equally desirable. The second-period objective function of…rm 2 remains the same as equation (2).

As a benchmark of comparison, we consider a complete information case where …rm 2 canperfectly infer …rm 1’s objective type. Then, the …rst-period output decision of …rm 1 has no
informational e¤ect and the two-period Cournot competition model with one-sided incomplete
14

information reduces to a one-shot Cournot competition over two periods. Since the output
level in each period can be adjusted without cost, the optimal …rst-period output levels of
pro…t-maximization-type of …rm 1 and …rm 2 depend only on a contemporaneous level of aand ". Let (q1 , q2 ) denote the output level which maximizes …rm i0s, i = 1, 2, one-shot pro…tqi 2 arg maxE i1 (a; qi1 ; qj1 ; "); i; j = 1; 2; i 6= j;
q1t

and

1 denote the obtained pro…t.

4

Equilibrium Analysis

In this section, we solve for the perfect Bayesian equilibrium in the two-period Cournot competition. Using backward induction, we …rst characterize the second-period market equilibrium(q12 (m); q12 (r); q22 ( 2 )); for a given level of the posterior belief

2 and the …rst-period random

shock: We then consider the …rst-period market equilibrium (q11 (m); q11 (r); q21 ), and interpretthe setting of on- and o¤-equilibrium path beliefs

2 : We especially consider …rm 2’s reaction

to …rm 1’s real activities manipulation in production for a higher …rst-period pro…t level, when…rm 1 might take advantage of its private information.
As mentioned earlier, since the earnings-target type …rm has a myopic preference, it attempts to reach some earnings target and pursues a higher …rst-period pro…t level and ahigher …rst-period output level than the pro…t-maximization-type’s …rst-period output level.
Moreover, once the …rst-period earnings target is reached, it is not necessary for this typeto pursue a higher second-period pro…t and thus has an incentive to signal itself out frompro…t-maximization-type …rm in period 1.

4.1

Market Equilibrium Strategies in Period 2

The second-period market equilibrium is di¤erent from the …rst-period market equilibriumin three aspects. First, …rm 1’s second-period market strategy has no signaling indication.
Second, …rm 2 uses the ex-post belief,

2 , instead of the ex-ante belief, to calculate the expected

pro…t. Third, the earnings-target-type …rm needs to meet a second-period earnings target
15

depending on the …rst-period market equilibrium and the …rst-period demand uncertainty: At
the beginning of the second period, both …rm 1 and …rm 2 can observe their …rst-period output
levels, the realization of …rst-period demand uncertainty, and the realization of their …rstperiod payo¤s. The second-period belief

2 (on- and o¤-equilibrium path) will be discussed

in more detail when we characterize the …rst-period outputs in the next subsection. For the
moment, the value of

2 is treated as constant. Firm 1 and …rm 2 determine (q 2 (m); q 2 (r); q 2 )1
1
2

simultaneously in the second period.
For the pro…t-maximization-type of …rm 1, let q12 (m)

2
1 =

Z"

(a

q12

bq22 ( 2 )arg max 12 ; where
q12c1 )q12 :"The pro…t-maximization-type of …rm 1’s best response to q22 is
q12 (m) =

bq22
2

(a

c1 )

:

(5)

For the earnings-target-type of …rm 1, q12 (r) is denoted as the output to satisfy equation (6),i.e.,q12 (r) 2 fq12 j 12b ( 1 ; q 1 (m); q 1 (r); q 1 ; ")g,1

where b ( 1 ; q11 (m); q11 (r); q21 ; ") =Next, …rm 2 chooses q22 to maximize fa

q22

1

2

1 1 1
1
1
1 ( ; q1 (m); q1 (r); q2 ; "):b[ 2 q12 (m) + (12 )q 2 (r)] + "2
1

(6)
c2 gq22 : Firm

2’s best response to q12 (m) and q12 (r) is
q22 =

fa

b[ 2 q12 (m) + (122 )q 2 (r)]
1

c2 g

:

(7)

From equations (5), (6), and (7), we can see what pro…t-maximization-type does in the face of…rm 2 being indi¤erent over a measurable set of options. The pro…t-maximization-type …rm’s
best response to q22 is determined by the …rst order condition of pro…t-maximization problem.
This could be characterized by q12 (m) =q12 (r) is determined by q22 =(a bq22 c1 )where …rm 2’s best response to q12 (m) and2

fa b[ 2 q12 (m)+(122 )q 2 (r)]1c2 g

. Thus, the pro…t-maximization-type…rm’s response to the output from the earnings-target-type …rm is a¤ected by …rm 2’s ex-post16

belief about …rm 1’s type where

2 is constant in second-period output competition.

As2decreases and approaches 0, the pro…t-maximization-type …rm responds proportionally to theearnings-target-type …rm’s output.
When we discuss the best replies of the rival …rm and the earnings-target-type …rm, wetake q12 (m) as a given. This is because this value will be uniquely determined by equation (5).
Then, we use a …gure to depict the best replies of the rival …rm and the earnings-target-type…rm.

The earnings-target-type …rm needs to choose among a range of feasible outputs to reach theearnings target. The best replies of q12 (r) are indicated by the shadow area in the diagram. As
the …rst period pro…t gets lower, b gets higher. The feasible outputs set to reach the target

will be smaller. Thus, it will be more di¢ cult for the earnings-target-type …rm to make up
for the shortfall in pro…ts earned in the …rst period.
The second-period equilibrium is determined by equations (5), (6), and (7) simultaneously.
As a benchmark of comparison, we consider that (q1o , q2o ) denote the output level thatmaximizes …rm i0s, second-period pro…t in a full information case, i.e.,qio 2 arg maxE i2 (a; qi2 ; qj2 ); i; j = 1; 2; i 6= j;
q12

and

o
1 is the respective pro…t.

To describe the equilibrium properties, notice …rst that the …rst-period equilibrium will affect the continuation payo¤ through Bayesian updating for
17

2 and through b ( 1 ; q 1 (m); q 1 (r); q 1 ; ");1
12

which will determine the second-period earnings target and a¤ect the second-period output
choices for meeting the earnings target. Speci…cally, when the …rst-period pro…t of earningstarget-type of …rm 1 is higher than2
1 ; it may set a q1 (r) to moderate the variation of

2 2 2
2 2
1 ( ; q1 (r); q2 ( )) for smoothing of its two-period payo¤, i.e.,

2 2 2
2 2
1 ( ; q1 (r); q2 ( ))

o
1

1 1 1
1
1 ( ; q1 (r); q2 ; ")1:

We will determine the equilibrium properties for the earnings-target-type …rm in the second
period.
Lemma 1 (i) For the earnings-target-type …rm to reach a second-period earnings target equal
to or lower thano
1 in the Cournot competition, it can set its second-period output level equal

at or lower than q1o :Proof. Since

2 2 2
2 2
2
2
1 ( ; q1 (r); q2 ( )) is concave in q1 (r) and decreasing in bq2 , if the earnings-

target-type …rm needs to meet a second-period earnings target level equal to lower thanrequires q12 (r) < q2o . Then, since …rm 2 faces an expected output
then q22 increases and q12 (m) responds with q12 (r) < q12 (m)( 2 q12 (m) + (1o
1 , it2 )q 2 (r)),
1

q2o .

Given that the earnings-target …rm engages in real activities manipulation through production in the …rst period, this lemma demonstrates the cost of engaging in real activities
manipulation where the earnings-target …rm has a lower output and lower pro…t in the second
period. This could happen when a myopic …rm overproduces for greater short-term pro…ts
but reverse the abnormal production subsequently. We will demonstrate shortly that there
exists equilibrium where …rms raise the …rst-period outputs and then lower the second-period
outputs.
Since the set of q12 (r) is a¤ected by the level of b ( 1 ; q11 (m); q11 (r); q21 ; "), we rewrite thesecond-period payo¤

2
1 as

2 2 b 22 2
1 ( ; ; q1 (r); q2 ( )):Lemma 2 (i) Given that the earnings-target-type …rm needs to reach a second-period earnings
target lower thano
1;2 2 b 22 2
1 ( ; ; q1 (r); q2 ( )) increases with

18

2:

(ii) The lower bound of

2 2 b 22 2
1 ( ; ; q1 (r); q2 ( )) for the earnings-target-type …rm will in-crease with b ( 1 ; q11 (m); q11 (r); q21 ; ") and decrease with ":Proof. (i) Given q12 (r) lower than q1o , q12 (m) responds with q12 (r) < q12 (m)+ (12 )q 2 (r)) decreases with12:(ii) As b increases, by de…nition, the required level ofthe earnings-target-type …rm increases. As " increases,
decreases. Thus, the required level ofdecreases.

( 2 q12 (m)2 2 b 22 2
1 ( ; ; q1 (r); q2 ( )) decreases with

2 : With the fact that

2 2 b 22 2
1 ( ; ; q1 (r); q2 ( )) increases with

q22 ,

q2o .

2 2 b 22 2b for
1 ( ; ; q1 (r); q2 ( )) to meet

1
1
1
b 1 1
1 increases and ( ; q1 (m); q1 (r); q2 ; ")2 2 b 22 2
1 ( ; ; q1 (r); q2 ( )) for the earnings-target-type …rm

Lemma 2 explains how the second-period earnings target b and the posterior belief ( 2 )a¤ect the equilibrium pro…t. Since both of them are in‡uenced by the …rst-period output of…rm 1, these e¤ects are important for the earnings-target type of …rm 1’s strategic concern in
the …rst period.
Corollary 3 The lower bound of q12 (r) will increase with b and decrease with ":Proof. This directly follows Lemma 2.

Lemma 2 and Corollary 3 show that as b increases the lower bound of q12 (r) will increase.

4.2

Market Equilibrium Strategies in Period 1

We characterize the …rst-period market equilibrium (q11 (m); q11 (r); q21 ), and consider the e¤ects
of …rm 1’s …rst-period output levels. First, …rm 1’s …rst-period output level with the realizationof …rst-period demand uncertainty a¤ects the required second-period pro…t for the earningstarget-type …rm to meet the second-period earnings target, which will a¤ect q12 (r) and q22 .
Second, …rm 1’s …rst-period output level will be taken as a signal about …rm 1’s type and then…rm 2 will update its ex-ante belief to2.

The impact of q11 (k) ; k = m; r; onwhether …rm 1 needs to set an earnings level higher than

2 depends on

1 in the …rst period.

Given the second-period equilibrium (q12 (m); q12 (r); q22 ( 2 )) as characterized above, the intertemporal payo¤s for each …rm are given as follows. The pro…t-maximization-type of …rm 1
19needs to …nd q11 (m) to solve the following problem:
max
q11

Z "

"

[(a-q11 -bq21 ( 1 )+"-c1 )q11 + 12 ( 2 ; b ( 1 ; q11 (m); q11 (r); q21 ; "); q12 (m); q12 (r); q22 )]

1d": (8)2"

The earnings-target-type of …rm 1 needs to …nd a q11 (r) such that:
q11 (r) 2 fq11 j

Z ""[(a-q11 -bq21 ( 1 )+"-c1 )q11 + 12 ( 2 ; b ( 1 ; q11 (m); q11 (r); q21 ; "); q12 (m); q12 (r); q22 )]Firm 2 chooses a q21 to solve the following problem given the ex-ante belief
max
q21

Z "

"

1
d"
2"
(9)

1 :

[(a-q21 -b( 1 q11 (m)+(1- 1 )q11 (r))+"-c2 )q21 + 22 ( 2 ; b ( 1 ; q11 (m); q11 (r); q21 ; "); q22 ; q12 (m); q12 (r))](10)

As described in Corollary 3, the level of b will a¤ect the lower bound of q12 (r), and b is inturn a¤ected by the …rst-period equilibrium and the …rst-period demand uncertainty ".
Let "(q11 (m), q11 (r), q21 ) denote the threshold value of " such that11 =

1 of the one-shot

earnings. For q1t 6= q1 :"(q11 (m); q11 (r); q21 )c1

q 1 q 1 q1 q2
a + q1t (r) + q1 + b 11 2:
q1 (r) q1

For "(q11 (m); q11 (r); q21 ) to exist, it must be the case that: q11 (r) 6= q1 and "(q11 (m); q11 (r); q21 ) 2[ "; "]: Lemma 4 describes the e¤ect of …rm 1’s output level on "(q11 (m); q11 (r); q21 ):Lemma 4 "(q11 (m), q11 (r), q21 ) increases with bq21 and increases with q11 (r), if q11 (r) > q1 .
Proof.

@"(q11 (m);q11 (r);q21 )q q2 q1 q21
q1 (q2 q21 )11= 1 + b (q11 (r)2 = 1 + b (q 1 (r) q )2 > 0; where q1 = q2 ; q1 > q1 > q2 :@q11 (r)
q
)
1
1
1
1

@"(q11 (m);q11 (r);q21 )q11 (r)
=
b
> 0:
1
1
@q2
q1 (r) q1

This lemma shows that a higher level of q11 (r), q11 (r) > q1 and a lower level of q21 , q21

q1 ;will induce a higher level of threshold value, "(q11 (m), q11 (r), q21 )5 : This implies that for theearnings-target-type …rm meeting a …rst-period earnings target higher thanbound of5

1 ; the lower

1 1 1
1
1
1
1
1
1 ( ; q1 (m); q1 (r); q2 ) will increase with "(q1 (m), q1 (r), q2 ). Moreover, by Lemma

Since 0 < b < 1, the net e¤ect of a higher level of q11 (r), q11 (r) > q1 and a lower of q21 , q21

q11 (r), q21 ) is still positive.

20:

q1 on "(q11 (m),

1
d":
2"

4, we will consider the likelihood in which the pro…t-maximization …rm may (or may not)mimics the earnings-target …rm’s …rst-period output decision.
We will consider …rm 1 taking pure strategy or mixed strategy in the …rst period. A purestrategy for …rm 1 is a map from the di¤erential objective functions (i.e., pro…t-maximizationand earnings-target) into the choice of …rst-period output. A mixed strategy for …rm 1 is a
probability distribution over a set of feasible …rst-period output choices for di¤erential objective functions. Given that …rm 1 knows its own type, it will choose each action from thefeasible set with some probability. We consider ; where 0 << 1, is the probability for some" that will result in the pro…t-maximization-type of …rm 1 randomizing between q11 (m) andq11 (r).

4.2.1

Firm 1 Taking a Pure Strategy in Period 1

In the separating equilibrium, di¤erent types of …rm 1 use di¤erent strategies. Therefore,
the type is learned exactly, and …rm 2 will set its output level to best …t each type of …rm
1 in the …rst period. We focus on the equilibria, (q11 (m); q11 (r)), with q11 (r) > q1 and q11 (m)responding with q11 (r) > q11 (m)q1 ; in which the earnings-target-type of …rm 1 sets its …rst-

period output level q11 (r) higher than q1 , which re‡ects the earnings-target-type …rm’s myopia
and this type of …rm will distort its …rst-period output level to pursue a higher …rst-period
pro…t level; the pro…t-maximization-type of …rm 1 pursues pro…ts maximization within two
periods and sets its …rst-period output q11 (m), with q11 (m)q1 . By Lemma 4, this could

happen once the random demand shock falls below the threshold value "(q11 (m), q11 (r), q21 ) in
which the masked e¤ect from the demand uncertainty on the …rst-period pro…t is low and ahigher level of …rst-period output level will not increase the …rst-period pro…t level. Thus, thepro…t-maximization-type of …rm 1 has no incentive to set a higher q11 and further mislead …rm
2 about …rm 1’s objective type. The probability for this case is21("+"(q11 (m); q11 (r); q21 )).
2"

Recall that q21 is determined by equation (10). We consider the following posterior beliefs:
2= 0;

for q11q11 (r);= 1;

for q11 < q11 (r).

In these posterior beliefs, after observing q11 with q11 < q11 (r); …rm 2 holds the belief that …rm
1 is a pro…t-maximization-type …rm,

2 = 1; after observing q 1 with q 1
1
1

the belief that …rm 1 is earnings-target-type …rm,q11 (r); …rm 2 holds

2 = 0: Note that this on-equilibrium pathbelief for the …rm 1’s output choices (i.e., value of q11 is either q11 (m) or q11 (r)) follow Bayes’rule, and the setup for the o¤-equilibrium path belief for …rm 1’s output choices (i.e., value ofq11 other than q11 (m) or q11 (r)) is referred to Gibbons (1992).
We replace

2 with the above setting and rewrite the expected intertemporal pro…ts forthe pro…t-maximization-type of …rm 1.
Z"(aq11 (m)bq21 ( 1 ) + "c1 )q11 (m)

1
d"
2"

"

"(q11 (m);q11 (r);q21 )

+

Z

"

+

Z"

"(q11 (m);q11 (r);q21 )

2
1
1
2
2
2 1
b 1 1
d"
1 (1; ( ; q1 (m); q1 (r); q2 ; "); q1 (m); q 1 (r); q2 )

2"

2
1
1
2
2
2 1
b 1 1
d":
1 (1; ( ; q1 (m); q1 (r); q2 ; "); q1 (m); q 1 (r); q2 )

2"

(11)

Henceforth, we denote q 21 (r) as the second-period output of the earnings-target-type …rm forcases where the targeted pro…t is higher thano2
1 : Similarly, q 1 (r) as the second-period outputof the earnings-target-type …rm for cases where the targeted pro…t is lower than thanAs for the earnings-target-type of …rm 1, denote

22

o
1:

as its expected intertemporal pro…ts,

whereZ"(aq11 (r)bq21 ( 1 ) + "c1 )q11 (r)

1
d"
2"

"

"(q11 (m);q11 (r);q21 )

Z

+

2
2 1
2
1
1
2
b 1 1
d"
1 (0; ( ; q1 (m); q1 (r); q2 ; "); q1 (m); q 1 (r); q2 )

2"

"

Z"

+

2 1
2
2
1
1
2
b 1 1
d":
1 (0; ( ; q1 (m); q1 (r); q2 ; "); q1 (m); q 1 (r); q2 )2""(q11 (m);q11 (r);q21 )Pro…t-maximization-type of Firm 1 In the separating equilibrium, the following are
required: (i) q11 (m) maximizes the pro…t in (11), meaning that the equilibrium pro…t is higher
00than any (q11 (m); q11 (r)) with q11 (m) 6= q11 (m) and2= 1: This condition is the marginal

condition that the partial derivation of (11) with respect to q11 (m) is equal to zero. (ii) The
equilibrium pro…t is at least greater than that of earnings-target type …rm and setting outputs
and belief to be (q11 (r); q11 (r)) and2 =1 . This condition requires the pro…t in (11) to be atleast as great as the following term:Z"(aq11 (r)bq21 ( 1 ) + "c1 )q11 (m)

1
d"
2"

"

"(q11 (m);q11 (r);q21 )

Z

2"

_

"

Z"

+

2 1 b 1 1
1
1
2
2
2 1
d"
1 ( ; ( ; q1 (m); q1 (r); q2 ; "); q1 (m); q 1 (r); q2 )2 1 b 1 1
1
1
2
2
2 1
d"
1 ( ; ( ; q1 (m); q1 (r); q2 ; "); q1 (m); q 1 (r); q2 )2""(q11 (m);q11 (r);q21 )Let the above condition bind, then we have
Z"

1
1 1
1 1
d"
1 (q1 (r); q2 ( ); ")][ 11 (q11 (m); q21 ( 1 ); ")2"""(q11 (m);q11 (r);q21 )

Z

+

_

"

+

Z"

"(q11 (m);q11 (r);q21 )[ 12 (1; b ; q12 (m); q 21 (r); q22 )[ 12 (1; b ; q12 (m); q 2 (r); q22 )1

23

2 1 b 222 1
d"1 ( ; ; q1 (m); q 1 (r); q2 )]2"

2 1 b 22
2 1d" = 0:1 ( ; ; q1 (m); q 1 (r); q2 )]

2"

(12)

where we have abbreviated the second-period earnings benchmark b ( 1 ; q11 (r); q21 ; ") as b for
simpli…cation.

Earnings-target-type of Firm 1 For the earnings-target-type of …rm 1, it is only
required that the expected intertemporal payo¤s satisfy: E( 11 +21) =: Hence, for q11 (r) tobe the equilibrium strategy, we need a q11 (r) to satisfy (15),q11 (r) 2 fq11 jZ"(a

q11 (r)bq21 ( 1 ) + "1c1 )q11 (r) d" +2"""(q11 (m);q11 (r);q21 )

Z

"

2
2
2 1
b 2
d"
1 (0; ,q1 (m),q 1 (r),q2 )]

2"

(13)

+

Z"

"(q11 (m);q11 (r);q21 )

2
2 1
2
b 2
d"
1 (0, ,q1 (m),q 1 (r),q2 )2"gOverall, the separating equilibrium is determined by the marginal condition in (11), equality(12) and marginal condition in (13). The following proposition describes the properties forseparating equilibrium.
Proposition 5 There exists separating equilibria in which the pro…t-maximization …rm andthe earnings-target …rm choose q11 (m) and q11 (r) in the …rst period, respectively, with q11 (r) >q11 (m)q1 ; and choose q12 (m) and q12 (r) in the second period, respectively, with q12 (m)q1o >

q11 (r):
Proof. See Appendix.
As mentioned above, …rm 1’s …rst-period output level could in‡uence …rm 2’s posterior
belief, which in turn a¤ects the size of the second-period earnings target for the earningstarget …rm. Given the earnings-target …rm’s myopic incentive, this type of …rm second-period
equilibrium pro…t could be lower than its …rst-period equilibrium pro…t (and could also be
lower than the pro…t-maximization type of …rm’s second-period equilibrium pro…t).
This proposition addresses the competitive e¤ects of meeting earnings target and illustrates
a grim picture of the long-term consequences of meeting earnings target. We show that whenthe earnings-target …rm prefers a higher …rst-period pro…t and a lower second-period pro…t24

and attempts to meet the two-period earnings target, this type of …rm will distort its outputs
decision to produce greater short-term pro…ts at the expense of long-term pro…t through overproduction in the …rst period and then lower the output in the second period. Moreover, this
proposition also implies the following corollary.
Corollary 6 When the earnings-target …rm faces higher earnings target, the rival …rm will
respond more aggressively in the second period.
This corollary predicts that …rms experiencing higher earnings target will shift their focus
toward generating current earnings by exercising market power and raising the outputs towarda higher level. Moreover, this earnings target will further a¤ect competitive interactions andencourage greater expansion by rival …rms subsequently.

4.2.2

Firm 1 Taking a Mixed Strategy in Period 1

In the hybrid equilibrium, a certain type of …rm 1 uses mixed strategy and chooses randomly
between q11 (m) and q11 (r). Therefore, …rm 2 does not perfectly learn the type of …rm 1, and thisparticular type of …rm 1 will take advantage of the impact on …rm 2’s uncertainty ( 2 ). Firm
2 will set an output level which best replies to a weighted sum of q12 (m) and q12 (r): We focus on
the equilibria, ( q11 (m) + (1)q11 (r); q11 (r)), 0 << 1, with q11 (r) > q11 (m)q1 ; in which thepro…t-maximization-type …rm takes a mixed strategy, and the earnings-target-type …rm selects
a pure strategy. By Lemma 4, this could happen once the random demand shock exceeds thethreshold value "(q11 (m), q11 (r), q21 ): The probability for this case isthis case, …rm 1 will take advantage of(" "(q11 (m); q11 (r); q21 ))
.
2"

In

1 , with the e¤ect of an expectation on high demand

uncertainty on its …rst-period pro…t level and raise its …rst-period output level in an attempt
to increase the …rst-period pro…t. The pro…t-maximization-type of …rm 1 has incentive to set
a higher q11 and further to mislead …rm 2 about …rm 1’s objective type.

25

Recall that q21 is determined by (10). We consider the following posterior beliefs:
2

=

1 (1

)
) + (1

1 (1

1)

;

for q11 = q11 (r);for q11 6= q11 (r).

= 1;

In these posterior beliefs, after observing q11 with q11 6= q11 (r); …rm 2 holds the belief that …rm
1 is a pro…t-maximization-type …rm,

2 = 1; after observing q 1 with q 1 = q 1 (r); …rm 2 holds
11
1

the belief that …rm 1 may be a pro…t-maximization-type …rm,

2 =

1 (1
1 (1

2 = 1; for q 1 6= q 1 (r) and1
1these on-equilibrium path beliefs, i.e.,

2 =

)
)+(1

1)

: Note that

1 (1
1 (1

)
)+(1

1)

; for

q11 = q11 (r) follow Bayes’rule. Novaes (2002) also used similar on-equilibrium path beliefs inwhich a manager uses leverage to convey information about his ability and avoids the threatof shareholders’activism under a takeover threat.
We replace

2 with the above setting and rewrite the expected intertemporal pro…ts forthe pro…t-maximization-type of …rm 1.
Z"

q11 (r)(abq21 ( 1 ) + "c1 )q11 (m)

1
d"
2"

"

"(q11 (m);q11 (r);q21 )

Z

+

2"

"

Z"

+

2 2 b 222 1
d"1 ( ; ; q1 (m); q 1 (r); q2 )]2 2 b 222 1
d":1 ( ; ; q1 (m); q 1 (r); q2 )]2""(q11 (m);q11 (r);q21 )As for the earnings-target-type of …rm 1, denoteZ"(aq11 (r)as its expected intertemporal pro…ts, where

bq21 ( 1 ) + "c1 )q11 (r)

1
d"
2"

"

"(q11 (m);q11 (r);q21 )

+

Z

"

+

Z"

"(q11 (m);q11 (r);q21 )2 2 b 222 1
d"1 ( ; ; q1 (m); q 1 (r); q2 )2"

2 2 b 222 1
d":1 ( ; ; q1 (m); q 1 (r); q2 )

2"

26

(14)

Pro…t-maximization-type of Firm 1 We replace2with the above setting, andrewrite the expected intertemporal payo¤s for the pro…t-maximization-type of …rm 1. In
the hybrid equilibrium, q11 (m) maximizes the pro…t in (11), meaning that the equilibrium00

pro…t is higher than any (q11 (m); q11 (r)) with q11 (m) 6= q11 (m) and2= 1: This conditionis the marginal condition that the partial derivation of (11) with respect to q11 (m) is equal
to zero. Moreover, the mixed strategy between q11 (m) and q11 (r) lead to the same expectedintertemporal pro…ts. This condition is equivalent to the following:
Z"

1
1 1
1 1
d"
1 (q1 (r); q2 ( ); ")][ 11 (q11 (m); q21 ( 1 ); ")2"""(q11 (m);q11 (r);q21 )Z+[ 12 (1; b ; q12 (m); q 21 (r); q22 )

_

"

+

Z"

[ 12 (1; b ; q12 (m); q 2 (r); q22 )1"(q11 (m);q11 (r);q21 )2 2 b 222 1
d"1 ( ; ; q1 (m); q 1 (r); q2 )]2"

2 2 b 22 1
2d" = 0:1 ( ; ; q1 (m); q 1 (r); q2 )]

2"

(15)

Earnings-target-type of Firm 1 For the earnings-target-type of …rm 1, it is only
required that the intertemporal payo¤s satisfy: E( 11 +. Hence, for q11 (r) to be the21) =equilibrium strategy, we need a q11 (r) to satisfy (16),q11 (r) 2 fq11 jZ"(a

q11 (r)bq21 ( 1 ) + "1

1c1 )q11 (r) d"1 +2"""(q11 (m);q11 (r);q21 )Z

2 2 b 222 1
d"1 ( , ,q1 (m),q 1 (r); q2 )]

2"

"

(16)

+

Z"

"(q11 (m);q11 (r);q21 )2
2 2 b 22 1
d"
1 ( , ,q1 (m); q 1 (r); q2 )2":Overall, the hybrid equilibrium is determined by the marginal condition in (11), equality in(15), and marginal condition in (16). The following proposition describes the hybrid equilibrium.
Proposition 7 There exists a hybrid equilibrium in which the pro…t-maximization-type …rmand the earnings-target-type …rm choose q11 (m) + (127

)q11 (r), 0 << 1 and q11 (r) in the…rst period, respectively, with q11 (r) > q11 (m)period, respectively, with q12 (m)q1 ; and choose q12 (m) and q12 (r) in the second

q1o > q12 (r):Proof. See Appendix.
For the informational impact of meeting earnings target, we show that the tendency for…rms to meet target is motivated by marketwide demand conditions in which once the expected…rst-period demand shock is high (E("1 ) > "(q11 (m), q11 (r), q21 )) the pro…t-maximization-type…rm is motivated to conceal its identity by exploiting the e¤ect of high level of expected demand
shock on its …rst-period output choice and mimicking the earnings-target-type …rm (so that…rm 2 does not perfectly learn the type of …rm 1). Consequently, the pro…t-maximizationtype …rm could boost its …rst-period output level for a higher pro…t level. Moreover, this
proposition also implies the following corollary.
Corollary 8 As the expected demand uncertainty further increases, there will be a higher
probability, 1; that the pro…t-maximization-type …rm pools with the earnings-target-type…rm and …rm 2 responds less aggressively in the second period.
This corollary predicts that as the expected level demand uncertainty further increases,
there will be a higher likelihood that the pro…t-maximization-type …rm pools with the earningstarget-type …rm. This further confuses …rm 2’s assessment of …rm 1’s type and thus the pro…tmaximization-type …rm’s absolute amount of output manipulation gain is higher. However, ahigher level of 1

will lead to a higher level of

2 ; in which the rival …rm will respond lessaggressively in the second period.
This corollary implies that the tendency for …rms to meet earnings target is positively
related to the marketwide business conditions. This is consistent with Cohen and Zarowin(2007) who provided evidence that the tendency for …rms to meet or beat earnings benchmarks
is positively related to marketwide P/E ratio. In addition, this corollary also suggests that thegreat economic booms further confound a rival …rm’s ability to identify opportunistic abnormal
output activities and enhance a market-leader …rm’s absolute amount of output manipulation

28

gain. Thereby, the rival …rm responds less aggressively later and this may improve the marketleader …rm’s long-term product market competitiveness. This enhances the market-leader…rm’s absolute amount of output manipulation gain and induces the rival …rm response lessaggressively later. Consequently, our analysis predicts that the negative impact of short-term
earnings pressure on long-term product market competition will be lowered when market
transparency (on the producer side) is lower.

5

Conclusion

This study investigates how a …rm manages earnings through real activities manipulation
triggered by product market consideration production, and how this a¤ects the real operating
decisions of other …rms in the same industry. To address this issue we consider a two-period
oligopoly model with one-sided asymmetric information in which a …rm has private information about its objective type (pro…t-maximization-type or earnings-target-type) and characterize the perfect Bayesian equilibria in which a …rm’s …rst-period real decisions are not only
strategically made but are also used to reveal its objective type to its rival.
We show that one …rm will engage in real activities manipulation through over-production
for greater short-term pro…ts at the expense of long-term pro…ts. For the informational impact
of meeting earnings target, we show that the tendency for …rms to meet target is motivatedby marketwide conditions. Speci…cally, once the expected level of demand uncertainty is high,the pro…t-maximization …rm partially acts as the earnings-target …rm to mask the e¤ect ofdemand uncertainty on its …rst-period pro…t. The analysis of our game implies that earnings
target will a¤ect competitive interactions, because it encourages expansion by competitors.
The analysis also yields the prediction that when a dominant …rm face a higher earnings
target, it will induce rival …rms to respond more aggressively. It is shown that the extent
to which …rms are involved in meeting earnings target may positively relate to marketwide
business conditions. Our analysis further yields the prediction that when the market is lesstransparent (on the producer side) is lower, there will be a higher probability that the pro…t-29

maximization-type …rm pools with the earnings-target-type …rm in which the earnings kinkphenomenon is less relevant to opportunistic real activities manipulation.
For extending our study, one can consider a two-way feedback game between a …rm andthe stock market: a …rm will devote more e¤orts on either real smoothing in production orintertemporal pro…t maximization to give the stock market what it wants; it can be rational
for the stock market to weigh either real smoothing measure or intertemporal pro…tability
measure based on investors’ knowledge about the …rm’s preference over possible strategy.
Brown and Revankar (1971) and Aghion and Stein (2008) proposed a generalized utility inwhich a …rm devotes e¤orts on both sales and pro…ts. More speci…cally, a …rm devotes e¤orts
on combined sales and pro…t-maximization in Brown and Revankar (1971) and on either sales
growth or pro…t margins in Aghion and Stein (2008). These studies and ours consider ageneralized setting in which a …rm can change its strategic orientation deviated from pro…tmaximization. However, di¤erent from Brown and Revankar (1971) and Aghion and Stein(2008), the …rms’deviated behaviors in our model are put into a multi-period environment inwhich the earnings target is taken as pre-commitment to a higher …rst-period output and used
to coordinate a …rm’s intertemporal output decisions. Thus, engaging in real smoothing overperiods versus intertemporal pro…tability may reduce real-side volatility which is contrast to
Aghion and Stein (2008). Moreover, consideration of the e¤ect of combined sales and pro…tmaximization may also alter Aghion and Stein (2008)’s results. We leave it to future research.

Appendix

Proof of Proposition 5. (i) The conditions for the hybrid equilibrium consist of the marginal
condition of (11), equality (12), and the marginal condition of (13).
Given that earnings-target-type …rm’s second-period output is q12 (r); with q12 (r) < q1o andthe second-period pro…t is

2
2
2
b 2
1 (0; ; q1 (m); q1 (r); q2 ); with

2
2 2
2
b 2
1 (0; ; q1 (m); q 1 (r); q2 ; " ) <o1;

Let q11 (r) satisfy the condition of (13). By Lemma 4, when q11 (r) > q1 and q11 (r) < q1 ; giventhat

1 is small enough and approaches 0, then

30

1 1 1
1
1 ( ; q1 (r); q2 ; ")1:

Let q11 (m) satisfy the marginal condition of (11),@E( 11 + 12 )@E 11
@ 12 @ 2=+= 0:@q11 (m)@q11 (m) @ 2 @q11 (m)Given that q11 (r) > q1 , since

1 1 1
1
1
1
1 ( ; q1 (r); q2 ; ") is concave in q1 (r) and decreasing in bq2 and…rm 2 faces an expected quantity ( 1 q11 (m) + (1be set to satisfy q11 (r) > q11 (m)q11@E1 )q 1 (r)), with 0 <1

1 < 1; q 1 (m) could
1

1

2 is equal to 0 for1= 0: Moreover, since
q1 ; with @q1 (m)1

q11 (r); and is equal to 1; for q11 < q11 (r), output competition in the second period is

reduced to full information case where q12 (m) is set to q1o , q22 is set to q2o ; and2
2 is equal to@ 12
2 : In this case, @q 1 (m) = 0:
1

Given the expected random demand shock in the …rst period falls below the threshold value"(q11 (m); q11 (r); q21 ), we have E( 11 (q11 (m); q21 ( 1 ); ")) < E( 11 (q11 (r); q21 ( 1 ); ")); where q11 (r) >q11 (m)q1 : For the equality (12) to hold, we needand q12 (m) >22
22
1 (1; q1 (m); q1 (r); q2 ) >

2 1 2
2
2
1 ( ; q1 (m); q1 (r); q2 )1 )q 2 (r): The latter condition implies that q 2 (r) < q o1
1
1

1 q 2 (m)+ (11q12 (m);where q12 (r) would be q 21 (r). By Lemma 1, if …rm 1 needs to meet a second-period earnings target equal to or lower thano2o1 , it could achieve this by setting q1 (r) < q1 where thesecond-period demand uncertainty lies within a high range.
In summary, (q11 (m); q11 (r)); with q11 (r) > q11 (m)q1 and q12 (r) < q1o

q12 (m) forms a

separating equilibrium.
Proof of Proposition 7. The conditions for the hybrid equilibrium consist of the marginal
condition of (11), equality (15), and the marginal condition of (16).
Given that earnings-target-type …rm’s second-period output is q12 (r); with q12 (r) < q1o andthe second-period pro…t is

2 2 b 22
2
1 ( ; ; q1 (m); q1 (r); q2 ); with

2 2 b 222 2
1 ( ; ; q1 (m); q 1 (r); q2 ; " ) <o1;

Let q11 (r) satisfy the condition of (16). By Lemma 4, when q11 (r) > q1 and q11 (r) < q1 ; giventhat

1 is small enough and approaches 0, then

1 1 1
11 ( ; q1 (r); q2 ; ")1:

Let q11 (m) satisfy the marginal condition of (11),@E( 11 + 12 )@E 1
@ 2 @ 2
= 1 1 + 21 1
= 0:
1
@q1 (m)@q1 (m) @ @q1 (m)Given that q11 (r) > q1 , since

1 1 1
1
1
1
1 ( ; q1 (r); q2 ; ") is concave in q1 (r) and decreasing in bq2 and…rm 2 faces an expected quantity ( 1 q11 (m) + (1311 )q 1 (r)), with 0 <1

1 < 1; q 1 (m) could be1

set to satisfy q11 (r) > q11 (m)

@E

1

1
q1 ; with @q1 (m)= 0: Moreover, since

2 is equal to

1

1 (1
1 (1

)
)+(1

1)

for q11 = q11 (r); and is equal to 1; for q11 6= q11 (r), output competition in the second period is
reduced to full information case where q12 (m) is set to q1o , q22 is set to q2o ; and2
2 is equal to@ 12
2 : In this case, @q 1 (m) = 0:
1

Given the expected random demand shock in the …rst period exceeds the threshold value"(q11 (m); q11 (r); q21 ), we have E( 11 (q11 (m); q21 ( 1 ); ")) < E( 11 (q11 (r); q21 ( 1 ); ")); where q11 (r) >q11 (m)q1 : For the equality (12) to hold, we need
1 (1

)
)+(1

q12 (m)+ (12222
1 (1; q1 (m); q1 (r); q2 ) >

1 (1

)
)+(1

2 2 2
2
2
1 ( ; q1 (m); q1 (r); q2 ))q12 (r): The latter condition implies thatand q12 (m) >1 (1q12 (r) < q1o

q12 (m); where q12 (r) would be q 21 (r). By Lemma 1, if …rm 1 needs to meet

1)

1 (1

1)

a second-period earnings target equal to or lower thano
1 , it could achieve this by setting

q12 (r) < q1o :Finally, the pro…t-maximization-type …rm takes a mixed strategy q11 (m) + (1the …rst period, where q11 (r) > q11 (m)q1 . Then, we can observe that q11 (m) + (1is higher than q11 (m); 8 2 (0; 1). In summary, ( q11 (m) + (1q11 (m)6)q11 (r) in)q11 (r))q11 (r); q11 (r)) with q11 (r) >q1 forms a hybrid equilibrium.

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