OSIPP Discussion Paper : DP-2006-E-004-Rev

Contracting with Self-Esteem Concerns
November 15, 2006
Junichiro Ishida
Associate Professor, Osaka School of International Public Policy (OSIPP)【キーワード】Self-esteem, Bayesian learning, Tradeoff between risk andincentives, Contract【要約】It is widely accepted in social psychology that the need to maintainand enhance self-esteem is a fundamental human motive. We incorporate
this factor into an otherwise ordinary principal-agent framework andexamine its impact on the optimal incentive scheme and the agent's
behavior, especially focusing on a form of intrapersonal strategy known as
self-handicapping. Incorporating self-esteem concerns into a contracting
situation yields an implication that goes against the conventional wisdom:
the standard tradeoff between risk and incentives may break down in thepresence of self-esteem concerns because uncertainty mitigates the need for
self-handicapping, providing a potential reason for why we do notempirically observe this tradeoff in a robust manner. We characterize an
intuitive condition for this anomaly to arise and present a set of testable
implications. Along the way, we also show that the fragility of self-esteem(the variance) is just as important as its level (the mean) in selecting agents.
Finally, this simple logic is applied to a team problem to show why and how
people are better motivated under team production than under individual
production.

I am grateful to Hideshi Itoh and seminar participants at CTW Summer
Conference for helpful discussion. Financial support from Grants-in-Aid forYoung Scientists (B) is gratefully acknowledged.

1Introduction

In most economic analyses, agents are typically assumed to possess precise knowledge of their own
attributes. As this assumption symbolically indicates, economists have paid relatively less attention
to potential consequences of learning about oneself. This aspect of economics perhaps draws clear
contrast with psychology where how people come to understand themselves in general, or the issueof self-esteem in particular, has always been the topic of utmost concern. Although self-esteem isdefined in a variety of ways, including perceived ability and competence, physical attractiveness andinterpersonal relations, it is now widely accepted in social psychology that the need to maintain andenhance self-esteem is a fundamental human motive (Leary and Downs, 1995).
Recently, there is also a growing amount of interest on the issues of self-esteem concerns among
economists, as exemplified most notably by Benabou and Tirole (2002). In this paper, we explore
implications of self-esteem concerns in a contracting situation by following this line of research froma different perspective. To this end, we start our analysis with two key presumptions: (i) the agent
in question is a rational Bayesian learner, but with vague knowledge about himself to begin with;and (ii) he benefits directly from having a positive image of himself, for various reasons. Under thissetup, an outcome of some action, which becomes a signal of his own unknown attributes, has a direct
effect on the payoffs, aside from compensations from the agreed-upon contract. The presence of selfesteem concerns has a critical bite especially when ability and effort are complementary to each other,as is often assumed in many economic analyses. Under this condition, the agent actually stretches
the distribution of outcome by exerting effort, thereby facilitating the learning process about oneself.
Conversely speaking, by not exerting effort and hence compressing the distribution of outcome, thefailure becomes relatively insignificant as the agent can still remain vague about his own attributes:
even if the task turns out to be unsuccessful, the agent can attribute it to the lack of effort rather
than the lack of ability.
An especially interesting situation arises when the agent is averse to having a negative self-image
or, more precisely, the utility gain from self-esteem is concave in its level. In such a case, given
1the same mean, the agent is actually made better off by not obtaining more information and hence
remaining vague about himself. This motive gives rise to a form of intrapersonal strategy, known
as self-handicapping in social psychology, where individuals create impediments to successful performances. In some instances, self-handicapping takes a highly active form where they take performanceimpairing drugs or alcohol before the achievement activity such as the exam;1 in others, it takes amore passive form where they intentionally withhold effort in order to make failure meaningless (e.g.,
not studying hard before the exam). In either case, people resort to self-handicapping as a strategy
to shield themselves from ‘facing the truth’ that can sometimes be painful. In this paper, we mostly
focus on the role of the latter form of (passive) self-handicapping in a principal-agent framework.2
Incorporating self-esteem concerns into a contracting situation yields an implication that goesagainst the conventional wisdom. The central tenet of the contract theory is the tradeoff between
risk and incentives, which asserts that the cost of inducing any given level of effort generally increases
with the extent of uncertainty faced by the agent. This general conclusion suggests that, because theagency cost increases with the uncertainty of the underlying environment, incentive pays would be
muted in risky situations. Despite its clear prediction, however, finding this tradeoff in actual data
has turned out to be a daunting task, as emphasized in a series of papers by Prendergast (2000, 2002a,
2002b).3
In those papers, Prendergast provides several plausible reasons why we may not observe thistradeoff by focusing on the neglected impact of uncertainty on various aspects of monitoring behavior(Prendergast, 2000, 2002b) or the allocation of responsibility (Predergast, 2002a).4 The basic stancethere is that there are some hidden aspects of uncertainty that tend to be overlooked, and those aspects
influence the optimal form of incentive structure. In contrast, this paper points out a channel through1 For instance, Tucker, Vuchinich and Sobell (1981) observe that college students who are not sure to perform wellat an intellectual task volunteer to drink alcohol before the task.
2 In what follows, we refer to self-handicapping simply as an act of withholding effort in an attempt to obscure one’s
own attributes.
3 See Jin (2002) and Core and Guay (2002) for more recent empirical evidence.
4 Several alternative explanations have also been suggested. For instance, Ackerberg and Botticini (2002) argue thatthe standard tradeoff may disappear if endogenous matching is explicitly considered. Raith (2003) emphasizes theimpact of market competition on the provision of managerial incentives.

2

which the presence of uncertainty itself directly yields a positive incentive effect which weakens oreven breaks down the standard tradeoff.5 The main contention of this paper is that uncertainty may
yield a positive incentive effect because the uncertainty associated with the task obscures the agent’strue worth, thereby reducing the need for self-handicapping. Since the need for self-handicapping
naturally increases the agency cost to induce any given level of effort, an increase in uncertainty may
actually decrease the agency cost; this is so even when the agent in question is a rational Bayesianlearner with no ability to manipulate information. Along the way, our analysis, and especially thereasoning mentioned above, give rise to a set of testable implications on the tradeoff between risk andincentives.
As an application of this logic, we also make a point that this mechanism explains why teamproduction can be more profitable, compared to individual production. As a recent trend, many firms
start adopting team production as a way to motivate workers. This trend is somewhat puzzling because the standard theory asserts that team production invites a notorious free-rider problem because
each agent’s contribution becomes less distinguishable in teams. To account for this trend, several
explanations have been offered, from the presence of complementarities to the importance of repeatedinteractions (e.g., Che and Yoo, 2001; Ishida, 2006). This paper provides yet another explanation
for why team production can be profitable based on self-esteem concerns. In short, team production
can be profitable because the outcome of some team projects is less reflexive of one’s own attributes
whereas the outcome more accurately reflects them under individual production. Since the need for
self-handicapping is lower under team production, the cost of inducing effort can also be lower, consequently making team production more profitable. Our framework thus provides an explanation for
why workers are better motivated under team production, especially to the extent that can overcome
the free-rider problem – the psychological side of team production often emphasized by managers andexecutives.
As already mentioned, there is a growing body of literature which incorporates psychological factors
5 Our stance here is that the presence of self-esteem concerns can provide one factor, possibly among many others,

which can break down the standard tradeoff. It should thus be noted that the purpose of this paper is simply tocomplement, but certainly not to deny, the existing views on this issue.

3into formal economic analyses. There are largely two strands of literature that explore consequencesof learning about oneself. The first strand deals with interpersonal situations, which can be seen
as a particular type of the informed-principal problem. For instance, Benabou and Tirole (2003)
analyze how disclosing information about the agent (or his surrounding environment) might affect his‘intrinsic motivation.’6 Ishida (2006) further extends this idea and analyzes optimal promotion rules
when the agent is ambiguous about his own attributes and gains some information about himself fromthe principal’s behavior.
The second strand, on the other hand, deals with intrapersonal situations. Economic consequencesof self-esteem concerns are broadly analyzed by Benabou and Tirole (2002), focusing mainly on problems that stem from time-inconsistent preferences along the line of Carrillo and Mariotti (2000). Using
intrapersonal games, they analyze issues such as why self-confidence can be beneficial and how theacquisition of information alters the behavior of future selves. Benabou and Tirole (2004) combine
imperfect recall with time-inconsistent preferences and develop a theory of personal rules arising fromself-reputation concerns. Within a framework that is similar to ours (unbiased Bayesian learning andself-esteem concerns), Koszegi (2006) shows how self-esteem concerns give rise to biased beliefs evenfor rational Bayesian learners and distort the choice of task. The present paper belongs to this second
strand where the agent gains some information about himself through his own actions (self-signaling).
As a departure from previous studies, we focus on a contracting situation and analyze how self-esteem
concerns affect the optimal incentive scheme, especially in its relation to the tradeoff between risk andincentives.7
The present setup is also closely related to models of career concerns, most notably by Holmstrom(1999), in that it deals with dynamic signaling incentives.8 The difference from this strand of literature
is subtle yet critical. In models of career concerns, signaling is directed to outside observers who only
6 Benabou and Tirole (2006) consider a different context where an agent possesses private information about his
tastes and attempts to signal them in order to appear ‘prosocial,’ and show how this reputation effect is contaminatedby extrinsic rewards.
7 There is recently an increasing number of works that incorporate behavioral factors into contracting situations.
Some examples along this line include Itoh (2004), Grund and Sliwka (2005) and Englmaier and Wambach (2006) justto name a few.
8 Also, see Dewatripont, Jewitt and Tirole (1999a,1999b)4

have a limited set of information about the sender. Career concerns then typically yield a positive
incentive effect because the agent can gain nothing by withholding effort when outside observers
expect him to do otherwise. This draws clear contrast to the present framework where the focus isplaced on self-signaling and the agent’s information set, on which the posterior belief is conditioned,
naturally includes his own actions. As we will see shortly, this seemingly slight difference amounts todifferent implications where self-esteem concerns actually yield a negative incentive effect under someconditions, ultimately working to counteract with the standard tradeoff between risk and incentives.
The paper proceeds as follows. Section 2 briefly discusses why we care about self-esteem as ourentire analysis rests on this presumption. Section 3 illustrates the environment where we introduce
self-esteem concerns into an otherwise ordinary principal-agent model. Section 4 derives the main
results and shows that self-esteem concerns have an effect that tends to negate the standard tradeoff
between risk and incentives. Section 5 extends the model and shows that the same logic also works
for team production, providing an explanation for why team production can be so profitable. Finally,
section 6 makes some concluding remarks.

2

Why do we care about self-esteem?

Before we proceed to the formal analysis, we first briefly discuss why we care about our self-images atall because our analysis hinges crucially on the presumption that people benefit from having a positive
image of themselves. It is argued, mostly in psychology, that one of the most basic human responses
when faced with some object is evaluation (Tesser and Martin, 1996). It is then only natural thatsince the most important object in one’s life is arguably the self, the evaluation of self, or self-esteem,
has been the central theme in social psychology from the very beginning (Tesser, 2001). Consequently,
this voluminous literature has produced a set of theories and hypotheses on why there is ever a needfor a positive view of self.
On the demand side for self-esteem, Benabou and Tirole (2002) cite three possible factors on
why we prefer to have a positive view of ourselves. The first factor is what they refer to as the5consumption value of self-esteem: we simply like to consider ourselves as able, attractive, caring andso on. A possible channel through which the consumption value arises is a connection between selfesteem and affect that is well recognized in social psychology (Tesser and Collins, 1988): a rise in
self-esteem is often associated with positive affect while a decrease is associated with negative affect.
This then implies that the need for self-esteem inherently arises when we have preferences for positive
affect. According to this view, self-esteem is just another argument in the utility function, along withthe consumption of private goods.9
The second factor is the motivation value of self-esteem which becomes valuable especially insituation where our willpower is tested periodically. Evidence in favor of this view is fairly abundantas it is often observed that high self-esteem helps people achieve their goals. For instance, there isa tendency that people with high self-esteem perform better and persist longer at tasks (Bandura,
1977). In fact, people with high self-esteem tend to persist longer even at impossible tasks (McFarlin,
Baumeister and Blascovich, 1984). Here, the need for self-esteem arises indirectly where high selfesteem is instrumental in inducing better performances which are expected to lead to higher payoffs
in future transactions.
Finally, high self-esteem can be valuable in interpersonal situations, which Benabou and Tirole(2002) label as the signaling value of self-esteem. The idea is that it is easier to convince others thata person has some favorable traits when he or she in fact possesses such qualities. In a world full of
information asymmetry, the ability to present ourselves favorably to others can be a valuable asset
in situations such as job interviews, business negotiations, and so on. Somewhat related to this is
Barkow’s (1980) notion that self-esteem is an indicator of dominance in a group. According to thisview, high self-esteem implies dominance in a group, which certainly helps convincing others.
While it is undoubtedly crucial to examine the origins of self-esteem concerns, we do not take any
specific position about which view is more appropriate in this paper, in order to focus our attention
9 The consumption value of self-esteem can also be explained by the terror management theory (TMT). According
to Greenberg, Pyszczynski and Solomon (1986), the awareness of death, and its finality, produces terror. Being a partof one’s culture reduces this terror since the culture lives on forever and also promises an afterlife. Self-esteem becomes
important in this sense as it is an indicator of the extent to which the individual is meeting cultural standards.

6

to the impact of self-esteem concerns on the optimal incentive scheme. In what follows, therefore, we
simply assume that the agent in question benefits from having a positive image of himself for someunspecified reasons. More precisely, the present framework should be interpreted as adopting the first
approach (the consumption value) or some reduced form of the other two (the motivation value andthe signaling value) for practical purposes.

3

The model

We illustrate our contention by a simple model of moral hazard, with discrete effort choices and linear
contracts.10 The main purpose here is to make a point that the agency cost to induce any given levelof effort may decrease with an increase in the extent of uncertainty of the underlying environment,
quite contrary to the conventional wisdom.
Consider a model with a principal (female) and an agent (male). The agent is characterized by
the ability type η ∼ N(µ, ση2 ), µ > 0, which is initially not known to anyone, including the agent
himself. The prior distribution of the ability type is common knowledge. Under this setup, the meanµ (the prior belief on the agent’s ability type) reflects the agent’s initial self-esteem level while thevariance ση2 reflects its fragility. We hence regard that the agent is more secure (fragile) about his
own self-images when ση2 is relatively small (large). When ση2 = 0, the agent is certain about his own
attribute, and the problem converges to the standard case.
The principal lets the agent engage in a task where the agent’s effort level is denoted by e ∈ {0, 1}.
The cost of exerting effort is given by c(e) where c(0) = 0 and c(1) = c. The observable outcomey ∈ R is a noisy signal of ability and effort, specified asy = ηe + ε,(1)where ε ∼ N(0, σε2 ) is a disturbance distributed independently of η. Among other things, this specification implies that ability and effort are complementary to each other. The variance of the disturbance
10 Although it is in principle possible and conceptually straightforward to extend the model to continuous effort choices,the derivation of optimal contracts can be quite complicated computationally. The current specification is simple andtractable enough (although still computationally highly tedious) to succinctly make our point.

7

σε2 measures the extent of uncertainty faced by the agent in this economy. Our ultimate concern is its
impact on the cost of inducing effort e = 1.
We assume that the outcome is the only contractible variable in this environment and focus on alinear contract contingent on it. More precisely, the principal offers
w = βy + γ,

(2)where γ denotes some (constant) transfer payment. Given this, the contract can generically be writtenas (β, γ).
Finally, we need to specify the agent’s preferences, which mark the sole departure from the conventional setup. While the agent gains utility from material benefits as usual, he also has vested interests
in his own ability type. Let µ̃ denote the agent’s posterior belief about his own ability type, whichis contingent on the effort level e and the outcome y. The agent’s preferences are specified by thefollowing CARA utility function:u(w − c(e) + α(µ̃ − µ)) = − exp{−r[w − c(e) + α(µ̃ − µ)]}, r > 0.

(3)

Throughout the analysis, we broadly refer to the last term α(µ̃ − µ) as the self-esteem concern, andthe parameter α ≥ 0 measures its relative strength. When α = 0, the self-esteem concern is totallyabsent, and the agent’s utility depends solely on material payoffs as is normally assumed.
The timing of the model is summarized as follows:
stage 1:The principal offers a contract (β, γ). If the agent rejects it, both receive the reservation

payoff, which is normalized to zero.
stage 2: The agent determines the effort level e.
stage 3: The outcome y is realized and the wage is paid as specified by the agreed-upon contract.

8

4

The optimal contract with self-esteem concerns

4.1

A tenuous tradeoff between risk and incentives

The crux of the model is how the agent’s behavior influences the extent of uncertainty that he faces.
Let π := w − c(e) + α(µ̃ − µ) denote the total net payoff. Then, the certainty-equivalent (CE) versionof the agent’s problem is defined asmax

e∈{0,1}r
πCE := βµe + γ − c(e) − var(π | e).
2

Note that E(µ̃ | e) = µ regardless of the agent’s effort choice e. The agent exerts effort if and only ifrβµ ≥ c + [var(π | e = 1) − var(π | e = 0)],2

(4)Provided that the agent’s reservation payoff is normalized to zero, the participation constraint is givenbyr
βµe + γ ≥ c(e) + var(π | e),2(5)

when the contract offered is designed to induce effort e. Define we (ση2 , σε2 ) := c(e) + (r/2)var(π | e) as
the agency cost of inducing effort e. We are generally interested in how w1 is related to an increasein the extent of uncertainty σε2 .
To explicitly solve this problem, we obviously need to obtain the conditional variance of the payoffvar(π | e). For this, we can obtain the following result which holds even if e can be chosen continuously
over [0, ∞).
Lemma 1³var(π | e) = β +αeση2 ´2 2 2(e ση + σε2 ) := Γ2e (e2 ση2 + σε2 ),σε2 + e2 ση2for any given e ∈ [0, ∞).
Proof: We proceed here as if the effort choice is continuous for more generality. The outcome y inthis environment contains some information about the agent’s ability type. The best estimate from9

that observation alone is given by η̂ := y/e = (ηe + ε)/e.11 Note that, given the true η, η̂ is distributed
normally with precision e2 /σε2 . The agent then updates his prior with this new information, and theposterior belief is hence given by
µ̃ =

e2
1
ση2 µ + σε2 η̂1e2
ση2 + σε2=σε2 µ + e2 ση2 η + eση2 ε
σε2 µ + e2 ση2 η̂
=.
σε2 + e2 ση2σε2 + e2 ση2(6)

See DeGroot (ch.9, 1970) for more detail. It then follows from this that the agent’s ex post payoff is
π = β(ηe + ε) + γ − c(e) + α

e2 ση2 (η − µ) + eση2 ε.
σε2 + e2 ση2(7)

Since α, β, γ and µ are all constant at this stage, we have³var(π | e) = βe +αe2 ση2 ´2 2 ³αeση2 ´2 2 ³αeση2 ´2 2 2
+
β
+
=
β
+
σ
σ
(e ση + σε2 ).
ηεσε2 + e2 ση2σε2 + e2 ση2σε2 + e2 ση2(8)

Q.E.D.
Several remarks are in order. First, as ση2 → 0, the problem evidently converges to the standard
case where var(π | e) = β 2 σε2 regardless of e, and the incentive compatibility constraint is naturally
reduced to βµ ≥ c. A decrease in α, on the other hand, yields a slightly different implication: as
α → 0, i.e., as the self-esteem concern ceases to exist, the self-esteem fragility ση2 is just another formof uncertainty, playing quite a similar role to σε2 .12 When both α > 0 and ση2 > 0, however, there
arises some interaction between them that works to negate the standard tradeoff between risk andincentives under some conditions.
It follows from lemma 1 that the incentive compatibility constraint can be written asrβµ ≥ c + [Γ21 (ση2 + σε2 ) − Γ20 σε2 ].
2(9)Define β ∗ as the minimum incentive needed to induce e = 1, which satisfies (9) with equality. The
next result establishes that there exists some nonempty interval of β that can satisfy (9) when theprior belief µ is sufficiently large.
11 Note that η̂ is not well-defined when e = 0. We know, however, that the posterior belief always coincides with theprior and its variance is zero when e = 0. We thus proceed as if it is well-defined at the moment and later verify thatthe derived solution is indeed what we need to obtain.
12 The only difference is that this uncertainty is complementary to the effort level so that more effort amplifies theextent of uncertainty. It is important to emphasize, however, that its impact is independent of σε2 .

10Lemma 2 Suppose that µ is large enough to satisfy(µ − αrση2 )2 > rση2 (rΦ + 2c).,
where
Φ :=

(αση )2.
ση2 + σε2

There then exists some nonempty interval of β that can satisfy (9), and the optimal contract (β ∗ , γ ∗ )is given byβ ∗ (ση2 , σε2 ) =Proof:µ − αrση2 −q(µ − αrση2 )2 − rση2 (rΦ + 2c)rση2,γ ∗ (ση2 , σε2 ) =r ∗2 2β σε .
2

It follows from (9) and lemma 1 that the minimum incentive needed to induce e = 1,

denoted as β ∗ , must solve
β∗

=
=

´i
αση2 ´2 2
r h³ ∗
c
∗2 2
2
)
−
β
σ
+
σ
+
β + 2
(σ
ε
ε
η
µ 2µ
σε + ση2h2αση2 (ση2 + σε2 ) ∗(αση2 )2 icr.
+
ση2 β ∗ 2 +β+µ 2µσε2 + ση2
σε2 + ση2(10)Note that the righthand side is always positive, meaning that the roots, if they exist, must be positive.
When µ is sufficiently large, there exist two positive roots, of which the smaller one constitutes thesolution for our purpose. Applying the quadratic formula we obtain the optimal incentive as follows:qµ − αrση2 − (µ − αrση2 )2 − rση2 (rΦ + 2c)
β ∗ (ση2 , σε2 ) =
,
(11)
rση2
where Φ := (αση )2 /(ση2 + σε2 ). It is evident from this that there exist two positive roots, and hence
the solution is well-defined, when(µ − αrση2 )2 > rση2 (rΦ + 2c).

(12)Finally, since the participation constraint must also hold with equality, we obtainγ ∗ (ση2 , σε2 ) =rrvar(π | e = 0) = β ∗ 2 σε2 .
2
2

(13)
Q.E.D.

11

In what follows, we restrict attention to the case where µ is large enough to satisfy the conditionin the lemma, so that the optimal solution β ∗ exists. With this well-defined solution, the agency costof inducing e = 1 can be written asαση2 i2 2rhr(ση + σε2 ).
w1 (ση2 , σε2 ) = c + Γ21 (ση2 + σε2 ) = c + β ∗ (ση2 , σε2 ) + 222
σε + ση2(14)

Given this, we first make the following observation that the agency cost generally increases with σε2under the conventional setup.
Proposition 1 The agency cost w1 increases with the extent of uncertainty σε2 if α = 0 and/orση2 = 0.
Proof:

If ση2 = 0, the incentive compatibility constraint is simply reduced to βµ ≥ c so thatβ ∗ = c/µ. Note also that Γ1 = β ∗ = c/µ under this condition. The proposition is then immediately
obtained from this.
If α = 0, the incentive compatibility constraint becomes βµ ≥ c + β 2 ση2 . Again, the optimal β ∗is independent of σε2 . Since Γ1 = β ∗ as above, the agency cost increases with σε2 , provided that awell-defined solution β ∗ exists.
Q.E.D.
This conclusion that generally and robustly holds true in the conventional setup may be overturned
because an increase in uncertainty obscures the self-evaluation process, mitigating the need for selfhandicapping. More precisely, we make the following claim which identifies the necessary and sufficientcondition for this reversal to occur.
Lemma 3 Let ∂var(π | e = 1)/∂σε2 denote the partial derivative with respect to σε2 when β ∗ is held
constant wherehαση2 σε2 i∂var(π | e = 1)
∗
β
−
=
Γ
.
1
∂σε2
(σε2 + ση2 )2The agency cost w1 then decreases with the extent of uncertainty σε2 if and only if∗∂var(π | e = 1)
2 ∂β
2
)
+
σ
+
2Γ
(σ
< 0.
1
ε
η
∂σε2
∂σε2

12

Proof: It is straightforward to obtain that∗∂w1r ∂var(π | e = 1)
2
2 ∂β
=
+
rΓ
(σ
+
σ
)
,
1
η
ε
∂σε2
2
∂σε2
∂σε2

(15)

h
h
αση2 σε2 i2αση2 (ση2 + σε2 ) i∂var(π | e = 1)
∗
β
−
Γ
−
=
Γ
.
=
Γ
1
1
1
∂σε2
(σε2 + ση2 )2(σε2 + ση2 )2

(16)

where

Q.E.D.
While this condition is not particularly intuitive, examining this more closely yields the next
proposition which constitutes the main contention of the paper.
Proposition 2 The agency cost w1 decreases with the extent of uncertainty σε2 for any given (c, α, ση2 , σε2 )if µ is sufficiently large.
Proof: We first show that ∂var(π | e = 1)/∂σε2 < 0 is actually a sufficient condition for ∂w1 /∂σε2 <0. To see this, note that β ∗ must satisfy
β∗ =

c
r
c
r
+
[var(π | e = 1) − var(π | e = 0)] = +[var(π | e = 1) − β ∗ 2 σε2 ].
µ 2µ
µ 2µ

(17)

It follows from this that an increase in σε2 decreases the righthand side with β ∗ held constant if∂var(π | e = 1)/∂σε2 < 0. Since β ∗ is the smaller root of (17) (see the proof of lemma 2 for moreon this), this also implies ∂β ∗ /∂σε2 < 0, proving that ∂var(π | e = 1)/∂σε2 is actually a sufficientcondition for ∂w1 /∂σε2 < 0. More precisely, given some optimal contract (β ∗ (ση2 , σε2 ), γ ∗ (ση2 , σε2 )), theagency cost decreases with σε2 , evaluated at σε2 , ifβ ∗ (ση2 , σε2 ) <αση2 σε2.
(σε2 + ση2 )2(18)

This condition holds for any given (c, α, ση2 , σε2 ) when µ is sufficiently large since limµ→∞ β ∗ = 0.
Q.E.D.
A straightforward way to interpret this result is that the standard tradeoff between risk andincentives tends to disappear when the agent is more self-confident. This interpretation should be13made with caution, however, because what a high µ means is only relative, especially to the costof performing the task c. Our preferred view is slightly different, though closely related. Fixing cconstant, an increase in µ alternatively implies that the task at hand is getting easier or less costly,
and weaker incentives are needed to induce effort (the optimal contract converging to a fixed-wage
scheme as µ → ∞). This means that the agent can earn less pecuniary rents by performing the task,consequently rendering the self-esteem concern more significant in a relative sense. This implication
thus leads to a potentially testable hypothesis: the tradeoff between risk and incentives becomes more
ambiguous when expected material rents are relatively small. Conversely, it is also expected thatthe standard tradeoff becomes more visible for those with more lucrative contracts, such as CEOsand professional athletes who can supposedly earn larger rents. Indeed, according to the evidence
presented by Prendergast (2002), the relationship between risk and incentives is ambiguous at best
for CEOs while there is a clear positive relationship for sharecroppers and franchisees.
Although more empirical studies along this line are certainly needed before we jump to a firm
conclusion, this argument seems to reveal something fundamental about any explanations that appeal
to psychological factors. Since psychological factors are normally exogenously given and the magnitudeof their effects is roughly fixed, those factors tend to be more accentuated when less material benefits
are at stake.13 For instance, it is well known in social psychology that incentives (explicit rewards)
may backfire as they often interfere with ‘intrinsic motivation.’14 Subsequent studies reveal that thisanomaly, which certainly contradicts with the conventional economic reasoning, is more likely to arise
when material benefits are not sufficient (e.g., Gnnezy and Rustichini, 2000). In other words, any
effect that stems from exogenously fixed psychological factors is more resounding when less is at stakematerially but tends to be blown away in the face of significant material incentives. A similar logic
certainly works in the present model: when less is at stake materially, the agent’s attention naturally
shifts towards psychological factors such as self-esteem concerns, which substantially weaken or even
13 This is especially true when the consumption value of self-esteem is more dominant because it is reasonable toregard its effect as exogenously fixed.
14 One of the famous examples is an observation by Titmus (1970) that paying for blood would reduce the willingness
to donate blood as it undermines its social value.

14

overturn the prediction made by the standard economic theory.
Besides this implication, the present model also sheds light on two key ingredients of the main
result, each of which yields a potentially testable hypothesis. First, we assume at the outset thatability and effort are complementary to each other, which is crucial in giving rise to the need for selfhandicapping. In fact, the conclusion is totally reversed when they are substitutive, i.e., when only
one of either ability or effort is sufficient to carry out a task. In that case, the agent actually exposes
himself less to relevant information by exerting effort since more effort can cover the lack of ability.
Note that this need to hide the lack of ability diminishes as the underlying environment becomesnoisier and the outcome loses its informational content. The model thus predicts an important,possibly testable, connection between the complementarity between ability and effort on the one hand
and the tradeoff between risk and incentives on the other: the standard tradeoff becomes less visible
in situations where effort and ability are more complementary.
Second, the way we model self-esteem concerns implicitly assumes that the agent is risk-averse
in his own self-images. In other words, we implicitly assume by design that the agent is relatively
averse to receiving a bad news about himself (which may be referred to as ‘information-aversion’).
This condition is critical because the conclusion is once again totally overturned if the agent is riskloving in his own self-images. Suppose that this is the case so that the agent is actually madebetter off by collecting more accurate information about himself, given the same mean. In this case,besides monetary compensations, the agent has an additional incentive to ‘discover himself’ when
he faces a task. This extra incentive is naturally stronger when the underlying situation involves
less uncertainty as the agent is likely to obtain a more accurate signal in that case. The effectarising from self-esteem concerns then works in the same direction as the standard tradeoff: anincrease in uncertainty diminishes this extra incentive, thereby increasing the agency cost. This
reasoning implies that information-aversion (or truth-aversion) constitutes a necessary component forour story to be valid when it is combined with the complementarity between ability and effort.15
15 The standard tradeoff also breaks down when the agent is risk-loving in his own self-images, and ability and effort

are substitutive. We do not explore much on this case since this combination seems to be less likely.

15

Although this assumption of information-aversion seems to be a reasonable specification for manycases, as exemplified by several episodes of self-handicapping behavior, this implication indicates thatthe question of how we value self-esteem (the sign of the second derivative), instead of just whether
we care about it (the sign of the first derivative), can be a critical agenda on this issue.

4.2

A numerical example

We conclude the section with a numerical example in order to present a clearer picture of the model.
More specifically, we are interested in how the optimal incentive β ∗ and the agency cost w1 vary withthe extent of uncertainty σε2 for given values of ση2 and α.16
Figures 1a and 1b illustrate β ∗ for α = 0.75 and α = 1. In each figure, three different values of ση2
are considered. As the figures indicate, the optimal incentive β ∗ decreases with σε2 for a wide range of
σε2 . Indeed, the optimal incentive decreases rather sharply when σε2 is relatively small. This tendency
is clearly more visible when the self-esteem concerns is stronger (α = 1).
[figures 1a and 1b about here]
Figures 2a and 2b illustrate how the agency cost w1 varies with σε2 . The figures confirm that there
indeed exists some range for which the agency cost does decrease with σε2 , due mostly to a decreasein β ∗ . They also indicate that the agency cost becomes larger when the self-esteem concern is strong(a large α).
[figures 2a and 2b about here]
The figures above also indicate that the stronger incentive is necessary and the agency cost islarger for more fragile individuals (one with a larger ση2 ), illustrating an inherent relationship thatexists between the self-esteem fragility ση2 and its level µ. The reason for why fragile self-esteem is notdesirable for the principal is intuitively clear and simple: more fragile individuals face more uncertainly
both for the outcome and the posterior belief and hence demand more to compensate for this loss.
16 For the example, we specify r = 1, c = 0.1 and µ = 2.

16This indicates that when it comes down to selecting an agent (say, a worker), how fragile (or secure)the individual is about his own self-images is a factor just as crucial as his expected productivity, e.g.,
the expected ability.

5

Why and how can team production be profitable?

It has recently been suggested that many firms adopt team production as a means to motivate workers
and improve productivity. This is somewhat puzzling, at least on purely theoretical grounds, because
team production invites the free-rider problem in standard moral hazard problems. In order to accountfor this gap, several explanations have been offered. An obvious explanation is to point to the presenceof complementarities or synergies among team members. A benefit of team production also arises ina long-term relationship where team members interact with each other repeatedly over time.17
We intend to offer an alternative view on a virtue of team production, with an emphasis on therole of self-esteem concerns. Since a failure can be attributed at least partially to the teammates,
team production inevitably introduces ambiguity into the self-evaluation process. It is therefore lessego-threatening to exert effort under team production than under individual production because theoutcome now reflects the teammates’ attributes as well as the agent’s own, and hence they can share
the blame in the case of an unsuccessful event.
For the sake of comparison, we consider exactly the same specification as in the previous section.
The only difference is that the principle now hires two agents, denoted by i = A, B, and lets them
perform a task jointly. The only available measure of performance is the aggregate outcome y, which
is given byy=(ηA eA + εA ) + (ηB eB + εB )
,
2

(19)

where εi is i.i.d. This additive nature of the production function implies that there are no technologicalcomplementarities between the agents, a potential source of the benefit of team production.
Under this setup, we show that the principle may induce effort ei = 1 from both agents at a lower
17 See Che and Yoo (2001) and Ishida (2006) for this approach.

17

cost when they work jointly. To see this, it is once again crucial to obtain the variance of the total
payoff πi . The following result is obtained by slightly modifying lemma 1.
Lemma 4var(πi | ei , ej ) =

³ βe

i

2

³β
αe2i ση2 ´2 2
αei ση2 ´2 2 ³ βej ´2 2
σ
+
2
σε +
+
ση , i 6= j.
η
2σε2 + ei 2 ση22
2σε2 + ei 2 ση22+

Proof: The result obtained here largely parallels to lemma 1. The outcome under team production
contains some information about the teammate’s ability type, which functions as a noise in the selfevaluation process. The best estimate from the aggregate outcome is (2y − µej )/ei = (ηi ei + εi +εj )/ei := η̂i , i 6= j. Note that η̂i is distributed normally with precision e2 /2σε2 . The posterior belief isthen given by
µ̃i =

1
e2
ση2 µ + 2σε2 η̂i
1
ση2 +

ei 2
2σε2

=

2σε2 µ + ei 2 ση2 η̂i
2σε2 µ + ei 2 ση2 ηi + ei ση2 (εi + εj )=.
2σε2 + ei 2 ση2
2σε2 + ei 2 ση2(20)

It then follows from this that the agent’s ex post payoff is
πi = βei 2 ση2 (ηi − µ) + ei ση2 (εi + εj )(ηi ei + εi ) + (ηj ej + εj )+ γ − c(ei ) + α.
2
2σε2 + ei 2 ση2(21)

Since α, γ and µ are all constant at this stage, we havevar(πi | ei , ej ) =

³ βe

i

2

+

³β
αe2i ση2 ´2 2
αei ση2 ´2 2 ³ βej ´2 2
+
2
+
σ
σε +
ση .
η
2σε2 + ei 2 ση22
2σε2 + ei 2 ση22(22)
Q.E.D.

Given this, the incentive compatibility constraint (for agent A) isrβµ≥ c + [var(πA | eA = 1, eB ) − var(πA | eA = 0, eB )],
2
2

(23)

while the participation constraint is
βµreA + eB+ γ ≥ c(eA ) + var(πA | eA , eB ).
2
2

(24)

Define β ∗∗ as the minimum incentive needed to induce effort eA = eB = 1 from both agents whichmust satisfy
β ∗∗ =³ β ´2 iαση2 ´22cr h³ β
2
2
+
+ 2
(2σ
+
σ
)
−
2
σε2 .
ε
η
µ
µ 2
2σε + ση2
2
18

(25)

The agency cost of inducing eA = eB = 1 under team production is then defined as
W1 (ση2 , σε2 ) = c +³ β ∗∗ (σ 2 , σ 2 ) ´2 iαση2 ´2r h³ β ∗∗ (ση2 , σε2 )
η
ε
2
2
ση2 .
+ 2
)
+
+
σ
(2σ
η
ε
2
2
2σε + ση22(26)Comparing W1 with w1 obtained in the last section, we can make the following claim which is very
similar in nature to proposition 2.
Proposition 3 The agency cost is lower under team production than under individual production,i.e., W1 (ση2 , σε2 ) < w1 (ση2 , σε2 ), for any given (c, α, ση2 , σε2 ) if µ is sufficiently large.
Proof: The agency cost decreases under team production if var(πi | eA = 1, eB = 1) < var(π | e =1), i.e.,³ β ∗∗ (σ 2 , σ 2 )
η

2

ε

+

³ β ∗∗ (σ 2 , σ 2 ) ´2³
αση2 ´2
αση2 ´2 2
ε
η
2
2
∗
2
)
+
+
σ
(2σ
(σε + ση2 ).
<
β
+
σ
η
ε
η
2σε2 + ση22
σε2 + ση2(27)Note that limµ→∞ β ∗ = 0 and limµ→∞ β ∗∗ = 0. As µ → ∞, therefore, (27) can be written as³³ ασ 2 ´2αση2 ´2η(2σε2 + ση2 ) <(σε2 + ση2 ),22
2σε + σησε2 + ση2(28)

which can be shown to hold for any given (c, α, ση2 , σε2 ).
Q.E.D.
There are now increasingly many firms that adopt internal team competition in various formats
as a means to motivate workers. Many managers and executives emphasize the psychological side ofteam production although it is not entirely clear through what channel team production can provide somuch motivation to team members, especially to the extent that can overcome the free-rider problem.
The present model suggests one possible channel through which that can happen: workers are better
motivated under team production because ambiguity inherent under team production is instrumental
in mitigating the need for self-handicapping. Although we do not necessarily claim that this factor
alone is strong enough to make team production more effective than individual production, it can bea factor that plays at least some role in it.

196Concluding remarks

This paper examines the role of self-esteem concerns in contracting situations via a simple model ofmoral hazard. When the agent is relatively averse to having a negative self-image, there arises an
incentive to remain ignorant about himself, ultimately amounting to the need for self-handicapping.
In this situation, uncertainty may have a positive incentive effect as it introduces ambiguity into theself-evaluation process. This actually mitigates the need for self-handicapping.
The main purpose of the paper is simply to illustrate the point that the presence of self-esteem
concerns yields an implication that goes against the conventional wisdom. For this reason, there areseveral avenues to extend the present analysis. First, it is an important extension to examine the roleof self-esteem concerns in more general settings, e.g., continuous effort choices and/or more general,
nonlinear, contracts. Of course, as is well known, it is hard enough to generally characterize theoptimal contract in moral hazard problems even without self-esteem concerns. It is nonetheless animportant agenda to see how far one can push this logic and generalize the results obtained in thepresent paper.
Second, this paper assumed that the agent in question is a rational Bayesian learner who can
objectively compute his posterior belief. In reality, though, it is well known that people often resort
to ways to manipulate their own beliefs, from self-serving bias and cognitive dissonance to downward
comparison. For instance, self-serving bias is another inherent human tendency which is though to bea part of the self-defence mechanism. Although we emphasize the aspect that the main results holdeven for rational Bayesian learners, it is of some interest to see interactions, if any, between self-esteem
concerns and biased information processing.

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23Figures
Β*

Β*
0.25

0.25

0.2

0.2

0.15

0.15
Σ2Η =1.5

0.1

Σ2Η =1.5

0.1

Σ2Η =10.05

Σ2Η =0.5Σ2Η =1Σ2Η =0.5

0.05

Σ2¶

Σ2¶
1

2

3

4

1

5

Figure 1a: α = 0.75

2

3

4

5

4

5

Figure 1b: α = 1

w1

w1

0.5

0.5
Σ2Η =1.5

0.4

0.4

0.3

0.3
Σ2Η =1.5

0.2

Σ2Η =10.2

0.1

Σ2Η =0.5

0.1

Σ2Η =1Σ2Η =0.5

Σ2¶
1

2

3

4

Σ2¶

5

1

Figure 2a: α = 0.75

23Figure 2b: α = 124