GCOE Discussion Paper Series
Global COE Program

Human Behavior and Socioeconomic Dynamics
Discussion Paper No. 263

Promotion without Commitment: Signaling, Time
Inconsistency and Decentralization of the Firm

Junichiro Ishida

May 2012

GCOE Secretariat
Graduate School of Economics

OSAKA UNIVERSITY

1-7 Machikaneyama, Toyonaka, Osaka, 560-0043, Japan

Promotion without Commitment: Signaling, Time
Inconsistency and Decentralization of the Firm∗
Junichiro Ishida
ISER, Osaka University
May 10, 2012

Abstract
This paper explores the consequences and implications of the “dual role of promotion” in an environment where a firm must simultaneously achieve two distinct goals –assignment and incentive provision – via the strategic use of promotions. We argue thatthe efficient promotion rule is generally not implementable, as it necessarily entails timeinconsistent objectives: the firm is always tempted ex post to promote the worker withthe highest upside potential rather than the one with the highest output. This ex post
bias towards the assignment role of promotion leads to inefficient task choices where too
many workers are induced to work on the difficult task to signal their productivities. The
framework identifies the costs and benefits of decentralization, in relation to factors suchas the levels of human and social capital, the degree of market competition, firm size, anddistance to the technology frontier, and provides predictions that are in line with recent
empirical evidence.

JEL Classification Codes: D82, M51.
Key Words: Assignment, Incentive provision, Tournament, Promotion, Commitment, Time
inconsistency.
∗

Correspondence to: Junichiro Ishida, Institute of Social and Economic Research, Osaka University, 6-1
Mihogaoka, Ibaraki, Osaka 567-0047, Japan. E-mail: jishida@iser.osaka-u.ac.jp.

1

Introduction

Promotion decisions are one of the most important decisions to be made within firm organizations. There are mainly two reasons for this. First, since positions higher up in a firm’s
hierarchy tend to assume a larger degree of authority and responsibility, promotions almost
inevitably function as an assignment mechanism of internal human resources. Second, promotions can also be a reward for workers, either directly or indirectly, and hence provide animportant strategic device for incentive provision. This latter aspect is particularly important when performance measures are not verifiable, though observable, so that a firm cannot
enforce complete contracts contingent on those measures. In the absence of complete wage
contracts, a firm may be forced to use promotions not only to assign but also to motivate its
workers.
In this paper, we explore the consequences and implications of this “dual role of promotion” in an environment where assignment cannot be separated from incentive provision
due to contractual incompleteness. We argue that the efficient promotion rule is generally
not implementable in such an environment, unless the firm possesses full commitment power,
because the efficient rule inherently entails time-inconsistent objectives: incentive provision
typically calls for a promotion rule which selects the worker with the highest output (who has
contributed most in the past) whereas assignment calls for a rule which selects the worker
with the highest upside potential (who is expected to contribute most in the future). A conflict between assignment and incentive provision then naturally arises when the worker withthe highest output differs from the one with the highest upside potential. The problem isthat, whenever the conflict surfaces, it is typically resolved in favor of the assignment role, as
the firm is always tempted ex post to promote the worker with the highest upside potential
rather than the one with the highest output. This ex post bias towards the assignment roleseverely limits the value of promotion as an incentive device and distorts workers’ behavior,
which yields a wide array of implications for organizational design.
We illustrate this problem though a simple tournament model in which a firm hires nworkers who compete for a promotion. Each worker differs in innate ability which is his
own private information. The key aspect of the model is that there are two distinct ways to
produce output, which we call tasks for expositional clarity, where one is standardized andmore labor-intensive (the easy task) while the other is less conventional and more ability-1intensive (the difficult task). The difficult task is more productive only if the worker’s ability
is sufficiently high, and we assume that there exists an ability threshold above which thedifficult task is more productive. The firm’s goal in this setup is to devise a promotion rule
which provides proper incentives for each worker to choose the right task (incentive provision)and still allows the firm to identify and select the most deserving worker (assignment).
Even though the firm is in a situation that it must “kill two birds with one stone,” thesolution to this problem is actually very simply, at least conceptually, if the firm can credibly
enforce a complete promotion rule. With full commitment power, the firm can realize theallocation which maximizes total output by simply promising to promote the worker with thehighest output, as this promotion rule makes each worker’s objective aligned squarely withthe firm’s objective of profit (output) maximization.1 The problem is that this rule, thoughsimple and clear, is not enforceable when the firm lacks the ability to commit to a contingent
promotion rule ex ante because it is not sequentially rational to abide by this rule once thetask choices have been made. Anticipating this, the workers’ attention naturally diverges
away from the firm’s objective of profit maximization, and consequently distorts their task
choices.
In this setup, we first show that, in the absence of full commitment, it is always thecase that too many workers opt for the difficult task in equilibrium compared to the firstbest efficiency level.2 The logic behind this result is as follows. Since the productivity ismore sensitive to the worker’s ability, the difficult task generates a more accurate signal ofunobservable ability. Conversely, since the easy task is a noisier signal, those workers whochoose the easy task are more or less “pooled” from the firm’s viewpoint. If the firm evaluates
its workers based purely on the perceived ability type, a worker who is just below the firstbest efficiency threshold always has an incentive to deviate and switch to the difficult task tosignal his ability. This distortion in task choice lowers the firm’s overall productivity as too
many workers work on the task that is actually too difficult for them to carry out.3
The tension between the two roles of promotion, as illustrated here, yields a range of
implications for the optimal design of organization, especially the optimal degree of decen1

In the present setup, as we will describe later, the firm and the workers simply split the total output withsome exogenous share, so that profit maximization is equivalent to output maximization.
2
The first-best allocation is defined as the one which maximizes total output. See section 3.1 where we
provide formal definitions of efficiency criteria in this model.
3
In a broad sense, this may be regarded as a form of influence activity because workers attempt to convey
information for private benefits at the expense of low productivity.

2

tralization (delegation of decision rights). Given that the root of the problem lies in the factthat there are more than one way to produce output, a potential (second-best) solution is tolimit the workers’ job discretion altogether and force them to follow the standardized way of
production. The cost of centralization in this context is then obvious: by limiting the extent
of job discretion and virtually forbidding its workers to experiment with new, potentiallymore innovative, ways of production, the firm effectively wastes opportunities to solicit andutilize their private information. Despite this apparent cost, the firm might still choose tocentralize when the output loss from distorted task choices outweighs the cost. Analyzing
this tradeoff explicitly, our framework clarifies the costs and benefits of decentralization, in
relation to factors such as the levels of human and social capital, the degree of market competition, firm size and distance to the technology frontier. We later discuss in greater depth
how those results can be interpreted in light of recent empirical findings on firm organization.
Identifying the determinants of decentralization also yields an implication of broader
interest, as it sheds light on one of the long-standing issues in economics. The literature
on firm productivity reveals that there exists an astonishingly large productivity dispersion
across firms and countries, even within narrowly defined sectors, a large portion of whichis left unexplained by observable factors. While this still remains largely a puzzle, twoobservations are suggestive on this account: first, there is a set of management practices,such as decentralization, effective monitoring, well-defined targets and incentives, that are
generally associated with high productivity;4 second, there is also a substantial variation in
the quality of management practices across firms as well as countries. These observations
have led to an argument that the difference in the quality of management practices canaccount for a large fraction of the large productivity dispersion across business units (Bloom
and Van Reenen, 2007, 2010; Bloom et al., 2010). In this paper, we shed light on thisproblem by clarifying the costs and benefits of decentralization and show, for instance, why
it is not optimal for some firms to decentralize despite all the potential benefits or why
low-productivity firms appear to be trapped with bad management practices.
The paper is related to several distinct strands of literature. First, it is related to works
which analyze the role of signaling via task choices (or promotions decisions) in organizations
4

See Bloom and Van Reenen (2007, 2011) for an association between productivity and human resource
management (HRM). Although these observations, which are based on cross-sectional data, do not necessarily
indicate the causational relationship, Bloom et al. (2011) run a randomized experiment and find that the lackof delegation results in inefficient decision making and reallocation of resources.

3and the distortions it causes. The most notable along this line is Waldman (1984) who
considers promotion as a signal.5 In this model and many other models of asymmetriclearning, a worker’s productivity is observable to the firm (the current employer) but not
to the market (outside employers).6 Assuming that promotion decisions are observable tothe market, it is then shown that the firm has incentives to distort task assignments inorder to exploit the value of private information. Ishida (2006) considers a different setup
where promotion also serves as a signal, but the uninformed party in that model is theworker who makes an inference about his own productivity through promotion decisions. The
current work belongs to this strand of literature in that task choices convey information. The
difference is that the informed party in our model is the workers who signal their productivities
though task choices to the firm.7
Although the two roles of promotion have been well recognized in the literature,8 few
works have explicitly focused on the potential conflict between them in a single framework.9
One of few exceptions is Waldman (2003) who analyzes the time-inconsistency problem arisingfrom the two conflicting roles of promotion. The source of time inconsistency in his model isthe possibility of external hiring, where a firm can fill a position by hiring an outsider. He
then shows that there are circumstances in which the firm is made better off by committing
to not hiring from outside, thereby giving a rationale for the common practice of internal
promotions. A key difference from this work is that time inconsistency in our model arises
because there are different ways to produce output, and the output alone is not necessarily thebest indicator of a worker’s qualifications. We then focus on the workers’ signaling incentives
and the distortion caused by them, in order to further inquire into the potential consequences
and implications of the dual role of promotion which, in our own view, have not been explored5

The possibility of asymmetric learning can also provide a possible explanation for why firms often ties
wages to ranks.
6
Models of asymmetric learning include Ricart i Costa (1988), Bernhardt (1995), Ishida (2004), Owan
(2004) and Limor (2005) among others.
7
It is also important to note that the meaning of “task choice” differs critically between those previous
models and the current one. In Waldman (1984) and others, a worker is said to be promoted when he isassigned to a more difficult task. Here, task choices are totally independent of promotion decisions, as they
simply refer to different ways to proceed the job at hand.
8
See, for instance, Gibbons and Waldman (1999a) for a survey.
9
The two roles of promotion have largely been analyzed separately. For instance, Gibbons and Waldman(1999b, 2006) provide a model of job assignment, combined with human capital accumulation and learning,that can capture a wide range of stylized facts. In these works, however, they sidestep the issue of incentive
provision. Similarly, works which take promotion as the incentive mechanism, such as the theory of tournament
by Lazear and Rosen (1981) and others, typically do not consider the issue of assignment.

4

fully yet.
The paper is also related to the large and diverse literature which examines the allocationof authority within the firm. Many studies depict decentralization as a means to solicit private
information that cannot be observed directly by the principal. Aghion and Tirole (1997)
analyze the impact of the allocation of authority on the incentive to acquire information withparticular focus on the distinction between real and formal authority. Dessein (2002) considers
cheap talk communication in organizations, and shows that decentralization emerges as the
optimal choice as long as the incentive conflict is not too large.10 Acemoglu et al. (2007)
examine a situation where a firm must decide whether to adopt a new technology and argue
that the firm delegates control to the manager when the value of local information is high. The
current paper shares this view that an important virtue of decentralization is to utilize theagent’s private information more effectively but approaches from an alternative perspective
which rests on the time-inconsistent nature of the efficient promotion rule. Moreover, while
the cost of decentralization in all of the works mentioned above originates from the agent’s
preference bias that is exogenously given, it stems from the lack of commitment on theprincipal’s part in our model, which yields some implications of practical importance.
Finally, the paper also intends to contribute to the literature on tournament. The current
model introduces a new dimension to the problem by incorporating a task choice problem intoa tournament setting. This addition gives rise to strategic interactions between the principal
and the agents – an aspect which is absent in the canonical tournament model, such as Lazer
and Rosen (1981), where the principal is virtually depicted as an impartial observer – whichallows us to shed light on a new type of inefficiency that could arise in this type of setup.11
This aspect is illuminated most clearly when we extend the baseline model to include effort
choices: in the extended version of the model, we show that there arises a novel tradeoff
between effort and task choices where an increase in rewards induces higher effort at theexpense of more distorted task choices.
The paper is organized as follows. In section 2, we briefly outline the baseline model.
Section 3 analyzes the model, characterizes the equilibrium and provides some comparative
10

There are now several works which employ cheap talk to analyze the optimal extent of decentralization.
For instance, Alonso and Matouschek (2007) incorporate cheap talk communication and show that thresholddelegation is optimal for a wide range of circumstances when the principal has some commitment power.
11
The previous literature focuses on types of inefficiency which arise from strategic interactions among
agents. One prominent example is the possibility of sabotage where the agents may exert effort to reduce therivals’ outputs. See Lazear (1989), Chen (2003) and Ishida (2012) along this line of works.

5statics exercises. Section 4 discusses the model’s implications, especially in relation to theexisting empirical evidence. Section 5 presents an extension of the baseline model where
effort choices are also endogenized. Finally, section 6 offers concluding remarks.

2

The baseline model: exogenous promotion bonus

Setup: There are a firm (principal) and n workers (agent), denoted by i = 1, 2, ..., n, whocompete for a promotion. Each worker i is characterized by his ability type, denoted by ηi ∈[0, 1], which is distributed according to F with full support over [0, 1]. Let µ(η) :=Rη00
0 η dF (η )F (η)

and µ := µ(1). The ability type of a worker is his private information which cannot be
observed by the firm.
Task choice and job discretion: Let yi ∈ [0, 1] denote worker i’s output level. There are
two tasks, easy (task E) and difficult (task D), and each worker must perform either one.
There are established and clearly defined procedures for task E where a worker can produce
output simply by exploiting the stock of existing knowledge. The productivity in task E ishence less sensitive to the worker’s ability. In contrast, there are no established proceduresfor task D where a worker needs to explore new ideas on how to proceed the task. Since task
D inevitably tests the worker’s creativity, the productivity depends more on his ability. To
capture this difference in the nature of the tasks, we specify that(θ if worker i works on task E,yi =ηi if worker i works on task D,
where θ ∈ (0, 1) is some constant which measures the current state of existing knowledge.
At the beginning, the firm determines whether to delegate task choice decisions to its
workers or not. If the firm chooses to delegate (the case of decentralization), each worker isallowed to choose whichever the task he prefers at his own discretion. We assume that theworkers make their decisions simultaneously and independently under decentralization. If thefirm chooses not to (the case of centralization), on the other hand, it retains full authority
over the task allocation and orders all the workers to work on task E.12
12

We assume that the firm can only order a worker to work on task E, because it is inherently much easierto force someone to work on a routine and standardized task. In contrast, since no one knows ex ante whatkind of resources is indispensable to come up with and carry out new procedures, the firm must grant theworkers full access to all the critical resources, which necessarily includes those that are indispensable to carryout the routine task. There is hence no realistic enforcement mechanism to prohibit a worker to work on task
E.

6

Information: Once the firm determines the extent of job discretion, it only plays a passiverole thereafter; its only remaining job is to choose which worker to promote, after observing
the outputs (y1 , ..., yn ).13 Let xi ∈ {0, 1} denote the promotion outcome for worker i, whereP
xi = 1 if he is promoted and xi = 0 otherwise, with the restriction that ni=1 xi = 1. We
assume that neither the output nor the task choice is verifiable, so that no contingent contract(wage and promotion rules) can be enforced.
Payoffs: Each worker receives a wage and, if he is promoted, a promotion bonus. In the absence of complete contracts, each worker’s wage is determined though ex post Nash bargaining
with some exogenous share λ. The payoff for worker i is then given by
ui = λyi + Bxi ,where B ≥ 0 measures the relative salience of the promotion bonus which includes all the
expected benefits accruing from a promotion, such as pay raises, various fringe benefits, highprestige, and so on. For now, we assume that B is determined largely by outside market
conditions and is hence given exogenously. Let b := Bλ for normalization.
The firm’s payoff, on the other hand, depends positively on each worker’s output andthe ability of the promoted worker. The fact that the firm cares about the ability of thepromoted worker directly gives rise to the assignment role of promotion. The payoff for thefirm, denoted by u0 , is given by
u0 = (1 − λ)Pni=1 yin+ Γn ηs ,where the promoted worker is denoted by i = s. The parameter Γn > 0 measures theimportance of managerial skills in the firm’s production process and hence the salience of theassignment role of promotion relative to the incentive role. Note that nΓn measures the total
value of assignment to the firm, where we assume that nΓn is weakly increasing in n withΓnsome finite upperbound limn→∞ nΓn = Γ < ∞. As above, let γn := 1−λ.

Timing: The sequence of events is summarized as follows:
1. Nature draws the ability types (η1 , η2 , ..., ηn ).
2. The firm chooses whether to delegate or not.
13
In this context, it does not matter whether the task choice is observable or not. Because of the way wespecify the model, the output level is effectively a sufficient statistic, and the observability of the task choice
is totally irrelevant.

7

3. If the firm chooses to delegate, each worker chooses which task to perform.
4. Upon observing the realized outputs (y1 , y2 , ..., yn ), the firm chooses a worker to promote.
5. The payoffs are realized.
Remarks on the underlying environment: Before we proceed to analyzing the model,
we would like to make some remarks about the current setup in order to clarify the scope of
the analysis. Two aspects of the model are especially critical and virtually define the natureof the underlying situation.
1. The contracting environment we consider is extremely incomplete in that nothing isdirectly tied to the observable output, possibly due to the unverifiability of performance measures. While this aspect gives rise to the incentive role of promotion, where
workers are motivated though the prospect of promotion, it also implies that the firmcannot commit to any contingent promotion rule either. The combination of these two
restrictions put the firm in a difficult situation where it must use promotions not only
to allocate but also to motivate its workers, and moreover must do so without any
commitment devices, i.e., contracts, at its disposal.
2. The second aspect, which appears more innocuous but is nonetheless equally important,is the fact that the production process inherently involves some uncertainty: although
there is an established routine (task E), it is not clear whether that would provide themost efficient way to produce output in this particular environment. The spirit of this
aspect is exemplified in the task choice problem where each worker chooses which task
to implement.
We argue that the problem of this kind abounds in typical firm organizations. First, inmany cases, it is either practically impossible or prohibitively costly to measure all dimensionsof performances objectively. In any event, it is in practice very rare to find a firm which
specifies fully contingent promotion rules in an unambiguous way. Moreover, there is little
doubt that workers get both tangible and intangible rewards from promotions: at the very
least, wages are tied strongly with ranks in most firms.14
14

There is a large literature which examines the so-called Baker-Jensen-Murphy puzzle (1988), i.e., why

8The second aspect is also common and relevant, particularly in newly emerging industries
where established procedures are not necessarily the most efficient. In such an environment,
the firm must rely on its workers’ creativity in search of new ideas and methods. If thefirm confers some discretion over task choice decisions, some workers may attempt to exploit
the existing knowledge more (task E) while others may attempt to explore and experimentwith what could prove to be truly innovative ideas (task D). In this uncertain environment,
the conflict between the two roles of promotion is more likely to surface because a worker’s
immediate output alone may no longer be an accurate indicator of how productive he will bein the future.

3

Analysis

3.1

The efficient task choice rules

Before we analyze the model, we first characterize the efficient task choice rules which thefirm would implement if it could enforce a complete contract contingent on the output yi(though not directly on the task choice). To this end, note first that since the surplus gained
from assigning a worker to task D is increasing in ηi , any efficient rule is characterized by athreshold η̃ such that a worker is assigned to task D if and only if ηi ≥ η̃. Then, the firm
can implement any efficient task choice rule by appropriately designing an incentive scheme.
To see this more clearly, suppose that each worker’s reservation payoff is zero, and the firm
offers a (take-it-or-leave-it) contract w(yi ). Then, for any η̃ ∈ [0, 1], the following contract
implements the desired task choice rule at almost no cost:
if yi ≥ η̃εw(yi ) = 0
if yi = θ,
−D if yi < η̃ and yi 6= θ,

where ε > 0 is some infinitesimally small number and D > 0. Given this contract, it is indeed
optimal for a worker to choose task D if and only if ηi ≥ η̃.
The efficient task choice rule is thoroughly characterized by the threshold η̃. Here, we

consider two different efficiency criteria. First, the problem would be much simpler in theabsence of information asymmetry because the firm only needs to concentrate on incentive
firms ever use promotions to reward workers when they can also use monetary rewards to induce worker
motivation. See Malcomson (1984), Prendergast (1993), Fairburn and Malcomson (2001) for various accounts
for this puzzle.

9

provision in this case. The first-best task choice rule – the task choice rule which the firm
would implement when each worker’s ability type is publicly observable – is such that aworker chooses task D if and only if ηi ≥ θ. Note that the first-best task choice rule is theone which maximizes the expected total output.
The notion of first-best efficiency is not necessarily appropriate, however, when eachworker’s ability type is his private information. In the presence of information asymmetry,
there is also a gain from experimentation, i.e., from assigning a worker to task D in order toinduce his private information, and the efficiency criterion may need to take this gain into
account. To this end, let S(η̃) denote the total surplus (per worker) when all workers with
ηi ≥ η̃ (η < η̃) are assigned to task D (E). We then obtain
S(η̃) = θF (η̃) +Z 1

ηdF + Γn µ(η̃n )F (η̃n )n +

Z 1
η̃n

η̃

!

ηdFη(n) ,where Fη(k) is the distribution of the k-th order statistic η(k) with its corresponding densityfη(k) . Define η SB as the second-best task choice threshold, which is given byη SB = argmaxη̃∈[0,1] S(η̃).
The first-order condition implies that the second-best threshold must solve!
Z ηSB
ηdF − η SB fη(n) (η SB ) = 0.
(θ − η SB )f (η SB ) + Γn η SB f (η SB )F (η SB )n−1 + fη(n−1) (η SB )0

Since fη(n) = nF n−1 f , we haveθ − η SB + Γn η SB F (η SB )n−1 + (n − 1)F (η SB )n−2

Z ηSB

ηdF − nη SB F (η SB )n−1

0

!

= 0,

which is further reduced toθ − η SB = (n − 1)Γn F (η SB )n−1 (η SB − µ(η SB )).
Because of the value of experimentation, the second-best threshold η SB is strictly lower than
the first-best threshold θ. Note, however, that the second-best threshold coincides with thefirst-best when n = 1 and also converge to the first-best as n → ∞.

3.2

Time inconsistency

As can be seen, the problem is quite straightforward when the firm can enforce complete
contracts contingent on each worker’s output. In many cases, though, it is not feasible to10

do so, e.g., because performance measures are often not verifiable, and the firm must instead
motivate its workers through the prospect of promotion. This restriction poses a serious
difficulty for the firm. To see this, recall that a worker’s (normalized) payoff is given by
yi + bxi . Note that the first term represents a common interest, so that any distortion in thiscontext must arise from the second term. Given this, it appears that the conflict of interest
would be alleviated by committing to a promotion rule under which the firm simply promotes
the worker who have produced the highest output. Because the workers are only concerned
about maximizing their own outputs under this rule and use their private information to that
end, the firm can effectively implement the first-best task choice rule.15
The problem is that given that contingent wage contracts are not feasible, it is also highly
unlikely that the firm can enforce such a contingent promotion rule. In the absence of credible
commitment, it is generally impossible to implement the first-best task choice rule since thefirm has no incentive to enforce this promotion rule ex post: once the task choices have been
made, the firm is always tempted to choose the worker with the highest expected ability,
inferred from the observed output level, rather than the one with the highest output. Thisis a typical time-inconsistency problem which occurs when one side of the parties must takean irreversible action, and the other side subsequently has an opportunity to take advantage
of it. The time-inconsistent nature of the two roles of promotion obviously influences theworkers’ incentives, as we discuss next.

3.3

The task choice problem

We first consider the problem faced by each worker, given that the firm chooses to decentralize.
For the analysis, we restrict our attention to symmetric equilibria of the following form: there
exists a common cutoff η̄n for all i such that worker i chooses task D if and only if ηi ≥ η̄n .
Let σi denote the firm’s belief concerning worker i’s ability type. Given the cutoff strategy,
the firm’s belief is obtained asσi = σ(yi ) =(yi
if yi 6= θ,µ(η̄n ) if yi = θ.

The ex post optimal promotion rule is to choose the agent with the highest σi rather thanthe one with the highest yi .16
15
Of course, if it is feasible to enforce a promotion rule contingent on the output, the firm can also design
a more complicated promotion rule and implement other task choice rules as well.
16
When there is a tie, we assume that the winner is determined by a coin flip.

11

Given the ex post optimal promotion rule and the cutoff η̄n , each worker computes thepromotion probability contingent on his task choice. Let qk (η) denote the promotion probability when a worker with ability η chooses task k, k = E, D. If a worker chooses task E,
he will be promoted only when all of the other workers choose task E as well (and win thetie-break). We thus have
F (η̄n )n−1,
nqE (ηi ) =which is totally independent of the ability type ηi . If a worker chooses task D, on the other
hand, the promotion probability depends on the ability type and is given by
n−1
for ηi ∈ [η̄n , 1],
F (ηi )n−1
qD (ηi ) = F (η̄n )for ηi ∈ [µ(η̄n ), η̄n ),
0for ηi ∈ [0, µ(η̄n )).
It follows from these that worker i chooses task D over task E if
ηi + bqD (ηi ) ≥ θ + bqE (ηi ),which must hold with equality at the cutoff ability type in equilibrium:η̄n + bqD (η̄n ) = θ + bqE (η̄n ).
Rearranging this yieldsθ−n−1
bF (η̄n )n−1 = η̄n .
n(1)

Proposition 1 For any given θ, n and b, there exists a unique cutoff ability level η̄n whichis strictly lower than θ for n ≥ 2 and b > 0. Moreover, η SB > η̄n if
b > nΓn (θ − µ(θ)).
Proof: Let
Hn (η; b) = θ −n−1
bF (η)n−1 ,nor simply Hn (η), so that the equilibrium cutoff level is given by a fixed point η̄ = Hn (η̄). Thereexists a unique cutoff because Hn0 < 0, limη→0 [Hn (η) − η] = θ > 0, and limη→θ [Hn (η) − η] =n−1 < 0 for any n and b. It also follows from this that η̄ < θ for n ≥ 2 and b > 0.
− n−1
nn bF (θ)

12Second, a sufficient condition for η SB > η̄n isn−1
bF (η)n−1 > (n − 1)ΓF (η)n−1 (η − µ(η)) ⇔ b > nΓn (η − µ(η)),
n
for all η ∈ [0, θ]. This is the case if and only ifb > nΓn (θ − µ(θ)).

The fact that θ > η̄n implies that task choice in this context is generally inefficientcompared to the first-best level in that too many workers opt for task D to signal theirabilities. Moreover, when b is sufficiently large, the threshold goes below the second-bestlevel. Figure 1 illustrate a typical equilibrium and the associated output loss. The root of the
problem lies in the firm’s inability to commit to the ex ante optimal promotion rule which
evaluates workers solely on how much they have produced and hence contributed to the firmin the past. Given that the firm cannot make credible commitments, however, the assignment
role of promotion always dominates the incentive role ex post, which provides workers withan excessively strong incentive to signal their abilities.
[Figure 1 here]
The cutoff level depends largely on two factors – the relative salience of the promotion
bonus b and the number of workers n. We first consider the impact of changes in b which isrelatively straightforward. An increase in b shifts each worker’s attention away from output
maximization to ability signaling, which exacerbates the inefficiency in task choice. In particular, as b tends to infinity, the signaling motive becomes so dominant that the cutoff level
goes down to the lowerbound and almost everyone chooses task D. One can also see thatthe first-best efficiency is achieved only when b = 0, i.e., there is no direct return to being
promoted.
Proposition 2 The cutoff level is monotonically decreasing in b. Moreover, limb→0 η̄n = θand limb→∞ η̄n = 0 for any n.
nProof: It is evident that an increase in b lowers the cutoff since ∂H∂b < 0 for any η. Notealso that Hn (η; 0) = θ which implies that η̄n = θ when b = 0. Finally, the cutoff level must13

satisfy
η̄n
θ n−1
−
F (η̄n )n−1 =.
bnb
As b → ∞, this becomes−n−1
F (η̄n )n−1 = 0,nwhich implies that limb→∞ η̄n = 0.

We now consider the effect of a change in n. Since only one worker will be promoted in theend, the number of competing workers n captures the intensity of the promotion competitionin the firm. An increase in n gives rise to two distinct effects. The first effect is that it
decreases qE , i.e., the probability that a worker who chooses task E is promoted, which inturn reduces the incentive to choose task E. There is also a countervailing effect, however,as an increase in n decreases the probability that all the other workers choose task E, whichworks to reduce the incentive to choose task D. The overall impact is determined by which
effect eventually dominates.
Proposition 3 There exists n̄ such that η̄ is decreasing in n for n̄ ≥ n and increasing forn > n̄ + 1. Moreover, η̄1 = limn→∞ η̄n = θ.
Proof: The second part of the proposition, i.e., η̄1 = limn→∞ η̄n = θ, is obtained straightforwardly from (1). For the first part, we treat n as if it is continuous. The cutoff level η̄nincreases with n if
∂H1
n−1
|η=η̄n = − 2 bF (η̄n )n−1 −bF (η̄n )n−1 ln F (η̄n ) > 0,∂nnnwhich is simplified to− ln F (η̄n ) >1.
n(n − 1)This means that η̄n is decreasing in n at n = 1 and increasing when n is sufficiently large.
Then, there must exist at least one ñ such that− ln F (η̄ñ ) =14

1.
ñ(ñ − 1)(2)

Let ñ0 is the smallest one which satisfies (2). We can then show that it is the only one which
can satisfy (2). To see this, suppose that there exists ñ1 > ñ0 which satisfies (2). Notice theslope of the right-hand side of (2) is always negative, meaning that the slope of the left-handη̄n|n=ñ1 = 0 and theside must also be negative at n = ñ1 . This is a contradiction because ∂∂nslope must be zero at this point by definition. Given the uniqueness of ñ, n̄ is defined as thelargest integer which satisfies n̄ + 1 > ñ > n̄.

The relationship between η̄n and n is U-shaped, where more intense competition lowers
the efficiency up to some point and then improves it thereafter. This suggests that the
inefficiency in task choice is most serious when n is in some intermediate range – the casethat can presumably be applied to many organizations. In contrast, task choice is fully
efficient at both ends. First, when n = 1, the worker is guaranteed to be promoted, andthere is hence no internal competition whatsoever. The worker’s incentive coincides exactlywith the firm’s regardless of b because he has no need to “show off” his talent. On the other
hand, when n is sufficiently large, the promotion competition now becomes so severe thatthe prospect of promotion is negligibly small for almost all workers. This again shifts eachworker’s attention more towards output maximization and hence makes his task choice more
efficient. In either case, when n is too small or too large, the task choice problem is lessstrategic in that each agent’s behavior is less dependent on what others do.
Note also that both η SB and η̄n converge to the first-best level θ as n → ∞. One can theneasily show that η SB > η̄ for all n if b > Γ(θ − µ(θ)). If Γ(θ − µ(θ)) > b, on the other hand,the speed of convergence is faster for η̄n , so that η̄n > η SB for n sufficiently large.

3.4

Promotion and job discretion

When the firm cannot commit to the ex ante optimal promotion rule, each worker’s careerconcerns distort his task choice if he is given full discretion over what to do. Given the firm’s
inability to commit, one way to mitigate this problem is to limit job discretion altogether
and unilaterally assign tasks to the workers. The cost of centralization is then evident.
One obvious problem which stems from this is that the task allocation becomes necessarily
inefficient in that some competent workers are forced to work on routine tasks. Moreover, inthe context where the assignment role of promotion is also important, centralization entails
an additional efficiency loss because by forcing every worker to work on the same set of routine
15

tasks, it becomes harder for the firm to differentiate the workers and identify the right one
to promote. Despite these apparent problems, however, centralization may still prove to be
optimal for the firm when the distortion under decentralization is severe enough.
To see when it is optimal to limit job discretion, consider first the case of decentralization
where each worker is conferred full authority over what to do. Under decentralization, theworkers are separated and sorted according to their own abilities. The expected payoff under
decentralization is computed asθF (η̄n ) +Z 1nηdF + γn µ(η̄n )F (η̄n ) +

Z 1
η̄n

η̄n

!

ηdFη(n) .

If the workers are restricted to work on task E, on the other hand, the expected output is θ
for any realization of (η1 , η2 , ..., ηn ). Since the workers are pooled and hence identical fromthe firm’s viewpoint, it must randomly pick one of them with the expected ability of µ. The
expected payoff is thus θ + γn µ.
Given the preceding argument, it is optimal to limit job discretion via centralization if!
ZZ1

θ + γn µ > θF (η̄n ) +ηdF + γn F (η̄n )n µ(η̄n ) +

1

η̄n

η̄n

ηdFη(n) ,which can further be reduced to
!
Z 1
Z 1
Z η̄n
(η − µ)dFη(n) .
(µ(η̄n ) − µ)dFη(n) +(θ − η)dF > γn
η̄n

0

(3)

η̄n

One can easily see that the right-hand side of (3) is always strictly positive for any γ > 0.
Centralization is then optimal if the right-hand side, which measures the loss of output due
to the inefficiency in task choice, is positive and sufficiently large.
The condition (3), along with (1), allows us to identify factors which could influence
the optimal degree of decentralization. Among those factors, we here focus on three ofthem, which offer some interesting implications to be discussed later. The first is the firm’s
productivity relative to the existing stock of knowledge θ: in the current context, a highproductivity firm can be regarded as the one in which the distribution is skewed more towards
the high end and F (θ) is relatively small. To see how the level of human capital affects thecost of decentralization, consider a high-productivity firm with F (θ) = ε. One can thenshow that as ε → 0, the cutoff ability level converges to the first-best level, meaning that
decentralization imposes no cost to the high-productivity firm (note that the second-best16

threshold η SB also converges to the first-best level, so that the allocation is fully efficient).
This is summarized as follows.
Proposition 4 Decentralization is optimal if F (θ) is sufficiently small.
Proof: As F (θ) → 0, η̄n → θ, and (3) becomesZ 1(θ − η)dF > γn

Z θ
0

θ

This never holds as(µ(θ) − µ)dFη(n) +Z 1θ(η − µ)dFη(n)

!

= γn

Z 1
θ

(η − µ)dFη(n) .

R1θ (θ − η)dF < 0.

The second key factor is the number of competing workers n which obviously bears critical
impacts on each worker’s signaling motives. As can be seen from proposition 2, task choice
is fully efficient when n = 1 and n → ∞, which implies that decentralization entails less costat both ends. We can then immediately obtain the following result.
Proposition 5 Decentralization is optimal when n is either sufficiently small or sufficiently
large.
Proof: For n = 1, (3) becomesZ 1(θ − η)dF > γ1(µ(θ) − µ)dF +0θwhich never holds since

Z θ

R1

Z 1

(η − µ)dF

θ

!

= 0,

θ (θ − η)dF < 0. Similarly, as n → ∞,Z 1
θ(θ − η)dF > lim γn (1 − µ) = 0,n→∞which never holds either.

The final factor is the value of managerial skills as captured by γn . As is clear from (3), an
increase in γn makes the assignment role of promotion a predominant concern for the firm.
Decentralization is indispensable to induce each worker’s private information, although it
necessarily means a loss of control by the firm. When γn is large enough, the assignment roleof promotion dominates the incentive role, and it becomes optimal to confer job discretionto the workers.
17

Proposition 6 There exists some γ̄n > 0, n ≥ 2, such that centralization is optimal for allγ̄n ≥ γn if θ is sufficiently close to one.
Proof: We simply need to show that the left-hand side of (3) is positive, i.e.,R1η̄n (θ−η)dF > 0.

We have already seen that θ > η̄n for n ≥ 2. Then, as θ → 1, this condition becomesR1η̄n (1 − η)dF > 0, which holds if 1 > η̄n .

4Discussion

4.1

Determining factors of decentralization

The current model provides a framework to clarify the determinants of decentralization,
which is of particular importance because decentralization is regarded as one of the key
modern management practices which have critical impacts on the firm’s overall productivity.
Three factors – the firm’s relative productivity (proposition 4), the number of competing
workers (proposition 5), and the importance of managerial skills (proposition 6) – are shown
to be crucial. In this subsection, we derive further implications of these results and interpretthem in light of recent empirical findings.
Human capital: A strong association seems to exist between human capital and decentralization. Caroli and Van Reenen (2001) and Breshnahan et al. (2002) find evidence for the
existence of complementarities between organizational changes, as characterized by decentralization of authority, and skills. Bloom et al. (2010, 2011) also find consistently that firms
with more skilled workers are more decentralized. This is consistent with one of our main
predictions that decentralization imposes no cost to high-productivity firms which are more
likely to diversify decision rights and confer a larger degree of autonomy among its workers.
Market competition: A broad view in economics is that market competition enhances efficiency since it weeds out any suboptimal behavior. Given that modern management practices
can be regarded as a form of innovation, there is a pervasive belief that market competition
encourages firms to adopt more modern, and more efficient, management practices including
the delegation of authority lower down the firm hierarchy. This view is roughly confirmed
by Bloom et al. (2010) who find that competition seems to foster decentralization. Rajun
and Wulf (2006) raise market competition as a potential factor behind the recent movement
towards delayering of corporate hierarchies. Similarly, Guadalupe and Wulf (2010) find that18

greater competition causes firms to adopt flatter corporate hierarchies, using the Canada-US
Free Trade Agreement (FTA) as a quasi-natural experiment.17 As more indirect evidence,
Acemoglu et al. (2007) also emphasize that firms tend to decentralize when the value of
local information, compared to that of public information, is high. Then, to the extent thatmarket competition raises the value of local information, greater competition induces more
firms to decentralize.
It is intuitively clear that once we accept that decentralization is a form of innovation,market competition exerts a direct impact on the extent of decentralization simply because
firms with less efficient management practices are less likely to survive in competitive environments. Aside from this direct effect, market competition could also induce firms todecentralize if it somehow raises the value of managerial skills.18 Besides its intuitive appeal,
there is some indication that this premise is indeed a valid one to assume. For instance, market competition is positively correlated not only with productivity (Nickell, 1996; Syverson,2004), but also with the quality of management practices (Bloom and Van Reenen, 2010),
which suggests that greater market competition could intensify the need for high-quality management. Moreover, market competition may also function as a disciplining device to mitigate
managerial slack. Several theoretical works establish that market competition is more likely
to result in higher effort provision by managers (Hart, 1983; Schmidt, 1997). The natureof competition also shapes the incentive structure within the firm: Cunat and Guadalupe(2005, 2009) find that a higher degree of market competition increases the performance pay
sensitivity of compensation schemes, which could result in higher effort provision. Given thateffort and managerial skills are complementary, these findings suggest that market competition generally raises the value of managerial skills, which in turn raises the importance ofassignment and hence favors decentralization.
Distance to the technology frontier: Using data on French and British firms, Acemoglu
et al. (2007) find that firms closer to the technology frontier are more likely to be decentralized.19 The distance to the technology frontier could have a profound impact on the extent
17

Of course, there is no inherent connection between delayering and decentralization, as the effect of delayering can go in either direction. There seems to be some indication, however, that delayering is positively
associated with decentralization. We explore more on this point in section 4.1.
18
It should be noted, though, that the correlation could in principle go in either direction. Since goodmanagement can be regarded as a form of technology, the argument runs parallels to that concerning therelationship between competition and innovation. The theoretical relationship between them is not clear, as
there are both positive (the Arrowian effect) and negative effects (the Schumpeterian effect).
19
Their argument emphasizes the role of local information as a determinant for the extent of decentralization.

19

of decentralization in the current setup as well.
There are two alternative ways to make this connection, each of which is closely related tothe argument made above. First, firms closer to the technology frontier can be interpreted as
the ones that are technologically advanced relative to the existing stock of knowledge. Since
each worker’s productivity is high relative to θ, one can argue that F (θ) is relatively small
for those firms. The same argument as in the case of human capital then applies here: thecost of decentralization is smaller when F is skewed upwards, and decentralization emerges
as the optimal choice when F (θ) is sufficiently small.
There is also a more indirect channel which works through its effect on the value ofmanagerial skills. As Acemoglu et al. (2006) argue, managerial skills matter more in environments where innovation, rather than adaptation, is the main concern.20 Applying thislogic, since a firm needs to rely more on innovation where there is little room to learn frompublic information, the value of managerial skills is expected to rise as the firm gets closer tothe technology frontier. The distance to the technology frontier then plays an identical role
to market competition: the value of managerial skills γn tend to be larger for firms closer tothe technology frontier which in turn face stronger incentives to decentralize.
Firm size and delayering: The number of competing workers within an organization isanother important determinant of decentralization. It follows from proposition 5 that thecost of decentralization decreases as the number of competing workers n gets larger (aftersome point), so that decentralization is more likely to prevail when n is sufficiently large.
There are two implications that can be derived form this observation.
First, in the long run, the number of competing workers is ultimately determined by
the size of the firm. The model then predicts that the cost of decentralization diminishes
as the firm size gets larger. When the firm size is sufficiently large, the probability that a
low-productivity worker is mistakenly promoted becomes very slim, because there is almost
surely someone who is more productive, leaving little room for manipulating information
through task choices. In this context, therefore, the cost of decentralization is less in larger
They argue that firms need to decentralize more when the value of local information is sufficiently highcompared to that of public information. This leads them to hypothesize that firms closer to the technology
frontier are more likely to be decentralized, because they are less likely to learn from public information.
20
Market competition may also play a role through this channel, if the value of innovation is higher in morecompetitive environments. For instance, Nickell (1996) and Blundell (1999) find a positive association between
market competition and innovation. Aghion et al. (2005) find that the relationship is non-monotonic andexhibits an inverted-U shape although the correlation seems to be positive for a substantial range of market
competition.

20

firms since severer competition works to discipline workers and makes their objectives morealigned squarely with the firm’s. This implication is largely consistent with recent evidence
by Bloom et al. (2010) and Bloom and Van Reenen (2010) that larger firms are more
decentralized.
In the short run, promotion competition may involve only workers in related divisions,and hence the number of competing workers depends crucially on how the firm organizationis layered into different business units. In general, there seems to be a movement towards
flatter and simpler corporate hierarchies, partly triggered by the recent advent of information
technology, which implies that there are less “intermediate positions” available, yielding aneffect analogous to an increase in n.21 The same logic then applies here: internal competition
among workers aligns their incentives more closely with the firm’s, and decentralization hence
imposes less cost to the firm when n is larger.22 This prediction is roughly in line with evidenceby Rajan and Wulf (2006) who find that delayering is often associated with pay increases ofdivisional managers, which they take as an indication of decentralization.23
Distorted promotion incentives: The driving force of the model is built on the premisethat the firm uses promotions to allocate workers where they belong and has an incentive to
identify and select the most deserving worker ex post. This logic is hence less applicable if thefirm’s incentives are distorted for some reasons, and it is not particularly concerned about
the assignment role of promotion, e.g., in a case where there is a predetermined winner,or the “heir apparent,” who is sure to be promoted. To see this, consider an asymmetric
tournament in which there is a worker who is promoted with probability r regardless of his
performances; with the remaining probability, the firm promotes the worker with the highest
ability. Letting ηp denote the ability type of the preferred worker and normalizing, the firm’s
21
For instance, Rajan and Wulf (2006) document that the span of control is increasing (the number ofmanagers reporting to the CEO has increased steadily over time, from 1986 to 1998) and the number of layers
in firm hierarchy is decreasing (the number of positions between the CEO and the division heads has decreased
over the same span).
22
It should be noted, though, that there is a caveat for these interpretations. In deriving these implications,
we only consider the effect of an increase n while taking b fixed. This may not necessarily be a fair comparison
since the gains that accrue from a promotion could also increase with n. Our logic implies, however, thatthe effect of an increase in n is exponential and typically dominates that of a proportional increase in b (seeproposition 7 in Appendix for more detail). In light of this, we claim that decentralization is more likely toprevail in larger organizations or business units.
23
It is important to note that it is not a priori clear whether delayering itself means more decentralizationor less: on one hand, middle managers can directly communicate with the CEO, which might imply moreautonomy for them; on the other hand, the large span of control could imply more direct control and intensemonitoring by the CEO.

21

payoff function becomes
u0 =

Pn

i=1 yin+ γn (rηp + (1 − r)ηs ).

Since ηp is exogenous to the model and can be ignored, the presence of the preferred worker
yields an impact equivalent to a decrease in γn , which in turn favors centralization.24
Promotion incentives are distorted whenever a person in charge derives private benefits
from promoting a particular worker regardless of his qualifications, as it diminishes the valueof experimentation through decentralization. One factor that bears a critical impact on thisis the ownership structure of a firm, where diversified ownership diminishes the role of private
benefits. One evidence in line of this argument is the finding that family firms, especiallythose in which the CEO is chosen by primogeniture, are on average badly managed andsubstantially less decentralized (Bloom and Van Reenen, 2007, 2010).
Social capital: Recently, economists have become increasingly aware of the importance of
culture as a potential determinant of economic outcomes (see Guiso, Sapienza, and Zingales,
2006, for a survey). Among those cultural factors, one critical factor seems to be the levelof social capital, often proxied by the level of trust. There is now an abundance of evidence
that trust fosters faster growth (La Porta et al., 1997). Although not much is know about
the underlying mechanism which links trust with economic performances, one convincing
evidence for why trust matters for economic performances is provided by Bloom, Sadun
and Van Reenen (2011) who find a strong association between trust and decentralization:
firms in a high-trust region are more decentralized. A firm with a high level of trust is able
to decentralize and hence effectively utilize local information available only to its workers,
which in turn spurs its productivity.
The current model provides one potential route through which intangible social capitalsuch as trust could influence the firm’s productivity though its choice on the extent of decentralization. As we have already argued, the firm can implement the first-best task allocationby committing to a rule which promotes the worker with the highest output. Under thispromotion rule, each agent uses his private information only to maximize the output, which
24

The presence of the preferred worker may also affect the other workers’ incentives as it severely limits theprospect of promotion for them. This could yield an effect equivalent to a decrease in B which favors decentralization. We argue, however, that the distorted incentive structure is more likely to result in centralization
because workers’ career concerns are not necessarily confined within the boundary of the firm organization:
if a worker can signal his productivity to outside firms to some extent, the distorted incentive structure does
not lower B as sharply as β, thereby favoring centralization.

22

can be done by choosing task D if and only if η ≥ θ. What is interesting here is that once thefirm makes a commitment, the ex post temptation for the firm totally dissipates: since theworker with the highest output is also the one with the highest ability, the efficient promotion
rule turns out to be ex post optimal as well. The commitment to the efficient promotion ruleis the almighty solution in this context, which makes each worker’s objectives roughly alignedwith the firm’s objectives and realizes the allocation which maximizes the total output. As
this argument indicates, the cost of decentralization in this context depends crucially on how
easily the firm can make the commitment credible without any enforcement by a third party.
The presence of mutual trust could work as a substitute for legal enforcement by making thecommitment feasible at a lower cost, which allows the firm to exploit the role of promotion
as an incentive device more effectively.25

4.2

On the productivity dispersion across firms

In the previous subsection, we have raised several potential determining factors of decentralization. While identifying the determinants of decentralization bears some importance in its
own right, it also offers an implication of broader scope as it can shed light on one of thelong standing puzzles in economics. It has long been argued that there exists a substantial
disparity in labor productivity across firms and countries which cannot easily be explained byobservable factors, even after controlling for all conceivable measures of inputs. For instance,
Syverson (2004a) shows that plants at the 90th percentile are four times as productive as
those in the 10th percentile. Only half of this difference in labor productivity could be accounted for by differences in inputs such as capital intensity. Similar observations have been
made by others who by and large find persistent and sizeable differences in labor productivity
even within narrowly defined sectors.
While the exact nature of this productivity dispersion still remains largely a puzzle, it
has been pointed out recently that variations in management practices can account for a
substantial portion of it (Bloom and Van Reenen, 2007, 2010; Bloom et al., 2010). There are
two sets of findings that have led to this hypothesis. First, the recent literature indicates thatthe quality of management can be objectively quantified, and moreover that there is a set of25

The way trust works here goes both ways. On one hand, to allow for greater job discretion, the firm needs
to trust its workers to behave closely in line with its objectives. One the other hand, the workers also needto trust the firm for evaluating them on what they have contributed and, more importantly, not rewarding aworker who deviates from the efficient task choice rule.

23

“good” management practices, such as well defined targets and performance measures, proper
incentive systems and decentralization of authority, which universally contribute significantly
to productivity improvements. Second, like productivity performances, there is also a wide
dispersion in managerial practices, indicating the coexistence of some well managed firms at
one tail of the distribution and some badly managed firms at the other tail. Putting thesepieces together, one can argue that the large productivity dispersion is due, at least in part,to variations in the way firms are organized and managed.
The true question that remains is then why there exist firms which continue to adopt
poor management practices. To answer this question, we take the stance that even when
decentralization is largely beneficial, its costs vary across firms, and it is simply too costly
for some firms to decentralize.26 More importantly, the cost of decentralization not only
varies across firms, but it is also strongly correlated negatively with the firm’ productivity:
as we have seen, decentralization imposes less cost to high-productivity firms or those closer
to the technology frontier. The implied complementarity between the productivity and thequality of management practices can be a powerful force behind the wide dispersion in firm
productivity as efficient firms can afford to adopt better management practices and become
even more efficient while inefficient firms are virtually trapped with less effective management
practices.

4.3

An application to the academic profession

The model environment here offers some relevance for many skill-intensive industries where
skills or talents – traits that are not easily quantified nor observed – are highly valued.27 .
One such example, which fits this description rather nicely, is the academic profession where
signaling undoubtedly plays a critical part. There are several obvious similarities. First,
researchers are rewarded mostly through “promotions” to higher ranks or better universities,
but there are obviously no specific promotion rules that are tightly contingent on observable
output. Second, each employer is naturally more concerned about an applicant’s upside potential, especially when she needs to hire young researchers, rather than past achievements.
26

As suggested by Bloom and Van Reenen (2010), an alternative story is that good management practices
are partially like a technology which slowly diffuses throughout the economy. Needless to say, our aim here is
not to deny this possibility; it is simply to shed light on one aspect, possibly among many others, of this issue.
27
An obvious difference is that there are many potential employers competing for researchers in the academic
community. While this is an important extension worth serious consideration, the main logic of this paper is
expected to survive even if there are multiple employers.

24

Finally and most importantly, research activities apparently require a high degree of creativity, and it is typically at our discretion to decide how to proceed our own research. The choice
we face is often similar to the task choice problem of the current model: some problems may
be intellectually stimulating but do not yield much social value while some others may be
intellectually dull but are nonetheless more beneficial. The current analysis predicts that insuch a situation, researchers, especially young ones, have excessively strong incentives to workon intellectually stimulating problems even when there are other more important problems.

5

An extension: endogenous effort and promotion bonus

In the baseline model, we show that the task choice threshold is monotonically decreasing
in b. The baseline model thus yields no interesting tradeoff regarding the promotion bonus:
if it is the firm’s choice to set b, the threshold is brought closer to the first-best level by
setting it as low as possible. This part of the model is not necessarily satisfactory andalso counterintuitive, as it implies that the promotion bonus in this context has no positive
incentive effect, which stems from the implicit premise that effort is costlessly supplied by
the workers. In this section, in order to address this issue, we consider an extension of thebaseline model which incorporates an effort choice problem, on top of the task choice problem
we have considered thus far, into the model. This extension, while preserving the main insightof the model, allows us to shed light on a novel tradeoff between task and effort choices which
is absent in canonical tournament models.

5.1

The general framework

We augment the baseline model by introducing two modifications. First, effort is now costly
for the workers, and it is their choice to decide how much effort to supply. Second, while
we have assumed thus far that the level of the promotion bonus b is determined by outside
market conditions and exogenously given, here we consider an alternative scenario and allow
the firm to set b freely to induce costly effort from the workers.28 For this extension we
restrict our attention to the case of decentralization.
More precisely, let ei ∈ {0, 1} denotes the effort level chosen by worker i. The output
28

Note, however, that whether b is the firm’s conscious choice is of secondary importance: the main purposeof this section is to illustrate a tradeoff between task and effort choices, which is present even when b isdetermined by market forces.

25level for worker i is now given by yi ei , instead of just yi , where yi is determined in the same
way as in the baseline model. The sequence of events in this extended model is summarized
as follows:
1. Nature draws the ability types (η1 , η2 , ..., ηn ).
2. The firm offers the promotion bonus b.
3. Each worker chooses which task to perform and how much effort to exert.
4. Upon observing the realized outputs (y1 , y2 , ..., yn ), the firm chooses a worker to promote.
5. The payoffs are realized.
The effort cost is given by C, and we assume θ > C > λθ, i.e., the effort cost is neither toolarge nor too small. The first inequality (θ > C) means that it is efficient to induce effort
from all workers, given that task choice is also efficient. The second inequality (C > λθ)is necessary to make the problem relevant because if the effort cost is too small, ex post
bargaining is enough to induce effort. Let c := Cλ for normalization.
We first consider the effort choice problem. Note that since the return to exerting effort
is weakly increasing in the ability, the effort choice problem can also be characterized by acutoff η̂n such that worker i chooses ei = 1 if and only if ηi ≥ η̂n .29 Given this, if a worker
n−1chooses not to exert effort, the promotion probability is F (η̂nn). Worker i then chooses toexert effort if and only if
max{ηi + bqD (ηi ), θ + bqE (ηi )} − c ≥ b

F (η̂n )n−1
,
n

(4)

where qk (η) is the modified promotion probability contingent on the task choice, given thatthe worker chooses to exert effort. If (4) does not hold, then the task choice problem becomes
totally irrelevant: we simply assume for clarity that the worker chooses task E in that case.
As this implies that η̄n ≥ η̂n without loss of generality, (4) can be written asθ + bqE (ηi ) − c ≥ b
29

F (η̂n )n−1
.
n

(5)

As we will see shortly, all the workers with ηi ∈ [0, η̄n ) face the same incentives, and there are also otherpayoff-equivalent equilibria with no cutoff property.

26

On the other hand, given that ei = 1, the task choice problem is virtually the same as before:
for ηi ≥ η̂n , worker i chooses task D if and only if
ηi + bqD (ηi ) ≥ θ + bqE (ηi ).

(6)

Given the cutoffs (η̂n , η̄n ), the workers are separated into at most three intervals: (i)those in [η̄n , 1] exert effort and choose task D; (ii) those in [η̂n , η̄n ) exert effort and choosetask E; and (iii) those in [0, η̂n ) exert no effort and choose task E. The modified promotion
probabilities are then computed as follows:(
Pn−1(n−1)!
Gm (1−G)n−1−m
F (η̄n )n−1 m=0
m+1
m!(n−1−m)!
qE (ηi ) = F (η̂n )n−1nF (ηi )n−1F (η̄ )n−1nqD (ηi ) =
n−1

F
(η̂

n)


0

for ηi ∈ [η̂n , 1),for ηi ∈ [0, η̂n ),for ηi ∈ [η̄n , 1],for ηi ∈ [µ̃(η̂n , η̄n ), η̄n )for ηi ∈ [µ(η̂n ), µ̃(η̂n , η̄n )),for ηi ∈ [0, µ(η̂n )),
R η̄

ηdF

η̂
where G := prob(ηi ∈ [η̂i , η̄i ) | η̄n > ηi ) and µ̃(η̂, η̄) := F (η̄)−F(η̂) . Define

P (η̂n , η̄n ) :=n−1
X

Gm (1 − G)n−1−m(n − 1)!
.
m!(n − 1 − m)!
m+1
m=0Note that limη̂n →η̄n P (η̂n , η̄n ) = 1, limη̂n →0 P (η̂n , η̄n ) = n1 , and P (η̂n , η̄n ) > n1 for any η̄n ≥η̂n > 0. It is also intuitively clear that P (η̂n , η̄n ) is strictly increasing in η̂n .
With some algebra, (5) and (6) can be written as follows:
!
n−1
F
(η̂
)
n
b F (η̄n )n−1 P (η̂n , η̄n ) −≥ c − θ.
nb(F (ηi )n−1 − F (η̄n )n−1 P (η̂n , η̄n )) ≥ θ − ηi .

(7)
(8)

If there exist interior solutions, these conditions must hold with equality at the cutoffs: let(η̂n (b), η̄n (b)) denote the equilibrium cutoffs. There are three remarks we would like to makehere.
1. (8) implies that task choice continues to be inefficient, i.e., θ > η̄n , as long as P (η̂n , η̄n ) <1. On the other hand, the efficiency in task choice can be achieved for a positive b whenb satisfiesb(n − 1)
F (θ)n−1 = c − θ,n27

which never happens in the baseline model. In any case, though, the task choice cutoff
never goes above θ.
2. (8) also indicates an intriguing interaction between the effort cutoff and the task choice
cutoff. A decrease in η̂n (an increase in the effort level) decreases P (η̂n , η̄n ) taking η̄nfixed. This raises the incentive to choose task D for the boundary worker with ηi = η̄because the promotion probability qE is now lower, pointing to a tradeoff such thatan increase in effort makes task choice less efficient by lowering η̄n . This is the force
which makes the efficiency in task choice attainable even when b > 0: in that case, theefficiency in task choice is achieved because low effort (a high effort cutoff) makes thedeviation to task E more profitable for the boundary worker.
3. b = 0 no longer achieves the first-best efficiency because no worker has an incentive
to exert effort if b is too small. More precisely, b needs to be at least large enough tosatisfyb(n − 1)
F (η̄n (b))n−1 ≥ c − θ.
n(9)

If this fails to hold, all workers choose to exert no effort and consequently choose task
E in equilibrium. It is evident that (9) does not hold when b = 0, under the assumptionthat c > θ.
Finally, the firm’s problem is to choose the promotion bonus b to maximize the expected
profit, which is defined as
Z 1
Z η̄n (b)
ηdF +
max θ
b

η̄n (b)η̂n (b)ηdF −λbn(1 − λ)+ γn µ(η̂n (b))F (η̂n (b))n + µ̃(η̂n (b), η̄n (b))

Z η̄n (b)η̂n (b)dFη(n) +Z 1

η̄n (b)!

ηdFη(n) .

The tradeoff of our focus can be most clearly be seen in the limiting case where γn → 0.30 In
this case, the first-order condition is obtained as
−θ

dη̄n
λ
dη̂n
+ (θ − η̄n )f (η̄n )
=
.
db
db
n(1 − λ)(10)

The first term indicates the loss due to a decrease in effort; the second term indicates the gain
due to an improvement in task choice. The optimal promotion bonus thus needs to balancethese two forces.
30

Note that γn can be arbitrarily small but needs to be strictly positive to maintain the assignment motive.

28

The general model, with an arbitrary n, is exceedingly complicated to fully characterize,
but it can be made much more tractable if we restrict our attention to the case with n = 2.
Although this example presents only a special case of the model described above, it contains
all the key elements of the extended model and is highly instructive to illuminate the tradeoffof our focus as we will see next.

5.2

A case with n = 2

With n = 2, it is straightforward to obtain
P (η̂, η̄) =(η̂)
F (η̂) + F (η̄)−FF (η̂) + F (η̄)
2=,
F (η̄)
2F (η̄)where we suppress the subscript n for the cutoffs for notational simplicity. The cutoffs, if
interior solutions exist, are then obtained as
F (η̄(b))= c − θ.
2

(11)

F (η̄(b)) − F (η̂(b))= θ − η̄.
2

(12)

b

b

One can then show that both η̂(b) and η̄(b) are decreasing in b. First, it directly follows from(11) thatdη̄F (η̄)=−< 0.
db
bf (η̄)(13)dη̂
F (η̄) − F (η̂) + b(f (η̄) dη̄dη̄
db − f (η̂) db )
=− .
2
db

(14)

Similarly, from (12), we obtain

Substituting (13) into (14) yields
F (η̄)1dη̂
F (η̄) − F (η̂) − (2 + bf (η̄))=
db
bf (η̂)bf (η̄)!

1
2F (η̄)=−F (η̂) +bf (η̂)bf (η̄)!

< 0.

The structure of the model is much simpler now, where η̄(b) is uniquely pinned down from(11) for a given b, and η̂(b) is then obtained from (12). As stated, b needs to be sufficiently
large for the existence of interior solutions. Since θ ≥ η̄ ≥ η̄, a necessary condition for interior
solutions to exist isb ≥ bmin :=292(c − θ).
F (θ)

Note that η̂(bmin ) = η̄(bmin ) = θ, so that task choice is first-best efficient at b = bmin . Ifb < bmin , no worker has an incentive to exert effort and the expected output level is zero.
Since the expected profit (per worker) is −b/2, it is strictly better for the firm to offer b = 0.
Then, the optimal promotion bonus is positive if and only if
Z 1
1 − θ22(c − θ)
bmin
⇔
≥
.
ηdF ≥
2
2
F (θ)
θ

(15)

The condition holds if c is sufficiently close to θ.
Given this, we can also obtain sharper predictions for the firm’s problem. The first-ordercondition (10) can now be written asθ
2F (η̄)F (η̂) +bf (η̂)bf (η̄)!

− (θ − η̄)F (η̄)λ=.
b2(1 − λ)where we maintain that γn → 0. Suppose that (15) is satisfied and it is optimal for the firm
to offer a positive b. The firm then raises b above the minimum level to induce more effort,
even though it results in more distortion in task choice, if!
!
θ
2F (θ)
θF (θ)
2F (θ)2λ.
F (θ) +=F (θ) +>
bmin f (θ)
bmin f (θ)
2(c − θ)f (θ)
2(c − θ)f (θ)
2(1 − λ)(16)

The condition again holds if c is sufficiently close to θ. The tradeoff faced by the firm is now
clear. To see this, note that the efficiency requires η̂ = 0 under the maintained assumption.
Since η̄(bmin ) = η̂(bmin ) = θ, an increase in b above bmin improves effort choice but lowers
the task choice cutoff away from the first-best level. This is the case when both (10) and(16) hold, in which case the loss of output due to low effort becomes too costly, and the firm
hence needs to induce higher effort by raising b even at the expense of more distortion in task
choice.31

6Conclusion

This paper provides a model where promotion carries two roles – assignment and incentive
provision – that often conflict with each other. When the principal is unable to commit to
the efficient promotion rule, too many agents are induced to work on the difficult task tosignal their productivities. To minimize this loss, the principal may centralize task choices
31

Of course, this distortion could enhance welfare in the presence of information asymmetry when the task
choice cutoff moves towards the second-best level.

30

despite the fact that it necessarily results in inefficient use of private information. The modelclarifies the costs and benefits of decentralization and provides several predictions that are
in line with recent empirical evidence on firm organization.

AppendixHere, we consider the effect of a simultaneous increase in b and n by multiplying them by thesame factor, so that the ex ante expected promotion bonus nb is kept constant. To this end,
define the cutoff ability level as a function of b and denote it by ηn (b). We can then show thefollowing.
Proposition 7 There exists ω̄ such that η(1+ω)n ((1 + ω)b) > ηn (b) for ω > ω̄. Moreover,ω̄ = 0 if n + (n − 1) ln F (θ) < 0.
Proof: By definition,θ−n−1
bF (ηn (b))n−1 = ηn (b).
n

It then suffices to show thatθ−

(1 + ω)n − 1(1 + ω)bF (ηn (b))(1+ω)n−1 > ηn (b),(1 + ω)n

which can be written as
1 > Jn (ω) :=(1 + ω)n − 1
F (ηn (b))ωn .
n−1First, since limω→∞ Jn (ω) = 0, this condition holds when ω is sufficiently large. Second, Jn
is strictly decreasing in ω if
n + ((1 + ω)n − 1) ln F (η̄n (b)) < 0.
Since Jn (0) = 1, Jn (ω) < 1 for all ω > 0 if
n + (n − 1) ln F (η̄n (b)) < n + (n − 1) ln F (θ) < 0.

31

References
Acemoglu, Daron, Philippe Aghion, and Fabrizio Zilibotti, 2006, Distance to Frontier, Selection, and Economic Growth, Journal of the European Economic Association, 4, 37-74.
Acemoglu, Daron, Philippe Aghion, Claire Lelarge, John Van Reenen, and Fabrizio Zilibotti,
2007, Technology, Information, and the Decentralization of the Firm, Quarterly Journalof Economics, 122, 1759-99.
Aghion, Philippe and Jean Tirole, 1997, Formal and Real Authority in Organization, Journalof Political Economy, 105, 1-29.
Aghion, Philippe, Nick Bloom, Richard Blundell, Rachel Griffith, Peter Howitt, 2005, Competition and Innovation: An Inverted-U Relationship, Quarterly Journal of Economics,
120, 701-28.
Alonso, Ricardo, Niko Matouschek, 2007, Relational Delegation, RAND Journal of Economics, 38, 1070-89.
Baker, Geroge P., Michael C. Jensen, and Kevin J. Murphy, 1988, Comepnsation and Incentives: Practice vs. Theory, Journal of Finance, 43, 593-616.
Bernherdt, Dan, 1995, Strategic Promotion and Compensation, Review of Economic Studies,62, 315-39.
Bloom, Nichilas and John Van Reenen, 2007, Measuring and Explaining Management Practicies across Firms and Countries, Quarterly Journal of Economics, 122, 1341-408.
Bloom, Nicholas and John Van Reenen, 2010, Why Do Management Practices Differ acrossFirms and Countries, Journal of Economic Perspectives, 24, 203-24.
Bloom, Nicholas and John Van Reenen, 2011, Human Resource Management and Productivity, forthcoming in Handbook of Labor Economics.
Bloom, Nicholas, Raffaella Sadun, and John Van Reenen, 2010, Does Product Market Competition Lead Firms to Decentralize? American Economic Review Papers and Proceedings,
100, 434-8.
Bloom, Nicholas, Raffaella Sadun, and John Van Reenen, 2010, Recent Advances in the
Empirics of Organizational Economics, Annual Review of Economics, 2, 105-137.
32

Bloom, Nicholas, Raffaella Sadun, and John Van Reenen, 2011, The Organization of Firms
across Countries, mimeo.
Bloom, Nicholas, Benn Eifert, Aprajit Mahajan, David McKenzie, and John Roberts, 2011,
Does Management Matter? Evidence from India, mimeo.
Blundell, Richard, Rachel Griffith, and John Van Reenen, 1999, Market Share, Market Valueand Innovation in a Panel of British Manufacturing Firms, Review of Economic Studies,66, 529-54.
Bresnahan, Timothy, Erik Brynjolfsson, and Lorin Hitt, 2002, Information Technology, Workplace Organization and the Demand for Skilled Labor: Firm-Level Evidence, Quarterly
Journal of Economics, 117, 339-76.
Caroli, Eve and John Van Reenen, 2001, Skill Biased Organizational Change, Quarterly
Journal of Economics, 116, 1449-92.
Chen, Kong-Pin, 2003, Sabotage in Promotion Tournaments, Journal of Law, Economics,
and Organization, 19, 119-40.
Cunat, Vicente and Maria Guadalupre, 2005, How Does Product Market Competition Shape
Incentive Contracts, Journal of the European Economic Association, 3, 1058-82.
Cunat, Vicente and Maria Guadalupre, 2009, Globalization and the Provision of Incentives
inside the Firm: the Effect of Foreign Competition, Journal of Labor Economics, 27,
179-212.
Dessein, Wouter, 2002, Authority and Communication in Organizaitons, Review of Economic
Studies, 69, 811-38.
Fairburn, James A. and James M. Malcomson, 2001, Performance, Promotion and the Peter
Principal, Review of Economic Studies, 68, 45-66.
Gibbons, Robert and Michael Waldman, 1999a, Careers in Organizations, in Handbool ofLabor Economics, Vol. 3, eds. Ashenfelter, Orley and David Card, Amsterdam: NorthHolland.
Gibbons, Robert and Michael Waldman, 1999b, A Theory of Wage and Promotion Dynamics
indise Firms, Quarterly Journal of Economics, 114, 1321-58.

33

Gibbons, Robert and Michael Waldman, 2006, Enriching a Theory of Wage and Promotion
Dynamics inside Firms, Journal of Labor Economics, 24, 59-107.
Golan, Limor, 2005, Counteroffers and Efficiency in Labor Markets with Asymmetric Information, Journal of Labor Economics, 23, 373-93.
Guadalupe, Maria and Julie Wulf, 2010, The Flattening Firm and Product Market Competition: the Effect of Trade Liberalization on Corporate Hierarchies, American Economic
Journal: Applied Economics, 2, 105-27.
Guiso, Luigi, Paola Sapienza, and Luigi Zingales, Does Culture Affect Economic Outcomes?
Journal of Economic Perspectives, 20, 23-48.
Hart, Oliver, 1983, The Market Mechanism as an Incentive Scheme, Bell Journal of Economics, 14, 366-82.
Ishida, Junichiro, 2004, Signaling and Strategically Delayed Promotion, Labour Economics,
11, 687-700.
Ishida, Junichiro, 2006, Optimal Promotion Policies with the Looking-Glass Effect, Journalof Labor Economics, 24, 857-77.
Ishida, Junichiro, 2012, Dynamically Sabotage-Proof Tournaments, forthcoming in Journalof Labor Economics.
La Porta, Rafael, Florencio Lopez de Silanes, Andrei Shleifer, and Robert Vishny, 1997, Trustin Large Organizations, American Economic Review, 87, 333-8.
Lazear, Edward P., 1989, Pay Equality and Industrial Politics, Journal of Political Economy,
97, 561-80.
Lazear, Edward P. and Sherwin Rosen, 1981, Rank-Order Tournaments as Optimum Labor
Contracts, Journal of Political Economy, 89, 841-64.
Malcomson, James M., 1984, Work Incentives, Hierarchy, and Internal Labor Markets, Journal of Political Economy, 92, 486-507.
Nickell, Stephen J., 1996, Competition and Corporate Performance, Journal of Political Economy, 104, 724-46.
Owan, Hideo, 2004, Promotion, Turnover, Earnings, and Firm-Sponsored Training, Journalof Labor Economics, 22, 955-78.
34

Prendergast, Canice, 1993, The Role of Promotion in Inducing Specific Human Capital Acquisition, Quarterly Journal of Economics, 108, 523-34.
Rajan, Raghuram G. and Julie Wulf, 2006, The Flattening Firm: Evidence from Panel Dataon the Changing Nature of Corporate Hierarchies, Review of Economics and Statistics,
88, 759-73.
Ricart i Costa, Joan, 1988, Managerial Task Assignments and Promotion, Econometrica, 56,
449-66.
Schmidt, Klaus M., 1997, Managerial Incentives and Product Market Competition, Review
of Economic Studies, 64, 191-213.
Syverson, Chad, 2004, Market Structure and Productivity: A Concrete Example, Journal of
Political Economy, 112, 1181-222.
Waldman, Michael, 1984, Job Assignments, Signalling, and Efficiency, Rand Journal of Economics, 15, 255-67.
Waldman, Michael, 2003, Ex Ante Versus Ex Post Optimal Promotion Rules: The Case ofInternal Promotion, Economic Inquiry, 41, 27-41.

35

efficiency loss

task E

task Dη̄nθ

Figure 1: An equilibrium and the output loss.

36

ηi