DISCUSSION PAPER

SERIES IN

ECONOMICS AND

MANAGEMENT

The Impact of Job Similarity along the Career

Path on the Firm’s Promotion Choice

Jakob Infuehr, Sebastian

Kronenberger

Discussion Paper No. 17-25

GERMAN ECONOMIC ASSOCIATION OF BUSINESS

ADMINISTRATION – GEABA

The Impact of Job Similarity along the Career

Path on the Firm’s Promotion Choice∗

Jakob Infuehr†and Sebastian Kronenberger‡

August 21, 2017

Abstract: Job promotions are one of the most important ways to incentivize

hard work from low-level employees. At the same time, they are also used to sort

employees according to their skills. These two functions are often in conflict. An

external job candidate might be the best qualified, but hiring him reduces motivation

for the existing workforce. We extend prior research by taking the effect of job

similarity between current and future job into account. We show that if the job

after promotion requires a vastly different skill set than the one currently performed,

then this makes it easier and thus more likely for a firm to promote only internal

candidates. Furthermore, we analyze competition on the demand-side of the labor

market and its effect on promotion decisions, depending on firm productivity.

∗We thank Volker Laux for valuable comments.†University of Texas at Austin, McCombs School of Business,

jakob.infuehr@mccombs.utexas.edu.‡University of Hanover, Institute for Accounting and Auditing, kronenberger@rewp.uni-

hannover.de.

1

1 Introduction

Promotions are an integral part of organizations. Typically, they serve two functions

simultaneously. First, they motivate employees to provide higher effort. In the

literature, the most common studied incentive is a (linear) cash bonus for output.

However, this type of incentive is only common for higher-ranking employees. Rank-

and-file employees often have no explicit bonuses in their contracts. Yet, it is still

important to ensure that these employees provide high effort. The possibility of a job

promotion provides this incentive. The difference in wage is usually large enough such

that even a small probability of promotion results in a significant increase in expected

future compensation if the candidate provides high effort today. The second function

of promotions is to sort workers according to their abilities. Higher skilled employees

are typically assigned a higher ranking, more important job to more effectively use

the better skill. However, the two functions of job promotions can be in conflict with

each other.

In this context, we extend prior literature by adding a new dimension to the

trade-off between the functions of promotions: job similarity. Many organizational

types require a vastly different skill set from their employees in each level along the

career path. The organizational structure in Big 4 audit firms is a good example.

At the entry-level, auditors are mostly responsible for structured auditing tasks. As

employees rise up in the ranks, the tasks switch more to managing the younger staff,

2

and eventually as they become partners they try to aquire new clients. A feature of

the Big 4 audit firms is the up-or-out culture. Auditors either receive a promotion or

leave the company (Kornberger et al. 2011). Law firms and the consulting industry

have a similar structure. Another example of reduced correlation is a teacher, who

could receive a promotion to principal. And yet, a good teacher is not necessarily

a good principal and vice versa. Contrary to these examples, a sales representative,

who is promoted to deal with more important clients, can probably use a very similar

skill set as before the promotion.

The research question being analyzed is whether it is optimal to restrict pro-

motions to internal candidates. Intuitively, one might think that a high degree of

job similarity increases the information the firm has about workers’ skills for the

higher-level job and thus commitment to internal promotion is more attractive. As

we explain in the following, this is not the case. The conflict between motivating

entry-level workers and sorting them according to their abilities arises because the

firm makes both decisions at different points in time, causing a time-inconsistency

problem. In the first period, the firm motivates workers to exert effort. In the second

period, the firm makes a promotion decision based on the observed output, which

is a noisy signal about the workers’performance. At this point in time, the firm is

only worried about the optimal assignment and might pick an external candidate,

if he is the best-qualified, since the effort of the workers is already sunk. This, in

turn, reduces incentives for its employees to provide high effort in the first period due

to the increased competition and thus lowered anticipated probability of receiving

a promotion (to be more precise, effort increases the chance of receiving a promo-

3

tion by a smaller amount). The firm anticipates this problem and as a solution

could commit to internal promotion. Both strategies - commitment to internal labor

market and non-commitment - create costs for the firm. Commitment increases the

likelihood of promoting a candidate not suitable for the managerial job since the

firm only chooses workers from within. Non-commitment, which resembles a real

option-to-wait with the promotion decision, increases the payroll in the first period

since internal promotion is less likely and does not provide the necessary incentives

to work hard for the entry-level worker. The key force is that the cost of the option-

to-wait does not depend on job similarity, while the cost of exclusively promoting

from within does. If correlation between the jobs is high, then the firm learns more

about future managerial skills of its employees, hence rendering commitment more

costly in expectation since low-performing candidates are also more likely to possess

less-than-average managerial potential. Thus, exclusive internal promotion could

backfire. On the flip side, in the case in which job levels are almost uncorrelated, it

is always optimal to commit to internal promotion because commitment creates no

costs.

While explicit commitment to internal promotion based on enforceable contracts

might be rare, firms in the real world find other ways to effectively accomplish

the same outcome. In multi-period settings, reputation concerns prevent firms from

breaking their commitment to internal promotion. Also, firms establish formal in-

ternal labor markets (see related literature) that ensure an increased probability

for promotion from within. We address both forms of implicit commitment in our

extensions.

4

We further analyze the scenario in which two competitors, who only differ in pro-

ductivity of the managerial job, compete for young talents and both have to choose

whether they commit to the internal labor market. Competition changes the setup

in that it offers the opportunity to hire personnel from outside the firm, whose per-

formance in period one can be observed. One might expect that competition harms

the smaller (less productive) firm since the larger (more productive) firm has the

power to poach the smaller firm’s entry-level worker for its own managerial position.

In contrast, we find that firm value for both firms can increase in equilibrium. The

reason for this result is that poaching does not change the smaller firm’s payoff. If

the small firm has as many candidates available as managerial positions, the large

firm, who wants to poach one of these candidates, needs to fully reimburse the small

firm for the loss in managerial talent. However, competition generates a positive

effect when one of the firms has suitable candidates in excess. Then, the competitor

can benefit from picking up the spared managerial talent, of which it observed an

above average performance, if it has only below average candidates amongst its own

entry-level workers. This beneficial effect of the outside hiring option also causes

both firms to use the internal labor market less often.

Our model contributes to the literature in that it allows predictions as to which

firms and industries should be expected to promote more from the inside versus

outside. We expect that firms, whose jobs along the hierarchical ladder require a

different set of skills, will promote internally with greater probability, such as the

above mentioned auditing networks or consulting firms.

In our extensions, we further allow for a potentially misleading worker’s report

5

about her first period output. Consistent with the earnings management literature,

the possibility of manipulating the report about the first period output makes effort

a less attractive option compared to the case without manipulation. The firm has to

promise a higher wage in the managerial position to ensure hard work from an entry-

level worker and manipulation serves as a lever for the costs of non-commitment.

Consequently, in order to keep the payroll relatively low, the possibility of report

manipulation causes a firm to more likely turn to internal promotions. Our model

therefore predicts that firms with worse corporate governance are more likely to

promote from within.

The remaining paper is organized as follows. Section 2 discusses related literature,

section 3 describes the model, section 4 contains the main analysis, section 5 shows

the competition scenario, section 6 provides the extensions, and section 7 concludes.

2 Related Literature

The tournament theory literature has analyzed the motivational aspect of promo-

tions. Rank-order tournaments pay employees based on their ordinal rank in an orga-

nization. Lazear and Rosen (1981) show that under risk neutrality this compensation

scheme is as good as a linear pay-for-performance scheme and achieves first-best em-

ployee effort. If workers are risk averse, then tournaments can even dominate a piece

rate under certain conditions. Rosen (1986) explains the disproportionate increase

in wage differences across the career ladder. A top-heavy distribution is needed to

incentivize high effort from workers who already received some promotions. Success

6

increases the compensation in case of eventual failure while simultaneously reducing

prizes that have yet to be achieved.

The other role of promotions is sorting workers to jobs according to their abilities.

Sattinger (1975) finds that comparative advantages will cause the distribution of

earnings to be more skewed than the distribution of skills to achieve the optimal

sorting of workers, even in the absence of market imperfections and institutional

peculiarities. Similarly, Rosen (1982) examines the top-heavy distribution of wages

and attributes it to the fact that the best-skilled employees make influential decisions

that affect the productivity of many workers below them.

Malcomson (1984) combined the two ideas and showed that an internal labor

market can solve the conflict. However, in this model, workers are homogeneous,

they do not differ in ability. At the time of the promotion decision, there is no time-

inconsistency problem because internal candidates are equivalent to external ones.

Milgrom and Roberts (1988) illustrated the time-inconsistency problem. Their focus

is on unproductive influence activities. At the time of the promotion decision, the

employer wants to select the best-suited workers for the high-level job. Anticipating

this behavior, employees will engage in wasteful behavior to signal a better ability.

The study most closely related to our paper is Waldman (2003). He focuses on

internal promotion and shows that, given a suffi ciently narrow distribution of skills,

it is optimal for the firm to commit to internal promotion. This leads to an ex-

post ineffi cient promotion rule as sometimes not the best worker for the next job is

promoted. However, this disadvantage is outweighed by the motivational effect that

increases effort. In his analysis, workers had one skill level that was relevant for both

7

the low-level and high-level task. This will be the assumption that we will relax.

Workers can have two different skills that can be more or less correlated.

An important aspect of these models is the ability of the firm to commit to internal

promotion. There are several ways this can be achieved in practice. Milgrom and

Roberts (1988) discuss the option to put the promotion decision into the hands of a

bureaucratic, rule-based personnel department that is unresponsive to complaints by

managers and whose only interest is folllowing the stated policy. Another possibility

is discussed in Waldman (2003). The analyzed models assume a short-lived firm. If

firms operate with a longer time-horizon, then reputation concerns can alleviate the

time-inconsistency problem. A firm will be punished in future periods by its workers,

if expectations of internal promotion are not met. A suffi ciently low discount rate and

an infinite number of periods is suffi cient to render the trigger strategy of deviating

from initial commitment detrimental.

The paper also contributes to the internal labor market (ILM) literature. Pfeffer

and Cohen (1984) and Baron et al. (1986) have found quite a few determinants that

are correlated with a firm’s use of ILMs. These determinants include "firm-specific

skills, organizational structure, gender distinctions, technology, occupational differ-

entiation, the institutional environment, and the interests of unions." Job similarity

along the career ladder has been overlooked, though. It is also worth pointing out

that our model is not motivated at all by firm-specific skills.

8

3 Model

Consider a two-period game with a risk-neutral firm and two representative risk-

neutral workers i ∈ {1, 2}.

Timing: There are three dates, t = {0, 1, 2}. At date t = 0, the firm hires two

workers for an entry-level job and offers them a long-term contract. After signing the

contract, the agents can exert costly effort that increases the probability of success

of their individual projects. At date t = 1, the project outcomes are publicly realized

and expectations of workers’skills are updated. Then, the firm chooses one worker

for a managerial job. At date t = 2, the project outcome for the managerial worker

is realized. Workers are paid according to negotiated wages, and firms collect the

cash flow from produced output net of wages. The game ends.

Effort: After signing a contract at t = 0, each worker takes an unobservable

effort choice eit ∈ {el, eh}. High effort improves the probability of project success

yH : Pr(yH |e = eh) > Pr(yH |e = el). Effort is costly, v(ei). The cost of high effort is

v(eh) = k, while the cost of low effort is normalized to zero, i.e. v(el) = 0, without

loss of generality. As will become clear below, effort choice in the second period is

always low, and hence we will drop the time subscript, when it is without ambiguity.

Let k be small enough such that the firm finds it optimal to incentivize high effort

in the first period.

Skills: Each worker has two skills θiE, θiM ∈ {θB, θG}. The first one, θiE, is the

relevant skill for the entry-level job, while the second one, θiM , is relevant for the

managerial position. Skills are unknown to all parties. If a worker is skilled, then the

project will succeed with higher probability: Pr(yH |θiE = θG) > Pr(yH |θiE = θB) as

9

well as Pr(yH |θiM = θG) > Pr(yH |θiM = θB). The ex-ante unconditional probability

that a worker is skilled at a particular job, is π = Pr(θiE = θG) = Pr(θiM = θG).

However, skills are not independently distributed. The correlation coeffi cient between

skills is ρ ∈ (0, 1]. It follows that E[θiM |θiE] = ρθiE+(1−ρ)E[θiM ]. Let the expected

ex-ante skill level be noted by E[θ] = θ∗ = πθG + (1− π)θB.

Projects: Each worker is in charge of a project. Project outputs are uncorre-

lated, observable, but noncontractible, and can either be high or low: yit ∈ {yL =

0, yH = 1}. The probability of high output for entry-level and managerial jobs are

Pr(yi1 = yH) = θiE + ei1 and Pr(yi2 = yH) = θiM + ei2 respectively. We define

p = θ∗ + eh to simplify notation. This is the success probability of a worker, who

puts in high effort. The output value for the entry-level job is normalized to one.

Value of the managerial job is greater than one by a factor of λ > 1.

Managerial hiring decision: At t = 1, after observing project outputs, the

firm has to hire a worker for the managerial job. At t = 0, it can commit to

promote only internally one of the two workers that worked for the firm in the

first period in an entry-level position. Firms that promote exclusively internally

are consistent with empirical evidence (see related literature section) and can be

explained in several ways, two of which will be explored in this paper (in addition

to a simple contractual obligation). If the firm did not commit, then in addition to

promoting from within, it can also pick a worker that was unemployed in the first

period. Expected skill levels for unemployed workers cannot be updated and remain

at θ∗. For all employed workers, skills can be updated. After first period success, we

have θ = π(θG+ei1)π(θG+ei1)+(1−π)(θB+ei1) , and after failure θ = π(1−θG−ei1)

π(1−θG−ei1)+(1−π)(1−θB−ei1) . The

10

following ordering of skills can be obtained: θB < θ < θ∗ < θ < θG.

Contracting: Since output is assumed to be non-contractible and effort is unob-

servable, the firm can only offer a flat wage in each period. Thus, a contract has the

following vector form: c = (WE,WM), where WE describes the wage paid in the first

period to a hired entry-level worker, and WM describes the wage paid in the second

period to a hired managerial-level worker. Workers can choose not to work for the

company, both at t = 0, and at t = 1 ("no-slave condition"). Their outside option

utility is U per period not working for the firm. Furthermore, to keep the model

simple, we exogenously assume that if a firm hires externally for the managerial job,

it has to pay at least WM to that worker as well.

4 Analysis

4.1 Results

Starting with the situation, when the firm commits to internal promotion, the con-

tract structure needs to satisfy two constraints. The agent needs to find it optimal

to choose work over shirk; and he needs to find it optimal to sign the contract in the

first place instead of choosing his outside option. The incentive constraint (IC) can

be simplified to the following expression (see appendix for details):

WM = U +2k

eh − el . (1)

The first thing to note is that WE is not present. This is driven by the fact

11

that the first-period compensation is constant, because output is by assumption not

contractible. Thus, the only way to incentivize hard work is via the wage for the

managerial position in the second period. High effort increases the chances that the

agent will receive the promotion and its associated payoff.

We introduce a variable that will be useful later:

τ ≡ WM − U. (2)

τ is the "surcharge" that the firm has to pay above the outside option to incen-

tivize hard work. However, as will become clear from the participation constraint

(PC), this surcharge does not always affect the bottom line because the workers can

be kept at their reservation utility.

WE +1

2WM +

1

2U − k ≥ 2U. (3)

The agent can accept the offer, work hard, and receiveWE in the first period, and

have a 50% chance to get WM in the second period (still analyzing the situation, in

which the firm will promote internally from its two symmetric entry-level workers).

This option has to be at least as good as declining the offer and receiving the outside

option in both periods.

Before we can describe firm profits, we need to analyze how beliefs about the

managerial skill of a worker are updated. For all j 6= i it is true that (θiE−θjE)∗ρ =

E[θiM |θiE]−E[θjM |θjE]. For more similar jobs, the expected difference in managerial

skill levels is bigger than for less similar jobs, holding the difference in low-level skill

12

constant. This is a standard result (e.g., Arya and Mittendorf 2011, p. 1434).

Basically, with greater correlation, the information that is learnt, makes for a better

predictor.

We now have the necessary foundation to describe the firm’s profit using the

strategy of always promoting internally.

V (C) = 2p︸︷︷︸exp. first period output

+ λ(θ∗ + 2p(1− p)(θ − θ∗)ρ)︸ ︷︷ ︸exp. skill of promoted worker

− (2WE +WM)︸ ︷︷ ︸=3U−2k

(4)

When the firm keeps all its options open, then two things change. First, the

expected skill of the promoted worker increases, which increases profits. Second, the

probability that an internal worker receives the promotion decreases. The ex-post

optimal promotion rule is to promote the best internal candidate ifmaxi

[E[θiM |θiE]] ≥

θ∗ and choose an external worker if this condition is not met. Concretely, the firm

finds it ex-post optimal to promote internally, if at least one of its workers had

success, because θ < θ∗ < θ. All non-promoted internal workers will voluntarily

quit and choose self-employment in the second period. However, ex-ante, the firm

needs to consider the effect of the promotion rule on the effort decision of its workers.

Since the principal also has to obey the participation constraint, he has to increase

promised wages to ensure that workers want to work for the company in the first

period. This effect decreases profits.

V (NC) = 2p+λ(θ∗+2p(1−p)(θ−θ∗)ρ+(1−p)2ρ(θ∗−θ))−2WE−WM −(1− p)2τ︸ ︷︷ ︸to keep workers’effort high

(5)

13

The difference in profits between the firm’s two strategies can be expressed in the

following way:

V (NC)− V (C) = (1− p)2(λρ(θ∗ − θ)− τ). (6)

V (NC) and V (C) are the firm profits after non-commitment and commitment

respectively. The first factor is the probability that both internal workers fail in the

first period. Only in that case will the firm’s promotion decision be different. The

first summand of the second factor is the increase in expected output. Note that

correlation ρ plays a crucial role as the firm can only learn about managerial abil-

ity, if it is correlated with the entry-level skill. The second summand of the second

factor is the surcharge τ . Since the externally promoted worker receives the man-

agerial wage, this expense does not contribute towards satisfying the participation

constraint. Using (6), we can calculate a threshold value ρ∗ for correlation when the

difference in profits is zero:

ρ∗ =τ

λ(θ∗ − θ) . (7)

This leads to the following propositon.

Proposition 1 There exists ρ∗ such that it is optimal for the firm to commit to only

promote from the inside if and only if ρ < ρ∗.

As jobs become more similar, the required skills will be more correlated. As

correlation increases, more information about the ability for the high-level job is

learned. Due to increased correlation, the updated distribution of the high-level skill

will shift more with respect to the information about the low-level skill. Hence, the

14

difference between ex-post expected value and ex-ante expected value will increase

and therefore also the difference to the expected value of the external candidates. As

a result, the cost of commitment increases with increasing correlation. At correlation

ρ∗, the cost exactly balances the benefit. As correlation becomes even stronger, the

cost will outweigh the benefit and thus commitment is no longer the optimal choice. It

should be noted here that it is possible that ρ∗ > 1, in which case internal promotion

always dominates.

On the other side of the spectrum, if skills between entry-level and managerial

jobs are almost independent, then there is virtually no cost to commitment. The

expected ability of the promoted worker is almost unchanged, regardless of first

period outcome. The possibility of an external candidate provides little extra benefit.

Yet, the advantage of increased motivation remains and the necessary managerial

wage can be lowered.

Corollary 1 If ρ→ 0, then it is always optimal for the firm to commit to promote

an entry-level worker.

This corollary can be deduced directly from equation (7), because ρ∗ is always

strictly positive.

4.2 Comparative Statics

Several variables determine the profitability of commitment to internal promotion

and thus ρ∗.

15

Corollary 2 Commitment to internal promotion becomes more profitable (ρ∗ in-

creases) if

(i) the variance of the distribution of skills (θG − θB) decreases,

(ii) the importance of the managerial position (λ) decreases,

(iii) the cost of effort (k) increases, or

(iv) the effect of high effort (eh − el) on output decreases.

(i) A decrease in the variance of the distribution of skills reduces the possibility

that a truely bad worker has to be promoted with commitment. Hence, internal

promotion will be more profitable.

(ii) Clearly, as the importance of the managerial position increases, it will be

crucial to have a competent person in charge and keeping the option of an external

hire is more benefitial. (iii) The influence of the cost of effort on ρ∗ is more subtle.

If k increases, then the promised managerial wage has to increase in order to still be

able to incentivize high effort. However, without commitment, part of the increase in

that wage will, in expectation, go to an external candidate. To compensate for this

loss in expected wage for internal workers, the firm has to increase the managerial

wage even more. As a result, not commiting to internal promotion becomes more

expensive.

(iv) A decrease in the output effect of high effort uses a similar argument. The

incentive compatibility constraint will be harder to satisfy because the probability

of receiving a promotion with low effort increases. The firm has to increase the

promised managerial wage and this, as described above, benefits commitment to

internal promotion.

16

One assumption of the model, that was unchanged thus far, is the expected skill

of the external candidate: θ∗. This is equivalent to assuming that the firm has no

information about external candidates. Trivially, if this expected value increases,

then internal promotion is less attractive. For exapmle, the firm has the option to

consider an experienced manager in the external pool of unemployed workers instead

of young talent. Contrary to the variables mentioned in the corrolary above, changing

the expected skill of the external candidate changes the result of Corollary 1 when

ρ→ 0. It will no longer be the case that it is always optimal to commit to internal

promotion because the difference in expected skills does not converge to zero any

more.

5 Competition

5.1 The Companies’Payoffs

Next, we turn to a scenario with two firms (Small, S and Large, L) on the market,

which compete in recruiting suitable candidates for the managerial position in t =

2. Both have two representative entry-level workers in t = 1 and a vacancy in

management in t = 2. They can either promote internally, hire from the external

pool of unemployed workers or they can try to hire the entry-level worker from

the competitor. To simplify the structure, we assume that the entry-level workers’

output in t = 1 is observable by the own firm and the competitor to the same

extent.1 Furthermore, the external pool provides enough candidates so that both

1We could also assume that the competitor only observes the cumulated output for both workers.If both workers are successful or unsuccessful, the competitor can see this in cumulated reports as

17

firms always have the option to hire from the pool. The firms only differ in the

productivity of the managerial position with λL > λS and both firms can either

commit to internal hiring or choose not to commit, which generates four possible

strategy combinations. We also use subscripts to the probability that an entry-level

worker produces high output in period one, pS and pL, to make the equations more

tracktable, even though we assume pS = pL = p. We call an entry-level worker

with such a high output a "star". In this section, we derive the firms’payoffs in all

four strategy combinations, a) - d), before we analyze the firms’equilibrium choices.

VS(C) describes the monopoly payoff from the small firm given commitment, while

VS(C,C) describes the competition payoffs, where the first strategy stands for the

small firm and the second for the large firm.

a) Both firms commit:

VS(C,C) = VS(C) (8)

VL(C,C) = VL(C) (9)

If both companies commit to internal hiring for the managerial position, each firm

operates independently of the competitor. Both companies focus on their internal

talent and their payoffs are as defined in (4) with their respective firm productivity

λS or λL.

well. If only one worker is successful, it depends on the distribution of skill levels, whether thecompetitor would be interested in poaching this successful worker. The same is true for the casethat both firms only observe aggregated reports. Then, also the internal promotion decision dependson the distribution of skill levels.

18

b) Small firm does not commit, large firm commits

VS(NC,C) = VS(NC) + (1− pS)2p2L(θ − θ∗)ρλS (10)

Similar to the monopoly case, the small firm can gain from not committing in

expectation whenever it has no stars available with probability (1− pS)2. In compe-

tition, the only difference to the monopoly payoffs from (5) is if the large firm has

two stars available. The large firm has only one managerial position available and

cannot retain the second skilled worker since she would either be too expensive for

the entry-level job or too ambitious to remain in the entry-level. Therefore, the large

firm has to let her go and the small firm can hire this second skilled worker without

additional surcharges. If the large firm has only one star available, the small firm

does not have the resources to poach the worker since λL > λS, which only leaves it

with the option to hiere from the external pool.

VL(NC,C) = VL(C) + p2L(1− pS)2τ (11)

The large firm’s payoff, if the small firm plays non-commitment, changes with

respect to one particular case. If the large firm has two stars, p2L, it can only promote

one to the managerial position and has to let go of the second star. If, at the same

time, the small firm has no suitable candidates in its own firm, (1− pS)2, the option

to change companies offers a new career path for the second star. Basically, the

competitor takes over the role of providing career incentives for the large firm. The

surcharge, τ , earned from the second star in the new company can be deducted from

19

the first period wage in the old company. If the large firm has one star only, it

will promote her to the managerial position. Even if the small firm has no star, it

does not have the resources to steal from the competitor. Nevertheless, the small

firm imposes a credible threat to the large firm which is why the large firm needs

to counter the offer. This essentially increases the compensation of the promoted

star in period two. However, all workers are kept at the reservation utility and an

increase in second period compensation means that the firm can reduce first period

compensation by the exact same amount. This second effect cancels out. In sum, the

large firm benefits from the non-commitment of the small firm, which also describes

the difference to the monopoly case in (4).

c) Small firm commits, Large firm does not commit

VS(C,NC) = VS(C) + (1− pL)2p2Sτ (12)

In this scenario, the small firm’s payoff mirrors the large firm’s payoff from b),

VL(NC,C), since in both scenarios the competitor does not commit while the com-

pany in focus commits. With two own stars, p2S, and no stars of the competitor,

(1 − pL)2, the logic remains unchanged. The large competitor takes over the career

incentive for the second star due to its ability to hire externally. But the explanation

for the second effect is slightly different. In case the small firm has only one star

available, it could indeed lose the star to the large firm. In order to extract this

star from her current employer, the large firm must pay a premium. This premium

must be high enough so that the small firm cannot counter the offer. Therefore,

the large firm pays exactly the small firm’s marginal benefit from the star in the

20

managerial position, which makes the small firm indifferent between keeping the star

or promoting its second worker. However, while the small firm loses the benefit of

promoting a highly skilled worker for the managerial position, the premium offered

from the large firm to this worker can be deducted from the first period entry-level

compensation, reducing the wage costs by the exact same margin. In sum, also the

small firm benefits from the non-commitment of its competitor.

VL(C,NC) = VL(C) + (1− pL)2[p2S(θ − θ)ρλL (13)

+(1− pS)2(θ∗ − θ)ρλL + 2(1− pS)pS((θ − θ)ρλL − (θ − θ)ρλS)− τ ]

Without commitment, the large firm can improve from internal promotion when-

ever it does not have any stars, (1−pL)2. Depending on the small firm’s endowment,

it hires from the external pool or from the competitor. If the small firm has two

stars, p2S, the large firm can hire one star without surcharge and receives benefit

(θ − θ)ρλL, as can be seen in the first line of the equation. If the small firm has no

star, (1− p2S), the large firm hires from pool and receives benefit (θ∗ − θ)ρλL. If the

small firm has one star, 2(1 − pS)pS, the large firm can poach this star and steal it

from the competitor for benefit (θ− θ)ρλL, but it must offer a premium, which must

be at least as high as the small firm’s loss in productivity, (θ − θ)ρλS.2 In all three

cases, the large firm needs to add τ to the existing payroll to compensate for the lack

of promotion incentives for its entry-level workers. As before, the difference to the

monopoly case in (5) is the option to receive the second star from the competitor if

2We assume that the productivity levels are suffi ciently different so that stealing is the betteroption for the firm compared to the external pool. (θ−θ)ρλL−(θ−θ)ρλS > (θ∗−θ)ρλL rearrangedyields λL/λS > (θ − θ)/(θ − θ∗).

21

available. In addition, the large firm now has the option to poach the only star from

the small firm.

d) Noone commits

VS(NC,NC) = VS(NC) + (1− pS)2p2L(θ − θ∗)ρλS + (1− pL)2p2Sτ (14)

The case where noone commits provides a combination of the effects from scenario

b) and c) to the small firm. The first term provides the basis from the monopoly

case, second term describes the small firm’s option from competition if it has no

stars available, and the third term describes the effect from the large firm’s non-

commitment if it takes over the career incentives for the smal firm’s second star.

VL(NC,NC) = VL(C,C) + p2L(1− pS)2τ + (1− pL)2[p2S(θ − θ)ρλL

+ (1− pS)2(θ∗ − θ)ρλL + 2(1− pS)pS((θ − θ)ρλL − (θ − θ∗)ρλS︸ ︷︷ ︸new price for S’s star

)− τ ]

The large firm’s payoff follows the same logic and corresponds to combination of

scenario b) and c). The career incentives for the second star from scenario b) can

be seen in line one and the hiring options from scenario c) are in line two. However,

there is one modification if the large firm wants to steal the only star of the small

firm. Since the small firm is not limited to the internal labor market as in scenario

c), the large firm has to pay less in order to poach the star. The small firm can

now replace the star from the external pool, which increases the value of its next

22

best option, which is why the large firm pays only the difference from the star to the

average skill, (θ− θ∗)ρλS. Without taken into accounting the equilibrium strategies,

we can already state the following proposition

Proposition 2 If at least one of the firm’s does not commit to the internal labor

market, competition increases firm value.

The payoffs from competition in scenario a), if both firms commit to the internal

labor market, are identical to the monopoly case. Both firms live in their own bubble

independent of the other firm and competition has no impact on their behavior.

However, in all other cases b) - d), the cash flows are higher. The reason for this

result is that the competitor offers the opportunity to hire personnel from outside the

firm, whose performance in period one can be observed. If one firm has more suitable

candidates than managerial positions, the competitor can benefit from picking up the

managerial talent, as in (10). At the same time, the firm with the excess candidates

does also benefit because the career incentives of this excess candidate is transfered

to the competitor. Hence, it pays a lower first period wage if it has more candidates

than managerial positions available.

5.2 The Companies’Strategy

The Small Firm. Similar to the monopoly situation, the small firm determines

the strategy based on a comparison of payoffs. Thereby, it needs to incorporate the

strategy of the other firm, which leads to the following lemma:

23

Lemma 1 Independent of the large firm’s strategy, there exists a threshold ρS such

that the small firm commits to the internal labor market for all ρ < ρS and does not

commit for all ρ > ρS.

Proofs are in the appendix.

ρS is the threshold value for the similarity in skills, which solves VS(C,C) =

VS(NC,C) from scenario a) and b) or VS(C,NC) = VS(NC,NC) from scenario c)

and d). Interestingly, the small firm’s strategy does not depend on the large firm.

If the big firm is willing to poach a worker from the small firm, it always pays the

marginal benefit such that the small firm does not lose in expectation. In addition,

the transfer of career incentives to the large firm in case the small firm itself has two

stars is also irrelevant. The effect arises given non-commitment of the large firm no

matter the action of the small firm. Consequently, the only remaining effect from

competition compared to the monopoly situation is the option to hire the second

star from the large firm.

The Large Firm. The large firm’s strategy is derived in a similar way based on

the comparison of the payoffs and the other firm’s strategy.

Lemma 2 (i) Given the small firm chooses to commit to the internal labor market,

there exists a threshold ρCL such that the large firm also commits for all ρ < ρCL and

does not commit for all ρ > ρCL .

(ii) Given the small firm chooses not to commit to the internal labor market,

there exists a threshold ρNCL such that the large firm commits for all ρ < ρNCL and

does not commit for all ρ > ρNCL .

Proofs are in the Appendix.

24

ρCL is the threshold value of the similarity in skills, which solves VL(C,C) =

VL(C,NC) from scenario a) and c) and ρNCL is the threshold value which solves

VL(NC,C) = VL(NC,NC) from scenario b) and d). The large firm is more produc-

tive than its smaller competitor, λL > λS. As a consequence, it holds the resources

to make an offer to the small firm’s star, which the small firm cannot refuse. At the

same time, the large firm is able to defend all possible offers from its competitor for

its own workers for the same reason. However, despite the large firm’s powerful posi-

tion, its strategy depends on the strategy of its smaller competitor, while the smaller

competitor chooses its strategy independently. In general, the large firm faces the

same effects than the small firm. It benefits from the option to hire the small firm’s

second star and, if it has two stars itself, from the transfer of career incentives to

the small firm. The reason for the small firm’s impact on its own strategy is the

following: When the large firm steals the only star from its competitor, the small

firm is either committed to internal promotion and has to take the worker left within

the company or it is not committed and can replenish the position from the external

pool. This second options makes it cheaper for the large firm to poach the only star

since it has to pay less if the small firm’s next best option is the external pool.

Equilibrium Strategies.

Proposition 3 Given that both companies have the same inherent correlation be-

tween the entry-level and the managerial position, it follows that ρCL < ρNCL < ρS.

(i) It is true that ρCL < ρ∗(λL) and ρS < ρ∗(λS).

(ii) For all ρ < ρCL , both firms commit to the internal labor market (Scenario a)).

25

For all ρ ∈ (ρCL , ρS), the large firm does not commit and the small firm commits

to the internal labor market (Scenario c)).

For all ρ > ρS, both firms do not commit to the internal labor market (Scenario

d)).

Proofs are in the Appendix.

Part (i) compares the strategies in the monopoly situation to the competition.

Both firms rely on the internal labor market less often. For both firms, the competitor

presents an intruiging opportunity to learn something about the skill level of the

outside hiring option. Excess talent in one firm will be hired from the other firm

when in need. The large firm has an additional benefit from non-commitment. Due

to its market power based on the higher productivity level, λL > λS, it can steal

one star from the small firm, which causes the large firm to choose non-commitment

more often than the small firm, ρCL < ρS. Note that threshold ρNCL is off-equilibrium.

The small firm always commits for all ρ < ρS and since ρNCL < ρS, the large firm

chooses its strategy in equilibrium given commitment from the small firm, ρCL . As a

consequence, the strategy ranges in part (ii) arise.

Competition on the labor market in this model does not lead to a deterioration

in any sense. Both firms have the chance to observe performance outside of their

company, which enables a better allocation of proven managerial talent. Instead of

releasing them to unemployment, the workers can be picked up by the competitor.

Competition pushes back the internal labor markets, which is not necessarily a bad

thing.

26

6 Extensions

6.1 Report Manipulation

In many situations, the principal cannot observe an agent’s output directly, but

has to rely on reports, generated by the agents themselves. This introduces the

possibility that these reports might be manipulated. Suppose that agent i can make

an unobservable manipulation decisionmi ∈ [0, 1] after low output. With probability

mi, her output will falsely be reported as high. The cost of manipulation to the agent

is gmi/2, where g is exogenously determined and describes how easily a report can

be manipulated. Assume that g is high enough that an interior solution (mi < 1)

prevails.

Again, starting with the incentive constraint to make sure that the agents find it

optimal to avoid shirking, we arrive at the following equation (details in appendix):

WM = U +2k − (eh − el)gm2

i

(1−m)(eh − el) . (15)

Comparing the surcharge τ in equation (15) with the one in equation (1), we can

show that the promised compensation to the agents in case of a promotion has to

increase, when manipulation is possible. This is a straight-forward result, consistent

with the earnings management literature. The possibility of manipulation makes

effort look like a less attractive option (compared to a no manipulation case). If

wages remained constant, then the worker would shirk and simply manipulate a

little bit to compensate for his loss in output. Thus, promised compensation has to

27

increase to keep incentives to work hard high enough.

The remainder of the analysis is unchanged. The key difference between always

promoting internally or not occurs when both agents report low output. Otherwise,

there is no reason to hire externally. However, the firm knows that a report of low

output is truthful, and therefore has the same information about its workers, as if

manipulation were not possible at all. Thus, we can simply take equation (7) and

notice that an increase in τ causes a proportional increase in ρ∗.

Proposition 4 The possibility of report manipulation causes a firm to more likely

go with exclusively internal promotions.

Internal promotion allows the firm to not worry about the higher managerial

wage, because it can recoup the higher expenses by lowering the entry-level wage.

This proposition also creates the empirical prediction that firms with worse corporate

governance are more likely to promote from within.

6.2 Implicit Commitment

6.2.1 Private Benefits

Explicit and contractually binding commitment to internal promotion is rare in the

business world. In this section, we assume that explicit commitment is not possible.

However, the firm can decide who gets to make the promotion decision after the first

period. Option 1 is to let the HR department decide. We assume that they will

simply pick the best qualified candidate for the manager job. On the other hand, the

firm could let the future immediate superior of the manager decide. We assume that

28

this person gains private benefits B from promoting an internal candidate. Maybe

the superior is already a golf buddy with the current entry-level workers. He could

simply have an aversion to new people. Alternatively, the benefit B can be viewed as

a benefit to the company from promoting internally, such as positive media coverage

or positive feedback from stakeholders. For instance, FC Bayern Munich recently

implemented a policy to focus on its own youngsters instead of hiring international

stars. They expect to gain a benefit due to the increased identification of the fans

with the young talents, who have their roots in the club. Hence, the club’s implicit

commitment is implemented in their general corporate identity "Mia san Mia" which

limits the operating decisions of the current club manager/coach to hire players

outside of the club.

Let the utility function of the immediate superior manager be UI = E[θiM |θiE]+B

if he promotes internal candidate i and UO = θ∗ in case of an external candidate

getting the job. Thus, he promotes internally, if B > θ∗ −maxi

[E[θiM |θiE]], which is

equivalent to maxi

[θiE] > θ∗ − ρB. If B is very large, then he will always promote

internally and the situation is equivalent to the situation analyzed in the previous

section. If B = 0, then the decision will be the ex-post optimal one for the firm.

For small private benefits, this will lead to an advantage for internal workers getting

the promotion. However, if all internal candidates are too weak, then the external

candidate can still get the job.

Proposition 5 Assuming a suffi ciently wide distribution of skills and ρ < ρ∗, there

exists B∗ such that it is optimal for the firm to let the person with the private benefits

decide the promotion if B > B∗.

29

The intuition is similar to the previous section. Giving the superior with the

private benefits the decision right increases the probability of a promotion for inter-

nal workers and thus motivation at the cost of reducing expected skill level of the

promoted person. The key difference is that for a small B, an internal worker will

not get promoted, if the external candidate is substantially better.

6.2.2 Infinite Horizon

Implicit commitment can also be derived via a simple trigger strategy over the course

of an infinite horizon. The idea is to earn the reputation as a firm to commit to

the internal labor market. If the firm deviates from this strategy once and hires

externally, it is not able to return to the internal labor market because the implicit

commitment is not credible anymore.

Suppose that ρ < ρ∗. Then, the firm commits to the internal labor market and

the entry-level workers provide high effort for as long as none of the players deviate

from these strategies. The firm’s present value of future cash flows from commitment

is

Π(C) = V (C) + δΠ(C)⇐⇒ Π(C) =V (C)

1− δ

where δ is the discount factor and V (C) is the firm value with the commitment

strategy from (4). The firm faces the same choice in every period and if it is optimal

to commit in this period, then it is also optimal to commit in the next period.

If the firm deviates from the commitment strategy, it can hire externally in this

period, which has the following consequences: After the deviation, the agent does

30

not deliver high effort with the firm’s commitment strategy in any future period

because she does not trust the incentives provided by the internal labor market

anymore. Thus, instead of the empty promise to promote internally, the firm needs

to switch to the non-commitment strategy, which provides a higher managerial-level

wage to incentivize the entry-level workers. The present value of a deviation from

the commitment to the internal labor market in the next period is given by

Π(D) = V (D) + V (NC)δ

1− δ

with V (D) = V (C) + (1 − p)2ρλ(θ∗ − θ) and V (C) from (5). The firm value in

the deviation period is higher than in commitment (or non-commitment), V (D) >

V (C) > V (NC), since the workers provide high effort but the firm never keeps

its promise to promote internally and never compensates otherwise. The firm will

deviate from commitment and accept the lower future payoffs if

Π(C) < Π(D).

Proposition 6 Assuming an infinite horizon, the firm commits to internal promo-

tion, if the jobs are suffi ciently different ρ < ρ∗ and the firm is suffi ciently patient

δ > δ∗ = V (D)−V (C)V (D)−V (NC) .

The first condition in the proposition is trivial. Without suffi ciently different jobs

ρ < ρ∗, the firm would choose non-commitment in every period and commitment is

never a problem. The second condition, δ > δ∗ is related to the patience of the firm.

31

If the interest rate is high (high in the sense of δt = (1 − r)−t and r is high), cash

flows today become relatively more important than cash flows in the future. Hence,

the incentive to deviate from commitment and to grasp the high cash flow V (D)

today increases. The benefit of hiring externally today exceeds the costs of not being

able to commit to the internal labor market in the future.

In sum, commitment is possible even if it is not explicitly contracted or enforce-

able in court. In an infinite horizon, the workers hold the firm accountable for its

actions.

7 Conclusion

This paper analyzes the effect of job similarity along the career path on the firm’s

promotion choice. The firm is concerned about optimally assigning workers to tasks

and motivating high effort. After the first period, the firm is only worried about the

optimal assignment and might pick an external candidate, if she is the best-qualified.

This, in turn, reduces incentives for its employees to provide high effort in the first

period due to the increased competition and thus lowered probability of receiving

a promotion. The firm anticipates this problem and as a solution could commit

to internal promotion. In the case of almost independence, it is always optimal to

commit to internal promotion because the influence of an optimal assignment of

workers on profits is negligible.

As jobs become more similar, the required skills will be more correlated. As

correlation increases, more information about the ability for the high-level job is

32

learned. Due to increased correlation, the updated distribution of the high-level skill

will shift more with respect to the information about the low-level skill. Hence, the

difference between ex-post expected value and ex-ante expected value will increase

and therefore also the difference to the expected value of external candidates. As

a result, the cost of commitment increases with increasing correlation and makes it

less likely that commitment is the optimal choice to achieve the benefit of increased

motivation and therefore reduced wage payments.

Furthermore, when there is labor market competition, then there will be less

internal promotion, and firm strategies might depend on the other firm’s actions.

Also, when report manipulation is possible, then internal promotion becomes more

attractive.

These results show that firms, whose jobs along the job ladder are more similar,

should be expected to hire more outsiders and promote less from within, while firms

with weak corporate governance may promote more internally.

8 Appendix

Proof of Proposition 1 and Corollary 1:

Let us start with the situation, when the firm will promote internally. The firm

needs to structure wages such that agents find it optimal to participate in the game

33

(PC), and that they find it optimal to work hard (IC).

IC : WE +1

2WM +

1

2U − k ≥ WE + (p(θ∗ + el)

1

2+

+ (1− p)(θ∗ + el) + (1− p)(1− θ∗ − el)1

2)WM+

+ (p(θ∗ + el)1

2+ p(1− θ∗ − el) + (1− p)(1− θ∗ − el)1

2)U. (16)

This simplifies to

WE +1

2WM +

1

2U − k ≥ WE +

1

2

(1− eh + el

)WM +

1

2(1− el + eh)U, (17)

and eventually

WM = U +2k

eh − el︸ ︷︷ ︸=τ

. (18)

PC : WE +1

2WM +

1

2U − k ≥ 2U. (19)

Plugging (18) into this formula, and simplifying gives

WE = U − (1− eh + el)k

eh − el . (20)

We now have the necessary foundation to describe the firm’s profit using the

strategy of always promoting internally.

V (C) = 2p+ λ(θ∗ + 2p(1− p)(θ − θ∗)ρ)︸ ︷︷ ︸exp. skill of promoted worker

− (2WE +WM)︸ ︷︷ ︸=3U−2k

(21)

34

Let us now analyze the situation, when the firm is free to promote whomever,

and compare it to the previous situation.

V (NC) = 2p+ λ(θ∗ + 2p(1− p)(θ − θ∗)ρ+

+ (1− p)2ρ(θ∗ − θ))− 2WE −WM − (1− p)2τ

V (NC)− V (C) = (1− p)2(λρ(θ∗ − θ)− τ) (22)

The expected compensation to internal workers has to stay constant (binding par-

ticipation constraint). Thus, when the firm is open to choosing an external worker, it

has to offset the expected loss in wages to its internal workers by increasing compen-

sation. The benefit from this is an improvement in expected skill. Note that ex-post

it is always optimal to choose an external worker, if both internal agents failed.

Using the above derived formula, we can solve for ρ∗, such that V (NC)−V (C) =

0.

ρ∗ =τ

λ(θ∗ − θ) . (23)

Proof of Lemma 1:

Threshold ρS

ρS is the threshold value of the similarity in skills, which solves VS(C,C) =

VS(NC,C) from scenario a) and b)

VS(C,C) = VS(C,C) + (1− p)2[(p2(θ − θ)

+((1− p)2 + 2p(1− p))(θ∗ − θ))ρλS − τ ]

35

The equation is fulfilled if the term in the squared brackets equals 0. This is true

for a threshold value of ρ:

ρS =τ

λS[p2(θ − θ) + (1− p2)(θ∗ − θ)]−1 (24)

The proof also works if the threshold ρS is solved with VS(C,NC) = VS(NC,NC)

from scenario c) and d)

Proof of Lemma 2:

(i) Threshold ρCL

ρCL is the threshold value of the similarity in skills, which solves VL(C,C) =

VL(C,NC)

VL(C,C) = VL(C,C) + (1− p)2[p2(θ − θ)ρλL + (1− p)2(θ∗ − θ)ρλL

+2(1− p)p((θ − θ)ρλL − (θ − θ)ρλS)− τ ]

The equation is fulfilled if the term in the squared brackets equals 0. This is true

for a threshold value of ρ:

ρCL =τ

λL

[p2(θ − θ) + (1− p)2(θ∗ − θ) + 2(1− p)p(θ − θ)(1− λS

λL)

]−1(25)

(ii) Threshold ρNCL

ρNCL is the threshold value of the similarity in skills, which solves VL(NC,C) =

36

VL(NC,NC)

VL(C,C) + p2L(1− pS)2τ = VL(C,C) + p2L(1− pS)2τ + (1− pL)2[p2S(θ − θ)ρλL

+ (1− pS)2(θ∗ − θ)ρλL + 2(1− pS)pS((θ − θ)ρλL − (θ − θ∗)ρλS)− τ ]

The equation is fulfilled if the term in the squared brackets equals 0. This is true

for a threshold value of ρ:

ρNCL =τ

λL

[p2(θ − θ) + (1− p)2(θ∗ − θ) + 2(1− p)p((θ − θ)− (θ − θ∗)λS

λL)

]−1(26)

Proof of Proposition 3:

In this proof, we show the following relations step by step: ρCL < ρNCL < ρS and

ρNCL < ρ∗(λL) as well as ρS < ρ∗(λS).

First, we show that ρCL < ρNCL :

The only difference in the thresholds in (25) and (26) is that given non-commitment

from the small firm, the large firm pays a lower price for poaching the star, (θ− θ) >

(θ − θ∗). This effect increases the nummerator of ρNCL . Hence, ρCL < ρNCL .

Second, we show that ρNCL < ρS

τ

λL

[p2(θ − θ) + (1− p)2(θ∗ − θ) + 2(1− p)p((θ − θ)− (θ − θ∗)λS

λL)

]−1<

τ

λS[p2(θ − θ) + (1− p2)(θ∗ − θ)]−1

37

We multiply both sides of the inequality with the denominator and numerators

⇐⇒ (p2(θ− θ) + (1− p2)(θ∗− θ))(λS−λL) < λL2(1− p)p((θ− θ)− (θ− θ∗)λSλL

) q.e.d

Due to λS < λL, the left hand side is negative and the right hand side is positive

which fulfills the proof.

Third, we show that ρNCL < ρ∗(λL)

τ

λL

[p2(θ − θ) + (1− p)2(θ∗ − θ) + 2(1− p)p((θ − θ)− (θ − θ∗)λS

λL)

]−1<

τ

λL(θ∗ − θ)

We multiply both sides of the inequality with the denominator and numerators

⇐⇒ (θ∗ − θ) < p2(θ − θ) + (1− p)2(θ∗ − θ) + 2(1− p)p((θ − θ)− (θ − θ∗)λSλL

)

We use (θ − θ) = (θ − θ∗) + (θ∗ − θ).

⇐⇒ 0 < p2(θ − θ∗) + 2(1− p)p(θ − θ∗)(1− λSλL

) q.e.d

Lastly, we show that ρS < ρ∗(λS)

τ

λS[p2(θ − θ) + (1− p2)(θ∗ − θ)]−1 < τ

λS(θ∗ − θ)

38

We multiply both sides of the inequality with the denominator and numerators

⇐⇒ (θ∗ − θ) < p2(θ − θ) + (1− p2)(θ∗ − θ)

We use (θ − θ) = (θ − θ∗) + (θ∗ − θ).

⇐⇒ 0 < p2(θ − θ∗) q.e.d

Proof of Proposition 4:

The full, unshortened incentive constraint is

WE + 12WM + 1

2U − k − (1− θ∗ − eh)gm2

i /2 ≥ WE + (p(θ∗ + el)12

+ (1− p)(θ∗ +

el)(1−m/2) + p(1− θ∗ − el)m/2 + (1− p)(1− θ∗ − el)12)WM+

+(p(θ∗ + el)12

+ p(1− θ∗ − el)(1−m/2) + (1− p)(θ∗ + el)m/2 + (1− p)(1− θ∗ −

el)12)U − (1− θ∗ − el)gm2

i /2.

This can be arranged and simplified to equation (15).

To prove the proposition, we need to show that

2k−(eh−el)gm2i

(1−mi)(eh−el) >2k

(eh−el) = τ old,

which is equivalent to

gmi <2k

(eh − el) = τ old. (27)

mi is a choice variable by the worker i. He will pick the value that maximizes his

expected utility.

p(mi(WM + U)/2 + (1−mi)U) + (1− p)(mimj(WM + U)/2 +mi(1−mj)WM +

(1−mi)mjU + (1−mi)(1−mj)(WM + U)/2− gm2i /2

39

Taking the first derivative and setting it to zero, yields after some algebra

(WM − U)/2 = gmi.

Plugging the solution for (WM −U) from the IC into this expression and solving

for mi gives

mi =(

1−√

1− τoldg

)Multiplying both sides with g, plugging into the inequality (27), proves the propo-

sition.

Proof of Proposition 5:

Given the assumptions about the utility function of the decision maker, it follows

that he will always promote internally, if

B > B∗ ≡ θ∗ − θρ

. (28)

If B < B∗, then he behaves like an unbiased person. Note that this result is

driven by the binary structure of the model. If project outcome were continuously

distributed, then it could be possible that even for ρ > ρ∗, there are parameter values

such that giving the biased decision maker the decision rights is optimal.

9 References

Arya, A., Mittendorf, B., 2011. The Benefits of Aggregate Performance Metrics in

the Presence of Career Concerns. Management Science 57, 1424-1437.

Baron, J., Davis-Blake, A., Bielby, W., 1986. The Structure of Opportunity: How

Promotion Ladders Vary Within and Among Organizations. Administrative Science

40

Quarterly 31, 248-273.

Lazear, E., Rosen, S., 1981. Rank-Order Tournaments as Optimum Labor Con-

tracts. Journal of Political Economy 89, 841-864.

Kornberger, M., Justesen, L., Mouritsen, J., 2011. “When you make manager,

we put a big mountain in front of you”: An ethnography of managers in a Big 4

Accounting Firm. Accounting, Organizations and Society 36, 514-533.

Malcomson, J., 1984. Work Incentives, Hierarchy, and Internal Labor Markets.

Journal of Political Economy 92, 486-507.

Milgrom. P., Roberts, J., 1988. An Economic Approach to Influence Activities

in Organizations. American Journal of Sociology 94, 154-179.

Pfeffer, J., Cohen, Y., 1984. Determinants of Internal Labor Markets in Organi-

zations. Administrative Science Quarterly 29, 550-772.

Rosen, S., 1978. Substitution and the Division of Labour. Economica 45, 235-250.

Rosen, S., 1986. Prizes and Incentives in Elimination Tournaments. Bell Journal

of Economics 13, 311-323.

Sattinger, M., 1975. Comparative Advantage and the Distribution of Earnings

and Abilities. Econometrica 43, 455-468.

Waldman, M., 2003. Ex ante versus ex post optimal promotion rules: the case of

internal promotion. Economic Inquiry 41, 27-41.

41