Corruption, Culture and Org-Form

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Corruption, Culture and Organizational Form1

Elena Duggar2

African Department

International Monetary Fund, Washington, D.C.

Madhur Duggar

Structured Bond Research and Strategy

Citigroup, New York, NY

Keywords: Bureaucracy, Corruption Control, Hierarchy,

Organization Form, Peer Pressure, Culture.

JEL Classification: O10, K42, D73, L20, Z13.

November 2004

1This paper is based on chapter one of E. Duggars Ph.D. dissertation at Univesity of California

at Berkeley. We thank Pranab Bardhan, Peter Evans, Joseph Farrell, Neil Fligstein, G erard Roland,

Suzanne Scotchmer and seminar participants at U.C. Berkeley. All errors are ours.2Corresponding author. Tel. +1-202-623-7562. Fax. +1-202-623-7095. Email: [email protected].


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Abstract

This paper examines the relationship between organizational form and the potential for corruption in two

polar opposite cultural settings. We build a theoretical model of a licensing bureaucracy consisting of honest

and dishonest officials, and study two types of corruption - collusion, where crooks try to bribe officials inorder to pass bad projects, and extortion, where officials extort bribes from good applicants in order to

process a good application. We examine two types of organizational culture - competitive culture, where

officials monitor each other and pressure each other to behave honestly, and cooperative culture, where

there is peer pressure from dishonest officials to cheat. We find that in the case of competitive culture,

when peer relationships are strong, flat hierarchies are less prone to collusion, less prone to extortion and

less costly to maintain than steep hierarchies. However, cooperative culture presents us with a trade-off:

when peer relationships are strong, steep hierarchies are less prone to collusion and less prone to extortion,

but flat hierarchies are less costly to maintain. We explore the implications of some reform policies aimed

at reducing corruption.


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1 Introduction

This paper investigates the following questions: What is the relationship between organi-

zational form and corruption within government? How does this relationship depend on

culture and social norms?In recent years accusations of corruption have brought down politicians, governments,

and in some cases, whole political classes. Concerned with corruption, many governments

have announced plans to improve the performance of state agencies. Public sector reforms

have been on-going in the developed countries, and since the 1980s, public sector reforms

in customs, tax administration and civil service have b een a major component of the World

Banks structural adjustment lending to developing countries. In 1999-2000 itself, civil

service reform had been a part of World Bank programs in as many as 45 countries.

In his classic study Controlling Corruption, R. Klitgaard describes one such reform -

the remarkable effort of Justice Plana to reduce corruption in the 1975 Philippines Bureau ofInternal Revenue (BIR). He concludes that in 4 years, Justice Plana succeeded in eliminating

job selling, embezzlement and fraud, greatly reduced the acceptance of bribes for lower

assessments, and the extortion of money from taxpayers with threats of high assessments

and the prospect of costly litigation, and moreover, achieved this in an environment where

other forms of corruption remained widespread.

Yet, there are only a few examples of reforms in developing countries that have made

such a noticeable progress. Part of this has been blamed on wage declines following World

Bank and IMF structural adjustment programs which have resulted in low morale and in-

creased petty corruption. However, case studies of successful and unsuccessful attempts of

reforming state agencies suggest that there is a much deeper connection between organi-

zational characteristics and the p otential for corruption than wage levels. Reform efforts

generally include firing existing officials, hiring new officials, creating new internal auditing

units, and re-organizing work processes1, all of which change the structure of the organi-

zation, emphasizing the need to understand the relationship between organizational form

and the incentives for corruption. Moreover, case studies suggest that this relationship is

different in organizations with different culture2.

This paper builds a theoretical model of a government bureaucracy, e.g. a licensing

agency, to explore the relationship between organizational form and the potential for cor-

ruption. We find that the potential for corruption depends not only on the benefits andcosts to both applicants and officials, but also on the size and shape of the organization.

Moreover, the type of organizational form that is preferred depends on the organizational

culture, and on the strength of peer relationships among officials.

1Mars (1982), Klitgaard (1988) and Anechiarico and Jacobs (1996)2Mars (1982) and Klitgaard (1988)

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We find that if peer relationships are strong and organizational culture is such that

peer pressure forces officials to behave more honestly, then the preferred organizational

form is a flat pyramid. Moreover, downsizing is likely to have adverse consequences for

corruption. On the other hand, if peer relationships are strong and organizational culture

is such that peer pressure forces officials to behave more dishonestly, then the preferred

organizational form is a steep pyramid. Moreover, downsizing is likely to be beneficial for

reducing corruption.

This paper is a first step in bridging the gap between the literature on corruption which

has not addressed the role of the organization as a whole, and the literature on organizations.

Moreover, this paper is a first attempt to model within the same framework the two opposite

cultural contexts, and the two different types of peer pressure, that sociologists have found

to exist in organizations3. The literature on corruption has explored the effects of wage

levels and wage dispersion in increasing the penalty for corruption4, increasing monitoring

effort in principal-agent frameworks5, and the effect of competition6, but has not looked atthe organizational form as a whole. The organizations literature, on the other hand, has

shown that organizational form is important with respect to effort incentives7, and with

respect to information aggregation broadly defined8, but has not addressed the problem of

corruption. Also, the few economics papers addressing peer pressure address it as being

only peer monitoring9.

We model two types of culture within the organization. The first type of culture is

competitive, where officials monitor each other and put pressure on each other to behave

honestly, as in most organizations of professionals and businessmen. The second type of

culture is cooperative, where there is pressure from dishonest officials to conform to thebehavior of the group and to cheat. This is the case in police departments, some government

agencies, and where family and ethnic ties are strong. We take the type of organizational

culture as exogenous, as it is historically determined, but the strength of peer pressure as

endogenous, as it depends on organizational characteristics.

We model two types of corruption: collusion where crooks try to bribe officials in

3Allen (1970), Alatas (1980), Mars (1982), Williams (2002)4See Becker (1968), Basu at al. (1992), Besley and McLaren (1993), Mookherjee and Png (1995) and

Carillo (1999).5See Tirole (1986), Kofman and Lawaree (1993), Bac and Bag (1998), and Laffont and Meleu (2001) in

the case of collusion, and Banerjee (1997) and Guriev (1999) in the case of bribe extortion.6See Rose-Ackerman (1986), Shleifer and Vishny (1993), Laffont and Martimort (1997), and Laffont and

NGuessan (1999).7See Alchian and Demsetz (1972), Calvo and Weillisz (1978) and Qian (1994).8See Keren and Levhari (1979, 1983), Sah and Stiglitz (1986), and Radner (1992).9See Arnott and Stiglitz (1991) in the context of insurance markets, Kandel and Lazear (1992)in part-

nerships, Barron and Gjerde (1997) in team production, and Stiglitz (1990) and Ghatak (1999) in credit

markets.

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order to pass bad projects, and extortion where officials ask good applicants for bribes

in order to process a good application. While traditionally the corruption literature has

focused on collusion10, bribe extortion is an equally important problem in many developing

countries, and is frequently considered to be most harmful to citizens morale and trust in

the rule of law11. Thus, we model b oth collusion and bribe extortion12. Each official has

an independent jurisdiction over the decision on an application, and we assume that it is

costless for officials to determine whether an application is good or bad.

The role of the bureaucracy in our model is to screen applications, to approve license

applications for good projects and to reject license applications for bad projects. The

bureaucracy is modeled as a hierarchy that consists of two types of officials: honest and

dishonest, where officials are subject to peer pressure.

The novel approach of this research is to look not only at the actual bribes being ex-

changed, but to look at the much more important question of corruptibility or the potential

for corruption. We analyze the decision of the crook to offer a bribe and the decision of theofficials to accept the bribe offered in the case of collusion, and similarly, the decision of the

official to extort the good applicant and the decision of the good applicant to pay the asked

bribe in the case of bribe extortion. We define corruptibility, a measure of the potential

for corrupt deals, as the distance between the maximum amount of bribe an applicant will

be willing to offer, and the sum of minimum amounts of bribe officials will require in order

to cheat. We find that both organizational form and culture determine the potential for

bribe-taking.

We find that under competitive culture, when peer relationships are strong, a flat orga-

nizational pyramid is less prone to collusion and less prone to bribe extortion compared toa steep pyramid. Under competitive culture peer pressure acts to force officials to behave

more honestly, and having a flat organization is a way of reinforcing peer pressure. However,

under cooperative culture, the opposite is true. When peer relationships are strong, a steep

organizational pyramid is less prone to both collusion and bribe extortion compared to a

flat pyramid. Under cooperative culture peer pressure acts to force officials to behave more

dishonestly, so having a steep organization is a way of breaking peer pressure.

In analyzing the social optimum we take into account the effect of bureaucracy both on

the good and bad projects that pass through the bureaucracy, and also on the distribution of

projects that approach the bureaucracy in the first place. We show that the very possibility

of collusion deters marginally profitable bad projects from approaching the bureaucracy in

the first place, but at the same time, the possibility of extortion deters marginally profitable

good projects from approaching the bureaucracy.

10Tirole (1986), Rose-Ackerman (1978, 1986)11Alatas (1980), Klitgaard (1986)12We follow Banerjee (1997) and Guriev (1999).

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Therefore, under a competitive culture, the social optimal organization is a flat pyramid

as it is less prone to collusion, less prone to bribe extortion, and less costly to maintain.

Cooperative culture, on the other hand, presents us with a trade-off: a steeper pyramid is

less prone to collusion and less prone to bribe extortion but also more costly to maintain

than a flatter pyramid. The lower wage levels and wage dispersion, the steeper the optimal

organizational form. The basic intuition behind these results is that under competitive

culture peer monitoring is effective, and since it is less costly than monitoring by superiors,

it is optimal to use peer monitoring by having a flat organization. Under cooperative

culture, however, peer monitoring is ineffective, so it becomes necessary to use monitoring

by superiors by having a steep organization.

Thus, we propose the use of organizational shape as a policy instrument in fighting

corruption: making the organization flatter under competitive culture, and making the

organization steeper under cooperative culture.

We also find that the relationship between corruption and organizational size depends onthe cultural context. Under competitive culture, increasing organizational size always acts

to reduce corruptibility, as it increases monitoring. Under cooperative culture, however,

increasing organizational size initially might reduce corruptibility as having more officials

checking an application makes it more likely that there will be an honest official among

them. But after a threshold, increasing size further starts increasing corruptibility as peer

pressure makes officials less likely to act honestly. Thus, we observe a domino effect of

corruption spreading: as officials meet more dishonest colleagues, they themselves become

less likely to act honestly.

This implies that a policy of downsizing will only be beneficial in reducing corruptionin organizations with cooperative type culture, thus supporting the push for downsizing in

developing countries, and especially in Africa, by international organizations. Moreover,

downsizing accompanied by increases in wage levels and wage dispersion is an appropriate

policy to aim at reducing corruption in developing countries, while downsizing accompanied

by decreases in wage levels or wage dispersion, is inappropriate. This points towards an

explanation of why past corruption-reducing reforms that happened in the context of falling

wage levels were not successful, and supports the shifted focus of international organizations

in recent years on increasing wages and wage dispersion.

Our framework allows us to easily analyze three other reform policies that have been

used in the fight against corruption. First, we address the debate of whether it is more

efficient to punish the bribe-taker or the bribe-giver, and find that it is more effective to

punish the bribe-giver. Second, we address the policy of raising officials wages in fighting

corruption, and find that it is most effective to rase the wages of officials at the bottom of

the hierarchy. Finally, we address corruption cleansing, and find that it is most effective

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to replace officials at the top of the hierarchy in order to affect the incentives of everybody

below them.

This paper is organized as follows. Section 2 outlines the model. It describes the bu-

reaucracy, how culture is modeled, the applicants that approach the bureaucracy, and the

timing and outcomes of the model. Section 3 analyzes the relationship between collusion

and organizational form and culture. It first describes the officials decision problem, the

applicants decision problem, and our measure of corruption. Then, it explores the rela-

tionship between collusion, culture and the shape of the organization. Finally, it explores

the relationship between collusion, culture and the size of the organization.

Similarly, Section 4 analyzes the relationships between extortion and organizational

form and culture. It describes the officials and the applicants decision problems, our

measure of extortion, and the difference between collusion and extortion. Then, it explores

the relationship between extortion, culture and the shape of the organization. Finally, it

explores the relationship between extortion, culture and the size of the organization.Section 5 analyzes the social optimal organization and level of corruption. It adds the

dimension of the cost of maintaining the bureaucracy to the above analysis. Finally, section

6 analyzes three other reform policies. Section 7 concludes and draws extensions. All proofs

are in the Appendix.

2 Outline of the Model

2.1 The Bureaucracy

We model the organization as a hierarchy consisting of K levels, with nk = nk number ofofficials in each level k, and total number of officials N. We assume that < 1, so that nk

is decreasing with k. The rank of the official increases as k increases from 1 to K. Assume

that officials wage is an increasing function of the rank k, so that Wk = Wk1, where is

the starting wage and W > 1 is the wage dispersion. We use the terms peers, superiors and

inferiors to describe officials in the same level, in the levels above and in the levels below a

given official respectively.

There exist two types of officials in the organization, where officials type is private

information and officials do not know the type of their colleagues. A fraction p of the

officials are dishonest, and a fraction (1p) are honest. Honest officials do not take bribes.Dishonest officials will sometimes take a bribe in order to approve a fraudulent application,

and will also extort money from applicants in order to process a good application, as long

as it is profitable for them to do so. Thus, with probability q the dishonest officials behave

corruptly and with probability 1 q they behave honestly. The size of q depends on the

strength of peer pressure, and the form of q depends on the type of peer pressure, that is,

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it depends on the organizational culture and the social relationships among officials. We

provide more details on the function q in the following section.

An application passes through the hierarchy starting at the bottom level and making its

way to the top. We assume division of labor within the levels of the organization, so that

if there are several officials in a level, they each work on a different part of the application.

For example, in a construction license application, one official looks at electricity, another

one at water, a third at fire safety, etc. Each official is able to observe the entire application

and is therefore able to judge whether the application is good or bad. As such, if a bad

application passes through a level k and is later caught, then all officials in level k are held

liable and fired.

We also assume that it is costless for the officials to determine whether an application is

good or bad. This is an important simplifying assumption and it is consistent with assuming

division of labor within the organization in settings where each official receives the whole

file and either it is easy to tell that there is something wrong with the application, or wordspreads around the office. The team of three customs inspectors that check cars for drugs

on the b order crossing is an example of the former: one official checks the back, another one

checks the front and a third one checks the tires, but they are all individually responsible

for letting the car go. The team of engineers that inspects a construction site is an example

of the latter: the water inspector cannot immediately determine whether the electricity

system is in order, but the length of the process allows more than enough time for rumors

to circulate13.

2.2 The Organizational Culture

We model two types of organizational culture. The first type is the culture in organizations

where colleague relationships are competitive, and colleagues tend to monitor each other and

put pressure on each other to behave honestly. This is the case when collegial relationships

and group norms are aligned with organizational goals and societal values, and work to

preserve the values of honesty and integrity. In this case, the more officials there are,

the more pressure to behave honestly, thus, the probability that dishonest officials behave

dishonestly, q, is a decreasing function of the number of peers nk and of the total number

of officials N. Mathematically,

Competitive organizational culture : q = qk = e[1nk+2N] (1)

where nk is the number of peers, N is the total number of officials, and 1 < 1 and 2 < 1

are constants.

13The alternative is to assume that officials can determine whether an application is good or bad with

some probability. This will not alter the main results, so we choose not to further complicate the model.

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The second type is the culture in organizations where colleague relationships are coop-

erative, and where there is strong peer pressure from dishonest officials to conform to the

behavior of the group and to follow suit in cheating. This is the case of collegial relation-

ships and group norms which deviate from organizational goals and societal values, and

which work to promote corruption. In this case, the more pervasive corruption is, that is,

the more dishonest colleagues one has, the more likely one is to succumb to peer pressures

and to cheat. Thus, the probability of behaving dishonestly is an increasing function of the

number of dishonest peers and of the total number of dishonest officials. Mathematically,

Cooperative organizational culture : q = qk = ep[1nk+2N] (2)

where nk is the number of peers, N is the total number of officials, p is the fraction of

dishonest officials, and < 1, 1 < 1 and 2 < 1 are constants. This formulation captures

the domino effect of corruption spreading: an official that meets enough number of dishonest

officials is more likely to behave dishonestly himself/herself no matter what fraction of the

total these officials represent. 1/2 is the weight one places on peer officials relative to

everybody else. It is realistic to assume that the weight placed on peer officials is larger,

since officials tend to socialize more with their peers than with their superiors or inferiors 14.

Sociologists have observed that organizational culture has historically developed over

long periods of time based on particular occupational characteristics, based on traditional

societal values, or based on particular historical developments (e.g. how colonial powers

transfered administration to the native population after independence). Occupations where

individual achievement and competition are valued, and where members are enabled to

work under conditions of relative autonomy, tend to be more conducive to competitive typeculture. While occupations where the nature of the work performed requires the formation

of a group and the cooperation of group members, tend to be more conducive to cooperative

type culture.

Thus, entrepreneurs, businessmen, and professionals in particular (Mars 1982), and cor-

porations and universities in general (Blankenship 1977), have tended to be more conducive

to competitive type culture. The community of commitment and integrity shared by aca-

demics has had profoundly positive results for society (Simmel 1964).

On the other hand, police departments have been a frequently cited example of cooper-

ative type culture. Police culture is a culture of group camaraderie where officers dependon each other for their very lives. As a result, peer pressure and the desire for continued

comradery with and acceptance by fellow police officers creates a culture in which bribery

and corruption are tolerated. An honest policemen who tries to inform on his corrupt col-

leagues comes under the most severe pressures from them (Kugler, Verdier and Zenou 2003,

14Mishler and Tropp (1956), Berkovitz (1961), Alderfer (1971)

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Williams 2002, Weisburd et al. 2001). Cooperative type culture also exists among dock

workers, dustcart crews (Mars 1982), and also in some government agencies, social service

agencies, and military organizations (Blankenship 1977).

Western values of individual achievement tend to be more conducive to competitive type

culture, while strong kinship and ethnic ties existing in many developing countries tend to

be more conducive to cooperative type culture. Allen (1970) describes the emergence of

culture of integrity in the (British) Malayan Civil Service. While Wertheim (1965) describes

how traditional family ties clash with morality in Indonesian public services, where all the

personnel in one particular office belonged to a single family group: that of the office chief.15

In the case of the Philippines Bureau of Internal Revenue (BIR), Magtolis-Briones (1979)

emphasizes

. . . the unusual closeness of the employees, especially at the middle management level with

each other. All respondents at the BIR have made mention of the strong ties of affection

and close interpersonal relationships that bind the BIR employees together. . . The tendency toprotect and to cover up for each other exists. The answer of one official interviewed about the

case of a dismissed employee is perhaps typical,I cannot comment on this case. It is difficult

to cut off the head of a member of the family.16

In this paper, we take the type of organizational culture and colleague relationships (i.e

the form of q) as exogenous, consistent with sociologists observations of their historical

determinance. We endogenize, however, the strength of colleague relationships and peer

pressure as dependent on organizational characteristics. Thus, the size ofq and the behavior

of dishonest officials are endogenous, and dependent on the organizational form.

2.3 The Applicants

The clients of the bureaucracy are also of two types and we distinguish two types of corrup-

tion accordingly. The first type are applicants with good pro jects, which could be subjected

to bribe extortion by the officials. Extortion is always harmful for the clients of the bureau-

cracy, and even though extortion is a transfer of money between the good client and the

officials, it is socially harmful as far as it deters some good clients from approaching the bu-

reaucracy in the first place. The second type are applicants with bad projects, which could

bribe officials in order to get a bad application approved. In keeping with the literature we

name this type of corruption collusion. Collusion is socially harmful as it leads to stealing

of output from society.

A crook has to bribe all officials in order to pass the whole bureaucracy. If an official is

caught cheating in passing a bad application, he gets fired and everybody below him also

gets fired, since everybody below him must have cheated in order for the application to get

15cited in Alatas (1980), p.1716cited in Klitgaard (1988), p.16-17

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so far. In the case of collusion, an official can get caught by his peer colleagues and by his

superiors. In the case of extortion, an official can get caught only by his peer colleagues. His

superiors have no way of verifying whether he extorted a bribe or not, since the superiors

themselves are looking at a good application. We do not model the possibility of the good

applicant complaining about extortion, to the media for example, since the goal of this

research is to determine the relationship between corruption and organizational form, and

there is no reason to believe that the possibility of complaining will have different effect

given different organizational forms.

2.4 The Timing of the Model

The timing of the model is the same both in the case of a bad and in the case of a good

application. First, the applicant submits their application and tries to bribe, or is extorted

for bribes by all officials starting from the bottom up the hierarchy. The application either

passes the whole bureaucracy or gets caught on the way. If the application passes the whole

bureaucracy, the officials receive their bribes. If the application gets caught on the way, in

the case of collusion all officials that cheated are fired and nobody receives any bribes. In

the case of extortion, only officials that cheated in the level that caught extortion are fired.

Lower level officials receive their bribes and do not get fired. Society pays wages to the

officials that are not fired by the end of the game. We assume that there is no uncertainty

in receiving the bribes.

Thus, there are three possible outcomes with respect to corruption in the bureaucracy.

First, if all officials cheat with probability one (p = 1, q = 1), everybody is corrupt, all bad

projects pass, and all good projects are extorted for bribes. Second, if all officials behavehonestly with probability one (q = 0), then nobody cheats, and there is no corruption.

Third, if dishonest officials behave dishonestly with probability between zero and one (p >

0, q > 0), then sometimes there is corruption and sometimes corruption is caught and

officials are fired. This is similar in spirit to the multiple equilibria models of corruption

of Cadot (1987) and Andvig and Moene (1990), however, in Cadot (1987) and Andvig and

Moene (1990) the expected punishment for corruption declines as more officials become

corrupt, and this gives rise to the two extreme equilibria. By modeling peer pressure, out

model allows not only for the two extremes, but also for intermediate outcomes.

3 Collusion

In this section we analyze the relationship between collusion and organizational form and

culture. We first describe the officials and the applicants decision problems, and use them

to construct a measure of the potential for corruption. Next, we take the constructed

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measure and explore the relationship between collusion, culture and the shape of the orga-

nization. Then, similarly, we explores the relationship between collusion, culture and the

size of the organization.

3.1 The Dishonest Officials Decision

We first describe the decision problem of the official. The dishonest official must decide

whether to accept the bribe offered by the crook or not. We assume that the official gets

the bribe only if the crook is not caught and passes free all steps of the application process.

If the crook gets caught, the bribe is discovered, the official loses his wage Wk, and gets

zero17. Let the bribe per official be xk.

In the case of collusion, an official processing a bad application could be caught both by

his peers and by his superiors. The crook will pass free and the official will receive his bribe

only if all other peer and superior officials are also dishonest or choose to act dishonestly.

The probability that an official acts dishonestly is pqk. Thus, the probability of all other

peers behaving dishonestly is (pqk)nk1. Finally, the probability of all superiors behaving

dishonestly is Ki=k+1(pqi)ni , where (pqi)

ni is the probability of passing free through level

i. Thus, the probability of all other peers and superiors behaving dishonestly, which will

depend on the organizational form, is ck = (pqk)nk1Ki=k+1(pqi)

ni . The dishonest officials

decision becomes - accept bribe if expected benefit of cheating is larger than expected cost:

(xk + Wk)ck + 0(1

ck) Wk (3)

Solving for xk, this expression will give us the minimum amount of bribe per person the

official will require in order to cheat:

xmink =Wkck

Wk =Wk

(pqk)nk1Ki=k+1(pqi)

niWk (4)

The minimum amount of bribe official require increases as their loss Wk increases, and

falls as the fraction of dishonest officials p increases. Moreover, for W > W, where

log(W) =ckk

1ck(1

ck) , the minimum amount of bribe officials require has an inverse-U

relationship with their rank.

As we move towards the top of the hierarchy, the potential loss (the lost wage) of the

official increases, but the probability of being caught decreases. The lowest ranking officialdemands a small bribe because their loss (the lost wage) if they get caught is relatively

small compared to other officials. The official at the very top also demands a small bribe

because they face little or no risk of b eing caught. The officials towards the middle of

17We assume for simplicity that the official loses only his wage when fired. Assuming that the loss is larger

than the wage, including fine, time in prison, loss of respect, etc, will not change the analysis

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the hierarchy, however, face a larger loss than those at the bottom, but also have a larger

probability of being caught than those at the top, so they demand the largest bribe. Figure

1 illustrates this relationship. The actual bribe each official will receive depends on their

relative bargaining power. If the top official has most or all of the bargaining power, as is

most often the case in reality, then it is possible that the topmost official receives the largest

bribe.

3.2 The Bad Applicants Decision

Next, we turn to the crooks decision. Assume that the value of the bad project is B, that

is, the crook can steal B from society if he gets his project application approved. Assume

a binomial distribution of bad projects in the population, where a fraction b of the bad

projects have a payoff value of BH and a fraction (1b) have a payoff value of BL. To the

crook, the benefit of passing the application process and not being caught is B. The payoff

of not trying to pass is zero. And the cost of trying to pass, but being caught is C.The crook will pass free with probability b = Ki=1(pqi)

ni , if all officials behave dis-

honestly. Thus, the crook will decide to pass if and only if his expected benefit minus his

expected cost is larger than the reservation utility of not applying, which is zero. So, the

crooks decision is to pass if

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(B sumx)b C(1 b) 0 (5)

where sumx is the total amount of the bribe paid to all officials. Solving for sumx, this

expression will give us the maximum amount of the total bribe the crook will be willingto pay. As the crook passes up through the hierarchy, the maximum amount he will be

willing to pay in bribes changes because as there are less officials to go through, there is

less uncertainty about being caught. However, in order to pass the application process, it

has to be beneficial for the crook to pass the whole hierarchy, therefore the decision has to

be made at the beginning:

sumxmax = B + CC

b= B + C

C

Ki=1(pqi)ni

(6)

The maximum amount of bribe the crook is willing to pay decreases as their benefit B

falls, as their cost C rises, and as the fraction of dishonest officials p falls.We assume that BH > B > BL, and B is the solution to x

max(B) = xmin. Thus,

the existence of the bureaucracy alters the distribution of bad projects that are going to

approach it in the first place by deterring bad projects with low value. The fact that the

crook has to pay a bribe to get a license for a bad project deters marginally profitable bad

projects from approaching the bureaucracy in the first place. Bribery increases the cost of

bad projects with value BL just enough to make them marginally unprofitable, so the only

bad projects that approach the bureaucracy are bad projects that have high payoffs, BH.

This is a benefit to having the bureaucracy in place.

Having the minimum amount of bribe the officials require in order to cheat and themaximum amount of bribe the crook is willing to pay, allows us to look at the corruptibility

of the system, or the potential for corrupt deals, which depends on the organizational form.

3.3 Corruptibility in the Case of Collusion

As long as sumxmin sumxmax, there will be collusion in the bureaucracy, as the amount

of bribe that the crook is willing to pay is more than the amount of bribe that the officials

require in order to help the crook. The true amount of each bribe xk will be between xmin

and xmax, and will depend on the relative bargaining power of the crook and the official.

In this paper we choose to abstract from the questions of bargaining, and we look at thebroader and more important question of corruptibility as a measure of the potential for

corruption.

Definition 1 We define corruptibility in the case of collusion as the distance between the

total maximum bribe the crook will be willing to pay, sumxmax, and the total of the minimum

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bribes the officials will require, sumxmin = Kk=1(nkxmink ).

Corruptibility = sumxmax sumxmin

= [B + C

C

b ]

K

k=1[nk(

Wk

ck

Wk)]

where b = Ki=1(pqi)ni and ck = (pqk)

nk1Ki=k+1(pqi)ni.

The smallest size of the bureaucracy needed to prevent collusion will be just above the

number of levels K with nk officials in each level k that solve sumxmax = sumxmin.

In the case of collusion, corruptibility increases as the crooks benefit of cheating, B,

increases and as the fraction of dishonest officials, p, increases; corruptibility falls as the p o-

tential loss to the official, Wk, increases and as the loss to the crook if caught, C, increases.

Figure 2 shows corruptibility decreasing as the fraction of honest officials (1 p) increases,

both in the case of competitive and in the case of cooperative culture. This implies thatmeasures increasing societys ethics and the fraction of honest people, such as education or

improved law-abiding, can reduce corruption and can reduce the size needed for the bu-

reaucracy to behave honestly.

Figure 3 shows corruptibility decreasing as wage dispersion increases, both for competi-

tive and cooperative culture. This result is consistent with the literature on using fines as a

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deterrent to crime18. Moreover, in our model, the fine required to deter cheating is less than

the maximum fine that will make the officials benefits of cheating negative, even though

there is a positive probability of not being caught. The fine required to deter cheating does

not need to be large enough to make the minimum bribe officials require infinitely large,

it only needs to make the minimum bribe larger than the maximum bribe the crook can

afford to pay. This is another explanation of why in reality individuals are rarely if ever

fined an amount approximating their wealth. In addition, unlike the argument of Polinsky

and Shavell (1979), this argument does not rely on risk aversion.

Figures 2 and 3 are shown for the case where corruptibility under competitive culture is

lower than corruptibility under cooperative culture. It is intuitive to suppose that organiza-

tions with cooperative type culture, where family and ethnic ties are important and where

group relationships are strong, are likely to be more prone to collusion than organizations

with competitive type culture, where individual achievement is valued more, where there is

fast turnover, frequent job rotation, and competition among officials for the same positions.However, whether organizations with cooperative culture are more prone to corruption than

organizations with competitive culture all else equal, is an empirical question.

18starting with Becker (1968) and Becker and Stigler (1974)

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3.3.1 Collusion, Culture and Organizational Shape

In this section, we explore the effect of organizational shape on corruptibility, as defined

above, and we show how organizational shape can be used as a policy instrument for fight-

ing corruption. In order to investigate how shape matters, we compare organizations ofthe same size, that is, organizations with the same number of officials. First, we compare

a flat pyramid, an organization with few levels and many officials per level, versus a steep

pyramid, an organization with many levels and few officials per level. Then, we investigate

numerically the relationship between collusion and the steepness of the organization, using

as a measure of the steepness.

There are three major differences between a flat pyramid and a steep pyramid in the way

they impact officials incentives to act corruptly. First, as wage increases up the hierarchy,

the wage dispersion is higher in the steep pyramid than it is in the flat pyramid (assuming

both start off with the same base wage at level 1). Since officials receiving higher wages

have more to lose when caught and fired for corruption, they behave more honestly. Thus,

the wage effect makes the steep pyramid less corrupt compared to the flat one. This

wage effect will be larger, the larger the wage dispersion.

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Second, at each level, the sum of peer and superior officials in the steep pyramid is

always greater than in the flat pyramid. We can think of creating the steep pyramid out

of the flat pyramid by moving a given number of officials from each level higher up the

hierarchy. This probability effect can be decomposed into two competing forces. Firstly,

for each official in levels 1 to Kflat, where Kflat is the number of levels in the flat pyramid,

the probability of there being at least one official who behaves honestly and who can tell

on them is larger in the steep pyramid than in the flat one, since there are more officials

monitoring them in the steep pyramid. This can easily be seen in Figure 4. Official A

in the flat pyramid and official B in the steep pyramid are both in level 2. Since b oth

pyramids have the same number of total officials, 12, but the steep pyramid is taller, official

A has only 6 peers and superiors, while official B has 7. Thus, the probability of getting

caught is larger for official B than for official A. This geometry effect makes the steep

pyramid less corrupt than the flat one.

Secondly, for each official in the steep pyramid in levels Kflat +1 to Ksteep, where Ksteep

is the number of levels in the steep pyramid, the probability of there being at least one

official who behaves honestly and who can tell on them is smaller than for officials in the

flat pyramid, since there are fewer officials monitoring them. To see this, compare official

C with official D in Figure 4. Official C in the flat pyramid is in level 2 and has 6 peers

and superiors. The same official has moved to level 4 in the steep pyramid, and now has

only 2 peers and superiors, thus he is less likely to get caught in the steep pyramid. This

height effect acts to make the steep pyramid more corrupt than the flat one. Thus, the

direction and the size of the probability effect depends on the shape of the organization

and on whether the geometry effect or the height effect dominates.Third, each official has less peers in the steep pyramid than in the flat pyramid. The

effect of peer pressure on corruptibility depends on culture. Under competitive culture,

less peer pressure will mean less pressure to behave honestly, and will make the steep

pyramid more corrupt than the flat one. Under cooperative culture, less peer pressure will

mean less pressure to cheat, and will make the steep pyramid more honest than the flat

one.

It follows from the definition of q in equation 1 and 2 that the size of the peer pressure

effect depends on how much officials care about their peers relative to everybody else, that

is on the weights 1/2 and 1/2. Under competitive culture, if 1/2 is high, that is if

officials care a lot about their peers and less about everybody else, then the effect of having

fewer peers in the steep pyramid will be strong, and honest officials will be a lot less likely

to behave honestly in the steep than in the flat pyramid (i.e. qsteep


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Similarly, under cooperative culture, if 1/2 is high, there is a lot less peer pressure

on officials to cheat in the steep hierarchy, and the peer pressure effect is strong (i.e.

qsteep >> qflat). On the other hand, if 1/2 is small, officials do not care much about their

peers and the effect of decrease in the number of peers will be small (i.e. qsteep is almost

equal to qflat).

Figure 5

Effect on Collusion as the Organization Becomes Steeper

Effect Comp etitive Culture Coop erative Culture

Wage Effect (-) (-)

Probability Effect:

Geometry Effect (-) (-)

Height Effect (+) (+)

Peer Pressure Effect (+) (-)

Thus, as Figure 5 shows, under competitive culture, the wage effect and the geometry

effect act to make the steep pyramid less corrupt, while the height effect and the peer

pressure effect act to make it more corrupt than the flat pyramid. Under cooperative

culture, the wage effect, the geometry effect and the peer pressure effect act to make

the steep pyramid less corrupt, while the height effect acts to make it more corrupt than

the flat pyramid. Which effect dominates, depends on wage dispersion, on organizational

shape and on the strength of peer relationships.

Proposition 3.1 Under competitive culture, for WsteepK < W and Ksteep < K, where

W =K

flat

k=1 (nflatk n

steepk )W

flatk [

1

c,flatk

1)]

[Kflat

k=1 (nflatk n

steepk )][

1c,steepK

1](7)

and where K is the solution to:

Kflat

i=1 [(pqflati )

nflati

(pqsteepi )nsteepi

] = Ki=Kflat+1(pqsteepi )

nsteepi (8)

the flat pyramid is less prone to collusion than the steep one.

Under cooperative culture, for 2Kflat Ksteep 1, and nk [(pqk)nk ] > 0, the steep

pyramid is less prone to collusion than the flat one.

Under competitive culture, under the above conditions, the height effect and the peer

pressure effect dominate the wage effect and the geometry effect, and make a flat pyra-

midal organization less prone to collusion than a steep one. As K increases beyond K and

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W increases beyond W, the wage effect and the geometry effect begin to dominate.

On the other hand, under cooperative culture, if peer relationships are strong enough,

the steep pyramid is less corrupt than the flat one. The figures below illustrate these

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results and show how organizational shape can be used as a policy instrument in reducing

corruption. We use as a measure of the steepness of the organizational pyramid: as

increases, the organization becomes flatter.

Figures 6 and 7 show that changing organizational shape has a different effect depend-

ing on organizational culture. In organizations with competitive type culture, the total

minimum bribe required by officials increases and the total maximum bribe offered by ap-

plicants falls as the organization becomes flatter. Thus, corruptibility, which is the distance

between them, decreases. In organizations with cooperative type culture, however, the total

minimum bribe required by officials falls and the total maximum bribe offered by applicants

rises as the organization becomes flatter, and thus corruptibility increases.

Figures 8 and 9 show corruptibility itself decreasing as a function of under competi-

tive culture and increasing as a function of under cooperative culture. We see that the

effect of wage dispersion is the same in both cultures: increasing wage dispersion decreases

corruptibility. This is consistent with the findings of a negative relationships between wagesand corruption in cross-section data by Van Rijckeghem and Weder (1997) and Haque and

Sahay (1996).

Finally, Figures 10 and 11 illustrate the opposite effect the strength of peer relationships

has on corruptibility in the two cultural contexts. Increasing 1 and increasing 1 increases

the importance placed on peer relationships relative to relationships with the rest of the

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officials. Under competitive culture, peer pressure acts to force officials to behave more

honestly, and we see that collusion falls. Under cooperative culture, however, peer pressure

act to force officials to b ehave more dishonestly and we see that collusion increases with the

strength of peer relationships.

This is consistent with the evidence. In the case of competitive type culture, Burrage(1972) and Gower and Price (1957) compare the strength of occupational group ties in

Britain and in the U.S. They find that occupational ties are stronger in Britain than in the

U.S., and that sanctions against deviance are more likely to be effective in Britain. They

observe that American layers are more likely to formulate ethical codes than the British,

but are less likely to observe them. Similarly, Ostrogorski (1902) observes that American

political parties are more likely to have paid officials and experts, and are more likely also,

to engage in corrupt or criminal practices than the British.

In the case of cooperative type culture, the change in the strength of peer relationships

and corrupt behavior that can occur when bureaucracies are under the threat of internal

investigations and monitoring is striking. Gary Marx describes the extreme effects of the

implemented undercover and sting operations in the New York City government: as officials

fear that they are constantly watched and tested, and that any colleague may be an informer

and any conversation may be recorded, conformity to the organization goals increases and

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risk-taking declines19. And while Marx (1992) doubts the effects on New York City officials

morale, Klitgaard (1988) describes the beneficial effect reducing trust among officials had

on corruption in the Philippines Bureau of Internal Revenue, when Justice Plana employed

secret agents to p ose as undercover tax inspectors. Because the undercover operations re-

duced trust and cooperation among tax officials, they were much more effective in reducing

corruption than just an increase in monitoring, and made possible reform efforts that had

failed in other countries, to succeed in the Philippines BIR.

3.3.2 Collusion, Culture and Organizational Size

In the previous section we discussed the effect of organizational shape on corruptibility.

In this section we explore the effect of increasing organizational size on corruptibility. We

analyze increasing organizational size by adding more officials to each level, that is by

increasing n so that nk = nk rises.

Under competitive culture, officials monitor each other, so adding more officials bothincreases the chances of there being more honest officials, and makes the honest officials

more likely to behave honestly. At the same time, however, increasing size provides for more

officials who could potentially take bribes. If peer relationships are important enough, the

former two effects dominate, and the probability of cheating falls. Figures 12 and 13 show

19cited in Anechiarico and Jacobs (1996), p. 200

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the probability of cheating, (pqk)nk for officials in a given level k as the size of the level

increases. Figure 12 shows the case of competitive culture where the probability of cheating

decreases as the size increases.

Under cooperative culture, however, officials put pressure on each other to behave cor-

ruptly. Here, increasing organizational size has the following two competing effects. As weincrease the size of the organization the chances of there being at least one official who be-

haves honestly increase. However, adding more officials increases peer pressure on officials

and induces them to behave less honestly, and also provides for more officials who could

potentially take bribes. Figure 13 shows that in the case of cooperative culture, the prob-

ability of cheating initially falls as we add more officials, but after a threshold size starts

increasing as the peer pressure effect starts to dominate.

Thus, under competitive culture, the minimum amount of bribe officials require in order

to cheat rises as the organizational size increases. However, if peer relationships are impor-

tant enough, under cooperative culture the minimum amount of bribe officials require falls

as organizational size increases. Figures 14 and 15 show the opposite effect that organiza-

tional size has on the minimum bribe required by an official in level k in the two cultural

contexts.

Similarly, under competitive culture, the total of the minimum bribes required by offi-

cials increases as organizational size increases, as each individual bribe required increases

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and as there are more officials in the organization. Under cooperative culture, however,

there are more officials added to the organization, but each individual official requires a

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smaller bribe to cheat. Therefore, if peer relationships are important enough and wage

dispersion is low enough, the total of the required bribes is lower as size increases.

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On the side of the applicants, the opposite is true. Under competitive culture, now

there are more officials to bribe and a higher probability of getting caught, so the maximum

bribe applicants will be willing to pay falls. Under cooperative culture, however, there

are more officials to bribe but also there is a lower probability of getting caught. Thus,

whenever the second effect dominates, the maximum bribe applicants are willing to pay

rises as organizational size increases.

Figure 16 shows how, under competitive culture, as organizational size increases, the

maximum bribe offered by the crook falls, and the minimum bribe required by the officials

increases, so that corruptibility, which is the distance between them, falls. Moreover, there

exists a large enough organizational size for which there is no corruption.

Under cooperative culture, however, in Figure 17, increasing organizational size initially

reduces corruptibility, but after a threshold starts increasing it. Initially, the effect of there

being more officials to check dominates, but as organizational size increases there is a thresh-

old size after which the peer pressure effect starts dominating. Thus, we observe a domino

effect of corruption spreading: when officials observe enough dishonest officials around them

behaving dishonestly, they themselves become more likely to cheat, so corruption spreads

through the organization and the overall corruptibility level rises. This implies that under

cooperative culture, there might be an optimal organizational size for minimizing corrupt-

ibility. Moreover, it may not always possible to eliminate corruption - if B is high enough

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and W is low enough it might be impossible to eliminate corruption, as illustrated in Figure

17.

Therefore, organizational culture influences the relationship between organization size

and collusion. Under competitive culture, increasing size reduces collusion. However, un-

der cooperative culture, when peer relationships are strong, increasing organizational sizeincreases collusion.

Proposition 3.2 Under competitive culture, a large pyramid is less prone to collusion than

a small pyramid.

Under cooperative culture, for nk

[(pqk)nk ] > 0 and n1large nsmall and

Klarge = Ksmall.

This suggests that a policy of downsizing will be appropriate in organizations withcooperative culture and inappropriate in organizations with competitive culture with respect

to reducing corruptibility. Thus, contrary to popular criticism, the frequently advocated by

international institutions policy of downsizing as part of civil service reform is appropriate

in the context of developing countries where culture is more likely to be cooperative, where

family and ethnic ties are strong, and where peer pressure is likely to be strong.

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4 Extortion

In this section we analyze the relationship between extortion and organizational form and

culture. Similarly to the section on collusion, we first describe the officials and the appli-

cants decision problems, and use them to construct a measure of the potential for extortion.Next, we take the constructed measure and explore the relationship between extortion,

culture and the shape of the organization. Finally, we explore the relationship between

extortion, culture and the size of the organization.

4.1 The Dishonest Officials Decision

Bribe extortion is frequently considered to be the most harmful type of corruption. It

happens when the dishonest official demands a bribe from the good applicant for processing

a good application. Bribe extortion could b e caught by the officials peers when peers

decide to act honestly. Bribe extortion cannot b e caught by superior officials because theapplication passed on up the hierarchy is a good application, and the superiors cannot verify

whether inferiors extorted a bribe for processing it or not. Thus, in the case of extortion,

the official will get the bribe if the applicant passes his level in the hierarchy. If the official

gets caught, the bribe is discovered, and the official loses his wage Wk. Let the extorted

bribe per official be yk.

The probability that all other peers behave dishonestly is e = (pqk)nk1. Thus, the

officials decision is - request bribe if expected benefit of cheating is larger than expected

cost:

(yk + Wk)e + 0(1 e) Wk (9)

Solving for yk, this expression gives us the minimum amount of bribe per person the

official will extort:

ymink =Wkek

Wk =Wk

(pqk)nk1Wk (10)

The minimum amount of bribe the official will extort increases as their loss, Wk, in-

creases, and falls as the fraction of dishonest officials, p, increases.

4.2 The Good Applicants Decision

Next, we turn to the applicants decision. We model the good applicants decision sym-

metrically to the crooks decision. Assume that the value of a good project is G. Assume

a binomial distribution of good projects in the population, where a fraction g of the good

projects have a payoff value of GH and a fraction (1 g) have a payoff value of GL. Thus,

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the benefit of passing the application process for the good applicant is G, and the payoff of

not trying to pass is zero. The cost of being caught paying bribes and being punished is S.

The good applicant will pass free with probability g = Ki=1(pqi)ni if all officials cheat.

Thus, the good applicant will decide to pay a bribe if and only if his expected benefit minus

his expected cost is larger than his reservation utility of not applying, which is zero. So,

the good applicants decision is pass if

(G sumy)g S(1 g) 0 (11)

where sumy is the total amount of the extorted bribe paid to all officials. Solving for sumy,

this expression will give us the maximum amount of the total bribe the good applicant will

be willing to pay:

sumymax = G + SS

g= G + S

S

Ki=1(pqi)ni(12)

The maximum amount of bribe the good applicant will be willing to pay decreases as

their benefit G decreases, and as their cost S increases; and increases as the fraction of

dishonest officials p increases.

The existence of bribe extortion alters the distribution of good projects approaching

the bureaucracy in the first place by deterring good projects with low value. The fact that

the good applicant has to pay a bribe to get a license for a good project deters marginally

profitable good projects from approaching the bureaucracy. We assume that GH > G >

GL, where G is the solution to ymax(G) = ymin. Thus, bribery increases the cost of good

projects with value GL just enough to make them marginally unprofitable. So only goodprojects with high payoff, GH, will approach the bureaucracy in the first place. This is a

cost to having the bureaucracy in place.

Having the minimum amount of bribe the officials will ask for and the maximum amount

of bribe the good applicant will be willing to pay, allow us to look at the potential for

extortion in the organization, which depends on the organizational form and culture.

4.3 Corruptibility in the Case of Extortion

As long as sumymin sumymax, there will be extortion in this bureaucracy, as the amount

of bribe that the good applicant is willing to pay is more than the amount of bribe that theofficials ask for. The true amount of each bribe yk will be between y

min and ymax, and will

depend on the relative bargaining power of the good applicant and the official. Again, we

abstract from the questions of bargaining and we look at the more important question of

corruptibility as a measure of the potential for corrupt deals:

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Definition 2 We define corruptibility in the case of extortion as the distance between the

total maximum bribe the good applicant will be willing to pay, sumymax, and the total of the

minimum bribes the officials will demand, sumymin = Kk=1(nkymink ):

Corruptibility = sumymax sumymin

Corruptibility = G + SS

gKk=1[nk(

Wkek

Wk)]

where g = Ki=1(pqi)ni and ek = (pqk)

nk1.

Corruptibility in the case of extortion rises as the good applicants benefit G increases

and as the fraction of dishonest officials, p, increases; and falls as the loss to the official, Wk,

increases and as the loss to the good applicant if caught paying bribes, S, increases.Solving

for corruptibility equal to zero will give us the number of people in each level above which

extortion will be prevented (or minimized).It is intuitive to suppose that cooperative culture is more prone to extortion than is

competitive culture, and this will be consistent with the observations in reality that extortion

is primarily a problem in developing countries, for example India and the Philippines in

Asia, and Nigeria and Uganda in Africa, where family and ethnic ties are strong, and where

culture is likely to be cooperative. However, whether organizations with cooperative culture

are more corrupt than organizations with competitive culture all else equal, is an empirical

question.

Proposition 4.1 All else equal, the potential for collusion is less than the potential for

bribe extortion. However, assuming that the bargaining power of the official is defined by ,

where

=

xxmin

xmaxxminfor collusion

yymin

ymaxyminfor extortion

(13)

is a r.v. with density f() on the interval [0, 1], the average bribe observed in the case of

collusion will be larger than the average bribe observed in the case of extortion.

Examining the possibilities for collusion and extortion, we see that, for the same costs

and benefits of the good and the bad projects, sumxmax = sumymax, but xmink > ymink .

From the perspective of the applicants, the probability of a bad application not passingthrough is the same as the probability of a good application not passing through, since they

both have to clear the whole bureaucracy. However, from the perspective of the officials, the

probability of getting caught for collusion is higher than the probability of getting caught

for extortion. This is b ecause officials do not have to worry about being caught by their

superiors in the case of extortion as they do in the case of collusion.

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Thus, the average bribe observed under collusion will be larger than the average bribe

observed under extortion. This result is consistent with reality. The typical bribe extorted

by officials for processing good applications is relatively small. The huge bribes that make

the news headlines are typically given for illegal projects and are examples of collusion.

Moreover, if the benefits and punishments for collusion and extortion are the same, all

else is equal, the bureaucracy size needed to prevent extortion will be larger than the size

needed to prevent collusion. However, if the payoff from bad projects is higher than the

payoff from good projects, then the bureaucracy size needed to prevent extortion might be

smaller than the size needed to prevent collusion. For example, in a competitive economy

like the US, good projects are likely to be only marginally profitable compared to bad

projects. In this case, bureaucracy size could be large enough to deter extortion while still

not large enough to deter collusion. On the other hand, in a monopolistic economy like

India, returns on both good and bad projects might be quite large so that bureaucracy size

is not enough to deter neither extortion nor collusion, and we observe both.

4.3.1 Extortion, Culture and Organizational Shape

In this section we analyze the effect of the steepness of the organizational pyramid on ex-

tortion, and show how organizational shape can be used as a policy instrument for reducing

extortion. We use the extortion measure constructed above. In order to investigate how

shape matters, we compare different organizational shapes for organizations with the same

size. We start by comparing a steep versus a flat hierarchy.

The intuition that we developed in the case of collusion carries through in the case

of extortion. There are three major effects that distinguish a flat pyramid from a steeppyramid. The wage effect makes the steep pyramid more honest than the flat one as it

has a larger wage dispersion.

Figure 18

Effect on Extortion as the Organization Becomes Steeper

Effect Comp etitive Culture Coop erative Culture

Wage Effect (-) (-)

Probability Effect:

Geometry Effect (+) (+)Height Effect (+) (+)

Peer Pressure Effect (+) (-)

The probability effect makes the steep pyramid more corrupt as each official has fewer

peers and thus is less likely to get caught when cheating in the steep pyramid. The proba-

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bility of there being at least one official who behaves honestly in each level is lower in the

steep pyramid than it is in the flat pyramid as there is less monitoring. (This is true for all

officials in the steep pyramid, and unlike the case of collusion, both parts of the probability

effect - the geometry effect and the height effect - act to make the steep pyramid more

corrupt in the case of extortion).

Finally, the peer pressure effect makes the steep pyramid more corrupt under compet-

itive culture and more honest under cooperative culture as there are fewer peers and less

peer pressure in the steep pyramid compared to the flat one. Figure 18 shows the three

effects.

The magnitude of the wage effect depends on the size of wage dispersion, the magnitude

of the probability effect depends on the organizational shape and size, and the magnitude

of the peer pressure effect depends on the strength of peer relationships.

Proposition 4.2 For WKsteep < W and Ksteep

< K, where

W =K

flat

k=1 (nflatk n

steepk )W

flatk [

1

e,flatk

1)]

[Kflat

k=1 (nflatk n

steepk )][

1

e,steepK

1](14)

and where K is the solution to:

Kflat

i=1 [(pqflati )

nflati

(pqsteepi )nsteepi

] = Ki=Kflat+1(pqsteepi )

nsteepi (15)

under competitive culture, the flat pyramid is less prone to extortion than the steep one.

For 2Kflat

Ksteep

1, and

nk [(pqk)nk ] > 0, under cooperative culture, the steep

pyramid is less prone to extortion than the flat pyramid.

Under competitive culture, if wage dispersion is low enough and peer relationships are

important enough, the flat pyramid is less prone to bribe extortion than the steep one.

Under cooperative culture, however, if the geometry effect is strong enough and peer rela-

tionships are strong enough, the steep pyramid is less prone to bribe extortion than the flat

one. Thus, in settings where peer relationships are strong, a flat pyramid will be preferred

under competitive culture, and a steep pyramid will be preferred under cooperative culture

both in the case of collusion and in the case of bribe extortion.

Changing allows us to explore the effect of changing organizational shape as increas-

ing makes the organization flatter. In Figure 19 we plot extortion as a function of the

organizational shape and as a function of peer relationships for competitive culture. We see

that as increases and as peer relationships become more important extortion decreases.

Similarly, in Figure 20 we plot extortion as a function of the organizational shape and as a

function of the strength of peer relationships for cooperative culture. Here, we see that as

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increases and as peer relationships become more important extortion increases.

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4.3.2 Extortion, Culture and Organizational Size

In the previous section we discussed the effect of organizational shape on extortion. In

this section we explore the effect of increasing organizational size on extortion. We analyze

increasing organizational size by increasing n so that the number of officials in each level,nk = n

k, rises.

Proposition 4.3 Under competitive culture, a large pyramid is less prone to extortion than

a small pyramid.

Under cooperative culture, for nk

[(pqk)nk ] > 0 and nlarge1 nsmall andKlarge =

Ksmall.

Similar to the case of collusion, under competitive culture, if peer relationships areimportant enough, adding more officials to each level k reduces corruptibility in the case

of extortion. Adding more officials both increases the chances of there being at least one

official who behaves honestly, and induces more monitoring and more competition, thus

increasing the probability that the existing officials behave more honestly. In addition,

it provides more officials who potentially can extort bribes. Therefore, as size increases

corruptibility will fall. The effect is weaker for bribe extortion than for collusion since in

the case of extortion only the incentives of peers are affected, while in the case of collusion

the incentives of peer and inferior officials are affected.

Under cooperative culture, however, if peer relationships are important enough, adding

more officials eventually increases corruptibility in the case of extortion. Adding more

officials increases the chances of there being at least one official who behaves honestly,

but at the same time increases peer pressure on existing officials to behave less honestly,

and also adds more officials that can extort bribes. Thus, if peer relationships are strong

enough, increasing size might initially reduce corruptibility, but after a threshold, it will

start increasing it. Again, the effect of changing organizational size is weaker for bribe

extortion than for collusion.

Figures 21 and 22 show the opposite effect that increasing organizational size has on

corruptibility for extortion in the two cultural contexts. Under competitive culture, in

Figure 21, as size increases, the maximum bribe the applicant is willing to pay falls andthe total minimum bribes that officials require increases, thus corruptibility, which is the

distance between the two, falls. Under cooperative culture, in Figure 22, as size increases,

the maximum bribe the applicant is willing to pay rises and the total minimum bribes that

officials require fall, thus corruptibility increases.

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Therefore, organizational culture influences the relationship between organizational size

and corruptibility. If peer relationships are strong enough, under competitive culture, in-

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creasing organizational size reduces corruptibility both for collusion and for extortion, while

under cooperative culture, increasing organizational size eventually increases corruptibility

both for collusion and for extortion.

These results imply that, all else equal, the problem of extortion will be especially bad in

bureaucracies with cooperative culture which also have a large size, as in India for example.

They also suggest that a policy of downsizing will be appropriate in organizations with

cooperative culture and inappropriate in organizations with competitive culture with respect

to reducing corruption. Thus, contrary to popular criticism, the policy of downsizing as part

of civil service reform, frequently advocated by international institutions, is appropriate in

the context of developing countries where family and ethnic ties are strong, and the effect

of peer pressure is likely to be strong.

5 The Social Optimal Bureaucracy and Corruption

This section adds the last dimension to the analysis in the previous sections - the cost of

maintaining the bureaucracy. In reality, having a large bureaucracy is costly, so eliminating

corruption might not be optimal. In this section we explore societys problem of choosing

the optimal organizational shape and size, and the optimal level of corruption. We present

some comparative statics on the optimal organizational shape and size.

The task that the bureaucracy performs is screening applications. It approves good

applications, and it catches some bad ones. In the absence of bureaucracy there will be no

screening and all projects, both good and bad, will be carried out. Thus, the benefit to

society of having a bureaucracy in place is stopping some of the bad projects that apply for

license, and also deterring some of the bad projects from approaching the bureaucracy in

the first place. The cost of having the bureaucracy, however, is throwing out some of the

good projects when the good applicants get caught for paying bribes, and also deterring

some of the good projects from approaching the bureaucracy in the first place because of

the possibility of extortion. In addition, there is also the monetary cost of maintaining the

bureaucracy. Thus, societys problem is

Max (Expected benefit from bad projects not passing or not applying)2

(Exp. loss from good projects not passing or not applying + Exp. wage costs)2

Let the fraction of good projects in the population be , and the fraction of bad projects

be (1 ). Thus, the fraction of good applications that the bureaucracy actually receives

is g, and the fraction of bad applications is b(1 ). That is, the existence of extortion

within the bureaucracy deters the good projects that have low payoffs from applying for

a license in the first place, and similarly, having to pay a bribe to get a license for a bad

project deters bad projects with low payoffs from approaching the bureaucracy.

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Thus, the probability that the application approaching the bureaucracy is a good appli-

cation is g and the probability that the application approaching the bureaucracy is a bad

application is b, where

g = g

g + b(1 ), b =

b(1 )g + b(1 )

(16)

The probability that a bad application will get caught inside the bureaucracy is (1b) =

[1 Ki=1(pqi)ni], and the probability that a good application will get thrown out by the

bureaucracy because of extortion is (1 g) = [1Ki=1(pqi)ni ], where ni is the number of

officials in level i. Thus,

Expected benefit from bad projects not passing or not applying =

b(1 )(1 b)BH + (1 b)(1 )BL

Expected loss from good projects not passing or not applying =

g(1 g)GH + (1 g)GL

Assuming that wages are paid at the end of the game, each official will receive a wage

if they behave honestly, or if they cheat and everybody else also cheats. Thus,

Expected wage costs = Kk=1(nkWkQk) (17)

where nk is the number of officials in level k, Wk is the wage per official in level k, and Qk

is the probability with which wage will be paid.

The officials in level k are paid a wage with probability one if they behave honestly. If

the officials behave dishonestly in the case of bad applications, they are paid a wage if allpeers and superiors also b ehave dishonestly. Thus they are paid a wage with probability

bck, where

ck = (pqk)

nk1Ki=k+1(pqi)ni . If the officials behave dishonestly in the case of

good applications, they are paid a wage if all peers also behave dishonestly. Thus they are

paid a wage with probability gek, where

ek = (pqk)

nk1. Therefore, the probability of

paying the wage, Qk, equals the probability of behaving honestly, (1p) +p(1q), plus the

probability of behaving dishonestly, (pq), multiplied by the probability that the application

is bad and all peers and superiors cheat, bck, plus the probability that the application is

good and all peers also cheat, gek:

Qk = (1p) + p[(1 q) + q(bck + gek)] (18)

Therefore, societys problem is to maximize output with respect to N and nks:

Max [b(1)(1b)BH+(1b)(1)BL]

2[g(1

g)GH+(1g)GL+Kk=1nkWkQk]

2

(19)

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We solve for the social optimal organizational form numerically. We find that if running

the bureaucracy is costly, it is optimal to choose a bureaucracy size which is too low to pre-

vent corruption, thus the optimal amount of corruption is positive. This result is consistent

with the conventional wisdom in the corruption literature (e.g. Rose-Ackerman 1978, 1999)

and holds irrespective of culture.

Societys objective function allows us to look at how changing parameters of the model

affects the optimal organizational form and thus allows us to address the question of whether

reform policies have different effects depending on organizational form and culture.

5.1 Comparative Statics: The Optimal Organizational Shape

The monetary cost of maintaining the organization needs to be added to the comparative

analysis of organizational shapes in the previous sections, as this cost effect acts in addition

to the wage effect, the geometry effect and the peer pressure effect described before. In

general, the flatter the organizational pyramid, the cheaper it is to maintain.

Analyzing corruptibility in the previous sections, we found that in settings where peer

relationships are strong, that is the weight, , placed on peer officials relative to everybody

else is high, a flat pyramid is less corrupt both in the cases of collusion and extortion under

competitive culture, but a steep pyramid is less corrupt both in the cases of collusion and

extortion under cooperative culture.

Analyzing the social optimal shape, we find that if peer relationships are strong enough,

in the case of competitive culture, the social optimal shape is a one-level horizontal organi-

zation. This completely flat structure is the least corrupt and the cheapest shape.

On the other hand, if peer relationships are strong enough, in the case of cooperativeculture, the social optimal shape is a pyramid. Since adding officials to the same level

eventually starts increasing corruption, it becomes more efficient to break peer cooperation

and to add officials in upper levels. Under cooperative culture, there exists a trade-off

between cost and corruption: the steeper the pyramid, the less collusion and extortion

there is, but the higher the cost of maintaining the organization. Therefore, for lower wage

levels and low wage dispersion, the social optimal shape will be a steeper pyramid, while for

higher wages and high wage dispersion, the social optimal shape will be a flatter pyramid.

The optimal shape will never be completely vertical, that is having just one official per

level, since in a completely vertical structure extortion cannot be caught.These results are intuitive with respect to the kind of monitoring an organization wants

to use. Monitoring by peer officials is cheaper than monitoring by superior officials. In an

organizational culture where peer officials put pressure on each other to behave honestly,

peer monitoring is effective and is more cost-efficient. On the other hand, in an organi-

zational culture where peer officials put pressure on each other to behave corruptly, peer

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monitoring is ineffective, and the organization has to resort to monitoring by superiors even

though it is more costly.

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Figures 23 and 24 illustrate some of these trade-offs and the potential of using orga-

nizational shape as a policy instrument in fighting corruption. We show how output level

changes as the slope of the organizational pyramid changes and as the strength of peer

relationships changes for the cases of competitive and cooperative cultures respectively. We

see that increasing the strength of peer relationships has the effect of increasing output in

the case of competitive organizational culture and has the effect of decreasing output in the

case of cooperative organizational culture. Similarly, we see that under competitive culture,

increasing the steepness of the organizational pyramid has the effect of reducing output,

while under cooperative culture, increasing the steepness of the organizational pyramid has

the effect of increasing output. This results also point towards the importance of p olicies

that can reduce cooperation among employees in organizations with cooperative type cul-

ture such as job rotation, faster turnover, and faster promotion, and the use of undercover

operations in anti-corruption reforms.

5.2 Comparative Statics: The Optimal Organizational Size

Irrespective of culture, increasing the size of the organization always makes it more expensive

to maintain, so next we turn to the social optimal bureaucracy size. The comparative statics

are illustrated in Figure 25.

Intuitively, we find that irrespective of organizational culture, as wage levels and wage

dispersion increase the optimal bureaucracy size decreases. When wage levels or wage

dispersion are high, it is expensive to have a large bureaucracy, and thus the optimal

bureaucracy is small. On the other hand, when wage levels or wage dispersion are low, it

is cheaper to maintain a larger bureaucracy. Therefore, the optimal organization is large.Thus, it appears that reforming civil service by downsizing accompanied by decreases in

wage levels or wage dispersion will move organizations away from the optimal. Downsizing

will be appropriate only if accompanied by increases in wage levels and wage differentials.

Earlier reform efforts in developing countries happened in the context of the strict fiscal re-

quirements of World Bank and IMF programs. According to these results, it is not surprising

that reforms did not succeed in curbing corruption. In the past eight years or so, the focus

in the international organizations had shifted towards promoting downsizing accompanied

by increases in wage levels and wage dispersion. This seems to be an appropriate response

and we should expect more recent reforms to be more effective in fighting corruption.Similarly, as the fraction of honest officials p increases, the optimal organizational size

decreases. For high honesty level p, the optimal bureaucracy is small since the amount of

corruption that exists will be low and fewer people will be needed to prevent it. For low

honesty levels p, there will be a lot of corruption, and the organization required to prevent

it will be large.

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Lastly, as the potential loss from bad pro

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Corruption, Culture and Org-Form