How to Fight Corruption: Carrots and Sticks Dmitriy Knyazev

Abstract I present a model of corruption with incomplete information where the bureaucrat may request a bribe from the citizen for providing a service. Two anti-corruption policies are considered: punishments for bribes and rewards for reporting about bribes. It is shown that neither of these policies alone can defeat corruption. However, if these policies are used simultaneously in a proper way, they can fully prevent corruption. I also show that reducing bureaucracy is a vital part of anti-corruption policies.

Keywords: Corruption, bureaucracy, bribery, punishments, rewards. JEL Classi…cation Codes: D73, K42, H83. I would like to thank Daron Acemoglu, Benny Moldovanu, Tymon Tatur and the participants of PET 2015 conference for their useful discussion and comments. Financial support from the German Science Foundation (DFG) is gratefully acknowledged. Humboldt University of Berlin, [email protected]

1

1

Introduction

During recent decades, corruption has become a signi…cant problem for a vast number of countries across the world. Corruption is one of the main concerns not only in developing economies and economies in transition but also in developed countries. I start with several stories about countries that have been able to substantially reduce their level of corruption. Singapore is one of the least corrupted countries in the world. In the 21st century, it is consistently placed in top-ten least corrupted countries according to the Corruption Perception Index. However, this has not always been the case. Before obtaining independence in 1965, Singapore was a highly corrupted country with a large number of other institutional problems. How was one of the most corrupted countries able to achieve one of the lowest levels of corruption? The key element of the anti-corruption policy in Singapore was the Corrupt Practices Investigation Bureau (CPIB). It is the sole agency in Singapore responsible for …ghting corruption and directly accountable to the Prime Minister of Singapore. The CPIB was founded in 1952 and the Prevention of Corruption Act (PCA) — enacted in 1960 — provided strong instruments and freedom to CPIB in investigating corruption. CPIB o¢ cers have the right to arrest without a warrant any person independent of his social status and position in a society. Moreover, every citizen of Singapore can complain about corrupted o¢ cials to CPIB and obtain the service without paying bribes. Corrupted o¢ cials will be severely punished with a huge …ne and penitentiary imprisonment. These methods have proven very e¤ective and the Independent Commission Against Corruption (ICAC) was adopted after the CPIB in 1974 in Hong Kong. Due to the ICAC, Hong Kong was also able to substantially reduce its level of corruption. Nowadays, even though Singapore and Hong Kong are located in a very corrupted region, they do not have serious problems related to corruption. Singapore also rewards citizens who report tax evasion or fraud. A reward of 15% on tax recovered and capped at $100,000 is given if the provided information has led to the recovery of tax. These rewards create incentives for citizens to report "wrong" behavior of bureaucrats. Recently, some other countries — e.g. China and Kazakhstan — have also started paying money rewards for information about corruption cases.

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In this paper, I show that the possibility of reporting corrupted o¢ cials and obtaining rewards for it is indeed an e¤ective mechanism to prevent corruption in the case of harassment bribery. Harassment bribes are the bribes paid by citizens for services to which they are legally entitled. In this paper, I consider the situation in which an entrepreneur wants to implement some project and needs to obtain a permit for this project from the bureaucrat. The project is legally allowed to be implemented if the entrepreneur can prove that it is socially desirable, namely that it satis…es some criteria stated in the law. Thus, the legal objective of a bureaucrat is to check whether these conditions are met and give the permission in the case when the project is desirable and to reject this project otherwise. However, even if the entrepreneur can prove that the project is desirable, in many countries bureaucrats often request bribes for the permission despite the fact that they are obliged to provide it. The entrepreneur has to pay this bribe if he wants to implement his project. The important feature of such kind of corruption is that it is the bureaucrat who requests the bribe and not the citizen who o¤ers it. Thus, these two parties are not equally responsible for corruption, namely the bureaucrat bene…ts from corruption and the entrepreneur su¤ers from it. Hence, the entrepreneur would like to implement the project without paying a bribe. The idea of the paper is to provide the entrepreneur with an opportunity to report about corruption to a special anti-corruption agency like CPIB and eventually obtain the permission without paying the bribe. Instead of the entrepreneur and the project, one could think about a model with a more general setup where a citizen applies for some service and the value of the service is his private information. I describe a model in the entrepreneur project terms as the main application of the model. I show that if the government does not …ght corruption, then the equilibrium in our model implies a substantial level of corruption. Next, I consider several ways of preventing corruption: 1) punishments for the o¢ cial who takes and extorts bribes; 2) rewards for the entrepreneur for reporting about the corrupted o¢ cial; and 3) combination of punishments and rewards. I show that an increase in punishments has two e¤ects: the level of bribes in the equilibrium decreases, but the percentage of projects implemented through a bribe transfer increases. Moreover, it is not possible to defeat corruption with this policy. In turn, the policy of rewards reduces the percentage of corruption cases, although the e¤ect 3

on the level of a bribe depends on the hazard rate of the revenue distribution. If the hazard rate increases then the equilibrium bribe decreases, whereas if the hazard rate decreases then the equilibrium bribe increases. The main problem with this policy is the same as with punishments: rewards are unable to defeat corruption completely. Precisely, for any …nite reward, there exists a level of bribe such that there is a positive probability that the entrepreneur would agree to pay the bribe. However, I show that if the government decides to use punishments and rewards simultaneously, then this mixture can be much more e¤ective. I show that it can fully prevent corruption for any distribution of the project revenue. Modeling corruption through bribe giving dates back to Beck and Maher (1986) and Lien (1986). Basu (2011) argues informally that in the case of harassment bribes, the punishment should not be symmetric for both parties. His proposal is to legalize the giving of harassment bribes and return the bribe to the citizen if corruption is detected. This should provide incentives for a citizen to report about corruption after obtaining the service through bribery. This would deter the bureaucrat from demanding bribes. Dufwenberg and Spagnolo (2015) propose a formal game-theoretic model for Basu’s conjecture. They model bribery as a game with complete information where the bureaucrat can request a …xed exogenously given amount of money from a citizen. Their results suggest that in a one-shot interaction Basu’s proposal is not e¤ective, although it can help in the case of repeated interaction. Basu et al. (2016) complement Dufwenberg and Spagnolo (2015) endogenizing a bribe in a bargaining game. Oak (2015) endogenizes the bribe type and constructs a model where bribes can be either harassment or non-harassment. He shows that caution is necessary in applying Basu’s proposal because in the case of non-harassment bribes it can reduce social welfare without eliminating bribery. Abbink et al. (2014) conduct a laboratory experiment on harassment bribes and provide support for asymmetric punishment for the citizen and the bureaucrat. For the case of non-harassment bribes, where the citizen pays the bribe to the bureaucrat to take some illegal action, Burlando and Motta (2016) show that it is also possible to avoid corruption with a so-called tax-and-legalize scheme. This scheme allows the citizen to take the sanctioned action by paying a tax or a reduced …ne. In our model, punishments can only be applied to the one side, namely o¢ cials who request bribes. Basu et al. (1992) discusses the recursive problem of the following form: when an o¢ cial (policeman, 4

auditor, etc.) bargains over a bribe with an agent who he has just caught, he must take into account the fact that he may in turn be caught for taking this bribe and participate in the same bargaining process, but from the other side. Many papers concentrate on a relation between corruption and economic activity, such as Mauro (1995), Bardhan (1997) and Fisman and Svensson (2007). The Causes of corruption are discussed in Treisman (2000), Ades and Di Tella (1999) and Glaeser and Saks (2006). Institutional aspects of corruption are discussed in Acemoglu and Verdier (2000), Fisman and Gatti (2002), Mauro (1998), Schleifer and Vishny (1993) and Rose-Ackerman and Palifka (2016). The persistence of corruption is shown in Damania et al. (2004) and Tirole (1996). Based on a …eld experiment, Olken (2007) reports that government monitoring can substantially reduce corruption. Brunetti and Weder (2003) show that more press freedom leads to less corruption. My model di¤ers from the literature in several ways. First, I propose a model with incomplete information, where the value of the project is a private value of the entrepreneur. Second, the size of the requested bribe is optimally chosen by the bureaucrat when she obtains an application from the entrepreneur and this bribe can be adjusted to anti-corruption policies. Thus, I characterize how the size of the bribe in equilibrium responds to di¤erent anti-corruption measures. The assumption that bureaucrats can choose bribes is supported by Svensson (2003), who shows that bureaucrats act often as bribe discriminators and request di¤erent bribes from di¤erent entrepreneurs. In my model, there are two parameters that I treat as measures of bureaucracy. The …rst one, T; re‡ects the costs incurred by the entrepreneur to prove that the project is socially desirable while applying for a permit. It can incorporate the time and money spent on preparation of documents. The second parameter,

, re‡ects the costs incurred by the

entrepreneur when he rejects giving a bribe and reports about bribery to an anti-corruption agency (like CPIB). In this case, since the project is still socially desirable, the project is still implemented, albeit with a delay. Hence, the project revenue is generated later and has to be discounted by (1

): The higher values of these parameters re‡ect the higher

level of bureaucracy. My results suggest two positive e¤ects from a decrease in the level of bureaucracy: …rst, a decrease of corruption itself; and second, lower bureaucracy levels make 5

it easier to …ght corruption. Thus, reducing the level of bureaucracy should be an important part of anti-corruption policies. The remainder of this paper is structured as follows. In the next section, I present the model. Then, I describe the solution without anti-corruption policies. Section 4 discusses the policy of punishment. Section 5 deals with the policy of rewards. In section 6, I combine both policies together. In section 7, I discuss the relation between bureaucracy and corruption. Section 8 concludes the paper.

2

Model

There are two sides, called the entrepreneur (he) and the o¢ cial (she). The entrepreneur has a project that could be implemented. In order to implement the project, he has to apply for a permission from the o¢ cial. The expected net revenue from implementation R is distributed on ( 1; +1) according to a continuously di¤erentiable distribution F and f (x) = F 0 (x) 6= 0 for any x: The project is either socially desirable or not. The revenue of the project and its social desirability are independent and both are private information of the entrepreneur. However, the social desirability of the project is veri…able. It costs T > 0 for the entrepreneur to prove that his project is socially desirable. I concentrate on those types of entrepreneurs who have socially desirable projects. Legally, all project proved to be socially desirable can be implemented. Thus, once the o¢ cial receives an application from the entrepreneur with a socially desirable project, legally she should give the permission. However, in this case, the o¢ cial can decide whether to give the permission immediately (p) or request a bribe (b), namely some monetary transfer b from The entrepreneur to the o¢ cial. If the bribe b is requested, the entrepreneur can take one of two actions: …rst, he can agree to give the bribe (g), whereby in this case the project is implemented immediately; and alternatively, instead of giving a bribe, the entrepreneur can report about the o¢ cial to the anti-corruption agency (r), whereby in this case the project is implemented without paying a bribe, albeit with a delay. Thus, the value of the project is discounted by (1 0<

< 1. Hence, instead of R; the entrepreneur expects to receive (1

about bribery. 6

);

)R if he reports

All agents are rational. The size of the requested bribe b is chosen by the o¢ cial in the optimal way to maximize her expected utility. The entrepreneur with an e¢ cient project expects that the o¢ cial can request a bribe and chooses optimally whether to apply for the permission and spend the cost T or not to incur any costs and not to apply at all. If the entrepreneur does not apply for the permission, he obtains zero reservation utility. If he applies, the payo¤ matrix is as follows1 : O¢ cial p Entrepreneur r

R

g R

b

T; 0 R(1 T; 0

R

) T

T; 0 b; b

The timing of the model is as follows: 1) The entrepreneur decides whether to apply or not. 2) The o¢ cial decides whether to request the bribe or not. If the o¢ cial requests the bribe, she also chooses the size of the bribe b: 3) If the bribe b is requested, the entrepreneur decides whether to pay the bribe or report. In order to obtain clear and analytically tractable results, we make the following technical assumptions. De…ne the hazard rate of the revenue distribution F as the inverse hazard rate hF (x) := 1= (x) =

1 F (x) : f (x)

F (x)

:=

f (x) 1 F (x)

and

We assume that the functions x + y and

hF (x) are single-crossing for any y 2 R. Namely, for any y, there exist at most one x

0

such that x + y = hF (x ); x + y < hF (x) for all x < x and x + y > hF (x) for all x > x . If for some y 2 R such a point does not exist, then it has to be the case that x + y > hF (x) for any x

0 because x+y can be in…nitely high for large x. We also de…ne 'F (x) := x hF (x).

The single-crossing condition does not imply that the function 'F (x) is invertible. However, for any x; we can de…ne 'F 1 (x) := maxfz : 'F (z) = xg: If this maximum does not exist, we set 'F 1 (x)

0:

1

One could think that " T " is redundant because it presents in every matrix …eld. However, this payo¤ matrix is relevant for the cases when the entrepreneur has already applied for the permission and …nds it bene…cial to spend the cost T on the application process.

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3

Solution without anti-corruption policies

I solve the model by backward induction. If the entrepreneur has applied and the o¢ cial has requested a bribe, it is optimal for the entrepreneur to pay if the gain from the immediate implementation is greater than the gain from the delayed implementation: R

T

b

R(1

)

(1)

T:

Thus, the entrepreneur would agree to pay the bribe if the expected revenue is su¢ ciently high, namely R

b

: Intuitively, if the entrepreneur has a project with a low expected

revenue, the …xed monetary loss from paying a bribe is greater than the loss due to the delay when he reports about the corrupted o¢ cial. On the other hand, if the project can generate a high revenue, it is bene…cial to pay the bribe and implement the project immediately. Denote G(x) as the revenue distribution of those projects with which the entrepreneur applies for the permission in equilibrium. This distribution is endogenously determined in the model. However, since the o¢ cial chooses the amount of the bribe after the entrepreneur has applied, she takes the distribution G(x) as given. If the bribe b is requested, then the probability that the entrepreneur would agree to pay it is equal to 1

G( b ): Hence, the

optimal bribe can be found from the following maximization problem:

b = arg max(1 b 0

b G( ))b:

(2)

The solution concept is a subgame perfect equilibrium. The next result characterizes the equilibrium without anti-corruption policies. Proposition 1 In equilibrium: 1) The o¢ cial requests a bribe b = maxf T

T 1

; 'F 1 (0)g:

2) The entrepreneur applies i¤ R

1

3) The entrepreneur pays b i¤ R

maxf 1 T ; 'F 1 (0)g:

:

8

Proof. see Appendix. T

The entrepreneur applies for the permission if and only if R

1

. If the value of cost T

)'F 1 (0); then the entrepreneur who applies already has

is su¢ ciently high, namely T > (1

a project of high quality. In this case, is it optimal for the o¢ cial to request the highest bribe such that the entrepreneur would always agree to pay, i.e.

T 1

. If T < (1

)'F 1 (0), then

the entrepreneur will also apply for the permission to implement less pro…table projects. In this case, the o¢ cial sets the bribe in such a way that the entrepreneur reports about bribery for R 2 [ 1 T ; 'F 1 (0)) and pays the bribe for R

'F 1 (0): The distribution of projects with

which the entrepreneur would like to apply is T

G(x) = F (xjx

)=

1

8 < :

0; x < F (x) F ( 1 T ) 1 F(1

T

)

T 1

; x

T 1

9 = ;

.

In the …rst-best without corruption, all socially bene…cial projects with R

T would be

implemented. Hence, corruption brings additional loss to e¢ ciency because only projects with R

T 1

are implemented.

In the next sections, we analyze the e¤ects of anti-corruption policies on the level of corruption. In our model, we de…ne two measures of corruption: 1) the total sum of bribes (m1 ), and 2) the probability of a bribe payment (m2 ). The …rst measure re‡ects the total amount of money paid as bribes in the economy. The second measure neglects the value of bribes but re‡ects the number of bribes. Thus, m1 = b (1

F(

m2 = 1

4

b

)) = 'F 1 (0)(1

G(

b

)=

1

F ('F 1 (0)) > 0;

F ('F 1 (0)) > 0: 1 F ( 1T )

Punishment

Suppose now that the government wants to …ght corruption and sets a punishment p for the o¢ cial who is caught engaging in bribery. This punishment can be implemented through a

9

monetary …ne, a prison sentence, etc. The new payo¤ matrix looks as follows:

Entrepreneur r

O¢ cial p

b

R

)

g R

T; 0 R(1 T; 0

R

T; p

T

b; b

Intuitively, we can expect that the law introducing such kinds of punishments should reduce the level of corruption. The o¢ cial should be afraid of being punished and this should prevent her from requesting bribes. However, I show below that the punishment is not that e¤ective. Although a punishment can lead to a decrease in the optimal bribe, it cannot prevent corruption completely. We start by calculating the optimal level of a bribe in this case. Since the o¢ cial incurs losses p when caught, the o¢ cial’s problem looks as follows: b G( ))b

b = arg max[(1 b 0

b pG( )]:

The next result characterizes the equilibrium under the policy of punishments. Proposition 2 In equilibrium under punishment: 1) The o¢ cial requests a bribe b = maxf

T 1

T

; 'F 1 (

2) The entrepreneur applies i¤ R

1

3) The entrepreneur pays b i¤ R

maxf 1 T ; 'F 1 (

p

(3)

)g:

: p

)g:

Proof. see Appendix. Again, only entrepreneurs with R >

T 1

apply for the permission. Thus, punishment on

the o¢ cial in equilibrium does not a¤ect the application behavior of the entrepreneur. One can notice that the o¢ cial can always request a bribe at least b =

T 1

and the entrepreneur

always agrees to pay this bribe provided that he has already applied for the permission. Thus, regardless how severe the punishment is, the o¢ cial asks for a strictly positive bribe 10

in equilibrium. To show the comparative statics of b with respect to the punishment level p, I formulate the following result. Corollary 1 When the punishment increases, the optimal bribe decreases until it reaches T 1

: Afterwards, it remains at a constant level.

Proof. Since the function '(x) is increasing, the inverse function is also increasing. Thus, the increase of p will reduce the value of the argument of the function ' 1 : Since b is chosen as a maximum of

T 1

and 'F 1 (

p

); the optimal bribe decreases until it reaches

T 1

.

The intuition here is as follows: when the punishment increases, the o¢ cial reduces the required bribe, which reduces the probability that the entrepreneur reports. This bribe reduction continues until the bribe is set at the level whereby the entrepreneur is always ready to give the bribe, namely b =

T 1

. This level is positive because due to the application cost

T; The entrepreneur would only apply with projects that can generate substantially high revenue. Hence, for any su¢ ciently small bribe, the entrepreneur would prefer to pay it rather than reporting about it. In this case, even for the huge punishment, the o¢ cial is not afraid of it because she is never punished in equilibrium. Thus, we obtain the following result: Corollary 2 The policy of punishments is unable to prevent corruption. This result suggests that the elimination of corruption is not achievable with the punishment policy. Nevertheless, the level of bribes can be decreased, as follows from Corollary 1. The next proposition shows how the increase in the punishment a¤ects the corruption measures. Proposition 3 Under the punishment policy, m1 (p) is a non-increasing function and m2 (p) is a non-decreasing function. Proof. see Appendix. Hence, we conclude that the total sum of bribes decreases, but at the same time the number of bribes increases with an increase of punishment. The o¢ cial requests smaller bribes, although they are paid more often. 11

5

Rewards

Here, I consider another possible government policy against corruption, which provides incentives for the entrepreneur to report about bribery. When The entrepreneur is requested to pay a bribe and reports about it, due to this policy he obtains a reward r: The payo¤ matrix looks as follows: O¢ cial p Entrepreneur r

R

g R

b

T; 0 R(1

)+r

T; 0

T

R

T; 0

b; b

Under the policy of rewards, the entrepreneur agrees to pay the bribe i¤

R

T

b

R(1

)

b+r

Thus, the entrepreneur gives the bribe i¤ R

T + r:

(4)

: The optimal bribe is the solution to the

following problem:

b = arg max[(1 b 0

G(

b+r

))b]:

The next result characterizes the equilibrium under the policy of rewards. Proposition 4 In equilibrium under rewards: 1) The o¢ cial requests a bribe b = maxf

T 1

r

r ; r + 'F 1 ( )g:

2) The entrepreneur applies i¤ R

T r : 1

3) The entrepreneur pays b i¤ R

maxf T1

r

(5)

; 'F 1 ( r )g:

Proof. see Appendix. Since the entrepreneur obtains r when he reports, the set of projects for which the entrepreneur would obtain the permission is larger. Now, the entrepreneur would apply if and 12

T r ; 1

only if R with R

T 1

while without any reward the entrepreneur would only apply with projects

: The comparative statics of the optimal bribe with respect to the announced

reward is more complicated than the comparative statics in the case of punishments. The next result shows that it depends on the hazard rate of the revenue distribution. Proposition 5 1) If 2) If

F (x)

F (x)

is non-decreasing, then b (r) is non-increasing.

is non-increasing, then there exists a value r such that for all b (r) is non-

decreasing for all r > r . Proof. see Appendix. The surprising result is that for the decreasing hazard rate and su¢ ciently large values of r; the optimal bribe is increasing. In this case, larger rewards will lead to the higher equilibrium level of bribes in the economy. In order to prevent the bribe-taking behavior of the o¢ cial, the reward for the entrepreneur has to be such that b

0: However, it turns out that the optimal bribe is positive

for any value of the reward because the second part of (5) is always positive. Thus, we can formulate the following proposition. Corollary 3 The policy of rewards is unable to defeat corruption. Proof. There is no corruption in equilibrium if and only if it is possible to …nd such a value of r that implies b

0: It is possible to make the …rst term of (5) less than or equal to zero by

imposing a su¢ ciently high reward r we should have

r

T: However, in order to satisfy

'F ( r ): Since 'F ( r ) =

r

r + 'F 1 ( r )

hF ( r ); we must have hF ( r )

0;

0; which is

impossible. The policy of rewards is unable to prevent corruption. However, there are some positive e¤ects of this policy. First, the share of projects that are implemented increases with r. Namely, all e¢ cient projects with R >

T r 1

are implemented. The next result shows that

both corruption measures are also non-increasing. Proposition 6 1) m2 (r) is a non-increasing function of r: 2) There exists r > 0; such that m1 (r) is a decreasing function for any r > r . 13

Proof. see Appendix. r depends on the bureaucracy measures

and T: The lower the values of

and T ,

the lower the value of r . Hence, decreasing bureaucracy makes the rewards policy more e¤ective. However, a substantial amount of money may be required from the budget to pay the rewards.

6

Combination of punishment and rewards

I have shown that neither the policy of punishments nor the policy of rewards separately is able to prevent corruption. In this section, I show that the proper combination of these policies can defeat corruption. If the government can use punishments and rewards simultaneously, the payo¤ matrix when the entrepreneur applies looks as follows: O¢ cial p Entrepreneur r

R

g R

b

T; 0 R(1 T; 0

)+r R

T

T; p b; b

The optimal bribe requested by o¢ cial is determined as the solution to the following problem:

b = arg max[(1 b 0

G(

b+r

))b

pG(

b+

)]:

The next result characterizes the equilibrium under the joint policy of punishments and rewards. Proposition 7 In equilibrium under punishment and rewards: 1) The o¢ cial requests a bribe b = maxf

T 1

r

; r + 'F 1 (

2) The entrepreneur applies i¤ R

T r : 1

3) The entrepreneur pays b i¤ R

maxf T1 14

r

; 'F 1 ( r

r

p

p

)g:

); 0g:

(6)

Proof. see Appendix. The next result provides necessary and su¢ cient conditions for values p; r such that the equilibrium level of corruption is 0. In this case, it is not pro…table for the o¢ cial to request any positive bribe. Hence, such a combination of punishments and rewards implies a zero level of corruption in equilibrium. Proposition 8 Any combination of punishments and rewards (p; r) such that r

T and

hF ( r ) is able to sustain a zero level of corruption in equilibrium. This inequality always

p

has a continuum of solutions in terms of (p; r): Proof. see Appendix For any values (p; r) such that r

T and p

hF ( r ); the entrepreneur would agree

to pay a bribe, but the o¢ cial never requests it. All projects with R

T are implemented.

Moreover, this scheme does not require paying rewards in equilibrium because the o¢ cial never requests a bribe and the right upper corner of the payo¤ matrix is never on the equilibrium path. Since the range of solutions to this inequality is in…nite, there is no need to …nd any speci…c values. The government needs to promise a high reward r greater than T and impose a su¢ ciently high punishment p; greater than

hF ( r ): I also notice that

these conditions are only su¢ cient, not necessary. In order to obtain necessary conditions, one has to …nd values (p; r) such that the solution to problem (6) is zero. In this case, it would be optimal for the o¢ cial not to request a bribe.

7

Bureaucracy and corruption

In this section, I discuss the relation between bureaucracy and corruption and explain how the reduced bureaucracy can help to …ght corruption. In this paper, there are two parameters responsible for bureaucracy, T and : Based on the previous discussion, we can formulate the following results: Only projects with R >

T r 1

are implemented. Hence, the lower the values of T and

, the more projects that are implemented in equilibrium. 15

The value of the optimal bribe is not smaller than when If

T r : 1

This expression goes down

or T decrease.

= 0, the entrepreneur loses nothing from reporting about the corrupted o¢ cial.

Then, there is no corruption even without anti-corruption policies. Indeed, the entrepreneur never agrees to give any bribe that is greater than zero. If T = 0; the entrepreneur does not incur any costs from applying for permission and applies with every project. Then, it is possible to prevent corruption through the policy of punishments. In this case, an increase of punishment will lead to a decrease of the optimal bribe until it reaches 0. The policy of rewards is still unable to defeat corruption. Summarizing, we obtain the following proposition: Proposition 9 The lower that bureaucracy is, the lower that corruption is. At the same time, …ghting corruption is more e¤ective under a lower level of bureaucracy. Now, I provide some empirical evidence on the relationship between corruption and bureaucracy. I use the Corruption Perception Index published by Transparency International as a measure of corruption (higher values of the index indicate less corruption) and Doing Business published by the World Bank to measure bureaucracy. I take "the total number of days required to build a warehouse" as a proxy for bureaucracy (higher values of the index indicate higher bureaucracy). Our sample includes 167 countries. I measure the correlation between corruption and bureaucracy using Spearman’s rank correlation coe¢ cient2 . The coe¢ cient of correlation equals -0.28 and the p-value is 0.00023 . Thus, there is indeed a strong positive correlation between corruption and bureaucracy, which supports the results of my model. 2

Simply looking for correlation in levels would be incorrect because all indices do not measure absolute values, but only relative ranking. 3 The correlation coe¢ cient and the p-value are computed for values of the indices in 2013. The signi…cant positive correlation between bureaucracy and corruption is also found for other years and other proxies for bureaucracy obtained from Doing Business.

16

8

Conclusion

In this paper, I have constructed a model of corruption with two counterparts: an o¢ cial and an entrepreneur. The entrepreneur has a project with privately-known expected revenue, but in order to implement it he has to obtain the permission from the o¢ cial. I have shown that if the government does not …ght corruption, then the equilibrium implies the substantial level of corruption, namely the o¢ cial always requires a bribe and the entrepreneur often gives the bribe. Then, I discuss several government policies to prevent corruption, namely punishments for the o¢ cial for requesting bribes, rewards for the entrepreneur for reporting about bribery and a mixture of both. It emerges that none of these policies applied separately can prevent corruption. Moreover, under the punishments policy the share of cases ending with giving bribes will be even higher than in the case without anti-corruption policies. Under the rewards policy, the equilibrium bribe may increase if the hazard rate of the project distribution decreases. However, I show that there always exists a combination of punishments and rewards that prevents corruption. If the reward is su¢ ciently large and the punishment is even larger, then it would be non-pro…table for the o¢ cial to request a bribe. Hence, there would be no corruption in equilibrium under the joint policy of punishments and rewards. My results also suggest that a reduced bureaucracy level also leads to reduced corruption. At the same time, it is easier to …ght corruption under the lower level of bureaucracy. In this paper, I have considered the situation in which the bureaucrat requests a bribe from the citizen for the service to which the citizen is entitled. However, one could think about the situation where the citizen o¤ers a bribe to obtain a service that he is not legally supposed to obtain. In this case, the roles of the sides are switched and the bureaucrat needs to be rewarded for rejecting a bribe and the citizen has to be punished for o¤ering a bribe. I believe that a proper combination of punishments and rewards can also prevent this type of corruption. This is a question for future research.

17

9

Appendix

Proof of Proposition 1 b

From (1), it follows in equilibrium that the entrepreneur agrees to pay the bribe i¤ R

.

b Then, it is not optimal to request b < bb; where bb is the highest number such that G( b ) = 0:

If the solution is interior and b > bb; then it satis…es the following F.O.C.: 1 Hence, 0=

b

1

G(

b

)

g(

b b ) = 0:

G( b ) b = b g( )

hG (

b

) = 'G (

b

(7)

):

Assume that hG (:) satis…es the single-crossing property. Below, we show that it is true when hF (:) satis…es it. Then, in the interior case, the solution to (7) is b = 'G1 (0). Thus, the solution to the initial problem is b = maxfbb; 'G1 (0)g:

The entrepreneur rationally expects that o¢ cial requests b . Hence, only the entrepreneur with a su¢ ciently good project will apply. Namely, the entrepreneur will apply if the expected revenue of his project is such that R(1 entrepreneur applies i¤ R

)

T

0 or R

T

b

0: Thus, the

minf 1 T ; T + b g. To continue the proof, I make the following

claim. Claim 1 T + b

T 1

.

Proof. Assume by contradiction that T + b < b

: Thus, if the entrepreneur applies, R

T 1

: Rearranging the terms implies T + b >

minf 1 T ; T + b g = T + b >

b

: Hence G( b ) = 0:

However, if the o¢ cial increases a bribe by a small " > 0 such that T + b + " > still holds that G( b

+"

b +"

; it

) = 0: Such an increase of the requested bribe does not reduce the

probability of paying it. Hence, the o¢ cial can increase her utility and b is not optimal.

18

. Hence, bb =

T

Thus, the entrepreneur applies if and only if R

1

T 1

: The distribution

of the projects with which the entrepreneur would apply is T

G(x) = F (xjx

For x >

T 1

)=

1

8 < :

0; x < F (x) F ( 1 T ) 1 F(1

T

)

9 =

T 1

; x

;

T 1

:

; the hazard rates of distributions G(x) and F (x) coincide because f (x)=(1 F ( 1 T )) g(x) f (x) = = : T 1 G(x) 1 F (x) (1 F (x))=(1 F ( 1 ))

Hence, if F (:) satis…es the single-crossing condition, then G(:) also does. Thus, b = maxfbb; 'G1 (0)g = maxf

T

; 'F 1 (0)g:

1

The entrepreneur prefers to give the bribe i¤ R

= maxf 1 T ; 'F 1 (0)g:

b

Proof of Proposition 2 As in the proof of Proposition 1, we can immediately notice that it is not optimal to b

request b < bb; where bb is the highest number such that G( b ) = 0: If the solution is interior and b > bb; then it satis…es the following F.O.C.: 1

G(

Hence, p

=

b

1

b

)

g(

b b +p ) = 0:

G( b ) b = b g( )

hG (

b

) = 'G (

b

):

Again, assume for a moment that in this case hG (:) also satis…es the single-crossing property. Then, we obtain for the interior case b = 'G1 (

p

):

Thus, b = maxfbb; 'G1 (

p

)g:

Using similar arguments as in Proposition 1, the entrepreneur will apply only with the

19

. Hence, bb =

T

projects that generate revenue R >

1

p

= maxf 1 T ; 'G1 (

b

entrepreneur agrees to give b i¤ R

and 'G1 (

T 1

p

) = 'F 1 (

p

): The

)g:This …nishes the proof.

Proof of Proposition 3 If T

)'F 1 (0); then expression (3) implies that an increase of p changes nothing in

(1

)'F 1 (0):

the behavior of both sides. Hence, consider the case with T < (1 'F ( 1 T ); the following holds:

Then, for all values of 0 < p <

= =

p

'F 1 (

@ @m1 (p) = @p

1 @'F @x @'F @x

p

1

('F ( p

f ('F 1 ( 1

('F (

@m2 (p) = @p

p

)(1 F ('F 1 ( @p

)

p

@

))

))

))) p

F ('F 1 (

(1

p

1

('F ('F (

1 F ('F 1 ( p )) 1 F ( 1T )

@p

= )) + 'F 1 (

p

p

p f ('F 1 (

))) =

@'F @x

)

p

1

('F (

f ('F 1 ( p )) ( 1 F ( 1T )

=

) ( f ('F 1 (

))

p

1 @'F @x

('F 1 (

p

< 0;

1 @'F @x

))(

('F 1 (

p

))

) > 0:

Proof of Proposition 4 From (4), it follows in equilibrium that the entrepreneur agrees to pay the bribe i¤ R b +r b

. Hence, it is not optimal to set b < bb; where bb is the highest number such that

G( b+r ) = 0: If the solution is interior and b > bb; then it satis…es the following F.O.C.: 1

G(

b +r

)

g(

b +r b ) = 0:

Then, hG (

b +r

)=

b

=

b +r

or

'G (

b +r

20

)=

r

:

r

;

))

)=

Assuming as earlier in the proofs of Propositions 1 and 2 that hG (:) satis…es the singlecrossing property, we obtain for the interior case b =

r + 'G1 ( r ):

Thus, r b = maxfbb; r + 'G1 ( )g:

Using similar arguments as in Proposition 1, the entrepreneur will apply only with the projects that can generate revenue R > Entrepreneur applies i¤ R

b +r

T r : 1

= maxf T1

r

Hence, bb =

T r 1

and 'G1 ( r ) = 'F 1 ( r ):

; 'G1 ( r )g: This gives the statement of the

proposition. Proof of Proposition 5 Notice that

T r 1

in (5) decreases with an increase in r: We now study the behavior of

r + 'F 1 ( r ): Its derivative with respect to r is as follows:

1+

1 @'F @x

('F 1 ( r ))

=

1+

From the proof of Proposition 3, hF ( b

1 = @hF ('F 1 ( r )) 1 @x

1 +r

)=

b

: Hence, 'F ( b

@hF ('F 1 ( r )) @x : @hF ('F 1 ( r )) @x +r

) = r : The single-crossing

property implies that @hF @hF b + r r ('F 1 ( )) = ( ) < 1: @x @x Thus, if the hazard rate is non-decreasing, then the inverse hazard rate is non-increasing, so

@hF @x

('F 1 ( r ))

0: Hence,

r+ 'F 1 ( r ) is non-increasing. In this case, b = maxf

T r ; 1

r+

'F 1 ( r )g is also non-increasing as a maximum from two non-increasing functions. If the hazard rate is non-increasing, then will exist a value r

r + 'F 1 ( r ) is non-decreasing. Thus, there

0 such that for all r > r the following holds:

r + 'F 1 ( r ) >

Thus, for r > r the optimal bribe will be a non-decreasing function of r: Proof of Proposition 6 With rewards, the corruption measures have the following form:

21

T r : 1

m1 = b (1 m2 = 1

F( G(

b +r

b +r

));

): T r 1

We start by analyzing the e¤ect of an increase in the reward r on m2 : If

>

r+

'F 1 ( r ); then by Proposition 4, if the entrepreneur applies, he is ready to give a bribe and G( b

+r

If

) = 0: Hence, an increase in r does not a¤ect m2 . r + 'F 1 ( r ); then we can obtain from Proposition 1 and Proposition 4:

T r 1

1

G(

b +r

)=

1

F ('F 1 ( r )) : 1 F ( T1 r )

Hence,

@m2 (r) = @r

@

1 F ('F 1 ( r )) 1 F(T 1

r

f ('F 1 ( r )) 1

)

=

@r

1

1 ('F 1 ( r )) F ( T1 r ) @'F @r

(1

F ('F 1 ( r ))) 1 1 f ( T1 (1

F ( T1 r ))2

r

)

< 0:

The last inequality is due to the single-crossing property. Now, we compute the derivative of m1 with respect to r: Take r : If r

r ; then b =

r + 'F 1 ( r ) and hF ( b

+r

)

b

T r 1

r + 'F 1 ( r ):

= 0: In this case,

+1 @m1 (r) @b b +r b + r @b = (1 F ( )) b f ( ) @r = @r @r b +r b b + r @b b +r b b = f( ) (hF ( ) ) = f( ) < 0: @r For r < r ; the sign of

@m1 (r) @r

depends on the revenue distribution of F (x) and cannot be

identi…ed without making additional assumptions. Proof of Proposition 7 As in the proof of Proposition 4, we can immediately notice that it is not optimal to b request b < bb; where bb is the highest number such that G( b+r ) = 0: If the solution is interior

22

and b > bb, then it satis…es the following F.O.C.: 1

G(

Rearranging the terms, hG ( b

b +r

+r

)=

)

g(

b +p

b +r b +p ) = 0:

or 'G ( b

+r

)=

r p

: Assuming as earlier in the

proofs of Propositions 1, 2 and 4 that hG (:) satis…es the single-crossing property, we obtain r + ' 1( r

for the interior case b =

p

):

Thus, r b = maxfbb; r + 'G1 (

p

); 0g:

Using similar arguments as in Proposition 1, the entrepreneur will apply only those projects that generate revenue R >

T r . 1

Entrepreneur agrees to give b i¤ R

b +r

Hence, bb =

= maxf T1

r

T r 1

; 'G1 ( r

p

and 'G1 ( r

p

) = 'F 1 ( r

p

):

)g: This gives the statement

of the proposition. Proof of Proposition 8 I will show that if r

p

T and

hF ( r ); then the optimal bribe is zero. Hence, it cannot

be optimal for the o¢ cial to request a bribe, and there will be no corruption in equilibrium. From (6), we need

T r 1

0 and

r + 'F 1 ( r

p

0 to have the optimal bribe equal to

)

zero. If r 'F 1 ( r

T; we immediately see that p

) > 0: Then,

r p

T r 1

0: Suppose, by contradiction, that

> 'F ( r ): Since 'F ( r ) =

Rearranging terms, we obtain

p

r

hF ( r ); we have

r p

>

r

r+

hF ( r ):

< hF ( r ): Thus, we obtain a contradiction. Hence, the

optimal bribe is zero.

10

References

1. Abbink, K., Dasgupta, U., Gangadharan, L., and Jain, T. (2014). "Letting the briber go free: an experiment on mitigating harassment bribes." Journal of Public Economics, 111, 17-28.

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2. Acemoglu, D., and Verdier, T. (2000). "The choice between market failures and corruption." The American Economic Review, 90(1), 194-211. 3. Ades, A., and Di Tella, R. (1999). "Rents, competition, and corruption." The American Economic Review, 89(4), 982-993. 4. Bardhan, P. (1997). "Corruption and development: a review of issues." Journal of Economic Literature, 35(3), 1320-1346. 5. Basu, K. (2011). "Why, for a Class of Bribes, the Act of Giving a Bribe should be Treated as Legal." Mimeo. 6. Basu, K., Basu, K., and Cordella, T. (2016). "Asymmetric punishment as an instrument of corruption control." Journal of Public Economic Theory, 18(6), 831-856. 7. Basu, K., Bhattacharya, S., and Mishra, A. (1992). "Notes on Bribery and the Control of Corruption." Journal of Public Economics, 48(3), 349-359. 8. Beck, P. J., and Maher, M. W. (1986). "A comparison of bribery and bidding in thin markets." Economics Letters, 20(1), 1-5. 9. Brunetti, A., and Weder, B. (2003). "A free press is bad news for corruption." Journal of Public Economics, 87(7), 1801-1824. 10. Burlando, A., and Motta, A. (2016). "Legalize, tax, and deter: Optimal enforcement policies for corruptible o¢ cials." Journal of Development Economics, 118, 207-215. 11. Damania, R., Fredriksson, P. G., and Mani, M. (2004). "The persistence of corruption and regulatory compliance failures: theory and evidence." Public Choice, 121(3), 363390. 12. Dufwenberg, M., and Spagnolo, G. (2015). "Legalizing bribe giving." Economic Inquiry, 53(2), 836-853. 13. Fisman, R., and Gatti, R. (2002). "Decentralization and corruption: evidence across countries." Journal of Public Economics, 83(3), 325-345. 24

14. Fisman, R., and Svensson, J. (2007). "Are corruption and taxation really harmful to growth? Firm level evidence." Journal of Development Economics, 83(1), 63-75. 15. Glaeser, E. L., and Saks, R. E. (2006). "Corruption in America." Journal of Public Economics, 90(6), 1053-1072. 16. Lien, D. H. D. (1986). "A note on competitive bribery games." Economics Letters, 22(4), 337-341. 17. Mauro, P. (1995). "Corruption and growth." The Quarterly Journal of Economics, 110(3), 681-712. 18. Mauro, P. (1998). "Corruption and the composition of government expenditure." Journal of Public Economics, 69(2), 263-279. 19. Oak, M. (2015). "Legalization of bribe giving when bribe type is endogenous." Journal of Public Economic Theory, 17(4), 580-604. 20. Olken, B. A. (2007). "Monitoring corruption: evidence from a …eld experiment in Indonesia." Journal of Political Economy, 115(2), 200-249. 21. Rose-Ackerman, S., and Palifka, B. J. (2016). "Corruption and government: Causes, consequences, and reform." Cambridge University Press. 22. Shleifer, A., and Vishny, R. W. (1993). "Corruption." The Quarterly Journal of Economics, 108(3), 599-617. 23. Svensson, J. (2003). "Who must pay bribes and how much? Evidence from a cross section of …rms." The Quarterly Journal of Economics, 118(1), 207-230. 24. Tirole, J. (1996). "A theory of collective reputations (with applications to the persistence of corruption and to …rm quality)." The Review of Economic Studies, 63(1), 1-22. 25. Treisman, D. (2000). "The causes of corruption: a cross-national study." Journal of Public Economics, 76(3), 399-457.

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