How to Fight Corruption: Carrots and Sticks

Transcription

1 How to Fight Corrution: Carrots and Sticks Dmitriy Knyazev Abstract I resent a model of corrution with incomlete information where the bureaucrat may request a bribe from the citizen for roviding a service. Two anti-corrution olicies are considered: unishments for bribes and rewards for reorting about bribes. It is shown that neither of these olicies alone can defeat corrution. However, if these olicies are used simultaneously in a roer way, they can fully revent corrution. I also show that reducing bureaucracy is a vital art of anti-corrution olicies. Keywords: Corrution, bureaucracy, bribery, unishments, rewards. JEL Classi cation Codes: D73, K42, H83. I would like to thank Daron Acemoglu, Benny Moldovanu, Tymon Tatur and the articiants of PET 205 conference for their useful discussion and comments. Financial suort from the German Science Foundation (DFG) is gratefully acknowledged. Humboldt University of Berlin, knyazevd@hu-berlin.de

2 Introduction During recent decades, corrution has become a signi cant roblem for a vast number of countries across the world. Corrution is one of the main concerns not only in develoing economies and economies in transition but also in develoed countries. I start with several stories about countries that have been able to substantially reduce their level of corrution. Singaore is one of the least corruted countries in the world. In the 2st century, it is consistently laced in to-ten least corruted countries according to the Corrution Percetion Index. However, this has not always been the case. Before obtaining indeendence in 965, Singaore was a highly corruted country with a large number of other institutional roblems. How was one of the most corruted countries able to achieve one of the lowest levels of corrution? The key element of the anti-corrution olicy in Singaore was the Corrut Practices Investigation Bureau (CPIB). It is the sole agency in Singaore resonsible for ghting corrution and directly accountable to the Prime Minister of Singaore. The CPIB was founded in 952 and the Prevention of Corrution Act (PCA) enacted in 960 rovided strong instruments and freedom to CPIB in investigating corrution. CPIB o cers have the right to arrest without a warrant any erson indeendent of his social status and osition in a society. Moreover, every citizen of Singaore can comlain about corruted o cials to CPIB and obtain the service without aying bribes. Corruted o cials will be severely unished with a huge ne and enitentiary imrisonment. These methods have roven very e ective and the Indeendent Commission Against Corrution (ICAC) was adoted after the CPIB in 974 in Hong Kong. Due to the ICAC, Hong Kong was also able to substantially reduce its level of corrution. Nowadays, even though Singaore and Hong Kong are located in a very corruted region, they do not have serious roblems related to corrution. Singaore also rewards citizens who reort tax evasion or fraud. A reward of 5% on tax recovered and caed at $00,000 is given if the rovided information has led to the recovery of tax. These rewards create incentives for citizens to reort "wrong" behavior of bureaucrats. Recently, some other countries e.g. China and Kazakhstan have also started aying money rewards for information about corrution cases. 2

3 In this aer, I show that the ossibility of reorting corruted o cials and obtaining rewards for it is indeed an e ective mechanism to revent corrution in the case of harassment bribery. Harassment bribes are the bribes aid by citizens for services to which they are legally entitled. In this aer, I consider the situation in which an entrereneur wants to imlement some roject and needs to obtain a ermit for this roject from the bureaucrat. The roject is legally allowed to be imlemented if the entrereneur can rove 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 ermission in the case when the roject is desirable and to reject this roject otherwise. However, even if the entrereneur can rove that the roject is desirable, in many countries bureaucrats often request bribes for the ermission desite the fact that they are obliged to rovide it. The entrereneur has to ay this bribe if he wants to imlement his roject. The imortant feature of such kind of corrution is that it is the bureaucrat who requests the bribe and not the citizen who o ers it. Thus, these two arties are not equally resonsible for corrution, namely the bureaucrat bene ts from corrution and the entrereneur su ers from it. Hence, the entrereneur would like to imlement the roject without aying a bribe. The idea of the aer is to rovide the entrereneur with an oortunity to reort about corrution to a secial anti-corrution agency like CPIB and eventually obtain the ermission without aying the bribe. Instead of the entrereneur and the roject, one could think about a model with a more general setu where a citizen alies for some service and the value of the service is his rivate information. I describe a model in the entrereneur roject terms as the main alication of the model. I show that if the government does not ght corrution, then the equilibrium in our model imlies a substantial level of corrution. Next, I consider several ways of reventing corrution: ) unishments for the o cial who takes and extorts bribes; 2) rewards for the entrereneur for reorting about the corruted o cial; and 3) combination of unishments and rewards. I show that an increase in unishments has two e ects: the level of bribes in the equilibrium decreases, but the ercentage of rojects imlemented through a bribe transfer increases. Moreover, it is not ossible to defeat corrution with this olicy. In turn, the olicy of rewards reduces the ercentage of corrution cases, although the e ect 3

4 on the level of a bribe deends 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 roblem with this olicy is the same as with unishments: rewards are unable to defeat corrution comletely. Precisely, for any nite reward, there exists a level of bribe such that there is a ositive robability that the entrereneur would agree to ay the bribe. However, I show that if the government decides to use unishments and rewards simultaneously, then this mixture can be much more e ective. I show that it can fully revent corrution for any distribution of the roject revenue. Modeling corrution through bribe giving dates back to Beck and Maher (986) and Lien (986). Basu (20) argues informally that in the case of harassment bribes, the unishment should not be symmetric for both arties. His roosal is to legalize the giving of harassment bribes and return the bribe to the citizen if corrution is detected. This should rovide incentives for a citizen to reort about corrution after obtaining the service through bribery. This would deter the bureaucrat from demanding bribes. Dufwenberg and Sagnolo (205) roose a formal game-theoretic model for Basu s conjecture. They model bribery as a game with comlete 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 roosal is not e ective, although it can hel in the case of reeated interaction. Basu et al. (206) comlement Dufwenberg and Sagnolo (205) endogenizing a bribe in a bargaining game. Oak (205) endogenizes the bribe tye and constructs a model where bribes can be either harassment or non-harassment. He shows that caution is necessary in alying Basu s roosal because in the case of non-harassment bribes it can reduce social welfare without eliminating bribery. Abbink et al. (204) conduct a laboratory exeriment on harassment bribes and rovide suort for asymmetric unishment for the citizen and the bureaucrat. For the case of non-harassment bribes, where the citizen ays the bribe to the bureaucrat to take some illegal action, Burlando and Motta (206) show that it is also ossible to avoid corrution with a so-called tax-and-legalize scheme. This scheme allows the citizen to take the sanctioned action by aying a tax or a reduced ne. In our model, unishments can only be alied to the one side, namely o cials who request bribes. Basu et al. (992) discusses the recursive roblem of the following form: when an o cial (oliceman, 4

5 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 articiate in the same bargaining rocess, but from the other side. Many aers concentrate on a relation between corrution and economic activity, such as Mauro (995), Bardhan (997) and Fisman and Svensson (2007). The Causes of corrution are discussed in Treisman (2000), Ades and Di Tella (999) and Glaeser and Saks (2006). Institutional asects of corrution are discussed in Acemoglu and Verdier (2000), Fisman and Gatti (2002), Mauro (998), Schleifer and Vishny (993) and Rose-Ackerman and Palifka (206). The ersistence of corrution is shown in Damania et al. (2004) and Tirole (996). Based on a eld exeriment, Olken (2007) reorts that government monitoring can substantially reduce corrution. Brunetti and Weder (2003) show that more ress freedom leads to less corrution. My model di ers from the literature in several ways. First, I roose a model with incomlete information, where the value of the roject is a rivate value of the entrereneur. Second, the size of the requested bribe is otimally chosen by the bureaucrat when she obtains an alication from the entrereneur and this bribe can be adjusted to anti-corrution olicies. Thus, I characterize how the size of the bribe in equilibrium resonds to di erent anti-corrution measures. The assumtion that bureaucrats can choose bribes is suorted by Svensson (2003), who shows that bureaucrats act often as bribe discriminators and request di erent bribes from di erent entrereneurs. In my model, there are two arameters that I treat as measures of bureaucracy. The rst one, T; re ects the costs incurred by the entrereneur to rove that the roject is socially desirable while alying for a ermit. It can incororate the time and money sent on rearation of documents. The second arameter,, re ects the costs incurred by the entrereneur when he rejects giving a bribe and reorts about bribery to an anti-corrution agency (like CPIB). In this case, since the roject is still socially desirable, the roject is still imlemented, albeit with a delay. Hence, the roject revenue is generated later and has to be discounted by ( ): The higher values of these arameters re ect the higher level of bureaucracy. My results suggest two ositive e ects from a decrease in the level of bureaucracy: rst, a decrease of corrution itself; and second, lower bureaucracy levels make 5

6 it easier to ght corrution. Thus, reducing the level of bureaucracy should be an imortant art of anti-corrution olicies. The remainder of this aer is structured as follows. In the next section, I resent the model. Then, I describe the solution without anti-corrution olicies. Section 4 discusses the olicy of unishment. Section 5 deals with the olicy of rewards. In section 6, I combine both olicies together. In section 7, I discuss the relation between bureaucracy and corrution. Section 8 concludes the aer. 2 Model There are two sides, called the entrereneur (he) and the o cial (she). The entrereneur has a roject that could be imlemented. In order to imlement the roject, he has to aly for a ermission from the o cial. The exected net revenue from imlementation R is distributed on ( ; +) according to a continuously di erentiable distribution F and f(x) = F 0 (x) 6= 0 for any x: The roject is either socially desirable or not. The revenue of the roject and its social desirability are indeendent and both are rivate information of the entrereneur. However, the social desirability of the roject is veri able. It costs T > 0 for the entrereneur to rove that his roject is socially desirable. I concentrate on those tyes of entrereneurs who have socially desirable rojects. Legally, all roject roved to be socially desirable can be imlemented. Thus, once the o cial receives an alication from the entrereneur with a socially desirable roject, legally she should give the ermission. However, in this case, the o cial can decide whether to give the ermission immediately () or request a bribe (b), namely some monetary transfer b from The entrereneur to the o cial. If the bribe b is requested, the entrereneur can take one of two actions: rst, he can agree to give the bribe (g), whereby in this case the roject is imlemented immediately; and alternatively, instead of giving a bribe, the entrereneur can reort about the o cial to the anti-corrution agency (r), whereby in this case the roject is imlemented without aying a bribe, albeit with a delay. Thus, the value of the roject is discounted by ( ); 0 < <. Hence, instead of R; the entrereneur exects to receive ( )R if he reorts about bribery. 6

7 All agents are rational. The size of the requested bribe b is chosen by the o cial in the otimal way to maximize her exected utility. The entrereneur with an e cient roject exects that the o cial can request a bribe and chooses otimally whether to aly for the ermission and send the cost T or not to incur any costs and not to aly at all. If the entrereneur does not aly for the ermission, he obtains zero reservation utility. If he alies, the ayo matrix is as follows : Entrereneur O cial b r R T; 0 R( ) T; 0 g R T; 0 R T b; b The timing of the model is as follows: ) The entrereneur decides whether to aly 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 entrereneur decides whether to ay the bribe or reort. In order to obtain clear and analytically tractable results, we make the following technical assumtions. De ne the hazard rate of the revenue distribution F as x) := the inverse hazard rate h x) := =(x) = x) f(x) f(x) x) and : We assume that the functions x + y and h x) are single-crossing for any y 2 R. Namely, for any y, there exist at most one x 0 such that x + y = h x ); x + y < h x) for all x < x and x + y > h x) for all x > x. If for some y 2 R such a oint does not exist, then it has to be the case that x + y > h x) for any x 0 because x+y can be in nitely high for large x. We also de ne ' x) := x h x). The single-crossing condition does not imly that the function ' x) is invertible. However, for any x; we can de ne ' x) := maxfz : ' z) = xg: If this maximum does not exist, we set ' F (x) 0: One could think that " T " is redundant because it resents in every matrix eld. However, this ayo matrix is relevant for the cases when the entrereneur has already alied for the ermission and nds it bene cial to send the cost T on the alication rocess. 7

8 3 Solution without anti-corrution olicies I solve the model by backward induction. If the entrereneur has alied and the o cial has requested a bribe, it is otimal for the entrereneur to ay if the gain from the immediate imlementation is greater than the gain from the delayed imlementation: R T b R( ) T: () Thus, the entrereneur would agree to ay the bribe if the exected revenue is su ciently high, namely R b : Intuitively, if the entrereneur has a roject with a low exected revenue, the xed monetary loss from aying a bribe is greater than the loss due to the delay when he reorts about the corruted o cial. On the other hand, if the roject can generate a high revenue, it is bene cial to ay the bribe and imlement the roject immediately. Denote G(x) as the revenue distribution of those rojects with which the entrereneur alies for the ermission in equilibrium. This distribution is endogenously determined in the model. However, since the o cial chooses the amount of the bribe after the entrereneur has alied, she takes the distribution G(x) as given. If the bribe b is requested, then the robability that the entrereneur would agree to ay it is equal to G( b ): Hence, the otimal bribe can be found from the following maximization roblem: b = arg max ( G( b ))b: (2) b0 The solution concet is a subgame erfect equilibrium. The next result characterizes the equilibrium without anti-corrution olicies. Proosition In equilibrium: ) The o cial requests a bribe 2) The entrereneur alies i R T : b = maxf T ; ' 0)g: 3) The entrereneur ays b i R maxf T ; ' 0)g: 8

9 Proof. see Aendix. The entrereneur alies for the ermission if and only if R T. If the value of cost T is su ciently high, namely T > ( )' F (0); then the entrereneur who alies already has a roject of high quality. In this case, is it otimal for the o cial to request the highest bribe such that the entrereneur would always agree to ay, i.e. T. If T < ( )' F (0), then the entrereneur will also aly for the ermission to imlement less ro table rojects. In this case, the o cial sets the bribe in such a way that the entrereneur reorts about bribery for R 2 [ T ; ' F (0)) and ays the bribe for R ' F (0): The distribution of rojects with which the entrereneur would like to aly is G(x) = xjx 8 T < ) = : x) 0; x < T T ) T ) ; x T 9 = ;. In the rst-best without corrution, all socially bene cial rojects with R T would be imlemented. Hence, corrution brings additional loss to e ciency because only rojects with R T are imlemented. In the next sections, we analyze the e ects of anti-corrution olicies on the level of corrution. In our model, we de ne two measures of corrution: ) the total sum of bribes (m ), and 2) the robability of a bribe ayment (m 2 ). The rst measure re ects the total amount of money aid as bribes in the economy. The second measure neglects the value of bribes but re ects the number of bribes. Thus, m = b ( b )) = ' F (0)( ' (0)) > 0; F m 2 = G( b ) = ' 0)) T ) > 0: 4 Punishment Suose now that the government wants to ght corrution and sets a unishment for the o cial who is caught engaging in bribery. This unishment can be imlemented through a 9

10 monetary ne, a rison sentence, etc. The new ayo matrix looks as follows: Entrereneur O cial b r R T; 0 R( ) T; g R T; 0 R T b; b Intuitively, we can exect that the law introducing such kinds of unishments should reduce the level of corrution. The o cial should be afraid of being unished and this should revent her from requesting bribes. However, I show below that the unishment is not that e ective. Although a unishment can lead to a decrease in the otimal bribe, it cannot revent corrution comletely. We start by calculating the otimal level of a bribe in this case. Since the o cial incurs losses when caught, the o cial s roblem looks as follows: b = arg max b0 [( G( b ))b G( b )]: The next result characterizes the equilibrium under the olicy of unishments. Proosition 2 In equilibrium under unishment: ) The o cial requests a bribe b = maxf T ; ' 2) The entrereneur alies i R T : 3) The entrereneur ays b i R maxf T ; ' )g: (3) )g: Proof. see Aendix. Again, only entrereneurs with R > T aly for the ermission. Thus, unishment on the o cial in equilibrium does not a ect the alication behavior of the entrereneur. One can notice that the o cial can always request a bribe at least b = T and the entrereneur always agrees to ay this bribe rovided that he has already alied for the ermission. Thus, regardless how severe the unishment is, the o cial asks for a strictly ositive bribe 0

11 in equilibrium. To show the comarative statics of b with resect to the unishment level, I formulate the following result. Corollary When the unishment increases, the otimal bribe decreases until it reaches T : Afterwards, it remains at a constant level. Proof. Since the function '(x) is increasing, the inverse function is also increasing. Thus, the increase of will reduce the value of the argument of the function ' : Since b is chosen as a maximum of T and ' T ); the otimal bribe decreases until it reaches. The intuition here is as follows: when the unishment increases, the o cial reduces the required bribe, which reduces the robability that the entrereneur reorts. This bribe reduction continues until the bribe is set at the level whereby the entrereneur is always ready to give the bribe, namely b = T. This level is ositive because due to the alication cost T; The entrereneur would only aly with rojects that can generate substantially high revenue. Hence, for any su ciently small bribe, the entrereneur would refer to ay it rather than reorting about it. In this case, even for the huge unishment, the o cial is not afraid of it because she is never unished in equilibrium. Thus, we obtain the following result: Corollary 2 The olicy of unishments is unable to revent corrution. This result suggests that the elimination of corrution is not achievable with the unishment olicy. Nevertheless, the level of bribes can be decreased, as follows from Corollary. The next roosition shows how the increase in the unishment a ects the corrution measures. Proosition 3 Under the unishment olicy, m () is a non-increasing function and m 2 () is a non-decreasing function. Proof. see Aendix. Hence, we conclude that the total sum of bribes decreases, but at the same time the number of bribes increases with an increase of unishment. The o cial requests smaller bribes, although they are aid more often.

12 5 Rewards Here, I consider another ossible government olicy against corrution, which rovides incentives for the entrereneur to reort about bribery. When The entrereneur is requested to ay a bribe and reorts about it, due to this olicy he obtains a reward r: The ayo matrix looks as follows: Entrereneur O cial b r R T; 0 R( ) + r T; 0 g R T; 0 R T b; b Under the olicy of rewards, the entrereneur agrees to ay the bribe i R T b R( ) T + r: (4) Thus, the entrereneur gives the bribe i R b+r : The otimal bribe is the solution to the following roblem: b = arg max b0 [( G(b + r ))b]: The next result characterizes the equilibrium under the olicy of rewards. Proosition 4 In equilibrium under rewards: ) The o cial requests a bribe 2) The entrereneur alies i R T r : b = maxf T r ; r + ' r )g: (5) 3) The entrereneur ays b i R maxf T r ; ' r )g: Proof. see Aendix. Since the entrereneur obtains r when he reorts, the set of rojects for which the entrereneur would obtain the ermission is larger. Now, the entrereneur would aly if and 2

13 only if R T with R r ; while without any reward the entrereneur would only aly with rojects T : The comarative statics of the otimal bribe with resect to the announced reward is more comlicated than the comarative statics in the case of unishments. The next result shows that it deends on the hazard rate of the revenue distribution. Proosition 5 ) If x) is non-decreasing, then b (r) is non-increasing. 2) If x) is non-increasing, then there exists a value r such that for all b (r) is nondecreasing for all r > r. Proof. see Aendix. The surrising result is that for the decreasing hazard rate and su ciently large values of r; the otimal bribe is increasing. In this case, larger rewards will lead to the higher equilibrium level of bribes in the economy. In order to revent the bribe-taking behavior of the o cial, the reward for the entrereneur has to be such that b 0: However, it turns out that the otimal bribe is ositive for any value of the reward because the second art of (5) is always ositive. Thus, we can formulate the following roosition. Corollary 3 The olicy of rewards is unable to defeat corrution. Proof. There is no corrution in equilibrium if and only if it is ossible to nd such a value of r that imlies b 0: It is ossible to make the rst term of (5) less than or equal to zero by imosing a su ciently high reward r T: However, in order to satisfy r + ' r ) 0; we should have r ' r ): Since ' r ) = r imossible. h r ); we must have h r ) 0; which is The olicy of rewards is unable to revent corrution. However, there are some ositive e ects of this olicy. First, the share of rojects that are imlemented increases with r. Namely, all e cient rojects with R > T r both corrution measures are also non-increasing. Proosition 6 ) m 2 (r) is a non-increasing function of r: are imlemented. The next result shows that 2) There exists r > 0; such that m (r) is a decreasing function for any r > r. 3

14 Proof. see Aendix. r deends 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 olicy more e ective. However, a substantial amount of money may be required from the budget to ay the rewards. 6 Combination of unishment and rewards I have shown that neither the olicy of unishments nor the olicy of rewards searately is able to revent corrution. In this section, I show that the roer combination of these olicies can defeat corrution. If the government can use unishments and rewards simultaneously, the ayo matrix when the entrereneur alies looks as follows: Entrereneur O cial b r R T; 0 R( ) + r T; g R T; 0 R T b; b The otimal bribe requested by o cial is determined as the solution to the following roblem: b = arg max b0 [( G(b + r + ))b G(b )]: The next result characterizes the equilibrium under the joint olicy of unishments and rewards. Proosition 7 In equilibrium under unishment and rewards: ) The o cial requests a bribe b = maxf T r ; r + ' r ); 0g: (6) 2) The entrereneur alies i R T r : 3) The entrereneur ays b i R maxf T r ; ' 4 r )g:

15 Proof. see Aendix. The next result rovides necessary and su cient conditions for values ; r such that the equilibrium level of corrution is 0. In this case, it is not ro table for the o cial to request any ositive bribe. Hence, such a combination of unishments and rewards imlies a zero level of corrution in equilibrium. Proosition 8 Any combination of unishments and rewards (; r) such that r T and h r ) is able to sustain a zero level of corrution in equilibrium. This inequality always has a continuum of solutions in terms of (; r): Proof. see Aendix For any values (; r) such that r T and h r ); the entrereneur would agree to ay a bribe, but the o cial never requests it. All rojects with R T are imlemented. Moreover, this scheme does not require aying rewards in equilibrium because the o cial never requests a bribe and the right uer corner of the ayo matrix is never on the equilibrium ath. Since the range of solutions to this inequality is in nite, there is no need to nd any seci c values. The government needs to romise a high reward r greater than T and imose a su ciently high unishment ; greater than h r ): I also notice that these conditions are only su cient, not necessary. In order to obtain necessary conditions, one has to nd values (; r) such that the solution to roblem (6) is zero. In this case, it would be otimal for the o cial not to request a bribe. 7 Bureaucracy and corrution In this section, I discuss the relation between bureaucracy and corrution and exlain how the reduced bureaucracy can hel to ght corrution. In this aer, there are two arameters resonsible for bureaucracy, T and : Based on the revious discussion, we can formulate the following results: Only rojects with R > T r are imlemented. Hence, the lower the values of T and, the more rojects that are imlemented in equilibrium. 5

16 The value of the otimal bribe is not smaller than T r : This exression goes down when or T decrease. If = 0, the entrereneur loses nothing from reorting about the corruted o cial. Then, there is no corrution even without anti-corrution olicies. Indeed, the entrereneur never agrees to give any bribe that is greater than zero. If T = 0; the entrereneur does not incur any costs from alying for ermission and alies with every roject. Then, it is ossible to revent corrution through the olicy of unishments. In this case, an increase of unishment will lead to a decrease of the otimal bribe until it reaches 0. The olicy of rewards is still unable to defeat corrution. Summarizing, we obtain the following roosition: Proosition 9 The lower that bureaucracy is, the lower that corrution is. At the same time, ghting corrution is more e ective under a lower level of bureaucracy. Now, I rovide some emirical evidence on the relationshi between corrution and bureaucracy. I use the Corrution Percetion Index ublished by Transarency International as a measure of corrution (higher values of the index indicate less corrution) and Doing Business ublished by the World Bank to measure bureaucracy. I take "the total number of days required to build a warehouse" as a roxy for bureaucracy (higher values of the index indicate higher bureaucracy). Our samle includes 67 countries. I measure the correlation between corrution and bureaucracy using Searman s rank correlation coe cient 2. The coe cient of correlation equals and the -value is Thus, there is indeed a strong ositive correlation between corrution and bureaucracy, which suorts the results of my model. 2 Simly 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 -value are comuted for values of the indices in 203. The signi cant ositive correlation between bureaucracy and corrution is also found for other years and other roxies for bureaucracy obtained from Doing Business. 6

17 8 Conclusion In this aer, I have constructed a model of corrution with two counterarts: an o cial and an entrereneur. The entrereneur has a roject with rivately-known exected revenue, but in order to imlement it he has to obtain the ermission from the o cial. I have shown that if the government does not ght corrution, then the equilibrium imlies the substantial level of corrution, namely the o cial always requires a bribe and the entrereneur often gives the bribe. Then, I discuss several government olicies to revent corrution, namely unishments for the o cial for requesting bribes, rewards for the entrereneur for reorting about bribery and a mixture of both. It emerges that none of these olicies alied searately can revent corrution. Moreover, under the unishments olicy the share of cases ending with giving bribes will be even higher than in the case without anti-corrution olicies. Under the rewards olicy, the equilibrium bribe may increase if the hazard rate of the roject distribution decreases. However, I show that there always exists a combination of unishments and rewards that revents corrution. If the reward is su ciently large and the unishment is even larger, then it would be non-ro table for the o cial to request a bribe. Hence, there would be no corrution in equilibrium under the joint olicy of unishments and rewards. My results also suggest that a reduced bureaucracy level also leads to reduced corrution. At the same time, it is easier to ght corrution under the lower level of bureaucracy. In this aer, 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 suosed 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 unished for o ering a bribe. I believe that a roer combination of unishments and rewards can also revent this tye of corrution. This is a question for future research. 7

18 9 Aendix Proof of Proosition From (), it follows in equilibrium that the entrereneur agrees to ay the bribe i R b. Then, it is not otimal to request b < b b; where b b is the highest number such that G( b b ) = 0: If the solution is interior and b > b b; then it satis es the following F.O.C.: G( b ) g(b )b = 0: Hence, 0 = b G( b ) g( b ) = b h G ( b ) = ' G( b ): (7) Assume that h G (:) satis es the single-crossing roerty. Below, we show that it is true when h :) satis es it. Then, in the interior case, the solution to (7) is b = ' G (0). Thus, the solution to the initial roblem is b = maxf b b; ' G (0)g: The entrereneur rationally exects that o cial requests b. Hence, only the entrereneur with a su ciently good roject will aly. Namely, the entrereneur will aly if the exected revenue of his roject is such that R( ) T 0 or R T b 0: Thus, the entrereneur alies i R minf T ; T + b g. To continue the roof, I make the following claim. Claim T + b T. Proof. Assume by contradiction that T + b < T : Rearranging the terms imlies T + b > b T : Thus, if the entrereneur alies, R minf ; 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 + " > b +" ; it still holds that G( b +" ) = 0: Such an increase of the requested bribe does not reduce the robability of aying it. Hence, the o cial can increase her utility and b is not otimal. 8

19 Thus, the entrereneur alies if and only if R of the rojects with which the entrereneur would aly is For x > G(x) = xjx 8 T < ) = : x) T. Hence, b = T : The distribution 0; x < T T ) T ) ; x T 9 = ; : T ; the hazard rates of distributions G(x) and x) coincide because g(x) G(x) = f(x)=( T ( x))=( T )) )) = f(x) x) : Hence, if :) satis es the single-crossing condition, then G(:) also does. Thus, b = maxf b b; ' T G (0)g = maxf ; ' 0)g: The entrereneur refers to give the bribe i R b = maxf T ; ' 0)g: Proof of Proosition 2 As in the roof of Proosition, we can immediately notice that it is not otimal to request b < b b; where b is the highest number such that G( b ) = 0: If the solution is interior and b > b b; then it satis es the following F.O.C.: G( b ) + g(b )b = 0: Hence, = b G( b ) g( b ) = b h G ( b ) = ' G( b ): Again, assume for a moment that in this case h G (:) also satis es the single-crossing roerty. Then, we obtain for the interior case b = ' G ( Thus, ): b = maxf b b; ' G ( )g: Using similar arguments as in Proosition, the entrereneur will aly only with the 9

20 rojects that generate revenue R > T. Hence, b = T and ' G ( entrereneur agrees to give b i R b = maxf T ; ' G ( ) = ' )g:this nishes the roof. ): The Proof of Proosition 3 If T ( )' F (0); then exression (3) imlies that an increase of changes nothing in the behavior of both sides. Hence, consider the case with T < ( )' 0): Then, for all values of 0 < < ' T ); the following ' = F (' )( ) ' F ))( ( ))(' ' ))) ))) = = )) + ' F ) ( f(' ) )) < 0; F ))) 2 ' )) T )) = f(' T ) F > 0: ))) Proof of Proosition 4 From (4), it follows in equilibrium that the entrereneur agrees to ay the bribe i R b +r. Hence, it is not otimal to set b < b b; where b b is the highest number such that G( b b+r ) = 0: If the solution is interior and b > b b; then it satis es the following F.O.C.: G( b + r ) + r g(b )b = 0: Then, or h G ( b + r ) = b = b + r r ; ' G ( b + r ) = r : 20

21 Assuming as earlier in the roofs of Proositions and 2 that h G (:) satis es the singlecrossing roerty, we obtain for the interior case b = r + ' G ( r ): Thus, b = maxf b b; r + ' G ( r )g: Using similar arguments as in Proosition, the entrereneur will aly only with the rojects that can generate revenue R > T r: Hence, b = T r and ' G ( r ) = ' r ): Entrereneur alies i R b +r = maxf T r; ' G ( r )g: This gives the statement of the roosition. Proof of Proosition 5 Notice that T r in (5) decreases with an increase in r: We now study the behavior of r + ' r ): Its derivative with resect to r is as follows: F r )) = (' r )) F r F r )): From the roof of Proosition 3, h b +r ) = b : Hence, ' b +r ) = r : The single-crossing roerty imlies (' r )) (b + r ) < : Thus, if the hazard rate is non-decreasing, then the inverse hazard rate is non-increasing, F r )) 0: Hence, r+' r ) is non-increasing. In this case, b = maxf T r; r+ ' r )g is also non-increasing as a maximum from two non-increasing functions. If the hazard rate is non-increasing, then r + ' r ) is non-decreasing. Thus, there will exist a value r 0 such that for all r > r the following holds: r + ' r ) > T Thus, for r > r the otimal bribe will be a non-decreasing function of r: r: Proof of Proosition 6 With rewards, the corrution measures have the following form: 2

22 m = b ( b + r )); m 2 = G( b + r ): We start by analyzing the e ect of an increase in the reward r on m 2 : If T r > r + ' r ); then by Proosition 4, if the entrereneur alies, he is ready to give a bribe and G( b +r ) = 0: Hence, an increase in r does not a ect m 2. If T r r + ' r Hence, ); then we can obtain from Proosition and Proosition 4: G( b + r ) = ' r )) T r) 2 ' r )) T r = f(' r (' r )) ( ' r ))) f(t r) T r) < 0: ( T r ))2 The last inequality is due to the single-crossing roerty. Now, we comute the derivative of m with resect to r: Take r : T r r +' r ): If r r ; then b = r + ' r ) and h b +r ) b = 0: In this @r ( = f( b + r ) F + r (b )) b f( b (h b + r ) b ) b = = f( b + r )b < 0: For r < r ; the sign identi ed without making additional assumtions. deends on the revenue distribution of x) and cannot be Proof of Proosition 7 As in the roof of Proosition 4, we can immediately notice that it is not otimal to request b < b b; where b is the highest number such that G( b b+r) = 0: If the solution is interior 22

23 and b > b b, then it satis es the following F.O.C.: G( b + r ) + r + g(b )b Rearranging the terms, h G ( b +r ) = b + or ' G ( b +r ) = r : Assuming as earlier in the roofs of Proositions, 2 and 4 that h G (:) satis es the single-crossing roerty, we obtain for the interior case b = r + ' ( r ): Thus, b = maxf b b; r + ' G (r = 0: ); 0g: Using similar arguments as in Proosition, the entrereneur will aly only those rojects that generate revenue R > T r. Hence, b = T r and ' Entrereneur agrees to give b i R b +r = maxf T r ; ' of the roosition. G ( r G ( r r ) = ' ): )g: This gives the statement Proof of Proosition 8 I will show that if r T and h r ); then the otimal bribe is zero. Hence, it cannot be otimal for the o cial to request a bribe, and there will be no corrution in equilibrium. From (6), we need T zero. ' r 0 and r + ' If r T; we immediately see that T r r r r ) > 0: Then, > ' r ): Since ' r ) = r h r ) 0 to have the otimal bribe equal to 0: Suose, by contradiction, that r + ); we have r > r h r ): Rearranging terms, we obtain < h r ): Thus, we obtain a contradiction. Hence, the otimal bribe is zero. 0 References. Abbink, K., Dasguta, U., Gangadharan, L., and Jain, T. (204). "Letting the briber go free: an exeriment on mitigating harassment bribes." Journal of Public Economics,,

24 2. Acemoglu, D., and Verdier, T. (2000). "The choice between market failures and corrution." The American Economic Review, 90(), Ades, A., and Di Tella, R. (999). "Rents, cometition, and corrution." The American Economic Review, 89(4), Bardhan, P. (997). "Corrution and develoment: a review of issues." Journal of Economic Literature, 35(3), Basu, K. (20). "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. (206). "Asymmetric unishment as an instrument of corrution control." Journal of Public Economic Theory, 8(6), Basu, K., Bhattacharya, S., and Mishra, A. (992). "Notes on Bribery and the Control of Corrution." Journal of Public Economics, 48(3), Beck, P. J., and Maher, M. W. (986). "A comarison of bribery and bidding in thin markets." Economics Letters, 20(), Brunetti, A., and Weder, B. (2003). "A free ress is bad news for corrution." Journal of Public Economics, 87(7), Burlando, A., and Motta, A. (206). "Legalize, tax, and deter: Otimal enforcement olicies for corrutible o cials." Journal of Develoment Economics, 8, Damania, R., Fredriksson, P. G., and Mani, M. (2004). "The ersistence of corrution and regulatory comliance failures: theory and evidence." Public Choice, 2(3), Dufwenberg, M., and Sagnolo, G. (205). "Legalizing bribe giving." Economic Inquiry, 53(2), Fisman, R., and Gatti, R. (2002). "Decentralization and corrution: evidence across countries." Journal of Public Economics, 83(3),

25 4. Fisman, R., and Svensson, J. (2007). "Are corrution and taxation really harmful to growth? Firm level evidence." Journal of Develoment Economics, 83(), Glaeser, E. L., and Saks, R. E. (2006). "Corrution in America." Journal of Public Economics, 90(6), Lien, D. H. D. (986). "A note on cometitive bribery games." Economics Letters, 22(4), Mauro, P. (995). "Corrution and growth." The Quarterly Journal of Economics, 0(3), Mauro, P. (998). "Corrution and the comosition of government exenditure." Journal of Public Economics, 69(2), Oak, M. (205). "Legalization of bribe giving when bribe tye is endogenous." Journal of Public Economic Theory, 7(4), Olken, B. A. (2007). "Monitoring corrution: evidence from a eld exeriment in Indonesia." Journal of Political Economy, 5(2), Rose-Ackerman, S., and Palifka, B. J. (206). "Corrution and government: Causes, consequences, and reform." Cambridge University Press. 22. Shleifer, A., and Vishny, R. W. (993). "Corrution." The Quarterly Journal of Economics, 08(3), Svensson, J. (2003). "Who must ay bribes and how much? Evidence from a cross section of rms." The Quarterly Journal of Economics, 8(), Tirole, J. (996). "A theory of collective reutations (with alications to the ersistence of corrution and to rm quality)." The Review of Economic Studies, 63(), Treisman, D. (2000). "The causes of corrution: a cross-national study." Journal of Public Economics, 76(3),