WPS6933 Policy Research Working Paper 6933 Asymmetric Punishment as an Instrument of Corruption Control Karna Basu Kaushik Basu Tito Cordella The World Bank Development Economics Vice Presidency Office of the Chief Economist June 2014 Policy Research Working Paper 6933 Abstract The control of bribery is a policy objective in many bribe sizes rise as expected penalties rise. Second, when developing countries. It has been argued that asymmetric detection rates are determined by the bribe-giver, a punishments could reduce bribery by incentivizing switch from symmetric to asymmetric punishment either whistle-blowing. This paper investigates the role played eliminates bribery or allows it to persist with larger bribe by asymmetric punishment in a setting where bribe size sizes. Furthermore, when bribery persists, multiple bribe is determined by Nash bargaining, detection is costly, sizes could survive in equilibrium. The paper derives and detection rates are set endogenously. First, when parameter values under which each of these outcomes detection rates are fixed, the symmetry properties of occurs and discusses how these could be interpreted in punishment are irrelevant to bribery. Bribery disappears the context of existing institutions. if expected penalties are sufficiently high; otherwise, This paper is a product of the Office of the Chief Economist, Development Economics Vice Presidency. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org. The authors may be contacted at kbasu@hunter.cuny.edu, kbasu@worldbank.org, and tcordella@worldbank.org. The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent. Produced by the Research Support Team Asymmetric Punishment as an Instrument of Corruption Control Karna Basu,yKaushik Basuzand Tito Cordellax This paper has bene…ted from conversations with Christian Ahlin, Jonathan Conning, Avinash Dixit, Aristomene Varoudakis, and seminar participants at the University of Penn- sylvania Law School. y Hunter College, City University of New York; E-Mail: kbasu@hunter.cuny.edu z The World Bank, 1818 H St. NW, Washington, DC 20433, USA; E-Mail: kbasu@worldbank.org x The World Bank, 1818 H St. NW, Washington, DC 20433, USA; E-Mail: tcordella@worldbank.org. 1 Introduction Corruption is a major concern in several countries. One reason it is di¢ cult to control is that those involved have an incentive to collude to prevent detection. While this is a feature of many criminal activities, the problem under corruption is heightened by criminal codes that, in most countries, penalize the bribe-giver and the bribe-taker equally.1 As a result, all participants in a bribing scheme, including those who might otherwise be considered victims and could be tempted to act as whistle-blowers, have a vested interest against doing so. How could such collusion be weakened and bribery reduced? A possible solution that we discuss in this paper lies in asymmetric punishments. The basic justi…cation for asymmetric punishments is that, by penalizing some parties less than others, the government can create ex-post incentives for agents to report the crime and thereby stop colluding. The idea of asymmetric punishment for crime is not new and it has been implemented in various forms around the world. For example, prosecutors in the United States sometimes o¤er immunity to those who reveal …nancial crimes that they might themselves have been complicit in. In Italy, similar schemes have been used to …ght organized crime. If asymmetric punishment is quite widespread in the case of …nancial and organized crime, it is relatively rare in the case of bribery.2 This is somewhat surprising, especially in the context of harassment bribes where (i) citizens are asked to pay a bureaucrat to receive services that they are legally entitled to, and (ii) the bribe does not itself change the nature of the services being exchanged.3 Harassment bribes are pervasive in developing countries (and sometimes be- yond) and directly a¤ect large segments of populations.4 This means that there might be signi…cant political returns to tackling such corruption with innova- tive solutions. In a note for India’s Ministry of Finance, one of us (Basu, 2011) proposed the following: decriminalize the giving (but not taking) of harassment bribes and require the bribe-taker to return the bribe to the citizen if caught.5 This would create ex-post incentives for citizens to reveal that bribes were paid, and could end up discouraging bureaucrats from demanding bribes in the …rst place. Inspired by the animated discussion that followed this proposal,6 and to 1 See Linklaters (2012) for a survey. 2 Thereare some exceptions, discussed in Li (2012) and Engel et al (2012). 3 As would be the case if, for example, an entrepreneur were paying a bribe to avoid complying with environmental standards. 4 While not relevant to this paper, the distinction between harassment bribes (a type of extortion) and other forms of bribery is a complex one. See, for example, Carson (1985) and Oak (2013). 5 According to India’s Prevention of Corruption Act (1988), the giver and the taker of a bribe are considered equally culpable and can be …nancially penalized and incarcerated for up to …ve years. 6 The proposal led to a large controversy with questions being raised by members of the Indian Parliament. It received wide publicity in the print and electronic media. See, for instance, The Economist (2011), Dreze (2011), Sainath (2011), Mitra (2011), Seabright (2011), Haider (2012), and Zakaria (2011). 2 assess its “robustness” , in this paper we study how di¤erent punishment schemes are likely to a¤ect the size and incidence of harassment bribes. This allows us to shed some new light on the conditions under which asymmetric punishment is able to deter bribe-giving e¤ectively. We develop a simple model in which a bureaucrat can costlessly provide a service that creates a surplus for the citizen, but might demand a bribe in exchange. If a bribe is demanded, the bureaucrat and the citizen split the surplus through a process of Nash bargaining. We …rst analyze a benchmark case where the …nes for bribe-giving and bribe- taking and the probability of detection are exogenous. In such a setting, a bribe is exchanged as long as the total expected penalty is small enough. Interestingly, the symmetry properties of the punishments are irrelevant to the incidence of bribery. Whether the penalty burden falls disproportionately on the bureaucrat or the citizen, and whether the bureaucrat is required to repay part of the bribe, do not matter: the bribe size will adjust to keep the surplus equally split. Furthermore, we show that bribe sizes could rise when anti-corruption en- forcement is strengthened. Intuitively, if penalties are at all asymmetric, as enforcement improves the citizen must pay a larger bribe to compensate the bureaucrat for his relatively larger expected penalty. This means that if bribery is measured by bribe size, an attempt to reduce bribery might instead increase it. Next, we relax the assumption that the probability of detection is exogenous, and we assume that it depends on costly actions undertaken by the state and/or the citizen. We show that asymmetric punishment increases the incentives for the citizen to whistle-blow. However, whether this leads to the elimination of bribery, as in Basu (2011), or to an exacerbation of the problem– in which bribery persists and the bribe size rises to account for the greater probability of detection– depends on the e¤ectiveness of law enforcement agencies in detecting corruption. Asymmetric punishments could also give rise to multiple equilibria with two possible outcomes– one where the bribe size is small and the probability of detection is also small, and another where both the bribe size and probability of detection are large. This necessarily complicates policy prescriptions. If it is su¢ ciently easy for a citizen to get the corrupt bureaucrat caught, asymmetric punishment can be an e¤ective tool to eliminate bribery. However, in countries where the marginal cost of improved detection is high, possibly the same countries where harassment bribes are a problem in the …rst place, bribery will survive under asymmetric punishment. When this is the case, bribe size might rise to account for the fact that the o¢ cial is more likely to be penalized due to the entrepreneur’ s e¤orts to report. Here, asymmetric punishment in fact creates an e¢ ciency loss through the costs associated with whistle-blowing. Our model could therefore partly ex- plain why a country like China, which implemented asymmetric punishments in 1997 but has high costs of reporting, has not experienced a discernible reduction in corruption (Li, 2012). Bribery and corruption have been subjects of economic inquiry for some time (see Bardhan, 1997, for a comprehensive survey). In their seminal paper, Shleifer 3 and Vishny (1993) show how institutions a¤ect the prevalence and e¢ ciency implications of corruption. More recently, several papers present theoretical analyses of approaches to reduce corruption (see, among others, Andrianova and Melissas, 2008 and Dixit, 2013). The present paper belongs to that tradition and relates closely to the growing academic literature on the possibilities and limitations of asymmetric punishment (see Rose-Ackerman, 1999; Lambsdor¤ and Nell, 2007; and Oak, 2013). On this topic, Rose-Ackerman (2010) and Dufwenberg and Spagnolo (2013) are particularly relevant to our analysis. The …rst paper, which is a critical survey of the law and economics of bribery and extortion, provides a wide-ranging discussion of how di¤erent punishment schemes a¤ect the bargaining between the bribe-giver and bribe-taker. While some of the intuition of our paper can be found there, our contribution lies in the formalization of the analysis and the endogenization of costly actions undertaken by the bribe-giver. Dufwenberg and Spagnolo (2013) provide a rigorous game theoretic formu- lation of Basu’ s (2011) proposal. In a non-cooperative framework, they show that, in a one shot game, asymmetric punishment either has no e¤ect or prevents bribery but at the cost of the service o¤ered. Which of these is realized depends on whether, in the absence of a bribe, institutions are e¤ective enough to incen- tivize the bureaucrat to o¤er the service. They then consider a repeated version of the game in which the bureaucrat has an incentive to build a reputation of being corrupt. In such a set-up, they show that asymmetric punishment indeed becomes an e¤ective instrument to …ght corruption but only if institutions are good. Our paper complements Dufwenberg and Spagnolo (2013) through the intro- duction of a new set of realistic and consequential considerations. By modeling the interaction between the bureaucrat and citizen as a bargaining game, we endogenize bribe size, making it a function of the punishment regime as well as the probability of detection. In addition, by endogenizing probabilistic detec- tion we generate some nuanced results including the possibility that asymmetric punishment could raise bribe size. Aside from the theoretical research, there is a limited but growing empirical literature on the e¤ectiveness of asymmetric punishment in deterring harassment bribes. On the one hand, Abbink et al. (2014) provide some experimental evidence supporting the use of asymmetric punishment. On the other, Engel et al. (2013) use a lab experiment to show that, when the bureaucrat can bestow favors in response to a bribe, asymmetric punishment raises the incidence of bribery. Additional empirical work, guided by economic theory, can continue to re…ne our understanding of how alternative forms of punishment may a¤ect incentives to demand and pay bribes. Our goal is to bring some carefully constructed game theoretic methods to investigate a subject of great practical signi…cance and vigorous public debate. Not surprisingly, the analysis does not lead to a unique prediction, but to con- ditional results which try to delineate where a certain kind of law will work and where it will not. Our model provides a stylized description of the mechanics that underlie bribery, and emphasizes the subtle interaction of two fundamental 4 choices– bribe size and detection probability. It is hoped that by bringing dis- passionate analysis to bear on this emotive subject, we are able to shed some light on what is ultimately a practical matter of policy in law and economics. 2 Setup 2.1 Assumptions Suppose an entrepreneur (denoted E ) needs a licence to conduct his business. The license gives him a bene…t of L > 0. The government o¢ cial (denoted O) is able to deliver the license costlessly. However, he considers the possibility of charging the entrepreneur for the license; that is to demand a bribe. Assume the o¢ cial has two choices– deliver the license for free, or make license delivery conditional on a bribe being paid. If he chooses the latter, he and the entre- preneur must bargain over the bribe size, and if they are unable to agree, no license is delivered. Suppose the o¢ cial decides to demand a bribe. If a bribe size is agreed upon and paid, it is detected with probability p 2 [0; 1]. If detected, the entrepreneur is penalized FE 0 and the o¢ cial is penalized FO 0. These penalties could constitute …nes or other non-pecuniary costs. In addition, the o¢ cial is required to return a fraction 2 [0; 1] of the bribe paid. We de…ne perfectly symmetric punishment as FE = FO and = 0, and perfectly asymmetric punishment as FE = 0 and = 1. We shall throughout assume that the …ne on the o¢ cial is at least as large as the …ne on the entrepreneur: A1. FO FE : In the case of harassment bribes this is a reasonable assumption and allows us to limit the cases we study without altering the qualitative conclusions of the analysis. 2.2 Bargaining We use the standard Nash bargaining solution to determine the bribe size. For s utility is: any bribe B 2 [0; L], the entrepreneur’ VE (B ) L B pFE + p B: (1) s utility is: Similarly, the o¢ cial’ VO (B ) B pFO p B: (2) If the players fail to agree on a bribe size, they both receive their outside options valued at 0. If a solution exists, it is given by the following: B arg max [VE (B ) 0] [VO (B ) 0] : (3) B 5 Since f(VE (B ) ; VO (B )) : B 2 [0; L]g is a compact and convex set, a Nash bargaining solution exists as long as the penalties are su¢ ciently small; that is, if there is some B~ such that VE B ~ ; VO B ~ (0; 0). We assume that the o¢ cial decides to demand a bribe if, and only if, a Nash bargaining solution exists (which, given the threat points, would automatically leave him weakly better o¤ than not demanding a bribe). Indeed, the exchange of a bribe comes closest to the kind of two-person nego- tiating situation that Nash (1950) had envisaged. Because of its illegal nature, there is seldom a third party or competitor involved during a transaction. It is a face-o¤ between two individuals– a classic bargaining situation. While there are competing bargaining models, such as the one by Kalai and Smorodinsky (1975), which have the advantage of a slightly wider domain of application (see Anant, Mukherji, and Basu, 1990), in this case they are unlikely to make any substantial di¤erence. 3 Benchmark Model Assuming a bribe is paid, the equilibrium bribe size is determined by: max (L B pFE + p B ) (B pFE p B) : (4) B This yields the following bribe size: L + p (FO FE ) B = : (5) 2 (1 p ) The corresponding utility is: L p (FO + FE ) VE (B ) = VO (B ) = : (6) 2 First, let us analyze the utility from a bribe. The Nash bargaining solution leaves the players with identical utility–they essentially agree to split the gains generated by the license. Any rise in penalties results in a smaller surplus to be shared, so utility drops. Observe that the resulting utility is una¤ected by , the fraction that the o¢ cial must return if caught. Since does not a¤ect the total surplus to be shared, any redistribution that emerges from punishment is accounted for in the bribe size– a larger results in a larger bribe size. Next, we analyze equilibrium bribe size. We can see that a solution exists if and only if p (FO + FE ) L. In other words, for a bribe to be exchanged, there must remain some surplus beyond the total expected punishment. Equation 5 lends itself to some natural comparative statics analysis. In particular, we might be interested in how the punishments and especially their symmetry properties a¤ect equilibrium outcomes. It can easily be veri…ed that @B @B @F0 > 0 and @FE < 0. Intuitively, the one who expects to get penalized more heavily needs to be given more up-front. Similarly, @B @ > 0 – if the o¢ cial 6 expects to have to return some of the bribe, more needs to be paid. Finally, consider how B changes in response to p: @B (FO FE ) + L = ; (7) @p 2(1 p)2 2 @ B [(FO FE ) + L] = ; (8) @p2 (1 p) The …rst and second derivatives are weakly positive if, and only if, FO FE L. This means that the bribe size rises in p if the rise in p hurts the o¢ cial su¢ ciently more than it hurts the entrepreneur. This condition is automatically satis…ed by Assumption 1. The results above are summarized in Proposition 1. Proposition 1 Suppose FO , FE , , and p are set by the government. (a) If p (FO + FE ) > L, bribes are eliminated. (b) If p (FO + FE ) L, a bribe is exchanged and the bribe size is strictly rising in FO , strictly dropping in FE , and strictly rising in . Given A1, the bribe size is strictly rising in p except if FO = FE and = 0, when it is constant in p. Two important lessons emerge even from this simple setting. The …rst is that the symmetry properties of the punishment are irrelevant to the elimination of bribery. Bribery is eliminated as long as (FO + FE ) is large enough. Whether the penalty burden is on the o¢ cial or the entrepreneur, and whether the o¢ cial is required to repay part of the bribe, do not matter, since the bribe size can adjust to account for them. To eliminate bribery, the state simply needs to drive up the expected total punishment high enough that the o¢ cial will not ask for a bribe. How it does so depends on its costs of adjusting p, FO , and FE . In the next section, we introduce a richer and arguably more realistic setting to further examine how asymmetric punishment might a¤ect bribery. The second lesson is that bribe sizes can rise when anti-corruption enforce- ment is strengthened. If bribery is measured by bribe size, an attempt to reduce bribery can instead increase it. In particular, if the penalty is low to begin with, a rise in the o¢ cial’s …ne or in the detection probability will result in a larger bribe. Our point here is that a larger bribe should not be interpreted as more severe bribery– it is simply a re‡ ection of the reallocation of surplus between entrepreneur and o¢ cial. Larger bribes seem to suggest a more acute problem, but policies designed to detect bribery might themselves raise the size of the bribe. 3.1 Bribe Size as a Function of Detection Probability As Equations (5) and (7) show, B is rising in p. Figure 1 depicts B (p) for some relevant parameter values. As noted before, the incidence of bribery is una¤ected by the symmetry properties of punishment. However, bribe size, and the e¤ect of p on bribe size, depend on whether punishment is symmetric or not. Under perfect symmetry, bribe size stays constant at L2 as long as punishment 7 is su¢ ciently small. If = 0 but …nes are asymmetric, bribe size rises linearly in p. If …nes are asymmetric and some of the bribe must be returned upon detection, bribe size is rising and convex in p. In fact, if FO + FE L (so that a bribe is feasible for all p) and = 1, bribe size rises to in…nity as p approaches 1. Intuitively, for high p, the o¢ cial gets a large bribe which he gets to keep with low probability, while the citizen pays a large bribe which is most likely returned to him. Figure 1: Equilibrium bribe size as a function of detection probability. 4 Endogenizing Detection Probability We continue with the assumptions above, but with one modi…cation. The en- trepreneur or the state can choose to incur a cost to raise p above a benchmark level (which could be zero). This is a reasonable and important assumption. Both the state and the players involved in bribery presumably have some con- trol over, and interest in setting, p. How they choose to exercise this control depends on their incentives– they must weigh the bene…ts of raising p against the costs. Therefore, it will be necessary to de…ne a cost function, c (p), over the relevant domain. It will also be necessary to modify our notion of equilibrium to accommodate an endogenous choice of p. We will assume that the selection of B and p satis…es rational expectations. First, suppose the entrepreneur controls p. Now, the anticipated costs of 8 whistle-blowing must be incorporated in the entrepreneur’s utility, so that:7 V E (B ) L B pFE + p B c (p) : (9) We use a modi…ed rational expectations approach to de…ne equilibrium: First, B (p) is determined taking p as given (if there is no solution, a bribe is not requested). Subsequently, the entrepreneur chooses p according to some function p (B ). In equilibrium, the p assumed during bribe size negotiations must be the same as the actual p the entrepreneur selects.8 For (p ; B ) to constitute an equilibrium, it must satisfy p = p (B ) and B = B (p ). Second, suppose the state controls p. On the one hand, bribe size is de- termined by Nash bargaining. Given p, the optimal bribe size depends on the function B (p), from equation (5). On the other hand, depending on the state’ s incentives, p possibly depends on bribe size, resulting in a function p (B ).9 An equilibrium with bribery, if it exists, is denoted by the pair (p ; B ) that satis…es p = p (B ) and B = B (p ). The bribe size must be a best response to the detection probability, and vice versa. 4.1 Entrepreneur Chooses p Suppose now the benchmark detection probability, set by the state, is p < 1, but the entrepreneur can raise the probability to some p 2 (p; 1] at a cost k .10 So, 0, if p = p; c (p) = k , if p = p: To make the problem interesting, we assume that p is low enough to support bribery: L A2. p < FO +FE The Nash bargaining solution, if it exists, for either p 2 p; p is given by: L p (FO FE ) c (p) B (p) = : (10) 2 (1 p) 7 This continues to satisfy the convexity requirements of the Nash Bargaining problem. 8 This is a non-standard concept of equilibrium as it combines cooperative and non- cooperative choices. Intuitively, a way to think of this within the standard framework of a non-cooperative game is the following: consider simultaneous moves made by two “play- ers,” where one player is the entrepreneur who must choose p and the other player is the entrepreneur-o¢ cial pair who must choose B according to their own objective function which, in this case, is provided by Nash bargaining. 9 It is not being assumed that the government knows in advance what the bribe size will be, but that it has a rational expectation about the size of bribe for this class of crime. Note that this includes the special case where p (B ) remains unchanged across di¤erent values of B. 1 0 For ease of exposition, we assume there are only two possible values of p. It is straight- forward to extend the analysis to a continuum of possible values. Notes are available upon request. 9 Note that B (p) may no longer rise in p; indeed, if k is su¢ ciently large, B (p) < B p . This is because there are now two forces at play as p rises: …rst, as before, a higher p reduces the surplus to be split, with a weakly greater burden imposed on the o¢ cial, causing the bribe size to rise; second, a higher p imposes a whistle-blowing cost on the entrepreneur, causing the bribe size to drop. 4.1.1 Symmetric Punishment The entrepreneur’ s optimal choice of p, p (B ), depends on the punishment regime. Clearly, under perfectly symmetric punishment, the entrepreneur gains nothing from raising p. Regardless of bribe size, he has no incentive to encourage detection since that would simply imply a higher probability of incurring FE . Therefore, p (B ) = p. The equilibrium outcome under symmetric punishment is depicted in Figure 2. p (B ) is constant at p. B (p) is now de…ned at only two points. Since we have symmetric punishment, B p < B (p). The equilibrium outcome lies at the intersection of the "best-response functions" B (p) and p (B ). Figure 2: Bribery survives under symmetric punishment and endogenous choice of p. 4.1.2 Asymmetric Punishment Now, consider a switch to perfectly asymmetric punishment. The entrepreneur must trade o¤ the cost of whistle-blowing against the potential bene…t in the form of greater expected bribe recovery.11 He will choose p = p if the potential 1 1 Over a continuous domain, she would raise p as long as c0 (p) > B . 10 recovery is su¢ ciently large, so:12 k p, if B p p p (B ) = (11) k p, if B < p p We can now analyze the impact of a switch from perfectly symmetric to perfectly asymmetric punishment in two cases. First, suppose the highest de- L tection probability still allows a bribe to be given (p < F O ). An equilibrium with a bribe size of B p and detection probability p exists if each is a best response to the other; that is, using (10) and (11), if k B p < p p L + pFO p p () k > kL : (12) 2 2p An equilibrium with bribe size of B (p) and detection probability p exists if each is a best response to the other; that is, using (10) and (11), if k B (p) p p (L + pFO ) p p () k < kH : (13) 2 p+p It can easily be veri…ed that kH > kL , so there is a range of parameter values that supports two equilibria– one with low detection and small bribes, and another with high detection and large bribes. L Next, suppose a bribe is impossible at p (p F O ). An equilibrium with low detection exists if k > kL as de…ned above. Otherwise, if k kL , an equilibrium with bribery cannot survive. This is summarized in the next proposition. Proposition 2 Consider a switch from symmetric to asymmetric punishment. L (1) If p < F O , bribery will not be eliminated. For k > kL , there will be a unique equilibrium with B p and p, as under symmetric punishment. For k kH , there will be a unique equilibrium with B (p) and p. For k 2 (kL ; kH ], there will be two equilibria. L (2) If p FO and k > kL , there will be a unique equilibrium with B p L and p, as under symmetric punishment. If p FO and k kH , the license is delivered without a bribe. We now discuss the proposition intuitively. For bribery to exist, there must be an equilibrium bribe size (B ) and detection probability (p ) such that p is a best response to the bribe size and B is a “best response” to the detection 1 2 We are assuming that, when indi¤erent, the entrepreneur chooses the higher detection probability. 11 probability. In other words, p should be such that the entrepreneur’ s bene…ts from whistle-blowing are greater than the costs of doing so. p (B ) is (step-wise) rising in B – under perfectly asymmetric punishment, a higher bribe means he stands to gain more from whistle-blowing. And B should be such that, given p, the bribe maximizes the Nash product or, in this case, divides the surplus equally across both parties. The possible equilibrium outcomes are depicted in Figures 3-6. A bribery equilibrium exists if the best response functions intersect. If k is low, whistle-blowing is cheap. So, for a given bribe size, the entrepre- neur is more willing to set a high p. The best response to a high p is a high bribe size. But if p is high enough, it is impossible to …nd a bribe size for which the probability of detection will be low enough to generate any surplus. So there will be no intersection of the best response functions (Figure 3). The o¢ cial will provide the license without asking for a bribe. The above analysis shows that, even in this more realistic framework, the basic logic of asymmetric punishment (Basu, 2011) remains intact in that it encourages whistle-blowing, but at the same time the model demonstrates that the control of corruption has greater complexity than suggested in that paper. If asymmetric punishment encourages enough whistle-blowing, bribery is elim- inated. But, if whistle-blowing is expensive or there are limits to how high detection probability could go, bribes might get bigger under asymmetric pun- ishment. If k remains low enough to encourage whistle-blowing and p is low enough to sustain bribery, asymmetric punishment simply leads to a rise in the bribe size which must occur to account for the higher likelihood of detection (Figure 4). Finally, if k is high enough, the low bribe outcome continues to survive in equilibrium. At such a bribe size, the entrepreneur does not have the necessary incentives to raise p. If k is very high, this is the only equilibrium (Figure 5). For intermediate values of k , two equilibria can coexist (Figure 6). However, in such cases, since the high detection equilibrium is Pareto dominated, we might conjecture that it is unlikely to be selected.13 4.2 Costly Adjustment of p by the State There are two reasons the state might prefer to encourage revelation by citizens rather than relying on its own detection. The …rst is that detection by the state could be particularly costly. To detect bribery, it has to be vigilant across all transactions, even those where no bribes are exchanged. On the other hand, it 1 3 Though Dufwenberg and Spagnolo (2013) emphasize a di¤erent and complementary set of considerations, it is useful to contrast our results to those in their benchmark game. In their model, if the o¢ cial incurs a cost of delivering the license, asymmetric punishment induces the o¢ cial to reject any o¤ered bribe but to also not deliver the license (a bribe functions as compensation for the o¢ cial’ s costs, and asymmetric punishment makes it impossible for the o¢ cial to be compensated). In the current paper, even if we were to introduce costs associated with license delivery, our results would remain qualitatively unchanged (asymmetric punishment could eliminate bribery or cause a rise in bribe size). This is because we implicitly treat not delivering the license as a dereliction of duty that subjects the o¢ cial to punishment as if he had demanded a bribe. 12 Figure 3: If k is low enough and p high enough, asymmetric punishment elim- inates bribery. Figure 4: If both k and p are low, bribe size rises under asymmetric punishment. 13 Figure 5: If k is high, the low bribe equilibrium survives. Also note that, because of the high cost of whistle-blowing, B p might be greater than B (p). Figure 6: With a low p and at intermediate values of k , both low bribe and high bribe equilibria are feasible. 14 might be cheaper for individuals to reveal that bribery has occurred, since they know exactly who was involved and how much was exchanged. The second is that a government that would like to detect bribery would still have to rely on an enforcer who is himself subject to a cost-bene…t analysis. As we argue next, while one can easily see how it would be in the interest of a decriminalized bribe-giver to have the bribe detected, this is less clear in the case of a government enforcer. Suppose p is set by a government enforcer at cost c (p). We could ask how the incentives for the enforcer should be set up. First, note that it is very hard to incentivize the enforcer to minimize the incidence of bribery. Since the state cannot distinguish between p = 0 (under which no bribes will be detected) and p = 1 (under which bribery will actually be eliminated), the enforcer has no incentive to exert any e¤ort to raise p. Bribe-enforcers have less of an incentive to eliminate bribery than bribe-givers do. Alternatively, suppose the bribe-enforcer is rewarded by the number of bribes detected or the amount in bribed detection. This actually incentives higher detection probabilities, but it is never in the enforcer’ s interest to raise detection so high that bribery is eliminated. 5 Discussion and Conclusion In the preceding sections, we built a simple model of harassment bribes. If a government o¢ cial demands a bribe in exchange for his service, he and the entrepreneur must bargain over the bribe size. The o¢ cial demands a bribe only if a Nash bargaining solution exists (given our construction of threat points, existence of a solution ensures that the o¢ cial is better o¤ by demanding a bribe than otherwise). Bribe size rises in detection probability, the o¢ cial’ s …ne, and fraction of bribe the o¢ cial must repay if detected. Bribe size drops in the entrepreneur’ s …ne. Importantly, these bribe size e¤ects exist solely to reallocate surplus. They should not be viewed as indicators of the severity of corruption. We …nd that the incidence of bribery does not depend on the symmetry properties of punishment. A bribe is paid as long as the total expected …nes are less than the surplus generated by the license. To eliminate bribery, the state must raise expected punishment to a su¢ ciently high level. If punishment is raised but inadequately, bribery will persist with higher bribe sizes. To examine more carefully the implications of asymmetric punishment, we expanded the model to endogenize detection probability. If the o¢ cial demands a bribe, the entrepreneur must choose detection probability. Now, the symme- try properties of punishment matter. Under symmetric punishment, endoge- nous selection of detection probability changes nothing since it is not in the entrepreneur’ s interest to have the bribe detected. However, under asymmetric punishment, the entrepreneur is willing to incur some costs to raise detection probability as this allows him to get his money back. If bribery survives, bribe size and detection probability must be best responses to each other. We …nd that asymmetric punishment eliminates bribery if whistle-blowing is e¤ective and cheap. Otherwise, bribery survives and bribe sizes can rise relative to sym- 15 metric punishment. Our results here are quite parameter-speci…c, and importantly so. Consider variation in k and p. These two variables describe the ease with which a cit- izen can reveal bribery to the government, and they depend on the ability to verify a bribe payment, the responsiveness of government departments to such claims, the extent to which the whistle-blower is protected after the act, the e¤ectiveness of the judicial system, etc. If k is low and p high, so the country has the infrastructure to allow reporting at low cost, asymmetric punishment is an e¤ective solution for eliminating bribery. The change in the entrepreneur’ s incentives drives detection probabilities so high that it is impossible to arrive at a bribe size that is large enough to make bribery worthwhile for the o¢ cial. As k rises and p drops (i.e. whistle-blowing gets more di¢ cult), we move from zero bribery to large bribe sizes. As k rises further, bribe sizes drop down to the levels under symmetric punishment. This leads to some unusual cross-country predictions. If countries were ordered by ease of reporting bribes, all else equal, we should see bribery appear the most severe for intermediate countries where whistle-blowing is cheap enough that a lot of it happens, but not so cheap that bribery can be eliminated. The possibility of multiple equilibria adds addi- tional complexity, as identical underlying conditions could lead to substantially di¤erent bribe sizes. This model suggests some ways to structure our thinking about anti cor- ruption policy. Clearly, one way to eliminate bribery is to make punishments severe and probability of detection high (see Becker, 1968). However, severe …nes are often politically infeasible and detection, if carried out by government enforcers, can be expensive (where should we look?) and hard to incentivize (how do we distinguish between eliminating bribery and failing to detect it?). In this context, it makes sense to transfer the task to signaling bribery to those who know it best– the parties involved. This can be incentivized through asym- metric punishment. But for asymmetric punishment to work, whistle-blowing needs to be su¢ ciently cheap– the state must not only encourage entrepreneurs to reveal bribery, it must allow them to do so easily. This requires careful at- tention to several aspects of bureaucratic and legal institutions. If the state is unable to make whistle-blowing su¢ ciently cheap to eliminate bribery, then somewhat perversely, it is best to make whistle-blowing expensive so it happens less. This is because the e¤ort expended in revealing a bribe creates a pure surplus loss unless bribery is actually eliminated. So, if countries with bribery problems are also countries with weak institutions for reporting, they can be stuck in corruption traps where asymmetric punishment makes matters worse, not better. The model above is stylized to isolate some key e¤ects. There are some natural extensions that could help build a richer understanding of the design and implications of anti-corruption policy. First, the model could be extended to non-harassment bribes. Consider the following example: the agent has violated the law and stands to lose L. Instead, he could pay a …ne B to the bureaucrat. The problem remains identical to ours but notions of e¢ ciency might change. This also creates room for thinking about endogenizing the agent’ s decision to 16 commit the crime in the …rst place. Second, it might be instructive to analyze a setting with heterogeneity in license bene…t and moral costs, where these are private information. Finally, recall that one prediction of our model is that if …nes are small, bribe sizes can get inde…nitely large as the probability of detection approaches one. While it could be argued that lim B (p) is not empirically relevant, this p!1 does raise a concern about the depths of entrepreneurs’ pockets. 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