The Welfare Effects of Consumers Reports of Bribery

Transcription

1 The Welfare Effects of Consumers Reports of Bribery J. ATSU AMEGASHIE Department of Economics and Finance Uniersity of Guelph Guelph, Ontario Canada N1G 2W1 A primary means of bureaucratic oersight is consumer complaints. Yet this important control mechanism has receied ery little attention in the literature on corruption. I study a signaling game of corruption in which uninformed consumers require a goernment serice from informed officials. A ictim of corruption can report corrupt officials whose superisors are negligent or conscientious but an official s type is his priate information. I find that social welfare may be nonmonotonic in the proportion of conscientious superisors. Seeral examples show that an increase in the proportion of conscientious superisors decreases social welfare if the mass of conscientious superisors is below a critical leel. I find that this pererse result does not hold if (a) the bribe is ery large, or (b) bribe-giing is legalized. I also find that there is an equilibrium in which no one reports corruption. 1. Introduction Goernment corruption is the sale by goernment officials of goernment property for personal gain (e.g., Bardhan, 1997). In many less-deeloped countries, one must pay a bribe to obtain a routine goernment serice such as getting a child into a public school, a drier s license, a building permit, a passport, a birth certificate, clearing goods at customs, etc. There is, of course, corruption in deeloped countries een if to a lesser extent. A primary means of bureaucratic oersight is consumers complaints. Ghana s 2006 Whistleblower Act, the Punjab Citizen Feedback Model, and I paid a bribe websites 1 in seeral countries recognize this point. In 2011, the Kingdom of Bhutan s Anti-Corruption Commission created an online form to allow the anonymous reporting of corruption. 2 And in October 2013, Kenya launched an anticorruption web site 3 for people to report incidents of corruption directly to the goernment. Users can upload ideos, photos and other documents and can choose from a long dropdown list of goernment departments I thank a coeditor, two anonymous referees, and Henry Thille for ery helpful comments. My thanks are also due to Kurt Annen, Zubair Bhatti, Ken Jackson, Olier Masakure, and Jun Zhang for helpful comments on an earlier ersion of this paper. I also thank seminar participants at the following uniersities: Florida State, Guelph, and Manitoba. 1. See a March 2012 New York Times article titled Web Sites Shine Light on Petty Bribery Worldwide : pagewanted=all&_r=0 2. Among others, the site states that [H]elp us be more efficient and effectie by proiding true complaints with specific details. You could also stand as witness and informer. Your identity and liability shall be protected as per the witness protection sections under chapter 7 of the Anti-Corruption Act of Bhutan : C 2015 Wiley Periodicals, Inc. Journal of Economics & Management Strategy, Volume 25, Number 2, Summer 2016,

2 Consumers Reports of Bribery 517 to complain about. The Punjab Citizen Feedback Model (Pakistan) inoles an audit (phone calls) to ascertain consumer feedback about a goernment serice, and whether or not they were made to pay a bribe for the serice. 4 Recently, Basu (2012) proposed that bribe-giing but not bribing taking should be legalized to encourage bribe-giers to report corruption. Surprisingly, this consumer-feedback mechanism has receied ery little attention in the literature on corruption. The literature on whistleblowers focuses on employees (not consumers) of an organization. In this paper, I study a model in which consumers of a goernment serice encounter corrupt officials whose superiors may be negligent or conscientious. Whether a corrupt official s superisor is conscientious or negligent is known to the official but not to the consumer. If a consumer rejects a demand for a bribe and reports corruption, he gets the serice without paying a bribe if the superisor is conscientious. This is the benefit of reporting corruption. If the superisor is negligent, nothing is done about the consumer s complaint and he does not get the serice. So he loses a positie surplus if the bribe he refused to pay was smaller than his aluation. This is the cost of reporting corruption. I find that in some cases, social welfare is nonmonotonic in the proportion of conscientious superisors. In particular, it may be decreasing in the proportion of conscientious superisors. The intuition is that although increasing the proportion of conscientious superisors results in higher reports, it may also result in an increase in the number of consumers who do not get the serice because their complaints were handled by negligent superisors. It is an elasticity issue in the sense that for social welfare to increase, consumers reports should not be too elastic with respect to an increase in the number of conscientious superisors. In some cases, an increase in the proportion of conscientious superisors decreases social welfare if the mass of conscientious superisors is below a critical leel. This suggests that piecemeal anticorruption measures may be counterproductie or welfare reducing. I find this result does not hold if the bribe is ery large or if bribe-giing is legalized. I find that there is an equilibrium in which no one reports corruption. This is because the equilibrium bribe is sufficiently small to make complaints not worthwhile. To the best of my knowledge, this is the first model of corruption in which consumers decision to report corruption is endogenized and studies the factors that affect the frequency of consumers reports and their effect on social welfare. Howeer, there are some related papers. Mookherjee and Png (1992) study a model with consumers complaints but these complaints are exogenous and there is no bribery. In Prendergast (2003), the superisors of corrupt officials are not negligent. Botero et al. (2013), using surey data on reporting crime and corruption, found that better-educated citizens are more likely to report crime and corruption, and argue that this may explain why better-educated countries hae better goernments. Empirically, they also found that the country-aerage assessment that a policeman iolating the law will be punished is a strong predictor of the probability of complaining about misconduct and reporting 4. The model is described at the official web site of the Goernment of Punjab as follows: When a citizen goes to a goernment office to aail a serice (e.g., driing license, character certificate, property registration) the office records his or her mobile number along with the transaction details. This data is passed on to local officers and to a call center through an online data entry form or through SMS. The local officers call some of the citizens. The call center sends SMS messages to citizens and also calls a much greater percentage to inquire about quality of serice receied. Thus, the state, instead of passiely waiting for the citizen to file a complaint, if there is indeed cause of such a grieance, proactiely engages the citizen and gets his feedback to improe serice deliery and, especially, weed out corrupt goernment officials.":

3 518 Journal of Economics & Management Strategy crime. I formally endogenize the latter mechanism to show that the probability (posterior belief) that a conscientious superior will handle a complaint increases the number of complaints. The paper is organized as follows. The next section presents and soles a model of incomplete information and consumers reports. A subsection considers the case of legalized bribe-giing. Section 3 discusses robustness and extensions and section 4 concludes the paper. 2. The Model Consider a goernment agency with a continuum of risk-neutral officials of unit measure who proide a serice to members of the public. Each official has a superisor who is conscientious or negligent. An official whose superisor is conscientious is C-type and is an N-type if his superisor is negligent. An official s type is his priate information and the proportion of C-type officials, which is common knowledge, is π (0,1). Each C-type official s per-period aluation of his job is s, where s is continuously distributed on [s, s] with distribution function F(s); s 0. An official s aluation of his job is his priate information. Each official has an infinite horizon and can sere only one consumer per period. The discount factor is δ (0,1). There is a continuum of risk-neutral consumers of unit measure each with aluation,, for the serice, where is continuously distributed on [, ] with distribution function G(); 0. A consumer s aluation is his priate information and he wants only a unit of the serice. Without loss of generality, assume that the official price of the serice is k = 0. 5 There is a bribe, b 0, demanded by a corrupt official. The bribe is a form of extortion or what Basu (2012) calls a harassment bribe. After an initial (costless) contact with an official, assume that further search is not possible. Allowing consumers to keep searching for an official till they meet an honest official makes reporting by consumers redundant, an undesirable feature of a model of consumers reports. Furthermore, there are certain serices for which you cannot search een if search is costless. For example, when an immigration official, customs official, or an official who issues passports demands a bribe, you cannot go to another official because the original official will not transfer your file and once he has denied your application, another official may not process your application unless you lodge a formal and successful complaint to a higher-ranking official. Paying a bribe is illegal, so consumers who intend to report corruption will not pay the bribe and those who paid a bribe will not report corruption. Conscientious superisors only act when a consumer reports an official. Alternatiely, they cannot fire their subordinates unless there is a report by consumers. This allows me to focus on the role of consumers reports. In the model, consumers do not report an official out of spite or hatred, so their reports are credible. When a corrupt C-type official is reported, he is fired immediately, no preious bribe collected is retrieed, is replaced by a random selection from the same population, 5. There are certain goernment serices (e.g., public schools) for which the price is zero. An extension which models an official s decision to engage in corruption without theft (extortion or harassment) or corruption with theft (collusion or nonharassment), as defined in Shleifer and Vishny (1993), considers the case of k > 0. This is necessary because corruption with theft would require a corrupt official to sell the serice at a price that is less than k, which does not make sense if k = 0. This extension is aailable on request. Oak (2015) considers a similar problem but in a model with no consumer reports.

4 Consumers Reports of Bribery 519 and the complainant gets the serice without paying a bribe. 6 A corrupt N-type official is not punished and his superisor ignores consumers complaints. Consumers who report corruption cannot rejoin the queue. This ensures that reporting corruption is potentially costly (i.e., when the complainant meets a negligent superisor and is a consumer who would hae been better off paying the bribe). Otherwise, all consumers will report corruption. Consumers who reject an official s bribe demand can rejoin the same official s queue if they did not report him. The sequence of actions is as follows: (1) Without obsering an official s bribe or his type, a consumer approaches an official for the goernment serice. (2) If the official is honest, the consumer is sered. If the official is corrupt, the consumer has two choices: (a) refuse to pay the bribe and report the official; or (b) pay the bribe and not report the official. (3) Payoffs for the consumer and official are realized. If the official is not fired in a gien period, another consumer approaches him in the next period and we repeat the process starting in stage 1. If the official is fired he is, as preiously, stated replaced by another official who is randomly chosen from the same population. Before I proceed to the solution of the model, let me reiterate that consumers cannot search after meeting an official. I need this friction in the model because a model of corruption cannot be a first-best model. After all, corruption tends to exist because we are not in a first-best enironment. Otherwise, eliminating or reducing corruption becomes a triial problem. For example, it is obious that corruption can be significantly reduced by combining a small monitoring probability with a ery seere punishment (e.g., fine) for offenders (e.g., Becker, 1968; Stigler, 1970) or ery high salaries for corruptible officials (e.g., Becker and Stigler, 1974). Howeer, there are standard second-best arguments in the law and economics literature for why these solutions cannot or should not be implemented (e.g., Stigler, 1970; Mookherjee and Png, 1992). But more importantly, the frictions in my model were not chosen arbitrarily. They were chosen with the goal of constructing a second-best enironment that gies a possible nontriial role to consumer complaints in the control of corruption Equilibrium Analysis If a consumer reports corruption to a conscientious superisor, his payoff is ; if the superisor is negligent, his payoff is zero. If he pays a bribe, he gets b if b ; if b < 0 and he does not report corruption, his payoff is zero. Let r [0,1] be the probability that an official who demands a bribe is reported. Gien a continuum of consumers, the law of large numbers imply that r is also the measure (proportion) of consumers who will report an official if the official demands a bribe. Gien that a consumer who is willing to report a demand for a bribe might end up meeting an honest official, r 6. For simplicity, I assume that since an official deals with one consumer per period in his office, firings are not obsered by consumers who are yet to be sered because a consumer does not know the identity of an official until he enters his (official s) office. This ensures that the consumers do not get additional information when an official is fired. Alternatiely, we may assume that consumers obsere firings of officials but there is replacement or death of superisors with some exogenous probability and this replacement of superisors is also obsered by consumers. This does not affect the analysis. The proof is aailable on request. 7. In the same ein, Lazear (2006), for example, assumes an exogenous and sufficiently small fine (punishment) in order to focus on alternatie measures of dealing with malfeasant behaior. The same is also true in many models of corruption (e.g., Mookherjee and Png, 1995).

5 520 Journal of Economics & Management Strategy is not the proportion of consumers who report demands for a bribe. Howeer, for the sake of exposition, I use the expressions the measure of reports and the measure of consumers who are willing to report interchangeably. The solution concept is perfect Bayesian equilibrium. I focus on pure strategies. In a perfect Bayesian separating equilibrium, N-type officials and C-type officials choose different bribes. In a pooling equilibrium, both types choose the same bribe. A semiseparating or hybrid equilibrium may take the following form: some C-types choose the same bribe with N-types and other C-types choose a different bribe. The following lemma eliminates one class of equilibria: Lemma 1: There is no separating equilibrium (i.e., an equilibrium in which N-type officials and C-type officials choose different bribes). Proof: Corrupt C-type officials cannot choose a positie bribe different from the bribe chosen by corrupt N-types because they would reeal their type; their demand for a bribe will be rejected and they will be reported for sure and fired. Therefore, a separating equilibrium, if it exists, must be such that all C-types will be honest (i.e., choose a bribe of zero) and all N-types will be corrupt (i.e., choose a positie bribe). But then the optimal response for consumers is not to report corruption (i.e., r = 0) because only N-type officials are corrupt. Howeer, gien r = 0, not being corrupt is not optimal for a C-type official; a C-type official is better off by deiating to the positie bribe being demanded by N-types. This contradiction implies that there is no separating equilibrium. Accordingly, I focus on perfect Bayesian pooling or semi-separating (hybrid) equilibria in pure strategies. 8 Definition: A pure-strategy perfect Bayesian pooling or semiseparating (hybrid) equilibrium of this game is a bribe-report probability pair, ( ˆb, ˆr), and consumers beliefs about an official s type (N-type and C-type) such that (a) gien ( ˆb, ˆr) and consumers beliefs, each official chooses to be corrupt or honest, where honest officials choose a zero bribe, corrupt officials choose ˆb 0, and no official has the incentie to change his bribe, (b) gien ( ˆb, ˆr) and a consumers beliefs, each atomistic consumer maximizes his payoff by choosing whether or not to report an official if the official demands a bribe; (c) gien ˆb, the measure of consumers in (b) who will report corruption is indeed ˆr, and (i) wheneer possible, the consumers beliefs are deried from the officials strategies using Bayes rule. I focus on equilibria with a bribe ˆb (0, ) for all corrupt officials and ˆr (0, 1). 9 Stage 3 is triial. I therefore moe to stage 2. Consider C-type officials in stage 2. Consumers approach an official sequentially and do not obsere an official s type or bribe before approaching him, so they approach officials randomly in stage 1. To a C- type official, each consumer s type is an identical and independent draw from the same distribution. Therefore, a C-type official s belief of the probability that a consumer will report corruption is the same for each consumer. For a C-type official with aluation s, the Bellman equation for a corrupt strategy is V t = (1 r)([s + b] + δv t+1 ), where V t is the alue function for period t. The preceding arguments, risk-neutrality, infinite 8. Notice, for example, that there cannot be an equilibrium in mixed strategies for consumers because the model has a continuum of consumers with different aluations. So for a gien bribe, when a consumer with a gien aluation is indifferent between reporting and not reporting corruption, then this condition will not hold for other consumers. 9. I discuss equilibria with b / (0, ) in an appendix aailable at: jamegash/ OnlineAppendixCorruption.pdf.

6 Consumers Reports of Bribery 521 horizon, and the fact that no preious bribe is retrieed imply that an official s problem is stationary. Then V t = V t+1 (for all t) gies the payoff from a corrupt strategy as V *B = (1 r)(s + b)/(1 δ[1 r]). The payoff from a noncorrupt strategy is V *NB = s/(1 δ). A C-type official will be corrupt if V B V NB. (1) Then (1) implies that C-types with aluation s ŝ will be corrupt and those with s > ŝ will not, where ŝ (1 δ)(1 r)b/r. Therefore, the measure of corrupt C-type officials is ŝ ( ) (1 δ)(1 r) ρ(b, r) = df(s) = F (ŝ) = F b. (2) s r Consider an N-type official in stage 2. Gien that an N-type official s job security does not depend on being corrupt or honest, his aluation of his job has no effect on his decision to be corrupt. Therefore, without loss of generality, I ignore an N-type official s aluation of his job. Furthermore, gien that an N-type official keeps his job when he is reported for demanding a bribe and there is a positie probability (i.e., [1 ˆr] [0, 1]), of a consumer paying the bribe, it triially follows that it is a strictly dominant strategy for all N-type officials to demand a bribe. Consider the consumers in stage 2. Gien the strategy of C-types and N-types, a consumer s belief that an official is a C-type gien a demand for a bribe is: λ(b, r) Pr ( C type b ) ρ(b, r)π = ρ(b, r)π + (1 π). (3) A consumer of type for whom b 0 will report corruption if λ(b, r) + (1 λ[b, r])(0) b. Consumers with b < 0 will report corruption because λ(b, r) + (1 λ[b, r])(0) 0 > b. Therefore, a consumer will report corruption if λ(b, r) + (1 λ [b, r])(0) max[0, b]. (4) The set of consumers who satisfy the inequality in (4) hae aluation [, ˆ], where λ(b, r)ˆ + (1 λ[b, r])(0) = ˆ b. This gies ˆ(b, r) = b/(1 λ[b, r]) > b. Consumers with aluation ˆ will report corruption and those with > ˆ will not. Hence, r = ˆ ( dg() = G(ˆ) = G b 1 λ(b, r) ). (5) For consumers with b, the cost of reporting corruption is zero. For those with (b, ˆ), the expected cost of reporting corruption is positie because they may meet a negligent superisor and thereby lose a positie surplus because they cannot rejoin the queue. Hence, the cost of reporting corruption is different for different consumers. The following lemmas are useful in subsequent analysis: Lemma 2: There is no equilibrium with ˆb (0, ) and ˆr = 1 (i.e., all consumers are willing to report corruption). Proof: Towards a contradiction, suppose ˆb (0, ) and ˆr = 1 is an equilibrium. Then no C-type official will be corrupt because, gien that bribe-giing is illegal, his demand for a bribe will be rejected and he will be reported with certainty. Howeer, gien that no C-type official is corrupt, it is not an optimal response for all consumers to report a

7 522 Journal of Economics & Management Strategy demand for a bribe because ˆb (0, ) and any official who demands a bribe is belieed to be an N-type (i.e., λ = 0). That is, the inequality in (4) does not hold for all if λ = 0 and ˆb (0, ). Hence, ˆr = 1and ˆb (0, ) cannot be an equilibrium. Lemma 3: Holding b fixed, ρ(b, r) = (1 δ)bf(ŝ)/r 2 < 0, (6) r λ r = πρ r (1 λ) < 0, (7) and r π = g(ˆ)bρr 2 > 0, (8) (1 π)[(1 π)r 2 + (1 δ)πg(ˆ) f (ŝ)b 2 ] where ρ r ρ/ r, ρ(b, r)π + (1 π) f (s) = F (s), and g() = G (). 10 The result in (6) means that an increase in the measure of consumers who are willing to report bribery reduces the measure of corrupt C-type officials whereas the result in (8) means that as the measure of C-type officials increases, there is also an increase in reports. These results are intuitie. The intuition behind the result in (7) is not so obious. It says that an increase in measure of consumers who are willing to report bribery reduces a consumer s posterior belief that an official who demands a bribe has a conscientious superisor (i.e., is a C-type). This is because an official who demands a bribe when there is a higher probability of being reported is likely to hae a negligent superisor. This follows from the result in (7) because when there are more consumers who are willing to report bribery, there are fewer corrupt C-type officials. Define Ĝ(r) G(ˆ[ ˆb, r]). The solution to equation (5) is a fixed point: r = Ĝ(r). Differentiating Ĝ(r) with respect to r gies Ĝ(r) r = g(ˆ) ˆbλ r < 0, (9) 2 (1 λ) because λ r λ/ r < 0 according to (7). Note that Ĝ(r) as r Also, Ĝ(1)= G( ˆb) < 1 because ˆb (0, ). 12 Then gien that Ĝ(r) is continuous and strictly decreasing in r, there exists a unique fixed point, ˆr (0, 1) of Ĝ(r). Recall that corrupt C-type officials cannot choose a positie bribe different from the bribe chosen by N-types because they would reeal their type; their demand for a bribe will be rejected and they will be reported for sure. Therefore, for corrupt C-type officials, b(s) = ˆb s. Any bribe, ˆb (0, ), is an equilibrium bribe. I support these equilibria with the following out-of-equilibrium beliefs: if a consumer obseres b ˆb, he beliees that the official is C-type and so he will report the official. Therefore, ˆb is the optimal bribe for all corrupt official (including N-types). 13 This gies: 10. To obtain (8), differentiate the LHS and RHS of r = G(b/(1 λ[b,r]) in equation (5) with respect to π, collect terms, and sole for π/ r. 11. To see this, note that ρ as r 0. By L Hopital rule, λ 1asρ. Finally, Ĝ(r) as λ When r = 1, then ρ = 0, so λ = 0. This gies G( ˆb/[1 λ]) = G( ˆb) = Ĝ(1). 13. It is important to recall the following points: (i) an official does not know if a consumer s type is ˆ, (ii) a consumer can rejoin an official s queue after rejecting his bribe demand if he did not report the

8 Consumers Reports of Bribery 523 Proposition 1: Consider ˆb (0, ) and let ˆr (0,1) be the solution to (5) gien ˆb. Suppose ŝ (1 δ)(1 ˆr)ˆb/ˆr (s, s). Then there exists perfect Bayesian semiseparating equilibria with bribes ˆb and reports ˆr such that all N-type officials are corrupt and the proportion of corrupt C-type officials is ˆρ = F (ŝ) (0,1). Each consumer s belief that a corrupt official has a conscientious superisor is λ( ˆb, ˆr) ˆλ = π ˆρ/[1 π + π ˆρ] if b = ˆb and λ = 1if b ˆb. Lemma 2 says that there is no equilibrium with ˆb (0, )andˆr = 1 and proposition 1 does not include equilibria in which ˆr = 0. Accordingly, I state the following proposition: Proposition 2: Gien π (0,1), suppose > 0. Then there exists perfect Bayesian pooling equilibria (with corruption) as follows: ˆb (0, b], ˆr = 0, and ˆρ = 1, where b = (1 π) > 0. That is, all officials demand the bribe, ˆb, and no consumer reports corruption. Each consumer s belief that a corrupt official has a conscientious superisor is ˆλ =π if b = ˆb and any official who demands b ˆb is belieed to hae a conscientious superisor. Proof: Consider the equilibrium with ˆb = b = (1 π) > 0. Recall that each consumer is atomistic. Suppose that each consumer beliees that all other consumers will not report corruption, so that r = 0. Then all officials will be corrupt. 14 So a consumer s posterior belief that an official who demands a bribe is C-type is π. Then a consumer will not report a demand for a bribe if ˆb >π, which is true for all, gien ˆb = (1 π) > 0. Gien the out-of-equilibrium beliefs, no official has the incentie to deiate. So ˆb= b, ˆr = 0, and ˆρ = 1 is an equilibrium. Then it is obious that ˆb (0, b), ˆr = 0, and ˆρ = 1is also an equilibrium. Notice that unlike the equilibrium in proposition 2, the equilibrium in proposition 1 does not require > 0. Therefore, if = 0, then only the equilibrium in proposition 1 holds. 2.2 Equilibrium Refinement The equilibria in propositions 1 and 2 satisfy the intuitie criterion (see appendix A). The game has infinitely many perfect Bayesian equilibria in propositions 1 and 2 that satisfy the intuitie criterion. In what follows, I use a stronger refinement and focus on the equilibrium in proposition 1 for the following reasons: (a) although there is a plethora of equilibrium bribes in proposition 2, the equilibrium measure of reports is unique (i.e., ˆr= 0). The result that no one reports corruption is interesting and independent of the bribes in proposition 2, and (b) one of the paper s main results (i.e., proposition 3) is based on proposition 1. The equilibria in proposition 1 also surie the stronger D1 refinement (Banks and Sobel, 1987; Cho and Kreps, 1987). 15 I proe this result in appendix B. official, and (iii) a consumer does not know that an official is C-type. These three obserations imply that a consumer cannot merely by rejecting an official s offer credibly threaten to report corruption expecting that such a threat will lead the official to demand a bribe smaller than ˆb. 14. Note, howeer, that ρ(b, r) in equation (2) is undefined for r = 0. This is because when r = 0, the weak inequality in (1) does not hold with strict equality for any b > 0. Gien that all C-type officials are corrupt when r = 0andb > 0, we may write the proportion of corruption C-type officials as max(1, ρ[b, r]). 15. If an equilibrium suries the D1 refinement, then it necessarily suries the intuitie criterion. But the conerse statement is not necessarily true. Howeer, using both refinements does not render the intuitie criterion redundant because both equilibria in propositions 1 and 2 surie the intuitie criterion but only the equilibria in proposition 1 surie the D1 refinement.

9 524 Journal of Economics & Management Strategy Gien that these commonly used refinements do not narrow the set of equilibria, 16 I use a range of equilibrium bribes in proposition 1 for subsequent analysis. Fortunately, proposition 3, which is based on proposition 1, holds for a wide range of equilibrium bribes. Therefore, it does not hinge on a particular equilibrium bribe. This is shown in Table I below. Note that proposition 3 below, which is based on proposition 1, holds for examples in which = 0, a case in which proposition 2 does not hold. 2.3 Social Welfare Treating bribes as redistributie transfers, the equilibrium expected social welfare is: Ŵ = ((1 π) + π ˆρ) ˆ g()d + π ˆρ ˆ g()d + π(1 ˆρ) g() d. (10) The first term is the payoff of consumers who are willing to pay the bribe weighted by the probability of meeting a corrupt official and the second term is the payoff of consumers who will report a demand for a bribe weighted by the probability of meeting a corrupt official whose superisor is conscientious (i.e., a corrupt C-type official). The final term is the payoff of all consumers weighted by the probability of meeting an honest C-type official. 17 Equation (10) simplifies to Ŵ = (1 π) ˆ g()d + π g() d. (11) Gien that ˆb is independent of π, it follows that when I undertake comparatie static exercises with respect π, the equilibrium bribe will not change. Howeer, when π changes, the measure of corrupt C-type officials and the measure of consumers who are willing to report corruption may adjust to changes in π. I return to this point in the discussion of the robustness of the results. Using Leibniz s rule, we get Ŵ π = ˆ g() d (1 π)ˆg(ˆ) ˆ π. (12) Gien that ˆr = G(ˆ), G(.) is an increasing function, and ˆr/ π > 0, it follows that ˆ/ π > 0. The sign of the deriatie in (12) is ambiguous because its first term is positie whereas its second term, gien ˆ/ π > 0and ˆ (, ), is negatie Numerical Examples Consider the equilibrium in proposition 1. Let δ = 0.1. Suppose is uniformly distributed on [0,2] and s is uniformly distributed on [0,1]. Seeral examples show that Ŵ is strictly 16. This signaling game has types in two nontriial dimensions: a two-type space for an official s superisor (C-type and N-type) and an infinite type space for a C-type s aluation of his job. It should not come as a surprise that the semiseparating equilibria in proposition 1 surie stronger refinements. The present game is not a standard signaling game in the sense of Cho and Sobel (1990). 17. At the risk of belaboring the obious, note that the bribe paid by a consumer to an official enters as b in the social welfare function, while the same bribe receied by the official enters as + b resulting in b + b = 0. This is why the bribes do not enter the social welfare function. In a preious ersion of this paper, I also treated the bribes receied by corrupt officials as costs to consumers by subtracting them from social welfare but not as a benefit to the officials. This added an additional term to social welfare as stated in (10). The issue of whether or not bribes should be treated as a cost or benefit in social welfare is reminiscent of an objection raised by Stigler (1970) against Gary Becker s formulation of the social welfare of crime wherein the gain to the criminal is included in social welfare. I shall later discuss why the exclusion of bribes in social welfare is sensible.

10 Consumers Reports of Bribery 525 conex in π on the domain [0,1] with a stationary point (i.e., it is U-shaped) for a wide range of equilibrium bribes. In Table I below, I indicate the alue of π at which the welfare function is at its minimum alue (for a gien ˆb): Table I. VALUE OF π AT WHICH Ŵ IS AT A MINIMUM FOR A GIVEN ˆb. THE DOMAIN Is π [0, 1) ˆb π To present an example of a typical case in a diagram, consider ˆb= 1. Gien the parameters and distribution functions aboe, it can be shown that 18 ( π + ) 340π 359π ˆr =. (13) 1 π Plotting the equilibrium social welfare, Ŵ, onπ [0, 1) gies 19 figure 1 below. The numerical results in Table I show that gien δ = 0.1, and s uniformly distributed on [0,2] and [0,1] respectiely, 20 social welfare, Ŵ,isU-shapedasfunctionofπ for ˆb (0, 1.4]. 21 As noted aboe, seeral examples confirm this result. This gies: Proposition 3: Below a critical mass of conscientious superisors, social welfare may decrease as the proportion of conscientious superisors increases. 18. I also plotted ˆr on the domain π (0,1) to confirm that ˆr was indeed in the feasible interal (0,1). I did the same for ˆρ. The equilibria in proposition 1 exist for all alues of π (0,1). These results and equation (13) were obtained with the help of the software, Maple V. 19. Using equation (13), we get ˆr = 0.5 when π = 0. Note that λ = 0whenπ = 0. So gien ˆb= 1andthe uniform distribution on [0,2], a measure ˆr = G( ˆb) = 0.5 of consumers report corruption. For these consumers, the cost of reporting corruption is zero because ˆb. So we get the triial case of some customers reporting corruption een though all officials are N-types. 20. The results hold for bigger parameter alues (e.g., δ = 0.42). But they do not hold when δ is too high. I shall explain the intuition for this result in section The exact upper bound of this interal actually lies between 1.4 and 1.5. I also looked at plots of the welfare function. Looking at plots of the equilibrium reports is consistent with the result in lemma 3 that the equilibrium measure of reports is increasing in π.

11 526 Journal of Economics & Management Strategy FIGURE 1. Social welfare and proportion of conscientious superisors. The intuition is as follows: as the proportion of conscientious superisors increases, the measure of reports also increases. Howeer, a proportion of these complainants will meet a negligent superisor and so will not get the serice (the cost of complaints). For a gien π,theexpected measure of complainants who did not get the serice because they met a negligent superisor is L = (1 π)ˆr. If the increase in π leads to a sufficiently high increase in ˆr, then L/ π = (1 π)( ˆr/ π) ˆr will increase; the expected measure of consumers who will not get the serice will increase. 22 The aluations of these disgruntled but unsuccessful consumers matters because consumers for whom > ˆb and, who preiously would hae paid the bribe but now report corruption, would hae been better off paying the bribe We can rewrite the deriatie aboe as, L π = ˆr π ([1 π]εˆrπ π), where εˆrπ ˆr π π ˆr is the elasticity of ˆr with respect to π. Then it follows sufficient but not necessary conditions for L/ π> 0areπ 0.5 and εˆrπ > 1. Therefore, if the proportion of conscientious superisors is not more than 50% and the equilibrium measure of reports is elastic with respect to the proportion of conscientious superisors, then an increase in the proportion of conscientious superisors increases the expected measure of consumers who do not get the serice. Howeer, note that this argument does not consider the important effect of the aluations of those who do not get the serice, which is subsequently discussed in the text. 23. As noted earlier, in a preious ersion of this paper, I also treated the bribes receied by corrupt officials as costs to consumers by subtracting them from social welfare. In cases where proposition 3 is oerturned because the bribes to officials are not treated as pure transfers but as costs, this is due to a pererse effect. In particular, if social welfare is monotonically increasing in π when it would otherwise be decreasing in π (oer a certain range), it is because although social welfare falls as a result of more consumers who report not getting

12 Consumers Reports of Bribery 527 Note that, gien a fixed ˆb, those who were willing to report corruption before the increase in π will continue to do so after the increase in π. Therefore, gien a fixed ˆb, the increase in reports is solely due to the fact that some consumers with > ˆb who were preiously willing to pay the bribe and not report corruption are now willing to report corruption because of the increase in π. To elaborate on the welfare implications of these changes in behaior, we can rewrite (11) as Ŵ = ˆ g()d + π ˆ ˆb g() d + π ˆb g() d. (14) When the proportion, π, of conscientious superisors increase, consumers whose aluations was smaller than the equilibrium bribe will be better off because the bribe remains unchanged and the probability of meeting a conscientious superisor increases; recall that these consumers report corruption so long as π>0. Their (expected) welfare is captured by the last term on the RHS of (14). For the same reason, the set of consumers represented by the middle term on the RHS before the increase in π will also be better off. The welfare of consumers who will pay the bribe and not report corruption is captured by the first term on the RHS of (14) whereas the middle term is the welfare of those whose aluation is greater than the bribe but report corruption. When the proportion of conscientious superisors increases the first term has a smaller magnitude and the middle term and last terms hae bigger magnitudes. We add more consumers to the set of consumers represented by the middle term. In effect, within the class of consumers with > ˆb, we moe mass from the first term to the middle term but the welfare of consumers in the middle term has a weight of π (0,1) (i.e., takes account of the fact that by reporting corruption, these consumers may not get the serice) while the welfare of consumers in the first term has a weight of 1 (i.e., these consumers will definitely get the serice because they will pay the bribe). If we only took account of the fact that the weight on the aluations in the first term is greater than the weight on the aluations in the middle term (i.e., 1 >π), then an increase in π will unambiguously lead to a fall in welfare. But we also hae to consider the fact that the change in the weight of the middle and last terms (i.e., π > 0) is greater than the change in the weight of the first term, which is zero. This welfare effect moes in an opposite direction to the welfare effect due to moing some mass of consumers from the first term to the middle term. This explains why the net effect of an increase in π on expected social welfare is ambiguous. If the increase in reports is too high, then we moe too much mass from the first term to the middle term, resulting in a fall in social welfare. In general, because social welfare is continuous in π and is maximized at π = 1, social welfare must necessarily increase in π if π is sufficiently close to 1. Note also that as π approaches 1, L = (1 π) ˆr approaches zero. Therefore, although social welfare can monotonically increase in the proportion of conscientious superisors for all π [0,1], it cannot monotonically decrease in π for all π [0,1]. For example, gien that the social welfare function has a unique minimum, Table I shows that social welfare is monotonically increasing in π for ˆb (1.5, 2). Based on Table I, the results suggest that proposition 3 does not hold when the bribe is sufficiently high (i.e., if ˆb is close to = the serice, this is counteracted by the effect that social welfare rises because more corrupt officials did not receie a bribe. So not sering consumers is socially desirable so long as this means that more corrupt officials do not receie a bribe. This strikes me as being oerly obsessed about the act of receiing a bribe relatie to what ought to be the ultimate goal of social policy (i.e., sering the consumers who want the serice). Therefore, treating bribes as pure transfers is sensible.

13 528 Journal of Economics & Management Strategy 2). To see why, note that as ˆb approaches, ˆ also approaches. That is, when the bribe is ery high, almost eeryone is willing to report corruption. Noting that ˆ approaches as ˆb approaches and that the last two terms on the RHS of (14) can be combined and rewritten as ˆ g() d, we can write social welfare, using (14), as: Ŵ + = limŵ = g()d + π g() d = π g() d. (14a) ˆb Then it is obious that Ŵ + / π >0. This result accords with intuition because if a ery large mass of consumers are not sered because they will get a negatie surplus by paying a bribe, then increasing the probability of these consumers getting the serice from conscientious superisors will increase social welfare. Proposition 3 implies that piecemeal anticorruption measures may be counterproductie or welfare-reducing. A big-push may be necessary. But, as shown aboe, in countries where bribes are ery high, a piecemeal approach that encourages people to report corruption increases social welfare. In proposition 2, no one reports corruption because the bribe is sufficiently low. Eeryone is sered and thus social welfare is maximized gien that bribes are treated as purely redistributie transfers. In this case, social welfare is independent of the proportion of honest superisors. This leads to the following comment: using an increase in consumer complaints as a measure of the success of an anti-corruption campaign may be misleading because the consumers may benefit in other ways (i.e., a ery small equilibrium bribe). 2.4 Legalizing Bribe-Giing Basu (2012) proposed that bribe-giing (but not bribe-taking) should be legalized in order to encourage people who pay harassment bribes (extortion) to report corruption and thus deter demands for bribes by goernment officials. 24 In the present model, this law will hae no effect on proposition 3 if reporting corruption does not result in a partial or full refund of the bribe paid een if the superisor is conscientious. This is because the model assumes that the consumers hae no non-pecuniary benefit from reporting corruption. Suppose instead that reporting corruption leads to a full refund of bribes paid. Then for any consumer who pays the bribe and therefore gets the serice, it is a strictly dominant strategy to report corruption so long as he has a positie belief that the official is a C-type. And, of course, the same argument holds for those who refuse to pay a bribe and do not get the serice. Consider an equilibrium in which eery corrupt official is reported. For this to be an optimal response for consumers, it must be the case that a positie measure of C-types pool with N-types, so that λ>0. Suppose this is the case. Let b = arg max b b(1 G[b]) be the equilibrium bribe. This is the bribe that any official will choose if there were no 24. Basu proposed this idea for India in 2011 when he was the Chief Economic Adiser to the Goernment of India. His proposal attracted the attention of The Economist in an article titled A Noel Way to Combat Corruption, May , p. 70: It was also coered in Fareed Zakaria s CNN show, GPS, May It attracted comments from many people including an article titled "The bribing game" in the Indian Express by Jean Dreze: et al. (2014) studied Basu s proposal in the lab and found mixed support for it as an effectie anticorruption strategy. In game-theoretic models with no reports but with different punishments for officials and customers, Basu et al. (2014) and Oak (2015) studied Basu s proposal.

14 Consumers Reports of Bribery 529 risk of being reported. Any consumer with b will pay the bribe and then report corruption because λ + (1 λ)( b) max[λ, b], (15) where the expression on the LHS is his expected payoff if he pays the bribe, then reports corruption, and gets a full refund if the superisor is conscientious; λ is his payoff if he does not pay the bribe and reports corruption; and b is his payoff if he pays the bribe and does not report corruption. Also, any consumer with < b will not pay the bribe and will report corruption. Recall when an official is reported and fired, any bribe collected is not retrieed. Then gien that eery corrupt official is reported, s/(1 δ) is the discounted payoff to a C-type of being honest, and only consumers with b pay the bribe, it follows that a C-type official with aluation, s, will be corrupt if (1 G[ b]) b s/(1 δ). All N-types will be corrupt. The measure of corrupt C-type officials is ρ = F ([1 δ](1 G[ b]) b). It is optimal for eery consumer to report corruption because there is a positie equilibrium probability, λ = π ρ/(π ρ + 1 π), of meeting a conscientious superisor who will either refund the bribe, if a bribe was paid, or will ensure that the consumer gets the serice without paying a bribe. Therefore, the equilibrium report is indeed r= 1. Gien that a corrupt C-type official will definitely be reported and fired, his choice of any positie bribe has no effect on the probability of being reported. Therefore, he cannot do better than choosing the bribe, b. Accordingly, there is no equilibrium in which a corrupt C-type official chooses b b. This is also the profit-maximizing bribe for N-types. Therefore, if bribe-giing is legalized and there is full refund of the bribe for those who report corruption, then we hae the following unique perfect Bayesian equilibrium: r= 1; the bribe is b; only consumers with b pay the bribe; all N-type officials are corrupt; ρ = F ([1 δ](1 G[ b]) b) of C-type officials are corrupt; and each consumer s belief that a corrupt official is a C-type is λ = π ρ/(π ρ + 1 π). If consumers see b b, they beliee that the official is a C-type. Gien that the equilibrium report is r= 1 and is independent of π, it follows that if bribe-giing is legalized, then the pererse result in proposition 3 can no longer hold. This conclusion does not depend on the fact that the refund is full. If there is partial refund, eery consumer will still report corruption. The key difference is that not eery consumer with b will pay the bribe and report corruption. Some of these consumers will report corruption without paying the bribe. Suppose only a proportion, (1 μ), of the bribe is refunded, where 0 <μ<1. Then a consumer with b will pay the bribe and report corruption if λ( μ b) + (1 λ)( b) max[λ, b]. (16) Note that the LHS of (15) is strictly bigger than b. So gien, b and comparing the LHS of (16) with λ, it follows that only those with (1 λ + λμ) b/(1 λ) will pay the bribe and report corruption. If μ = 0 (full refund), then (1 λ + λμ) b/(1 λ) becomes b. The analysis in this section also implies that lemma 2 does not hold when bribegiing is legalized and there is partial or full refund of the bribe for those who report corruption. I summarize the main result here in the following proposition:

15 530 Journal of Economics & Management Strategy Proposition 4: If bribe-giing (but not bribe-taking) is legalized and there is full or partial refund of the bribe for those who report corruption, then an increase in the proportion of conscientious superisors will not result in a decrease in social welfare. 3. Robustness and Extensions The comparatie static result in proposition 3 was based on the argument that the equilibrium bribe, ˆb, is independent of π (i.e., ˆb/ π = 0). Gien the multiplicity of equilibrium bribes, the corrupt officials could be seen as soling a coordination problem. Therefore, once they are able to settle on a specific ˆb gien π, it could become a focal point which leads them to choose the same ˆb if π changes, although the measure of corrupt officials may change. This is a plausible argument, especially for small changes in π. Howeer, for the sake of robustness, consider the two other cases, ˆb/ π > 0and ˆb/ π < 0, in addition to ˆb/ π = 0. Proposition 3 is strengthened if an increase in π leads to an increase in the equilibrium bribe. This is because the increase in the bribe increases the measure of consumers who report corruption. On the other hand, if an increase in π reduces the equilibrium bribe, this will weaken the result in proposition 3 but will not completely oerturn it. Formally, we can demonstrate this point as follows: write ˆ( ˆb, ˆr) as ˆ( ˆb[π], ˆr[π, ˆb]). Then ˆ π = ˆ b ˆb π + ˆ r( ˆr π + ˆr b ˆb π ) = (ˆ b + ˆ r ˆr b ) ˆb π + ˆ r ˆr π, where ˆ r ˆ/ r and so on. Putting this into (12) gies: Ŵ π = ˆ g() d (1 π)ˆg(ˆ)ˆ r ˆr π (1 π)ˆg(ˆ)( ˆ b + ˆ r ˆr b ) ˆb π. (12a) It is obious that if ˆb/ π = 0, as assumed aboe, then the expressions in (12a) and (12) are identical. The difference between (12) and (12a) arise when the last term on the right-hand side of (12a) is not zero (i.e., ˆb/ π 0). Suppose ˆb/ π > 0and Ŵ/ π in (12) is negatie. Then noting that ˆr b > 0, ˆ b > 0, and ˆ r > 0, it follows that Ŵ/ π in (12a) is also negatie. On the other hand, if ˆb/ π < 0and Ŵ/ π in (12) is negatie, it does not necessarily follow that Ŵ/ π in (12a) is also negatie. Howeer, Ŵ/ π in (12a) is negatie if the absolute alue of ˆb/ π is sufficiently small. If ˆb/ π < 0andits absolute alue is sufficiently high, then reports will not increase, if π increases. There is, of course, nothing in the analysis that guarantees that if ˆb/ π < 0, its absolute alue will be so high that reports will not increase. Therefore, the case of ˆb/ π < 0 weakens, but does not oerturn, the result in proposition 3. Proposition 3 does not hold if δ is ery close to 1. The intuition is that for an official whose job aluation is s, the payoff from being honest, s/(1 δ), is ery high when δ is close to 1 and so ery few C-type officials are corrupt. That is, an increase in δ has an effect that is analogous to an increase in the officials compensation (salary). It is well known that a sufficiently high salary will deter corruption by officials who face a risk of losing their job for being corrupt (e.g., Becker and Stigler, 1974). It can be shown that ˆρ/ δ< 0and ˆr/ δ = [ ˆbπg(ˆ)/(1 ˆλ)(π ˆρ + 1 π)]( ˆρ/ δ)< 0. Therefore, gien that a ery high alue of δ leads to ery few C-type officials and a low leel of reports, an increase in π only leads to a ery small increase in reports and so this does not lead to a fall in social welfare. As appendix A shows, the equilibria in propositions 1 and 2 are supported by the following out-of-equilibrium belief: if a consumer obseres b ˆb, he beliees that the official is C-type. This satisfies standard refinements. But one may argue that a more plausible refinement would be that the bigger the out-of-equilibrium bribe demanded,