Does Transparency Reduce Political Corruption?

Transcription

1 Does Transparency Reduce Political Corruption? Octavian Strîmbu and Patrick González March 15, 2015 Abstract Using a common agency game with imperfect information, we show that increasing the transparency of the political process raises the offered bribes as it increases the competition between the interests groups. Keywords : Political Corruption, Transparency, Common Agency JEL Codes : D73, D80 1 Introduction Democratic political systems provide the citizen effective means to observe and to influence the officials decisions. Nevertheless, even in well-established democracies, assuming that the officials decisions always reflect the voters preferences is overly optimistic. Every now and then the medias report cases of policies that hardly maximize any kind of social welfare function: contracting public procurements at exorbitant prices, supporting hazardous economic Department of Economics, University of Ottawa and Department of Economics, CRE- ATE, Université Laval. The authors thank Gustavo J. Bobonis, Arnaud Dellis and Nicolas Jacquement for their comments on an earlier draft. 1

2 activities in environmentally protected areas, providing useless public facilities, are just a few examples. The matter is even worse for new democracies and authoritarian regimes. Pretending to act for the benefit of the public, high-level officials often appear corrupted. Political corruption is an instance of government failure; to correct this failure, one of the most popular solutions is to improve the transparency of the political decision process. 1 In this paper we challenge this view by arguing that more transparency increases the competition between the public and the corruptors to influence the official, so that the bribes offered to the latter actually increase. In an opaque system, the public has little incentive to influence the official. As a result, the corruptors don t have to do much to influence the official: political corruption is widespread but the bribes are low. Increased transparency empowers the public which then fight more aggressively to counteract the influence of the corruptors. But the corruptors fight back and the bribes increase. Our point is not that increasing transparency is a bad policy. We show that expected welfare actually increases with transparency as the official is led to favor more often efficient actions. What transparency does is to enhance the shadow value of the official s power. The expected bribe increases because the corruptor is now ready to pay more to influence that power. We make our point with a common agency model in which the public and the corruptor (the principals) try to influence the choice of an action by an official (the agent). The principals favor different policies; yet, although the public s preferred policy would lead to a greater increase in total welfare, the corruptor may get a better deal by bribing the official to implement his preferred policy. We innovate by introducing an information gap between the principals: while the corruptor always observes the official s action, the public does so with some probability and has to trust the official s word otherwise. In this 1 See for example Transparency International (2003). 2

3 setting, the celebrated efficiency result of the common agency model (there is always an equilibrium with bribes where the official chooses the efficient action favored by the public) holds if the information gap between interest groups is small. When there is a sufficient chance for the official to have her cake and eat it too by pretending to act in the public interest while accepting a bribe from the corruptor to do otherwise, this result vanishes. In equilibrium, both principals compete in mixed strategies by varying their compensation offers to the official. As a result, the corruptor s offer sometimes surpasses that of the public and the official willingly accepts the bribe. Our main result is that the expected bribe increases as the information gap is reduced; that is, as transparency increases. Political corruption: definition and literature The concept of political corruption has significantly changed over time (see Heidenheimer and Johnston, 2002). Besley (2006) defined political corruption as: a situation where a monetary payment a bribe is paid to the policy maker to influence the policy outcome. As helpful as it is, this definition raises further questions. For one, who gains from influencing the policy outcome? In other words, whose welfare is altered by the policy? Almost any decision of an official affects the welfare of more than one interest group. Awarding a government contract, for example, affects the welfare of the firm executing the contract, but also that of the taxpayer who ultimately foots the bill. Hence, when analyzing political corruption, we must presume that there are at least two interest groups in presence. Furthermore, are bribes any different from legitimate political contributions? The above definition states that a monetary transfer from an interest group to an official is a bribe if it is contingent on an official s action. This is not the sole characteristic of bribes, though. Corruption is famously a secret phenomenon. If a firm pays a bribe to an official to get a government contract, they will keep the deal secret. We see two reasons why both the 3

4 corruptor and the official want the bribe to be a hidden, private payment. First, when the corruptor favors an inefficient policy, political corruption destroys surplus and would not survive a round of public renegotiation with all the parties involved. Second, both the corruptor and the official gain at the expenses of the public in a manner that might be deemed illegal. Since the development in the mid-80s of Principal-Supervisor-Agent model (hereafter PSA; see Tirole, 1986), the microeconomic formalization of corruption has reached undisputed success. Besley and McLaren (1993), Mookherjee and Png (1995) or Acemoglu and Verdier (2000) among others bring useful insights into this phenomenon and at the same time relate to its essential characteristics. Aidt (2003) suggests as well that by setting up an agency framework in which one benevolent principal (the policy-maker) tries to prevent the collusion between a corrupt supervisor (the bureaucrat) and a corrupt agent, the PSA model became a powerful tool for analyzing corruption. Unfortunately, though, the PSA model applies only to bureaucratic corruption. Probably because in the microeconomics of corruption literature the line between political and bureaucratic corruption is often fuzzy, this important clarification is overlooked. We argued above that a model of political corruption should feature at least two interest groups and an official. Since it features only one principal and the role of the policy-maker is basically inverted, the PSA model doesn t have any chance to fit the realities of political corruption. Paradoxically, the success of the PSA model has left a gap in the formalization of political corruption. To fill this gap, two models of the political economy literature may be considered. They are not models of political corruption per se, but they do include rents or monetary transfers associated with political corruption. The first one is the political agency model (Barro, 1973; Ferejohn, 1986; Persson and Tabellini, 2000; and Besley, 2006). It explains the behavior of officials facing elections. In its simplest form the political agency is a principal-agent model: a decision affecting the welfare of the citizen (the 4

5 principal) is delegated to an official (the agent). The official may shirk and acquire a rent. The citizen s only mean of disciplining the official is to vote her out of office. Focusing on the electoral process, the political agency model proposes a fairly simple type of rents which can be interpreted as corrupt gains. 2 However, they do not correspond to the definition of political corruption used here because they are not monetary transfers contingent on an official s action. More precisely, in the political agency model the potential rents are settled at the beginning of the elections and the official can decide to get (a part of) them by risking her office. In this respect these rents resemble rather the embezzlement of public funds than actual political bribes. The second one is the common agency model first devised by Bernheim and Whinston (1986a and 1986b) and further developed as a branch of the lobbying literature by Grossman and Helpman (1994, 2001), Le Breton and Salanié (2003) and Martimort and Semenov (2007). Within a common agency, many principals (the interest groups) compete to influence an agent (the official). As Harstad and Svensson (2011) mentions, there is something puzzling about the lobbying literature, though. The monetary transfers from the interest groups towards the official are frequently called bribes but that creates confusion between lobbying and political corruption. This puzzle is easy to solve if one considers the distinction between bribes and political contributions we made earlier. The lobbying models built on common agency feature equilibrium transfers that are known by all the players. Therefore, these payments should be interpreted as legitimate political contributions. Bribes are hidden, private payments and the current applications of the common agency to lobbying fall short of reflecting this reality. The remainder of the paper is organized as follows. In Section 2, we outline the model and solve for the standard complete information equilibrium and the asymmetric information equilibrium when the information gap is small. We also cover the political corruption scenario. When the informa- 2 In a famous definition corruption is an abuse of public office for private gain. 5

6 tion gap is large, the principals adopt mixed strategies in equilibrium and political corruption occurs with some probability when an illegitimate principal outbids a legitimate one. In Section 3, we compute that equilibrium probability and we proceed with comparative statics to establish our claims about the effect of transparency on expected bribes and efficiency. Section 4 is a conclusion. 2 The Model Consider a common agency game with two principals, the public and the corruptor, and a single agent, the official. The game takes place during the official s term of office. The official must choose an action within a set A = {1, 2}. The principals have opposite preferences over this set: the public prefers the first action and the corruptor the second one. Without loss of generality, we normalize at zero the expected utility of each principal for his least-preferred action and we normalize at 1 the expected utility for the public of pursuing the first action. Let ɛ denotes the expected utility for the corruptor of pursuing the second action. We assume that 0 < ɛ < 1 so that the public s choice is the efficient choice (the official has no preference over A). Undertaking the inefficient action entails a loss of 1 ɛ in welfare. Hence, a high value of ɛ means both a strong minor interest (a high corruptor s stake) and a low potential loss in welfare. Both concepts are confounded in this model. To influence the official s choice, the public offers the official a menu contract (u 1, u 2 ) that specifies the utility u i he shall transfer to the official if she chooses action i. Likewise, the corruptor offers simultaneously a menu contract (b 1, b 2 ) to the official that specifies the bribes. By choosing action i, the official gets a total transfer u i + b i. Both transfers are assumed to be bounded below by zero. Although we measured them here in money units, the interpretation of 6

7 these transfers may be quite rich. For instance, the transfer u could be interpreted as the likelihood that the public will support the official in a forthcoming election. Such soft commitment would count as an opportunity cost for the public and as a gain for the official because staying in office brings her an utility. 3 Our analysis of political corruption rests on imperfect monitoring of the agent s action by the principals. Specifically, the public observes this action with probability θ while the corruptor observes it with probability ξ θ (both observations being independent events). A corruptor is then someone who has a private minor interest (he prefers the inefficient action) and who is in a better position to deal with the official (since ξ θ). To account for the possibility that one or both principals do not observe the official s action, we assume that she reports a message m about the action i she plans to select. The public pays u i if it observes the action and u m otherwise. The same applies for the corruptor. The effect of an increase in transparency on political corruption is best seen in the special case where ξ = 1 > θ; that is when the corruptor always monitors the official. There, the parameter θ is a measure of transparency useful for comparative statics. We shall analyze that case below but notice first that the case ξ = θ = 1 is a special instances of the common agency model developed by Bernheim and Whinston (1986b) with full monitoring of the agent s action. This is an extreme case with (ex ante) complete and (obviously) symmetric information. In that case, there exists a unique truthful Nash equilibrium 4 where the corruptor tries to bribe the official with b 2 = ɛ, but the public matches this bribe with u 1 = ɛ and the official chooses the efficient action. Both principals offer nothing if their preferred action is not chosen. So, in equilibrium, the corruptor gets b 1 = 0, the public gets 1 u 1 = 1 ɛ > 0 and the official 3 In the political economy literature this utility is usually called ego rent. 4 Truthfulness is a refinement that excludes equilibria where the principals promise unreasonable transfers for actions that are not undertaken in equilibrium. See Bernheim and Whinston (1986b). 7

8 gets u 1 + b 1 = ɛ + 0 = ɛ which is at least as good as what she would have get by selecting the other action u 2 + b 2 = 0 + ɛ = ɛ. Now suppose that θ = 0. This is the extreme case with asymmetric information where the public is powerless to monitor the official. It is then fruitless to match the corruptor s bribe since the official would only pretend to choose the efficient action and would pocket the corruptor bribe anyway by choosing the latter preferred action. Consequently, the corruptor has little incentive to offer a big bribe. Indeed, this game has a unique subgame perfect equilibrium where both principals offer nothing and the official chooses the inefficient action. 5 The public gets u 2 = 0, the corruptor gets ɛ b 2 = ɛ 0 = ɛ and the official gets u 2 + b 2 = Going from the asymmetric case just described (with θ = 0) to the complete information symmetric case described above (with θ = 1) a transition that we associate to an increase in transparency the incidence of political corruption goes from widespread (the official always chooses the corruptor s preferred action) to none and the level of bribes offered rises from zero to ɛ. If we measure political corruption by the likelihood that official s choice matches the public s choice, then transparency reduces political corruption. But if we measured it by the level of bribes, an increase in transparency led to an increase in bribes. As for the expected or average bribe actually paid, it is zero in both these extreme cases. We shall now analyze the equilibrium in the intermediate cases 0 < θ < 1 (keeping ξ = 1) and proceed with comparative statics along the same line. In particular, we want to confirm the intuition expressed above that an increase in transparency (an increase of θ) leads to less instances of political corruption yet to higher bribes. In addition, we want to establish that an increase in transparency enhances welfare and to check whether it leads or not to higher 5 Suppose there is a subgame perfect equilibrium where the corruptor plays b 2 > 0 Then the official surely plays the second action. It follows that the corruptor would strictly increase his payoffs by halving his bribe. This implies that b 2 should vanish but a null bribe would not belong to an equilibrium strategy profile if the official did not choose the second action. 8

9 expected accepted bribes. To simplify the analysis, notice that paying the official for one s non preferred action is a weakly dominated strategy for both principals. Since we shall find an equilibrium that do not use such strategies, we may assume that u 2 = b 1 = 0 and that the public pays 0 if it is revealed by chance that the official lied about choosing action 1. We thus simplify the notation by writing u = u 1 and b = b 2. Besides, since the corruptor always observes the official s action, the choice of the message matters only in the latter s deal with the public and since the public don t pay for the inefficient action, pretending to choose the inefficient action can t improve the official s payoff. Hence, we may assume that the official always pretend to choose the efficient action. Thus, a (behavioural) best-response for the official resumes to a correspondence φ that associates to every pair (u, b) a subset of A. Given a pair (u, b), the efficient action is a rational choice for the official if u (1 θ)u + b. She always pretends to choose the efficient action: if she does it, she gets u whether the public actually observes her move or not; if she chooses the inefficient action instead, she pockets the bribe b and she still has a chance 1 θ of not being exposed and getting u anyway. Hence, {2} if θu < b φ(u, b) = A if θu = b {1} if θu > b Recall that when the public always observes the official (θ = 1), it can match in equilibrium the corruptor s bribe b = ɛ, ensure that the official will undertake the efficient action and still obtain a gain since 1 ɛ > 0. Now we show that this solution will still hold if θ is big enough, more precisely if 9

10 θ ɛ. Offering u = ɛ will no longer do since then {2} if θɛ < b φ(ɛ, b) = A if θɛ = b {1} if θɛ > b and the corruptor could compel the agent into choosing the inefficient action by offering a bribe b (θɛ, ɛ) and make a profit ɛ b > 0. Imperfect transparency (θ < 1) lessens the potency of the public s incentive. In equilibrium, we find that u = ɛ/θ, b = ɛ and the official rationally chooses the efficient action since 1 φ(ɛ, ɛ/θ). This is an equilibrium since the corruptor would loose by offering a higher bribe and the official would reverse her choice should the public reduce marginally u, at a loss for the latter. We sum things up so far in the first proposition. Proposition 1. Let θ ɛ. Let π denotes the official s equilibrium payoff. There is a pure strategies equilibrium where the public offers u = ɛ/θ, the corruptor offers b = ɛ and the official plays i φ(u, b) if θu b and i = 1 otherwise. In equilibrium, the public gets 1 ɛ/θ, the corruptor gets 0 and the official gets π = ɛ/θ. Proof. We refer the reader to the discussion above. Notice though that the official must choose the efficient action whenever she reaches an indifference point so that the public has no incentive to increase slightly his bid beyond that point. In the light of proposition (1), a discussion about the effect of an increase in transparency upon political corruption would conclude that it shifts surplus from the official toward the public: as θ increases, the official s payoff ɛ/θ decreases and the public s payoff 1 ɛ/θ increases. On could also emphasizes the effect of competition, through ɛ, on both payoffs: as ɛ increases, the value of the official s action on the political corruption market increases so that her payoff increases and that of the public decreases. In both comparative static 10

11 analysis, the corruptor s payoff stays constant at zero but that is no surprise since no political corruption actually takes place in this equilibrium! A classic proposition of the microeconomics of corruption literature states that a better paid agent is less likely to accept a bribe. In essence, the proposition states that the public should pay the agent according to her value on the political corruption market, but that is the logic of competition, not of corruption. In our view, political corruption is a phenomenon associated with imperfect information. No official in her right mind would willingly admit that she is corrupted. Political corruption involves some form of deception where a venal official publicly pretends to do something but actually does something else. In the game we have set up, the official has this strategy to have her cake and to eat it too. Proposition 1 establishes that this is a loosing strategy if transparency is high enough. Now suppose that the information gap is more severe; that is, θ < ɛ. This will result in an inherently unstable situation: The corruptor may counter any rational attempt by the public to obtain the official s favor. Yet, if the official is to be corrupted anyway, there is no rational for the public to pay her for false promises when she is not caught accepting bribes (i.e. playing the inefficient action). If the public does not compete, the corruptor should economize on the bribe; but if the bribe is low, the public should compete for the official s favour. So no pure strategies equilibrium exists in these cases. In the following proposition, we thus look for an equilibrium where both the public and the corruptor bid for the official s favour with mixed strategies. Proposition 2. Let θ < ɛ and consider the distribution functions F and G 11

12 over R + such that ɛ θ if u 1 F (u) = ɛ θu 1 otherwise; 1 θ b if b θ G(b) = θ 1 b 1 otherwise. (1) (2) There is an equilibrium where the public plays F, the corruptor plays G and the official plays i φ(u, b) if u > 0 and i = 2 otherwise. Let P be the equilibrium probability that the official accepts the bribe and plays i = 2. Then the equilibrium payoffs are 0 for the public, ɛ θ for the corruptor and π = θ + (1 P )(1 ɛ) (3) for the official. Proof. Notice that the official always chooses her action from her best-response correspondence. To prove that we have an equilibrium, we need only to verify that both principals do so as well. Suppose that the corruptor plays G. Given the public bid u, the probability that the official selects the efficient action is Prob (θu > b) = G(θu). By bidding u [0, 1], the public then gets a zero expected payoff G(θu)(1 u) (1 G(θu))(1 θ)u = 0 (4) independent of u (the second additive term on the left accounts for the possibility that the public pays the official but receives nothing in return because it fails to observe the latter s move). Besides, increasing its bid beyond 1 could only result in a loss. It follows that bidding over [0, 1] is a best response to G for the public. Likewise, if the public plays F, then Prob (θu b) = F (b/θ) and, if he bids b [0, θ], the corruptor gets an expected payoff F (b/θ)(ɛ b) = ɛ θ > 0 (5) 12

13 independent of b. If he bids more, that is b > θ, he surely wins but he ends up with ɛ b < ɛ θ. Hence, bidding over [0, θ] is a best response to F for the corruptor. We specify that the official selects the inefficient action if the public offers nothing. This is to ensure that the support of the corruptor s strategy is compact: since the public offers zero with a positive probability, the corruptor would never offer zero if there was any chance the official could select the efficient action in case of a tie at zero. To prove (3), consider total surplus which is one minus 1 ɛ if there is political corruption. Hence, total expected surplus amounts to 1 (1 ɛ)p (6) The corruptor gets a share ɛ θ of that amount and the public gets none: the residual has to accrue to the official. Rearrange 1 (1 ɛ)p (ɛ θ) to get (3). When the transparency problem is severe enough to make full deterrence a loss-making option, political corruption randomly occurs when the corruptor s bribe beats the (discounted) public reward (b > θu). We contend that this mixed strategies equilibrium (which can be purified) captures the essence of the political corruption phenomenon. Transparency has clearly an effect on the competition between the principals. Both distributions F and G are strictly decreasing in θ over their respective supports. So a larger value of θ induces an increasing first-order stochastic dominance: both random bids become stochastically larger and their expected values increase. 6 A reduction of ɛ has a similar effect on F (as F increases with ɛ) but no effect whatsoever on G. A key expression in the political corruption equilibrium is the corruptor s expected payoff ɛ θ (in equation 5) which decreases with transparency. 6 All others being equal, say G 1 and G 2 denote the corruptor mixed strategies σ 1 and σ 2 respectively when θ = θ 1 and θ = θ 2 with θ 2 > θ 1. Then G 2 (b) G 1 (b) for all b [0, θ 2 ], so σ 2 first-order stochastically dominates σ 1. First-order stochastic dominance implies dominance in expected values. 13

14 The effect of transparency on the total expected surplus and on the official s payoff depends on the probability of political corruption. In proposition 3 below, we show formally that P decreases with θ so that both values increase as transparency improves. Recall that under perfect information, the value of the official s action induced by the competition between the principals is π = ɛ/θ which peaks at 1 when θ ɛ. Under imperfect information, equation (3) offers an interesting decomposition into two effects of that value. The first part, θ, reflect the competition effect: as θ ɛ, the moral hazard problem disappears and the value of the official s action increases (toward ɛ). The second part (1 P )(1 ɛ) reflects the efficiency effect: political corruption destroys surplus and whatever is saved, that is 1 ɛ with probability 1 P, accrues to the official; as θ ɛ, political corruption disappears and the official s total payoff tends to 1 ɛ + θ 1 ɛ/θ; that is, to its value under the pure strategies equilibrium. From propositions 1 and 2, we see that the structure of payoffs and the effect of transparency on those payoffs depends critically on θ and ɛ. When θ < ɛ, there is political corruption and the total expected surplus (6) is shared between the corruptor and the official. When θ ɛ, there is no political corruption and the unitary surplus (6) is shared between the official and the public. The corruptor s share ɛ θ decreases from ɛ to zero as transparency improves from θ = 0 to θ = ɛ. The public s share 1 ɛ/θ increases from 0 to 1 ɛ as transparency improves from θ = ɛ to θ = 1. The official s share is hump-shaped: it is given by (3) and increases from 0 to 1 as transparency improves from θ = 0 to θ = ɛ; it is given by π = ɛ/θ and decreases from 1 to ɛ as transparency improves from θ = ɛ to θ = 1. Figure 1 provides an illustration for the case ɛ = 1. The line in the upper 3 quadrant is the official s expected payoff π as a function of θ. It rises from 0 to 1 as transparency improves from θ = 0 to θ = ɛ as described by (3). It then decreases to ɛ as θ reaches 1, following π = ɛ/θ. In the lower panel, where the curves are drawn upside down, we have first the corruptor s payoff 14

15 1 ε = 1/3 θ + (1 P) (1 ε) ε/θ π 1/3 π 0 1/3 θ 1 1/3 ε θ 1 ε/θ 2/3 Figure 1: The figure is drawn for the case ɛ = 1 ; that is, the stake of the 3 corruptor is one third of that of the public. The official s expected payoff π is drawn in the upper panel as a function θ. The corruptor s and public s expected payoff are drawn in the lower panel (the public has a zero payoff when the the corruptor has a positive payoff, and vice-versa). The difference between both curves is the total expected surplus: it starts at ɛ = 1 3 in θ = 0 and plateaus at 1 in θ = ɛ, when transparency becomes sufficient enough to prevent the occurrence of political corruption. 15

16 which decreases linearly from ɛ to 0 over θ [0, ɛ]. Then, we have the public s payoff which starts positive at ɛ and increases toward 1 ɛ as θ reaches 1 along 1 ɛ/θ. The distance between the curve in the upper panel and that in the lower panel equals total expected surplus: it starts at ɛ in θ = 0 and plateaus at 1 in θ = ɛ when political corruption disappears. Improved transparency beyond that point translates into a reallocation of surplus from the politician to the public, the total remaining fixed at 1. 3 Comparative Statics Our theory of political corruption combines two features: competing principals and observability of actions which we dubbed transparency. We started from a multiprincipals model with imperfect information. We showed that when transparency was an issue, the official could be corrupted: she might accept a bribe to implement the inefficient action. Political corruption is a form of moral hazard where the value of the outside option (the bribe) results from the competition between the principals for the agent s services. Although our model is pretty simple and quite abstract, we are confident that it does capture an important part of the political corruption phenomenon. In this section, we perform comparative statics to derive testable empirical propositions. Suppose we had access to a rich data set about political corruption in a given jurisdiction that provides A measure of transparency (θ). The pecuniary incentives for the principals (1 and ɛ). The prevalence of political corruption (the probability P that a randomly picked official is corrupted). The attitude of officials towards transparency and political corruption. The average bribe offered to officials. 16

17 The average bribe paid to corrupted officials. All these measures are obviously related but often, as we shall see, in non obvious ways. To analyze the sensitivity of theses measures, we need a richer characterization of the equilibrium probability of political corruption. Let T = {(θ, ɛ) : 0 θ < ɛ 1} denotes the subset of parameters values for which there is mixed strategy equilibrium; S(θ) = [0, 1] [0, θ] the support of the equilibrium mixed strategies profile. The probability of political corruption is given by the function P : T [0, 1], P (θ, ɛ) = θ 0 F (b/θ) G b (b)db which depends on ɛ through the definitions of F and G. For a start, equations (6) and (3) depends on θ through P = P (θ, ɛ). As we have promised it above, we establishes that P decreases with θ in the next proposition. Proposition P (θ, ɛ) = θ ɛx Let x = θ(1 ɛ)/(ɛ θ). Then ( ) 1 + x ln (1 + x) ɛ x 2. P is strictly decreasing in θ and strictly increasing in ɛ. 3. P is strictly concave in θ. 4. P has the following limits: lim P (θ, ɛ) = 1 lim θ 0 P lim θ 0 P (θ, ɛ) = 0 lim θ ɛ θ (θ, ɛ) = 1 2ɛ P (θ, ɛ) = 0 ɛ lim lim θ 0 P lim θ ɛ θ θ ɛ 5. P is strictly supermodular ( P θ ɛ > 0). Proof. See the appendix. 17 P (θ, ɛ) = 1 θ/2 ɛ 1 (θ, ɛ) = P (θ, ɛ) = ɛ

18 1 0 ε Increased efficiency C D Increased transparency θ 0 1 Figure 2: The figures illustrates P (θ, ɛ) over T with a set of iso-probability curves. 18

19 Notice that P is not defined at (θ, ɛ) = (0, 0) and (θ, ɛ) = (1, 1), so one must be careful before making inference around these values. 7 In Figure 2, we have represented the equilibrium probability function P. The triangle denotes the set T rotated 45 clockwise. Within that triangle, a set of strictly concave iso-probability curves illustrates P as a strictly quasiconvex function. The level of these curves is given by 1 θ/2 on the rightmost side of the triangle. Hence, the probability of political corruption is 1 at the very top (where θ = 0) and higher along curve C than along curve D. The probability is always 1 on the left side of the triangle (where θ = 0). It approaches zero at the base of the triangle but one must exclude the left and right vertices were it is not defined. From this graph, we see that an improvement in transparency leads to a decrease in the probability of political corruption while an improvement in efficiency has the opposite effect. This is because an increase in efficiency also means that the corruptor bids more aggressively for the official s favor as his stake increases relatively to that of the public. The same incentive explains the effect of transparency on the corruptor s bid. Since more transparency reduces the probability of political corruption, transparency improves both the expected total surplus (6) and the official s payoff (3) when there is political corruption. The opportunity of political corruption is not a boon for the official: it creates moral hazard and lowers the value of her services. She gets paid less by the public, so the corruptor can secure her services for less. From her point of view, θ = ɛ is an ideal point since she then gathers all the surplus (see figure 1). She benefits from a high surplus environment because there is no political corruption and from a high transfer from the public because of the tough potential competition from the corruptor. If transparency is low (θ < ɛ), the official would support an effort to improve it. If it is high, she would advocate relaxing it: doing so would not increase the political corruption (there is none since θ > ɛ) but 7 We show in the appendix that although the probability of political corruption vanishes in the limit when θ ɛ, this is not true when ɛ 0 or ɛ 1. 19

20 would increase her transfer from the public. The effect of a change in ɛ is more ambiguous. A marginal increment in efficiency increases total surplus by P (θ, ɛ) (1 ɛ) P (θ, ɛ) (7) ɛ Using proposition 3, we compute that, when ɛ (0, 1), expression (7) worths 1 when θ 0 and when θ ɛ. The cross derivative yields P θ (θ, ɛ) (1 ɛ) 2 P (θ, ɛ) < 0 θ ɛ It follows that expression (7) decreases from 1 to over [0, ɛ]. Since the corruptor captures 1 at the margin and total surplus increases by at most 1, such a marginal increase never benefits the official when θ < ɛ. Yet, a non marginal increase could benefit the official as it is illustrated in figure 3. Like in figure 1, both curves peaks at 1 in θ = ɛ. Although a marginal increase in ɛ necessarily lowers the official s payoff when there is political corruption, a non marginal increase (switching from the full to the dotted line) could increase it if θ is higher than the point where the two curves crosses. In this scenario, a non corrupted official (along the decreasing portion of the thick line) benefits from an empowerment of the corruptor (along the dotted line) even if transparency is still good enough to prevent political corruption. In the discussion that followed proposition 2, we saw that transparency motivates the corruptors to bid more aggressively, hence the average bribe offered to officials should increase with θ. Paradoxically, such increase is thus a sign that a transparency policy is working as the corruptors are compelled to increase their bids to maintain their influence. Yet, it is quite unlikely that we could reliably observe such measure. A compilation of exposed political corruption cases would instead inform us about the average bribe paid to corrupted officials. Such measure depends on transparency in more complex way: A corruptor may increase his bid but if the official is not tempted, the incidence of political corruption remains low. 20

21 Figure 3: The figures illustrates the value of the official s payoff as a function of θ for two values of ɛ (ɛ is higher for the dotted curve). Let b denote the actual bribe paid b if b θu, b = 0 otherwise. The interpretation being that should we audit a hundred officials, we would expect on average to observe 100 E(b ) dollars paid in political corruption, or E(b ) on average per official. The measure E(b ) is directly related to the amount of money that goes into political corruption. Proposition 4. The average bribe amounts to E(b ) = P (θ, ɛ)ɛ (ɛ θ) (8) As a function of θ, that value is hump-shaped: as transparency improves from 0 to ɛ, E(b ) first increases and then decreases with θ. Proof. First, notice that E(b ) = P (θ, ɛ) E(b b θu) (9) where E(b b θu) denotes the expected bribe given that political corruption occurs. The corruptor gets ɛ minus the bribe b in the event when the official 21

22 accepts the bribe and zero otherwise. Since his unconditional expected payoff is ɛ θ, it must be that P (θ, ɛ)(ɛ E(b b θu)) = ɛ θ Substitute (9) and rearrange to get (8). In proposition 3, we showed that lim θ 0 P (θ, ɛ) = 1 and that lim θ ɛ P (θ, ɛ) = 0. From (8), it follows that E(β) = 0 when θ = 0 and when θ = ɛ. Besides, we showed that P is strictly concave in θ so E(β) is strictly concave as well, hence hump-shaped. There is no easy intuition behind proposition 4 although it flows logically from our simple assumptions. Notice that when transparency is low and political corruption is pervasive, the official gets most of her compensation from the corruptor; when transparency is high and political corruption is rare, the official gets most of her compensation from the public. Since an improvement in transparency motivates the corruptor to offer the official higher bribes, this phenomenon is more acute when transparency is low. As convincing as this argument may be, it does not take into account that the corruptor bids are much higher when transparency is high. Proposition 4 is a reminder that observing more money into political corruption is not necessarily a sign that political corruption is a bigger problem than it was. It might be a necessarily stage for a society that starts with a very low level of transparency and that wants to develop a more efficient public service. 4 Conclusion Political decision process implies the existence of multiple interest groups which try to influence the officials choices. Employing multiple-principal models (such as common agency) to formalize corruption should, in the first place, help to draw a line between political and bureaucratic corruption. Then, we argue that one way to formally distinguish political corruption 22

23 from lobbying consists in assuming that there is an information gap between principals. One implication of this assumption is that the better informed interest group has to hide his transfers towards the official. Hence, these transfers qualify as political bribes rather than political contributions. More importantly than distinguishing concepts, a common agency model with information asymmetry between principals brings useful insights into the issue of interest groups influence. In our model the efficiency outcome of the complete information common agency model holds if the information gap between principals is small. On the contrary, if transparency is low, the official may choose inefficient policies and accept private transfers from the informed interest group. We identify this scenario as political corruption. As long as political bribing occurs, the main finding of this paper is that marginally increasing transparency of the political process only increases the expected bribe. On the other hand, the expected welfare increases with transparency. To eradicate political corruption, it takes an important jump in transparency. References Acemoglu, D., and T. Verdier (2000): The Choice between Market Failures and Corruption, The American Economic Review, 90(1), Aidt, T. S. (2003): Economic Analysis of Corruption: A Survey, The Economic Journal, 113(491), F632 F652. Barro, R. J. (1973): The Control of Politicians: An Economic Model, Public Choice, 14, Bernheim, B. D., and M. D. Whinston (1986a): Common Agency, Econometrica, 54(4),

24 (1986b): Menu Auctions, Resource Allocation, and Economic Influence, The Quarterly Journal of Economics, 101(1), Besley, T. (2006): Principled Agents? Oxford University Press. Besley, T., and J. McLaren (1993): Taxes and Bribery: The Role of Wage Incentives, The Economic Journal, 103(416), Ferejohn, J. (1986): Incumbent Performance and Electoral Control, Public Choice, 50(1/3), Grossman, G. M., and E. Helpman (1994): Protection for Sale, The American Economic Review, 84(4), (2001): Special Interest Politics. The MIT Press. Harstad, B., and J. Svensson (2011): Bribes, Lobbying and Development, American Political Science Review, 105(01), Heidenheimer, A. J., and M. Johnston (eds.) (2002): Political corruption: concepts and contexts. Transaction Publishers. Le Breton, M., and F. Salanie (2003): Lobbying under political uncertainty, Journal of Public Economics, 87, Love, E. R. (1980): Some Logarithm Inequalities, The Mathematical Gazette, 64(427), Martimort, D., and A. Semenov (2007): Political Biases in Lobbying under Asymmetric Information, Journal of the European Economic Association, 5(23), Mookherjee, D., and I. P. L. Png (1995): Corruptible Law Enforcers: How Should They Be Compensated?, The Economic Journal, 105(428),

25 Persson, T., and G. Tabellini (2000): Political economics: explaining economic policy. Massachusetts Institute of Technology. Tirole, J. (1986): Hierarchies and Bureaucracies: On the Role of Collusion in Organizations, Journal of Law, Economics, and Organization, 2(2), Transparency International (ed.) (2003): Global Corruption Report Special Focus : Access to Information. Profile Books Ltd. 25

26 Appendix Proof. Proof of Proposition 3 The following inequalities hold for x > 0. x 1 + x/2 < ln(1 + x) < x(1 + x/2) 1 + x (10) The first one is established by Love (1980). To prove the second one, let x(1 + x/2) f(x) = ln(1 + x). Notice that f(0) = 0 and consider that its 1 + x derivative f (x) = 1 ( ) 2 x x is null in x = 0 but strictly positive for x > Let T = {(θ, ɛ) : 0 θ < ɛ 1} denotes the subset of parameters values for which a mixed strategy equilibrium exists and P : T [0, 1] denotes the function that yields the equilibrium probability of political corruption as a function of (θ, ɛ). Let 1 + x x x = θ 1 ɛ ɛ θ = ɛ 1 ɛ 1 θ θ 1 + x = ɛ 1 θ ɛ θ x 1 + x/2 = 2 θ(1 ɛ) 2ɛ θ θɛ 26

27 Then P (θ, ɛ) = = θ 0 θ 0 F (b/θ) G b (b)db ɛ θ ɛ b 1 θ θ θ 1 (1 b) db 2 = (ɛ θ) 1 θ 1 1 θ 0 ɛ b (1 b) db 2 = (ɛ θ) 1 θ [ ( ) 1 1 b ln 1 ɛ ] θ θ (1 ɛ) 2 ɛ b 1 b 0 = (ɛ θ) 1 θ ( ( 1 ln ɛ 1 θ ) ) θ (1 ɛ) θ (1 ɛ) 2 ɛ θ 1 θ = ɛ θ ( ( 1 1 θ ln ɛ 1 θ ) ) 1 1 ɛ 1 ɛ θ ɛ θ = θ ( ) 1 + x ln (1 + x) ɛ ɛx x 2. P is strictly decreasing in θ and strictly increasing in ɛ. The partial derivative of P with respect to θ is P (θ, ɛ) = ɛ θ θ2 θ 2 (1 ɛ) 2 ( (1 + θ)θ(1 ɛ) ɛ θ 2 ln (1 + x) ) (11) Given that 1 > ɛ > θ > θ 2 > 0, the sign of this expression is the same of that of the term with parentheses, which can be rewritten 1 + θ 2ɛ θ θɛ 2 θ(1 ɛ) ln (1 + x) ɛ θ 2 [ 2 2ɛ θ θɛ ] 1 + θ 2ɛ θ θɛ x ln (1 + x) (12) ɛ θ x/2 Given the first inequality in (10), we establish that (12) is negative by showing that the bracketed term is smaller than 1. 27

28 θ 2 (1 ɛ) < θ(1 ɛ) θɛ θ 2 ɛ θ < θ 2 (2ɛ θ 2 ) + θɛ θ 2 ɛ θ < (2ɛ θ 2 ) θ 2 (1 + θ)(2ɛ θ θɛ) < 2(ɛ θ 2 ). The partial derivative of P with respect to ɛ is P ɛ 1 θ (θ, ɛ) = θ 1 + ɛ 2θ (1 ɛ) 3 ( ln(1 + x) x 1 + x/2 [ 2ɛ θ θɛ ɛ ɛ ]) ɛ 2θ Notice that 1 > ɛ > θ implies that 1 + ɛ 2θ > 0. Hence, to show that this expression is positive, we need only to show that the bracketed term within the parentheses is smaller than 1. 2ɛ(1 θ + ɛ) < 2ɛ(1 θ + ɛ) + θ(1 ɛ) 2 2ɛ(1 θ + ɛ) θ θɛ 2 < 2ɛ + 2ɛ 2 4θɛ (2ɛ θ θɛ)(1 + ɛ) < 2ɛ(1 + ɛ 2θ). 3. P is strictly strictly concave in θ. P is strictly concave in in θ since the second derivative is negative. The second derivative with respect to θ can be written as ( ln (1 + x) 2 P 2ɛ (θ, ɛ) = θ2 θ 3 (1 ɛ) 2 x(1 + x/2) 1 + x which is negative because of the second inequality in (10). 4. P has the following limits: lim P (θ, ɛ) = 1 lim θ 0 P lim θ 0 P (θ, ɛ) = 0 lim θ ɛ θ (θ, ɛ) = 1 2ɛ P (θ, ɛ) = 0 ɛ lim lim θ 0 28 P lim θ ɛ θ θ ɛ ) < 0 P (θ, ɛ) = 1 θ/2 ɛ 1 (θ, ɛ) = P (θ, ɛ) = ɛ

29 The partial derivative can be rewritten P θ (θ, ɛ) = 1 θ(1 + θ)(1 ɛ) (ɛ θ 2 ) ln (1 + x) (1 ɛ) 2 θ 2 Applying the l Hospital s rule twice, we establish that P lim θ 0 θ (θ, ɛ) = 1 2ɛ P lim (θ, ɛ) = θ ɛ θ 5. P is not defined at (θ, ɛ) = (0, 0) and (θ, ɛ) = (1, 1). Although (0, 0) and (1, 1) do not belong to S, does P reach a limit at these values? Define the following functions that maps R + to a probability p [0, 1]. m(k) = k ln(1 + 1/k) n(k) = (1 + k) ln(1 + k) k k 2 The function m is strictly increasing and strictly concave with lim k 0 m(k) = 0 and lim k m(k) = 1. The function n is strictly decreasing and strictly convex with lim k 0 n(k) = 1 2 and lim k n(k) = 0. We then consider the limit of P as we approach the origin within S along the line ɛ = (1 + k)θ. lim P (θ, (1 + k)θ) = m(k) θ 0 It follows that the probability is not defined at the origin: it yields 0 coming along the line ɛ = θ (when k 0) and 1 along the line θ = 0 (when k ). Likewise, the limit of P as we approach the point (1, 1) within S along the line ɛ = (1 + kθ)/(1 + k) is lim P (((1 + k)ɛ 1)/k, ɛ) = n(k) ɛ 1 29

30 Again, the value of this limit depends on the value of k: the limit probability is 0 when we take the limit along ɛ = θ (when k ) and 1 2 when we follow ɛ = 1 (when k 0). 6. P is strictly supermodular ( P θ ɛ > 0). 30