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Strategic Analysis of Petty Corruption: Entrepreneurs and Bureaucrats Ariane Lambert-Mogiliansky a, Mukul Majumdar b, Roy Radner c a Paris-Jourdan Sciences Economiques (CNRS, EHESS, ENPC, ENS) 48 bd Jourdan,

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Strategic Analysis of Petty Corruption: Entrepreneurs and Bureaucrats Ariane Lambert-Mogiliansky a, Mukul Majumdar b, Roy Radner c a Paris-Jourdan Sciences Economiques (CNRS, EHESS, ENPC, ENS) 48 bd Jourdan, Paris, FRANCE b Economics Department, 416 Uris Hall, Cornell University, Ithaca, NY c Stern School of Business, KMC 8-8, New York University, 44 West Fourth Street, New York, NY Corresponding Author: Roy Radner Stern School of Business, KMC 8-87, New York University, 44 West Fourth Street, New York, NY tel: , fax: June 16, 2006 Abstract This paper develops a game-theoretic model of petty corruption by government officials. Such corruption is widespread, especially (but not only) in developing and transition economies. The model goes beyond the previously published studies in the way it describes the structure of bureaucratic tracks, and the information among the participants. Entrepreneurs apply, in sequence, to a track of two or more bureaucrats in a prescribed order for approval of their projects. Our firstresultestablishesthatinaone-shot situation no project ever gets approved. This result leads us to consider a repeated interaction setting. In that context we characterize in more detail the trigger-strategy equilibria that minimize the social loss due to the system of bribes, and those that maximize the expected total bribe income of the 1 bureaucrats. The results are used to shed some light on two much advocated anti-corruption policies: the single window policy and rotation of bureaucrats. JEL Classification Numbers: D73, C73, O17 Keywords: corruption, economic development, repeated games 2 Corruption is found to be one of the most damaging consequences of poor governance characterized by lack of both transparency and accountability. Corruption lowers investment and hinders economic growth and human development, by limiting access to basic social services as well as increasing the cost of their delivery. It also increases poverty, subverts the financial system, and undermines the legitimacy of the state. Thus, corruption is anti-poor, anti-development, anti-growth, anti-investment, and inequitable. The cost of corruption to a nation is very high. Transparency International (Report 2003) 1 Introduction 1.1 Background Corruption, defined roughly as the abuse of public office for private gain, 1 has generated an immense literature. The well-known book by Rose-Ackerman (1999) has some four hundred items in the list of references, and, for shorter useful surveys, one canturntoandvig(1991),bardhan (1997), Lambsdorff (2001), and the collection of articles edited by Elliott (1997). Perhaps the sheer volume of this literature (which we do not attempt to survey here) is a testimony to the fact that corruption in its many forms is not of recent origin, and not just limited to developing economies or the economies in transition from a command to a market system. Indeed, over the years, allegations of corruption have been important in political debates and in ushering major political changes in many countries at different stages of development. 2 However, in many recent estimates or rankings of corruption, developing countries and transition economies have figured prominently, and policy makers in those economies as well as international agencies interested in accelerating the pace of economic development have been justifiably concerned with the impact of corruption on productive efficiency, growth, poverty and the proper utilization of economic assistance. In this paper we focus on game-theoretic modeling of petty corruption. In some cases the term petty corruption is used in the context of relatively small bribes. However, even in this usage it has been rightly noted that pettiness of corruption refers only to the size of each transaction and not to its total impact on government income or policy (Scott, 1972, p. 66). In typical examples of petty corruption, the private citizens (often owners of businesses or managers of firms) are engaged in dealing with low-level government bureaucrats regarding transactions involving the filing of appropriate tax returns, payment of important duties, clearance of regulatory or licensing requirements, application for government benefits (loans 3 from state-owned banks, subsidies, jobs...) or approval of specific privileges (driver s license, passport, registration of a new firm as a legitimate business activity that complies with the laws on minimum wages, workers safety, safe construction standards, environmental hazards,...). The basic ingredients of corruption emphasized by Klitgaard (1988, p. 75) include (1) government monopoly, (2) discretion in interpreting laws, in deciding who is eligible for benefits, and in what constitutes proper documentation and procedure, and (3) lack of direct accountability. These appear in various ways. Some are subtle - a polite request or suggestion for a small baksheesh (in the Indian subcontinent) to expedite decision-making, the much discussed speed money, - and some are crude - a threat to derail the review and approval process; to stop the file immediately (Bardhan, 1997, p. 1324)]. As one might expect from elementary economic analysis, the exercise of the monopoly power of the bureaucrat typically results in a redistribution of income from the applicant to the official, but it may also result in a loss of efficiency, a so-called dead-weight loss. The latter can occur if an economic activity (i.e., a project) that would have been profitable without the payment of a bribe becomes unprofitable net of the bribe, and hence is curtailed or even abandoned in the presence of the extortionary regime. In the theoretical models that we develop, conditions for the persistence of petty corruption and consequent social losses can be precisely identified. The game-theoretic approach typically leads to models with multiple equilibria, and the presence of multiple equilibria in turn raises the possibility of moving from a current bad equilibrium to one that is socially superior. The question of how to make such a move has apparently not received much attention in game theory (see, however, Tirole, (1996)). Our analysis enables us to provide information about the set of equilibria and how this set depends on the parameters of the model. We indicate in some detail applications of our analytical framework to two themes of particular interest in the literature on anti-corruption policy: (a) the single window or one stop shop procedure (replacement of a track of bureaucrats by a single bureaucrat) and (b) rotation of bureaucrats. 3 One of the motivations behind our model specifications is the extensive discussion of the system of multiple approvals or multiple verifications that characterize the interaction between the citizens and the bureaucrats in the Indian subcontinent, and on the link between such systems and pervasive petty corruption, and the resultant effects on India s development programs. 4 N. Vittal, India s Vigilance Commissioner argued, (citing UNDP calculations) that India s GDP will go up by 1.5 per cent if the corruption levels of India are brought down to those of Scandinavian countries [Vittal in Gupta (2001, Chapter 2)]. And even after some fifteen years of liberalization and reforms, the project approval process has remained a source of 4 major irritation. 5 In their widely cited article, Shleifer and Vishny (1993) argued that competing bureaucracies, each of which can stop a project from proceeding, hamper investment and growth around the world, but especially in countries with weak government and gave Russia as a prime example (pp ). Rose-Ackerman (1999) specifically referred to corruption discouraging the flow of foreign direct investment to developing countries (p. 3). 6 Thus, the models we are developing should be of interest to a broad group of developing and transition economies. Compared to the entire published literature on corruption, the literature on gametheoretic analyses is rather limited. Various aspects of corruption have been studied from this point of view, such as: bribery to avoid the payment of taxes (Marjit et al., 2000) or the enforcement of regulations against pollution (Mookerjee and Png, 1992, 1995); bribery to avoid prosecution for crimes or to influence anti-crime policies (Dal Bo et al., 2003); corruption in procurement auctions (Burguet and Che, 2004; Compte et al., 2005). Further references can be found in these publications, in (Bardhan, 1997), and in (Mishra, 2005). We are not aware of any previous gametheoretic analysis of bribery to obtain permits that explicitly models the structure of bureaucratic tracks, the sequence of applicants, and the information flows among the participants. 1.2 Summary of Results In our basic model, entrepreneurs apply sequentially to a track of bureaucrats. Each entrepreneur has a project that she wants approved, and must apply to each of the bureaucrats in the track for approval. If the project is approved, she will realize some positive value, but each bureaucrat may demand a bribe in return for his approval. Each bureaucrat s goal is to maximize his total discounted expected bribe income. (See Section 1.3 for a more detailed sketch of the model, and Section 2 for a complete description of the formal model.) The resulting sequential game has many equilibria, which differ in the bribes demanded. Any one equilibrium is characterized by a set of normal bribes, one for each bureaucrat in the track. An entrepreneur will apply to the track and pay the normal bribes if the value of her project exceeds the sum of the normal bribes. In any particular equilibrium, a bureaucrat is said to defect if he attempts to charge a bribe larger than his normal one for that equilibrium. Bureaucrats are deterred from defecting by the threat that the other players of the game will revert to a bad equilibrium in which his future bribe income will be reduced to zero. In an equilibrium with positive normal bribes, some of the projects with positive value will not be implemented because the sum of the normal bribes exceeds the value. 5 This results in a dead-weight loss, or social loss, for the system. We call an outcome socially efficient if the total value of the implemented projects maximized, which means that all of the bribes are zero. Unfortunately, no equilibrium of the game has this desirable property. However, we can characterize those equilibria that minimize the the social loss in the set of all equilibria. Following standard terminology, these are called second-best. We also show that themorepatientthebureaucratsare(the closer their discount factor is to zero), the closer are the second-best equilibria to being socially efficient. At the other extreme, we characterize the equilibria that maximize the total expected bribe income of the bureaucrats, and show that the more patient the bureaucrats are the larger is their maximum bribe income. As is intuitively clear, the total expected bribe income is positively related to the social loss. We can deepen the analysis to shed some light on two oft-proposed policy recommendations. One such recommendation is that in any jurisdiction the track of multiple bureaucrats should be replaced by a single window to which the entrepreneur can apply. We show that the single window policy does not unambigously lead to a reduction in social loss. On the one hand, if we look only at second-best equilibria, then a switch to a single window does indeed reduce the total bribe income, and hence the social loss. On other hand if we look at bribe-income-maximizing equilibria, the switch to a single window will increase the social loss! Our analysis also enables us to assess another much-advocated reform, the rotation of bureaucrats among tracks. The multiplicity of equilibria again makes the results ambiguous, but in the opposite direction. If we focus on the second-best equilibria, an increase in the frequency of rotation leads to an increase in social loss. On the other hand, if we focus the bribe-income-maximizing equilibria, an increase in the frequency of rotation leads to adecreaseinsocialloss. As is standard in the theory of sequential games, a part of the analysis is the identification of a bad equilibrium such that the threat to revert to it in case of a defection is credible. In our case, this bad equilibrium is the repetition of the one-stage game, in which the players are a single entrepreneur and the track of bureaucrats. We show that in this one-stage game there is no equilibrium in which the entrepreneur s project is approved. On the other hand, there is an equilibrium in which the bribes demanded are so high that entrepreneur does not apply, no matter what the value of her project. The one-stage game is exhibits an extreme example of hold up, and has an independent interest. For a more detailed discussion of these results, see Section 3. 6 1.3 Sketch of the Model As noted above, in the basic model a sequence of entrepreneurs may apply to a track of two or more bureaucrats for approval of their projects. Each entrepreneur has a project that has a specific (expected present) value that would be realized if the project were approved. This value is known to the entrepreneur, but not to the bureaucrats. However, its probability distribution is common knowledge. The entrepreneur must apply to each bureaucrat in the track in a prescribed order, and her project is approved if and only if every bureaucrat in the track approves it. Each bureaucrat may demand a bribe as a condition of approval. At any step in the period the entrepreneur may refuse to pay the bribe, in which case she leaves the process and the value of her project is not realized, although she loses the total amount of bribes paid up to that point. If her project is approved by the entire track, she then receives the value of the project, minus the total amount of bribes paid. The payoff to a bureaucrat in that period is the amount of the bribe he receives, if any, and the bureaucrat s total payoff in the game is the expected sum of discounted bribes he receives. It is important to distinguish between two types of interventions by a bureaucrat when an entrepreneur plans an investment project. In order to get formal approval, each project typically has to conform to certain requirements (e.g., by satisfying some safety standards or meeting appropriate financing norms...) A bureaucrat may reject a qualified project if a demanded bribe is not paid. On the other hand, abureaucratmay approve an unqualified project in exchange for receiving a corresponding bribe that he demands. Thus the bribes demanded for the approval of qualified and unqualified projects may be different. We refer to the phenomenon of the approval of unqualified projects as capture, as distinct from the phenomenon of demanding a bribe for the approval of a qualified project, which we refer to as hold up or pure extortion. For simplicity of exposition, in the formal model (Section 2) we assume that all the projects are qualified, and focus on hold up. Section 3 provides some informal comments on capture. A more complete formal treatment (with detailed proofs) of both types of intervention is given in Lambert-Mogilianky, Majumdar and Radner (2006) [to be referred to as L-M-R]. We make the following assumptions about the information that the players have about the actions of the other players: 1. Players remember their own actions and those of the players they transact with. 2. Within any single period, no bureaucrat knows the bribes demanded by the other bureaucrats. 3. Every player learns the actions of the other players in previous periods, 7 perhaps with some delay. Section 2 presents the details of the formal model and results. The reader who is not interested in these details can skip to Section 3, where we discuss the assumptions of our basic model and the policy implications of the results. Finally, we suggest various extensions of the analysis, some of which we have completed, and some of which will be the subject of future research. 2 A Formal Model 2.1 A One-Stage Game The players in the one-stage game consist of a single entrepreneur (EP) and a single track of N bureaucrats (BUs), with N 2, arranged in a specific sequence. In order to get her project approved, EP must apply to and obtain approval from each of the BUs in the prescribed order (i.e. BU 1 first, then BU 2 etc.). If the project is rejected by any one BU, the game ends and EP does not proceed further in the track. Here is the complete description of the extensive form of the game. Let V denote the project s potential value, which is uniformly distributed on some closed interval, which we may normalize to be [0, 1]. The probability distribution of V (the prior ) is common knowledge, but the realized value of V is known only to EP. If and when EP applies to BU n she incurs a cost c 0. For convenience of exposition, this cost is assumed to be the same for all BUs. The cost c is known to all theplayers. IfEPappliestoBU n,letb n 0 denote the bribe demanded by him. The project is approved if and only if the bribe is paid. The bribe is demanded on a take-it-or-leave-it basis, so that if EP refuses to pay the bribe the game ends. It is assumed that the BUs do not observe the bribes demanded by the other BUs. Let a n =1or 0 accordingasepdoesordoesnotapplytobu n. If she does apply, she incurs the application cost c 0 and then learns the magnitude b n of the bribe demanded by BU n. Let p n =1or 0 accordingasepdoesordoesnotpaythe bribe. Note that if a n =0or p n =0then the game is over. Thus, if a n =0we have p n =0and if p n =0then a m =0 for all m n. Call the part of the game in which EP faces BU n the nth step (n =1,..., N). The action taken by EP in step n is the pair (a n,p n ). The action taken by BU n in step n is, of course, b n. For n 1, leth n denote the history of the game through step n, i.e., the sequence of actions taken by all players through step n. A strategy for EP is a sequence of 8 functions, α = {A 1,P 1,..., A N,P N },whichdetermineep sactionsaccordingto: a n = A n (V,H n 1 ), (1) p n = P n (V,H n 1,a n,b n ). (Here H 0 denotes an exogenous constant, the prehistory of the game. ) Since BU n does not know the magnitudes of any previously demanded bribes, his strategy for the game is the magnitude of the bribe he demands: b n 0. (2) To complete the description of the game, we must describe the players payoff functions. The payoff for BU n is the bribe he demands, if it is paid, i.e., U n = p n b n. (3) The payoff for EP is the value of the project if the project is approved, less the sum of the application costs and bribes paid (whether or not the project is completely approved). Thus EP s payoff is U 0 = p N V X (a n c + p n b n ). (4) 1 n N Finally, without loss of generality, assume: 0 Nc 1. (5) (Otherwise, no project would be profitable.) As usual, a Bayes-Nash equilibrium ofthegameisaprofile of strategies such that no player can increase his or her expected pay-off by unilaterally changing his or her strategy. A strategy is (weakly) undominated if there is no other strategy that yields the player as high a payoff for all strategy profiles of the other players, and a strictly higher payoff for some strategy profile of the other players. For our first result, we shall confine ourselves to equilibria in undominated strategies. Theorem 1 There is no equilibrium in which the project is approved with positive probability. We sketch here a proof of the theorem by contradiction. First observe that for an equilibrium in undominated strategies, the bribes demanded by the BUs must be strictly positive. Hence, if EP ever applies to the last BU N,heinfersthatEP 9 has already incurred a positive cost, [and this is true even if the application cost is zero]. This inference influences the size of the bribe he demands. One can verify the following c

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