Inefficient lobbying, populism and oligarchy

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1 Inefficient lobbying, oulism and oligarchy The Harvard community has made this article oenly available. Please share how this access benefits you. Your story matters Citation Camante, Filie R., and Francisco H.G. Ferreira Inefficient Lobbying, Poulism and Oligarchy. Journal of Public Economics 91 (5-6) (June): doi: /j.jubeco Published Version doi: /j.jubeco Citable link htt://nrs.harvard.edu/urn-3:hul.instreos: Terms of Use This article was downloaded from Harvard University s DASH reository, and is made available under the terms and conditions alicable to Other Posted Material, as set forth at htt:// nrs.harvard.edu/urn-3:hul.instreos:dash.current.terms-ofuse#laa

2 Inefficient Lobbying, Poulism and Oligarchy Filie R. Camante and Francisco H. G. Ferreira December 1, 2006 Abstract This aer analyses the efficiency consequences of lobbying in a roduction economy with imerfect commitment. We first show that the Pareto efficiency result found for truthful equilibria of common agency games in static exchange economies no longer holds under these more general conditions. We construct a model of ressure grous where the set of efficient truthful common-agency equilibria has measure zero. Second, we show that under fairly general assumtions, the equilibrium will be biased against the grou with the highest roductivity of rivate caital, reflecting the fact that, on the margin, less roductive grous find lobbying relatively more rewarding. Finally, as an alication, if lobbies reresenting the oor and the rich have identical organizational caacities, we show that the equilibrium is biased towards the oor, who have a comarative advantage in olitics, rather than in roduction. If the ressure grous differ in their organizational caacity, both ro-rich (oligarchic) and ro-oor (oulist) equilibria may arise, all of which are inefficient with resect to the constrained otimum. We are grateful to Alberto Alesina, Abhijit Banerjee, Francesco Caselli, Quoc-Anh Do, Jan Eeckhout, Elhanan Helman, Richard Holden, Humberto Moreira, and Andre Sant Anna for their helful comments. Many suggestions by the editor, Emmanuel Saez, and two anonymous referees are also gratefully acknowledged. Finally, we thank seminar articiants at Harvard University, the University of Pennsylvania, the World Bank, PUC-Rio, the NBER Summer Institute, the V Meeting of the Political Economy Grou of LACEA (Cartagena, Colombia), NEUDC 2004 (Montreal), and the ASSA Meetings 2005 (Philadelhia). The usual disclaimer on remaining errors alies. Financial suort for the early stages of this research was rovided by Faerj. Deartment of Economics, Harvard University. Contact: camante@fas.harvard.edu The World Bank Research Deartment. Contact: fferreira@worldbank.org 1

3 1 Introduction Lobbies and ressure grous emloy roductive resources time and money in the ursuit of influence over government decisions. There is widesread evidence that such rent-seeking activities have real imact on olicy-making. Farm lobbies have successfully sought to maintain high levels of rotection for domestic roduction in a number of laces, including the Euroean Union, Jaan and the United States. In federal countries, such as the United States, India or Brazil, regional and state reresentatives often lobby central governments to attract ublic sending to their states including sending on education and infrastructure that are subsequently used as inuts by rivate businesses in those areas. In develoing countries, it is not uncommon for richer grous to lobby for government sending on high-end infrastructure rojects such as airorts and universities, while oorer grous lobby for sending on basic sanitation and rimary schooling. Is the influence of lobbies over governments costly, in terms of the aggregate efficiency of resource allocation? And, in addition to any aggregate efficiency losses, do the distortions they romote on government activities benefit somegrousattheexenseofothers? Theimortanceoflobbyingas an economic activity has of course long been recognized, as have its otentially deleterious effects on the efficiency of resource allocation. 1 But the initial view that lobbying was inefficient, which characterized the original literature on rent-seeking, derived from its treatment of the contributions made by lobbies to government agents as deadweight losses. 2 Once the government is exlicitly recognized as an agent in its own right, with its own references and resources, the economic analysis of ressure grou olitics changes. A dominant theoretical aroach to lobbies when ayments to the government are not dismissed as deadweight losses is that of common agency, in which lobbying is modeled as a menu auction. 3 If rincials behave truthfully in the sense of revealing their true references, and hence aying as contributions to the agent the maximum amount that they are wiling to exchange for the agent s decision then it has been shown (by Bernheim and Whinston, 1986, and with greater generality by Dixit, Grossman and Helman, 1997, henceforth cited as DGH) that the equilibrium of the common agency game is Pareto efficient. This result has been very influential in the olitical economy literature, having been alied, inter alia, to tax rate olicy (DGH,1997, and Dixit,1996) 1 A seminal early treatment can be found in Krueger (1974). 2 See, for instance, Rodríguez (2004), which follows this rent-seeking literature. 3 A common agency roblem is one in which several rincials, with different and ossibly conflicting interests, try to influence the decisions of a single agent. Unlike most rincial-agent setus, common agency games resent a non-trivial efficiency issue even under erfect information, as they raise the question of whether an efficient allocation of resources can be achieved when the several rincials act in a noncooerative way. 2

4 and to the determination of trade tariffs (by Grossman and Helman,1994, 1995a, and 1995b). Against this background, this aer makes three oints. First, we show that the result that truthful equilibria in common agency games are Pareto efficient hinges on the existence of erfect commitment mechanisms between rincials and the agent. While this requirement aears both natural and inconsequential in a static exchange economy setu, it turns out to matter a great deal if time and roduction are introduced. When the DGH framework is extended to incororate roduction and imerfect commitment (due, say, to contract enforcement roblems or credit market failures), the truthful equilibrium of the game is almost surely Pareto inefficient, because rincials cannot commit to use the outut from roduction to make contributions to the agent. Second, we make a general rediction about the nature of the inefficiency that arises from lobbying without commitment. We consider a simle model in which two grous have access to different technologies, each combining rivate caital with a different ublicly rovided inut. These grous therefore have conflicting interests over the comosition of ublic sending, and they make olitical contributions seeking to influence it. In the absence of enforceable contracts, the equilibrium allocation is shown to be inefficient, because it is excessively tilted towards the grou which has the lowest marginal roductivity of rivate caital in equilibrium. The intuition for this general result is that the grou which is relatively inefficient in using rivate resources (wealth) for roduction, allocates a greater share of these resources to lobbying, thus distorting ublic decisions in its favor. This would not occur if future gains from roduction were also available for lobbying. But, in the absence of commitment, the full surlus from roduction cannot be used, and the roduction vs olitical contribution decision is effectively a ortfolio investment decision. Those with a comarative advantage in roduction lobby relatively less, and the equilibrium is distorted in favor of the other grou, which may be said to have a comarative advantage in olitics, rather than roduction. 4 Third, we consider the distributional imlications of these results in a secific variant of the model, in which access to the more roductive technology is endogenized by requiring a minimum level of wealth. This causes the two ressure grous to have different wealth levels, with one oorer than the other. Since the richer grou gains access to a more roductive technology by virtue of having greater wealth the equilibrium of the basic model is inefficiently ro-oor, in the sense 4 This resembles the result from the classic model of cometition among ressure grous by Becker (1983), in which the equilibrium deends on relative olitical roductivity between grous. That model, however, does not include roduction exlicitly, so it does not address the issue of olitical roductivity relative to efficiency in roduction er se. Our results also contrast with those in the model by Acemoglu, Aghion and Zilibotti (2006), in which lobbying under credit constraints always benefits those who have more resources. 3

5 that the equilibrium allocation of ublic sending is excessively tilted towards the oorest lobby (relative to the efficient allocation). Since this is the result of a relatively larger lobbying effort on the art of the oor, we call this a oulist equilibrium. Allowing for different levels of organizational caacity within each lobby so as to cature a ossible Olsonian effect of grou size (Olson, 1965) generates a richer gamut of outcomes. In articular, if the richer grou is sufficiently smaller and better organized, it is ossible to obtain inefficiently ro-rich equilibria, which we call oligarchic. Other aers have studied conditions under which the Pareto efficiency roerty of the equilibria of common-agency games fails. Besley and Coate (2001) obtain inefficiency results within the common-agency framework by abandoning the notion of truthful behavior. 5 Besharov (2002) generates inefficiency by returning to the notion that contributions are directly wasteful. Of course, the common agency framework is not the only way to model the behavior of interest grous, and adiscussionofdifferent aroaches can be found in van Winden (2003). Another recent treatment aears in Felli and Merlo (2006), who substitute bargaining for the menu auction formulation. Our results are also related to those in Loury (1981), Galor and Zeira (1993), and Banerjee and Newman (1993), in the sense that the initial distribution of wealth affects the efficiency roerties of the long-run equilibrium of the economy. As in those aers, imerfect commitment (which may arise from credit market imerfections) lays a crucial role, although here it does so in a different context, namely a non-electoral olitical rocess. In this context, the key inefficiency generated by the absence of commitment arises through a distortion in equilibrium ublic olicy, and is additional to the one stemming simly from the existence of individuals restricted to a less roductive technology due to lack of access to credit. In common with the literature on wealth distribution and olitical economy (Bertola, 1993; Alesina and Rodrik, 1994; Persson and Tabellini, 1994; Bénabou, 2000), we find that wealth inequality can lead to inefficient equilibria, due to the existence of conflicting references over ublic olicy. In contrast with most of it, however, in our model inefficiency does not arise from distortions inherent to the nature of redistribution (such as a tax on caital holdings). Instead, it arises from the very nature of the olitical rocess. Whereas those authors emhasize the inefficiencies caused 5 Besley and Coate, 2001,. 79 state that "Bernheim and Whinston (1986), Grossman and Helman (1994), and DGH (1997) have all argued that we should exect equilibria with truthful contribution schedules to be layed. At the end of the day, however, they do not offer an account of the decision making rocess which guarantees convergence to these equilibria (our abbreviation). We do not find the original three arguments in suort of truthful behavior as unersuasive as Besley and Coate do: (i) the efficiency result itself may cause truthful equilibria to be focal; (ii) truthful contribution schedules are always a best resonse (which imlies the existence of truthful equilibria), and (iii) they are the only coalition-roof equilibria. 4

6 by tax choices arising from electoral outcomes, we consider inefficient sending decisions, as a result of lobbying from interested ressure grous. 6 Other aers that are related to ours are Esteban and Ray (2000, 2006) and Do (2004), which also look at wealth distribution and olitical cometition over government decisions. Esteban and Ray (2006) consider an imerfect information setu, in which agents lobby in order to signal rofitability. The signal can be jammed, however, by the confounding effect of wealth. Governments do not directly benefit from contributions, which are urely wasteful, but their allocation decisions can be distorted by the suerior lobbying ability of the wealthy, conditional on roductivity. The result is driven owerfully by the assumtions that wealth and roductiviy are uncorrelated, and that the cost of lobbying declines with wealth. Although the setu is quite different from our erfect information common agency game, a comarison of our results (articularly in Section 4) with Esteban and Ray s hels shed light on the central issue of how the correlation between wealth and roductivity determines the direction of the biases that arise from government decisions under lobbying. We return to this issue in the Conclusions. Do (2004) also analyzes ressure grou interaction under credit market imerfections, but it focuses on the endogenous emergence of barriers to entry in regulated industries, rather than on the allocation of government sending. Finally, our aer also relates to the literature studying oligarchies versus oulism, of which Bourguignon and Verdier (2000), Acemoglu (2005), and Mejía and Posada (2005) are examles. These aers, however, do not study a olitical rocess based on lobbying, which is our main focus. The aer is organized as follows. Section 2 makes our first oint, by showing that truthful equilibria in common agency games layed without commitment in a roduction economy are generally inefficient. Section 3 makes our second oint: it resents a basic model of two ressure grous that have access to different technologies using different ublicly rovided inuts, and shows that the equilibrium is distorted towards the grou with lowest marginal roductivity of rivate caital. Section 4 makes our third oint: when access to the different technologies deends on wealth, the efficiency roerties of the game have distributional consequences. With identical organizational abilities, the equilibrium is inefficiently ro-oor (or oulist ). If the richer lobby is sufficiently better organized, inefficiently ro-rich (or oligarchic ) equilibria are also ossible. Section 5 concludes. 6 The need to move beyond voting rocesses in order to understand the economic effects of olitics was emhasized by Atkinson (1997,. 316), [it seems] imortant to see how far the findings deend on whether the outcome is governed by the references of the median voter, or by the ideology or references of olitical arties, or by olitical ressure from different interest grous (...). There has been relatively little research by economists which has set side by side different ossible exlanations of income redistribution. 5

7 2 Inefficient Lobbying: Introducing Production and Imerfect Commitment to the Common Agency Framework In this section, we investigate the consequences of relaxing the assumtion of erfect commitment for the efficiency result of the common agency game roosed by DGH (1997). Since commitment issues are essentially immaterial in a one-shot exchange economy, we extend the DGH framework to an economy in which there is roduction, and roduction takes time. 2.1 The Basic Setu Following DGH, let there be a (finite) set L of rincials ressure grous, for instance in which every rincial i L has continuous references denoted by U i (a, c i ),wherea is the vector chosen by the agent - e.g. the olicy-maker. Princials wish to influence this choice, and c i is a scalar that stands for the ayment made with that urose by rincial i to the agent. It is assumed that U i is decreasing in c i. The agent has continuous references G(a, c), wherec is the ayment vector, and G is assumed to be increasing in each comonent of c. In words, the agent enjoys being aid, while the rincials do not like to make contributions. Princial i chooses a ayment schedule C i (a) C i, which mas every ossible action a A into a contribution to the agent. Sets C i and A reresent institutional and feasibility constraints on ossible choices, and it is assumed that C i C i imlies that C i (a) 0 for every a A, and also that if C i C i then any Ci, such that Ci (a) 0 and C i(a) Ci (a) for every a A, also belongs to C i. That simly means that ayments must be nonnegative, and that any (nonnegative) ayment smaller than some feasible ayment must also be feasible. The analysis then focuses on a two-stage game: in the second stage, the agent chooses the otimal action given the ayment functions chosen by each rincial, which were defined noncooeratively in the first stage, taking account of the agent s eventual resonse. Such a game has a multitude of ossible equilibria. Following DGH, most of the literature has focused on truthful Nash equilibria, which are Nash equilibria in which all layers adot truthful strategies. A truthful strategy, in this context, is a truthful ayment schedule relative to some utility level: each rincial offers the agent a contribution schedule C i (a) that transfers to the agent the full comensating variation that arises from the the agent s action, rovided that such ayment is feasible. 7 Truthful equilibria are an attractive refinement because truthful strategies are always a best resonse; the equilibria are focal, and coalition-roof. The fundamental result of the common agency literature, due to Bernheim and Whinston (1986) 7 For this reason, truthful ayment schedules are also known as comensating ayment schedules (see Grossman & Helman, 2001). 6

8 and generalized by Proosition 4 in DGH (1997,. 761), establishes the Pareto efficiency of truthful Nash equilibria in this game. It is helful to go through the argument that underlies its roof: 8 Denote the set of agent actions and rincial contributions in the truthful equilibrium by {a 0,C 0 }(with resect to utility levels u 0 i ). Now suose there were a olicy vector a and a ayment vector c that Pareto-dominated the truthful equilibrium air of {a 0,C 0 }.Asrincialimust be at least as well off as in equilibrium, and once ayments reduce its utility, it must be the case that c i CT i (a,u 0 i ), for this is by assumtion a truthful schedule. Hence the agent cannot strictly refer a and c to the equilibrium values, following a revealed reference logic: once a and {C T i (a,u 0 i )} i L were available, yet he chose {a 0,C 0 }, then he must not refer the former to the latter. Given that c i CT i (a,u 0 i ), it follows that he also does not refer a and c to the former, for his utility is increasing in each rincial s ayment. It must therefore be true that the strict inequality that is required to characterize Pareto-dominance is valid for some rincial i: some of the rincials must strictly refer a and c i to the equilibrium values. This would mean, however, that such rincial would not be otimizing in equilibrium: he could have offered c i in exchange for a, and the agent would have acceted, for he would still be receiving the truthful contributions Cj T (a,u 0 j ) from every other rincial j (and C T j (a,u 0 j ) c j, as was seen above). This means that {a0,c 0 } was not an equilibrium, and this contradiction establishes the Pareto efficiency of truthful equilibria. The intuition for this result is that cometition between the rincials enables the agent to extract all of the surlus in the game, and it is therefore in her best interest to maximize that surlus via an efficient allocation. It should be clear that this result relies critically on commitment. The rincials commit to the contribution schedules, and the agent commits to the vector of actions she chooses. This reliance on full commitment is imlicit in DGH, and it seems both natural and innocuous when we think of both actions being taken simultaneously, in which case adherence to the announced actions is ultimately enforced by the credible threat by either arty to renege on its art of the deal, in case of deviation by the other arty. But this is not the case if, say, the contributions are to be aid after the agent has already imlemented his action. In this case there must be an exlicit commitment device, otherwise the agent will anticiate that the rincials will renege on their contributions, and the equilibrium will unravel. 9 8 The heuristic argument is rovided by DGH (1997). In order to findaformalroof,however,onemustreferto Dixit, Grossman and Helman (1999). 9 The issue of commitment arises, in a different context, within the dynamic extension of the common agency game exlored by Bergemann and Valimaki (2003). They consider the case where there is no commitment across eriods in a reeated game, but not within one game. 7

9 2.2 Production Imerfect commitment would be articularly imortant in a roduction economy. The key feature of a roduction economy, in the resent context, lies in the distinction between the resources available before and after the roductive activity is undertaken. Let us therefore extend the common agency game to the case of a roduction economy: the agent s choice (of a)affects the rincials roduction function, Ψ i, and individual utilities deend on this function s (scalar) outut. The roduction technology also uses as an inut the resources directly invested by each rincial, which will be denoted k i. Therefore our setu may be summed u as follows: each rincial has continuous references U i [Ψ i (a, k i ),c i ], which is increasing in Ψ i and decreasing in c i. Ψ i is increasing in k i and satisfies the Inada conditions; the agent has continuous references G[a, c; Ψ(a, k)], whereψ is the vector of roduction oututs and k is the vector of k i. 10 The existence of a roductive activity means that time now matters in this common agency game: resource availability after roduction is not the same as before it takes lace. Under imerfect commitment, it is the availability of resources before roduction that determines the feasibility constraints for individual rincials. To cature this oint formally, let us rewrite the common agency roblem in a generalized framework, as a three-stage game, rather than the two stages in which it is usually modeled. At stage one, rincials announce ayment schedules C i (a) C i, just as usual. At the second stage, the agent chooses a olicy vector a A, and the rincials decide how much they will ay simultaneously with the imlementation of the chosen olicy, c s i. Finally, at the third stage, roduction is realized and rincials decide how much will be aid at the end of the game, c d i. In other words, it is ossible to ay art of the contribution immediately, while ostoning some of it, at each rincial s discretion, therefore otentially deferring effective ayments. Production takes lace between the second and third stages. Denote individual i s wealth by w i and assume, for simlicity, that each rincial s utility deends only on own consumtion, which takes lace in the final eriod and equals outut minus the final eriod contribution. 11 Assume also that credit markets are missing entirely from this economy, and that the wealth distribution is bounded above, so that 1 < Ψ i (a i,w i )/ w i, i,,where a i arg max a A Ψ i (a, w i ) imlying that all rincials find it referable to invest all of their wealth, 10 Alternatively, and more generally, one could think of Ψ i as reresenting the rofits resulting from a roductive activity, and of the agent s decision as affecting those rofits in some way. In that case, a could still reresent ublicly-rovided inuts for rivate roduction, but it might also include decisions on subsidies or tariff rates, or indeed anything that enhanced the rofitability of rivate roduction. 11 Allowing for consumtion in earlier eriods obviously changes the levels of investments and contributions, but does not qualitatively affect the main results of the aer. This is discussed in more detail in Section 3. 8

10 rather than to save any of it across the two eriods. 12 This effectively means that the roduction function Ψ i is the only conduit between initial wealth and final consumtion. The absence of credit markets means that rincials can not have access to resources beyond their initial wealth, before roduction takes lace. Individual outut then deends on the action chosen by the agent and on the resources invested by the rincial, k i = w i c s i.wealsoassumethatthereisnodiscounting. We can then formally define the strategic form of the generalized common agency game as follows: Definition 1 The strategic form of the generalized common agency game is Γ {N,(S i ) i N, (u i ) i N } such that (i) N = L {j}, (setoflayers,wherel is the set of rincials and j refers to the agent) (ii) u i = U i [Ψ i (a, w i c s i ) cd i ],i L, u i = G[a, c s + c d ; Ψ(a, w c s )],i= j, (ayoffs) (iii) S i = C e i C e i C e i 0,i L, S i = A, e i = j (where C e i is the sace of functions f : A C i, C e i 0 is the sace of functions g : A C e i C i such that g(a, c i )+c i C i,anda e is the sace of functions h : C A), (strategy saces). Let us first assume that there is erfect commitment by the rincials, meaning that each rincial can somehow commit to the announced ayment schedule in a credible manner. This may be formally stated by imosing c s i + cd i = C i (a) for every ossible a chosen by the agent, indicating that the latter is indifferent between being aid in the second or in the third stage. The set of ossible contributions in equilibrium is now conditioned by the ossibility of aying after roduction. Indeed, the maximum ossible ayment by rincial i, C i, is given by his total outut when: (i) the agent chooses the action that maximizes the rincial s utility, and (ii) all of the resources initially available are invested in roduction: C i (w i ) Ψ i (a i,w i ). Given that ayments can be made after roduction and that the rincial s utility is increasing in Ψ i, which is increasing in k i, it is otimal for rincial i to invest w i on the roduction function, setting c s i =0in any subgame-erfect Nash equilibrium. This in turn imlies that w i may be considered a arameter in the ayoff functions, which can thus be written as U i (a, c i ) and G(a, c): this is recisely how they aear in DGH (1997). It is then ossible to directly aly their Proosition 4, and to conclude that truthful equilibria lead to Pareto-efficient allocations in generalized common agency games with erfect commitment by the rincials with resect to announced ayment schedules. In fact, within a erfect commitment framework, the introduction of a roduction activity merely changes the set of ossible equilibrium contributions, C i. 12 While the missing credit market assumtion is crucial for the results, the uer bound on the wealth distribution is an innocuous simlification. It simly revents us from having to account for some agents investing u to the oint where Ψ 0 i (k) =1, and saving k i thereafter. 9

11 Let us now consider the case in which there is no such erfect commitment mechanism. In this case, roceeding by backward induction in Γ, a subgame-erfect equilibrium necessarily involves c d i =0: once the olicy chosen by the agent has been imlemented, rincials have no incentive whatsoever to make any further ayment, for it would decrease their utilities. Any romise of a strictly ositive c d i would not be credible, and the agent will take account of that by demanding that ayments be made simultaneously to olicy imlementation. This means that all ayments must be made before roduction, and that affects the amount of resources available for roductive investment in equilibrium, since contributions and investments must both come from initial wealth, w i. Formally, there is a new level of the maximum ossible contribution by rincial i, C i 0,given by C i 0(w i ) w i. The utility functions must now be corresondingly written as U i [Ψ i (a, w i c s i )] and G[a, c s ; Ψ(a, w c s )]. Given that roduction in this economy is more efficient than a storage technology, C i 0 is a strict subset of C i. A careful analysis of the aforementioned heuristic argument behind the roof of Proosition 4 of DGH (1997) shows that this suffices to break the validity of the roosition as a general result: it could be the case that there existed a and c such that Ci T (a,u 0 i ),c i C i and C T i (a,u 0 i ),c i / C i0, forsomei L, so that the revealed reference argument is no longer valid. To ut it another way, the absence of erfect commitment reduces the set of ayments that are ossible in equilibrium: there may be an allocation which Pareto-dominates the constrained equilibrium one and which is feasible in C i, but which is not feasible in the restricted set C i The crucial element in the above argument is the imossibility of having access to roduced resources before engaging in the roductive activity. In this sense, the existence of erfect credit markets could lay the role of erfect commitment, in that it would allow for the anticiation of future resources. Of course, erfect credit markets require erfect commitment between borrowers and lenders, in the sense of erfect enforcement of contracts. This reveals the very nature of the inefficiency under analysis: it is linked to some institutional roblem which gives rise to a contract enforcement failure, either within credit markets or between rincials and agent. 14 As elsewhere in the literature (e.g., Grossman and Helman, 1994a), this discussion of efficiency alies to the allocation of resources among the layers taking art in the game. If there are 13 The maintained assumtion here is that the relevant set for efficiency analysis is the one which embodies the technological roduction ossibilities of the economy. The imlication is that an equilibrium reached subject to the feasibility constraints imlicit in the constrained set of ossible equilibrium contributions need not be Pareto efficient in that larger set. This efficiency assessment is analogous to stating that a general equilibrium with a missing market is no longer Pareto efficient (as comared to one with comlete markets). 14 It is ossible that commitment devices might emerge in a context in which the game is reeated. As with the standard Folk theorem, their existence would require some uer bound on discount rates. 10

12 other individuals in the economy who are not art of the common agency game, there can (and, in general, will) be inefficient outcomes for the economy as a whole, where the outsiders end u being exloited by the layers, to the detriment of efficiency. 15 In this section, we have shown that truthful equilibria in generalized common agency games without erfect commitment need not be efficient. In the next section, we consider a simle illustration, in which two exogenously formed grous have access to different technologies. Each uses a different ublicly rovided good as an inut into roduction, and they lobby the government over the comosition of ublic sending between these goods. The results will shed light on the nature of the ensuing inefficiency, in which ublic sending is distorted towards the least economically roductive grou. 3 A Model of Inefficient Lobbying over the Comosition of Public Exenditures In order to analyze the nature of the inefficiency generated by lobbying in a roduction economy with imerfect commitment, some additional structure is necessary. In this section we rovide a simle common agency model that incororates both a time-consuming roduction rocess and imerfect commitment, by considering two ressure grous that use different ublicly rovided inuts, which we denote g and s, into their own rivate roduction rocesses. The vector of government actions will now be the vector of the quantities of these two ublicly rovided goods: a = {g, s}. Let the economy consist of a continuum of rivate individuals forming a oulation of size one, and of a searate agent, called the government, whose attributes are discussed below. In this section, let each individual in the continuum be endowed with an identical initial wealth level, w. This initial wealth consists of a single good, which we can be used to ay taxes; to invest in roduction (in the form of caital good k); or to make contributions to the government agent. The government uses tax revenues to roduce two different kinds of ublicly-rovided caital, g and s. As in the revious section, consumtion of the final good takes lace after roduction. 16 The objective function of the government agent, which will be resented below, imlies that it is amenable to rivate contributions, which can influence its allocation decision between g and s. It will thus be rational for rivate agents to make contributions out of their initial wealth, contingent on the government s actions: C(g, s). 15 Felli and Merlo (2006) show that, in a context where lobbying is modelled as bargaining between an elected official and organized grous, not all grous will actively lobby in equilibrium. 16 Later in this section we show that our main results are robust to allowing consumtion of the initial good. 11

13 Private roduction occurs by means of atomistic rojects with inelastic and unit labor suly. Each individual has access to only one of two different technologies, which we will denote Technology 1 and Technology 2, described resectively by the roduction functions ψ 1 (k 1,g) and ψ 2 (k 2,s). These functions are assumed to be differentiable, increasing and concave in both arguments, homogeneous of degree one, and to satisfy the Inada conditions. A roortion of the oulation has access to Technology 1, while the remaining 1 has access to Technology 2. For the moment, we assume that access to technology is determined exogenously. We relax that assumtion in the next section. Since each individual lives for a single eriod and derives utility only from his own final consumtion, his objective will be to maximize disosable income, which will be totally consumed. Caital markets are assumed to be non-existent. A key but not necessarily the only distinction between Technologies 1 and 2 is that the former makes use of g, whereas the latter utilizes s. Thegovernmentfinances the roduction of g and s through taxation. It is assumed that the government s taxation technology is such that it can only raise funds through a linear wealth tax at the beginning of the eriod. The government is subject to a balanced budget constraint: τw = g +(1 )s (1) where τ is the exogenously given tax rate on initial wealth. 17 This is what gives rise to a conflict of interests between Grous 1 and 2 over the amount of g and s to be roduced by the government. Note also that (1) imlies that s may be exressed as a function of g, so that with a slight abuse of notation we can rewrite C(g, s) as C(g) The Political Process In keeing with standard ractice in the common agency literature, we assume that the two grous have exogenously solved the collective action roblem and are articulated as ressure grous, each trying to influence the government s choice between the two tyes of exenditure, by means of olitical contributions. Each grou romises to ay some amount to the government, deending on the olicy vector {g, s}. These contributions actually stand for a lethora of real-life ractices, such as money (or time) devoted to camaign contributions, ure bribery, etc., as in Grossman and 17 Note that olitical contributions do not enter the budget constraint. One should think of them as going to a arty fund, or simly being shifted towards rivate consumtion of the government agent. 18 This is made ossible by the assumtion of an exogenous tax rate. If the tax rate were endogenous - say, art of the vector a - then the agent s contribution schedule would be a function of two dimensions: both the level and comosition of ublic sending. Results might then be otentially quite different, and this is an interesting question for further research. 12

14 Helman (1994). We also assume that individuals can only influence government behavior through this channel if they are art of an organized ressure grou: each individual erceives himself as too small to influence olicy decisions on their own (Grossman and Helman, 1994). In line with the revious section, we assume imerfect commitment: there is no way by which either grou can credibly commit to meeting their announced olitical contributions after the government has imlemented its decision. As we have seen, this imlies that contributions must be aid before roduction, hence resources available for roductive investment must be net of such ayments. To summarize the time structure of the model, we can reresent life in this one-eriod economy in the timeline deicted in Figure 1. [FIGURE 1 HERE] Following Grossman and Helman (1994) and DGH (1997), we assume that the government s objective function is a convex combination (with weight x) of the contributions it receives and of a social welfare function. This ositive weight (1 x) on social welfare can either be interreted as allowing for some benevolence on the art of the government agent, or simly as caturing the fact that actual olitical rocesses are not limited to the interaction of ressure grous, and may also include more democratic channels, such as elections, which may induce the government to care about the welfare of the eole. These features may be exressed, drawing uon Grossman and Helman (1994), by modeling a government that maximizes the following objective function: G = x C 1 (g)+(1 )C 2 (g) +(1 x) ψ 1 ((1 τ)w C 1 (g),g)+(1 )ψ 2 ((1 τ)w C 2 (g),s) (2) where C j (g) is the olitical contribution from an individual member of grou j as a function of the comosition of government exenditures. We assume this function to be continuously differentiable. x (0, 1) is the weight attached to contributions vis-à-vis social welfare (considering, for simlicity, a Benthamite welfare function in which every individual has the same weight). The individual s utility which is identical to its ost-roduction disosable income is written in (2) taking into account the fact that, in light of the absence caital markets, initial wealth is fully exhausted by taxes, olitical contributions and rivate investment. Assuming erfect information, the roblem is therefore written exactly as a generalized common agency game where ressure grous are the rincials and the government is the agent and its 13

15 solution may be obtained as such. 3.2 Results As with the standard common agency game discussed in DGH (1997), this game comorts a multilicity of subgame erfect Nash equilibria. As anticiated, we follow Bernheim and Whinston (1986), Grossman and Helman (1994) and DGH in restricting our attention to truthful symmetric Nash equilibria, since truthful contribution schedules are always a best-resonse strategy and are the only coalition-roof equilibria of these games. 19 In this subsection we therefore turn to the efficiency roerties of truthful Nash equilibria within this model Inefficiency of the truthful olitical equilibrium First let us characterize in Proosition 1 the efficient allocation in this economy, which will serve as a benchmark for comarisons with the olitical equilibrium allocation: Proosition 1 For any given {k 1,k 2}, a Pareto-efficient allocation {g,s } must have ψ 1 2(k 1,g )=ψ 2 2(k 2,s ) (3) where the subscrit indicates the artial derivative with resect to the corresonding argument. Proof: See Aendix. Proosition 1 simly states the obvious requirement that the efficient allocation should equate the marginal roduct of ublic caital across the two sectors. It follows directly from the firstorder condition of the roblem faced by a hyothetical social lanner who wished to maximize a Benthamite social welfare function (or, equivalently, total outut) in this economy, by choice of ublic exenditure, subject to the government budget constraint. On the other hand, a truthful olitical equilibrium may be characterized as follows: Proosition 2 Afeasibleallocation{k 0 1,k 0 2,g 0,s 0 } is a truthful (olitical) equilibrium only if Proof: See Aendix. ψ 1 2(k1,g 0 0 ) 2(k2,s 0 0 ) ψ 1 1(k1 0,g0 ) =ψ2 ψ 2 1(k2 0,s0 ) (4) Proosition 2 is obtained by imosing the requirements that the equilibrium allocation be otimal for the government agent, given the rincials contribution schedules; and otimal for each of 19 Since these truthful symmetric Nash equilibria are equilibria of a game that models a olitical rocess - of lobbying to influence government decisions - we sometimes refer to them as "olitical equilibria" in what follows. 14

16 the grous (rincials), given the government s feasibility and rationality constraints. The intuition behind the resulting equation (4) is that a olitical equilibrium equates (across grous) the marginal rates of technical substitution between investments in roduction and in olitical contributions. This is the result of the rincials effectively having to urchase the ublic caital inut, through olitical contributions, which makes the decision on olitical contributions inextricable from the decision on roductive investment. The interesting question now is to comare (3) and (4), in order to determine the efficiency roerties of the truthful olitical equilibrium. It is easy to see that the olitical equilibrium will only be efficient when the grous have the same marginal roductivity of rivate caital at the equilibrium allocation. If the only differences between ψ 1 and ψ 2 were their use of different ublic caital inuts, that equality might be attained. But if the two roduction functions are different also in terms of the marginal roductivity of rivate caital, equality between the marginal rates of technical substitution at any inut ratio will not, in general, imly equality between the marginal roducts. Generally seaking, therefore, the ratio of the marginal roducts of rivate caital ψ1 1 (k0 1,g0 ) ψ 2 1 (k0 2,s0 ) will not be equal to 1, and hence ψ 1 2(k1,g 0 0 ) 6= ψ 2 2(k2,s 0 0 ). As long as the grous differ in their rivate caital rodutivity, the allocation of ublic caital across tyes will fail to equalize their marginal roducts, and the equilibrium will be inefficient. It should also be stressed that what is meant by an efficient allocation here does allow for the role of the government as a layer: resources used as olitical contributions are not being considered a deadweight loss, as is usual in the literature on rent-seeking. 20 The inefficiency that arises in our model is due to the fact that lobbying distorts two key decisions: the comosition of government exenditures and the rivate investment decision of the rincials. If there were erfect commitment, the extraction of the full roductive surlus by the agent would lead him to searate roduction from olitics in equilibrium and what would revail would be erfectly analogous to the outcome of the common agency game without roduction. Without commitment, the two cannot be disentangled, and resource allocation is distorted. Moreover, such inefficiency is not a mere consequence of corrut government behavior: erfect commitment allows for an efficient outcome desite the fact that the government still receives contributions and derives utility from them. 20 To use the terminology of Esteban and Ray (2000), our model features allocational losses. If one were willing to judge all olitical contributions as socially wasteful, our model would also feature the "conflictual losses that are tyical of rent-seeking models. 15

17 This olitical inefficiency does not deend on the weight that the government attaches to olitical contributions vis-à-vis social welfare as long as this weight remains strictly ositive 21 which can be seen from the fact that x does not aear in either (3) or (4). This remark reinforces the observation that the inefficiency stems from the mere existence of lobbying, in the absence of erfect commitment or credit markets. In this sense, it does not deend on how democratic the olitical rocess turns out to be Understanding the inefficiency This very simle model illustrates that generalized common agency games without erfect commitment may indeed be Pareto inefficient a result which was derived more generally in Section Let us now briefly analyze the nature of this inefficiency. Since the technologies are assumed to have constant returns to scale, the marginal roducts will be homogeneous of degree zero, and we can think of the terms in (3) and (4) as functions of the ublic-rivate caital ratios. Suose, without loss of generality, that Grou 2 has a larger marginal roductivity of rivate caital than Grou 1 at the equilibrium allocation, i.e. ψ 1 1(k 0 1,g 0 ) < ψ 2 1(k 0 2,s 0 ). This imlies, from (4) that ψ 1 2(k 0 1,g 0 ) <ψ 2 2(k 0 2,s 0 ). In order to achieve the equality rescribed by the efficient allocation, we must decrease g k 1 relatively to s k 2, so that the RHS will decrease, and the LHS will increase (keeing in mind the assumtion of concavity of the roduction functions). We can thus conclude that, in the olitical equilibrium, Grou 2 will have relatively less ublic caital er unit of rivate caital than what would be efficient. In this sense, the olitical equilibrium is biased towards Grou 1. It allocates too much ublic sending towards ublic good g, which is used by Grou 1 recisely the grou with lower rivate caital roductivity. Since the distortion occurs on the margin, the result does not imly that the least roductive grou receives a greater allocation of ublic inuts in absolute terms. The most roductive grou might well receive more in total, but it will receive less than it would have received in an efficient allocation. This result is driven by the comarative advantages of each grou. Since Grou 2 is assumed to have an absolute advantage in roduction (a larger marginal roductivity of rivate caital), 21 There is a discontinuity at x =0, because as soon as the government laces no value on contributions, those go to zero: all rincials invest their full initial wealth in rivate caital, and the government agent rovides ublic inuts efficiently, so as to maximize social welfare. If there is any scoe for contributions, the rincials will be driven to comete with one another, and in a truthful equilibrium they will offer their comensating variation. 22 Formally, this result stems from the enveloe theorem: when the government considers the imact of a change in the comosition of exenditures, the effect on the agents welfare - the democratic comonent - vanishes because of the first-order condition for agents otimization. This is a consequence of the concet of truthful equilibrium. 23 It is easy to check that introducing erfect commitment in our model actually leads to an efficient allocation, which is a mere alication of the result due to DGH (1997), but can also be verified by an argument identical to the oneusedintheroofofproosition2. 16

18 identical olitical roductivities imly that this grou also has a comarative advantage in roduction, while Grou 1 has a comarative advantage in olitics. Each grou will tend to secialize (artially, rather than comletely, due to decreasing returns to both tyes of caital) in the activity in which it has a comarative advantage. Grou 1 thus secializes in lobbying, shifting the olitical equilibrium towards them. The Inada conditions satisfied by the roduction function ensure that each grou does value access to ublic caital, even when w is very low. This simle model therefore delivers two key results. First, in the absence of commitment, the truthful olitical equilibrium of a common-agency lobbying game in an economy with roduction is generally inefficient. Second, this equilibrium will be biased in favor of the grou that has a comarative disadvantage in roduction. So long as these grous are formed by eole who use different technologies, which require different inut mixes from the government, one should observe those grous that are relatively less efficient in roduction sending a greater share of their scarce initial resources lobbying the government, and thereby successfully shifting the government s (marginal) actions to their advantage. Anecdotal evidence of less roductive grous being more successful in lobbying for ubliclyrovided inuts, relative to comaratively more roductive ones, is not hard to come by. One examle is rovided by the 2005 transortation bill in the US. A lot of ress coverage was devoted to the fact that Alaska obtained over $1 billion for transortation rojects. In comarison, the state of Washington, with a oulation nearly ten times as large, received about $500 million in total. It is not hard to gauge which state would claim the more roductive use of the money: Washington s to transortation roject, relacing an earthquake-damaged viaduct used by 110,000 vehicles a day, received just over $200 million, which was about the same amount earmarked for Alaska to build a bridge (about as long as the Golden Gate Bridge, and taller than the Brooklyn Bridge) linking a town with 8,000 inhabitants to an island inhabited by 50 eole. 24 In addition, a slightly broader interretation of the results is ossible. As discussed in Section 2, within the context of our model one could think of the vector of government actions as comrising not only different ublicly roduced inuts, but as also encomassing a broader set of ublic olicies, such as sector-secific tariffs, taxes or regulations, which affect the rofitability of rivate roduction. Such an interretation would be consistent with the casual observation that traditional (or declining) sectors are often seen to exend greater effort in lobbying the government than do firms in dynamic, 24 This information was obtained from Bloomberg.com, from Se. 2, 2005, in an article intitled Alaska s $223 Mln Bridge to Nowhere Envied in U.S. Northwest. 17