7. Special-interest politics
Motivation Why do some groups in society receive more generous support than other (e.g. farmers)? Homogeneity in interests which allows more efficient organization of lobby group Group members might be less ideologically biased Geographic clustering: Overrepresentation in democratic system (rural areas) We focus on bullet points 1 (lobbying through contributions) and 2 (electoral competition)
A model of local public goods We develop our arguments by means of a simple public good model We assume that governments can target payments (local public goods) to specific interest groups Expenditures are financed from a pool of tax revenues
A model of local public goods Consider a society with J distinct groups of identical individuals Group J = 1,..., J has size (mass) N J, J NJ = N, where N is the size of the population Individuals in group J have the following quasi-linear preferences w J = c J + H(g J ), (90) where c J captures consumption of private goods and g J denotes per capita supply of a locally provided good.
A model of local public goods The increasing and concave function H( ), with H(0) = 0, is defined over a good that only benefits members of that particular group. It must be provided in an equal amount per capita Income in each group is identical, y J = y One unit of income can be converted into any of the J publicly provided goods at no costs Taxation is lump sum to avoid further distortions in the model
Normative benchmark We derive the utilitarian optimum by maximizing the Benthamite welfare function N J N w J (91) J subject to the resource constraint N J (g J + c J ) = Ny (92) J As the marginal social cost of the publicly provided good is unity by assumption, the optimal vector g g J implies that the average marginal benefit has to be unity: H g (g ) 1 = 0. We denote aggregate spending for this benchmark vector as G = Ng.
Normative benchmark It is straightforward to see that group-specific lump-sum taxes could achieve this benchmark allocation so that c J = y τ J = y g J However, this type of tax instrument might not be available in many real world scenarios Rather, governments have to finance group-specific expenditures from a common pool of tax revenues This would generate incentives to influence the government in one s own favor as the benefits to a particular group clearly exceed the costs that have to be borne by that group More precisely, there is a common lump-sum tax for all groups such that the budget constraint reads Nτ = J NJ g J G, where G is aggregate expenditure.
The basic common pool problem Now assume that each group decides freely on the provision of each publicly provided good whereas the tax rate is residually determined Utility of an individual from group J can be written as W J (g) = y τ + H(g J ) = y I g I NI N + H(gJ ). (93) Every group J maximizes (93) taking expenditures by all other groups as given which leads to overexpenditure in each group. Equilibrium spending now satisfies H g (g J,D ) = NJ N. (94)
The basic common pool problem As the right-hand side of (94) is negative each group demands too much of the publicly provided good compared to the social optimum Furthermore, smaller groups "overdemand" to a larger extent Intuition: Each group only internalizes the fraction N J /N of the social marginal cost of higher taxes The root of the problem lies in the institutional framework of decentralized spending and determining the tax rate residually after the spending decisions have been made Practically, full decentralization of financing may not be achievable. And even if it could be enforced, the incentive remains for each group to influence the decision makers to finance a higher share of publicly provided goods for them
Lobbying Policy decisions centralized in the hands of a semibenevolent government Government can be influenced via contributions of organized lobby groups Obviously, there is a free rider problem as all members of the group benefit irrespective of whether they have contributed We circumvent the difficult field of coalition formation and assume that an exogenous fraction L is successful in doing so
Lobbying We study a two-stage policy game: 1 Every lobby non-cooperatively and simultaneously sets a binding C J (g) as to maximize net welfare of its members: N J (W J (g) C J (g)) 2 The government sets g so as to maximize a weighted sum of social welfare and contributions: W (g) = η J N J W J (g) + (1 η) J L N J C J (g), (95) where 0 η 1 is a measure of the government s benevolence. We restrict the analysis to truthful contribution schedules satisfying C J (g) = max[w J (g) b J, 0], where b J is a constant the lobby sets optimally.
Lobbying Political equilibrium: Note that truthful strategies must be jointly Pareto optimal for the government and all lobbies The equilibrium vector g therefore maximizes the sum of the net welfare of the organized lobbies N J (W J (g) C J (g)) J L and the government objective W (g) In particular, g is chosen to maximize η N J W J (g) + N J W J (g). (96) J / L J L
Lobbying Political equilibrium cont d: In other words, the equilibrium coincides with a planning problem where the non-organized groups are underweighted according to the degree of government benevolence. The first-order conditions to the maximization problem (96) define the equilibrium allocation: H g (g J,L ) 1 = (1 λ L )(1 η) 0, J L H g (g J,L ) 1 = λ L (1 η)/η 0, J / L, (97) where 0 λ L = J L NJ N 1 is the share of the population organized in a lobby.
Lobbying Several results are apparent from (97): 1 The lobbying equilibrium can be optimal if the government is perfectly benevolent (η = 1) if no groups seek for influencing activities (λ L = 0) if more surprisingly all groups are organized in lobbies, i.e. λ L = 1 2 Public consumption is generally misallocated, however. The degree of misallocation decreases in η and in λ L. 3 There is no presumption of aggregate overspending as lobby groups get more at the expense of unorganized groups.
Electoral competition Special interest politics might also come in another form than lobbying. Office-seeking politicians might have an incentive to target special groups in society before elections Question: Which groups have the greatest influence on policy outcome? We address this question by applying the probabilistic voting model
Electoral competition Two competing candidates P = A, B maximize their probability of winning the elections by making binding promises to interest groups ex ante, g A and g B They take into account which groups are more likely to be swayed when choosing their announcements Parties differ with respect to "ideology"
Electoral competition Voter i of group J has the following utility function: w ij = κ J W J (g) + (σ ij + δ)d B, (98) where D B takes the value of one if party B wins the election and zero otherwise. Furthermore, σ ij is an individual-specific parameter (σ ij > (<)0 implies a bias in favor of (against) party B), κ J is a group-specific parameter, and δ is a random variable capturing the party preferences of the whole population. Moreover, groups also differ in the strength of their ideological motives: κ J
Electoral competition The swing voter in group J is defined by σ J (g A, g B, δ) κ J [W J (g A ) W J (g B )] δ. (99)
Electoral competition Political equilibrium: The two parties simultaneously and non-cooperatively announce their platforms so as to maximize the probability of winning the election. Party A s vote share can be expressed as π A = J N J [ N φj σ J (g A, g B, δ) + 1 ] 2φ J. (100)
Electoral competition Hence, party A s probability of winning the election results as p A = prob[π A 0.5] = 0.5+ ψ φ [ J N J [ ] ] N φj κ J W J (g A ) W J (g B ), (101) where φ N J N φj is the average density of party bias across groups.
Electoral competition As both parties face the same budget constraint, we get a convergence result: g A = g B By the definition of the swing voter, this implies that σ J (g A, g B, δ) = δ As the expected value of δ is zero, both parties try to get the votes of the ideologically neutral swing voters in each group
Electoral competition Against this background, the first-order conditions can be written as N J N φ J φ κj H g (g J ) NJ N I φ I N N φ κi = 0. (102) I Intuitively, parties compete for the same voters as mentioned above by buying electoral support. As a result, the distribution of voters preferences alone decides the unique equilibrium election outcome.
Electoral competition Rewriting (102) allows us to characterize equilibrium spending g E as H g (g J,E ) 1 = I NI N φi κ I φ J κ J φ J κ J. (103) Again, the right-hand side determines deviations from the utilitarian optimum.
Electoral competition We derive a number of insights: 1 Electoral competition installs the utilitarian optimum g E = g if the ideological bias is identical across groups such that φ J and κ J coincide for all J 2 The term φ J κ J summarizes the clout of a specific group J. If this term is higher than the weighted average of all groups, the right-hand side of (103) becomes negative implying that g J,E > g 3 Group size plays no role in determining political power
Lobbying and elections Motivation: Lobbying without elections can rather be interpreted as bribes to politicians In this section, we combine the lobbying model with the elections model to motivate official campaign contributions What is the role of campaign contributions in representative democracies?
Lobbying and elections We use a simplified version of the probabilistic voting model: All groups are of equal size normalized to unity such that N J N = 1 J We place the same weight on economic outcome and ideology, also normalized to unity (i.e. κ J = 1)
Lobbying and elections Voters in group J possess preferences of the following kind w ij = W J (g) + (σ ij + δ)d B, (104) but now δ is driven by δ = δ + h(c B C A ). Thus, party B s average popularity has two components now: δ and contributions C P
Lobbying and elections Following the same logic as in the basic probabilistic voting model, we can determine the swing voter as σ J = W J (g A ) W J (g B ) + h(c A C B ) δ. (105) Campaign spending now influences the identity of the swing voter! The probability that party A wins the election is given by [ [ 1 p A = 0.5+ψ J J φ J φ ( W J (g A ) W J (g B )) ] ] + h(c A C B ). (106)
Lobbying and elections A subset L is organized in lobbies so that λ L describes the share of the "organized" population. Lobby J maximizes p A W J (g A ) + (1 p A )W J (g B ) (C J ) 2 /2, (107) where C J = CB J + CJ A is the per member campaign contribution by lobby J to both parties. As each group owns the share 1/J of the population, total contributions received by party P are C P = 1 J CP J. (108) J L
Lobbying and elections The timing of the game is as follows: 1 Parties simultaneously announce their policy platforms 2 All lobbies simultaneously set their campaign contributions 3 Elections are held. NOTE: In contrast to the previous section, stages (1) and (2) are reversed in this model.
Lobbying and elections Equilibrium: The problem is solved by backward induction. Since the electoral outcome at stage (3) has already been discussed, we can directly jump to the lobby maximization problem for given policy platforms. Maximizing (107) with respect to CA J and CJ B, subject to (106), yields C J A = Max [ 0, hψ C J B = Min ] J (W J (g A ) W J (g B )) [ 0, hψ J (W J (g A ) W J (g B )) ]. Each lobby only campaigns in favor of one party at most (109)
Lobbying and elections Summing this expression across all lobbies in L, we get C A C B = hψ ( ) J 2 W J (g A ) W J (g B ). (110) J L This equation states that campaign contributions go to the party that is more successful in pleasing the lobbies.
Lobbying and elections We next turn to the party optimization problem. Here maximizing the vote share and the probability of winning yield the same result. By (106), (107) and (110), party A s objective function can then be written as [ max ψ φ J J φ [W J (g A ) W J (g B )] + γ ] [W J (g A ) W J (g B )], J J L (111) where γ = ψh 2 /J > 0 is an extra weight on the lobbies utility related to how effectively campaign spending influences the voters. Since party B solves the same problem, we observe convergence in announcements such that g A = g B, which then implies zero campaign spending.
Lobbying and elections However, this does not mean that the presence of lobbies is irrelevant for the equilibrium outcome. Taking the first-order conditions of problem (111) and rearranging allows us to determine the allocation as follows: H g (g J ) 1 = φ [1 φ J φj + γφ H g (g J ) 1 = φ φ J [ 1 φj φ + γλ L ] φ γ(1 λ L) J L ] J / L. (112)
Lobbying and elections Conclusions: g J is overprovided if φ J is larger than φ If group J is organized as a lobby, there is also overprovision, and the lobbying effect is stronger the higher is γ Also, a smaller fraction among the groups (λ L ) increases the amount of overprovision for the organized groups, but decreases the underprovision for the unorganized groups Bottomline: The lobbying and probabilistic voting models complement each other.
Lobbying à la Grossman and Helpman Idea: Politicians have incomplete information and can thus be influenced/ consulted by special interest groups Assumptions: Lobbying is potentially informative, i.e. it allows politicians to make better policy decisions Policy maker cannot easily verify the lobbyists claims Objectives of politicians and lobbies are not perfectly matched
Lobbying à la Grossman and Helpman Two questions: 1 What statements will be persuasive? 2 What can a lobby do to enhance credibility?
Costless lobbying One lobby We consider costless lobbying first There is only one lobby that has information relevant to the policymaker s decision Welfare of policymaker is given by G(p, θ) = (p θ) 2, where p is a policy variable (i.e. desire to be reelected, partisan preferences) and θ captures the true state of the world (which only the lobby knows). We note that the value of this function is maximized when p = θ.
Costless lobbying One lobby The interest group s (or similarly the lobbyist s) preferences are given by U(p, θ) = (p (θ + δ)) 2 The lobby has an ideal policy of p = θ + δ in state of the world θ Divergence among politicians and individuals is driven by δ (bias in the group s preferences)
Costless lobbying One lobby For simplicity, we assume only two states of the world, θ L and θ H Policymaker sets p = θ when the lobbying group reveals the true state of the world She sets p = E θ when she remains uncertain about the true state (where θ should be interpreted as a random variable) Policymaker takes the lobbyist s claims at face value and then investigates the incentives of the lobbyist
Costless lobbying One lobby U L H L H θ L θ L +δ θ H θ H +δ p Figure 30: One lobby Two states of the world
Costless lobbying One lobby The left curve LL represents welfare as a function of the chosen policy variable p if the state of the world is θ L Similarly, HH describes welfare if θ H is realized A trusting policymaker will implement p = θ L if the lobby reports θ L as the true state (similarly for θ H ) this is not the welfare maximizing policy for the lobby as long as δ 0! Will the lobbyist reveal the correct information?
Costless lobbying One lobby Results: If the true state is θ H then the lobbyist has no incentive to misrepresent the facts. This is because by claiming that the true state is θ L the utility will always be lower If the true state is θ L then the lobbyist has no incentive to misrepresent the facts if (θ L + δ) θ L θ H (θ L + δ), which is the same as if δ θ H θ L 2 Thus, when this condition is satisfied there exists an equilibrium with informative lobbying
Costless lobbying One lobby If this condition is not satisfied that is when δ > θ H θ L 2 ) then the lobbyist s report lacks credibility The politician knows that the lobbyist has an incentive to announce the state θ H no matter what the true state happened to be The politician ignores the report prepared by the lobby and sets the policy p = θ H+θ L 2, which matches her prior about the mean value of θ
Costless lobbying One lobby When the inequality condition is fulfilled: There is also another outcome known as a "babbling equilibrium" In this scenario, the policymaker generally distrusts the interest group and sets p = θ H+θ L 2, independently of what the interest group says Interest group has no incentive to lobby
Costly lobbying One lobby Preferences of the interest group are now depicted by U = (p (θ + δ)) 2 l, where l is new and represents the cost of lobbying If the group does note choose to lobby, then l = 0, otherwise l = l f > 0 The objective function of the policymaker remains the same G(p, θ) = (p θ) 2.
Costly lobbying One lobby Timing of the lobbying game is as follows: 1 The interest group learns the true value of θ 2 It decides whether to bear the cost l f 3 The policymaker updates her beliefs based on the lobby s report 4 The policymaker chooses the policy level to maximize her expected utility
Costly lobbying One lobby When l f = 0, the problem is identical to the previous section For θ H, there is no risk of false reporting But when the state is θ L the group may be tempted to misrepresent its case If there are costs for lobbying, the policymaker now takes a group s willingness to lobby to imply that θ = θ H and a failure to lobby to means that θ = θ L Paradoxically, the group might fare better with costly lobbying as the investment (to lobby) can serve as a means to gain credibility
Costly lobbying One lobby Let s solve the equilibrium: The group is willing to pay the lobbying cost in state θ H if and only if (θ H (θ H + δ)) 2 l f (θ L (θ H + δ)) 2, or δ 2 l f (θ L (θ H + δ)) 2 l f (θ H θ L )(2δ + θ H θ L ) k 1.
Costly lobbying One lobby The group must also prefer to refrain from lobbying when the state is θ L (which we initially assumed). The condition for this is: (θ L (θ L + δ)) 2 (θ H (θ L + δ)) 2 l f, or δ 2 (θ H (θ L + δ)) 2 l f, or l f (θ H θ L )(2δ θ H + θ L ) k 2. Since k 1 > k 2 there is a range of lobbying costs for which both conditions are satisfied
Costly lobbying One lobby Welfare implications I: Policymaker Recall that if δ > θ H θ L 2, then the policymaker sets p = θ H+θ L 2, which is not her ideal point When l f lies between k 1 and k 2, the costly lobbying allows the policymaker to infer the true value of θ, in which case she achieves her ideal policy in both states of the world. This is better than in the no-cost case when the politician sometimes gets distorted information
Costly lobbying One lobby Welfare implications II: Interest group If δ > θ H θ L 2, then their utility in the no-cost case is U l=0 = ( θ H+θ L 2 (θ H + δ)) 2 + ( θ H+θ L 2 (θ L + δ)) 2. 2 In the case of positive costs, she achieves δ 2 l f in state θ H and δ 2 in state θ L so U l>0 = δ 2 l f 2 Positive lobbying costs may enhance utility for interest groups: U l>0 > U l=0 if l f < (θ H θ L ) 2 2
Costly lobbying One lobby Intuition: Policymaker knows that the costs reduce the incentives to falsely report the low state of the world θ L This implies that she picks p = θ H+θ L 2 less frequently As p = θ H+θ L 2 is a bad policy from the interest group s point of view it may be better off when there are costs of lobbying.
References Grossman, G.M. and E. Helpman (2001), Special Interest Politics, Cambridge, Mass: MIT Press. Chapter 4.1 and 5.1