Should we tax or cap political contributions? A lobbying model with policyfavors and access☆
Christopher Cotton ⁎Department of Economics, University of Miami, Coral Gables, FL 33146, United States
☆ I greatly appreciate comments and advice from Talia BJayant Ganguli, Bard Harstad, Ben Ho, Justin Johnson, AntoPrice, Josh Teitelbaum, two anonymous referees, and escomments from participants at various seminars and con⁎ Tel.: +1 305 284 4064.
1 Interest groups and individuals may also provide contribcompete for and win (re)election (e.g., Coate, 2004b). Thergroups provide political contributions to influence electiocontributions in an effort to influence the votes of sittingSnyder, 1992; Stratmann, 2005). Howmoney affects the votdebate, as the empirical evidence supports both concontributions-for-access stories. In both cases, higher cofavorable votes; and there is little data available to distingumaking the choice between selling access and sellingdetermines when the politician prefers to engage in either a
This paper develops amodel of political contributions inwhich a politician can either sell policy favors, or sell access.Access allows interest groups to share hard informationwith the politician in support of their preferred policy. Hereselling accessmaximizes policy utility, while selling policy favorsmaximizes total contributions. Imposing a bindingcontribution limit makes it more likely that the politician sells access, which can improve expected constituentwelfare. However, a contribution limit distorts the signals associatedwith the contributions, which tends to result inworse policy. Alternatively, a tax on political contributions can ensure that the politician sells access withoutdistorting his information. Therefore, from the viewpoint of a representative constituent, a tax on contributions isstrictly preferred to a contribution limit or no reform. The politician, however, may prefer regulation in the form of acontribution limit, evenwhen a tax is better for the constituent.
Howmightpolitical contributions influence thedecisionsofpoliticians?Theeconomicsandpoliticalscience literaturehighlighttwomeansof influence.First,moneymaybecontributed inaquidproquoexchange forapolicy favoror favorable vote on an issue. Second, money may be contributed to helpsecure access to a politician, where access allows one to influence policythrough the provision of evidence in favor of one policy, or against another.1
ar, Kaushik Basu, Dan Benjamin,nio Merlo, Ted O'Donoghue, Joepecially Steve Coate, as well asferences. Mistakes are my own.
utions to help certain politicianse is evidence that some interestns, while other groups providelegislators (e.g., Herndon, 1982;es of sitting legislators is open totribution-for-policy favors andntributions are correlated withish between the two stories. Byfavors endogenous, this paperctivity.
ll rights reserved.
The theoretical literature includes both models in which politicianssell favors (e.g., Grossman and Helpman, 1994; Baye et al., 1993;Tullock, 1980) and models in which politicians sell access (e.g.,Austen-Smith, 1998). This paper allows for both of these possibilities,developing a game theoretic model in which a politician chooseswhether to sell favors or to sell access. It then uses the framework toassess two different campaign finance reforms, including taxingcontributions and imposing contribution limits.
This is the first paper inwhich a politician chooses between sellingpolicy favors and selling access.2 If the politician sells favors, he doesso using an all-pay auction, rent-seeking mechanism as is common inthe lobbying literature (e.g., Gavious et al., 2002; Che and Gale, 1998;Baye et al., 1993). Interest groups simultaneously submit contributionsto the politician, then the politician votes in favor of the highestcontributor. Alternatively, the politician may sell access through asimilar process in which groups submit contributions and the highcontributor wins access. An interest group with access can presenthard evidence to the politician in support of its preferred policy. A
2 Bennedsen and Feldmann (2006) and Dahm and Porteiro (2008a,b) allow interestgroups to influence policy through both the disclosure of hard evidence and the quidpro quo exchange of contributions for policy favors. In these previous models, however,the politician does not control which groups can disclose information, and he is unableto provide access based on contributions.
5 Cotton (2008) incorporates the evidentiary structure developed in this paper intoa model of price setting similar to Austen-Smith (1998). Most other papers thatincorporate “access” either do not consider verifiable or hard information, or they donot give the politician control over which groups can disclose evidence. For example,Austen-Smith (1995), Ball (1995), and Lohmann (1995) develop models in whichinterest groups receive private, unverifiable signals about the impact of a certain policy.
6 How politicians actually do award access is open to debate. Although there issubstantial data on political contributions in the U.S., there is little data available howpoliticians spend their time and with whom they meet. See Stratmann (2005) for anoverview of the empirical literature concerning money in politics.
7 Such an effect is similar to the impact of contribution limits in the policy favorgames by Prat (2002a,b) and Coate (2004a), where limits decrease the monetaryincentives to provide policy favors and increase the likelihood that a politician choosesthe policies preferred by his constituents rather than the policies preferred by aninterest group. In these other papers, however, the identity of the ideal policy is knownex ante; there is no role for access, and contributions do not help the political learnabout the best policy.
8 In Wittman (2002) and Coate (2004b), limits decrease the amount of advertising,
832 C. Cotton / Journal of Public Economics 93 (2009) 831–842
politician who learns all evidence can identify and implement hisfully-informed policy, which maximizes constituent welfare.
The contributions-for-access model developed here is a tractableframework that is relatively straightforward to incorporate into asimilarmodel of policy favors. Interest groups provide contributions incompetition for access, just as they provide contributions in competi-tion for favors in more traditional lobbying games, including the oneused to model the allocation of policy favors in this paper.3 In theequilibrium of the competition for access game, an interest groupwithstronger evidence in support of its preferred policy is willing tocontribute more in an effort to win access than is an otherwise similargroup with weaker evidence. When the politician sells access, helearns about interest group evidence through the revelations ofgroups with access, and through the signaling power of interest groupcontributions. In equilibrium, selling access allows the politician tobecome fully informed about the evidence of both interest groupseven when he only gives access to one of the groups.
When the politician sells access, contributions allow him tobecome more informed about the issue, and to choose better policythan he otherwise could. In addition to caring about policy, however,the politician also cares about collecting political contributions.Although selling access results in the politician collecting somecontributions, he expects higher total contributions when he sellspolicy favors instead of access.4 Therefore, his choice of whether to sellfavors or sell access depends on the issue. For important-enoughissues—those for which the politician has the most to gain fromchoosing the best policy—the politician sells access. For less-importantissues he sells favors, sacrificing policy utility and constituent welfarein order to collect larger contributions.
A contribution limit (i.e., bid cap) can reduce expected totalcontributions both when the politician sells policy and when he sellsaccess. The limit tends to have a larger impact on contributions in thepolicy favor game, making selling policy favors relatively lessattractive compared with selling access. A contribution limit canresult in the politician selling policy favors for a smaller range of issue.The downside of a limit, however, is that it distorts the signalingpower of the contributions when the politician does sell access. Thismeans that, conditional on the politician selling access, he tends to beless informed and chooses worse policy when there is a contributionlimit compared to when there is no limit. Although I show that thereexists a binding contribution limit that improves expected constituentwelfare, this is not necessarily true of all limits. It is never optimal toban contributions.
Alternatively, society may tax political contributions. Similar to alimit, a tax reduces the politician's expected revenue both when hesells policy andwhen he sells access. The impact of the tax is greater inthe policy favor game, and it therefore makes selling policy relativelyless attractive compared with selling access. A tax decreases the rangeof issues for which the politician sells policy favors. Unlike a limit,however, a tax does not distort the interest groups' willingness tocontribute in competition for either policy favors or access. Therefore,the tax does not distort the signaling power of the contributions in theaccess game.When the politician sells access, he is able to identify andimplement the fully-informed policy even under a high tax rate.
Unlike a limit, a tax unambiguously improves expected constituentwelfare. Furthermore, one can always set a tax such that expectedconstituent welfare is higher than under any limit or no regulation.Here, taxes are strictly better than limits at regulating contributions.Although a tax is better for constituent welfare than a limit, however,
3 See for example the models by Che and Gale (1998), Gavious et al. (2002), Holt(1979), Holt and Sherman (1982), Baye et al. (1993, 1996), Anderson et al. (1998).
4 When the politician sells access, he maximizes his expected policy utility, but nottotal contributions. When the politician sells policy favors, he maximizes expectedtotal contributions, but not policy utility and constituent welfare.
the politicianmay prefer for contributions to be regulated by a limit, asa limit may have less of an impact on total contributions.
The primary contributions of this paper are twofold. First, itdevelops the first model of political contributions inwhich a politicianchooses whether to sell favors or sell access. By giving the politicianthis choice, the model should provide a better understanding of theinteraction between interest groups and politicians, and the influencethat political contributions may have on the decision making process.In this paper, the means by which the politician may sell favors isrelatively standard for the literature, building on the work of Hillmanand Riley (1989), Baye et al. (1996), Che and Gale (1998), Gaviouset al. (2002) and others. The means by which the politician may sellaccess, however, is relatively novel and represents its own contribu-tion to the lobbying literature. To my knowledge the competition foraccess model developed here and Austen-Smith (1998) represent theonly two theoretical frameworks in which buying access allows anagent (or interest group) to share verifiable evidence with a decisionmaker.5 The primary difference between the access model in thepresent paper and Austen-Smith (1998) is the mechanism throughwhich the politician allocates access: In this paper the politicianawards access to the highest contributor; in Austen-Smith (1998) thepolitician announces prices for access and any interest group that paysthe announced price gains access.6 For the purpose of this paper, thecompetition for access framework offers the distinct advantage of itbeing straightforward to incorporate with a standard model of policyfavors. Section 8 discusses why the main results of the paper shouldcontinue to hold if the politician sells access through a pricing gamerather than an auction.
The second primary contribution of this paper is the considerationof contribution limits and taxes. The paper shows that both limits andtaxes can cause the politician to switch from selling favors to sellingaccess.7 A tax, however, is strictly preferred to a limit since it can causethe politician to sell access without distorting the signals associatedwith the contributions and the politician's information.8 This result isin contrast to Drazen et al. (2007) which also allows for both acontribution limit and tax. Drazen et al. (2007) considers interestgroup formation in a variation of the money-for-policy-favor game,and shows that a contribution tax can offset the negative impact of thecontribution limit; suggesting that a limit and tax should be used incombination.9 In the current paper, in which the politician may alsosell access and there is no concern about interest group formation, atax is strictly preferable to a contribution limit, and there is no benefitto using them in combination. Other papers focus on contribution
which results in a less-informed electorate. In a game with access, a limit may alsoresult in a less-informed politician.
9 In Drazen et al. (2007) politicians and lobbyists bargain over a policy choice. There,a binding contribution limit can increase the bargaining power of lobbyists, increasingthe expected returns from lobbying. When this is the case, a limit can result in theformation of more lobbying groups, and therefore worse policy from the perspective ofthe politician's constituents. A contribution tax can offset the negative impact of thecontribution limit.
833C. Cotton / Journal of Public Economics 93 (2009) 831–842
limits alone.10 Austen-Smith (1998) shows how a limit may result in amore informed politician in an access game where interest groupsdiffer in terms of their evidence reliability. In such a model, a limit cancause the politician to provide access to more-informed interestgroups rather than groups with higher willingness to pay for access.This is not the case in the present paper, as there is no reliability issueswith the evidentiary structure. Instead, the present paper focuses ondifferences in issue importance. Incorporating reliability issues willlikely weaken, but not eliminate this paper's results.
The model is described in Section 2 and solved in Section 3.Sections 4 and 5 consider the impact on equilibrium behavior andpolicy outcomes of a contribution limit and a tax, respectively. Thewelfare effect of a limit and a tax are compared in Section 6. Section 7incorporates interest group asymmetries into the model. Allowing forwealth or valuation differences does not change the results. Section 8discusses alternative assumptions about the underlying mechanismsfor awarding policy and access. It also discusses the cases of noisyinterest group evidence, and costly evidence production. Section 9concludes the paper.
2. Model
A politician must choose a policy from a continuous, single-dimensional policy space [−1,1]. Denote his choice of policy by p.There are two interest groups associated with the issue; group Lstrictly prefers lower (leftward) p and group R prefers higher(rightward) p all else equal. The politician experiences policy utilityW(p) from his policy choice, where
W pð Þ = αRp + αL −pð Þ− p2
2
" #γ:
The analysis assumes that the politician's policy utility is equivalentto thewelfare function forhis representative constituent (anonplayer inthe game). The politician is ex ante uncertain about the valuesαR andαL
which represent the benefits and costs of marginal changes in policy.The value−p2
2 incorporates intoW(p) a tendency for the representativeconstituent to prefer moderate policy. The value γN0 represents issueimportance, and is the realization of a random variable continuouslydistributed on R++ according to distribution G and density g.11
Let p̂ denote the policy the politician prefers when he is fullyinformed. Therefore, p ̂≡argmaxp W(p)=αR–αL. If the politicianchooses p=p ̂, he maximizes both his own policy utility and thewelfare of the representative constituent.12
Each interest group ja {L,R} observes its own αj, but not that of theother group. Each group's αj is the independent realization of a
10 For example, Dahm and Porteiro (2008b) show how contribution limits may deterinformational lobbying in a game in which interest groups have free access to apolitician. In Reizman and Wilson (1997), a politician may choose to sell additionalpolicy favors in order to make up for a decrease in contributions that result from alimit. Both Che and Gale (1998) and Gavious et al. (2002) consider the effects ofcontribution limits on total revenue.11 Campaign finance reforms may be implemented before the realization of γ. Bymodeling γ as the realization of a continuously distributed random variable, theanalysis is able to capture the reality that campaign finance reforms apply across many,different issues.12 The specified equation forW simplifies the analysis. AssumingW(p)=−(αR−αL−p)2
would not change the results. Alternative functionsmay also be used. For example, onemayincorporate bias into the policy utility function by setting W pð Þ = αRp + αL −pð Þ−½− jp−Bias jð Þ2
2 �γ, where p̂ then equals αR−αL+Bias. Such Bias represents the political leaningsof the politician or his constituent. In another example, the politicianmay be responsible forchoosing a trade tariff p a (0,1), for which W(p)=[αRln p+αLln(1−p)]γ, and where p̂equals αR
αR + αL. For the full-information result to hold, without other modifications to the
model, W must be such that ∂p̂/∂αR=-∂p̂/∂αL. However, as long as ∂p̂/∂αRN0 and ∂p̂/∂αLb0, the politician can still become fully informed by selling access, so long as he grantsaccess to the group that signals the highest α. See for example the discussion concerninginterest group asymmetries in Section 7.
random variable uniformly distributed on [0.1].13 The distribution of αis common knowledge. Each interest group has private, verifiableevidence about its own αj. Formally, the evidentiary structure meetsthe requirements of Lipman and Seppi (1995)'s full reports conditionand Bull and Watson (2007)'s evidentiary normality condition, whichrequire that higher-type agents (i.e., agents with higher αj) can alwaysprovide evidence not available to lower-type agents. An agent canunder represent but not exaggerate its evidence. If group j a {L,R} hasaccess to the politician, it can costlessly present any evidence amountej a [0,αj], or he can refuse to present any evidence setting ej=Ø.14
The politician controls which interest groups receive access. Due totime constraints, I assume the politician can only grant access to one ofthe groups; however, this assumption may be relaxed.15 If he grants agroup access, that group is able to present evidence ej.
In this framework, the politician is able to sell policy favors andaccess to interest groups. Let cj≥0 denote the political contributionthat group j pays the politician.
Payoffs—The politician prefers to set policy as close to the fully-informed policy as possible. He also benefits from collecting politicalcontributions. His payoff is given
UP = W pð Þ + cL + cR:
Interest groups prefer more extreme policies, and they findproviding political contributions costly. Given implemented policy p,groups L and R earn respective payoff
UL = − pv2− cL; and
UR = pv2− cR:
The value v2 N 0 represents how much interest groups care about
policy relative to money. For now, interest groups differ in terms oftheir evidence, and not in terms of their valuation. They share acommon v, which is common knowledge. Section 7 allows for groupasymmetries.
Game Order—The politician can sell access or a policy favor. If hesells access, the group that receives access can present evidence to thepolitician. If he sells a policy favor, the group that receives the favorgets to choose the policy that is implemented.
The game takes place as follows:
1. The politician chooses whether to sell access or a policy favor at thebeginning of the game. Denote this choice by α, where α=1 if thepolitician sells access and α=0 if he sells a policy favor.
2. Whether the politician sells access or a policy favor, interest groupscompete for the “prize” in the same way. Both interest groupssimultaneously contribute to the politician, and the group thatprovides the highest contribution wins the prize.
3. If the politician sells a policy favor, then the winner of the prizecompetition chooses a policy. If the politician sells access, then thewinner of the prize competition chooses evidence to reveal to thepolitician; then, after updating his beliefs about the evidencequality of both interest groups, the politician chooses a policy.
13 Assuming that draws of α are uniformly distributed and uncorrelated simplifiesthe analysis, but is not necessary. The αs may be (negatively) correlated and drawnfrom less-straightforward distributions.14 One may think of an interest group’s evidence as a collection of verifiabledocuments. For a detailed discussion, see Bull and Watson (2004, 2007).15 The time constraint is reasonable if one thinks of the game being repeated acrossmany issues and many different interest groups. Alternatively, the politician could findgranting access costly, in which case he prefers to give access to one group rather thanboth groups. So long as the cost of access is small enough, the results of the analysiscontinue to hold.
16 If instead the politician’s beliefs are such that EμαjN0 when ej=Ø, then all groupswith αj≤Eμαj (and no groups with αjNEμαj) have an incentive to announce ej=Ø. Thepolitician recognizes this and his beliefs therefore must account for the types of agentsthat do announce ej=Ø, which requires him to lower Eμαj. Again however, only groupswith actual qualifications lower than the updated expected qualifications have anincentive to refuse to reveal their evidence. The reasoning repeats, and the requiredEμ(αj|ej=Ø)→0; only then do no groups have an incentive to deviate. See Milgrom andRoberts (1986) for a formal proof.17 To show this, solve for the equilibrium under the assumptions that C is strictlydecreasing in α, or that C is not strictly monotonic. Either alternative assumptionresults in a contradiction when solving for the equilibrium contribution function.
834 C. Cotton / Journal of Public Economics 93 (2009) 831–842
Let w a {L,R} denote the identity of the prize winner.Player Strategies and Equilibrium Concept—In both the access and
policy-favor subgames, interest groups must choose how much tocontribute to the politician. In the access subgame, groups must alsochoose the evidence ej a [0,αj] or Ø to reveal. A complete descriptionof an interest group's strategy must describe its choice of cj and ej foreach possible (γ,αj,a) triple.
The politicianmust choosewhether to sell access or policy, and if hesells access he must also choose a policy at the end of the game. Acomplete description of his strategy must give his choice of α for eachpossibleγ, aswell as his choice of p for each possible (γ,cL,cR,ew) vector.
Let μ represent the politician's beliefs about the state of the worldat the time he chooses policy in the access subgame. Eμ denotesexpectations given beliefs μ, and E (without the subscript) denotes exante expectations before the start of the game.
The analysis solves for the symmetric Perfect Bayesian Equilibriumof the game, which I label the contribution equilibrium. A completedescription of the equilibrium must include the strategy profiles forthe interest groups and the politician, as well as the politician's beliefsabout the state of the world at the time he chooses policy in the accesssubgame. The politician's beliefs must be consistent with Bayes' Ruleon the ex ante distribution of α given the strategies of the interestgroups. Each player's strategymust be a best response to the strategiesof the other players, given the player's beliefs.
3. Contribution equilibrium
The paper first determines interest group behavior and policychoice in the access and policy-favor subgames, then it considers thepolitician's choice of whether to sell access or sell policy.
3.1. Selling policy favors
When the politician chooses to sell a policy favor, the interestgroups compete in a traditional all-pay auction, rent-seeking game(e.g., Hillman and Riley, 1989; Baye et al., 1996). The interest groupthat wins the contest will choose to implement the most extreme p inits preferred direction. Group L prefers to implement policy pL≡−1,and group R prefers policy pR≡1. The winning group earns policypayoff of v
2, and the other group receives policy payoff equal to − v2.
Therefore, holding contributions constant, an interest group valueswinning the contest at v.
If group w wins, it sets p=pw. The winning group earns payoffUw = v
2 − cw . The non-winning group (denoted −w) earns payoffU−w = − v
2 − c−w . There is no pure strategy equilibrium in theall-pay auction game with complete information about playervaluations. The mixed strategy Nash equilibrium of the policy favorsubgame involves each interest group contributing c according todistribution H, where H cð Þ = c
v. Since both interest groups share acommon valuation for the prize, no one is willing to bid (on average)more than the other group in an effort to secure the prize. Inequilibrium, the politician is equally likely to award the policy favor tointerest group R as he is to award the favor to interest group L.
Expected total contributions from selling the policy favor equal v.The politician is able to extract all of the expected rent from theinterest groups. The resulting policy choice, however, is at the extremeend of the policy space. The politician's expected policy utility fromselling a favor for issue γ equals E W ja = 0ð Þ = − γ
2. Therefore,E UP ja = 0ð Þ = − γ
2 + v.
3.2. Selling access
Policy Choice—When the politician sells access, he retains the rightto choose policy. Since the policy decision is made at the end of thegame, it cannot affect contributions. Therefore, the politician choosesp to maximize EμW(p). He sets p equal to his expectation regarding p̂
or p=EμαR−EμαL. Only when the politician is fully informed about αL
and αR is he able to identify and implement the fully-informed policyp̂.
Evidence Revelation—Any interest group with access reveals all ofits evidence, ej=αj. This is a standard result in the hard evidenceliterature (e.g., Milgrom and Roberts, 1986; Bull and Watson, 2004). Ifa group with access revealed ejbαj, then the group could costlesslyrepresent higher α by revealing ej=αj instead. Only when each typeof agent reveals ej=αj do no groups have an incentive to deviate.Similarly, no agent with αjN0 will ever refuse to reveal evidence. Ifej=Ø, the principal updates his beliefs putting probability 1 onαj=0.16
In equilibrium, any group j with access reveals ej=αj. Therefore,when group j reveals evidence ei to the politician, the politician'sbeliefs μ must put probability 1 on αj=ej and probability 0 on anystate in which αj≠ej. This means that if the politician gives access togroup j, then he fully learns its type and Eμαj=αj.
Interest Group Contributions—In equilibrium, all interest groupscontribute according to the contribution function C. It is straightfor-ward to show that C is strictly increasing in αj.17 Since C is strictlyincreasing, it is invertible, where α⁎(c)=C−1(α), and there exists aone-to-one mapping between a group's contribution and its evidencequality. It immediately follows that a rational agent can determine aninterest group's α if he observes its contribution.
To solve for the equilibrium contribution function, the analysissolves for the contribution decision of interest group j assuming thatinterest group −j contributes according to the equilibrium function.Because group −j contributes according to C, the politician cancorrectly infer α−j from c−j. Interest group j chooses contribution cj tomaximize its expected utility
v2
Z α4 cjð Þ0
αj − α− j
h idα− j +
v2
Z 1
α4 cjð Þα4 cj� �
− α− j
h idα− j − cj: ð1Þ
Interest group j wins access so long as c−jbcj, which happenswhenever C(α−j)bcj or α−jbα⁎(cj). The first integral in the expressionrepresents the group's payoff when it wins access, in which case thegroup reveals its evidence and αj to the politician and the politicianchooses p=αj−α−j. Even though the politician does not give group−jaccess, his expectations regarding α−j are correct because group −jcontributes according to the strictly increasing equilibrium contribu-tion function. The second integral in the expression represents thegroup's payoff when it does not win access, and the politician relies onits contributionwhen updating his expectations regarding αj. Inwhichcase, the politician chooses p=α⁎(c)−α−j.
The first order conditions of the interest group's expected utilitymaximization problem are
v2
Aα4 cj� �
Acjαj − α4 cj
� �h i+
v2
Z 1
α4 cjð ÞAα4 cj
� �Acj
dα− j − 1 = 0:
Fig. 1. Example contribution function.
835C. Cotton / Journal of Public Economics 93 (2009) 831–842
In equilibrium, α⁎(cj)=αj, and strict monotonicity implies that[∂α⁎(cj)/∂cj]−1=C ′ (αj). Therefore, the first order conditions simplifyto
C′ αj
� �= 1− αj
� � v2: ð2Þ
It is straightforward to show that the initial requirement that C′(αj)N0 holds. Integrating with respect to αj gives the equilibriumcontribution function18
C αj
� �= 1−
αj
2
� �αj
v2: ð3Þ
Information Revelation and the Role of Access—Because thecontribution function is strictly increasing in αj, there exists a one-to-one mapping between each group's contribution and its evidencequality. A group with the highest-possible α contributes C 1ð Þ = v
4, anda group with the lowest-possible α contributes C(0)=0. For all valuesα a [0, 1], a higher α means a larger contribution. The politicianrecognizes this and in equilibrium he correctly infers the evidencequality of both interest groups, even though he only gives access toone of them. In equilibrium, Eμαj=αj for both interest groups, and thepolitician chooses p= p̂.
If interest group j contributes more than C(αj), then the politicianwill overestimate αj when the group does not receive access. In orderfor no interest group to have an incentive to deviate from theequilibrium contribution function, the expected policy benefit frommarginally increasing one's contribution in order to signal higherevidence must be completely offset by the monetary costs ofsubmitting a higher contribution. This is the condition given byEq. (2). Fig. 1 shows an example contribution function. At low α, aninterest group is relatively unlikely towin access; therefore the benefitof marginally increasing its contribution is relatively large. Over suchvalues of α the slope of the contribution function must be relativelysteep to offset the incentive to increase one's contribution. Alterna-tively, an interest group with a high α is relatively likely to submit thehigh contribution and win access. Therefore, the politician is likely tolearn its true α even if it over contributes in order to signal higherevidence. Over such α the benefit of signaling a higher α is relativelysmall; therefore, the slope of the contribution function does not needto be as steep to offset these benefits.
In equilibrium, the politician becomes fully informed about theevidence quality of both groups by observing their contributions alone.This does not imply that the politician becomes fully informed evenwhen he provides no access. If the politician does not provide access toeither group, then the contributions become uninformative.19
Politician Payoffs—In equilibrium, the politician sets p= p̂, max-imizing his policy payoff and constituent welfare at W p̂
� �=
αR −αLð Þ22 γ. The politician's ex ante expected policy utility when he
sells access is E W ja = 1ð Þ = R 10
R 10 W p̂
� �dαLdαR = γ
12. Total ex anteexpected contributions equal E cL + cR ja = 1ð Þ = 2
R 10 C αð Þdα = v
3.The politician's expected utilitywhenhe sells access is E UP ja = 1ð Þ =γ12 + v
3.
18 The interest group's expected payoff is strictly increasing in cj up to cj=C(αj), andstrictly decreasing in cj for all higher values. If the group provides no contribution, thepolitician expects that the group has αj=α(0)=0. Thus, interest groups do not preferto provide any other contribution than C(αj). Any off-equilibrium contribution cjNC(1)is interpreted by the politician as representing some feasible α a [0,1] (rather thansome larger αN1).19 Without access, all interest groups face the same incentives when choosing theircontributions; a group with a high α is no longer willing to provide a largercontribution than a group with a lower α. The politician recognizes this and does nottake the size of the contributions into account when updating his beliefs. This meansthat Eμαj=Eαj for both j a {L,R}, and the access selling politician chooses p=0.
3.3. Selling policy v. selling access
By selling policy the politician maximizes his expected total con-tributions, but does so at the cost of implementing a less-than-idealpolicy. By selling access, the politician maximizes his policy utility, butcollects lower contributions.
Lemma 1. In the contribution equilibrium
• selling policy favors results in the highest possible expected contribu-tion revenue, but does not maximize policy utility;
• selling access results in the highest possible policy utility, but does notmaximize expected contribution revenue.
It is straightforward to determine when he prefers each course ofaction.20 The politician prefers to sell access when E(UP|α=1)≥E(UP|α=0), or γ
12 + v3 z − γ
2 + v. This result is restated in the followingproposition.
Proposition 1. In the contribution equilibrium:
1. For important-enough issues (i.e., γ z 87v), the politician sells access
and p=p ̂.2. For less-important issues (i.e., γ b 8
7v), the politician sells policy favorsand p≠p ̂ with probability 1.
The variable γ represents how much the politician cares aboutpolicy relative to how much he cares about political contributions.This means that the politician prefers to sell access rather than policyfavors if the issue is important enough—if he cares enough about thepolicy outcome relative to contributions. For less important issues, hechooses to sell policy favors which results in higher revenue and lowerpolicy utility.
Throughout the paper, γ ̅ denotes the cutoff value at which thepolitician is indifferentbetweensellingaccess andsellingpolicy favors. Letγ t� �
= 87v denote this value for the case without campaign finance
reform(i.e., no contribution limitor tax). The following sectionsderive thecutoff values when there is a limit and a tax, γ (̅c )̅ and γ (̅τ) respectively.
4. Contribution limit
This section considers the impact of a contribution limit onequilibrium behavior and policy outcomes. An interest group cannotcontribute more than the limit, denoted c ̅ a [0,v). If c ̅=0, there is acontribution ban. The limit is assumed less than v since without thelimit no interest group will ever contribute more than v.
4.1. Policy favor game with limit
Equilibrium contributions depend on the size of the limit. For thecase when c V v
2, each interest group contributes c ̅, and each wins the
20 I assume that the indifferent politician sells access.
Fig. 2. Example contribution function with limit c .̅
836 C. Cotton / Journal of Public Economics 93 (2009) 831–842
prize with equal probability. Total revenue equals 2c ̅ which is strictlyless than the no-limit expected revenue of v.
For the case when c N v2, groups contribute according to a mixed
strategy. Their contributions are made according to distribution Hc ̅,where
Hc cð Þ =
cv
for ca 0;2c − vð �2c − v
vfor ca 2c − v; cð �
1 for c = c:
8>>>>><>>>>>:
Each group wins the prize with equal probability, and has anexpected contribution of v
2. Just as in the case without a contributionlimit, a high enough limit (i.e., c N v
2) results in the interest groupscompeting away all of their expected rent. The politician continues tocollect v in expected contributions.
Only a strict enough contribution limit affects politician utility inthe policy favor subgame. To impact the politician's expected payoffsfrom selling policy, it must be that c b v
2. Otherwise, the politician'sexpected payoff from selling policy is unchanged.21 Independent of c ̅,the politician's expected policy utility equals −γ
2 whenever he sellspolicy favors.
4.2. Access game with limit
Under a limit, the politician will still choose the policy he expectsmaximizes W(p) given his beliefs; although the limit might influencethe policy choice be influencing the politician's information and hisbeliefs about p̂. Furthermore, regardless of the limit, an interest groupwith access will always fully reveal its evidence. The limit can affectthe interest groups' equilibrium contribution strategy.
Without a limit, the maximum interest group contribution in theaccess game is v
4. Therefore, any c z v4 has no impact on behavior in the
access game. For c b v4, interest groups contribute according to
function Cc_, where
Cc αð Þ = 1− α2
� �αv2
forα b α cð Þc forα z α cð Þ
8><>: ð4Þ
where
α cð Þ = max 0;1−ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2− 8c
v
r( ): ð5Þ
Appendix section 1 provides details about the derivation of Cc ̅.22
Fig. 2 provides an example contribution function. An interest groupwith α equal to the cutoff value α ̅(c ̅) is indifferent between con-tributing according to the increasing contribution function and con-tributing the maximum amount c ̅. The cutoff value α ̅ takes on valuesbetween 0 and 1 as c ̅ increases from v
8 to v4. If c V
v8, then α ̅=0 and all
interest groups contribute the limit independent of their evidencequality.
Any contribution limit c b v4 results in a pooling equilibrium in
which any interest group with αj a [α ̅ (c ̅),1] contributes c ̅. Apolitician who observes cj=c ̅ can no longer infer αj from observing
21 Che and Gale (1998) assume that interest groups differ in terms of their valuations.In that case, they show that a limit can actually increase expected total contributions.Allowing for such differences in this paper would mean an ever stricter contributionlimit is required in order to decrease the politician's expected utility from selling policyfavors.22 The analysis in this section is most closely related to Gavious et al. (2002), whichincorporates bid caps into an all pay auction game with agents who are privatelyinformed about their valuations. In the current model, however, agents are privatelyinformed about their evidence, not their valuations.
the contribution alone. Without granting the group access, thepolitician only learns that αj a [α ̅(c ̅),1]. The potential for poolingresults in a less-than-fully informed politicianwhenever both interestgroups contribute c ̅; in which case the politician randomly awardsaccess to one of the groups and remains less than fully informed aboutthe other group's evidence. If neither or only one of the groupscontributes c ̅, the politician remains fully informed as he gives accessto the high contributor and can fully infer the low contributor'sevidence from its contribution.
With probability (1−α ̅(c ̅))2 both groups contribute c ̅ in whichcase he remains less than fully informed about one group's α.When he chooses policy, he relies on his expectation of α, whereE α jαa α;1½ �ð Þ = α + 1
2 . The politician's ex ante expected utility equals
E UP jc;α = 1ð Þ= ½ γ12 − 1−α cð Þð Þ4 γ24 � + 2 1− α cð Þð Þc + v
2αðcÞ22
−αPðcÞ36
!" #:
ð6Þ
The term in the first set of brackets denotes the politician'sexpected policy utility E(W|c ̅, α=1), where− 1−α cð Þð Þ4 γ
24 is the lossin expected utility from potentially being less informed compared tothe case without a limit. The term in the second set of bracketsdenotes the expected contribution from each group. It is straightfor-ward to show that both expected policy utility and expected revenueare lower in the access game under a limit thanwhen there is no limit(or when c z v
4 which means the limit is not binding). For any c b v4
expected contribution revenue is strictly increasing in c ̅; the stricterthe limit, the lower the revenue. Similarly policy utility is strictlydecreasing in c ̅, for ca v
8 ;v4
. For any c N v
4, the limit does not changethe access game, and for any c b v
8 both groups always contribute thelimit and further decreasing c ̅ has no impact on policy utility.
4.3. Selling access v. selling policy with limit
As in the case without a contribution limit, the politician sellsaccess whenever his expected utility in the access subgame is at leastas large as his expected utility in the policy favor subgame. It isstraightforward to calculate γ ̅(c ̅), the issue importance for which thepolitician is indifferent between selling access and selling policy inequilibrium. The cutoff value depends on the contribution limit.
For c z v2, the limit does not affect politician payoffs in either the
policy favor game or the access game. Therefore, such a limit cannotaffect the politician's choice of whether to sell access or sell policyfavors, and the cutoff value equals γ ̅(Ø).
For ca v4 ;
v2Þ
, the limit affects expected payoffs in the policy favor
subgame, but not in the access subgame. In this case, the politicianchooses to sell access if γ
12 + v3 z 2c − γ
2. Rearranging this gives thecondition that the politician sells access if γ z 24
7 c − 47 v, otherwise he
sells policy.For ca v
8 ;v4
� , the limit impacts expected payoffs in both the policy
favor and access subgames. In this case, the politician sells access if his
837C. Cotton / Journal of Public Economics 93 (2009) 831–842
expected payoff fromdoing so (given by Eq. (6)) is at least as great as hisexpected utility from selling favors (i.e., 2c − γ
2). He therefore sellsaccesswheneverγ≥[2v α (̅ c )̅ (3−α̅(c )̅2)]/[13+4 α (̅ c )̅−6α(̅ c )̅2+4α (̅c )̅3− α (̅c )̅4], where α (̅c )̅ is given by Eq. (5).
For ca 0; v8
, both interest groups always contribute the limit inboth the access and policy favor games, independent of their evidencequalities. Therefore, both games result in the same revenue (i.e., 2c )̅for the politician. The access game, however, results in strictly higherexpected policy utility, as the politician learns one of the group'sevidence before selecting policy. He therefore strictly prefers to sellaccess rather than sell policy under such a limit for all γN0.
In summary,
γ cð Þ =
87v for c z
v2
247
c − 47v for ca
v4;v2
h �2vα cð Þ 3− α cð Þ2
� �13 + 4α cð Þ − 6α cð Þ2 + 4α cð Þ3 − α cð Þ4 for ca
v8;v4
� i
0 for ca 0;v8
h i
8>>>>>>>>>>>><>>>>>>>>>>>>:
ð7Þ
For any c b v2, the politician sells access for a larger range of γ than he
does without a limit. However, any limit c b v4 influences contributions
in the access subgame, limiting the amount of information that thepolitician can infer from each group's contribution.
Lemma 2.
1. For any c b v2, γ cð Þ b γ t
� �. The limit results in the politician selling
access for a larger range of issues, and selling policy for a smaller rangeof issues.
2. For any c b v4, the limit decreases the probability the politician is fully
informed about both αR and αL when he sells access.
4.4. Effect of limit on constituent welfare
A contribution limit causes the politician to sell access (rather thanpolicy favors) for a larger range of γ. This effect tends to improveconstituent welfare, as the politician more often chooses the policy hebelieves is best, rather than choosing an interest group preferredpolicy.23 When the politician does sell access, however, a limit alsodecreases the politician's ability to learn about evidence by observingcontributions. This effect decreases expected constituent welfare, asthe politician tends to have less accurate beliefs about p̂ and is lesslikely to choose the welfare maximizing policy in the access game.24
The optimal limit, from the standpoint of constituent welfare,depends on the distribution of γ. Even without additional assump-tions regarding the distribution of γ, it follows that the optimal limit(1) will result in a pooling equilibrium in the access game, whichtends to decrease the accuracy of the politician's beliefs about p̂, and(2) will always be positive. Banning contributions is never optimal.
Let EW(c )̅ denote ex ante expected constituent welfare underlimit c ,̅ and let EW(t) denote expected welfare when contributionsare not limited.
23 Selling policy always results in lower expected constituent welfare than sellingaccess. This is because selling policy results in an outcome that is independent of thefully-informed policy p̂. If the politician retains the right to choose policy – as when hesells access – then he chooses the policy he believes is best. Even when he is less-thanfully informed about the evidence, his policy choice tends to be closer to the idealpolicy than when an interest group chooses policy.24 This negative affect is only true of a limit that is strict enough to influence behaviorin the access game (i.e., c b̅v/4).
Proposition 2. There exists some Pc ⁎a v8 ;
v4
� �such that
1. EW(c ⁎̅)≥EW(c )̅ for all c ̅≥0, and2. EW Pc ⁎
� �N EW Fð Þ
Let binding limit refer to any limit below the maximum equilibriumcontribution in the access game; therefore, a binding limit is any c b v
4.Proposition 2 shows that there exists a binding limit that results inhigher expected constituent welfare compared to no limit or any otherlimit, and that banning contributions is never optimal. In fact, it is neveroptimal to impose a limit resulting in all interest groups contributing c̅independent of their type. To seewhy a limit of v4 is not optimal, considerimplementing amarginally lower limit. This decrease in the limit causesthe politician to sell access for more issues—a good thing. It alsodecreases politician informationwhen he does sell access, but only by avery small amount.25 Similar reasoning rules out a limit of v
8 or below.
5. Taxing contributions
This section considers the impact of a contribution tax. I show thata proportional tax can have similar benefits as a contribution limit, butwithout the information loss.
Consider a tax rate τ a [0,1]. Any political contribution c is taxed atrate τ such that the politician receives payment (1−τ)c. Theremainder of the tax may go towards some public good which I donot model.26 I assume that neither the politician nor his constituentsbenefit from the tax revenue. If the constituents benefited from thetax, then taxing contributions would be even more attractive.
Unlike a limit, a tax does not distort the interest groups' incentivesto contributewhether they are competing for access or policy favors. Itdoes, however, influence the politician's incentives to sell policy ratherthan access.
5.1. Policy favor game with tax
A tax does not change interest group behavior in the policy favorgame, and equilibrium contribution strategies are identical to those inthe original game without a tax or a limit. The equilibrium is in mixedstrategies, with each interest group randomly drawing a bid from auniform (0,v] distribution. Each group wins with an equal ex anteprobability, and Ecj = v
2 for both j. Total expected after-tax revenue forthe politician is (1−τ)v. Expected politician utility from selling apolicy favor is E UP jτ; a = 0ð Þ = − γ
2 + 1− τð Þv.
5.2. Access game with tax
Interest groups have the same incentives to contribute as in theoriginal game, and the equilibrium contribution function isunchanged. Both groups submit contributions according to the originalfunction C defined in Eq. (3). Total expected contributions equal v3, andexpected politician revenue is 1− τð Þ v
3. C is strictly increasing for all αa [0,1]. Therefore, unlike in the case of a contribution limit, inequilibrium the politician can always correctly infer an interest group'sα from its contribution. The politician remains fully-informed aboutinterest group evidence. He is able to implement p ̂, which results in themaximum policy utility. His expected utility from selling access isE UP jτ; a = 1ð Þ = γ
12 + 1− τð Þ v3.
25 A limit just below v4 means a small positive probability that both groups contribute
c ,̅ and since the politician can only give access to one group he remains less than fullyinformed about the other group's evidence. However, because this other groupcontributed the limit, the politician correctly infers that the group had high enoughevidence quality to make such a contribution. In this case, the range of α for which aninterest group is willing to contribute the limit is very small; therefore, the politicianremains almost-fully informed about the group's evidence.26 One possibility is that the taxes fund the bureaucratic system necessary to enforceand collect the taxes.
838 C. Cotton / Journal of Public Economics 93 (2009) 831–842
5.3. Selling policy v. selling access with tax
When contributions are taxed at rate τ, the politician prefers to sellaccess if γ
12 + 1− τð Þ v3 z − γ
2 + 1− τð Þv. Rearranging this expres-sion gives the condition γ z 1− τð Þ 87 v. Therefore, for any τ a [0,1],γ τð Þ = 1− τð Þ 87 v, and Aγ
Aτ b 0. The cutoff value γ̅ is strictly decreasingin the tax rate, where γ̅(1)=0.
Lemma 3. For any τ a (0,1]:
1. γ τð Þ b v2. The tax results in the politician selling access for a larger
range of issues, and selling policy for a smaller range of issues.2. The politician remains fully informed about αR and αL when he sells
access.
27 Such a tax is distinctly different from a contribution ban, even through bothregulations result in the politician collecting no revenue. Under a high tax, the interestgroups still make payments that are observed by the politician and used to determinewhich group receives access. This is equivalent to “burning money.” A ban couldpotentially also lead to such an outcome if interest groups donate money to thepolitician's favorite charity or community organization in place of providing acampaign contribution. The politician will remain fully informed in such a situation,so long as he observes the charitable donations of all groups and grants access to thegroup that provides the largest donation.28 When c = v
8, both groups contribute c_independent of their α, and the politician
randomly awards access to one of the groups.
5.4. Effect of tax on constituent welfare
For any τ, if the politician sells access then he becomes fullyinformed about interest group evidence in equilibrium, and he is ableto identify and implement his fully-informed policy p̂. Therefore,selling access results in the maximum possible constituent welfare.Furthermore, given any issue γ, it is possible to set τ such that thepolitician chooses to sell access.
Lemma 4. For each γ, there exists a τ'a [0,1) such that for any τ≥τ' thepolitician sells access and p=p ̂.
Before the realization of γ, it is optimal from the standpoint of theconstituents to set τ=1. When τ=1, the politician, who cares aboutidentifying his fully-informed policy, chooses to sell access to thegroup who submits the highest (fully-taxed) contribution. He doesthis for all γ, and he remains fully informed in the process.
Proposition 3. A tax τ⁎=1 achieves the maximum possible constituentwelfare with probability 1.
A tax rate of 1 results in the politician selling access for all possibleissues. He therefore becomes fully informed independent of γ andimplements p= p̂ with probability 1. This represents the first-bestoptimal outcome for constituents, which is not achieved in theunregulated game or under a limit.
The model assumes that politician revenue does not directlybenefit constituents. Contributions may, however, provide some socialbenefit if they are used to run advertisements during campaigns.Coate (2004b), for example, develops a model in which contributionsfund ads that help inform voters about politician quality. If contribu-tions are used for such purposes, fully taxing contributions may not beoptimal. Although it is feasible that a high tax combined with somesystem to public campaign financing may be optimal for constituentwelfare. This issue is not further addressed in the present paper.
6. Tax versus limit
Both a tax and a limit can cause the politician to switch from sellingpolicy favors to selling access, which results in better policy choicesand improves constituent welfare. However, a limit decreases thepolitician's available information in the access game. This is not thecase with a tax; the politician remains fully-informed when he sellsaccess.
The optimal tax rate τ⁎=1 results in expected constituent welfareof EW(τ⁎)=0, which is strictly greater than the expected constituentwelfare under any possible limit. If constituents receive additionalbenefits from the collected taxes, then the advantage of taxing, ratherthan limiting contributions is further increased. The tax rate need notbe at τ⁎ in order for taxing contributions to result in higher expectedconstituent welfare than a contribution limit.
Proposition 4. There exists a tax rate τ̂b1 such that for all τ≥τ ̂,
• EW(τ)NEW(c_⁎), and
• EW τð ÞN EW t� �
.
A tax is clearly better than a limit when it comes to achieving thebest policy and highest constituent welfare. A tax rate of τ=1achieves the maximum possible expected constituent welfare in thepolicy favor and access game.27
This doesnot however imply that thepoliticianprefers a tax. First notethat the politician prefers no regulation to a contribution tax, as a taxsimply limits the revenue associated with any action. Suppose, however,there is outside pressure for campaign finance reform. To model this,assume that thepolitician can select either a limit or a tax to achieve someminimum required cutoff value γ '̅. Does the politician prefer to achieveγ '̅ through the use of a limit or a tax? Remember that γ = 8
7 v withouteither a limit or a tax; therefore, only γ′ b 8
7 v are of interest.
Proposition 5. To achieve any γ′ b 87 v, the politician prefers the use of a
limit rather than a tax so long as v is sufficiently large.
Proposition 5 shows that the politician may support the use of alimit rather than a tax, even when a tax results in higher constituentwelfare. This will be true whenever interest groups are sufficientlywealthy. Consider an extreme case where γ ̅'=0. The politician canachieve γ ̅' through a tax rate of τ=1, which maximizes policy utilitybut results in the politician collecting no contribution revenue.Alternatively, the politician can achieve the required cutoff by settinga limit c = v
8, which results in the politician collecting 2c ̅ in revenue,but being fully uninformed about one of the interest group's α inequilibrium.28 In this case, total expected politician policy utilityequals γ
24. The politician prefers to achieve γ ̅' through a limit c = v8
rather than a tax τ=1 so long as γ12 b 2 v
8 + γ24 or equivalently v N γ
6.Such a v cutoff exists for any γ′ b 8
7 v. This result may help explainwhycontribution limits are popular policy instruments, but contributiontaxes are uncommon.
7. Interest group asymmetries
There are various ways to incorporate interest group asymmetriesinto the model. I do so by allowing interest groups to differ in terms oftheir valuation parameter v. Without loss of generality, assume thatgroup R is more wealthy than group L; therefore, vRNvL. This may alsobe interpreted as group R caring more about the issue than group L.Both interpretations are reasonable, and justify consideration of thisextension. The values vL and vR are common knowledge.
In the policy favor game, the model takes the form of the all-payauction analyzed by Hillman and Riley (1989) and Baye et al. (1996).Because the interest groups differ in terms of their valuations, they nolonger follow the same mixed strategies. Instead, group R is more likelyto submit a higher contribution compared to group L, and is more likelytowin the policy favor. Group Rwinswith probability 1− vL
2vRN 1
2. Totalexpected contributions collected by the politician equal vL vR + vLð Þ
In the access game, I assume that the politician gives access to theinterest group that signals the highest quality evidence, rather than
839C. Cotton / Journal of Public Economics 93 (2009) 831–842
the group that provides the largest contribution.29 In this case, interestgroup contribution functions are unchanged from the earlier analysis,except they now depend on a group's v as well as its α. Therefore,Cj αð Þ = 1− α
2
� � αvj2 . Because a group's contribution function is strictly
increasing in its α, the politician continues to be able to correctly infera group's α from its contribution. He remains fully informed andimplements p ̂. Allowing interest groups to differ in terms of vtherefore does not change the policy outcome of the access game. Itdoes, however, change the expected total contributions. Now,expected politician revenue equals vR + vL
6 .The politician sells access whenever γ
12 + vR + vL6 z − γ
2 +vL vR + vLð Þ
2vR. Rearranging gives
γ z27
vR + vLvR
� �3vL − vRð Þ:
When interest groups have the same v, selling policy favors alwaysresults in higher expected revenue than selling access. However, whengroups differ in terms of v, this is not necessarily the case. WhenvL b vR
3 , selling access results in higher expected contributions, andhigher policy utility; for this range of values the politician prefers tosell access for all realizations of γ. For larger vL, the politician prefersto sell access only for important enough issues—those issues with highenough γ.
Just as in the game without interest group asymmetries, introdu-cing either a contribution limit and a tax can cause the politician toswitch from selling policy to selling access. Selling access is alwaysbetter for constituents than selling policy favors. While a limit mayhave averse affects on politician informationwhen he does sell access,however, a tax does not have such affects. Therefore, introducing a taxcan assure that the politician sells access, and that he continues to beable to identify and implement his fully informed policy.
8. Discussion
This paper combines a stylized model of policy favors with astylizedmodel of access to help gain a better understanding of the roleof political contributions and the effects of campaign finance reforms.The mechanisms through which this paper assumes the politicianawards favors or access are not the only means by which a politicianmay trade policy choices or access for contributions. Allowing thepolitician to award policy or access through alternative means shouldnot change the main results, so long as the politician continues tochoose “better” policy in the money-for-access subgame than in themoney-for-policy subgame.
In this paper, the politician gives access to the interest group thatprovides the highest contribution (or in the case of interest groupasymmetries, to the group that signals the highest α). Alternatively,the politician may set a price for access, and any group that pays theset price receives access (e.g., Austen-Smith, 1998). Cotton (2008)considers such a mechanism while assuming an underlying eviden-tiary structure similar to the one developed in this paper. Under suchan alternative mechanism for awarding access, the politician becomesfully informed about the evidence of any group with access, and hebecomes partially informed about the evidence of any group that doesnot pay for access. This is because only groups with high-enough α arewilling to pay the set access fee, and the politician can correctly inferthat any group who does not pay the fee has a lower α. Selling accessthrough access fees still results in a more informed policy decision
29 Such an assumption simplifies the analysis, and is reasonable given the accounts ofpoliticians and interest groups (see for example, Schram (1995); Makinson (2003)).Smaller local organizations often need to contribute less to achieve access than larger,more wealthy organizations. Without this assumption, there is pooling amongst thehighest α rich groups. However, the politician will remain fully informed, as a richgroup with such high α will win access, as the pooling contribution amount is greaterthan the contribution from any type of poor group.
than selling policy favors. Therefore, the main results of the papershould continue to hold: the representative constituent tends to bebetter off when the politician sells access rather than favors, both alimit and a tax can make selling access more likely, and a tax does sowithout further distorting the politician's information.
There are also alternative means through which the politician maysell policy. For example, the politician may sell policy through a menuauction inwhich each interest group provides a contribution schedulethat assigns a payment to each possible policy choice (e.g., Grossmanand Helpman, 1994; Bernheim and Whinston, 1986). Such a mechan-ism may result in a moderate equilibrium policy choice (e.g., p=0);however the policy choice is still made by a less informed politicianand does not result in as good of policy as in the access subgame inwhich the politician is more-fully informed. Again, the main results ofthe paper should continue to hold.
Another means of generalizing the model is to allow for noisyinformation in the access game. For example, interest groups may notknow exactly how the politicianwill interpret their evidence. Onewayto model this is for each interest group to observe a signal correlatedwith its αj. In this case, the contribution function is increasing in agroup's signal rather than its α, which the groups do not observe. If agroup wins access, the politician still becomes fully informed about αj.Otherwise, the politician remains less than fully-informed about thegroups αj, although he can infer the group's signal from itscontribution. To the extent that a group's signal is correlated withits true type, contributions still enable the politician to become betterinformed about a group's type. Here, the politician continues to bebetter informed and choose better policy when he sells access ratherthan favors.
The access framework in this paper also assumes that interestgroups are endowed with evidence about their respective issues, butpoliticians are ex ante uncertain about the evidence. This assumptionis supported by the idea that interest groups are actively involvedwiththeir issues, but politicians must make decisions regarding manyissues, some of which they likely know little or nothing about.30 Itwould also be reasonable, however, to assume that the acquisition orpresentation of evidence is costly for the interest groups. So long asthe costs to an interest group are low enough, such an assumptionshould weaken, but not significantly change the results. For example,if the presentation of evidence is costly, only groups with high-enoughevidence quality pay to present it if they gain access. This would likelycreate pooling amongst the groups with low quality evidence, whowill not find it worthwhile to pay the presentation costs. If the costsare small enough, most groups will continue to behave according tothe original model. The same should be true if the politician can pay toconduct his own research, so long as his costs are sufficiently largecompared to the research costs of the interest groups.
9. Conclusion
This paper makes two primary contributions. First, it develops anew model of lobbying and money in politics. The frameworkcombines a traditional money-for-policy model with an informationallobbying and money-for-access game. The model shows that for someissues, the politician provides policy favors in exchange for contribu-tions. For other issues (those of great enough importance), thepolitician provides access in exchange for contributions, whereinformation revealed through access allows him to make better policydecisions.
30 In this way, this paper's model probably does not apply to an issue like abortion,for which politicians are already well informed or likely to publicly commit to aposition, and for which constituents likely have strong beliefs. Instead, such a model islikely a better fit for an issue such as steel tariffs in which the domestic automobileproducers have arguments against a tariff, the domestic steel industry has argumentsin favor of a tariff, and most politicians are not well informed about the optimal level oftariff for their constituents.
840 C. Cotton / Journal of Public Economics 93 (2009) 831–842
Second, the paper compares two types of campaign financereform: imposing contribution limits, and taxing contributions. Theanalysis shows that both a contribution limit and a tax may result inbetter policy outcomes. This is because either reform may cause thepolitician to sell more access and fewer policy favors. When theanalysis compares the effects of a contribution limit and a contribu-tion tax, however, a tax is clearly the better type of campaign financereform for the representative constituent. A limit makes selling accessmore likely, but at the same time reduces the politician's ability toidentify and implement his fully-informed policy. A tax, on the otherhand, makes selling access more likely without reducing politicianinformation.
Future work may further improve this framework by consideringrepeated interactions between a politician and interest groups,analyzing legislative decision making, or formally modeling howpoliticians use contributions to fund elections in the presence of bothpolicy favors and access.
Appendix A
A.1. Access game equilibrium contribution function with limit
The contribution limit constrains the possible contributions, butdoes not directly influence the interest groups' willingness tocontribute. Interest groups with high enough evidence quality preferto contribute more than the limit, but are unable to do so. Groups withlowenough evidence quality are happy contributing less than the limit.Let α ̅(c ̅) denote the α cutoff associated with limit c
_such that groups
with αNα ̅ contribute the limit, and those with α≤α ̅ contribute lessthan the limit. If both groups contribute c ̅, eachwins accesswith equalprobability. If a group receives access, the politician observes itsevidence directly. If a group contributes c ̅ and does not receive access,the politician acts as if the politician has α equal to Eμ αð Þ = α + 1
2 .A group with α≤α ̅ has the same incentives to contribute as
without a limit; therefore, Cc ̅(α)=C(α) for α≤α ̅. If group jcontributes cbc ̅, then it receives expected payoff equal to Eq. (1).For α in this range, a group's expected payoff is maximized when itcontributes according to the contribution function C derived in theprevious section; doing so results in expected payoffs
v2
Z 1
0αj − α− j
h idα− j − 1−
αj
2
� �αj
v2: ð8Þ
If group j contributes cj=c ̅, it receives payoff
v2
Z α
0αj − α− j
h idα− j +
v2
Zα
1 12
αj − α + 12
� �+
12
α + 12
− α− j
� �� �dα− j − c:
ð9Þ
If the other group contributes less than the limit (which it doeswhen αLb α̅), group j receives access and the politician also correctlylearns group −j's evidence through its contribution. If −j alsocontributes the limit, each group receives access with equalprobability, and the politician only learns the evidence quality of thegroup that receives access.
For any αbα (̅c )̅, the benefit of contributing the limit (i.e., Eq. (9)minus Eq. (8)) is strictly increasing in the group's α. The higher αj, themore attractive j finds contributing the limit, rather than any value lessthan the limit. The cutoff value α (̅c )̅ is the evidence value at whichthe interest group is indifferent between contributing c ̅ and contribut-ing C(α )̅ (i.e., a r α solves for αj the equality Eq. (9)=Eq. (8)). Solvingfor α ̅givesα = 1−
ffiffiffiffiffiffiffiffiffiffiffi2 − 8c
v
q.When α̅≤0, the interest group contributes
the limit for all α. This happens whenever c V v8.
A.2. Proofs
Formal proofs of Proposition 1 and Lemmas 2 and 3 are omitted.They follow directly from the analysis in the body of the paper andAppendix section 1.
Proof of Lemma 1. Consider first the maximum equilibriumcontribution revenue. The worse-possible policy utility for an interestgroup equals− v
2, which happens when the politician implements theother group's policy. For any p, group R receives policy payoff p v
2 andgroup L receives policy payoff−p v
2. Suppose interest group i contributesaccording to an equilibrium strategy si, and that F(·|sL, sR) isthe equilibrium distribution of policy choice p given the equilibriumstrategies. The expected policy benefit to interest group R of participat-ing is
R 1−1 f p jsL;sRð Þ p v
2 − − v2
� �� �dp. Independent of how policy is
chosen (i.e., through the sale of access, the sale of policy favors, or insome other way), an interest group's equilibrium contribution willnot exceed the expected benefit from making the contribution. There-fore, EcR sR;sLð ÞV R 1−1 f p jsL;sRð Þ p v
2 − − v2
� �� �dp, and similarly for EcL.
Together, this means EcR + EcL VR 1−1 f p jsL;sRð Þ v + p v
2 − p v2
� �dp = v.
Therefore, total expected revenue cannot exceed v. Selling policy favorsachieves v; while selling access results in total expected contributions ofv3 b v.
Next, consider the maximum equilibrium politician policy utility.By definition p̂≡argmaxpW(p). In the access subgame, p= p̂ withprobability 1; thus maximizing policy utility and constituent welfare.In the policy favor subgame, p≠ p̂ with probability 1, thus achievinglower expected policy utility. □
Proof of Proposition 2. Expected constituent welfare as a function ofthe contribution limit is given by
EW cð Þ =
Z γ
0cð Þg γð Þ −γ
2
h idγ +
Zγ cð Þ∞
g γð Þ γ12
h idγ for c = tor c z
v4Z γ
0cð Þg γð Þ −γ
2
h idγ +
Zγ cð Þ∞
g γð Þ γ12
− 1−α cð Þð Þ4 γ24
h idγ for ca
v8;v4
h iZ ∞
0g γð Þ γ
24dγ for ca 0;
v8
h i;
8>>>>>>>>><>>>>>>>>>:
where γ (̅c )̅ is defined by Eq. (7). First, it should be clear from EW(c )̅above that a limit of c = v
4 is strictly better (for constituent welfare)than any higher limit, or no limit at all. This follows because Aγ
Ac z 0 forall c z v
4 and AγAc N 0 for all ca v
4 ;v2Þ
. Remember g(γ)N0 for all γN0.
Consider now ca v8 ;
v4
. For this range of limit,
AEW cð ÞAc
= g γ cð Þð Þ −γ cð Þ2
� �γ′ cð Þ− g γ cð Þð Þγ′ cð Þ
γ cð Þ12 − 1−α cð Þð Þ4γ cð Þ
24
" #
+ 4 1−α cð Þð Þ3α′cð ÞZ ∞
γ cð Þg γð Þ γ
24dγ:
The derivative evaluated at the upper bound of this range, c = v4, is
AEW v4
� �Ac
= − v6g 2v = 7ð Þγ′ v= 4ð Þ:
The derivative of the cutoff value with respect to the limit, Aγ cð ÞAc , is
strictly positive for all ca v8 ;
v4
. Therefore, AEW v
4ð ÞAc b 0. Given an initial
c = v4, marginally decreasing c̅ strictly increases expected constituent
welfare. Thus, c b v4.
Similarly, the derivative evaluated at the lower bound of this range,c = v
8, is
AEW v8
� �Ac
=23v
Z ∞
0g γð Þγdγ N 0:
841C. Cotton / Journal of Public Economics 93 (2009) 831–842
Given an initial c = v8, marginally increasing c ̅ strictly increases
expected constituent welfare. Thus, c N v8. Taken together these
conditions imply v8 b c b v
4.
Proof of Lemma 4. Define τ′umax 0;1− 78γv
�. Given some tax rate
τ, the politician sells access if γ z γ τð Þ = 1− τð Þ 87 v. Rearranging,the politician sells access if τ z 1− 7
8γv. Since τ≥0, it follows that the
politician sells access iff τ≥τ'. From the analysis in the body of thepaper, it follows that whenever the politician sells access in the gamewith a contribution tax, the politician becomes fully informed inequilibrium. A fully-informed politician chooses his fully-informedpolicy, setting p=p ̂.
Proof of Proposition 3. For any tax rate τ a [0,1], ex ante expectedconstituent welfare is
EW τð Þ =Z 1 − τð Þ87v
0g γð Þ −γ
2
h idγ +
Z ∞
1 − τð Þ87vg γð Þ γ
12
h idγ; ð10Þ
which is strictly increasing in τa [0,1]. Therefore, EW(τ) is maximizedat the maximum tax rate, τ=1. Therefore, EW τ = 1ð Þ =R∞0 g γð Þ γ
12
dγ
Proof of Proposition 4. From the proof to Proposition 3, it is clearthat EW(τ) is strictly increasing in τ, and ranges from
R∞0 g γð Þ γ
12
dγ
when τ=1 toR 8
7v0 g γð Þ − γ
2
dγ +
R∞87vg γð Þ γ
12
dγ when τ=0.
From the proof to Proposition 2, it is clear that for any c_≥0,
EW cð Þ b R∞0 g γð Þ γ12
dγ. Therefore, EW(c
_)bEW(τ=1). Let EW(c
_⁎)
denote the maximum possible ex ante expected welfare under alimit. Let τ′ solve EW(τ)=EW(c
_⁎) for τ, where EWτ is given by Eq.
(10). Given that EW(τ) is strictly increasing in τ and that EW(c_)bEW
(τ=1) for all c_, it follows that τ′b1. Given that EW(τ) is strictly
increasing in τ, it follows that for any τNτ′, EW(τ)NEW(c_). □
Proof of Proposition 5. First consider the case when γ′a 27 v;
87 vÞ
.
The required limit to achieve γ ̅=γ ′̅ solves 2c − γ′
2 = γ′
12 + v3
; therefore,
c = 124 4v + 7γ′� �
. The politician's expected utility in the game withsuch a limit equals
Z γ′
0g γð Þ 2c − γ
2
� �dγ +
Z′
γ∞g γð Þ γ
12+
v3
� �dγ: ð11Þ
To achieve γ ′̅ through a tax, the required τ solves γ′
12 +1− τð Þ23 v = − γ′
2 + 1− τð Þv; therefore, τ = 8v − 7γ′
8v . This is truefor any γ′ b 8
7 v. The politician's expected utility in the game with sucha tax equals
Z γ′
0g γð Þ −γ
2+ 1− τð Þv
� �dγ +
Z 87v
γ′
g γð Þ γ12
+ 1− τð Þ v3
� �dγ
+Z ∞
87v
g γð Þ γ12
+v3
� �dγ:
ð12Þ
The politician prefers the limit whenever Eq. (11) is greater than Eq.(12). This condition simplifies towhenever
R 87v0 g γð Þ 8v − 7γ′
� �124 dγ N 0,
which holds for all v, given that γ′ b 87 v.
Next consider the case when γ′a 0; 27 v
. For values in this range,the required limit to achieve γ ′̅ solves Eq. (7) as an equality. Therequired tax is the same as in the first case. To prove that there exists av large enough such that the politician prefers regulation through alimit, it is sufficient to show that there exists a v large enough suchthat the politician prefers the limit to the tax for each possiblerealization of γ, with strict preference for some potential realizations.
For γb γ ′̅, the politician sells favors and the politician's realizedutility is independent of the type of regulation. Here the politician is
indifferent between both types of regulation. For γa γ′; 27 vh i
, thepolitician earns expected payoff γ
12 − 1−α cð Þð Þ4 γ24 + 2 1− α cð Þð Þc +
v α cð Þ22 + α cð Þ3
6 Þ�
under required limit c_, and the politician earns
expected payoffγ12 + 7γ′
24 under the required tax. For this range of γ,the expected payoff under the tax is independent of v, while theexpected payoff under the limit is strictly approaches ∞ as v → ∞.Thus, the politician will strictly prefer the limit for large enough v. Forγa 2
7 v;87 v
� , the politician earns expected payoff γ
12 + v3 under a limit.
Under the required tax, the politician earns the same expected payoffas in the case when γa γ′; 27 v
h i. The politician's expected payoff is
strictly increasing in v under the limit, with EUP → ∞ as v→ ∞, and thepolitician's expected payoff is again independent of v under the tax,given γ. Again, the politician will strictly prefer the limit for largeenough v. Finally, for γ z 8
7 v, the politician earns the same expectedpayoff γ
12 + v3 under either regulation and is therefore indifference.
For large enough v, the politician strictly prefers the limit for somepotential realizations of γ, and is indifferent between the tax and thelimit for all other realizations of γ. Therefore, if v is large enough, thepolitician earns a strictly higher ex ante expected utility under thelimit, and thus strictly prefers the limit to the tax. □
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