Informational lobbying and political contributions

Journal of Public Economics 90 (2006) 631 – 656 www.elsevier.com/locate/econbase

Informational lobbying and political contributions Morten Bennedsen a, Sven E. Feldmann b,* a

b

Copenhagen Business School and CEBR, Denmark MEDS Department, Kellogg School of Management, Northwestern University, 2001 Sheridan Road, Evanston IL 60208-2009, United States Received 20 August 2004; received in revised form 3 August 2005; accepted 14 August 2005 Available online 3 October 2005

Abstract Interest groups can potentially influence political decision-makers by offering contributions and by providing relevant information that sways the decision in the group’s favor. What mix of these two instruments should an interest group choose, and how does the use of one instrument affect the effectiveness of the other? In this paper we identify an information externality that raises the cost of offering contributions and show that this indirect search cost reduces the group’s incentive to gather information when contributions are allowed. Furthermore, we analyze how competition among lobby groups as providers of information and contributions affect the choice and effectiveness of the instruments. We show that the information externality rewards the group that can abstain from information search and focus its influence on contributions. D 2005 Elsevier B.V. All rights reserved. JEL classification: D72; D82 Keywords: Lobbying; Political contributions; Asymmetric information; Common agency

1. Introduction Interest groups participate directly in the political process in several ways; they provide substantive information to policy makers and, at least in the U.S., they offer financial incentives by contributing to politicians’ campaigns.1 In order to influence a political decision an interest group thus faces the choice of providing the decision-maker with information, lobbying via contributions, or doing both. The first part of this paper analyzes how the choices of acquiring * Corresponding author. E-mail address: [email protected] (S.E. Feldmann). 1 In addition to interacting directly with decision-makers, interest groups also provide information or cues to voters via issue ads or candidate endorsement. We ignore this (equally strategic) aspect of interest group behavior in this paper. 0047-2727/$ - see front matter D 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.jpubeco.2005.08.003

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information and providing it to the decision-maker and supporting her campaign interact, and under what circumstances an interest group uses one or both of these two different strategies. The second part of the paper studies how competition among interest groups affects the groups’ choices and to what extent it changes the amounts of information and influence the decisionmaker receives. The framework of this paper is a follows: interest groups and a decision-maker are uncertain about some aspect of a policy decision; depending on the true nature of the uncertain aspect, the decision-maker prefers either an outcome that favors an interest group or one that harms it. The interest group has the ability to gather information that may reduce the uncertainty, and it may therefore be in the position to provide the decision-maker with useful information. Obviously, the interest group will only gather and transmit the information if it is in its interest to do so. Alternatively or additionally, the interest group may take advantage of the decision-maker’s ignorance and induce her to choose the favorable outcome by offering campaign contributions. Collecting information and deciding not to provide it to the decision maker is information in and of itself, and a rational decision-maker will make use of it. Independently of whether the interest group’s search for information is observed by the decision-maker, the collection of information creates an informational externality when it leads the decision-maker to infer that the group is knowledgeable and is withholding its information. In conjunction with contributions, however, this information externality increases the cost of bribing the decision-maker ex post. We show in Proposition 1 that the information externality reduces a single lobby group’s incentive to search for information. It is often argued that competition among information providers increases the incentive to provide (truthful) information (see e.g. Austen-Smith and Wright, 1992 and Dewatripont and Tirole, 1999). This insight no longer holds without qualification when information providers can also use contributions. In Proposition 2 we first show that in the absence of contributions the introduction of a competing interest group leads to (weakly) more information search, which is consistent with the bconventional wisdom.Q Allowing for contributions, however, changes the picture somewhat. The information externality implies that searching provides benefits to the opponent. A group will try not to search, and the group with the less powerful information technology receives on average a rent, as it benefits from the information externality generated by its opponent. The results are robust in that they do not depend on the parametric assumptions of the model. This suggests that the interaction of information and incentive provision should be carefully considered in principal–agent models. Campaign contributions as well as the strategic use of information to influence policy choice have been the subject of tremendous scholarly interest and research (see surveys by Schlozman and Tierney, 1986; Persson and Tabellini, 2000; Grossman and Helpman, 2001). A growing number of formal models assess the role of campaign contributions and party or candidate competition for interest group influence on policy outcomes (Austen-Smith, 1987; Baron, 1989, 1994; Snyder, 1990, 1991; Grossman and Helpman, 1994, 1996; Dixit et al., 1997; Besley and Coate, 2001). In these models, contributions serve as an incentive device with which interest groups induce policy choices. Following a fundamental result by Bernheim and Whinston (1986), the policy choice induced by contingent contributions maximizes a weighted sum of the interest of organized groups and that of the decision-maker, where the latter can be interpreted to reflect the preferences of the decision-maker’s electoral constituents. The second strand of literature relating to this paper addresses the role of strategic information provision. Information originating from interested parties is potentially biased; by using costly signals or sporadic verification of the information by the decision-maker, the interest group can

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credibly inform the decision-maker (Crawford and Sobel, 1982; Calvert, 1985; Gilligan and Krehbiel, 1987; Austen-Smith, 1994). The influence a group has on the decision provides an incentive to acquire information, even if the acquisition is costly. Most papers in the literature focus on one of these means of influence. It is likely that different instruments interact, both with respect to incentives and with respect to the outcome they produce. The contribution of the present paper is to analyze the interaction of campaign contribution and information provision as means of influence. Austen-Smith (1995) considers a two-stage model in which in the first stage contributions serve to gain access and partially signal the group’s preference, followed by a second stage game of costless information provision. Lohmann (1995) analyzes the situation where several heterogeneous interest groups seek access and influence. Interest groups with preferences similar to the decision-maker’s obtain access at zero cost and can transmit private information credibly, while extreme lobby groups must pay positive contributions. In both models contributions serve to gain access and to enhance the credibility of the sender. Austen-Smith and Banks (2002) also analyze a two-stage game in which the sender can incur a utility loss that increases the credibility of the information. The present paper takes a different approach from these papers: It contrasts the cynical view of interest groups as influence seekers by means of contributions with the more optimistic view of interest groups as providers of useful information. It bstacks the deckQ in favor of information by making information as credible as possible, by assuming it to be costlessly verifiable. We show that even with this strong assumption in favor of informational lobbying, which makes the model tractable, interesting and non-trivial interactions between information provision and contributions result. In a related paper Dahm and Porteiro (2004) examine the incentives of a single interest group to provide information and to exert pressure on a decision-maker. Their analysis builds on an earlier working paper version of this paper and extends its framework by allowing the interest group to choose between public or private information search. Dahm and Porteiro derive interesting results about the policy effects of campaign finance reforms by characterizing when a campaign finance reform induces an interest group to provide more information. The paper proceeds as follows: Section 2 lays out the simple generic decision problem used in the subsequent sections. Section 3 shows that allowing an interest group to use financial incentives decreases its incentive to search. In Section 4 we extend our model by introducing a competing interest group and analyze how the competition among information providers changes the incentives to gather information. We show that competition increases the lobby’s search activity when contributions are not permitted, but that the benefits of the search accrue in part to the opposing lobby group when contributions are allowed due to the information externality. Section 5 discusses the findings and concludes. 2. The model A decision-maker (DM) needs to choose between three alternative policies, d l , d r, and d B. Whether d l or d r is the best choice depends on the state of the world, h a {h l , h r }, while d B is never best nor worst and in this sense can be considered a bneutralQ alternative. The state of the world is unknown to the decision-maker, and each state has an equal probability ex ante.2 We assume that d B is preferred to either d l , and d r under ex ante beliefs, so that d B allows the DM to partially hedge against uncertainty. 2

The symmetry of the probability between the states is immaterial for what follows but provides a convenient choice for the analysis.

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In addition to her preference over projects, the decision-maker derives utility from potential contributions from an interest group. The utility from contributions c is additively separable and linear, with a (marginal) value of campaign contributions to the decision-maker of a.3 Her total utility is given by VDM ðd; c; hÞ ¼ uDM ðd; hÞ þ ac: For simplicity of exposition we choose an explicit functional form for u as follows:4 8 if ðd; hÞafðdl ; hl Þ; ðdr ; hr Þg < us ¼ 0 uDM ðd; hÞ ¼ uB ¼  1 if d ¼ dB : ufs ¼  4 if ðd; hÞafðdl ; hr Þ; ðdr ; hl Þg: There is one interest group (L) in the basic influence model, and it prefers the d l project independently of the state of the world. The lobby group’s preference is additively separable in the utility from the project, the cost of gathering private information, and the contributions it pays to the decision-maker: VL ðd; s; cÞ ¼ uL ðd Þ  sk  c; 8 < 2b if d ¼ dl if d ¼ dB where uL ðd Þ ¼ 1 : 0 if d ¼ dr : k z 0 is the cost incurred by the group if it decides to search for information, s a {0, 1}. b z 1 / 2 parameterizes the lobby group’s intensity of preference between the projects. Notice that the group’s utility function is concave (convex) with respect to the project choice if b b (N) 1: When b N 1 the interest group has more to gain from the choice of their most preferred outcome than between the two other choices, and we refer to such an interest group as having intense preferences for its preferred outcome. When b b 1 then the interest group is relatively more concerned about averting the worst outcome, d r.5 The contractual framework between interest group and decision-maker is incomplete. We assume that the decision-maker and the lobby group are unable to write binding ex ante contracts that tie the decision maker’s choice to the lobby’s search activity or to the information transmitted by the group, or contracts that require payments by the decision-maker to the lobby group contingent on the chosen policy. We believe this to be a defining aspect of lobby groups. The decision-maker always retains the right to choose the ex post optimal outcome; it would be politically infeasible and practically problematic to bind the decision-maker to the lobby group’s recommendation. If the decision-maker were to make such a commitment, the information provider becomes a (government) agency or contractor.6 3 This means that the decision-maker is risk neutral with respect to contributions. If the decision-maker were risk averse, contingent contributions could influence the decision-maker additionally by providing an insurance. 4 Choosing a specific functional form reduces the parameter space and yields algebraic solutions in the remaining parameter space. Any choice of utility function yields similar results as long as u s N u B N u ~s (where s denotes that the decision correctly reflects the state) and where d B provides a partial hedge of ex ante uncertainty, i.e. u B N pu s + (1  p)u ~s with p being the probability of the more likely state. Our choice of utility function is equivalent to a continuous outcome space in which the alternatives d l , d B, and d r are equally spaced with unit distance and the state contingent utility functionis negative quadratic over all alternatives. 5 Given the flexibility of b, u L (d ) is without loss of generality. 6 In addition, we also assume that commitment to a third party, e.g. the public, is not enforceable. The consequences of contracting with third parties are analyzed in Maskin and Tirole (1999).

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t=0

Nature chooses state θ

1

2

3

4

Group chooses whether or not to search s

Group receives signal σ

Group sends message m, offers contributions c

decision-maker chooses project d

635

Fig. 1. Time line.

The sequence of moves in the game applies both to lobbying in a democratic society through legal campaign contributions to political parties and to corruption with bribes in an autocratic regime. In the first stage of the influence game the lobby group decides whether it wishes to search for information about the state of the world. If the group decides to search (s = 1), it receives a signal r, which with probability q contains hard information about the state of the world, r = h, and with probability 1  q is uninformative, r = t (if the group does not search r = t). We denote the decision-maker’s belief of whether or not she expects the group to search by e and ~e, respectively.7 Next, the interest group sends message m to the decision-maker, where m a {r, t }. We assume that the group can withhold knowledge about the state of the world, but it cannot blie,Q i.e. it cannot forge information. We can interpret this assumption of bhard informationQ as the decision-maker requiring a high evidentiary standard that makes it prevents the group from offering bogus information but allows it to remain silent. Alternatively, information may be difficult for the decision-maker to generate but easy to verify once submitted.8 Given this information structure, m = t means that either the group is uninformed or that it is not willing to provide the information it has. In addition to sending a message, the interest group can also seek influence by offering contributions, understood as non-negative payments to the decision-maker contingent on the chosen project (similar to Bernheim and Whinston, 1986). Finally, given messages and contingent contributions, the decision-maker chooses the project. The time line of the influence game is given in Fig. 1. When the interest group searches, it receives a favorable signal r = h l with probability q / 2, and will reveal this to the decision-maker. If the lobby group receives unfavorable information (r = h r ), it will hide this from the decision-maker and will send the same message as if its search was uninformative (r = t ). Given this message strategy and her belief about the group’s search activity, the decision-maker uses Bayes’ rule to update his beliefs about the state of the world. When the DM but receives a message m = t , her  expects the 1 group to search (e) posterior belief is: p hr jm ¼ t ¼ 2q and p(h l |m = t ) = 1q 2q . 7 More generally the DM’s belief regarding the group’s search is a probability g a [0, 1]. In a pure strategy equilibrium the belief is dichotomous, either g = 1 or g = 0, and we adopt the notation above for mnemonic and notational convenience. 8 The following scenario illustrates the bhard informationQ assumption: the interest group commissions an independent study on the impact of a certain policy; while the research institutionTs scientific reputation lends the study credibility and prevents manipulation of the studyTs results, the lobby group strategically chooses to publish the results, or parts of them, only when they are supportive of its interests. The assumption is similar to Milgrom and Roberts (1986), Laffont and Tirole (1990), Bennedsen and Feldmann (2002a,b). Milgrom and Roberts (1986) uses free verification as justification for truthtelling. More generally, the information structure of this sender-receiver game can be characterized according to whether or not the information is manipulable and whether or not it can be withheld. In Section 5 we discuss the role of alternative assumptions about the informational structure.

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3. A single interest group’s incentive to lobby In this section we solve the influence game with one interest group. Before doing so fully, we first illustrate the basic information externality and its effect on the size of contributions. To this end we consider the simplest instance in which the ability to make contributions affects an interest group’s incentive to collect information, which should provide an intuition for the subsequent, more complex, analysis. Consider a single lobby group whose search effort can be observed by the decision-maker. When contributions are not feasible and search is quite informative, i.e., when q N 2 / 3, an unsuccessful search increases the likelihood of state h r sufficiently so that the decision-maker chooses d r, the worst outcome for the group. Provided the group cares enough about its most preferred outcome, it is willing to take the gamble of getting the favorable information at the expense of potentially ending up with the worst outcome.9 When contributions are permitted, the indirect cost of searching takes on a different form: an unsuccessful search not only potentially changes the decision-makers optimal choice, but it also raises the contributions necessary to induce the group’s favorite outcome. Even though the decision-maker, after a successful search, chooses the lobby’s preferred outcome for free, the net effect is that searching increases the ex ante expected contributions necessary to obtain the lobby groups’s favored outcome. Thus, even if the search activity is costless, a group that is willing to use contributions after a failed search will never search.10 The reason for the group not wanting to use information is the following. The group’s search-whether successful or not-increases the information available to the decision-maker about the state of the world, and this binformation externalityQ increases the decisionmaker’s ex ante expected utility. In the case where the group’s interest is sufficiently strong so that it will induce its preferred outcome independently of the search result, the final decision is known ex ante and thus the total surplus created by the decision is fixed. Since the decision-maker is made better off by the information, the group must be worse off. In other words, searching for information transfers welfare from the lobby group to the decision-maker, while this is not the case when the group induces its choice via contributions only. The conclusion is that the ability to use contributions as a means of influencing the decision-maker reduces, and in this case eliminates, the lobby’s incentive to acquire information. We now move on to solve the influence game with one interest group and unobservable information search. Due to the cost of monitoring interest groups, decision-makers in general do not observe whether or not lobby groups’ are actively acquiring information about policy. We solve for the rational expectation equilibria (REE) in which the decision-maker correctly infers the lobby group’s equilibrium search behavior and both players’ strategies maximize their expected utilities given their beliefs.11

9 The condition for searching when search is observable and informative (i.e., q z 2 / 3) is b N 1þk q . We note that only an intense interest group (b H 1) is willing to take this gamble. 10 Then lobby group is sufficiently interested, or extreme, to induce d l after a failed search with q N 2 / 3 iff o 2q 2þq 1 bzmax að2q Þ ; 2 þ 2að2qÞ . 11 A rational expectations equilibrium of this game is a Perfect Bayesian equilibrium: actors behave sequentially rational, and beliefs about the group’s search and about the state of the world are determined by Bayes’ rule along the equilibrium path; out-of-equilibrium beliefs are updated correctly whenever hard information is provided.

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As is commonly the case in models of imperfect information, the game has multiple equilibria; however, since non-empty messages are restricted to be truthful, the set of possible equilibria is small. Consider first the situation in which no contributions can be paid (~c), and suppose the decision-maker expects the lobby group not to search (~e). Since no search is expected, the decision-maker does not update her beliefs when the lobby group provides no information (m = t ) and chooses d B. If, instead, the group searches and in the event of a positive outcome sends message m = h l , then the decision-maker chooses d l with probability q / 2. Thus, the lobby group’s expected benefit of searching in this case is Bð¨e;¨cÞ ¼

 q q ð2bÞ þ 1  d1  1 2 2

  1 ¼q b : 2

ð1Þ

An equilibrium in which the group does not search obtains when the group behaves according to expectation, requiring B (~e,~c) b k, or bb 12 þ kq. If the decision-maker expects the lobby group to search (e), she updates her beliefs whenever the group does not provide information. The optimal behavior depends on how informative the search technology is: If q V 2 / 3, the decision-maker chooses d B after m = t , and the group’s benefit of searching is the same as in (1). If q N 2 / 3, the decision-maker chooses d B unless the lobby group communicates m = h l . The group’s expected benefit of searching is    if qV 23 q b  12 ð2Þ Bðe;¨cÞ ¼ qb otherwise: An equilibrium with search exists, in the absence of contributions, whenever B (e,~c) N k. In the case q N 2 / 3, we have B (~e,~c) b B (e,~c). Thus, both search and no-search equilibria exist for the range of parameter values that satisfy both Eqs. (1) and (2).12 When the interest group can offer contributions, it can induce any decision d by offering contributions c(d) if the contributions are sufficient to compensate the decision-maker for her expected utility loss from d relative to the optimal decision d* that would be chosen in the absence of the contributions. The minimal contribution13 inducing d is   EuDM d 4  EuDM ðd Þ : ð3Þ cð d Þ ¼ a Eu DM(d ) and d* depend on the decision-maker’s belief about h and thus on whether or not she expects the group to search and on the message she receives from the group. The contributions and the benefit of searching are simple to calculate for the case when the decision-maker does not expect the group to search. In this case the decision-maker does not update when she receives no information, hence d* = d B and the contributions necessary to h i Both conditions are satisfied for b a kq ; 12 þ kq for q N 23 . 13 To assure existence and single-valuedness of the best response correspondence we break indifference in the following ways: the DM always accedes to the group’s wishes whenever she is indifferent, and the group contributes more rather than less when it is indifferent. 12

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induce d l are c(d l |~e) = 1 / a. The group chooses to induce d l if this improves its utility, i.e., if 2b  1 / a N 1. The group’s benefit from searching becomes

(

Bð¨e;cÞ ¼

q 2a   1 q b 2

if bN

1þa 2a

ð4Þ

otherwise:

Comparing (4) with (1) shows that B (~e,~c) z B (~e,c), with strict inequality when bN 1þa 2a , i.e., when the group strictly prefers to induce d l . In other words, the incentive for the group to search is reduced when contributions allow the group to obtain its favorite outcome. The contributions necessary to induce the optimal decision and the benefit of searching when search is expected, B (e,c), are given in the proof of Proposition 1. The proposition extends the above observation and shows that B (~c) z B (c) whether or not the DM expects the group to search. Proposition 1. In the influence game with one interest group, the interest group’s incentive to search is always greater when no contributions can be offered than when contributions are available, strictly so when after an unsuccessful search the interest group prefers to induce a decision dˆ p d*. As before, an equilibrium without search exists when contributions are possible when B (~e ,c ) V k, and equilibrium with search exists when B (e ,c ) z k. We generally have B (~e,c) b B (e,c),14 implying that there exist both search and no-search equilibria, as well as mixed strategy equilibria.15 The intuition for the result is analogous to the introductory discussion with observable search activity. Here, with search being unobservable, the decision-maker either learns the true state of the world from the interest group when its search was successful or, if no information is provided, he updates his belief thanks to his knowledge of the group’s equilibrium search strategy. Since the group cannot extract the decision-maker’s benefit when it reveals the true state of the world, the decision-maker over all receives an informational rent whenever the group searches in equilibrium. When contributions are available the decision-maker’s higher information level works against the group as the expected gain caused by the reduction in contributions when finding favorable information is more than outweighed by the increased cost of contributions when no favorable information can be delivered. The result that the group’s incentive to search is smaller when contributions are feasible implies that the range of circumstances in which the group searches in equilibrium is more restrictive with contributions than when no contributions are allowed. In other words, when contributions are allowed, the group is bless likelyQ to search for information, as specified in the following Corollary. Corollary 1. Suppose after an unsuccessful search the interest group prefers to induce a decision dˆ p d* The possibility of offering contributions (i) strictly reduces the range of parameters for which a rational expectation equilibrium exists in which the interest group

14 B (~e,c) = B (e,c) obtains only for case (i) in Eq. (13) and b V 1þa 2a , as well as for a null-set in the parameter space. We assume that bb Q holds balmostQ w.l.o.g. 15 The mixed strategy equilibria are characterized in Lemma 1, given in Appendix B.

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searches and (ii) strictly increases the range of parameters for which there exists a rational expectations equilibrium where the interest group does not search. Corollary 1 presumes that after an unsuccessful search the group would still want to induce its preferred outcome d l (i.e., dˆ p d*). This condition depends on the relative strengths of the two means of influence. Consider the following: a more informative search technology ( q large) implies that while the group is more likely to obtain its preferred outcome without contributions, search also causes a greater information externality to the decision-maker in case of an unsuccessful search, causing the cost of contributions to increase for this event. The condition presumes that after an unsuccessful search the group would still want to induce the outcome d l , which requires that either the group cares enough about d l (as expressed by parameter b) or that contributions are bcheapQ enough (as expressed by a) to render influence via contributions worthwhile. Provided this condition is met, the group is strictly less likely to provide information in equilibrium when contributions are allowed than when contributions are not permitted.16 The upshot of Proposition 1 and Corollary 1 is that an interest group may lack the incentives to provide information if it has the ability to induce its favored outcome via contributions. The reason is not that contributions provide a cheaper means for obtaining the preferred outcome— although they may—(i.e., a pure substitution effect); rather, the presence of contributions reduces the benefit to the group of providing information. As a result, a group that is willing to incur direct search cost in order to influence and convince the decision-maker when contributions are not allowed may no longer have this incentive when contributions are available. We have shown that when contributions are allowed, the indirect costs caused by the decision-maker’s belief updating when the information collection is unsuccessful always dominates the gain from inducing the lobby’s favored outcome through successful information collection. 4. Competition among lobby groups A standard result in the information economics literature holds that competition among information providers increases the incentive for each side to offer information and thus to render the decision-maker better informed.17 In this section we extend our model of lobbying to the case of multiple, competing interest groups and first show how this bconventional wisdomQ holds as long as groups are not allowed to offer contributions. We then show that when contributions are permitted, the standard result no longer holds. The intuition for the standard result is that searching by a second, competing lobby group with opposing interest mitigates the first group’s indirect search cost, thereby pro-viding the first group with a greater incentive to search, and vice versa. The following shows the intuition for this: Consider two groups, L and R, who prefer outcomes d l and d r, respectively. Suppose R’s search is successful and reports the true state h = h r ; then L’s decision whether or not to search is irrelevant, as the DM is already informed. Thus, L incurs an indirect (i.e., updating) cost for an unsuccessful search only conditional on the other group’s search being unsuccessful. At the same time the benefit of L’s search (i.e., the likelihood to find h = h l ) is independent of R’s search.

16

In fact, when contributions are allowed the group searches in equilibrium only if the search costs are too low so that the group cannot commit not to search. If the group could commit to reveal its search activity, then under the premise of Corollary 1 the group would never search when contributions are allowed (see Bennedsen and Feldmann, 1998). 17 See, e.g., Milgrom and Roberts (1986), Austen-Smith and Wright (1992), Dewatripont and Tirole (1999).

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Hence the net effect of R’s search is to mitigate L’s information externality and to increase the incentive for L to search. The twist occurs when interest groups can also induce decisions via monetary contributions. As we observed in the last section, contributions alter the benefits and costs of information search: the benefit is the amount of contribution saved when search produces favorable evidence, while the costs are the additional contributions necessary when search did not provide favorable information. Competition alters these benefits and costs as the contributions necessary to induce any outcome depend on the success or failure of either of the groups’ searches: a group gains directly in form of saved contributions from the information externality generated by the other group’s search activity. Conversely, and in contrast to the situation without contributions above, with competition present and contribution feasible the indirect search cost accrues both when the other group’s search was successful and when it was not. In the result in this section we show that with contributions feasible, competition raises or lowers the incentives to engage in information provision depending on whether the opposing group is endowed with an equal, inferior, or superior information technology. 4.1. The model with competing lobby groups In this game two lobby groups with conflicting (and state independent) interests simultaneously try to influence the decision-maker in a model of common agency. As before, we first allow the groups to only use information to affect the decision-maker; then we allow contributions to be offered. The models are identical in all other aspects to the ones presented in the previous sections: each interest group may withhold information it learned but may not fabricate information. The decision-maker cannot monitor the interest groups’ search activity but has correct equilibrium beliefs about the group’s behavior. We denote the lobby groups L and R. L prefers the outcome d l and R prefers d r. To rule out the case where one group simply outbids the other, assume that both groups’ preference for their preferred outcome is the same, 2b and that they face the same search cost k. However, the groups’ search technology may be differently informative: the signals r i are independent, and each reveals the true state h with probability q i , for i = L, R. Each group’s contributions are equally valuable to the decision-maker (ac i ); we address possible differences in the ability to raise or use contributions in the Discussion of the results. 4.2. The decision-maker’s choice If group i searches, it benefits from revealing the state that favors its preferred outcome; thus, group i’s message strategy is m i = r i if r i = h i and m i = t whenever it is uninformed or knows that h p h i . If both groups search, each follows this message strategy. No informative message is sent only if neither group’s search is successful, which occurs with probability PrfmL ¼ mR ¼ tg ¼ 1  q2L  q2R . Thus, the decision-maker’s updated beliefs in this event are

and

pðhl jmL ¼ mR ¼ tÞ ¼

1  qL 2  qL  qR

pðhr jmL ¼ mR ¼ tÞ ¼

1  qR : 2  qL  qR

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Given these beliefs the decision-maker’s best response is18 8 if qL V 3qR  2 ðRegion 1Þ dl > > > < 2 þ qR  ðRegion 2Þ if 3qR  2 V qL V d 4 tÞud4ðmL ¼ mR ¼ tÞ ¼ dB 3 > > 2 þ qR > : dr : ðRegion 3Þ if qL z 3

641

ð5Þ

Fig. 2 illustrates Eq. (5) and shows how the optimal choice depends on the strength of each lobby group’s searching ability measured by q i : the decision-maker’s best response divides the q L –q R -space into three regions. The optimal choice is d B when the group’s search technology is similarly informative, and bswitchesQ to the preferred outcome of the group with the weaker searching technology when there is a significant difference in the information content of the two group’s search activity. 4.3. The case of no contributions We first characterize the informational equilibria when no contributions are possible. The results replicate the bconventional wisdomQ of information economics, which holds that competition among information providers increases information provision. To rule out trivial search equilibria we always assume positive search cost, k N 0. There are two types of (pure strategy) perfect Bayesian equilibria with search: In the first, asymmetric equilibrium, only one group searches, and in the second, symmetric equilibrium, both groups search. Since the groups have different search technologies q i , we cannot restrict our attention to symmetric equilibria only. We characterize all three types of equilibria where one, two, or no group searches. Asymmetric search equilibria without contributions. Assume group i is expected to search. Since i is the only group searching, it has the same incentive to search as derived in (2) for a single group, i.e., 8   2 > < qi b  12 if qi V i 3 ð6Þ B ðe;¨e;¨cÞ ¼ 2; > : qi b if qi N 3 where we denote by B i group i’s benefit from searching. The subscript indicates whether the group itself and its opponent are expected to search and whether contributions are allowed; in this case i is expected to search, j is not, and no contributions are permitted: (e,~e,~c). The benefit from searching for group j differs from that for a single group whenever group i’s unsuccessful search induces d*(t ) = d j , i.e., if q i N 2 / 3. If this happens, the group has no incentive to search as it cannot improve the outcome and rather free rides on the information externality generated by group i. Its benefit is thus: (   1 2 qj b  if qi V j 2 3: ð7Þ B ð¨e;e;¨cÞ ¼ 2 0 if qi N 3 18

This follows from u DM (d B) = 1, u DM (d l | m) = p(h r )(4), u DM(d r | m) = p(h l )(4).

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qR 1 d* = d 1 2/3 d* = do d* = dr

2

3

qL 2/3

1

Fig. 2. Decision-maker’s best response d*(t ). j Thus, an equilibrium in which i searches while j one does not, exists if B(~e,e,~c) Vk V This interval for k is non-empty whenever q j V q i or q i z 2 / 3. In words, the group that searches in an asymmetric search equilibrium either has the more informative search technology ( q i z q j ), or its own search technology is sufficiently informative ( q i z 2 / 3).

B i(e,~e,~c) .

Symmetric search equilibria without contributions. Consider now a symmetric equilibrium in which both lobby groups search. The lobby group’s benefit from searching depends on the DM’s decision d*(t ):

Biðe;e;¨cÞ

8   1 > > < qi b  2 ¼ > q b i > : 0

if d4ðtÞ ¼ dB if d4ðtÞ ¼ dj if d4ðtÞ ¼ di

:

ð8Þ

A symmetric search equilibrium exists if mini=L,R B i(e,e,~c) z k. Inspection of (8) shows that this is only possible for d*(t ) = d B. The reason for this is that in Region 1 of Fig. 2, L cannot gain anything by searching: even if its message is m L = t , the decision-maker chooses d l ; thus, if searching is at all costly, L will never search if ( q L , q R ) is in Region 1. Likewise, R does not benefit from searching in Region 3. Thus, a symmetric search equilibrium can only exist in Region 2, for parameters s.t. b z 1 / 2 + maxi k / q i . No search equilibria without contributions. In this case, as in (1), B i(~e,~e,~c) = q i (b  1 / 2). An equilibrium of the game with competing interest groups in which neither group searches exists if maxi=L,R B i(~e,~e,~c) V k, or b V 1 / 2 + mini k / q i . In order to determine whether competition among interest groups increases the amount of information provided to the decision-maker, we now compare the incentives for interest groups to search in the game with one or two interest groups, respectively. Letting q L = q, we observe by comparing Eqs. (1) and (2) with Eqs. (7) and (8) that B L(d ,d ,~c) V B (d ,~c). That

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is, L has a weakly lower incentive to search when there is a competing interest group. The incentive is strictly lower, however, only when R searches in equilibrium. We thus obtain the following result: Proposition 2. Consider an influence game without contributions. If q = q L such that a search equilibrium exists in the game with only one interest group, then there also exists an equilibrium in the game with competing interest groups in which L, R, or both search. Proposition 2 states that if there is a search equilibrium in the game with only one interest group, then there is an equilibrium in which at least one group searches in the game in which a second group provides competition. It is important to note, however, that it may be the case that the group with the less informative search technology searches, provided that the search technology creates a large enough information externality ( q i N 2 / 3) to sustain the asymmetric search equilibrium. Thus, it need not be the case that more information is generated by the presence of the second interest group. For a subset of the parameter space both groups have an incentive to search and provide the DM with more information in equilibrium than with one group only. The condition for both groups to search is that b z 1 / 2 + maxi k / q i and that search technologies ( q L , q R ) are in Region 2 (cf. Fig. 2). The result echoes Austen-Smith and Wright (1992) and Dewatripont and Tirole (1999) in that competition among lobbyists may avail the decision-maker with more information. It is interesting to observe that in the case where unsuccessful search leads the DM to choose the opposite outcome ( q i N 2 / 3), the group that does not search is better off. In a symmetric search equilibrium, however, the group whose search technology is more informative is better off than its opponent as it is more likely to obtain its preferred outcome while the information externality by the other group assures that the decision-maker does not choose the opposite outcomes when the search fails. 4.4. Allowing contributions We now introduce contributions into the game with two interest groups. We model the part of the game in which the groups simultaneously offer contributions to the decisionmaker contingent on her decision as a common agency game (Bernheim and Whinston, 1986). In our discrete choice space, complete contribution schedules for L and R are given by the triples ci = (cil, c Bi , c ri), i = L, R, where i promises to pay the contribution c hi if decision d h is chosen. The common agency framework provides that the following properties characterize the equilibrium choice and contribution schedules:19 1. The equilibrium decision dˆ maximizes joint welfare, where the lobby groups’ welfare is discounted by a due to the limited transfer technology between lobby group and decisionmaker.

19 See Lemma 2 in Bernheim and Whinston, 1986. We adopt their bglobal truthfulnessQ refinement to rule out inefficient equilibria, and we adapt the framework to the discrete choice space and the partially transferable utility of this model. (See also Dixit et al., 1997).

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Accordingly, let W(d) = u DM(d) + au L (d) + au R (d) be the joint welfare. If dˆ is the decisionmaker’s equilibrium choice, then dˆ maximizes W(d). 2. Contribution schedules are truthful: whenever a group offers positive contributions for two decisions, the different offers reflect exactly the group’s compensating variation (or difference in willingness to pay) between the two decisions. i.e.,   ui dg  cig ¼ ui ðdh Þ  cih ; whenever cig ; cih N0 ð g; hafl; o; rgÞ: 3. Each lobby group contributes zero to the policy choice that maximizes the joint welfare of the decision-maker and the other lobby group, and lowers its payments uniformly until the decision-maker is indifferent between that choice and dˆ , if this is possible. Using these facts successively to obtain the contribution strategies for the contributions subgame, we solve the full game in which the lobby groups can search and offer contributions.20 We first characterize the symmetric search equilibria. 4.4.1. Symmetric search equilibria with contributions Suppose both groups are expected to search. Without loss of generality we assume q R N q L . To limit the number of cases we have to consider we make the following assumptions: A1. The decision after unsuccessful searches is contested, i.e., if only one group were to offer contributions after m i = t , then this group induces its preferred outcome.21 A2. If both searches fail, then the decision induced in equilibrium is dˆ (t ) = d l .22 The two assumptions apply when both groups send non-informative messages. Assumption A1 assures that preferences are strong enough (or the transfer technology sufficiently effective) for one group to induce its preferred outcome if the other group fails to make contributions. Assumption A2 states that preferences are strong enough (or the transfer technology sufficiently effective) for L to capitalize on its ex post informational advantage. If either group searches successfully, its preferred outcome becomes the efficient choice, as the decision-maker now also prefers this outcome. Suppose R finds h r ; then L’s truthful contribution schedule is c L = (2b, 1, 0). With this, the decision-maker needs no further inducement to choose d r unless a(2b) N 4, in which case R will have to offset L’s contributions.

20 The following benchmark case without search illustrates the nature of the equilibrium strategies for the contribution subgame. Suppose w.l.o.g. p z 1 / 2, where p is the decision-maker’s posterior belief for h l . Then (by (1)), dˆ = d B or dˆ = d l . Specifically, dˆ = d l if b z 1 + 3  4p / 2a, d B otherwise. Suppose dˆ = d l . Then R offers contribution c RB = 0, as dˆl would be chosen without R’s contributions (following (3)), and, further, c RB = 1, c Rr = 2b (by (2)). Along this contribution schedule R’s net utility remains constant: u R (d h )  c hR = 0. L’s contributions are as follows. Define dˆ i be the choice induced by i’s contributions alone, i.e., the choice induced if j p i were absent. Consider the case dˆ R = d r. [dˆ R = d r if p(4) + a(2b) N 1 + a, or b N 1 / 2 +( 4p  1 / 2a).] By (3), L will not contribute for the outcome dˆ R , c Lr = 0, and offers just enough contributions so that dˆ is chosen: If dˆ = d l this requires Þ (1  p)(4) + acLl = p(4) + a(2b), or cLl ¼ 2b  4ð 2p1 , or if dˆ = d B, then cLB ¼ 2b  4p1 a a . Notice that L is advantaged by the decision-maker’s belief and therefore receives a positive net utility in equilibrium, while R’s net utility in equilibrium is zero. qi qj 21 1 Formally, dˆ R (t ) = d r and dˆ L (t ) = d l . Using p = p(h l | t ) this implies bzbi u 12 þ 2a þ a 2q . Since q R N q L Z ð i qj Þ R L R b N b , b is binding (i.e., necessary and sufficient) for A1 to hold. 22 ˆ 1 L 3qR d ( t ) = d l if the lobby groups care intensely enough, specifically, if bzbˆ u1 þ 2a2þq ð2qL qR Þ ¼ 1 þ 2a  qR qL R R : bˆ ab , depending on the parameters. Thus, A1 and A2 together require b z max{bˆ, b }.

að2qL qR Þ

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Thus, after potential contributions R’s brentQ (net utility) in this case is V R (d r, c rR | h r) = min {2b, 4 / a}. A similar rent is obtained for L if L’s search is successful in producing h l . If neither group searches successfully, the decision-maker updates her beliefs to 1qL pðhl jtÞ ¼ 2q . Given A2, d l becomes the equilibrium choice dˆ (t ). R offers its truthful L qR contribution schedule c R = (0, 1, 2b), which is insufficient to avert the final choice d l , while L ðqR qL Þ (invoking A1) offers contributions cLl ¼ 2b  að42q , which induce dˆ = d l at least cost. After L qR Þ these contributions L’s net utility, or information rent, is   4ð qR  qL Þ : VL dl ; cLl jt ¼ 2b  cLl ¼ að 2  qL  qR Þ L’s information rent is increasing in the difference of the q i ’s, reflecting the fact that L benefits from R’s information externality and suffers from his own. As a result, the larger the difference in effectiveness of the information technology between the groups, the greater the net utility for the group with the less informative technology in the contribution game, whenever the searches are unsuccessful. At the same time, of course, R’s search is more likely to be successful the better its search technology. From an ex ante perspective, the groups’ expected utilities in an equilibrium in which both groups search, are: EV R ¼ qR minfb; 2=ag and

EV L ¼ qL minfb; 2=ag þ ð2=aÞðqR  qL Þ:

It follows that EVL z EVR , and L, the group with the (strictly) less informative search technology, is strictly better off iff b b 2 / a: Provided the groups do not care too much about their preferred alternative, the group with the inferior search technology obtains an ex ante rent. A symmetric search equilibrium exists if the incentive to search is sufficiently large for each group. As before, the incentive is given by the payoff the group can expect to gain from searching compared to not searching when the group is expected to search. This yields: BRðe;e;cÞ ¼ qR minfb; 2=ag and

BLðe;e;cÞ ¼ qL minfb; 2=ag  qL

2ð qR  qL Þ : að 2  qL  qR Þ

ð9Þ

Since q L b q R , we have B L(e,e,c) b B R(e,e,c) and a symmetric search equilibrium exists if and only if B L(e,e,c) z k. We can now examine whether the incentive to search is greater when contributions are allowed or not allowed. Define 8 2a 2 > < if bV 4 þ a a ð10Þ k ¼ 8 þ 2a  4ab > : otherwise 8 þ a  2ab and let  K¼

ðqL ; qR Þa½0; 12 j 1  k V

1  qR 1 V : 1  qL 1  k

K is a compact cone in [0, 1]2 with vertex at (1,1).

ð11Þ

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Proposition 3. Consider an influence game with competing interest groups and assume A1 and A2. Suppose both groups are expected to search; then for the group with the less informative search technology the incentive to search is smaller in the game with contributions than in the game without contributions, whenever the search technologies are sufficiently different. Specifically, n o n o min BLðe;e;cÞ ; BRðe;e;cÞ b min BLðe;e;¨cÞ ; BRðe;e;¨cÞ

iff

ðqL ; qR ÞgK:

Proposition 3 states that in any symmetric search equilibrium the incentive for the group with the weakest information technology (in our case with q L b q R , group L) is weaker when contributions are allowed than without, unless q L and q R are similar in magnitude so that they fall into a cone-shaped area along the main diagonal of the unit square. Inside the cone the incentive for L to search is greater with contributions than without. Fig. 3 illustrates the situation. The cone is narrower the larger is b and the smaller is a, and K vanishes as k V 0 f b z 2 / a + 1 / 2. Since the incentive to search is weaker with contributions when the search parameters lie outside the cone-shaped area, allowing contributions strictly reduces the set of parameters for which a symmetric search equilibrium exists if the search technologies lie outside the cone, and strictly increases the set when the search parameters lie inside the cone. We interpret the result as follows: if the groups’ information technologies are similarly informative, then allowing contributions intensifies the competition among the groups in terms of both information and contributions. However, when one group has a (sufficiently) better search technology than the other, then the information externality allows the other group to commit not to search and to induce its preferred outcome with contributions instead, while such commitment is impossible when contributions are not allowed. In this case, the availability of contributions reduces the incentive for one group to search, and the decision-maker obtains less information in equilibrium than without contributions.

qR 1


,e, ~c

)

,c


Λ

B(

B

(e

,e,

c)

>

(e,e

B

(e

B (e,e

)

,~c

(e,e

,~c)

2/3

qL 2/3

1

Fig. 3. Area where symmetric search equilibria exist. In the shaded area along the main diagonal the incentive to search is greater with contributions, otherwise it is weaker.

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Why does competition (in the presence of contributions) increase the incentive to search when search technologies are similar but reduce the incentive when the technologies are different? We can distinguish two opposing effects that are introduced with competition. First, competition mitigates the information externality. When both groups search, L’s unsuccessful search causes the negative information externality (i.e., the DM’s update against L) only when group R’s search is unsuccessful; for when R’s search is successful, then R conveys the true state of the world to the DM, and L’s search result is irrelevant. Thus, the presence and search of the opposing interest group mitigates the negative effect of L’s search activity and thus increases L’s incentive to search. The same holds for R. This mitigation of the information externality, incidentally, is responsible for why in the absence of contributions competition unambiguously increases the groups’ incentive to search. With contributions, a second effect is present. Consider the case where L and R have dissimilar search technologies and L’s technology is less informative. As observed in the previous paragraph, L’s search only matters when R’s search is unsuccessful. In this case, thanks to its less informative search technology, L receives a brentQ when its own search is unsuccessful, as the DM’s updated beliefs are more favorable to L than they were ex ante. This means that L can induce its preferred outcome at lower contributions cost following R’s (unsuccessful) search. The amount of contributions L saves with a successful search is thus smaller than when R is absent. Thus, R’s presence reduces L’s incentive to search, allowing L to directly benefit from, and bfree-rideQ on, R’s information externality. The free-riding effect becomes more important and starts to dominate the mitigation effect the more dissimilar the two search technologies are. This causes the incentive to search for the less informed group to decline monotonically as the search technology of its opponent gets more informative, as represented in Fig. 3. For simplicity the analysis has so far assumed that the two groups’ ability to use—or raise— contributions is identical. We can relax this assumption by allowing the groups to have different influence parameters, a i . We discuss this case informally. The interesting question for our analysis is how a difference in the ability to use contributions interacts with differences in information technology. We can provide a clear intuition for some cases. If the groups’ influence technologies differ but Assumptions A1 and A2 are satisfied for each, then the main results remains unchanged as both groups are willing to use contributions ex-post independently of the outcome of the information searches. In such circumstances the group that benefits from the information externality (with sufficiently low q) will refrain from searching for information whenever contributions are allowed, as it prefers to save contributions by exploiting the information externality generated by the other group. Another clear case is when the ability to use contributions and the search technology correlate negatively: Suppose group R has superior information technology (larger qR ) and inferior contribution technology (lower aR ). In this case the competition between interest group clearly lowers group L’s incentive to engage in information provision because avoiding searching makes the group both benefit from R’s large information externality and enable it to use its superior contribution technology. A more ambiguous case arises when R enjoys an advantage in both technologies to the extent that group L’s contribution technology is so weak that it will not implement its favorite outcome when group R does not provide information. In this case group L’s weakness in influencing through contributions implies that it cannot fully exploit R’s information externality. Hence, this limits the free riding effect of competition among the groups and will thus not necessarily

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decrease L’s incentive to search. In the extreme case, where group L cannot use contributions (a L approaches zero) we end up in the standard result where competition increases L’s incentive to provide information. 4.4.2. Asymmetric search equilibria with contributions When one group’s incentive to search is less than its direct search cost while the other’s exceeds it, an asymmetric equilibrium obtains. To complete our analysis we focus on the question whether the availability of contributions decreases the incentive to engage in information provision. The assumptions that limit the number of possible equilibrium behaviors, A1 and A2, need to be slightly modified to reflect the groups’ respective roles:23 A1V: if L makes no contributions after R does not provide favorable information, R induces its preferred outcome; and A2V: L’s informational advantage after R has not provided favorable information is sufficient for L to induce its preferred outcome.24 The formal analysis is relegated to the Appendix. Due to the possibility of multiple equilibria as we move between the games without and with contributions, stating the effect of contributions on the incentive for the groups to search is somewhat cumbersome. Given this, the following proposition provides sufficient conditions for when contributions (weakly) reduce the overall incentive for groups to search for information for parameters in which the game with contributions has an asymmetric search equilibrium. Proposition 4. Consider an influence game with competing interest groups and assume A1V and A2. Suppose that in the game with contributions an asymmetric search equilibrium exists in which R searches. 1. If q R N 2 / 3, then in the game without contributions an asymmetric search equilibrium also exists and the incentive for R to search is (weakly) lower in the game with contributions. 2. If q R N 2 / 3 and b z 1 / 2 + 2 / a, then in the game without contributions an equilibrium exists in which at least R searches. Furthermore, if q L V k, then the asymmetric equilibrium in which R searches exists. The proposition states that if q R N 2 / 3 or b z 1 / 2 + 2 / a, the game without contributions has at least as much search as the game with contributions. In part 1 of the proposition the same type of asymmetric equilibria exists in the game without contributions as with contributions, and the incentive for R to engage in information provision is weakly reduced. In part 2 the same asymmetric equilibrium or a symmetric search equilibrium exists in the game without contributions whenever the game with contributions has an asymmetric equilibrium; switching from an asymmetric to a symmetric search equilibrium of course increases the amount of information generated, given the groups’ search technologies q L and q R . The only case when the incentive to search may increase occurs when b z 1 / 2 + 2 / a. Recall that A1V and A2 provide lower bounds on b, so that this area of the parameter space may be small or even empty, depending on the remaining parameters. We thus conclude that, compared to an asymmetric equilibrium of the game with contributions, the game without contributions balmost alwaysQ induces at least as much search in equilibrium. 23

We assume w.l.o.g. that R is the group that searches. A1V Z A1 and A2 Z A2V. Hence this assumption ensures that dˆ R (t ) = d r and dˆ (t ) = d l in both the symmetric and the asymmetric search equilibria of the game with contributions. 24

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Over all, while the game with competing interest groups is harder to analyze, we showed that allowing contributions generally reduces the incentive to provide information when the groups have sufficiently different search technologies, while the incentive to search is increased when the search technologies are similar. In the latter case, the groups compete both along the information and the contribution dimension-making the DM both more informed and, in addition, leaving her a rent in the common agency contribution game. In this case the information stage of the game does not affect much the second contribution stage of the game when both searches are unsuccessful. By contrast, when the search technologies are sufficiently different, the information stage very much affects the contribution stage, as the DM’s posterior changes in favor of the group with the less informative technology when both searches are unsuccessful. This changes the relative benefits the two groups obtain from searching: the group with the lesser search technology has less to gain from its search in the second stage. This reduces its incentive to search—not because its technology is less informative, but because its outside option (i.e., not searching) is better. As a result the DM will generally receive less information in equilibrium in the presence of contributions. A particularly strong effect obtains in the case where in the game with contributions the unique equilibrium is asymmetric with only one group searching while the corresponding game without contributions would have both groups search. 5. Discussion Interest groups often have privileged access to information and are thus in the position to provide a political decision-maker with knowledge that is crucial for making the correct decision. At the same time, interest groups arguably have the ability to influence the decision maker’s choice via financial incentives in form of campaign contributions. The models we presented in this paper show under what circumstances interest groups have the incentive to collect and provide such information, to offer contributions, or to do both. When equipped with the ability to make contributions, a group weights the direct and indirect costs of searching against the cost of inducing a favorable outcome via contributions to the decision-maker. We point out that an unsuccessful search partially informs the decision-maker and thereby raises the cost of inducing the group’s preferred outcome ex post. The information externality, or indirect search cost, is thus reflected in higher contributions necessary to induce a desired outcome. The ability to offer contributions thus conflicts with the group’s willingness to search and to provide useful information to the policy maker. Proposition 1, which characterizes the rational expectations equilibria of this game, shows that a group’s incentive to search for information is reduced when they are able to use contributions to influence political decision making. Thus, the result states that rather than being strategically independent of (or orthogonal to) one another, two instruments are substitutes. Our second contribution in this paper is to analyze how the choice between information and contribution is affected by the presence of competition among lobby groups. A standard result in the information economics literature holds that search activity and information provision increases when lobbyists compete for influence. We show that this result holds as long as interest groups do not have the ability to make contributions. When monetary incentives are allowed, the presence of a competing information provider makes the group that does not provide information or that has the weaker information technology better off. The information structure in this paper is one of hard information: information can be withheld but not directly manipulated by an interest group. These two attributes of

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information—ability to withhold and non-manipulability—can in principle vary independently and the best modeling choice likely depends on the context. In this paper we have analyzed but one of the four possible combinations.25 Proposition 1 carries over to the case where the interest group cannot withhold an unfavorable signal. The intuition is the same as for the case analyzed: By searching, an interest group without the ability to use contributions takes a gamble between a preferred and a less preferred outcome than the DM’s ex ante choice (from the group’s ex ante perspective, searching does not change the expected outcome, due to the law of iterated expectation). The group may well take this gamble if it cares sufficiently about the preferred outcome relative to the loss from the worst possible outcome, as it gains more from a successful search than it looses from finding evidence that works against its interests (in this case it is costless to have an uninformative search result, as the DM observes this too). The situation, however, is different for a group that can induce its preferred outcome with contributions. Searching (with or without the ability to withhold adverse results) makes the DM more informed; since the group cannot extract the entire information rent, a more informed DM is on average more expensive to bribe, thus making it unattractive for the group to provide the information for most parameter constellations.26 Note that in this case the decision-maker’s expectation about the interest group’s search activity is irrelevant, as all information is revealed. The opposite case in which information can be fully manipulated turns the information game into a bcheap-talkQ game. The complexity of analysis in bcheap-talkQ games have generally limited that amount of robust institutional results in the literature (see, e.g., survey by Farrell and Rabin, 1996). It is a challenging future research question to analyze to what extent our results are robust to such an informational environment. The analysis shows the relationship between two major interest group activities, campaign financing and information provision to political decision-makers, which the literature has largely treated as separate issues. Our results show that the two activities are strategic substitutes, as information inherently raises the price of contributions. A group that can commit not to search will do so and obtains its preferred outcome at lower cost via contributions. In the case of competing groups, the group with the less informative search technology is advantaged, both in the ex post contribution subgame and from an ex ante perspective. Thus, to the extent that interest groups might choose the search technologies available to them, our results suggest that a campaign finance regime that allows contributions discourages groups from obtaining effective search technologies. Acknowledgement We would like to thank Daniel Diermeier, Skip Lupia, Eric Maskin, Torsten Persson, Ken Shepsle, and Jim Snyder for valuable comments. Financial support from the Danish Social Science Research Council and CEBR (www.cebr.dk) is gratefully acknowledged. 25

One might argue that there exists a trade-off for the group between the inability to manipulate information (which lends credibility to the group’s message) and the ability to withhold undesirable outcomes: e.g., information generated by an independent research institute will be less manipulable but hard to conceal, while in-house research is easy to conceal but is also easily manipulated. We thank a referee for this suggestion. 26 Dahm and Porteiro (2004), analyzing this case of bpublicQ search with a continuous state space, find that for a subset of the parameter space the group combines search with contributions. This follows from the fact that while information creates a more informed (and hence more expensive) DM, common information also allows the group to induce the jointly optimal decision. It is possible that this gain dominates the cost of a more informed DM.

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Appendix A Proof of Proposition 1. The incentives to search derived in the text are   1 Bð¨e;¨cÞ ¼ q b  ; 2 8   1 2 < q b if qV ; Bðe;¨cÞ ¼ 2 3 : qb otherwise;

Bð¨e;cÞ

8 q > <   ¼ 2a 1 > :q b  2

if bN

1þa 2a

otherwise;

and it is obvious that B (~e,~c) z B (~e,c). It remains derive the incentive to search with contributions when search is expected, B (e,c), and to verify that B (e,c) V B (e,~c). In order to do so, we first identify the equilibrium contribution schedules and induced outcome with search. Assume contributions are allowed and that search is expected. After receiving m = t the DM optimally chooses d* = d B if q V 2 / 3 and d* = d r otherwise. Applying (3), the minimal contributions necessary to induce d l given the DM’s beliefs, are 8 2þq 2 > > if qV < að 2  qÞ 3 cucðdl jm ¼ tÞ ¼ 4q > > otherwise; : að 2  qÞ while the contributions to induce d B when q N 2 / 3 are   3q  2 : cB uc dB jm ¼ t ¼ að 2  qÞ Let dˆ be the decision the group optimally induces with contributions after an unsuccessful search (m = t ). If d* = d r (i.e., q N 2 / 3), the group prefers to induce d B rather than accept d r iff 1  c B z 0, which is the case iff azaVu 3q2 2q . Furthermore, the group prefers to induce d l after m = t iff 2b  c l z 1 when q V 2 / 3 and 2b–c l z max{1 c B, 0} when q N 2 / 3, which is equivalent to 8 1 2þq 2 > > if qV or abaV < þ 2 2að2  qÞ 3 ð12Þ b z bVu 2q 2 > > if qN and azaV: : að 2  q Þ 3 In other words, as does the size of the contributions, the outcome the group induces depends on three factors: how informative the search is ( q), how much the group cares about the outcome (b), and how effective contributions are (a). The decision-maker’s induced choices after an unsuccessful search are as follows: dˆ = d l if b z bV; dˆ = d B if ( q V 2 / 3 and b b bV) or ( q N 2 / 3, b b bV and a z aV); dˆ = d r if ( q N 2 / 3 and b b bV and a b aV). This means that dˆ p d* and contributions are strictly positive [c(dˆ | m = t) N 0] iff b N bV or ( q N 2 / 3 and a N aV). With dˆ and c(d ) thus established, the benefit of searching can now easily be calculated. We present the case where q V 2 / 3 and dˆ = d l (case (iv) below); the other cases follow analogously.

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Assume b z bV. The benefit of searching is that in the event of a successful search the group obtains d l bfor free,Q while in all other events the group induces d l by offering c l . Thus, in this case, the benefit of searching (when search is expected and contributions feasible) is Bðe;cÞ ¼ q2 að2þq 2qÞ . Proceeding similarly for the remaining cases we obtain:

Bðe;cÞ

 8  1 > > q b  > > 2 > > > > > > qb > > >   > < 1 aV ¼ q b þ >  2 2a > > > q 2þq > > > > > > 2a  2  q  > > q 4q > > : 2a 2  q

2 3 2 bbbV and qN and abaV 3 2 bbbV and qN and azaV 3 2 bzbV and qV 3 2 bzbV and qN : 3

if bbbV and qV

ðiÞ

if

ðiiÞ

if if if

ðiiiÞ

ð13Þ

ðivÞ ðvÞ

Finally, we verify that B (e,~c) z B (e,c), strictly so when contributions are positive: For (i) and (ii), B (e,~c) = B (e,c) and c(d ) = 0. In case (iii) we have B (e,c) V qb since a z aV. In (iv) and (v) the inequality holds due to the condition on b given in (12). In (iii)–(v) the benefit is strictly higher whenever the a or b, respectively, strictly exceed their lower-bound conditions, which is necessary and sufficient for c(dˆ | m = t ) N 0. 5 Proof of Corollary 1. Let X ¼ R3þþ  ð0; 1Þ be the space of the parameters (a, b, k, q) in the influence game. (i) Let S v be the set of parameters for which a REE with search exists, for v=c, ~c: S v = {(a, b, k, q) a X | B(e, v) z k}. Then B (e,~c) z B (e,c) (strict for some a, b, q) Z S c o S ~c . (ii) Let N v be the set of parameters for which a REE without search exists, for v = c, ~c: N v = {(a, b, k, q) a X | B (~e,v) V k}. Then B (~e,~c) z B (~e,c) (strict for some a, b, q) Z N ~c o N c . 5 Proof of Proposition 2. Assume q L = q such that a search equilibrium exists in the game with only one interest group, i.e., B (e,~c) N k. In the game with group competition, B L(e,~e,~c) = B (e,~c) by Eq. (2) and (6). Thus, L searches provided R does not, which requires B R(~e,e,~c) V k. (By Eq. (7) this implies q R b q L or q L z 2 / 3.) Otherwise, R must be searching. Thus, at least one group searches in equilibrium. Suppose R searches; then an asymmetric search equilibrium exists where L does not search, if B L(~e,e,~c) b k (requiring q L b q R or q R N 2 / 3); a symmetric search equilibrium exists where L also searches if mini q i (b  1 / 2) z k and ( q L , q R ) a Region 2. 5 Proof of Proposition 3. In the text we derived (under Assumptions A1 and A2):   1 Biðe;e;¨cÞ ¼ qi b  whenever d4ðtÞ ¼ dB ; i ¼ L; R 2

ð8Þ

BRðe;e;cÞ ¼ qR minfb; 2=ag and BLðe;e;cÞ ¼ qL minfb; 2=ag  qL

2ð qR  qL Þ : að 2  qL  qR Þ

ð9Þ

M. Bennedsen, S.E. Feldmann / Journal of Public Economics 90 (2006) 631–656

Suppose q L V q R . Then B L(e,e,c) V B R(e,e,c) and B L(e,e,~c) V B R(e,e,~c). Thus consider   2ðqR  qL Þ 1 L L N qL b  f qL minfb; 2=ag  qL Bðe;e;cÞ N Bðe;e;¨cÞ að 2  qL  qR Þ 2  1 2ð qR  qL Þ 1  N /umax b  ; 0 2 að2  qL  qR Þ 2 Solving (16) for q R and letting k ¼

2að12/Þ 4það12/Þ ,

653

f ð16Þ

we obtain

qR b k þ ð1  kÞqL :

ð17Þ

Substituting / into k we get the formula for k given in Eq. (10), above the proposition. Suppose now that q L N q R . Then q L b k + (1  k)q R . Hence, together with (17) we obtain Eq. (11). 5 Proof of Proposition 4. Proof. Consider that R is the group that searches in the asymmetric 1 equilibrium. If R’s search is unsuccessful, we have pðhl jtÞ ¼ 2q . After m = t , the assumptions R R 27 ˆ ˆ imply: A1V f d (t ) = d r, and A2V f d (t) = d l . R’s incentive schedule after an uncessful search is c R = (0, 1, 2b) and its utility V R (dˆ | c R ,t) = 0. L offers the decision-maker her reservation utility for d l , such that 1qR 4qR L 1 L 2b  að2q . Thus, in the event of m R = t, L 2qR ð  4Þ þ acl ¼ 2qR ð  4Þ þ  a2b; or cl ¼ RÞ 4qR L ˆ receives an information rent VL d jc ; t ¼ að2qR Þ . If R’s search is successful, its payoff is, for the same reason as in the case of a symmetric search equilibrium, min {b, 2 / a}, and L’s payoff is zero. Ex ante the incentive for L and R to search when only R is expected to search, are, respectively, BRðe;¨e;cÞ ¼ qR minfb; 2=ag and BLð¨e;e;cÞ ¼ qL minfb; 2=ag  qL

2qR : að 2  qR Þ

ð15Þ

An asymmetric search equilibrium in which R searches and L does not search exists if B L(~e,e,c) V k V B R(e,~e,c). If q R N q L and R is expected to search, then R faces the same incentive with asymmetric search as in a symmetric search equilibrium, B R(e,~e,c) = B R(e,e,c), while L has a lower incentive if it is not expected to search. Thus, multiple equilibria exist whenever B L(~e,e,c) V k V B L(e,e,c). From the text we have  8  1 2 > < qR b  if qR V R 2 3 ð6Þ Bðe;e;cÞ ¼ 2 > :q b if qR N ; R 3

27

1 2a

qR 1 Since only R is expected to search, A1V: dˆ R ðtÞ ¼ dr fbzbVR u 12 þ 2a þ að2q ; and A2V: dˆ ðtÞ ¼ dl Zbzbˆ Vu1þ RÞ qR ˆ ˆ  að2qR Þ . Note that b V N b (see footnote 22), hence A2 Z A2V.

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BLð¨e;e;¨cÞ

 8  1 > < qL b  2 ¼ > :0

2 3 2 if qR N ; 3

if qR V

ð7Þ

1. Suppose q R N 2 / 3. Then B R(e,~e,~c) z B R(e,~e,c) and B L(~e,e~,c) = 0 and, since an asy. search eqm. exists for the game with contributions, B L(~e,e,c) V k V B R(e,~e,c). Hence B L(~e,e,c) V k V B R(e,~e,c). 2. Suppose q R V 2 / 3. B R(e,~e,~c) z B R(e,~e,c) f 1 / 2 z max{b  2 / a, 0} f b V 1 / 2 + 2 / a. Since an asy. search eqm. exists for the game with contributions, k V B R(e,~e,c). Hence k V B R(e,~e,c) = B R(e,e,c), so an asymmetric equilibrium or a sym. search eqm. exists. BLðe;¨e;¨cÞ V BLðe;¨e;cÞ f Þ 2qR b  minfb; 2=agu/V 12  að2q f qR V 2að12/ ¼ að1  2/Þuk. Thus, if q L b k, we 4 RÞ have B L(~e ,e ,~c ) V B L(e ,~e ,c ) V k and an asy. eqm. exists. Otherwise, it may be that B L(~e,e,c) V k b B L(e,~e,~c) and the only equilibrium in the game without search is a sym. search eqm. 5 Appendix B. Mixed strategies for the single interest group case In this section we characterize the mixed strategy equilibria for the case with one interest group, referred to in fn. 15 above. Lemma 1. [Mixed strategies] Suppose that there is one interest group, that contributions are feasible, and that k a [B (~e,c) , B (e,c) ] (where B (~e,c) is defined in (4) and B (e,c) is defined in (13). Then there exists a mixed strategy rational expectation equilibrium that is characterized as follows. Define 4ak  2q 2ak s1 ¼ 2 and s2 ¼ 2 : q þ 2aqk 2q þ aqk (i) If q b 2 / 3, then the interest group searches with probability s = s 1 . If it does not search or does not find favorable information, it offers contributions C ðsÞ ¼ 2þsq 2sq =a for the choice of d l , 0 otherwise. (ii) If q N 2 / 3, then the interest group searches with probability s 1 if k a [B (~e,c) , k*] and with probability s 2 if k a [k*, B (e,c) ], where k* = q / a. If it does not search or does not find 4sq favorable information, it offers contributions C ðsÞ ¼ 2sq =a for the choice of d l , 0 otherwise. In both cases the decision-maker always chooses d l upon receiving hard evidence for h l or for contributions of at least C(s). Proof. Assume that the group uses a mixed search strategy in which it searches with probability s, and that the decision-maker expects the group to search with probability s˜ . Whenever the decision-maker does not receive hard information m = h l , she updates her beliefs about h, which 1=2 1 becomes pðhr jm ¼ tÞ ¼ 1˜ s q=2 ¼ 2˜s q . With this belief the optimal decision independently of contributions dswitches’ at s˜ q = 2 / 3, i.e. ( 2 if s˜ qb d4 ¼ dB 3 dr otherwise:

M. Bennedsen, S.E. Feldmann / Journal of Public Economics 90 (2006) 631–656

655

The decision-maker’s expected utility from the project choice is

uDM ðd4jm ¼ tÞ ¼

while uDM ðdl jm ¼ tÞ ¼

8 > < 1

if s˜ qb

 4ð1  s˜ qÞ > : 2  s˜ q

otherwise;

4 2˜s q .

2 3

The contributions necessary to induce d l are therefore



8 4 > > a < 1þ 2  s˜ q 

C ðs˜ Þ ¼   4ð1  s˜ qÞ 4 > > : þ a 2  s˜ q 2  s˜ q

2 þ s˜ q a 2  s˜ q

4˜s q ¼ a 2  s˜ q

¼

if s˜ qb 23 otherwise:

In a mixed strategy rational expectations equilibrium the interest group must be indifferent between searching and not searching, or ( q / 2)2b + (1  q / 2)(2b  C(s˜ ))  k = 2b  C(s˜ ), which implies q C ðs˜ Þ ¼ k: ð14Þ 2 Furthermore, the expected search probability must equal the actual one, s˜ = s. sq Case 1. Assume s˜ q b 2 / 3. Plugging C(s˜ ) into (14), we get q2 2þ˜ 2˜s q =a ¼ k. Solving for the search probability yields s˜ ¼

4ak  2q us1 : q2 þ 2aqk

It is easy to show that s 1 is a valid probability (s 1 a [0, 1]) for k a [B (~e,c), B (e,c)]. Furthermore, s 1 is decreasing in q and increasing in k and a. q b 2 / 3 guarantees that s˜ q b 2 / 3. Thus, s˜ = s 1 constitutes an equilibrium mixed strategy for the interest group and decision-maker equilibrium belief whenever q b 2 / 3 and k a[B (~e,c), B (e,c)]. 2 If q N 2 / 3, then s˜ q b 2 / 3 requires that q4ak2q 2 þ2aqk qb 3 . Solving for k we get as condition for a valid probability q k b uk4: a It is easy to show that in this case B (~e,c) b k* b B (e,c). Thus, s˜ = s 1 also constitutes a mixed strategy equilibrium for the interest group and decision-maker equilibrium belief whenever q N 2 / 3 and k a[B (~e,c), k*]. 4˜s q Case 2. Assume s˜q N 2 / 3. Plugging C(s˜) into (14) for this case we have q2 2˜ s q =a ¼ k. Solving for s˜ we get s˜ ¼

2ak us2 : 2q2 þ aqk

Again, one can show that s 2 is decreasing in q and increasing in k. For k a [0, B (e,c)], s 2 is a valid probability. Naturally, s˜ q N 2 / 3 implies q N 2 / 3 and k N k*. Thus, s˜ = s 2 constitutes an equilibrium mixed strategy for the interest group and decision-maker equilibrium belief whenever q N 2 / 3 and k a [k*, B (e,c)]. 5

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