Lobbying legislatures

Bennedsen, Morten; Feldmann, Sven E. Working Paper Lobbying legislatures Working paper, No. 7-2000 Provided in Cooperation with: Department of Economics, Copenhagen Business School (CBS) Suggested Citation: Bennedsen, Morten; Feldmann, Sven E. (2000) : Lobbying legislatures, Working paper, No. 7-2000, Copenhagen Business School (CBS), Department of Economics, Frederiksberg, https://hdl.handle.net/10398/7621 This Version is available at: https://hdl.handle.net/10419/208429 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by-nc-nd/3.0/ Institut for Nationaløkonomi Handelshøjskolen i København Working paper 7-2000 LOBBYING LEGISLATURES Morten Bennedsen Sven E. Feldmann Department of Economics - Copenhagen Business School Solbjerg Plads 3, DK-2000 Frederiksberg Lobbying Legislatures Morten Bennedsen Copenhagen Business School [email protected] Sven E. Feldmann University of Chicago [email protected] June 2000 Abstract We analyze informational lobbying in the context of multi-member legislatures. We show that a single decision maker and a decentralized majoritarian legislature provide widely different incentives for interest groups to acquire and transmit policy relevant information. The paper also shows a difference in the opportunity to affect policy through lobbying between a parliamentary legislature and a legislature with low voting cohesion, such as the U.S. Congress. We show that the incentives to lobby a parliamentary legislature are much lower than to lobby Congress. The results provide a rationale for why lobby groups are more active in the U.S. Congress. The key institutional feature to explain the different behavior of lobby groups is the vote of confidence procedure, which creates voting cohesion in a parliamentary system across policy issues. We show that the flexibility of creating majorities in the Congress creates an incentive for interest groups to play an active role in the design of policy in the congressional system, while the voting cohesion in the parliamentary system dissuades interest group’s incentive to engage in information provision. We are grateful to David Baron, Massimo Morelli and Christian Schultz for helpful comments on an earlier draft. 1 Introduction Studies of interest group influence on legislative decision making fall into two categories. In the first category, interest groups offer campaign contributions or other politically valuable resources in exchange for services or legislative favors. Many of these models study how a group optimally allocates its resources between the various members of the legislature in order to secure the required support (Snyder 1991, Stratmann 1992, Groseclose and Snyder 1996, Baron 1999, Dharmapala 2000). Papers in the second category study the extent to which interest groups can affect policy outcomes by providing relevant information to the lawmaker. Interest groups have an incentive to offer information if they can influence the outcome in their favor (Calvert 1985, Austen-Smith and Wright 1992, Austen-Smith 1995, Lohmann 1994, 1998, Ball 1995, Laffont 1999, and others). Informational theories focus conspicuously on a single decision maker and do not address the fact that in a legislature decisions are made by compromise and via (some form of) majority rule. The institutional structure of the legislature, whose importance is extensively studied by the theories of legislative decision making, is absent in all papers of informational lobbying we are aware of. This paper analyzes informational lobbying in the context of multi-member legislatures. We show that the difference between a single decision maker and a legislature can be crucial for the interest group to provide information at all. As we suggested in an earlier paper (Bennedsen and Feldmann 1998), if an uninformed lobby with known and certain preferences confronts a single decision maker who is uncertain about the state of the world, it prefers not to search for information. The reason is that the benefit of providing positive information from the lobby’s point of view is offset by the cost incurred when the policy maker updates her beliefs as the lobby does not provide any information. An interest group that lobbies a majoritarian institution must be con1 cerned with the effect of its information on the composition of the majority that supports a proposal. We show in this paper that the majority coalition may change in response to the information provided, and that the lobby group can internalize the benefit of providing positive information without bearing the cost of negative signals. Therefore, it may be beneficial for a lobby to engage in informational lobbying vis-`a-vis a legislature, even if it is not so for a group that faces a single decision maker. A second focus of the paper is to explain how different legislative structures change interest groups’ incentives to lobby the legislature. Empirical evidence suggests a significantly different role of private interests in the legislative process in the United States and in European parliamentary democracies. Large and well-entrenched interest groups form important constituencies in European parliamentary decision making. By comparison, however, Capitol Hill teems with lobbying organizations and lobbyists trying to influence political decisions in their favor. Observers of the policy process are often struck by the intensity of lobbying—or lack thereof—in the system on the other side of the Atlantic. Our model allows a comparison of the incentive to lobby a parliamentary legislature versus a legislature with low voting cohesion, such as the U.S. Congress. As others (e.g. Huber 1995) have argued, a crucial difference between the two systems is the vote of confidence procedure, a mechanism that allows the proposer of a bill in the parliamentary system to link the government’s survival to the passage of the bill. Diermeier and Feddersen (1998) show that this procedure engenders discipline within the governing coalition and leads to a high degree of voting cohesion in the parliamentary system. The results derived in our informational lobbying game provide a rationale for the different intensity of legislative lobbying in the two systems. We show that the voting cohesion induced by the confidence procedure diminishes the ability of information to change the policy coalition. As a result the incentive to lobby the legislature in the parliamentary system is reduced, and lobbying activity may be diverted to other parts of the policy process, 2 such as the ministerial level or the bureaucracy. The relative importance of U.S. Members of Congress and their exposure to lobbyists may exactly be a consequence of their low coalitional loyalty. Our model assumes that legislators care about policy outcomes and update their beliefs rationally, i.e. according to Bayes’s Rule. It might be tempting to argue that legislators do not learn from information they do not receive, i.e., that they fail to update their beliefs in this situation. This paper takes a game theoretic approach and assumes that all actors make the best use of the information available. Another common caveat is that lobby groups are sometimes thought to be better informed than politicians without any search effort. While we do consider the case where the group can acquire the information costlessly, we believe that becoming informed is a conscious choice for the group, in which case the group considers the consequences of this choice. A model in which lobby groups are simply “born” with the relevant information seems less satisfactory on this account. Persson and Helpman (1998) and Baron (1999) analyze the importance of legislative structure for interest groups’ lobbying behavior. In both papers the means of influence are campaign contributions, or financial incentives. Our analysis extends the comparative institutional analysis of lobbying behavior to interest groups’ use of information as means of influencing policy outcomes. The paper is organized as follows. In Section 2 we present the generic structure of the lobbying and legislative game. Section 3 solves the model for a legislature without the vote of confidence procedure (“congressional legislature”). We provide a sufficient condition for the lobby to engage in information transmission and argue that this condition is generally satisfied. We then characterize the optimal search strategy for the lobby group in a large legislature. In Section 4 we introduce the vote of confidence procedure and show how it reduces the lobby group’s incentive to search for information. We provide a sufficient condition for the lobby not to search at all. Up to that point the benefit of belonging to the governing coalition is exogenously given. Section 5 presents a simplified dynamic version of the model that 3 determines the benefit of remaining in the governing coalition endogenously. We provide a condition for which the introduction of a vote of confidence procedure strictly decreases the expected benefit from lobbying. Section 6 concludes. 2 A model of lobbying for a public good We analyze lobbying and the legislative process in a simple model of public goods provision of distributive nature, i.e. goods whose incidence is local to geographic districts while being financed through general taxation. Examples may be local highway construction, environmental clean-up or regional development projects, or grants-in-aid, whose benefits accrue mainly locally and costs are shared through the general tax bill.1The benefits accrue directly to the public and are, via the electoral connection, internalized in the representative’s decision making. Districts differ in the degree to which their residents value the public good. A national interest group that benefits from the provision of public goods in all districts seeks to promote its overall provision. Such a group might be the national trade organization of private suppliers or contractors for the projects to be built, or a national public interest organization such as the Sierra Club or organized beneficiaries like the AARP. In order to promote the provision of the public good the group can collect decision-relevant information about the good’s positive impact in each district and can transmit this information to the legislators to influence their policy choice. The decision to provide information is naturally strategic. To be specific, consider a country with ndistricts of equal size, each represented by one legislator i=1...n. We assume that nis odd and define N={1,... ,n}as the set of legislators. The legislature decides on the size and distribution of public goods gi that are to be built in the districts. Let g=(g1,... ,g n) be the vector of the 1See Lowi (1964) and Wilson (1980) for a discussion of such projects. Weingast, Shepsle and Johnsen (1981) is a classic model of such pork barrel projects. 4 public good allocation and 1 2G=i∈Ngithe total amount of public good provided. The total cost Cis increasing in gi. For simplicity we assume that Cis a convex function of the total amount of public good, C(g)=1 2G2, which reflects the fact that inefficiencies or monitoring cost increase with the size of the federal bureaucracy or that the opportunity cost of taxation increases with the size of tax levied. Costs are shared equally among the districts through lump sum taxation, ti=1 nC(g). Each legislator iis interested in net benefits for his or her district and thus has the utility function ui=rigi−1 2nG2+bii∈N. The benefit of the public good to the district depends on the marginal valuation ri, which is a random variable that can take on two values, rwith probability (1 −p◦ i) and rwith probability p◦ i, with r>r(>0).2The superscript ‘◦’ indicates the common ex ante beliefs, that is, before any information is generated or transmitted. For simplicity let the beliefs be identical for all districts, p◦ i=p◦. Furthermore, the ri’s are uncorrelated across the districts; the interpretation is that the benefit of the public good to the district depends on some unknown, district specific properties. Bills, or proposals to allocate the public good, are introduced by a proposer, or agenda setter. The proposer is chosen randomly from a governing coalition M⊂N.3The proposed bill gpasses if a majority of the legislature votes for the bill. We refer to the collection of legislators supporting the bill as policy coalition. As will become clear presently, being member of the governing coalition and thus having a chance to be selected as proposer conveys a benefit, bi. For simplicity we first assume that bi=b>0 for all i∈M and bi= 0 for all i/∈M. In Section 5 we endogenize the value of biin a simplified dynamic version of the lobbying game. 2Any non-degenerate probability distribution on the positive domain would do. 3In the U.S. Congress Mis the majority party, in the parliamentary system it is the governing party or coalition. Since we are not concerned with the election and the coalition formation stage, we assume Mto be determined exogenously by Nature’s move. 5 The interest group that benefits from the provision of the public good can search for high valuation of the public good in the districts (ri=r) and can strategically provide this information to the legislators. We assume that the lobby’s decision to search in a district is a long term one, i.e. it is made before the government coalition or the agenda setter are chosen. To make the analysis succinct and relatively straightforward, we assume throughout the paper that the group’s search activity can be observed by the legislature.4 Given the symmetry of the model the lobby is indifferent about in which district to search. Its search strategy is therefore simply the number of districts in which to search, s. Furthermore, let Is∈{0,1}indicate whether 0<s≤n. With this notation we can now state the lobby group’s utility as uL=G−IsZ, where Z≥0 is the lobby’s cost of searching for information on the districts’ valuations. We think of the search cost as the organizing cost for engaging in information search and transmission, and not as a district specific cost; it is only incurred once when the group decides to search.5Note also that the lobby group is risk neutral in the provision of the public good. When the interest group searches for information about district i’s valuation of the public good, it receives a signal σi, which with probability q reveals the true benefit, σi=ri, and with probability 1 −qis uninformative, σi=∅. After the proposer (and in the parliamentary system the government coalition) is chosen, the interest group sends messages µ=(µ1,... ,µ n)to the legislature, where µi∈{σi,∅}. In words: the group can transmit the information it found, or pretend it found nothing, but it cannot “lie” by forging information. After the messages are sent, the proposer makes a policy proposal and submits it to a vote. The only difference between the congressional and the 4The insight of the present paper carries over to the case where the group’s search activity cannot be monitored, as shown in Bennedsen and Feldmann (1999). 5This provides the greatest incentive to search in as many districts as possible and is in no way restrictive. 6 when confronting a multi-member majoritarian institution. The reason is that the majoritarian nature of decision maker enables the group to benefit from positive information about districts, while at the same time to avoid the detriment of negative (or nil) information. Since it is in the agenda setter’s and the lobby group’s interest to identify high-valuation coalition partners, lobbying is most effective in the multi-member congressional structure. Optimal search strategy in large legislatures The previous section shows that an interest group has an incentive to search for information in the congressional legislature when the legislature is large and the group reveals the information it finds strategically to the legislature. It remains to derive the optimal search strategy. Given that it is in the group’s interest to search, in how many districts will the group optimally search? When the group searches for information, four different circumstances can arise, in each of which searching either raises or lowers the proposer’s allocation of the public good, or leaves it unaffected. Let K⊆Nbe the set of districts in which the lobby group searches, k=|K|>0. Furthermore, let H={i∈K|σi=rand i=a}, i.e. the non-agenda setter districts for which the group found favorable evidence; h=|H|. When the group considers to search in an additional district j∈ K, the following four cases can arise: (1) j=a. If jis chosen to be the agenda setter, the group incurs an expected loss for searching due to the concavity of G∗in ra. The next three cases assume that j=a: (2) h<n−1 2,k−h<n−1 2. If the search in jis successful, jwill be included in the majority; if σj=r, it will not receive positive allocation of public good. In expectation, G∗increases. 13 (3) h<n−1 2,k−h≥n−1 2. If the number of unsuccessful searches is larger than half of the number of districts (excluding the agenda setter’s), then some districts for which µi=∅have to be in the majority coalition, and search in jincreases that number. Thus, additional search reduces G∗. (4) h≥n−1 2. The number of districts with successful searches is already sufficient to form a majority. Additional search does not affect G∗. The expected gain from searching in kdistricts involves summing up the best-response public goods allocations resulting from each possible outcome, i.e. with hranging from 0 ...k, and weighting each case by the probability with which it occurs. Case 1, of course, occurs with a constant probability of 1/n, while the probability of the other three cases is given by the cumulative of the binomial distribution B(k,pq). Suppose the lobby group has an incentive to search in at least kdistricts. The following Lemma establishes the condition under which the group has an incentive to increase its search, i.e. to search in at least k+ 1 districts. Lemma 3. If C1 holds, then in the congressional system the group has an incentive to increase the number of districts kin which it searches whenever h<n−1 2and k−h<n−1 2. Proof. Suppose the group searches in kdistricts, and h<n−1 2,k−h<n−1 2. Then, if the group searches in k+ 1 districts, the expected change in public good allocation is ∆Gk=pqG∗(r,ErM\{i})−G∗(Er¯ C)+1−pq nG∗(Esr, Er¯ C\{a})−G∗(Er¯ C) =pq n rE◦r (h+1)E◦r+(m−h−1)r)−rE◦r hE◦r+(m−h)r +(1−pq)rE◦rEsr rE◦r+hE◦rEsr+(m−h−1)rEsr−rE◦r hE◦r+(m−h)r) =pq n rE◦r(r−E◦r) ((h+1)E◦r+(m−h−1)r)(hE◦r+(m−h)r) −(1−pq)r2E◦r(E◦r−Esr) (rE◦r+hE◦rEsr+(m−h−1)rEsr)(hE◦r+(m−h)r) =pq rE◦r(r−E◦r) hE◦r+(m−h)rn (h+1)E◦r+(m−h−1)r−r rE◦r+hE◦rEsr+(m−h−1)rEsr, 14 where the last equality follows since E◦r=(1−pq)E sr+pq r. Denote the difference in the parentheses by ψ. The term premultiplying ψis positive; hence ∆Gk>0 if and only if ψis positive. Rearranging terms we have ψ(h)= n E◦r+(m−1)r−h(r−E◦r)−1 E◦r+(m−1)Esr−hEsr r(r−E◦r) =n a−hb −1 c−hd. Condition C1 implies that ψ(h)>0 for h= 0. Furthermore, it is easy to show that b a−hb >d c−hd. Thus, ψ(h)= nb (a−hb)2−d (c−hd)2>0 and ψ(h)= nb2 (a−hb)3−d2 (c−hd)3>0. Thus, as ψis convex, it is increasing and positive throughout. Hence C1 implies that ∆Gk>0. Lemma 3 shows that condition C1 is sufficient so that whenever case 2 occurs, the group has an incentive to search in more districts. Countervailing this incentive, of course, is any (possible) occurrence of cases 3 and 4; this is considered below. An immediate consequence of Lemma 3 however is that, whenever C1 holds, the group always searches in at least half the districts: If k≤n−1 2, then the premise of Lemma 3 is guaranteed to be satisfied (because cases 3 and 4 cannot occur), and the group has a strict incentive to increase the number of districts in which it searches until it searches in at least half of the districts. Calculating the optimal number of districts using the binomial distribution of successful and unsuccessful searches is analytically cumbersome. For large n, however, the calculation becomes relatively simple, since the distribution of successful searches approaches the expected value pq·k. Proposition 2 shows that the optimal fraction of districts in which the group searches in the congressional system converges to a fixed number greater than one-half 15 and less than all of districts. The exact proportion depends on the search parameters (pand q). Let α=k nbe the proportion of districts in which the group searches. Proposition 2. For large nin the congressional system the proportion of districts in which the group searches in equilibrium is α∗→min 1 2pq,1 2(1 −pq). Proof. Assume the group searches in kdistricts, and let (as before) ∆Gkbe the expected gain from searching in one additional district. First, notice that as n→∞, C1 in Proposition 1 is satisfied. Thus, by Lemma 3, if max{h, k −h}<n−1 2, then ∆Gk>0 and the group has an incentive to increase k. Second, if k−h≥n−1 2, case 3 or case 1 occurs, implying that ∆Gk= G∗(Esr, r¯ C\{i})−G∗(r¯ C)<0. Alternatively, if h≥n−1 2, case 4 or (with a 1/n chance) case 1 occurs, so that ∆Gk=1 nG∗(Esr, r¯ C\{a})−G∗(r¯ C)<0. h, of course, is a random variable distributed binomially B(k,pq), with E[h]=pq k. As n→∞the Central Limit Theorem implies that h k a.s. −→ pq ⇔ h n a.s. −→ pq k n=pq α. Suppose by contradiction that the optimal proportion of districts in which the group searches for large n,α∗=k∗(n) n<min 1 2pq ,1 2(1−pq). Then for arbitrarily small ε, ε>0 there exists an n, large, such that ε, ε<1 nand such that h n≤pq α∗+ε<1 2and k∗(n)−h n≤α∗−pq α∗+ε<1 2with probability one. For such n∆Gk∗>0; thus, the group has an incentive to increase k, and α∗cannot be optimal. Suppose on the other hand, also by contradiction, that for large nα ∗> min 1 2pq ,1 2(1−pq). Then for some small ε, ε>0 there exists an n, large, such that h n≥pq α∗−ε>1 2and k−h n≥α∗−pq α∗−ε>1 2with probability one. For such n∆Gk<0. Thus, the group has an incentive to decrease k, and α∗is not optimal. It follows that α∗∈min 1 2pq ,1 2(1−pq)±max{ε, ε}for large n, where ε, εare arbitrarily small. 16 0 0.2 0.4 0.6 0.8 1 α 0 0.2 0.4 0.6 0.8 1 pq min{ , } 2pq 2(1-pq) 1 1 ___ ______ Figure 1: Optimal search strategy without vote of confidence procedure The optimal search strategy—and thus the optimal number of districts— depends, as Proposition 2 shows, on the parameters of the search. Figure 1 shows the optimal proportion of search districts α∗for a large legislature as a function of pq. As we observed earlier, the group optimally searches in at least one-half of all districts and (generically) never in all districts. In the congressional system, interest groups can actively seek to affect the composition of policy coalition. Since the agenda setter and the interest group’s interests are aligned, the group can affect policy by identifying “high demand” districts. Negative search results do not affect the policy negatively since they can be externalized, to some degree, to non-majority members. Thus, interest groups have an incentive to provide policy-relevant information that allows the agenda setter—or other leaders—to construct most favorable policy coalitions. 17 4 Lobbying a Legislature With Vote of Confidence Procedure Policy making in a parliamentary system is characterized by a high degree of cohesion within the governing coalition. Diermeier and Feddersen (1998) show how this voting cohesion can be induced by the vote of confidence procedure, since coalition partners derive benefits being in the government only if the governing coalition is maintained. We show that this voting cohesion reduces an interest group’s incentive to provide information. Government membership is valuable. In a first step and to keep the model as simple as possible we assume in this section that this value is exogenously given and that members of the governing coalition lose the benefit bif the government is dissolved. In Section 5 we derive the value of bin a simple dynamic policy game. Our focus is on the policy making process and lobbying, and we are less concerned with the coalition formation stage; we thus simply assume that Nature chooses a governing coalition Mand a proposer, a∈M.aproposes a policy vector and decides whether or not to attach a vote of confidence to the proposal. To simplify the analysis, we assume that |M|=n−1 2, i.e. the governing coalition is a minimum majority.6 By attaching a vote of confidence to policy gthe proposer can exploit the coalition partners’ incentive of maintaining the governing coalition. When b is large enough the proposer proposes a policy that receives the support from the members of the governing coalition and extracts the surplus b. When b is small, the proposer may be better off choosing the best policy coalition C, irrespective of M. Let C⊂Ndenote the best policy coalition that constitutes a majority. From the previous section we know that Cwill never be a super majority, i.e. |C|=n−1 2. If the proposer seeks support from policy coalition C=M, she will not attach a confidence vote to the proposal in order not to risk the dissolution of the government, and bremains unaffected 6An alternative assumption would be to let Mbe of any size, but assume that a vote of confidence requires unanimity among the coalition partners. 18 by the outcome of the vote on the proposal in this case. The proposer’s problem when seeking support from Mby attaching a vote of confidence is, max graga−1 2nG2+b s.t. rigi−1 2nG2+b≥0∀i∈M gi≥0∀i∈N. The solution, G∗ +v, in terms of the aggregate amount of public good to this problem is given by G∗ +v=   n i∈M 1 Eri if b≤n 2r2 a nr aotherwise. The first row is the case where the proposal makes the majority partners indifferent between supporting or not. However, if bis very large, it is possible that the rent transfer from coalition partners to the proposer through an increase of public good in the proposer’s district is so inefficient that the proposer prefers to leave the coalition partners with some rent in equilibrium. This is captured by the second row in the definition of G∗ +v. If the proposer instead chooses support from Cwithout invoking the confidence procedure, her problem is identical to the one in Section 3: max graga−1 2nG2+b s.t. rigi−1 2nG2≥0∀i∈C gi≥0∀i∈N. The aggregate solution G∗ −vto the problem without the use of the confidence procedure is G∗ −v=n i∈¯ C 1 Eri . Proposition 3 below states the main result of this section, namely that an interest group’s incentive to engage in information provision is smaller in the parliamentary system than in the congressional system. To derive the proposition, the following lemma will be useful. 19 Lemma 4. If in all possible equilibria the proposer chooses support for the policy proposal from the governing coalition Mby attaching the vote of confidence, then the interest group is strictly better off not searching for information. Proof. Suppose aseeks support for her proposal from the governing coalition M, and the group searches in k∈{0,... ,n−1}districts. Let Kbe the set of districts in which the group searches and B=K∩M(possibly empty). Denote by ErBthe vector of expected valuations for the districts in Bafter the group has sent messages to the proposer (i.e., each element in ErBwill be either ror Esr). The allocation of public good the proposer chooses is given by G∗(ErB,E◦rM\B).(∗) Now consider that the group searches in k+1 districts, by adding district j. In case 1, j∈M, which implies the expected allocation pq G∗(r,ErB,E◦rM\(B∪{j}))+(1−pq)G∗(Esr, ErB,E◦rM\(B∪{j}))(∗) By concavity and Jensen’s inequality (∗) is less than (∗). In case 2, j∈ M, in which case the allocation is not affected by the search (i.e., as given in (∗)). Since both cases have a positive probability of occurring, the expected allocation after searching in k+ 1 districts is less than for searching in k districts. Since kis any number between 0 ...n−1, this means that the group is strictly worse off searching in any district. Lemma 4 builds on the following fact. If the policy coalition is fixed and cannot be affected by the interest group’s message, then searching in a coalition member’s district is a risky undertaking for the interest group: If the search is successful, it increases the total amount of public good provided; if it is not successful, it reduces the amount. As shown in Lemma 1 the proposer’s optimal allocation of public good G∗is concave in the districts’ 20 valuations for the good; thus, by Jensen’s inequality, the expected allocation is lower than if the group does not search. We are now ready to state our main result. Proposition 3 establishes the conditions under which a proposer chooses support from Monly, leaving interest groups with no incentive to search. Proposition 3. The vote of confidence procedure reduces the interest group’s incentive to search for information. In particular, the group never searches if b≥r(r−r)2n n2−1≡¯ b(5) Proof. After the lobby has delivered its message two situations can arise. Either the proposer selects as policy coalition the group of legislators with the highest expected ri,C, or she proposes a policy supported by the members of the governing coalition M. In the former case the lobby has the same benefit from its search activity as in the case without vote of confidence procedure (congressional case). In the latter case, when the proposer chooses support from M, the lobby group’s benefit from searching can never be higher than in the congressional case, since Mmay include legislators who ex-post do not have the highest expected ri. It remains to show that b≥¯ bis a sufficient condition for the proposer to choose a policy supported by Mindependently of the information transmitted by the lobby. To show this, consider the most adverse case, where the proposer has the largest incentive to include legislators from outside the governing coalition. This case occurs when the lobby has delivered messages µi=rfor all i/∈M and µi=rfor all i∈M\{a}. If the proposer chooses support from the governing coalition she will link the policy to a vote of confidence. The aggregate amount of public good will be, G∗(Era,rM)= n (m−1)1 r+1 Era . 21 The utility, u+v a, of the proposer in this case is, u+v a=n 2 Er2 ar (m−1)Era+r+Era r(m−1)b+b. If the proposer instead chooses support from outside the governing coalition, she will not use the vote of confidence procedure and the aggregate public good will be, G∗(Era, r)= n (m−1)1 r+1 Era . The utility, u−v a, of the proposer in this case is, u−v a=n 2 Er2 ar (m−1)Era+r+b. The proposer, therefore, prefers to find support within the governing coalition if u+v a−u−v a≥0, which reduces to, (m−1) b≥nrEra 2r (m−1)Era+r−r (m−1)Era+r(6) Since r (m−1)Era+r<r mEraand r (m−1)Era+r>r mErawe get an upper bound on the right hand side of equation (6) by substituting these latter terms (note that this is a least upper bound as m→∞), which reduces to b≥nr(r−r) 2m(m−1) =r(r−r)2n n2−1. Proposition 3 establishes that an interest group has no incentive to lobby a legislature with the vote of confidence procedure than when b, the value of keeping the government in office, is large enough. The reason is that with b≥¯ b, the proposer always chooses policy that is supported by members of the governing coalition. Thus, following the logic of Lemma 4, the interest group has no incentive to search for information. 22 The proposition implies that the interest groups’ incentive to engage in information search is strictly smaller in legislatures with the confidence procedure than in legislatures without this procedure, for periods t>t ∗. Clearly, the relevance of this result depends on the size of t∗. Simulations show that for a large range of plausible parameter values t∗=1, 9that is, the two legislative structures provide different incentives for lobby groups to engage in information search in all but the final policy period. 6 Discussion Our model of lobbying legislatures for favorable policy has shown that the incentive interest groups have to lobby depends, not too surprisingly, on the legislative structure in which the group operates. The results roughly correspond to the empirical observation that lobbying is far more active in the U.S. Congress than in European parliamentary systems. The distinguishing feature we have identified between the parliamentary and congressional systems is the ability of parliamentary leaders to induce voting cohesion through the use of the confidence procedure. On the other hand, leaders in Congress craft legislative coalitions according to the policy preferences of legislators for each policy issue at a time. As the analysis has shown, it is this feature that provides interest groups with influence by passing on information that helps the agenda setter identify the most favorable supporters for the proposal. In the absence of this coalitional flexibility, as in parliamentary systems when the value of government membership is significant, the proposer has nothing to learn about the composition of the winning coalition. Therefore, the only way the interest group can affect outcomes is by providing informa9For example let r= 1 then ∀q,p ∈[0,1] and ∀r≤2,t ∗=1. For smaller variation between districts the result is even stronger. In this numerical example, r≤1.4 is a sufficient condition for b1>u p(r,r)−up(r,r), which is the highest gain a proposer can ever achieve from breaking the governing coalition. Thus, in this case the lobbies will never search in any policy period before the final one, since the composition of the policy majority is not affected by any transmitted information. 29 tion about a given set of districts. As we show, it is a feature of Bayesian updating that the ex ante (uninformed) beliefs are a weighted average of the posterior (informed) beliefs. Therefore, the degree to which the proposer’s beliefs are influenced by favorable information as well as the potential detriment from the failure to do so cancel each other out in expectation. Moreover, since the proposer’s reaction function is concave in her expectation, the group is strictly worse off trying to lobby a proposer who is wedded to the districts she needs to favor. Thus, without the flexibility to customize winning coalitions there is no scope for informational lobbying. An interesting sideline to our results is that lobbying in the congressional system always yields coalitions of “high demand” districts, i.e., districts whose preference for the public good are above the average and who are willing to support the agenda setter’s over-provision of public good to some districts. In this regard the model suggests that the congressional system is more prone to inefficient allocation of policy than the parliamentary system (although this assessment lies beyond the scope of our model for the present time). A variation of our model could relax the assumption that the interest group is organized at the national level and benefits from the provision of the public good in any district. An interest group’s benefit is often localized, and it may have a particular knowledge of the local incidence of the public good that it might want to convey to the legislators. First results along these lines indicate that if interest groups are local, they compete for inclusion of their district in the majority by providing information. Since such an incentive is absent in the parliamentary system, our general result prevails and may even be amplified. In the present paper we assume that the lobby’s search activity is observable for the legislature; this allow us to highlight the mechanism of Bayesian inference engendered by the group’s search for favorable information. In practice, legislators cannot be expected to monitor interest group activities all too closely. However, if we maintain the standard assumption of Bayesian games, namely that players are rational and make the best (equilibrium) 30 predictions about other players’ unobserved behavior and that players’ actions are optimal given their beliefs, then the main observation10from the present analysis obtains when the search activity is unobservable, albeit in a qualified form: the congressional system provides an interest group with a greater incentive to lobby via information search than the parliamentary system. The principal difference is that when the search activity is not observable, searching itself does not induce the proposer to revise her beliefs, so that the activity itself does not impose a Bayesian cost. Instead, the proposer infers whether or not the group has an incentive to search and forms her expectations accordingly. Thus, in equilibrium the failure to report a positive finding still carries the Bayesian updating cost. Some observers of lobbying argue that interest groups in Europe far more actively lobbying bureaucrats rather than legislators, relative to their US counterparts. The standard explanation is that legislators are less important in the design of policy. Our analysis provides a different explanation for this observation: Lacking the ability to influence policy coalitions and outcomes in the legislature, interest groups focus their attention on the implementation of policy. Further empirical work will need to shed light on the merits of either explanation. 10The following argument is developed in Bennedsen and Feldmann 1999. 31 Appendix: Proof of Lemma 5. Proof. Since the lobby cannot distinguish between the proposer and the coalition partner when it picks its search strategy, there are five search strategies with different expected values. With a slight abuse of notation we can write these strategies as s1(one coalition member’s district), s3(the minority district), s12 (both coalition members’ districts), s13 (one coalition member’s district and the minority district), s123 (all three districts). Similarly, we write the lobby’s expected value (relative to not searching) from using these strategies as V1,V3,V12,V 13, and V123. V3=pq(G∗(r,E◦r)−G∗(E◦r, E◦r)) >0, V1=1 2(pq G∗(r,E◦r)+(1−pq)G∗(Esr, E◦r)) +1 2(pq G∗(r,E◦r)+(1−pq)G∗(E◦r, E◦r)) −G∗(E◦r, E◦r)<V 3, V13 =1 2(pq)2G∗(r,r)+pq(1 −pq)(G∗(Esr, r)+G∗(r,E◦r))+(1−pq)2G∗(Esr, E◦r) +1 2(pq +(1−pq)pq)G∗(r,E◦r)+(1−pq)2G∗(E◦r, Esr)−G∗(E◦r, E◦r) <1 2[pq G∗(E◦r, r)+(1−pq)G∗(E◦r, E◦r)] +1 2[pq G∗(r,E◦r)+(1−pq)G∗(E◦r, E◦r)] −G∗(E◦r, E◦r)=V3, V12 =(pq)2G∗(r,r)+pq(1 −pq)(G∗(r,E◦r)+G∗(r,Esr)) +(1−pq)2G∗(Esr, E◦r)−G∗(E◦r, E◦r) <pqG ∗(r,E◦r)+(1−pq)G∗(E◦r, E◦r)−G∗(E◦r, E◦r)=V3, V123 =pq[pq(2 −pq)G∗(r,r)+(1−pq)2G∗(r,Esr)] +(1−pq)[pq(2 −pq)G∗(Esr, r)+(1−pq)2G∗(Esr, Esr)] −G∗(E◦r, E◦r). <pq[pq G∗(r,r)+(1−pq)G∗(r,E◦r)] +(1−pq)[pq G∗(Esr, r)+(1−pq)G∗(Esr, E◦r)] −G∗(E◦r, E◦r). <pqG ∗(E◦r, r)+(1−pq)G∗(E◦r, E◦r)−G∗(E◦r, E◦r)=V3. where each inequality (except the first) follows from Jensen’s inequality and from concavity of G∗(·). 32 References [1] David Austen-Smith. “Campaign Contributions and Access.” American Political Science Review 89(3), 1995, pp. 566–81. 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