Lobbying: Buying and utilizing access

Mayer, Wolfgang; Mujumdar, Sudesh Article Lobbying: Buying and utilizing access Economics: The Open-Access, Open-Assessment E-Journal Provided in Cooperation with: Kiel Institute for the World Economy – Leibniz Center for Research on Global Economic Challenges Suggested Citation: Mayer, Wolfgang; Mujumdar, Sudesh (2014) : Lobbying: Buying and utilizing access, Economics: The Open-Access, Open-Assessment E-Journal, ISSN 1864-6042, Kiel Institute for the World Economy (IfW), Kiel, Vol. 8, Iss. 2014-2, pp. 1-35, https://doi.org/10.5018/economics-ejournal.ja.2014-2 This Version is available at: https://hdl.handle.net/10419/90642 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. 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Licensed under the Creative Commons License - Attribution 3.0 Vol. 8, 2014-2 | January 13, 2014 | http://dx.doi.org/10.5018/economics-ejournal.ja.2014-2 Lobbying: Buying and Utilizing Access Wolfgang Mayer and Sudesh Mujumdar Abstract This paper develops a lobbying-by-firms model that draws on a more realistic characterization of the lobbying process; influence-seeking requires both money to ‘buy access’ and managerial time to ‘utilize access’. This, more realistically grounded, modeling approach furnishes theoretical support for why one encounters different numbers of lobbying firms of varying sizes in different industries, without casting the (unrealistic) lifeline of the ‘money-buyspolicies’ assumption or (unrealistically) casting out the role of money from the lobbying process. Theoretical legs are also furnished for the empirical finding of a negative and statistically significant (at the 1% level) relationship between industry concentration and “direct lobbying” by the industry. Additional insights emerge from the model regarding how a cap on the lobbying-contributions of firms results, in fact, in an expansion of the amount of access-time purchased by some firms, and how a decline in the world price of an industry’s good can generate greater inequality in access to politicians. JEL H0 F16 L1 Keywords Lobbying; free-rider problem; size-distribution-of-firms; world-price; labormarket-flexibility Authors Wolfgang Mayer, University of Cincinnati, USA Sudesh Mujumdar, Department of Economics and Marketing, University of Southern Indiana, 8600, University Blvd., Evansville, Indiana 47712, USA, [email protected] Citation Wolfgang Mayer and Sudesh Mujumdar (2014). Lobbying: Buying and Utilizing Access. Economics: The Open-Access, Open-Assessment E-Journal, Vol. 8, 2014-2. http://dx.doi.org/10.5018/economicsejournal.ja.2014-2 www.economics-ejournal.org 1 1 Introduction Lobbying is an integral part of economic policymaking. In the United States, the First Amendment to the Constitution lays the legal foundation for individuals and groups to “petition the government for a redress of grievances.” The recent economic literature on economic policy making has accounted for the influence of lobbying groups to explain governments’ choices of ‘actual’ as opposed to ‘socially-optimal’ policies. A standard assumption made in this literature is that interest groups make monetary contributions to policy makers in return for adopting desired policies. In other words, money is accorded the role of directly purchasing policies. Empirical evidence of monetary contributions is strong.1 The assertion that firms and interest groups are buying policies through these contributions has, however, been seriously disputed. Austen-Smith (1991) and others have argued convincingly that the assumption of money directly affecting policy choices is both simplistic and unrealistic. First, information transmission is a more important channel for influencing policies than financial contributions. On many issues, policy-drafting legislators possess far less information than firms affected by these policies. Consequently, legislators actively seek information and gladly listen to lobbies. Second, paying money in return for policies is clearly illegal; and, at least in the United States, there is evidence of reasonably consistent law enforcement.2 A more acceptable characterization of lobbying contributions is to view them as ‘buying access’ to legislators.3In recent discussions on campaign finance reform in the United States, former representative Lee Hamilton (1998: 1-2) writes that “special interests gain access to Members (of Congress) through campaign _________________________ 1 In 2010, the estimated spending on lobbying by firms and interest groups was $3.52 billion. In 1998, this estimate was $1.44 billion. Thus the time period: 1998-2010 has witnessed an increase in lobbying expenditures of more than 140%. Note that these lobbying expenditures do not include campaign contributions. All data are from the Center for Responsive Politics (its website: www.opensecrets.org). 2 The conviction of James Trafficant, a United States Congressman from Ohio, of bribery, racketeering, and tax evasion is an example. 3 There is further debate as to what ‘buying access’ really means, as Austen-Smith (1995) points out. Is it a euphemism for receiving favorable policies, is it just a way to signal a group’s concerns, or does it provide the opportunity to meet and convey the group’s concerns, as this paper postulates. www.economics-ejournal.org 2 contributions and determined lobbying, and often put pressure on Members to vote with them on their key votes…But the ease by which special interests can manipulate the system and push things through is exaggerated by the public.” Lending further support to the claim that ‘money buys access’ is a quote by Prof. James Thurber in Attkisson (2012), “I think that when people give campaign contributions, they are not there simply to improve the workings of democracy. They’re there to buy access.”4 Both politicians and political analysts, when asked about financial contributions, are quite careful in emphasizing that they buy access rather than policies. This ‘money-buys-access’ characterization also explains why many firms and individuals contribute to more than one party or candidate in a given election. Firms buy access to potential winners even when they do not share their policy preferences.5,6 The characterization of money directly buying policies, besides being unrealistic, harbors dire implications for industry lobby formation by firms with common interests. Olson’s (1965; 28) classic lobbying model, which links policy outcomes directly to financial contributions, yields the finding that “no one in the group will have an incentive independently to provide any of the collective good once the amount that would be purchased by the individual in the group with the largest Fi was available”, where Fi stands for the ith individual’s fraction of total benefits. Hence, at most one firm has an incentive to contribute in return for a policy that benefits all of an industry’s firms. This conclusion, therefore, raises serious questions about the logical consistency of the lobbying literature’s standard _________________________ 4 The following remark of Attkisson (2012) generates confidence in Prof. Thurber’s claim: “No one knows the business of Washington lobbying better than Thurber. He helped write a report on lobbying reform for the American Bar Association, and he teaches a course to aspiring lobbyists at American University.” 5 37% of the top of political donors (firms and other organizations, such as trade associations) over the period: 1989 – 2012, split their campaign contributions (in the 40% to 59% range) between Republicans and Democrats (http://www.opensecrets.org/orgs/list.php). 6 While the real-world phenomenon of politicians selling access has been embraced by the literature concerning itself with modeling their (politicians’) behavior – see, e.g., Cotton (2009) – it has been cast aside in the lobbying-by-firms literature. The literature on modeling a politician’s behavior, however, given its focus, sidesteps the role of firms in the lobbying process (especially the opportunity cost of such activity), and hence does not uncover any related insights (such as those in this paper). www.economics-ejournal.org 3 pairing of the assumptions that all of an industry’s firms lobby and that policies are adopted in return for monetary contributions.7 A small, but growing literature has addressed the issue of endogenous lobby formation when monetary contributions directly affect policies. Pecorino (1998) employs a repeated game framework with a trigger strategy to show that all of an industry’s firms of equal size might have an incentive to lobby. Pecorino’s framework was later adopted by Magee (2002) who endogenized both lobby formation and policy choices. Mitra (1999), on the other hand, established lobby formation without a repeated game by assuming that firms engage in pre-play communication. His model also assumes that industries are made up of identical firms and that money is the lobbying instrument. The assumption of identical firms was finally relaxed by Bombardini (2008). Based on the menu-auction approach of Grossman and Helpman (1994), she lets each of the industry’s heterogeneous firms decide on whether to enter the lobbying game and what individual contribution schedule to present to its government. Hillman (1991), in a little-known but truly important paper, discards the assumption of lobbying through monetary contributions. Lobbying by his firms requires that managers spend costly time to influence policy makers. Hillman demonstrates that more than one of many heterogeneous firms might lobby. In fact, all of an industry’s firms will participate, even if they are of different size, provided all firm managers possess the same entrepreneurial ability. To reiterate, monetary contributions play no role in Hillman’s model. Hillman’s insights emerge from a lobbying-by-firms model that corresponds to the classic private-provision-of-public-goods model of Bergstrom et al. (1986). Consequently, the implications from Hillman’s model are equally strong. First, all CEOs of lobbying firms spend the same amount of time on entrepreneurial activities even if they differ with respect to entrepreneurial abilities. Different abilities show up as differences in lobbying activities only. When all CEOs possess the same entrepreneurial talent, then all of them lobby if one has an incentive to do so, and all spend the same amount of time on lobbying. Second, there emerges a neutrality relationship between total industry lobbying and the degree of concentration of the lobbying industry: for a given number of lobbying _________________________ 7 To avoid confronting this ‘uncomfortable’ issue, some authors simply assume that organized groups already exist and that the free-rider problem has ‘somehow’ been overcome. www.economics-ejournal.org 4 firms, total industry lobbying depends only on the group’s total profit and not on the distribution of total profit among its members, irrespective of whether the CEOs have equal or unequal entrepreneurial abilities (Hillman 1991: 132). In other words, if profit serves as a proxy for size, the group’s lobbying effort depends on the group’s aggregate size but is independent of the contributing firms’ size distribution. Hillman’s conclusion on the independence of industry lobbying from the industry’s firm-size distribution is not supported by empirical evidence. For example, Gawande (1997) finds a positive and (statistically) highly significant (at the 1% level) relationship between an industry’s degree of concentration and its lobbying-contribution level. The underlying reason for why, say, a high degree of concentration yields a large contribution level is that “the same barriers to entry that allow a high degree of concentration also allow firms to reap the full benefits from lobbying” and hence as a group they contribute more.8 Our alternative lobbying formulation assumes that it takes both money and time to lobby effectively. Lobbying a legislator first involves the making of a financial contribution by the firm to gain access to the legislator. The larger the contribution, the greater is the amount of ‘access-time’ obtained.9 Thus, as in Olson and in accord with empirical reality, financial contributions form an essential component of the lobbying process. However, different from Olson, financial contributions do not buy policies. Once a firm gains access, it can utilize this access to inform and influence the legislator. Preparing for and meeting with legislators, however, requires time on _________________________ 8 Some studies find no effect and some a negative effect between the industry’s degree of concentration and its ‘policy-effectiveness’ – see, Potters and Sloof (1996; 417). These studies, however, suffer from one or both of the following methodological shortcomings: 1) There is no ‘direct’ test of the relationship between industry concentration and industry lobbying but an indirect one – mediated through the ‘policy effectiveness’ variable, and 2) While the ‘policy-effectiveness’ variable (e.g., the level of industry-protection) is considered to be a function of the industry lobbying-contribution level, the latter variable is treated as independent of the ‘policy-effectiveness’ variable, resulting in the usual, statistically-related ‘endogeneity issues’. 9 The Center for Public Integrity (2000), for example, reports, that there exist different price tags for joining the Republican Attorneys General Association (RAGA), which pushed for “nonparticipation by Republican attorneys general in lawsuits against corporations’ interests.” $25,000 provided “preferred seating” at events, offering private conversations; $15,000 secured tickets to events and access to conference calls; while $5,000-10,000 offered less access. www.economics-ejournal.org 5 the part of the firm’s manager(s).10 Hence, the firm must reallocate resources away from production and towards access-utilization. One might argue, however, that lobbying is often “conducted by the ‘public communication’ departments or is outsourced to specialized firms.”11 In such cases, the management of a firm must still indirectly be involved in matters of lobbying. It would be naïve to expect that the ‘public communication’ department or the outsourced agency are acting independently of the management of the firm (that is, without any input, monitoring, and follow-up work by the management). To restrain one from succumbing to such naïveté, in what follows, we discuss a piece of evidence of management involvement in lobbying matters, even though the operational aspects of lobbying are outsourced. In the article by Attkisson (2012: 1), noted earlier, there is the following quote by Gary Lauer, CEO of eHealth Insurance: “I was interested in getting some lobbyists a) who had high credibility, and b) who could frankly get some doors open so that we could explain what the situation was and what we think the remedy would be,” Lauer said. So, it appears that the main job of the outsourced firm was to obtain access to the legislators. It still falls upon the management to “explain the situation” and suggest “the remedy”. Here’s how one can infer the involvement of the CEO/management in the lobbying process (again, quoting from Attkisson (2012: 3), where Gary Lauer, CEO of eHealth Insurance is being interviewed by Attkisson): …In the end, eHealth's lobbying was successful in changing the rules. Low income Americans will be allowed to use their subsidies to buy insurance on eHealth. “Did you have to write a proposed regulation to hand them?”Attkisson asked. _________________________ 10 For instance, Fitzgerald (2011: 1) reports that 18 CEOs and other management-staff of various Technology companies met with U.S. legislators to push for protection of government spending and tax deductions for “corporate research and development.” Further, Schwab (1994: 170), in her detailed examination of the making of the Omnibus Trade and Competitiveness Act, notes concerning the plant closing provision that “it was primarily a small hard core group of individual firms and the administration that did the most lobbying against the provision.” 11 As one referee pointedly noted. www.economics-ejournal.org 6 “We've written a lot,” Lauer replied. “At the end of the day, the regulation didn't use all of our language, and that was fine, but it caught the essence of this, and it included some things that these people in health and human services thought were important, which we agreed with ... “I would say that the process here is far from elegant. The process here involves influence.” Thus it is apparent that the management of eHealth Insurance must have been involved in writing the proposed regulation that was presented to the legislators once access was secured through the outsourced lobbying firm. It is hard to imagine that the ‘public communication’ department of eHealth Insurance would have written the proposed regulation independently of the input of the management of the firm. So, all we are claiming is that if the management of a firm is involved in ‘nonmanagement’ activities, such as lobbying, then this must impose ‘productivitycosts’ on the firm (otherwise, why hire management–staff at all). Hence, in so much as lobbying uses up ‘entrepreneurial time’ or ‘management time’, we draw on Hillman (1991) in building our model. The above-described, more realistic characterization of the process of lobbying by firms was initially laid out (in less detailed fashion) in Mayer and Mujumdar (2002) – the Working paper version of the current paper. This characterization was then drawn upon in Mayer and Mujumdar (2003) – henceforth, M&M (2003) – to examine the lobbying responses of the import sector and the export sector to a decline in the world price of the import industry’s good in a two-sector general equilibrium model. Given its focus, the analytical treatment of lobbying behavior by firms in M&M (2003) is relatively rudimentary. Specifically, while the current paper fully characterizes and derives the lobbying equilibrium for firms of different sizes and demonstrates that the equilibrium is unique, M&M (2003) reports a lobbying equilibrium for firms of only two sizes, and this equilibrium is neither fully derived nor demonstrated to be unique. Consequently, the important insights on firm and industry lobbying uncovered by this paper (discussed below) do not obtain in M&M (2003). This paper builds a lobbying-by-firms model that captures two, key real-world dimensions of this lobbying process; a) money buys ‘access’, and b) utilizing www.economics-ejournal.org 7 access consumes ‘management-time’. Further, the model allows for firms of different sizes. The following main insights emerge from analyzing the model: 1) Any particular firm’s incentive to engage in lobbying is larger, the lower is the amount of lobbying undertaken by the other firms in the industry. This result sheds light on a link that is not intuitively apparent - the one between a firm’s incentive to lobby and lobbying activity by other firms in the industry. 2) The lobbying equilibrium (as we explicitly demonstrate) may be characterized by just ONE lobbying firm or MULTIPLE lobbying firms. That is, it is endogenously determined that one, some or all of an industry’s firms can be engaged in lobbying. This result helps explain the real-world phenomenon of why we encounter lobbying by different numbers of firms (of different sizes) in different industries, without being beholden to the unrealistic assumption that ‘money-buys-policies’ (as in Bombardini 2008) – or by banishing the role of money in the lobbying process (as in Hillman 1991). 3) If the size-distribution of lobbying firms in an industry were to become more unequal, then this would result in a decline in the industry’s lobbying of politicians through ‘direct-access’ (and vice-versa). This finding furnishes theoretical support to a similar empirical finding by Vannoni (2013). Specifically, Vannoni (2013) uncovers a negative and statistically significant (at the 1% level) relationship between industry concentration and “direct lobbying” by the industry –for firms in the European Union.12 4) In examining the effects of laws that impose a limit on the lobbyingcontribution of firms, we find that lobbying firms, on whom the limit is not _________________________ 12 At first blush, our finding appears to run counter to the theoretical result in Bombardini (2008), where a more unequal size-distribution, implies a larger industry-level of lobbying-contribution (for a given level of output) and, consequently, a higher level of protection. Our finding is driven by the fact that the increase in lobbying by the expanding firm is smaller than the decline in lobbying by the contracting firm. In a more elaborate model of lobbying, which accounts for both ‘direct’ as well as ‘indirect’ means (such as contributions towards relevant issue-advocacy adverts or interest groups) of ‘petitioning the government’, it is conceivable that the contracting firm’s total monetary contributions for lobbying purposes decreases by a relatively smaller amount, as these contributions are now funneled more towards indirect channels since their relative cost is now lower. This is due to the fact that for the contracting firm, the cost of ‘direct-access’ (including ‘productivity-cost’) per unit of capital is now higher. The opposite would hold true for the expanding firm. So, it is quite possible that total monetary contributions for lobbying purposes actually increase – in line with Bombardini’s (2008) result. However, our new insight is that a more unequal size distribution of firms results in less lobbying through ‘direct-access’. www.economics-ejournal.org 14 (10) )( )1()]([)(' 11 λ π fK B gApAp H HH > ′ +− −− and (11) )( )1()]([)(' 1 λ π fK B gApAp H HH + < ′ +− where ∑ = = H jj H AA 1 is total lobbying time spent by the H largest firms (where M H≤≤ 1 ). The second part of Proposition 2 states that, in equilibrium, each of the M equal-sized firms lobbies, if the representative firm has an incentive to lobby when no other firm lobbies. This follows from a comparison of (9) with (8’) when M K KK == =... 21 We have demonstrated that the number of endogenously determined lobbying firms can be one, some, all or none. In what follows, we examine the forces behind this finding by relating our model to the specifications of Olson and Hillman. Olson’s (1965) model rests on the assumption that lobbying consists of making monetary contributions for directly purchasing policies. Since lobbying has no impact on a CEO’s management input, this implies in the context of our model that )( j Hg is independent of j A , making 1 )1()( == gHg j . This, in turn, implies that equations (9) and (8’) – constituting the conditions for more than one firm to lobby – reduce to )]([)(' 1 * 1 λ fKBAp = and )]([)(' * 1 λ fKBAp j > , respectively. Clearly the inequality of the second condition cannot hold if the equality of the first one does. Whereas the LHS is the same for both equations, 1 KK j≤ implies that the RHS of the second condition cannot be less than the RHS of the first condition. Consequently, no other firm has an incentive to lobby if the largest firm lobbies – just as Olson concludes. We note in this context that Olson’s characterization of the use of money to obtain the desired policy measures turns lobbying into a constant-cost activity – that is, the marginal cost of lobbying becomes constant. Hillman’s (1991) model rests on the assumption that lobbying requires no financial contribution on the part of a firm; instead, it calls for involvement by its www.economics-ejournal.org 15 CEO who faces a trade-off between managing and lobbying. This leads Hillman to the conclusion that, when all CEOs have the same ability, either none or all of an industry’s firms lobby. Now, the management trade-off assumption is reflected in our characterization of the lobbying process, but the absence of money is not. Eliminating monetary contributions simply implies that our 0=B . Substituting 0=B in (8), the th j firm has an incentive to lobby when no other firms lobbies if 0)]1 ()]0( [)0 ('[ > ′ +− g pp π . But if this condition is satisfied for one firm, then it must be satisfied for all N of the industry’s firms, independent of their size. Hence, they all lobby in equilibrium. Lobbying by NH <≤1 firms cannot occur. Were only the H largest firms to lobby, then 0 )]1( )]([ )1()(' [* *= − ′ + −− h H h HAg ApAg Ap π would be satisfied for the th h firm choosing 0 *> h A , where H A is again total lobbying by the H largest firms and Hh ..., ,1= . But then it also must be that 0)]1()]([)('[ > ′ +− gApAp HH π for each non-lobbying firm since )1()1(1 * h Agg −>= and )1()1( * h Agg − ′ < ′ . Hence, in equilibrium, all N firms have an incentive to lobby and, in equilibrium, 0)]1()]([)1()('[ ** =− ′ +−− j N j NAgApAgAp π for all Nj ..., ,1= .Since this yields the same * j A for all j ,it follows that NAA N j= * . Thus without financial contributions, the trade-off between lobbying and managing introduces a strong bias in favor of collective lobbying by all the industry’s firms.21 This bias is the consequence of lobbying being an increasing-cost activity when, as assumed, managing raises output at a decreasing rate. _________________________ 21 Hillman allows entrepreneurial ability to vary among firms. How heterogeneity in management abilities affects the number of lobbying firms depends on the way heterogeneity is introduced. If, for example, γ α jjj Hg = and N ααα >>> ... 21 where jj AH −=1 , then all firms lobby if one does. If, on the other hand, γ jj Hg = and jjj ATH −= , where N TTT ... 21 >> , then it is quite possible that firms with less entrepreneurial ability do not lobby. www.economics-ejournal.org 16 4 Lobbying Equilibrium An industry lobbying equilibrium is established when none of the Malready lobbying firms has an incentive to adjust their lobbying and none of the (N-M) non-lobbying firms has an incentive to start lobbying. Hence, in a non-cooperative lobbying equilibrium (where firms can be of different sizes): (12) )( )1 ()]([)1()(' ** λ π fK B AgA pAgAp m m M m M=− ′ +−− for Mm ..., , 1= (13) )( ) 1()]([)(' λ π fK B gApAp n MM ≤ ′ +− , for NMn ..., ,1 += where ∑ = =M mm MAA 1 * represents total industry lobbying and M is endogenously determined. The M equations of (12) are best-lobbying-response functions of the lobbying firms. A sufficient condition for the equilibrium to be unique is that the best-response functions’ slopes are less than one in absolute value for all firms (Eichberger, 1993: 105). Differentiating (12) with respect to j A , where Mj ..., ,1= and mj ≠ , the slope of any such response function is: (14) )( * mm m j m dA dA ρσ σ + − = where [ ] 0)1 ()(' )1() (" * * <− ′ − −= m M m M m AgA pAg Ap σ and [ ] 0)1( )(')1()]( ** <− ′ −− ′′ += m M m M mAgApAgAp πρ . Clearly, the absolute value of the slope of the response function is less than one for all m and j . www.economics-ejournal.org 17 We next consider the influence of a firm’s size on its lobbying. Looking at (12), note that the equilibrium value of M A is the same for all firms, as are the values of B and )( λ f . What differs among firms is the value of Km,, such that ( ) [ ] 0)( 2* >−=∂∂ λρ fKBKA mmmm implies: Proposition 3: Larger firms always lobby more than smaller firms. Although larger firms lobby more than smaller firms, this does not mean that they also lobby more relative to their size. If one defines mmm KAa ** = as the th m firm’s optimal lobbying per unit of capital, then ( ) 0 *>∂ ∂mm Ka if ) ( * λ ρ fA KB mmm −> . This condition is likely to be satisfied for the smallest lobbying firms since m K is very small. The RHS’s value, however, rises with m K and the condition might no longer be satisfied for the largest firms. Lobbying per unit of capital is not necessarily greater for the largest firm than for slightly smaller firms. 5 Contribution Limits and Lobbying Incentives Suppose an upper limit of 0>C is imposed on how much money a firm can contribute to legislators’ election campaigns (or more generally, for lobbying purposes). This, in turn, implies an upper limit (of, say, 0>A ) on how much access-time an individual firm can acquire. Concerning such a lobbying constraint, we establish: Proposition 4: The imposition of a lobbying constraint that is binding on some but not all lobbying firms: a. Definitely raises the lobbying of firms on whom the constraint is not binding. b. Weakly increases the number of firms that lobby in equilibrium, as it heightens the incentives of non-lobbying firms to the join the lobby. www.economics-ejournal.org 18 With NM < lobbying firms and no lobbying constraints, equations (12) and (13) must hold, where ∑ = =M mm MAA 1 * . If a lobbying constraint, A , is imposed such that * h AA < for firms MHh <= ..., ,1 , then the H largest firms are directly affected. If this were the only departure from the unconstrained equilibrium, such that the remaining (M-H) firms would still exert lobbying efforts Am*, then (12) would change to: (12’) )( ) 1()] ([)1()(' λ π fK B A gApAgAp h M M>− ′ +−− ′ ′ for Hh ..., ,1= (12”) )( )1()]([)1()(' ** λ π fK B AgAp A gAp m m M m M >− ′ + −− ′′ for MH m ..., , 1+= where ∑∑ =+= ′=<+= M mm M M Hm m MAAAAHA 1 * 1 * .22 Consequently, all lobbying firms have incentives to lobby more. While the contribution limit prevents the H largest firms from making adjustments, the smaller ) (H M− lobbying firms are able to expand their engagement. Also, since [ ] [ ] )1()]([)(')1()]([)(' gApApgApAp MMMM ′ +−< ′ +− ′′ ππ , so far non-lobbying firms have stronger incentives to lobby. It, therefore, is quite possible thatfor the largest of the )( MN − pre-constraint non-lobbying firms, we have: [ ] [ ] )()1()]( [)(' λπ fKBgApAp n MM ≤ ′ +− without constraint, but _________________________ 22 Since AM’< AM, the equality of (12) turns into the inequality of (12’) for firms with binding constraints; and it turns into the inequality of (12”) for firms with no binding constraint when lobbying of the firm under consideration is evaluated at the original lobbying equilibrium. www.economics-ejournal.org 19 [ ] [ ] )()1()]([)(' λπ fKBgApAp n MM > ′ +− ′′ with constraint. 6 Size Distribution of Firms and Industry Lobbying Concerning the relationship between the size-distribution of firms and the industry’s lobbying effort, we state: Proposition 5: Provided 0)( ≥ ′′′ Hg , a more unequal size-distribution of lobbying firmsimplies less total lobbying by the industry. The number of lobbying firms,however, might grow as the size-distribution becomes more unequal. Given an initial cumulative firm-size distribution, ) , (1 s KG , a new distribution, ) ,( 2 sKG , is considered to be more unequal if, at a constant mean, [ ] 0) ,() ,( 0 12 ≥ − ∫dKsKG sK G j K for all KK j≤≤0 , where K denotes the largest firm’s size.23 If any two of the M currently lobbying firms changed their sizes such that 0=+ ji dKdK , then the mean of the distribution would remain the same. If, furthermore, ji KK > and 0> i dK , then the distribution becomes more unequal, as defined above. Stated more intuitively, if a larger firm expands at the expense of a smaller firm, the industry’s size distribution becomes more unequal. Accordingly, we evaluate the impact of a more unequal size distribution on total industry lobbying by evaluating: (15) i j M i MdK K A K A         ∂ ∂ − ∂ ∂ for ji KK > and 0> i dK _________________________ 23 For further explanations, see Laffont (1989). www.economics-ejournal.org 20 where ∑ = = M mm M AA 1 * and we assume, for the time being, that the number of lobbying firms, M , remains unchanged. Based on differentiating the M equations of (12) with respect to j K , as shown in Appendix A, equation (16) expresses the lobbying response by the jth firm itself, equation (17) shows the lobbying response of each of the other firms, and equation (18) states the entire industry’s lobbying response to a change in the size of firm j: (16) () ( ) 0 1 1 )( 1 2 * >                    +        +         −= ∂ ∂ ∑ ∑ = ≠ M mmmj M jm m m j j j fK B K A ρσρ ρσ λ (17) () 0 1 )( 1 2 * <                  +         = ∂ ∂ ∑ = M mm mj i i j j i fK B K A ρ σρ ρ σ λ (18) () () 0 1 )( 1 2 1 * >                  + − =         ∂ ∂ = ∂ ∂ ∑ ∑ = =M mmm jj M mj m j M f K B K A K A ρσ ρλ . Substitution of (18) into (15) for i and j then yields: (19) ( ) 0 1)( 11 1 22 <                  +        + − =                 ∂ ∂ −         ∂ ∂ ∑ = i M mmm jjii i j M i MdK f B KK dK K A K A ρσλ ρρ for 0> i dK . www.economics-ejournal.org 21 The value of [ ] 0)1()(')1()]([ ** >− ′ −− ′′ +−=− m M m M mAgApAgAp πρ rises with m K , provided 0)( ≥ ′′′ Hg , since AM is given and * m A is positively related to m K . It follows that 22 jji i K K ρρ − > − for ji KK > in the first bracket of the RHS of (19). And since the expression of the second bracket on the RHS in (19) is always positive, a more unequal size distribution of firms reduces the industry’s overall lobbying effort. The intuition underlying the above finding, focusing on the role of access cost – since this is the key feature that distinguishes our setting from that of Hillman – runs as follows. For the contracting firm j , the percentage increase in the price of access per unit of capital is greater than the percentage decrease in the price of access per unit of capital experienced by the expanding firm i . This leads firm j to cut its lobbying by more than the corresponding lobbying expansion by firm i , resulting in a fall in the total lobbying of the industry. In Hillman’s setting, since access is costless (although time spent lobbying is not), firm j does not undertake as sharp of a cut in its lobbying time. In fact, in Hillman, the cut in lobbying time by firm j matches the expansion in lobbying time by firm i , leaving total industry lobbying unchanged. Finally, if the more unequal size-distribution of firms is associated with less industry lobbying for a given number of M firms, there now emerge added incentives for so-far non-lobbying firms to become active lobbyists under the more unequal distribution. Hence, an industry with a more unequal-size distribution of firms might have more lobbying firms but lobby less in total than an industry with a more equal-size distribution of firms. 7 Lobbying Responses to an Exogenous Price Change when Labor Employment is not Variable Firms can adjust their profits either through lobbying for a higher price or through producing more. When managerial resources are required for both lobbying and producing, there exists a trade-off between the alternative ways of influencing profits. A CEO’s optimal allocation of management time between lobbying and managing is, therefore, critically affected by any exogenous change, such as a change in the world price of the good produced by the firm. www.economics-ejournal.org 22 Concerning the impact of a change in the world price, π ,on individual firms’ and the entire industry’s lobbying, we obtain (assuming that firms cannot alter their respective labor-employment levels): Proposition 6: If the world price of the industry’s good declines, a. The largest lobbying firm always lobbies more. b. The smallest lobbying firm’s response is indeterminate. In fact, it might lobby less, and possibly even turn into a non-lobbying firm. c. The industry as a whole always lobbies more. Assume initially that the number of lobbying firms before and after the fall in price remains the same (say, at M ). As shown in Appendix B, the impact of a declining world price on the th j firm’s profit-maximizing lobbying response is: (20) ( ) ( )( ) ()      +        ′ − ′ + ′ = ∂ ∂∑∑ =≠ m mm m M jm mjj mmj j jj gg g A 1 * 1 ρσ ρρσσ ρπ . The denominator of the above expression is always positive, since ( ) 0> mm ρσ . Concerning the numerator, the first component, ( ) jj g ρ ′ , is always negative. The sign of the second component, on the other hand, is not determinate as it depends on the signs of ( ) jm m jgg σσ ′ − ′ for all m = 1,..,M other than j. With the substitution of the full expressions for m σ and j σ , we get: ( ) [ ] jmmj M jmmj ggggApgg ′ − ′ = ′ − ′)(" σσ , where )1()1( ** mmjj Ag gAgg − ′ = ′ >− ′ = ′ and )1()1( ** mmjj AggAgg −=<−= for mj KK > , using Proposition 3. Accordingly, for the largest firm of size ( ) 0 , 111 < ′ − ′ σσ mm ggK for all 1≠m and the price-fall always results in more lobbying. On the other hand, for the smallest lobbying firm of size ( ) 0 , > ′ − ′MmmMM ggK σσ for all Mm ≠ . So, accounting for both the first and second component in the numerator, the smallest lobbying firm’s response to the price-fall is indeterminate; one cannot preclude the possibility that this firm’s lobbying declines when the world price falls. For the next smallest firm 1−M , www.economics-ejournal.org 23 ( ) 0 11 > ′ − ′−− MmmM gg σσ for all 1 , −≠ MMm , while ( ) 0 11 < ′ − ′ −− MmmM gg σσ for m = M. It thus is quite possible that this second-smallest lobbying firm lobbies less as well; but this response is less likely than it is for the smallest lobbying firm M. More generally, one can see that, as the influence of these negative terms rises with the size of the firm, larger and larger firms are increasingly likely to lobby more as the world price falls. To highlight the different influences on a firm’s lobbying response, we substitute the domestic price function of (6) in the firm’s first-order condition of (12) and differentiate it with respect to π, yielding: (21) πρ σ ρπ d dA Ag d dA M m m m mm − − =)1(' ** . The first term on the RHS is always negative, meaning that, at constant industry lobbying, M A , all already lobbying firms increase their lobbying in response to a world price decline. The second term on the RHS, on the other hand, is positive since, as will be shown in (22), total or industry lobbying must rise in response to the price decline. Accordingly, an individual firm’s lobbying effort can decline only if the rise in industry lobbying is sufficiently large to more than offset the decreased lobbying of the firm (at constant industry lobbying). The industry’s total lobbying response to a price decline can be ascertained by summing of (20) for all M lobbying firms and noting that ( ) ∑∑ = ≠ = ′ − ′ M j M jm jmmj gg 1 0 σσ . This yields: (22) ( ) ∑∑ ∑ = = =<      +        ′ = ∂ ∂ = ∂ ∂M jm mmm M jj j j M g A A 1 1 1 * 0 1 ρσ ρ ππ . www.economics-ejournal.org 30 Appendix A: Derivations of the Expressions for jj KA ∂∂ * and j i K A∂∂ * [Note: MiMj ..., ,1 ; ..., ,1 == ] The M equations of (12) describe a non-cooperative equilibrium for the M actually lobbying firms. Differentiating these functions with respect to j K yields: (A.1)                     =                     ∂∂ ∂∂ ∂∂ ∂∂                     + + + + m m m m jM j j j MMMMM S S S S KA KA KA KA . . / . . / / / )(.. ...... ...... ..)( ..)( ..)( * * 3 * 2 * 1 33333 22222 11111 ρσσσσ σρσσσ σσρσσ σσσρσ where: [ ] 0)1()(')1()(" ** <− ′ −−= m M m M mAgApAgAp σ , [ ] 0)1()(')1()]([ ** <− ′ −− ′′ += m M m M mAgApAgAp πρ for Mm ..., ,1= ; 0= m S for jm ≠ and [ ] 0)( 2<−= λ fKBS jm for jm = Now, whether we can determine the expressions for jj KA ∂∂ * and ji KA ∂∂ * by simply applying Cramer’s rule would depend, of course, on whether the first matrix on the LHS of (A.1) is non-singular. Let us check if this is so. The determinant, ∆ , of this matrix is given by: (A.2) ( ) ∏∑ ==     +=∆ M m M mmmm 11 1 ρσρ Since 0< m σ and 0 < m ρ , 0>∆ if M is even and 0<∆ if M is odd.With 0≠∆ , the matrix is non-singular and we can indeed apply Cramer’s rule. Applying this rule, then, it is easily determined that: www.economics-ejournal.org 31 (A.3) ( ) ( ) 0 1 1 )( 1 2 * >                    +        +         −= ∂ ∂ ∑ ∑ = ≠ M mmmj M jm mm j j j fK B K A ρσρ ρσ λ (A.4) () 0 1 ) ( 1 2 * <                  +         = ∂ ∂ ∑ = M mm mj i i j j i f K B K A ρ σρ ρ σ λ . www.economics-ejournal.org 32 Appendix B: Derivation of the expression for π ∂∂ * j A Differentiating the M equations of (12) with respect to π , we obtain: (B.1)                     ′ ′ ′ ′ =                     ∂∂ ∂∂ ∂∂ ∂∂                     + + + + M M M MMMM g g g g A A A A . . / . . / / / )(.. ...... . ..... .. )( . .)( ..)( 3 2 1 * * 3 * 2 * 1 3 3333 22 222 11 11 1 π π π π ρσσ σσ σρσσ σ σ σρσ σ σ σσρσ where M iA gg i i ..., ,1 ),1( * = − ′ = ′ and mm ρσ , (where Mm ..., ,1= ) are as defined earlier. Note that we can obtain the expression for π ∂∂ * j A by once again applying Cramer’s rule. Applying this rule, then, it is determined that: (B.2) ( )( ) ( )      +        ′ − ′ + ′ = ∂ ∂∑∑ =≠ M mmm M jm mjjmm j j jj gg gA 1 * 1 )( ρσρρσσ ρπ . www.economics-ejournal.org 33 References Attkisson, S. (2012). Behind the Closed Doors of Washington Lobbyists. CBS News. October 7. http://www.cbsnews.com/8301-3445_162-57527490/behind-the-closed-doors-ofwashington-lobbyists/ Austen-Smith, D. (1991). Rational Consumers and Irrational Voters: A Review Essay on Black Hole Tariffs and Endogenous Policy Theory by Magee, S.et al., Cambridge University Press 1989. Economics and Politics 3 (1): 73–92. http://onlinelibrary.wiley.com/doi/10.1111/j.1468-0343.1991.tb00040.x/abstract Austen-Smith, D. (1994). Strategic Transmission of Costly Information. 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