Lobbying: The theory of America’s (other) favorite pastime

1. Lobbying: The theory of America’s (other) favorite pastime Presented by: Sharon Poczter November 26, 2007

2. Lobbying is economically and politically significant in the U.S. *Data from opensecrets.org

3. Top 10 U.S. Lobbying Spenders 1998-2007

4. What is the definition of lobbying? “Meetings between representatives of interest groups and policymakers in which the former try to persuade the latter that their preferred positions would also serve the policymaker’s interests and perhaps those of the general public.” (Grossman, Helpman 2001)

5. As always, a tradeoff… Tradeoff in collective action: Advantages Pooling resources Increased bargaining power Disadvantages Free Riders • The logic of collective action first challenged by Olson, 1965

6. What would we like to model? What statements by the lobby will be credible, i.e. under what conditions is it optimal for a SIG to communicate the truth about the state of the world and the policymaker to believe the SIG? Are there other equilibrium?

7. Dimension of Variation in Lobbying Models • Information • Two states of the world • Three states of the world • Continuous • Number of lobbies • One, two • Bias of lobbies • Favored direction of policy relative to policymaker, like and opposite bias

8. Equilibrium Notions in Costless Lobbying Models • Truth-telling equilibrium (truth and trust) • Babbling equilibrium (lying and distrust) • Partial information equilibrium • Partition equilibrium (ranges)

9. Equilibrium Results for Different Environments

10. Setup of the One Lobby, Two States Lobbying model Policy variable p Information described by θ policy environment information Welfare functions: G(p,θ)=-(p-θ)² U(p,θ)=-(p-θ-δ)² Policymaker ideal: p=θ SIG ideal: p=θ+δ Policymaker behavior: Set p=θ when lobbying reveals true state Set p=E(θ) when uncertain about state

11. Conditions of Truth-Telling Equilibrium in Two States Policymaker accepts any claim the lobbyist makes as the truth, lobbyist reports truth No incentive to lie when θ=θH Conditions not to lie when θ=θL δ≤ (θH-θL)/2

12. Conditions of Another Equilibrium: Babbling Equilibrium • Policymaker distrusts everything the lobbyist reports • Policymaker always implements: • p=(θH+θL)/2 • Lobbyist does not report truthfully

13. Conditions for Truth-Telling in Three States of the World Conditions for SIG truth-telling: δ ≤ (θM- θL )/2 δ ≤ (θH- θM )/2 As we can see, more states, more restrictions

14. Partial Information Equilibrium: Truth-telling Violated • SIG can report “low” versus “not low” • Policymaker implements: • p= θL when “low” • p=(θH+θL)/2 when “not low” • SIG incentive to lie • θH: no lying • θM,θL : policy resulting from truth report result closer to ideal than policy resulting from false report, no lying • Conditions for SIG truth-telling: • δ≤ (θH–θM)/4 +(θH–θM) /2 (IC for θM) • δ≥ (θH–θM)/4 +(θM–θL) /2 (IC for θL)

15. Equilibrium Analysis with Continuous Information: Partition Equilibrium • Truth-telling harder and harder • Lobbyist can indicate ranges • “θ is in range n” means • θn-1≤ θ≤ θn • Equilibrium conditions • θj≥ (j/n) θmax+(n-j/n)θmin-2j(n-j)δ • 2n(n-1) δ< θmax-θmin (Necessary and sufficient condition)

16. Welfare Analysis in the Partition Equilibrium EGⁿ=-(1/(12(θmax- θmin))∑(θj–θj-1) EUⁿ=-(1/(12(θmax- θmin))∑(θj–θj-1) -∑(θj–θj-1)3= - (θmax- θmin)2 -4δ2(n2-1) θmax- θmin n2 Ex-ante welfare increasing in n more reports, everyone better off

17. Important Conclusions • Bias important and information transmission • Equilibrium driven by δ • As the information space becomes more “complex” (increase in number of states), full information transmission harder • Both parties prefer outcomes with greater n

18. Lobbying: Part II Presentation to 279B Dec 3, 2007

19. Agenda • Recap the key results from last week • Extending the model to 2 lobbies • Costly lobbying • Final thoughts 071202-279-Lobbying presentation v4

20. The basic setup Policy Space: θ δ θL “Low State” θH “High State” • Information: • Policy maker does NOT know the true state of the world, and believes each state to be equally likely • Interest group knows the state of the world, but can only convey this through messages • Preferences: • Policy maker prefers the true state of the world • Interest group prefers the true state plus δ, with symmetrically falling preferences around θ + δ 071202-279-Lobbying presentation v4

21. The problem is that the interest group may not have any credible message space 2-state world: Policy Space: θ δ δ θL “Low State” θH “High State” If the true state is “low” SIG reports “high” If the true state is “high”, SIG reports “high” • Two types of equilibrium emerge: • No-content equilibrium if δ too large • Fully communicative equilibrium if δ small enough • Adding additional ‘medium’ states narrows the δ over which fully-communicative equilibria occur • Rationale: Once the SIG has an incentive to mis-report, the policy maker will ‘shade’ their policy choice. Knowing this the SIG has incentive to over-report, etc. 071202-279-Lobbying presentation v4

22. In continuous space, there are no fully-informative equilibria Continuous states-of-the-world: θ* θ** Policy Space: θ δ θL “Lower Support” θH “Upper Support” • If the interest group must communicate a specific θ, there are no informative equilibria • Breakdown of fully-informative equilibrium: • Assume that the true state of the world is θ* which is reported and believed • Then the interest group has incentive to report θ**= θ*+δ • Knowing this the policy maker discounts the report by δ • Knowing the discount, the interests group reports θ*+2δ • The policy maker knows this and discounts by the bias, now 2δ • Etc. 071202-279-Lobbying presentation v4

23. Partial information can, however, be conveyed through communicating ranges Continuous states-of-the-world: 1. SIG truthfully reports the range of the state-of-the-world Range 1 Range 2 Policy Space: θ p1 p2 θL θH δ 2. Policy maker trusts the report and makes best available prediction 3. δ must be small enough that at the highest State of the World in Range 1, the SIG indifferent between p1 to p2 • The number (and narrowness) of informative ranges depend on δ 071202-279-Lobbying presentation v4

24. Agenda • Recap the key results from last week • Extending the model to 2 lobbies • Costly lobbying • Final thoughts 071202-279-Lobbying presentation v4

25. Broadening our scope to multiple SIGs, we can examine 3 types of messages Other SIG meeting with PM Content of other SIG’s message There are no 100% secret equilibria, since this would require belief of non-communication by the other SIG, which is incorrect. 071202-279-Lobbying presentation v4

26. Private messages: A truth-telling equilibrium exists, but is fragile • Truth-telling equilibrium: • Policy maker interprets with p* = min(m1,m2) • Both assumed to tell the true state of the world • Unilateral deviation if unprofitable: • mi lower than θ results in p<p* yielding lower utility • mi higher than θ results in no change to p • Therefore deviation is unprofitable • But consider the following alternate strategy • Play mi=θ+δi (ideal state for SIG i) • If mi>m-i=θ no impact of message • But if m-i>θ then mi>m-i yields p>p* which is preferred • Therefore truth-telling is a Nash equilibrium, but is not trembling-hand perfect 071202-279-Lobbying presentation v4

27. Public messages:No complete truth-telling equilibrium exists • Assume a truth-telling equilibrium exists • SIG 1: reports m1=θ • SIG 2: confirms with m2=θ • Policy-maker sets p=θ • Consider a deviation by SIG 1 • SIG 1: Reports m1=θ+ epsilon • SIG 2: Confirms with m2=m1 • Policy-maker sets p=θ+ epsilon • Therefore SIG 1 will want to deviate • Notice this works because messaging is sequential, so SIG 2’s strategy space is: • F(m1,θ) = m2 • So only 1 is deviating, 2 is just responding 071202-279-Lobbying presentation v4

28. Public messages:Partial-information equilibria exist Continuous states-of-the-world: θL θH Steps: 1. SIG 1 indicates a credible partition m1- m1+ 2. SIG 2 sub-divides one of the SIG 1 message spaces m2- m2+ 3. Policy maker learns about subdivided spaces m1-, m2- m1+, m2- m1+, m2+ p1 p2 p3 071202-279-Lobbying presentation v4

29. Public messages:Notes on 2-SIG, partition equilibria • In equilibrium, SIG 1 anticipates SIG 2’s message when deciding m1 • Equilibrium is then the solution to the corresponding linear system • Many equilibria exist, depending on chosen SIG order and partitions • Krishna and Morgan have shown • No more information is conveyed in 2-SIG messaging, than if just the more-moderate SIG messaged on their own • Ex Ante welfare of all participants is higher for any n-division with just the moderate SIG messaging, than both 071202-279-Lobbying presentation v4

30. 2 lobbies, with opposite bias:Equilibria can be more informative, but not perfect • Truth-telling equilibrium does not exist • Assume the policy-maker accepts the SIGs advice only if m1=m2, in which case p*=mi • If SIGs advice is not credible, policy maker chooses p (say as the midpoint of θ) • Then both will have incentive to report truthfully unless the true θ is not ‘too close’ to the mid-point (where one would prefer the default result) • Krishna and Morgan have shown that: • Partial revelation can occur if both lobby groups are nonextreme (don’t prefer one support in all states of the world) • Ex Ante welfare is higher under these than any single SIG lobbying result This is just an example showing the difficulty, but the result holds in general 071202-279-Lobbying presentation v4

31. Agenda • Recap the key results from last week • Extending the model to 2 lobbies • Costly lobbying • Final thoughts 071202-279-Lobbying presentation v4

32. Lobbying costs • Introduces signaling into the message space • Choosing costly signals conveys extra information • Recall that in the 2-state world, communication was impossible if δ was too large Policy Space: θ δ θL “Low State” θH “High State” If falsely reporting the low-state as ‘high’ is costly, the SIG will choose not to do it under some circumstances • Solution requires: • Incentive constraint to hold • Participation constraint to hold (new) 071202-279-Lobbying presentation v4

33. When Lobbying is Costly 3 Types of Costs: Fixed Varied Imposed by policymaker

34. Equilibrium Notions in Costly Lobbying Models

35. Signaling Equilibrium with Costly Lobbying Whether or not the SIG chooses to lobby provides a signal Policymaker implements p=θH if lobbyist shows up, p= θH otherwise SIG willing to pay cost in θH iff: lf≤ (θH – θL)[2δ+ θH-θL] ≡ k1 SIG refrain from lobbying in state θl iff: lf≥ (θH – θL)[2δ-( θH-θL)] ≡ k2

36. Mixed Strategy Equilibrium with Costly Lobbying Strategy: Lobby with probability 1 when θ=θH Randomize when θ=θL Lobby with probability ς<1 Policymaker uses Bayes Rule: Expectation of p|SIG lobby p=(θH+ ς θL)/(1+ ς) Set p= θL when no lobby SIG must be indifferent between lobbying and not lobbying when θ=θL ς = (θH- θL) ((δ ± √ δ2-lf)/lf) – 1

37. Equilibrium with One Lobby, Continuous Information • 2 partition equilibrium : • Lobbying informs the policymaker whether θ exceeds a critical value or not • Situations where partition equilibrium does not exist without cost • Equilibrium exists if for some value of θ between θmin and θmax , SIG indifferent between costly lobbying and obtaining p from higher range, and obtaining p from lower range, with no cost

38. Two Lobbies, Costly Lobbying • Like biases • δ1>δ2>0 • Free-rider equilibrium where one group is the credible informant, lobbying in high state, not lobbying in low: • SIG j≠i does not lobby, gets benefit • SIG i lobbies iff: (from earlier) • lf≤ (θH – θL)[2δi+ θH-θL] and • lf≤ (θH – θL)[2δi+ θH-θL]

39. Two Lobbies, Costly Lobbying • Opposite Biases • δ1>0>δ2 • Free-rider equilibrium • Policymaker relies on SIG 1 for information • SIG 1 lobbies if θ=θH, refrains otherwise • SIG 2 free rides • If θ=θH no incentive to lobby (policymaker won’t believe) • If θ=θL prefers to under-report anyway • Each group lobbies in one state • If θ=θH policymaker only expects SIG 1 to lobby • If θ=θL policymaker only expects SIG 2 to lobby

40. Two Lobbies, Costly Lobbying • Unknown Biases • Interest groups know the state of the world • Prevalence of political activity serves as a signal of most likely state • p increasing in number of groups lobbying • Interest groups do not know the state of the world • More extreme group is pure advocate (conditions under which preferable to lobby even if indication is of low state) • Less extreme group provides information • Equilibrium where policymaker chooses relatively high level of policy if both show up, low level if only one shows up

41. Two Lobbies, Costly Lobbying Bias Unknown • Moderate willingness to lobby implies σH • p(2) = ζθH+(1-ζ)θL • p(1)=(1-ζ)θH+ζθL • p(0)=(1-ζ)θH+ζθL

42. Two Lobbies, Costly Lobbying Bias Unknown • Moderate Lobbies iff: • lf≤(θH+θL)(2ζ-1)[2δ1+(θH-θL)(2ζ-1)] • Moderate refrains iff: • lf≥(θH+θL)(2ζ-1)[2δ1-(θH-θL)(2ζ-1)] • Extreme Always Lobbies iff: • lf≤4δ2(θH-θL) ζ(1-ζ)(2ζ-1)

43. Important Conclusions • Costly lobbying can serve as a signal • Extremism may lead to pure advocacy, regardless of the state of the world • Free riders may exist (whether biases are in the same direction or not) • Other things to consider? • Selling favors

44. All things considered… • Lobbying is noisy, but full revelation may exist under certain conditions • Theoretically, a purpose to cost of lobbying • Also theoretically, show why pure advocacy exists (guns are good, no matter what the truth is)

45. Access costs • The policy-maker can charge for access to their time • If SIGs make this choice after finding out the state of the world, we this is just the costly lobbying described earlier • If SIGs make this choice before finding out the state of the world (e.g. election campaign donations), then: • Modestly-biased groups pay more for access because more informative partition equilibria exist (more divisions, better splits) • Cost of access can vary, involving a bargaining split of the residual between the policy-maker’s benefit of hearing the signal and the SIGs benefit from the policy • Implies varying access costs can exist for issues of different value to the policy-maker 071202-279-Lobbying presentation v4

46. Agenda • Recap the key results from last week • Extending the model to 2 lobbies • Costly lobbying • Final thoughts 071202-279-Lobbying presentation v4

47. Critique • Very dependent on the linear modeling of the policy space • Parallel between the Hotelling’s linear beach vs. circular beach • Strongly dependent on the weak order assumption of preferences (ie. θ+δ > θ+δ+1 > θ+δ+2, etc.) • But SIG’s preferences may not be continuous • Real lobbying is characterized by: • Strong reputational effects • Repeated interactions 071202-279-Lobbying presentation v4