Lobbying & Costly Lobbying

Lobbying & Costly LobbyingSpecial Interest Politics – Chapters 4-5

G. Grossman & E. HelpmanMIT Press 2001

Presented by:Victor BennettRichard WangFeb 13 2006

Overview

Lobbying– One Lobby

• Two States of the World• Three States of the World• Continuous Information• Ex Ante Welfare

– Two Lobbies• Like Bias• Opposite Bias• Multidimensional Information

– More General Lobbying Game

Overview

Costly Lobbying

– Fixed Exogenous Costs• Out to SIG’s control

– Variable Endogenous Costs• Depend on Actions of the SIG

– Policymaker-imposed costs• Costs as a choice variable for the policymaker

How do these costs affect equilibria under different model conditions?

Basic Model Setting

Players: Policymaker Lobby / Special Interest Group (SIG)

Utilities: G(p,)=-(p-)2 U(p,)=-(p--)2

p Policy Variable State of the World Bias (>0, unless otherwise stated)

Basic Model Setting

Assumptions:Lobbyist knows the state of the world () but the policymaker does not

The policymaker has a prior belief on the state of the world (realization of a random variable, ):

~ U[min,max] ~~

One Lobby, Two States of the World

The Setting

• Two states – Low or High є {L,H}, L<H

• Policymaker:– Initially regards L,H are equally likely– Sets p = when the lobbying reveals the true state– Sets p = E when uncertain about the state

• Lobbyist knows the true state

• Discuss 2 equilibria: Full Revelation and Babbling

~


Full Revelation Equilibrium

• The lobbyist tells the truth to inform the policymaker.

• The policymaker:– Believes the state of the world as told by the lobbyist

– Sets the policy p = H or p = L when the state is High or Low, respectively.

One Lobby, Two States of the World• When the true state is H, the lobbyist will tell the truth

because:U(p=H, H) > U(p=H, L)

=> (H+)-H < (H+)-L

• When the true state is L, the lobbyist will tell the truth iff:

U(p=L, L) > U(p=H, L)

=> (L+)-L ≤ H -(L+)

=> ≤ (H- L)/2 (4.1)


• Eq (4.1) measures the degree of alignment between the interests of the policymaker and the lobbyist.

• When Eq (4.1) is satisfied, the equilibrium is fully revealing.

• If Eq (4.1) is not satisfied, the lobbyist’s report lacks credibility.


Babbling Equilibrium

• The policymaker:– Distrusts the lobbyist about the reported state– The policymaker remains uninformed.

– Sets the policy p = (H+L)/2

• The lobbyist has no incentive to report truthfully.

One Lobby, Three States of the World

The Setting

• Low, Medium, High States: є {L,M ,H}, L<M <H

• Policymaker:– Initially regards L, M,H are equally likely– Sets p = when the lobbying reveals the true state– Sets p = E when uncertain about the state

• Lobbyist knows the true state

• We will show 3 equilibriums:– Full Revelation Equilibrium– Partial Transmission Equilibrium– Babbling Equilibrium

~


Full Revelation Equilibrium

• The lobbyist tells the truth to inform the policymaker.

• The policymaker:– Believes the state of the world as told by the lobbyist

– Sets the policy p = H, p = M, or p = L when the reported state is High, Medium, or Low, respectively.


• When the true state is L, the lobbyist will tell the truth iff:

(i) U(p=L, L) > U(p=M, L) and

(ii) U(p=L, L) > U(p=H, L)

• Since L<M <H, reporting H when the state is L is unattractive to the lobbyist anytime it is unattractive to report the state as M. Therefore, we only need to consider (i):

=> (L+) – L ≤ M - (L+)

=> ≤ (M- L)/2(4.2)


• When the true state is M, the lobbyist has no incentive to report L because the SIG prefers a policy larger than M.

• The lobbyist will tell the truth at state M iff:

U(p=M, M) > U(p=H, M)

=> (M+) - M ≤ H - (M+)

=> ≤ (H- M)/2(4.3)


• When the true state is H, the lobbyist has no incentive to report either state M or L because these will result in a policy level that is lower than p = H.

• Therefore, there is no restriction needed for truthful reporting in state H.


Partial Transmission Equilibrium

• When either (4.2) or (4.3) is violated.• Lobbyist cannot communicate full information to

policymaker.• Lobbyist communicates more-limited information.

One Lobby, Three States of the World• Say, (4.3) is violated.

• Lobbyist communicate the state as “Low” or “Not Low”.

• Truthful report of “Not Low” requires:(M+) - L ≥ (M+H)/2 - (M+)

=> ≥ (H- M)/4 - (M- L)/2 (4.4)

• Truthful report of “Low” requires:(L+) - L ≤ (M+H)/2 - (L+)

=> ≤ (H- M)/4 + (M- L)/2 (4.5)


Babbling Equilibrium

• The policymaker:– Distrusts the lobbyist about the reported state

– Sets the policy p = (H+M+L)/3 whether the state is High, Medium, or Low.

• The lobbyist has no incentive to report truthfully.

• The policymaker remains uninformed.


Which Equilibrium?

• For both the policymaker and the lobbyist, the ex ante expected utilities for each equilibrium:

EU(Full) > EU(Partial) > EU(Babbling)

• The lobbyist and the policymaker might coordinate on Full Revelation Equilibrium.

One Lobby, Continuous Information

• In the discrete state case, for a lobbyist to distinguish between all possible states, the bias, , must be smaller than one-half of the distance between any of the states.

• In the case where the state variable is continuous, the lobbyist can never communicate to the policymaker the fine details of the state.

• Compromise: The lobbyist can credibly report to the policymaker a range that contains the true state – Partition Equilibrium.

One Lobby, Continuous InformationThe Setting:• The policymaker has a prior belief on the state of the world (random

variable, ):

~ U[min,max]

• Lobbyist knows the state of the world (the realized value of ) but cannot credibly communicate to the policymaker.

• Lobbyist indicates a range (R) that contains the true value of .

Example: Lobbyist report in R1 min≤ ≤ 1

Lobbyist report in R2 1 ≤ ≤ 2

Lobbyist report in Rn n-1 ≤ ≤ n

• Policymaker will set p = (k+k-1)/2 when the lobbyist report Rk.

~~

~

One Lobby, Continuous Information

Objective:

Find values of 1, 2 … n such that the policymaker sees the lobbyist’s report as credible.

Question:

What values of k-1, k, and does the lobbyist prefer to tell the truth when is in Rk?

One Lobby, Continuous InformationIdea: • Suppose is in R1, the greatest temptation for the lobbyist to

lie is when is a bit less than 1. So we set:

(1+) - (min+1)/2 ≤ (2+1)/2 - (1+)

=> 2 ≥ 21+4-min (4.6)

• Now suppose is in R2. To prevent false report that is in R1, we set:

(1+) - (min+1)/2 ≥ (2+1)/2 - (1+)

=> 2 ≤ 21+4-min (4.6’)

• (4.6) & (4.6’) => 2 = 21+4-min (4.7)

One Lobby, Continuous Information• Extending the argument to R3, R4, and so on, we have:

j = 2j-1+ 4–j-2 (4.8)

• The top most value must coincide with the maximum support of the distribution:

n = max (4.9)

• (4.8) & (4.9): j = (j/n)max+ ((n-j)/n)min - 2j(n-j) (4.10)

• Eqm condition requires that 1 > min, which is satisfied iff:

2n(n-1)< max - min (4.11)

One Lobby, Continuous Information• Inequality (4.11) is a necessary and sufficient condition

for the existence of a lobbying equilibrium with n different reports.

• Three observations:– n=1 always exists -> Babbling Equilibrium– The smaller is , the larger is the maximum number of feasible

partitions, n.– If an equilibrium with n reports exists, then an equilibrium with k

reports also exists for all k < n.

• Question: Given n equilibria, which one will the lobbyist and policymaker agree to coordinate on?

Ex Ante Welfare• If the policymaker and lobbyist agree on their rankings of

the equilibria, the players might be able to coordinate on a particular equilibrium that yields each of them the highest ex ante welfare.

• The expected welfares in an n-partition equilibrium are:

– Policymaker: EGn = (4.12)

– Lobbyist: EUn =(4.13)

• Both players do agree on their ranking of possible equilibria.

n

jjj

1

31

minmax

)()(12

1

2

1

31

minmax

)()(12

1

n

jjj

Ex Ante Welfare• Using (4.10) to obtain the form of j and j-1, combining

with (4.12) and (4.13) and simplifying, we have:

(4.14)

• RHS of (4.14) is an increasing function of n for all n that satisfy (4.11).

• Therefore, both parties would agree, ex ante, the equilibrium using the maximum n allowable by (4.11) is the best among all equilibrium outcomes.

)1(4)(

)(

)(22

2

2minmax

minmax

1

31

nn

n

jjj

Two LobbiesThe Setting• Same information assumptions as one lobby case,

except we have two lobbies now.

• The two lobbies may have different direction of biases:– Like Bias: Both i,j > 0 or < 0; |i| < |j|; i ≠ j– Opposite Bias: sign(i) ≠ sign(j); |i|≤|j|; i ≠ j

• Three types of messages:– Secret: Each lobbyist is ignorant of the alternative info source– Private: Each lobbyist is aware that another has

offered/will offer advice but ignorant on the content

– Public: Subquent lobbyist can condition the report on the info that the policymaker already has.

2 Lobbies, Like Bias, Secret Message

Outcome• No strategic interaction between the lobbyists.

• Each lobbyist will act according to the prescription of one of the equilibria discussed in the one lobby case.

• The policymaker will take action based on the combined info from the two lobbyists.


Example

• Lobbyist 1 sends either m1 (indicates ≤ 1) or m2 (indicates ≥ 1).

• Lobbyist 2 sends either 1 (indicates ≤ 1) or 2 (indicates ≥ 1), where 1 < 1.

m m


m

Message Inference

m1 and 1 min≤ ≤1

m2 and 2 1≤ ≤max

m2 and 1 1≤ ≤ 1

m

m

min max

m1 m2

mm1 2

1

2 Lobbies, Like Bias, Private MessageFull Information Equilibrium

• Many different outcome possible, including Full Information Equilibrium.

• Policymaker:– Believes each lobbyist report precisely and truthfully.– Sets optimal strategy: p = min{m,m^}

• Lobbyists:– Each lobbyist’s report can be used to discipline the other’s– Truthful revelation is an equilibrium

2 Lobbies, Like Bias, Private MessageFull Information Equilibrium

• Example:– = 5– Lobbyist 1 expects m^=5 (truth telling by Lobbyist 2)– No gain for lobbyist if report m>5 (p = 5)– Lobbyist 1 will worsen own situation if report m<5– So truth telling by Lobbyist 1– Similarly, truth telling by Lobbyist 2

• But Full Information Equilibrium is fragile.

2 Lobbies, Like Bias, Private Message

Full Information Equilibrium

• Illustration:– Lobbyist 1 might believe that Lobbyist 2 announces

m^>5 (e.g. error by Lobbyist 2)– If Lobbyist 2 really did report m^>5, then Lobbyist 1

would wish he had reported m>5– If Lobbyist 2 report m^=5, there is no loss for Lobbyist

1 to report m>5 (p is still at 5)– Weakly dominant strategy for each Lobbyist to reveal

his ideal point in every state.

2 Lobbies, Like Bias, Public Message

• Lobbyists report their information sequentially.• Second Lobbyist learns what the first reported.• Full Revelation Equilibrium cannot occur.

• Illustration:– Suppose that there is a full revelation equilibrium– Policymaker believes she learned the true state and set p = – Lobbyist 1 will have an incentive to report ’> , and if Lobbyist 2

follows suit, the policymaker would believe and set p = ’– Both Lobbyists will be better off, while the policymaker will be

worse off.– Therefore, full revelation equilibrium cannot occur.


• Every equilibrium with 2 lobbies can be represented as a Partition Equilibrium (Krishna and Morgan 2001).

• In Partition Equilibrium, the policymaker learns the true lies in one of a finite number of non-overlapping ranges.

• Policymaker’s information comes from the combined information of the two lobbyists.


Example:

• When each lobbyist partition the set of possible values into 2 subsets, the combined information leads to a 3-partition equilibrium.

• Setup:– Policymaker’s Belief: lies between 0 and 24 with equal

probability.

– Lobbyists’ Bias: 1=1, 2=2

2 Lobbies, Like Bias, Public MessageExample

• Setup continued:

– Lobbyist 1 reports first.

– Lobbyist 1 (L1) sends either m1 (indicates ≤ 1) or m2 (indicates ≥ 1).

– Lobbyist 2 (L2) sends either m^1 (indicates ≤ ^1) or m^2 (indicates ≥ ^1), where ^1 <1.

– Hypothesize 1 be reasonably large, so Lobbyist 2 wants to distinguish between “very low” (between min and ^1) or “reasonably low” (between ^1 and 1).

2 Lobbies, Like Bias, Public Message• Scenarios:

– If L1 announces m2,• L2 reporting m^2 will add no new info

• L2 reporting m^1 indicates one of report is false – not equilibrium

– If 1 announces m1, • 2 reporting m^1 informs policymaker the state is “very low”;

policymaker sets p=p(m1,m^1)

• 2 reporting m^2 informs policymaker the state is “reasonably low”; policymaker sets p=p(m1,m^2)

m1 m2

mm1 2

1

p(m1,m^1) p(m1,m^2) p(m2,m^2)

2 Lobbies, Like Bias, Public Message• Equilibrium conditions: L1 and L2 should have no

incentive to report falsely.– For L2, this requires at state = ^1:

(^1+2) – p(m1,m^1) = p(m1,m^2) - (^1+2); 2 =2;

=> ^1 = 1/2 – 4(4.15)

– For L1, this requires at state = 1:

(1+1) – (1+^1)/2 = (1+24)/2 - (1+1); 1 =1;

=> 1 = 10 + ^1/2(4.16)

m1 m2

mm1 2

1

p(m1,m^1) p(m1,m^2) p(m2,m^2)

2 Lobbies, Like Bias, Public Message• Solution:

– Solving (4.15) and (4.16) simultaneously, we have:

^1 = 4/3

1 = 32/3

1

2/3 18/3 52/3

4/3 32/3

2 Lobbies, Like Bias, Public Message• Solution:

– Another possible equilibrium (reverse role of L1 and L2):

^1 = 28/3

1 = 8/3

1

4/3 18/3 50/3

8/3 28/3

2 Lobbies, Like Bias, Public MessageOther findings by Krishna and Morgan (2001):

• It does not matter which lobbyist report first. The set of possible equilibria unchanged by sequence.

• For given parameter values, there exists a maximum number, n, of subset in an equilibrium partition.

• As 1 or 2 approaches zero (less bias from policymaker), n increases and more detailed the information convey.

• Max n with two lobbies ≤ Max n of the more moderate of the two lobbyists

• Ex ante welfares for all parties are higher when the more moderate of the two lobbyists lobbies than that when both lobbyist lobby.

Two Lobbies, Opposite Bias

• Opposite Bias: sign(i) ≠ sign(j); ; |i|≤|j|; i ≠ j

• Policymaker cannot gain complete information (Krishna and Morgan 2001).

• However, policymaker can learn more from the two lobbyist together than from either one alone.


Example:

• 1 = -3; 2 = 3

• lies between 0 and 24.

• With only either one lobbyist, outcome would be either babbling equilibrium or 2-partition equilibrium with: 1 = 18 and ^1 = 6

• 3-partition equilibrium is not possible with either one lobbyist alone, but 3-partition equilibrium is possible when both lobbyist lobby together.


Illustration:

• 1 = -3; 2 = 3

• lies between 0 and 24• L1 reports first, then L2

• Let 1 > ^1

m1 m2

mm1 2

1

p(m1,m^1) p(m1,m^2) p(m2,m^2)


Illustration:• To ensure truth telling by L1 and L2:

L2: ( ^1+3) - ^1/2 = ( 1+ ^1)/2 – ( ^1+3)

=> ^1 = 1/2 – 6(4.17)

L1: ( 1-3) – ( 1+ ^1)/2 = ( 1+24)/2 – ( 1-3)

=> 1 = ^1/2 + 18(4.18)

m1 m2

mm1 2

1

p(m1,m^1) p(m1,m^2) p(m2,m^2)

Two Lobbies, Opposite BiasIllustration:• Solving (4.17) and (4.18) simultaneously, we have a 3-

partition equilibrium with: ^1 = 4 and 1 = 20; p = 2, 12, and 22.

• All parties have higher ex ante welfare if both lobbyists lobby than only one lobbyist lobby.

• Krishna and Morgan (2001) showed partial revelation equilibrium exists whenever both lobbyists are non-extreme.

1

2 12 22

204

Multidimensional InformationBattaglini (2000):• Increasing the dimensionality of the policy problem may improve the

prospects for information transmission.

• Setting:– Policy: 2-dimensional vector p = (p1, p2)

– State: 2-dimensional vector = (1, 2)

– Bias: 2-dimensional vector i = (i1, i2); i ≠ i– Policymaker’s utility: G(p,) = - ∑(pj - j)2

– Lobbyist’s utility: Ui(p,) = - ∑(pj - j- ij)2

• Each lobbyist knows but the policymaker doesn’t.

• Each lobbyist meet with the policymaker in private.

Multidimensional Information

• Given i ≠ i, there exists an equilibrium with full revelation of :

– L1 reports m = 211 + 222

– L2 reports m = 111 + 122

– Based on L1 and L2 reports, policymaker draws two lines:

LL: 211 + 222 = 0

L^L^: 111 + 122 = 0

– Ensures truth telling by both lobbyists (see Figure 4.5)

Multidimensional Information2

1

L^

L

L

L^M

M^

M^

M

Reported by L2

Reported by L1

Figure 4.5

Multidimensional Information

Other results by Battaglini (2000):

• Small reporting mistakes by lobbyists– Probabilities of errors are small and independent for two lobbyist– Lobbyists unaware of the errors

=> There exists an equilibrium with (nearly) full revelation of when the dimension of uncertainty is 2 but not 1 (i.e. both

lobbyists observes the state with error.)

• Can generalize to other utility functions– Relies on the alignment of the different policy dimensions with the

different dimensions of policy uncertainty.

General Lobbying Game

The Setting:

• One policymaker and one lobbyist• Welfare Functions - policymaker: G(p,); lobbyist: U(p,)• Properties of G, U:

– Differentiable– Strictly concave in p

– Gp and Up > 0

• Properties of :– CDF: F(

– PDF: f()=F’(> 0 for all between min and max.

= 0 otherwise


The Setting:

• Lobbyist’s ideal policy > Policymaker’s ideal policy

arg maxp U(p,) > arg maxp G(p,) for all є [min,max]

• Lobbyist:– Learns and communicates m є M to Policymaker. – Strategy: m = ()

• Policymaker:– Suspects Lobbyist’s strategy: ^()

– Forms posterior belief distribution: F^(∙|m,^


The Setting:

• Policymaker chooses p to maximize expected welfare:

pG(m|^) = arg maxp ∫G(p,)dF^(∙|m,^

• Lobbyist will construct () such that U[pG(m|^) ,] is maximized.

• In equilibrium, Policymaker’s belief must be consistent with the incentive faced by the lobbyist: ^() = () .


• No Full Revelation Equilibrium

• Babbling Equilibrium exists

• Partition Equilibrium (Crawford and Sobel 1982)– Lobbyist chooses one of finite n messages:

m є {m1,m2, …., mn}

– Policymaker interprets mi indicates i-1≤ ≤ i

– {1, 2, … , n }, 0 = min and n = max

– Policymaker chooses the policy:

p(mi) = arg maxp

dmfpG

i

i

i )|(ˆ),(1


• Truth telling requires:U[p(mi),i] = U[p(mi+1),i]

• Maximum number of partition exists, nmax.

• The more aligned the interests between the policymaker and the lobbyist are, the greater the nmax.

• If the policymaker and the lobbyist can agree on the ranking of equilibrium, the can agree to coordinate on nmax.

Costly Lobbying

• Fixed Exogenous Costs– Out to SIG’s control

• Variable Endogenous Costs– Depend on Actions of the SIG

• Policymaker-imposed costs– Costs as a choice variable for the policymaker

How do these costs affect equilibria under different model conditions?

Single SIG, Dichotomous Information

With low costs there is an equilibrium where the act of lobbying transmits information and both actors are better off.

Requirement that SIG is willing to pay lobbying cost in H

If ≤ (H –L)(2+H – L) ≡ k1

Requirement that SIG won’t lobby in L

lf ≤ (H –L)(2+H – L) ≡ k2

Because k1>k2, there is a range where both are satisfied and the equilibrium exists.

Players: Policymaker SIG Costs

Utilities: G(p,)=-(p-)2 U(p,l)=-(p--)2-l

lf ≤ (H –L)/2

Single SIG, Dichotomous Information

High costs mean that the SIG can’t tie its own hands, so if the policymaker believes the SIG will lobby if H, the SIG lobbies, but is actually worse off in

expectation if p = (H –L)/2 always and costs are 0.

With this condition of high costs, the pure strategy equilibria are either to make the SIG worse off, or offer no additional information to the policy maker

A mixed strategy, however, might provide information if the SIG always lobbies

if H and mixes when L.



lf > (H –L)/2

Single SIG, Dichotomous InformationPlayers: Policymaker SIG Costs

Utilities: G(p,)=-(p-)2 U(p,l)=-(p--)2-l lf > (H –L)/2

When will a mixed strategy occur?

Beliefs of Policymaker P(Lobbying| H)=1, P(Lobbying| L)=ζ < 1

→ P(H|Lobbying)= 1/(1+ ζ ), P(H|Lobbying)= ζ /(1+ ζ )

→ plobby = (H+ζL)/(1+ζ), pno lobby = L

For mixing, SIG must be indifferent when L, so

ζ = (H – L)(δ+- √δ2 – lf)(1/ lf) - 1

Single SIG, Continuous InformationPlayers: Policymaker SIG


From 4.1.4 we know that with costless lobbying a moderately biased group can convey information, but no group can communicate θ exactly.

The cost allows the policymaker to split the space into two where the act of lobbying per se indicates which partition contains θ if there exists a point θ1 for which the SIG is indifferent between paying lf and the associated policy.

If we assume that the policy makers beliefs are P(θ≥θ1|Lobbying)=1, P(θ≤θ1|Lobbying)=0 then the condition for informative equilibrium is

-(12-θ1/2-δ)2-lf = -(-θ1/2-δ)2

→ θ1 = θmax/2 - 2δ + lf /(θmax/2 )

Two Lobbies, Dichotomous Information, Like Biases

Players: Policymaker SIGs Biases

Utilities: G(p,)=-(p-)2 U (p,l)=-(p--)2-l δ2>δ1>0

When firms have like bias, there exist equilibria where one SIG lobbies and the other free rides

If

lf ≤ (θH-θL)(2δ1+θH-θL) and

lf ≥ (θH-θL)(2δ1-θH+θL)

→ SIG1 only lobbies when θH and SIG2 never lobbies

If

lf ≥ (θH-θL)(2δ1+θH-θL) and

lf ≤ (θH-θL)(2δ1-θH+θL)


Is there an equilibrium where both lobby? Yes, but not a very satisfactory one. If all four conditions are met, and the Policymaker on believes reports of θH from both, both lobby on θH and not θL. One lobbying never happens, so the beliefs are never tested, which means that this survives as a PBE.

Two Lobbies, Dichotomous Information, Opposite Biases


Utilities: G(p,)=-(p-)2 U (p,l)=-(p--)2-l δ2>0>δ1

Despite conflicting interests there exists an equilibrium where one SIG lobbies and the other free rides

If

lf ≤ (θH-θL)(2δ1+θH-θL) and

lf ≥ (θH-θL)(2δ1-θH+θL)


For example, if these equations are satisfied, SIG1 represents the world, and the policy maker ignores 2.

Is there a symmetric equilibrium where both lobby? Yes!

Two Lobbies, Dichotomous Information, Opposite Biases


Utilities: G(p,)=-(p-)2 U (p,l)=-(p--)2-l δ2>0>δ1

A symmetric equilibrium exists where each SIG lobbies in the case it cares most about, and not in the other case, and the policymaker keeps its priors if both or neither lobby.

(θH-θL)(δ-(θH-θL)/4) < lf < (θH+θL)(δ-(θH-θL)/4)

lf must be in the range where SIG1 is unwilling to lobby in θL to force a higher policy, and unwilling to not lobby at θH to avoid the cost. Similar for SIG2.

Two Lobbies, Dichotomous Information, Unknown Biases


Utilities: G(p,)=-(p-)2 U (p,l)=-(p--)2-l δ2>δ1

Lohmann (1993) suggests that extremists may always be willing to lobby but moderates will only do it when situations merit it. Thus, if some groups are active, they are likely the extremists, but if all are active then conditions may be more extreme.

An equilibrium exists where both lobby in θH but not in θL because they are both prefer higher policy levels than the policymaker.

Endogenous Costs, Single SIG, Dichotomous Information

With fixed costs full revelation equilibria occur only for a range of possible values of lf. With variable costs, however, full revelation equilibria always exist. The SIG will never lobby in θL, and in θH will spend enough to tie his hands to show that this is the case.

-δ2 ≥ -(θH-θL-δ)2-lH is necessary and sufficient so the SIG doesn’t pretend the state is θH.

If ≤ (qH –qL)(2d+qH – qL) ≡ k1

lf ≤ (qH –qL)(2d+qH – qL) ≡ k2

Just as in the fixed cost state, a cost between k1 and k2 is necessary for separating equilibrium. In this case, however, the SIG can choose the cost, and thus can always make themselves credible.

Players: Policymaker SIG Bias


δ> (H –L)/2

Endogenous Costs, One SIG, Three States of Nature

Suppose that the policy maker expects the SIGs to not lobby at all if θL, to pay lM if θM, and to pay lH when θH. So we want to find the smallest values that meet these constraints.

lM=(θM – θL)[2δ-(θM-θL)]

However, to keep the SIG from stepping up a campaign in θM to force policy appropriate for θH, we need the following constraint as well:

lH = 2δ(θH – θL) – (θH – θM)2 – (θM – θL)2

This assures that the additional cost of lobbying for the higher level is to burdensome to be worth it when it is not merited, specifically when θM.



lL=0, lH> lM

Endogenous Costs, One SIG, Continuous States of Nature

The policymaker believes that l(θ) uniquely indicates a policy level p = θ. Additionally, the marginal cost of signaling a higher level must be equal to the associated marginal gain from a higher policy level. This is enumerated above. Combining these two yields:

l(θ)=2δ(θ-θmin)

The SIG has no incentive to lie because its utility for a policy it supported, x, is:

U(x) = -(x – θ – δ)2 - 2δ(x- θmin)

Which reaches its maximum at θ, the true state of the world, so the SIG reveals truthfully when there is no fixed costs.


Utilities: G(p,)=-(p-)2 U(p,l)=-(p--)2-l l(θmax)>l(θmin)=0

l’(θ)= 2δ

Fixed and Variable Costs, Continuous States of Nature

Suppose the policy maker becomes fully informed.

In state θ’ ≈ θmin, the policy makers utility is very close, i.e. U(θ’) ≈ U(θmin). For a small enough difference, the difference in utility for the SIG between lobbying and not is too low to justify spending lf. Contradiction. There is not full revelation. However an equilibrium with truthful revelation of all states θ ≥ θ1 exists under the following conditions:

θ1 = θmin + 2(√(δ2 + lf) – δ) → USIG(θ1|Lobbying) = USIG(θ1|Not Lobbying)

l’(θ)= 2δ → marginal benefit of signaling = marginal cost of signaling, i.e. for all θ ≥ θ1 l(θ)= θ


Utilities: G(p,)=-(p-)2 U(p,l)=-(p--)2-Σl l(θmax)>l(θmin)=0

l’(θ)= 2δ

Policymaker-Imposed Access Costs

When the information provided by SIGs is valuable to policymakers, why would they charge access costs?

• Time is a scarce resource and policy maker wants to make sure their time is well used

• Policymaker my have utility over contributions per se• My use access costs to differentiate levels of bias

Also whether access costs are paid before or after realization of θ matters. Since post realization fees regress to the cases we just studied, We’ll focus on imperfectly informed SIGs.

Access Costs, Known BiasPlayers: Policymaker SIG

Utilities: G(p,τ)=-λ(p-)2+(1-λ)c-τ U(p,c)=-E(p--)2-c

With known bias, the policymaker can extract the maximum the SIG is willing to pay. To check for equilibria, however, we must verify that this will be enough to be worth the policymaker’s time.

cmax = [(n2max – 1)/12]*[(((θmax – θmin)2)/ n2

max) - 4δ2]

Notice that bias δ is inversely correlated to cmax. This is because information transmitted for a given n is better and the maximum number of partitions grows as bias decreases.

Also notable is that the total gain to the policymaker from charging c is λcmax+(1-λ)cmax = cmax. This indicates that if cmax > τ then the policymaker charges cmax and gets it, otherwise the policymaker makes herself inaccessible.

Access Costs, Known BiasPlayers: Policymaker SIG


What does this suggest? Low bias makes lobbying worth while to you. Higher bias will make the policymaker pay you so little heed, you are willing to spend little, to nothing, for the opportunity to lobby.

Access Costs, Unknown BiasPlayers: Policymaker SIG


For tractability, the paper constrains δ so that a two partition equilibrium exists even for the highest and lowest biases.

δmin > (θmax – θmin)/12

δmax < (θmax – θmin)/4

Here lobbying is compelling for groups with high or low bias, opposite from before, where propensity to lobby decreased monotonically with δ. We need a point θ1(δ) where the SIG is indifferent between reporting low or high when its bias is δ. The indifference conditions is:

θ1(δ) + δ – pl = ph - θ1(δ) – δ → θ1(δ) = (1/2)(pl + ph) – δ

Updating with Bayes’ Rule (where δ’ is the average of δs that result in lobbying):

pL = E[θL|θL reported] = (3θmin + θmax)/4 – δ’



What does the firm gain from lobbying? The difference between the policy it would report, and the policy the policymaker would enact as a default from its priors:

B(δ, δ’) = (1/2)(δ-δ’)2 – δ’2 + (1/16)(θmax – θmin)2

This function reaches its min at δ’, which means that the group with the average bias for lobbying SIGs. It reaches its maxima at the extrema.

The IR requirements, will always be satisfied at B(δi, δ’) = c. An equilibrium at a given c is thus characterized an equation guaranteeing consistency of beliefs for the policy maker. Some algebra and noting the symmetry of the indifference points about δ’ yields:

δ’ = (1/2)(δmin + δmax)

But how does the policymaker choose the c you’ve been talking about?



Raising c narrows the range where the SIGs will lobby, with the following effects:

1. Reducing the expected impact of τ.

2. Changes the likelihood of lobby, which lowers the quality of p

3. Increases revenues in some cases

The policymaker will maximize utility given λ and τ.

Lobbying & Costly Lobbying

Documents

Transcript of Lobbying & Costly Lobbying