# Lobbying & Costly Lobbying

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Lobbying & Costly Lobbying. Special Interest Politics – Chapters 4-5 G. Grossman & E. Helpman MIT Press 2001. Presented by: Victor Bennett Richard Wang Feb 13 2006. Overview. Lobbying One Lobby Two States of the World Three States of the World Continuous Information Ex Ante Welfare - PowerPoint PPT Presentation

### Text of Lobbying & Costly Lobbying

• Lobbying & Costly LobbyingSpecial Interest Politics Chapters 4-5G. Grossman & E. Helpman MIT Press 2001

Presented by:Victor BennettRichard WangFeb 13 2006

• OverviewLobbyingOne LobbyTwo States of the WorldThree States of the WorldContinuous InformationEx Ante Welfare

Two LobbiesLike BiasOpposite BiasMultidimensional Information

More General Lobbying Game

• OverviewCostly Lobbying

Fixed Exogenous CostsOut to SIGs controlVariable Endogenous CostsDepend on Actions of the SIGPolicymaker-imposed costsCosts as a choice variable for the policymaker

How do these costs affect equilibria under different model conditions?

• Basic Model SettingpPolicy VariableqState of the WorlddBias (d>0, unless otherwise stated)

• Basic Model SettingAssumptions:Lobbyist knows the state of the world (q) but the policymaker does not

The policymaker has a prior belief on the state of the world (realization of a random variable, ): ~ U[qmin,qmax]

• One Lobby, Two States of the WorldThe Setting

Two states Low or High q {qL,qH}, qL

• One Lobby, Two States of the WorldFull Revelation Equilibrium

The lobbyist tells the truth to inform the policymaker.

The policymaker:Believes the state of the world as told by the lobbyistSets the policy p = qH or p = qL when the state is High or Low, respectively.

• One Lobby, Two States of the WorldWhen the true state is qH, the lobbyist will tell the truth because:U(p=qH, qH) > U(p=qH, qL)

=> (qH+d)-qH < (qH+d)-qL

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

U(p=qL, qL) > U(p=qH, qL)

=> (qL+d)-qL qH -(qL+d)

=> d (qH- qL)/2(4.1)

• One Lobby, Two States of the World

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 lobbyists report lacks credibility.

• One Lobby, Two States of the WorldBabbling Equilibrium

The policymaker:Distrusts the lobbyist about the reported stateThe policymaker remains uninformed.Sets the policy p = (qH+qL)/2

The lobbyist has no incentive to report truthfully.

• One Lobby, Three States of the WorldThe Setting

Low, Medium, High States: q {qL,qM ,qH}, qL

• One Lobby, Three States of the WorldFull Revelation Equilibrium

The lobbyist tells the truth to inform the policymaker.

The policymaker:Believes the state of the world as told by the lobbyistSets the policy p = qH, p = qM, or p = qL when the reported state is High, Medium, or Low, respectively.

• One Lobby, Three States of the WorldWhen the true state is qL, the lobbyist will tell the truth iff:

(i)U(p=qL, qL) > U(p=qM, qL)and(ii)U(p=qL, qL) > U(p=qH, qL)

Since qL d (qM- qL)/2(4.2)

• One Lobby, Three States of the WorldWhen the true state is qM, the lobbyist has no incentive to report qL because the SIG prefers a policy larger than qM.

The lobbyist will tell the truth at state qM iff:

U(p=qM, qM) > U(p=qH, qM)

=> (qM+d) - qM qH - (qM+d)

=> d (qH- qM)/2(4.3)

• One Lobby, Three States of the WorldWhen the true state is qH, the lobbyist has no incentive to report either state qM or qL because these will result in a policy level that is lower than p = qH.

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

• One Lobby, Three States of the WorldPartial 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 WorldSay, (4.3) is violated.

Lobbyist communicate the state as Low or Not Low.

Truthful report of Not Low requires:(qM+d) - qL (qM+qH)/2 - (qM+d)

=> d (qH- qM)/4 - (qM- qL)/2(4.4)

Truthful report of Low requires:(qL+d) - qL (qM+qH)/2 - (qL+d)

=> d (qH- qM)/4 + (qM- qL)/2(4.5)

• One Lobby, Three States of the WorldBabbling Equilibrium

The policymaker:Distrusts the lobbyist about the reported stateSets the policy p = (qH+qM+qL)/3 whether the state is High, Medium, or Low.

The lobbyist has no incentive to report truthfully.

The policymaker remains uninformed.

• One Lobby, Three States of the WorldWhich 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, d, 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[qmin,qmax]

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

Lobbyist indicates a range (R) that contains the true value of q.Example: Lobbyist report q in R1 qmin q q1Lobbyist report q in R2 q1 q q2Lobbyist report q in Rn qn-1 q qn

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

• One Lobby, Continuous Information

Objective: Find values of q1, q2 qn such that the policymaker sees the lobbyists report as credible.

Question: What values of qk-1, qk, and d does the lobbyist prefer to tell the truth when q is in Rk?

• One Lobby, Continuous InformationIdea: Suppose q is in R1, the greatest temptation for the lobbyist to lie is when q is a bit less than q1. So we set: (q1+d) - (qmin+q1)/2 (q2+q1)/2 - (q1+d)=> q2 2q1+4d-qmin(4.6)

Now suppose q is in R2. To prevent false report that q is in R1, we set: (q1+d) - (qmin+q1)/2 (q2+q1)/2 - (q1+d)=> q2 2q1+4d-qmin (4.6)

(4.6) & (4.6) => q2 = 2q1+4d-qmin (4.7)

• One Lobby, Continuous InformationExtending the argument to R3, R4, and so on, we have: qj = 2qj-1+ 4d qj-2(4.8)

The top most value must coincide with the maximum support of the distribution: qn = qmax (4.9)

(4.8) & (4.9): qj = (j/n)qmax+ ((n-j)/n)qmin - 2j(n-j)d (4.10)

Eqm condition requires that q1 > qmin, which is satisfied iff:2n(n-1)d < qmax - qmin (4.11)

• One Lobby, Continuous InformationInequality (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 EquilibriumThe smaller is d, 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 WelfareIf 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.

• Ex Ante WelfareUsing (4.10) to obtain the form of qj and qj-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.

• Two LobbiesThe SettingSame information assumptions as one lobby case, except we have two lobbies now.

The two lobbies may have different direction of biases:Like Bias: Both di,dj > 0 or < 0; |di| < |dj|; i jOpposite Bias: sign(di) sign(dj); |di||dj|; i j

Three types of messages:Secret: Each lobbyist is ignorant of the alternative info sourcePrivate: Each lobbyist is aware that another has offered/will offer advice but ignorant on the contentPublic: Subquent lobbyist can condition the report on the info that the policymaker already has.

• 2 Lobbies, Like Bias, Secret MessageOutcomeNo 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.

• 2 Lobbies, Like Bias, Secret MessageExample

Lobbyist 1 sends either m1 (indicates q q1) or m2 (indicates q q1).

Lobbyist 2 sends either 1 (indicates q 1) or 2 (indicates q 1), where q1 < 1.

• 2 Lobbies, Like Bias, Secret Messageq1qminqmaxm1m2121

MessageInferencem1 and 1 qminq q1m2 and 2 1q qmaxm2 and 1 q1q 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^

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