A Model of Party Discipline in Congress

Introduction Model Results Appendix

A Model of Party Discipline in Congress

Galina Zudenkova

University of Mannheim

December 2012

Galina Zudenkova A Model of Party Discipline in Congress

Introduction Model Results Appendix Motivation Questions Roadmap

Motivation

Party Discipline refers to control that party leadership has overits legislature

– ability of party leaders to get their partisancongress members to support party line.



Motivation

Party Discipline refers to control that party leadership has overits legislature – ability of party leaders to get their partisancongress members to support party line.



Motivation

Party Discipline refers to control that party leadership has overits legislature – ability of party leaders to get their partisancongress members to support party line.



Research Questions

What determines the level of party discipline?

Is party discipline weaker in the majority party or in the minorityparty?

What are the impacts of party discipline on policy outcomes?

How does party discipline affect distribution of governmentspending among national districts?

I analyze distribution of government spending in a two-partylegislature within the presidential system.



Research Questions








Research Questions








Research Questions








Research Questions








Roadmap

Allocation of scarce government spending is modeled as anasymmetric contest between congress members.

Majority party has relative advantage in directing spending intoits partisan districts.

Party leaders can enforce discipline in their correspondingparties to make their congress members support party line –maximize party’s total share of spending (rather than followinterests of their home districts).

I show that party discipline favors minority party and leads toless biased distribution of government spending amongnational districts.



Roadmap







Roadmap



Party leaders can enforce discipline in their correspondingparties to make their congress members support party line

–maximize party’s total share of spending (rather than followinterests of their home districts).




Roadmap







Roadmap






Introduction Model Results Appendix Outline Congress Members Discipline Timing

Model

Congress (legislative branch of government), two-party system.

One congress member for each of national districts.

Each congress member is affiliated with one of two politicalparties.

Party that holds a majority – majority party maj.

Other party – minority party min.

nmaj and nmin – number of congress members affiliated with majand min.



Model









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Model

Congress performs purely distributive task of allocatinggovernment spending to nmaj + nmin national districts.

Distributive policies benefit only districts in which spendingoccurs.

Size of government spending is normalized to 1.

To bring spending into home district, each congress memberexerts effort ai ≥ 0, i = 1, ..., nmaj + nmin.

Cost of effort:C (ai) = ai.



Model








Model








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Model

Legislative process of the US Congress:

A bill is introduced to the congress (by any congress member).

It is referred to appropriate committee (where it may beaccepted, amended, or rejected).

If approved, the bill is reported to the congress, and majorityparty leadership decides when to place it for consideration.

When the bill comes up for consideration, debate starts whereeach congress member may introduce amendments or filibusterit.

Once debate is over, the vote of simple majority passes the bill.



Model









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Model

This suggests:

1 Government spending to district i, si ∈ [0, 1], increases witheffort ai and decreases with effort of all other congress membersaj, j 6= i.

2 Legislative process is biased in favor of majority party maj.Ceteris paribus, congress member affiliated with maj finds iteasier to bring spending to home district than congress memberaffiliated with min.

Spending allocation is modeled with the Tullock contest successfunction (1980):

si(a1, ..., anmaj+nmin

)=

βiai∑nmaj+nmin

j=1 βjajif max

a1, ..., anmaj+nmin

> 0,

1nmaj+nmin

otherwise,

where βi = β > 1 if i ∈ maj, βi = 1 if i ∈ min.



Model

This suggests:





)=

βiai∑nmaj+nmin

j=1 βjajif max

a1, ..., anmaj+nmin

> 0,

1nmaj+nmin

otherwise,




Model

This suggests:





)=

βiai∑nmaj+nmin

j=1 βjajif max

a1, ..., anmaj+nmin

> 0,

1nmaj+nmin

otherwise,




Model

This suggests:





)=

βiai∑nmaj+nmin

j=1 βjajif max

a1, ..., anmaj+nmin

> 0,

1nmaj+nmin

otherwise,

where βi = β > 1 if i ∈ maj, βi = 1 if i ∈ min.Galina Zudenkova A Model of Party Discipline in Congress


ModelCongress Members and Party Leaders

Congress members want to bring spending to their homedistricts:

maxai


)− C (ai) .

Party leaders (majority leader and minority leader) care abouttotal share of spending directed into party’s partisan districts.Party leadership’s objective – party line.

Majority party line – to maximize∑i∈maj


).

Minority party line – to maximize∑i∈min


).





maxai


)− C (ai) .

Party leaders (majority leader and minority leader) care abouttotal share of spending directed into party’s partisan districts.

Party leadership’s objective – party line.



).



).





maxai


)− C (ai) .




).



).





maxai


)− C (ai) .




).



).





maxai


)− C (ai) .




).



).



ModelParty Discipline

Party leaders can impose a certain type of control – partydiscipline – on their congress members.

Party discipline – ability of party leader to get his congressmembers to support party line rather than to follow specialinterests of their home districts.Party leaders can impose discipline levels λmaj ≥ 0, λmin ≥ 0,which determine strength with which congress members sharepreferences of their party leadership.Net objective function of congress member i ∈ maj:


)+ λmaj

∑j∈maj

sj(a1, ..., anmaj+nmin

)− C (ai) .

Net objective function of congress member i ∈ min:


)+ λmin

∑j∈min


)− C (ai) .




Party leaders can impose a certain type of control – partydiscipline – on their congress members.Party discipline – ability of party leader to get his congressmembers to support party line rather than to follow specialinterests of their home districts.

Party leaders can impose discipline levels λmaj ≥ 0, λmin ≥ 0,which determine strength with which congress members sharepreferences of their party leadership.Net objective function of congress member i ∈ maj:


)+ λmaj

∑j∈maj


)− C (ai) .



)+ λmin

∑j∈min


)− C (ai) .




Party leaders can impose a certain type of control – partydiscipline – on their congress members.Party discipline – ability of party leader to get his congressmembers to support party line rather than to follow specialinterests of their home districts.Party leaders can impose discipline levels λmaj ≥ 0, λmin ≥ 0,which determine strength with which congress members sharepreferences of their party leadership.

Net objective function of congress member i ∈ maj:


)+ λmaj

∑j∈maj


)− C (ai) .



)+ λmin

∑j∈min


)− C (ai) .




Party leaders can impose a certain type of control – partydiscipline – on their congress members.Party discipline – ability of party leader to get his congressmembers to support party line rather than to follow specialinterests of their home districts.Party leaders can impose discipline levels λmaj ≥ 0, λmin ≥ 0,which determine strength with which congress members sharepreferences of their party leadership.Net objective function of congress member i ∈ maj:


)+ λmaj

∑j∈maj


)− C (ai) .



)+ λmin

∑j∈min


)− C (ai) .




Party leaders can impose a certain type of control – partydiscipline – on their congress members.Party discipline – ability of party leader to get his congressmembers to support party line rather than to follow specialinterests of their home districts.Party leaders can impose discipline levels λmaj ≥ 0, λmin ≥ 0,which determine strength with which congress members sharepreferences of their party leadership.Net objective function of congress member i ∈ maj:


)+ λmaj

∑j∈maj


)− C (ai) .



)+ λmin

∑j∈min


)− C (ai) .




Party leaders bear costs c (λmaj) = λmaj and c (λmin) = λmin ofimposing party discipline.

Majority leader’s problem:

maxλmaj

∑i∈maj


)− c (λmaj) .

Minority leader’s problem:

maxλmin

∑i∈min


)− c (λmin) .

Party leaders’ incentives are negatively aligned.

Intra-party alignment of incentives: congress member caresnot only about her home district’s interests but also about partyline.






maxλmaj

∑i∈maj


)− c (λmaj) .


maxλmin

∑i∈min


)− c (λmin) .








maxλmaj

∑i∈maj


)− c (λmaj) .


maxλmin

∑i∈min


)− c (λmin) .








maxλmaj

∑i∈maj


)− c (λmaj) .


maxλmin

∑i∈min


)− c (λmin) .








maxλmaj

∑i∈maj


)− c (λmaj) .


maxλmin

∑i∈min


)− c (λmin) .





ModelTiming

Timing of events:

Party leaders impose discipline levels λmaj and λmin.

Congress members exert efforts ai, which determine shares ofspending si in each national district.

Game is analyzed backwards to find subgame perfectequilibrium.



ModelTiming

Timing of events:






ModelTiming

Timing of events:






ModelTiming

Timing of events:





Introduction Model Results Appendix Related Literature

Results

Discipline level is higher in min party: λ∗min > λ∗maj > 0.

Intuition: min leader has more stake in imposing discipline than majleader (”disadvantaged” min party gains more than ”advantaged” majparty from same increment of discipline level).

min members exert higher effort: a∗min > a∗maj > 0.

Intuition: maj member has more members from her own party tocare about and less rivals to compete with for spending than minmember⇒ with party discipline, maj member has less incentive toexert effort than does min member.

Total share of spending is greater in maj party:nmajs∗majnmins∗min

= β > 1.

s∗maj > s∗min if β > nmajnmin

, s∗maj ≤ s∗min if β ≤ nmajnmin

.



Results






= β > 1.



.



Results






= β > 1.



.



Results




Intuition: maj member has more members from her own party tocare about and less rivals to compete with for spending than minmember

⇒ with party discipline, maj member has less incentive toexert effort than does min member.


= β > 1.



.



Results






= β > 1.



.



Results






= β > 1.



.



Results






= β > 1.



.



Results

With party discipline, per district spending share of maj partydecreases, while that of min party increases, relative to allocationwith no party discipline:

s∗maj < s0maj, s∗min > s0

min.

Party discipline favors min party and leads to less inequitabledistribution of government spending.

min members exert higher effort under party discipline:

a∗min > a0min.

maj members’ effort might increase or decrease with partydiscipline (depending on parameters’ values).



Results



min.



a∗min > a0min.




Results



min.



a∗min > a0min.




Results



min.



a∗min > a0min.




Results

no discipline party disciplineλmaj = λmin = 0 λ∗min > λ∗maj > 0

amaj a0maj ? a∗maj

efforts ∨ ∧amin a0

min < a∗min

smaj s0maj > s∗maj

per district ∨ ?spending smin s0

min < s∗min

nmajsmaj nmajs0maj > nmajs∗maj

total ∨ ∨spending nminsmin nmins0

min < nmins∗min



Results




min < a∗min



min < s∗min



min < nmins∗min



Results




min < a∗min



min < s∗min



min < nmins∗min



Results




min < a∗min



min < s∗min



min < nmins∗min



Results

Discipline level of minority party is higher than that ofmajority party.

Minority party members exert more effort and might evenget a higher per district share of government spending thanmembers of majority party. (The latter happens if relativeadvantage of majority party in allocating government spending issufficiently low.)

⇒ Party discipline favors minority party, which gets greaterper district share of spending relative to the allocation with noparty discipline.

Party discipline leads to less biased distribution of federalresources among national districts.



Results


Minority party members exert more effort and might evenget a higher per district share of government spending thanmembers of majority party.

(The latter happens if relativeadvantage of majority party in allocating government spending issufficiently low.)





Results







Results







Results







Empirically Testable Predictions

Per district spending share is increasing in discipline strength incorresponding party and decreasing in discipline strength in rivalparty.

Minority leader imposes stronger discipline on his party’scongress members than majority leader.

Total share of government spending of majority party exceedsthat of minority party regardless of discipline strength in bothparties.















Research

This presentation focuses on specific stylized framework.

More general framework:

relative advantage of maj party β might be related to maj partysize nmaj and min party size nmin;

maj party may take credit for passing a bill, which benefits minmember district;

other powers of congress such as powers to lay and collect taxesand imposts, to pay debts, to provide defense and general welfareof the society, etc.;

endogenous size of government spending.



Research









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Literature – Formal Models

Informational argument: Strong party discipline informs votersabout candidate’s future policy (Ashworth and Bueno de Mesquita2004, Castanheira and Crutzen 2010, Cox and McCubbins 1993,Snyder and Ting 2002).

Commitment to party platforms: Party’s ability to induce ex-postadherence to pre-announced position (Grossman and Helpman 2008).

Ability of party leadership to control its legislators such that theyvote in line with party ideological position (Colomer 2005, Eguia2011, Iaryczower 2008, McGillivray 1997, Patty 2008, Volden andBergman 2006).

Institutional explanation: Vote-of-confidence procedure common inparliamentary democracies creates incentives for cohesion in voting(Diermeier and Feddersen 1998).

Little done with regard to impacts of party discipline on policyoutcomes. This paper contributes to this line.



































Related Literature

Empirical literature: Heller & Mershon (2008), Krehbiel(2000), McCarty, Poole & Rosenthal (2001), Snyder &Groseclose (2000).

Literature on inter-group contests: Katz, Nitzan & Rosenberg(1990), Baik (1993), Riaz, Shogren & Johnson (1995), Esteban& Ray (2001), Konrad & Morath (2012).


Introduction Model Results Appendix Congress Members’ Efforts Shares Party Discipline

AnalysisCongress Members’ Problem




Problem of congress member i ∈ maj:

maxai


)+λmaj

∑j∈maj


)−C (ai) .

Problem of congress member i ∈ min:

maxai


)+λmin

∑j∈min


)−C (ai) .

Due to symmetry, congress members affiliated with same partywill exert same effort.

amaj – effort of congress member affiliated with maj.

amin – effort of congress member affiliated with min.





maxai


)+λmaj

∑j∈maj


)−C (ai) .


maxai


)+λmin

∑j∈min


)−C (ai) .








maxai


)+λmaj

∑j∈maj


)−C (ai) .


maxai


)+λmin

∑j∈min


)−C (ai) .








maxai


)+λmaj

∑j∈maj


)−C (ai) .


maxai


)+λmin

∑j∈min


)−C (ai) .







TheoremGiven discipline levels λmaj ≥ 0, λmin ≥ 0, congress members’ exertefforts amaj (λmaj, λmin) and amin (λmaj, λmin):

amaj (λmaj, λmin) = fmaj (λmaj, λmin, β, nmaj, nmin) if β < (1+λmin)nmajnmaj−1 ,

nmaj−1n2

majotherwise,

amin (λmaj, λmin) =fmin (λmaj, λmin, β, nmaj, nmin) if β < (1+λmin)nmaj

nmaj−1 ,

0 otherwise.




TheoremGiven discipline levels λmaj ≥ 0, λmin ≥ 0, congress members’ exertefforts amaj (λmaj, λmin) and amin (λmaj, λmin):

amaj (λmaj, λmin) = fmaj (λmaj, λmin, β, nmaj, nmin) if β < (1+λmin)nmajnmaj−1 ,

nmaj−1n2

majotherwise,

amin (λmaj, λmin) =fmin (λmaj, λmin, β, nmaj, nmin) if β < (1+λmin)nmaj

nmaj−1 ,

0 otherwise.



Appendix: Congress Members’ Efforts

Congress Members’ Efforts

amaj (λmaj, λmin) =1β ((1 + λmaj)βnmin − (nmin − 1)) Ω if β < (1+λmin)nmaj

nmaj−1 ,nmaj−1

n2maj

otherwise,

amin (λmaj, λmin) =((1 + λmin) nmaj − β (nmaj − 1)) Ω if β < (1+λmin)nmaj

nmaj−1 ,

0 otherwise,

where

Ω =(1+λmin)nmaj((1+λmaj)βnmin−(nmin−1))+(nmin−1)((1+λmin)nmaj−β(nmaj−1))

(nmaj((1+λmaj)βnmin−(nmin−1))+nmin((1+λmin)nmaj−β(nmaj−1)))2 .




Congress members’ efforts increase with discipline levels intheir corresponding parties:

∂amaj(λmaj,λmin)∂λmaj

> 0, ∂amin(λmaj,λmin)∂λmin

> 0.

Spending share increases with discipline level of the party butdecreases with discipline level of the rival party:

∂smaj(λmaj,λmin)∂λmaj

> 0, ∂smaj(λmaj,λmin)∂λmin

< 0,∂smin(λmaj,λmin)

∂λmin> 0, ∂smin(λmaj,λmin)

∂λmaj< 0

maj party relative advantage β increases smaj but decreases smin:

∂smaj(λmaj,λmin)∂β > 0, ∂smin(λmaj,λmin)

∂β < 0.







> 0.






∂λmaj< 0



∂β < 0.







> 0.






∂λmaj< 0



∂β < 0.




TheoremGiven discipline levels λmaj ≥ 0, λmin ≥ 0, spending sharessmaj (λmaj, λmin) and smin (λmaj, λmin) are:

smaj (λmaj, λmin) =gmaj (λmaj, λmin, β, nmaj, nmin) if β < (1+λmin)nmaj

nmaj−1 ,1

nmajotherwise,

smin (λmaj, λmin) =gmin (λmaj, λmin, β, nmaj, nmin) if β < (1+λmin)nmaj

nmaj−1 ,

0 otherwise.




TheoremGiven discipline levels λmaj ≥ 0, λmin ≥ 0, spending sharessmaj (λmaj, λmin) and smin (λmaj, λmin) are:

smaj (λmaj, λmin) =gmaj (λmaj, λmin, β, nmaj, nmin) if β < (1+λmin)nmaj

nmaj−1 ,1

nmajotherwise,

smin (λmaj, λmin) =gmin (λmaj, λmin, β, nmaj, nmin) if β < (1+λmin)nmaj

nmaj−1 ,

0 otherwise.



Appendix: Pork-Barrel Shares

Government Spending Shares

smaj (λmaj, λmin) =1∆ ((1 + λmaj)βnmin − (nmin − 1)) if β < (1+λmin)nmaj

nmaj−1 ,1

nmajotherwise,

smin (λmaj, λmin) =1∆ ((1 + λmin) nmaj − β (nmaj − 1)) if β < (1+λmin)nmaj

nmaj−1 ,

0 otherwise,

where

∆ = nmaj ((1 + λmaj)βnmin − (nmin − 1)) +

nmin ((1 + λmin) nmaj − β (nmaj − 1)) .



AnalysisParty Leaders’ Problem




Problem of maj leader:

maxλmaj

∑i∈maj


)− c (λmaj) .

Problem of min leader:

maxλmin

∑i∈min


)− c (λmin) .

Party leaders simultaneously choose discipline levels.

In equilibrium, λmaj > 0 and λmin > 0 only if nmin >(1+β)2

1+β−β3

where 1 + β − β3 > 0.

Otherwise, either λmin > 0, λmaj = 0 or λmaj = λmin = 0(depending on parameters’ values).





maxλmaj

∑i∈maj


)− c (λmaj) .


maxλmin

∑i∈min


)− c (λmin) .



1+β−β3

where 1 + β − β3 > 0.






maxλmaj

∑i∈maj


)− c (λmaj) .


maxλmin

∑i∈min


)− c (λmin) .



1+β−β3

where 1 + β − β3 > 0.






maxλmaj

∑i∈maj


)− c (λmaj) .


maxλmin

∑i∈min


)− c (λmin) .



1+β−β3

where 1 + β − β3 > 0.






maxλmaj

∑i∈maj


)− c (λmaj) .


maxλmin

∑i∈min


)− c (λmin) .



1+β−β3

where 1 + β − β3 > 0.





TheoremIf min party has sufficient number of seats in congress and maj party

advantage is not very high (formally, nmin >(1+β)2

1+β−β3 where

1 + β − β3 > 0) then there is a unique equilibrium:

λ∗maj = nmin−1nmin

1β −

1+β+β2

(1+β)2 ,

λ∗min =nmaj−1

nmajβ − 1+β+β2

(1+β)2 ,

a∗maj =nmajnmin(1+β+β2)

2−(nmaj+β2nmin)(1+β)2

n2majnmin(1+β)4 ,

a∗min =nmajnmin(1+β+β2)

2−(nmaj+β2nmin)(1+β)2

nmajn2min(1+β)4 ,

s∗maj = βnmaj(1+β) ,

s∗min = 1nmin(1+β) .Galina Zudenkova A Model of Party Discipline in Congress

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A Model of Party Discipline in Congress