17 November, 2017
Masa Kudamatsu
The models we have discussed so far in this course
Many elected politicians negotiate with each other to enact policies
The single elected politician can unilaterally implement policies
In reality
e.g. Fiscal budget has to be approved by legislature
The legislative bargaining model
is a framework to analyze such collective decision-making
The legislative bargaining model
is another way to pin down an equilibrium policy in such cases
For policy issues where there is no median voter (cf. Lecture 1)
e.g. The division-of-a-pie problem
We need a model that allows us to find an equilibrium
e.g. Probabilistic Voting Model (cf. Lecture 3)
The legislative bargaining model is an extension to allow
(1) multiple players
(2) majority voting, rather than unanimity
In game theory
The Rubinstein bargaining game is a framework
to analyze the negotiation between two persons
Originally proposed by Baron and Ferejohn (1989)
Here we follow Section 5.4 of Persson and Tabellini (2000)
Three legislators, \(J \in \{L,M,R\}\)
Think of each as a citizen-candidate elected in each constituency
Each legislator \(J\) is endowed with income \(y^J\) with \(y^L<y^M<y^R\)
where \(y\) is per capita income w/ pop size 1
where \(y\) is per capita income w/ pop size 1
Plugging the budget constraint into legislator J's preference...
First order condition yields:
First order condition yields:
So we have:
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Nature picks \(J \in \{R,M,L\}\) as the agenda setter
Denote this legislator by \(A\)
Legislator \(A\) proposes \(g_A\)
All legislators vote on the proposal \(g_A\)
If at least two parties vote yes, \(g_A\) will be implemented
Otherwise, the default policy, \(\bar{g}\), will be implemented
Cabinet ministers in parliamentary systems (UK, etc.)
Legislative committees in presidential systems (US etc.)
Agriculture Appropriations Armed Services Budget
Education and the Workforce Energy and Commerce Ethics
Financial Services Foreign Affairs Homeland Security
House Administration Judiciary Natural Resources
Oversight and Government Reform Rules
Science, Space, and Technology Small Business
Transportation and Infrastructure Veterans' Affairs Ways and Means
Source: www.congress.gov/committees
Committees in U.S. Lower House
We will see this committee in action later
Government shutdown in U.S.
October 1st-16th, 2013
Due to the deadlock between the Republican-controlled House
and the Democrat-controlled Senate over Obamacare
Most recent case:
e.g. Art. 312 of Treaty on the Functioning of the European Union
Where no Council regulation determining a new financial framework has been adopted by the end of the previous financial framework, the ceilings and other provisions corresponding to the last year of that framework shall be extended until such time as that act is adopted.
"
"
(Quoted by Piguillem and Riboni (2015), footnote 8)
The policy adopted in the previous fiscal year
Government shutdown in U.S.
October 1st-16th, 2013
Due to the deadlock between the Republican-controlled House
and the Democrat-controlled Senate over Obamacare
Most recent case:
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Nature picks \(J \in \{R,M,L\}\) as the agenda setter
Denote this legislator by \(A\)
Legislator \(A\) proposes \(g_A\)
All legislators vote on the proposal \(g_A\)
If at least two parties vote yes, \(g_A\) will be implemented
Otherwise, the default policy, \(\bar{g}\), will be implemented
Legislators \(J \neq A\) vote yes to \(g_A\) as long as
Since \(W^J(g)\) is single-peaked, this means
Legislators \(J \neq A\) vote yes to \(g_A\) as long as
Since \(W^J(g)\) is single-peaked, this means
Accept
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Nature picks \(J \in \{R,M,L\}\) as the agenda setter
Denote this legislator by \(A\)
Legislator \(A\) proposes \(g_A\)
All legislators vote on the proposal \(g_A\)
If at least two parties vote yes, \(g_A\) will be implemented
Otherwise, the default policy, \(\bar{g}\), will be implemented
Suppose
Suppose
Legislator R will vote yes if
Suppose
Legislator L will vote yes if
Legislator M's bliss point \(g^M\) will be accepted by L
It's optimal to propose \(g_A = g^M\)
Suppose
Legislator L will vote yes if
Suppose
Legislator R will vote yes if
Suppose
Legislator M's bliss point \(g^M\) will be accepted by R
It's optimal to propose \(g_A = g^M\)
For all \(\bar{g}\),
Legislator M proposes \(g_A = g^M\)
Then
R votes in favor if \(\bar{g} > g^M \)
L votes in favor otherwise
So far the prediction is the same as the median voter theorem
Suppose
Suppose
Legislator R will vote yes if
Suppose
Legislator M will vote yes if
Suppose
Legislator M will vote yes if
Legislator R will vote yes if
Legislator L's bliss point \(g^L\) will be accepted by both
It's optimal to propose \(g_A = g^L\)
Default policy | Equilibrium policy |
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Suppose
Suppose
Legislator R will vote yes if
Suppose
Legislator M will vote yes if
Suppose
Legislator M will vote yes if
Legislator R will vote yes if
Default policy \(\bar{g}\) yields the highest payoff to L
among those to be approved
It's optimal to propose \(g_A = \bar{g}\)
Default policy | Equilibrium policy |
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Suppose
Suppose
Legislator R will vote yes if
Suppose
Legislator M will vote yes if
If
it's optimal to propose
and M will vote yes
Suppose
Legislator M will vote yes if
If
it's optimal to propose
and M will vote yes
Default policy | Equilibrium policy |
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Default policy | Equilibrium policy |
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Whatever \(\bar{g}\) is, L can implement \(g_A \in [g^M, g^L] \)
Whatever \(\bar{g}\) is, L can implement \(g_A \in [g^M, g^L] \)
Whatever \(\bar{g}\) is, L can implement \(g_A \in [g^M, g^L] \)
M is always better off than R
because M's support is cheaper for L to buy than R's
By the symmetric argument, R can implement
Three legislators, \(J \in \{1,2,3\}\)
Think of each as a citizen-candidate elected in each constituency
where \(T\) is exogenous revenue
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Nature picks \(J \in \{1,2,3\}\) as the agenda setter
Without loss of generality, let legisator 1 be chosen
Legislator 1 proposes the allocation \(\mathbf{g} = (g^1, g^2, g^3)\)
All legislators vote on the proposal \(\mathbf{g}\)
If at least two parties vote yes, \(\mathbf{g}\) will be implemented
Otherwise, the default policy, \(\bar{\mathbf{g}} = (\bar{g}^1,\bar{g}^2,\bar{g}^3)\), will be implemented (with \(\sum_J \bar{g}^J < T\))
Legislator \(J \neq 1 \) will vote yes if
Legislator 1's payoff
To minimize \(\sum_{J\neq 1}g^J\)
Majority voting implies only one more legislator's support is needed
for all \(J \neq 1\)
if \(\bar{g}^2 \leq \bar{g}^3\)
if \(\bar{g}^2 \geq \bar{g}^3\)
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The equilibrium exists where the Downsian model has none
Agenda-setter keeps the largest share of the pie
If \(\bar{g}^2 < \bar{g}^3\)
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The equilibrium exists where the Downsian model has none
Agenda-setter keeps the largest share of the pie
Minimum winning coalition: one legislator gets zero
The legislator with worse outside option (i.e. default policy)
is chosen to be part of the winning coalition
We can modify the timing of events in the following way
If the proposal is voted down,
nature picks a new agenda-setter
and repeat the same bargaining protocol
Then the legislator who's likely to be a next agenda setter
has a higher outside option
Will be excluded from the winning coalition
e.g. Negotiation on the coalition government formation
when no political party won the majority of legislative seats
The largest party is usually given the role of proposer
If the negotiation breaks down, the second largest party is chosen
Probability of becoming an agenda setter
= Seat share in the legislature
See Merlo (1997 JPE)
Pioneer: Baron (1996 APSR) on one-dimensional policy model
If the proposed bill is rejected
the previous-period policy continues to be implemented
Kalandrakis (2004 JET) considers the division-of-a-pie policy
Diermeier and Fong (2011 QJE) allow the same legislator to remain as the agenda-setter
Knight (2005 AER) tests these two predictions in U.S.
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Majority
voting
Some non-agenda
setters receive zero
Agenda setters
propose the allocation
Their district receives
more funds
2
Consider the allocation of funds across districts each represented by a legislator
Drivers
Federal govt
Gasoline tax
State govts
Fiscal transfer
Highways
Construct & Maintain
Congress chooses
which highways to be financed
($5b in 1991, $8b in 1998)
Testing ground:
House of Representatives (435 members)
House Committee
on Transportation
and Infrastructure
(55 or 72 members)
Fund allocation bill
Propose
Vote
Testing ground:
Based on project descriptions in the bill,
match each highway project with a congressional district
Knight (2005 AER) tests these two predictions in U.S.
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Majority
voting
Some non-agenda
setters receive zero
Agenda setters
propose the allocation
Their district receives
more funds
2
Consider the allocation of funds across districts each represented by a legislator
Committee members' | The others | |
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1991 | 0 | 72 |
1998 | 0 | 21 |
Source: Table 1 of Knight (2005)
Knight (2005 AER) tests these two predictions in U.S.
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Majority
voting
Some non-agenda
setters receive zero
Agenda setters
propose the allocation
Their district receives
more funds
2
Consider the allocation of funds across districts each represented by a legislator
Committee members' | The others | |
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1991 | $54.8m | $6.1m |
1998 | $38.5m | $13.8m |
Source: Table 1 of Knight (2005)
For each year of 1991 and 1998, estimate with OLS:
Highway fund spending in district \(d\) (in millions of 1998 dollars)
Indicator of district \(d\)'s representative being in the committee
District \(d\)'s characteristics
Source: Table 2 of Knight (2005)
Legislators may join the committee
because their districts need more highways
In need of highways
Restrict the sample to those districts that can be matched
District fixed effects
Control for unobservable time-invariant district characteristics
But due to the redrawing of districts in 1992,
some districts cannot be matched between 1991 and 1998
Aggregate at the state level by taking the averages
State fixed effects
Source: Table 5 of Knight (2005)
Committee members in 1991 leave the committee
because their districts no longer need more highways
Decline in the need of highways
Newly elected legislators are more likely to join the committee
Use the indicator of being newly elected as an instrument
First-stage does work: 8.5 pt increase (sample mean 15%)
Newly elected legislators are less powerful
This may directly affect the allocation of funds to their district
The positive correlation
between committee membership & allocated funds
Consistent with theoretical predictions
from legislative bargaining model
Adapted from Persson et al. (2000 JPE)
(See also sections 10.2-10.3 of Persson and Tabellini 2000)
We have seen the impacts of
Electoral rules (Lecture 3)
Term limits (Lecture 4)
Another major difference in political institutions across countries
Presidentialism vs Parliamentarism
Three legislators, \(J \in \{1,2,3\}\)
Each represents a region (or a group of voters)
Without loss of generality, assume:
Legislator 1 is in charge of proposing the tax policy
Legislator 2 is in charge of proposing the expenditure policy
Legislator 3 is the minority party member
Legislator \(J\)'s payoff
Exogenous income
Lump-sum tax
Public goods (benefiting all legislators)
Transfer to region \(J\)
Legislator \(J\)'s payoff
Each legislator can be thought of as
a citizen-candidate who won the election in each region
Legislator 1 proposes \(\tau\)
Legislator 2 proposes \(g\), \(\{f^J\}\)
e.g. Finance Minister
Member of Congress Committee on Taxation
e.g. Other Ministers
Members of Congress Committees on Expenditure
All legislators vote on these proposals
Legislator 1 proposes \(\tau\)
Legislator 2 proposes \(g\), \(\{f^J\}\)
All legislators vote on these proposals
Major difference: how the chief executive is elected
Other important differences: How legislature makes policies
But we do not model this here
Different congressional committees hold proposal power over different policy issues
Ruling party legislators propose almost all bills
A disagreement within ruling party members leads to a government crisis (vote of no confidence 「内閣不信任決議」)
June 1993: Vote of no confidence against Prime Minister Miyazawa was approved as some LDP members voted in favour
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Legislator 1 proposes total tax revenue, \(\tau\)
Legislators vote on the tax proposal
If rejected, the default policy, \(g=f^1=f^2=f^3=0\), is implemented
Legislator 2 proposes expenditures on public goods (\(g\)) and transfer to each region (\(f^1, f^2, f^3\))
Legislators vote on the expenditure proposal
If rejected, the default policy, \(\bar{\tau}=0\), is implemented
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Legislator 1 proposes total tax revenue, \(\tau\)
Legislators vote on the tax proposal
If rejected, the default policy, \(g=f^1=f^2=f^3=0\), is implemented
Legislator 2 proposes expenditures on public goods (\(g\)) and transfer to each region (\(f^1, f^2, f^3\))
Legislators vote on the expenditure proposal
If rejected, the default policy, \(\bar{\tau}=0\), is implemented
Both prefer anything only slightly better than the default policy
Legislator \(J\) accept the proposal if
(Assuming they will accept when indifferent between the bill and the default policy)
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Legislator 1 proposes total tax revenue, \(\tau\)
Legislators vote on the tax proposal
If rejected, the default policy, \(g=f^1=f^2=f^3=0\), is implemented
Legislator 2 proposes expenditures on public goods (\(g\)) and transfer to each region (\(f^1, f^2, f^3\))
Legislators vote on the expenditure proposal
If rejected, the default policy, \(\bar{\tau}=0\), is implemented
Choose policies to solve
subject to
First, there is no need to provide positive \(f^1, f^3\) to pass the bill
First order condition:
The remaining tax revenue is used for transfer to region 2
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Legislator 1 proposes total tax revenue, \(\tau\)
Legislators vote on the tax proposal
If rejected, the default policy, \(g=f^1=f^2=f^3=0\), is implemented
Legislator 2 proposes expenditures on public goods (\(g\)) and transfer to each region (\(f^1, f^2, f^3\))
Legislators vote on the expenditure proposal
If rejected, the default policy, \(\bar{\tau}=0\), is implemented
Choose \(\tau\) to solve
subject to
Starting with \(\tau=0\), legislator 2 will first spend any increase in \(\tau\) on \(g\)
Starting with \(\tau=0\), legislator 2 will first spend any increase in \(\tau\) on \(g\)
Until the marginal utility from \(g\) reaches 1
Then legislator 2 will spend any extra increase in \(\tau\) on \(f^2\)
Legislator 1 benefits as well
Legislator 1 no longer benefits
So it's optimal for legislator 1 to set
Both legislators are happy to accept
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Legislators 1 & 2 (i.e. the cabinet) jointly propose the policy package, \(\tau, g, f^1, f^2, f^3\)
Legislators vote on the proposal
If rejected, the cabinet resigns; the default policy, \(\bar{\tau}=g=f^1=f^2=f^3=0\), is implemented
No support from the opposition is needed to pass the bill
Legislators 1 & 2 jointly maximize their payoffs
Given \(\tau\), they choose \(g\) to solve
Govt budget constraint & \(f^3=0\)
FOC w.r.t. \(g\)
Legislators 1 & 2 jointly maximize their payoffs
Given the optimal \(g^{PA}\), they choose \(\tau\) to solve
FOC w.r.t. \(\tau\)
Extracting income from region 3
to split it among the two regions
Public good provision
Regional transfer
Tax revenue
Hard to prove causality running from forms of govt to policies
Forms of government rarely change
Thus impossible to separate their impact
from that of country characteristics
We can only check
if correlation is consistent with the theoretical prediction
See also Persson and Tabellini (2003) and Acemoglu (2005)
Run cross-country regressions of fiscal policies on forms of govt
Indicator of presidentialism in country \(i\)
Theory predicts \(\beta < 0\) when \(y_i\) is the size of government
See also Persson and Tabellini (2003) and Acemoglu (2005)
Run cross-country regressions of fiscal policies on forms of govt
Per capita GDP
Trade openness
Population
% of those aged 16-54
% of those aged over 65
Years of being democracy
Quality of democracy (Freedom House Index)
Dummy for majoritarian elections
(cf. Lecture 3)
Dummy for federal states
Dummy for OECD countries
Dummies for continents
Dummies for legal origins
Source: Figure 4.1 of Persson and Tabellini (2003)
Presidential
Parliamentary
Not democratic
(excluded from the sample)
Fiscal policy (as % of GDP) |
Central govt expenditure | Social protection |
Presidential system | 22.2% (7.2) |
4.8% (4.6) |
Parliamentary system | 33.3% (10.0) |
9.9% (7.0) |
p-value for two-sample t-test |
Source: Table 1 of Persson and Tabellini (2004)
Note: Standard deviation in parentheses
0.00
0.00
Dep. Var. (as % of GDP) |
Central govt expenditure | Central govt revenue | Government deficit | Social protection |
Presidentialism | -5.18*** (1.93) |
-5.00** (2.47) |
0.16 (1.15) |
-2.24* (1.11) |
# observations | 80 | 76 | 72 | 69 |
Source: Tables 2 and 4 of Persson and Tabellini (2004)
Countries with presidential system
have a smaller size of government
spend less on social protection (pension, unemployment benefits, child allowance, etc.)
Motivation
Almost all countries in Latin America and Africa
have adopted presidentialism
Source: Table 1 of Robinson and Torvik (2016)
Only 3 countries are parliamentary
No transition to parliamentary
Minority parties: more powerful in parliamentarism
They can hold a minority government
President as agenda-setter always excludes them from coalition (at least until next presidential election)
Presidents: more powerful than prime minister in parliamentarism
Cannot be kicked out by parliament
Prime minister needs to maintain the support of MPs
Politicians from the majority group
Parliamentarism is better to control political leader
Presidentialism is better to silence minority groups
Support presidentialism if losing power to minority groups is very costly
Preference between groups is polarized
Govt budget is small so the benefit of parliamentarism is small as well
e.g. Ethnic diversity in Africa
e.g. Weak fiscal capacity in Latin America and Africa
When legislators want to increase current spending and procrastinate spending cut...
Disagreement in legislature attenuates over-spending
Derived from the assumption that more legislators in favor
only increase the prob. of passing the bill.
e.g. Minority opposition can delay the discussion of the bill
Formation of political parties
Formation of coalition government (structural estimation)
Macroeconomic policies