Motivation #1

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

Motivation #2

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)

Motivation #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

Basic Model

with one-dimensional policy space

Originally proposed by Baron and Ferejohn (1989)

Here we follow Section 5.4 of Persson and Tabellini (2000)

Players

Three legislators, $J \in \{L,M,R\}$

Think of each as a citizen-candidate elected in each constituency

Endowments

Each legislator $J$ is endowed with income $y^J$ with $y^L<y^M<y^R$

Preference

W^J(g) = (1-\tau)y^J+H(g)

W^J(g) = (1-\tau)y^J+H(g)

Government budget constraint

\tau y = g

\tau y = g

where $y$ is per capita income w/ pop size 1

Timing of Events

1

2

3

4

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

Default policy in reality #1

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

Image source: www.ibtimes.com/government-shutdown-2013-impact-national-parks-museums-us-travel-1413078

Most recent case:

Analysis

Backward induction

1

2

3

4

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

Backward induction

1

2

3

4

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

Case 2: Legislator L as the agenda setter

g^M

g^M

g^R

g^R

g^L

g^L

g_A

g_A

Case 2: Legislator L as the agenda setter

g^M

g^M

g^R

g^R

g^L

g^L

g_A

g_A

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

Extension to

the division-of-a-pie problem

Players

Three legislators, $J \in \{1,2,3\}$

Think of each as a citizen-candidate elected in each constituency

Preference

W^J(g^J) = H(g^J)

W^J(g^J) = H(g^J)

Government budget constraint

T = \sum_J g^J

T = \sum_J g^J

where $T$ is exogenous revenue

Timing of Events

1

2

3

4

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 $\sum_J \bar{g}^J < T$ )

Analysis

Legislator $J \neq 1$ will vote yes if

g^J \geq \bar{g}^J

g^J \geq \bar{g}^J

Legislator 1's payoff

W^1(g^1)= H(T-\sum_{J\neq 1} g^J)

W^1(g^1)= H(T-\sum_{J\neq 1} g^J)

To minimize $\sum_{J\neq 1}g^J$

Majority voting implies only one more legislator's support is needed

g^J = \bar{g}^J

g^J = \bar{g}^J

for all $J \neq 1$

(g^1, g^2, g^3) = (T-\bar{g}^2, \bar{g}^2, 0)

(g^1, g^2, g^3) = (T-\bar{g}^2, \bar{g}^2, 0)

if $\bar{g}^2 \leq \bar{g}^3$

(T-\bar{g}^3, 0, \bar{g}^3)

(T-\bar{g}^3, 0, \bar{g}^3)

if $\bar{g}^2 \geq \bar{g}^3$

Implications

1

2

The equilibrium exists where the Downsian model has none

Agenda-setter keeps the largest share of the pie

g^1> \max\{g^2, g^3\}

g^1> \max\{g^2, g^3\}

g^1 - g^2= T-2\bar{g}^2

g^1 - g^2= T-2\bar{g}^2

If $\bar{g}^2 < \bar{g}^3$

> T - (\bar{g}^2 + \bar{g}^3) = \bar{g}^1 \geq 0

> T - (\bar{g}^2 + \bar{g}^3) = \bar{g}^1 \geq 0

Implications

1

2

3

4

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

Extension to multiple rounds of bargaining

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

Likelihood of becoming an agenda-setter

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

Diermeier, Eraslan, and Merlo (2003 Econometrica)

See Merlo (1997 JPE)

Endogenous default policy

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

Evidence

Predictions from legislative bargaining model

Knight (2005 AER) tests these two predictions in U.S.

1

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

Data

Based on project descriptions in the bill,

match each highway project with a congressional district

Image source: en.wikipedia.org/wiki/List_of_United_States_congressional_districts

Predictions from legislative bargaining model

Knight (2005 AER) tests these two predictions in U.S.

1

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

% of congressional districts receiving zero

	Committee members'	The others
1991	0	72
1998	0	21

Source: Table 1 of Knight (2005)

Predictions from legislative bargaining model

Knight (2005 AER) tests these two predictions in U.S.

1

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

Average Allocated Spendings

	Committee members'	The others
1991	$54.8m	$6.1m
1998	$38.5m	$13.8m

Source: Table 1 of Knight (2005)

Takeaway

The positive correlation

between committee membership & allocated funds

Consistent with theoretical predictions

from legislative bargaining model

Application:

Presidentialism

vs

Parliamentarism

Adapted from Persson et al. (2000 JPE)

(See also sections 10.2-10.3 of Persson and Tabellini 2000)

Motivation:

Impacts of political institutions

on economic policies

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

A Model of

Fiscal Policy-making

Players

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

Modelling

forms of government

Differences between

Presidentialism and Parliamentarism

Major difference: how the chief executive is elected

Other important differences: How legislature makes policies

But we do not model this here

Presidentialism

Different congressional committees hold proposal power over different policy issues

Separation of Power

=

Taxation

Spending

Parliamentarism

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

Image source: www.huffingtonpost.jp/2014/11/20/general-election_n_6190126.html

Legislative cohesion

=

Fiscal policy in

presidentialism

Timing of Events in Presidentialism

1

2

3

4

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

Backward induction

1

2

3

4

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

Legislators 1 & 3's optimal voting

on the expenditure proposal

Both prefer anything only slightly better than the default policy

Legislator $J$ accept the proposal if

g \geq 0, f^J \geq 0

g \geq 0, f^J \geq 0

(Assuming they will accept when indifferent between the bill and the default policy)

Backward induction

1

2

3

4

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

Backward induction

1

2

3

4

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

Fiscal policy in

parliamentarism

Timing of Events in Parliamentarism

1

2

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

Transfer to opposition's region

No support from the opposition is needed to pass the bill

f^3=0

f^3=0

Public goods & transfer to ruling party's regions

Legislators 1 & 2 jointly maximize their payoffs

Given $\tau$ , they choose $g$ to solve

\max_{g, \{f^J\}} 2[y-\tau+H(g)]+f^1+f^2

\max_{g, \{f^J\}} 2[y-\tau+H(g)]+f^1+f^2

=\max_g2[y-\tau+H(g)]+3\tau-g

=\max_g2[y-\tau+H(g)]+3\tau-g

Govt budget constraint & $f^3=0$

FOC w.r.t. $g$

2H_g(g)=1

2H_g(g)=1

Size of government

Legislators 1 & 2 jointly maximize their payoffs

Given the optimal $g^{PA}$ , they choose $\tau$ to solve

\max_{\tau\in[0,y]} 2[y-\tau+H(g^{PA})]+3\tau-g^{PA}

\max_{\tau\in[0,y]} 2[y-\tau+H(g^{PA})]+3\tau-g^{PA}

FOC w.r.t. $\tau$

1>0

1>0

Extracting income from region 3

to split it among the two regions

\tau^{PA}=y

\tau^{PA}=y

Comparative politics

Presidentialism

Parliamentarism

H_g(g^{PR})=1

H_g(g^{PR})=1

2H_g(g^{PA})=1

2H_g(g^{PA})=1

g^{PR} < g^{PA}

g^{PR} < g^{PA}

Public good provision

Regional transfer

f^1=f^2=f^3=0

f^1=f^2=f^3=0

f^1+f^2=y-g^{PA}

f^1+f^2=y-g^{PA}

f^3=0

f^3=0

Tax revenue

\tau = g^{PR}

\tau = g^{PR}

\tau = y

\tau = y

<

<

Evidence on the impact of forms of government

Persson and Tabellini (2004 AER)

Causal evidence?

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

Causal evidence?

We can only check

if correlation is consistent with the theoretical prediction

Forms of government across the world in 1998

Source: Figure 4.1 of Persson and Tabellini (2003)

Presidential

Parliamentary

Not democratic

(S_i=1)

(S_i=1)

(S_i=0)

(S_i=0)

(excluded from the sample)

Unconditional mean comparison

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

OLS estimation results

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