Political Economy - Political Agency January 29, 2013 1/20 - - PowerPoint PPT Presentation

Introduction Model Equilibrium Results

Political Economy - Political Agency

January 29, 2013

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Introduction Model Equilibrium Results

Political Agency Key Idea

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Introduction Model Equilibrium Results

Political Agency Key Idea

Politicians are the agents of voters

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Introduction Model Equilibrium Results

Political Agency Key Idea

Politicians are the agents of voters Voters discipline politicians via the ballot box

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Introduction Model Equilibrium Results

Political Agency Key Idea

Politicians are the agents of voters Voters discipline politicians via the ballot box

Voters face two problems

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Introduction Model Equilibrium Results

Political Agency Key Idea

Politicians are the agents of voters Voters discipline politicians via the ballot box

Voters face two problems

Adverse selection - unobservable type

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Introduction Model Equilibrium Results

Political Agency Key Idea

Politicians are the agents of voters Voters discipline politicians via the ballot box

Voters face two problems

Adverse selection - unobservable type

Politicians may be of different types - competence, objectives, honesty

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Introduction Model Equilibrium Results

Political Agency Key Idea

Politicians are the agents of voters Voters discipline politicians via the ballot box

Voters face two problems

Adverse selection - unobservable type

Politicians may be of different types - competence, objectives, honesty Voters cannot perfectly observe a politicians type

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Introduction Model Equilibrium Results

Political Agency Key Idea

Politicians are the agents of voters Voters discipline politicians via the ballot box

Voters face two problems

Adverse selection - unobservable type

Politicians may be of different types - competence, objectives, honesty Voters cannot perfectly observe a politicians type

Moral hazard - unobservable action

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Introduction Model Equilibrium Results

Political Agency Key Idea

Politicians are the agents of voters Voters discipline politicians via the ballot box

Voters face two problems

Adverse selection - unobservable type

Politicians may be of different types - competence, objectives, honesty Voters cannot perfectly observe a politicians type

Moral hazard - unobservable action

Politicians actions may not be perfectly observable

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Introduction Model Equilibrium Results

Political Agency Key Idea

Politicians are the agents of voters Voters discipline politicians via the ballot box

Voters face two problems

Adverse selection - unobservable type

Politicians may be of different types - competence, objectives, honesty Voters cannot perfectly observe a politicians type

Moral hazard - unobservable action

Politicians actions may not be perfectly observable Voters may not be able to perfectly deduce the actions that politicians took, but they can often observe something of the results

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Introduction Model Equilibrium Results

Political Agency Simple Model

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Introduction Model Equilibrium Results

Political Agency Simple Model

Two time periods t ∈ {1, 2}

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Introduction Model Equilibrium Results

Political Agency Simple Model

Two time periods t ∈ {1, 2} Politician elected at the beginning of each period

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Introduction Model Equilibrium Results

Political Agency Simple Model

Two time periods t ∈ {1, 2} Politician elected at the beginning of each period Politician if elected makes a single decision et ∈ {0, 1}

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Introduction Model Equilibrium Results

Political Agency Simple Model

Two time periods t ∈ {1, 2} Politician elected at the beginning of each period Politician if elected makes a single decision et ∈ {0, 1} Payoffs to politician and voters depends on the state of the world st ∈ {0, 1}

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Introduction Model Equilibrium Results

Political Agency Simple Model

Two time periods t ∈ {1, 2} Politician elected at the beginning of each period Politician if elected makes a single decision et ∈ {0, 1} Payoffs to politician and voters depends on the state of the world st ∈ {0, 1}

Each state is equally likely to occur

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Introduction Model Equilibrium Results

Political Agency Simple Model

Two time periods t ∈ {1, 2} Politician elected at the beginning of each period Politician if elected makes a single decision et ∈ {0, 1} Payoffs to politician and voters depends on the state of the world st ∈ {0, 1}

Each state is equally likely to occur

2 types of politician

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Introduction Model Equilibrium Results

Political Agency Simple Model

Two time periods t ∈ {1, 2} Politician elected at the beginning of each period Politician if elected makes a single decision et ∈ {0, 1} Payoffs to politician and voters depends on the state of the world st ∈ {0, 1}

Each state is equally likely to occur

2 types of politician

Congruent - share voters interests

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Introduction Model Equilibrium Results

Political Agency Simple Model

Two time periods t ∈ {1, 2} Politician elected at the beginning of each period Politician if elected makes a single decision et ∈ {0, 1} Payoffs to politician and voters depends on the state of the world st ∈ {0, 1}

Each state is equally likely to occur

2 types of politician

Congruent - share voters interests Dissonant - have own agenda

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Introduction Model Equilibrium Results

Political Agency Simple Model

Two time periods t ∈ {1, 2} Politician elected at the beginning of each period Politician if elected makes a single decision et ∈ {0, 1} Payoffs to politician and voters depends on the state of the world st ∈ {0, 1}

Each state is equally likely to occur

2 types of politician

Congruent - share voters interests Dissonant - have own agenda

State of the world only observed by the incumbent politician ⇒ Moral Hazard

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Introduction Model Equilibrium Results

Political Agency Simple Model

Two time periods t ∈ {1, 2} Politician elected at the beginning of each period Politician if elected makes a single decision et ∈ {0, 1} Payoffs to politician and voters depends on the state of the world st ∈ {0, 1}

Each state is equally likely to occur

2 types of politician

Congruent - share voters interests Dissonant - have own agenda

State of the world only observed by the incumbent politician ⇒ Moral Hazard Politicians type only observed by the incumbent politician ⇒ Adverse Selection

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Introduction Model Equilibrium Results

Political Agency Simple Model - Payoffs

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Introduction Model Equilibrium Results

Political Agency Simple Model - Payoffs

Voters Payoffs

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Introduction Model Equilibrium Results

Political Agency Simple Model - Payoffs

Voters Payoffs

∆ if et = st

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Introduction Model Equilibrium Results

Political Agency Simple Model - Payoffs

Voters Payoffs

∆ if et = st 0 otherwise ⇒ Only get a payoff if politician makes the ”right decision”

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Introduction Model Equilibrium Results

Political Agency Simple Model - Payoffs

Voters Payoffs

∆ if et = st 0 otherwise ⇒ Only get a payoff if politician makes the ”right decision”

Politicians Payoffs

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Introduction Model Equilibrium Results

Political Agency Simple Model - Payoffs

Voters Payoffs

∆ if et = st 0 otherwise ⇒ Only get a payoff if politician makes the ”right decision”

Politicians Payoffs

All politicians experience an ”ego-rent” of E

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Introduction Model Equilibrium Results

Political Agency Simple Model - Payoffs

Voters Payoffs

∆ if et = st 0 otherwise ⇒ Only get a payoff if politician makes the ”right decision”

Politicians Payoffs

All politicians experience an ”ego-rent” of E

Congruent Politicians Payoffs

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Introduction Model Equilibrium Results

Political Agency Simple Model - Payoffs

Voters Payoffs

∆ if et = st 0 otherwise ⇒ Only get a payoff if politician makes the ”right decision”

Politicians Payoffs

All politicians experience an ”ego-rent” of E

Congruent Politicians Payoffs

Share voters objectives - always choose et = st

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Introduction Model Equilibrium Results

Political Agency Simple Model - Payoffs

Voters Payoffs

∆ if et = st 0 otherwise ⇒ Only get a payoff if politician makes the ”right decision”

Politicians Payoffs

All politicians experience an ”ego-rent” of E

Congruent Politicians Payoffs

Share voters objectives - always choose et = st So payoff is E + ∆

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Introduction Model Equilibrium Results

Political Agency Simple Model - Payoffs

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Introduction Model Equilibrium Results

Political Agency Simple Model - Payoffs

Dissonant Politicians Payoffs

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Introduction Model Equilibrium Results

Political Agency Simple Model - Payoffs

Dissonant Politicians Payoffs

If et = st

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Introduction Model Equilibrium Results

Political Agency Simple Model - Payoffs

Dissonant Politicians Payoffs

If et = st Get random private benefit (dissonance rents) rt ∈ [0, R]

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Introduction Model Equilibrium Results

Political Agency Simple Model - Payoffs

Dissonant Politicians Payoffs

If et = st Get random private benefit (dissonance rents) rt ∈ [0, R] rt drawn independently from a stationary distribution with c.d.f . of G(r)

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Introduction Model Equilibrium Results

Political Agency Simple Model - Payoffs

Dissonant Politicians Payoffs

If et = st Get random private benefit (dissonance rents) rt ∈ [0, R] rt drawn independently from a stationary distribution with c.d.f . of G(r) µ - mean of r

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Introduction Model Equilibrium Results

Political Agency Simple Model - Payoffs

Dissonant Politicians Payoffs

If et = st Get random private benefit (dissonance rents) rt ∈ [0, R] rt drawn independently from a stationary distribution with c.d.f . of G(r) µ - mean of r β - discount rate common to all agents

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Introduction Model Equilibrium Results

Political Agency Simple Model - Payoffs

Dissonant Politicians Payoffs

If et = st Get random private benefit (dissonance rents) rt ∈ [0, R] rt drawn independently from a stationary distribution with c.d.f . of G(r) µ - mean of r β - discount rate common to all agents Receive E + rt in t

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Introduction Model Equilibrium Results

Political Agency Simple Model - Payoffs

Dissonant Politicians Payoffs

If et = st Get random private benefit (dissonance rents) rt ∈ [0, R] rt drawn independently from a stationary distribution with c.d.f . of G(r) µ - mean of r β - discount rate common to all agents Receive E + rt in t

Assume R > β(µ + E) - guarantees that dissonant politicians do not do what voters want some of the time

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Introduction Model Equilibrium Results

Political Agency Simple Model - Payoffs

Dissonant Politicians Payoffs

If et = st Get random private benefit (dissonance rents) rt ∈ [0, R] rt drawn independently from a stationary distribution with c.d.f . of G(r) µ - mean of r β - discount rate common to all agents Receive E + rt in t

Assume R > β(µ + E) - guarantees that dissonant politicians do not do what voters want some of the time Let et(s, i) with s ∈ {0, 1} and i ∈ {c, d} denote the politicians action in t

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Introduction Model Equilibrium Results

Political Agency Simple Model - Timing in period 1

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Introduction Model Equilibrium Results

Political Agency Simple Model - Timing in period 1

Nature plays first and chooses

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Introduction Model Equilibrium Results

Political Agency Simple Model - Timing in period 1

Nature plays first and chooses

State of the world - s1 - observed only by politician

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Introduction Model Equilibrium Results

Political Agency Simple Model - Timing in period 1

Nature plays first and chooses

State of the world - s1 - observed only by politician Type of politician - i1 - observed only by politician

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Introduction Model Equilibrium Results

Political Agency Simple Model - Timing in period 1

Nature plays first and chooses

State of the world - s1 - observed only by politician Type of politician - i1 - observed only by politician Dissonance rent - r1 - observed only by politician if dissonant

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Introduction Model Equilibrium Results

Political Agency Simple Model - Timing in period 1

Nature plays first and chooses

State of the world - s1 - observed only by politician Type of politician - i1 - observed only by politician Dissonance rent - r1 - observed only by politician if dissonant

Incumbent politician plays second and chooses

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Introduction Model Equilibrium Results

Political Agency Simple Model - Timing in period 1

Nature plays first and chooses

State of the world - s1 - observed only by politician Type of politician - i1 - observed only by politician Dissonance rent - r1 - observed only by politician if dissonant

Incumbent politician plays second and chooses

Action e1 ∈ {0, 1} - observed only by politician

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Introduction Model Equilibrium Results

Political Agency Simple Model - Timing in period 1

Nature plays first and chooses

State of the world - s1 - observed only by politician Type of politician - i1 - observed only by politician Dissonance rent - r1 - observed only by politician if dissonant

Incumbent politician plays second and chooses

Action e1 ∈ {0, 1} - observed only by politician

Voters play last observe their payoffs and choose either

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Introduction Model Equilibrium Results

Political Agency Simple Model - Timing in period 1

Nature plays first and chooses

State of the world - s1 - observed only by politician Type of politician - i1 - observed only by politician Dissonance rent - r1 - observed only by politician if dissonant

Incumbent politician plays second and chooses

Action e1 ∈ {0, 1} - observed only by politician

Voters play last observe their payoffs and choose either

To reelect the incumbent politician

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Introduction Model Equilibrium Results

Political Agency Simple Model - Timing in period 1

Nature plays first and chooses

State of the world - s1 - observed only by politician Type of politician - i1 - observed only by politician Dissonance rent - r1 - observed only by politician if dissonant

Incumbent politician plays second and chooses

Action e1 ∈ {0, 1} - observed only by politician

Voters play last observe their payoffs and choose either

To reelect the incumbent politician Replace the incumbent with random draw from the pool

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Introduction Model Equilibrium Results

Political Agency Simple Model - Timing in period 2

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Introduction Model Equilibrium Results

Political Agency Simple Model - Timing in period 2

Nature plays first and chooses

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Introduction Model Equilibrium Results

Political Agency Simple Model - Timing in period 2

Nature plays first and chooses

State of the world - s2

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Introduction Model Equilibrium Results

Political Agency Simple Model - Timing in period 2

Nature plays first and chooses

State of the world - s2 Type of politician - i2 - if they are replaced

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Introduction Model Equilibrium Results

Political Agency Simple Model - Timing in period 2

Nature plays first and chooses

State of the world - s2 Type of politician - i2 - if they are replaced Dissonance rent - r2

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Introduction Model Equilibrium Results

Political Agency Simple Model - Timing in period 2

Nature plays first and chooses

State of the world - s2 Type of politician - i2 - if they are replaced Dissonance rent - r2

Incumbent politician plays second and chooses

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Introduction Model Equilibrium Results

Political Agency Simple Model - Timing in period 2

Nature plays first and chooses

State of the world - s2 Type of politician - i2 - if they are replaced Dissonance rent - r2

Incumbent politician plays second and chooses

Action e2 ∈ {0, 1}

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Introduction Model Equilibrium Results

Political Agency Simple Model - Timing in period 2

Nature plays first and chooses

State of the world - s2 Type of politician - i2 - if they are replaced Dissonance rent - r2

Incumbent politician plays second and chooses

Action e2 ∈ {0, 1}

All agents realize their payoffs

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Introduction Model Equilibrium Results

Political Agency Simple Model - Timing in period 2

Nature plays first and chooses

State of the world - s2 Type of politician - i2 - if they are replaced Dissonance rent - r2

Incumbent politician plays second and chooses

Action e2 ∈ {0, 1}

All agents realize their payoffs Game ends at the end of period 2

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Introduction Model Equilibrium Results

Political Agency Simple Model - Equilibrium

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Introduction Model Equilibrium Results

Political Agency Simple Model - Equilibrium

Perfect Bayesian Equilibrium

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Introduction Model Equilibrium Results

Political Agency Simple Model - Equilibrium

Perfect Bayesian Equilibrium

All politicians behave optimally given the reelection rule of voters

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Introduction Model Equilibrium Results

Political Agency Simple Model - Equilibrium

Perfect Bayesian Equilibrium

All politicians behave optimally given the reelection rule of voters Voters use Bayes Rule to update their beliefs

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Introduction Model Equilibrium Results

Political Agency Bayes Rule

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Introduction Model Equilibrium Results

Political Agency Bayes Rule

The probability that two events a and c occur together may be written

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Introduction Model Equilibrium Results

Political Agency Bayes Rule

The probability that two events a and c occur together may be written

p(a|c)p(c) or p(c|a)p(a) = ⇒ p(a|c)p(c) = p(c|a)p(a)

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Introduction Model Equilibrium Results

Political Agency Bayes Rule

The probability that two events a and c occur together may be written

p(a|c)p(c) or p(c|a)p(a) = ⇒ p(a|c)p(c) = p(c|a)p(a) Rearranging p(a|c) = p(c|a)p(a)

p(c)

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Introduction Model Equilibrium Results

Political Agency Bayes Rule

The probability that two events a and c occur together may be written

p(a|c)p(c) or p(c|a)p(a) = ⇒ p(a|c)p(c) = p(c|a)p(a) Rearranging p(a|c) = p(c|a)p(a)

p(c)

Now suppose c can also occur with b so

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Introduction Model Equilibrium Results

Political Agency Bayes Rule

The probability that two events a and c occur together may be written

p(a|c)p(c) or p(c|a)p(a) = ⇒ p(a|c)p(c) = p(c|a)p(a) Rearranging p(a|c) = p(c|a)p(a)

p(c)

Now suppose c can also occur with b so

p(c) = p(c|a)p(a) + p(c|b)p(b)

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Introduction Model Equilibrium Results

Political Agency Bayes Rule

The probability that two events a and c occur together may be written

p(a|c)p(c) or p(c|a)p(a) = ⇒ p(a|c)p(c) = p(c|a)p(a) Rearranging p(a|c) = p(c|a)p(a)

p(c)

Now suppose c can also occur with b so

p(c) = p(c|a)p(a) + p(c|b)p(b)

Combining these facts gives Bayes Rule

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Introduction Model Equilibrium Results

Political Agency Bayes Rule

The probability that two events a and c occur together may be written

p(a|c)p(c) or p(c|a)p(a) = ⇒ p(a|c)p(c) = p(c|a)p(a) Rearranging p(a|c) = p(c|a)p(a)

p(c)

Now suppose c can also occur with b so

p(c) = p(c|a)p(a) + p(c|b)p(b)

Combining these facts gives Bayes Rule

p(a|c) =

p(c|a)p(a) p(c|a)p(a)+p(c|b)p(b)

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Introduction Model Equilibrium Results

Political Agency Bayes Rule

The probability that two events a and c occur together may be written

p(a|c)p(c) or p(c|a)p(a) = ⇒ p(a|c)p(c) = p(c|a)p(a) Rearranging p(a|c) = p(c|a)p(a)

p(c)

Now suppose c can also occur with b so

p(c) = p(c|a)p(a) + p(c|b)p(b)

Combining these facts gives Bayes Rule

p(a|c) =

p(c|a)p(a) p(c|a)p(a)+p(c|b)p(b)

Employing Bayes rule will allow the voters to make their best guess of a politicians type given their observations

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Introduction Model Equilibrium Results

Political Agency Solving for the Equilibrium

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Introduction Model Equilibrium Results

Political Agency Solving for the Equilibrium

Start with period 2

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Introduction Model Equilibrium Results

Political Agency Solving for the Equilibrium

Start with period 2

There are no reelection concerns

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Introduction Model Equilibrium Results

Political Agency Solving for the Equilibrium

Start with period 2

There are no reelection concerns Each politician takes their short term optimal action

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Introduction Model Equilibrium Results

Political Agency Solving for the Equilibrium

Start with period 2

There are no reelection concerns Each politician takes their short term optimal action

Congruent chooses

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Introduction Model Equilibrium Results

Political Agency Solving for the Equilibrium

Start with period 2

There are no reelection concerns Each politician takes their short term optimal action

Congruent chooses

e2(s, c) = s2

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Introduction Model Equilibrium Results

Political Agency Solving for the Equilibrium

Start with period 2

There are no reelection concerns Each politician takes their short term optimal action

Congruent chooses

e2(s, c) = s2

Dissonant chooses

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Introduction Model Equilibrium Results

Political Agency Solving for the Equilibrium

Start with period 2

There are no reelection concerns Each politician takes their short term optimal action

Congruent chooses

e2(s, c) = s2

Dissonant chooses

e2(s, d) = (1 − s2)

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Introduction Model Equilibrium Results

Political Agency Solving for the Equilibrium

Start with period 2

There are no reelection concerns Each politician takes their short term optimal action

Congruent chooses

e2(s, c) = s2

Dissonant chooses

e2(s, d) = (1 − s2)

All agents in the model can work this out

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Introduction Model Equilibrium Results

Political Agency Solving for the Equilibrium

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Introduction Model Equilibrium Results

Political Agency Solving for the Equilibrium

Now consider period 1

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Introduction Model Equilibrium Results

Political Agency Solving for the Equilibrium

Now consider period 1

A congruent politician will always do what voters want

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Introduction Model Equilibrium Results

Political Agency Solving for the Equilibrium

Now consider period 1

A congruent politician will always do what voters want A dissonant politician may also do what voters want so as to get reelected for period 2

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Introduction Model Equilibrium Results

Political Agency Solving for the Equilibrium

Now consider period 1

A congruent politician will always do what voters want A dissonant politician may also do what voters want so as to get reelected for period 2

Define

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Introduction Model Equilibrium Results

Political Agency Solving for the Equilibrium

Now consider period 1

A congruent politician will always do what voters want A dissonant politician may also do what voters want so as to get reelected for period 2

Define

λ - probability dissonant politician does what voters want in period 1 - Political Discipline

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Introduction Model Equilibrium Results

Political Agency Solving for the Equilibrium

Now consider period 1

A congruent politician will always do what voters want A dissonant politician may also do what voters want so as to get reelected for period 2

Define

λ - probability dissonant politician does what voters want in period 1 - Political Discipline π - probability a randomly drawn politician is congruent

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Introduction Model Equilibrium Results

Political Agency Solving for the Equilibrium

Now consider period 1

A congruent politician will always do what voters want A dissonant politician may also do what voters want so as to get reelected for period 2

Define

λ - probability dissonant politician does what voters want in period 1 - Political Discipline π - probability a randomly drawn politician is congruent Π - voters updated probability a politician is congruent after they observe a payoff of ∆ in period 1

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Introduction Model Equilibrium Results

Political Agency Solving for the Equilibrium

Now consider period 1

A congruent politician will always do what voters want A dissonant politician may also do what voters want so as to get reelected for period 2

Define

λ - probability dissonant politician does what voters want in period 1 - Political Discipline π - probability a randomly drawn politician is congruent Π - voters updated probability a politician is congruent after they observe a payoff of ∆ in period 1 If voters observe a payoff of 0 they know that the politician is dissonant

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Introduction Model Equilibrium Results

Political Agency Solving for the Equilibrium

Now consider period 1

A congruent politician will always do what voters want A dissonant politician may also do what voters want so as to get reelected for period 2

Define

λ - probability dissonant politician does what voters want in period 1 - Political Discipline π - probability a randomly drawn politician is congruent Π - voters updated probability a politician is congruent after they observe a payoff of ∆ in period 1 If voters observe a payoff of 0 they know that the politician is dissonant

Dissonant chooses

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Introduction Model Equilibrium Results

Political Agency Solving for the Equilibrium

Now consider period 1

A congruent politician will always do what voters want A dissonant politician may also do what voters want so as to get reelected for period 2

Define

λ - probability dissonant politician does what voters want in period 1 - Political Discipline π - probability a randomly drawn politician is congruent Π - voters updated probability a politician is congruent after they observe a payoff of ∆ in period 1 If voters observe a payoff of 0 they know that the politician is dissonant

Dissonant chooses

e2(s, d) = (1 − s2)

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Introduction Model Equilibrium Results

Political Agency Solving for the Equilibrium

Now consider period 1

A congruent politician will always do what voters want A dissonant politician may also do what voters want so as to get reelected for period 2

Define

λ - probability dissonant politician does what voters want in period 1 - Political Discipline π - probability a randomly drawn politician is congruent Π - voters updated probability a politician is congruent after they observe a payoff of ∆ in period 1 If voters observe a payoff of 0 they know that the politician is dissonant

Dissonant chooses

e2(s, d) = (1 − s2)

All agents in the model can work this out

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Introduction Model Equilibrium Results

Political Agency Solving for the Equilibrium

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Introduction Model Equilibrium Results

Political Agency Solving for the Equilibrium

Applying Bayes Rule if ∆ is observed gives p(c|∆) = p(∆|c)p(c) p(∆|c)p(c) + p(∆|d)p(d) = π π + λ(1 − π) = Π ≥ π

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Introduction Model Equilibrium Results

Political Agency Solving for the Equilibrium

Applying Bayes Rule if ∆ is observed gives p(c|∆) = p(∆|c)p(c) p(∆|c)p(c) + p(∆|d)p(d) = π π + λ(1 − π) = Π ≥ π Dissonant politicians choice

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Introduction Model Equilibrium Results

Political Agency Solving for the Equilibrium

Applying Bayes Rule if ∆ is observed gives p(c|∆) = p(∆|c)p(c) p(∆|c)p(c) + p(∆|d)p(d) = π π + λ(1 − π) = Π ≥ π Dissonant politicians choice

Will choose e1(s, d) = s1 if E + r1 ≤ E + β(µ + E) = ⇒ r1 ≤ β(µ + E)

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Introduction Model Equilibrium Results

Political Agency Solving for the Equilibrium

Applying Bayes Rule if ∆ is observed gives p(c|∆) = p(∆|c)p(c) p(∆|c)p(c) + p(∆|d)p(d) = π π + λ(1 − π) = Π ≥ π Dissonant politicians choice

Will choose e1(s, d) = s1 if E + r1 ≤ E + β(µ + E) = ⇒ r1 ≤ β(µ + E) Probablity of which (political discipline) is λ = G(β(µ + E))

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Introduction Model Equilibrium Results

Political Agency Equilibrium

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Introduction Model Equilibrium Results

Political Agency Equilibrium

In the Perfect Bayesian Equilibrium

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Introduction Model Equilibrium Results

Political Agency Equilibrium

In the Perfect Bayesian Equilibrium

Congruent politicians always set e = s

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Introduction Model Equilibrium Results

Political Agency Equilibrium

In the Perfect Bayesian Equilibrium

Congruent politicians always set e = s Dissonant politicians set e2 = 1 − s2

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Introduction Model Equilibrium Results

Political Agency Equilibrium

In the Perfect Bayesian Equilibrium

Congruent politicians always set e = s Dissonant politicians set e2 = 1 − s2 Dissonant politicians set e1 = s1 if r1 ≤ β(µ + E) which

• ccurs with probability λ

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Introduction Model Equilibrium Results

Political Agency Equilibrium

In the Perfect Bayesian Equilibrium

Congruent politicians always set e = s Dissonant politicians set e2 = 1 − s2 Dissonant politicians set e1 = s1 if r1 ≤ β(µ + E) which

• ccurs with probability λ

Dissonant politicians set e1 = 1 − s1 if r1 > β(µ + E) which

• ccurs with probability 1 − λ

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Introduction Model Equilibrium Results

Political Agency Equilibrium

In the Perfect Bayesian Equilibrium

Congruent politicians always set e = s Dissonant politicians set e2 = 1 − s2 Dissonant politicians set e1 = s1 if r1 ≤ β(µ + E) which

• ccurs with probability λ

Dissonant politicians set e1 = 1 − s1 if r1 > β(µ + E) which

• ccurs with probability 1 − λ

All politicians that choose e1 = s1 are reelected, those that do not are replaced

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Introduction Model Equilibrium Results

Political Agency Quality of Government

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Introduction Model Equilibrium Results

Political Agency Quality of Government

Voters Expected Payoffs

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Introduction Model Equilibrium Results

Political Agency Quality of Government

Voters Expected Payoffs

Period 1 V1(λ) = [π + (1 − π)λ]∆

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Introduction Model Equilibrium Results

Political Agency Quality of Government

Voters Expected Payoffs

Period 1 V1(λ) = [π + (1 − π)λ]∆ Period 2 V2(λ) = π[1 + (1 − π)(1 − λ)]∆

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Introduction Model Equilibrium Results

Political Agency Quality of Government

Voters Expected Payoffs

Period 1 V1(λ) = [π + (1 − π)λ]∆ Period 2 V2(λ) = π[1 + (1 − π)(1 − λ)]∆ Discounted Voter Welfare W (λ) = V1(λ) + βV2(λ) = [π + (1 − π)λ]∆ + βπ[1 + (1 − π)(1 − λ)]∆

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Introduction Model Equilibrium Results

Political Agency Quality of Government

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Introduction Model Equilibrium Results

Political Agency Quality of Government

Discounted Voter Welfare W (λ) =[π + (1 − π)λ]∆ + βπ[1 + (1 − π)(1 − λ)]∆ so Wλ =(1 − π)(1 − βπ)∆ > 0

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Introduction Model Equilibrium Results

Political Agency Quality of Government

Discounted Voter Welfare W (λ) =[π + (1 − π)λ]∆ + βπ[1 + (1 − π)(1 − λ)]∆ so Wλ =(1 − π)(1 − βπ)∆ > 0 An increase in political discipline raises voter welfare

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Introduction Model Equilibrium Results

Political Agency Quality of Government

Discounted Voter Welfare W (λ) =[π + (1 − π)λ]∆ + βπ[1 + (1 − π)(1 − λ)]∆ so Wλ =(1 − π)(1 − βπ)∆ > 0 An increase in political discipline raises voter welfare

Dissonant politicians are more likely to behave as voters wish in period 1

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Introduction Model Equilibrium Results

Political Agency Quality of Government

Discounted Voter Welfare W (λ) =[π + (1 − π)λ]∆ + βπ[1 + (1 − π)(1 − λ)]∆ so Wλ =(1 − π)(1 − βπ)∆ > 0 An increase in political discipline raises voter welfare

Dissonant politicians are more likely to behave as voters wish in period 1 But more of them then survive to misbehave in period 2

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Introduction Model Equilibrium Results

Political Agency Quality of Government

Discounted Voter Welfare W (λ) =[π + (1 − π)λ]∆ + βπ[1 + (1 − π)(1 − λ)]∆ so Wλ =(1 − π)(1 − βπ)∆ > 0 An increase in political discipline raises voter welfare

Dissonant politicians are more likely to behave as voters wish in period 1 But more of them then survive to misbehave in period 2 The first effect dominates

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Introduction Model Equilibrium Results

Political Agency Quality of Government

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Introduction Model Equilibrium Results

Political Agency Quality of Government

Discounted Voter Welfare W (λ) =[π + (1 − π)λ]∆ + βπ[1 + (1 − π)(1 − λ)]∆

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Introduction Model Equilibrium Results

Political Agency Quality of Government

Discounted Voter Welfare W (λ) =[π + (1 − π)λ]∆ + βπ[1 + (1 − π)(1 − λ)]∆ Political Discipline λ = G(β(µ + E))

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Introduction Model Equilibrium Results

Political Agency Quality of Government

Discounted Voter Welfare W (λ) =[π + (1 − π)λ]∆ + βπ[1 + (1 − π)(1 − λ)]∆ Political Discipline λ = G(β(µ + E)) So by substitution W (π, µ, β, E) =[π + (1 − π)G(β(µ + E))]∆ +βπ[1 + (1 − π)(1 − G(β(µ + E)))]∆

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Introduction Model Equilibrium Results

Political Agency Quality of Government

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Introduction Model Equilibrium Results

Political Agency Quality of Government

Discounted Voter Welfare W (π, µ, β, E) ={[π + (1 − π)G(β(µ + E))] +βπ[1+(1 − π)(1 − G(β(µ + E)))]}∆

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Introduction Model Equilibrium Results

Political Agency Quality of Government

Discounted Voter Welfare W (π, µ, β, E) ={[π + (1 − π)G(β(µ + E))] +βπ[1+(1 − π)(1 − G(β(µ + E)))]}∆ Change in the Discount Rate - β Wβ(π, µ, β, E) ={G ′(.)(µ + E)[1 − π − βπ] +[π + (1 − π)G(β(µ + E)]}∆

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Introduction Model Equilibrium Results

Political Agency Quality of Government

Discounted Voter Welfare W (π, µ, β, E) ={[π + (1 − π)G(β(µ + E))] +βπ[1+(1 − π)(1 − G(β(µ + E)))]}∆ Change in the Discount Rate - β Wβ(π, µ, β, E) ={G ′(.)(µ + E)[1 − π − βπ] +[π + (1 − π)G(β(µ + E)]}∆ So a sufficient condition for Wβ(π, µ, β, E) > 0 is [1 − π − βπ] > 0

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Introduction Model Equilibrium Results

Political Agency Quality of Government

Discounted Voter Welfare W (π, µ, β, E) ={[π + (1 − π)G(β(µ + E))] +βπ[1+(1 − π)(1 − G(β(µ + E)))]}∆ Change in the Discount Rate - β Wβ(π, µ, β, E) ={G ′(.)(µ + E)[1 − π − βπ] +[π + (1 − π)G(β(µ + E)]}∆ So a sufficient condition for Wβ(π, µ, β, E) > 0 is [1 − π − βπ] > 0

As β increases dissonant politicians are more likely to behave correctly in the first period

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Introduction Model Equilibrium Results

Political Agency Quality of Government

Discounted Voter Welfare W (π, µ, β, E) ={[π + (1 − π)G(β(µ + E))] +βπ[1+(1 − π)(1 − G(β(µ + E)))]}∆ Change in the Discount Rate - β Wβ(π, µ, β, E) ={G ′(.)(µ + E)[1 − π − βπ] +[π + (1 − π)G(β(µ + E)]}∆ So a sufficient condition for Wβ(π, µ, β, E) > 0 is [1 − π − βπ] > 0

As β increases dissonant politicians are more likely to behave correctly in the first period If π small - dissonant politicians are proportionately greater in number, therefore their good behavior is more valuable to voters

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Introduction Model Equilibrium Results

Political Agency Quality of Government

Discounted Voter Welfare W (π, µ, β, E) ={[π + (1 − π)G(β(µ + E))] +βπ[1+(1 − π)(1 − G(β(µ + E)))]}∆ Change in the Discount Rate - β Wβ(π, µ, β, E) ={G ′(.)(µ + E)[1 − π − βπ] +[π + (1 − π)G(β(µ + E)]}∆ So a sufficient condition for Wβ(π, µ, β, E) > 0 is [1 − π − βπ] > 0

As β increases dissonant politicians are more likely to behave correctly in the first period If π small - dissonant politicians are proportionately greater in number, therefore their good behavior is more valuable to voters If π is small we are less likely to replace a dissonant with a congruent in the second period so we are less concerned with detecting them and voting them out of office in period 1

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Introduction Model Equilibrium Results

Political Agency Quality of Government

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Introduction Model Equilibrium Results

Political Agency Quality of Government

Discounted Voter Welfare W (π, µ, β, E) ={[π + (1 − π)G(β(µ + E)] +βπ[1+(1 − π)(1 − G(β(µ + E)))]}∆

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Introduction Model Equilibrium Results

Political Agency Quality of Government

Discounted Voter Welfare W (π, µ, β, E) ={[π + (1 − π)G(β(µ + E)] +βπ[1+(1 − π)(1 − G(β(µ + E)))]}∆ Change in the Dissonant Politician’s Payoffs - µ + E Wµ(π, µ, β, E) =WE (π, µ, β, E) =(1 − π)βG ′(β(µ + E))[1 − βπ] > 0

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Introduction Model Equilibrium Results

Political Agency Quality of Government

Discounted Voter Welfare W (π, µ, β, E) ={[π + (1 − π)G(β(µ + E)] +βπ[1+(1 − π)(1 − G(β(µ + E)))]}∆ Change in the Dissonant Politician’s Payoffs - µ + E Wµ(π, µ, β, E) =WE (π, µ, β, E) =(1 − π)βG ′(β(µ + E))[1 − βπ] > 0

Dissonants care more about being reelected therefore behave better in the first period

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Introduction Model Equilibrium Results

Political Agency Quality of Government

Discounted Voter Welfare W (π, µ, β, E) ={[π + (1 − π)G(β(µ + E)] +βπ[1+(1 − π)(1 − G(β(µ + E)))]}∆ Change in the Dissonant Politician’s Payoffs - µ + E Wµ(π, µ, β, E) =WE (π, µ, β, E) =(1 − π)βG ′(β(µ + E))[1 − βπ] > 0

Dissonants care more about being reelected therefore behave better in the first period More dissonance survive to the second period where they misbehave

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Introduction Model Equilibrium Results

Political Agency Quality of Government

Discounted Voter Welfare W (π, µ, β, E) ={[π + (1 − π)G(β(µ + E)] +βπ[1+(1 − π)(1 − G(β(µ + E)))]}∆ Change in the Dissonant Politician’s Payoffs - µ + E Wµ(π, µ, β, E) =WE (π, µ, β, E) =(1 − π)βG ′(β(µ + E))[1 − βπ] > 0

Dissonants care more about being reelected therefore behave better in the first period More dissonance survive to the second period where they misbehave The first effect dominates

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Introduction Model Equilibrium Results

Political Agency Quality of Government

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Introduction Model Equilibrium Results

Political Agency Quality of Government

Discounted Voter Welfare W (π, µ, β, E) ={[π + (1 − π)G(β(µ + E)] +βπ[1+(1 − π)(1 − G(β(µ + E)))]}∆

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Introduction Model Equilibrium Results

Political Agency Quality of Government

Discounted Voter Welfare W (π, µ, β, E) ={[π + (1 − π)G(β(µ + E)] +βπ[1+(1 − π)(1 − G(β(µ + E)))]}∆ Change in the Proportion of Congruent Politicians - π Wπ(π, µ, β, E) ={(1 − G(β(µ + E)) +β[1 + (1 − G(β(µ + E))[1 − 2π]]}∆ > 0

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Introduction Model Equilibrium Results

Political Agency Quality of Government

Discounted Voter Welfare W (π, µ, β, E) ={[π + (1 − π)G(β(µ + E)] +βπ[1+(1 − π)(1 − G(β(µ + E)))]}∆ Change in the Proportion of Congruent Politicians - π Wπ(π, µ, β, E) ={(1 − G(β(µ + E)) +β[1 + (1 − G(β(µ + E))[1 − 2π]]}∆ > 0 Raises voter welfare

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Introduction Model Equilibrium Results

Political Agency Quality of Government

Discounted Voter Welfare W (π, µ, β, E) ={[π + (1 − π)G(β(µ + E)] +βπ[1+(1 − π)(1 − G(β(µ + E)))]}∆ Change in the Proportion of Congruent Politicians - π Wπ(π, µ, β, E) ={(1 − G(β(µ + E)) +β[1 + (1 − G(β(µ + E))[1 − 2π]]}∆ > 0 Raises voter welfare

More likely to get a congruent politician in period 1

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Introduction Model Equilibrium Results

Political Agency Quality of Government

Discounted Voter Welfare W (π, µ, β, E) ={[π + (1 − π)G(β(µ + E)] +βπ[1+(1 − π)(1 − G(β(µ + E)))]}∆ Change in the Proportion of Congruent Politicians - π Wπ(π, µ, β, E) ={(1 − G(β(µ + E)) +β[1 + (1 − G(β(µ + E))[1 − 2π]]}∆ > 0 Raises voter welfare

More likely to get a congruent politician in period 1 More likely to get a congruent politician in period 2 to replace a dissonant politician that is not reelected

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Introduction Model Equilibrium Results

Political Agency Quality of Government

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Introduction Model Equilibrium Results

Political Agency Quality of Government

Term Limits

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Introduction Model Equilibrium Results

Political Agency Quality of Government

Term Limits

Suppose politicians are term limited to one period in office

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Introduction Model Equilibrium Results

Political Agency Quality of Government

Term Limits

Suppose politicians are term limited to one period in office That period is then their last period

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Introduction Model Equilibrium Results

Political Agency Quality of Government

Term Limits

Suppose politicians are term limited to one period in office That period is then their last period No political discipline λ = 0

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Introduction Model Equilibrium Results

Political Agency Quality of Government

Term Limits

Suppose politicians are term limited to one period in office That period is then their last period No political discipline λ = 0 Dissonant politicians always choose e1(s, d) = (1 − s1)

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Introduction Model Equilibrium Results

Political Agency Quality of Government

Term Limits

Suppose politicians are term limited to one period in office That period is then their last period No political discipline λ = 0 Dissonant politicians always choose e1(s, d) = (1 − s1) Reduces voter welfare

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