Dynamic Bargaining over Redistribution in Legislatures Facundo Piguillem*

Alessandro Riboni**

´ * EIEF, ** Ecole Polytechnique

December 4, 2013

Motivation

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In most democracies policies are decided by elected representatives who bargain over changes to the current policies, i.e., the status quo

Motivation

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In most democracies policies are decided by elected representatives who bargain over changes to the current policies, i.e., the status quo

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The chosen policy becomes the new status quo

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⇒ the status quo is endogenous

go

What is the paper about? Economy where capital taxes are used to finance redistribution I

Optimal policy: high tax today, low in the future ⇒time inconsistent

What is the paper about? Economy where capital taxes are used to finance redistribution I

Optimal policy: high tax today, low in the future ⇒time inconsistent

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Standard approach (in macro-political-economy): I I

MPE: median voter outcome Key state variable: capital

What is the paper about? Economy where capital taxes are used to finance redistribution I

Optimal policy: high tax today, low in the future ⇒time inconsistent

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Standard approach (in macro-political-economy): I I

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MPE: median voter outcome Key state variable: capital

Our approach: I I

MPE: with Legislative Bargaining Additional state variable: endogenous Status Quo

What is the paper about? Economy where capital taxes are used to finance redistribution I

Optimal policy: high tax today, low in the future ⇒time inconsistent

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Standard approach (in macro-political-economy): I I

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Our approach: I I

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MPE: median voter outcome Key state variable: capital

MPE: with Legislative Bargaining Additional state variable: endogenous Status Quo

Quantitative implications I I

Standard approach: very high taxes Our approach: lower taxes

The mechanism

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Endogenous status quo creates a trade off

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Status quo: default option in case of disagreement I

⇒ It affects bargaining power

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High status quo ⇒ more power to poor legislators

The mechanism

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Endogenous status quo creates a trade off

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Status quo: default option in case of disagreement

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⇒ It affects bargaining power

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High status quo ⇒ more power to poor legislators

High taxes I

Redistribute today ⇒ moving the status quo

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And give more power to poor legislators tomorrow

Other Implications

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Political growth Cycles

Other Implications

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Political growth Cycles

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Strategic interactions I

Politicians’ strategy respond to changes of environment/institutions

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Example: an increase in the mass of representatives of rich constituents

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⇒ Polarization of policy preferences

Related Literature

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Median Voter approach: Meltzer and Richard (1981), Krusell and Rios-Rull (1999), Corbae et al. (2009), Azzimonti et al. (2006)

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Legislative Bargaining:

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Baron and Ferejohn (1989) consider a ”divide the dollar” problem

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Battaglini and Coate (2008): pork and public good decisions

Legislative Bargaining with endogenous status quo: Baron (1996), Kalandrakis (2004), Battaglini & Palfrey (2012) Duggan & Kalandrakis (2008), Nunnari(2011), Bowen & Zahran (2012), Piguillem & Riboni (2013)

Roadmap

1. Environment 1.1 Economy given taxes 1.2 Legislative Bargaining

2. Example 3. Simulations 4. Concluding remarks

The Model

Overview

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Standard growth model, heterogeneous agents (in initial capital)

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Capital income taxed to finance equal lump-sum transfers

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Capital taxation: redistribution from agents with high wealth to agents with low wealth

Timing inside a period (time t = 0, 1, ....)  

t.1  t 

Firms rent  kt and Lt to  produce  States:   Capital:       kt   Status quo: qt 

t.2

Legislature  bargains  over tax τt 

t.3

t.4

Capital  income is  taxed 

Consumption  and saving 

States:   Capital: kt   Tax         qt+1=τt 

t+1 

The consumers: given tax process I

Markov process for τ ∈ [0, τ¯]: Γ(τt+1 |τt , kt )

I

Unit measure of agents

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Each agent (consumer) is defined by his wealth share. θ0i = k0i /k0

max Et

X∞ j=t

 β j−t u(cji ) ,

(1)

subject to i cti + at+1 = wt + Tt + Rt ati i at+1

(2)

≥ 0, ∀t

where Rt = 1 + rt (1 − τt ),

(3)

Technology, Government and Market clearing

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Government budget: τt rt kt = Tt ∀ t

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Technology: f (kt ) = ktα

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Prices: rt = f 0 (kt ) − δ

wt = f (kt ) − kt f 0 (kt ) I

Feasibility : ct + kt+1 = f (kt ) + (1 − δ)kt

(4)

Optimal policy with commitment I

For any agent θ < 1 optimal (commitment) policy is: I

τ0 in upper bound I I

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Capital is fixed: no distortions from taxation The lower θ the stronger the incentive to raise τ0

τt equal to zero in the long run I I

All τt , t ≥ 1, generate distortions Similar to Chamley-Judd result. Bassetto & Benhabib, (2006)

Optimal policy with commitment I

For any agent θ < 1 optimal (commitment) policy is: I

τ0 in upper bound I I

I

Capital is fixed: no distortions from taxation The lower θ the stronger the incentive to raise τ0

τt equal to zero in the long run I I

All τt , t ≥ 1, generate distortions Similar to Chamley-Judd result. Bassetto & Benhabib, (2006)

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But this policy is time inconsistent

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Without commitment?

Legislature: bargaining protocol Continuum of legislators: distribution µL (θ) Payoffs: legislator θ maximizes utility of agent θ

Legislature: bargaining protocol Continuum of legislators: distribution µL (θ) Payoffs: legislator θ maximizes utility of agent θ I

Agenda setter is selected with probability µa (θ)

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Makes a take it or leave it offer τt ∈ [0, τ¯]

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All members simultaneously vote: either yes or no

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Acceptance is probabilistic: measure of legislators in favor

Legislature: bargaining protocol Continuum of legislators: distribution µL (θ) Payoffs: legislator θ maximizes utility of agent θ I

Agenda setter is selected with probability µa (θ)

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Makes a take it or leave it offer τt ∈ [0, τ¯]

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All members simultaneously vote: either yes or no

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Acceptance is probabilistic: measure of legislators in favor

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If proposal is rejected ⇒ qt is implemented

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If proposal passes ⇒ tax for the current period. ⇒ qt+1 = τt : endogenous status quo

Politico-Economic Equilibrium Definition (PEE) Given µL (θ) and µa (θ), a PEE is I I I I

Proposal rules: τ (θs ) : <+ × [0, τ¯] → [0, τ¯]

Voting rules: α(θ) : <+ × [0, τ¯] × [0, τ¯] → {yes, no}

Markov process for taxes: Γ(τ |q, k),

Law of motion of aggregate capital: G : <+ × [0, τ¯] → <+

Such that b (k, q, θ) and G (k, τ ) constitute a CE. a) Given Γ(τ |q, k), V b (k, q, θ), b) Given G (k, τ ) and V b.1) α(θ) maximize legislators utilities b.2) τ (θs ) solves the agenda setter problem. b.3) Γ(τ |q, k) is generated by µa (θ), µL (θ), τ (θs , q, k) and α(θ, q, k).

Example

Example I

Log utility and full depreciation

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Legislature only meets at t = 0 and t = 1 I

I

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τ1 stays for all t ≥ 1

Two types of legislators I

Median: θm < 1, with measure 1 − µ > 0.5

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Poor: θp < θm , with measure µ < 0.5

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Both like redistribution

Difference in bargaining protocol I

Majority voting rule

Optimal constant tax (t = 1)

I

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Value functions from t = 1 onwards v1 (τ1 , k1 , 1)

=

v1 (τ1 , k1 , θ)

=

φ1 (τ1 , θ)

=

  1 βα log((1 − τ1 )αβ) α log(k1 ) + log(1 − (1 − τ1 )αβ) + 1 − βα 1−β 1 − βα log(φ1 (τ1 , θ)) + v1 (τ1 , k1 , 1) 1−β (1 − τ1 )(θ − 1) 1 + (1 − β)α 1 − (1 − τ1 )αβ

The optimal τ1 satisfies 1 −(θ − 1) τ1 β − =0 φ(τ1 , θ) 1 − (1 − τ1 )βα (1 − τ1 )(1 − βα)

Value functions (from t = 1 onwards)

Value function for each type

0

poor median

τ*(θm) 0.5

τ

τ*(θp) 1

Example: period 1 bargaining

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pic

endo

With prob. 1 − µ: θm is recognized as setter: I

She gets what she wants regardless of the status quo

Example: period 1 bargaining

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endo

With prob. 1 − µ: θm is recognized as setter: I

I

pic

She gets what she wants regardless of the status quo

With prob. µ: θp is recognized I I

She has to make the policy proposal acceptable to the median What is acceptable depends on the status quo

If θp is recognized: q is low

0

agenda setter median

0.1

0.2

τ*m 0.3

0.4

q

0.5

τ*p 0.6

τ

0.7

0.8

0.9

1

If θp is recognized: q is low

0

agenda setter median

0.1

0.2

τ*m 0.3

0.4

q

0.5

τ*p 0.6

τ

0.7

0.8

0.9

1

If θp is recognized: q is low

0

agenda setter median

0.1

0.2

τ*m 0.3

0.4

q

0.5

τ*p 0.6

τ

0.7

0.8

0.9

1

If θp is recognized: q is high

endo

0

agenda setter median

0.1

0.2

τ*m 0.3

0.4

0.5

τ*p 0.6

τ

0.7

0.8

0.9

q

1

If θp is recognized: q is high

0

agenda setter median

0.1

0.2

τ*m 0.3

0.4

0.5

τ*p 0.6

τ

0.7

0.8

0.9

q

1

If θp is recognized: q is in between

0

agenda setter median

0.1

0.2

τ*m 0.3

0.4

0.5

no change if q is here 0.6

τ

0.7

τ*p 0.8

0.9

1

Proposals at t = 1

0.8 τ*p

proposal by θp

0.75 0.7

τ1

0.65 0.6

τ*m

proposal by θm

0.55 0.5 0.45 0.4 0

0.1

0.2

0.3

τL

0.5

τ0

τ*m

0.7

τ*p

0.9

1

Example: decisions at t = 0

pic

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By looking at current payoff, all legislators want maximum taxes at t = 0

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But policy at t=0 strategically affects future outcomes

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What is the median’s preferred policy?

Example: decisions at t = 0

pic

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By looking at current payoff, all legislators want maximum taxes at t = 0

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But policy at t=0 strategically affects future outcomes

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What is the median’s preferred policy? I

As θp → θm , τ0 goes to upper bound

Example: decisions at t = 0

pic

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By looking at current payoff, all legislators want maximum taxes at t = 0

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But policy at t=0 strategically affects future outcomes

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What is the median’s preferred policy? I

As θp → θm , τ0 goes to upper bound

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The same when the poor never control the agenda µ → 0. (MV)

Example: decisions at t = 0

pic

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By looking at current payoff, all legislators want maximum taxes at t = 0

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But policy at t=0 strategically affects future outcomes

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What is the median’s preferred policy?

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As θp → θm , τ0 goes to upper bound

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The same when the poor never control the agenda µ → 0. (MV)

If q were exogenous: τ0 would be in the upper bound

Numerical Results

Agenda setter problem

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Given state (k, q), optimal proposal by agenda setter θa solves b (θa , k, τ ) + [1 − Pr (k, τ, q)] V b (θa , k, q) max Pr (k, τ, q) V τ

subject to k 0 = G (k, τ );

∀τ

Agenda setter problem

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Given state (k, q), optimal proposal by agenda setter θa solves b (θa , k, τ ) + [1 − Pr (k, τ, q)] V b (θa , k, q) max Pr (k, τ, q) V τ

subject to k 0 = G (k, τ );

I

∀τ

Prob. of acceptance of proposal τ vs prob. of rejection

Agenda setter problem

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Given state (k, q), optimal proposal by agenda setter θa solves b (θa , k, τ ) + [1 − Pr (k, τ, q)] V b (θa , k, q) max Pr (k, τ, q) V τ

subject to k 0 = G (k, τ );

∀τ

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Prob. of acceptance of proposal τ vs prob. of rejection

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Life-time utility when τ is accepted

Agenda setter problem

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Given state (k, q), optimal proposal by agenda setter θa solves b (θa , k, τ ) + [1 − Pr (k, τ, q)] V b (θa , k, q) max Pr (k, τ, q) V τ

subject to k 0 = G (k, τ );

∀τ

I

Prob. of acceptance of proposal τ vs prob. of rejection

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Life-time utility when τ is accepted

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Life-time utility when q is kept

Agenda setter problem

I

Given state (k, q), optimal proposal by agenda setter θa solves b (θa , k, τ ) + [1 − Pr (k, τ, q)] V b (θa , k, q) max Pr (k, τ, q) V τ

subject to k 0 = G (k, τ );

∀τ

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Prob. of acceptance of proposal τ vs prob. of rejection

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Life-time utility when τ is accepted

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Life-time utility when q is kept

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Aggregate law of motion of capital

Prob. of Acceptance

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Pr (k, τ, q): probability of τ being accepted given state q and k

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What is this?

Prob. of Acceptance

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Pr (k, τ, q): probability of τ being accepted given state q and k

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What is this? n o b (k, θ, τ ) ≥ V b (k, θ, q) . A(k, τ, q) = θ ∈ ΘL : V Then

Z Pr (k, τ, q) = A(k,τ,q)

µL (θ)dθ

Policy proposals in the full model

more

Proposed tax (given capital) 1 0.9

Proposed tax: τ (θ,q, K)

0.8

θ=0.26 θ=0.63

0.7

θ=0.7 θ=0.77

0.6 0.5 0.4 0.3 0.2 0.1 0 0

0.1

0.2

0.3

0.4

0.5

q

0.6

0.7

0.8

0.9

1

Summarizing

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A tax increase involves following trade-off:

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Redistributes w/out distorting the economy

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But it has future consequences via status quo: 1. High tax may persist. 2. It affects future proposals (and acceptance probabilities)

Results I I

Calibration: α = 0.3, β = 0.96, τ¯ = 0.95 δ = 0.08 Calibration: measures pic I I

µa = µL distribution of net worth SCF 2007 θm ≈ 0.25 and Prob(θ > 1) = 0.20

Results I I

Calibration: α = 0.3, β = 0.96, τ¯ = 0.95 δ = 0.08 Calibration: measures pic I I

µa = µL distribution of net worth SCF 2007 θm ≈ 0.25 and Prob(θ > 1) = 0.20

Tax on Capital Income

E (τ ) 0.51

corr (τ ) 0.51

std(τ ) 0.39

consumption 0.96

Results I I

Calibration: α = 0.3, β = 0.96, τ¯ = 0.95 δ = 0.08 Calibration: measures pic I I

µa = µL distribution of net worth SCF 2007 θm ≈ 0.25 and Prob(θ > 1) = 0.20

Tax on Capital Income I

corr (τ ) 0.51

std(τ ) 0.39

consumption 0.96

If Legislators represent themselves (data: opensecrets.org) Tax on Capital Income

legis

E (τ ) 0.51

E (τ ) 0.25

corr (τ ) 0.48

std(τ ) 0.46

consumption 1.09

Importance of Legislators’ Distribution

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If legislators are distributed as in the population, median legislator has θ = 0.25

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Using actual legislators’ wealth distribution, the median legislator is very rich, θ = 1.76

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With latter calibration taxes go down (but not to zero) and volatility goes up

Benevolent vs Self Interested Politicians with the same θ behave differently in the two cases.

Rich Legislature (θm = 1.76)

”Poor” legislature (θm = 0.25 ) Proposed tax (given capital) 1

0.9

0.9

0.8

0.8

Proposed tax: τ (θ , q, K )

Proposed tax: τ (θ , q, K)

Proposed tax (given capital) 1

0.7 0.6 0.5 θ=0.63 θ=0.76 θ=0.83 θ=0.96

0.4 0.3 0.2

θ=0.63 θ=0.76 θ=0.83 θ=0.96

0.7 0.6 0.5 0.4 0.3 0.2

0.1

0.1

0

0

0

0.2

0.4

q

0.6

0.8

1

0

0.2

0.4

q

0.6

Polarization (more extreme policy preferences) in left panel.

0.8

1

Bicameralism

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Suppose we require two votes to pass legislation

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If benevolent Legislators Tax on Capital Income

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E (τ ) 0.34

corr (τ ) 0.73

std(τ ) 0.32

consumption 1.04

If Legislators represent themselves (data: opensecrets.org) Tax on Capital Income

E (τ ) 0.12

corr (τ ) 0.68

std(τ ) 0.41

consumption 1.13

Bicameralism and gradualism Unicameral

Bicameral

Proposed tax (given capital)

Proposed tax (given capital)

0.8

0.8

0.7 Proposed tax

Proposed tax

0.6 0.5 0.4 θ=-0.72 θ=0.05 θ=0.48 θ=0.83

0.3 0.2 0.1

θ=-0.72 θ=0.05

0.6

θ=0.48 θ=0.83

0.4

0.2

0

0 0

0.1

0.2

0.3

0.4 0.5 Status quo

0.6

0.7

0.8

0

0.1

0.4 0.5 Status quo

0.6

0.7

0.8

1 Probability of acceptance

Probability of acceptance

0.3

Probability of acceptance(given capital)

Probability of acceptance(given capital) 1 0.8 0.6 0.4 q=0.00 q=0.25 q=0.53 q=0.80

0.2 0

0.2

0.8 0.6

q=0.00

0.4

q=0.25 q=0.53 q=0.80

0.2 0

0

0.1

0.2

0.3

0.4 0.5 Proposed tax

0.6

0.7

0.8

0

0.1

0.2

0.3

0.4 0.5 Proposed tax

0.6

0.7

0.8

Expected Proposal and tax

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Expected proposal as function of capital 0.5

Proposal: E[τ ∗(θ)|q, K]

0.45 0.4 0.35 0.3

q=0 q=0.18 q=0.47 q=0.95

0.25 0.2

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

K

Expected tax as function of capital 0.9 0.8 q=0 q=0.18 q=0.47 q=0.95

0.7

E[τ |q,K ]

0.6 0.5 0.4 0.3 0.2 0.1 0

0

0.5

1

1.5

2

2.5

K

3

3.5

4

4.5

5

Sample Paths: τ and k: Politics and Business Cycle Sample path of Taxes 1

0.8

τt

0.6

0.4

0.2

0 100

110

120

130

140

150

160

170

180

190

200

170

180

190

200

t(years) Sample path of Capital 2.6 2.4

Kt

2.2 2 1.8 1.6 1.4 100

110

120

130

140

150

t(years)

160

tax

Concluding Remarks

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Taxes lower than usually obtained in macro literature with MV

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Key mechanism: threat of politicians eager for redistribution

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Interesting implications: I

Adding more rich-wealth legislators induces less discipline in the poorer legislators

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Politics and business cycle: redistribution is cheaper in booms

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Value of bicameral system: more persistence, less taxation

Distributions of θ’s −3

8

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Distribution in Legislature

x 10

6 4 2 0 −2

0

2

4 6 8 theta Probability of being recognized agenda setter

10

0.01

0.005

0 −2

0

2

4 theta

6

8

10

Distribution of Legislators

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Democrats House Average Median Prop richer than average Senate Average Median Prop richer than average Boths Chambers together Average Median Prop richer than average

Summary Republicans

Difference (%)

4,488,893 654,006 0.58

7,561,302 848,035 0.61

68% 30%

19,383,524 2,579,507 0.85

7,153,985 3,025,002 0.83

-63% 17%

7,209,600 891,506 0.63

7,491,000 1,075,002 0.65

4% 21%

Distribution of Net Worth (all legislators) 0.25 Democrats Republicans

kernel density

0.2

0.15

0.1

0.05

0 −20

−10

0 10 20 30 40 (Net Worth)/(Average net worth in economy)

50

60

Acceptance Probabilities

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1 0.9

Probability of acceptance

0.8 0.7 0.6 0.5 0.4 0.3 q=0.00 q=0.25 q=0.53 q=0.80

0.2 0.1 0

0

0.1

0.2

0.3

0.4 Proposed tax

0.5

0.6

0.7

0.8

Budget Negotiation in EU

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“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.” (Para 4, Art 312, European Union 2010).