Voting over Selfishly Optimal Income Tax Schedules with ... · Voting over Sel shly Optimal Income Tax Schedules with Tax-Driven Migrations Darong Dai Department of Economics Texas

Voting over Selfishly Optimal Income Tax Scheduleswith Tax-Driven Migrations

Darong Dai

Department of EconomicsTexas A&M University

Darong Dai (TAMU) Voting over Income Taxes 11/03/2017 1 / 26

Introduction

Motivation

Labor income tax design: work incentive and participation incentive.

Large income tax-induced mobility elasticities:

Highly paid football players: Kleven et al. (2013, AER).High income foreigners in Danish: Kleven et al. (2014, QJE).Foreign superstar inventors (employees): Akcigit et al. (2016, AER).

Geographic mobility in designing redistributive taxation:

Conventional wisdom (Stigler, 1957): limits redistribution.The classic paper: Mirrlees (1971, RES).Mirrlees (1982), Simula and Trannoy (2010, 2012), Piketty and Saez(2013) and Lehmann et al. (2014).They focus on the normative perspective.Lack of research from the positive perspective.


Introduction

The Combination of Labor Mobility and Majority Voting

Political process:

A direct democracy with citizen candidates.Pairwise majority voting.Each worker has one vote.

Hand-voting: Equilibrium tax schedule is selected by majority voting.

Foot-voting: Workers can move between alternative jurisdictions.

This combination generates a complex interaction whereby:

The taxation policies chosen determine whom they attract.Whom they attract determine their choices of taxation policies.


Introduction

Question

How would labor mobility affect income redistribution in a votingequilibrium?

To my knowledge, the answer is not yet well established.

To answer this question:

Establish a voting equilibrium.Compare to autarky (without migrations), qualitatively andquantitatively.


Introduction

Related Literature

Combine migrations and voting:

Cremer and Pestieau (1998), Hindriks (2001), Hamilton and Pestieau(2005), Brett (2016).

Selfishly optimal nonlinear taxation determined by the majority rule:

Roell (2012), Bohn and Stuart (2013), Brett and Weymark (2016,2017).

How the change of skill distribution affects equilibrium tax:

Leite-Monteiro (1997), Hamilton and Pestieau (2005), Brett andWeymark (2011), Lehmann et al. (2014).


Model

Environment

Two jurisdictions: A and B, not necessarily symmetry.

Both jurisdictions adopt majority voting.

Workers differ in

Skill/labor productivity, w ∈ [w ,w ] and w > 0.Migration cost/foot-voting capability, m ∈ R+.

Information structure:

Distributions F (w) =∫ w

wf (t)dt and G (m|w) =

∫ m

0g(x |w)dx are

common knowledge.Values of w and m are the private information of each worker.

Quasilinear-in-consumption preferences (Gruber and Saez, 2002).

Labor markets are perfectly competitive.

Labor income taxes are levied according to the residence principle.


Model

Individual Choices: Behavior Responses

For a worker of type (w ,m) born in jurisdiction A:

How much to work and consume?:

U(w) ≡ max{c,l}

c − h(l)

s.t.c = y − T (y) and y = wl .

FOC: T ′(y(w)) ≡ τ(w) = 1− 1w h′ ( y

w

), i.e., MTR = 1−MRSc,y .

Allowed: τ(w) < 0 for some w .

Where to work and consume?:

not to migrate ⇐⇒ U(w)︸︷︷︸stay

≥ U−(w)−m︸︷︷︸move

, (participation constraint)

following Lehmann et al. (2014, QJE).


Model

Migration Elasticity

The ex post mass of residents of skill w in jurisdiction A:

φ(∆(w); w) ≡

f (w) + G−(∆(w)|w)f−(w)n−︸︷︷︸

inflow

for ∆(w) ≥ 0,

f (w)− G (−∆(w)|w)f (w)︸︷︷︸outflow

for ∆(w) ≤ 0

with ∆(w) ≡ U(w)− U−(w).

Ex post skill density: f (w) ≡ φ(∆(w); w).

Following Lehmann et al. (2014, QJE), migration elasticity is:

θ(∆(w); w) ≡ ∂ f (w)

∂∆(w)

c(w)

f (w)≡ θ(w).


Model

Government Budget Constraint

Government budget constraint (GBC) under pure redistribution:∫ w

wT (y(w))f (w)dw ≥ 0.

Ex post tax base, denoted by

Γ(w ,w) ≡∫ w

wf (w)dw ,

is endogenous.


Model

Selfishly Optimal Nonlinear Tax Schedules

By Taxation Principle, a worker of type k ∈ [w ,w ] proposes an income taxschedule by solving the problem:

max{c(w),y(w)}w∈[w,w ]

U(k)

s.t.

U(k) = c(k)− h

(y(k)

k

)(IU);∫ w

w[y(w)− c(w)]f (w)dw ≥ 0 (GBC);

U ′(w) = h′(

y(w)

w

)y(w)

w 2, ∀w ∈ [w ,w ] (FOIC);

y ′(w) ≥ 0, ∀w ∈ [w ,w ] (SOIC).


The Voting Equilibrium

Theorem

By imposing pairwise majority-voting rule to the continuum of selfishlyoptimal income tax schedules, the one for the median skill type turns outto be a Condorcet winner.

By establishing weak single-peakedness of preferences (invertedU-shape):

U(w ,w) ≥ U(w , k1) ≥ U(w , k2), ∀proposers’ type︷︸︸︷w > k1 > k2

U(w ,w) ≥ U(w , k1) ≥ U(w , k2), ∀w < k1 < k2

then appealing to Black’s Median Voter Theorem (1948, JPE).

Recent empirical evidences: Agranov and Palfrey (2015), Corneo andNeher (2015) and Grundler and Kollner (2016).


Three Characteristics of Equilibrium Tax Schedule

The First Characteristic

Proposition

It coincides with the maximax tax schedule for types below the medianskill level and coincides with the maximin tax schedule for types above themedian skill level.

It redistributes incomes from the poor and rich toward the middle.

Intuition: Median voter is selfish.

Autarky equilibrium: Brett and Weymark (2017, GEB).

Director’s Law (Stigler, 1970): labor mobility and inter-jurisdictionaltax competition.



The Second Characteristic

Proposition

For low incomes below the median skill type, marginal tax rates arenegative. For high incomes above the median skill level, marginal tax ratesare positive if their migration elasticities are endogenously bounded above(this upper bound is in general different for different types).

Intuition:

The tradeoff between:

Maximizing resources extracted from other types.Maximizing resources available for extraction.

Tax higher skills because:

High wage rate implies a high opportunity cost of leisure.

Subsidize lower skills because:

Low wage rate implies a low opportunity cost of leisure.Taxing them strengthens their motive to mimic high types.



The Third Characteristic

Proposition

Truth-telling calls for bunching (pooling), namely imposing the same taxrate, in middle-income class, low-income class and/or high-income class.

w

y

yR∗(·)

yM∗(·)

0 w wk

y M∗(w)

wη wα wβwγ

y R∗(w)

Figure: Income schedule with three bridges.



The Third Characteristic (Cont’d)

w

y

yR∗(·)

yM∗(·)

0 w wk

y M∗(w)

wα wβwγ

y R∗(w)

w

y

yR∗(·)

yM∗(·)

0 w wk

y M∗(w)

wη wα wβ

y R∗(w)

Figure: Income schedule with two bridges and an upward discontinuity.


Identifying the Effect of Migrations on Equilibrium Taxes

Qualitative Characterization: Case I

Proposition

SupposeΘM(w) < θ(w) < ΘMR(w) for ∀w ∈ (w ,wm]

andΘR(w) < θ(w) < ΘMR(w) for ∀w ∈ (wm,w),

then we have:(i) If wm ≥ wm, then distortions and redistribution for ∀w ∈ (w ,w) aresmaller than in autarky.(ii) If wm < wm, then (i) still holds for ∀w ∈ (w , wm] ∪ (wm,w), whereasredistribution and distortions for ∀w ∈ (wm,wm] turn out to be greaterthan in autarky.



Graphic Illustration: Case I

Black ones represent the autarky equilibrium.

w

y

yR (·)

yM (·)yM (·)

yR (·)

0 w wwmwm

w

y

yR (·)

yM (·)yM (·)

yR (·)

0 w wwmwm



Contribution and Intuition: Case I

Contribution:

Derive endogenous lower bounds ΘM(w) and ΘR(w).

Intuition:

For high skills:

Large migration elasticity implies strong threat.Lower MTRs to prevent the shrink of tax base.

For low skills:

Lower MTRs on high skills provide more incentives to mimic high types.High migration possibility strengthens this.More transfers to prevent mimicking (more information rents).

Types between median types:

The income class they belong to totally changes!From the group receiving transfers to that paying taxes, or vice versa.



Qualitative Characterization: Case II

Proposition

Suppose

θ(w) < ΘM(w),

inflow︷︸︸︷f (w)/Γ(w ,w) > f (w)/F (w) for ∀w ∈ (w ,wm], and

θ(w) < ΘR(w),

outflow︷︸︸︷Γ(w ,w)− Γ(w ,w)

f (w)>

1− F (w)

f (w)for ∀w ∈ (wm,w),

then we have:(i) If wm ≤ wm, then distortions and redistribution for ∀w ∈ (w ,w) aregreater than in autarky.(ii) If wm > wm, then (i) still holds for ∀w ∈ (w ,wm] ∪ (wm,w), whereasredistribution and distortions for ∀w ∈ (wm, wm] turn out to be smallerthan in autarky.



Graphic Illustration: Case II

Black ones represent the autarky equilibrium.

w

y

yR (·)

yM (·)yM (·)

yR (·)

0 w wwmwm

w

y

yR (·)

yM (·)yM (·)

yR (·)

0 w wwmwm



Contribution and Intuition: Case II

Contribution:

Derive endogenous upper bounds ΘM(w) and ΘR(w).

Reasonable counterexamples to the conventional wisdom.

Intuition:

For high skills:

Small migration elasticity implies weak threat.Outflow implies the shrink of tax base (brain drain) relative to autarky.Higher MTRs to make up for the shrink of tax base.

For low skills:

Higher MTRs on high skills weaken incentives to mimic high types.Low migration possibility strengthens this.Less transfers to prevent mimicking (less information rents).Inflow implies more people to share the transfers.

Types between median types: the same as Case I.



Numerical Experiments: Functional Forms

Pareto distribution (Saez (2001) and Atkinson et al. (2011)).

As in Diamond (1998), h(l) takes the form h(l) = l1+1/ε/(1 + 1/ε).

The difference of MTRs is

δMTR ≈

τR (w)=︷︸︸︷1a

(1 + 1

ε

)1 + 1

a

(1 + 1

ε

) −τR (w)≈︷︸︸︷

1a

(1 + 1

ε

)− θ(w)ξ(w)

1 + 1a

(1 + 1

ε

)for top incomes, with τR(w) denoting autarky-equilibrium tax rate.

An approximation (quasilinear-in-consumption preferences) of theelasticity of utility with respect to pre-tax income:

ξ(w) ≡ ∂U(w)

∂y(w)

y(w)

c(w).



Numerical Experiments: Parameter Values

Table: Parameter Values (U.S.)

Value Description Source

θ 0.25 Global migration elasticity Lehmann et al. (2014)ε [0.12, 0.4] Labor-supply elasticity Saez et al. (2012)a 1.5 Pareto index Diamond & Saez (2011)τ top 42.5% Real top tax rate Diamond & Saez (2011)

Case (a): a = 1.5, ε = 0.25, θ = 0.25, ξ = 5.96 ⇒ τR = τ top.

Case (b): a = 1.5, ε = 0.40, θ = 0.25, ξ = 3.64 ⇒ τR = τ top.



Numerical Experiments: Results

Holding everything else constant.

How large the difference can be made by migrations?

Table: The difference of MTRs (%) under case (a)

a 1.35 1.4 1.5 1.7 2.0 3.0

δMTR 36.2 35.6 34.4 32.1 28.9 20.0

Table: The difference of MTRs (%) under case (b)

a 1.35 1.4 1.5 1.7 2.0 3.0

δMTR 29.6 28.9 27.5 24.8 21.1 11.4


Conclusion

Implications and Insights

Emphasize the interaction between tax rate and tax base.

Avoid the emergence of extreme extraction:No dictator: majority voting (democracy).No tyranny of middle class: informational constraint and foot-voting.

Achieve certain balance between efficiency and equity:Tax high skills while subsidize low skills.Without resorting to a benevolent social planner.Without resorting to other-regarding social preferences.The key is institutional arrangement.

Joint effect of hand-voting and foot-voting:Hand-voting endogenizes social welfare function.Foot-voting endogenizes reservation utility.

No laissez faire: democracy + skill heterogeneity.

A possible low-efficiency trap: high redistribution ⇒ brain drain ⇒poorer median voter ⇒ higher redistribution ⇒ more brain drain.


The End

Thank You!


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Voting over Selfishly Optimal Income Tax Schedules with ... · Voting over Sel shly Optimal Income Tax Schedules with Tax-Driven Migrations Darong Dai Department of Economics Texas