Voting over Selfishly Optimal Income Tax Schedules with Tax-Driven Migrations

Transcription

1 Voting over Selfishly Optimal Income Tax Schedules ith Tax-Driven Migrations Darong Dai Department of Economics Texas A&M University Darong Dai (TAMU) Voting over Income Taxes 11/03/ / 26

2 Introduction Motivation Labor income tax design: ork 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 isdom (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. Darong Dai (TAMU) Voting over Income Taxes 11/03/ / 26

3 Introduction The Combination of Labor Mobility and Majority Voting Political process: A direct democracy ith citizen candidates. Pairise majority voting. Each orker has one vote. Hand-voting: Equilibrium tax schedule is selected by majority voting. Foot-voting: Workers can move beteen alternative jurisdictions. This combination generates a complex interaction hereby: The taxation policies chosen determine hom they attract. Whom they attract determine their choices of taxation policies. Darong Dai (TAMU) Voting over Income Taxes 11/03/ / 26

4 Introduction Question Ho ould labor mobility affect income redistribution in a voting equilibrium? To my knoledge, the anser is not yet ell established. To anser this question: Establish a voting equilibrium. Compare to autarky (ithout migrations), qualitatively and quantitatively. Darong Dai (TAMU) Voting over Income Taxes 11/03/ / 26

5 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: Röell (2012), Bohn and Stuart (2013), Brett and Weymark (2016, 2017). Ho the change of skill distribution affects equilibrium tax: Leite-Monteiro (1997), Hamilton and Pestieau (2005), Brett and Weymark (2011), Lehmann et al. (2014). Darong Dai (TAMU) Voting over Income Taxes 11/03/ / 26

6 Model Environment To jurisdictions: A and B, not necessarily symmetry. Both jurisdictions adopt majority voting. Workers differ in Skill/labor productivity, [, ] and > 0. Migration cost/foot-voting capability, m R +. Information structure: Distributions F () = f (t)dt and G(m ) = m g(x )dx are 0 common knoledge. Values of and m are the private information of each orker. Quasilinear-in-consumption preferences (Gruber and Saez, 2002). Labor markets are perfectly competitive. Labor income taxes are levied according to the residence principle. Darong Dai (TAMU) Voting over Income Taxes 11/03/ / 26

7 Model Individual Choices: Behavior Responses For a orker of type (, m) born in jurisdiction A: Ho much to ork and consume?: U() max {c,l} c h(l) s.t. c = y T (y) and y = l. FOC: T (y()) τ() = 1 1 h ( y ), i.e., MTR = 1 MRSc,y. Alloed: τ() < 0 for some. Where to ork and consume?: not to migrate U() U }{{} () m, (participation constraint) }{{} stay move folloing Lehmann et al. (2014, QJE). Darong Dai (TAMU) Voting over Income Taxes 11/03/ / 26

8 Model Migration Elasticity The ex post mass of residents of skill in jurisdiction A: f () + G ( () )f ()n for () 0, }{{} φ( (); ) inflo f () G( () )f () for () 0 }{{} outflo ith () U() U (). Ex post skill density: f () φ( (); ). Folloing Lehmann et al. (2014, QJE), migration elasticity is: θ( (); ) f () c() () f () θ(). Darong Dai (TAMU) Voting over Income Taxes 11/03/ / 26

9 Model Government Budget Constraint Government budget constraint (GBC) under pure redistribution: Ex post tax base, denoted by Γ(, ) is endogenous. T (y()) f ()d 0. f ()d, Darong Dai (TAMU) Voting over Income Taxes 11/03/ / 26

10 Model Selfishly Optimal Nonlinear Tax Schedules By Taxation Principle, a orker of type k [, ] proposes an income tax schedule by solving the problem: s.t. max U(k) {c(),y()} [,] ( ) y(k) U(k) = c(k) h (IU); k [y() c()] f ()d 0 (GBC); ( ) y() y() U () = h, [, ] (FOIC); 2 y () 0, [, ] (SOIC). Darong Dai (TAMU) Voting over Income Taxes 11/03/ / 26

11 The Voting Equilibrium Theorem By imposing pairise majority-voting rule to the continuum of selfishly optimal income tax schedules, the one for the median skill type turns out to be a Condorcet inner. By establishing eak single-peakedness of preferences (inverted U-shape): U(, ) U(, k 1 ) U(, k 2 ), proposers type {}}{ > k 1 > k 2 U(, ) U(, k 1 ) U(, k 2 ), < k 1 < k 2 then appealing to Black s Median Voter Theorem (1948, JPE). Recent empirical evidences: Agranov and Palfrey (2015), Corneo and Neher (2015) and Gründler and Köllner (2016). Darong Dai (TAMU) Voting over Income Taxes 11/03/ / 26

12 Three Characteristics of Equilibrium Tax Schedule The First Characteristic Proposition It coincides ith the maximax tax schedule for types belo the median skill level and coincides ith the maximin tax schedule for types above the median skill level. It redistributes incomes from the poor and rich toard the middle. Intuition: Median voter is selfish. Autarky equilibrium: Brett and Weymark (2017, GEB). Director s La (Stigler, 1970): labor mobility and inter-jurisdictional tax competition. Darong Dai (TAMU) Voting over Income Taxes 11/03/ / 26

13 Three Characteristics of Equilibrium Tax Schedule The Second Characteristic Proposition For lo incomes belo the median skill type, marginal tax rates are negative. For high incomes above the median skill level, marginal tax rates are positive if their migration elasticities are endogenously bounded above (this upper bound is in general different for different types). Intuition: The tradeoff beteen: Maximizing resources extracted from other types. Maximizing resources available for extraction. Tax higher skills because: High age rate implies a high opportunity cost of leisure. Subsidize loer skills because: Lo age rate implies a lo opportunity cost of leisure. Taxing them strengthens their motive to mimic high types. Darong Dai (TAMU) Voting over Income Taxes 11/03/ / 26

14 Three Characteristics of Equilibrium Tax Schedule The Third Characteristic Proposition Truth-telling calls for bunching (pooling), namely imposing the same tax rate, in middle-income class, lo-income class and/or high-income class. y y M ( ) y R ( ) y R () y M () 0 η α k β γ Figure: Income schedule ith three bridges. Darong Dai (TAMU) Voting over Income Taxes 11/03/ / 26

15 Three Characteristics of Equilibrium Tax Schedule The Third Characteristic (Cont d) y y M ( ) y R ( ) y R () y y M ( ) y R () y R ( ) y M () y M () 0 α k β 0 γ η α k β Figure: Income schedule ith to bridges and an upard discontinuity. Darong Dai (TAMU) Voting over Income Taxes 11/03/ / 26

16 Identifying the Effect of Migrations on Equilibrium Taxes Qualitative Characterization: Case I Proposition Suppose and Θ M () < θ() < Θ MR () for (, m ] Θ R () < θ() < Θ MR () for ( m, ), then e have: (i) If m m, then distortions and redistribution for (, ) are smaller than in autarky. (ii) If m < m, then (i) still holds for (, m ] ( m, ), hereas redistribution and distortions for ( m, m ] turn out to be greater than in autarky. Darong Dai (TAMU) Voting over Income Taxes 11/03/ / 26

17 Identifying the Effect of Migrations on Equilibrium Taxes Graphic Illustration: Case I Black ones represent the autarky equilibrium. y y M ( ) ŷ M ( ) y y M ( ) ŷ M ( ) y R ( ) ŷ R ( ) y R ( ) ŷ R ( ) 0 m m 0 m m Darong Dai (TAMU) Voting over Income Taxes 11/03/ / 26

18 Identifying the Effect of Migrations on Equilibrium Taxes Contribution and Intuition: Case I Contribution: Derive endogenous loer bounds Θ M () and Θ R (). Intuition: For high skills: Large migration elasticity implies strong threat. Loer MTRs to prevent the shrink of tax base. For lo skills: Loer 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 beteen median types: The income class they belong to totally changes! From the group receiving transfers to that paying taxes, or vice versa. Darong Dai (TAMU) Voting over Income Taxes 11/03/ / 26

19 Identifying the Effect of Migrations on Equilibrium Taxes Qualitative Characterization: Case II Proposition Suppose inflo {}}{ θ() < Θ M (), f ()/Γ(, ) > f ()/F () for (, m ], and θ() < Θ R (), outflo {}}{ Γ(, ) Γ(, ) f () > 1 F () f () for ( m, ), then e have: (i) If m m, then distortions and redistribution for (, ) are greater than in autarky. (ii) If m > m, then (i) still holds for (, m ] ( m, ), hereas redistribution and distortions for ( m, m ] turn out to be smaller than in autarky. Darong Dai (TAMU) Voting over Income Taxes 11/03/ / 26

20 Identifying the Effect of Migrations on Equilibrium Taxes Graphic Illustration: Case II Black ones represent the autarky equilibrium. y ŷ M ( ) y M ( ) y ŷ M ( ) y M ( ) ŷ R ( ) y R ( ) ŷ R ( ) y R ( ) 0 m m 0 m m Darong Dai (TAMU) Voting over Income Taxes 11/03/ / 26

21 Identifying the Effect of Migrations on Equilibrium Taxes Contribution and Intuition: Case II Contribution: Derive endogenous upper bounds Θ M () and Θ R (). Reasonable counterexamples to the conventional isdom. Intuition: For high skills: Small migration elasticity implies eak threat. Outflo implies the shrink of tax base (brain drain) relative to autarky. Higher MTRs to make up for the shrink of tax base. For lo skills: Higher MTRs on high skills eaken incentives to mimic high types. Lo migration possibility strengthens this. Less transfers to prevent mimicking (less information rents). Inflo implies more people to share the transfers. Types beteen median types: the same as Case I. Darong Dai (TAMU) Voting over Income Taxes 11/03/ / 26

22 Identifying the Effect of Migrations on Equilibrium Taxes Numerical Experiments: Functional Forms Pareto distribution (Saez (2001) and Atkinson et al. (2011)). As in Diamond (1998), h(l) takes the form h(l) = l 1+1/ε /(1 + 1/ε). The difference of MTRs is δ MTR ˆτ R ()= { ( }} ) { 1 a ε ( ) a ε τ R () { ( }}{ 1 ã ε) θ()ξ() ( ) ã ε for top incomes, ith ˆτ R () denoting autarky-equilibrium tax rate. An approximation (quasilinear-in-consumption preferences) of the elasticity of utility ith respect to pre-tax income: ξ() U() y() y() c(). Darong Dai (TAMU) Voting over Income Taxes 11/03/ / 26

23 Identifying the Effect of Migrations on Equilibrium Taxes 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) ã 1.5 Pareto index Diamond & Saez (2011) τ top 42.5% Real top tax rate Diamond & Saez (2011) Case (a): ã = 1.5, ε = 0.25, θ = 0.25, ξ = 5.96 τ R = τ top. Case (b): ã = 1.5, ε = 0.40, θ = 0.25, ξ = 3.64 τ R = τ top. Darong Dai (TAMU) Voting over Income Taxes 11/03/ / 26

24 Identifying the Effect of Migrations on Equilibrium Taxes Numerical Experiments: Results Holding everything else constant. Ho large the difference can be made by migrations? Table: The difference of MTRs (%) under case (a) a δ MTR Table: The difference of MTRs (%) under case (b) a δ MTR Darong Dai (TAMU) Voting over Income Taxes 11/03/ / 26

25 Conclusion Implications and Insights Emphasize the interaction beteen 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 beteen efficiency and equity: Tax high skills hile subsidize lo 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 elfare function. Foot-voting endogenizes reservation utility. No laissez faire: democracy + skill heterogeneity. A possible lo-efficiency trap: high redistribution brain drain poorer median voter higher redistribution more brain drain. Darong Dai (TAMU) Voting over Income Taxes 11/03/ / 26

26 The End Thank You! Darong Dai (TAMU) Voting over Income Taxes 11/03/ / 26