Voting over Selfishly Optimal Income Tax Schedules with Tax-Driven Migrations Darong Dai Department of Economics Texas A&M University Darong Dai (TAMU) Voting over Income Taxes 11/28/2017 1 / 27
Outline 1 Introduction 2 Model 3 The Voting Equilibrium 4 Three Characteristics of Equilibrium Tax Schedule 5 Identifying the Effect of Migrations on Equilibrium Taxes 6 Conclusion 7 The End Darong Dai (TAMU) Voting over Income Taxes 11/28/2017 2 / 27
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 approach. Lack of research from the positive (political-economy) approach. Darong Dai (TAMU) Voting over Income Taxes 11/28/2017 3 / 27
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. Voice : Equilibrium tax schedule is selected by majority voting. Exit : Workers can move between alternative jurisdictions. A real example: Switzerland (26 cantons), top tax rate: 22.5%-46%. This combination generates a complex interaction whereby: The taxation policies chosen determine whom they attract. Whom they attract determine their choices of taxation policies. Darong Dai (TAMU) Voting over Income Taxes 11/28/2017 4 / 27
Introduction Question How would labor mobility affect income redistribution in a voting equilibrium? To my knowledge, the answer is not yet well established. To answer this question: Establish a voting equilibrium. Compare to autarky (without migrations), qualitatively and quantitatively. Darong Dai (TAMU) Voting over Income Taxes 11/28/2017 5 / 27
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: R¨ oell (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 and Weymark (2011), Lehmann et al. (2014). Darong Dai (TAMU) Voting over Income Taxes 11/28/2017 6 / 27
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: � w � m Distributions F ( w ) = w f ( t ) dt and G ( m | w ) = 0 g ( 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. Darong Dai (TAMU) Voting over Income Taxes 11/28/2017 7 / 27
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 . w h ′ � y � FOC: T ′ ( y ( w )) ≡ τ ( w ) = 1 − 1 , i.e., MTR = 1 − MRS c , y . w Allowed: τ ( w ) < 0 for some w . Where to work and consume?: not to migrate ⇐ ⇒ U ( w ) ≥ U − ( w ) − m , (participation constraint) � �� � � �� � stay move following Lehmann et al. (2014, QJE). Darong Dai (TAMU) Voting over Income Taxes 11/28/2017 8 / 27
Model Migration Elasticity The ex post density of residents of skill w in jurisdiction A : f ( w ) + G − (∆( w ) | w ) f − ( w ) n − for ∆( w ) ≥ 0 , � �� � inflow φ (∆( w ); w ) ≡ f ( w ) − G ( − ∆( w ) | w ) f ( w ) for ∆( w ) ≤ 0 � �� � outflow 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 ) c ( w ) ≡ ˜ θ ( w ) . ˜ ∂ ∆( w ) f ( w ) Darong Dai (TAMU) Voting over Income Taxes 11/28/2017 9 / 27
Model Government Budget Constraint Government budget constraint (GBC) under pure redistribution: � w T ( y ( w ))˜ f ( w ) dw ≥ 0 . w Ex post tax base, denoted by � w ˜ Γ( w , w ) ≡ f ( w ) dw , w is endogenous. Darong Dai (TAMU) Voting over Income Taxes 11/28/2017 10 / 27
Model Selfishly Optimal Nonlinear Tax Schedules By Taxation Principle , a worker of type k ∈ [ w , w ] proposes an income tax schedule by solving the problem: max U ( k ) { c ( w ) , y ( w ) } w ∈ [ w , w ] s.t. � y ( k ) � U ( k ) = c ( k ) − h (IU); k � w [ y ( w ) − c ( w )]˜ f ( w ) dw ≥ 0 (GBC); w � y ( w ) � y ( w ) U ′ ( w ) = h ′ w 2 , ∀ w ∈ [ w , w ] (FOIC); w y ′ ( w ) ≥ 0 , ∀ w ∈ [ w , w ] (SOIC) . Darong Dai (TAMU) Voting over Income Taxes 11/28/2017 11 / 27
The Voting Equilibrium Theorem By imposing pairwise 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 winner. By establishing weak single-peakedness of preferences (inverted U-shape): proposers’ type � �� � U ( w , w ) ≥ U ( w , k 1 ) ≥ U ( w , k 2 ) , ∀ w > k 1 > k 2 U ( w , w ) ≥ U ( w , k 1 ) ≥ U ( w , k 2 ) , ∀ w < 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 Gr¨ undler and K¨ ollner (2016). Darong Dai (TAMU) Voting over Income Taxes 11/28/2017 12 / 27
Three Characteristics of Equilibrium Tax Schedule The First Characteristic Proposition It coincides with the maximax tax schedule for types below the median skill level and coincides with the maximin tax schedule for types above the median 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-jurisdictional tax competition. Darong Dai (TAMU) Voting over Income Taxes 11/28/2017 13 / 27
Three Characteristics of Equilibrium Tax Schedule The Second Characteristic Proposition For incomes below the median skill type, marginal tax rates are negative. For 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 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. Darong Dai (TAMU) Voting over Income Taxes 11/28/2017 14 / 27
Three Characteristics of Equilibrium Tax Schedule The Third Characteristic Proposition Truth-telling implies that workers with heterogenous skills may face the same marginal tax rate. y y M ∗ ( · ) y R ∗ ( · ) y R ∗ ( w ) y M ∗ ( w ) w 0 w w η w α w β w γ w k Figure: Income schedule with three bridges. Darong Dai (TAMU) Voting over Income Taxes 11/28/2017 15 / 27
Three Characteristics of Equilibrium Tax Schedule The Third Characteristic (Cont’d) y y y M ∗ ( · ) y M ∗ ( · ) y R ∗ ( w ) y R ∗ ( · ) y R ∗ ( · ) y R ∗ ( w ) y M ∗ ( w ) y M ∗ ( w ) w w 0 0 w w α w β w γ w w η w α w β k w k w Figure: Income schedule with two bridges and an upward discontinuity. Darong Dai (TAMU) Voting over Income Taxes 11/28/2017 16 / 27
Identifying the Effect of Migrations on Equilibrium Taxes Qualitative Characterization: Case I Proposition Suppose Θ M ( w ) < ˜ θ ( w ) < Θ MR ( w ) for ∀ w ∈ ( w , w m ] and Θ R ( w ) < ˜ θ ( w ) < Θ MR ( w ) for ∀ w ∈ ( w m , w ) , then we have: (i) If ˜ w m ≥ w m , then distortions and redistribution for ∀ w ∈ ( w , w ) are smaller than in autarky. (ii) If ˜ w m < w m , then (i) still holds for ∀ w ∈ ( w , ˜ w m ] ∪ ( w m , w ) , whereas redistribution and distortions for ∀ w ∈ (˜ w m , w m ] turn out to be greater than in autarky. Darong Dai (TAMU) Voting over Income Taxes 11/28/2017 17 / 27
Identifying the Effect of Migrations on Equilibrium Taxes Graphic Illustration: Case I Black ones represent the autarky equilibrium. y y y M ( · ) y M ( · ) y M ( · ) y M ( · ) ˆ ˆ y R ( · ) y R ( · ) y R ( · ) y R ( · ) ˆ ˆ w w 0 0 w w m ˜ w w m w w w m w m ˜ Darong Dai (TAMU) Voting over Income Taxes 11/28/2017 18 / 27
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