International Tax Competition: Zero Tax Rate at the Top Re-established Tomer Blumkin, Efraim Sadka and Yotam Shem-Tov April 2012, Munich
Some Background � The general setting examined in Mirrlees (1971) provides fairly limited insights regarding the desirable properties of the optimal non- linear tax schedule, except that its marginal rate is nonnegative. � Confining attention to bounded skill distributions, Sadka (1976) and Seade (1977) demonstrate that the marginal tax rate levied on the individual with the highest skill level is optimally set to zero. � By continuity consideration marginal tax rates must decline at the top.
� Prima-facie , this stands in sharp contrast to observed patterns of progressive income tax schedules in most OECD countries, where statutory marginal tax rates increase with respect to income, usually in a piece-wise linear fashion (notice however the difference b/w statutory and effective marginal tax rates). � The controversial zero tax at the top result has been challenged by two influential papers: Diamond (1998) and Saez (2001).
� Both studies show that with unbounded distributions (random draw from underlying distribution), the zero tax at the top fails to hold under reasonable parametric assumptions regarding the skill distribution (top approximated by Pareto ). � Diamond and Saez (2011) conclude that the result is of little policy relevance and in any case, is only a local property which applies to the very top earner, even when bounded distributions are allowed for.
Our Contribution � In this paper we revisit the zero tax at the top result. We deviate from the standard Mirrleesian setting and the bulk of the subsequent literature which focus on the closed economy case, by allowing for labor migration. � Incorporating this extensive margin consideration into the standard framework, we examine the role played by international tax competition in shaping the optimal tax-and-transfer system.
� We show that the optimal asymptotic marginal tax rate is zero when migration is taken into account. We further demonstrate by simulations that there exists an income threshold above which the optimal marginal tax rate is approximately set to zero. � Notably, the 'lump-sum' tax over this range of high income levels is set at its Laffer rate, maximizing tax revenues against the backdrop of the disincentive associated with migration.
The Model � Two identical countries producing a single consumption good employing labor inputs. � Production technology exhibiting CRS and perfect substitution across skill-levels. � Individuals differ in two attributes: earning ability and mobility costs (between the two countries).
� Individual skill level, � , is distributed according to some CDF, F � , ( ) � � , and assumed to be private information. over the support [ , ) � Migration cost, m , is assumed to be distributed uniformly over the support � � for each skill level � . � 0, / 2 � Quasi-linear preferences given by: � � � � � � � � � (1) , U c l d ( , , ) c h l ( ) d m c h y ( / ) d m �� �� � � ( ) V where d is an indicator function (1 when migrating, 0 otherwise).
The Government Problem � A Rawlsian government is seeking to maximize: � V � (2) W ( ), subject to a revenue constraint, � � � � � � � � � � (3) y t ( ) V t ( ) h y t ( ( ) / ) t ( ) t dt 0, � where,
� � � � � � � � � � � � � � � (4) ( ) f ( ) 1 2 V ( ) V ( ) / , 2 and a self-selection constraint [Salanie (2003)]: � � � � y ( ) h y '( ( ) / ) � � (5) V '( ) . � 2 Remarks: (i) Actual skill distribution is generally different from that of permanent residents due to migration (but in the symmetric equilibrium both coincide). Autarky is obtained for � � � .
(ii) Welfare is depending on the utility of the least well-off permanent resident.
Solution � We solve the program as an optimal control problem, choosing y ( θ ) as a control variable and V ( θ ) as the state variable. � Formulating the FOCs for the Hamiltonian , employing the transversality conditions, yields upon re-arrangement the following expression for the optimal marginal tax rates: � � � � 2 T t ( ) � � g t dt ( ) � � � � T '( ) y 1 1 G y ( ) � � y � � . � � (6) 1 � � � � 1 T '( ) y 1 G y ( ) g y ( ) y � � y � �
Characterization y � for all y ; (ii) lim � . Proposition : (i) T '( ) 0 T y '( ) 0 �� y
Implications � The asymptotic marginal tax rate is zero. � In simulations we demonstrate that the zero-marginal tax result is far from being a local property by showing that there exist a whole range of income levels at the higher end of the income distribution for which the optimum tax is approximately given by a lump-sum.
� The lump-sum tax is set at its Laffer rate; namely, set at the rate which maximizes total tax revenues (taking into account the disincentive effect on migration). � In the limiting cases ( δ → 0 and δ →∞ ) we obtain, respectively, the case of costless (free) migration, inducing a race to the bottom and no taxation; and, the case of autarky [the standard formula in the literature as in Diamond (1998)].
Interpretation � In the absence of migration, the incentive constraint faced by the local government is related to the intensive margin, that is, the tax schedule is designed in a way that ensures no mimicking by the high skilled. � With migration in place, an extensive margin comes into play, as the government attempts to attract/maintain high-skill migrants/residents.
� Although the government can increase the tax burden shifted on the high-skill residents without inducing the latter to mimic, when the IC constraint of the latter is non-binding, the reduction in the tax base due to the ensued migration is large enough to offset the gain from increasing the tax rate. � There is no need to impose positive marginal tax rate as IC constraints are not binding [an extension of the two-type model of Piaser (2007)].
Numerical Analysis: Assumptions (i) Iso-elastic disutility from labor with pre-tax income elasticity of � � 0.4 . [Gruber and Saez (2002)]. y (ii) Skill level is distributed according to a (truncated) Pareto � � � f ( ) � distribution with a Pareto coefficient of [Saez 2 � � [1 ( )] F (2001)]. (iii) The support for the income distribution is given by the interval [100,1000]
Results Figure 1: The effect of migration on the optimal tax schedule 300 200 Tax schedule 100 0 -100 0 200 400 600 800 1000 Gross income (skill) Delta = 50 Delta = 100 Delta = 150 Delta = 400 Delta = 700
Interpretation � There exists an income threshold above which the tax schedule becomes approximately flat; namely, individuals are faced with a zero marginal tax rate. � The lump-sum tax in this income range is given by � , the Laffer / 2 rate.
� The interval of incomes over which individuals are faced with a zero marginal tax rate is expanding as the costs of migration decrease [as in the two-type setting of Piaser (2007)]. � The marginal tax rates are declining over the entire range of incomes (can be proved for empirically plausible parametric assumption).
Illustrative Example � Setting the cost of migration to 70 (7 percent of top income), a fraction of 4 percent of the population is facing MTR lower than 1 percent , and 7.9 percent of the population is facing MTR lower than 5 percent . The increase in consumption (of the least well-off individual) due to the tax schedule is 35.8 percent .
Conclusions � Zero MTR at the top property due to Sadka (1976) and Seade (1977) has been recently challenged by Diamond (1998) and Saez (2001). � Focusing on skill distributions with unbounded support, Diamond and Saez show that under plausible assumptions, the zero MTR property fails to hold.
� Extending the model to allow for labor migration and tax competition over mobile labor, we show that the zero MTR property holds even with unbounded skill distributions. � We further show that the result is not local but rather holds (approximately) over a whole range of incomes at the top end of the distribution.
� The optimal lump-sum tax levied on individuals at the top should be set at its Laffer rate, maximizing tax revenues against the backdrop of migration threats. � The range in which MTR is (approximately) zero expands as migration costs decrease.
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