Tax Competition, Income Differentials and Local Public Services

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Keywords: tax competition, migration, local public goods, coordination equilibria ... crowd out public services, the incentives faced by local authorities hinge on ...

International Tax and Public Finance, 8, 675–691, 2001.  C 2001 Kluwer Academic Publishers. Printed in The Netherlands.

Tax Competition, Income Differentials and Local Public Services ERIC SMITH [email protected] Department of Economics, University of Essex, Wivenhoe Park, Colchester, CO4 3SQ, England TRACY J. WEBB [email protected] Department of Economics, University of Wales Swansea, Singleton Park, Swansea, SA2 8PP, Wales

Abstract This paper examines strategic tax setting between fiscal authorities in the presence of mobile workers who locate across these jurisdictions in response to differing tax structures and congestable local public amenities. We find that the nature of the tax setting outcomes depend crucially on the proximity between cities. For “distant” cities with the same size populations, the pressure on tax rates of a more mobile workforce depends on the whether mobile workers are net beneficiaries or net contributors. If mobile workers are either high or low income earners, cities lower tax rates. If mobile workers are middle income earners, cities raise tax rates. For “close” or neighbouring cities, workers locate in one of the cities and tax rates and local public amenities are dispersed. Keywords: tax competition, migration, local public goods, coordination equilibria JEL Code: H73, H21, J61

1.

Introduction

International co-operation, most notably in Europe but elsewhere as well, has made consumers, producers and workers more mobile. Within national borders, improved technology and lower transportation costs have likewise enhanced the movement of buyers and sellers. These changes and their impact on the formulation of tax policy have generated considerable attention amongst academics and policymakers. Indeed, the issues and policy questions raised have spawned a large and extensive public finance literature. The hallmark of many of these papers is that freer commodity trade, capital or labour mobility generates tax competition across local jurisdictions as authorities attempt to lure in business. The key point is that by altering its own tax rate, each jurisdiction is able to change both its own tax base and the tax base of other jurisdictions. The significance of these fiscal spillovers is that they are likely to result in “a race to the bottom” with low and suboptimal tax rates.1 This paper analyses tax competition across local jurisdictions in the presence of mobile labour. Tax competition arises as each local authority levies a proportional income tax on mobile workers who consume congestable public amenities in the region where they work. The contribution of the paper is twofold. First, we explicitly allow for distance between the tax setting authorities. This distance, modelled as a transportation cost, is crucial in

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partitioning outcomes and allows us to draw an analogy to club goods.2 Second, we allow mobile and immobile workers to differ in terms of their incomes. These income differentials, together with congestion effects, play an important role in determining public policy. In this system, the pressure on tax rates of a mobile workforce depends on whether local authorities have an incentive to deter or attract additional residents. Of course, the effect on tax rates also depends on the location response of mobile workers. Since consumers crowd out public services, the incentives faced by local authorities hinge on whether the tax contributions from an increased tax base are large enough to offset the additional revenue required to produce a given level of amenities.3 If so, incoming migrants are desirable and they are net fiscal contributors. If not, incoming migrants are net fiscal beneficiaries and they are undesirable. Wellisch and Wildasin (1996) also focus on this distinction and show that this is important for determining the welfare effects of immigration in a model of income redistribution.4 The key aspect in this paper is that tax contributions are related to an individual’s ability to pay and as such, the desirability or not of additional residents depends on relative income levels. Moreover, the location decision of mobile workers also depends on income. If mobile workers have higher incomes than immobile residents, they prefer lower tax rates while if they have lower incomes, they prefer higher tax rates.5 It is this interaction between the location response of mobile workers to changes in tax rates on the one hand and the incentives faced by local authorities on the other which determines tax rates across jurisdictions. The main result that emerges from this analysis is that reduced barriers to labour mobility may exert upward pressure on tax rates. This occurs if mobile workers are net fiscal contributors but earn less than the immobile group. Intuitively, if mobile workers are net fiscal contributors, they are desirable to local authorities. Moreover, with lower incomes than the immobile group, they prefer higher tax rates than do the residents: as income falls, individuals prefer to consume relatively less private goods and relatively more public goods. This implies local authorities raise tax rates to lure in these additional workers. This, as far as we are aware, is one of the few examples of the base stealing motive which does not point to downward pressure on taxes. The policy message is that local authorities need to assess not only the fiscal contribution of each migrant but also the way in which the relative income of migrants affects their response to local public financing choices. The above result occurs in competition between sufficiently distant jurisdictions. When transportation costs are high, transport outlays are important to mobile workers who are spread between competing tax authorities. To reduce these costs, mobile workers consume in the nearest city. In this case, there is a marginal worker who is responsive to differences in tax rates and public services and this creates the potential for competition over the tax base. On the other hand, when transportation costs are sufficiently low, mobile workers are able to take advantage of the nature of local public goods and they move to the same city. For this outcome to occur, however, mobile workers must be net fiscal beneficiaries. Moreover, mobile workers must be willing to pay the cost of moving. If there is a sufficiently small cost to relocating, then even the worker who is furthest away will move to the other city. With one way population flows, the end result is that tax rates and public good expenditures are dispersed.

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2.

677

The Model

Two regions, each containing a city, exist on the interval [0, 1]. The two regions (and the cities) are labelled j = a, b. Region a is defined over the distance from zero (the location of city a) to a border positioned at one half. Region b is the distance from that border to one (the location of city b) .Within each city, there are a large number of firms which produce output. Labour is the only input and production is linear. Within each region, there are mobile and immobile workers. The immobile work and reside in the cities. The number of these workers is equal in both cities and is denoted by s > 1. On the other hand, there is a unit mass of mobile workers uniformly distributed across the two regions. Mobile workers can work in either of the two cities but not simultaneously in both. Moreover, if a mobile worker decides to work in a particular city, he must also reside there and once this location decision has been made it cannot be altered—there is no commuting. For these mobile workers, however, travelling to either city involves a transportation cost which is proportional at rate c > 0 to the distance from that city. We interpret these costs as a proxy for the distance between the two cities but they may also be thought of literally as moving costs. Mobile and immobile workers also differ in terms of their productivity. Each immobile worker produces one unit of output while each mobile worker produces α > 0 units. Hence, α represents the relative efficiency of mobile labour. Clearly, if α < 1, mobile workers are less efficient than immobile workers whereas α > 1 implies that they are more efficient. We allow for both possibilities. There are two stages of the decision making process. In the first stage, majority voting in each region determines proportional tax rates t j for j = a, b, the revenues from which finance local public amenities. Since the mobile group is smaller than the resident population of each city, majority voting implies that immobile workers choose taxes.6 Since these workers are identical, we can proceed with a representative from each group. In each city, this individual chooses his preferred tax rate by maximising his own welfare, taking as given the tax rate set by the other city and the migration response of mobile workers. In the second stage, mobile workers analyse tax rates and public services and make location decisions.7 Along with immobile workers, they produce output, receive a wage for each unit of output produced and are taxed on this income. Notice, however, that since workers consume where they work (there is no cross border shopping) there is no difference between taxes on income and taxes on consumption. Moreover, since individuals also live where they work, residence (destination) based taxes which are levied on labour where it lives are equivalent to origin based taxes which are levied on labour where it works.8 Competitive profit maximisation implies that the real wage in each city equals the constant marginal product of labour and that at that wage, firms are willing to hire any number of workers. Since all firms are identical, the wage per unit of output (w) is equal in each city. Given this, differences in income arise due to differences in taxes and productivity. Normalising hours of work to one, income for an immobile worker in city j is w(1 − t j ) while the income of a mobile worker in city j is αw(1 − t j ). Tax revenues in each city accrue to the local government there and these revenues finance local public services. For any ta and tb , individuals expect all mobile workers to participate; that is, to move to a city and work with xˆ (ta , tb ) entering city a and the remaining 1 − xˆ (ta , tb ) entering

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city b.9 Thus they expect a population in city a of Na = s + xˆ with government expenditure ¯ a = ta w(s + α xˆ ) and a population in city b of Nb = s + (1 − x) ˆ with public expenditure G ¯ ˆ G b = tb w(s + α(1 − x)). In each city, the benefits of public spending on amenities such as recreation facilities, education, libraries, police protection and sanitation accrue equally to all individuals in that city (the immobile group plus incoming mobile workers) but not to individuals who reside outside of the city. Let φ(Gj ) denote the benefit to an individual in city j from Gj units β of per capita public good consumption, where Gj = G¯ j /N j . The congestion parameter β can take on the values 0 ≤ β ≤ 1, where pure public goods and publicly provided private goods correspond respectively to β = 0 and β = 1. Assume φ(Gj ) is increasing, continuous, strictly concave and differentiable. Utility for both groups of workers is quasilinear over consumption and the local public good less any transportation costs. Since an immobile worker residing in city j = a, b has no migration opportunities, utility is given by ˆ = w(1 − t j ) + φ(Gj ) V j (t j ; x)

j = a, b

(1)

A mobile worker, on the other hand, pays transportation costs. Hence, for a mobile worker who is located at x, the utility he receives if he resides in city a is ˆ x) = −cx + αw(1 − ta ) + φ(G a ) Ua (ta ; x,

(2)

Similarly, if he resides in city b, he receives ˆ x) = −c(1 − x) + αw(1 − tb ) + φ(G b ) Ub (tb ; x, 3.

(3)

The Location Decision

If workers are allowed to choose, they move to the city which yields the highest utility. Given ta , tb and the associated expectation of xˆ , a mobile worker may be indifferent between the ˆ x ∗) = two cities. If so, this is true only for workers at the location defined by Ua (ta ; x, ∗ Ub (tb ; xˆ , x ). Equating (2) and (3) defines x ∗ = (1/2c)[αw(tb − ta ) + φ(G a ) − φ(G b )] + 1/2

(4)



Workers located at x < x strictly prefer city a (those closest to city a) while those located at x > x ∗ (those closest to city b) strictly prefer city b. Substituting xˆ for x ∗ into (4) implicitly defines xˆ . This indifference, however, may not occur. If the spillover effects associated with public good provision are large enough, workers may rationally expect all other mobile workers to move to one city. Given tax rates ta and tb , all mobile workers move to city a if Ua (ta ; 1, 1) > Ub (tb ; 1, 1) ⇔ c < αw(tb − ta ) + φ[ta w(s + α)/(s + 1)β ] − φ[tb ws 1−β ] (5) Likewise, all mobile workers move to city b if Ua (ta ; 0, 0) < Ub (tb ; 0, 0) ⇔ c < αw(ta − tb ) + φ[tb w(s + α)/(s + 1)β ] − φ[ta ws 1−β ] (6)

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Intuitively, for all mobile workers to move to city a (xˆ = 1), it must be the case that an individual who is located at city b (the furthest distance away from city a) is willing to pay the cost of moving given tax rates ta and tb and given that he expects all others to do the same. This is the case if the costs of moving are sufficiently low. The net fiscal spillovers which arise when all taxpayers contribute towards local public good provision in city a must outweigh the transportation costs of the individual located the furthest distance away from city a. Condition (6) has a similar interpretation. Hence, from (4), (5) and (6), we have  0 for c < αw(ta − tb ) + φ[tb w(s + α)/(s + 1)β ] − φ[ta ws 1−β ]      1 for c < αw(tb − ta ) + φ[ta w(s + α)/(s + 1)β ] − φ[tb ws 1−β ] xˆ (ta , tb ) = (7)  (1/2c){c + αw(tb − ta ) + φ[ta w(s + α xˆ )/(s + xˆ )β ]     − φ[tb w(s + α(1 − xˆ ))/(s + (1 − xˆ ))β } Notice that there may exist a ta , tb and a sufficiently small c such that xˆ simultaneously takes on three values in (7).10 In the second stage subgame, multiple equilibria occur for some parameterisations of taxes and transportation costs. When all three solutions exist, however, the interior solution is unstable under standard naive dynamics and is not considered. We show in the appendix that when xˆ only satisfies the third value in (7), xˆ (ta , tb ) is well defined for all (ta , tb ) ∈ [0, 1]2 . In the symmetric case, which we focus on later, ta = tb = ts and hence xˆ = 1/2 is a solution to (7). In this case, stability requires ∂Ua (ts ; xˆ , xˆ )/∂ xˆ = −∂Ub (ts ; xˆ , xˆ )/∂ xˆ < 0 which implies D = c − [φs ts w/(s + 1/2)1+β ] · s > 0

(8)

where s = [α(s + 1/2) − β(s + α/2)] and φ(G j ) ≡ φ j .

4.

Tax Setting

In each city, a representative immobile worker determines the tax rate by maximising his own welfare as given by (1). When the border between the two regions is closed, migration is restricted and xˆ is fixed. In this case, the first order condition for the policymaker in city a is given by   s + α xˆ φa · =1 (9) (s + xˆ )β The resident worker chooses a level of per capita local public good consumption such that the marginal benefit from these services equals the amount which he must pay towards financing them. The fractional share of providing public expenditure level G¯ a is 1/(s + α xˆ ) while the fractional cost share of providing per capita consumption G a is (s + xˆ )β /(s + α xˆ ). For the symmetric closed border case in which xˆ = 12 , ta = tb = tc and φa = φb = φc . Hence, the first order condition becomes   s + α/2 φc · =1 (10) (s + 1/2)β

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When the border is open, however, labour movements are unrestricted and in the second stage of the game mobile workers respond to the decisions made by policymakers in the first stage. As such, the policymaker in city a maximises (1) taking into account the subsequent migration response of mobile workers as characterised by (7). This implies that given tb , the optimal tax for city a solves max Va (ta , tb ; xˆ ) = w(1 − ta ) + φ[ta w(s + α xˆ (ta , tb ))/(s + xˆ (ta , tb ))β ] ta

subject to (7)

(11)

Given an analogous problem for city b, a Nash equilibrium is a tax pair (ta∗ , tb∗ ) such that ta∗ = arg max w(1 − ta ) + φ[ta w(s + α xˆ (ta , tb∗ ))/(s + xˆ (ta , tb∗ ))β ]

(12)

tb∗ = arg max w(1 − tb ) + φ[tb w(s + α(1 − xˆ (ta∗ , tb )))/(s + 1 − xˆ (ta∗ , tb ))β ]

(13)

ta

tb

Equation (7) leads us to focus on two types of equilibria. First, we consider the symmetric interior equilibrium in which the marginal worker responds to fiscal incentives. We then turn to agglomeration equilibria in which each mobile worker rationally expects all other mobile workers to locate in one of the two cities (say, city b) and given this belief, the strategy which maximises his utility is to move to that city. In this case, it is as if there is no marginal worker. Each tax authority sets tax rates in the first stage as if to satisfy a fixed population and as if without consideration of the other city’s tax policy.

4.1.

The Symmetric Interior Equilibrium

An open border interior equilibrium is a tax pair (ta∗ , tb∗ ) which satisfy equations (12) and (13) with xˆ (ta∗ , tb∗ ) ∈ (0, 1) implicitly defined by Ua (ta ; xˆ , x ∗ ) = Ub (tb ; xˆ , x ∗ ). Recall from Section 3 that a stable equilibrium requires high transportation costs as given by (8). In this case, the optimal strategy for city a solves (14) while the second stage response of the marginal worker is given by (15)     s + α xˆ φa ta a ∂ xˆ −1 + φa + =0 (14) β 1+β (s + xˆ ) (s + xˆ ) ∂ta ∂ xˆ w[α − φa · [(s + α xˆ )/(s + xˆ )β ]] = ∂ta −2c + [φa ta w/(s + xˆ )1+β ] a + [φb tb w/(s + 1 − xˆ )1+β ] b

(15)

where a = [α(s + xˆ ) − β(s + α xˆ )] and b = [α(s + 1 − xˆ ) − β(s + α(1 − xˆ )]. In the symmetric case, ta∗ = tb∗ = ts , xˆ = 12 and φa = φb = φs . Evaluating (14) and (15) at xˆ = 12 implies     s + α/2 φs ts s ∂ xˆ

−1 + φs + =0 (16) (s + 1/2)β (s + 1/2)1+β ∂ts ∂ xˆ −w[α − φs · [(s + α/2)/(s + 1/2)β ]] = ∂ts 2D

(17)

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Inspection of (16) and (17) reveals that the effect on the tax rate of opening the border depends crucially on the relative incomes of mobile and immobile workers. Consider first the benchmark case in which all individuals are identical (α = 1). In this case, mobile workers have the same preferences over tax rates and public expenditure levels as the resident population and they prefer the closed border solution to any other tax rate. As such, these workers do not respond to fiscal incentives (α = 1 implies ∂ xˆ /∂ts = 0) so that the effect of opening the border is to leave tax rates unchanged.11 If individuals are not identical, however, a change in the tax rate induces mobile workers to change their location decision which in turn impacts on the marginal utility (and hence tax setting behaviour) of immobile residents. This indirect or strategic interaction effect, captured by the third term in (16), depends on whether mobile workers have higher or lower incomes than the resident population. If mobile workers have higher incomes than the resident population, they prefer lower tax rates than the closed border solution. Hence, an increase in a city’s tax rate deters these workers from entering that city (α > 1 implies ∂ xˆ /∂ts < 0). On the other hand, if mobile workers earn less than the resident population, they prefer higher tax rates than the closed border solution. In this case, an increase in a city’s tax rate attracts these workers (α > 1 implies ∂ xˆ /∂ts > 0). Given these reactions of mobile workers to tax policy, each local authority can alter its own tax rate to either deter or attract additional residents. Of course, the incentives for local authorities to either deter or attract residents depends on whether additional residents are attractive in terms of their net tax contributions. This attractiveness depends on the sign of

s in (16). If this term is positive, mobile workers are net fiscal contributors and they are desirable; that is, an additional worker contributes more in tax revenues than he congests. If it is negative, mobile workers are net fiscal beneficiaries and they are undesirable; that is, the congestion cost imposed on others outweighs each individual’s tax contribution. > Notice that s > < 0 as α < αˆ where αˆ ≡ βs/[s + (1 − β)/2]. Since β ≤ 1, this implies αˆ ≤ 1. Hence, if mobile workers are high income earners (α > 1), they are also net contributors.12 On the other hand, when α < 1, the desirability of mobile workers depends on the degree of congestion as given by β. For αˆ < α < 1, mobile workers earn less than immobile workers but are net fiscal contributors; refer to these as middle income earners. For α < α, ˆ mobile workers again earner less than the immobile group but in this case they are net beneficiaries; refer to these as low income earners. Both lower and middle income earners prefer higher tax rates than immobile residents whereas high income earners prefer lower tax rates. As income increases, there are two effects. An individual who alone experiences a rise in income will want to adjust tax rates downward: here the increased demand for private consumption outweighs the desire for more public good provision. In addition, there is an ambiguous effect when other agents experience a rise in income. When others have more income, there is an incentive to take greater revenue through higher taxes. On the other hand, the rise in income generates more revenue for a given tax rate. Rather than taking this benefit as public good provision alone, the individual may want to take some of the gain through private good consumption and hence lower taxes. The overall effect here is that preferred tax rates fall with income. Now consider how tax authorities will respond in each of the three case. First, suppose that mobile workers are high income earners (α > 1). In this case, mobile workers prefer lower tax rates than the closed border solution. Since they are also net contributors, local

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authorities have an incentive to lower tax rates so as to lure in these additional tax payers. Now suppose that mobile workers are low income earners (α < α). ˆ Low income earners prefer higher tax rates than the closed border solution. In this case, however, mobile workers are net beneficiaries and are undesirable. As a result, local authorities have an incentive to lower tax rates to deter these workers. Proposition 1 If mobile workers are either high income earners or low income earners, taxes in the open border symmetric Nash equilibrium are lower than taxes in the closed border economy. Proof: See Appendix. In contrast, when mobile workers are middle income earners, local governments raise taxes, a result which differs from the standard tax bidding outcome in the literature. Middle income mobile workers (αˆ < α < 1) are net contributors and they want taxes raised from the closed border solution (since these workers earn less than immobile residents). To attract these additional tax payers, local governments raise tax rates which stands in contrast to standard tax bidding results. Proposition 2 When mobile workers are middle income earners, taxes in the open border symmetric Nash equilibrium are higher than taxes in the closed border economy. Proof: See Appendix. In the extreme case when there is no congestion (β = 0), mobile workers are always net contributors. Hence, the mobility shock of opening the border depends simply on whether mobile workers have higher or lower incomes than the resident population. If α > 1, mobile workers want lower tax rates than the closed border solution and hence ts < tc . If α < 1, they want higher tax rates than the closed border solution and hence ts > tc . In contrast, if there is full congestion (β = 1), mobile workers are net contributors if and only if α > 1. For α < 1, they are a fiscal burden. In both cases, cities set ts < tc . In the first case, cities attempt to lure in additional workers who want lower taxes. In the second, cities try to deter additional residents who want higher taxes.13 These results are similar in spirit to those in Starrett (1980) who analyses jurisdictions which compete for residents using a variety of taxation schemes. Starrett, however, does not explicitly model the migration response of mobile individuals. The assumption is that increases in public expenditure lead to in-migration. Boadway (1982) corrects for this feature but assumes that all individuals are identical. He finds that local communities behave optimally when taxes are incident on domestic residents only, independent of whether the local government takes into account the migration response to their own policy. In this case, local authorities can do no better by acting strategically rather than myopically. This is consistent with our result that if mobile workers earn the same as immobile workers, then mobile workers do not respond to tax changes, a result which highlights the role that income differentials play in determining fiscal policy.

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4.2.

683

Agglomeration Equilibria

To consider the agglomeration equilibrium in which all workers move to city b(xˆ = 0), let ta0 = arg max w(1 − t) + φ[tws 1−β ] t

tb0 = arg max w(1 − t) + φ[tw(s + α)/(s + 1)β ] t

For all mobile workers to migrate to city b in the second stage (given tax rates ta0 and tb0 set in the first stage), the costs of doing must be sufficiently low: 



c < cˆ (α, β) ≡ αw ta0 − tb0 + φ tb0 w(s + α)/(s + 1)β − φ ta0 ws 1−β The net benefits from agglomeration spillovers must more than compensate for the transportation costs of each migrant. For workers to benefit from moving to the same city, there has to be enough “publicness” of the public good. If an additional worker congests more than he contributes independent of city size, there are no positive spillover effects from public services and an agglomeration equilibrium does not exist.14 We show in the appendix that if migrants are undesirable, cˆ (α, β) < 0. It is also straightforward to show that if migrants are desirable, cˆ (α, β) > 0 for (φ

/φ ) · G < −1. This is sufficient to ensure cˆ (α, β) > 0 but it is not necessary. The existence of an agglomeration equilibrium also requires that the tax rates set in the first stage are optimal responses to each other as well as to the migrant’s location decision in the second stage. We do not characterise all possibilities. Instead, we establish existence and characterise this equilibrium for the simpler special case when migrants are desirable and xˆ (t, tb0 ) = 0 for all t. In this case, migrants are unresponsive to city a’s tax rate and ta0 is a best response to tb0 . On the other hand, city b has all of the mobile group and has its optimal tax rate: this is the best possible outcome for city b. A sufficient condition for xˆ (t, tb0 ) = 0 for all t is that 

αw t − tb0 + φ tb0 w(s + α)/(s + 1)β − φ[tws 1−β ] > c for all t ∈ [0, 1] This condition holds as c approaches zero and a approaches one. When transportation costs are very low, initial location is unimportant and the incentive to coordinate is high. Provided that immobile and mobile workers have similar preferences over tax rates, immobile workers will be willing to set taxes which lead to these agglomerating outcomes. Suppose that mobile workers are net contributors. Differentiation of (9) with respect to xˆ demonstrates that (exogenously) expanding a city’s tax base leads to a higher level of public good expenditure per capita. As a result, the high population city in the agglomeration equilibrium has a higher level of public good expenditure per head than in the closed border case whereas the low population city has a lower level of expenditure per head. Tax rates, however, depend on preferences. Again differentiation of (9) reveals that moving from the closed border solution to the agglomeration equilibrium in which all mobile workers move to city b increases the tax rate in city a. The tax rate decreases in city b if and only if (φb

/φb ) · G b < −1. Intuitively, for a given tax rate in city b, an increase in the number of net contributors leads to an increase in revenue and public amenities. The marginal benefit of public good provision falls and there is an incentive to reduce tax rates. At the same time, however, there is a fall in the marginal cost of public good provision and this provides

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an incentive to raise taxes. If (φb

/φb ) · G b < −1, the marginal benefit effect outweighs the marginal cost effect and the tax rate falls.

5.

Conclusion

Moving from the closed border economy to the open border symmetric equilibrium leads to changes in tax rates and per capita public amenities. Migration flows, however, remain unchanged. As a result, welfare effects arise only through changes in local public policy. In this case, immobile workers are always worse off; mobility ties the hands of the majority. The welfare of mobile workers, however, depends on their incomes relative to the earnings of residents. If mobile workers are net contributors, they gain. If they are net beneficiaries, they lose. High income mobile workers are net contributors who prefer lower taxes than in the closed border solution. To attract these workers, cities lower taxes. Redistribution is from the lower income resident population to the higher income mobile group and inequality increases. Middle income mobile workers are also net contributors but they prefer higher taxes than the closed border solution. To attract these workers, cities raise taxes. In this case, redistribution favours middle income mobile workers and inequality falls. Whether welfare improves depends on the weights attached to the two groups in the social welfare function. When migrant workers are low income, however, both the mobile and the immobile groups are made worse off. Low income earners crowd out public amenities more than they contribute in tax revenue but they prefer higher taxes than in the closed border economy. Since these workers are net beneficiaries, cities try to discourage in-migration by lowering taxes. As both cities behave in this way, the end result is that populations remain the same but taxes and public amenities are lower. These results provide scope for rationalising a variety of policies. For instance, when additional residents are desirable, each local authority would like to restrict out-migration. Since local governments have little direct control over out-migration, however, authorities may want to co-operate and restrict in-migration. Qualification requirements across jurisdictions, such as those observed in Canada, may be one example of this type of behaviour. On the other hand, when mobile workers are net burdens, there is an incentive for authorities to unilaterally restrict in-migration. Perhaps the most obvious policy response is to restrict access for low income workers through residency requirements. Alternatively, limiting access to publicly provided private goods such as health care, housing and welfare benefits weakens the incentive for mobile workers to move to high benefit states and slackens the constraints on local authorities to pursue optimal first best domestic tax policies. More generally, if local governments are able to diversify across different types of public amenities, they may wish to target expenditures towards services which attract net contributors rather than assign revenues to services which appeal to low income groups. That low income workers respond positively to more generous social service systems is an important aspect of the welfare reform debate in North America (see The Vancouver Sun, August 1995). Winer and Gauthier (1982), for instance, find that out-migration from the Atlantic provinces is inhibited by increases in the generosity of UI payments in the Atlantic region and is stimulated by increases in UI payments in other regions. Evidence in the US

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also finds that given one parent families receiving AFDC (Aid to Families with Dependent Children) benefits move, they are more likely to move to a state which pays out more. (See Ermisch, 1991.)15 Of course, local authorities may require higher levels of government to enforce a cooperative outcome; that is, lower levels of government may require higher levels of government to assist in the provision and/or financing of social services in order to forestall undesirable equilibrium outcomes. Co-operation at the local level, however, may not always appeal to central governments. For example, if mobile workers are middle income earners, fiscal externalities actually lower inequality. In this case, higher levels of government may prefer the “let tax competition rip” outcome. As we move from the closed border solution to the open border agglomeration equilibrium, population flows determine (at least in part ) the welfare effects of opening the border. Since the agglomeration equilibrium occurs only if mobile workers are net contributors, an increase in city size implies an increase in net revenues and public amenities. As a result, when transportation costs are low, allowing workers to move increases per capita expenditure on public services in the high population city but lowers per capita expenditure in the low population city. As we have seen, the effect on tax rates is ambiguous. In the agglomeration equilibrium, immobile residents in the high population city are better off; they choose their preferred tax rate but they have a higher tax base than in the closed economy. If they choose lower tax rates, mobile workers are also better off since private and public good consumption increase. If they choose higher taxes, however, there is a possibility that the loss in private good consumption outweighs the gain in public good consumption. This does not hold for common parameterisations of the utility function and reasonable specifications of relative income. On the other hand, residents in the low population city are always worse off as they are constrained by a lower tax base. Fewer taxpayers and lower revenues may contribute to a downward spiral as more people leave these cities (see Rybezynski, 1995). This suggests that stark differences in public services may arise across neighbouring cities as local governments adjust their expenditures in line with tax revenues. On the other hand, if local governments commit to public expenditure levels, cities with falling tax revenues may find it increasingly difficult to finance public expenditure projects and balance their budgets. This is consistent with anecdotal evidence on many cities across the U.S. Camden (New Jersey) and Philadelphia (Pennsylvania), for example, are neighbours but have very different tax patterns and levels of public amenities. Camden, in contrast to Philadelphia, has a low and dwindling tax base. With services deteriorating, residents who have the resources are moving across the Delaware River to Philadelphia and are leaving Camden with severe public financing problems.16,17 From a federal perspective, such sharp differences in public services across neighbouring cities may be politically undesirable and may lead to interregional policies aimed to overhaul downtown districts. These initiatives may involve building projects as well as attracting companies and businesses to these areas through tax incentives and the provision of local services. Locally, one response by authorities without sufficient concentrations of people may be to close sections of the city which are not viable and to concentrate resources in selected areas. Housing alternatives in other parts of the city may be offered and zoning for depopulated areas changed to zero occupancy (Rybezynski).

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Appendix The function xˆ (ta , tb ) is non empty for all (ta , tb ) ∈ [0, 1]2 . Consider values of ta and tb for which xˆ is defined only by Ua (ta ; xˆ , x) = Ub (tb ; xˆ , x). Under this assumption, the corner solutions in (7) do not hold. Hence, c ≥ αw(ta − tb ) + φ[tb w(s + α)/(s + 1)β ] − φ[ta ws1−β ] β

c ≥ αw(tb − ta ) + φ[ta w(s + α)/(s + 1) ] − φ[tb ws

1−β

]

(A1) (A2)

Let (xˆ ) = (1/2c)[c + αw(tb − ta ) + φ[ta w(s + α xˆ )/(s + xˆ )β ] − φ[tb w(s + α(1 − xˆ ))/(s + 1 − xˆ )β ]] Conditions (Al) and (A2) imply (respectively) (0) = (1/2c)[c + αw(tb − ta ) + φ[ta ws 1−β ] − φ[tb w(s + α)/(s + 1)β ]] ≥ 0 (1) = (1/2c)[c + αw(tb − ta ) + φ[ta w(s + α)/(s + 1)β ] − φ[tb ws 1−β ]] ≤ 1 By continuity of (xˆ ), there must exist at least one xˆ such that (xˆ ) = xˆ . Proof of Proposition 1: (i) The open border tax rate is lower than the closed border tax rate when mobile workers are high income earners. Suppose ts > tc . By concavity of (1) in ta , the direct effect of a change in the tax rate from the closed border solution is nonpositive φs ·

s + α/2 0 1+β (s + 1/2) ∂ts Since α > 1, migrants are desirable and s > 0. Hence, the indirect effect is positive if and only if ∂ xˆ /∂ts > 0. Since D > 0, ∂ xˆ /∂ts > 0 if and only if α < φs ·

s + α/2 (s + 1/2)β

which is a contradiction since α > 1. (ii) The open border tax rate is lower than the closed border tax rate when mobile workers are low income earners. Since it is possible for residents to deter migration through excessively high tax rates as well as through excessively low tax rates, the above approach does not immediately apply. We therefore adopt a slightly different approach. Suppose that ts > tc . For ts to be an equilibrium, ta = ts must be a best response to tb = ts . To see that this is not the case, suppose that there exists a t < ts such that xˆ (t, ts ) = 1/2. For the mobile

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worker positioned at x = 1/2, xˆ (t, ts ) = 1/2 implies αw(1 − t) + φ[tw(s + α/2)/(s + 1/2)β ] = αw(1 − ts ) + φ[ts w(s + α/2)/(s + 1/2)β ] However, since t < ts , (1 − α)(1 − t)w > (1 − α)(1 − ts )w. Solving the above for αw(1 − t) and substituting into this condition implies Va (t, ts ) = w(1 − t) + φ[tw(s + α/2)/(s + 1/2)β ] > w(1 − ts ) + φ[ts w(s + α/2)/(s + 1/2)β ] = Va (ts , ts ) Hence, ta = ts is not a best response to tb = ts . Therefore, it follows that xˆ (t, ts ) =  1/2 for all t < ts . We now show that xˆ (t, ts ) > 1/2 for all t < ts . Recall that due to the concavity of (1) in ta , ts > tc implies that the direct effect of the first order condition (16) is negative. Hence, for (16) to hold, the indirect effect must be positive   φs · ts · s ∂ xˆ >0 1+β (s + 1/2) ∂ts But since mobile workers are undesirable, s < 0 which implies that the indirect effect is positive if and only if ∂ xˆ /∂ts < 0. By continuity, this implies that xˆ (t, ts ) > 1/2 for all t < ts . Given xˆ (t, ts ) > 1/2 for all t < ts , the mobile worker located at x = 1/2 strictly prefers city a to city b. Setting t = 0 implies ˆ ts )))/(s + 1 − xˆ (0, ts ))β ] αw + φ[0] > αw(1 − ts ) + φ[ts w(s + α(1 − x(0, Rearranging in terms of αwts and noting that α < 1 implies wts > αwts gives wts > φ[ts w(s + α(1 − xˆ (0, ts )))/(s + 1 − xˆ (0, ts ))β ] − φ[0] Manipulating this condition now gives Va (0, ts ) = w + φ[0] > w(1 − ts ) + φ[ts w(s + α(1 − xˆ (0, ts )))/(s + 1 − xˆ (0, ts ))β ] Since xˆ (t, ts ) > 1/2 for all t < ts , lower congestion implies w(1 − ts ) + φ[ts w(s + α(1 − xˆ (0, ts )))/(s + 1 − xˆ (0, ts ))β ] > w(1 − ts ) + φ[ts w(s + α/2)/(s + 1/2)β ] = Va (ts , ts ) But this implies Va (0, ts ) > Va (ts , ts ). Hence ta = ts is not a best response to tb = ts . Proof of Proposition 2: Suppose that ts < tc . By concavity of (1) in ta , it follows that the direct effect of a change in the tax rate from the closed border solution is positive φs ·

s + α/2 >1 (s + 1/2)β

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Hence, for the first order condition (16) to hold, the indirect effect must be negative   φs · ts · s ∂ xˆ 0 and the indirect effect is negative if and only if ∂ xˆ /∂ts < 0. Given D > 0, ∂ xˆ /∂ts < 0 if and only if α > φs ·

s + α/2 (s + 1/2)β

which is a contradiction since α < 1. If migrants are undesirable for all levels of migration, an agglomeration equilibrium does not exist. Suppose not and let there be an agglomeration equilibrium at xˆ = 0. For all mobile workers to move to city b, we must have   Ua ta0 ; 0, 0 < Ub tb0 ; 0, 0 



⇔ αw 1 − ta0 + φ ta0 ws 1−β < −c + αw 1 − tb0 + φ tb0 w(s + α)/(s + 1)β (A3) In equilibrium, the following condition must also be satisfied 



    β w 1 − ta0 + φ ta0 ws 1−β ≥ w(1 − t) + φ tw s + α xˆ t, tb0 / s + xˆ t, tb0 for all t ∈ [0, 1] Since migrants are undesirable, this condition implies 

w 1 − ta0 + φ ta0 ws 1−β > w(1 − t) + φ[tw(s + α)/(s + 1)β ]

for all t ∈ [0, 1]

From (A3) and (A4) respectively, 



c < αw ta0 − tb0 + φ tb0 w(s + α) (s + 1)β − φ ta0 ws 1−β 



w ta0 − tb0 + φ tb0 w(s + α) (s + 1)β − φ ta0 ws 1−β < 0

(A4)

(A5) (A6)

Now suppose that > If migrants are undesirable, then α < 1. Hence, (A5) and (A6) imply c < 0 which is a contradiction. Now suppose that ta0 < tb0 . Given xˆ , G a = ta w(s + α xˆ )/(s + xˆ )β . Hence   ∂G a w ∂ta ta a (A7) = (s + α xˆ ) + ∂ xˆ (s + xˆ ) ∂ xˆ (s + xˆ )β ta0

tb0 .

and from the first order condition (9)



 ∂ta φa ta w(s + α xˆ ) φa a = −

+1 ∂ xˆ φa · w(s + xˆ )1+β [(s + α xˆ )/(s + xˆ )β ]2 φa (s + xˆ )β

(A8)

Substituting (A8) into (A7) now gives ∂G a φa · a = −