taxation and migration in a federal system

International Tax and Public Finance, 5, 345–355 (1998)c© 1998 Kluwer Academic Publishers, Boston. Manufactured in The Netherlands.

Taxation and Migration in a Federal System

KJETIL BJORVATN* [email protected] of Economics, The Norwegian School of Economics and Business Administration, Helleveien 30,5035 Bergen-Sandviken, Norway

Abstract

This paper discusses how taxation may affect migration, economic efficiency and income distribution. Theinstitutional framework is a federal system, in which local authorities are responsible for the supply of publicservices and the financing of these services, and where the central authorities are in charge of income redistribution.The main conclusion is that a moderate policy of income redistribution is associated with greater centralization ofthe work force and greater economic inefficiency than is the case with both radical and more limited policies ofredistribution.

Keywords: Fiscal federalism, public provision of private goods, migration

JEL Classification: F22, H42, H53, H72

Introduction

An important task for governments is the design and implementation of policies of incomedistribution. These policies include, on a general level, schemes of taxation and transfers,and, on a more specific level, the supply of public services such as health and education.1

A major issue in the literature on fiscal federalism is the optimal allocation of responsibil-ities between levels of government. The main conclusion from that literature is that localredistribution creates fiscal incentives for migration, and that redistribution for this reasonshould be a function carried out by the central level of government, see for instance Brownand Oates (1987), Wildasin (1991, 1994), Burbidge and Myers (1994), and Fernandez andRogerson (1996). This conclusion, however, rests on the assumption that the central gov-ernment is both willing and able to implement policies of redistribution which lead to aPareto efficient outcome. Both the literature on second best taxation, and the literature onpublic choice, shed some doubt on this assumption.

Rather than assuming that the central government automatically solves any efficienciesstemming from local redistribution, the present model considers how a particular policytool, namely central redistribution of income, may affect migration, economic efficiency,and the distribution of income. The institutional framework is a federal system, in whichlocal authorities have autonomy in the provision of local public services and responsibilityfor raising the taxes necessary to finance these services. The relatively high degree of localfiscal autonomy described in this model certainly does not fit reality everywhere.2 In most

* I would like to thank Shanta Devarajan, Rune Jansen Hagen, Aanund Hylland, Toshihiro Ihori, Kjell ErikLommerud, Fred Schroyen, Steinar Vagstad, and two anonymous referees for useful comments. Remaining errorsare of course mine.

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countries, the central government influences the choice of local public services both throughthe definition of certain minimum standards of supply, and through arrangements such asmatching grants. However, in view of the process of fiscal decentralization that we observein a number of countries, the relevance of the model is likely to increase over time.

The set of policies is, on the central level, lump sum redistribution of income, and onthe local level, the supply of public services financed by linear income taxes. The level ofpublic services, and hence the level of taxation needed to finance these services, dependson the population structure in the region, which is endogenously determined in the modeldue to the possibility of labor migration. The degree of central redistribution, on the otherhand, is exogenous, and used for comparative static analysis. It turns out that central andlocal taxation may interact in rather interesting ways to determine the locational outcomeof the model. More specifically, a moderate level of central redistribution causes morecentralization of the work force than do both a more limited and a more radical levelof redistribution. And since there are certain costs associated with centralization of thework force in this model, a moderate level of central redistribution also causes maximuminefficiency.

The paper is organized as follows. Section 1 presents the model in the absence of anyintervention from the central government. Section 2 introduces a central government to themodel. Section 3 concludes.

1. Model without Central Redistribution

1.1. Private Agents

The important decision made by private agents in the present analysis is where to live. Themodel therefore consists of different areas, or regions, which may be interpreted in variousways; as districts in a metropolitan area, as regions in a country, or as countries in a union.For simplicity, we include only two regions,j = 1, 2. The workers may freely choose theregion in which they want to live. Each individual is however assumed to live and work inthe same region, perhaps due to high costs of commuting. To make the model interesting,and probably more realistic, we assume that there are certain costs associated with a highdegree of centralization of the work force. These costs could be due to increased pressureon local infrastructure leading to congestion, high costs of living due to scarcity of land, orreduced labor income due to some factor of production in fixed supply.

In this paper, the costs of centralization arise indirectly, through a productivity loss asso-ciated with immigration, or more precisely, a productivity loss associated with working ina “foreign” region. As will become evident in the next section, immigration may be a costnot only for the migrant, but also for the non-migrants in the destination region, since itmay lead to a reduction in the level of local public service supply. Immigration is obviouslyalso a cost for the economy as a whole, since total output goes down.

The productivity loss from migration is assumed to differ across types of workers. Assumethat there are two kinds of people in the economy, the educated and the less educated. Thesetwo groups differ on two dimensions. First, educated people are richer than less educated

TAXATION AND MIGRATION 347

people. Second, educated people are equally productive in both regions, whereas lesseducated people are more productive in their “home” region than in the “foreign” region.

One can think of education as providing people with general skills which enable them toadapt to a new environment quickly. Or, as suggested by Schwartz (1973), more educatedworkers are more informed about job openings in other places, and therefore move morefrequently and further away from their place of origin than do less educated workers. Theinformational disadvantage of less educated workers could also imply that this category ofworkers would have to accept a lower wage in a foreign region than in the home region ifhe or she were to move. Moreover, this reduction in wages could persist for a considerableperiod of time, since it takes time to build up the social network which may provide immi-grant workers with information about relevant employment opportunities. In any case, theimportant assumption here is that a high degree of centralization of the work force impliesa large number of “foreign” workers, and hence high productivity losses for the economy.

Let the gross income of a rich person exceed that of a non-migrant poor person by a factorr > 1, i.e.,yR = r yP, whereyi is the gross income of an agent of typei . Gross incomesare assumed to be exogenously given. And let the gross income of a poor person livingabroad be a fractionα < 1 of his or her income at home, i.e.,y f

P = αyP, where superscriptf stands for “foreign.” For later use, note that the above assumptions imply that averagegross income in regionj can be written as:

yaj = βj yP (1)

where

βj =rnRj + nP j + αn f

P j

nj(2)

and subscripta denotes the average,ni j is the number of workers of categoryi in region j ,nj = nRj + nP j + n f

P j is the total number of workers in regionj , of whichn fP j are the less

educated immigrants. Income is spent on two goods, call themg andx. Preferences aredescribed by the following Cobb-Douglas utility function:

Ui j = xγi j g1−γi j (3)

Let the marginal rate of transformation be unity, which means that we can abstract fromrelative prices in the economy. For simplicity, let prices equal unity.

1.2. Local Governments

The tasks of local governments are assumed to be the determination of the supply of localpublic services, such as health and education, and the collection of the taxes necessary tofinance these services. Letgj denote the level of public services in regionj . In practice,public services may or may not be provided by the public sector, and the standard may beabsolute or may define a minimum level of quality and supply. Since the present modeldoes not include different sectors of production, the question of who provides the good is

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irrelevant. What is important to note, however, is our assumption that the public servicesare provided uniformly to the local population, i.e.,gP j = gRj. In other words, standardsmay differ between regions, but within a region the local government defines an absolutestandard of supply.

The funds required for the financing of the public services in practice come from differentsources. This paper assumes that the public services are financed by local taxes only.Furthermore, balanced budgets are required. This is certainly a simplification of reality inmost countries, since central governments, for instance through matching grants, contributein this respect. The central government in this paper, however, is concerned with thedistribution of income and not with the distribution of public services. In each region,the tax instrument employed is assumed to be a proportional income tax, call ittj . Thedisposable income of agenti in region j can then be written as:

xi j = yi j (1− tj ) (4)

which also defines the individual budget constraint. The budget constraint of the localgovernment is defined as:

tj

nj∑h=1

yhj = gj nj (5)

Turning to the supply of public services, let the choice of the local government in regionj be guided by a utilitarian welfare function defined over the utilities of the people in thatregion, i.e.,Wj =

∑nj

h=1 xγhj g1−γj . Maximizing this welfare function with respect totj and

gj , given the local government budget constraint in (5), it is straightforward to demonstratethat the optimal level of public services and the optimal tax rate in regionj are:

g∗j = (1− γ )yaj (6)

t∗j = 1− γ (7)

The optimal tax rate is independent of the regional average income level and thereforeidentical across regions. The provision of public services, on the other hand, depends onthe average income in the region. The richer region, in the sense of higher average income,has a higher supply of, say, education than the poorer region. For simplicity, we shallassume that policies are continuously updated. A change in the population structure in aregion therefore immediately translates into a change in the supply of public services inthat region. Note in particular that immigration of less educated workers reduces the levelof public service supply in the destination region by lowering the region’s average income.And since the tax rate is unaffected by such migration, the welfare of the local populationin the destination region must go down. For later use, note also that by inserting (7) into(4), income after optimal local taxation is simply a fraction of gross income:

xi j = γ yi j (8)

In the absence of central redistribution, the disposable income of the different categories ofworkers is ranked as follows:x f

P1 < xP1 = xP2 < xR1. Note in particular that the poorestgroup of workers is the less educated immigrants.


1.3. Equilibrium

Workers in this model are assumed to move to whichever region offers the higher level ofutility. We shall assume that the choice of location is an individual decision. Given that theeconomy consists of a large number of individuals, this implies that the migrants take thelevel of regional public services as given when making their locational choice. Of course,in the process of migration, average incomes will change, and so will the regional supply ofpublic services. In equilibrium, the potential migrant must be indifferent between locatingin region 1 and 2 given the level of public services in the two regions.

Location of the Rich

It can easily be shown that, in the absence of central redistribution, all rich people chooseto live in the same region. The reason is simply that by clustering together, the averageincome in that region increases, and the level of the publicly provided good will be closerto the preferred level of the rich. To see this, note that by inserting (6) and (7) into (3), andusing the definitionyR = r yP and (2), the utility of a rich person in regionj can be writtenas:

URj = k(βj /r )1−γ yR (9)

wherek = γ γ (1−γ )1−γ . It is clear that the utility of a rich person is increasing in regionalaverage income, sinceβj is increasing in regional average income. Hence, rich peoplesettle in the region with the higher average income. This is the familiar Tiebout-effect, seeTiebout (1956). Assume that the ratio of educated relative to less educated native workers ishigher in region 1 than in region 2. The resulting higher level of public services in region 1attracts the educated workers from region 2 to region 1, leading to a clustering of rich peoplein that region. Region 1 may therefore be called “the rich region” and region 2 “ the poorregion.”

Location of the Poor

Using the same procedure as above, the utility of a non-migrant poor individual can beexpressed as:

UP j = kβ1−γj yP (10)

Clearly, since all rich people have left region 2, prior to any migration of the poor,UP1 > UP2

sinceβ1 > β2 = 1. Differences in standard of living between regions do not automaticallytrigger migration, the reason being that moving to a new place is associated with a reductionin productivity and hence a loss in income. The utility of a less educated migrant can befound as:

U fP j = kαγ β1−γ

j yP (11)

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Sinceα < 1, UP1 > U fP1. Migration of less skilled workers to region 1 only takes place if

the following expression is positive:

sign(U fP1−UP2) = sign

(α − 1

β(1−γ )/γ1

)(12)

In words, if the cost of moving due to the productivity loss is not too high, i.e.,α nottoo low, relative to the benefit of moving due to the higher level of public services in thedestination region, as captured by theβ1 term, then less skilled people move to region 1.For convenience, we shall in the following assume that this is indeed the case. Note thatmigration of the less skilled workers into region 1 generates an inefficiency, since it involvesa loss in the productivity of these workers. The source of the market failure is the implicitregional redistribution of income, attracting poor workers to the rich region.

The interior migration equilibrium is characterized byUP2 = U fP1, which from (12)

impliesα = 1/β(1−γ )/γ1 . Using this equilibrium condition and the fact thaty fP = αyP, and

inserting this information in (8), we can derive the following expression for the less skilledmigrants’ disposable income, which takes account of both the optimal tax policy of localgovernments and the migration equilibrium:

x fP1 = γ yP/β

(1−γ )/γ1 (13)

Condition for Interior Equilibrium

To make sure that we have an interior migration equilibrium, we need to assume that thenumber of low-skilled workers originating from region 2 exceeds a certain minimum. Notethat migration of poor people to region 1 necessarily reducesβ1. From (12) it is clear thatfor sufficiently low values ofβ1, immigration to region 1 must come to a halt. For instance,β1 = 1 ⇒ UP2 > U f

P1. At this point, clearly the pull is towards region 2 rather thantowards region 1. As will become evident in the next section, with national redistributionthe minimum level ofβ1 is unity. From (2), we can derive the number of low-skilledimmigrants in region 1 for whichβ1 = 1 as:

n fP1

∣∣∣β1=1= nR1(r − 1)

1− α (14)

Hence, to make sure we have an interior equilibrium in both the present version of themodel and the version which includes national redistribution, we assume that the number ofpoor people originating from region 1 exceeds the number defined in (14). The migrationequilibrium is then always an interior one, characterized byUP2 = U f

P1.

2. Central Redistribution

Redistribution of income is obviously one of the most important tasks of governments.Redistribution of income is carried out through various welfare programs, such as minimum


wage legislation and unemployment benefits, and through the tax system which normallyassigns a higher tax burden on people with higher income than those with lower income.Since we wish to focus only on the distributional aspects of central government policies,we shall abstract from the supply of public goods and services on this level of government,and assume that the central government is assigned a single task; lump sum redistributionof income. The budget constraint of the central government can be expressed as:∑

i, j

τi j = 0 (15)

whereτi j denotes the lump sum tax, or subsidy in case it is negative, levied by the centralgovernment on the worker of typei in region j . The level of central redistribution is deter-mined by the size ofτi j , which is an exogenously determined policy variable in this model.Given the budget constraint facing the central government, the aim is to equalize disposableincomes in the economy. For simplicity, we shall assume that income is transferred onlyfrom those with the highest disposable income to those with the lowest disposable income.

2.1. Central Redistribution and Migration

To see how central redistribution affects migration, we know from (8) that the less educatedimmigrants are those with the lowest disposable income and the rich those with the highestdisposable income, prior to any central redistribution. Hence, starting from zero centralredistribution, a small transfer from the rich benefits only the low-skilled immigrants. Thisclearly affects the migration equilibrium, since given the regional distribution of labor, theintroduction of the welfare program leads toU f

P1 > UP2. In this way, central redistributionon a small scale stimulates further migration into region 1.

Migration reduces the attractiveness of living “abroad,” and hence stabilizes the system,through two channels. First, since the transfer is distributed equally between the immigrants,an increase in migration to region 1 means less money for each immigrant. Second, anincrease in migration reduces the average income in region 1, which again leads to areduction in the level of public services in that region. Note here that in the presence ofcentral redistribution, equation (6) needs to be modified to:

g∗j = (1− γ )(yaj − τaj ) (6′)

where the last parenthesis in(6′) denotes average income net of the redistributive tax, or“average net income” for short.3 These two effects reduce the attractiveness of living in therich region, and restore the migration equilibrium.

What happens if the central government increases the level of redistribution? Would thiscause further migration to region 1? The answer is yes, but only up to a certain point. Theeffect of central redistribution on the location of labor can be analysed by studying equation(13). As long as the less educated immigrants are the sole beneficiaries of central transfers,the transfer remains in region 1, i.e.,τa1 = τa2 = 0. The utility of workers in region 2 istherefore not affected by these transfers. The migration equilibrium is still described byUP2 = U f

P1 in (12), and hence the disposable income of less skilled migrants is described

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by (13). From (13) it is also clear that forβ1 > 1, i.e., as long as the average income inregion 1 exceeds that of region 2, the less skilled migrants remains the poorest group. Aslong as the number of less skilled immigrants in region 1 is not too high, i.e., as long asβ1 > 1, an increase in national redistribution therefore stimulates further centralization ofthe work force.

But migration into region 1 reduces average income in that region. From (13) it is evidentthat in equilibrium this reduction in average income must be balanced by an increase inthe disposable income of the low-skilled immigrants. And at a certain level of nationalredistribution, the degree of centralization of the work force must be such that the averageincome in region 1 equalsyP, which makesβ1 = 1. At this point, the less skilled immigrantshave the same level of disposable income as their fellow non-migrants, and equal toγ yP.Moreover, from (6) we know that equal average income between regions means equalregional supply of public services. Since the consumption of both types of goods now hasbeen equalized for all less skilled workers, obviously their utility levels have also beenequalized. The number of low-skilled immigrants at this point is given by (14).

What is the level of central taxation which results in this level of immigration? We knowthat the gross income of low-skilled migrants isαyP. Since the disposable income forpoor people has been equalized, then clearly each low-skilled migrant receives a transferof γ (1− α)yP, and hence total transfers from the rich at this critical level of redistributionis n f

P1γ (1− α)yP. Using (14), and the fact thatyR = r yP, total transfers from the rich arenR1γ (r − 1)yR/r , which gives us the following critical redistributive tax rate imposed onthe rich:

θR = γ (r − 1)

r(16)

whereθR ≡ τR/yR. The total tax rate on the income of the rich at this point, includingboth local and central taxes, equalstR + θR = (r − γ )/r . For instance, forγ = 0.6 andr = 1.5, the total tax rate at this point is 60%, where the central tax rate is 20% and 40%is local taxation. We shall refer to the tax rateθR, or more preciselyθR − ε, whereε isan infinitely small number, as a “moderate” level of redistribution, taxes higher thanθR as“radical” redistribution, and taxes lower thanθR as “limited” redistribution.4

So far we have seen that limited redistribution is associated with less centralization ofthe work force than is moderate redistribution. But what happens if the level of nationalredistribution is raised from a moderate level to a radical level? Since at this stage allpoor people qualify for aid, part of an increase in national transfers would now leak outof region 1, and benefit also those living in region 2, i.e.,τa1 > 0, τa2 < 0. Holding theregional distribution of labor constant, this would clearly lead to a decrease in the averagenet income in region 1, and an increase in the average net income in region 2. This inturn leads to a higher level of public services in region 2 than in region 1. And since poorpeople’s disposable incomes have been equalized through the welfare program, the resultmust beUP2 > U f

P1, which constitutes a pull towards region 2. In other words, equilibriumunder radical redistribution must involve a lower number of low-skilled immigrants thanthat given by (14).

For levels of central taxation up to the critical level defined in (16), all rich people clusterin region 1. This is no longer necessarily the case for central taxation above this critical


level. The reason is that in equilibrium with radical redistribution there is equal supply ofpublic services in both regions (which must be true since the disposable incomes of the lessskilled workers now are equalized). The equilibrium condition for migration is thereforethat the average net income is equalized across regions.

There are a number of locational configurations which satisfy this condition, and themodel cannot predict which equilibrium the economy coordinates on.5 In any case, it stillholds true that an increase in central redistribution in the radical redistributional regimereduces the degree of centralization. This must be so, since the more populous region mustbe the one with the larger number of rich inhabitants. Hence, an increase in central taxationincreases the transfer of funds from the larger region to the smaller one, which leads to aflow of people in the same direction.

Let me sum up the discussion above by offering the following intuition for the mainresult, namely the non-monotonic relationship between national redistribution and regionalconcentration of labor. For radical levels of central redistribution, the regions are fairlyequal in terms of income and provision of public services, and the incentive to leave thehome-region is small. Moderate levels of central redistribution imply greater differencesbetween regions, and hence an incentive to move to the richer region in order to receivea share of the local policy of redistribution, implicitly taking place through local taxationand the supply of local public services. With only a limited level of central redistribution,however, moving to the richer region becomes less attractive, since there is little nationalwelfare to compensate for the loss in income due to migration. This reduces the degree ofcentralization in the economy.

2.2. Policy Implications

We have seen that forθR < θR, an increase in central redistribution leads to increasedmigration into region 1. Increased migration involves an efficiency loss to the economy,since low-skilled workers are less productive in the foreign region. At the same time, it isevident that this limited level of redistribution does not improve the standard of living ofthe poor. This is because migration equilibrium is characterized byUP2 = U f

P1, which tiesthe utility of migrants to the level of utility in their home-region, which for limited policiesof central redistribution is constant. Note that migration in this case amounts to a form ofrent-seeking, where the rent is the level of central redistribution. Moreover, there is fullrent-dissipation in the economy, since the reduced productivity of migrants fully crowdsout any improvement in the welfare of the poor.

We have also seen that radical redistribution reduces the incentives for centralization ofthe work force. In this way, the worst policy from an efficiency viewpoint is moderateredistribution, since such a policy generates the largest number of immigrants into region 1.This kind of policy reduces the welfare of the rich without improving the standard of livingof the poor.

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3. Conclusion

The paper demonstrates that moderate programs of redistribution within a federal system canbe expected to be rather unsuccessful. The reason is that moderate programs of redistributionare likely to increase the pressure for centralization of the work force. Migration may beinterpreted as a form of rent-seeking, the result of a moderate program of redistributionbeing rent-dissipation rather than the improvement in the standard of living of the poor.6

For redistribution to work, such programs should either be rather limited or fairly radical.In other words, there may be a non-monotonic relation between central redistribution andeconomic efficiency, with the least attractive welfare programs being those involving mod-erate redistribution. In this way, building down the welfare state from a radical to a moremoderate level, can be expected to trigger increased centralization, increased economicinefficiency and increased inequality. Building down the welfare state from a moderatelevel to a fairly limited level, on the other hand, is likely to have rather different effects onthe economy, namely increased decentralization of the work force and improved efficiency,without significantly affecting the welfare of the poor.

Several interesting extension of the model and alternative formulations are possible. First,it would be interesting to study the case where the rich, rather than the poor, suffer a pro-ductivity loss from migration. If the poor mainly carry out manual labor, their performancemay be independent on the region in which they operate. The rich, on the other hand, mayhave their wealth tied to some immobile factor such as land, capital, or a network of busi-ness associates, which makes them less prone to migrate. The assumption that poor peopleare manual workers, suggests that this approach perhaps is more suitable in a developmenteconomy context. Second, there could be emotional costs in addition to the productivityloss. Third, both the productivity costs and the emotional costs of living in another regionmay decrease with the number of “compatriots” in that region. Fourth, a geographicallyfixed factor of production, such as land, could be introduced to model. This would makegross labor income a function of the regional distribution of labor, and modify the pulltowards the rich region. Fifth, and probably more ambitious, other political mechanisms,such as lobbying or majority vote, could be considered as determinants of public choice.

Notes

1. Income distribution is certainly not the only explanation or justification for government involvement in healthand education. Other factors such as externalities and information asymmetries are also relevant.

2. See Hughes and Smith (1992) for a description of fiscal decentralization in the industrialized world.

3. We therefore reserve the term “disposable income” for income net of both central and local taxation, i.e.,γ yi − τi .

4. Some readers would perhaps object to the characterization of a tax rate around 60% as “moderate.” Remember,however, that in this model, all locally provided public services are financed through direct taxation, whichexplains the high income tax levied by local governments.


5. Note that the assumption that workers take the regional supply of public services as given when making theirdecision on location, is important here. The reason is that, given equal average net income in both regions,moving a rich person from, say, region 1 to region 2, would always lead to an increase in the average netincome of region 2, and a reduction in region 1. In other words, we would have a game of “matching pennies,”in which no Nash equilibrium in pure strategies would exist. The assumption that the workers take the regionallevel of public services as given, guarantees the existence of migration equilibria in the radical redistributionregime. These equilibria are however not stable. The model therefore predicts that in the radical redistributionregime, small incidences may create imbalances which trigger migration as the economy moves from oneequilibrium to another.

6. Note that taxes are assumed to be lump-sum in this paper. Introducing distortative taxation would naturallymake the radical program of redistribution less attractive from an efficiency viewpoint.

References

Brown, C. C., and W. E. Oates. (1987). “Assistance to the Poor in a Federal System.”Journal of Public Economics32, 307–330.

Burbidge, J. B., and G. M. Myers. (1994). “Redistribution within and across the Regions of a Federation.”Canadian Journal of Economics27(3), 620-636.

Fernandez, R., and R. Rogerson. (1996). “Income Distribution, Communities, and the Quality of Public Educa-tion.” Quarterly Journal of Economics444, 135–164.

Hughes, G., and S. Smith. (1992). “Economic Aspects of Decentralized Government: Structure, Functions, andFinance.”Economic Policy13, 426–459.

Schwartz, A. (1973). “Interpreting the Effect of Distance on Migration.”Journal of Political Economy81,1153–1169.

Tiebout, C. M. (1956). “A Theory of Local Expenditure.”Journal of Political Economy64, 416–424.Wildasin, D. E. (1991). “Income Redistribution in a Common Labor Market.”American Economic Review81,

757–774.Wildasin, D. E. (1994). “Income Redistribution and Migration.”Canadian Journal of Economics3, 637–656.

taxation and migration in a federal system

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