Factors that Affect Fiscal Externalities in an Economic Union
Timothy J. Goodspeed
Hunter College - CUNY
Department of Economics
695 Park Avenue
New York, NY 10021
USA
Telephone: 212-772-5434
Telefax: 212-772-5398
E-mail: tgoodspe@shiva.hunter.cuny.edu
October, 1999
Abstract: The literature on tax competition suggests that a country's public sector
will be influenced by an economic union. For instance, the horizontal tax
competition literature suggests that the expectation that a mobile factor will leave a
jurisdiction in the face of a non-benefit tax will result in downward pressure on
mobile tax bases within a jurisdiction, and hence lower than desired levels of nonbenefit taxes and spending. Despite these important insights, little work has been
done to assess the factors that affect fiscal externalities and the resulting impact of
these externalities on public spending, taxation, and migration. This paper uses a
simulation model to gauge the impact of the fiscal externalities in an economic union
under alternative assumptions concerning expectations of tax base responsiveness,
the time frame, the relative progressivity of member country tax systems, and the
variance of incomes in the union.
JEL Classification: H23, H73
Keywords: Fiscal federalism, Fiscal externalities, Tax competition
This paper is a revised version of “The Effect of the Characteristics of New Members of an
Economic Union on Redistributional Policies” initially presented at the International Seminar in
Public Economics, May 27-29, 1995, University of Essex. The revision was inspired by the research
and discussions presented at the ZEW conference on “Fiscal Competition and Federalism in Europe”
June 1-3, 1999. My thanks to participants in both seminars and Howard Chernick for helpful
discussions.
I. Introduction
The economies of the nations of the world are becoming increasingly integrated. This
integration has been in part a natural consequence of increased trade and the mobility of financial
capital between countries, but has been hastened by the emergence of economic unions such as the
European Union (EU) and the North American Free Trade Agreement (NAFTA). The literature on
tax competition suggests that a country's public sector will be influenced by an economic union.
For instance, the horizontal tax competition literature, such as Wildasin (1988, 1989) and
Zodrow and Mieszkowski (1986), develops a concept of a fiscal externality. The basic insight is that
the expectation that a mobile factor will leave a jurisdiction in the face of a non-benefit tax will
result in downward pressure on mobile tax bases within a jurisdiction, and hence lower than desired
levels of non-benefit taxes and spending. A similar point is made in Goodspeed (1989). Migration
incentives are created if non-benefit taxes are levied on mobile resources because the mobile factor’s
tax-price is lower in a jurisdiction with a higher mean tax base. If migration results in the factor
contributing less to revenue than it consumes in public services, its’ migration imposes an externality
on other factors resident in the jurisdiction.
These insights have important consequences for redistributional policies. Redistribution by
definition entails taxes that do not reflect benefits. If the factors that are so taxed become mobile
because of an economic union, redistributive taxes will result in an inefficient spatial allocation of
resources and will tend to be competed down.
Despite these important insights, little work has been done to assess the factors that affect
fiscal externalities and the resulting impact of these externalities on public spending, taxation, and
2
migration. What factors influence the impact of fiscal externalities? This paper uses a simulation
model to gauge the impact of the fiscal externalities in an economic union under alternative
assumptions concerning expectations of tax base responsiveness, the time frame, the relative
progressivity of member country tax systems, and the variance of incomes in the union.
In a base case in which two jurisdictions use proportional income tax systems, the time frame
(reflected by the elasticity of supply of housing) is found to have a large impact on migration, but
much smaller effects on tax rates and public spending. In contrast, the expected responsiveness of
the tax base has a large impact on public spending and tax rates, but little impact on migration.
When the tax systems of the two jurisdictions differ in their progressivity, the expected
responsiveness of the tax base has a profound impact on migration patterns. Finally, the variance
of the income distribution is found to have a strong impact on tax rates and public spending, and
relatively small effects on migration patterns.
The results have some interesting implications for fiscal competition in Europe. First, they
emphasize that fiscal externalities affect not only movements of factors, but also internal public
spending and taxation decisions. Empirical work should examine the impact of fiscal externalities
on public good levels, not just on the movement of factors from one jurisdiction to another. Second,
the results concerning the variance of the income distribution suggest that the addition of new
members with incomes substantially different from current members can have a strong impact on
current members’ taxation and spending decisions.
The paper is organized in the following manner. The next section discusses fiscal
externalities in a simplified version of the model to be simulated. Section 3 briefly discusses the
simulation model used. Section 4 presents the results of three sets of nine simulations each that
3
attempt to gauge the impact of the fiscal externalities in an economic union under alternative
assumptions. Section 5 concludes.
II. The Fiscal Externality
The fiscal externalities discussed in this paper combine the work of Goodspeed (1989) with
that of Wildasin (1988, 1989) and Zodrow and Mieszkowski (1986). Before considering a
simulation model based on Goodspeed (1989) and results designed to measure changes in the fiscal
externality, it is useful to discuss the fiscal externality in a simpler framework. To do this, we
consider the simulation model that follows, but ignore the housing market. The elasticity of the
supply of housing is used in the simulations to allow for real income differences that could arise in
the short or intermediate run in an economic union. The housing market is unnecessary to discuss
fiscal externalities, however.
Consider a simple world of two jurisdictions and the optimization problem of one of the
governments, calling this jurisdiction 1. We assume that the preferences of the median voter are
defined over a private good, X, and the per-capita level of a publicly provided private good, G1:
(1)
Jurisdiction 1 is assumed to finance expenditures using a linear income tax; hence, local government
one’s budget constraint is given by
(2)
4
where ym1 is the mean income of jurisdiction one. The tax base of each jurisdiction will be influenced
by its own fiscal decisions and those of the other jurisdiction; hence, ym1 = ym1 (a1, a2, t1, t2). We
assume that this is due solely to the mobility of the tax base; that is, we assume that an individual’s
(before tax) income is exogenous and hence does not depend on tax rates. We will interpret this
function as jurisdiction 1's expectation of its tax base given its choice of tax parameters and those
of the other jurisdiction.
Voting models that attempt to explain the progressivity of a tax system quickly run into
difficulties. Even a simple linear income tax is problematic because there are three voting
parameters, the level of the public good and the two tax parameters, only one of which is determined
by the government budget constraint. Kramer (1973) shows that if all combinations of the remaining
two dimensions are admitted as possible candidates, majority rule will fail to generate an
equilibrium. Denzau and Mackay (1981) and Inman (1985) provide excellent discussions of some
of the proposed solutions to this problem. One approach is what Shepsle calls "structure induced
equilibrium." Shepsle (1979) uses a serial election process (with myopic expectations) in which the
essential institutional constraint is that each dimension is voted on one at a time. Denzau and
Mackay (1981) extend this analysis to consider the case of perfect foresight expectations, and show
that the equilibrium generated will generally be different than that under myopic expectations. A
different solution is that of Roberts (1977), who holds one of the parameters, G, fixed and hence
reduces the problem to one of voting over a single dimension.
Migration models that consider voting and redistribution have proceeded by simplifying the
5
problem in different ways.1 We will assume a linear income tax, and consider a variant of the
Roberts solution in which we hold the intercept term fixed. A set of simulations that follow will
change the exogenous intercept parameter for one of the jurisdictions to gauge the impact of differing
degrees of progressivity. The problem of jurisdiction 1 is to choose the tax rate to maximize the
median voter’s utility subject to the median voter’s budget constraint and his expectation of
jurisdiction 1's budget constraint:
(3)
where ym1 (a1, a2, t1, t2) is the function noted above. Substituting the constraints into the objective
function and differentiating yields the first order condition
(4)
1
Goodspeed (1989) considers a proportional income tax and hence eliminates the
constant term of the linear income tax. Epple and Romer (1991) use the approach of Roberts
(1977) and essentially set G equal to zero; a proportional property tax is used to generate a lumpsum subsidy that is added to each person's income. The analysis in Goodspeed (1995) assumes
that the intercept is greater than or equal to zero, interprets the intercept as a head tax, and
investigates the choice between financing by a proportional income tax or a head tax. His
approach can be thought of as a hybrid of the serial voting and Romer approaches. Goodspeed's
voters consider the optimal choice of each parameter holding the other parameters fixed; it turns
out that each voter will choose one of the two tax parameters to be zero. In a sense, this reduces
the public choice problem to a single dimension as in Roberts, but unlike the Roberts case, no
parameter is exogenously fixed. Each voter endogenously fixes one of the tax parameters to be
zero.
6
Rewrite the first order condition as
(5)
The right hand side is the perceived tax-price of public spending. The work of Goodspeed (1989)
takes Mym1 / MtL1 to be zero. Nevertheless, a fiscal externality is present and location decisions are
distorted in Goodspeed’s model as long as the mean income of jurisdiction one differs from that of
jurisdiction two. The distortion in location incentives results because an individual’s tax-price is
lower in a jurisdiction with a higher mean tax base. This is illustrated by the two solid budget
constraints plotted in Figure 1. For a given level of public service, an individual will always prefer
the wealthier jurisdiction since the tax price is lower. (Indifference curves are plotted as concave
functions with utility rising as one moves toward the southeast of Figure 1). An incentive is created
for a migrant to move to a wealthier jurisdiction where he will contribute less to revenue than he
consumes in public services. He will thus impose an externality on everyone else, as explained in
Oates (1972) and Goodspeed (1989, 1995).
The term Mym1 /MtL1 is the focus of the fiscal externality discussed in the horizontal tax
competition literature such as in Wildasin (1988, 1989) and Zodrow and Mieszkowski (1986). That
literature argues that tax base mobility imposes a fear that non-benefit taxes will drive out the mobile
tax base, and leads to lower tax rates. The effect of this externality is similar to that explored in
Goodspeed (1989): if Mym1 / Mt1 is negative, the price of local public services is higher than it would
be if the decisive voter ignored the mobility of the tax base. This is illustrated by the dotted budget
7
constraints in Figure 1. While this will clearly have an impact on the internal choice of spending
levels and tax rates in both jurisdictions, the impact on migration of the taxed factor is less clear
since this depends on relative prices between jurisdictions one and two. The impact of this fiscal
externality on migration and the public sector may therefore be quite different than that explored in
Goodspeed (1989).
The simulations that follow are designed to gauge the impact of these fiscal externalities on
public spending, tax rates, and migration under different scenarios. This is achieved by considering
three sets of nine simulations. In each set, the simulations consider 3 values for Mym/Mt and 3 values
for the elasticity of the housing supply. (The housing supply elasticity is interpreted in terms of the
time frame under consideration.) The first set of simulations assumes that both jurisdictions use
proportional income taxes. The second set of simulations considers a proportional tax system for
one jurisdiction and a progressive tax system for the other. The third set of simulations again
assumes that both jurisdictions use proportional income taxes as in the first set of simulations, but
considers a larger variance of the income distribution.
III. The simulation model
The simulation model is based on the model developed in Goodspeed (1989) that is in turn
based on the models of Westhoff (1977) and Epple, Filimon, and Romer (1984). These models
embed a median voter model in a migration model and both the voting equilibrium and the migration
equilibrium are determined endogenously. Two important assumptions of the model that are used
to establish both equilibria is that income is a continuous variable and indifference curves are single8
crossing in income.
As the equilibrium properties of these models are well known, and this is not the focus of the
current paper, I will not dwell on proving existence in the model. Two differences from previous
versions of the model are worth noting. First, a linear income tax is used, but the intercept term is
taken as exogenous. Second, a jurisdiction has some expectation of its tax base function, and hence
some expectation of how the tax base will change as it changes its tax rate. A value for Mym/Mt is
exogenously specified in the simulations.
Other than these differences, the model is similar to that developed in Goodspeed (1989).
The model will be simulated for two jurisdictions. The voting equilibrium of the model is
determined by the equality of the slope of the median voter's indifference curve and the government
budget constraint within each of the two jurisdictions. The migration equilibrium is determined by
a single equation that generates indifference for a particular income level between the pair of
jurisdictions. This partition of the income distribution allocates the population to jurisdictions such
that everyone is satisfied with the jurisdiction in which he resides. This also defines the jurisdiction
population and tax base. Within each jurisdiction, the supply and demand for housing determines
the equilibrium price of housing in that jurisdiction. The model thus consists of 7 equations to be
solved for the 7 endogenous variables: the tax rates and level of public spending in each jurisdiction,
the price of housing in each jurisdiction, and the income level of the indifferent individuals.
The simulations will assume that utility is of the Stone-Geary form. The continuous
distribution of incomes will be assumed to be uniform; hence mean and median incomes are
identical. The housing supply function is of the form assumed in Epple, Filimon, and Romer (1984)
and Goodspeed (1989).
9
IV. Results
Before presenting results of the simulations, a word on the interpretation of the model is
useful. In the very long run, migration suggests that real incomes will be equalized. However, this
is not likely to happen across country borders, even with free migration, for a very long time. The
model here allows for real income differences through the housing market. Over time, such
differences may become less important. This will be reflected in the simulations by increasing the
elasticity of the supply of housing.
As mentioned, we consider three sets of nine simulations. The first set of simulations
assumes that both jurisdictions use proportional income taxes (a1 = a2 = 0). The results for the
equilibrium population, tax rate, and public spending in each jurisdiction are presented in Table 1
for the nine simulations. Each simulation row corresponds to a different value for Mym/Mt and each
simulation column corresponds to a different value for the housing supply elasticity. The striking
feature of the simulations is the differing impact on migration and public sector spending of the
externalities explored in Wildasin (1988, 1989) and Goodspeed (1989). The first row assumes no
expectation of a decline in tax base, yet the migration impact in the very long run is extremely large.
The impact on public spending is modest in the first row simulations. In contrast, the first column
simulations show that a larger expectation of a decline in the tax base has a very large impact on
public spending and tax rates, even in the very short run. The impact on migration is minimal in the
first column simulations.
The second set of simulations considers a proportional tax system for one jurisdiction and
a progressive tax system for the other. Prior to presenting these results, a word on the definition of
10
progressivity is in order. Many measures of progressivity may be considered, but we consider the
derivative of the average tax rate with respect to income. If the derivative of the average tax rate is
positive, the tax system is said to be progressive. Since the tax paid by an individual with income
y is T = -a + ty, the average tax rate is -a/y + t and the derivative of the average tax rate with respect
to y is a/y2, which is positive as long as a is positive, so the tax is progressive. Further, a change in
a parameter of the tax system increases the progressivity of the tax system if the derivative of the
progressivity measure with respect to the parameter (i.e. the cross partial of the average tax rate) is
positive. Since the cross-partial of the average tax rate with respect to income and t is zero and with
respect to income and a is positive, an increase in the parameter a will increase the progressivity of
the tax system and an increase in t will not affect its progressivity. This characteristic of the linear
income tax will be exploited in the next set of simulations; the more progressive tax system will have
a higher value for the intercept term.
Table 2 presents the results of the second set of simulations that assume a proportional tax
system for jurisdiction one (a1 = 0) and a progressive tax system for jurisdiction 2 (a2 = .2). Again,
the results for the equilibrium population, tax rate, and public spending in each jurisdiction are
presented for the nine simulations. The first row of simulations shows a somewhat more accentuated
migration from the poor to the wealthy jurisdiction. The most striking feature of these simulations
compared to those of Table 1 comes from the next two rows, however. In these last two rows, the
progressivity of the tax system of jurisdiction 2 combined with the expected reduction in tax base
reverses the migration pattern. Instead of a migration from the poor to the wealthy jurisdiction, we
find a pattern of migration toward the poorer jurisdiction. The problem for jurisdiction 2 is that it
must impose a higher tax rate to achieve the same level of public spending as in Table 1. Public
11
spending becomes so much more expensive that the high tax base incentive for locating in the
wealthy jurisdiction is overwhelmed. The expected tax base mobility parameter is much more
important for migration patterns when two jurisdictions have diversely progressive tax systems.
The third set of simulations again assumes that both jurisdictions use proportional income
taxes as in the first set of simulations, but considers a larger variance of the income distribution. The
larger variance is modeled by increasing the support from [2, 3] to [2, 3.5]. For comparison to the
other simulations, the height of the uniform distribution is reduced to .67 to maintain the same
aggregate income and population. The results are presented in Table 3. While somewhat more
migration towards the wealthier jurisdiction than in Table 1 is seen, the most striking difference from
the results in Table 1 is substantially lower tax rates and public spending. A wider distribution of
income in itself induces a reduction in tax rates and public spending.
V. Conclusion
The economies of the world are becoming increasingly integrated, in part because of the
emergence of economic unions. The literature on horizontal tax competition suggests that an
economic union can have an impact on the public sector of member countries.
Despite important insights provided in the tax competition literature, little work has been
done to assess the factors that affect fiscal externalities and the resulting impact of these externalities
on public spending, taxation, and migration. This paper uses a simulation model to gauge the impact
of the fiscal externalities in an economic union under alternative assumptions concerning
expectations of tax base responsiveness, the time frame, the relative progressivity of member country
12
tax systems, and the variance of incomes in the union.
In a base case in which two jurisdictions use proportional income tax systems, the time frame
is found to have a large impact on migration, but much smaller effects on tax rates and public
spending. In contrast, the expected responsiveness of the tax base has a large impact on public
spending and tax rates, but little impact on migration. When the tax systems of the two members
of an economic union differ in their progressivity, the expected responsiveness of the tax base has
a profound impact on migration patterns. Finally, the variance of the income distribution is found
to have a strong impact on tax rates and public spending, and relatively small effects on migration
patterns.
The results have some interesting implications for fiscal competition in Europe. First, they
emphasize that fiscal externalities affect not only movements of factors, but also internal public
spending and taxation decisions. Second, the results concerning the variance of the income
distribution suggest that the addition of new members with incomes substantially different from
current members can have a strong impact on current members’ taxation and spending decisions.
Empirical work is needed on the impact of fiscal externalities. Such work should examine the
impact of fiscal externalities on public good levels and tax structure, not just on the movement of
factors from one jurisdiction to another.
13
Bibliography
Denzau, Arthur T. and R. J. Mackay. 1981. "Structure-Induced Equilibria and Perfect-Foresight
Expectations." American Journal of Political Science. 25: 762-779.
Epple, D. and T. Romer. 1991. "Mobility and Redistribution." Journal of Political Economy. 99:
828-858.
Epple, D., R. Filimon, and T. Romer. 1984. "Equilibrium Among Jurisdictions: Toward an
Integrated Treatment of Voting and Residentail Choice." Journal of Public Economics. 24:281-308.
Goodspeed, Timothy J. 1989. "A Re-examination of the Use of Ability to Pay Taxes by Local
Governments." Journal of Public Economics. 38:319-342.
Goodspeed, Timothy J. 1995. "Local Income Taxation: An Externality, Pigouvian Solution, and
Public Policies." Regional Science and Urban Economics. 25: 279-296.
Inman, Robert P. 1987. "Markets, Governments, and the 'New' Political Economy," in A.J. Auerbach
and M. Feldstein, eds., Handbook of Public Economics. Amsterdam: North-Holland.
Kramer, Gerald. 1973. "On a Class of Equilibrium Conditions for Majority Rule." Econometrica.
41: 285-297.
Roberts, K.W.S. 1977. "Voting over Income Tax Schedules." Journal of Public Economics. 8: 329340.
Shepsle, Kenneth. 1979. "Institutional Arrangements and Equilibrium in Multidimensional Voting
Models." American Journal of Political Science. 23: 27-59.
Westhoff, F. 1977. "Existence of Equilibria in Economies with a Local Public Good." Journal of
Economic Theory. 14:84-112.
Wildasin, D., 1988. “Nash Equilibria in Models of Fiscal Competition.” Journal of Public
Economics. 35: 229-40.
Wildasin, D., 1989. “Interjurisdictional Capital Mobility: Fiscal Externality and a Corrective
Subsidy.” Journal of Urban Economics. 25: 193-212.
Zodrow, G., Miezskowski, P., 1986. “Pigou, Tiebout, Property Taxation, and the Underprovision
of Local Public Goods.” Journal of Urban Economics. 19: 296-315.
14
Figure 1
15
Table 1
Migration and Public Sector Impact of Fiscal Externalities:
Similarly Progressive Tax Systems
(a1 =a2 = 0 for all simulations)
Housing
supply
elasticity
tax base
responsiveness
Mym
----- = 0
Mt
My
region
elasticity=1
elasticity=3
elasticity=9
region 1
region 2
region 1
region 2
region 1
region 2
tax rate
.21
.22
.28
.28
.30
.30
public good
expenditure
.48
.62
.68
.76
.62
.76
percent of
population
49
51
39
61
14
86
tax rate
.12
.12
.14
.13
.14
.14
public good
expenditure
.28
.34
.30
.36
.29
.35
percent of
population
48
52
35
65
10
90
tax rate
.09
.09
.09
.09
.10
.09
public good
expenditure
.20
.24
.20
.25
.19
.24
percent of
population
48
52
31
69
5
95
variable
m
----- = -5
Mt
Mym
----- = -9
Mt
16
Table 2
Migration and Public Sector Impact of Fiscal Externalities:
Diversely Progressive Tax Systems
(a1 = 0; a2 = .2 for all simulations)
Housing
supply
elasticity
tax base
responsiveness
My
region
elasticity=1
elasticity=3
elasticity=9
region 1
region 2
region 1
region 2
region 1
region 2
tax rate
.22
.29
.29
.36
.30
.38
public good
expenditure
.49
.61
.62
.76
.62
.75
percent of
population
49
51
36
64
9
91
tax rate
.12
.16
.14
.16
.14
.16
public good
expenditure
.27
.24
.32
.26
.33
.28
percent of
population
55
45
64
36
80
20
tax rate
.08
.11
.09
.11
public good
expenditure
.20
.11
.23
.12
percent of
population
81
19
99
1
variable
m
----- = 0
Mt
Mym
----- = -5
Mt
My
m
----- = -9
Mt
17
no
viable
equilibrium
found
Table 3
Migration and Public Sector Impact of Fiscal Externalities:
Similarly Progressive Tax Systems (a1 =a2 = 0 for all simulations),
Greater Variance of Income Distribution
Housing
supply
elasticity
tax base
responsiveness
My
region
elasticity=1
elasticity=3
elasticity=9
region 1
region 2
region 1
region 2
region 1
region 2
tax rate
.13
.14
.21
.21
.28
.28
public good
expenditure
.31
.43
.47
.61
.58
.73
percent of
population
47
53
33
67
12
88
tax rate
.09
.09
.12
.12
public good
expenditure
.22
.29
.27
.34
percent of
population
47
53
30
70
tax rate
.07
.07
.09
.08
public good
expenditure
.18
.22
.19
.25
percent of
population
46
54
25
75
variable
m
----- = 0
Mt
Mym
----- = -5
Mt
Mym
----- = -9
Mt
18
no
viable
equilibrium
found
no
viable
equilibrium
found