Preliminary version; Comments Invited.
Strategic Fiscal Interactions Among Atomistic Governments:
A Comparative Statics Analysis †
David E. Wildasin
Martin School of Public Policy
University of Kentucky
Lexington, KY 40506-0027
USA
February, 2014
Abstract: Characteristically, people in metropolitan areas are employed in one locality
(a “central city”) even though they reside in another (a “suburb”). Through this economic linkage, local property taxes affect neighboring localities within a metropolitan
area even when the entire region is small and open with respect to the external markets
for freely-mobile labor and capital. Comparative statics analysis shows how one locality
can use its property tax to transfer rents from neighbors, giving rise to small-number
strategic fiscal interactions among atomistic governments.
† To
be presented at the University of Georgia, February 20, 2014.
1
Introduction
A now vast literature on “fiscal competition” investigates the interdependent choices of
tax and expenditure policies in a system of governments.1 The objective of the present
paper is to develop a new theoretical framework that can be used to analyze policy
interdependence among local governments that are linked by commuting, as exemplified by the localities found within metropolitan areas. Within such regional economies,
households residing within one locality are often employed in a different locality. Due
to this residence/employment linkage, policy choices implemented in one locality affect
neighboring localities within the same metropolitan area, even if, as is assumed here, the
regional economy as a whole is only a small part of a larger national or global economy.
Goods and services, labor, and capital are freely mobile within this larger economy, with
respect to which the regional economy as a whole, and the individual localities within
it, are thus “small” and “open”, i.e., “atomistic”. As will become clear, these atomistic
jurisdictions should nonetheless be expected to act strategically, vis-a-vis each other, in
setting their fiscal policies.
Research on fiscal competition owes much to seminal contributions by Mieszkowski (1972),
Zodrow and Mieszkowski (1986), and others (see Zodrow (2007) for discussion and references), initially applied to the study of local property taxes. These taxes underpin the
fiscal systems of many local governments – tens of thousands in the US alone – throughout the world. One main theme of the literature on property tax incidence is that the
long-run mobility of capital results in equalization of net rates of return across localities.
Since no locality contains more than a very small share of the aggregate stock of capital,
many analyses of local public finance, both theoretical and empirical, postulate that no
one jurisdiction’s tax policy has a perceptible impact on the economy-wide net rate of return on capital. Under these conditions of atomistic or perfect competition for capital, no
strategic interactions arise among localities when they choose their tax policies. Indeed,
no country in the world, and, a fortiori, no subnational economy, contains more than a
relatively modest share of the world’s GDP, capital stock, or population. Population and
capital mobility at the international and, a fortiori, at the subnational levels, may thus
create a strong presumption in favor of treating governments – local, state/provincial,
and even national – as atomistically fiscal competitive.
The assumption of perfect competition, however, is by no means universal in the literature. On the contrary, many studies, both theoretical and empirical, assume instead
that there is only a small number of competing jurisdictions (often, just two, in theoretical models) capital (or perhaps some other mobile resource, like labor) is allocated
(see Keen and Konrad (2013) for an up-to-date survey, with many references). Strategic
1 For surveys with varying emphases and extensive references, see Wilson (1999), Wildasin and Wilson (2004), Brueckner
(2003), Revelli (2005) and, most recently, Keen and Konrad (2013).
1
interactions naturally arise in this context because each jurisdiction’s policy can have
non-negligible impacts on the economy-wide net return to the mobile resource (price
effects) and on the stock of the mobile resource that locates in other jurisdictions (quantity effects). In this case, each locality’s choice of tax policy is important for the policy
choices of other localities, that is, they are strategically interdependent. For instance, in
one pioneering study, Brueckner and Saavedra (2001) study local property taxes within
the Boston metropolitan area, attempting to discern whether an increase in the property tax within one locality results in an increase, a decrease, or no change at all in the
property taxes of neighboring localities.
Overall, it is fair to say that previous literature on fiscal competition reveals no clear-cut
consensus on the a priori appeal of large-number (atomistic) or small-number (strategic)
specifications of fiscal policymaking. Under these circumstances, it is difficult to know
how to best to model fiscal policymaking by jurisdictions in open-economy settings, and
how to interpret empirical findings.
The analysis to follow presents a model that, like much of the literature, postulates
that labor and capital are freely mobile among numerous small governments which are
therefore atomistic with respect to the economy-wide markets for labor and capital. The
model departs from the standard framework of atomistic fiscal competition, however,
by recognizing that local economies are sometimes highly economically integrated, and
that such economic linkages can give rise to strategic interactions among these integrated
local economies.2 Although there are many potentially important types of such linkages,
the analysis here focuses on the linkages that, in the US, define “metropolitan areas”,
namely, as local economies where suburban populations are linked to urban core areas
by commuting.3 Needless to say, this is not the only way in which local economies may
be linked, and, indeed, previous studies have examined other types of fiscal interactions.4
2 Hoyt (1993) analyzes local fiscal policies in a metropolitan area where households select among several residential
locations that use taxes on housing to finance public services. Unlike the analysis presented here, Hoyt focuses on symmetric
jurisdictions and abstracts from interactions between suburban policies and urban labor markets, instead taking household
incomes as exogenously fixed.
3 A metropolitan area must contain an urban core and it includes localities that meet at least a minimum threshold
level of “employment interchange” – i.e., of people residing in one location while working in another. In most instances,
this threshold is 25%. See OMB (2010), p. 37250.
4 Although labor and capital mobility are the focus of attention in the present analysis, they are by no means the only
reasons why fiscal policies in one jurisdiction may affect and be affected by policies elsewhere, whether jurisdictions act
atomistically or strategically. As one example, retail sales and other taxes on commercial transactions create incentives for
buyers to make purchases in low-tax jurisdictions. If transportation costs constitute a significant impediment to commerce,
however, such taxes primarily affect commerce with nearby jurisdictions. Since each jurisdiction has only a very limited
number of neighboring jurisdictions, the desired policy of each depends importantly on the policies chosen by only a
small number of others, so that the assumption of atomistic policy setting is inappropriate. Kanbur and Keen (1993)
and Nielsen (2001) analyze strategic tax setting with cross-border shopping. See Keen and Konrad (2013) for a survey
and additional references, as well as Agrawal (2012, 2013), and Agrawal and Hoyt (2014) for recent theoretical extensions
and empirical applications. Strategic interactions can also arise from informational interactions, with no market linkages
whatsoever. See Besley and Case (1995); Bordignon et al. (2003), among others, emphasize the need to distinguish
empirically among different theories of strategic interactions, a theme further developed in Revelli (2005). Still other
approaches – as for example Wildasin (1993), which studies fiscal interactions among regions that are connected through
upstream/downstream industrial linkages – have been investigated. Needless to say, these and other alternative theoretical
2
Section 2 outlines a highly stylized model of such a metropolitan area in which people
reside in suburbs while working in a city, the key interjurisdictional economic linkage
that underlies the entire analysis. In suburbs, land and capital are used to provide the
housing in which people reside, while, in the city, land and capital are used along with
workers to produce goods and services. City and suburban governments impose taxes on
freely-mobile capital (“property taxes”) but, because these localities are small relative to
the economy-wide market for capital, their tax policies can have no perceptible effect on
the net return to capital. Nevertheless, by affecting housing markets, suburban policies
indirectly affect the urban labor market, and, by affecting productive urban activity, city
policies affect suburbs.
Section 3 is devoted to the comparative statics analysis of city and suburban tax policies.
Section 4 examines the welfare implications of these policies and shows, in particular, that
both city and suburban governments have incentives to impose taxes on freely mobile
capital, even if they have ideal lump-sum taxes at their disposal as alternative revenue
sources. In essence, even though no local government can have a significant affect on
the net return to capital, a tax on such capital allows each to capture some rents from
its metropolitan-area neighbors. While Sections 2-4 focus on a starkly simplified model
for the sake of analytical clarity, Section 5 shows how the model and key findings can
be extended to accommodate a richer and more realistic policy environment. Section
6 presents some preliminary results concerning city-suburban fiscal reaction functions.
Section 7 concludes with a short summary and suggestions for further research.
2
The Model
This section presents the basic structure of the model in its simplest form. Relaxation of
some of its strong simplifying assumptions is discussed later; suffice it to say here that
many generalizations and alternative interpretations are possible, many of which do not
change the essential findings.
First, there are two or more local jurisdictions, henceforth called the “city” and the
“suburbs”, that constitute a regional economic system. In the city, productive activities
take place using three inputs, called “capital” (denoted by kc ), “labor” (denoted by `),
and “land”. Workers each provide a single unit of labor and reside in housing that is
situated in the suburbs and that is produced using capital (ks ) and land. No other
productive activities take place in the suburbs. The amount of land in both the city and
the suburbs is exogenously fixed. Each worker requires precisely one unit of housing, so
that `, the size of the city work force, is also the size of the total stock of housing in the
suburbs.
and empirical models of strategic interaction need not be mutually exclusive.
3
The production activities in the city yield outputs that are freely traded with the rest of
the world at prices that are unaffected by local policies. These prices, taken as given, allow
outputs to be aggregated into a single homogeneous product that serves as numéraire,
with a price of one. The price of housing in the suburbs is denoted by p. Capital and
labor can both move freely between the regional economy and the rest of the world, and,
as a condition of equilibrium, must earn the same net incomes or utilities within the
regional economy as can be obtained in the rest of the world.
Output in the city is a strictly increasing and strictly concave function f (kc , `) of the
amounts of capital and labor employed there. The amount of housing produced in the
suburbs is a strictly increasing and strictly concave function g(ks ) of the amount of capital
used there. Both production functions are twice continuously differentiable. Both are
strictly concave because both the production of the all-purpose good in the city and the
production of housing in the suburbs depends on land inputs, and land is strictly fixed
in supply. All production is carried out by profit-maximizing firms operating in perfectly
competitive markets.
City and suburban governments can each impose a tax on capital employed within their
boundaries, at per-unit rates denoted by tc and ts , respectively, thus yielding revenues of
tc kc and ts kx . The disposition of these revenues, and the possible use of other revenue
instruments, is discussed further below. (Although positive tax rates are observed empirically, the formal analysis to follow can accommodate negative tax rates, i.e., subsidies,
if desired.) Because capital is freely mobile, the long-run equilibrium before-tax rates of
return on capital in the city and in the suburbs are given by r + tc and r + ts , respectively,
where r is the prevailing net rate of return on capital in the rest of the world.
Let w denote the wages earned by workers in the city, and assume that each worker’s
utility depends solely on earnings net of the price of housing, w − p. Under conditions of
free labor mobility, equilibrium requires that
w̄ = w − p
(1)
where w̄ is the prevailing net income of workers in the rest of the world, taken as exogenously fixed.
Land rents are determined as residuals, that is, as the value of production minus the
costs of variable inputs. Land rents in the city are thus
Rc = f (kc , `) − w` − (r + tc )kc
(2)
while land rents in the suburbs are
Rs = pg(ks ) − (r + ts )ks .
(3)
The assumption that each unit of labor requires one unit of housing means that housing
4
demand must equal housing supply, or
` = g(ks ).
(4)
The assumption that firms employ profit-maximizing amounts of labor and capital means
that
f` (kc , `) = w,
(5)
fk (kc , `) = r + tc ,
(6)
pg 0 (ks ) = r + ts .
(7)
and
where, as usual, subscripts on f denote partial derivatives.
This completes the formal setup of the model. The model can be expressed in a more
condensed form by using the migration equilibrium condition (1) to express p in terms of
w, using the marginal-productivity condition (5) to express the wage rate as a function
of (kc , `), and inverting the housing market equilibrium condition (4) to solve implicitly
for ks as a strictly increasing and convex function of `, denoted by κs (`), satisfying
κ0 (`) = 1/g 0 > 0. (7) can then be written
(f` (kc , `) − w̄)g 0 (κs [`]) = r + ts
(8)
which, together with (6), constitutes a two-equation system that determines the variables
(kc , `) as implicit functions of the policy variables (tc , ts ).
This system is analyzed in more detail in the next section. Before doing so, it is helpful to
recapitulate the basic economic structure of the model, which hinges on the assumption
that the same people who reside in the suburbs also work in the city, creating a fundamental economic linkage between the two. Suburban policies – specifically, the property
tax rate ts – affect the suburban housing stock and thus the size of the urban work force.
In turn, this affects the urban labor market, the return to investment in the city, land
rents in the city, and other endogenous variables. Similarly, city policies – specifically,
the property tax rate tc – affect the size of the urban labor force and thus the suburban
housing market, the price of residential housing, and suburban land rents. Even though
the entire regional economy is small relative to the labor, capital, and goods markets in
the rest of the world, the taxation of capital in one jurisdiction has a non-negligible effect
on economic conditions in the other jurisdiction.
As so far described, the model postulates just two jurisdictions, namely, one city and one
suburb. However, one can interpret the single suburb as an aggregate of many identical
suburbs. A change in ts must then be understood as a simultaneous or coordinated
change in the property tax rates of all suburbs taken together. From the viewpoint of
any one small suburb in a system of many suburbs with one city, the situation is rather
5
different, since any one suburb by itself has only a negligible impact on the total size of
the regional work force and thus must take w, the city wage, as exogenously fixed. In this
case, migration equilibrium (1) implies that the price of housing in this one suburb must
also be taken as exogenously given. Each suburb, in this interpretation, is atomistic. The
implications of atomistic policy choices by suburbs are discussed further below; at this
stage, it is important simply to note that the model can accommodate either atomistic
or unitary suburbs.
3
The Effects of Local Policy Changes: Comparative Statics
This section shows how the two-equation system (6) and (8) can be used to solve implicitly for the variables (kc , `) in terms of the local policy instruments (tc , ts ), deriving
comparative statics in the usual way.
The implicit function theorem can be applied to (6) and (8) provided that the determinant
of the Jacobian matrix
fkk
fk`
H= 0
(9)
g f`k
g 0 f`` + pg 00 κ0s
is non-vanishing. Since g 0 > 0 > g 00 and since κ0s = 1/g 0 > 0, and since the Hessian matrix
of f (kc , `) is negative definite, with determinant |F | = fkk f`` − fk` f`k > 0, it follows that
the determinant of H is given by
|H| = g 0 |F | + pg 00 fkk > 0.
(10)
Let Hij denote the (i, j) element of H.
In order to sign the comparative-statics responses to changes in tax policies, assume that
flk = fkl > 0, that is, that an increase in one variable input raises the marginal product
6
of the other.5 It then follows that (6) and (8) for
∂kc
H22
=
<0
∂tc
|H|
(11a)
∂`
H21
= −
<0
∂tc
|H|
(11b)
H12
∂kc
= −
<0
∂ts
|H|
(11c)
∂`
H11
=
< 0.
∂ts
|H|
(11d)
In words, (11a) and (11b) show that a tax on capital in the city reduces its capital stock
and urban employment. A tax on capital in the suburbs reduces the size of the regional
population, and thus urban employment, as well as the size of the urban capital stock.
Since the size of the labor force and the suburban housing stock are positively related and
since the suburban housing stock is produced using capital, it follows that the suburban
housing stock and stock of capital are both reduced at ts rises.
Having determined the effects of policy changes on employment and investment, it is
possible to explore the impacts of policy on other endogenous variables. For instance, it
is straightforward to observe that an increase in the city property tax reduces the price
of suburban housing, since a reduction in employment implies a reduction in housing
demand and, given the concavity of g, a reduction in p. Specifically, from (7),
∂p
g 00 ∂`
= −p 02
< 0.
∂tc
g ∂tc
(12)
Since migration equilibrium (1) requires that w and p move together unit for unit, it
follows that
∂w
∂p
=
< 0.
(13)
∂tc
∂tc
Suburban land rents are also depressed by an increase in the city property tax rate since,
by the envelope theorem,
∂Rs
∂p
=g
< 0.
(14)
∂tc
∂tc
Analogously, an increase in suburban property taxation raises the equilibrium wage rate
5 This
is true for standard production functions used in empirical studies, such as the CES.
7
w, which can be seen by differentiating (5) to get
∂w
∂`
∂kc
= f`` + f`k
∂ts
∂
∂ts
2
f`` fkk − f`k
=
|H|
|F |
=
> 0.
|H|
(15)
Remembering that the price of suburban housing and the wage rate must move together,
by (1), it follows that
∂p
> 0.
(16)
∂ts
Also, again using the the envelope theorem,
∂w
∂Rc
= −`
< 0,
(17)
∂ts
∂ts
that is, an increase in suburban taxation of property reduces land rents in the city.
4
Local Policy Choices: Rent Maximization and Rent Transfers
Public policies are determined through complex institutions that respond, to varying
degrees, to the interests of local households, businesses, workers, or bureaucracies, sometimes formally organized into lobbying or other pressure groups, sometimes acting through
voting for representatives or through referenda, through direct involvement in electoral
processes, and through financial contributions and other payments to political parties,
politicians, and others. No simple model can capture all of these complexities.
Economic analyses of policymaking, however, are generally grounded in the hypothesis
that agents attempt to influence policies that advance their own interests. By showing
how local policies can affect market prices in an integrated regional economy, the preceding analysis clarifies the gains and losses from different policy choices and thus the
economic incentives that may come to bear on the policymaking process.
Let us begin by noting that there are agents in the model whose welfare is unaffected
(or imperceptibly affected) by local policies. In particular, local policies have a negligible
impact on the net return to capital and on the net incomes of workers since the region
is small and open relative to the capital and labor markets in the rest of the world.6
6 Although the impacts of local policies on economy-wide returns to labor and capital are tiny, they are not literally zero.
In fact, a local tax on freely-mobile labor or capital can reduce the worldwide return to these resources by approximately
as much as the amount of local revenue collected – a non-negligible but highly diffuse global impact. See, e.g., Bradford
(1978) for a concise treatment.
8
Capital owners and workers are thus indifferent about local policies, and, within the
model, have no incentive to vote or otherwise participate in the local political process.
The only agents whose welfare is affected by local policies are the owners of immobile
resources which, so far, we have designated as “land” (Wildasin (2006)). Let us therefore
suppose that policies in each jurisdiction are chosen in accordance with the interests of
local landowners7 Let us therefore consider what policies might be chosen in order to
maximize the welfare of landowners (see also Fischel (2001)).
At this stage, it becomes important to consider the use of tax revenues. The most transparent hypothesis is that tax revenues are used solely to finance lump-sum transfers to
local landowners, the group whose interests are supposed to be served in the local policymaking process. This assumption, which is relaxed in subsequent sections, is imposed
here in order to suppress complications relating to other uses of revenues. In some applications, however, this assumption may be a reasonable first approximation, for instance
when governments can tax land directly or, indirectly, through the use of administrative
tools such as property assessment practices.
Given the assumption that property tax revenues are transferred to landowners, we may
define the net land rent in the city and the suburbs, respectively, as
Rcn = Rc + tc kc
Rsn = Rs + ts ks ,
which show the net incomes accruing to landowners in each jurisdiction, inclusive of the
proceeds of local taxation, and consider what policies maximize welfare, i.e., net land
rents, in the city and in the suburbs. These policies are the joint solutions of
M ax<tc > Rcn
(C)
M ax<ts > Rsn .
(S)
and
Consider first the solution of (C). Using the envelope theorem, the first-order condition
for this problem is
∂w
∂kc
∂Rcn
= −`
+ tc
=0
(18)
∂tc
∂tc
∂tc
with the second-order condition ∂ 2 Rcn /∂t2c ≤ 0 assumed to hold as a strict inequality.
Recalling (13) and (11a), we see that (18) can only be satisfied at t∗c > 0, where the
asterisk denotes the value of tc that maximizes net land rents.
7 As discussed further below, the immobile resource may be interpreted as some particular type of labor (e.g., lowskilled labor), or as some particular type of fixed capital (an “economic base” with long-lived capital built around a
specific industry), or in some other way. These different interpretations about the nature of the immobile resource give
rise to mutatis mutandis changes about what types of agents (low-skilled workers, industry lobbies, etc.) would seek to
influence local policymaking.
9
Suburban net land rents are likewise maximized when
∂p
∂Rsn
∂ks
=g
+ ts
= 0.
∂ts
∂ts
∂ts
(19)
Using (16), it is evident that this condition can only be satisfied when t∗s > 0.
If there are many identical suburbs, however, each of them takes p as exogenously given.
Under this assumption, the first term on the right-hand side of (19) vanishes, so that net
land rents in each suburb is maximized when ts = 0.
To summarize:
Proposition 1: To maximize the net returns to landowners, the city imposes a positive
tax rate on capital, i.e., t∗c > 0. Aggregate net returns to suburban landowners are also
maximized with a positive tax rate on capital, i.e. when t∗s > 0. The net incomes of
landowners in small suburbs, are maximized by setting a tax rate equal to 0.
The results in Proposition 1 contrast sharply with standard models of fiscal competition
in which there are no labor-market linkages between jurisdictions. When the revenues
from a property tax or other source-based capital tax can be returned in a lump-sum
fashion to the owners of immobile resources, and when a jurisdiction is small relative
to the world market for freely-mobile capital, no jurisdiction would choose to impose a
non-zero tax rate on capital. Here, all jurisdictions are assumed to employ only a small
portion of the world capital stock, and yet they have incentives to tax this freely-mobile
capital. They do so because of the economic linkages within the regional economy. When
the city taxes capital, it drives down suburban land rents, resulting in a rent transfer
from suburban to urban landowners. The same is true, in reverse, when the suburban
property tax rate is increased. If there are many suburban governments, however, and if
each is small relative to the entire regional economy, none can have a perceptible effect
on the price of suburban housing, on the urban wage rate, or on urban land rents, and
a suburban property tax then merely depresses the net land rent accruing to the owners
of land in any single suburb. Thus, in a world with a single city and many suburbs, the
model predicts t∗c > 0 = t∗s .
It should be noted that Proposition 1 presupposes that there do exist values of (tc , ts )
that maximize net city and suburban land rents. This assumption is relatively innocuous. Proposition 1 is otherwise quite general. In particular, only mild and standard
assumptions have been imposed on the production functions f and g.
10
5
Extensions: Property Taxes, User Fees, Public Goods, and
Welfare
The treatment of local policies in the preceding analysis has been deliberately simplified
in order to clarify the essential workings of the model in a stark form. Here, the model is
embedded in a richer framework, showing that how its essential findings survive in a much
more general context and highlighting their potential policy and empirical implications.
First, consider the expenditure side of local government policies. So far, tax revenues
have assumed merely to finance lump-sum transfers to the owners of immobile resources.
Suppose instead that each unit of government can raise revenues, if desired, through a
lump-sum tax Ti on the local immobile resource, i = c, s, in addition to a tax on local
capital at rate ti , and that it must spend an exogenously-fixed amount Ḡi on the provision
of a Samuelson-pure local public good. Assuming that the local budget must balance,
Ḡi = ti ki + Ti , and net land rents are given by
Rin = Ri − Ti = Ri − Ḡi + ti ki .
Suppose that the utility of workers depends on public good provision in either or both
jurisdictions in addition to earnings net of housing costs, as given by an indirect utility
function v(wi − p, Gc , Gs ), and that workers can obtain a utility level v̄ in the rest of the
world. Instead of (1), free mobility of workers now requires that v̄ = v(wi − p, Ḡc , Ḡs ).
This modification has no effect at all on the preceding analysis, since w − p is still
exogenously fixed by the condition of free labor mobility.
Next, suppose that suburban governments must provide a congestable public service to
their residents, that is, a public service whose cost rises as the size of the residential
population rises. (Education is one classic and important example of such a public
service.) For simplicity, suppose that the level of this service (“quality”) is exogenously
fixed, and that the cost of providing the service is strictly proportional to the local
population, requiring a public-sector outlay of Z = `z where z is expenditure per resident.
The local government budget constraint is now
Ḡs + `z = ts ks + Ts
(20)
so that net suburban land rents are given by
Rsn = Rs − Ts = Rs − Ḡs − `z + ts ks .
The value of ts that maximizes net land rents, t∗s , is now determined from the first-order
condition
∂p
∂ks
∂Rsn
=g
+ (ts − zg 0 )
= 0.
∂ts
∂ts
∂ts
11
In the case where suburban governments act atomistically, the first term on the righthand side vanishes which implies that t∗s = zg 0 , i.e., the local property tax rate is chosen
so that each resident pays a tax equal to the marginal cost of provision of the congestable
local public service. This implies that the lump-sum tax on the immobile resource is used
to finance any expenditures for the pure local public good. This is precisely the standard
result for the welfare-maximizing mix of taxes for the financing of a mix of pure and
congestable local public goods for an atomistic locality. If, on the other hand, there is
only one suburban government, or if many suburban governments coordinate their tax
policies, they will select a tax rate on mobile capital t∗s > zg 0 , that is, a tax rate in excess
of that needed to finance the incremental expenditures on congestable local public goods
provided for residents. Thus, in this richer specification, the proper interpretation of
Proposition 1 is not that the suburban property tax rate is literally zero when suburban
governments act atomistically, but rather that it is set so as to finance the incremental
cost of congestable local public services. If there are no pure local public goods, this
is equivalent to saying that the local property tax is just sufficient to cover the entire
cost of local public expenditures. In the non-atomistic case, the property tax rate is set
higher than this, helping to finance any expenditure requirement for pure local public
goods and, beyond this, to provide lump-sum transfers to the owners of local immobile
resources.
In a well-known paper, Hamilton (1975) discusses the use of zoning requirements by local governments that use property taxes to finance their public expenditures. Hamilton
interprets zoning requirements as a mechanism by which to insure that residents in a
locality cannot escape some of the burden of paying for local public services by buying
cheaper housing – houses that utilize less capital. The effect of zoning in that model, in
other words, is to make each household in a locality consume a fixed amount of housing,
which, in effect, has been assumed in (4) above. The preceding remarks regarding the
choice of t∗s when local governments provide congestable public services parallel wellknown findings in the literature on “fiscal zoning” in the tradition of Hamilton. In this
literature, the local property tax is sometimes called a “benefit tax”, which means, in
effect, that it serves as a user fee for the financing of a congestable local public service.
This result reappears in the present analysis under the assumption that suburban governments compete atomistically with one another. If they can coordinate their policies,
however, so as to act as a single unit within the regional economy, they will select a
property tax rate higher than this in order to effectuate a transfer of rents from urban
to suburban owners of the immobile resource.
As mentioned in Section I, the basic modeling framework used in the analysis of fiscal
competition has been used to study the implications of taxes on households, often simply
by reinterpreting the variables of the model. The same may be done in the present context. As an illustration, suppose that there are two types of labor, skilled and unskilled,
or high- and low-wage, that are employed in a city, and suppose that high-skilled workers
12
reside in suburbs while unskilled workers are immobile and reside in cities. Technically
speaking, this is only a minor variation on the preceding model, merely requiring that the
“immobile resource” in the city be reinterpreted to include unskilled workers. The policy
implications of the model in this case are, however, rather different. In particular, suburban property taxation now depresses not only urban land rents (assuming that urban
land constitutes one portion of the composite stock of immobile resources in the city),
as in (17), but also the earnings of immobile unskilled urban workers. The suburban
property tax, in this setting, transfers rents from low-wage urban workers to suburban
landowners. In this interpretation of the model, urban workers now have an incentive
to influence city policies, perhaps through voting, in order to increase their net incomes.
Positive city property taxes (t∗c > 0, as in Proposition 1) would reduce the fiscal burden
on urban residents of financing public goods and services in the city and could also help
to finance redistributive transfers – in cash, or in kind – for their benefit.
Finally, consider some of the welfare implications of Nash noncooperative equilibria in
this model. As we have noted, both city and suburban governments have incentives to
impose taxes on freely mobile capital, even if they have ideal lump-sum taxes at their
disposal. Since suburbs and cities are intrinsically asymmetric, Nash noncooperative
equilibria must generally be characterized by unequal tax rates on mobile capital, which
implies that the marginal productivity of capital in cities will differ from that in suburbs.
It follows that decentralized local tax policies result in inefficient allocation of capital
among localities, even when they compete atomistically in the economy-wide markets
for labor and capital. From a distributional perspective, it is also noteworthy that the
taxation of capital by many atomistic localities reduces the economy-wide net rate of
return on capital, provide that the aggregate supply of capital is fixed or, at least, not
perfectly elastic. Insofar as the aggregate stock of capital depends on the net rate of
return on capital, local property taxes not only distort the allocation of the stock of
capital among localities but also distort the incentives to supply capital.
6
Fiscal Reaction Functions
Let us now revert to the stripped-down model of Sections II-IV in which the property tax
is the sole revenue instrument at the disposal of local governments. Within this simplified
setting, it may be of interest to analyze possible strategic interactions between city and
suburban governments. This section presents some initial results, which may perhaps be
extended in future research.
One potentially interesting question concerns the non-cooperative determination of the
tax rates (t∗c , t∗s ) by the city and suburban governments, a question that has been studied
extensively in previous literature and that will be explored further here. Before turning to
13
the analysis, however, it should be noted that there is no necessarily compelling reason
to suppose that tax rates are the strategic variables over which competition occurs;
governments might just as well compete over expenditure levels, over the size of tax
bases, or other variables. Furthermore, it is worth recalling that fiscal competition occurs
in real time, and, indeed, many empirical studies have estimated the period-by-period
responses of policy interactions among governments. The simple static models discussed
here and in most of the theoretical literature obviously cannot provide a foundation for
the evolution of policies over time.
With these provisos in mind, let us follow much of the previous literature and consider the
non-cooperative determination of city and suburban tax rates. Following the analysis of
previous sections, it might be natural to assume that policies are chosen to maximize net
land rents, as discussed above. Two cases may be distinguished, depending on whether
the suburbs are numerous and act atomistically or, instead, act as a single unit. In the
former case, as shown in Proposition 1, t0s = 0, and, in this case, the only non-trivial
problem is to determine the city tax rate that solves (C) when ts = 0. In the latter case,
it is necessary to find the tax rates that simultaneously solve the problems (C) and (S).
The customary approach in the literature is to use the first- and second-order conditions
for optimal local policies to solve for the Nash equilibrium. In the present context, it is
possible to solve (18) implicitly for t∗c as a function τc (ts ) of the suburban tax rate ts , and,
likewise, to use the first- and second-order conditions for a solution of (S) to determine
t∗s as a function τs (tc ) of tc , in a neighborhood of a Nash non-cooperative equilibrium
(t∗c , t∗s ). In particular, the “reaction functions” τi (tj ) must satisfy
τi0 (tj ) = −
∂ 2 Rin /∂ti ∂tj
∂ 2 Rin /∂t2i
(21)
where the second-order conditions for a maximum insure that the denominator on the
right-hand-side is negative. The difficulty, however, is that the numerator of (21) cannot
be signed in general.
This is a typical problem for theoretical models of strategic fiscal interactions. The usual
approach in the literature is to impose strong (and, unfortunately, empirically poorlyjustified) assumptions on functional forms in order to obtain more definite results. The
most common assumption that has been used in the standard tax competition models,
which assume that there is only a single variable productive factor, is that production
functions are quadratic in that one input.8 That approach cannot be applied here,
however, at least in any simple way, as the complementarity of the two productive inputs
(kc , `) in the city production function is essential to the model. In future analysis, it may
8 See, e.g., Wildasin (1991)). As noted by Keen and Konrad (2013), “In the asymmetric case, ..., general results are hard
to find. For that one must look to further restrictions on functional form, as for example, assuming a quadratic production
function”. (The present model is, of course, intrinsically asymmetric.)
14
be possible to obtain additional results using numerical methods, but that task is not
pursued here.
It is nevertheless still possible to obtain some reasonably general analytical results that
highlight some crucial and novel features of city/suburban tax competition. To do so,
let us focus first on strategic tax base interactions.
As already observed, an increase in property taxation in one locality has a negative
impact on economic activity in the other. Specifically, holding the suburban tax rate
fixed, an increase in the city tax rate on capital reduces the size of the labor force and
thus the size of the suburban housing stock and the suburban property tax base, as
shown in (11b) and (14). Similarly, an increase in the suburban tax rate ts , holding
tc fixed, causes the levels of employment and of the capital stock in the city to fall, as
shown in (11c) and (17). This is a striking contrast with the canonical tax competition
models with mobile capital, in which a tax increase in one jurisdiction causes an outflow
of capital to one or more other jurisdictions and thus increases the size of the capital
stock(s) and the level(s) of output elsewhere. In the present model, it is still the case
that local taxes cause capital (and labor) outflows to the rest of the economy, and thus
an increase in capital stocks, employment, and output elsewhere. However, local taxes
reduce economic activity and tax revenues in neighboring jurisdictions.
Now suppose that local governments use their revenues to finance provision of local public
goods, rather than paying lump-sum transfers to landowners and, initially, suppose that
these are pure local public goods that benefit landowners. Under these assumptions, the
local governments face the budget constraints
Gi = ti ki , i = c, s.
(22)
Suppose that local governments choose their tax rates non-cooperatively to maximize
the utility of local landowners. Landowner preferences for local public goods now must
be taken into account in the choice of tax policies, as landowners face tradeoffs between
public and private consumption, with the latter depending on land rents. Assuming a
utility function ui (Gi , Ri ), the first-order condition for optimal local policy is
M RSi −
∂Ri
=0
∂ti
(23)
where M RSi = uiG /uix is the marginal rate of substitution between public and private
consumption for local landowners. It follows from (23) that local revenues must be
increasing in the local tax rate for each jurisdiction, i.e., ∂Ri /∂ti = 0, at an optimal local
policy.
The demand for local public goods may be more or less elastic, depending on the form
of local preferences. In one extreme case, the demand may be highly or even perfectly
15
inelastic, that is, each locality chooses whatever tax rate is needed to finance a nearly
or completely fixed level of public expenditures Ḡi . Although this is certainly a special
case, it is at least illustrative. In this special case, each locality must in effect raise some
fixed (or nearly fixed) level of revenues,9 that is, it must set its tax rate ti such that
Ri (ti , tj ) = Ḡi ,
i = c, s.
(24)
This equation may be solved for the constant-revenue reaction function τi |Ḡi (tj ), showing
how ti must vary with tj . We now have
Proposition 2: Local constant-revenue reaction functions are upward-sloping in the
neighborhood of any Nash non-cooperative equilibrium, that is,
dτi
| > 0.
dtj Ḡi
This result follows (see (14) and (17)) from ∂Ri /∂ti > 0 > ∂Ri /∂tj .
Although a more thorough analysis of reaction functions must remain on the agenda for
future research, Proposition 2 at least provides a baseline reference point. It confirms
that changes in the taxation of freely-mobile capital by a small and open locality increase
the preferred tax rate in a neighboring that also is small and open relative to external
factor markets.
7
Conclusion
As noted at the outset, the literature on fiscal competition, both theoretical and empirical,
displays no consensus about whether jurisdictions act strategically or atomistically in
setting their policies.
Focusing only on the issue of factor mobility, the foregoing analysis has shown how
strategic fiscal interactions can arise among economically-linked localities – specifically,
local economies in metropolitan areas, where households reside in suburban locations
and work in central cities – even when these localities, and the entire economic region of
which they are a part, are atomistic competitors in the markets for freely mobile labor
and capital. Despite their small size and their corresponding inability to use local policies
to affect the “terms of trade” on which they obtain mobile resources, local governments
can still use their fiscal policies to transfer rents from the owners of immobile resources in
9 It could also conceivably be the case that each locality faces a regulatory mandate to raise some specified level of
revenues. Many local governments in the US have been forced to meet specified expenditure levels as a result of judicial
action, especially in the sphere of education spending.
16
neighboring localities. Since the number of neighboring localities within a metropolitan
area is comparatively small, these governments choose their policies strategically. The
equilibrium of a system of localities acting in this way is sure not to be first-best efficient,
as mobile resources are taxed unequally and are not allocated with maximum efficiency.
Although detailed analysis of strategic interactions among localities must be left for
future research, it is clear that the economic nature of these interactions is quite different
from that discussed in previous research. In standard models, strategic interactions arise
because the taxation of a mobile resource shifts the tax base from one jurisdiction to its
strategic rival. Here, by contrast, a local tax reduces the tax base of neighboring localities.
Although these cross-effects of local policies differ in sign, it is still possible that fiscal
reaction functions are upward-sloping, as, for example, if localities are committed to
raising target amounts of revenues regardless of the tax policies of their rivals.
All models of fiscal competition must, in the end, be built upon some hypothesis about
how local policies are determined. Under the assumption that labor and capital are freely
mobile and that localities are small and open, it is natural to postulate that local policies
reflect the interests of the owners of immobile resources. The analysis here has focused on
land as an immobile resource, but we have noted that the basic modeling approach can
also be applied in situations where other productive resources – low-skilled workers, for
example – are immobile. A more satisfying modeling strategy, however, is to recognize
that labor and capital are, in truth, neither perfectly mobile nor perfectly immobile.
Rather, while migration and investment flows among jurisdictions tend to equalize net
factor returns over time, local stocks of labor and capital do not adjust instantaneously
to changes in local policies or other local economic conditions. One potentially fruitful
but challenging path for future research, then, is to investigate fiscal competition among
economically-linked jurisdiction in an explicitly dynamic framework with endogenouslydetermined migration and capital flows (see, e.g., Wildasin (2011)). In such a setting,
quasi-rents accrue to the owners of imperfectly mobile resources such as workers and the
owners of local capital. Assuming that these agents discount the future, they then have
incentives to influence local policies, even if all quasi-rents disappear in the long run.
17
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