The structure of each level of government in the United States has changed over the last 200 years. Wallis (2000) has presented empirical evidence that relates the dominance of each level not to the functions government decides to undertake (the expenditures it commits to), but to the costs and benefits of the financial instruments each level has available (the way each level extracts revenues). In this paper we provide theoretical evidence for this hypothesis. We show why two different levels of government (e.g. state and federal) would not want to use a common instrument to finance the same good.

Maravall Rodríguez, Carlos

English

Research Papers in Economics

 
 
Working Paper  05-22   
Economics Series 13 
April 2005 
 
 
Departamento de Economía 
Universidad Carlos III de Madrid 
Calle Madrid, 126 
28903 Getafe (Spain) 
Fax (34) 91 624 98 75 
 
 
 
 
 
FISCAL FEDERALISM WITH A SINGLE INSTRUMENT TO FINANCE 
GOVERNMENT 
 
Carlos Maravall  Rodríguez  
1
 
 
  
 
Abstract 
 
The structure of each level of government in the United States has changed over the last 200 
years. Wallis (2000) has presented empirical evidence that relates the dominance of each level not 
to the functions government decides to undertake (the expenditures it commits to), but to the costs 
and benefits of the financial instruments each level has available (the way each level extracts 
revenues). In this paper we provide theoretical evidence for this hypothesis. We show why two 
different levels of government (e.g. state and federal) would not want to use a common instrument 
to finance the same good. 
 
 
 
Keywords: Fiscal Federalism; Community Models; Publicly Provided Private Goods. 
 
JEL Classification: D78, E62, H42, H77 
 
                                                           
1   Carlos Maravall,  Departamento de Economía. Universidad Carlos III de Madrid  C/ Madrid 
126, 28903 Getafe (Madrid). E-mail:  carlos.maravall@uc3m.es
 
 Fiscal Federalism with a Single Instrument
to Finance Government
Carlos Maravall Rodríguez∗
March 15, 2005
Abstract
The structure of each level of government in the United States has changed over the
last 200 years. Wallis (2000) has presented empirical evidence that relates the dominance
of each level not to the functions government decides to undertake (the expenditures it
commits to), but to the costs and beneﬁts of the ﬁnancial instruments each level has
available (the way each level extracts revenues). In this paper we provide theoretical
evidence for this hypothesis. We show why two diﬀerent levels of government (e.g. state
and federal) would not want to use a common instrument to ﬁnance the same good.
Keywords: Fiscal Federalism; Community Models; Publicly Provided Private Goods.
JEL Classiﬁcation: D78, E62, H42, H77
∗carlos.maravall@uc3m.es. Departamento de Economía, Universidad Carlos III de Madrid, 28903 Getafe
(Madrid).
11 Introduction
In the United States the structure of government has changed over the last 200 years. Wal-
lis (2000) has presented empirical evidence that relates (i) the growth of government to the
functions it decides to undertake (the expenditures it commits to) but (ii) the dominance of
each level (State 1790-1840, Local 1840-1933 and Federal 1933-) to the costs and beneﬁts of the
ﬁnancial instruments each level has available (the way each level can extract revenues). In this
paper we provide theoretical evidence for this second hypothesis. In particular, we show why
two diﬀerent levels of government, deﬁned by the extent of their franchise (e.g. a country made
up of diﬀerent communities with a central government and community governments) would not
want to use a common instrument to ﬁnance the same good.
It is not immediately obvious why two diﬀerent levels of government would not want to
use the same instrument to ﬁnance themselves. For example, Wallis (2000) himself has argued
that:
“Governments raise revenues and spend money. Raising revenues is politically
costly, but spending money generates political beneﬁts. [...] When there are multiple
levels of government, with multiple revenue instruments and multiple purposes on
which money can be spent, then marginal costs and beneﬁts should be equated
across all governments, revenue sources, and expenditures functions.”
(pp. 64).
T h er e a s o ni st h a tt h eb e n e ﬁt from using an instrument at one level is at the expense of
another: marginal costs and beneﬁts cannot be aligned at diﬀerent levels of government. The
2use of one instrument at one level at the expense of another implies that marginal conditions
will remain unequal and there will be corner, not interior solutions.
Related Literature
The capacity that centralized government has to extract resources from its citizens has been a
source of concern for political scientists since, at least, the time of the Federalist papers. The
recent work of Persson and Tabellini (1996) has analyzed this problem from the perspective
of redistribution from rich to poor regions. They show that a system of government which
is centralized (a federation, as the U.S.) will provide higher levels of redistribution than a
system of government in which the diﬀerent states bargain over intergovernment transfers (a
confederation, as the E.U.). The complaints inhabitants in rich regions in Germany, Italy, and
Spain, express against the beneﬁts their poor counterparts get because they belong to the same
country provide an example of this problem.
In contrast, the study of Fiscal Federalism (Oates, 1972) or Economic Federalism (Inman
and Rubinfeld, 1997) considers the possibility that government can be designed with diﬀerent
levels (local, state and federal in the U.S.) to optimally provide a good or service. The limits
that deﬁne the activities performed by a higher or a lower level of government, are determined,
among others, by intrastate externalities, the geographical diﬀerences in tastes, etc. The recent
surveys of Inman and Rubinfeld (1997), Oates (1999), and Wallis (2000) give an overview of
this literature.
This paper presents one clariﬁcation with respect to how much we can expect from the
latter principle, given the power that centralization entails. In particular, it does not negate
3the possibility of an optimal assignment of expenditures across diﬀerent levels of government,
but it asserts that it better be that the diﬀerent levels collect their revenues with diﬀerent
instruments.
2 The Model
There is a population of individuals who only diﬀer in their initial endowment of income, yi.
The density function of income across the whole country is f, with median, ymed,a n dm e a n ,
_
y.
Mean and median income satisfy the inequality ymed <
_
y as is observed in actual distributions.
Individuals have preferences over two goods: a numeraire private good (consumption) and a
publicly provided private good, c and g, respectively. Preferences are:
u(c,g)
with uc,u g > 0 and ucc,u gg < 0,i . e . u is strictly increasing, and strictly quasi-concave. All
individuals value a positive level of consumption and public provision, i.e. lim
c→0 uc = lim
g→0 ug = ∞.
The good g is ﬁnanced with proportional taxes on personal income, yi, across the country,
tf, and within each community, ti. Initially, no restrictions are imposed on tax schedules,
allowing them to be positive or negative, i.e. progressive or regressive: tf,t i ∈ <.O n l y
feasibility conditions will constrain these. The country includes all individuals in the economy,
whilst communities are mutually exclusive and collectively exhaustive (i.e. individuals cannot
belong to two communities at a time and they must belong to at least one). For simplicity,
I consider communities that are perfectly homogenous. This allows us to focus on issues of
distribution across communities, instead of within.
4In community i an individual is constrained, as (s)he cannot consume more income than
is available, and the community is constrained as it cannot allocate more funds than there are
available:
ci 6
¡
1 − t
f − t
i¢
yi (1)
g
i 6 t
f_
y + t
iy
i. (2)
Note that as communities are homogenous, mean income is equal to the community’s represen-
tative individual’s income and, as uc,u g > 0, in equilibrium both constraints will be satisﬁed
with equality. Moreover, as lim
c→0 uc = lim
g→0 ug = ∞,i tw i l la l s ob et r u et h a tc,g > 0, i.e.
t
f + t
i < 1,
t
f_
y + t
iy
i > 0.
Finally, individual feasibility constraints require that an individual cannot be taxed more
income than (s)he has available:
t
f,t
i,t
f + t
i 6 1.
The problem with no feasibility constraints
Unless mean income in the federal level and the community where a voter lives are equal, the
diﬀerence between them can be used to ﬁnance the good at less expense than if there was a
single level of government. For the sacriﬁce of being taxed by any of the two levels is the same
(see equation (1)), but the return is higher for one than the other (see equation (2)), as long as
their mean incomes diﬀer, and the amount taxed at one level, can be neutralized by the other.
Moreover, even if the federal tax is completely neutralized by the state tax, ti = −tf,w h e n
5yi <
_
y funds are increasing in the federal level tf,a sgi = tf_
y + tiyi = tf ¡_
y − yi
¢
is increasing
in tf.T h i si m p l i e sag a i nw i t hn oc o s t ,a si fti = −tf, ci =
¡
1 − tf − ti¢
yi = yi.
Proposition 2.1 The preferred tax rates of individuals when there are no feasibility constraints
are:
(i) if yi <
_
y: tf = ∞,t i = −∞,w i t htf + ti < 1 and tf_
y + tiyi > 0,
(ii) if yi >
_
y: tf = −∞,t i = ∞, with tf + ti < 1 and tf_
y + tiyi > 0.
Proof. As long as we do not consider the individual feasible tax constraints tf,t s 6 1,t h e
problem has no solution. The Kuhn Tucker conditions show that the ﬁrst order conditions of
max
tf,ti u
£¡
1 − t
f − t
i¢
yi,t
f_
y + t
iyi
¤
s.t.
t
f + t
i < 1,
t
f_
y + t
iy
i > 0.
cannot hold in space tf × ti as
−uc (ci,g i)yi + ug (ci,g i)yi =0
−uc (ci,g i)yi + ug (ci,g i)
_
y =0 .
and it is immediate to note that both equations cannot hold unless yi =
_
y.
As there can be neutralization at any level of taxation, and the higher the level of taxation,
the higher the level of funds available, a voter who is decisive can ﬁnance the good at no cost.
The problem is analogous to that of an individual who has two assets available with the same
6variance but diﬀerent expected value. A pure arbitrage condition allows for an inﬁnite (!) proﬁt
by short selling the asset with the lower return (indebting oneself with it) and leveraging on the
asset with a higher return (investing in it). The spread is pure proﬁta n dw i t h o u tac o n s t r a i n t ,
it can be made inﬁnite.
Figures 1 and 2 present the solution with feasibility constraints, but it is immediate to
note the nature of the problem if one removes them.
Feasibility constraints
The intuition described above shows that in this economy the population is divided into two
groups with respect to their preferences over taxes: those who want as high a federal tax as
possible and as low a state tax as possible, i.e. those with with yi <
_
y,a n dt h o s ew i t hyi >
_
y
who want as low a federal tax as possible and as high a state tax as possible. By assumption,
the number of individuals in the former group dominates the latter as ymed <
_
y; hence the
federal tax will be positive. Is it possible to be more speciﬁc about the federal tax? And, can
we determine the state schedules? Indeed we can, once we introduce feasibility constraints.
Proposition 2.2 The preferred tax rates of individuals are:
(i) if yi <
_
y: tf =1 , ti < 0 s.t. tiyi = constant, tf + ti < 1 and tf_
y + tiyi > 0,
(ii) if yi >
_
y: tf < 0, ti =1 , with tf + ti < 1 and tf_
y + tiyi > 0 satisﬁed.
In equilibrium, as ymed <
_
y, taxes are set as in (i).
7Proof. The problem to solve for each individual is
max
tf,ti u
£¡
1 − t
f − t
i¢
yi,t
f_
y + t
iyi
¤
s.t.
t
f 6 1, with multiplier α1 > 0,
t
i 6 1, with multiplier α2 > 0,
t
f + t
i < 1,
t
f_
y + t
iy
i > 0.
The set deﬁned by the constraints in tf × ti space is shown in ﬁgure 1 when yi >
_
y and
ﬁgure 2 when yi <
_
y. Utility is increasing in the North-West direction, as shown in ﬁgure 1, as
when ti = −tf if yi >
_
y utility is decreasing in tf.I na n a l o g y ,ﬁgure 2 shows what is true for
av o t e rw i t hyi >
_
y. In this case, utility is increasing away from the origin in the South-East
direction.
The Kuhn-Tucker conditions provide the same information. Ignore the ﬁrst two inequality
constraints, by considering their interior, as lim
c→0 u0 (c)=l i m
g→0 v0 (g)=∞.T h e ﬁrst order
conditions are
−uc (ci,g i)yi + ug (ci,g i)
_
y = α1,
−uc (ci,g i)yi + ug (ci,g i)yi = α2.
For those individuals with yi <
_
y we ﬁnd that tf =1as α1 >α 2 > 0 because α1 − α2 =
ug (ci,g i)
¡_
y − yi
¢
> 0. With respect to ti,w eﬁnd, ﬁrst, that as tf =1and tf + ti < 1,t h e n
ti < 0 (and α2 =0 ). Second, if tf =1all income is equally redistributed through the federal
8tax. But, if all income is redistributed, then all individuals have access to the same amount
of income, ex-post, to allocate to the publicly provided private good or the numeraire. As
we have considered individuals who do not diﬀer in their preferences, only in their income,
then if they all have access to the same pool of ex-post income, then they will all want the
same allocation of numeraire and publicly provided private good. That is, given tf =1 ,t h e
solution to u
£
−tiyi,
_
y + tiyi
¤
must be identical across individuals. Thus, we can conclude that
tiyi = tjyj,∀i,j. For this to be true then state taxes must be decreasing, in absolute value, in
income. That is,
dti
dyi
= −
[ucc (ci,g i)+ugg (ci,g i)]tiyi
[ucc (ci,g i)+ugg (ci,g i)](yi)
2 > 0,
and, given that state taxes are negative, they are increasing in income, and, hence, decreasing
in absolute value. Finally,
d(tiyi)
dyi
=0 , and hence
ci = c,
gi = g.
For individuals with yi >
_
y it is immediate to note that ti =1and, as tf +ti < 1,t h e ntf <
0. However, we cannot go further than this analysis without making further assumptions on
their relative preferences between the two goods. But, given that a majority of the individuals
satisfy ymed <
_
y the analysis for these individuals is what is informative as individuals with
yi >
_
y will take tf =1as a given.
Figure 3 is a graphical description of this solution and ﬁgures 1 and 2 present the optimal
solution for each set of voters in the population.
93C o n c l u s i o n
How is a publicly provided good to be ﬁnanced? The literature on ﬁscal federalism suggests
that if there are diﬀerent levels of government, its provision will be Pareto superior to that when
it can only be provided at a uniform rate by a central government. Similarly, with a political
economic context in mind, Epple and Romano (1996) have shown that public provision of a
private good supplemented by private purchases is preferred by a majority to pure public pro-
vision. Fernández and Rogerson (2003) reinterpret private provision as a supplement provided
by an individual’s community using the same instrument of funding as the central government.
If the community is homogenous, as they assume, then they share the same result with Epple
and Romano (1996). However, the analysis implicitly assumes that each level of government
is restricted to use progressive taxes (i.e. tf,t i > 0 in our model), a counterfactual assumption
(Klor, 2003). Instead, if no restrictions beyond feasibility conditions are imposed on these, it
might be of little practical use to have several levels of government to ﬁnance a good. A single
level, the central government, will provide all the funding, as a majority of individuals who live
in poor communities will prefer central funding using the rich communities’ income. This is
shown in this paper, i.e. interregional redistribution funds the whole “cake” and community
taxes are used to transfer funds across diﬀerent categories of goods within a region. Hence, to
avoid this expropriation of the rich communities by the poor regions, the former will have an
interest in developing diﬀerent ﬁscal instruments for each level.
10References
[1] Epple, D., Romano, R.E. 1996. “Public Provision of Private Goods.” Journal of Political
Economy, 104: 57-84.
[2] Fernández, R., Rogerson, R. 2003. “Equity and Resources: An Analysis of Education
Finance Systems.” Journal of Political Economy, 111: 858-97.
[3] I n m a n ,R . P . ,R u b i n f e l d ,D . L .1997. “Rethinking Federalism.” The Journal of Economic
Perspectives, 11: 43—64.
[4] Klor, E.F. 2003. “A Positive Model of Overlapping Income Taxation in a Federation of
States.” mimeo, Hebrew University of Jerusalem.
[5] Oates, W.E. 1972. Fiscal Federalism. New York, NY: Harcourt Brace Jovanovich.
[6] Oates, W.E. 1999. “An Essay on Fiscal Federalism.” Journal of Economic Literature, 37:
1120-49.
[7] Persson, T., Tabellini, G. 1996. “Federal Fiscal Constitutions: Risk Sharing and Redis-
tribution.” Journal of Political Economy, 104: 979-1009.
[8] Wallis, J.J. 2000. “American Government Finance in the Long Run: 1790 to 1990.” The
Journal of Economic Perspectives, 14: 61—82.
11t f
1
-1
t f  y + t i yi = 0
Figure 1
t i
u
t f = 1
t i = 1
Preferences and constraints
of a voter with yi >  y
t f + t i = 1
-1 1
•
Optimumt f
-1
t i
u
Figure 2
1
t f = 1
t i = 1
  y
  yi
t f + t i = 1
-1 1
•
Optimum
Preferences and constraints
of a voter with yi <  y
t f  y + t i yi = 0t f
Figure 3
poor
t i
rich
Tax schedules:
 Federal: yi < y are a
majority, & set t f = 1,
State: complete equality
ti yi = ty, as rich set a
lower ti, in absolute
value, than poor.
-1 1

Fiscal federalism with a single instrument to finance government.

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Fiscal federalism with a single instrument to finance government.

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