Optimal Federal Taxes with Public Inputs Author(s): Diego Martínez Source: FinanzArchiv / Public Finance Analysis, Vol. 64, No. 4 (December 2008), pp. 422-433 Published by: Mohr Siebeck GmbH & Co. KG Stable URL: http://www.jstor.org/stable/40913199 . Accessed: 13/06/2014 07:46 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp . JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. . Mohr Siebeck GmbH & Co. KG is collaborating with JSTOR to digitize, preserve and extend access to FinanzArchiv / Public Finance Analysis. http://www.jstor.org This content downloaded from 62.122.77.48 on Fri, 13 Jun 2014 07:46:16 AM All use subject to JSTOR Terms and Conditions
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Optimal Federal Taxes with Public InputsAuthor(s): Diego MartínezSource: FinanzArchiv / Public Finance Analysis, Vol. 64, No. 4 (December 2008), pp. 422-433Published by: Mohr Siebeck GmbH & Co. KGStable URL: http://www.jstor.org/stable/40913199 .
Accessed: 13/06/2014 07:46
Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp
.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact [email protected].
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422 FinanzArchiv/ Public Finance Analysis vol.64 no. 4
Optimal Federal Taxes with Public Inputs Diego Martinez*
Received 10 November 2007; in revised form 2 June 2008; accepted 13 October 2008
This paper deals with the solution to vertical expenditure externalities in a federation with two levels of government sharing taxes. Under these circumstances, the Nash equi- librium does not satisfy the condition for production efficiency in the provision of public inputs. This vertical expenditure externality is removed when the federal government, behaving as Stackelberg leader, chooses the optimal tax rate on labor income. The sign of this tax rate depends on the elasticity of marginal productivity of the public input with respect to employment. Moreover, the previous result that the two vertical (tax and expenditure) externalities are independent of each other is confirmed here.
Keywords: vertical externalities, public inputs, federal taxes
JEL classification: H 2, H 4, H 7
1. Introduction
The study of interactions between different levels of government has tradi- tionally been focused on vertical tax externalities. As is well known, they arise when taxes of one level of government affect the tax revenues of an- other level of government. Their origin lies in the federal version of the problem of commons, which usually leads to overexploitation of tax bases and to excessively high taxes. A number of papers have dealt with the effi- ciency implications of this issue, highlighting its consequences for the fiscal gap (Boadway and Keen, 1996; Kotsogiannis and Martinez, 2008), the dif- ferences between Leviathan and benevolent governments (Flowers, 1988; Johnson, 1991), the existence of heterogeneous agents and redistribution (Boadway et al., 1998), or the qualifications that have to be made when fiscal competition at the horizontal level is considered as well (Keen and Kotsogiannis, 2002).
* I am very grateful to G Kotsogiannis for his intensive work on this paper. I have ben- efited from comments by T. Aronsson, M. A. López, the editor Alfons J. Weichen- rieder, two anonymous referees, and seminar participants at the European Central Bank, Umea University, University Pablo Olavide, Universität Autonoma de Barcelona, 60th Congress of the IIPF, IEB Workshop on Fiscal Federalism, and XIII Spanish Meeting on Public Economics. The usual disclaimer applies. I acknowledge the financial support from the Spanish Ministry of Science and Technology (Project No. SEC 2006-04803).
However, this general prediction of overtaxation must be qualified when ad valorem taxes are involved. While it is commonly accepted that specific taxes lead to overtaxation, that is, to inefficiently high tax rates, the conclusion may be the opposite in the case of ad valorem taxes. The intuition behind this fact can be clarified if we focus on labor taxes. With specific taxes, it is easy to see that the tax base (employment) always decreases when tax rates increase. If, for instance, the federal government decides to levy a higher tax rate on a tax base shared with the states, the federal revenues will probably increase because the effect of raising the tax rate on revenues overcomes the negative effect of a smaller tax base1. But state revenues will decrease as long as the same state tax rates are levied on smaller tax bases. This negative effect is the reason why states underestimate the marginal cost of public funds and, consequently, set inefficiently high tax rates.
Things are quite different with ad valorem taxes. Note that, in this case, the tax base is the wage income, that is, employment times wage. As a result of increasing the federal tax rate, similarly to the case of specific taxes, the employment decreases but the wage may rise because of the smaller labor supply2. Therefore, it is possible to find increases in the state tax bases and in their tax revenues after the federal government has set higher tax rates on wage income. The situation is the opposite of specific taxes: the perceived marginal cost of public funds is higher than the true marginal cost, and accordingly, state tax rates are inefficiently small.
On the other hand, vertical expenditure externalities have been less studied. These situations appear when the expenditures decided by one level of government affect other levels' revenues. The case of productivity- enhancing public spending (say, public infrastructure) is a good example of this. A highway built by a state government has a clear impact on the productivity of production factors and consequently on tax revenues levied by federal and local authorities. The point here is that things become more complex when vertical expenditure externalities are involved. Indeed, public inputs have a positive effect on labor productivity and hence on income taxes, but the profit tax base may either increase or decrease, affecting ambiguously the federal and local tax revenues based on rents.
Dahlby (1996) finds that the federal government can overcome vertical expenditure externalities by providing a matching grant to states equal to the additional federal revenue that is generated from each dollar spent by states on productivity-enhancing expenditures. Dahlby and Wilson (2003) show how the government providing the public input may overestimate or
1 A welfare-maximizing government would not raise tax rates to a point where tax rev- enues decrease. Consequently, tax rates always will fall on the upward-sloping part of the Laffer curve.
2 This is true assuming that the demand for labor is inelastic (Dahlby and Wilson, 2003).
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underestimate the marginal benefit, leading to inefficient provision. To undo this externality and replicate the second-best outcome, they propose to offer the state governments a matching grant that is defined on the basis of the federal tax rates on labor income and profits.
This paper extends the contribution of Dahlby and Wilson (2003) in two directions. First, the second-best outcome is replicated here with the federal government behaving as a Stackelberg leader; this implies a more elaborate framework than that of Dahlby and Wilson (2003), with the federal gov- ernment moving first and taking account of the states' reaction functions with respect to the federal policy variables. Second, their finding (in their Proposition 3) that the vertical tax and expenditure externalities are inde- pendent of each other is confirmed here, but using an alternative approach. Instead of arguing in terms of the bias in the provision of public inputs and its relationship with the tax externality as they do, I use separately two con- ditions neutralizing both vertical externalities by replicating the second-best outcome.
Therefore, this paper shows how the federal government can replicate the second-best unitary outcome in the provision of public inputs. The high- est level of government sets an optimal tax rate on labor income, whose sign depends on the elasticity of marginal productivity of public input to employment: if this is elastic, the federal government should tax the labor income; if inelastic, the federal government ought to subsidize this tax base. The type of public input entering the production function (factor- or firm- augmenting) also matters in defining the federal tax rate. Additionally, the paper finds that the two vertical externalities have to be faced by the federal government independently each other.
After this introduction, the paper sets up the general framework of the model. Section 3 obtains the optimal solutions for the provision of public inputs and public goods in a unitary country, serving us as a benchmark that can be compared with the fiscal decisions taken by states in a federal country. Section 4 describes how the federal government can replicate the unitary outcome, and finally section 5 concludes.
2. The Theoretical Framework
The model I use is simple and well known from Boadway and Keen (1996), in which two levels of government occupy the same tax bases on labor. How- ever, by contrast to Boadway and Keen (1996), two new relevant features are included here. First, instead of using specific taxes on labor, I consider ad valorem taxes on labor income. In such a case, the vertical tax externality can be positive, and overlapping tax bases may result in inefficiently low tax
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rates. Second, this paper deals with public inputs, affecting the productivity of labor, which means scope for vertical expenditure externalities. In a sense, the theoretical framework I present here is a mix between Boadway and Keen (1996) and Dahlby and Wilson (2003).
In particular, I characterize a model where different levels of government provide two types of public expenditure. The federal country consists of k (symmetric) states, populated by nk identical, but immobile, households. Each representative household has the following utility function:
k(x, /) + 5(G) , (1)
where x is a private good (and numeraire), / is labor, and G is a federal public good. The subutility u(x, I) has the usual properties (quasiconcave, increasing in jc, and decreasing in /), and B(G) is increasing and concave.
The representative consumer maximizes (1) subject to the constraint x = (1 - r)wl, where r is the tax rate on labor income and w denotes the gross wage rate. It yields the labor supply l(w), where w = (1 - t)w is the net wage. It is assumed that l'{w) > 0.3 The indirect utility is then given by v(vv) = u(wl(w), /(vv)), with V = uxl by Roy's identity.
Each state is endowed with the same amount of some fixed factor. Output in each state is produced by applying the services of labor and public input to the fixed factor according to the technology /(n/, g), with g being the state public input. This production function has the usual properties/L,/g,/Lg > 0, fLg = /gL, and fLL,fgg < 0, with L = nl. Output can be used for x, g, and G. The private sector maximizes profits, given by it = /(L, g) - wL, and thus chooses a labor demand that satisfies
fL(L,g) = w. (2)
On this basis, and given /(vv), the equilibrium gross wage rate w(l - r, n, g) can be obtained. For later use, it can be proved that wT > 0 and wg > 0. The positive sign of wT comes from differentiating (2) totally:
-fLLnl'w +fLLtïl'(l - t)wt -wt = 0. (3)
Solving for wT gives -fLLnl'w
wT = - , (4) l-fLLnl'l-T)
which is positive given the properties of the production function. The positive sign of wg is obtained in a similar way. Differentiating (2), totally, we have
kg +fLLnl'{' - r)wg -wg = 0,
3 A subscript denotes the derivative of a function of several variables, whereas a prime de- notes the derivative of a function of one variable.
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w' = wi?(i-rr (5) which is positive in view of the properties of the production function.
Comparative statics on profits (rents) Jt gives nx = -nlwT < 0 , (6)
ng=fg- nl [fLg + (1 - r) fLLnrwg] ^ 0 . (7) The intuition behind the ambiguity of the sign in (7) is clear. Additional units of public input increase production, and consequently it, but the positive effect of g on wages through improving labor productivity may reduce the rents4.
3. Governments and Vertical Externalities
As is usual in fiscal federalism literature, the analysis now aims at obtaining the equilibrium solution that would be achieved by a unitary country. This will serve as a benchmark for efficiency comparisons when fiscal policies are chosen by different levels of government. Equilibrium in a unitary country involves maximization of v(w) + B(G), choosing r, G, g, subject to the con- solidated budget constraint G + kg = nkrw(l - r, n, g)l(w) + ji (1 - r, n, g).
From the first-order conditions of this optimization problem, it is straight- forward to show that the optimality rules for the provision of the national public good G and the state public input g are given, respectively, by
nkB'jG) 1 "V =
Pf' <8>
h = ! • <9> Equation (8) simply states that at the unitary optimum the tax rate r is set such that the sum of the marginal rates of substitution between the federal and the private good x must be equal to the marginal cost of public funds (MCPF), given by 1/(1 - xwl' '//). Equation (9) is the condition for production efficiency in the public sector, familiar from Diamond and Mirrlees (1971). In essence, it means that, at optimum, the marginal productivity of the public input is just equal to its marginal cost of production, which is 1 in the present model; and that occurs in spite of using distortionary taxation.
I turn now to the characterization of the equilibrium when different levels of government are involved in deciding on fiscal policy. Under the new federal
4 It can be proved that ng is always positive with a Cobb-Douglas technology. In general, only for values of the elasticity of the marginal product of the public input with respect to labor input higher than 1 is a negative sign for Jtg to be expected.
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structure for the country, each state government provides the local public input g, which is financed by taxing, at the rate r, the labor income wl. The federal government provides the national public good G, financed by taxing labor income at the rate T. Consolidated taxation is denoted by r = t + T. Profits it are taxable by the federal government at a fixed rate #, and by the state governments at the rate 1 - 6. Denoting by S the vertical transfer, the state public input is then given by
g(i, 7' r, S, n, 6) = ntw(l - r, n, g)l[l- nv(l - r, w, g))] (10)
+ l»0jr(l-r,/i,g)+S, and the federal public good by
G(t, T, r, S, n, 0) = nkTwQ - r, n, g) I [(1 - r)w(l - z, n, g))] (11)
Notice, from (12) and (13), that GT = nkwl + Gt. Equations (13) and (14) are central to the present analysis. They show the effects of states' fiscal decisions on the federal budget constraint, i.e., they are measures of the two vertical externalities existing in the model. The signs of both of them are indeterminate here because ad valorem taxation and the provision of public inputs at state level may increase or decrease the federal revenues (Dahlby and Wilson, 2003).
Nevertheless, the best way of showing how the equilibrium in a federal country moves away from the second-best solution is to discuss the case in which state governments behave as Nash players. In such a situation, each state government ignores the impact of its fiscal decisions on federal revenues, and consequently, vertical externalities are expected to appear.
The typical state chooses (i, g) to maximize v(w) + B(G) subject to (10), taking as given n, 6, and the decision variables of the federal government (r, 5, G). The necessary conditions for this are given by
where (16) comes from manipulations on the first-order conditions for t and g, and (17) from the state's budget constraint (10). Obviously, the con- dition for production efficiency in the provision of the public input does not hold in this scenario, and this is an indication of the existence of a vertical ex- penditure externality. Anyway, consistent with intuition, the condition fg = 1 is trivially achieved when T = 0 = 0 is imposed in (16), that is, when only one level of government is considered.
4. Equilibrium with the Federal Government Behaving as Stackelberg Leader
Assume now that the federal government is able to act as first mover (or Stackelberg leader), deciding on its fiscal variables and anticipating the ef- fect of them on states' behavior. Before focusing on the problem of federal government, a characterization of the response of states to federal policy vari- ables is needed. With this aim, I take as basis the expressions (16) and (17). Both of them implicitly define the states' reaction function
f = £(7'0,S,n) , (18)
g = y(T,0,S,n). (19)
Differentiating (16) and (17) totally, we obtain a two-equation system that provides information on comparative statics of the states' reaction function:
gT = A (VtQT - QtVT) , (20)
gs = A (Vti2s - Ws) , (21)
tT = a (-vgnT + ngvT) , (22)
ts = A (-VgQs + VgVs) , (23)
where A = - Q^_%Qr The federal government chooses (7' S), and residually G, to maximize
v(w) + B(G) subject to (11) and the states' reaction functions (18) and (19). First-order conditions for T and S are respectively
rV + (GT + GttT + GggT)B' = 0 , (24)
<PV' + (Gs + Gtts + Gggs)B' = 0 , (25)
where r = ((1 - z)wT - w)(l + tT) + (1 - r)wggT and 0 = ((1 - t)wt - w)ts + (1 - r)wggs. Combining the two expressions, we have
r^_0 + r^^sa_09i!i±^ii = o, (26) GT GT (jt
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and taking into account wg, vvr, (20)-(23), and that Qs = 0, we have
Í: (1 - T)nlfl-Vt ) JLs
nlfLgVg + Í: (1
- T)nlfl-Vt ) JLs = o , (27)
where the conditions Gt = Gg = 0 have been imposed. Solving (27) for/g = 1, the optimal federal tax rate is obtained:
r = eEg~ , (28) Eg
where Eg is the elasticity of marginal productivity of g with respect to em-
ployment. The sign of T* depends on the value of Eg' we have T* ̂ 0 when
Eg^.l. The more intense the complementary relationship between labor and public inputs, the higher the optimal federal tax rate.
This optimal federal tax rate is closely related to the optimal matching- grant rate obtained by Dahlby and Wilson (2003)5. Indeed, they overcome the vertical expenditure externality with the federal government providing a matching grant equal to the federal share of the marginal benefits coming from the state public input. The matching rate they derive is (p = EgT + (1 -
Eg)6. In the model I study here, without matching grants available for the federal government, if the previous equation is solved for 0 = 0, the optimal federal tax rate in (28) is obtained. The underlying intuition in both cases is that the level of government that causes the externality (states) must get the full marginal benefits from the provision of public inputs to provide the socially optimal productive public expenditure.
Given that the elasticity Eg appears as the relevant variable for determin- ing the sign of the optimal federal tax rate, it is interesting to elaborate on its magnitude. Certainly, this elasticity is quite sensitive to the specification of the production function, and, since I am dealing with public inputs, it is illustrative to use the distinction between the following two cases: factor- augmenting public inputs and firm-augmenting public inputs (Feehan and Matsumoto, 2002).
Assuming a Cobb-Douglas technology, the first case is that in which the private production factor (labor) exhibits constant returns to scale and, con- sequently, increasing returns in all inputs (labor and public inputs). There- fore, taking a production function f(nl, g) = Lgf' with/? > 0, it is straightfor- ward to see that Eg is equal to 1 and hence T* = 0. This is consistent with intuition as long as, in a framework with factor-augmenting public inputs, the gains generated by the provision of public inputs are captured entirely by labor according to the manner in which its marginal productivity increases. Consequently, the federal government does not need to encourage the pro- vision of public inputs by states, because they have already gotten the full
5 I thank a referee for suggesting to me this insightful interpretation.
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marginal benefits of productivity-enhancing public spending through wage income taxation.
The case of firm-augmenting public inputs is different. If the Cobb- Douglas production function exhibits constant returns to scale in all the inputs (i.e., /(ft/, g) = Lagx~a, with 0 < a < 1), then the elasticity Eg is equal to a and therefore the federal optimal tax rate T* must be negative. In such a context, the public input creates firm-specific rents, and the output is not exhausted by payments to the private factor L. Since the state govern- ments do not capture the complete marginal benefits of public inputs, the federal government has to subsidize the wage income as a way of transfer- ring to states its share of the marginal benefits (rents) created by the public input.
By contrast, apart from the standard distinction between factor-augment- ing and firm-augmenting public inputs, a constant elasticity of substitution (CES) production technology may result in Eg > 1. According to (28), this would lead to a positive federal tax rate. Dahlby and Wilson (2003) showed that Eg > 1 is a necessary condition for being in the presence of a negative vertical expenditure externality - that is, one in which the state public in- put affects federal revenues negatively and therefore the state governments overprovide it. They suggest a negative matching grant from the federal gov- ernment to states. In this paper, the solution consists in a positive tax on wage income by the federal government.
In essence, while Dahlby and Wilson (2003) suggest a matching grant for correcting both vertical externalities, this paper provides an alternative policy tool based on the asymmetry of government behaviors at state and federal levels. Additionally, the conditions Gt = Gg = 0 appear sufficient to achieve the unitary outcome6. Note that Dahlby and Wilson (2003) and Kot- sogiannis and Martinez (2008) show that both conditions characterize the second-best solution with ad valorem taxation for the provision of public inputs and public goods, respectively. In this context, I have confirmed that the two vertical externalities are independent of each other as long as the federal government neutralizes separately the effect of sharing taxation and the effect of state public input on its revenues, dealing with both external- ities. The rule for replicating the second-best solution does not consist in taking account of a combination of Gt and Gg (which should be zero), but the federal government cancels out the tax externality Gt = 0 and the ex- penditure externality Gg = 0 without considering reciprocal links between them. And this is done with the federal tax rate conveniently chosen. To summarize:
6 Assuming a Cobb-Douglas utility function, it can be numerically proved that the condi- tions Gt = Gg = 0 become necessary and sufficient to replicate the unitary second-best.
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Proposition 1 The federal government facing vertical tax and expenditure ex-
ternalities replicates the unitary solution with the optimal federal tax rate T* = 6
(Eg - I)/ Eg. More specifically, (a) if the marginal productivity of g with respect to employment is elastic, then
the federal government taxes labor income,
(b) if the marginal productivity of g with respect to employment is inelastic, then
the federal government subsidizes labor income, and
(c) the two vertical externalities are independent of each other.
5. Concluding Remarks
The study of vertical expenditure externalities has not been so intense as that of vertical tax externalities. However, the study of the real federations shows a number of cases in which the public spending decided by one level of government affects revenues of other levels of government. Public invest- ment constitutes a good example of this as long as local, state, and national (and even supranational) governments have spending responsibilities with respect to productivity-enhancing public expenditures.
This paper has dealt with a model in which vertical expenditure external- ities appear in a federal country with taxes on rents and ad valorem taxation on labor income. State governments provide a public input affecting the federal government's revenues, which in turn are used to finance a national public good. It is clear that the unitary government would achieve the second- best outcome in the provision of both public expenditures, which in the case of public inputs means preserving the production efficiency condition. But when different levels of government are involved in policy decisions, vertical externalities damage efficiency.
A way of correcting them is to assume that the federal government behaves as Stackelberg leader, that is, moving first by deciding its fiscal policy and taking account of the reaction of states to changes in federal variables. The result is the optimal federal tax rate, which crucially depends on the elasticity of marginal productivity of public input with respect to employment. The higher this elasticity, the more likely one is to have a positive federal tax rate. Moreover, this paper confirms a previous result on the absence of links between the two vertical externalities.
Regarding policy implications, one has to recognize that the matching- grant formulation is probably a more plausible option in real federations than the design of the optimal federal tax rate. In fact, in a situation in which the elasticity Eg is less than one, the federal government would set a negative tax rate, and, in the case of not having enough resources coming from its profit tax, it should receive a lump-sum grant from the
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states7. Although this is an unusual result, some cases can be found in the real world. One of them is Spain, where two regions (Basque Country and Navarra) enjoy a special financing system in which their levels of fiscal cap- acity are higher than their spending responsibilities, and consequently a nega- tive fiscal gap arises. In particular, the Spanish case is quite appropriate for drawing a parallel between this model and the real world in that the re- gions and the central government share taxes on wage income, and regional governments have relevant spending responsibilities with respect to public infrastructure.
Also from a normative view, it is worthy of note that the distinction between factor-augmenting and firm-augmenting public inputs becomes rel- evant. Examples of the former include education and training of workers and the provision of transport infrastructure; and, as was shown above, the second-best equilibrium requires a federal tax rate equal to zero. By con- trast, firm-augmenting public inputs such as legal, promotional, or security services imply a negative federal tax on wage income. Consequently, the type of public input determines how the policy interactions between different lev- els of government have to be designed to replicate the unitary outcome. In this framework, the power of federal government to replicate the second- best outcome dramatically depends on its ability to behave as a Stackelberg leader. In this view, one can guess that a strong federal government is a ne- cessary condition for avoiding inefficient decisions on public spending.
7 This idea of a negative fiscal gap was first set out by Boadway and Keen (1996).
References
Boadway, R., and Keen, M. (1996), Efficiency and the Optimal Direction of Federal-State Transfer, International Tax and Public Finance 3, 137-155.
Boadway, R., Marchand, M., and Vigneault, M. (1998), The Consequences of Overlapping Tax Bases for Redistribution and Public Spending in a Federation, Journal of Public Economics 70, 383-398.
Dahlby, B. (1996), Fiscal Externalities and the Design of Intergovernmental Grants, International Tax and Public Finance 3, 3, 397-^12.
Dahlby, B., and Wilson, L. S. (2003), Vertical Fiscal Externalities in a Federation, Journal of Public Economics 87, 917-930.
Diamond, P. A., and Mirrlees, J. A. (1971), Optimal Taxation and Public Production I, II, American Economic Review 61, 8-27, 261-278.
Feehan, J. P., and Matsumoto, M. (2002), Distortionary Taxation and Optimal Public Spending on Productive Activities, Economic Inquiry 40 (1), 60-68.
Keen, M., and Kotsogiannis, C. (2002), Does Federalism Lead to Excessively High Taxes?, American Economic Review 92, 363-370.
Kotsogiannis, C, and Martínez, D. (2008), Ad Valorem Taxes and the Fiscal Gap in Federations, Economics Letters 99 (3), 431^34.
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