1. Introduction

In modern economies, citizens receive goods from (and pay taxes to) multiple levels of governments that each have their own objectives and implement (possibly) uncoordinated fiscal policies. In this context, the literature has emphasized the fiscal consequences of coordination failures that lead to vertical and horizontal fiscal externalities. For the case of horizontal externalities, the mobility of households and firms induces subnational governments to overestimate the marginal cost of public funds, leading to sub-optimal levels of state taxation and spending (see ^{Wilson, 1999}).¹ On the contrary, for the case of vertical fiscal externalities, ^{Johnson (1988)}, ^{Boadway and Keen (1996)}, among many others, argue that federal and sub-national governments will underestimate the marginal costs of public funds associated with raising tax revenue leading to too high taxation and spending.

In this paper we analyze a federation with multiple levels of governments implementing uncoordinated policies. The central government implements a linear redistributive policy that seeks to redistribute welfare by redistributing income while sub-national governments provide local public goods (such as health services, local security, parks, bridges, trash recollection, etc.). The objective of this paper is to identify conditions that explain, first, why the central government exerts a high or low level of effort to redistribute income for an economy with multiple governments? Second, what is the role of politics in determining whether the uncoordinated actions of multiple governments lead to a highly effective (or ineffective) redistributive policy of the central government?

To answer these questions, we consider a political economy model with sequential elections and centralized leadership in which parties have fiscal policy preferences (see ^{Wittman 1973}, ¹⁹⁸³).² In our economy, national elections take place and voters elect a party that implements its ideal policy on income redistribution. Moreover, a set of simultaneous elections at the sub-national level leads elected parties to provide local public goods.

In our economy, the redistributive policy of the central government changes, i) The distribution of welfare in the society by increasing (reducing) the full income of poor (rich) families and, ii) The level of spending of sub-national governments. Public redistribution affects local spending through the following channels: first, the provision of local public goods is determined by an elected party that represents the preferences over public spending of a coalition of activist-voters who rule the party. Hence, the party designs public spending to maximize the preferences of the coalition of voters subject to the constraint that local spending is financed by local taxes. If sub-national governments provide an inferior local public good and localities are ruled by parties that represent a coalition of voters with a wage higher than the nationwide average wage then the linear redistributive program of the central government induces a fall in full income and the demand for public goods of the coalition controlling the local government increases.

Second, by redistributing income, the transfer policy of the central government affects the demand of households for private goods and the ability of local governments to raise tax revenue (and the supply of local public goods). Whether a given locality is a net winner or loser on tax revenue as a result of the central government policy depends on the difference between the aggregate transfers from the redistributive program to residents of a given locality and the aggregate tax payments of residents of the locality to the central government. This in turn, depends on the population density of the economy and on the original distribution of income.

In this paper, we contribute to the literature by identifying conditions that map the distribution of political power, the effort, and effectiveness of public redistribution in a federation. Even though in the literature it is well understood that elections and party preferences matter to determine fiscal outcomes (see ^{Reed, 2006}; ^{Alt and Lowry, 2000}; ^{Caplan, 2001}; ^{Rogers and Rogers, 2000}; ^{Chernick, 2005}; and ^{Fletcher and Murray, 2008}), we have little understanding of how the structure of political power in a federation might affect the policies of the central and subnational governments.

In this paper we contribute to filling this gap. In particular, we find that for a large economy, the central government implements a strictly positive universal transfer if the federal government is ruled by a party that represents a coalition of voters with a wage below the nationwide average wage. The effort of the central government in redistributing income will be high (that is the per capita transfer is high at the political equilibrium) if the local governments of both localities are ruled by parties representing voters with wages above the nationwide average wage.

Moreover, we find that if the following conditions are met: (i) Local public goods are inferior, (ii) The central government is ruled by a party that represents a coalition of voters with a wage below the nationwide average wage, (iii) Local governments represent voters with a wage above a certain threshold, (iv) The willingness to pay for local public spending of key activists inside the ruling party of local governments is high, and (v) Localities have sufficiently high densities of population; then the welfare of key voters-activists in the central government is increased above the direct effect of the redistributive program. This outcome implies that the central government is highly effective at redistributing welfare by redistributing income for key voters-activists inside the party in control of the central government. As a result, the strategic interaction among governments leads to a non-cooperative welfare-superior allocation of resources in which the per capita public transfers from the central government are high and the welfare gains associated with public redistribution for key voters-activists in the central government are high as well.

The paper is structured as follows: section 2 reviews the literature on the topic. Section 3, characterizes the politically driven redistribution and the reaction functions of sub-national governments. Section 4, analyzes the structure of political power, the effort to redistribute income and identifies sufficient conditions that lead to the equilibrium with non-cooperative welfare-superior redistribution. Section 5 includes a comparative analysis of our political equilibrium with the Pareto efficient outcome in which the government is ruled by a benevolent social planner. Section 6 concludes.

2. Literature review

In a federation, citizens are represented by a central government and by several sub-national governments who have different preferences and abilities to provide public goods and services. In this context, the literature has emphasized the possibility of coordination failures among governments that lead to vertical and horizontal fiscal externalities and its fiscal consequences. For the case of horizontal externalities, ^{Wildasin (1991)} argues that state governments ignore the effect of local taxes on other jurisdictions. Hence, in presence of mobile households and firms, state governments will overestimate the marginal cost of public funds leading to too little sub-national taxes and spending.³ For the case of vertical fiscal externalities, the basic argument by ^{Johnson (1988}), ^{Boadway and Keen (1996)}, ^{Dahlby (1996)}, ^{Boadway, Marchand and Vigneault (1998)}, and more recently ^{Rizzo (2008)} and ^{Dahlby and Wilson (2003)}, is that the federal and sub-national governments might not take into account how their policies affect each other. Therefore, these governments will underestimate the marginal costs of public funds associated with raising tax revenue leading to too high taxation.

Another branch of the literature has recognized that, in a Stackelberg game with leadership from the central government, the federal government could eliminate the vertical externality (see ^{Keen, 1997}; ^{Dalhby, 1996}; ^{Caplan, Cornes and Silva, 2000}; ^{Gong and Zou, 2002}; ^{Aronsson, Andersson, and Wikström, 2004}; and ^{Aronsson and Blomquist, 2008}). The theory of coordination failures usually emphasizes how self-interested agents might fail to cooperate and reach a Pareto superior allocation. While there is a large body of literature that studies the case of negative externalities, an issue that has received little attention is the case of uncoordinated policies leading to Pareto superior allocations. However, this topic is highly relevant for policy making. In this paper we study such a case and we call it non-cooperative welfare-superior redistribution. That is, we focus on whether the fiscal policy of the central government is complemented (from the point of view of the underlying objectives of the central government) by uncoordinated policies of sub-national governments leading to a high (or low) effectiveness of the policy of the federal government.

In this type of equilibria, public redistribution changes not only the distribution of welfare in the society but also affects local public spending. One likely outcome is that the local public good might be inferior and its provision might increase as a result of the redistributive policy of the central government. In this case, the welfare of poor families could also be increased by more than just the direct effect of the redistributive program. Hence, the redistributive policy of the central government is highly effective to redistribute welfare in favor of pivotal voters-activists by redistributing income. Our analysis complements the study of ^{Kochi and Ponce (2013)}, in which they analyze the behavioral effects of redistribution on subnational spending. However in their paper there is no policy design by the central government while in our paper we introduce a Stackelberg game to analyze the strategic interaction between the central and subnational governments.⁴

Our paper is also related to the theory of partisan politics and fiscal outcomes. This theory is concerned with the consequences of political outcomes and its effects on fiscal policy. A great deal of the literature has focused on the partisan consequences on the US fiscal policy. For instance, ^{Reed (2006)}, ^{Alt and Lowry (2000)}, ^{Caplan (2001)} and ^{Rogers and Rogers (2000)} find evidence that state taxes increase when Democrats have significant control of the executive and legislative bodies of state governments.^{5 Caplan (2001)} finds that corporate and income taxes tend to rise under Democratic control of state legislatures and fall with larger Republican majorities. ^{Chernick (2005)} finds that party control by Republicans is associated with more regressive state tax structures. ^{Fletcher and Murray (2008)} find that party control by the Democrat party is positively associated with higher top income tax rates, higher income threshold for the first bracket of the income tax, and higher earned income tax credits.

Our analysis is also related to the theory of political economy of fiscal federalism. For instance, ^{Lockwood (2002)} studies the allocation of public funds by the party with a majority, ^{Besley and Coate (2003)} show that the sub-national provision of local public goods with and without inter-regional spillovers is not Pareto efficient in a model with legislatures. ^{Ortuño-Ortin and Sempere (2006)} study the role of politics in determining the degree of fiscally autonomy regions versus fiscal centralization. Finally, ^{Bolton and Roland (1997)} study how political conflicts over redistributive policies might either lead nations to breakup or to increased unity.

Even though in the literature it is well understood that elections and party preferences help to determine fiscal outcomes, we have little understanding of how the structure of political power of the central and sub-national governments might affect fiscal outcomes in a federation. This paper seeks to contribute to filling this gap since our theory identifies sufficient conditions for the outcome of the national election to determine the level of effort of the central government to redistribute income (whether tax and transfers are high or low) and for the political structure of sub-national governments to determine whether the redistributive policy of the central government is effective or not.

3. Politically driven redistribution and the reaction functions of sub-national governments

In this section we study the role of political competition in determining the design of the central government of a redistributive program for an economy with strategic interaction among multiple governments. Our economy is a federation constituted by a central government and two sub-national governments (associated with localities 1 and 2). The central and sub-national governments have different tasks mandated by the constitution of the country. We take these constitutional mandates as given. Local governments provide local public goods (such as local security, education, bridges, parks, trash recollection, etc.) and the central government redistributes income.⁶

4. The structure of political power and the effort to redistribute income

The political equilibrium for this economy can produce multiple fiscal outcomes.¹⁹ However, in this section we focus on a type of equilibrium we call non-cooperative welfare superior redistribution. In this equilibrium, as we have mentioned before, public redistribution not only changes the distribution of welfare in the society by increasing (reducing) the full income of poor (rich) families but this policy also affects the spending of sub-national governments. If local governments provide inferior local public goods and the provision of these goods increase as a result of the redistributive policy of the central government, then the welfare of poor families is increased above the direct effect of the redistributive program. In this case, government action to redistribute welfare in favor of key voters-activists by redistributing income is highly effective.

The purpose of this section is to identify sufficient conditions to obtain the fiscal outcome described above. On what follows, proposition 3 characterizes the equilibrium level of the redistributive policy of the central government

τ ^*Z ,T ^*Z ∀ Z = {L,R}.

Proposition 4 identifies how election outcomes in a federation determine the level of effort that parties must spend to redistribute income. Proposition 5 identifies sufficient conditions for an allocation of resources with non-cooperative welfare superior redistribution.

PROPOSITION 3. In this economy the government’s per capita transfer T ^*Z ∀ Z is given by

Where

is the average wage income in the economy, and

Where μgZi = ∂μ ^*Zi /∂g ^*Zi , and the aggregate elasticity of labor supply and the federal tax, ε𝓁*i-τz, is given by²⁰

The term ∂TR ^Z /∂T ^Z is the marginal tax revenue when the government returns $1 to households through transfers, and

is the tax revenue from labor income,

is a weighted average labor income of the coalition controlling the national government, and the response of local governments ∀i on local public spending to national tax and transfer policies are given by^{21 , 22}

PROOF. The problem of policy design for party Z = {L, R} controlling the national government is defined as follows:

Where Y ^Z is a Lagrange multiplier and g*Zi τZ,TZ, nZi is given by condition 5 and satisfies the following:

Find the first order conditions and re-arrange terms to obtain condition (10). Condition (9) follows from (10) and from the budget constraint of the government. Conditions (12) and (13) follow from the equilibrium condition (5) in proposition 2.

PROPOSITION 4. THE STRUCTURE OF POLITICAL POWER AND THE EFFORT TO REDISTRIBUTE INCOME. At the politico-economic equilibrium of a large economy, T ^*Z is strictly positive if a party that represents a coalition of voters with a wage n ^Zi below the nationwide average wage rules the central government. Moreover, T ^*Z also depends on the distribution of political power at sub-national governments: T ^*Z is high (low) if local governments of both localities are ruled by parties representing voters with wages nLZi∀i above (below) the nationwide average wage.²³

PROOF. To prove this proposition it is sufficient to show that increases of n ^Zi reduce T ^*Z and increases of nLZi∀i increase T ^*Z . The first part of the proposition follows from the fact that

For a large economy hZinZi>0, but small implies hZinZi≅0 thus ∂T*Z∂nZi≅1-2τ*Z∂τ*Z∂nZi∑∀i∫∀nihininidni<0

since ∑∀i∫∀nihininidni>0,1-2τ*Z>0 and ∂τ*Z/∂nZi<0.

Note that ∂τ*Z/∂nZi<0 because ∂𝓁 ^*i /∂n ^Zi > 0∧h ^Zi (n ^Zi ) ≈ 0 imply

Moreover, 1-2τ*Z>0 since ∂T ^*Z /∂τ ^*Z > 0. To see this, note that at the equilibrium it must be satisfied that ∂T*Z/∂τ*Z>0⇒1-2τ*Z>0, otherwise

implying τ*Z,T*Z, Υ*Z∉ argmax δZτZ,TZ, ΥZ.

Therefore, since τ*Z,T*Z, Υ*Z∈ argmax δZτZ,TZ, ΥZ then ∂T*Z/∂τ*Z>0∧1-2τ*Z>0 ∀Z=L,R.

For the second statement in the proposition, we recognize that ∂T ^*Z /∂τ ^*Z > 0, hence

To see this, recall hZinLZi≈0, and

Hence 1-2τ*Z>0∧∂τ*Z/∂nLZi>0∧∑∀i∫∀nihininidni>0⇒∂T*Z/∂nLZi>0∀Z,∀i.

PROPOSITION 5. NON-COOPERATIVE REDISTRIBUTION WITH WELFARE SUPERIOR GAINS. Consider an economy with:

v.1) Inferior local public goods

v.2) A central government ruled by a party that represents a coalition of voters with a wage below the nationwide average wage.

v.3) Local governments ruled by parties that represent a coalition of voters with a wage nLZi and MRSgZi-αZi>1 (their willingness to pay for local public spending is high enough) such that:

v.4) Localities have sufficiently high densities of population such that:

In this case, the spending policy of sub-national governments complements the redistributive policy of the central government. As a result, the strategic interaction among governments leads to a non-cooperative allocation of resources in which T ^*Z is high and the welfare gains associated with public redistribution for the pivotal voters-activists of the central government are high as well.

PROOF. To see that condition v.1) is satisfied, note that we can generalize condition (5) in proposition 2 for any voter in every district. Hence, ∀ ni∈nmini,nmaxi, the ideal size of local public spending for a voter type n ⁱ is g*Zini=12Eni-niMRSg-αni+TZHini-τZEni-TZ-τZniMRSg-αni where Eni=∫∀nihininidni. It follows that ∂g*ni/∂ni=121-τZhini-1MRSg-αni.

Note that 1-τZ> 0. For a large economy h ⁱ (n ⁱ ) > 0 but small and MRSg-αni > 0 implies hini-1MRSg-αni<0 hence ∂g*ni∂ni< 0

Therefore, the ideal size of local public spending is a decreasing function of the voter’s earning ability.

By proposition 4, ∂T ^*Z /∂n ^Zi < 0 (this is condition v.2). In addition, recall ∂T ^*Z /∂τ ^*Z > 0 and

(see condition 10 in proposition 3). Thus, condition v.3nLZi>MRSL-gZi-αZi∫∀nihininidni implies that ∂g*Zi/∂τ*Z>0 (see condition 12) and ∂T*Z/∂∂g*Zi∂τ*Z>0.

Moreover, condition v.4Hini>1MRSL-gZi-αZi implies ∂g*Zi/∂T*Z>0, and ∂T*Z/∂∂g*Zi∂T*Z>0.

Thus, conditions v.1 to v.4 mean that the effort to redistribute income (i.e. the size of T ^*Z ) is high at the equilibrium which means that politicians can effectively redistribute welfare in favor of politically influential coalitions by redistributing income.

Propositions 4 and 5 say that election outcomes (that is the structure of the identity of the party controlling public office at each level of government) can explain not only the size of public redistribution and sub-national public spending but also whether the policy of the central government is effective or not in redistributing welfare by redistributing income in a federation.²⁴

To see this, we first need to recognize that the linear redistributive program of the central government entails a net positive (negative) transfer to any individual with a wage that is lower (higher) than the nationwide average wage. This explains why parties in control of the central government representing a coalition of voters with a wage lower than the average wage choose a positive level of T ^*Z (see proposition 4 and condition v.2 in proposition 5).

Moreover, parties seeking to win the national election to form the central government recognize that the gains from the net fiscal exchange associated with public redistribution depend on subnational election outcomes because the structure of inter-regional political power explains the reaction of local governments to the redistributive policy of the central government.

Public redistribution affects local spending through the following channels: first, in our economy sub-national governments provide an inferior local public good, hence the demand for sub-national public spending increases with a fall in the after tax and transfer income (or full net income). If local governments are ruled by a coalition of voters with a wage higher than the nationwide average wage then the linear redistributive program of the central government induces a fall in full income and the demand for public spending of the coalition controlling the local government increases (this effect is also characterized by conditions v.3 and v.4 in proposition 5).

Second, by redistributing income, the transfer policy of the central government affects the demand of households for private goods and the ability of local governments to raise both tax revenue and the provision of public goods (this is also characterized by conditions v.3 and v.4 in proposition 5). Whether the locality i is a net winner or loser on tax revenues as a result of the redistributive program of the central government depends on the difference between the aggregate transfers from the redistributive program to residents of locality i and the aggregate tax payments of residents of the district to the central government. This in turn, depends on the density of the population and the original distribution of income (see condition 5 in proposition 2).

The lack of quid pro quo of the fiscal exchange from public redistribution requires that the effects of taxation and transfers be analyzed separately. An increase in taxes on wage income tends to reduce local spending by reducing the available resources in localities for the supply of local public goods and simultaneously tends to increase the supply of local public goods since taxes reduce full income and the demand for public spending of the coalition of voters controlling the local government increases.

Condition v.3 says that if there is a level of income which is high enough so that the latter effect dominates then ∂g*Zi/∂τ*Z>0 which in turn means that the size of public transfers is higher at the political equilibrium because ∂T*Z/∂∂g*Zi∂τ*Z>0.

An increase of public transfers tends to increase the supply of local public goods through a positive local tax revenue effect (the higher the density of the population of the district the higher is the share of resources of the redistributive program that is allocated into the district, this in turn increases the demand of residents for private goods, the district’s tax collection, and the provision of the local public good). An increase of public transfers also reduces local public spending because the demand of the coalition of voters controlling the local government falls. Condition v.3 characterizes a sufficient condition in which the first effect dominates implying that ∂g*Zi/∂T*Z>0 and, because ∂T*Z/∂∂g*Zi∂τ*Z>0, the size of public transfers is higher at the political equilibrium.

5. The political equilibrium versus the Pareto efficient out-come

It is interesting to compare our political equilibrium with a cooperative Pareto efficient outcome. If all governments cooperate to design policies to maximize the wellbeing of their citizens, then these coordinated policies will lead to a Pareto efficient outcome maximizing the sum of utilities of all members involved in the agreement. In our case, this outcome is equivalent to a policy that maximizes the sum of utilities of all individuals in the economy. Therefore, the efficient outcome can be characterized by solving an optimization problem with a benevolent social planner in which the central government provides local public goods in all districts, and determines the optimal size of public redistribution, as well as the different forms of taxation.

In this case, the government’s problem of policy design for redistribution (T), local public goods, (g ⁱ , g ⁻ⁱ ), labor income taxation (τ), and commodity taxation (t ⁱ ) is characterized as follows:

subject to

Where Ξ is a nationwide social welfare function and condition (23) is the government’s budget constraint where total tax revenue depends on nationwide collections of public revenue from labor and commodity taxation.

PROPOSITION 6. Optimal tax and spending policies are given by

T ^** ,τ ^** ,g ^**i ,t ^**i ∀i:

For T**:

Where

is the social marginal utility of income, λ _Ξ is the social marginal cost of raising tax revenue from taxation, ξ_𝓁 −T is an aggregate weighted elasticity of the supply of labor with respect income transfers from the government

and