Public Goods in Federal Systems

Transcription

1 Public Goods in Federal Systems Catherine Hafer Department of Politics, New York University Dimitri Landa Department of Politics, New York University Abstract We study a politico-economic model of federations with both federal and supplemental regional provision of a local (impure) public good with spillover effects. Regional differences in average income levels and externalities of provision induce differences in preferences over federal and regional levels of provision. Although the voters preferences are not single-peaked, we provide sufficient conditions for the existence of a voting equilibrium and characterize its properties under alternative federal institutional arrangements. The voting equilibrium is unique but displays markedly different substantive characteristics under different conditions on parameters. We show that the inter-regional redistributive tensions present in federations lead to differences in regional preferences over federal institutions and may help to explain otherwise puzzling patterns in state support for federal programs.

2 Introduction The issue of the composition and structure of political unions or federations is as timely as it has ever been, with the expansion of the European Union leading to some of the most heated debates in European politics in the last decade. In many cases of political unions, the joint action of the members is a function of distinctly political phenomena, such as the perception of a common military threat or the political salience of domestic ethnic groups with cultural or historic affinities for neighboring states. The unions that lead to the creation of common political institutions charged with the implementation of common economic policies are, however, rarely products of political calculations alone (see, e.g., Inman and Rubinfeld 1998, Emerson et al for the EU, and Hardin 1999, Ch. 3, for the US), and call for the analysis of distinctly political-economic mechanisms of their formation, maintenance, and internal organization. The present paper analyzes one such mechanism by considering the political and economic incentives within federal structures with public good provision on both local and federal levels and spillover effects between regions - features that often characterize contemporary federal systems. Although such systems rarely have institutional provisions that explicitly authorize the duplication of services or public goods on the federal and the local levels, in practice, public goods provided at the two levels of government are often de facto substitutes, with fiscal federalism emerging less as a constitutional and juridical reality and more as a dynamic economic one. Sometimes the substitution effect is immediate and direct, as with the financing of the creation of new stem-cell lines in the US, which, before President Bush s ban, was done with federal money, but has now been picked up by the state of California. At other times, federal and regional/state programs may have different explicit targets, e.g., different categories of the population, but their substantive closeness gives rise to explicit budgetary fungeability - as with the US federal Medicaid spending on retirees, which is used by state health care facilities to help offset their overall operating expenses (Hernandez 2005). With many other spending programs, there is what may be called article-byarticle substitutability, whereby, within a given policy area there is a division of responsibilities 1

3 between the state and the federal governments, but a drop in spending by one level on an article within its purview, leads another level to pick up the slack by spending more on articles within its own budgetary purview. A prominent example of such a policy area is higher education financing, where the US federal government is typically understood to be responsible for the provision of low-interest student loans and faculty research funds, and state governments finance faculty and staff salaries and the physical plants of state universities. Other policy areas exhibiting substantial substitutability in the US and other federal states include highway construction, environmental regulation, etc., and in these and other policy areas mentioned, this substitutability is best thought of as a feature of what are, in effect, dual-provision fiscal federal mechanisms. Although the latter point is less true of the EU, whose budget is still rather small relative to those of its wealthiest member-states, the range of policy areas in which the substantive policy control is, effectively, shared by the EU and its members is long and growing, including a number of economic policy areas, most notably monetary policy, agriculture and fisheries, etc., with respect to which the EU is more and more resembling a federal state with a robust policy-making and implementing apparatus (Alesina and Wacziarg 1999). In analyzing such dual-provision systems, our model of federations could be seen as combining some of the key elements of two approaches to analyzing the political economy of federations, which have been the focus of the existing analyses and which may be referred to as the scale and the spillover mechanisms. The first of these, requiring more explicit cooperation among members, posits federal structures as outcomes of the economies of scale, which make it profitable for states to join forces in the selection of policy because the returns to joint economic action exceed the sum of the returns to the independent actions by the members (see Alesina, Perotti, and Spolaore (1995), and Bolton, Roland, and Spolaore (1996) for surveys of some of the models analyzing this mechanism). Examples of models that explore this mechanism include Casella (1992) and Alesina and Spolaore (1997), which focus on the scale effects of trade and Persson and Tabellini (1996a and b), which draws on the scale effects of risk sharing. Difficulties in enforcing agreements on which such unions are based are considered in Bednar (2001) and De Figuiredo and Weingast (2001). The second political-economic mechanism prominent in the extant work focuses on the possi- 2

4 bility of members enjoying spillovers in the provision of local public goods in the federation. Less explicitly cooperative than the first mechanism, the spillover mechanism more immediately lends itself to the analysis of the distributive properties of policy-making in federations, which are, arguably, the central source of tension in this conception of federalism. Papers exploring various elements of this mechanism include Cremer and Palfrey (2002), who analyze the distributive effects of unfunded federal mandates, and Alesina et al. (2005), who consider the possibility of supplementing local provision at the federal level. Like Alesina et al., we analyze a model with dual (federal and regional) provision and interregional spillovers, but unlike in their model, the presenceofincomeheterogeneityplaysacentral role in our causal account of the distributive effects of federal politics. Empirically, that heterogeneity is, indeed, substantial: in the US, the highest state-level median household income is nearly twice the lowest, and the highest national GDP per person in the EU (measured at PPP) is nearly three and a half times the lowest. Rather than assuming primitive differences in regional demands for public goods, we induce these differences endogenously from the interaction between the relevant spillover factors and the differences in regional incomes, which enables us to develop predictions in terms of these empirically obervable regional characteristics. 1 Our model also offers a framework for analyzing a wide range of different types of dual-provision mechanisms, including the previously unexplored and both theoretically and empirically important cases in which federal provision may exploit economies of scale in production, as well as the case in which federal provision is equivalent to the equal division of federal revenues among the member regions, who then produce the public good locally just as they would using locally raised revenue (as in Alesina et al. 2005). 1 Our basic setup is also related to Epple and Romano s (2003) model of collective public good provision with supplemental voluntary provision, which could be re-interpreted as a model of federation in which the federal and local means of provision are identical and in which the public good is a pure one. The model presented here is complicated not only by impure public goods and technological differences between the federal and local means of provision, but also by the fact that local provision must be determined by a collective choice rather than by an individual one. 3

5 We show that, in the presence of income heterogeneity across regions, the dual structure of public good provision induces redistributive tensions within the federation, with significant empirical and theoretical implications for our understanding of federal politics. Our key technical results characterize and provide sufficient conditions for the existence of a voting equilibrium with public good provision at two levels of government. Substantively, we show that the presence of spillovers in dual-provision federations results in political conflicts between the region-members of the federation and between the federal and the regional levels of government. These conflicts manifest themselves in regions attempting to increase or decrease the role of the federal government, relative to the regional governments, in order to force other regional governments into making particular political and economic choices. 2 We show that these attempts (1) may help account for the otherwise puzzling empirical patterns in state preferences over federal programs, e.g., opposition from poorer states that are their net beneficiaries and support from wealthier states that effectively subsidize them (Lacy 2004); (2) may give rise to politically potent ends-against-the-middle majority coalitions that often elude directly political explanations; and (3) lead to conflicts over the choices of institutional structures organizing the decision-making in federations, though not necessarily to the instability of collective institutional choice. The remainder of the paper is organized as follows. In the first section to follow we present our results on the existence and properties of equilibrium in federations with joint provision. The next section addresses issues of constitutional variation, including the comparative institutional analysis of political (de-)centralization. It is followed by a brief discussion section and an appendix that gathers the proofs of all the formal propositions in the paper. 2 In explaining the rivalry between the federal and some of the regional governments, this mechanism complements the credit claiming incentives that are highlighted in Bednar (2004) and Volden (2005), though it does suggest that, unlike in the case of credit-claiming, we should not expect this rivalry to be uniform across regions. 4

6 The Model Notation and Primitives The sequence of the game is as follows. First, the citizens of the federal union choose their federally provided level of public good. Then, citizens of each region comprising the union simultaneously choose their respective regional levels of provision. At both levels, decisions are made by majority rule. Following the realization of the federal and the regional provision levels, citizens of the union consume their public and private goods. 3 There are n regions in the union, where n is odd, and let l be the number of regions that choose (by domestic majority) to engage in supplemental local provision. The corresponding sets of member regions are denoted as N and L respectively, with L N. In the interests of tractability, all regions are assumed to have equal populations. 4 Although this assumption may appear restrictive initially, it does not affect the spirit of the substantive results. 5 Let u i j be the utility of agent i in region j. We assume generalized Cobb-Douglas preferences u i j(x i j,y j )=(x i ) a y b j, (1) where y j is the amount of public good enjoyed by each individual in region j and x i j is i s private 3 We comment on both the extension of the results to the case in which a representative federal legislature chooses federal policy and the possibility of reversing the order of provision in the Discussion. 4 It is straightforward, though notationally more cumbersome, to generalize to the case in which regions are of different sizes. We comment further on the possibility of such an extension below. 5 The mobility of voters across regions is beyond the scope of the present paper and is left to the future work extending the model developed here. Not modeling it explicitly here has the advantage of allowing us to evaluate the independent impact of spillovers on federal political economy, as well as to compare our results to the results in other papers that model federal system with spillovers and which, at the moment, do not allow for voter mobility. 5

7 good. This functional form treats public and private goods as essential in some measure and as complements, e.g. as complementary inputs to the productive economic activities of individual agents. Consequently, the agent requires positive amounts of both goods, and the marginal productivity of each input is increasing in the presence of greater amounts of the other. In many cases of public good provision, especially those of large-scale legal, physical, and financial infrastructure, this assumption is particularly plausible and warrants considerable attention in the analysis of political economy of federal unions. Additionally, we use the following notation to denote the corresponding income variables: h i j is the income of agent i in region j; H j = P i h i j is the total income of a generic region j; and H =(H 1,...,H j,...,h n ) is the vector of total regional incomes. H T = P j H j is the total income of the federation. We assume that the private good is numeraire, i.e., the monetary unit. One unit of private good purchases one unit of local public good, that is, one unit of an impure public good that can be enjoyed fully by citizens in the region in which it is provided, but only partly by the citizens of other regions. Let s L < 1 be the proportion of that local public good that citizens of other regions are able to enjoy. The federal-level policy we analyze imposes a uniform tax rate and spends equal amounts (per capita) on the provision of public goods in each region. The benefits from federal provision directed to one region spill over to other regions also at the rate of s L. Hence, a dollar spent on public good provision by the federal government increases the amount of public goodenjoyedinanygivenregionbyγ (1+s L(n 1)) n, where γ is a measure of the relative efficiency of federal provision. If γ < 1, then the federal means of provision is inherently less efficient than the local means of provision, and if γ > 1 then federal provision is more efficient. 6 As noted in the introduction, our assumptions here are flexible enough to cover the cases in which federal provision may exploit economies of scale in production, as well as the case in which federal provision amounts 6 Note that whether or not γ > 1 is distinct from the question of whether membership in the federation is attractive, in part because the existence of spillovers may make it attractive even if γ < 1. 6

8 to the equal division of federal revenues among the member regions, who then produce the public good locally just as they would using locally raised revenue. For notational convenience, we let γ (1+s L(n 1)) n = s F represent the amount of public good enjoyed in a region for each unit the federal government spends on public goods. We thus interpret s F to reflect both the direct impact (from the federal provision for region j) and the indirect impact (via cross-regional spillovers from the federal provision for other regions) of federal provision. Note that s L and s F can be treated as the rates of substitution of the individual s own region s locally provided public good for other regions or federal public goods. We return to the expression of s F in terms of s L below in the evaluation of the conditions that characterize the equilibrium levels of provision. Although, in the interests of brevity, we focus our interpretation of the model on the effects of positive externalities, it is fully consistent with the presence of negative externalities as well. In the latter case, the rationale for the the existence of the federal government may be thought to be the alleviation of such externalities, which is analytically equivalent to the production of positive ones. 7 The federal tax rate is t F and the vector of local tax rates is t = (t 1,t 2,...,t n ), with the understanding that t j,t F [0, 1]. The government faces a balanced budget constraint, so all revenue is invested in public goods at the corresponding level of government. Thus, for individual i in region 7 Suppose that regions produce negative externalities in the form of pollution and that the federal government creates an abatement program to eliminate them. Then the federal government may be thought to be producing a public good, in the form of cleaner air or water, or equivalently it may be thought to be eliminating a negative externality (pollution). If the government action constitutes an actual restriction on some beneficial activity that creates a negative externality as a by-product, then the assumption y j 0 implies that (1) the net benefit of government actions is positive, so that adequate benefits are always provided to compensate for losses, and (2) government abatement programs prevent firms from increasing their rate of pollution in response to government efforts. 7

9 j, X y j = t F H T s F + t j H j + s L t k H k (2) x i j = h i j(1 t F t j ) k L\j The Politico-Economic Equilibrium Our solution concept is subgame-perfect Nash Equilibrium in undominated strategies. More specifically, the equilibrium is characterized as the pair (t F,t ), such that the federal tax rate t F is in the majority rule core of the federation as a whole, given the equilibrium best response of t (t F ), and, for every region j, t j is in the majority rule core of region j, giventf and t j. Solving by backward induction, we first find the induced preferences of a voter in region j over regional tax rates, t j, given her expectations of the other regions simultaneously chosen tax rates, t j, and the known federal tax rate t F. Substituting (2) into (1) yields X u i j(t F,t, ) =((1 t F t j )h i j) a (t F H T s F + t j H j + s L t k H k ) b. (3) k N\j Because both private and public goods are essential, no agent ever prefers to tax away all of her private endowment. She may, however, prefer no supplemental local provision of the public good (t j = 0) if enough public good is provided at the federal level or locally in other districts. To locate any interior solution, we obtain the Kuhn-Tucker conditions, which (combined with the conditions for the corner solution) yield the most preferred local tax rate as a function of the federal tax rate: t j (t F )= 1 a+b " b(1 t F ) a(t F HT H j s F + s L if b(1 t F ) >a(t F HT H j s F + s L 0 otherwise P k N\j P k N\j t k H k H j ) # t k H k H j ) (4) The first thing to note in relation to (4) is that, because voters have identical marginal rates of substitution between private and public goods and the tax is a flat rate on endowment, domestic 8

10 politics (i.e., the politics of determining the supplemental level of public good provided at the local level) is essentially trivial: holding constant the federal tax t F, agents within a region have identical preferences over the internal tax financing the supplemental provision of the public good. Thus the choice of regional tax rate depends on the region s total income, H j, but does not otherwise depend on voter i s income, h i j. For the same reason, the equilibrium local tax rate is robust to the specification of the domestic collective choice rule. This simplicity of the intra-regional politics helps place the inter-regional politics in the spotlight, and will make it easier to see the causes and consequences of disagreements between regions over federal taxation and provision. These disputes will turn on the combination of the redistributive pressures inherent in income heterogeneity across regions and the possibility of free-riding implicit in inter-regional spillovers. We begin our analysis of these effects with two lemmata, which establish the unique relationship between the set of local providers and the federal tax rate that is instrumental in proving the main results of the model. Lemma 1 In any equilibrium, for any pair of regions j and k such that H j <H k,ifregionj provides a positive amount of the public good at the local level, then region k provides a strictly greater amount. Proof See Appendix. Let L(t F ) be the set of members which engage in supplemental local production at federal tax rate t F,i.e.,forwhicht j > 0att F. Let L(t F ) = l(t F ). If we index the regions from richest to poorest, i.e., so that H 1 H 2... H l... H n, the key consequence of this lemma for the present model is that l(t F )mustbethehighestintegersuchthatt l (t F )H l > 0, i.e., it has to be such that both t l (t F )H l > 0andt l+1 (t F )H l+1 = 0 (where the lower bound on tax rate may be P binding). Hence, t j (t F )H j = P t j (t F )H j, and from (4) we can write j N j L X t j (t F )H j = j N = X j L(t F ) t j (t F )H j 1 a + b + as L (l(t F ) 1) (b(1 tf ) X k L(t F ) H k as F t F H T l(t F )). (5) Substituting (5) into (4) and solving for t j (t F )H j at t F such that t j > 0, we get: 9

11 t j(t F )H j = b (1 t F )H j (6) a + b as L 1 a + b + as L (l(t F ) 1) (as F t F H T abs L X + (1 t F ) H k ), a + b as L k L(t F ) where, from the above ordering of H j and (6), l(t F )andl(t F ) are formally defined by the following system of inequalities: (a + b + as L (l(t F ) 1))b(1 t F )H l(t F ) >abs L (1 t F P ) H k +(a + b as L )as F t F H T (a + b + as L (l(t F ) 1))b(1 t F )H l(t F )+1 abs L (1 t F ) k L(t F ) P k L(t F ) H k +(a + b as L )as F t F H T (7) Together (6) and (7) determine the Nash equilibrium in the simultaneous-move local provision game. Lemma 2 For each federal tax rate t F, there is a unique group of regions, L(t F ), that are local providers at that tax rate. Proof See Appendix. By Lemma 1, this group of regions must include the wealthiest l(t F ) regions in the federation. Given this solution to the subgame, we next determine the agents preferences over federal tax rates. These preferences depend critically on the relative merits, from an individual s point of view, of the federal and the local means of provision, taking into account the strategic responses of other regions to changes in each. Two features of voters induced preferences over federal tax rates, each of which is established formally in the appendix, play prominent roles in the characterization of the equilibrium federal tax rate (below). First, we show that voters within a given region j have identical induced preferences over federal tax rates even though they may have different private endowments, and hence different utilities at any given tax rate. In addition to aiding the characterization of the majority rule core, this feature of the model facilitates the extension of the results to both a wider variety of institutions 10

12 for collective choice, including representative government, and the case in which regions differ in their populations. Second, we show that voters in any two regions that do not engage in local provision for some interval of federal tax rates have identical induced preferences over federal tax rates on that interval. Both of these properties are consequences of the fact that the citizens in question enjoy the same spillovers from other regions local provision, the same federal provision of the public good, and the same local provision from their own regional government. Hence, they enjoy the same amount of public good. This induced simplicity of regional politics in the model allows us to focus our attention on the consequences of inter-regional redistributive tensions. Because 0 is a binding lower bound on all local tax rates, the expression for the indirect utility of a voter in region j as a function of federal tax rate, given the equilibrium behavior in the local provision game, is different when some other region k engages in local provision than when it does not. Let l max = L(0) be the number of regions that engage in local provision when there is no federal provision of the public good, i.e. such that H lmax > as L a + b + as L (l max 1) Ã lmax! X H k H lmax +1 (8) 1 The conjunction of Lemmata 1 and 2 implies that the range of t F can be partitioned into [0, ˆt F l max ), [ˆt F l max, ˆt F l max 1 ),...,[ˆt F 1, 1], so that each of these intervals defines a range of tf corresponding to a given value of L. These intervals are bounded by the federal tax rates, ˆt F j (not necessarily optimal, from the perspective of a voter in region j), at which region j ceases local provision, i.e., at which t j (ˆt F j )=0. (For j>l max, t F j = 0.) Substituting t j =0andl = j into (6) and solving for tf ( ˆt F j ), we obtain ˆt F j = (a + b + as L (j 1))H j as L jp, (9) (a + b + as L (j 1))H j +(a + b as L ) a b s jp F H T as L H k 1 H k 1 which j l max is greater than 0. Then, for t F < ˆt F j and t j [0,t j (ˆt F j, )), voters in region j wish to procure more public good through some form of increased taxation. Given this partition of the policy space, we proceed by identifying the extrema on each interval. 11

13 In the presence of spillovers, there may exist multiple local optima, and regions preferences are neither necessarily single-peaked nor necessarily order-restricted. Although this means that we cannot rely immediately on standard theorems for aggregating preferences over t F, we can provide sufficient conditions for the existence of a unique stable outcome of majority rule and characterize that outcome. The next two propositions identify such conditions, and characterize two qualitatively different and mutually exclusive equilibria that obtain when they are satisfied. These equilibria differ dramatically in the composition of the coalitions supporting a greater or lesser degree of federal provision: in the first equilibrium, it is the citizens of the wealthiest regions (whether or not they are wealthy themselves) that prefer greater federal provision in opposition to the poorer regions preference for local provision; in the second equilibrium, the citizens of the wealthiest and sometimes also of the poorest regions prefer local provision, in opposition to the middle-income regions preferences for federal provision. Our sufficiency conditions for the existence of these equilibria identify the preference profiles that are order-restricted, and, as we show in Claim 1 in the Appendix, together they identify all such preference profiles. The restrictions on the preference profiles of the federation they entail are expressed in terms of two functions f(j; a, b, s L,s F,H)andg(j; a, b, s L,s F,H), such that the sign of f( ) determines whether the utilities of the citizens of the jth region are increasing in federal tax rate at a federal tax rate of 0, and the sign of g( ) whether their utilities are decreasing in federal tax rate at the federal tax rate at which that region ceases to provide locally, ˆt F j. We use these functions to establish necessary and sufficient conditions for all voters in regions that are local providers to have monotonic preferences over those federal tax rates at which they would engage in supplemental local provision, and then show that, if the voters have such preferences, the preference profile is order-restricted. In Proposition 1, the relevant ordering is by regional income; however, in Proposition 2, it is not. We characterize both functions explicitly in the Appendix and discuss their responsiveness to changes in parameter values later in this section of the paper. Recall that all citizens of a given region have identical induced preferences over tax rates and that j indexes regions in the descending order of their total (or average) income. Letting m index the median region region in this ordering, we can now formulate the following result: 12

14 Proposition 1 If f(1; a, b, s L,s F,H) > 0, then there exists an equilibrium with the following properties: (1) regions that engage in local provision at t F strictly prefer a higher tax rate, and each region s most-preferred tax rate is one at which it does not engage in local provision; (2) most preferred federal tax rates are weakly increasing in regional income; (3) there exists a Condorcet winner t F, which coincides with the most-preferred federal tax rate of the median income region, i.e., t F = t F m ; (4) the m poorest regions (comprising the majority of member regions of the federation) do not engage in local provision at the equilibrium federal tax rate. Proof See Appendix. Proposition 1 characterizes one set of strategic incentives that heterogenous-income regions face in federal systems with two levels of public good provision. Under the specified conditions, a majority of regions (and so of the citizens of the federation) select a low federal tax rate, anticipating that a minority of wealthier regions will provide additional amounts of the public good. 8 Because members enjoy positive externalities from public goods provided by other regions, free-riding on the provision of the wealthier regions at a lower level of federal provision is sometimes more attractive for the citizens of a poorer regions than is a more efficient level of provision that entails paying a higher federal tax. The properties of the equilibrium characterized in Proposition 1 are consistent with the seemingly puzzling fact that in the United States (poorer) federal units, which would seem to benefit most from redistributive federal programs, tend to oppose the expansion of the federal government, while the states that bankroll the federal programs tend to support it (Lacy 2004). Proposition 1 suggests that when its antecedent condition holds, this fact need not be paradoxical. When the public goods are substitutes, the presence of across-states externalities may make it so that the net 8 A similar logic underlies the equilibrium pattern of provision characterized in Alesina et al. (2005) for regions differing in their primitive taste for the public good, rather than in wealth as in our model. 13

15 receipt of federal funds to finance public good provision, coming at some non-zero price, is in the end worse for some states than free-riding on the spillovers from the public good provision in other states. The poorer (and hence, net federal financing recipient) regions/states object to the increases in federal provision, whereas the wealthier (and hence, net federal taxpayer) regions/states prefer relatively higher levels of federal provision. If so, then the states may be expected to respond precisely in a way consistent with the observed red states / blue states pattern. 9 We next provide another sufficient condition for the existence of the Condorcet winner, under which t F j (t, ) is weakly non-monotonic. Proposition 2 If there exists ˆl l max such that g(j; a, b, s L,s F,H) < 0 for every j ˆl, and,for ˆl <lmax,f(ˆl +1;a, b, s L,s F,H) > 0, then there exists an equilibrium with the following properties: (1) the wealthiest ˆl regions strictly prefer to decrease t F, and have a most-preferred federal tax rate of 0; every other region that engages in local provision at t F strictly prefers to increase it, and its most-preferred tax rate is one at which that region does not engage in local provision; (2) the most-preferred federal tax rate is weakly non-monotonic in regional income, with middle income regions preferring higher tax rates than do wealthier and poorer regions; (3) a unique Condorcet winner t F exists and is (a) 0 if m ˆl,or(b)t F if m>ˆl; m+ˆl (4) the wealthiest ˆl regions engage in local provision at the equilibrium federal tax rate t F. Proof See Appendix. 9 As an empirical matter, this pattern is surely overdetermined by other causal antecedents as well. Our point here is only that that data pattern is consistent with the causal mechanism we expect to be widely operative in federal structures. Moreover, in the context of public good provision accounts, the mechanism we identify is more appealing than those that rely on differences in the demand for public good induced by the differences in production technologies across states. Such differences (which are not modeled in this paper) are likely to work in the opposite direction from that which would be necessary to produce the observed pattern: it is unlikely that poorer states, with, among other things, worse economic infrastructures, have a lower need for the public good component in their production technologies. 14

16 The preference profiles that satisfy the conditions identified in Proposition 2 may give rise to majority coalitions with very different compositions. While some profiles result in an equilibrium in which the voters are divided by differences in regional income - i.e. the richer regions, which favor no federal provision, versus the poorer ones - other profiles produce an equilibrium in which the richest and poorest regions ally against the middle-income regions. In such cases, the rich and the very poor regions prefer little or no federal provision, and the middle-income regions champion higher federal tax rates. To be sure, the rich and the poor regions favor low taxes for different reasons. The citizens of the richer regions oppose the redistributive effects of federal provision. The poorest regions are, in such profiles, so poor relative to the rich regions, and obtain so much public good from the local provision of other regions (in the total absence of federal provision), that their demand for additional private good is greater than their demand for additional public good. This ends-against-the-middle result is the opposite of that of Epple and Romano (2003), in which the rich and poor desire higher taxation than do the middle-income voters. Because in their model, the public good is assumed to be truly global, every agent prefers additional federal provision to her own voluntary (local) provision of the good, since she bears only a fraction of the cost under the former scheme that she bears under the latter, while enjoying access to the same amount of the public good. Hence, in their model, the richest agents always demand high levels of federal taxation. Lower-income agents may demand higher levels of federal provision than middle-income agents, however, producing a coalition of rich and poor in support of higher taxation. By contrast, in the present paper, because the quantity of public good that an agent enjoys depends not only on the resources allocated to its production, but also on the location of its production in the federal system, wealthy regions may experience a decrease in the amount of public good that they enjoy as federal taxation increases. It is also the case that different regions engaging in local provision enjoy different amounts of the public good, giving rise to the possibility that, while some may be harmed by increases in federal provision, other local providers benefit from it. Thus citizens of middle-income regions may prefer higher levels of federal provision than do citizens of the rich and poor regions. 15

17 The Induced Preferences Over Federal Tax Rates: the Intuitive Characterization Figure 1 depicts the indirect utilities u(t F,t (t F )) over federal tax rates for the members of a federation composed of five regions, where the antecedent condition of Proposition 2 holds. Because, as already established, all the citizens of a given region have identical induced preferences over tax rates, we depict the indirect utility of one citizen in each region, with an individual income equal to the region s average per capita income. Without loss of generality, we will refer to the preferences of the citizens of a given region as the region s preferences throughout the following discussion. FIGURE 1 ABOUT HERE Regions 1 and 2, which are the wealthiest members, have strictly decreasing utility. Both 1 and 2 engage in local provision at Region 3 s most-preferred federal tax rate, t F 3. Regions that do not engage in local provision over a given interval of federal tax rates share the same preferences over those tax rates, e.g. regions 1, 2, and 3 all have a maximum at t F 3, and 1 and 2 both have a higher maximum at t F 2, indicating that they both prefer tf 2 to t F 3. Region 3 does not have a maximum at t F 2 because it engages in local provision at that tax rate, t F 2 < ˆt F 3 tf 3. Because regions not engaging in local provision over a given interval of federal tax rates have the same preferences, and because poorer regions stop providing locally at lower tax rates than do richer regions, a poorer region may prefer a lower tax rate than does a richer region, but it will never prefer a higher one. For this reason, most-preferred tax rates are weakly increasing in income among all regions that strictly prefer higher tax rates when they are local providers (i.e. all local providers under the conditions of Proposition 1, and {ˆl +1,...,l max } under the conditions of Proposition 2). Regions that do engage in local provision over a given interval of federal tax rates do not necessarily share the same preferences over those tax rates, however. Although Regions 1, 2, and 3 all engage in local provision on [0, ˆt F 3 ), 3 prefers higher tax rates on this interval, whereas 1 and 2 prefer lower tax rates. This difference is a result of the unequal distribution of wealth and the fact that different local providers enjoy different amounts of public good, insofar as they obtain greater benefit from public goods produced in their own districts (s L < 1). The conditions for the existence of a voting equilibrium in Propositions 1 and 2 are closely 16

18 related. In each case, the relevant conditions are those necessary to guarantee that, in every region, the voters have monotonic preferences on the interval of federal tax rates for which their own region does engage in local provision, [0, ˆt F j ], i.e., each must either strictly prefer higher taxation or lower taxation over those tax rates for which its own region is a local provider. The direct effect of increasing the federal tax rate on the amount of public good j enjoys is positive, but it is offset by all local providers reducing their local provision in response. While the marginal increase in federal provision is constant, the marginal decrease in local provision grows smaller as fewer regions engage in local provision, since regions who have ceased local provision entirely cannot reduce their local provision further in response to increases in federal provision. Thus if, for a citizen of region j, theformereffect dominates the latter effect for some number of local providers, then it does so for fewer local providers as well. Therefore to insure that her consumption is strictly increasing in federal tax rate (for as long region j is a local provider), it is sufficienttoinsurethatitisincreasing on [0, ˆt F l max ), as in Proposition 1. Similarly, to insure that consumption is strictly decreasing in federal tax rate, it is sufficient to insure that it is decreasing on [ˆt F j+1, ˆt F j ), as in Proposition 2. Because the citizens of a richer region pay more than those of a poorer one for a given increase in federal provision, the richer region reduces its local provision more quickly than does the poorer one as the federal tax rate increases. Thus the amount of public good enjoyed, and hence consumption, decreases more quickly or increases more slowly for the richer region. It follows that, given two local providers for whom consumption is decreasing at t F = 0, the consumption of a citizen of the poorer region will reach its minimum at a lower federal tax rate. Thus if the richest region s consumption is increasing on [0, ˆt F l max ), as required in Proposition 1, then all poorer local providers must also have increasing consumption on [0, ˆt F l max ). To insure that consumption is strictly decreasing on [0, ˆt F j ], as for the citizens of the ˆl richest regions in Proposition 2, it is sufficient to require that the citizens of the poorest such region providing locally at t F have decreasing consumption. Because poorer regions stop providing locally before richer regions, as established in Lemma 1, this requirement is equivalent to the statement in Proposition 2. 17

19 Evaluating Sufficiency Conditions To understand the weight of the sufficient conditions in Propositions 1 and 2, note first that the number of regions that provide the public good locally in the absence of federal provision, l max, is independent of the benefits of federal provision, s F. Given this independence, it is evident that f s F > 0and g s F > 0. Consequently, as s F increases, the antecedent of Proposition 1 is more easily, and the antecedent of Proposition 2 less easily, satisfied. Benchmark: pure public good, s L =1 µ lmax a P When s L = 1, then (8) reduces to H lmax > b+al max H k H lmax +1. The conditions for 1 Proposition 1, then, reduce to f(1; s L =1, ) =bs F H T b l max P H k > 0, which is satisfied whenever lmax P H k 1 s F >. Note that this ratio is always less than 1. This means that the wealthy regions H T may prefer federal provision to local provision even when the technology of federal provision is less efficient than that of local provision. The special case in which s F = s L = 1 may be thought to correspond to the world in which federal tax revenue is divided equally amongst the districts to fund the local production of the public good (using the same technology as the one they use for producing a locally financed public good). If s L =1, then f(j; s L =1, ) > 0 reduces to bs F H T b l Pmax H k > 0andg(j; s L =1, ) < 0 1 reduces to bs F H T P b j H k < 0. These conditions are jointly satisfied only if ˆl = l max. It follows 1 that a necessary and sufficient condition for the satisfaction of the conditions for Proposition 2 is g(1; s L =1, ) < 0, which reduces to s F < H 1 < 1. This condition is satisfied when s H T F is relatively small (i.e., federal technology of provision is relatively inefficient) or the wealthiest region controls most of the wealth of the federation. 1 Impurepublicgood,s L < 1 In this, more general, case, it is useful to return to the formulation of s F as a function of s L, s F = γ (1+s L(n 1)) n. Recall that the federal means of provision is inherently less efficient than the local means of provision if and only if γ < 1. (Recall also that the existence of spillovers may make membership in the federation attractive even if γ < 1.) Table 1 below shows the values of γ that 18

20 correspond to different values of the spillover coefficients s L and s F. A line is drawn demarcating the cases in which the federal means of production is more efficient, corresponding roughly to the upper-right portion of the table, and cases in which the local means is more efficient. Because the number of regions engaging in local provision in equilibrium at any given tax rate is defined implicitly by a system of inequalities, it is difficult to obtain comparative statics for f(j, a, b, s L,s F,H)andg(j, a, b, s L,s F,H) analytically for most parameters of the model, and so here we report results of numerical estimations of the determinants of sustaining the existence results in Propositions 1 and 2. For a particular set of parameter values (a = 0.6, b = 0.4, H = (100, 90, 80, 70, 50)) we estimate l max, represented here by superscripts, and the values of f(j, a, b, s L,s F,H)andg(j, a, b, s L,s F,H). The bold-faced cells to the left of the s F =.5 column correspond to cases in which Proposition 2 holds, and the bold-faced values in the cells to the right of it to cases in which Proposition 1 holds. TABLE 1 ABOUT HERE We might expect, absent strategic and redistributive effects, that members would prefer federal provision when it is more efficient, i.e. when γ > 1, and local provision when it is more efficient, i.e. when γ < 1. However, the redistributive features of federal provision and the voluntary nature of local provision complicate the effect of relative technological efficiency on induced preferences in equilibrium. Because a condition of federal provision is that each region enjoys equal amounts of the federally-provided good, and because the regions have unequal wealth, federal provision is redistributive, dampening the richest region s enthusiasm for that means of provision. Redistribution does not explain a second interesting feature of the results, however: satisfaction of the antecedent of Proposition 1 is non-monotonic in γ. For example, although it is satisfied for {s L =.9, s F =.7, γ =.76} and {s L =.9, s F =.9, γ =.98}, itisnotsatisfied for {s L =.7, s F =.7, γ =.92} or for {s L =.5, s F =.5, γ =.83}. Similarly, it is satisfied for {s L =.5, s F =1.5, γ =2.50}, but not satisfied {s L =.3, s F =1.1, γ =2.50}. This non-monotonicity is the result of the voluntary nature of local provision and the strategic response of regions local provision choices to increases in federal provision. While the citizens 19

21 of each local provider may benefit directly from switching to federal provision because it is technologically more efficient sufficiently more efficient to compensate for redistributive effects they suffer indirectly from other regions reducing local provision in response to the increase in federal provision. The condition f(1,a,b,s L,s F,H) > 0issatisfied only if the former effect is greater than the latter. Not all regions are necessarily able to reduce their provision of the public good in response to federal provision, however. When spillovers from local provision are sufficiently large, the poorest regions will not engage in local provision even in the total absence of federal provision, because they consume enough of the public good locally provided in other regions. It follows, then, that they will not be able to respond to increases in federal provision, and thus the net effect of increasing federal taxation on the utility of the richer regions will be greater than it would be if all regions were initially engaged in local provision. For this reason, citizens of richer regions find federal provision more appealing when, ceteris paribus, fewer regions are engaging in local provision, and, as the entries in Table 1 show, the antecedent condition of Proposition 1 is more likely to be satisfied, for a given value of γ, whenl max is lower. Given that redistribution is inherent in federal provision, and given the dependency of the above results on the number of regions that engage in voluntary provision, the satisfaction of the existence conditions also depends on the dispersion of the distribution of regional income. The antecedent of Proposition 2 is more easily satisfied for more dispersed income distributions. The satisfaction of the antecedent condition of Proposition 1 is non-monotonic in the dispersion of the income distribution, however. It is satisfied for sufficiently egalitarian distributions of income because there is little redistribution and little difference in the behavior of the regions in such cases. It is also satisfied for sufficiently inegalitarian distributions, because in such cases the poorer regions do not engage in local provision at any federal tax rate. For intermediate levels of dispersion in the income distribution, the condition is not satisfied because the poorer regions reduction in levels of local provision outweighs the additional direct benefits to the richer regions of federal provision, as discussed above. The effects of increasing the dispersion of the distribution are the same whether the median is less than the mean or vice versa. 20

22 The Effects of Spillovers To determine the effect of introducing positive spillovers into the model of federations with two levels of public good provision, we next provide the properties of the equilibrium in the federation when s L =0. LetH m be the total income in the median region of the income distribution. Then: Proposition 3 In the federation without inter-regional spillovers (s L =0): (1) if s F > Hm H T, then t F = b a+b and the median and all poorer regions choose t j =0; (2) if s F < Hm H T, then t F =0and all regions j choose t j = Proof See Appendix. In the federation without inter-regional spillovers, if s F > H 1, then all citizens of all regions H T prefer pure federal provision, i.e., t F = b a+b and t j = 0, for all j N; ifs F < Hn then all H T, citizens of all regions prefer pure local provision, i.e., t F =0andt j = b a+b, for all j N. The inter-regional disagreement occurs when the efficiency of federal provision is in the middle-range, i.e., when s F ( H n, H H T 1 ). In that case, citizens of some regions prefer federal, and citizens of H T others pure local, provision. Since within each region, voters share induced preferences over t F, the outcome of majority rule in the federation as a whole is identical to the outcome of weighted voting b a+b. among member states, where weights are proportional to states populations. Moreover, since, by assumption, all regions have equal populations, we can, in this and the subsequent results, restrict our attention to simple majority rule among regions. Because the regional preferences are single-peaked, the Condorcet winner always exists, and the prediction is straightforward. We can now ascertain the direct effects of the existence of spillovers in a federal system with joint federal and local provision, by comparing the results of Proposition 3 with those in the model with positive local (inter-regional) spillovers. The following proposition summarizes the salient features of this comparison: Proposition 4 (1) If s F < H m, the presence of local spillovers lowers local provision in the median H T and richer regions, leaving constant the majority s preferences over federal provision. (2) If s F > H m, the presence of local spillovers (weakly) lowers federal provision, leaves local H T provision unchanged for the majority of regions, and (weakly) increases local provision for a minority 21