MICHEL LE BRETON and SHLOMO WEBER^*

The world political map has undergone dramatic changes since World War II. The number of independent countries in the world almost tripled over the second half of the last century, rising from a mere 74 in 1946 to 193 today; 45 percent of countries that exist today have a population under five million people. The abolition of colonial rule in Africa in the 1960s created 25 new countries. The last decade brought the next major wave of border changes, highlighted by the breakups of the former Soviet Union, Yugoslavia, and Czechoslovakia and the reunification of Germany. Quebec’s recent secession bid was defeated by a majority of less than 1 percent. One can also point to Belgium’s process of “defederalization” and Scotland’s and Wales’ paths to devolution. Various types of separatist movements are active in Africa (Nigeria, Senegal, Angola, Côte d’lvoire), Asia (China, India, Indonesia), and Europe (Denmark, Spain, France, Italy, Russia, Yugoslavia), and conflicts over fiscal redistribution, regional power, and autonomy mushroom all over the globe.

The purpose of our paper is to examine distributive policies of the central government that would prevent a threat of secession by any of a country’s regions. The government’s objective is to design a transfer policy that would render the advantages of secession for every region inferior to the benefits of remaining within an integrated country. The analysis of advantages and disadvantages of a secession points out the trade-off between economies of scale in big countries and the costs of heterogeneity in large populations. As Barro (1991) puts it, “We can think of a country’s optimal size as emerging from a trade-off: A large country can spread the cost of public goods over many taxpayers, but a large country is also likely to have a diverse population that is difficult for the central government to satisfy.” Larger political jurisdictions bring about several benefits: the per capita cost of producing public goods declines with the population size of the country¹; larger countries rely more heavily on more efficient taxes² and enjoy economies of scale in the utilization of computer hardware and software systems in their tax collection³; the size of a country’s potential market is affected by the size of the jurisdiction in a world with barriers to trade⁴; larger countries are better equipped to absorb uninsurable shocks in different regions⁵; influence and security considerations may also matter.⁶ On the other hand being small has its advantages, as relative ethnic, religious, and cultural homogeneity is positively correlated with a country’s institutional efficiency⁷; small countries are usually more open to trade⁸ and adjust better to dealing with technological changes in the world markets; and interest groups and unproductive activities play a lesser role in smaller countries.⁹

Since the focus of our paper is the analysis of secessions, we consider a model with one nation and do not address the more general issue of border redrawing. It might be possible that in some situations a secession would necessitate redrawing of borders in several countries (e.g., the idea of “Greater Albania” consisting of Albania itself, Kosovo, and parts of the former Yugoslavian province of Macedonia; creation of the Basque country from the Basque areas in France and Spain; and the formation of Kurdistan from the Kurdish enclaves in Turkey, Iran, and Iraq). It is quite obvious that the probability of any of those scenarios coming true anytime soon is not very high; and indeed, most secessionist movements and tensions are internal to nations.

In our framework, a national policy consists of two components: a choice of public policy, which can be interpreted as composition of public expenditure, location of the central government, tax rates, immigration quotas, or any other issue of national interest; and a citizen-specific cost allocation designed to cover fixed government costs. This model allows us to examine the trade-off between heterogeneity of citizens’ preferences and increasing returns to scale in larger countries. The heterogeneity of preferences is described by the density function representing a number of citizens of each type, whereas the advantages of size are captured by sharing the fixed government costs among a larger number of citizens.

To address the issue of secession we first examine¹⁰ whether, given heterogeneity of citizens’ preference, it is desirable and socially efficient to maintain the unified country. We consider a notion of efficiency of cooperation among different regions of a country that is the case when all regions are better off under a single national government. The efficiency of cooperation does not necessarily imply that the gains from cooperation can be allocated in such a way that no region can ensure all its citizens a higher payoff than guaranteed by the central government. If no such allocation is feasible, some regions may become secession-prone. We investigate the existence of cost allocations that do not create secession-prone regions. If such an allocation exists, we call it secession-proof and the cooperation would be stable and sustainable. The requirement of stability is, in principle, stronger than that of efficiency. However, our first result suggests that, under quite general assumptions, high government costs eliminate the gap between efficiency and stability, thus reconciling these two notions. Then, whenever the cooperation is efficient, it is also stable, and the unified country is not subject to secession threats.

It is important to mention the way a cost allocation assigned to country’s citizens represents a transfer policy of the central government. The crucial element in designing a secession-proof transfer scheme is the degree of equalization between advantaged and disadvantaged regions of the country. Indeed, some equalization is required in order to support disadvantaged regions that may be vulnerable to secessionist threats in the absence of equalization transfers. Thus, one of the central government’s objectives is to design an equalization scheme that would eliminate, or at least reduce, the horizontal imbalances among the regions and deter their threat of secession. Ter-Minassian (1997) argues for a need for transfers to address this issue: “If local jurisdictions must rely on their own revenue sources, the poorer jurisdictions will have less resources than the richer ones. Therefore, they will not be able to finance services at the same level as the richer jurisdictions. Should a country accept this differentiation in the quality of services? If not, there is a need for the transfer of resources from rich to poor jurisdictions.” Ahmad and Craig (1997) point out that, indeed, “national governments may wish to ensure that citizens in different regions and localities have access to a certain modicum of publicly provided services.” To achieve this goal, horizontal imbalances in fiscal capacity should be addressed by equalization transfers from the center or among regions. Our second result derives a structure of equalization transfers under the requirement of secession-proofness. It establishes the principle of partial equalization, which asserts that

• in order to prevent a threat of secession by disadvantaged regions, they must be subsidized by advantaged regions; and

• in order to deter a threat of secession by advantaged regions, their required contributions should not be excessive.

We specifically determine a degree of partial equalization generated by secession-proofness and show that, in the case of the uniform distribution of citizens’ preferences, the equalization rate is exactly 50 percent. We also demonstrate that, in the absence of a redistribution mechanism, no intervention approach may leave disadvantaged areas of the country prone to secession. On the other hand, the Rawlsian transfer scheme, which completely equalizes the fiscal capacities of all regions, would cause advantaged regions to threaten to secede.

The principle of partial equalization suggests that, although the gap between advantaged and disadvantaged regions must be reduced, it should not be completely eliminated.

Before proceeding with the body of our analysis, let us briefly discuss how this work connects to the most closely related literature.¹¹

I. Some Related Literature

First, we would like to compare our analysis with that of Alesina and Spolaore (1997) (AS, henceforth). The only relevant difference between the two definitions of secession-proofness¹² is the set of policy instruments available to the country or any of its potentially seceding regions: AS consider the equal share of the government cost, whereas we allow for the full range of compensation schemes. The AS result reconciles stability and efficiency in the sense that, when the number of countries reaches the efficient threshold, no region would want to break away. In our single-country setup this translates into the elimination of a threat of secession in an efficient nation. As an entry-deterring instrument, transfers, therefore, become redundant if the nation and potential seceding regions are limited to the equal-share cost allocations.

The AS result has, however, been derived under the assumption of the uniform density of citizens’ preferences. The uniform distribution is a case of a nonpolarized society, and the natural question is whether the irrelevance of equalization schemes as a secession-deterring device would hold under an increased degree of polarization of a country’s citizens. Haimanko, Le Breton, and Weber (2003) provide a negative answer to this question and show that if the degree of polarization of citizens’ characteristics is sufficiently high, then, in the absence of transfers, an efficient cooperation, in general, is not stable and the efficiency alone does not eliminate a threat of secession by a country’s regions. This argument strengthens the need for an examination of equalization schemes as a device against possible secessions in countries where the citizens’ preferences exhibit a high degree of polarization and heterogeneity.

The heterogeneity of citizens’ preferences over the provision of public goods has been studied by Casella (1992), Casella and Feinstein (2002), Feinstein (1992), Perroni and Scharf (2001),¹³ and Wei (1991) who (implicitly or explicitly) utilized the Hotelling location model. Cremer, De Kerchove, and Thisse (1985) develop a model that examines the number and location of public facilities. There is also a literature rooted in the Tiebout tradition (Wooders, 1978; Guesnerie and Oddou, 1981, 1987; Greenberg and Weber, 1986; Weber and Zamir, 1985), where the heterogeneity of preferences among individuals and the impossibility of lump-sum financing of public good provision lead to the formation of small jurisdictions. These papers focus on the existence and the characterization of stable partitions of the individuals into jurisdictions, where equilibrium and stability notions capture various scenarios concerning the mobility of individuals and groups of individuals across jurisdictions and the decision-making process about the level of public good provision. The equilibrium and stability notions used in these papers represent a mix of cooperative and noncooperative concepts. The noncooperative nature comes through the usage of the concept of Nash equilibrium and its refinements, and a partition of individuals into jurisdictions is an equilibrium if no individual would find it beneficial to move to another jurisdiction. The cooperative features are introduced by allowing coalitional considerations, where it is assumed that coalitions can enforce specific feasible plans of action if they desire to do so. The mere knowledge of the payoffs of each coalition is sufficient to make predictions on the likely outcome of the game. Our paper follows this tradition by recognizing the role of coalitions without constraining the rules of their formation.

Another related group of papers focuses primarily on the heterogeneity in income rather than individuals’ preferences. The first contribution to this line of research was made by Buchanan and Faith (1987), who explore the limits that the threat of secession puts on the tax burden imposed by the majority (which can be rich or poor). This question is the subject of Bolton and Roland (1997), who develop a model of a two-region nation with different gross income distributions. Their main focus is to examine how the threat of secession determines the choice of a purely distributive taxation rate, under the assumption that if secession takes place, all gross incomes are deflated by a common factor. They show that fiscal accommodation in the union reduces the likelihood of secession, but by no means prevents the breakup of the nation under all circumstances. In addition, fiscal accommodation may, surprisingly, lead to higher taxes. As explained in Persson and Tabellini (1999), the identification of the equilibrium secession-proof tax rate is not straightforward, due to the fact that individual preferences may fail to be single-peaked. The Bolton and Roland model has been extended to allow for mobility across borders (Olofsgard, 1999) and the introduction of region-specific shocks (Fidrmuc, 1999).

Federations may also be considered from a contractual perspective. What sort of arrangements or constitution, including secession clauses, should be considered to promote efficiency? Drèze (1993) investigates how assets and liabilities should be appointed at the time of a secession and argues in favor of distributive neutrality. Bolton and Roland (1997) have interesting insights on the determinants of the most preferred arrangement. Persson and Tabellini (1996a,b) examine a risk-sharing argument under moral hazard considerations. More recently, Bordignon and Brusco (2001) offered an analysis of secession rules, arguing that the absence of explicit secession rules can be seen as a commitment device to increase the stability of the federation. A comprehensive analysis of constitutional provisions on country formation was provided by Jehiel and Scotchmer (2001).

Finally, our paper also relates to the huge empirical public finance literature on transfers across regions targeted at reducing their horizontal imbalances. Implicit transfers across regions are often generated by taxation systems and the design of public spending programs. Many countries, including Canada, Belgium, Germany, and Switzerland, have also adopted explicit interregional transfer rules that are motivated mostly by equity and solidarity considerations. The literature has focused on whether these rules lead to underequalization or overequalization. Although equalization is not driven by equity considerations in our paper, it turns out that secession-proof transfer schemes will entail some form of partial equalization.

II. The Model

We consider a country whose citizens have preferences over the unidimensional policy space I, given by the interval [0, 1] with a mass of 1. Each citizen has symmetric single-peaked preferences over the set I and we identify each citizen with an ideal point. The distribution of all ideal points (and, thus, of all citizens’ preferences) is given by a cumulative distribution function F, defined over the space I. We assume that F has a density function f that is positive and continuous everywhere on the interval [0, 1].

The country chooses a policy in the issue space I. In this paper we adopt a spatial interpretation of our model and identify a policy with a location of the government and we do not distinguish between geographical and preference dimensions. The country has to cover the cost of provision of public good g, which we will simply call a government cost. We assume that the cost of the government g is fixed, so if a region of the country secedes from I, it will have to cover the same cost g. For simplicity, we restrict our analysis of possible secessions to those subsets of I that consist of the union of a finite number of intervals and we will use the term region for such a subset of citizens.

the minimal transportation cost of the citizens of S.¹⁴

Let us introduce the notion of an S-cost allocation that determines the monetary contribution of each individual t towards the cost of government g.

For notational simplicity we assume hereafter that a, the marginal rate of substitution between money and the distance to the location of the government, is equal to I.¹⁵

Since the transportation costs incurred by citizens are represented by the distance between their location and the policy chosen by the country or the region to which they belong, it again points to the aforementioned conflict between heterogeneity and increasing returns to size. Indeed, on the one hand, a larger country would require a smaller per capita contribution toward government costs g given by an S-cost allocation x. On the other hand, the bigger the country, the greater the chance that the government’s location is far away from citizens living on the margin. One would expect that higher government costs would strengthen the cooperation, so that increasing returns to size would outweigh secession tendencies created by heterogeneity of citizens’ preferences.

To examine this issue formally, we introduce the notions of efficiency and stability of cooperation. Cooperation among the different regions of the country would be efficient if no breakup of the country into smaller parts can provide a total benefit exceeding that generated by the united country. As Wittman (1991) puts it: “Two nations would join together (separate) if the economies of scale and scope and the synergy produced by their union created greater (smaller) benefits than the cost.”

Consider all possible partitions of the interval I into several connected or disconnected intervals. A typical partition P of I would consist of a number of smaller regions {S₁, S₂, …, S_K}, where each individual t ∈ I belongs to one and only one region in P. The following definition in the game-theoretic terminology amounts to super-additivity:

Let us now turn to stability of cooperation, which requires not only positive gains from cooperation but also a mechanism that will allocate those gains in such a way that no separate region S can generate a higher payoff to all its members than that guaranteed to them by the central government. Given a cost allocation and location of the central government, regions of a country may contemplate the possibility of secession. If a region S can make its members better off than under the central government, then S would be prone to secession:

If no region is prone to secession, then the pair (p; x) is called secession-proof. The cooperation is called stable if there exists a secession-proof allocation.

Since throughout the rest of the paper we deal only with cost allocations defined for the entire interval I, we shall call an I-cost allocation simply a cost allocation.

We now state an important property of secession-proof allocations. It implies that under secession-proof allocation each region is required to make a nonnegative contribution toward government costs. That is, secession-proofness rules out direct subsidization. The reason is obvious: If region S receives a net transfer via cost allocation, the burden of government costs will fall on the rest of the country T= I \ S that would make region T prone to secession.

Lemma 2.4: Let x be a cost allocation. Suppose that there exists a region S such that $\begin{array}{c}{\int }_{s}x\left(t\right))f\left(t\right)\mathrm{dt}<0.\end{array}$. Then for any location of the government p, the region T=I\S is prone to secession, and therefore the pair (p, x) is not secession-proof.

To complete this section we would like to point out that gains from cooperation will emerge only if the government cost is sufficiently high. If the government cost is low, then no cooperation would emerge, that is:

Proposition 2.5: There is a cutoff value of government costs g_e such that cooperation is efficient if and only if g ≥ g_e.

Similarly, if government cost is low, there is little incentive for different regions to stay together in one country. (In the extreme case where g is zero, every cost allocation would be secession-prone.) Conversely, if the government cost is prohibitively high, no region would be able to pose a threat of secession.

Proposition 2.6: There is a cutoff value of government costs g_s such that cooperation is stable if and only if g ≥ g_s.

As we mentioned above, stability of cooperation requires not only positive gains from being together but also the ability to distribute these gains without creating secession-prone regions. That is, the stability requirement is stronger than the efficiency one:

Proposition 2.7: If cooperation is stable, it is also efficient, i.e., g_s ≥ g_e.

In the next section we derive the conditions under which stability and efficiency yield the same cutoff value, g_s = g_e. This would determine the lower bound on government costs yielding a secession-proof allocation.

III. The Main Result

As we have stressed above, the designer of the transfer scheme will have to meet two possibly conflicting objectives. On the one hand, it is important to identify the conditions under which the mere existence of gains from cooperation yields the possibility of reallocating these gains without creating regions that are prone to secession. It is also much easier to verify whether cooperation is efficient by simply observing the economies of scale rather than examining threats of secessions by every region. Our main result reconciles the two objectives: we establish that, under some general conditions, the bounds on efficiency and stability are the same.

We use two conditions to obtain our equivalence result. The first is

Symmetry: f(·) is symmetric with respect to the center, i.e., f(t) = f(1-t) for all t ∈ I.

This assumption is quite standard. It implies that the midpoint of the country, ½, is not only its geographic center but is also the median of the distribution of citizens’ location. In our analysis of secession-proof allocations, we therefore restrict our attention to the situations where the government is located in the middle of the country. Thus, instead of considering a pair (p, x) in Definition 2.3, we focus only on cost allocation, assuming that the national government is always located at the point ½.

Our second assumption is:

Gradually Escalating Median (GEM): l′(t) < 1 on the interval [0, 1.

This assumption implies that if we increase the length of the interval L_t = [0, t] by a small positive number δ, then the median of the interval L_{t + δ} = [0, t + δ] increases by an amount less than δ. Obviously, the symmetry of the distribution represented by (2) immediately implies that if l′(t) < 1, then r′(t) < 1. The class of distribution functions satisfying the condition of gradual escalation is quite large. In particular, it includes all log-concave functions,¹⁶ i.e., those for which the logarithm of the cumulative distribution function F is concave on the interval [0, 1]:

Remark 3.1: If the distribution function is log-concave it satisfies GEM.

The log-concavity assumption is satisfied for a wide range of symmetric distribution functions. For example, all symmetric distribution functions that are concave and have an increasing density on the interval [0, ½] are log-concave. It is important to note, however, that the assumptions of GEM and log-concavity allow for populations exhibiting higher density on the borders than in the center. For example, the distribution function whose density is given by

$\{\begin{array}{ccc}-t+1.25& \mathrm{if}& t\le \frac{1}{2}\\ t+0.25& \mathrm{if}& t\ge \frac{1}{2}\end{array}$

is log-concave (and therefore satisfies GEM). Moreover, the function whose density is

$\{\begin{array}{ccc}-1.2t+1.3& \mathrm{if}& t\le \frac{1}{2}\\ 1.2t+0.1& \mathrm{if}& t\ge \frac{1}{2}\end{array}$

is not log-concave but nevertheless satisfies GEM and, therefore, also belongs to the class of functions covered by our main result (see Figure 1).

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Bimodal Distribution That Satisfies GEM

Citation: IMF Staff Papers 2003, 003; 10.5089/9781589062030.024.A004

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In order to formally state our main result, let us turn to a closer examination of secession-proof allocations. Lemma 2.4 implies that every citizen makes a nonnegative contribution toward government costs. Since we assume the symmetry of the citizens’ distribution with respect to the median, it is crucial to examine how the contribution of each citizen is correlated with distance to the location of the government. We have to take into account horizontal imbalances among regions and design an equalization mechanism between advantaged citizens (those close to the center) and disadvantaged ones (those close to the borders). To what extent, if at all, should the more disadvantaged regions be compensated via resulting cost allocation?

For this purpose, consider the cost allocation x_g(t), which is defined as follows:

$x_g\left(t\right)\{\begin{array}{ccc}r\left(t\right)+\lambda & \mathrm{if}& t\le \frac{1}{2}\\ r(1-t)+\lambda & \mathrm{if}& t\ge \frac{1}{2}\end{array},$

where the value of λ is chosen to satisfy the country’s budget constraint:

$\lambda =g-2{\int }_0^{\frac{1}{2}}r\left(t\right)f\left(t\right)\mathrm{dt}\mathrm{.}$

It is important to note that the assumption of gradually escalating median guarantees that the allocation x_g(t) satisfies the principle of partial equalization. Indeed, the cost allocation x_g(t) = r(t) + λ is increasing, whereas the total cost |t − ½| + x_g(t) = ½ − t + r(t) + λ is decreasing on the interval [0, ½]. This means that the closer citizens are to the center, the larger their contribution toward government costs, while the total cost is still higher for those close to the borders. Thus, while some equalization takes place, it is not full. It is interesting to note that in the case of uniform distribution, the equalization rate is 50 percent (see Section 4). Then we have:

The Main Result: The symmetry and gradually escalating median assumptions imply g_e = g_s. Moreover, if the level of government costs g satisfies g ≥ g_e, then the allocation x_g(t) is secession-proof.

To prove this result, we consider a level of government costs g which guarantees that cooperation is efficient, i.e., g ≥; g_e. Then we consider the cost allocation x_g and show that it is secession-proof. Thus, the cooperation is stable, yielding g_e ≥ g_s. Since by Proposition 2.7, g_e ≤ g_s, it would imply that g_e = g_s.

Note that Remark 3.1 yields the following:

Corollary 3.2: Under symmetry and log-concavity we have g_e = g_s.

Although the complete proof of the main result is relegated to the Appendix, we would like to describe the method of the proof, which is of independent interest.

Let us first indicate the major difficulty with verifying secession-proofness. It stems from the fact that one cannot rule out a possibility of secession-prone regions that consist of disconnected intervals. If we were able to restrict our analysis to connected regions only, we could have used the Greenberg and Weber (1986) result, which yields a stable outcome when only connected, or “consecutive,” coalitions are considered. Unfortunately, it does not hold that if there exists a secession-prone disconnected region, there also exists a connected region prone to secession. The assumption of gradually escalating median plays a major role in removing this obstacle and allows us to consider connected regions as the only ones potentially prone to secession.

We proceed in two steps. First we show that for the set of secession-proof cost allocations, only a specific class of connected regions may be prone to secession. Then we show that the issue of secession-proofness translates into a variational problem. More specifically, we consider a set X of cost allocations that satisfy:

• (α) x is a continuous and nonnegative function on the interval [0, 1];

• (β) x is symmetric: x(t) = x(1 − t) for all t ∈ [0, 1];

• (γ) x is increasing on the interval [0, ½]

• (δ) x(t) − t is decreasing in t on the interval [0, ½].

This simply implies that individuals close to the center make larger contributions toward government cost. However, the total burden, which includes transportation costs, is still heavier for citizens who live close to the borders.

The following lemma, the proof of which heavily relies upon the GEM assumption, plays the central role in our proof:

Lemma 3.3: Let x ∈ X be a cost allocation that is not secession-proof. Then there exists t ∈ [0, 1] such that either L_t = [0, t] or R_t = [t, 1] is prone to secession.

The intuition is as follows. If a cost allocation entailing some degree of partial equalization is prone to secession by a disconnected region, it is also prone to secession by a connected region that contains at least one of the endpoints of the interval [0, 1]. Then we are left with an easier task whose technique consists in examining threats of secession only of connected regions.

Lemma 3.3 implies that for any secession-proof allocation x ∈ X, neither L_t nor R_t are prone to secession for any t ∈ I or, equivalently, the following two conditions should be satisfied for all t ∈ [0, 1]:

${\int }_{\mathrm{Lt}}\left(x\left(t\right)+|t-\frac{1}{2}|\right)f\left(t\right)\mathrm{dt}\le g+D\left(L_t\right)\mathrm{and}$

${\int }_{\mathrm{Rt}}\left(x\left(t\right)+|t-\frac{1}{2}|\right)f\left(t\right)\mathrm{dt}\le g+D\left(R_t\right),$

where, we remember, D(S) denotes the minimum of the aggregated transportation cost of members of S. For every t, denote by H(t) the aggregated transportation cost of citizens of L_t to the location of the government at ½, i.e.,

$H\left(t\right)={\int }_0^t\left|t-\frac{1}{2}\right|f\left(t\right)\mathrm{dt}\mathrm{.}$

Using the symmetry of the citizens’ distribution and rearranging the above inequalities, we obtain the necessary and sufficient conditions for a cost allocation x ∈ X to be secession-proof, namely, that the inequalities

$\begin{array}{cc}D\left(I\right)-D\left(R_t\right)-H\left(t\right)\le {\int }_0^{t}x\left(t\right)f\left(t\right)\mathrm{dt}\le g+D\left(L_t\right)-H\left(t\right)& \left(3\right)\end{array}$

hold for all t ≤ ½.

The problem is now reduced to a variational problem: find a cost allocation in X to satisfy the integral conditions in (3). The complete details of the solution to this problem are presented in the Appendix. In the next section we illustrate this problem by considering a special case of a uniform distribution that will help illustrate both difficulties and their resolution in the general case.

IV. Uniform Distribution

In this section we consider the density function that is uniform on the interval I, i.e., f(t) = 1 for all t ∈ [0, 1].

This means that in order to obtain a secession-proof cost allocation, one has to find, for a given value of g, a function y sandwiched between t²/4 and Ψ(t), with y(0) = 0, y(½) = g/2, y′ > 0, and 0 < y″ < 1. Therefore, the search for a secession-proof cost allocation amounts to finding an increasing and convex (but not “too convex”) function that connects 0 and A and whose graph lies within the shaded area depicted in Figure 2.

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The Secession-Proof Area

Citation: IMF Staff Papers 2003, 003; 10.5089/9781589062030.024.A004

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Our first result of this section derives the explicit value of the minimal threshold g_s that guarantees efficiency and stability of cooperation:

Proposition 4.1: The efficiency bound g_e is equal to 1/8.

The compensation rate generated by this allocation is 50 percent. This means that for every two citizens t < t′ < ½, the contribution of citizen t′ toward government costs exceeds that of citizen t by one half the distance between t and t′. To reinforce the need for a balanced (partial) equalization, we consider two extreme allocations, no-compensation allocation, under which each citizen contributes an equal amount toward government costs (no equalization), and Rawlsian Egalitarian allocation, which assigns equal total contributions (including the transportation cost) to every citizen (full equalization), and show that both are not necessarily secession-proof. The intuitive reasons are that in the case of no-compensation allocation a heavy burden (a lack of subsidy) is put on the distant regions, which may then be prone to secession. In the full compensation mechanism the burden is almost squarely on the shoulders of central regions, which can make them prone to secession. This intuition is supported by our results.

• No-compensation allocation NC. This allocation assigns an equal burden to all citizens.

Thus, for every t ∈ I

• NC(t) = g.

We have the following proposition:

Proposition 4.2: There exists a level of government costs g* = 0.134 > ⅛ such that for all g, ⅛ ≤ g ≤ g*, the no-compensation allocation NC is not secession-proof.

Note that the left side of inequality (4) is always satisfied for g ≥ ⅛ as t ≤ ½. This means that for t ≤ ½ no region R_t is prone to secession. The reason is that the citizens in the middle of the country are spared from equalization transfers to support distant regions, which would not wish to secede. The secession-prone candidates are, therefore, the regions L_t (t < ½), which contain border citizens but do not occupy the center of the country. It is interesting to mention that only relatively large regions, containing more than 33 percent of the population, could be prone to secession. Indeed, small regions on the margin are not prone to secession because of a heavy burden of per capita government costs if they wish to go alone.

• Rawlsian Egalitarian allocation RE. This allocation guarantees an equal total cost (including transportation) for all citizens. Thus, RE(t) + |t − ½)| is the same for all t.

(Three cost allocations, NC, RE, and x_g, are depicted in Figure 3.)

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Graphs of No-Compensation Allocation (NC), Rawlsian Egalitarian Allocation (RE), and Secession-Proof Allocation (x_g)

Citation: IMF Staff Papers 2003, 003; 10.5089/9781589062030.024.A004

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Hence for the range of government costs ⅛ ≤ g < ¼, the values of RE(t) are negative for all t satisfying 0 ≤ t < ¼ − g. This implies that for every t < ¼ g, the citizens of the region L_t will receive a net subsidy. Lemma 3.4 yields that it would not be acceptable for the rest of the country. Indeed, since full equalization puts a heavy burden on citizens close to the center, the corresponding regions R_t will be prone to secession. This immediately yields the following:

Proposition 4.3: For any level of government costs g such that ⅛ ≤ g < ¼, the Rawlsian Egalitarian allocation is not secession-proof.¹⁷

V. Concluding Remarks

In this paper we provide an analytical study of interregional fiscal policies in a country with heterogeneous citizens, when different regions may pose a threat of secession. We focus our analysis on the study of compensation schemes that would make the possible advantages of secession for every region inferior to the benefits of remaining within an integrated country.

To address the issue of secession we first examine whether, given heterogeneity of citizens’ preferences, it is desirable and socially efficient to maintain a unified country. We consider the notion of efficiency in a country when all regions are better off under a single national government. Efficiency does not necessarily imply that the gains from being together in the integrated country can be allocated in such a way that no region can guarantee all its citizens a higher payoff than guaranteed by the central government. We investigate the existence of compensation schemes (cost allocations) across regions that guarantee that no region will want to secede and break up the country. Such a scheme is called secession-proof and such a country is stable.

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Secession-Proof Rates as g Varies

Citation: IMF Staff Papers 2003, 003; 10.5089/9781589062030.024.A004

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The first result of the paper is to show that, under quite general distribution of citizens’ characteristics, efficiency and stability can be reconciled. That is, if a country is efficient, there is always a secession-proof compensation scheme that guarantees the country stability. We then examine secession-proof transfer schemes and the degree of equalization between advantaged and disadvantaged regions these schemes entail. We establish the principle of partial equalization; that the gap between advantaged and disadvantaged regions should be reduced, but it should not be completely eliminated. We determine a degree of partial equalization generated by secession-proofness and show that in the case of the uniform distribution of citizens’ preferences, the equalization rate is exactly 50 percent. We also demonstrate that, in the absence of a redistribution mechanism, some disadvantaged areas of the country could be prone to secession and that the no-compensation allocation is not secession-proof. On the other hand, the Rawlsian transfer scheme, which completely equalizes the fiscal capacities of all regions, would cause advantaged regions to threaten to secede.

The study presented in this paper can be extended in several directions. The focus of this paper was a study of compensation schemes under unanimity procedures. An analysis of alternative mechanisms, such as majority voting, would be a worthwhile contribution. One could also consider a multidimensional policy in which the citizens are distinguished by more than one parameter, say, income, geography, and ethnicity. This extension poses a difficult theoretical challenge but its resolution would be very promising from both theoretical and empirical points of view. Finally, it would be useful to look at the issue of migration, in particular, given heterogeneous tax burdens and living conditions across regions. All those extensions, as well as some other interesting related issues, are left to future research.

We conclude this section with a brief examination of some empirical evidence and a review of partial equalization in the real world. In general, the principle of partial equalization prevails in many countries, especially developed ones, and, in fact, Australia, Canada, Denmark, and Germany, among others, use horizontal imbalances as a basis for equalization policy among regions.

Canada.

The principle of equalization is a part of the Canadian Constitution and receives broad national support. There are a variety of transfer programs that attempt to reduce regional inequalities based on capacity, population, and needs (Krelove, Stotsky, and Vehorn, 1997). Equalization payments were redistributed to only seven relatively poor provinces (in terms of 1990–91 data), while Alberta, British Columbia, and Ontario received no payments from this fund (see Table 1).

Table 1.

Provincial Per Capita Notional Revenues Before and After Equalization, 1990–91, in Canada

Source: Boadway and Hobson (1993), p. 59.

¹Per capita yield of tax bases at national average tax rates.

²Notional revenue before equalization relative to the national average.

³Notional revenue yield after equalization relative to the national average.

Table 1.

Provincial Per Capita Notional Revenues Before and After Equalization, 1990–91, in Canada

Provinces	Notional Revenue Yield1	Equalization	index of Tax Capacity2	Index of Fiscal Capacity3
Newfoundland	2,898	1,686	0.63	0.93
Prince Edward Is.	2,988	1,595	0.65	0.93
Nova Scotia	3,517	1,066	0.76	0.93
New Brunswick	3,295	1,288	0.71	0.93
Quebec	3,973	610	0.86	0.93
Ontario	5,085	…	1.10	1.03
Manitoba	3,737	847	0.81	0.93
Saskatchewan	4,058	525	0.88	0.93
Alberta	6,306	…	1.36	1.28
British Columbia	4,8 38	…	1.04	0.97

Source: Boadway and Hobson (1993), p. 59.

¹Per capita yield of tax bases at national average tax rates.

²Notional revenue before equalization relative to the national average.

³Notional revenue yield after equalization relative to the national average.

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Table 1.

Provincial Per Capita Notional Revenues Before and After Equalization, 1990–91, in Canada

Provinces	Notional Revenue Yield1	Equalization	index of Tax Capacity2	Index of Fiscal Capacity3
Newfoundland	2,898	1,686	0.63	0.93
Prince Edward Is.	2,988	1,595	0.65	0.93
Nova Scotia	3,517	1,066	0.76	0.93
New Brunswick	3,295	1,288	0.71	0.93
Quebec	3,973	610	0.86	0.93
Ontario	5,085	…	1.10	1.03
Manitoba	3,737	847	0.81	0.93
Saskatchewan	4,058	525	0.88	0.93
Alberta	6,306	…	1.36	1.28
British Columbia	4,8 38	…	1.04	0.97

Source: Boadway and Hobson (1993), p. 59.

¹Per capita yield of tax bases at national average tax rates.

²Notional revenue before equalization relative to the national average.

³Notional revenue yield after equalization relative to the national average.

Clark (1997) points out the success of equalization efforts in reducing regional inequalities. For example, in 1994–95, Alberta’s fiscal capacity index before equalization was almost twice as high as that of Newfoundland. However, the equalization entitlement reduced this gap by almost 75 percent.

Australia.

Here, substantial funds are relocated away from the larger states of New South Wales and Victoria, whereas Southern Australia, Tasmania, and the Northern Territory serve as major recipients (Craig, 1997). (See Figure 5.)

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Impact of Horizontal Equalization Grants Relative to Equal Per Capita Allocation, 1996/96

(in millions of Australian dollars)

Citation: IMF Staff Papers 2003, 003; 10.5089/9781589062030.024.A004

Source: Craig (1997).

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Germany.

It is interesting to point out that, due to the heavy economic burden of the unification of West and East Germany, the transfer scheme used there exhibited a degree overequalization. Spahn and Fottinger (1997) (Figure 6) show that the fiscal capacity of poorer former East German provinces increased after the transfer, but the contribution paid by rich former West German states reduced their fiscal capacity below the average.

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Germany: Per Capita Fiscal Capacity of States Before and After Equalization

(In percent of average)

Citation: IMF Staff Papers 2003, 003; 10.5089/9781589062030.024.A004

Source: Spahn and Föttingcr (1997).

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At first glance, the German case seems to be incompatible with our model, where a threat of secession (or integration as in the German case) rules out a possibility of overequalization. One has to recall, however, that the decision on the German reunification has been made in a manner dictated by the political circumstances of that particular period. Had there been public debate in Germany on the consequences of reunification, including its enormous cost, followed by national elections or a referendum, the final decision might have been quite different.

Russia.

Triesman (1996, 1998) argues that direct financial transfers from the federal budget to regions in Russia in 1992—1994 were a function of the lobbying power of the regions, and the issues of horizontal imbalances were not properly addressed in that period. Indeed, Dabla-Norris, Martinez-Vasquez, and Norregaard (2000) and Dabla-Norris and Weber (2001) demonstrated that the principle of partial equalization was not implemented in Russia over the first part of the last decade and, in fact, the gap between rich and poor Russian regions has even widened. The best-off region (Moscow) in 1993 spent close to 12 times more in capital expenditures than the worst-off regions, with the gap widening to more than 24 times what it was in 1998 (see Table 2).

Table 2.

Measure of Horizontal Fiscal Imbalance in Russia: Per Capita Regional Expenditures, 1993–98

Source: Dabla-Norris, Martinez-Vasquez, and Norregaard (2000).

Table 2.

Measure of Horizontal Fiscal Imbalance in Russia: Per Capita Regional Expenditures, 1993–98

Year	Mean	Coefficient of Variation	Minimum	Maximum
1993	219.7	0.775	100.6	1,198.2
1994	959.7	1.191	359.8	8,000.7
1995	1,904.9	1.023	720.2	13,004.3
1996	2,835.7	1.067	1,050.3	16,521.1
1997	3,730.1	1.187	1,336.7	30,543.5
1998	3,184.4	1.022	1,121.5	22,559.8

Source: Dabla-Norris, Martinez-Vasquez, and Norregaard (2000).

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Table 2.

Measure of Horizontal Fiscal Imbalance in Russia: Per Capita Regional Expenditures, 1993–98

Year	Mean	Coefficient of Variation	Minimum	Maximum
1993	219.7	0.775	100.6	1,198.2
1994	959.7	1.191	359.8	8,000.7
1995	1,904.9	1.023	720.2	13,004.3
1996	2,835.7	1.067	1,050.3	16,521.1
1997	3,730.1	1.187	1,336.7	30,543.5
1998	3,184.4	1.022	1,121.5	22,559.8

Source: Dabla-Norris, Martinez-Vasquez, and Norregaard (2000).

China.

Hu and Tan (1996) have demonstrated that, due to governmental policies, the gap between rich and poor provinces in China declined in the 1980s. One of the tools cited in this regard is the “anti-mega city” policy that was initiated in 1986. It aimed to achieve a certain equalization across the country by placing restrictions on the largest cities: Shanghai, Beijing, and Tianjin. Ahmad, Li, Richardson, and Singh (2002) argue, however, that “the overall transfer system [in China] continues to be sharply regressive, rewarding wealthy regions with increased transfers.” (See Figure 7.)

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Total Transfers Per Capita and GDP Per Capita in 1998, in China

Citation: IMF Staff Papers 2003, 003; 10.5089/9781589062030.024.A004

Source: Ahmad, Li, Richardson, and Singh (2002).

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In fact, Hu and Fujita (2001) show that regional disparity between the coastal and interior provinces in China has increased since the mid–1980s and even accelerated after 1990. (For example, the per capita income in Shanghai is ten times larger than in the province of Guizhou.) Both Ahmad and others (2002) and Hu and Fujita (2001) consider the increasing gap between rich and poor regions a serious problem that needs to be addressed at the national level.

It is important to point out that central governments often use transfer schemes as an appeasement policy toward “target” regions. We have already mentioned the transfer policy of the Russian Federation in the early nineties when “trouble-making” regions received a disproportionately large share of the total transfer budget. In China, Tibet receives a large amount of subsidies from the central government, and its regional GDP growth reached almost 12 percent over the period 1993–1999, thus surpassing the national average for six consecutive years (People’s Daily, 2000). There are also special privileges granted to the Basque country in Spain. The Basque country is allowed to collect its own income tax, corporate tax, and VAT, as well as gasoline, tobacco, and alcohol taxes. Then a previously agreed quota is transferred to the Spanish treasury as compensation for Spanish common expenditures and the cost of running state bodies. Thus, the per capita level of public expenditure in the Basque country is much higher than in the rest of Spain. In fact, it is 80 percent higher than the level of public spending in Catalonia and Galicia (Moreno, 2001).