Can Centralization Stabilize Federations? A Dynamic Reconsideration of the Centralization Problem. Jean-Denis Garon Queen s University

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1 Can Centralization Stabilize Federations? A Dynamic Reconsideration of the Centralization Problem Jean-Denis Garon Queen s University January 9, 2012 Abstract In this paper, we consider the costs and benefits of centralization in a federation. In our model model, centralization affects the probability of survival of the union. For environments in which the members of the federation can or cannot commit not to unilaterally secede in future periods, we show that the level of centralization of the public sector endogenously modifies the probability of dissolution of the federation. In our dynamic analysis, we put to the test the intuition that centralization may improve the political stability of the federation, as seceding from a centralized federation may be costlier, as it would require the newborn country to massively re-invest in its own institutions. We show that this is the case only if the immediate secession costs associated to a centralized public sector outweigh the long-term welfare costs it also generates under a united federation. We derive optimal centralization rules under both full and no-commitment, namely when the constitution is either a complete or an incomplete contract. In the latter case, centralization can either be used as a commitment device to avoid inefficient unilateral secessions, or as a way to reduce the transaction costs associated to the negotiation of future constitutional amendments. Keywords: Centralization, Fiscal assignment, Fiscal federalism, Secessions JEL classification: H11, H41, H76, H77 Contact information: garonjd@econ.queensu.ca. Please download the most recent version of this paper here. The Fonds Québecois de la Recherche sur la Société et la Culture (FQRSC) and the Ontario Graduate Scholarship (OGS) programs provided funding for this research. The author is grateful to Robin W. Boadway, Sumon Majumdar, Marie-Louise Viero, Dan Usher, Nicolas Marceau, Nicolas-Guillaume Martineau and Maria Gallego for their comments and suggestions. Early versions of this project have been presented a the annual meetings of the Canadian Public Economic Group (2010) and of the Canadian Law and Economics Association (2010). 1

2 1 Introduction In this paper, we reconsider one of the most fundamental questions in public finance, namely that of determining the costs and benefits of delegating to a central government the task of providing public goods and services (Oates, 1972). In a dynamic framework in which, each period, the regions comprising the federation can decide to unilaterally secede, thereby imposing costs on the rest of the federation, we analyze whether centralization of the public sector may be used as a commitment mechanism to prevent inefficient dissolutions of the federation. Political and fiscal unions in general, are subject to political instability. Thus, their unity is rarely guaranteed in the long-term, and threats of dissolutions are common. This comes at no surprise, as by their very nature federations are generally composed of several regions with well-defined borders, and linguistic, ethnic and cultural traits. The economic characteristics of the regions forming the union can also sharply diverge over time, thereby generating interjurisdictional tensions. The ongoing sovereign debt crisis in the European Union, where many are still wondering whether countries such as Greece, Italy or Portugal will be able to remain in the union, is a clear example of that. In reality, centralization and decentralization have often been implemented, with the objective of reducing political instability and secessionist pressures. 1 federations have tamed separatist pressures by decentralizing. In recent history some This happened with Catalonia (Spain), with the devolution processes to Scotland (U.K.) and in Malaysia, or with the decentralization efforts of General Musharraf in Pakistan during the last decade. Some federations have simply been dismantled by common agreement (Czechoslovakia), and in others regions have unilaterally claimed their independence (Kosovo). 2 We have observed 1 Henceforth we will use the term federation to simplify the exposition, although we are conscious that the political structure of the countries discussed is varied. Spain, for instance, is not a federal country per se but still faces national unity challenges. 2 One can count the USSR among the federations that have been dissolved. The Soviet Union, despite its socialist nature, experienced episodes of extreme centralization especially under and after Stalin (1922 2

3 cases where a province came close to claiming its independence after running a referendum (Québec in Canada) or where the referendary strategy ended up being successful (South Sudan). The simple intuition we study here is that seceding from a federation in which most of the public sector belongs to the central tier of government may be very costly, because it would require some large reinvestments in the newborn country s public sector (as suggested in Dion (1996) among others). If a federal constitution cannot be written as a complete contract (Grossman and Hart, 1986; Hart and Moore, 1990) in which regions formally and credibly commit not to unilaterally secede, intuitively it would appear that increasing the size of the central government may be used as an alternative commitment device, as it would reduce the future incentives to secede. Our analysis shows that this simple intuition may be incomplete, and that blindly relying on such a mechanism and encouraging further centralization can be misleading. We show that although the immediate costs from seceding may be higher in a centralized federation, centralization may reduce the welfare generated by the federation in the long run. Therefore, whether centralization is likely to reduce political instability in the federation rests on its relative effect on the immediate gain of utility to secede but also on the expected utility not to do so, both of them being affected by the size of the centralized government. As it turns out, centralizing the federation may induce immediate costs of secessions and reduce their likelihood, but at the same time it may reduce the ability of the centralized public goods to suit local preferences, thereby reducing the long-term benefits of remaining in the union. This last effect is due to the dynamic nature of the model, and enriches the already existing ones that have been used to study problems of time-inconsistency and lack of commitment in federations (such as in Bordignon and Brusco (2001)). A theoretical contribution to this question, we believe, is useful and warranted for two main reasons. First, despite its relevance for policy, the effect of centralization on national unity onwards). 3

4 and political stability has been given little attention by theoretical economists. But more substantially, the limited evidence we have on the subject, mostly consisting of case studies, is at best ambiguous about whether it increases or reduces the likelihood of secessions. Among recent empirical works that have been conducted by social scientists and economists on the subject, all have concluded that centralization can be a double-edged sword on this matter. Brancati (2006) empirically finds, using cross-country panel data, that decentralization can alleviate ethnic conflicts and secessionism by bringing governments closer to the people and create opportunities for minorities to participate in government. On the other hand, he shows that decentralization may increase ethnic conflicts and bolster secessionism by encouraging the development of regional parties. Tranchant (2007) finds that decentralization dampens all forms of ethnic violence for groups which are geographically concentrated or which have a local minority, whereas it fuels conflicts when they are lacking one. He comes to the same conclusion in Tranchant (2010). Tranchant (2008) also obtain mixed results about the effect of decentralization and devolution on secessionism and conflicts. In an extensive review of the literature on the subject, Bird et al. (2010) conclude that no one has either generally persuasive ideas or evidence about the impact of decentralization on national unity. In their view, decentralization can either be a glue or a solvent for the unity of a federation. Analyzing the centralization of the public sector as a commitment mechanism that may be able to mitigate time-inconsistency problems in federations also contributes to a developing literature on in social contracts. As far as centralization is concerned, the main piece of work is that of Alesina et al. (2005), who analyze the effect of increasing centralization 3 on the optimal size of a coalition of countries, called the union. In the context of federalism, the work which is the closest to ours is Bordignon and Brusco (2001) who show that writing a constitution which is ambiguous about regions formal rights to secede is likely to reduce the frequency of secession threats. In the literature on constitutional design and social contracts, the use of super-majorities to amend constitutions have been studied by Aghion and Bolton (2003). Finally, we build on some previous works on political stability and secessions, such 3 They call it the scope of the union. 4

5 as Buchanan and Faith (1987) and Bolton and Roland (1997) who have analyzed the effect of secession threats on inter-jurisdictional redistribution in federations. 4 We also contribute to the theoretical literature on the costs and benefits of centralization, which has ignored so far its effect on national unity. The economic problem of determining whether the power to regulate and to make policies in a given area of responsibility should be centralized or decentralized is known as the assignment problem. When writing a federal constitution, one has to clearly identify what are the costs and benefits of centralizing a given legislative responsibility, in order to choose the optimal assignment of powers across tiers of government. Although the costs and benefits of centralization are manyfold and complex, an intuitive and well-established criterion which is often used to think about the assignment problem is that of comparing the preference-matching costs of centralization to its efficiency benefits. Analyses based on this criterion rest on the assumption that a centralized provision of public goods and services will not match the local preference of each member state of the federation as much as if lower tiers of government did it according to the preferences of their own constituents. On the other hand, centralizing provision generates efficiency gains such as economies of scale. According to this criterion, the provision of public goods and services should be centralized only if the efficiency gains of doing so are at least as large as the preference-matching cost. The preference-matching versus gains from centralization is an obvious normative criterion that had been widely used by both theoreticians and practitioners. For example, Alesina et al. (1995) identify the trade-off between specificity and economies of scale as fundamental in the attribution of powers to tiers of governments in fiscal and political unions. Boadway and Shah (2009) also identify a similar trade-off as they suggest guidelines to practitioners for the making of good policies. Our results show that this analysis should be enriched by taking into account the endogenous effect of centralization on the life expectancy of the federation. Also, if centralization increases (decreases) the probability that the federation be 4 Economic theories of secessions are surveyed in Buchanan (1997). 5

6 dissolved in equilibrium, the opportunities which regions will potentially miss (gain) by not seceding should also be accounted for in the costs (benefits) of centralization. Finally, if the constitution is an incomplete contract, then centralization can have a commitment benefit if it prevents inefficient unilateral secessions to happen, and can also increase or reduce the cost of negotiating constitutional amendments. The remainder of the paper is structured as follows. In section 2 we develop a simple, tworegion model of federalism where a federation has two roles, namely insuring its members against a risky future and providing public goods more efficiently. Before uncertainty is realized about the future economic conditions, a constitution is written. The latter specifies whether the provision of a public good, called the public sector, is centralized or not. Using this model, we derive a complete constitution in section 3. This benchmark version of the model achieves the highest possible level of joint surplus for the members of the federation since it precludes any unilateral secessions. We relax this last assumption in section 4 where we assume that unilateral secessions are allowed. Section 5 concludes. 2 The model The institutional problem at hand is that of evaluating whether two regions which have decided to form a single country together should centralize their public sector and jointly produce public goods and services. To tackle this issue and obtain clear and insightful intuitions, we use a simple model featuring two regions, labelled i = 1, 2. For simplicity in the analysis, we assume that they are equally populated, which allows us to normalize their populations to one and to define all the variables in per-capita terms. Citizens are identical within a region, but their preferences with respect to the provision of public goods differ across borders. The game goes on for an infinity of periods, denoted with the typical time index t = 0,.... In the context of this model, an insightful way to think about a time period may be in terms of generations, one period being one generation of citizens. 6

7 At the beginning of the game, both of them are independent jurisdictions. In that period representative citizens one from each region meet and have to decide: whether a federation is created in the first place and; and if so, whether the provision of public goods, called the public sector for simplicity and denoted by g, will be centrally provided by a the federal government or individually provided by each region separately, in a decentralized fashion. This decision, which happens only once, at t = 0, is made behind a veil of ignorance, in the sense that it is made before the realization of any region-specific uncertainty. Decentralizing or centralizing the public sector is modelled as a binary decision choice, denoted by c = 0, 1 respectively. The decision c {0, 1}, which is made unanimously and only once at t = 0, is enshrined in a constitution. If it is agreed that a federation should not be created at all, the game ends and regions remain independent forever. 5 Otherwise the federation lives on for at least one more period and the dynamic game begins. The game consists of two types of decision nodes: the veil of ignorance and the ex-post ones. The first decision node happens only once, at t = 0 and is called the veil of ignorance decision period. As the game is dynamic the objective function of the representative of region i (henceforth called region i only in period t = 0) is to maximize the discounted lifetime utility of its citizens, which is denoted max c {0,1} EW i = U i 0(c) + E 0 where U i 0(c) is the utility of the initial generation, U i t β t Ut i (c) (1) t=1 is the utility of each subsequent generation. Both are a function of the initial centralization decision c {0, 1}. β < 1 is the inter-generational discount factor and is common to both regions. 6 5 Howefer, we set-up our model in a way that guarantees that a federation be formed at t = 0, as we focus on the criteria that should drive the policy decision to centralize. 6 There is no unanimity among economists as to how the inter-generational discount factor should be or is determined. See Dasgupta et al. (1999) for an interesting normative interpretation. 7

8 As our model considers federations from an institutional point of view, we assume that developing institutions may be very costly, and doing so jointly instead of separately may substantially reduce its per-capita cost. For instance, building a set of institutions (i.e. the public sector) that allows a government to provide public goods and services requires a large investment in period t = 0. To make this idea clear, we express the utility term under the veil of ignorance as U i 0(c) = K(c) (2) where K(c) is the per-capita initial investment required to develop a public sector. As the notation suggests, we model this initial cost as an investment in capital. It is defined as k > 0, c = 0 K(c) = k k, c = 1 (3) where k > 0 represents the initial per-capita cost of the public sector under decentralization and k k is the initial per-capita cost of setting up institutions jointly with the other region. The parameter k, which plays an important role through the model, can be thought of as being the cost-saving benefit due to centralization. The sources of such cost savings may be due to the fact that regions can share expertise, resources, or benefit from economies of scales in setting up their institutions. An important feature of this initial investment is that it represents all the costs which have to be paid for up-front at time t = 0 and which are not-recurrent. 7 The centralization decision c is made once and for all behind the veil of ignorance. The dynamic game then begins at time t = 1 onwards, taking c as a state variable. As one can see, the utility terms in all subsequent time periods are subject to an expectation operator in equation (1) since regions do not know whether or not being members of a federation will be advantageous to them in each future period. Let us first present the utility representation 7 See Boadway and Shah (2009) for an extensive discussion about the sources of cost-savings in a centralized federation. We do not exclude, however, that centralizing the public sector may generate further welfare gains in future periods, for example due to a better internalization of inter-jurisdictional externalities and spillovers. 8

9 for each future node, denoted by ex-post periods, before we provide more details about its components. Every period t > 0, generation t derives utility U i t (c) = b c b + θ i t, t = 1, 2,... (4) We describe each component of this utility function below. The first component, b, in equation (4) is the benefit generated by having a public sector, and is invariant to whether the latter is centralized or decentralized. The second component, b which appears only under centralization, is called the net preference-matching cost. It captures all costs and benefits associated to a centralized provision of public goods which are recurring every period. It first encompasses the cost associated to the central government being unable to provide them in a way that matches local preferences as well as if each region had provided them in a decentralized fashion. 8 The existence of preference-matching costs under centralization have been found to be an element of foremost importance in the costbenefit analysis of centralization. It lies at the forefront of the theory of fiscal federalism since Oates (1972). It has been emphasized theoretically by Oates (1999) and Alesina et al. (2005) and empirically in Panizza (1999), among others. They also figure in the cost-benefit analysis guidelines for practitioners, such as in Alesina et al. (1995) and Boadway and Shah (2009). The term b also encompasses some potential benefits of centralization, such as the internalization of inter-jurisdictional externalities, from which citizens benefit as long as the federation is not dissolved. Because b represents either a net cost or benefit, we do not constraint its sign. By convention, it takes a positive value when it is a net preference-matching cost, and a negative value when it represents a net benefit. Apart from the possibility to centralize the public sector, another major role of a federation 8 Usher (1995) provides an interesting discussion on the preference-matching costs due to linguistic compromises in the Canadian federation. 9

10 is that it potentially gives regions the opportunity to centralize the provision of public goods, but also that forming a single jurisdiction allows them to face a less uncertain world at every future time period. If the two regions form a federation at t = 0 this utility term will take on a fixed value that equals θ (0, 1) i as long as the federation exists. On the other hand, if the decision is made not to form a federation at t = 0 or if, alternatively, the federation is eventually dissolved later in history, each independent region will be subject to a utility lottery. We adopt a simple binomial distribution for this lottery, whereby a high utility shock θ i t = 1 is realized with probability p and a low utility shock θ i t = 0 is realized with probability (1 p). Formally, under independence 9 1 w.p. p θt i = 0 w.p. 1 p. (5) It is assumed that the realized value of θt i is independently drawn from the distribution for each region. The assumption that the probability p is the same for the two regions, which simplifies the analysis by imposing symmetry, is not important for the the main conclusions of our model. Also, assuming that the shocks are independently distributed across time, thus ruling out persistence, does not drive our results as well. The idea that forming a federation may be used as a way to reduce the impact of idiosyncratic shocks is at the core of our model. This may be due to several factors if smaller and independent countries face more uncertainty about their future opportunities than larger ones (Alesina and Spolaore, 1997; Alesina et al., 2000, 2005). A a larger country is more efficient at protecting its own borders thus reducing the probability of wars (Ruta, 2005). Also, being part of a larger jurisdiction also increases the size of the domestic market, therefore reducing the vulnerability of its regions to trade wars or international trade disruptions. This assumption is strongly supported by historical and empirical evidence, and has been used 9 Constraining the possible realized values of this lottery to zero and one is not particularly important. The important factor is the value of θ relative to the expected realized value of θ i t with the lottery. 10

11 in the modelling of a federation, for example in Bordignon and Brusco (2001). Historically, the idea of commonly sheltering regions from future external shocks has been a fundamental factor in the decision to create the Canadian federation (Masters, 1963) and in the design of the second constitution of the United States (Hamilton et al., 2003;1788). It is therefore natural to assume that, from an ex-ante point of view, the formation of a federation generates an expected risk-hedging benefit: Assumption 1 θ > E(θ i t) = p. Uncertainty about ex-post states of the world As the probability of secession is central to our model, we now discuss what happens if a federation is ever dissolved at time t > 0. The fact that the shocks are identically and independently distributed each period generates one out of four possible states of the world (θt 1, θt 2 ) for each ex-post period. To keep the notation simple, we simply denote the possible ex-post states of the world at t > 0 by (1,1), (1,0), (0,1) and (0,0). The probability measure over these states of the world by z where z(1, 1) = p 2 z(1, 0) = p(1 p), z : (6) z(0, 1) = (1 p)p, z(0, 0) = (1 p) 2. We assume that that both regions observe their realized shock θt i and that of the other region even if they belong to a federation. In other words, for each ex-post node t > 0 at which regions are not independent they realize, so to speak, what they are currently missing by being in the federation. This is, in fact, what will generate an incentive to secede: regions are conscious that they may benefit immediately from leaving the federation by seizing an 11

12 otherwise missed opportunity if θ i t > θ. Capturing this immediate benefit requires dissolving the federation, which comes at the cost of not being able to insure against future low shocks. The ex-post capital costs of dissolving the federation Developing the institutions that are necessary to provide public goods and services is costly, and these costs are paid for once and for all at t = 0. As we will show below, in some ex-post states of the world, it may either be optimal to dissolve a federation or, if regions are allowed to do so, to unilaterally secede from it. This raises the issue of what happens in such cases with the public sector g if it had previously been centralized. As we have seen, there is a benefit to centralize the public sector ex-ante because doing so reduces the initial cost of developing the public sector by k, driving down the initial per-capita cost to k k. In our analysis, we will assume that if for some reason a centralized federation is dissolved ex-post, a portion δ of the initial investment in the centralized public sector is lost. This may happen for several reasons. If the capital required to produce public goods is spread all over the country, each region naturally recovers only some part of it after a dissolution of the federation and has to invest anew. Another reason is that producing public goods and services requires some knowledge, know-how and expertise that may be lost if both regions decide to provide their own public sector. A third possibility may be that the cost of providing the public sector may be driven up by a reduction in the credit rating of independent regions. As Dion (1996) observes, secession entails surmounting some big obstacles which undermine confidence in the success of secession. Taking over all the public services dispensed by a modern, centralized welfare state appears an almost impossible task. We formalize this last idea as follows. If a centralized federation is dissolved ex-post, each region has to decentralize its public sector at per-capita cost k (1 δ)(k k) = δk + (1 δ) k. Thus only a proportion (1 δ) of the initial investment k k can be used towards building the new institutions after decentralization. Thus, if a centralized federation is being 12

13 dissolved at time ˆt, then the total price that will have been paid for a decentralized public sector in present-value terms is k k + βˆt [δk + (1 δ) k] k. (7) Therefore, at t = 0 regions anticipate that the federation will be dissolved in some state(s) of the world, meaning that they have to balance the benefits of a cost reduction under centralization against that of a future cost increase in case of a dissolution. A decentralized federation is not subject to this tradeoff. Furthermore, whenever a federation is dissolved, both regions are no longer subject to the reduction of utility due to the net preferencematching cost b for all subsequent periods nor do they enjoy the reduction in uncertainty due to the federal nature of the state. We now present the timing of the game. General timing of the game As mentioned earlier, at period t = 0, decisions are made about whether or not to have a federation and if so, a constitution is drafted. Apart from the centralization decision, it is possible to specify in exactly what future states of the world the federation will be dissolved and in which ones it will not, but only if full commitment is possible and if the constitution can be written as a complete contract (Grossman and Hart, 1986; Hart and Moore, 1990). In section 3 we first analyze the centralization decision under full commitment, and later in section 4 we characterize the optimal centralization decision when only the centralization decision can be enshrined in the constitution. In the latter case the constitution is essentially an incomplete contract. In such case, after the realization of (θt 1, θt 2 ) at each period t it is possible that a region threatens to secede and requests the constitution to be redrafted. This fundamental difference of whether it is possible to commit ex-ante to a complete constitution changes the nature of the game, because renegotiating and amending the constitution ex-post can only happen under an incomplete constitution. We now elaborate on the timing 13

14 of the game and on the sequence of decisions. t = 0 Veil of ignorance. At period t = 0 a federation is formed. If a federation is formed both representatives decide whether the public sectors g i will be decentralized or centralized. This decision is denoted by c {0, 1}. Under a complete constitution only, a rule specifying whether the federation is preserved or dissolved for every possible realization of shocks is written in the constitution. This decision is denoted by µ t ((θt 1, θt 2 ), c) t where where µ t ( ) = 0 when the federation is dissolved and µ t ( ) = 1 if it is maintained. If a federation is not formed both regions remain independent forever. t > 0 (a) If a federation exists, at the beginning of any period t > 0 the value of θ i is realized for both regions, and is public information. Under a complete constitution the rule µ t ((θt 1, θt 2 ), c) is implemented. Under an incomplete constitution the constitution can be renegotiated and amended with unanimous consent. If regions cannot reach an agreement they can secede unilaterally. If the federation is maintained, citizens in each region enjoy b b from the public sector and θ. t > 0 (b) t > 0 (c) If the federation is dissolved and if g i had been centralized at time t = 0, then both regions have to invest anew in their own decentralized public sectors. Both regions are then independent forever. Otherwise a new time period starts and the game is repeated at t + 1. Subsequently the game is repeated next period. Several elements in this timing are worth noting. First, we simplify the environment by assuming that the regions face a one-time window of opportunity to create a single country, 14

15 and that if it is missed they remain independent forever. This rules out the problem of modelling what would happen if this window of opportunity happened late in history, at a moment where institutions already exist. 10 We leave this question for further research. Secondly, we assume that if the federation is dissolved (that it be of a common accord or through unilateral secessions), it remains dissolved forever. This assumption simplifies the analysis and is justified, for after unilateral secessions there may be a serious breach of trust between the two regions. Also, historically there are very few instances of countries reuniting after breaking up. 10 Such windows of opportunity can happen, for example, following a civil war or after having achieved independence from a colonial power. 15

16 Independence Independence Independence Independence Independence Decision to form a federation (yes) Centralization decision c {0, 1} (no) Dissolution decision µ t ((θ 1 t, θ 2 t ) c) {0, 1} (θ 1 1, θ 2 1) Dissolve Reneg. if allowed (θ2, 1 θ2) 2 Reneg. if allowed Dissolve Dissolve (θ 1 3, θ 2 3) Reneg. if allowed (θ4, 1 θ4) 2 Figure 1: Timing of the game 16

17 3 Constitutions as complete contracts - centralization under full commitment Constitutions are sophisticated contracts which often live on for generations. At the time of drafting them, it is impossible to determine with precision in exactly what circumstances it will be warranted to either amend or abrogate them. Even if making them contingent on all possible future events was possible at all, doing so would be very costly and such a contract would hardly be enforceable by a third party. This is why, typically, social contracts try to cope with unforeseen occurrences using various rules of procedures requiring, for example, super-majorities for the ratification of amendments. 11 Some rules also strictly forbid secessions, as is explicitly the case in the French constitution. Thus, in reality, a constitution cannot be a a complete contract which foresees all possible future events. Nor can regions commit, at the time of its ratification, to abide with it at all time and in all circumstances. Nevertheless, deriving an optimal complete contract will prove useful. In the transaction-cost literature in general (Grossman and Hart, 1986; Hart and Moore, 1990) such contracts are shown to maximize the joint welfare of the parties and can therefore be seen as a benchmark case. On the other hand, incomplete contracts, because they are subject to renegotiation, generate hold-up effects and call for various other transaction costs, generally provide less welfare than the complete contract. In our model, because the complete constitution is agreed upon behind a veil of ignorance by two regions that are identical ex-ante, this benchmark social contract maximizes their joint surplus from an ex-ante point of view and, thus, maximizes the expected social welfare. The assumption of full-commitment that underlies this type of contract is crucial here, since it may prescribe not to dissolve the federation in states of the world where, after the uncertainty has been resolved, one region is at disadvantage. The complete constitution can therefore 11 Aghion and Bolton (2003) worked on the design of optimal amendment rules on social contracts. 17

18 not be incentive-compatible ex-post. This problem is ruled out by the assumption of full commitment. The optimal constitution that we derive in this section is defined as follows: Definition 1 A complete constitution is a social contract unanimously agreed on at time t = 0. It specifies whether the federation is initially decentralized or centralized, a decision we denote by c {0, 1}. For every future possible state of the world (θt 1, θt 2 ) t > 0 it determines whether the federation must be dissolved forever or maintained for one more period, a decision denoted by µ t ((θt 1, θt 2 ) c) {0, 1}. The states of the world (θt 1, θt 2 ) are verifiable and are public information, and the constitution is enforceable by an third party t. The expected payoff of each region is described by equation (1). The timing of the game is the one we have introduced in section 2. We solve the model in two parts. As the centralization decision c {0, 1} is made at t = 0 by comparing whether the discounted expected utility, as accounted for in equation (1), is higher under centralization than under decentralization, we must solve the game from t = 1 onwards separately for both cases. Given a specific c, the equilibrium probability of dissolutions is a subgame-perfect equilibrium. We therefore solve the game backwards and first characterize the optimal dissolution decision given the realization of a state of the world (θt 1, θt 2 ), t > 0. The optimal decision µ t ((θt 1, θt 2 ) c) {0, 1} is presented in subsection 3.1. We then exploit the stationarity property of the game and use this information to derive the expected probability of future secessions, from an ex-ante point of view, in subsection 3.2. This probability is denoted by q t ( θ c) and depends on the ability of the federation to insure regions against shocks, as represented by θ. We finally analyze whether or not it is optimal to centralize the public sector g in subsection

19 3.1 Optimal dissolutions We denote the dissolution decision by µ t ((θt 1, θt 2 ) c) {0, 1} where µ t = 1 means that the federation must be maintained at time t and if (θt 1, θt 1 ) is realized, and where µ t = 0 if it is optimal to dissolve it. It is the rule µ t ( ) that will be enshrined in the constitution, to which regions can fully commit. In each possible state of the world, namely (1, 1), (1, 0) and (0, 0) it is optimal to maintain the federation if, at time t, doing so maximize the expected lifetime joint utility of all the members of the federation. 12 The dissolution decision is made after the initial investment has been made in the public sector at t = 0. If the federation had been centralized, which is denoted by c = 1, then dissolving the federation implies that each region has to re-invest ex-post in its own public sector. They therefore incur a cost that is absent if the federation is maintained or if the public sectors had simply been decentralized ex-ante. Whether c = 1 or c = 0 therefore influences the optimal dissolution decision. At this point c is therefore taken as a state variable. Prior to characterizing the optimal dissolution decision for each possible resolution of the shocks, let us discuss the trade-off at work in this decision. After shocks are realized, there may be an immediate payoff to dissolving the federation, which is that of benefiting from the high shock(s). However doing so comes at the cost of not being able to insure against low shocks in the future, plus that of (re)creating public services, if they were centralized. Therefore, dissolving the federation is warranted if it the immediate payoff under dissolution outweighs the future costs. On the other hand, it is optimal not to dissolve the federation if the immediate benefits of seceding are smaller than those of remaining insured in the future. Given the recursive nature of the game, this tradeoff between the short-term benefits of seceding and its long term costs can be expressed by using Bellman equations. At time t and given the realized shocks (θt 1, θt 2 ) if the federation is dissolved, the regions have an expected 12 We omit (0,1) since the analysis is symmetric with that of (1,0). 19

20 continuation value of E t v t+1 if they become independent from the next period onwards. This continuation value satisfies E t v t+1 = b + E t+1 (θ i t+1) + βe t+1 v t+2, i = 1, 2. (8) If the federation is not dissolved at time t, it is preserved for at least one period. However, the continuation value has to take into account that it may either be dissolved or maintained next period. The continuation value if the federation is maintained is denoted E t V t+1 and satisfies E t V t+1 (c) = (1 q t ( θ c))[b + θ c b + E t+1 βv t+2 ( θ c)] (9) +q t ( θ c)[b + θ t+1 (c) cδk c(1 δ) k + βe t+1 v t+2 (c)]. The probability q t ( θ c) is the expected probability, at time t, that the federation will be dissolved next period. The first line in equation (9) thus establishes that if the federation is maintained at period t and is not dissolved next period, which happens with probability 1 q t, then each region will benefit from the public good b, will pay the cost-matching costs (or benefits) if b > 0 (< 0), will obtain the fixed payoff θ and will develop a new continuation value E t+1 V t+2 ( θ c). The second line shows that if the federation is maintained at t, then it may be dissolved next period with probability q t. The first part of the payoff in such case is the benefit from the public sector b. The term θ is a shortened notation to denote the expected one-time shock θ i t that each region will obtain, conditional on dissolution being optimal. This term is defined as θ t+1 (c) = E(θ i t+1 µ t+1 ( ) = 0, c) = m {0,1} n {0,1} [1 µ t+1((, ) c)]z(m, n)m. (10) q t+1 ( θ c) Finally, equation (9) clarifies the fact that if a dissolution happens next period, the ex-post decentralization cost δk (1 δ) k will have to be paid only once, and only if the federation is a centralized one. On the other hand, it encompasses the fact that as long as the federation is maintained, the net preference-matching cost b is being paid each period. 20

21 Optimal dissolution in state (1, 1) It becomes much easier to characterize the optimal dissolution decision on a state-by-state basis if we use the recursive form of the game. As the federation must be dissolved if it maximizes the joint expected utility of the citizens in both regions, it is optimal to maintain the federation in state (1, 1) at time t only if 2 θ + 2b 2c b + 2βE qt V t+1 ( θ c) θt i + 2b c[δk + (1 δ) k] + 2βE t v t+1 (11) i=1,2 where θ i = 1, i = 1, 2. Re-expressing (11) using this latter fact gives the condition 2 θ + 2βE qt V t+1 ( θ c) 2 + 2βE qt v t+1 + cψ (12) where the left-hand side of the equation represents the lifetime value of maintaining the federation and the right-hand side represents the joint utility of regions if the federation is dissolved. We can finally pin down the values of θ for which the federation is maintained in state (1, 1), which satisfy θ 1 β(e qt V t+1 ( θ c) E t v t+1 ) + cψ. (13) One can see, from equation (13) that the higher is the value of θ with respect to the righthand side of the equation, and the more likely it is optimal to maintain the federation in state (1,1). One can also see the two competing effects of centralization. First, via βe qt V t+1 ( θ c) it increases the likelihood that it be optimal to maintain the federation, by changing the continuation value within a preserved federation. immediate interest in dissolving it through ψ, which is defined as Secondly, it modifies the ψ = b δk (1 δ) k 0. (14) 21

22 This cost will hold a central role in our analysis, as it emphasizes the fact that the immediate cost to secede depends not only on the fact that a reinvestment in the public sectors is required, but also on the fact that dissolving the federation allows regions to recover any preference-matching cost b. As a result, ψ can take either sign. Optimal dissolution in state (1, 0) Doing the same for states (1,0) and (0,1) which happen to be qualitatively identical from an ex-ante point of view, we know that the federation must be optimally dissolved if 2 θ + 2b + 2βE qt V t+1 ( θ c) 1 + 2b + 2βE t v t+1 + 2cψ which implies that the federation must be preserved in this state if and only if θ 1/2 β(e qt V t+1 ( θ c) E t v t+1 ) + cψ. (15). Optimal dissolution in state (0, 0) Finally the condition for maintaining the federation in state (0, 0), is 2 θ + 2b + 2βE qt V t+1 ( θ c) 2βE t v t+1 + 2cψ which is necessarily satisfied when θ β(e qt V t+1 ( θ c) E t v t+1 ) + cψ. (16) Summary of optimal dissolutions From these last equations one can easily see that if the federation has to be maintained in 22

23 state (1, 1), the state in which the relative value of the federation is the smallest as compared to the value of dissolving it, then it must be maintained in all other states since satisfying equation (13) implies that equations (15) and (16) are necessarily satisfied. Also, equation (15) being satisfied implies equation (16) and so on. By transitivity we can express the optimal state-contingent dissolution decision at time t as µ 0 t ( ) = 1 : always, θ 1 βeqt (V t+1 ( θ c) v t+1 ) + cψ] (1, 0) & (0, 0), θ [ 1 2 βe q t (V t+1 ( θ c) v t+1 ) + cψ, 1 βe qt (V t+1 ( θ c) v t+1 ) + cψ[ (0, 0), θ [ βeqt (V t+1 ( θ c) v t+1 ) + cψ, 1 2 βe q t (V t+1 ( θ c) v t+1 ) + cψ[ never θ < βeqt (V t+1 ( θ c) v t+1 ) + cψ (17) Equation (17) therefore tells us when it is welfare maximizing to keep the federation united or to dissolved depending on the value of θ, which is the relative ability of a federal system to be a risk-hedging device. 3.2 Expected probability of dissolution The optimal dissolution decisions depend on the parameters of the model, but also on the probability that the federation will be dissolved in the future, which is endogenous. The latter is denoted q t ( θ c) and has to be consistent with equation 17 in equilibrium. Deriving this probability of dissolution could be a difficult task if it was allowed to change over time. As it turns out, we can exploit the fact that the game is stationary to confirm that the equilibrium probability of dissolution is time-invariant, a fact that is being established in proposition 1. Proposition 1 The optimal dissolution decision is state-dependent but time-invariant, which is µ t ((θt 1, θt 2 ) c) µ t+j ((θt+j, 1 θt+j) c) 2 µ((θt 1, θt 2 ) c) whenever (θt 1, θt 2 ) (θt+j, 1 θt+j). 2 The continuation values are also time-invariant, which is E t V t+1 ( θ c) E t+1 V t+2 ( θ c) EV ( θ c) t > 23

24 0. Proof: The proposition flows from the fact that the game has a stationary structure for t > 0. If at any two time periods t and t + j the same state of the world realizes, the decision space µ {0, 1} is the same both at t and t + j, the game ahead is identical in both cases due to the fact that times goes to infinity, and past history does not matter for the payoffs ahead. This implies that V t (c) V t+j (c) is off the equilibrium path, and then that µ t ( ) µ t+j ( ) = µ( ). Therefore the expected probability that the federation will be dissolved next period is also constant over time and can be denoted q( θ c). This last result clarifies that if, at any time period t regions expect the federation to be maintained at period t + 1 with probability q next period, and that this probability remains unchanged over time. Using this fact, as well as of the stationarity of the game, allows us to isolate the continuation value in equation (8) and obtain that in equilibrium the value function under independence, which is Ev = 1 1 β [b + E( θ i )]. (18) Similarly, from equation (9) we can isolate the equilibrium continuation value when the federation is being maintained, which is EV ( θ c) = q( θ c) 1 β(1 q( θ c)) [b + θ 1 q( θ c) cδk c(1 δ) k + βv] + [b c b + θ]. 1 β(1 q( θ c)) (19) Note that the value function v, as is being clarified by equation (18), is fully determined by the parameters of the model. It is therefore no problem if it appears in equation (19). The two latter value functions, with the exception of q( θ c) and of θ which is also a function of q( θ c), are thus determined by the parameters of the model as well. To find the equilibrium probability of dissolution q( θ c) we can simply make use of the optimal dissolution rules presented in equation (17) and make use of the stationarity of the game derived in proposition 24

25 1. We thus obtain that 0 if θ 1 βe q( ) (V ( θ c) v) + cψ z(1, 1) if θ [1/2 βe q( ) (V ( θ c) v) + cψ, 1 βe q( ) (V ( θ c) v) + cψ[ q( θ c) = z(1, 1) + 2z(0, 1) if θ [ βe q( ) (V ( θ c) v) + cψ, 1/2 βe q( ) (V ( θ c) v) + cψ[ 1 if θ < βe q( ) (V ( θ c) v) + cψ (20) which gives us, given all parameters of the model, the probability that the federation be dissolved at period t + 1 if it is maintained at period t. Although equation (20) gives us the equilibrium q( θ c) as a function of θ, it is not totally obvious why it would necessary provide us with a unique equilibrium, or with an equilibrium at all for all values of θ. This is the case because as the value of E q( ) V ( θ c) increases with q( ) in equilibrium, and that it also increases with θ. Proposition 2 shows that the equilibrium exists and is unique. Proposition 2 The equilibrium probability of dissolutions q( θ c) exists and is unique. Proof: Denote by Z the set of all possible probabilities of secession, where Z = {0, z(1, 1), z(1, 1)+ 2z(0, 1), 1}. For each possible probability in this set, define the function E q V ( θ c) as derived in equation (9) and define v as it is defined in equation (8). Then the equilibrium probability of secession satisfies arg max ξ Z [ θ+e ξ V ( θ c)] which provides a unique equilibrium. Existence of the equilibrium is also straightforward. Because θ E q V ( θ c) 0 and is linear, then we q know that any θ [0, 1] has to satisfy at least one of the cases in equation (20) The (de)stabilizing effect of centralization As we have solved the entire dynamic model under both centralization and decentralization, the last step to solve the model is to analyze if, under the veil of ignorance at t = 0, it is optimal to centralize. But prior to solving for this last step, it is instructive to analyze under what conditions a centralized federation will be more stable than a decentralized one. 25

26 One of the characteristics of the equilibrium presented in equation (20) is that the probability of dissolution generally differ, depending on whether the federation is centralized or not. It can also be seen in equation (20) that centralization affects the equilibrium probability q through two channels. First, the immediate net cost of secession ψ reduces the incentive to secede if it is smaller than zero, but can induce regions to secede more often it it is larger than zero. Under decentralization, this net cost is trivially null. The second channel through which centralization affects the stability of the federation is by modifying the level of utility that the regions expect to obtain if they decide to maintain its unity. If the expected continuation value is such that E q V ( θ 1) < E q V ( θ 0), then maintaining the federation, in the long run, is less interesting under centralization than under decentralization, and vice-versa. Therefore, the equilibrium probability of dissolution q( θ 1) under centralization is smaller or equal than under decentralization, q( θ 0), if and only if β[e q( θ 1) V ( θ 1) E q( θ 0) V ( θ 0)] ψ. (21) In words, centralization stabilizes the federation if the short-term net secession costs are at least as large at the long-term loss in utility due to centralization. Otherwise, centralization destabilizes the federation in equilibrium. Proposition (3) provides us with a clear condition under which the probability of secession is smaller or equal under centralization. This condition links three elements: the net preference-matching cost b, the ex-post cost of decentralization δk + (1 δ) and the factor β at which region discounts the future costs and benefits of maintaining the federation. Proposition 3 The (de)stabilizing effect of centralization. A centralized federation is at least as stable as a decentralized one if b (1 β)(δk + (1 δ) k). Proof : Let us take as given the value of (δk + (1 δ) k) and assume that there exists a value for b such that q(0 θ) = q(1 θ), which we simply denote q. Under these conditions, 26

27 we know that equation (21) must hold. Substituting equation (9) equation (21) implies that b (1 β)(δk + (1 δ) k). It is worth discussing in more depth the condition provided by proposition 3, both because of the economic insight it provides but also because we will use it repeatedly in the rest of the paper. First, it shows that the higher is the weight being put on the welfare of future generations, which is represented by the discount factor β, the lower the net preference-matching costs must be for a centralized federation to be associated with less frequent dissolutions. This makes intuitive sense, as increasing b increases the immediate costs to secede, which enhances political stability but at the same time reduces the level of utility associated with maintaining the federation. By extension, the proposition thus shows that if absolutely no weight is put on the utility of future generations, which is if β = 0 then only the short-run secession cost ψ matters and centralization is associated with more political stability as long as ψ < 0. At the other extreme, if the weight being put on the welfare of future generations is very high, for example if β 1 then the centralized federation is more stable only if the net preference-matching actually represent a utility gain. 3.3 Centralization decision and policy implications We now have at hand all the necessary information to derive the optimal centralization rule. This is the first step of the game at which, behind the veil of ignorance and prior to the realization of any shocks, the regions decide whether the public sector is centralized. The rule driving the centralization decision is one of the main contributions of this paper, as it enriches the existing literature on the costs and benefits of centralization. Before the realization of any shocks, the expected utility associated with being in a centralized federation equals βe q( θ 1) V ( θ 1), whereas the expected welfare of a decentralized federation equals βe q( θ 0) V ( θ 0). Therefore, taking into account the fact that the initial cost of the public sector is (k k) in a decentralized federation but k in a centralized one, it is optimal in 27