LICOS Discussion Paper Series Making exit costly but efficient: the political economy of exit clauses and secession

This article presents a political economic analysis of exit from federations. Over time, members’ benefits from being in a federation can fluctuate because of changes in the state of the world. If a member stops benefitting, it may wish to secede i.e. exit the federation. Based on a real options model, we show that state-contingent exit penalties can induce socially efficient exit decisions. In addition to the substantive implications, this represents a methodological contribution to real options theory. Even if ex-ante specified exit penalties cannot be made state-contingent, they may still enhance social welfare by preventing secession wars. This finding runs counter to the dominant view in the literature that exit clauses should be avoided in federations. As a first test of the model, we derive five hypotheses and show that they hold for the breakup of Yugoslavia and all cases known to us of federations with an exit clause.

2 This article develops a political economic model of secession and the potential role of exit clauses. Generally speaking, an exit clause specifies the conditions of exit or withdrawal from an agreement. Examples of exit clause conditions are the payment of a penalty or waiting out a notice period. In most types of international treaties, safeguard clauses regulating temporary escape or withdrawal clauses regulating permanent exit are relatively prevalent (Koremenos and Nau 2010;Rosendorff and Milner 2001). As an alternative way of ensuring flexibility, international agreements may be concluded for a limited duration (Koremenos 2005). This is not the case for federations, which almost by definition have indefinite durations and in which exit clauses regulating secession are relatively rare. To the best of our knowledge, the only current examples are the secession clauses in the 1991 constitution of Ethiopia (Habtu 2005) and the 1983 constitution of Saint Kitts and Nevis (Weinstock 2001). 3 The European Union (EU), which has many characteristics of a federation, also has a withdrawal clause (Athanassiou 2009). 4 A historical example is Article 72 in the constitution of the Soviet Union (Sunstein, 1991: 645-647): "Each Union Republic shall retain the right freely to secede from the USSR".
Depending on how a secession takes place, it can be peaceful and swift, or painful and costly (Tir et al. 1998;Young 1994). If there is no exit clause in the federal constitution, exit from a federation requires an ex-post negotiated solution, i.e. consent from the remaining members. If a negotiated exit cannot be reached, embarking on a destructive secession war may be the only alternative for a member wishing to secede (Helfer 2005). We analyze three modes of exit: exit based on an exit clause, unilateral exit through a secession war, and negotiated exit. Considering 3 The conditions in the Federal Republic Ethiopia include a two-thirds majority in the Parliament of the seceding region. Saint Kitts and Nevis allows for secession by Nevis in case a two-thirds majority is reached in an independence referendum in Nevis. 4 Article 50 of the Treaty on European Union specifies that any Member State may withdraw from the Union by notifying the Council, and is guaranteed the right to leave unilaterally within two years.
the Soviet case, we allow for the possibility that the federation meets the triggering of an exit clause with an anti-secession war. Based on a real options model, we show that state-contingent exit penalties can induce socially efficient exit decisions even if there are barriers to ex-post negotiation.
In addition to the substantive implications, this is a methodological contribution to real options theory.
This paper is structured as follows. First we introduce the notion of efficient breach and review the literature on exit clauses. Then we introduce our model, of which we formally solve a decision theoretical version. Based on the insights from this analysis, we discuss the game-theoretical aspects of exit. Because a formal game-theoretical model incorporating barriers to negotiated exit would not be tractable, we offer a discussion instead. We demonstrate the plausibility of our conclusions by showing how the dynamics of the breakup of Yugoslavia can be explained based on our theory, and review all cases known to us of exit clauses in federations. While the evidence is supportive of the predictions of our model, it is by nature inconclusive in any statistical sense due to the small number of cases. In the conclusion, we identify three tentative reasons why exit clauses are actually rare in federations, in spite of their potential benefits.

Efficient breach and the literature on exit clauses
The idea that not respecting a contract may be socially desirable is known as efficient breach (Goetz and Scott 1977). In theory, if exit is efficient those better off outside could offer an acceptable side-payment for exit and make everyone better offan application of Coase (1960).
In this light, Drèze, De Grauwe, & Edwards (1993) discuss a practical rule suggested by Drèze to ex-post reapportion national debt at the time of secession. However, as pointed out by De Grauwe, ex-post renegotiation may be very difficult politically. Hence ex-ante negotiated exit clauses may be necessary to enable efficient breach.

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In spite of the potential benefits of secession clauses, the dominant position in the constitutionalist literature is that they should be avoided. This position was pioneered by Sunstein (1991), who sees constitutions as pre-commitment strategies in the presence of multiple equilibria. Chen & Ordeshook (1994) take the same starting point, but develop a formal three-player gametheoretical model which is taken up further in Filippov, Ordeshook, & Shvetsova (2004). Their conclusion is that there should be a constitutional ban on exit, in order to coordinate on nonsecession equilibria, which are assumed to be Pareto superior.
The strength of the conclusions drawn by Chen & Ordeshook (1994) is limited because of three strong assumptions. First, they assume that maintaining the federation is always socially efficient (efficient breach does not exist by assumption). Second, they assume that without an exit clause, exit cannot occur. In reality a party wishing to exit may embark on a destructive secession war.
Third, they assume that exit clauses are necessarily unconditional, i.e. free in use. In reality, exit will necessarily cause one-off transaction costs, and exit clauses could conceivably stipulate a penalty to be paid to the remainder of the federation. Bordignon & Brusco (2001) analyze optimal secession rules in a two-player game with two periods and a discrete stochastic state. In period two, members of the federation decide between accepting a federal allocation or starting a secession war. The conclusion is that secession clauses may be inefficient if the benefits from the federation depend significantly on its perceived stability.
While this model allows for stochastic shocks and hence the possibility of efficient breach, it still has some important limitations. The discretized set-up with only two periods and four states of the world precludes the analysis of optimal exit timing. In addition, they introduce a new restrictive assumption compared to Chen & Ordeshook (1994), namely that countries are ex-ante identical.
Using a formal model of costly exit clauses, we show that the position of Sunstein (1991) and Chen & Ordeshook (1994) against exit clauses is tenuous. By modeling the dynamic aspect of exit 5 decisions in continuous time, we introduce considerations of optimal exit timing absent in Bordignon & Brusco (2001). In addition, our model allows for members of the union to be different ex-ante, so that the distributional consequences of exit clauses can be studied. We also show that appropriately costly exit clauses do not increase the likelihood of exit given the implicit option of unilateral exit through a secession war.

The model
The following continuous time model describes a political union between two federated entities or members indexed by ∈ { , }. 5 For tractability, we assume that the entities of the federation are composed of identical inhabitants, and leave the incorporation of within-entity heterogeneity for future work. This means that each federal entity can be modeled as a unitary actor. For each such entity or member of the federation , the net benefits of being in the federation versus outside depend on the rules of the federation and a member's characteristics. Consistent with the literature on the size of nations, we assume that the benefits and costs from being part of a federation comprise economies of scale in the provision of public goods, the internalization of externalities, fiscal transfers, and welfare losses from centralized decision-making in the presence of heterogeneity between the federated entities (Alesina and Spolaore 2003;Desmet et al. 2011;Hug 2005). Each of these components is determined by the substantive terms of the federation, such as the rules for computing fiscal transfers, and the characteristics of the entities, such as their average income. We denote an entity's net benefits at the time of the creation of the federation by its type, . A high type indicates high benefits from the union. Forcefully incorporated members of the federation may have a negative type.

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Over time a member's benefits from being in the federation versus outside may change because of changes in the state of the world. For instance, a member may become richer. While this may be good for the member per se, it may also decrease its benefits from the federation, because it will have to pay higher fiscal transfers. This may be the case for Catalonia in Spain and Flanders in Belgium. As another example, consider changes in heterogeneity: over time, the culture and preferences of people across the federated entities may converge (diverge) such that the benefits of the federation for each federated entity increase (decrease). As a third example, two key external parameters can decrease the benefits from economies of scale: free trade and peace (Alesina and Spolaore 2003). With more free trade outside of the union the economies of scale from having a large internal market become less important. Likewise, the lower external military threats, the less important the economies of scale in the provision of national defense. Finally, consider changes in the attractiveness of the outside option, such as through the emergence of a free trade bloc like the European Union.
In our model, we capture all changes in the state of the world that are relevant for a member's benefits of being in the federation versus outside by its state . A high state means that a member is currently enjoying the federation more than when it was created, and vice versa. We assume that the link between the state of the world and benefit flows is exogenous. Substantively, this assumption means that the terms of the union cannot be renegotiated, e.g. the rules for computing fiscal transfers cannot be changed. While this is a limitation, we leave for future work a model where the link between the state of the world and benefits is endogenous.
To summarize, the net benefits for both members from being in the union versus outside depend on the stochastic state of the world at time , ( ) = ( ( ), ( )), and on the members' types ( , ). Concretely, member 's net benefit flow ( ) at time is given by: A positive correlation means that both members' benefits tend to move together. A negative correlation means that changes in the state of the world tend to have an opposite effect on both members.
Without loss of generality, suppose that the union starts at = 0 and set (0) = 0.
where ( ; , 2 ) is the probability density function (pdf) of the normal distribution with mean and variance 2 , and ( ) is the pdf of the standard normal distribution. Substantively, this means that the expected change in over any time period − is zero and that large changes are less likely than small changes. However, since the variance increases linearly with the time period − the expected magnitude of changes increases with time.
Assume that the members have a common discount rate , so that the expected discounted Hence, member only voluntarily enters the union if its type > 0. Members with < 0 may be coerced to join the union, but clearly such members want to secede from the federation if the exit costs are not prohibitive. Even if the union is ex ante beneficial for all, in some states of the world ( ) it may turn out so bad for one or both members that they may wish to exit.
In the model, we consider two types of ex-ante fixed exit conditions: penalties and one-off costs. An exit penalty consists of the payment of an amount by the exiting party to the remaining party . All other costs associated with exit are grouped in the one-off costs . This parameter comprises all non-transfer costs required explicitly or implicitly by the exit clause, such as the costs of organizing a referendum (if required), and the legal costs of creating a new state. The costs 9 and have the same effect on party , but only will be received by as a compensation for exit.
While is partly endogenous, can be freely specified.
As an example, consider the EU's Article 50. This clause does not specify a penalty, although it does stipulate a waiting period of two years. An example of a penalty that could have been included would be the payment of an additional year's budget contribution. The clause does not specify one-off costs such as the organization of a referendum, but clearly exit from the EU requires a substantial amount of legal costs. As an important side note, by triggering Article 50 a Member State can only guarantee full departure from the EU. This means losing all of the associated benefits, such a access to the Single Market, and all of the costs, such as the budget contribution.
The leaving state may attempt to negotiate more favorable terms with the rest of the EU, but such negotiations are legally distinct from the exit.

Optimal exit in a decision theoretical setting
To analyze the consequences of exit clauses, this section formally solves a decision-theoretical version of the model, in which only one member can exit. We start below by situating our model in real options theory. Following this, the first subsection discusses optimal exit with a fixed penalty , assuming that any clause is fully binding. In the second subsection the possibility of a secession war is incorporated. The next three subsections address the uncertainty of exit costs, the consequences of exit for the rest of the union, and the possibility of an anti-secession war initiated by the rump of the federation. The sixth subsection derives conditions for socially efficient exit, and the seventh and final subsection shows that state-contingent exit penalties can induce socially efficient exit.
In the model, we treat exit clauses as so-called real options. The theory of options was initially developed to study financial instruments such as put options, which give the holder a right to sell a stock at a pre-determined price in the future. Once developed, this theory has also been leveraged to study other optional decisions, such as the option to acquire a Joint Venture (Kogut 1991). Such applications of options theory outside of financial applications are called real options theory. The main technique used is dynamic stochastic programming, which requires the use of stochastic differential equations (Øksendal 1991;Stokey 2008). Our model builds on Dixit (1989) and Dixit & Pindyck (1994), who study firms' decisions to enter and exit markets with changing output prices. Since output prices are normally positive, they focus on geometric Brownian motions. In contrast, the model presented here assumes a standard Brownian motion because the benefits from a federation can become negative.
Our methodological contribution to real options theory is twofold. First, we extend the basic model of exit by a firm from a market to exit by a member from a federation. Unlike in a market, exit by one member of a federation implies a loss of benefits for the other members. Second, we formalize the mathematics of state-contingent exit penalties which depend on the state of the other member in a union. Jointly, these two methodological contributions allow us to derive conditions for socially efficient exit from a federation.
In what follows, we assume for simplicity that exit is definitive and that there is no possibility of re-entering later. However, even if re-entry is free the qualitative conclusions from our model would still hold, but the solution process would be complicated as the optimal exit decisions and optimal entry decisions would be mutually interdependent.
In the decision-theoretical version of the model, we assume that only one member can exit from the union, and only consider that member. Hence for now we drop the index to lighten notation.
When thinking about exit in a continuous time set-up, a member compares the expected value of maintaining the union to the value of exiting right now. Assuming rationality, the expected value of maintaining the union right now should take as a given optimal exit behavior in the future. This is captured by the notion of continuation value: the continuation value ( ) is the expected discounted benefit from maintaining the union when the current state is , assuming optimal exit behavior in the future (Dixit and Pindyck 1994).
We show in the Appendix that the continuation value is composed of two parts: the expected perpetuity value from maintaining the union, plus the option value of being able to terminate the union. At state , the benefit flow is + . Since on average the future value of a Brownian motion is equal to the current value, the expected perpetuity value at state is + . The more important the future, the lower the discount rate and the higher the perpetuity value. As we show in the Appendix, the option value of terminating the union depends on the exit terms. Specifically, the option value is , with = −√ 2 2 and a constant to be determined. Combining the expected perpetuity value and the option value, the continuation value can be written as Optimal exit with an exit penalty The continuation value is the value of maintaining the union for now, assuming optimal behavior for the future. Hence the constant depends on the optimal exit state . In the Appendix, we show that when facing an exit penalty , the optimal exit state and the corresponding value for The optimal exit state consists of three components. The first one, − , is the most intuitive.
When reaches -, the benefit flow drops to zero: ( | ( ) = − ) = − + = 0. The higher a member's type , the longer it is optimal to stay in the union, i.e. the more negative the optimal exit state.: < 0. The second term, − ( + ), reflects the deterring effect of exit costs since = < 0. The benefit flow needs to drop to − ( + ) to make exit worth considering, since the corresponding expected perpetuity value at that state would be equal to minus the exit costs −( + ).
The third term, 1/ , is the least intuitive but can be interpreted as the optimal forbearance level.
It reflects sophisticated rational behavior: given that re-entry is precluded, one should be willing to sustain some losses in the hope that the state improves again. 6 Intuitively, the higher the variance of the benefits, the higher the possibility that a bad state turns around, and the more reluctant one should be to exit. This intuition is confirmed: , it is easy to show that < 0.
Given (7) and (8), the continuation value at state is As the state deteriorates to the optimal exit state, the continuation value converges to the cost of exit: lim → ( ) = −( + ). The higher the cost of exit, the lower the value of the exit option and hence the continuation value: = < 0. Members prefer for themselves an exit penalty of = 0.
In summary, optimal exit decisions take into account the exit penalty . The higher the penalty, the lower the optimal exit state. This is intuitive: the costlier exit, the worse things need to be before exit becomes an optimal decision. 6 In fact, even if re-entry is free one should be willing to sustain some losses before exiting (Dixit 1989).

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Enforcement problems: the possibility of a secession war Up to now, we have assumed that any exit clause was fully binding. A member could only exit by paying the ex-ante agreed exit penalty . However, given that federal constitutions are not enforced by supranational courts, exit clauses may not be fully binding. In particular, the members may decide to renegotiate, or a member wishing to exit may do so unilaterally. By secession war, we denote any unilateral exit which does not respect a pre-agreed exit clause or has not been negotiated. We model a secession war as a pair of costs ( , ), where is the cost the exiting member would have to incur to win the secession war (including both the direct costs and the reputational costs) and is the corresponding damage to the remaining member.
The direct costs of a secession war hinge on the relative ease of exerting military force over a federal entity's territory. The stronger the presence of a loyal federal army within a federal entity, the more costly a secession war for that entity. Geography also plays a role: overseas regions or regions on the outer border of a federation incur less costs in seceding unilaterally than regions which are geographically contained within a federation. The reputational costs of a secession war depend both on the international norm against unilateral exit and on the circumstances. For instance, regions with oppressed ethnic minorities generally incur low reputational costs, as they tend to be quickly welcomed by the international community, i.e. recognized by other countries, the UN and the WTO (Buchanan 1997;Sorens 2016). For an analysis of third countries' recognition strategies, see Coggins (2011).
Arguably, if a member of the federation has the choice between using an exit clause and engaging in a secession war, it will pick the option with the lowest cost. Hence exit clauses with costs + above are ineffective as they cannot be enforced: the exit clause will never be used, but a secession war will occur if the state drops below ( ) = − − + 1 and a negotiated 14 exit is not forthcoming. The higher the cost , the less relevant the secession war option and hence the less severe the enforcement problem.

The uncertainty of exit costs
The model assumes that both the costs of exit per an exit clause, + , and the cost of a secession war are certain. This assumption is not restrictive under two conditions: (1)  Until now, we have only considered the member with exit option and dropped the index , temporarily reducing our two-player model to a one-player model. We now reintroduce the index for the member with the exit option, and introduce the index for the member subject to potential exit by member . For , the value ( , ) of being in the union depends on both and : 's benefit flow depends only on , but will be stopped by depending on .
In the Appendix, we show that if only has an exit option, 's value of being in the union is 7 For instance by observing cases of other federal entities seceding unilaterally, as suggested by Walter (2006).

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The first term again reflects the expected perpetuity value from the union, and is higher the higher 's state and type . The second term reflects the option value from 's potential exit.
This option value can be positive or negative; it is higher the higher the penalty that would receive, the lower 's one-off costs , and the lower 's benefit flow + that would be lost upon 's exit. As 's state deteriorates to its optimal exit state, 's value function converges to the penalty it receives upon exit minus the one-off costs associated with exit: lim Given the initial state of the world = = 0, the ex-ante expected value for is (0,0) = + ( − − ) − . The first order condition corresponding to the optimal exit penalty from 's perspective is (1 + ( − − )) − = 0. It is easy to verify that this penalty is = + − 1 and that it indeed corresponds to a maximum. This is the exit penalty preferred by for the other member . If only has an exit option, then would prefer for 's exit penalty to be higher the higher 's expected benefits, i.e. the higher 's type . Similarly, the higher 's one-off costs, the higher would like 's exit penalty to be.

The possibility of an anti-secession war
We have argued that federal unions may not be fully binding because of the possibility of a secession war and of a negotiated exit. A further enforcement problem is the possibility of an antisecession war. Even if the union includes an exit clause, a member trying to make legal use of this clause may be faced with an anti-secession war by the remaining member. Something to this effect occurred during the break-up of the Soviet Union, which tried preventing the secession of some Soviet republics. In the case of the American Civil War, some Southerners claimed there was an implicit secession right and that hence the North was conducting an illegal anti-secession war (Buchanan, 1997: 36).
Conducting an anti-secession war is an option for if has exercised its exit option. Intuitively, this option is more attractive for the worse off it would be by accepting 's legal exit. From (10) Government said "… it is worthwhile reminding the Convention that the former Soviets did have an exit clause, but if you chose to exercise it they would send gentlemen in tanks to talk to you".

Socially efficient exit
In this section we study exit from the point of the entire union. In a union with two members, exit by one member leads to the end of the union. By deriving the impact of exit on the combined benefits of the two players , we derive a condition for socially efficient exit. Taking the benefits of both members into account, this condition stipulates in which states of the world ( , ) the union should be preserved, and in which states it should be terminated. To ease the exposition, we present the derivation of the socially efficient exit state as stemming from a social planner who has as an objective function the sum of the members' benefits. We Socially efficient exit requires taking into account the states of both members, as well as the total one-off costs of separation of = + and the optimal forbearance level 1/ . If the combined state + drops below the threshold specified in (12) (23) and (28) for the individual members exit penalties do matter. The higher the exit penalty , the lower the state at which member exits. In the next section, we show that the exit penalty can be defined so as to induce to make socially efficient exit decisions.

State-contingent exit penalties
In the Appendix, we derive 's optimal exit behavior if the exit penalty can be made statecontingent. We show that if the penalty is of the form ( ) = + , then exits in states ( , ) satisfying + = − − ( + ) + 1 , = − √ 2 2 + 2 2 2 + 2 For this condition to lead to socially efficient exit as in (12), one finds = 1 , so that = and = + . Hence the socially efficient exit penalty for is * = + + The higher the state of the other member , the higher 's exit cost should be to induce it to take socially efficient exit decisions. This is intuitive: the more member is enjoying the union, the higher should be 's penalty for ending the union. Conversely, if member is in a very bad state, member would receive a positive payment for ending the union. The second term of * , equal to , reflects that for socially efficient exit needs to be incentivized to take 's one-off costs of 's exit into account.
Under the socially efficient exit penalty * , 's option value coincides with the social planner's option value: This is because has the same costs and benefits from stopping the union as the social planner: the payment of + , and the loss of the perpetuity value + . The loss of / is direct: by stopping the union, stops its benefit flow. The loss of / is indirect: the socially efficient exit penalty requires that pay / to .

Optimal exit in a game-theoretical setting
In the previous section, we formally analyzed the case where only one member had an exit option. In this section, we discuss exit in a game-theoretical setting. If both members have an exit option, member 's optimal exit strategy will depend on member 's exit strategy and vice versa.
In such a setting, no analytical solutions are available because the exit options are no longer perpetual: member 's (stochastic) exit time is the expiration date of member 's exit option. In addition, the analysis in this setting depends crucially on the possibility of a negotiated exit, which is hard to formalize appropriately.
If there are no obstacles to negotiating exit, socially efficient exit occurs irrespective of a potential exit clause. Although in this case the conditions of the exit clause do not matter for the timing of exit, the exit costs stipulated in the exit clause may affect the side-payments made to forestall or obtain exit, similar to the distribution of property rights in Coase (1960).

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In reality many obstacles may limit the scope for negotiating exit. Politicians or voters may be loss-averse or boundedly rational. Moreover, transfers may be costly or members' states may be privately observed (Fearon 1995). The importance of such impediments to a negotiated exit is ultimately an empirical matter. But because these impediments are hard to measure, we prefer not to formally model the role of negotiated exit and provide a discussion instead.
If negotiating exit is not frictionless, the possibility of an inefficient secession war reemerges, and with it the scope for exit clauses to improve social welfare. In particular, setting the exit cost + equal to the cost of a secession war would be welfare enhancing: when 's state drops to ( ), it will pay the penalty = − to , instead of starting a secession war which costs to . If the state of the world is fully contractible, efficiency could be further increased in the absence of renegotiation by making member 's exit cost conditional on 's state as in (15).
However, since the lack of observability of 's state by may precisely be one of the impediments to a negotiated exit, it seems optimistic to assume that state-contingent exit clauses could fully restore social efficiency.
To conclude this section we summarize the predictions of our theory based on the decision theoretical model and our discussion of negotiated exit. We identified three potential modes of exit: ex-post negotiation, unilateral exit, and exit based on an ex-ante agreed exit clause. If both members of a union are benefitting from it (are in a good state), neither will consider exit. Hence in states of the world ( , ) where both and are high the union continues. If both and are in a bad state, i.e. and are both low, exit will be negotiated and the union is dissolved.
If is in a bad state (low ) while is in a good state (high ), 's decision whether to exit depends on the exit costs of its cheapest mode of exit. If there is an exit clause, the associated exit costs consist of the penalty and the one-off costs . The costs of unilateral exit (secession war) are . The higher 's exit costs and the lower the variance , the lower the state can drop until exit becomes optimal for . If there are no barriers to ex-post negotiation, exit occurs when it is socially efficient, i.e. when the combined benefits of both members drop below a critical level. The side-payment made for such a negotiated exit depends on 's exit costs, and on 's costs of an antisecession war. If faces low exit costs and high anti-secession costs, makes a side-payment to for staying in the union. If a negotiated exit is not possible because dissolving the union would not be efficient (i.e. is benefitting more from the union than is losing), or because of barriers to negotiation, then considers unilateral exit.

Empirical evidence
In this section we derive testable hypotheses from our analysis. We focus on hypotheses that have to our knowledge not been tested yet in the literature. The lack of previous testing for these hypotheses is likely due to difficulties with gathering the necessary data. We provide a first stab by analyzing the breakup of Yugoslavia. Since the number of federations with exit clauses is very small, we are also able to test our hypotheses related to exit clauses for all cases known to us of federal exit clauses. While the evidence is supportive of the predictions of our model, it is by nature inconclusive in any statistical sense due to the small number of cases.

Testable hypotheses
The theory presented in this article centers on four key concepts: (1) the net benefits of being in the union versus outside, (2) the costs of unilateral secession through a secession war, (3) the presence of an exit clause and the associated exit costs, and (4) the costs of an anti-secession war.
In particular, the theory predicts that exit will occur if a member's net benefits drops below a critical value defined by the exit costs of the cheapest available mode of exit, whether it be a negotiated exit, exit based on an exit clause, or a secession war. Each of the four key concepts is defined by several components. Finally, we concluded that in response to the triggering of an exit clause, the rump of the federation may start an anti-secession war. However, since trying to prevent an exit clause-based secession carries reputational costs, we argued that anti-secession wars may only be relevant in autocracies, leading to the following testable hypothesis: H5: Democracies never meet an exit clause-based secession with an anti-secession war.

The breakup of Yugoslavia
After World War II, Josip Broz Tito united Yugoslavia as a Socialist Federal Republic consisting of six republics: Slovenia, Croatia, Bosnia-Herzegovina, Serbia, Montenegro, and Macedonia (Lampe, 2000: 233-235). In 1974, a confederal constitution was adopted (Fine, 2003: 182). While the preamble of this constitution made a reference to a national right to selfdetermination, Article 5 stated that border changes required the consent of all republics and 24 provinces (Iglar, 1992: 219). The 1974 constitution hence did not have an exit clause in any real sense.
In 1980 the Yugoslav President Tito died. In November 1989 the Berlin Wall fell and over the period 1990-1991 the Soviet Union disintegrated. In June 1991 Slovenia and Croatia unilaterally declared their independence from Yugoslavia, and by the end of the year Macedonia did the same (Hupchick & Cox, 2001: 49). Serbia, controlled by Milošević and considered the dominant republic in the Yugoslav federation, was opposed. In Slovenia, fighting only lasted ten days and its independence was quickly recognized. In Croatia, more fighting took place before its independence Based on the breakup of Yugoslavia, H1 clearly still stands. Croatia and Slovenia, the first republics to declare independence, were not only economically more advanced, but they were indeed paying transfers to the rest of Yugoslavia (Fine, 2003: 182). One key mechanism for such transfers was the Yugoslav Federal Fund, which provided investment capital for the less developed regions (Bookman, 1993: 97).

The evidence on exit clauses
As indicated in the introduction very few federations have exit clauses. We provide an overview of all cases known to us in Table 1. permitting secession was adopted after the collapse of military rule and the start of Eritrea's independence process. However, scholars are pessimistic about the secession clause, corroborating H5: "The provisions of a liberal democratic constitution conflict with the reality of authoritarian centralist practice and therefore jeopardize the future of federalism. Although the secession clause has symbolic value, it is unlikely that any Ethiopian government would allow secession to take place" (Habtu, 2005: 313 Our results beg the question why exit clauses are not more prevalent in real-world federations.
We tentatively advance three reasons. First, politicians negotiating federations may wish to tie their successors' hands. In our model, we assumed that each member of the political union could be represented as a unitary actor. In practice, political unions may have heterogeneous effects on different parts of the population within one member. If that is the case, politicians whose electorate favors the union may want to prevent exit in the future by not having an exit clause.
Second, political unions may not be rationally designed. This may be especially true for longestablished federal countries. But even for modern federations there may be a norm against exit clauses because these are perceived as going against the spirit of collaboration embedded in such unions. Such a norm may also explain why most real-world examples of exit clauses (such as the EU's Article 50) have no exit penalties, in spite of the theoretical importance of exit costs to achieve socially efficient exit decisions.
Third, exit clauses may not be prevalent in the real world because powerful members of the federation may be able to impose their terms. Given favorable substantive terms of the union, they would expect to benefit a lot from being in it. In turn, this would lead them to prefer a high exit cost for the other members. Expecting to be able to easily negotiate exit if the union would ever stop being beneficial to them, they may prefer not having an exit clause altogether and successfully impose this.
We leave for future research the negotiation of exit clauses. Given the distributional implications of exit clauses, the bargaining process will be important and socially efficient exit clauses are not guaranteed. However, to the extent that members are negotiating behind a veil of ignorance, their ex-ante preferences will be closer to the social optimum and negotiations will be easier. A second area for future research is to make the link between the state of the world and payoffs endogenous. In the model presented here, the payoff-relevant state of the world is exogenous. In practice members may be able to change how the state of the world affects their payoffs by renegotiating the terms of the union. For instance, federal laws affect how the state of the world maps to federal transfers and hence to the benefits from the union. If at some point the prevailing transfers make the federation undesirable to a member, this member will likely try to renegotiate the federal laws before considering exit.
with constants and to be identified. Note that > 0 and = − < 0. For a particular solution, we try ( ) = + . This yields the solution ( ) = + . This is the expected perpetuity value from the union starting from state . Combining the particular solution with the homogeneous part, the general solution is Since ( ) represents the value from maintaining the union perpetually, ℎ ( ) represents the option value of exit, which should be positive. As the state improves, the value of the exit option should converge to 0: the better the state, the higher your benefit flow and the less valuable the exit option. This implies that = 0 since > 0. We now have an expression for the continuation value ( ) up to the constant . This constant will be determined by a boundary condition corresponding to optimal exit.

Optimal exit with a penalty
Two conditions are needed for optimal exit in a continuous time stochastic model (Dixit and Pindyck 1994).
Ito's lemma in two dimensions (Øksendal 1991 ]. Fill this out in (24) to obtain the partial differential equation If exits, receives the exit penalty and incurs one-off cost . Since will exit at = − − ( + ) + 1 , the appropriate value-matching condition is 37 ∀ : ( , ) = − VM (27) Since undergoes 's exit decision, there is no smooth-pasting condition for optimality. The solution for ( , ) needs to satisfy both the partial differential equation (26)

State-contingent exit penalties
If the penalty can be made state-contingent, then 's continuation value will depend on .
Assume only has an exit option but the exit cost is a function of , specifically  ]. Fill this out in (33) to obtain the partial differential equation As in the main text, a particular solution is ( , ) = + , the perpetuity value of the union.
Since upon exit has to pay the penalty ( ) = + and incurs the one-off cost , the value-matching condition at an exit state = ( , ) is 40 Filling this out, one finds that optimal exit for is defined in terms of the following linear combination of and The higher or the more is made contingent on , the higher the weight of in 's exit decision. Member 's continuation value depends on its own state for the perpetuity value, and on the linear combination of and for the option value It is easy to verify that with a non-state contingent exit penalty ( ) = , i.e. = 0, = , the solution reduces to non-state contingent solution presented in the main text.