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The Political Economy of Sovereign Default

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Sebastian Hohmann

1. Theory

Texte intégral

  • 9  The two sets are, as defined in the introduction, the Selectorate {S} and the Winning Coalition {W(...)

1This section presents a model of the political economy of sovereign borrowing. I show that changes in the sizes of two sets – one composed of the group of people potentially with political say in a country, the other, a subset of the former, containing the government’s supporters9 – have an unambiguous influence on sovereign borrowing. Everything else equal, governments maintained in power by smaller (and thus more loyal) groups of supporters tend to default more often. Since lenders expect to be compensated for a higher risk of default with higher interest rates, governments maintained only by a few loyal supporters face higher borrowing costs.

1.1. General setup

  • 10 In particular, the concept of “affinities” between selectors and governments is completely omitted. (...)

2The model builds on the intuition of the Selectorate theory presented by Bueno de Mesquita et al. (2003), but departs from the authors’ original model to focus on sovereign borrowing.10 The model is an infinitely repeated game with one round presented here. There are three actors in the model. They are the members of the Winning Coalition W, the members of government and lenders to the government. All are assumed to be infinitely lived, risk neutral, maximising their utility and discounting the future at the common rate δ, with 0 < δ < 1. Only governments that have not yet defaulted are able to borrow. A country can, however, regain access to sovereign borrowing if the government is replaced. The people responsible for making this decision are the members of W. A government that is able to borrow does so at the rate at which lenders are willing to lend. The timing in each round is as follows: At the beginning of each period, governments that have not yet defaulted take out a loan at the competitive rate. The economy then rolls along for one period. Output is produced and taxed and the government doles out a mix of public and private goods to the country’s residents. At the end of the period, governments must make a payment on the loan they have taken out or decide to default. If they default, the members of the government’s Winning Coalition decide whether or not to depose the government.

3My solution of the game will take the form of two comparative statics conditions, which show a definitive effect of changes in political institutions on the likelihood of default. Before these conditions can be established, it is necessary to describe how institutions affect government resource allocation.

4To make decisions, governments need to survive politically. The Selectorate theory therefore assumes that politicians seek to maximize the time spent in office. Each period, the government has R resources at its disposal. R consists of tax income T plus borrowing L if credit is available. Hence

  • 11 Bueno de Mesquita et al. (2003), p. 139-143 discuss how changes in W and S influence the tax rate.
  • 12 This might be used for personal enrichment of leaders or some other purpose.

5I assume T to be given exogenously.11 Given R, the government chooses optimally what fraction of R to allocate to discretionary spending D12 and allocates the rest to non-discretionary spending N. Non-discretionary spending consists of spending on public goods G benefiting everyone in society and bribes b to keep the members of the government’s Winning Coalition happy. Figure 1 shows this carve-up of resources schematically.

6All Selectors are assumed to have the same additively separable preferences over government provided goods. That is the utility they receive from government provided goods may be written as

Figure 1: Distribution of resources R available to government

Figure 1: Distribution of resources R available to government

7I also assume

8Selectors receive utility from the non-discretionary portion of government spending. Those excluded from W receive the benefit of G, which consists of public spending t financed out of taxation and additional credit-financed spending l if the government can borrow. Members of W receive t and, if available l, plus a bonus of an additional b in private goods to keep them loyal, where b is a function of the size of the Winning Coalition. Hence the utility of members of W equals U (t, l, b(w))=u1(t) + u2(l) + u3(b(w)) under a government which has always repaid and U(t,l,b(w))=u1(t)+u3(b(w)) under a government, which has already defaulted. Selectors excluded from W receive U(t,l,b(w))=u1(t)+u2(l) in the former and U(t,l,b(w))=u1(t) in the latter case.

Comparative statics of institutional change for government goods provision

9Governments will only spend just enough of R on non-discretionary purposes to keep their Winning Coalition from withdrawing support.

10Should the current W decide to withdraw support from its government, whether or not its members end up again in the new W depends on the size of w/s. I assume that all members of S are the same a priori, and so the probability of being a part of the new Winning Coalition equals w/s, while the probability of being excluded equals 1-w/s.

  • 13  This section follows Bueno de Mesquita et al. (2003), p. l47-160.

11To keep its Winning Coalition from defecting, the government must take into account the loyalty norm w/s as well as the absolute size of W. I now examine how the government’s resource allocation decision is affected by institutional change.13

An increase in s

  • 14 This consideration is taken up below in the discussion of the effects of changes in w.
  • 15 Selectorate size does not influence the relative importance of public or private goods in determini (...)

12Holding w constant, an increase in the size of the Selectorate implies that w/s falls and hence the probability of exclusion from future Winning Coalitions following defection from the incumbent rises for current members of W. This increases the loyalty of the government’s Winning Coalition and thus discretion for the government, which can consequently appropriate a larger share of R as D. This shift in the division of R between D and N does not affect the division of N. Increased loyalty means simply that more resources go to the government and less to the Selectorate. t and, if available l will fall, but the size of b(w) relative to the size of t and l remains unaffected. The loyalty of W is ensured by rewarding its members above and beyond the public goods that ordinary Selectors enjoy, while taking account of the relative efficiency of spending on public and private goods.14 In their decision to maintain an incumbent in power, members of W compare the pile of goods they would receive as ordinary Selectors to their allocation of resources. An increase in s means both of these shrink in absolute terms, but the loyalty maintaining relative advantage b(w) that members of W enjoy remains unaltered.15

An increase in w

13An increase in the size of the Winning Coalition has several effects. First, the loyalty norm w/s increases, which reduces the loyalty of the Winning Coalition through the potential of future exclusion effect and therefore the amount of resources D the government can appropriate for itself. Changes in w do not influence the relative importance of public goods accruing to all Selectors and privative goods going only to W through this channel. Their level rises, making the Winning Coalition and the excluded Selectors better off, but the edge the Winning Coalition enjoys is the same.

  • 16  Consider, as an example, the case of pollution. Faced with the alternative between receiving a mod (...)
  • 17 […] as the coalition becomes larger, the relative difference in the value of goods received between (...)

14A second effect does, however, influence b(w). As w expands, private goods need to be spread more thinly among the members of W. This by itself will reduce the per capita bonus b(w) each member of W receives. Further, as W expands, spending resources to buy off its individual members is an increasingly inefficient way for the government to deliver utility to its supporters.16 Thus, as w increases, a larger proportion of N is spent on public goods, which, combined with the dilution effect of a larger Winning Coalition means that b(w) declines.17

15This discussion leads to the following comparative statics for b(w).

16where the last four conditions follow from changes in the loyalty norm w/s.

1.2. The Winning Coalition’s reaction to a default

17To stay in power, a government needs the support of its Winning Coalition. More goods are allocated to members of a W sustaining a government in power that is still able to borrow. But the edge that members of W enjoy over excluded Selectors does not disappear if a government that has once defaulted is no longer able to borrow. That government will not provide its Winning Coalition with resources as plentiful as before the default, but the benefits accruing to W may still be worth continued support. I now consider the problem facing the members of W once their government has defaulted.

1.2.1. A member of W loyal to a defaulting government

18Assume one representative member of W. If this member chooses to maintain his government in power indefinitely following a default, his utility is

1.2.2. A member of W that deposes a defaulting government

19If the Winning Coalition instead chooses to withdraw its support from the government, a new government takes over. This new government then needs one period to re-establish credibility as a borrower, following which it once again can and does borrow. Therefore, a member of W that deposes its government and ends up once again as a member of the W supporting the new government receives a utility of

20If he is shut out of the new Winning Coalition, his utility will be

21Should the current W decide to withdraw support from its government, whether or not its members end up again in the new W depends on w/s. It follows that the expected utility of a member of a W that deposes a defaulter government equals

1.2.3. To depose or not to depose

22The members of W will decide to depose a defaulting government if the expected utility from doing so exceeds the utility from keeping a defaulting government in power as a member of W. That is, a defaulting government will be removed if

23This can be arranged as

  • 18 This benefit is discounted, since it accrues only after one period, which the new government needs (...)

24Therefore, when (6) holds, deposing the defaulting government is the better option and members of W will do so. (6) has a straightforward interpretation. The potential benefit members of W deposing their government can incur is the renewed access to benefits from government borrowing u2 (l(w,s)).18 The risk they run is losing the benefit attached to belonging to the Winning Coalition, u3 (b(w)) times the probability of incurring this loss – the probability of exclusion from future Winning Coalitions 1-w/s. If the discounted benefit from future borrowing opportunities exceeds the expected loss from gambling on the membership in future Winning Coalitions, a defaulting government loses support.

1.2.4. Showing the possibility of continued support and deposition

25I now show that (6) can be such that either the LHS or the RHS is larger. I consider two cases.

26The first is that of a democracy, where the Selectorate comprises essentially the whole adult population and the Winning Coalition is a large subset of this group. l (w, s) must be large in this case because a substantial amount of government borrowing opportunities benefit the Selectors, since the government cannot funnel off resources effectively, given the weak loyalty of its Winning Coalition. Further, public goods provision is more effective than bribes to the members of W, given their number. At the same time, b(w) will be small, since again, public goods provision is more effective than private goods in keeping the Winning Coalition happy. The dilution effect that comes with a large w reinforces this, making individual benefits attached to membership in W small. Therefore the LHS of (6) will exceed the RHS and a defaulting government will be deposed.

  • 19  This arrangement is exemplified by the system developed by Lenin in Soviet Russia, Bueno de Mesqui (...)

27Second, consider a rigged election autocracy with the government depending for support on only a small Winning Coalition drawn from a large Selectorate.19 In this case, given the strong loyalty of its Winning Coalition, the government can expropriate a substantial part of borrowing for discretionary purposes, leaving little for public goods provision and thus l (w, s). Also, given the small size of W, private goods are a more effective loyalty-inducing device than public goods. Even though non-discretionary spending is smaller overall in this case, given the small number of individuals in W, the per capita benefit b(w) each of them receives is still large enough to offer a substantial advantage over the meagre public goods excluded Selectors receive from the government. Consequently, the RHS of (6) is large and exceeds the LHS, meaning that the Winning Coalition will maintain its government in power after a default.

1.2.5. Comparative statics of institutional change for the loyalty of the Winning Coalition post default

28I now consider what happens to the incentives of the members of W when institutions change.

An increase in s

29Taking partial derivates with respect to s on both sides of (6), I obtain

30(7) cannot hold, since the LHS is negative while the RHS is positive. Therefore an increase in s increases the RHS of (6) while decreasing the LHS, thereby making it less likely that a defaulting government will be deposed, everything else equal.

An increase in w

31Taking partial derivates with respect to w on both sides of (6), I obtain

32(8) necessarily holds, since the LHS is positive while the RHS is negative. Therefore an increase in w increases the LHS of (6) while decreasing the RHS, thereby making defaulting governments more likely to be deposed, everything else equal.

1.3. The government

  • 20  One objection that might be raised here is that borrowing carries only risks for politicians (bein (...)

33Governments want to survive politically. For each period in office, politicians receive utility Ψ. This is the extra utility politicians obtain above and beyond the enjoyment they would get from living as ordinary Selectors. Once in power, governments take out a loan each period, provided they have not defaulted yet. Once a default has occurred, access to credit is lost. Defaulting, however, does not automatically entail being deposed. Whether a government loses the support of its W depends on whether the latter’s members receive a utility by continuing to support a defaulting government that is greater than their expected utility after overthrowing their government. If the government is deposed, politicians lose the utility Ψ attached to office.20

34A member of a government that chooses to honour the country’s debt receives utility Ψ from being in office today plus the discounted utility of occupying office at the beginning of next period. Repaying debt costs the government θ, which can be thought of as the political penalty that servicing debt entails. The more difficult debt is to repay, for instance because of negative macroeconomic shocks, the larger θ. I assume this difficulty to lie outside the government’s control and treat θ as a random variable such that θf(θ) over [0, θ         ]. If a government repays its debt in the current period it finds itself in the next period again with the choice of honouring its debt or defaulting. After some algebra, I can write the expected utility of a government that chooses to honour its debt as

35where F (θT) = 0θT ƒ (θ) = P (θ < θT ), i.e. the probability that cost of repayment lies below the threshold θT defined below, and gD is the expected utility of a defaulting government.

36If the government defaults, it is retained in office by its Winning Coalition with probability q (w, s). As I showed in section 1.2, members of W are more likely to depose a government following a default, the larger w and are less likely to do so, the larger s. I therefore have the following comparative statics for the probability of governments being retained in office, following default.

37If a government is deposed, its members lose the extra enjoyment Ψ attached to office. I can therefore write the expected utility of a defaulting government as

1.3.1. To default or not to default

38To determine whether a government defaults or not, I must pin down the threshold cost of repayment θT, which leaves the government indifferent between repayment and non-repayment of debt. This is given as the solution for θ of

39namely

40(12) has the following interpretation. The cost of debt repayment θT that makes a government indifferent between repayment and non-repayment is equal to the discounted utility from political life Ψ, weighted by the probability of the government being deposed following a default. Intuitively, debt repayment means incurring a cost θ. This cost is worth incurring if it is smaller than the discounted expected loss in utility, following a default. If the cost of repayment exceeds this discounted expected loss in utility, repayment is not worth while and the government defaults.

1.3.2. Comparative statics of institutional change for the threshold cost of repayment

41I now examine how changes in the institutional environment affect government incentives.

An increase in s

42Taking partial derivatives on both sides of (12) with respect to s yields the partial effect on θT of an increase in the size of the Selectorate.

An increase in w

43Taking partial derivatives on both sides of (12) with respect to w yields the partial effect on θT of an increase in the size of the Winning Coalition.

44The signs of expressions (13) and (14) follow directly from the comparative statics developed in Section 1.2. There I showed that governments are more likely to be retained in power following a default, the larger s, and are less likely to be retained, the smaller w, everything else being equal in both cases.

45The interpretation of (13) and (14) is clear: a marginal change in the likelihood of being deposed following a default means that a government considering a default incurs a change in expected utility should it decide to stop honouring the country’s debt. The change in utility equals the discounted utility Ψ from political life weighted by the change in probability of being retained in office, following default. Politicians suffering an increased chance of being deposed following default as a result of an increase in the size of the Winning Coalition are prepared to incur higher threshold costs and hence will default less often. Politicians operating in environments with larger Selectorates are less likely to be deposed following defaults. Consequently, such governments will be prepared to incur only lower threshold costs of repayment and hence default more frequently.

1.4. Lenders and interest rates

46Lenders have funds equal to L to lend out each period. They face the following trade-off: Either they invest their money abroad and receive a certain return, which I normalize to zero. Or they invest their money in sovereign debt, in which case they receive a return of r if things go well, but lose all their money if the sovereign defaults. Let Θ denote the probability of default. Then the interest rate r that leaves lenders indifferent between lending and not lending (the competitive rate) is given by

Threshold cost, default risk and interest rate

47Now recall that the cost of repayment is a random variable θf (θ) over [0, θ        ]. The sovereign defaults if the realization of the cost of repayment in a particular period exceeds his threshold θT. Therefore a default occurs with probability

48Combining (15) and (16), the interest rate can be written as

49(17) can now be used to investigate what happens to interest rates when θT rises.

50Thus, when θT rises, the threshold cost of repayment at which it is better to default than not to has become bigger and so defaults become less common. Hence interest rates fall. As I showed previously, increases in w lead to increases in θT, while increases in s lower it. Thus changes in these institutional parameters contribute to changes in interest rates.

1.5. Conclusion

51In this section I have demonstrated how changes in the sizes of two groups termed Selectorate and Winning Coalition influence sovereign borrowing behaviour. Governments supported by Winning Coalitions that are small relative to the Selectorate have more loyal supporters, since the latter have a greater likelihood of being excluded from future Winning Coalitions, should they decide to depose their government. More loyal support means greater discretion for the government, which in turn translates into a greater incentive for the government to default, should the need arise. Other things equal, an increase in the size of the Winning Coalition increases the likelihood of a defaulting government’s members being punished by losing office, while increases in the size of the Selectorate reduces this likelihood. Governments attached to their jobs are therefore willing to incur larger political costs in repaying debt when operating under a larger Winning Coalition, and are prepared to incur lower costs when operating under a larger Selectorate. Thus governments operating in small s and large w systems default less often. Lenders who care about default risk then lend to such governments at more favourable terms.

Notes

9  The two sets are, as defined in the introduction, the Selectorate {S} and the Winning Coalition {W}. I will use capital letters S and W to denote these sets, omitting the braces, and lower case letters s and w to denote their respective cardinalities.

10 In particular, the concept of “affinities” between selectors and governments is completely omitted. Further, governments are assumed to be obtaining utility only from occupying office. The issue of how many resources they have for discretionary use each period, and the utility they derive from having these resources, is ignored.

11 Bueno de Mesquita et al. (2003), p. 139-143 discuss how changes in W and S influence the tax rate.

12 This might be used for personal enrichment of leaders or some other purpose.

13  This section follows Bueno de Mesquita et al. (2003), p. l47-160.

14 This consideration is taken up below in the discussion of the effects of changes in w.

15 Selectorate size does not influence the relative importance of public or private goods in determining the policy mix that the incumbent provides, but it does help determine the risk of exclusion from future coalitions, Bueno de Mesquita et al. (2003), p. 158.

16  Consider, as an example, the case of pollution. Faced with the alternative between receiving a modest boost to their utility from a small bribe in form of a cheque from the government and a government policy of pollution control (a public good making everyone better off), members of a large Winning Coalition might well opt for the latter. The assumption made is that Coalition members will value the increase in environmental quality more than the small individual payoff they would receive alternatively as members of a large Winning Coalition.

17 […] as the coalition becomes larger, the relative difference in the value of goods received between those in and those outside the coalition becomes smaller, Bueno de Mesquita et al. (2003), p. 149.

18 This benefit is discounted, since it accrues only after one period, which the new government needs to re-establish credibility.

19  This arrangement is exemplified by the system developed by Lenin in Soviet Russia, Bueno de Mesquita et al. p. 83-86.

20  One objection that might be raised here is that borrowing carries only risks for politicians (being deposed after an eventual default) and no additional benefits. Therefore rational governments would seem well advised to avoid borrowing altogether. However, looking at the problem from the point of view of the Winning Coalition, it is clear that a government that refuses to borrow can only deliver its W the payoff of a government that has already defaulted. In essence, default and non-borrowing are the same from the point of view of a government’s supporters. Since the supporters decide whether or not a government is retained, it is always better to borrow in order to increase a government’s chances of being maintained in office.

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