The Design of an Optimal Sovereign Debt Restructuring Mechanism
Carlos A. Abadi
August 14th, 2019
Debates on sovereign debt restructuring typically emphasize a trade-off between ex-ante and ex-post efficiency. Proponents of bankruptcy procedures highlight the ex-post inefficiency posed by costly default and emphasize the importance of mitigating these via statutory or market-based remedies. Critics of such proposals counter that sovereign debt is feasible and affordable only because of the threat of costly crises. In this article, we consider the design of an optimal sovereign debt restructuring mechanism where countries choose their bankruptcy provisions depending on the economic circumstances.
Debates on sovereign debt restructuring typically emphasize a trade-off between ex-ante and ex-post efficiency. Proponents of bankruptcy proceedings (e.g., Krueger, 2002; IMF, 2002) highlight the ex-post inefficiency posed by costly default, and emphasize the importance of mitigating these via institutional or market-based remedies. Critics of such proposals (e.g., Dooley, 2000; Schleifer, 2003) counter that sovereign debt is feasible and affordable only because of the threat of costly crises. Bankruptcy mechanisms that lower the ex-post costs of debt crises or shield the debtor from the threat of holdout litigation may do more harm than good by increasing moral hazard problems ex-ante.
Statutory approaches to balancing ex-ante incentives and ex-post crisis costs have tended to highlight a “double trigger” mechanism for a viable sovereign bankruptcy regime (Gai, Hayes, and Shin, 2004; Brookings-CIEPR, 2013). A sovereign first makes a request for assistance in a manner akin to filing for Chapter 11 of the US bankruptcy code, and then a bankruptcy code (or the IMF) rules on the case. Gai et al. (2004) show formally that statutory mechanisms enhance welfare even though the bankruptcy court is only able to imperfectly judge if repayment problems are the result of genuine bad luck on the part of the sovereign.
In an important contribution to the debate, Bolton and Skeel (2004) question the feasibility of statutory approaches to sovereign debt restructuring. Drawing on US bankruptcy history, they suggest that tailored approaches may become more politically palatable. Allowing sovereigns to have the choice of opting out of the provisions of a bankruptcy framework depending on their economic circumstances would increase their willingness to adopt a sovereign bankruptcy framework. Bolton and Skeel (2004) also emphasize the importance of preventing the dilution of the claims of existing creditors to ensure ex-ante efficient levels of borrowing. The enforcement of absolute priority emerges as a key element of a robust sovereign bankruptcy framework.
The changing nature of holdout litigation has also altered the balance between ex-ante and ex-post efficiency. In the past, ad hoc debt exchanges were largely smooth because a sovereign could unilaterally bypass holdout creditors through take-it-or-leave-it offers backed by the agreement of a simple majority of bondholders. But the New York District Court rulings on Argentina in 2012 have made it easier for holdout creditors to litigate other creditors and, hence, indirectly harass the sovereign (Brookings-CIEPR, 2013). By lowering the costs of litigation, such developments have made participation in debt exchanges harder to coordinate.
In this article, we present a model in which countries can tailor a sovereign bankruptcy framework to fit their own circumstances, but must contend with the market discipline of holdout litigation.
In our optimal contracting framework, a sovereign issues bonds to fund a risky project and chooses the bankruptcy provisions and exemptions (a “haircut”) ex-ante to maximize domestic consumption. The ex-ante choice of the haircut has two important ex-post incentive effects. First, it influences the sovereign’s willingness to repay. All other things being equal, a larger haircut means that the sovereign can more easily restructure its debts. This, in turn, increases the sovereign’s incentives to default and file for bankruptcy. The second effect is on the creditors’ incentives to hold out during the restructuring. In our model creditors are ex-post heterogeneous and have different costs of pursuing litigation against the sovereign. Litigants who reject the sovereign’s haircut on their claims petition a bankruptcy judge that they be repaid in full. The judge’s ruling reflects the extent to which creditors; rights are favored in the restructuring mechanism. Successful litigants are paid in full, while unsuccessful litigants walk away with nothing. Thus, a large haircut means that more creditors will hold out and pursue litigation. The sovereign seeks to mitigate the costs to output from default and so offers a lower haircut in equilibrium.
The optimal haircut is shaped by creditors’ ability to trade their claims in the secondary market prior to the restructuring phase. If the ex-ante haircut is high, then creditors with high litigation costs have a strong incentive to sell their bonds to the more litigious creditors; i.e., those with low litigation costs. This, in turn, exacerbates holdouts and litigation. In our model, if the most litigious creditor has deep pockets and sufficiently low marginal litigation costs, they can buy all the bonds from the other creditors. But if the ex-ante haircut is low, then the incentives for high-litigation cost creditors to sell their claims to more litigious creditors are eliminated and there is no trade in the secondary market.
Our model predicts that countries with weak and risky macroeconomic fundamentals will voluntarily seek lower haircuts (i.e., harsher bankruptcy provisions) ex-ante. Adverse shifts in the distribution of output have the effect of widening the range of economic outcomes over which the sovereign prefers to default. But if the threat of litigious holdout creditors is material, then the sovereign counters adverse holdout costs by offering a lower haircut ex-ante.
The legal environment also influences the choice of haircut. If the bankruptcy regime is more creditor-friendly, then the ex-ante haircut will tend to be lower by operation of two ex-ante effects. First, an improvement in the rights of holdout creditors implies that it is more likely that the sovereign will ultimately have to satisfy the holdouts. This reduces the incentive to file for bankruptcy. Secondly, creditors’ incentives to hold out and litigate increase. In order to avoid this, the sovereign lowers the ex-ante haircut, offering more to creditors. To the extent that the ability of the bankruptcy framework to mitigate the output costs imposed by the holdout creditors is increased, this raises the incentive for the sovereign to default and file for bankruptcy. This, in turn, enables the sovereign to increase the haircut and offer less to creditors during the restructuring.
Finally, our model suggests that it is optimal to prioritize the rights of holdout creditors during litigation so that they are always paid in full. This is consistent with the notion of strict adherence to absolute priori ty during debt restructuring that Bolton and Skeel also emphasize in their proposal.
Our work is related to the literature on creditor litigation in sovereign debt, notable Haldane, Penalver, Saporta, and Shin (2005), Engelen and Lambsdorff (2009), Pitchford and Wright (2012), Bai and Zhang (2012), and Schumacher, Trebisch, and Enderfein (2015). But those papers focus on the ex-post renegotiation stage rather than the ex-ante implications for sovereign borrowing and the design of the bankruptcy framework. Recent work has also highlighted the importance of the creditor base in sovereign debt enforcement. Broner, Martin, and Ventura (2010) develop a model in which, once it becomes apparent that default is looming and penalties are insufficient, foreign creditors can sell their bonds to domestic buyers. Since domestic residents expect the government to enforce domestic debts , they purchase the securities at face value. Trading in the secondary market thus allows foreign creditors to circumvent default. The secondary market channel through which debt is enforced in our model is very different, however.
This article is also related to recent work on pre-emptive sovereign debt restructuring. While many papers simply assume that restructurings are preceded by a default, Asonuma and Trebesch (2016) assume that this is not the case. They develop a quantitative sovereign debt model that emphasizes the Nash bargaining game between the debtor and its creditors, and which incorporates the possibility of both pre-emptive and post-default restructuring. Asonuma and Trebesch show that pre-emptive restructuring is optimal if the sovereign expects a high probability of default and faces high output costs as a result. In their model, pre-emptive deals also lead to lower haircuts, quicker renegotiations, and lower crisis costs. Empirical studies of pre-emptive restructuring include Diaz-Cassou, Erce-Dominguez, and Vazquez-Zamora (2008) and Erce (2013).
A small open economy extends over two periods, . here is a single consumption good and a representative domestic agent, the sovereign, which is risk-neutral and cares only about consuming in period 1.
At , the sovereign can borrow funds from the international capital markets to finance a risky project that yields units of output at . We suppose that the sovereign issues one unit of debt under international law — an infinitely divisible one-period bond that pays at maturity, . The realized ex-post return on the project is a random variable , drawn from the cumulative distribution function . There are foreign creditors who are ex-ante identical and risk-neutral. These creditors are not capital-constrained and are able to borrow and lend as much as needed at the constant risk-free world interest rate, .
In the presence of absolute sovereign immunity in international law, it is difficult (if not impossible) for foreign creditors to attach a sovereign’s property in the event of a default. Even though trading and credit relationships may be impaired in ways that diminish the sovereign’s output as a result of a default, lenders receive nothing. Denoting the fraction of output lost due to a default as , the sovereign is only willing to repay creditors in full provided that
To mitigate the costs associated with default, we allow the sovereign to tailor bankruptcy procedures ex-ante. Specifically, the contract with foreign creditors at stipulates a haircut, , that creditors will be offered at in the event that the sovereign files for bankruptcy in international courts to seek a restructuring. Filing for bankruptcy has two effects. First, it helps reduce the output loss from a default to , where captures the ability of the bankruptcy mechanism to shield the sovereign from output losses. But this also has the effect of increasing the sovereign’s incentive to default. Secondly, the recourse to a bankruptcy procedure ensures that creditors receive some payment in states of the world where they would have otherwise received nothing.
If the sovereign files for bankruptcy at , creditors are offered a haircut, , on their claims. Each creditor must decide whether to accept the haircut or litigate to recover the full claim. We assume a litigation cost per unit of claim for each creditor such that if creditor ‘s claim is , then the cost of litigation is . The assumption that the cost of litigation scales with the size of the claim is consistent with economic analyses of litigation behavior. The marginal litigation costs, , are independently and identically drawn at the start of from a uniform distribution for each creditor.
Litigation is risky since the full claim can only be recovered with success probability . Litigation fails with probability , in which case the holdout receives nothing. Following Schumacher et al. (2015), can be interpreted as a measure of the strength of creditor rights. Holdouts are costly for the economy and reduce output by the fraction , where is the ratio of holdout creditors to all bondholders. The cost of holdouts is increasing in , and .
Finally, creditors have access to the secondary market at . Upon discovering their litigation cost, creditors with high litigation costs may opt to sell their claims to those with low litigation costs. The secondary market for bonds is perfectly competitive with market-clearing price, , per unit of claim.
We solve the problem by backward induction. The pure strategy sub-game perfect Nash equilibrium consists of a bankruptcy threshold, , litigation threshold, , ratio of holdout creditors to all bondholders, , secondary market clearing price, , repayment, , and haircut, , such that at :
Incentives to Hold Out
If the sovereign files for bankruptcy and offers creditors a haircut, , then an individual creditor, , who accepts the offer receives . But if the creditor rejects the offer and litigates with success probability , the expected payoff after litigation costs is . so creditor holds out whenever:
Secondary Market for Bonds
Upon learning their litigation costs at , creditors can buy or sell bonds in a perfectly competitive secondary market. Since all creditors are ex-ante identical, they each hold an equal share , , of the bond. Without loss of generality, we can order all creditors based on their marginal litigation costs. The first creditor has the smallest litigation cost, , while the second creditor has the second smallest litigation cost, , and so on. We thus have . Suppose that the first creditors all have marginal litigation cost less than . It would be optimal for each of these creditors to reject the offered haircut, , and litigate against the sovereign. While, for the remaining creditors, it would be optimal to accept the haircut. But, with a secondary market, these creditors prefer to sell their claims to the litigious creditors instead. In equilibrium, insofar as , all other creditors sell their claims to the first creditor.
Proposition 1 If the first creditor has a small enough marginal litigation cost, , then bonds are traded in the secondary market. the first creditor buys all the bonds, and the equilibrium price is . If, however, the marginal litigation cost for the first creditor is large, , then it is optimal for all creditors to accept the haircut, and there is no trade.
The equilibrium bond price is indeterminate. However, since all creditors are risk-neutral, the exact price is immaterial when deriving the participation constraint. What matters, instead, is whether or not the first trader is litigious, , thus satisfying the condition for trade.
The Sovereign’s Willingness to Pay
Turning to the sovereign’s decision to file for bankruptcy, there are two cases to consider: (i) when bonds are traded, i.e. ; and (ii) when bonds are not traded, i.e. . We consider each in turn.
If the first creditor has a small enough litigation cost, then bonds are traded in the secondary market. The first creditor buys all the bonds from all other creditors. the first creditor subsequently rejects the haircut and pursues litigation, so . In this case, the willingness to pay constraint is:
The above equation can be rearranged to obtain that the sovereign will repay whenever the output is greater than a bankruptcy threshold, i.e. .
If the first creditor’s marginal litigation cost is greater than , then it is optimal for all creditors to accept the haircut, . As such, there are no holdout creditors, and the sovereign’s willingness to pay constraint is:
On rearranging, this yields that the sovereign will repay in full whenever the output is greater than an alternate bankruptcy threshold, i.e., . we can order the two thresholds such that .
Proposition 2 summarizes the equilibrium at .
Insofar as , a marginal increase in the haircut has no further effect on the equilibrium. But if then an increase in the haircut has potentially two effects. First, the bankruptcy threshold, , increases, implying that the sovereign is more likely to file for bankruptcy even for larger realizations of the output. At the same time, the critical litigation threshold, , increases. As long as remains above the threshold, the secondary market remains closed, and all creditors choose to accept the haircut. But once falls below the threshold the equilibrium switches to one where there is an active secondary market; the first creditor buys all the bonds from all the other creditors and the first creditor rejects the haircut and litigates.
At , the sovereign chooses the haircut to maximize expected consumption, which is expected output net of bankruptcy and holdout costs, and repayments to creditors. Denoting the unconditional expected output by , expected consumption, , then becomes:
is the cumulative distribution function for the smallest marginal litigation cost. If the sovereign expects that then, upon default, the first creditor will buy all the bonds form all the other creditors, reject the haircut and litigate. While, if the sovereign expects , then all creditors accept the haircut, and there is no further output loss from holdouts.
We now make the following three assumptions. First, output is uniformly distributed over . second, the bankruptcy regime is creditor-friendly, . And third, for a given , the output cannot be too large, implying . The first assumption is for analytical tractability. The second assumption ensures that the optimal haircut is an interior solution, while the third ensures that the expected consumption is maximized at the optimal haircut. Proposition 3 summarizes our results.
Proposition 3 For any given repayment, there exists a unique haircut, , that maximizes consumption. The optimal haircut is decreasing in the repayment. A leftward shift in the output distribution, i.e., a decrease in , lowers the optimal haircut, as does increased riskiness (in the sense of a mean-preserving shift in the output distribution). The optimal haircut is lowered if the bankruptcy regime is more creditor-friendly, and if the maximal output costs that holdouts can inflict increases.
As repayments increase, they induce two opposing effects on the sovereign’s choice of haircut. First, an increase in heightens the sovereign’s incentive to file for bankruptcy. Second, insofar as the first creditor’s marginal litigation cost is low, all other bondholder will sell their bonds to the first creditor following the bankruptcy filing. The first creditor, in turn, rejects the haircut and pursues litigation. The first effect induces the sovereign to opt for a higher haircut, while the second effect acts in the opposite direction. From the first-order condition, the second effect always dominates.
Our model predicts that countries with weak and risky macroeconomic fundamentals will seek lower haircuts ex-ante. A leftward shift in the output distribution lowers expected output. the range of over which the sovereign would default is larger. But, and as before, if the first creditor’s marginal litigation cost is sufficiently small, the first creditor buys all the bonds on the secondary market and litigates. This inflicts a large holdout cost for the sovereign. The sovereign can mitigate these costs by lowering the haircut, and thereby reducing the likelihood that the first creditor will be litigious.
Increasing the variance of the output distribution, while leaving the mean unchanged also has the effect of widening the range of over which the sovereign defaults and incurs holdout costs. The greater risk of suffering an output cost again induces a lower haircut.
An improvement in the creditor-friendliness of the bankruptcy regime induces two effects. First, it becomes more likely that the sovereign must repay the holdouts. This reduces the sovereign’s incentives to file for bankruptcy. And, second, the creditors’ incentive to hold out and litigate increase. To counter this, the sovereign lowers the ex-ante haircut, thereby offering more to creditors during the restructuring so as to offset their incentives to hold out.
Finally, an increase in the maximum holdout cost reduces expected consumption whenever bonds are traded in the secondary market. The sovereign can mitigate these costs by reducing the likelihood that the first creditor’s marginal litigation cost is below the threshold, . This, in turn, is achieved by reducing the haircut and offering more to creditors during the restructuring.
Pricing Sovereign Debt
The total repayment, , due at is determined by aggregating the breakeven conditions of individual creditors. Since all creditors are ex-ante identical, the typical creditor holds a claim, , against the sovereign. If the first creditor’s marginal litigation cost is greater than the threshold, , then the typical creditor accepts the haircut during the restructuring if the sovereign files for bankruptcy. Integrating over output, the claim is worth:
Nest, suppose that the first creditor’s litigation cost is below . If the sovereign files for bankruptcy, there are two further cases to consider. First, if the typical creditor does not have the smallest marginal litigation cost (with probability ), then the creditor will sell the bonds for price . Second, if the typical creditor has the smallest marginal litigation cost (with probability ), then the creditor will purchase bonds from the others for price . The typical creditor will then reject the haircut and pursue litigation. Integrating over output, the value of holding a claim for the typical creditor is which, on rearranging, gives:
Integrating over the first creditor’s marginal litigation cost, and aggregating over all creditors, the repayment, , is given by the solution to:
For to be unique, we require that the world interest rate is sufficiently small, .
Proposition 4 summarizes the properties of .
Proposition 4 For any given haircut, the repayment, , is unique. The repayment is increasing in the haircut. A decrease in expected output increases repayment. Greater creditor-friendliness of the bankruptcy regime decreases repayment. Finally, higher world interest rates also lead to greater repayment.
An increase in the haircut has several effects. First, the likelihood that the first creditor will be litigious increases. It is more likely that creditors trade bonds in the secondary market if the sovereign files for bankruptcy, and for the first creditor to pursue litigation. At the same time, the expected litigation cost increases. Second, conditional on there being no secondary market trade, an increase in the haircut increases the sovereign’s incentives the sovereign’s incentives to file for bankruptcy and settle with the creditors. To the extent that the secondary market effect is dominated and all creditors must accept the haircut, a higher repayment is required for creditors to break even.
The intuition behind the remaining results of Proposition 4 are more easily understood. A change to the output distribution that increases the risk of default (a fall in ) leads to an increase in repayment demanded by creditors faced with greater default risk. As the creditor-friendliness of the bankruptcy regime increases, the sovereign’s incentives to default are reduced. Moreover, if the sovereign did file for bankruptcy, more creditors would hold out and claim the full repayment with greater probability. Thus, the value of creditors’ claims against the sovereign increases and, hence, the required repayment decreases. High world interest rates increase the outside option for creditors who must, therefore, be compensated for sovereign lending with higher repayments.
We close the discussion of our model with a description of the joint equilibrium. The comparative statics directly follow from our earlier analysis of the schedules and in Propositions 3 and 4, respectively.
Proposition 5 The optimal haircut and repayment, i.e., and , respectively, jointly solves:
An increase in the world interest rate, , leads to a decrease in the haircut and an increase in the repayment. An increase in the maximum output, , leads to an increase in the haircut and a decrease in the repayment. An improvement in the creditor-friendliness of the bankruptcy regime leads to an increase in the haircut, but has an ambiguous effect on repayment. Finally, an increase in the maximum holdout cost has an ambiguous effect on but leads to a decrease in **.
Implications for Sovereign Debt Restructurings
Early proposals for sovereign bankruptcy frameworks (Krueger, 2002; IMF, 2002) typically assumed a “one-size-fits-all” approach based on a uniform and mandatory set of provisions. In an important contribution to the debate, Bolton and Skeel (2004) propose that sovereigns be permitted to opt out of some aspects of the bankruptcy procedure ex-ante. They argued that a tailored approach to sovereign bankruptcy would be politically easier to sell than more ambitious statutory approaches. Debtor nations that typically expressed strong reservations about sovereign debt restructuring regimes would be more willing to participate if they were able to obtain exemptions to provisions in accordance to local conditions. But there was a risk that countries may adopt overly harsh provisions ex-ante, for fear of losing their access to credit.
Our model helps shed light on this debate and the disciplining role played by holdout litigation in determining ex-ante exemptions (or haircuts). Our findings suggest that tailored frameworks will vary across countries according with their default risk — countries with weak or risky macroeconomic fundamentals will be more likely to settle for harsher provisions. Debtors are also more likely to adopt harsh provisions ex-ante , the more creditor-friendly is the bankruptcy regime and the greater the output losses that can be inflicted by holdout creditors. But it should be noted that, in our framework, contractual flexibility results in an efficient outcome. As such, we are unable to address the normative issue of whether sovereigns should be precluded from adopting overly harsh provisions that make restructuring more, rather than less, painful.
The analysis also clarifies the extent to which a sovereign debt restructuring should favor creditors. To the extent that an international body seeks to maximize welfare, i.e. the sum of domestic expected consumption and repayment to creditors, it can choose the degree of creditor protection, , to maximize:
which is the sum of expected output, loss to the sovereign from default and holdouts, and the cost to creditors from litigation. The effect of a change in can be decomposed into direct and indirect effects. We treat each one in turn.
First, for given , and , a marginal increase in implies that creditors who reject the sovereign’s haircut offer in a bankruptcy and litigate are more likely to succeed. This, in turn, implies that if the sovereign were to default, it is more likely that all other creditors will sell their bonds to the most litigious creditor, who will hold out. So the expected holdout cost to the sovereign and expected litigation cost to the litigant both increase, which reduces welfare.
The second effect of an increase in is on the haircut, repayment, and the sovereign’s default incentives. As Proposition 5 indicates, following an increase in , the repayment decreases. Since the litigation cost scales with the size of the claim, this indirect effect via helps improve welfare. At the same time, insofar as creditors sell their claims to the litigious creditor via the secondary market, the sovereign’s incentives to default and file for bankruptcy are reduced. This helps lower the expected holdout costs, which also improves welfare. Finally, the effects via the optimal haircut are, in general, ambiguous. If the haircut is also decreased, then this reduces the incentives of creditors to trade bonds and litigate against the sovereign in bankruptcy. This also improves welfare. However, if the haircut increases following a marginal increase in , then not only are the sovereign’s incentives to default, , also increased, but so also are the incentives for creditors to trade bonds and litigate. This would reduce welfare.
To assess how welfare depends on , we resort to numerical methods. The result is that the lower the , which captures the ability of the bankruptcy mechanism to shield the sovereign from output losses, the lower is the output loss to the sovereign from defaulting. We readily note that, irrespective of , welfare is always maximized at , i.e., whenever creditors litigate they always succeed. This suggests that the indirect effects via the haircut, repayment, and the sovereign’s bankruptcy incentives dominate over the creditors’ incentives to litigate and hold out. Furthermore, the maximum value of welfare is independent of .
The situation is consistent with the notion of absolute priority, namely the prioritization by the bankruptcy regime of the payments of bonds issued first before those issued later. Bolton and Skeel (2004) emphasize the importance of enforcing absolute priority as the basis of any bankruptcy procedure and our model confirms this perspective. The lack of adherence to absolute priority is damaging for global welfare in our model since, by diluting the claims of existing creditors, it curbs market discipline and results in higher borrowing costs for sovereigns. Reinforcing creditor priorities within the bankruptcy mechanism, thus, helps balance the tradeoff between ex-post crisis costs and ex-ante incentives.
Institutional solutions to debt restructuring entailing uniform and mandatory bankruptcy provisions are often criticized because there are too many political obstacles to implementation. As a result, contractual and market solutions have tended to be favored by many policymakers and commentators.
In this article, we have sought to examine a middle ground in which sovereigns are given the choice of opting out of a statutory bankruptcy framework by crafting their own provisions. We present a model that sheds light on the role played by holdout creditors, macroeconomic fundamentals, and the legal environment on the choice of exemptions (or haircut) sought ex-ante. Our model formalizes some of the insights of the Bolton and Skeel (2004) proposal advocating “Designer SDRMs” as a possible transitory step on the road to a statutory bankruptcy regime.
The lack of sufficient support for a statutory mechanism has led the IMF to follow a related path, namely encouraging countries to restructure their debts preemptively (i.e., launched prior to default) in an effort to ensure orderly sovereign bankruptcy (IMF, 2013). Our paper contributes to a broader policy debate on mechanisms the ensure that unsustainable debt situations are recognized in a timely way. Extending the model to allow for government myopia would also allow analysis of whether sovereigns should be precluded from adopting overly harsh provisions.