A. Assumptions

I consider a world with one consumption good and three periods (t = 0, 1, 2). There are a number of countries indexed by j = 1,…, n. Each country is populated by a continuum of mass 1 of atomistic individuals and the utility of the representative resident is

where $c_t^j$is the level of period t consumption of the representative individual in country j, and γ(e^j) is the cost of domestic effort (to be defined later). Domestic consumption must be larger than the subsistence level, which is normalized to zero.

Each country has the opportunity to make an indivisible public investment of size k in period 0. The investment increases domestic welfare by raising the country’s expected output in period 2. For example, it could be thought of as a transportation infrastructure that reduces transportation costs, or a schooling or health care system that enhances the productivity of domestic workers. The decisions concerning this investment are made by a benevolent government that acts on behalf of the representative resident and maximizes his welfare.

The representative citizen of country j receives a quantity of good $y_t^j$in period t (the country’s output net of the subsistence consumption level). Domestic output can be consumed by residents in all periods. In period 0, it can also be used to finance the investment in the home country or abroad.

The levels of output in period 0 and 1 are exogenous and both perfectly known in period 0. The level of output in period 2 depends on whether the country has made the investment in period 0 or not. In the absence of investment, period 2 output is deterministic, and denoted by ${\underset{¯}{y}}^j$. Making the investment gives the country the chance (not the certainty) of increasing its period 2 output by an amount Δy. Output is equal to ${\underset{¯}{y}}^j+{\Delta }y$if the investment is successful, and to ${\underset{¯}{y}}^j$if it fails (as if there had been no investment).

In period 1 the private sector assesses the probability that the investment will pay off on the basis of three pieces of information: the level of domestic policy effort, an exogenous signal, and the fraction of the investment that will remain in place in period 2,

Variable ϕ ∈[0, 1] is the fraction of the investment that remains in place in period 2. A fraction 1–ϕ of the investment is liquidated by foreign creditors in period 1. If the investment is completely liquidated, the probability of high output is equal to zero, as if the country had not made the investment. The probability of success of the investment is increasing with ϕ

The level of policy effort can be high (e^j= h) or low (e^j= l) with the costs normalized to γ(h) = γ and γ(l) = 0. A high level of effort enhances the impact of the investment on domestic output. It could be interpreted as a complementary investment in domestic human capital that costs γ to the representative resident. High effort could also be interpreted as a fiscal or governance policies that prevent the resources earmarked for the investment from being diverted to other uses, such as domestic consumption (in which case γ is the foregone benefit of diversion for the representative resident). Other things equal, a high level of policy effort increases the probability of high output, i.e., for all s and ϕ,

Finally, variable s^j is stochastic and captures the developments in the exogenous determinants of the investment’s success (productivity, terms of trade) that become observable in period 1. The probability of success of the investment is increasing with s^j. The signals s^j could be correlated across countries or not.

The model is stochastic because of the signal s. Let us denote by f_e(·) the probability distribution function of p conditional on no liquidation and the effort level e. The pdf f_h(·) and f_l(·) are strictly positive on the same support $[\underset{¯}{p},1]$. High effort tends to shift the probability distribution function of p to the right, an assumption that is captured more formally by assuming the existence of a threshold p* such that,

(see Figure 1).

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Conditional Probability Distribution Function of the Project’s Probability of Success

Citation: IMF Working Papers 2004, 137; 10.5089/9781451855944.001.A001

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Country j can finance the investment with domestic output, $y_0^i$, and by selling sovereign debt to foreign individuals. Capital-scarce countries (with $y_0^j<\kappa$) must borrow from the residents of capital-abundant countries (with $y_0^j>\kappa$) to finance the investment. There is enough wealth in the world to finance the investment in all countries, ${\displaystyle {\sum }_j}{y}_0^j>n\kappa$. The international debt market is perfectly competitive so that the expected return on sovereign debt must be equal to zero in equilibrium.

Sovereign debt is a promise by country j to repay $d_1^j$in period 1 and $d_2^j$in period 2 to foreign creditors. For simplicity, I abstract from the willingness-to-pay problem and assume that in each period, the country repays its debt up to its output (net of susbsistence consumption). I define the disposable wealth of country j as the sum of its output in all periods conditional on no investment,

This is the maximum of amount of good that the country can invest in period 0 without pledging any of the investment’s payoff in to foreign lenders.

In addition, the debt contract may involve the liquidation of the project in period 1. The project is completely liquidated if the probability of success conditional on no liquidation, p(e,s,1), falls below a threshold $\widehat{p}$. The threshold $\widehat{p}$is specified ex ante in the debt contract, which is thus summarized by the triplet ${\mathbf{d}}^j=(d_1^j,d_2^j,{\widehat{p}}^j)$. It will be shown in section 2.3 how such contracts can be implemented with demandable debt. For now, $\widehat{p}$can be interpreted as a reduced-form measure of the riskiness of debt. If $\widehat{p}\le \underset{¯}{p}$debt is safe in the sense that liquidation occurs with zero probability. By contrast if $\widehat{p}>\underset{¯}{p}$debt is risky: it makes the country vulnerable to the risk of inefficient liquidation with a strictly positive probability.

The policy effort e is set “between” period 0 and period 1, that is, after the debt contract with foreign investors is signed, but before the signal s is revealed. Importantly, the country cannot credibly commit to the level of domestic policy effort in period 0, and the debt contract cannot be made contingent on e. These commitment and contract incompleteness problems will explain why some countries resort to dangerous forms of debt in equilibrium. A country can reduce the probability of liquidation by producing a high level of effort $(F_1(\widehat{p})>F_h(\widehat{p})>0).$

I further make the following assumptions. Denoting by $p(e)\equiv {\displaystyle {\int }_0^1{\mathit{\text{pf}}}_e}(p)\mathit{\text{dp}}$the probability of success of the investment conditional on the level of effort, I assume that

The investment is efficient only conditional a high level of effort. Implementing the high level of effort will sometimes be referred to as the “good” policy. This assumption simplifies the analysis by restricting it to the case where sovereign debt must be incentive-compatible.

In addition, liquidation is assumed to be always inefficient,

where λ denotes the liquidation value of the investment. This assumption is not essential but focuses the attention on the ex ante incentives effect of liquidation as opposed to its efficiency ex post.

The sequence of events is the following. First, in period 0, governments auction their external debts ${\mathbf{d}}^j=(d_1^j,d_2^j,{\widehat{p}}^j)$in the international market. Then governments set the level of the policy efforst, e^j, after which the signals s^j are observed. The investment is liquidated in countries where $p^j<{\widehat{p}}^j$. In period 2, output is realized, international payments are made and consumption takes place. I consider perfect Bayesian equilibria in which all individuals maximize their utility and governments maximize domestic welfare.

B. Optimal Crises

This section shows why some capital-scarce countries may have to issue risky external debt and characterizes the optimal risky debt contracts. A capital-scarce country looks for the debt contract that solves the following problem

subject to

(the country index j is ommitted to alleviate notations). Equations (4), (5) and (6) are the country’s budget constraints in periods 0, 1 and 2 respectively. In period 1 the country’s resources are equal to its output plus the price foreigners have paid for its external debt. In equilibrium, this price must be equal to the expected value of the payments to foreigners, including the proceeds from liquidation. Subject to the feasibility constraints (8), debt is repaid with certainty, except the share of the project’s return that is pledged to foreign creditors,

which is repaid with probability p. Condition (7) says that the government sets policy so as to maximize the country’s welfare conditional on its external debt structure.

Using the budget constraints (4), (5), and (6) to substitute consumption out of (3), the country’s ex ante welfare can be written as

The country’s welfare is equal to domestic wealth plus the investment’s expected payoff minus its cost and the cost of the policy effort. Because of assumption (2), it is worth investing only if this will be followed by good policy. An external debt that is not incentive-compatible bears an interest rate that is too high for the country to be able or willing to borrow.

For a given external debt structure $\mathbf{d}=(d_1,d_2,\widehat{p})$to be incentive-compatible, the benefit of a good policy in terms of expected output net of debt repayment should be larger than its cost:

where Δf (·) is a shorthand for f_h(·) – f_l(·). This implies an upper bound for the level of long-term debt,

The maximum incentive-compatible level of debt is strictly below $\underset{¯}{y}+{\Delta }y$because of the classical debt-overhang problem. External debt acts as a tax on policy effort and thus discourages good policy. The incentive-constraint can be relaxed (up to a point) by making debt risky because $\overline{d}$is increasing with $\widehat{p}$over some range. Differentiating (12) gives

which is strictly positive if $\widehat{p}\in [\underset{¯}{p},p^{*}].\overline{d}$reaches its maximum for $\widehat{p}=p^{*}$(see Figure 2). Risky debt induces the country to implement a good policy by making bad policy relatively more costly. This is the sense in which risky debt disciplines domestic policies—a deviation from good policy is more likely to be sanctioned by a crisis than with safe debt. However, the punishment is not always fair since liquidation can occur even after the country has implemented the good policy, because of a bad signal.

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Maximum Levels of Incentive-Compatible Debt and Pledgeable Output

Citation: IMF Working Papers 2004, 137; 10.5089/9781451855944.001.A001

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A country issues risky debt only if the investment cannot be financed with safe debt. A country that issues risky debt, furthermore, minimizes the riskiness of debt subject to the constraints (8) and (11). This is achieved by pledging as much as possible of the country’s disposable wealth, $w=y_0+y_1+\underset{¯}{y},$, to foreign creditors, so as to minimize d₂ and so the level of $\widehat{p}$required by the incentive constraint (11). This requires that the country set domestic consumption to the subsistence level in periods 0 and 1. An optimal risky debt contract, therefore, must satisfy the following property.

C. World Equilibrium

The world has many countries with different output profiles $y_0^j,y_1^j,{\underset{¯}{y}}^j$. Capital-abundant countries (with $\begin{array}{c}{y}_0^j\ge \kappa \end{array}$) do not need to borrow abroad in order to finance the investment. They could borrow abroad to finance domestic consumption, but this does not affect their welfare as long as their debt is safe. The capital structure of capital-abundant countries is indeterminate conditional on their external debt being safe.

In order to determine which countries are going to issue risky debt in equilibrium, let me define a country’s financing capacity as its period 0 output plus the maximum quantity of funds that it can levy abroad by issuing incentive-compatible debt. Using Proposition 1, country j ‘s financing capacity can be written

Where

is the maximum share of the investment’s payoff that can be pledged to foreigners subject to the incentive compatibility constraint. The first derivative is of (13) is,

There are two effects at work. Increasing the riskiness of debt reduces the country’s financing capacity if the creditors’ expected payoff is reduced by a liquidation (first term), but increases it to the extent that it relaxes the incentive constraint (second term). If the latter second dominates, V increases with $\widehat{p}$(Figure 2).⁴

A capital-scarce country may fall in one of the following three cases, depending on its level of wealth. First, the country can finance the investment with safe, incentive-compatible debt, if w^j+ V (0) ≥ κ, that is if its wealth is larger than a critical threshold,

A country for which this condition is not satisfied can finance the investment with incentive-compatible but risky debt, provided that $w^j+{\max }_{\stackrel{⌢}{p}}V(\hat{p})\ge \kappa$, or

The country’s welfare is lower than the first-best level, but may be higher than in the absence of investment. Finally, if (15) is not satisfied the investment cannot be financed at all.

Proposition 2 describes a two-tiered world economy with a rich core (countries with $w^j\ge \overline{w}$) and a poor periphery (countries with $w^j<\overline{w}$). International credit flows inside the core are safe.⁵ Credit flows from the core to the periphery are fickle, and involve the risk of a liquidation by foreign creditors in period 1.

The debt overhang problem is more severe for poor countries, because these countries must issue more external debt to finance the same level of investment. Poor countries, therefore, need higher-powered incentives to implement good policies. These incentives are produced in some countries by making their external debt risky. The poorer the country, the riskier its external debt must be in equilibrium (i.e., the optimal $\widehat{p}$decreases with w in the interval $[\underset{¯}{w},\overline{w}]$

As shown in Figure 3, the welfare inequality between rich and poor countries is aggravated by the financial friction, which rations some poor countries out of the international debt market, and submits some others to the risk of unwarranted liquidation. The welfare of countries in the periphery is strictly below the (commitment) first-best level.

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Domestic Wealth and Welfare

Citation: IMF Working Papers 2004, 137; 10.5089/9781451855944.001.A001

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D. Implementation

A risky debt contract is not renegotiation-proof. Ex post, both domestic residents and foreign creditors would be better off not liquidating and sharing the renegotiation surplus pΔy −λ. This section shows how the creditors’ commitment to liquidate can be achieved by granting them uncoordinated liquidation rights, following a logic similar to Diamond and Rajan (2000). The uncoordination of creditors is a substitute for their ability to commit.

Let us assume that countries in the periphery offer a demandable debt contract to foreign investors. This contract gives each creditor the choice in period 1 between two sequences of repayments, (d₁,d₂) and (d₁ + δ₁, d₂ − δ₂) That is, each creditor has the option of accelerating the repayment of his claim, by asking a higher repayment d₁ + δ₁ in period 1 in exchange of a lower repayment d₂ − δ₂ in period 2.⁶ This formulation captures some well-known debt contracts as special cases. For example a deposit contract a la Diamond-Dybvig gives each depositor the choice between a late repayment (d₁ = 0, d₂ > 0) and an early repayment (δ₁ > 0, d₂ − δ₂ = 0). Opting for (d₁, d₂) can be interpreted as a decision by the creditor to roll over his claim in period 1. A contract is characterized by a vector (d₁, d₂, δ₁, δ₂)

I assume that like in the Diamond-Dybvig model, each unpaid creditor has the right to liquidate the investment up to the value of his claim in period 1. The nonoptional repayment d₁ is fully repaid with y₁ and the optional repayment δ₁ is repaid, if necessary, with the proceeds from liquidation. If the country’s resources are insufficient to cover the creditors’ demands, then the investment is fully liquidated and λ is shared between the creditors (or equivalently distributed according to a sequential service constraint) to repay δ₁.

Then it is possible to show the following result.

The intuition behind this proposition is straightforward (the proof may be found in appendix). The creditors ask for early repayment if δ₁ is larger than p δ₂, that is if the probability of success of the investment falls below a threshold,

So for demandable debt to have the same liquidation threshold as the optimal risky debt contract, the ratio δ₁/δ₂ must be set equal to $\widehat{p}$The liquidation is complete, furthermore, if the liquidation value λ is small enough.

As shown in the appendix, the demandable debt contract makes the country vulnerable to self-fulfilling roll-over crises that would not occur with the optimal risky debt contract. The strategic complementarity behind this multiplicity is the same as in the self-fulfilling bank runs of the Diamond-Dybvig model: by not rolling over his claim a creditor reduces the country’s future ability to repay the other creditors. I do not emphasize these self-fulfilling crises in the paper, as they have already received so much attention in the literature.⁷

E. Discussion

The analysis has been simplified by several assumptions. First, I have assumed that foreign creditors can enforce their rights to liquidate the investment. One might object to the realism of this assumption because, first, a public asset is difficult to liquidate, and second, the liquidation rights of foreign creditors might be difficult to enforce in court. However, the concept of “liquidation” does not have to be interpreted literally, and could be seen as a metaphore for all the uncoordinated actions that creditors can take and that are costly for the debtor country. An example is uncoordinated litigation against the sovereign in the foreign courts under whose jurisdiction the debt has been issued.⁸

Second, I have not considered the role that liquid reserves could play in dealing with a rollover crisis. Reserves could be introduced into the model as an investment in a zero return storage technology. However, it is easy to see that in equilibrium, capital-scarce countries will hold no reserves. These countries would have to finance the reserves by raising more funds abroad, which is possible, given the incentive compatibility constraint, only if they raised the liquidation threshold $\widehat{p}$that is, if they made their debt more risky. In other words, the reserves would have to be financed by an increase in demandable debt that is larger than the reserves.

Third, I considered contracts that involved either no liquidation or complete liquidation of the investment. The debt contract could be generalized by assuming that the fraction of the project that is liquidated in period 1 is an arbitrary function of p. However, as shown by Dewatripont and Tirole (1994), the optimal function ϕ (.) would satisfy the bang-bang property that has been assumed here.⁹

Fourth, the investment was assumed to be indivisible. What if the payoff of the investment, Δy, were an increasing and concave function of κ ? The analysis would be complicated by the fact that a poor country now would have the option of keeping its external debt structure safe by scaling down the size of the project. However, it will not generally be the case that all poor countries will chose this option in equilibrium. Some countries will prefer a larger investment financed by risky debt to a smaller investment financed by safe debt. These countries will be faced with the same tradeoff between incentives and risk as I have modeled here.

Fifth, the assumption that the policy effort e is chosen before the realization of the signal s can also be relaxed. In order to solve for the equilibrium, one has to determined how e is set in period 1 conditional on the knowledge of s. It remains true that other things equal, making debt demandable induces more policy effort, and so from an ex ante perspective it expands the range of s for which the effort is implemented. The countries that need discipline will make their debt demandable in equilibrium.

An assumption that is less innocuous is that the country cannot issue new debt is period 1. Allowing the government to borrow in period 1 would result in the dilution of period 0 lenders. Dilution gives rise to a set of issues that are interesting, but from which I have abstracted here.

A. Contractual Approach

To some extent, renegotiability is a feature that is built into the structure of debt ex ante, at the time of lending. Syndicated bank loans are easier to renegotiate than international bonds held by many dispersed creditors. Bonds themselves may or not include clauses that facilitate a successful renegotiation between the debtor and its creditors. These so-called “collective action clauses” include collective representation clauses that allow the debtor to negotiate with a representative of the creditors, and majority enforcement and restructuring clauses that restrict the rights of individual creditors to litigate before and after an agreement has been reached with a majority (Eichengreen, 2003). For example, UK law bonds, unlike those issued in New York, enable the holders of debt securities to call a bondholder assembly in which a majority of bondholders may change the bond’s terms of repayment.¹¹ Buiter and Siebert’s (1999) proposal of a contractual clause giving the debtor the option to roll over its debt for a short period could also be classified in this category.

The contractual approach has been endorsed by several academics and in some official reports (Eichengreen, 1999; Kenen, 2001; G-10, 1996; G-22, 1998). However, this apparent consensus on renegotiation-friendly clauses masks different views on how intrusive public policy should be in promoting their use. The official community has insisted that although educational efforts might be useful in advertising the merits of collective action clauses, their adoption by market participants should be purely voluntary. By contrast, some proponents of renegotiation-friendly clauses have suggested that their adoption should be subsidized, or even be made mandatory (Eichengreen, 1999; Kenen, 2001; Buiter and Siebert, 1999).¹²

In order to analyze the welfare properties of such clauses, I now consider an extension of the model in which the renegotiability of debt is endogenous. Let us assume that capital-scarce countries have the option to put a collective action clause in their demandable debt. A collective action clause specifies that conditional on an incipient debt roll-over crisis,¹³ the debtor country may ask the creditors to delegate a representative to negotiate a final repayment ${\stackrel{\sim }{d}}_2$(collective representation) and that the negotiated agreement binds all creditors (collective enforcement). Thus, the debt contract is the same as before, except that $p<\widehat{p}$triggers a negotiation between the debtor and the creditors rather a liquidation.

If the negotiation takes place like in the Rubinstein (1982) model of alternating offers, there will be no deadweight loss¹⁴ and the surplus will be shared between the creditors and the debtor according to their relative patience, or cost of waiting. In practice, the cost of waiting is determined, on the side of the creditors and that of the debtor, by different considerations. The debtor government is impatient to reach an agreement with creditors to the extent that staying in default disrupts trade credit and domestic borrowing abroad, or maintains an uncertainty about future fiscal policy that depresses domestic investment and reduces confidence in the domestic economy. A prolonged default may also be costly for creditors to the extent that it reduces the value and the liquidity of their claims. Here, I shall simply assume that the creditors’ share of the renegotiation surplus is known ex ante, when the contract is signed. This share (the creditors’ bargaining power) is denoted by α.

Assuming for simplicity that the liquidation value of the investment is equal to zero, the renegotiation surplus is equal to the expected payoff of the investment, pΔy. If p falls below $\widehat{p}$, there is a negotiation in which the government promises a repayment ${\tilde{d}}_2=\alpha {\Delta }y$. The incentive condition to implement a good policy becomes

The first term on the l.h.s. is negative, implying that the maximum level of incentive-compatible debt, ${\overline{d}}^r$, is lower than without collective action clause (compare with (10)). By softening the punishment for bad policy, the clause reduces the maximum level of incentive-compatible debt.

The collective action clause puts the ex ante welfare of the countries that adopt it at the first-best level. The interesting question is which countries adopt the clause in equilibrium. The financing capacity of a country that puts a collective action clause in its debt is given by $w+V^r(\widehat{p})$with

$V^r(\widehat{p})$is increasing with the creditors’ bargaining power from a level that is strictly lower than $V(\widehat{p})$if α = 0 to a level that is strictly higher than $V(\widehat{p})$if α = 1 (compare with (13)). It follows that the wealth threshold above which countries can borrow with a collective action clause,

could be higher or lower than $\underset{¯}{w}$, depending on whether α is lower or higher than a threshold $\overline{\alpha }$. For very low values of α, ${\underset{¯}{w}}^r$is larger than $\overline{w}$, implying that no country puts a collective action clause in its debt (the countries that could adopt the collective action clause do not need it because they do not issue demandable debt).

A collective action clause involves a trade-off between a benefit (increasing the repayment to creditors conditional on a crisis) and a cost (aggravating debtor moral hazard). Other things equal, increasing the bargaining power of creditors enhances the benefit and reduces the cost of the clause for all countries, inducing more of them to adopt it.

The cost of the clause in terms of moral hazard is larger for poor countries, for which the debt overhang problem is more severe. Below a certain level of wealth, therefore, it may be undesirable or impossible for countries to include a collective action clause in their debt. Including the clause would raise the cost of borrowing to a level where the countries are unable or unwilling to borrow.¹⁵

Although the countries that adopt the collective action clause see their welfare raised to the first-best level, the model does not imply that public policy has an active role to play in encouraging or mandating the use of these clauses. Some countries will chose not to include them in their debt even after they have been fully informed of their benefits, because it raises excessively their cost of borrowing. This choice is efficient ex ante conditional on the constraints.

Paradoxically, imposing a tax on risky debt may lead to an increase in the riskiness of debt in equilibrium. Assume that risky debt (defined as demandable debt without a collective action clause) is taxed at rate τ. The debtor country (or the creditors) must pay τd⁺ to an international agency in period 0. Then the financing capacity of a country issuing risky debt is given by

The country’s financing capacity is reduced by the tax, implying that in equilibrium the debt’s riskiness $\widehat{p}$must increase in order to levy the same quantity of funds. If some countries issue risky debt in the laissez-faire equilibrium (i.e., if $\underset{¯}{w}<{\underset{¯}{w}}^r$), then the tax strictly decreases their welfare, by rationing some of them out of the international credit market and by increasing the probability of liquidation for the others.¹⁶

B. The Statutory Approach

The renegotiation of debt could also take place in the context of a new legal regime applying the bankruptcy reorganization principles to the resolution of sovereign debt crises.¹⁷ The notion of a bankruptcy regime for sovereigns was promoted by the IMF’s First Deputy Managing Director, Anne Krueger (2002) proposal of establishing a Sovereign Debt Restructuring Mechanism (SDRM). This project failed to gain the support of the international community in 2003, after it had been criticized by the investor community and some scholars, on the grounds that it was going to weaken creditor rights and dry up the market for sovereign debt ex ante (Institute of International Finance, 2002; Shleifer, 2003).

The case for the statutory approach rests on the belief that efficient renegotiation between sovereigns and their creditors cannot be achieved in a purely contractual way (Schwarcz, 2000; Krueger, 2002; Bolton, 2003). This skepticism is related to the fact that in the real world (unlike in my model), sovereign debt is composed of many debt isues. In order to achieve efficient renegotiation it would be necessary make each debt issue contingent on the other ones, which is difficult to do without a statutory mechanism.

The multiplicity of debt issues raises at least two problems for the contractual approach. First, coordination failures could arise between creditors holding different debt issues. Bond clauses can help to coordinate the restructuring of a single bond, but do not provide a framework to coordinate creditors across different bond issues (Schwarcz, 2000; Krueger, 2002). This is likely to be a problem in debt restructuring negotiations as complex as the one currently underway in Argentina, which requires changing the terms of more than 90 international bonds.

Second, the lenders might accept a collective action clause in their bonds only at the condition that all future issues contain a similar clause—a commitment that sovereigns cannot credibly make at any given point in time. This nonexclusivity problem might result in debt being excessively difficult to restructure in equilibrium under the contractual approach, even from an ex ante point of view (Bolton, 2003; Bolton and Jeanne, 2004).

These two problems reflect a plausible form of incompleteness in sovereign debt contracts—the impossibility of making each contract contingent on the whole set of contracts. In this perspective, the role of a bankruptcy regime for sovereigns is to “complete the contracts” by specifying the rules by which individual bond issues will be restructured in a default conditional on the aggregate debt structure.¹⁸

Coming back to the model, let me represent a bankruptcy court as an institution that allows sovereigns to negotiate with their creditors in the same conditions as with a collective action clause. The difference with collective action clauses is that the bankruptcy regime is not optional: countries cannot opt out of the right to file for bankruptcy in the event of a roll-over crisis.¹⁹ The impact of the bankruptcy court, therefore, is the same as that of making collective action clauses mandatory in the previous section.

A statutory bankruptcy regime increases the welfare of the countries that retain access to the international debt market, but may aggravate credit rationing. In the latter case, the welfare inequality between rich and poor countries is aggravated, since it is the richest countries of the periphery that gain and the poorest that loose.

If α is large enough (i.e., if the court puts a large weight on the interest of creditors) the court generates a Pareto improvement in world welfare. This illustrates the importance of distinguishing renegotiation-friendly and creditor-friendly reforms. Renegotiation will not harm the creditors if they have a lot of bargaining power in the renegotiation. In fact, the objective of the reform should be to make debt both renegotiation-friendly and creditor-friendly, while keeping the deadweight loss of the renegotiation to a minimum.

This raises the question of how the bargaining power of creditors, α, can be raised in the bankruptcy regime. This may be difficult in practice, especially in the sovereign context where the position of creditors is already weakened by the absence of collateral (Shleifer, 2003). As mentioned above, if the negotiation involves alternate offers, the bargaining power of each party is determined by their relative cost of waiting, which in turn depends in a complex and unpredictable way on the broader context of the crisis. One question for future research is whether one can design robust bargaining rules that enhance the power of creditors while keeping the negotiation short.²⁰

One reason that the bankruptcy regime weakens the incentives is that it grants its protection to all debtors conditional on a crisis, irrespective of their pre-crisis policies. This suggests that a system of gate-keeping restricting the protection of the court to countries with good pre-crisis policies could enhance the incentives, even relative to laissez-faire. Indeed, one can show that such a scheme, if feasible, would put the world economy at the first-best, independently of the creditors’ bargaining power (the proof is given appendix).

Establishing a bankruptcy regime with gate-keeping is the best of the reforms we have considered so far and it is important to understand why. Essentially, the reason is that gate-keeping addresses the basic source of inefficiency in this model, which is not the creditors’ failure to coordinate but the incompleteness of sovereign debt contracts.

Risky debt debt contracts are made contingent on e indirectly, by means of a threat of a liquidation contingent on p. Coordination failures between creditors are just a way of making the threat of liquidation credible. However, risky debt involves a collateral damage: costly crises may occur even if e is high, following a low realizations of s. A bankruptcy regime with gate-keeping removes the collateral damage by introducing a direct contingency on e. In other words, the bankruptcy regime should complete the sovereign debt contracts not only in the sense of making them renegotiable, but also in making this renegotiation contingent on pre-crisis policies.

I conclude this section with two remarks on the feasibility of gate-keeping. First, effective gate-keeping requires the bankruptcy court to develop some jurisprudence on what constitute good and bad policies. It is the clearsightedness of the court in judging the quality of debtor country pre-crisis policies that allows the contracting parties to effectively complete the sovereign debt contracts. Although reaching a clear-cut judgment on the causes of a debt crisis is certainly very difficult in the real world,²¹ the optimality of gate-keeping does not require the court to be right 100 percent of the time.²²

The other problem that may undermine the effectiveness of gatekeeping is the risk of excessive forbearance. Gate-keeping is not time consistent. Ex post, the court may be tempted to restructure the debt of insolvent sovereigns irrespective of their pre-crisis policies, given that a liquidation decreases the welfare of both the debtors and creditors. In order to minimize this risk, it is important that the bankruptcy regime have a governance that insulates it from short-term political influences.²³