APPENDIX I Mathematical Derivations
(A) Conditions for the existence of a solution to (9): The necessary first-order condition for a maximum is
The sufficient second-order condition is
(B) Proof that the objective function in (18) is strictly concave in x2: Differentiating the LHS of (19),
Since the utility function and the output functions are increasing and strictly concave and the default state z* is decreasing in the policy effort x2, the expression above is unambiguously negative.
(C) Proof that dX/dℓ1 > 0: Because of (B), it is sufficient to show that the derivative of the LHS of (19) with respect to ℓ1 is positive. This derivative is
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I wish to thank Peter Wickham and Stijn Claessens for helpful comments and suggestions.
Providing new money may be optimal for creditors who are already exposed even if the country has lost its creditworthiness, because such a strategy (sometimes referred to as “defensive lending”) may increase the value of loans already outstanding. The analysis in the paper focusses on situations in which the borrower is creditworthy, meaning that new lending is profitable also for creditors who are not exposed yet. The potential coordination failures in the provision of defensive loans are the same as in the provision of debt forgiveness, and are well known.
For a recent, comprehensive account of the LDC debt crisis of the 1980s see Cline (1995).
On new mechanisms to deal with sovereign illiquidity and insolvency, see Eichengreen and Portes (1995).
Sachs (1995) argues that the Mexican crisis prompted by the peso devaluation in December 1994 was a liquidity crisis of this sort, and suggests that the international community should create a new institution along the lines of an international bankruptcy court for sovereign debtors.
In his paper, Calvo suggests that the literature on sovereign debt has ignored multiple equilibria because the usual assumption that the cost of a default is not increasing in the degree of default yields a unique equilibrium. The analysis in the paper shows that multiple equilibria are possible also with a fixed cost of default.
If debt could be renegotiated at no cost, then the locus would have a vertical asymptote and no backward-bending portion. However, if debt renegotiation involves some deadweight costs the locus always has a backward-bending portion.
The outcome is not first best for two reasons: first, by assumption the only financial asset is debt, so state contingent contracts are ruled out; second, potential default limits the possible debt contracts that can be written. Since the option to default makes debt repayment de facto state-contingent, the two distortions may partially offset each other.
Because the indifference curves need not be concave everywhere, the same indifference curve may have more than one tangency point with the zero-profit locus. In this case, there would be more than one Pareto-efficient contract. Obviously, this type of multiplicity is not very interesting because both the creditor and the debtor get the same utility in all equilibria. To avoid confusion, I will neglect the possibility of multiple Pareto-efficient contracts in the rest of the analysis.
To be precise, to control the probability that her loan will be repaid the creditor needs to impose a strict seniority covenant. This issue is discussed in detail in Detragiache (1992).
In Calvo’s model all debt is internal and it is denominated in domestic currency. The government can “default” by following a monetary policy that leads to high inflation, thereby reducing the real value of its liabilities. There is no randomness in the economy, but the interest rate includes a premium to compensate creditors for a future partial default. Partial default is optimal in equilibrium because the cost of default is increasing in the rate of inflation.
This may not be true if bonds are sold through an underwriter who takes on all of the placement risk. This will be discussed further below.
Another way to eliminate the bad equilibrium is for the borrower to set a ceiling on the interest rate that he is willing to accept (see Calvo (1988)).
In contrast with the exogenous output case, here the zero-profit locus would have a backward-bending portion even if debt could be renegotiated at no cost.
Recent work in corporate finance indicates that the inability to commit to invest in sound project may also force borrowers to finance long-term projects with short-term instruments (Flannery (1994)).
This does not mean that conditionality is not useful, of course. Agreeing on a borrowing program accompanied by conditionality may help a government overcome domestic opposition to its desired policy course, for instance.
For a recent attempt to classify financial crises and to connect theories with case studies, see Davis (1992).
Spreads on junk bonds widened considerably starting in March 1989, when Drexel’s junk-bond king Michael Milken was indicted. Drexel filed for bankruptcy in February 1990. For an account of Milken’s activities, see for instance Akerlof and Romer (1993). On the collapse of the junk bond market, see also Davis (1992). Davis contends that the collapse of the floating rate notes (FRN) Euro-market in December 1986 shared the same basic features of the junk-bond market crisis.
A similar episode is the bankruptcy of LTV in July 1986, which led to an overall price decline in the junk bond market (Hirtle (1989)).