Abstract
When a country encounters external debt problems, the question at the center of the policy debate is usually whether the problems are temporary or permanent, or, in other words, whether the country is illiquid or insolvent. Voices sympathetic to the debtor usually claim that the problem is il-liquidity, and that creditors would do well to provide new financing. Other voices caution against throwing good money after bad and encourage creditors to cut their losses and “exit” as soon as possible.1 If liquidity is not provided voluntarily, involuntary rescheduling or the accumulation of arrears follow, sometimes accompanied by emergency loans from foreign governments or international institutions. In the aftermath of the crisis, the debtor country usually improves its external accounts but only at the cost of a severe recession that worsens the country’s creditworthiness. A vicious cycle that perpetuates the initial debt problems then starts.2 Because a temporary external debt problem may lead to long-run economic disruption, the possibility that a liquidity shortfall will trigger a crisis should be a source of serious concern. Furthermore, policies that maintain creditworthiness may not be sufficient in these circumstances to avoid debt problems, and the question arises of whether an appropriate debt-management strategy or the intervention of multilateral institutions, such as the International Monetary Fund (IMF) may be necessary even for countries that normally have full access to world capital markets.3
When a country encounters external debt problems, the question at the center of the policy debate is usually whether the problems are temporary or permanent, or, in other words, whether the country is illiquid or insolvent. Voices sympathetic to the debtor usually claim that the problem is il-liquidity, and that creditors would do well to provide new financing. Other voices caution against throwing good money after bad and encourage creditors to cut their losses and “exit” as soon as possible.1 If liquidity is not provided voluntarily, involuntary rescheduling or the accumulation of arrears follow, sometimes accompanied by emergency loans from foreign governments or international institutions. In the aftermath of the crisis, the debtor country usually improves its external accounts but only at the cost of a severe recession that worsens the country’s creditworthiness. A vicious cycle that perpetuates the initial debt problems then starts.2 Because a temporary external debt problem may lead to long-run economic disruption, the possibility that a liquidity shortfall will trigger a crisis should be a source of serious concern. Furthermore, policies that maintain creditworthiness may not be sufficient in these circumstances to avoid debt problems, and the question arises of whether an appropriate debt-management strategy or the intervention of multilateral institutions, such as the International Monetary Fund (IMF) may be necessary even for countries that normally have full access to world capital markets.3
In this paper, I examine under what circumstances debt crises owing to illiquidity may arise. The most common argument used to dismiss concerns about liquidity problems is that rational creditors should always be willing to provide financing to a creditworthy borrower. Cooper and Sachs (1985) and Sachs (1984, 1995) challenge this view, arguing that a creditworthy borrower may be unable to obtain liquidity because creditors have “pessimistic” beliefs that become self-fulfilling: creditors do not lend because they think that the debtor will not repay. Without the option of rolling over some of his debt, the debtor ends up defaulting, thus validating the pessimistic expectations. This view seems to imply a model of sovereign borrowing with multiple rational expectations equilibria and no mechanism to ensure that the Pareto-superior outcome will be selected.4
Pursuing this line of inquiry, the first part of the paper explores potential liquidity crises arising from self-fulfilling beliefs. The first result found is that, if loans are negotiated by a few large banks, as in the case of the syndicated loans of the 1970s, “bad” equilibria can be easily avoided through coordination and communication among creditors.
As most of the existing literature on sovereign debt adopts a representative creditor framework, it is no wonder that the possible existence of multiple equilibria has generally been ignored.5 As sovereign debtors in developing countries are financing an increasing share of their external debt through bonds, it is important to consider the case in which the creditor side of the market consists of a large number of small claim holders. As it turns out, liquidity crises owing to self-fulfilling pessimistic beliefs can arise under these conditions in a very standard model of sovereign debt. Two distinct mechanisms can generate the multiplicity of equilibria: the first is that pessimistic expectations on the part of creditors increase the risk premium charged to the country. With a larger burden of debt service, the probability of a future default also increases, and a large enough increase can validate the expectations. This mechanism has been highlighted by Calvo (1988) in a model of domestic government borrowing in which the debt is nominal and default takes place through “surprise” in flation.6 Liquidity crises of this type can be avoided if the debtor can prevent the creditors from setting too high an interest rate; one such way is to offer a given amount of bonds for sale and let investors determine the price. Pessimistic expectations on the part of the creditors would then affect only the size of the proceeds from the bond issue but not the cost of future debt service, and the “Calvo mechanism” would not generate multiple equilibria.
A second mechanism can lead to self-fulfilling liquidity crises: if the proceeds from the bond issue are small because creditors have pessimistic beliefs, the borrower is less liquid and may cut investment to prevent current consumption from falling by too much. Lower investment leads to smaller future output and to a higher probability of future default. If the liquidity effect is strong enough, pessimistic expectations can then be validated even if they do not affect the cost of debt service. However, the sovereign borrower can also avoid the bad equilibrium possible under this mechanism by declaring that the bond issue will be automatically withdrawn if the average price is below an appropriately chosen minimum price. This solution can work if all the external debt is issued by a centralized agency, such as the treasury, but it would be difficult to implement in countries where provincial governments or public enterprises also issue substantial amounts of external liabilities.
These results suggest that liquidity crises driven by self-fulfilling beliefs may be an unfortunate by-product of the recent trend toward debt securitization in developing country financing. Although designing the debt issue appropriately can greatly reduce the danger of a crisis, the potential for multiple equilibria is one of the factors that makes access to emergency loans from the IMF or from foreign governments an important safeguard in international capital markets (Masson and Mussa (1995)).
Liquidity crises involving sovereign debtors can arise because these countries cannot make credible policy commitments to their creditors. If the debtor could ensure lenders that a certain amount of policy effort would be undertaken regardless of how much liquidity the country received from abroad, the “crisis” equilibrium would disappear. Credibility can be achieved by developing a reputation. For instance, Diamond (1989) shows how a borrower can improve his access to the credit market by building a reputation for being a “good risk” over time. From the perspective of Diamond’ s model, countries with recent histories of defaults and rescheduling owing to bad policies or countries that do not have long track records of international borrowing should be more vulnerable to liquidity problems. Because the cost of losing a good reputation is relatively small for these countries, modest increases in the (economic or political) costs of policy adjustment could destroy their credibility. Thus, creditors may be discouraged from lending even if other “fundamentals” do not appear to have changed.
The second part of the paper briefly explores another source of potential liquidity crises: disruptions in the bond market. Various studies in corporate finance have highlighted events that may temporarily “short-circuit” security markets, including the bankruptcy of a major issuing house, the default of a major debtor in the market, and a large drop in security prices that renders highly leveraged traders illiquid. When such events occur, external funds are likely to dry up temporarily for even creditworthy borrowers. The analysis briefly reviews past experience with security market disruption, evaluates the possibility that similar problems will arise in the emerging sovereign bond market, and discusses implications for external debt management.
The paper is organized as follows. Section I develops a simple model of sovereign borrowing in which output is exogenous and shows that multiple equilibria can arise because pessimistic beliefs can increase the cost of debt service, which, in turn, increases the probability of default. In the model of Section II, output is a function of policies undertaken in the previous period (that is, output is endogenous). In this model, pessimistic beliefs on the part of creditors can reduce liquidity in period 1, crowd out the policy effort, and increase the probability of a future default. (This is the second mechanism, as discussed above, that can generate multiple equilibria.) Ways to reduce the potential for this type of liquidity crisis are discussed. Section III contains an overview of factors that can disrupt bond markets, and Section IV summarizes the paper.
I. Self-Fulfilling Beliefs in a Model with Exogenous Output
Basic Model
The borrower is a benevolent government whose objective is to maximize the welfare of the representative consumer. There are two periods, denoted by t = 1, 2. Output in each period, denoted by yt, is the realization of the random variables Yt: [y, Y] → [0, 1]. The cumulative distribution function of Yt is F(yt) and the density is f(yt). Let ℓ1 denote the amount of new funds that the country receives from foreign creditors at date 1, while b2 denotes the amount of debt service due at t = 2 on the loan ℓ1. Thus, the interest rate that the country pays on the loan is b2ℓ1 – 1. If the debt contract is in the form of a pure discount bond, the face value of the bond is b2 and the price is ℓ1/b2. Also, the country is assumed to have debt obligations contracted in the past; dt denotes the amount of debt service due on these obligations at t = 1, 2.
At each date the country has the option to default on its foreign debt. If debt is repudiated, the country is unable to borrow new funds and incurs a penalty st = s(yt), with s’(yt) > 0. For simplicity, I will ignore the possibility of debt renegotiation, but I will point out cases (see footnote 7) in which renegotiation would change the results. Let ct denote consumption at t. The preferences of the representative consumer are captured by the utility function
where δ ∈ (0, 1) is the discount factor and u(ct) is a concave utility index. Let us examine the equilibrium in the second period. As t = 2 is the last period, no new borrowing takes place at this date, and the period 2 consumption levels if the country repays and if the country defaults are, respectively,
Hence, if s(y2) = b2 + d2, the country is exactly indifferent between repaying and defaulting on the loan; if s(y2) < b2 + d2, the country strictly prefers default. Let y* be the realization of output for which s(y2) = b2 + d2. Then, the probability of a default at t = 2 is F(y*). As the cost of default increases in output, the probability of default increases in the amount of new debt that the country incurs at t = 1:
Using these results, the maximum utility that a country with scheduled debt service b2 + d2 expects to receive in period 2 is
Before examining the borrowing decision at t = 1, let us consider the decision on repaying or defaulting at t = 1. If the country expects to borrow ℓ1 and make debt-service payments of b2 the maximum expected utility from repaying at t = 1 is
while the utility from defaulting is
Hence, the country will repay whenever Wr(y1, ℓ1, b2 + d2) > Wd(y1). Notice that Wr is increasing in ℓ1 and decreasing in b2. Thus, whether a debt crisis occurs in the first period depends not only on the default penalty but also on the terms at which the country expects to receive new financing.
Equilibrium with a Representative Creditor
In this scenario, the lender side of the market consists of a risk-neutral representative lender, whose opportunity cost of funds is r. The loan contract is the pair (ℓ1, b2). The expected zero-profit condition for the lender is
Curve AA’ in Figure 1 corresponds to the expected zero-profit locus. If the debt inherited from the past is very large [d2 > s(Y)], the probability of a default in period 2 is one even if b2 = 0, and the creditor is unwilling to lend new funds at any interest rate. In this case, the debtor is insolvent, and, at t = 1, the choice is between defaulting immediately or waiting until period 2. Immediate default is preferred if and only if d1 < s(y1). However, if d2 < s(Y), the creditor is willing to offer a new loan, provided that the interest rate is sufficient to cover the risk of default.
Multiple Equilibria with Exogenous Output
Citation: IMF Staff Papers 1996, 003; 10.5089/9781451973440.024.A003
The slope of the zero-profit locus is
As the amount borrowed and the interest rate increase, the zero-profit locus becomes steeper because the probability of repayment falls. Because dy*/db2 is positive (equation (4)), the denominator of equation (8) turns negative as debt repayment continues to grow, and the locus bends backward.7 With a representative lender, the set of competitive equilibria of the credit market is just the set of (constrained) Pareto-efficient loan contracts that yield expected zero profits to the lender.8 Hence, the equilibrium loan contract is the solution to the following problem:
subject to equation (7). Under appropriate assumptions (see Appendix), this problem has a solution represented by contract (ℓc, bc) in Figure 1.9
Is the Pareto-efficient contract also the (unique) equilibrium when there is a multiplicity of potential lenders? If an individual investor or coalition of investors (such as a bank syndicate) can raise sufficient funds to cover the borrowing needs of the country, the answer is affirmative. In this scenario, although many potential lenders compete with one another in supplying the most attractive set of contracts, the country need not borrow from more than one lender (or coalition of lenders) in equilibrium, and the lender can control the total amount disbursed and the total amount of debt service due. Hence, the probability of repayment does not depend on the actions of other creditors, and, in equilibrium, each lender is willing to supply any of the loan contracts on the zero-profit locus.10 The debtor, of course, will choose the contract that gives the most utility, namely, (ℓc, bc).
Equilibrium with Atomistic Creditors
Consider now a scenario in which the creditor side of the market consists of a multiplicity of small investors. As these investors have access to a limited amount of funds, each loan must be subscribed by several investors. Because of their large number, investors cannot coordinate or communicate among themselves. To simplify the analysis, it will be assumed that each investor is atomistic, so that her decision on how much to lend and at what interest rate does not affect the total loan amount and the average interest rate for the borrower. In contrast to the representative lender case, individual lenders cannot in this situation control the probability that their loans will be repaid, because this probability depends on the total amount of debt service due. In fact, from the point of view of an atomistic investor, the aggregate loan contract (ℓ1, b2) is exogenous. Hence, to decide their lending strategies, individual investors must form expectations about the aggregate amount of debt that the debtor will take on in equilibrium. All investors must expect to break even in equilibrium, and their expectations must be rational. Because investors are assumed to be identical, attention will be restricted to symmetric equilibria, in which all investors play the same strategy.
Before deriving the equilibrium, it is necessary to make assumptions as to the mechanism through which the loan is marketed. To begin with, let us assume (following Calvo (1988)) that the country announces the total amount that it wants to borrow, ℓ1, and invites investors to make bids consisting of pairs of quantity and interest rates. The borrowing country will then choose the bids that minimize the average interest rate. In Calvo’s model, investors know the total loan amount ℓ1 with certainty, but they must form expectations concerning b2. Let be denote the total amount of additional debt service that an investor / expects the country to take on. Then, investor i expects the country to default with probability F(y*(be)), where y*(be) is the solution to s(y2) = be + d2. Accordingly, the expected zero-profit condition for investor i if she lends ℓi at the interest factor Ri is
Hence,
Under symmetric strategies and rational expectations, Ri, = be/ℓ1 in equilibrium; hence, the aggregate loan contract is a solution to
All values of b2 that correspond to ℓ1 on the zero-profit locus satisfy this condition, and, because the locus is backward bending, there are two possible equilibria for any announced value of ℓ1. If the borrower announces that he wants to borrow the Pareto-efficient amount ℓc, the contract (ℓc, bc) is a rational expectation equilibrium under symmetric strategies because bc is on the zero-profit locus. However, the contract (ℓc, bp) is also an equilibrium: if an investor believes that all the others will lend at the higher interest factor bp, ℓc because they expect a high probability of default, she is better off offering the high interest factor as well, because offering a lower interest rate would not change the average rate paid by the country and, therefore, would not change the probability of default. In this equilibrium, creditors still expect to break even, but the borrower is worse off than in the Pareto-efficient equilibrium, as all the losses are borne by the borrower.
Hence, as in Calvo (1988), pessimistic beliefs on the part of the creditors can become self-fulfilling, and a creditworthy borrower may have to pay an exceedingly high interest rate.11 This situation, in turn, may trigger a debt crisis at t = 1 because the maximum utility from repaying at t = 1, Wr decreases in b2. In fact, it may be that, while full repayment is preferred to default if the creditors are “optimistic” at t = 1, default becomes the best option if the bad equilibrium is expected to occur. Hence, illiquidity owing to self-fulfilling pessimistic creditor beliefs may lead to an immediate default. Note, however, that in this model illiquidity in period 1 is not what increases the likelihood of future default: what lowers the probability of repayment at t = 2 is simply the high interest rate that the debtor has to pay.
This simple model suggests that liquidity crises owing to self-fulfilling beliefs are more likely to occur when debt is securitized than with large syndicated bank loans, because the inability of the creditors to coordinate their expectations makes the bad equilibrium possible.12 The crisis equilibrium, however, is very sensitive to the assumption that the sovereign borrower sells a given amount of debt and lets investors determine the interest rate. Under this assumption, the amount of debt service at t = 2 (b2) and, consequently, the probability of default (F(y*)) depend on investors’ expectations. This linkage gives rise to the multiplicity of equilibria. But the sovereign borrower could sell the debt so that b2 is independent of expectations. For instance, the borrower could put up for sale n bonds with face value Q and coupon rate i, and ask creditors to determine the price of the bonds. Incidentally, this is how most bonds and government securities are marketed (Smith (1995) and Bartolini and Cottarelli (1994)). If this sale succeeds, debt service in period 2 is b2 = n Q (1 + i), which is independent of creditor expectations. Thus, in choosing which price to offer, a small individual creditor need not form expectations about the behavior of the other creditors, because such behavior does not affect the probability of default or, thus, the profitability of the bonds. Therefore, an investor with rational expectations should always be willing to lend at the break-even price ℓc/bc, and the possibility of a belief-driven liquidity crisis should disappear.13
More generally, the existence of multiple equilibria can easily be checked by using Figure 1: if the debt is sold so as to fix the amount of debt service to bc, there cannot be another equilibrium besides the Pareto-optimal contract because the only loan amount on the zero-profit locus corresponding to bc> is ℓc. However, if the borrower fixes ℓc two equilibria exist because two values of b2 correspond to ℓc on the zero-profit locus.
This model is perhaps too simple to capture all the mechanisms that can generate self-fulfilling liquidity crises in the sovereign debt market. In particular, as remarked above, the probability of default at t = 2 in this model does not depend on the liquidity of the borrower in the previous period. In the next section, the model is extended by allowing output to depend on a policy action, thereby establishing the connection between liquidity and future insolvency.
II. Self-Fulfilling Beliefs in a Model with Endogenous Output
Basic Model
Suppose that output in the indebted country is a function of a random shock zt and of an endogenous variable xt that captures the extent of a “policy effort” undertaken in the previous period (such that, at t, xt is predetermined). The policy effort variable can be interpreted as investment in physical capital, human capital, or technology acquisition; more broadly, it can be understood as investment in economic reforms such as trade liberalization, financial liberalization, and fiscal reform. The production function is
The random shock zt takes values in [z, Z] and has the cumulative distributive function F(zt). The cost of undertaking the policy effort xt is borne at t — 1, and it is given by the following function:
Let z* be the realization of the shock making the borrower indifferent between default and repayment in period 2. Then,
As y is increasing in both of its arguments, dz*/dx2 < 0. The maximum expected utility at t = 2 is
Consider now the policy effort decision at t = 1. It will be assumed that the policy effort is chosen after the new loan is disbursed, and that the government cannot make a credible commitment with its creditors as to the choice of the policy effort x2. Suppose that, at t = 1, the country repays its obligations in full, the amount of new borrowing is ℓ1 and total debt service due at t = 2 is b2 + d2. Then, the optimal policy effort is the solution to
The first-order condition for an interior solution is
In the Appendix, it is shown that the objective function in equation (18) is strictly concave, so that the solution to equation (19) is the unique maximum. Let Χ = Χ (ℓ1, b2) denote this solution. The Appendix also demonstrates that Χ is increasing in the loan amount ℓ1. The intuition is that, with more liquidity (a larger first-period loan ℓ1), the utility cost of undertaking a large policy effort at t = 1 is smaller and, ceteris paribus, the optimal x2 is larger. In other words, liquidity “crowds in” the policy effort. In this new framework, the creditors’ expected zero-profit condition is
and the slope of the locus is
The main difference from the model with exogenous output is the presence of the second term at the numerator. This term is the composition of two effects: dχ/dℓ1 measures the extent to which the policy effort is crowded in by an increase in the loan disbursement, while f(z*) dz*/dx2 measures the decline in the probability of default owing to an increase in the policy effort. If this term is large enough, the numerator may be negative for some values of ℓ1 and b2, and, keeping debt service constant, an increase in the amount disbursed increases the probability of repayment by so much that expected profits actually increase. The implication for the shape of the zero-profit locus is shown in Figure 2: as in the model with exogenous output, the denominator of equation (20) changes sign for large values of b2, and the zero-profit locus bends backward.14 Furthermore, the numerator may also change sign for even larger values of b2, and the locus may slope upward. This is more likely to occur the more sensitive the output is in period 2 to policy rather than to the exogenous shock (which makes f(z*) dz*/dx2 larger), and the stronger is the crowding in effect. Cohen (1993) estimates that, for developing countries that rescheduled their external debt in the 1980s, a decrease in the external transfer of one dollar reduced private investment by 0.30; Cohen also observes that this figure confirms earlier studies on the effect of foreign aid on private investment. Hence, if we interpret the policy effort as private investment, a plausible size for the “crowding out” coefficient dχ/dℓ1 is 0.30.
As before, (ℓc, bc) is the Pareto-efficient contract, and (ℓc, bp) is the bad equilibrium that can arise when the borrower chooses the loan amount and lets creditors determine the interest rate. In contrast to the model of the previous section, however, a bad equilibrium may now arise even if the borrower issues bonds by fixing b2 and letting creditors determine ℓ1. In Figure 2, this equilibrium is the contract (ℓc, bc). In this equilibrium, each creditor believes that the others will offer a low price because they consider a default very likely. With a low price, the bond issue yields small proceeds. The debtor, faced with illiquidity at t = 1, must reduce the policy effort, thereby increasing the probability of default. The pessimistic expectations are thus validated.
Multiple Equlibria with Endogenous Output
Citation: IMF Staff Papers 1996, 003; 10.5089/9781451973440.024.A003
Preventing Liquidity Crises
As described above, a self-fulfilling crisis can be generated when the borrower chooses the loan amount and let creditors determine the interest rate. However, the borrower can avoid the bad equilibrium by selling the bonds through an appropriate technique. Specifically, a borrower who offers bonds for sale with face value bc should also announce that the offer will be automatically void unless the average price at which the bonds are purchased exceeds a minimum price p, where p is a number between ℓp/bc and ℓc/bc. With the minimum price provision, the bad equilibrium (ℓp, bc) is no longer possible because each investor knows that, if the other investors have pessimistic beliefs and the proceeds from the loan are too small, the offer will be withdrawn, thereby eliminating the risk of lending at a risk premium that is too low. With a minimum price, the only rational expectations equilibrium is (ℓc,bc), the Pareto-efficient outcome. It should be emphasized that to eliminate the bad equilibrium it is not enough for the borrower to reserve the right to void the sale; the offer must be automatically void if the minimum price rule is not met. Otherwise, if the bad equilibrium were better than an equilibrium with no borrowing, the borrower would choose not to void the sale if the price turned out to be low, and (ℓP,bc) could still be an equilibrium.
Note also that, if liquidity crises driven by self-fulfilling pessimistic beliefs can cause large welfare losses, the two loan contracts (ℓp, bc) and (ℓC, bc) must be “far apart.” The range within which the minimum price must be set to eliminate the bad equilibrium is therefore also large, so that, even if the borrower does not know the bond demand curve with much precision, the likelihood of choosing the wrong minimum price is small. An underwriter can also assist the borrowing country in obtaining information about the demand curve. If an underwriter is used, an alternative way to avoid coordination problems among bondholders is to use the so-called bought deal. In a bought deal, a very popular issuance technique in the Euromarket, the underwriter effectively takes on all of the issuance price risk (Smith (1995)), and there is no residual uncertainty about the size of the proceeds or the amount of debt-service payment that the country will have to make. Of course, the underwriter needs to be compensated with a fee.
These potential ways to avoid bad equilibria presume that all of the country’s external debt is issued by a centralized authority, such as the treasury or central bank. If independent branches of the government, such as local governments or public enterprises, can issue securities for which the central government bears ultimate financial responsibility (a common occurrence in emerging economies), an appropriate “minimum price clause” must be included in all bond contracts to eliminate the bad equilibria. This action, of course, can be taken only if the central government maintains a degree of control over the external borrowing decisions of all its branches. The problem is even more severe where the domestic banking system is a large issuer of external debt covered by an implicit government guarantee.
Liquidity Crises and Credibility
At the core of the liquidity crises described above is the inability of the debtor country to commit to a given level of policy effort before negotiating the new loan. Because of this inability, individual investors fear that the policy effort will be reduced if other investors are unwilling to provide sufficient external financing to the country; as a result, they offer a low price for the bonds. If the country could credibly commit ex ante to a certain amount of policy effort irrespective of the level of external financing, the bad equilibrium could be eliminated altogether. In equation (20), dz*/dy would be zero; the numerator of the expression would always be positive, as in the exogenous output model; and, as in that model, liquidity crises could arise only through the Calvo mechanism. Hence, if the sovereign borrower could make credible commitments about its policy stance, one of the mechanisms that can generate self-fulfilling liquidity crises would no longer be at work.
The literature on sovereign debt has often emphasized how the inability to commit to a given level of investment or policy effort before borrowing results in an equilibrium at which the country invests too little, pays a higher interest rate, and borrows less than in an equilibrium with precommitment (Atkeson (1991) and Rodrik (1996)). The welfare loss highlighted in the literature, however, is quite distinct from the welfare loss arising from multiple equilibria; the former does not depend on a lack of coordination among the creditors. In terms of the model with endogenous output, it can be easily shown that, if the country could make a credible commitment ex ante, not only would the bad equilibrium disappear but the country could also achieve an equilibrium that dominates the (constrained) Pareto-optimal equilibrium (ℓc, bc).15 The intuition is that the debtor, when deciding on the policy effort ex ante, takes into account that an increase in policy effort (x2) improves the terms of the new loan, such that the optimal amount of effort is higher than what is optimal ex post.
This point can be illustrated by showing that, starting from the Pareto-efficient equilibrium derived in the previous subsection (ℓc, bc) and keeping b2 = bc, an increase in x2 that changes the borrowing terms makes the debtor country better off. As the probability of default depends on the policy effort x2, the expected zero-profit condition for the creditors implicitly defines the function
Because the probability of repayment increases in the policy effort, this function increases in its first argument. When the borrowing country receives a loan that satisfies the expected zero-profit condition for the creditors, its expected utility at t = 1 is then
Suppose that this expected utility is evaluated at ℓ1 = ℓc, b2 = bc, and xc = χ(ℓc, bc), that is, the Pareto-efficient equilibrium derived in the preceding subsection. Differentiating equation (22),
(The second equality follows from equation (18)). With precommitment, an intensified policy effort can increase the amount that creditors are willing to disburse for a given debt-service payment, because the increased policy effort decreases the probability of default. This effect, captured by the term ∂λ/∂x2, is not taken into account in the model without precommitment because the loan amount is predetermined when the policy effort decision is made. Hence, if the indebted country could precommit to engage in a stronger policy effort, it would be able to obtain more favorable terms and would be better off than in the Pareto-efficient outcome without precommitment. Furthermore, precommitment would reduce the risk of self-fulfilling liquidity crises described at the beginning of this section.
Thus, the ability to make credible commitments can be very valuable to a sovereign borrower. Credibility can be achieved by developing a reputation for maintaining high levels of policy effort even if these efforts are not optimal ex post. The intuition behind the game-theory concept of reputation is that, when players interact over long periods of time, it may make sense to choose actions that are suboptimal from a myopic perspective because such behavior may induce other players to be more “cooperative” in the next stages of the game. Diamond (1989) provides an interesting illustration of how reputation effects may work in credit markets. In his model, the borrower can be one of three types: a “good risk,” a firm that has only a safe investment project; a “bad risk,” a firm that has only a risky project; and an “intermediate risk,” a firm that can choose between the two projects. The creditors cannot observe either the true identity of the borrower or the choice of project. The risky project is socially inefficient, but it is profitable for the borrower because the downside risk is shifted onto the creditors. Hence, in a one-shot game, the intermediate type would always choose the risky project. However, when the firm expects to borrow repeatedly over time, the intermediate type may choose the safe project instead: by building a track record of debt repayment, the borrower expects the default risk premium to fall as creditors assign a higher and higher probability to the firm’s being a good risk. Hence, the hope of developing a reputation for being a low risk induces the intermediate-risk firm to choose the safe investment project, even though such a choice is time inconsistent. The incentives to follow the time-inconsistent (but ex ante optimal) policy become stronger as time goes by. Hence, a good credit record is in Diamond’s model an asset whose value appreciates over time.
This framework, which could be easily adapted to the problem of sovereign borrowing, suggests that countries with histories of debt problems or with no track records in international capital markets are more vulnerable to liquidity crises. By establishing good track records, these countries can gain the confidence of foreign investors, but this process can occur only gradually over time. Events that suddenly increase the cost (economic or political) of undertaking policies that improve creditworthiness, then, may trigger a liquidity crisis for a sovereign borrower.
Rodrik (1996) argues that loans from the IMF and the World Bank containing “conditionality” clauses help remedy the time-inconsistency problem. In these programs, loans are disbursed little by little, and each disbursement is contingent on the country complying with a number of performance criteria agreed upon at the start. Other authors have raised doubts about Rodrik’s view of conditionality. In particular, they question whether conditionality can really induce a government to follow policies that it does not want to follow (Killick (1995) and Claessens (1996)).16
For conditionality to work as envisioned by Rodrik, several conditions must be met. First, the IMF and the World Bank staff must be able to monitor compliance with performance criteria. Second, the institutions must be willing to stop disbursement when the country goes off track even if, once the first tranches are committed and the creditors are “locked in,” the creditors may be better off to continue lending. Third, the debtor must at every stage be better off continuing with the program rather than going off track. For the third requirement to be satisfied, loan disbursements must be sufficiently large in the early stages of the program to compensate for the costs of undertaking a strong policy effort; when the time comes for the debtor to start making net repayments to the IMF and the World Bank, the policy changes must have become “self-sustaining.”
III. Liquidity Crises and Disruption of Securities Markets
The “rational” liquidity crises investigated in the preceding sections are events limited to an individual borrower. But liquidity problems may also arise when the entire market is disrupted. This section briefly reviews some of the factors that may cause temporary disruptions in bond markets. The literature on this subject is fairly large—although not as large as that on the related subjects of stock market crashes and banking crises—and, with a few notable exceptions, it is mostly descriptive.17 Various mechanisms have been identified as leading to bond market disruption. For instance, a sudden increase in the cost of issuing new bonds may originate from a drop in secondary market prices. Secondary bond markets differ from the stereotypical market in that they are often “dealer’s markets”: would-be buyers do not purchase securities directly from would-be sellers; rather, both buyers and sellers trade with dealers, who “make the market” for the particular security by quoting bid and offer prices. The willingness and ability of dealers to stand ready to buy and sell a security are crucial for the smooth functioning of the market, as they enable buyers and sellers to carry out their desired trades quickly. The width of the bid-ask spread measures the liquidity of a particular bond issue.18
If a market is dominated by a small number of dealers, and if one or more dealers withdraw (perhaps because they have become insolvent), the market may become illiquid and trading may come to a standstill. This is what happened to the junk bond market in 1989–90 when Drexel Burnham Lambert collapsed. Drexel was the dominant dealer in junk paper, accounting for 40 percent of the market in 1988 (Hirtle (1988)), and, in the wake of its demise, no other trading house was able to take its place and maintain liquidity in the market. As a result, prices of junk bonds dropped dramatically although no independent change in the borrowers’ creditworthiness had taken place, and new issues of junk bonds all but dried up until the market started to recover at the end of 1991.19 Emerging bond markets should be less vulnerable than the junk bond market to this type of crisis because dealing is not as concentrated: according to the Institutional Investor (“Emerging-Markets Debt,” April 1994), the Emerging Markets Trading Association had 125 members in 1993, with as many as half a dozen dealers in a dominant position.
A second type of market disruption can occur when the default of a large issuer leads to a generalized price fall (“contagion”). Here, the classic example is the default of the Penn Central railroad in 1970, which severely disrupted the U.S. commercial paper market (see, among others, Calomiris (1995)).20 Further defaults were avoided only because the Federal Reserve promptly intervened, encouraging commercial banks to provide liquidity to firms that could no longer roll over their short-term liabilities in the commercial paper market. Encouragement took the form of making liquidity available to the banks through the discount window. Because commercial paper has a very short maturity (30 days on average), rollover risk is of paramount concern, and a shortage of liquidity could have brought a number of large (and solvent) U.S. companies to the verge of default.
Although it did not give rise to formal sovereign default, the crisis following the Mexican devaluation in December 1994 led to a generalized fall of emerging sovereign bond (and equity) prices, which, in turn, forced a number of prospective borrowers to postpone new issues (International Monetary Fund (1995) and Andrews and Ishii (1995)). Argentina was perhaps the hardest hit, and it had to resort to increased borrowing from the IMF and the World Bank to face its short-term liquidity needs. Folkerts-Landau and Ito (1995) and Calvo and Reinhart (1996, forthcoming) discuss the evidence on the extent of the contagion in the Mexican crisis.
The Penn Central case and other similar episodes raise the question of why the troubles of one issuer can spill over to the rest of the market even if the fundamentals of other debtors have not changed. A possible explanation is that it takes time for the market to process the information revealed by an unexpected default. Initially, market participants mistakenly believe adverse shocks specific to particular borrowers to be of a more general nature. Only with time is the true nature of the shock discovered and the contagion ended. An alternative explanation may be that dealers, having lost money on the defaulting issue, lose their ability to deal in other securities and have to withdraw, thereby impairing the liquidity of the entire market. If at least a few prominent dealers in the market are well diversified and do not have large exposures to the defaulting borrower, however, this explanation would not be very relevant.
Another potential source of market disruption is explored in a recent paper by Aiyagari and Gertler (1995). In their model, a moderate price fall may trigger margin calls for highly leveraged traders. To meet the calls, the traders have to liquidate some of their assets, which typically consist of other securities. This liquidation worsens the initial price decline and may spread the selling spree from one market to another. Hence, the margin requirements that limit the ability of traders to leverage their positions give rise to price “overshooting” in securities markets. Of course, the more leveraged are the traders, the more vulnerable is a particular market to this type of crisis. Interestingly, the financial press mentioned the need to meet margin calls as one of the factors that contributed to the downturn in emerging markets in February 1994. According to the Institutional Investor (“Emerging-Markets Debt,” April 1994, p. 65):
Steep losses in the yen-dollar market then led several highly leveraged hedge funds and proprietary trading desks to unwind their long positions in the emerging-debt market to offset the losses. And margin calls on investors that had leveraged their positions, but lacked the ready cash to meet the calls, compelled them to aggressively hit market makers’ bids to unwind their long positions, thus adding to the downward momentum.
What can borrowers do to shelter themselves from the potential liquidity problems caused by these types of market disruptions? After the Penn Central crisis, market participants reacted by taking two types of precautions. First, the number of commercial paper issues rated by credit rating agencies such as Standard & Poor, Moody’s, and Fitch increased markedly, and rating standards were tightened (Stigum (1983)). Ratings provide the market with borrower-specific information, and they should increase investors’ ability to distinguish between adverse events that affect only one borrower or category of borrowers and shocks that affect the entire market, thus limiting the risk of contagion.
The second response to the Penn Central crisis was to back up commercial paper with lines of credit with banks. As documented by Post (1992), almost all of the commercial paper issues in the United States are completely backed up at present by such lines. These backup lines are distinct from guarantees or other forms of credit enhancement because they usually contain a “material-adverse-change” (MAC) clause stating that the bank can refuse to provide the loan if the debtor’s financial condition has deteriorated substantially. The borrower, therefore, has access to the line of credit only if the inability to roll over the commercial paper stems from market disruptions and not from a loss of creditworthiness. Therefore, commercial paper holders still bear default risk and have an incentive to scrutinize the issuer (Calomiris (1984)). Conversely, while it is no longer subject to the risk that its working capital will evaporate because of a temporary crisis in the commercial paper market, the issuer still has an incentive to maintain its creditworthiness.
The arrangements in the U.S. commercial paper market suggest that both extensive rating by specialized agencies and backup credit lines with banks may help countries participating in the emerging bond market to reduce the potential impact of market disruption. The viability of backup lines, of course, hinges on the banks’ ability to distinguish between situations in which the bond market has become too expensive because of a deterioration in creditworthiness (so that the MAC clause can be invoked) and situations in which the source of the trouble is generalized market disruption. Companies with access to the U.S. commercial paper market are generally large, well-known companies with extremely good credit ratings, and events that can trigger the MAC clause are likely to be events that dramatically change the situation of those companies. These large shocks are probably easy to detect. In the case of the emerging sovereign bond market, however, the risk of default is relatively high for most issuers, and it may be more difficult to distinguish material adverse changes from temporary market disruption. In any event, the reliance on bank credit lines in the commercial paper market suggests that maintaining an ongoing relationship with banks, so that bank financing can become available quickly in moments of crisis, may greatly help debt management. Interestingly, in the wake of the 1994 Mexican crisis, a revival of bank loan commitments to sovereign developing country borrowers has been observed (Andrews and Ishii (1995)).
Another precaution that a sovereign borrower can take against liquidity crises is to maintain a sufficiently large stock of foreign exchange reserves. To protect the country against rollover risk, reserves should be sufficient to cover not only imports but also debt service coming due in the near future, net of the amount that can be raised through existing credit lines.
IV. Summary and Concluding Remarks
In the debate over debt crises, the distinction between liquidity and solvency problems plays an important role. It is often argued that, when the creditor side of the market is rational and efficient, liquidity problems should never occur unless they are also accompanied by a loss of creditworthiness (insolvency): as long as the debtor is creditworthy, new loans are profitable, and as long as creditors are rational and compete with one another, all loans that are profitable should be on offer. However, the results in this paper show that this line of reasoning is not entirely correct. First, there is the possibility of multiple rational expectations equilibria, one of which can be identified as a “liquidity crisis” equilibrium. Multiple equilibria may arise when the creditor side of the market consists of many small investors who cannot coordinate their lending strategies. The potential for this type of liquidity crisis can be greatly reduced by marketing the debt appropriately, by developing a reputation for following policies that enhance the country’s repayment capacity, or by pursuing both these courses of action. Because reputation takes time to build, countries with a history of debt problems or no track record in international financial markets are more vulnerable to self-fulfilling liquidity crises. Access to emergency loans from the IMF and the World Bank in case of liquidity shortfalls is likely to be important for these countries.
The market for emerging sovereign bonds may be disrupted not only by multiple equilibria but also, like other securities markets, by events unrelated to the loss of creditworthiness of a particular borrower. In these circumstances, a creditworthy country may be unable to access the bond market for a limited time or may have to pay excessively high spreads. Market characteristics, such as the number and financial health of secondary market dealers, the leverage of the traders, and the use of underwriters, affect the extent to which a particular market is vulnerable to temporary disruption. Young markets (such as the emerging bond market) are likely to be more vulnerable because the institutional and contractual arrangements needed to ensure their smooth functioning may not be fully developed. Thus, sovereign borrowers with substantial bond issues that may have to be rolled over might need to maintain access to bank loans, perhaps through backup credit lines or other forms of emergency arrangements.
Appendix
This Appendix presents mathematical derivations related to equations (9), (18), and (19).
The necessary first-order condition for a maximum in equation (9) is
The sufficient second-order condition is
Proof that the objective function in equation (18) is strictly concave in x2 can be derived by differentiating the left-hand side of equation (19):
Because the utility function and the output functions are increasing and strictlyconcave and the default state z* is decreasing in the policy effort x2, the expressionabove is unambiguously negative. Because of equation (A3), it is sufficient to show that the derivative of the left-hand side of equation (19) with respect to ℓ1, is positive to prove that dΧ/dℓ1 > 0. This derivative is
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Enrica Detragiache is an Economist in the IMF Research Department. She received a Ph.D. in economics from the University of Pennsylvania. Before joining the Fund, she was an Assistant Professor at Johns Hopkins University.
Even if the country has lost its creditworthiness, providing new money may be optimal for creditors who are already exposed because such a strategy (sometimes referred to as “defensive lending”) may increase the value of loans already outstanding. The analysis in the paper focuses 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 developing countries’ 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. He suggests that the international community should create a new institution along the lines of an international bankruptcy court for sovereign debtors.
See, for instance, the recent survey by Eaton and Fernandez (1995).
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 his paper shows that multiple equilibria are possible also with afixedcost of default.
If debt could be renegotiated at no cost, 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. As the option to default de facto makes debt repayment 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, the creditor needs to impose a strict seniority covenant to control the probability that her loan will be repaid. This issue is discussed in detail in Detragiache (1994).
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.
Bad equilibria may not occur if bonds are sold through underwriters who take on all of the placement risk. This possibility 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 to the exogenous output case, the zero-profit locus here 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 projects may also force borrowers to finance long-term projects with short-term instruments (Flannery (1994)).
These doubts do 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 (1995).
For a theoretical model of a dealer’s market, see Glosten and Milgrom (1985).
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 (1995). Davis contends that the collapse of the Euromarket for floating rate notes in December 1986 shared the same basic features as the crisis in the junk bond market.
A similar episode is the bankruptcy of the LTV Corporation in July 1986, which led to an overall price decline in the junk bond market (Hirtle (1988)).
