International institutional lending arrangements to sovereign borrowers

Journal of International Money and Finance 22 (2003) 459–481 www.elsevier.com/locate/econbase

International institutional lending arrangements to sovereign borrowers Steven E. Plaut a, Arie L. Melnik b,∗ a

University of Haifa, School of Business Administration, Haifa 31905, Israel b University of Haifa, Department of Economics, 31905 Haifa, Israel

Abstract Recent financial crises in east Asia and elsewhere have illustrated the problems that plague emergency liquidity arrangements and the ‘lender of last resort’ role of the International Monetary Fund and other international institutions. In particular, these act under conditions of extreme uncertainty, where potential sovereign borrowers, as well as private financial institutions, are ‘kept in the dark’ regarding the intentions of the emergency lenders and the amounts and terms of emergency liquidity that can be tapped. From April 1999, longer-term credit lines are being offered by the IMF, designed to be awarded to ‘healthy’ countries before they experience contagion or distress. The paper evaluates the advantages of this form of IMF lending and this new trend in IMF operations. It is argued that provision of IMF financing through such long-term lending facilities is better in some senses than shorter-term lending. Long-term contracts reduce the uncertainty with respect to IMF intentions. Moral hazard problems are reduced for the borrowing country and financial markets know the future level and terms of IMF support. Another advantage is that long-term loan contracts improve the allocation of resources within the borrowing country. Much as private-sector facility lending is the dominant mode of finance in many markets, so facility lending has efficiency advantages when it is provided by the IMF. This efficiency advantage is derived formally. It is shown that sovereign borrowers are actually better off when utilizing these as backup lines of credit, instead of emergency borrowing that is conducted after distress occurs. Facility lending by international institutions can lead to a welfare improvement and superior resource allocation for sovereign borrowers. The intuition for this is that when financial distress drives these borrowers to increase their debt, risk premia in borrowing rates would not rise, at least up to the limits established by the size of the facility.  2003 Elsevier Science Ltd. All rights reserved.

∗

Corresponding author. Fax: +972-4-824-9245. E-mail address: [email protected] (A.L. Melnik).

0261-5606/03/$ - see front matter  2003 Elsevier Science Ltd. All rights reserved. doi:10.1016/S0261-5606(03)00015-9

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Keywords: IMF; Sovereign debt; Credit facilities; Signalling

1. Introduction As sovereign debt markets have expanded, there has been concern about the extent to which IMF lending stabilizes or destabilizes these markets. On the one hand, the IMF is presumed to act as a sort of lender of last resort and provider of emergency financing to sovereign debtors, especially during times of crisis. On the other, there is concern that the operations of the IMF create moral hazard problems, by which sovereign borrowers over-extend themselves in debt markets and hence financial crises become more frequent or severe. All of this has of course become much more acute following the ‘Asian crisis’ of the 1990s. The role of the IMF is central in any discussion of sovereign debt markets and their stability.1 One aspect of the functioning of the IMF that has attracted relatively little attention until recently is the contractual form through which the IMF provides financing, including emergency liquidity and financing of ‘last resort’. Recently the IMF changed its policy in this regard. On April 23, 1999 the board of governors of the International Monetary Fund altered the way in which the IMF does business with member countries. The board approved the implementation of a program establishing ‘contingent credit line facilities’ to help avert financial crisis. Guidelines for its implementation were formulated on November 1, 2000. These new facilities are supposed to assist countries that are not currently undergoing financial distress, providing them with facilities that entitle them to rapid funding should they later undergo problems or fall victim to ‘financial contagion’. The basic idea of the facilities is to establish lines of credit long before a financial crisis hits.2 The introduction of contingent credit lines represents an important change in the way the IMF operates.3 In the past, IMF loan facilities were generally set up as treatments for country financial/monetary problems after they had already appeared. In contrast, the new facilities are intended to serve more as preventive medicine.4 There was intensive debate, and there is still argument, over how the new facilities should operate. Some IMF members support facilities without specific quantity limi-

1

For reviews of the issues involved in multilateral lending see Rodrik (1995); Cassard and FolkertsLandau (1997); Rodrik and Valesco (1999) and Jeanne and Zetteelmeyer (2001). For discussions of the creation and resolution of international financial crisis see Bordo and Schwartz (1999) and Kamin (1999). 2 According to the Economist, May 1, 1999, Wall Street Journal, April 30, 1999, Business Times (Singapore), April 28, 1999, IMF Managing Director Michel Camdessus said, ‘The contingency reserve facility we are announcing today is for the country to establish a supplementary line of defense before it is hit by contagion. Contingent credit will be advanced at an interest rate between 3 and 5% above other IMF loans to members (currently about 4.75%).’ 3 IMF facilities and their operations are reviewed in http://www.imf.org/np/exr/facts/howland.htm. 4 It is quite possible, however, that the very application for such facilities may signal that distress is more likely to be relevant in the future.

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tations and without rules stipulating conditions for utilization. Others have been lobbying for a tighter set of restrictions due to concerns over ‘moral hazard problems’. The new program is just the latest outcome of a more general debate that has been going on for many years over how the IMF should conduct its operations. At one extreme might be ‘spot arrangements’ under which the IMF waits until financial stress develops and then offers some sort of remedial credit provision. At the other extreme could be long-term credit lines, somewhat resembling long-term loan contracts and credit facilities that are common in the private sector. Until now, the existing IMF programs have included some elements of both these alternatives. Technically IMF financing has been provided through relatively shortterm (usually a couple of years or so) financing facilities. These, however, have usually been provided in response to emerging financial distress, and so resemble, in nature, the sort of after-the-fact spot rescue financing noted above. The implementation of the contingent credit lines indicates a shift in the direction of longer-term financing established before financial crises, rather than in their aftermath. This paper addresses the relative advantages and disadvantages of different forms of IMF financing. We will address two polar alternatives, ‘spot’ financing and longterm facility financing. As noted, the actual IMF financing arrangements to date contain some elements of each of these alternatives, and the introduction of the new contingent credit lines represents a movement away from the first prototype and in the direction of the second. The paper addresses the efficiency implications of the two financing modes and argues that the movement in the direction of longer-term IMF facility financing makes economic sense. This paper is organized as follows. In the next section, lending under commitment is reviewed and possible applications to IMF financing are elaborated. Following that, we model IMF lending formally. We discuss conditions under which IMF lending dominates private-sector lending. We then show that, under broad assumptions, lending through commitment dominates spot lending for both private-sector and IMF financing. It does so because it leads to superior welfare and resource utilization for the borrowing sovereign.

2. IMF financial contracting There has been debate over the ‘proper role’ of the International Monetary Fund ever since it was created.5 In particular, as sovereign debt markets have expanded there has been concern over the extent to which IMF lending may destabilize these markets. On the one hand, the IMF is presumed to act as a lender of last resort and provider of emergency financing to sovereign debtors, especially during times of crisis. On the other, there is concern that the operations of the IMF create moral hazard problems. That is, sovereign borrowers may over-extend themselves in debt

5

For recent reviews see Bird (1995); Guitian (1995); Krueger (1998) and Uzan (1996).

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markets and hence financial crises become more frequent or severe.6 As a result, resolving and controlling sovereign debt crises has become the subject of a large body of literature.7 One aspect of the functioning of the IMF that attracted relatively little attention until recently is the contractual form through which the IMF provides financing ‘of last resort’. On the one hand, it seems generally accepted that the IMF does not have a significant financial comparative advantage over private-sector lenders, such as in the costs of raising funds. Its ‘comparative advantage’ must lie in its political role of supporting economic stabilization and in providing emergency (subsidized) liquidity. In the absence of such ‘non-commercial’ considerations in lending decisions, it is doubtful whether the IMF would ever make loans. On the other hand, as a large lender the IMF transactions resemble—at least in part—comparable transactions by private-sector lenders, where loans are structured to take into account borrower behavior and risk-taking tendencies. This may explain in part the role of ‘conditionality’ in IMF lending. While acting from motivations that differ from those of commercial banks and similar private-sector lenders, there are advantages to the adoption and implementation of some private-sector lending practices by the IMF. In particular, there are advantages to the adoption of private-sector loan commitment contracting forms. In recent years a growing body of research has analyzed the roles of loan commitments in the private banking sector. The bulk of corporate borrowing from banks takes place through commitments, as do many other forms of private-sector financing. Under a loan commitment, a ‘line of credit’ is established in advance by the lender for use by the borrower, with loan terms (often floating rates) determined in advance and a quantity ceiling established for the amount of funds that may be so utilized. Theoretical and empirical analysis of commitment lending has been done in recent years by (among others) Avery and Berger (1991); Berkovitch and Greenbaum (1991); Boot et al. (1991); Campbell (1978); Duan and Yoon (1993); Ham and Melnik (1987); Martin and Santomero (1997); Melnik and Plaut (1986a), and Thakor and Udell (1987). Recently there has been some discussion about the possible adoption of loan commitment facilities by public-sector institutions. Goodfriend and Lacker (1999) have argued that central bank lending, including the operations of the discount window, could benefit from implementing loan commitment facility forms, including standard facility features such as covenants, collateral and monitoring. One of the main advantages of such financial arrangements (in their view) would be the establishment of credibility to lending ceilings established by the credit facilities provided by the

6

See Bulow and Rogoff (1990); Cassard and Folkerts-Landau (1997); Cline (1984); Cole and Kehoe (1998); Eaton et al. (1986); Krugman (1989) and Lindert and Morton (1989). 7 There is some interesting literature that deals with sovereign debt negotiations. Representative references are Bulow and Rogoff (1989); Eaton (1990) and Kenen (1990). In these models debt renegotiation in stressful circumstances involves debt restructuring and partial debt forgiveness. The interaction between bad debts and new loan to sovereign borrowers—who encounter debt-servicing problems—is discussed by Krugman (1988); Landskroner and Paroush (1993) and Paroush and Landskroner (1990).

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central bank. They argue that this could prevent the well-known problem according to which anticipation of central bank financing leads to over-lending by ‘insured’ or covered banks. This in turn forces the hand of the central bank to provide the expected financing.8 Many of these arguments could be extended to the operations of the International Monetary Fund and other international financial institutions. As is well recognized, the operations of the IMF are themselves a major source of international uncertainty and moral hazard (Calomiris (1998); Cline (1984); Eaton (1993); Rosenthal (1991)). The world community, including financial markets, cannot know in advance when and under which circumstances the IMF will intervene in the affairs of individual countries, how much financing will be advanced, and at what terms. Debtor countries themselves know they can rely on IMF ‘bailouts’, at least with some degree of probability. But they are not informed in advance what the limits to such bail-out financing will be. Hence a moral hazard problem arises by which ‘insured’ debtor countries may have motivation to over-extend themselves in terms of borrowing with the expectation that the IMF stands ready to intervene and eventually to rescue them. There are at least two distinct advantages to the adoption of loan commitment financing by the IMF as its principal mode of operation. The first is the same as that identified by Goodfriend and Lacker (1999) for central banks: namely, the communication in more credible terms of the limits of emergency liquidity to sovereign debtors that the IMF is willing to provide. It has been recognized in the literature that one reason for lending through commitments in the private sector is the attribution of credibility to lending limits (Boot et al. (1991); Duan and Yoon (1993)). If IMF financing took the form of a well-defined credit line, then the financial community would know where each debtor ‘stands’ in terms of its ability to tap IMF funds. This would reduce uncertainty, which creates potential instability in markets for sovereign debt. It would also act as a clear and unambiguous communication of IMF intent to the sovereign debtors themselves. Voters and taxpayers in borrowing countries would know ‘the rules of the game’ and when their own governments are becoming over-extended in debt markets. Since this commitment would have a declared limit, its revelation would serve to inform all market participants and they could alter their own behavior accordingly.9 The conditions and restrictions attached to provision of IMF emergency financing, including ‘conditionality’, would be spelled out in advance, much as are covenants and restrictions governing the operations of private-sector loan commitments. It is also possible that the cost of monitoring would be lower under facility lending. There is, however, a second advantage to using loan commitment facilities by the IMF that is not as obvious. It has already been noted in previous research that loan commitment facilities have different incentive structures from spot lending and result in different borrower behavior and different welfare results for borrowers. For 8 Holmstrom and Tirole (1998) also consider various contractual forms for governmental provision of emergency liquidity. 9 Goodfriend and Lacker (1999) make a similar claim for imposing limits on borrowing through the discount window facility.

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example, Melnik and Plaut (1986b) argue that loan commitment financing results in higher utility or profits (on average) for corporate borrowers, compared with spot borrowing. Other papers, such as Berkovitch and Greenbaum (1991), and Thakor and Udell (1987), have also noted the ‘welfare’ or efficiency gains from operations within the framework of loan commitments. Commitments reduce some aspects of uncertainty present in spot markets. Commitments with fixed interest rates eliminate interest risk, at least for ‘takedowns’ within the quantity limits of the contract. More commonly, under floating-rate commitments the contract eliminates leverage-rising markups and uncertain risk premia above the interest basis (such as LIBOR or prime). These changes in pricing alter borrower behavior and affect efficiency of resource allocation. For simplicity we are ignoring here problems with the representation of sovereign borrowings as similar to private borrowing. In reality there are likely to be political considerations involved in borrower demands as well as principal-agent issues at play. The assumption being used here that all borrowings by the country are welfareaugmenting for that country are, of course, challengeable and hardly unambiguous. Indeed, in the cases of some countries, the very decision to borrow might be best understood as an indicator that the country is already in financial distress. However our point here is to emphasize the ability to hedge uncertainty of future foreign exchange earnings using credit facilities of different forms, and so we will ignore the signaling aspect and these other complications of real-world utilization of facilities by sovereign borrowers.

3. A framework for modeling international lending 1. There are three ‘players’ in the model. The first is called the country, a sovereign borrower which is a potential customer of either the private banking system, the International Monetary Fund (IMF) or both (the other two players). The country has an endowment of income, which could be thought to represent its initial foreign exchange reserves. It faces stochastic earnings thereafter, representing its foreign exchange earnings. The second player is known as the ‘bank’, but in fact could be thought of as a composite representation of the private banking sector. The third player is called the IMF, and is an international institution that provides financial aid. 2. The model takes place over three periods, the middle one being that in which we are most interested. In period 0, the country receives an initial endowment equal to Y0 dollars. The country also decides on its initial debt position L0. This latter amount is the size of the 0-period borrowings from the bank, and the loan is for a single period. Default by the country is allowed only in period 2, the last or terminal period. So this initial one-period loan is never lost in default and will play a minor role throughout most of the discussion. At time 1, the bank advances the funds at the riskless interest rate r0. Hence ‘consumption’ during the period

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3.

4.

5.

6.

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time 0 is equal to C 0 = Y 0 + L 0, which is the foreign reserve budget constraint of the country at that time.10 At time 1, the initial loan must be paid back with interest (i.e. L 0(1 + r 0)) by the country to the bank. The country receives stochastic income Y 1ⱖ0 at this time, and may also borrow a second loan for the period from 1 to 2, to be called L1. The probability density function of Y1 is f{Y1}. If Y1 is insufficient to repay the initial loan, L0, it will always be repaid out of the new L1. We will consider various borrowing arrangements, where the lender will be either the bank or the IMF, and borrowing could be either in ‘spot loans’ or through commitments. In a more complex model, short-term financing could be distinguished from longterm facilities. Short-term debt could allow the lender greater flexibility in terms of ‘pulling the plug’ on borrowers pursuing problematic policies, as in Rodrick and Valesco (1999). In our simplified model, the loan L1 carries an interest rate r, which we will consider at length under different assumptions shortly. The rate r will depend on various assumptions and arrangements under which the loan is made. Consumption at time 1 by the country is C 1 = Y 1⫺L 0(1 + r 0) + L 1. We will restrict L0 and L1 to the positive range. That is, the country in our model is never a net lender in the international debt market. At time 2, either the loan L1 is repaid in full with interest or default occurs. The total amount of resources available to the country at time 2 is the stochastic Y2. Y2 is defined over the finite range 0ⱕY2ⱕY¯ , and f{Y2} is the probability density function for all values of Y2, such that the integral of f{Y2} over 0⫺Y¯ equals 1. For our purposes Y2 is assumed to be exogenous, and we ignore the moral hazard of having it and the default endogenous. The f function is assumed continuous and differentiable, and for simplicity Y2 is presumed to be independent of Y1.11 Whenever Y 2ⱖL 1(1 + r), the loan is repaid in full and the residual is ‘consumed’ by the country. If default occurs, all of Y2 is used to pay off part of the debt and none is available for consumption. Hence consumption at time 2 is C 2 = Max{0, Y 2⫺L 1(1 + r)}. The bank is risk neutral, all other players are expected welfare-maximizers. When both the bank and the IMF lend to the country, the loans made by the bank are always senior claims on the country. When both spot loans and loans under commitment are made, the spot loans are always junior to the latter, regardless of who is the lender. When default occurs, the lender loses out-of-pocket the excess of the loan plus interest above Y2. But there are also negative impacts on the country itself and on the IMF. The latter is assumed to have a welfare function (W) it seeks to maximize, where the amount of funds lost in default appears as a negative argu-

10 Strictly speaking this is not consumption of all domestic and imported resources, but rather only foreign exchange purchases. We ignore consumption of domestic goods in the model. 11 If Y1 and Y2 are positively correlated, this would mean that when income drops in period 1 the probability of default in period 2 increases. Under such circumstances, the country can be shown to prefer borrowing under commitment more so than under the simpler assumption of independence. See discussion below.

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ment. In effect, this may be regarded as the capture of all ‘spillover’ effects or externalities caused to the international economy from default (such as risk of ‘chain reaction’ collapses in banks or other effects outside the lending institution taking the direct loss). The country also has a welfare function (U) that depends negatively on the magnitude of default, but for different reasons. The negative impact of default in U is regarded as capturing all future damages and consequences to the country from the default, such as loss in reputation or loss of access to world credit markets in the future. Hence the partials of U and W with respect to default D are negative, but differ from one another. The time framework of the model is summarized in Fig. 1. Formally, the welfare function of the country is: U ⫽ U{C0, C1, C2, D},

(1)

where the C’s are the consumption levels at time 0, 1 and 2, respectively, and D is the amount of funds in default at time 2. In the event of default, C2 is zero. All first partials of U with respect to the Cs are positive, the first partial with respect to D is negative, and all second partials are negative. Note that C0 ⫽ Y0 ⫹ L0, C1 ⫽ Y1⫺L0(1 ⫹ r0) ⫹ L1 ⫽ Y1⫺(C0⫺Y0)(1 ⫹ r0) ⫹ L1 C2 ⫽ Max{0,Y2⫺L1(1 ⫹ r)] ⫽ Max{0,Y2⫺L0(1 ⫹ r0) ⫹ (C1⫺Y1)(1 ⫹ r)} ⫽ Max{0,Y2⫺[(C0⫺Y0)(1 ⫹ r0) ⫹ (C1⫺Y1)](1 ⫹ r)} The IMF is assumed to have a welfare function W equal to: W ⫽ W{U,D} ⫹ Q

(2)

where U is the country’s welfare level defined in (1), D is the amount of funds lost in default at time 2, should the country in fact default on some of its obligations. Q is the amount of ‘income’ the IMF will realize from its lending activities to the country. The first partial of W with respect to U is positive and the first partial with respect to D is negative. The second partials with respect to U and D are negative. Q plays a role for the IMF roughly analogous to the role of bank income for the bank, where the IMF is ‘risk neutral’ with respect to its own cash flow, other things being equal.

Fig. 1. Time framework of the model.

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If W{U,D} were always zero, the IMF would behave exactly like the privatesector bank. In other words, we assume the IMF has no special financial advantage, such as in terms of its cost of funds, over the bank. It behaves differently from the bank due to this W function. In general, the W function could be either positive of negative. The presence of U as an argument within W is in a sense the raison d’eˆ tre of the IMF; the IMF plays a sort of ‘welfare’ function internationally, by which it seeks to enhance the national utility of the country. Without this role, the IMF would never participate in lending to the country. The IMF’s income, Q, could be a negative amount if the IMF were to lend funds that are not repaid, due to default by the country. If all funds borrowed by the country are from the private-sector bank only, then Q = 0. There is no ‘budget constraint’ as such on the IMF, in the sense of a liquidity constraint, although any funds lent by the IMF have opportunity costs or alternative returns equal to r0. If the IMF lends funds to the country at time 1 in the amount L1, charging interest rate r1, and if it is repaid in full at time 2, then Q = L 1(1 + r 1⫺r 0). If any funds are lost due to default on IMF loans, Q would be adjusted accordingly. Finally the bank, as noted, is assumed to lend in period 0 for one period at the riskless interest rate r0 for one-period loans. For the second period, from 1 to 2, default risk is present. In that case, banks always price loans such that the expected profit from the loan minus its opportunity costs is zero. The bank refuses to lend at all unless the expected profit equals the return it could have had from riskless lending.

4. ‘Spot’ loan markets Let us first consider ‘spot loan’ markets, where the country must approach either the bank or the IMF (or both) at time 1 for financing that initiates at time 1 and ends at time 2. ‘Spot loans’ are those contracted on the spot, which here will mean after Y1 is revealed. First, let us consider the option of bank financing. 4.1. Bank financing The bank is risk neutral. As noted, it lends at the riskless rate at time 0, but lends at a higher rate at time 1 due to risk. Bank income is L 1(1 + r), whenever Y2 is larger than this amount and Y2 otherwise. Hence expected bank income is: E[P] ⫽

冕

L1(1 ⫹ r)

0

Y2 f{Y2}dY2 ⫹

冕

⬁

L1(1 ⫹ r) f{Y2}dY2

(3)

L1(1 ⫹ r)

where f{} is the probability density function of Y2, and where E is the expected value operator. Bank profits must take into account the opportunity costs of the funds loaned, assumed to be measured by the riskless rate. This is equivalent to saying that E[P] ⫽ Pr{Def}ED(Y2) ⫹ Pr{Pay}L1(1 ⫹ r) ⫽ L1(1 ⫹ r0),

(4)

where Pr{Def} is the probability of default occurring, Pr{Pay} is 1⫺Pr{Def}, where

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ED is the expected value conditional on default occurring, and EP is the expected value conditional on default not occurring. The right hand side of (4) is the opportunity or alternative investment, at the riskless interest rate, and the left hand side is the expected income from the loan. Rearranging terms, (4) may be rewritten E[P] ⫽

冕

冕

L1(1 ⫹ r)

[Y2⫺L1(1 ⫹ r0)]f{Y2}dY2 ⫹

0

⬁

(5)

[L1(r⫺r0)]f{Y2}dY2 ⫽ 0.

L1(1 ⫹ r)

Eq. (5) says the bank’s income is equal to the default loss in states where default occurs (the difference between Y2 and the opportunity cost of the funds loaned) plus net profits in non-default states based on the difference between r and the opportunity cost rate r0. For a given f{} function, total differentiation of (5) yields the loan-specific interest offer curve provided by the bank ⫺[(1 ⫹ r)Pr{Pay}⫺(1 ⫹ r0)] [Pr{Def}EDY2] dr ⫽ ⬎ 0. ⫽ dL1 L1Pr{Pay} Pr{Pay}L21 Here

冕

Pr{Def}

is

the

probability

that

default

will

occur

(6) and

equals

L1(1 + r)

f{Y2}dY2; and Pr{Pay} is the probability that default will not take place and 0

so is equal to 1⫺Pr{Def}. The last equality before the inequality sign follows from (4). The entire expression must be positive, meaning the bank charges a rising risk premium as the loan size increases. The slope of the curve becomes infinite when L1 reaches Y2, because Pr{Def} becomes 1. The bank spot loan offer curve is shown in Fig. 2. The offer curve is a convex function of L1. It becomes vertical when L1 approaches Y¯ . Beyond that point, banks will not lend at any interest rate because they know that they will not be repaid by the country for any addition to the loan. 4.2. IMF loans Next, let us consider the supply function for IMF loans. IMF loans will be priced differently from loans made by the bank for two reasons: The IMF’s welfare function explicitly takes into account the welfare level U of the country as an argument in its own welfare function W, and it also includes the amount of funds lost in default D as a separate argument in the same function. Assume that the bank makes no loans for the moment and all loans are made by the IMF only. Assume also that in providing IMF funding, the IMF must always maintain EW ⫽ EW{U, D} ⫹ E Q ⫽ W0.

(7)

Here E is, again, the expected value operator, and W0 is a given level of expected

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Fig. 2.

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Spot offer curves of bank and IMF.

‘welfare’, perhaps imposed upon the IMF by its sponsors or members from the international community (which play no role here other than management of the IMF). The total differentiation of Q in (2) yields exactly the same expression as (6). The total differentiation of the entire expected W function, holding W equal to W0, would then be the expected value of

冋

册

冋

册

∂U ∂D ∂W ∂U ∂U∂D ∂W ∂D ∂W∂D ∂W ∂U ⫹ dL1 ⫹ dr ⫹ dL1 ⫹ ⫹ dr ∂U ∂L1 ∂D∂L1 ∂U ∂r ∂D ∂r ∂D ∂L1 ∂D ∂r ⫹

(8)

∂Q ∂Q dL1 ⫹ dr ⫽ 0 ∂L1 ∂r

Replacing some of the terms in (8) with their numerical expressions would yield the expected value of

冋

册

冋

册

∂U ∂W ∂U ∂U ∂W ∂W ∂U ⫹ (1 ⫹ r) dL1 ⫹ ⫹ L dr ⫹ (1 ⫹ r)dL1 ∂U ∂L1 ∂D ∂U ∂r ∂D 1 ∂D ⫹

(9)

∂W L dr⫺[Pr{Def}ED(Y2) / L1]dL1 ⫹ L1Pr{Pay}dr ⫽ 0 , ∂D 1

where the probabilities Pr{Def} and Pr{Pay} are defined as before. In the special case where the partials of W with respect to U and D vanish, Eq. (9) reduces to Eq. (6). More generally, the total derivative dr/dL1 for IMF loans is now equal to

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dr ⫽ dL1

冋 冋

册

册

∂U ∂W ∂W ∂U ⫹ (1 ⫹ r) ⫺(1 ⫹ r) ∂U ∂L1 ∂D ∂D . ∂W ∂U ∂U ∂W L1E Pr{Pay} ⫹ ⫹ ⫹ ∂U ∂r ∂D ∂D

Pr{Def}ED(Y2) / L1⫺E

冋

冉

冊 册

(10)

∂U ∂U will be developed below. and ∂L1 ∂r Proposition 1 follows directly. Proposition 1: The IMF offer curve could in general lie above or below the bank offer curve, and its curve could be either steeper or flatter than the latter’s in different ranges. Proof: Eq. (10) differs from Eq. (6) due to additional terms in the numerator and denominator. The denominator in (10) is smaller than the denominator in (6) due to the extra terms that take into account the additional impact of increases in interest rates on W (because of their impact on U and D). The numerator of (10) also includes additional terms, compared with the numerator of (6), capturing the impact on W of changes in L1 that operate through U and D. The last term in the numerator must be positive, but the term in the middle of the numerator has an ambiguous sign. Hence, on net, the expression in (10) could be either higher or lower than that in (6). The IMF offer curve is illustrated in Fig. 2. Another way to put this is to note that the gap between the bank’s and the IMF’s offer curves in Fig. 2 is precisely W{U, D} from Eq. (2). Whenever W{U, D} is a positive (negative) value, the IMF offer curve lies below (above) the bank’s offer curve. As both positive and negative values of W{U, D} are permitted, there may be regions over which the one offer curve sometimes lies above and sometimes below the other. The IMF offer curve differs from the bank’s in other ways as well. It does not necessarily become infinitely sloped when L1 = Y¯ , unlike the bank curve. Indeed, proposition 2 follows directly from this. Proposition 2: It is possible that the IMF will offer funds at finite lending rates even beyond the amount Y¯ (the highest possible income for the country in period 2). Proof: This is lending where—at the margin—it is certain that the funds will be lost in default. The reason for this has to do with the ‘welfare/aid’ role being played by the IMF, that is, by the presence of U within the W function in (2). An additional dollar could be loaned by the lender such that—with added interest—the debt of country would amount to more than the highest possible value of income in period 2 or Y¯ , making the loss of that dollar a certainty. But if the increase in utility to the country and the partial of W with respect to U are sufficiently high, the IMF will still knowingly make this ‘loan’, ensuring the loss of its funds through default. Formal expressions for

4.3. The presence of both bank and IMF lending In the event that both the bank and the IMF offer loans, obligations by the country to the bank are assumed always to have a senior claim on the resources of the country, and so the IMF’s loans are always junior. The country presumably will always take out loans from the cheaper supplier. It is possible that some loans will

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be taken initially from the bank, with additional funds borrowed from the IMF (as suggested in Fig. 2). We noted above that, in general, the position of the IMF offer curve relative to the bank’s curve is ambiguous. When both are together in the market, the country will utilize IMF loans only if they are cheaper than private-sector loans. So we will never see both lenders in the market unless the IMF offer curve lies below the bank’s curve, at least in the relevant region. Because of the seniority of private-sector loans, IMF loans will be priced ‘at the margin’, based on risk and default rates that bear in mind the presence of the senior bank loans. This is illustrated in Fig. 3. If the bank lends LB to the country at time 1, the loan will be priced according to the bank’s simple offer curve. If the IMF then lends LF beyond that, this loan will be priced as if the IMF had in fact lent on its own the entire L B + L F principal, that is, where each dollar advanced is priced at the margin as if all previous dollars had come only from the IMF. In terms of the figure, it is as if the IMF’s offer curve is truncated, and the vertical axis shifts to run through LB. 4.4. Demand for loans by the country The demand curve for the country may be derived by taking the total differendr functions defined in (6) tiation of the U function in (1) and bearing in mind the dL1 and (10). The first order conditions for maximizing U, subject to the various budget constraints, are:

Fig. 3.

Borrowing from both lenders.

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∂U ∂U E ⫽ (1 ⫹ r0)E and ∂C0 ∂C1

冋

册冋 冉 冊册

冉 冊

冉 冊册

∂U ∂U dr ∂U ∂U ⫺(1 ⫹ r)E ⫹ (1 ⫹ r) ⫹ L1 Pr{Def}ED ⫺Pr{Pay}EP E ∂C1 ∂C2 dL1 ∂D ∂C2

冋

∂U ∂U ∂U E ⫺(1 ⫹ r)q E ⫹ Pr{Def}ED ∂C1 ∂C2 ∂D

⫽

⫽0 (11)

L1 dr , and is in effect the elasticity of supply of the interest ratewith (1 + r)dL1 respect to the loan size, along the relevant offer curve. The term with the θ indicates that the country faces an upward sloping loan offer curve. There will be different values of θ for the bank and the IMF offer curves, reflecting the different expressions in (6) and (10). As noted before, it is ambiguous which will be the higher.12 ∂U ∂U ∂U It should also be noted that E = E ⫺(1 + r)E and ∂L1 ∂C1 ∂C2 ∂U ∂U ∂U = ⫺L1Pr{Pay}EP(L1) E + L1Pr{Def}ED , and these may be substituted into ∂r ∂C2 ∂D Eq. (10). The demand curve for loans at time 1 is shown in Fig. 4. The amount of funds Here q = 1+

冉 冊

Fig. 4.

12

Offer curves for loan commitment facilities.

The last term in Eq. (11) resembles somewhat the ‘marginal factor cost’ expression in the monopsony maximization equation. From second-order conditions, it can also be shown that when optimizing, L1 always moves in the opposite direction from Y1.

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demanded is lower than the amount that ordinarily would be demanded by a simple price-taking borrower, equating the expected marginal rate of substitution in utility to a fixed interest factor. There are two reasons for this. Since the country faces an upward-sloping offer curve, it looks at the marginal cost of funds (somewhat like a monopsonist looks at ‘marginal factor cost’) and not merely the interest rate, and this is captured in the θ term. In addition, the country is concerned with possible default D and this lowers the marginal utility from borrowing. At the optimum the UU curve in Fig. 4 is set equal to the marginal financing costs (MFC) curve, which is derived from the offer curve, and equals (1 + r) θ. Note that the position of the UU curve depends upon, among other factors, the value of Y1, the income of the country during period 1. When Y1 increases (decreases), other things equal the demand for L1 decreases (increases). This variation will play an important role shortly in the discussion of loan commitment contracts.

5. Borrowing under loan commitments We will now alter the assumptions concerning the manner in which time 1 lending takes place. Let us assume that at time 0, the country signs a commitment contract with either the bank or the IMF or both. In this contract, the lender agrees to provide funds up to some limit, to be called Lˆ , at a fixed interest rate to be called r∗ (see Fig. 5). The country cannot borrow funds beyond Lˆ under the contract. It is free, however, to go into the spot market, in which case spot loans would presumably be priced ‘at the margin’, based on Eqs. (6) or (10) for spot loans from the bank or IMF, respectively.13 For simplicity, the pricing of the commitment or credit line will

Fig. 5.

Offer of funds within a commitment facility.

13 To avoid situations where the country first borrows spot below r∗ and only then utilizes the commitment contract, spot loans are presumed always to be junior to funds taken under commitment.

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be assumed to be unidimensional, with no facility fee as such, merely the interest rate.14 Let us begin with bank loan commitments alone. The bank will provide commitments such that the following condition holds:

冕冕 冕冕 ˆ L

¯ Y

0

L1(1 ⫹ r)

ˆ L

L1(1 ⫹ r)

0

0

L1(r∗⫺r0)f{Y2}dY2h{L1}dL1 ⫹ (12)

(Y2⫺L1(1 ⫹ r0))f{Y2}dY2h{L1}dL1 ⫽ 0

or

再 冕

冎 冕

ˆ L

E Max Y2,

ˆ L

L1h{L1}(1 ⫹ r∗)dL1 ⫹ E

0

(Lˆ ⫺L1)h{L1}(1 ⫹ r0)dL1

(12⬘)

o

⫽ Lˆ (1 ⫹ r0). Here h{} is the probability density function of L1. It is based on the borrower maximizing conditions to be developed shortly, and depends on Y1. Eq. (12) says that the profits of the bank from funds utilized under the commitment, plus the profit from funds not so utilized (assumed invested at the riskless rate of r0) must be equal, on average, to the profits from investing the entire Lˆ at the riskless rate. Totally differentiating (12) yields the ‘offer function’ for loan commitments:

冋 册

∂P ∂L1 [(1 ⫹ r )Pr {Pay}⫺(1 ⫹ r0)] dr ⫽⫺ ⫽ ˆ ∗ ⬎ 0. ∗ ˆ d(L) Pr {Pay} LPr {Pay} ∗

∗

∗

E∗

(13)

Here E∗ and Pr∗ indicate the expected value and the probability (respectively) conditional on L1 equaling Lˆ (the full commitment being drawn down). Eq. (13) is roughly analogous to (6), except that here we are showing the ‘facility offer curve’ for commitments rather than the offer curve for spot loans. For IMF commitments, the derivation is similar, except that the same terms added to (6) to produce (10) must also be added to the equation here.15 The ‘facility offer curve’ for the IMF is:

14

Real-world commercial and other lines of credit generally use two-part pricing where facility fees are charged in addition to interest (see for example Berger and Udell (1995); Melnik and Plaut (1986b) and Schockley (1995)). 15 For simplicity we will ignore cases where the country has two commitments, one from the IMF and one from the bank.

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dr∗ ⫽ d(Lˆ )

475

(14)

冋 冋 冉

册

册

∂U ∂W ∂W ∂U (1 ⫹ r∗)Pr∗{Pay} ⫹ (1 ⫹ r0)⫺E ⫹ (1 ⫹ r) ⫺(1 ⫹ r) ∂U ∂L1 ∂D ∂D ⫺ ⬎ 0. ∂W ∂W ∂U ∂U ∗ Lˆ Pr {Pay} ⫹ ⫹ ⫹ ∂U ∂r ∂D ∂D

冋

冊 册

Eq. (14) stands to (13) as does (10) to (6). Note that the conditions under which (14) is smaller (flatter) than (13) are roughly the same conditions as those for comparing between the two offer curves for spot loans. Since the ‘added’ terms to (14) are the same as those in (10), it is approximately correct to say that whenever the IMF dominates bank lending in the spot market, it will also do so in the commitment market. The offer curves for loan commitment facilities are illustrated in Fig. 6. They resemble, but are not the same as, the spot offer curves. 5.1. Demand for commitment facilities by country For borrowing within an existing facility the demand for funds is described by the same first-order conditions as were found in eq. (11). The interest rate used would be r∗, because the offer curve is flat within the confines of the commitment; the q term reduces to 1 for utilization of commitment up to the limit of Lˆ . We now turn to the selection of commitments themselves. The first-order condition for maximizing expected country utility, and hence the condition describing the demand for credit facilities contingent on this form of facility having been chosen, can be derived from (1) as:

Fig. 6. Supply and demand for loan facilities (optimal IMF facility shown).

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冋

冉

冊册

∂U ∂U ∂U Pr{L1 ⫽ Lˆ } E ⫺(1 ⫹ r∗)q E ⫹ Pr{Def}ED ∂C1 ∂C2 ∂D

⫽ 0.

(15)

Here the θ value selected will be that from either (13) or (14), depending on whether bank of IMF financing, respectively, is being used. The expression in (15) differs from (11) only in the definition of θ and the use of r∗ instead of r.

6. Comparison between spot and commitment financing Because of the way we have modeled lender behavior, the bank ultimately derives the same levels of expected profit regardless of its lending arrangements and the IMF receives the same levels of expected welfare regardless of its lending arrangements. Thus the interesting welfare comparison is for the country. This brings us to the paper’s main finding. Proposition 3: Regardless of whether the bank or the IMF is acting as lender, the country is always at least as well off using commitment facilities as it would be under spot financing. Proof: The proof is somewhat complex and will be argued in stages. The proof is based on the following argument. Suppose that the demand curve for funds by the country at time 1 were non-stochastic. Since its position would be known by all in advance, any ‘commitment’ offered to the country by either lender would effectively be the same thing as a spot loan. In this case, the borrowing ceiling (Lˆ ) purchased by the country would be the same as the amount to be borrowed de facto. The supply curve for facilities would be the same as that for spot loans and the facility would always be fully drawn down. Hence, in this special case, the welfare of the country would be the same regardless of whether it used spot or facility financing. Having noted this, proposition 3 would be proved if we could show that whenever the variance of the position of the demand curve of the country increased, the relative advantage of facility financing over spot borrowing would increase. This is precisely what we shall now prove. Before doing so, let us define an alternative and simplified reduced representation of the welfare function of the country, which may be used to describe time 0 decisions. It is based on all known information as of time 0 and on decision variables controlled at that time (that is, whether to borrow under commitment or through the spot market at time 1). It can be used to describe the amount of funds to be borrowed at time 1, and it depends on the still unknown incomes Y1 and Y2. We shall denote this new representation as w{L1,Y1,Y2), where w is a reduced representation of U in (1). The country maximizes w subject to the loan pricing constraints under various financing modes. Let us first examine the demand function for funds during period 1. To derive this, we must take the first partial of w with respect to L1. This is in effect the ‘marginal utility’ to the country of an additional dollar in utilized financing, and takes into account the impact of debt on default chances and losses from D. The partial will be written w = l{L 1,Y 1}, meaning that the marginal utility is a function

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477

of the amount borrowed and period 1 income. l is assumed to be a negative function of both arguments, meaning that marginal utility of funds borrowed falls (rises) when the principal and when period 1 income increase (decrease). In the case of ‘financial distress’, Y1 will drop to ‘very low values’ and the country’s demand for credit will be ‘very high’. In the case of borrowing facilities, the elasticity of the interest rate (or θ⫺1) would equal zero as long as borrowing is confined to utilization of facility funds alone, and the interest rate r∗ would be the relevant facility interest rate. In the case of spot financing, (1 + r) θ would be the marginal cost of an extra dollar borrowed by the country from the relevant lender. The l function traces out the demand curve UU as shown in Fig. 6. Expected utility is maximized when l is set equal to the marginal cost of funds. While Y1 is restricted to the non-negative range, it will prove useful if the w and l functions are defined for negative values of Y1 as well. Now in order to prove our proposition we need only to show that the country’s expected welfare is higher within the range of the borrowing facility (up to Lˆ at a rate of r∗), compared with spot borrowing over the same range. The reason for this is that, given that facility debt is always senior to spot debt, should the borrowing country return to the spot market after fully drawing down its facility, the terms for additional funds at the margin are the same whether or not a facility was used for the first Lˆ dollars borrowed. Hence the entire proposition rests on comparing country expected welfare under facility and spot financing for the borrowing range up to Lˆ . Under spot borrowing alone, up to a maximum of Lˆ borrowed, the expected welfare ‘surplus’ of the country would be

冕冕 ¯ Y

ˆ L

0

0

(max[l{L1,Y1}⫺(1 ⫹ L1)q],0)dL1 g{Y1}dY1,

(16)

and the expected welfare ‘surplus’ from facility borrowing only would be

冕冕 ¯ Y

ˆ L

0

0

(max[l{L1,Y1}⫺r∗],0) dL1g{Y1}dY1,

(17)

where r∗ is the interest rate for facility lending, and where r and r∗ must satisfy Eqs. (6) and (13) for bank lending, or Eqs. (10) and (14) for IMF lending. Welfare ‘surplus’ here is defined in a manner equivalent to consumer surplus in microeconomics, and captures the net welfare of the country above the costs of financing. The remainder of the proof of the proposition holds regardless of whether bank or IMF financing is being used. Let us define GAP as the difference between expression (16) and (17), and so is the difference in country welfare surplus under the two financing modes. Let us also define Z 1 = aY 1 + (1⫺a) E(Y 1), and replace all Y1 in the resulting expression with Z1. The parameter aⱖ0 is a transformation parameter; when a = 1, then Z1 reduces to Y1. Z1 is a transformation of Y1, having exactly the same expected value, but with variance equal to a2 times the variance of Y1. By evaluating the partial of GAP with

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respect to a, we capture the effect of increasing the variance of Y1, other things being equal. Now we have already noted that in the special case where this variance is zero (when a = 0), spot and commitment financing are equivalent, meaning that GAP would be zero. In that case the two financing arrangements are equivalent. In all other cases, including when a = 1, the partial of GAP with respect to a shows how increasing variance affects the relative advantage of facility financing over spot financing. The partial of GAP with respect to a can be shown to be exactly the same expression GAP, but evaluated where Y1 is replaced with Y 1⫺E(Y 1) in (16) and (17). In other words, the partial has the same sign as would GAP itself when deducting E(Y1) across the board (in all states of nature) from Y1. Now at a = 0, we know the GAP is zero, and the partial also has zero sign. But for any value of a larger than zero, the GAP must be positive. This is because deducting income in the amount of E(Y1) from the income level in each state of nature must raise the demand for funds in each state of nature. It causes an upward shift in UU of Fig. 4. Since the interest rate is fixed under the facility, but rises with demand under spot lending, then interest rates for spot loans must always be considerably higher if income were to be reduced across the board by E(Y1). This implies that borrowing must drop by a greater amount under spot lending than under facility lending if E(Y1) is deducted across the board from income, lowering expected welfare for the spot welfare function more so than for the facility function. The partial of GAP with respect to a must therefore be positive for all a ⬎ 0. This means that the relative advantage of facility financing rises with variance.16

7. Concluding comments A major problem in recent ‘bailouts’ in east Asia and elsewhere has been the ambiguity in terms of the magnitude and extent of the commitment of international institutions (especially the IMF). These institutions did not specify how far they would ultimately go in providing liquidity to sovereign powers in distress and how quickly. Arranging international emergency financing through long-term credit facilities would eliminate much of this uncertainty, and would then allow private-sector lenders to make more informed and careful decisions. It would eliminate much of the financial and political uncertainty currently plaguing the international emergency financial arrangements. One important benefit from creating well-defined IMF facility size is to convey 16 We have left out of the discussion the impact on facility size selected at time 0 from the raising of a. In fact, facility size rises when variance of period 1 income rises, but it can be shown that this only strengthens the conclusion of the proposition. The intuition is that when variance rises, the relative advantage of an unchanged facility size improves, and keeping the old unchanged facility size is only one borrowing country option. By transitivity and revealed preference, if any new value for facility size is chosen, country welfare must have improved even more so than when facility size remains unchanged.

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information to the markets, information that reflects the IMF’s own cumulative monitoring activity. A better indicator regarding future actions by the IMF can lead to a superior level of investment in the private sectors of borrowing countries. Publically enunciated limitations to future IMF lending to a member country would convey valuable information to creditors and may improve the timing of lenders’ decisions, such as when to file for bankruptcy. Of course, the most significant role of defining the limits IMF’s commitment would be regarding the borrowing behavior of sovereign debtors. Provision of emergency liquidity through loan commitments by those international institutions serving as emergency lenders of last resort has a number of advantages. It reduces uncertainty about the behavior of the international institutions themselves in times of emergency. It also acts as a better, faster and more stable source of emergency funding to sovereign debtors facing financial crises. Furthermore, it allows the sovereign debtors themselves to decide how much emergency backing is ‘enough’, and how much backup financing to purchase from international institutions. This in turn would increase the credibility of the claims of international institutions that their willingness to extend emergency financing is limited to specific quantities, and this may reduce moral hazard problems that have long plagued sovereign debt markets. Debtors could also signal their intentions to the private sector by increasing and decreasing the magnitude of their emergency facilities. There were two main themes in this paper. The first is that international lending institutions would have no financial role to play in sovereign debt markets unless they are prepared to play a ‘welfare’ role in aiding sovereign countries facing financial distress. While this idea may seem straightforward, the implications are not always well thought through. Lending to countries in financial distress is almost by definition lending at subsidized terms, and it is lending that increases the total amount of funds at risk should the debtor country in question default. Such a danger is unavoidable unless international institutions are to cease altogether playing the roles of lenders of last resort to sovereign debtors or sources of emergency liquidity to countries in distress. The second theme is that there are technical advantages to providing emergency liquidity facilities through the IMF in the form of well-defined long-term credit lines (or financing facilities) of the sort that were introduced by the IMF’s board in April 1999. As was shown, without adversely affecting the objective function of the international institutions, such arrangements can lead to welfare improvements for the sovereign borrowers, at least whenever the funds are used for economically justified projects. These borrowers can access their credit facilities at terms that are well defined and where risk premia are flat within the range of the commitment. This improves their domestic economic welfare and resource allocation, while at the same time lowering uncertainty for all, i.e. for both the sovereign borrowers and for financial institutions. In particular, it allows sovereign borrowers facing financial crises to draw down their emergency credit lines at fixed risk premia, without being forced to pay much higher premia in the spot market. The picture is, of course, more complex if the borrower is already in financial distress when signing up for such a facility. The advantages of long-term commitment financing are valid for private-sector

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lending, as well as for lending by international institutions. But sovereign borrowers are already free to purchase credit commitments in private markets. The international institutions have tended to act as emergency ‘spot lenders’, with all the uncertainty and damage that this implies. In effect, we are arguing that the IMF and other international institutions should provide products more closely structured like privatesector financial facilities.

Acknowledgements We are grateful to Amit Boniel, Dominik Egli, Yoram Landskroner, Sylvia Marchese and Claudia Rosett, for useful ideas and comments. An earlier version was presented at the 14th Annual Congress of the European Economic Association, Santiago de Compostela 1999. We are particularly grateful for the comments and suggestions of an anonymous referee and the editor, James Lothian.

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