Preferred and non-preferred creditors

Cordella, Tito; Powell, Andrew Working Paper Preferred and non-preferred creditors IDB Working Paper Series, No. IDB-WP-1215 Provided in Cooperation with: Inter-American Development Bank (IDB), Washington, DC Suggested Citation: Cordella, Tito; Powell, Andrew (2021) : Preferred and non-preferred creditors, IDB Working Paper Series, No. IDB-WP-1215, Inter-American Development Bank (IDB), Washington, DC, https://doi.org/10.18235/0003109 This Version is available at: https://hdl.handle.net/10419/237494 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by-nc-nd/3.0/igo/legalcode Preferred and Non-Preferred Creditors Tito Cordella A ndrew Powell IDB WORKING PAPER SERIES Nº IDB-WP-1215 March 2021 Department of Research and Chief Economist Inter-American Development Bank March 2021 Preferred and Non-Preferred Creditors Tito Cordella* A ndrew Powell** * World Bank ** Inter-American Development Bank Cataloging-in-Publication data provided by the Inter-American Development Bank Felipe Herrera Library Cordella, Tito. Preferred and non-preferred creditors / Tito Cordella, Andrew Powell. p. cm. — (IDB Working Paper Series ; 1215) Includes bibliographic references. 1. Debtor and creditor-Econometric models. 2. Financial institutions, International- Econometric models. 3. Debt relief-Econometric models. I. Powell, Andrew (Andrew Philip). II. Inter-American Development Bank. Department of Research and Chief Economist. III. Title. IV. Series. IDB-WP-1215 Copyright © Inter-American Development Bank. This work is licensed under a Creative Commons IGO 3.0 Attribution- NonCommercial-NoDerivatives (CC-IGO BY-NC-ND 3.0 IGO) license (http://creativecommons.org/licenses/by-nc-nd/3.0/igo/ legalcode) and may be reproduced with attribution to the IDB and for any non-commercial purpose, as provided below. No derivative work is allowed. Any dispute related to the use of the works of the IDB that cannot be settled amicably shall be submitted to arbitration pursuant to the UNCITRAL rules. The use of the IDB's name for any purpose other than for attribution, and the use of IDB's logo shall be subject to a separate written license agreement between the IDB and the user and is not authorized as part of this CC-IGO license. 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The opinions expressed in this publication are those of the authors and do not necessarily reflect the views of the Inter-American Development Bank, its Board of Directors, or the countries they represent. http://www.iadb.org 2021 Preferred and Non-Preferred Creditors Tito Cordellayand Andrew Powellz March 15, 2021 Abstract International …nancial institutions (IFIs) generally enjoy preferred creditors treatment (PCT). Although PCT rarely appears in legal contracts, when sovereigns restructure bilateral or commercial debts they normally pay IFIs in full. This paper presents a model where a creditor, such as an IFI, that can commit to lend limited amounts at the risk-free rate and can refrain from lending into arrears is always repaid and adds value. The analysis suggests that IFIs and market lenders can both enhance welfare, even if banning commercial borrowing can sometimes be optimal. To maintain their status, preferred lenders should o¤er low cost …nancing in volumes that are consistent with countries’incentives to repay even in bad states. This suggests such lenders should not di¤erentiate lending interest rates according to risk and should not participate in the restructuring of commercial debt. JEL Classi…cation Numbers: F34, H63, O19, P33. Keywords: Preferred Creditor Treatment, Preferred Creditor Status, Sovereign Debt, Sovereign Defaults, International Financially Institutions, Emergency Financing. We would like to thank Shanta Devarajan, Aitor Erce, Paolo Garella, Bernardo Guimaraes, Aart Kraay, Leonardo Martinez, Alessandro Missale, Andy Neumeyer, Ugo Panizza, Anushka Thewarapperuma, Vasileios Tsiropoulos, Harold Uhlig, as well as participants at the 2018 ESM Workshop on “Debt sustainability: Current Practices and Future Perspectives,”at the DebtCon3 conference at Georgetown University, at the 2019 World Bank ABCDE conference, and at seminars at the University of Milan, at the IDB and the IMF, for many thoughtful suggestions. A particular thanks goes to Fernando Broner, our editor in charge, and to two anonymous referees for their constructive comments. The usual disclaimers apply. yThe World Bank, [email protected] zInter-American Development Bank, [email protected] 1 Introduction The role of international …nancial institutions (IFIs) in the global …nancial architecture has been widely analyzed both by academics and by the international policy community.1Much has been discussed about their role as providers of emergency funding but a long-standing central puzzle remains. Namely, the International Monetary Fund (IMF) and the main multilateral development banks (MDBs) enjoy Preferred Creditor Treatment (PCT) in relation to their sovereign lending, meaning that they are expected to be repaid even if the borrower restructures private or bilateral debt. And yet, while PCT is critical for the operating model of IFIs, and the Paris Club Agreed Minutes exonerate IFIs from a “comparability of treatment”clause, their preferred standing is not strongly backed in international law.2 At times, the preferred treatment of IFIs has been called into question. For example, Greece fell into arrears with the IMF in July 2015.3On August 28, 2019, the Argentine economy minister announced the intention to repro…le domestic and external debt and appeared to include amortizations to the IMF.4Still, during the prolonged “trial of the century”following Argentina’s 2002 default, the outstanding debts to the IMF were paid early and in full. Indeed, it is notable in that case that while there were many attempts from hold-outs to disrupt payments to creditors that accepted the 2005 restructuring and subsequent o¤ers, there was virtually no mention of Argentina’s preferred lenders, nor any serious attempt to crowd them in.5 And in several recent bond restructurings, including Argentina’s in 2020, private creditors su¤ered changes in contracts and present-value haircuts, but IFIs continued to be paid in full.6 The persistence of IFIs’ preferred-standing is intriguing, especially given that it is a market practice, which is not backed by any contractual clause. The resilience of PCT, together with the lack of any strong legal foundation, suggests that it should be understood as an “equilibrium outcome.”And yet we know of no economic model to date that shows this to be the case. Sovereign debt models that focus on “willingness to pay”do not consider seniority,7while those that focus on seniority8assume it, without explaining its origin. Despite the extensive literature on the international …nancial architecture and sovereign debt restructuring, and despite the critical nature of PCT to the operations of the main IFIs, to our knowledge there is no model that explains why sovereign borrowers treat such lenders as preferred. This paper attempts to …ll this gap. Our contribution is to develop a model that endogenizes the repayment decision of both commercial and IFI creditors9to show how such decisions are interdependent, and to describe the potential advantages and 1We review relevant academic literature in the next section. As examples of the policy discussion, see Council of Foreign Relations (2018) and the section on the global …nancial safety net in G20 Eminent Persons Group on Global Financial Governance (2018). 2“The Paris Club Agreed Minutes ‘comparability of treatment’ clause aims to ensure balanced treatment of the debtor country’s debt by all external creditors. In accordance with this clause, the debtor country undertakes to seek from nonmultilateral creditors, in particular other o¢ cial bilateral creditor countries that are not members of the Paris Club and private creditors (mainly banks, bondholders and suppliers), a treatment on comparable terms to those granted in the Agreed Minutes.” See: http://www.clubdeparis.org/en/communications/page/what-does-comparability-of-treatment-mean On the other hand, see Martha (1990) and Schadler (2014) on the lack of strong legal standing for PCT in international law. 3See, for example, “Defaulting on the IMF: A stupid idea whose time has come,” Financial Times, Alphaville, July 1st, 2015. 4See (in Spanish) “Hernán Lacunza: Propusimos al FMI dialogar para reper…lar los vencimientos de deuda” in La Nación newspaper August 28, and “Argentina seeks to restructure $101bn of debt” Financial Times August 29, 2019. 5For example, in Cruces and Samples (2016) account of Argentina’s “trial of the century” there is virtually no mention of Argentina’s senior creditors. 6Recent cases include Argentina, Barbados, and Ecuador. Previous cases include Belize, the Dominican Republic and Uruguay. A set of low income countries obtained debt relief under the Multilateral Debt Relief Initiative (MDRI). Broadly speaking, these countries did not have market access. Our focus is to understand why countries may treat IFIs as preferred in relation to market lending. Still, only two countries were in arrears with the IMF in 2019 and Oeking and Simlinski (2016) argue that persistent arrears to that organization may be a thing of the past. At the time of writing, Eritrea, Somalia, Sudan, the Syrian Arab Republic, and Zimbabwe were in arrears with the World Bank and Venezuela was in arrears with the Inter-American Development Bank. 7See, for instance, the classic papers by Eaton and Gersovitz (1981), Bulow and Rogo¤ (1989), Kletzer and Wright (2000) or, for a more up-to-date discussion, Aguiar and Amador (2014). 8See, e.g., Bolton and Jeanne (2009), Boz (2011), Chaterterjee and Eyigungor (2015), Gonçalves and Guimaraes (2015), Hatcheondo et al (2017), and Corsetti et al (2018). 9Throughout the paper we use IFIs and multilateral lenders/debt interchangeably. We thus ignore the fact that some 1 trade-o¤s faced by countries that may borrow from both the market (commercial lenders) and IFIs. In what follows, we develop a relatively simple model of emergency …nancing10 that allows us to obtain a set of analytical results. This contrasts with much of the recent literature, which tends to rely on numerical simulations. Our model abstracts from several important real-world features such as liquidity and creditor coordination issues as well as reforms and conditionality. The aim is to understand the fundamental di¤erences between IFIs and private lenders, focusing on the underlying incentives for a country to borrow and to repay each type of creditor. We show that IFIs are preferred because their bylaws allow them to commit to i) lend limited amounts at close to the risk-free rate under most circumstances, and ii) refrain from lending until any unpaid arrears are cleared. In contrast, atomistic private lenders are unable to coordinate and commit to a maximum amount of lending; they then face a type of dilution. This sets IFI lending aside from that of private lenders, and explains why, in many instances, the presence of IFIs may add value. However, we also …nd that preferred lending may be constrained by a country’s willingness to honor the commitments made, with the constraint depending on the probability and the severity of future shocks, on repayment costs, and on the country’s access to private lenders, which, in turn, depends on similar parameters. In a similar vein to the common statement in corporate …nance that if all …nancing is debt then none is (it turns into equity), we may quip that if all lending is preferred then no lending is. Preferred lending cannot be increased without limit, otherwise borrowers may cease to consider it preferred. Moreover, if emergency …nancial assistance is required frequently, or is extremely rare market solutions may be just as good. Finally, we …nd situations in which a country is better o¤if it cannot borrow from the market, providing a justi…cation for restrictions on commercial lending under certain conditions. In the next section, we review the literature on di¤erent aspects of PCT. In Section 3, we introduce the basic model and study the case in which the country borrows from an IFI. In Section 4, following the standard sovereign debt literature, we assume that the country relies only on private lenders. In Section 5, we allow for the simultaneous presence of multilateral and private lenders. Section 6 discusses extensions of the model analyzing cross-default clauses, conditionality, and the possibility of evergreening. Section 7 investigates how robust our results are to the relaxation of some critical assumption, while Section 8 provides an interpretation of the di¤erent parameters of the model and elaborates on whether our results would hold true in a more general set-up. Finally, Section 9 provides a set of policy implications and concludes. 2 On Preferred Creditor Treatment: A Brief Review Our paper borrows from several strands of literature on IFIs and PCT. First, a number of papers have discussed potential explanations for why IFIs enjoy PCT, although none to our knowledge contains a model illustrating how it can be supported as an equilibrium outcome. Buiter and Fries (2002) suggest countries may confer PCT to IFIs in return for competitive lending rates. Levy Yeyati (2009) argues that PCT is related to insurance–namely the expectation that IFIs will extend credit during a crisis. Humphrey (2015) stresses IFIs’mutual ownership structure. Risk Control (2017) collects statistics related to three potential “drivers” of PCT (favorable rates, counter-cyclical lending and the cooperative nature of the institutions) and …nds support for each. The paper also compares the degree of “mutuality” of each institution and discusses how that may a¤ect preferential treatment. Second, within the large empirical literature on sovereign defaults, a subset of papers considers the role of IFIs. Schlegl et al. (2015, 2019) analyze World Bank data on 127 countries from 1980 to 2006 and …nd a de facto hierarchy, with the IMF and MDBs as the most senior creditors. Bonds appear below MDBs in the pecking order, and then come bilateral lenders, banks and trade credit. Not all multilateral lenders are treated equally; for instance, during the European crisis the EFSF/ESM was not as preferred as other IFIs. Steinkamp and Westermann (2014) analyze the European crisis and present survey evidence on market participants’ perception of seniority levels and claim the IMF was perceived as the most senior o¢ cial multilateral lenders such as the IFC (the private sector arm of the World Bank Group) do not generally claim preferred status. 10 Focusing on emergency lending (and abstracting from lending for consumption-smoothing motives in normal times) provides a clean way to illustrate how a preferred lender could exist as an equilibrium outcome. 2 creditor. Finally, MDBs issue bonds on international markets and the IBRD and the four main regional MDBs (ADB, AfDB, EBRD and IDB) maintain AAA ratings. Moody’s and Standard and Poor’s both suggest these …ve organizations enjoy PCT, although methodologies vary regarding how much of a bonus this provides in formulating ratings.11 A set of papers shows that senior creditors may yield bene…ts but their status is assumed. Bolton and Jeanne (2009) argue that a seniority structure within creditors may ease the debt restructuring process without generating much ine¢ ciency ex ante. In Gonçalves and Guimaraes (2015), a country can commit to a speci…c …scal policy and borrow from a senior creditor–the IMF. Hatchondo, Martinez and Onder (2017) demonstrate that a country might be able to borrow more when there is a senior creditor. Our contribution, in contrast to these papers, is to show that seniority may be an equilibrium outcome consistent with the notion that preferred creditor status is a market norm, which, in general, is not written into legal contracts. Welfare improves through somewhat di¤erent mechanisms across these three papers and in ours. Our paper follows in the spirit of Grossman and van Huyck (1988). In their equilibrium, creditors default given a bad draw on income (an excusable default) but, otherwise, the long run value of the borrower’s reputation exceeds the short-run bene…ts of default. In our case, we allow for two types of creditors and, as we discuss below, the preferred creditor may commit to a low interest rate and a low lending volume such that the long-run value of access outweighs the short-run bene…ts of default. Figure 1 shows12 the number of countries “in default” in each year from 1960 to 2016 classi…ed by the type of creditor. These data stem from the Bank of Canada-Bank of England Sovereign Default Database— see Beers and Mavalwalla (2017) and Beers, Jones and Walsh (2020). As noted by these authors, there is no single accepted de…nition of default. For the purposes of the database “a default has occurred when debt service is not paid on the due date or within a speci…ed grace period.” For IFIs these “defaults” are arrears precisely because they expect at some point full repayment to be made. Each IFI has its own rules on provisioning against such events. We use the label “default” in the …gure following the convention of the database. Private creditors here refers to foreign currency lending by commercial creditors including loan and bond …nancing. Note that very few countries are in arrears with the IMF or with the IBRD. The maximum number of countries in arrears with the IMF was 16 in 1989, and this …gure falls to 2 in 2019. For the IBRD, there was a maximum of 9 countries in arrears in 1992, falling to just 1 in 2019. Arrears are much more frequent with the Paris Club group of bilateral lenders, with a peak of 46 countries in the year 2000, but falling to 12 in 2019. Regarding private creditors, there was a peak of 91 countries in 1994 and 1995, falling to 39 by 2019. Emergency lending is commonly seen as a potential driver of PCT. At times of stress, private creditors perceiving higher default probabilities will demand higher interest rates. If IFIs act benevolently and the expectation is that they will be repaid, then they can lend at low interest rates (just above the riskless rate to support their operating costs) even during di¢ cult times. For a country that may su¤er future emergencies, this relationship may be very valuable. In our model, it is the value of this relationship that provides the incentives for repayment. This implies that the amount that IFIs can lend to a country, and expecting to be repaid, will be related to the probability the country needs …nancial assistance in the future (e.g., because it is hit by a shock). Assuming that preferred lenders can credibly commit not to lend if a country has defaulted on its loans, this implies that a greater amount of preferred lending may be supported as the probability of shocks rises, suggesting a positive relationship between the probability of stress periods and the amount of preferred lending.13 11 See Humphrey (2015), Perraudin et al (2016), and Risk Control (2017) for relevant commentary. Moody’s (2017) and Standard and Poor’s (2017) contain information on the ratings methodologies. 12 The …gure plots the number of countries “in default” for each group of creditors following the de…nition of default as employed in the Bank of Canada and Bank of England dataset on sovereign defaults. The IMF is the International Monetary Fund. IBRD is the International Bank of Reconstruction and Development (the non-concessional balance sheet for sovereign lending of the World Bank Group), Paris Club refers to those bilateral lenders that are members of the Paris Club (essentially OECD member countries) and Private Creditors here includes both bond and loan …nancing exclusively in foreign currency. Source: Bank of Canada–Bank of England Sovereign Default Database. 13 In the working paper version of this paper, Cordella and Powell (2019), we provide evidence of a positive relation between 3 Figure 1: Number of Countries in “Default” 3 The Model In this section, we present a stylized model where it is assumed that, with a certain probability, a country may require emergency …nancial assistance. In our set-up, time, ; is discrete and runs from the initial period, t, to in…nity. In the initial period, the country requires assistance with probability ; but if there is no such need in t, then we assume there will never be a need thereafter. One interpretation of this is that the country has then “graduated”from requiring emergency lending. If, instead, the country has not graduated, then with the same probability that need reoccurs in t+ 1, and so forth. These assumptions imply a simple Markovian structure and allow us to solve the model analytically rather than relying on numerical simulations. All borrowing in the model is short term: the full amount of the loan plus the interest should be repaid at the end of each period, which we refer to as +. Figure 2 illustrates the timing of the model. For the sake of simplicity, the country’s discount factor and the (gross) risk-free interest rate are both set equal to 1, and we also normalize the utility in all states where no assistance is needed (the non-shock states) to zero; in those states where assistance is needed (the shock states), absent lending, we instead assume utility to be equal to to C. However, by borrowing an amount L; the country can reduce the loss in utility by aL L2 2. This speci…cation implies that the value of emergency lending rises with a, and exhibits decreasing marginal returns. Finally, there is some utility cost for the country to repay debt. This cost may vary depending on political, economic, or other considerations. To capture this, while keeping things simple, we assume that there are just two states, so this cost may be either high or low. We refer to these states as the high- and the low-repayment-cost states. We label the probability of the low-repayment-cost state as , and we normalize the cost of repayment in that low-repayment-cost state to 1. We denote by kthe cost of repayment in the high-repayment-cost state. Our model employs …ve key parameters, namely the probability of requiring …nancial assistance (), the utility value of that assistance (a), the probability of the realization of a state in which the cost of repayment of the debt is low (), the cost of repayment in the high repayment-cost state (k), and the loss in the probability of a country having IMF liabilities and the size of those liabilities, lending some support to this view. 4 5 Market and IFI Lending: The Blended Case In the previous section, we discussed IFI and market borrowing separately and independently of each other. However, in general, countries may borrow both from the market and from IFIs; in such a situation, the volume of market lending will a¤ect optimal IFI lending and vice versa. In addition, even if the market does not lend, the very possibility that it can lend may a¤ect the volume of lending extended by a preferred creditor. In this section, we thus allow the country to borrow both from a set of competitive private lenders and from an IFI. Once again we will investigate feasible and optimal lending allocations, imposing the restriction that the preferred lenders should be repaid in all states. We refer to this as the blended case, denoted by the subscript B. When there are two types of lenders present, a critical assumption is what happens to the country in terms of access to further borrowing if it defaults. Our …rst approach is to say that if there is default on one type of lender, the borrower is excluded from further lending from that lender but there is no cross default. In other words, if there is default on the IFI, this curtails access to further borrowing from that source but not from the market. And if there is default on private lenders, this curtails access from that source but not from the IFI. Under this symmetric assumption of no cross-default, the space for the IFI to lend is constrained relative to a setting where default on the IFI also triggers a loss of access to the private market. The IFI would typically be able to lend more, and still expect to be repaid, under that arguably more realistic assumption . We start by exploring the stricter, symmetric, assumption as we wish to show that even under these unfavorable conditions IFI preferred lending may be supported in equilibrium. In the case where there is cross-default, preferred lending is supported for a wider set of parameter values, as we show in Section 6. Assuming that the country always repays the IFIs, and that the country repays the market in the lowrepayment-cost state and defaults in the high-repayment-cost state, the value function can be written as VBt=VIBt+VMBt;(14) where VIBt=(C+aLIBtLIBt 2 2LIBt(+ (1 )k) + VIBt+1 );(15) VMBt=(aLMBt(LIBt+LMBt)2L2 IBt 2LMBt+VMBt+1 );(16) and where (15) denotes the value of the relation with the IFI, in a similar vein to (1), and (16) represents the additional utility associated with borrowing LMB from the market at an interest rate of 1=, when the country has already borrowed LIB from the IFIs: As discussed previously, IFIs di¤er from the market in that they can commit to the amounts they lend, while commercial lenders are not able to make a similar commitment. It is therefore natural to solve the blended case assuming that the IFI moves …rst (as a Stackelberg leader) and decides how much to lend anticipating the volume of loans that the country would then choose to take from the market, with the interest rate charged by private lenders re‡ecting the default risk. When we solve for the optimal amount of market lending for a given level of IFI lending, we obtain Lemma 2 If the country defaults on the market in the high-repayment-cost state, and honors its debt in the low-repayment-cost state, for any given amount of risk-free IFI lending LIB, the optimal amount of market borrowing is given by L MB(LIB)8 > < > : a1LIB;if 0< LIB <b La+ 1 2  ; 2((aLIB )1)  ;if b L < LIB < L a1  ; 0;if LIB > L; (17) 11 and the associated utility by VB(LIB) = 8 > > < > > : VB1=C (1)+LIB (2aLIB 2((1)k+) 2(1)+(1a+LIB )2 2(1);if 0< LIB <b L; VB2=C (1)++LIB (2aLIB 2((1)k+) 2(1)+2((aLIB )1) 2;if b L < LIB < L; VB3=C (1)+LIB (2aLIB 2((1)k+) 2(1);if LIB > L: (18) Proof: In Appendix. Once again, there are three di¤erent regimes and, in this case, we choose to di¤erentiate them by the amount of IFI lending o¤ered, so that (17) can be thought of as a reaction function— how market lending responds to the chosen volume of lending by the IFI.17 The reaction function has a di¤erent speci…cation in each regime. In the …rst regime, the volume of IFI lending is low and the optimal volume of market lending is unconstrained. This implies that, for each additional dollar of o¢ cial lending, market lending is reduced one to one. In the second regime, the volume of IFI lending is higher, and the market-repayment constraint in the low-repayment-cost state is now binding. Here, for each additional dollar of IFI lending, market lending must thus fall more steeply. In the third regime, IFI lending is higher still and no market lending is supported. The constraint that the private sector must be repaid in the low-repayment-cost state is embedded in these reaction functions but, so far, the fact that preferred creditors must be repaid in all states has been ignored. A necessary and su¢ cient condition for the IFI to always be repaid is that, in the high-repayment- cost state, the country is better o¤ repaying, rather than defaulting and relying henceforth solely on the market.18 Formally: De…nition 1 LIis risk free if VB(LIB)kLIB > VM;(19) and the set L IB where IFI lending is risk free is L IB =fLIB jVB(LIB)kLIB > VMg:(20) Let us now start investigating under which conditions IFI lending is risk free and how the di¤erent variables a¤ect the set L IB. We begin by proving that Lemma 3 If kaa 1> k > ((a1)2) 4(1)kb;for a su¢ ciently high probability of requiring …nancial assistance ( > a> I) the set L IB where o¢ cial lending is risk free is non-empty. Proof: In Appendix. The blue/gray shaded area in Figure 4 depicts the set of the IFI’s risk-free lending as a function of the di¤erent parameters of the model. At very low values of (the probability of requiring …nancial assistance), neither preferred lending (the green line) nor market lending (the red line) is supported. As rises, market lending becomes feasible and then, at still higher values of ; preferred lending also becomes feasible and the amount of IFI preferred lending increases as increases. In cases where the value of …nancial assistance is large (high a) and when such assistance is required more frequently (high ), countries are able to borrow more as they have greater incentives to repay. Note that the volume of feasible IFI lending also increases 17 Note that we do not allow IFIs to re-optimize should the country default on the private sector. A justi…cation for this is that countries’lending envelopes with IFIs tend to be relatively …xed. Moreover, re-optimization would imply greater lending from IFIs, but this is generally frowned upon as it may be seen as rewarding a country that had defaulted on the market. Technically, the continuation value of only being able to borrow from IFIs is like a constant outside option and so this assumption has little bearing on the overall nature of most of the results. 18 To simplify the analysis and to focus on the policy relevant cases, we rule out the possibility that the country would default on the IFI, then borrow from the market, and use the lending proceeds to repay its IFI arrears and resume IFI borrowing. 12 with , that is, when the probability of the high-repayment-cost state declines. However, as ,aand  increase, at a certain point preferred lending becomes infeasible. This happens when the market becomes willing to o¤er loans on terms similar to those o¤ered by IFIs, in which case there is very little cost19 in defaulting on the IFI and thus no risk-free IFI lending can be supported in equilibrium.20 Figure 4: Optimal and safe lending (I) 5.1 Optimal Lending Let us now switch our attention to the optimal amount of IFI lending. To compute the optimal lending levels, we not only take into account the reaction functions (17), computed assuming that the country defaults on the market in the high-repayment-cost state, but we also consider the possibility that the market can mimic IFIs, lending the same amount risk-free at the risk-free rate of interest. In the most interesting cases, from the standpoint of this paper, the country will choose to borrow both from the IFI, which o¤ers the risk-free rate, and from the market, which o¤ers a more expensive contract, anticipating default in the high-repayment-cost state. Figure 4 also plots the optimal volume of IFI (preferred) and private (defaultable) lending as a function of ,, and . For the sake of brevity, we will focus our discussion on the …rst case, depicted in panel 4a. The optimal lending volume by the market is depicted by the red line and that of the preferred IFI lending by the green line. At very low values of ; lending is infeasible. As this region is not of interest we do not show it in the …gure. At higher (the probability of negative shocks), market lending is feasible and the optimum consists of solely borrowing from the market. As rises, risk-free IFI lending becomes feasible but it is constrained and it rises with. As IFI lending rises, market lending falls in the blended optimum. To understand fully the interaction between the market and IFI schedules (the red and the green lines) it is useful to note (comparing Figure 4 with Figure 3 or considering Figure 5 below) that when both the market 19 To be precise, if >c, for low values of k,k < kT1+ , there are no gains for the country to borrow defaultable debt at the risk-adjusted rate and thus there is no cost in defaulting from the IFI. If k > kTit would instead be optimal for the country to borrow both from the IFI and from the market. However, such gains are not large enough to induce the country to repay the IFI. 20 For this particular result to hold, the assumption that IFIs do not re-optimize the volume of lending when the country default on the market is critical. Were this not the case, we could end up in a situation where, notwithstanding the fact the risk-free lending is feasible, neither the market nor IFIs would be willing to lend because it would always be in the country’s interest to default on one type of lender and borrow from the other thereafter. 13 and IFI lenders are present, preferred IFI lending is feasible only for values of that are higher than those for which, absent market borrowing, IFI lending is feasible. The reason is that the very presence of a market alternative increases the incentives to default on IFI loans. Intuitively, when the VIand the VMB schedules cross, at =e, the value of market and IFI lending are the same. Hence, it would be in the country’s interest to default on the IFIs (saving on debt service) and borrow from the market; this makes preferred lending infeasible. For higher values of ,>a2k 2k+(1)+p(1)(4(a1)k+(1), the advantages of IFI lending vis-à-vis market lending are greater and a positive volume of both IFI and market lending may be sustained in equilibrium. But then, at a higher value of (=c), the market is also able to o¤er risk-free loans, as we showed in Section 4, and this undermines IFIs’ability to lend risk free and be repaid in equilibrium. Formally, we can prove the following, Proposition 4 If k2[kb; ka]and 2(a; c),L IB >0and the presence of IFIs strictly improves welfare. Proof: In Appendix As IFI safe lending becomes feasible, it is at …rst constrained (the optimum is at the frontier of the feasible set), and as rises, the optimal level of IFI lending increases and market lending falls. At higher values of , IFI lending becomes unconstrained— this is where the optimum for IFI lending leaves the frontier of the feasible set. In this region, the IFI o¤ers loans at lower interest rates, but those may become onerous to repay in the high-repayment-cost state; in contrast, the market o¤ers loans at higher interest rates but will face default should the high-repayment-cost state materialize. Of course, the higher the probability of requiring emergency lending , the higher is the appeal of relying on IFI vis-à-vis market lending so that, as rises, optimal IFI lending also rises, while optimal market lending falls. In order to better understand the welfare implications of the three di¤erent types of lending, in Figure 5, we plot the value of the di¤erent lending relation (5a), the lending volumes (5b), and the welfare associated with the blended case with that of only the market and only IFI lending— to assess the welfare contribution of IFI lending (5c and 5d). As discussed, for low values of ( < e), relying solely on market lending is clearly preferred. Things become more interesting in the interval [e; a]where IFI lending would be optimal but it is not feasible in the blended case. This is because the very presence of market lenders would induce the country to default on IFIs. In this region, it would be in the country’s self-interest to be barred from borrowing from private creditors and only borrow from IFIs. In the interval [a; b]market lending does not completely crowd out IFIs’but, if private lending could be barred in this region, the country can borrow larger amounts from IFIs, and this would strictly improve welfare— see Figure 5d. Note that having the possibility of blended lending adds value (relative to just market) in the intermediate region for — see Figure 5c. This is when the presence of IFIs strictly improves welfare. 6 Extensions 6.1 Allowing for Cross-Default In the previous analysis, we assumed that if a country defaults on one type of lender (the market or the IFI), this would not a¤ect its ability to borrow from the other type of lender. Even under this strict assumption, we demonstrated that an equilibrium with value-added IFI lending could be sustained for a range of parameter values. However, default on IFIs would no doubt a¤ect a country’s credit standing with private lenders and could indeed curtail the ability to borrow from the private market. Risk managers in pension funds, commercial banks and other institutions, exercising their due diligence, or fearful of a regulator’s actions, may well prevent the purchase or continued holding of bonds issued by countries that had defaulted on a lender with a preferred status. 14 Figure 5: IFI, market, and blended (I) In this section, we consider alternative assumptions. First, assume that if the country defaults on the preferred lender then it has no further access to both types of lending. In that case, VMin (19) is replaced with a value function that assumes there is no subsequent access to borrowing, VNA =C (1). As VM> VNA;It follows immediately that the set e L, where IFI lending is risk free, namely e L IB =fLIB jVB(LIB)kLIB > VNAg:(21) contains the set for risk-free lending, as previously de…ned in (20), where a default on the IFI does not a¤ect the country’s ability to borrow from the market. The main result in the paper, that preferred lending can be supported in equilibrium, is then reinforced by this change in assumptions. From the fact that the feasible set for lending contains the previous set, it immediately follows that welfare must be at least as high as in the previous case and it could be greater. To illustrate, Figure 6 presents the results from a numerical simulation in similar vein to Figure 5. The impact of cross-default on the feasibility of greater IFI lending may be substantial. In the second panel, where cross-default is assumed, the feasible set is considerably larger and optimal IFI lending becomes positive at lower values of . Note that as IFI lending increases, this crowds out private borrowing. As IFI lending was not feasible before, at these values of , welfare is higher than in the case of no cross default. Indeed, whenever optimal IFI lending was constrained by the feasibility constraint in the case of no cross-default— that is, IFI lending was on the border of the feasibility set— welfare rises when there is cross-default and reputations are shared. This is clear from a simple inspection of Figure 7 where, for the same parameter values as in Figure 4a, we compare how the introduction of a reputational cost of IFI default (green line) increases welfare by relaxing the IFI constraint. There is also the logical possibility of cross default in the opposite direction: that default on commercial lenders might exclude countries from borrowing from an IFI. This seems hard to square with the current thinking in global …nancial architecture debates, which calls for “private sector involvement”(meaning the 15 Figure 6: Optimal and safe lending (II) private sector taking a haircut) in the context of international support packages from preferred lenders. Moreover, in our model such an assumption would lead to the peculiar result that a country would default on the IFI in all situations in which it defaults on the market, since the relationship with the IFI becomes worthless after market default. In addition, if default on the IFI precludes market lending, then the only possible equilibrium is with only private lenders. Hence, shared reputation in this direction, if it does anything, reduces welfare. 6.2 Conditionality An interesting further possibility is if commercial lending is made contingent on good standing with the IFI and, in addition, IFI lending is contingent on the repayment of market lenders in the low-repayment cost state. In other words, in this case we combine the idea that there would be no access to private lenders if there is default on the IFI with that of no IFI lending if the borrower defaults in the good state, which might be thought of as a non-excusable default. This could be considered a form of conditionality, where the condition is that countries should only default in bad states and not expect to borrow from the IFI if they do not repay private creditors in a good state of the world. This combination would be clearly welfare-improving for all situations in which market borrowing is constrained by the constraint that the country should repay the market in the low-repayment-cost state, as it would increase the amount that the country can borrow ex ante. Again, a numerical simulation exercise is helpful to illustrate this point— see Figure 6c. The main e¤ect of introducing such a form of conditionality is that, now, an increase in o¢ cial lending can relax the lowrepayment-cost state default constraint. This means that IFI and market lending may become complements rather than substitutes— the slope of the reaction function changes and may even change sign. In other words, an increase in IFI lending will increase the cost of defaulting on the market in the low-repayment-cost state, and this may relax the market borrowing constraint. This conditionality leads to a better mix of IFI and market borrowing, thus increasing welfare. Welfare is increased both with respect to the benchmark case and to the case where only reputation is shared so the country cannot borrow from the market if there is default on the IFI, see Figure 7, blue line. 16 Figure 7: Welfare under di¤erent cross-default rules 7 Robustness The results outlined above rely on two critical assumptions raised in section 3 when we described the basics of the model. In this section we consider the implications of relaxing these assumptions. First, we assumed that the cost of repayment in the high-repayment-cost state is large enough so that the country would wish to borrow from the market and default in the high-repayment-cost state, k > a a1, but that it is not so large that the country is tempted to default on the IFI (in the high-repayment-cost state) and then wait until a low-repayment-cost state materializes, clear the arrears and regain access to borrowing, k < 1 + 1 (21) . If k < a a1then, for low values of , no lending (from the IFI or from the market) can be supported in equilibrium. However, at higher values of ;  > I, o¢ cial lending is supported but market lending is not. It is only at somewhat higher values of ;  > M;that the market can now lend as well. As before, at still higher values of , the market may be able to replicate the IFI and also lend risk free. The utility associated with IFI lending is always higher than that associated with market lending, except, of course, in the cases in which the market can replicate the IFI and lend the same amounts, that is for  > c. Again, these general results can be illustrated via a numerical simulation— see Figure 8. In the blended case, the picture is a more complicated one, see Figure 9. Now, for low values of , o¢ cial lending is the only possibility, but it is crowded out by market lending when the latter becomes an option. And it is only for much higher values of the two can coexist in equilibrium. However, it is worth pointing out that in this situation market lending does not add value. This general observation is illustrated through a numerical simulation shown in Figure 10. Interestingly, this would imply that o¢ cial lending should be contingent on no market borrowing in this case. The second assumption is that k < 1 + 1 (21) , which rules out the case that private creditors would default in a high-repayment-cost state but would repay if a low-repayment cost state materializes. This constraint puts an upper bound to the amount that the IFI can lend risk free, namely LI2(a(k1)1(1 ) ): If the constraint is not met (k > 1 + 1 (21) ), then the set L IB, where o¢ cial lending is risk free shrinks, reducing the amount the IFI can lend in equilibrium— see Appendix 1. This is a general result but there 17 Figure 8: IFI and Market Lending: Volumes and Value (II) are di¤erent forces at play. To illustrate those forces a numerical simulation is again useful. In Figure 11 below, the yellow area denotes the reduction in the amount the IFI can lend risk-free in this case. Again, the red and the green lines denote, respectively, the optimal IFI and market lending in this constrained equilibrium— while the light blue and pink lines (labelled as “no evergreening” in Figure 11 illustrate the optimal amount of lending that would occur if the IFI could commit not to resume lending, if payment to the IFI is delayed but occurs in a future low-repayment-cost state. In other words, if the IFI is unable (or unwilling) to ban countries in default from borrowing again once arrears are cleared in a low repayment-cost state, then this reduces the amount that the IFI can lend risk-free. The associated welfare loss can be viewed as the cost of IFIs’inability to commit not to pursue this rather speci…c form of evergreening. These arguments relate to the internal consistency of the model. In the real world, countries and IFIs may make decisions that are driven by forces beyond the logic of the model. For example, suppose an IFI, for whatever reason, lends more than it “should” if it wishes for its debt to remain default free. If this is the case, then we might speculate that the IFI may pursue a di¤erent type of evergreening, and it may also be in the interests of the country to agree to that. As this lies outside of the logic of our model, we simply suggest it as a possibility. To understand this fully would require a di¤erent approach and perhaps one that incorporates political as well as economic forces; we leave this as an interesting future line of research. 18 Figure 9: Optimal and safe lending (III) 19 Figure 10: IFI, market, and blended (II) 8 Interpretation of the Results In our modeling strategy, we stripped the problem down to a set of core elements. This allowed us to obtain a set of closed-form, analytical results, something relatively rare in the current sovereign debt literature. However, questions may arise on how we should interpret the di¤erent parameters of the model and on whether our results would hold true in a more general set-up. In this section we address these questions. In the characterization of the analytical solutions to our model, we have mostly focused on the parameter , the probability that a country requires …nancial assistance. A main …nding is that IFI lending is more valuable for intermediate values of . The intuition is that if is low, no lending would be supported because the country will be tempted to default and, if is very large, the value of the lending relationship is so high that the country will always repay and can thus borrow risk free from the market. An important assumption behind these results is that the probability of requiring such assistance and its value (or intensity governed by the parameter a) are orthogonal, which in reality may not be the case. Had we assumed that frequency and intensity were correlated, perhaps negatively, both components would a¤ect the value of the lending relationship.21 In addition, in the case of a high probability of requiring assistance but where such assistance had a relatively low value, we then …nd that the market could provide lending with a value similar to that of IFIs. This could be considered akin to normal business-cycle lending, perhaps more common in some advanced economies. 21 It is worth noting that in a more general model the relative weight of the two might also depend on risk aversion. 20 that is, b LMD =a1:(31) Hence, the solution will be constrained, if b LMD LMD =2(a+1)  >0()  < 2 (a+1) bM. So the optimum lending will be the constrained solution, L MD =LMD if  < bM;and the unconstrained solution, L MD =b LMD;if bM. Substituting L MD into (7), we can then solve for the optimal value of the value function V MD for each case. Derivation of Condition 12: Assuming that if emergency lending is required, the country borrows b LMD at the risk-free interest rate, and the country repays both in the high and in the low repayment cost state, then the value function is given by: VND =(C+ab LMD b L2 MD 2b LMD ((1 )k+) + VND):(32) Solving for VND, and using (31), we have that VND =((2K(a1)2)2(a1)(1 )k) 2(1 );(33) and substituting this value into that condition (11), and using (31), we obtain 2k (a+ 2k1)c() VND kL MD   C 1. Proof of Proposition 3: To prove Proposition 3, it is useful to start by proving two Lemmas. Lemma 4 If 2[I;1),VIVMD increases with : Proof: Under Assumption (A1), we have that either M< I<bM<bI, or M<bM< I<bI. We show that @(VIVM D ) @ is positive in all the di¤erent sub-intervals of . Let …rst consider the case M< I< bM<bI: (i) In the interval 2(I<bM],@(VIVM D ) @ =2(k221) 22>0, because of (A1). (ii) In the interval 2(bM;bI],@(VIVM D ) @ =2k2 2(a1)2 2(1)2. We further have that Lim !b+ M @(VIVM D ) @ = (a+1)2(k21) 2>0, and Lim !b I @(VIVM D ) @ =(k+1)(1)(2a1+k(1))(a+k+(k1))2 2(a+k(1+k))2>0. Notice further that @(VIVM D ) @ = 0 i¤ k= 2 a1 1 . This means that there is at most one value of k > 0in the interval for which the expression can change sign. Hence the expression is positive in the whole interval. (iii) In the interval [bI;1);@(VIVM D ) @ =1 2((ak+k)2 (1)2(a1)2 (1)2). We further have that Lim !bI @(VIVM D ) @ = (k+1)(1)(2a1+k(1))(a+k+(k1))2 2(a+k(1+k))2>0and that Lim !1 @(VIVM D ) @ >0. Notice further that @(VIVM D ) @ = 0 i¤ =k1 a1+(k1)dor =2a1k+(k1) a(1+)1(k(k1) e. Since k < a () f>1, then there is at most one value of 2(bI;1] for which the expression can change sign. Hence @(VIVM D ) @ is positive in the interval. As per the case M<bM< I<bI, we should just consider the interval 2(I<bI], where VI increases in and VMnot. This, together with the fact that VIVMD is a continuous function proves the Lemma. Lemma 5 There is a e2[I;1) , such that for  > e() VI> VMD. 27 Proof: In the interval [M; I],VM> VIfollows directly for the fact that LM> LI= 0. We further have that in the interval 2(bI;1),VIVMD = 2((1)k)2 (1)(a1)2 (1), so that Lim !1(VIVMD)>0:This together with the fact that VM> VIat =I, and that VIVMis increasing in in the interval 2[I;1), because of Lemma 4, proves the Lemma. Now, to prove Proposition 3, …rst, notice that, if  < e,VMD > VI, and hence L M=L Icannot be an equilibrium, so that L M=L MD. For su¢ ciently high values of , > c, we have that L M=L I. Thus if c<1, that is when  < b, we have that there is a non-empty interval 2[c;1] for which V M=V I. It remains to prove that that the interval [e; Minfc; 1g]is non-empty so that the interval in which V I> V  M is also non-empty. Since, c>bI>bM, where the right inequality follows from A1, it is enough to show that c>  :V MD >bM=V I>bIf. Using (5) and (10), we have that f=(a1)2(ak(1 ))2 (a1)2(ak(1 ))2; with f<1and (after some algebra) a > 1 =)c> f. This proves the Proposition. Proof of Lemma 2: For a given LIB, the additional utility associated with borrowing LMB at an interest rate 1= from the market VMBtis given by (16). Equating VMBtwith VMBt+1 the value of market borrowing (on top of o¢ cial borrowing) can be written as: VMB =LMB(2(a1) LMB 2LIB) 2(1 ):(34) For the market to be willing to o¤er risky loans, the country must be willing to service this debt in the low-repayment-cost state. This condition can be written as VMB LMB :(35) Substituting (34) into (35) at equality, the maximum amount of lending that will be repaid in the lowrepayment-cost state is given by: LMB =2((aLIB)1)  :(36) We further have that LMB >0() LI< a 1  L: Absent default constraints, in period t, the country would choose b LMB arg max LM B VMBt=a1LIB:(37) Hence, the solution will be constrained, if b LMB LMB =a+ 1 LI2  >0() LI< a + 1 2  b L. We thus have that L MB(LIB) = 8 > < > : a1LIB;if 0< LIB <b L; 2((aLIB )1)  ;if b L < LIB < L; 0;if LIB > L: (38) Substituting these values into (34) 28 VMB 8 > < > : (1a+LIB )2 2(1);if 0< LIB <b L; 2((aLIB )1) 2;if b L < LIB < L; 0;if LIB > L: (39) We further have that the value of the relation with o¢ cial lenders in the blended case, VIBt, is given by VIBt=(C+aLIBtLIBt 2 2(1 )kLIBtLIBt +VIBt+1 );(40) and equalizing VIBtand VIBt+1 we have that VIB(LIB) = 2C +LIB (2aLIB 2((1 )k+) 2(1 ):(41) Finally, the overall value function (o¢ cial and market lenders) is then given by VB=VIB(LIB)+VMB(LIB ): Using (39), and (41), and assuming that the country is always willing to repay any LIB 2[0; L];we obtain (18). This proves the Lemma. Proof of Lemma 3: First notice that if Ithere is no risk-free lending in the IFI lending scenario and thus, a fortiori, there can be no risk-free IFI lending in the blended case. Consider now the interval  > b > I. A su¢ cient condition for the existence of risk-free IFI lending if the market does not o¤er the risk-free loan is k < Lim LIB!0 @(VB1V MD3) @LIB =Lim LIB!0 @VB1 @LIB ()  > a2k 2k + (1 ) + p(1 )(4(a1)k+ (1 ); (42) and a<1() k < a 1ka. It remains to verify that the market does not o¤er the risk-free loan; this is the case if ca= 2kp(1 p)(4k(a1) + 1 p)+1ap p(a+ 2k1) p(p1)((4ak 4kp+ 1)) + 2kp + 1 p>0 and a> c() k > ((a+ 1) 2) 1kb: The fact that ka> kbcompletes the proof. Proof of Proposition 4: From Lemma 3, we know that o¢ cial lending is feasible if >aand that Lim LIB!0 @VB1 @LIB >0. Hence, in the interval k2[ka; kb]there is a level of o¢ cial lending that strictly improves welfare. 29