Policy Research Working Paper 8941 Preferred and Non-Preferred Creditors Tito Cordella Andrew Powell Development Economics Vice Presidency Knowledge and Strategy Team July 2019 Policy Research Working Paper 8941 Abstract International financial institutions (IFIs) generally enjoy always repaid and adds value. The analysis suggests that IFIs preferred creditors treatment (PCT). Although PCT rarely should not mimic commercial lenders, but exploit their appears in legal contracts, when sovereigns restructure complementarity, even if banning commercial borrowing bilateral or commercial debts they normally pay IFIs in can sometimes be optimal. IFIs should also focus on coun- full. This paper presents a model where a creditor, such as tries with limited market access and should not be forced an IFI, that can commit to lend limited amounts at the into debt restructurings. risk-free rate and can refrain from lending into arrears is This paper is a product of the Knowledge and Strategy Team, Development Economics Vice Presidency. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/prwp. The authors may be contacted attcordella@worldbank.org and andrewp@iadb.or. The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent. Produced by the Research Support Team Preferred and Non-Preferred Creditors Tito Cordellayand Andrew Powellz JEL Classification 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, Andrew Neumeyer, Ugo Panizza, Anushka Thewarapperuma, 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 and at the Research Department of the IDB for constructive comments and suggestions. The usual disclaimers apply. y The World Bank, tcordella@worldbank.org z Inter-American Development Bank, andrewp@iadb.org 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.1 Much has been discussed about their role as providers of emergency funding but a long-standing central puzzle remains. Namely, the Interna- tional 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. Perhaps, the most emblematic of such discussions to date has been when Greece fell into arrears with the IMF in July 2015.3 On the other hand, during the prolonged “trial of the century” following Argentina’ s 2002 default, IMF liabilities were paid early and in full. 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 in those cases, nor any serious attempt to crowd them in.4 Similarly, in many recent bond restructurings, private creditors su¤ered changes in contracts and present-value haircuts but IFIs were eventually paid in full.5 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,6 while those that focus on seniority7 assume it, without explaining its origin. Despite the vast literature on 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 creditors,8 to show how such decisions are interdependent, and to describe the potential advantages and 1 We 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 non- multilateral 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. 3 See, for example, “Defaulting on the IMF: A stupid idea whose time has come,” Financial Times, Alphaville, July 1st, 2015. 4 For example, in Cruces and Samples (2016) account of Argentina’ s “trial of the century” there is virtually no mention of Argentina’ s senior creditors. 5 Such cases include Belize, the Dominican Republic, Jamaica and Uruguay. A set of low income countries also obtained debt relief under the Multilateral Debt Relief Initiative (MDRI). Broadly speaking these countries did not have market access and, as we are most interested in understanding why countries may treat IFIs as preferred in relation to market lending, they are special cases. Still one interpretation is that IFIs extended loan volumes greater than those consistent with risk-free lending. Moreover, there have been cases of arrears with IFIs. Still, with just three countries in long-standing arrears to the IMF, Oeking and Simlinski (2016) argued that persistent arrears to that organization may be a thing of the past. At the time of writing, the República Bolivariana de Venezuela is accumulating arrears with the Inter-American Development Bank (IDB). In keeping with the expectation of being paid both capital and interest in full, the IDB is making provisions solely on interest on interest payments, which is not charged. Five countries are currently in arrears with the World Bank: Eritrea, Somalia, Sudan, the Syrian Arab Republic, and Zimbabwe. 6 See, 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). 7 See, e.g., Bolton and Jeanne (2009), Boz (2011), Chaterterjee and Eyigungor (2015), Gonçalves and Guimaraes (2015), Hatcheondo et al (2017), Corsetti et al (2018). 8 Throughout 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 …nancing9 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. To keep things straightforward, our model abstracts from several important real-world features such as liquidity and creditor coordination issues as well as reforms and conditionality. Our aim is to under- stand 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 circum- stances, and (ii) refrain from lending until any unpaid arrears are cleared. This avoids the possibility of debt dilution, sets IFI lending aside from private lenders, and explains why, in many instances, the presence of IFIs adds 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 unlimited, otherwise it may not be considered as preferred. From a normative standpoint, our analysis suggests that if the capital or resources of preferred lenders are restricted, they may wish to concentrate their activities in countries where there is a signi…cant bene…t to having access to such emergency lending when needed but where that need may be relatively infrequent. If emergency …nancial assistance is required frequently, or is extremely rare, market solutions may be just as good and private lenders may even dominate IFIs. In addition, we …nd that there are 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 speci…c 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 on private lenders. In section 5, we allow for the simultaneous presence of multilateral and private lenders. Section 6 discusses how a capital constrained IFI should optimally allocate its resources, while section 7 looks at some of the key assumptions of the model and discusses the robustness of the results. Finally, section 8 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 may enjoy PCT, although none contains a model illustrating how it can be supported as an equilibrium outcome. Among these, 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 an insurance motive–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 these three potential “drivers” of PCT (favorable rates, countercyclical lending, cooperative nature of the institutions) and …nds evidence that IFIs do indeed extend funds at lower rates than the market, that they are counter- cyclical, and that they lend in bad times. 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 consider defaults (and the building up of arrears) on IFIs. Schlegl et al (2015, 2019) claim a hierarchy in seniority with the IMF and MDBs at the top. Their analysis is based on World Bank data and covers 127 countries from 1980 to 2006. Considering arrears, bonds appear below MDBs in the pecking order, and then come bilateral lenders, banks and trade credit. The analysis also shows that not all multilateral lenders are treated equally; multilateral lenders such as the IFC (the private sector arm of the World Bank Group) do not generally claim preferred status. 9 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 Figure 1: Sovereign defaults by type of creditors for instance, during the European crisis the EFSF/ESM was not as preferred as other IFIs. Steinkamp and Westermann (2014) also analyze the European crisis and present survey evidence on market participants’ perception of seniority levels and report that the IMF was perceived as the most senior creditor among o¢ cial lenders. Finally, since MDBs regularly issue bonds on international markets, another way of looking at their seniority is through the lens of credit ratings and the methodologies adopted by credit rating agencies. The IBRD and the four main regional MDBs (ADB, AfDB, EBRD and IDB) all maintain AAA ratings. Moody’ s and Standard and Poor’ s both suggest these …ve organizations enjoy PCT although they have slightly di¤erent methodologies for how much of a bonus this provides in terms of formulating ratings.10 To motivate our work, Figure 1 shows the number of countries in “default” in each year from 1960 to 2016 classi…ed by the type of creditor.11 In default here means with outstanding arrears, as noted above, in the end, IFIs are virtually always repaid. 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 13 during the 1980s and this …gure falls to 3 in recent years. The IBRD had between 7 and 9 countries in arrears during the 1990s and a peak of 11 in 2000.12 Arrears are much more frequent with Paris Club (bilateral) lenders, with a peak of 43 countries in arrears in the year 2000, but falling to 11 in 2016. Defaults on private creditors reached a peak of 88 countries in arrears with at least some private creditors in 1994. This number falls to 32 by 2016. As reviewed above, much of the literature considers emergency lending as a potential driver of PCT. During emergencies, default probabilities are likely considerably higher and private creditors anticipating greater risks will require considerably higher interest rates as compensation. If there is an expectation that IFIs will be repaid, then they can lend in these di¢ cult times at more competitive rates. If the default probability is close to zero, then IFIs can charge rates very close to the riskless rate of interest and still make 1 0 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, the latter discusses recent changes to the S&P approach. 1 1 The data come from the Bank of Canada sovereign default database, Beers and Mavalwalla (2017). Private creditors here refers to foreign currency lending by commercial creditors including loan and bond …nancing. 1 2 The Bank of Canada dataset does not separate other MDBs normally considered as being senior from other o¢ cial creditors that are not considered as senior. 3 Figure 2: Probability of IMF lending and lending volumes enough returns to support their operating costs. For a country that may su¤er emergencies in the future this relationship may be very valuable. In the model developed below, it is the value of this relationship that then provides the incentives for repayment. This implies that the amount that IFIs can safely lend to a country is related to the probability the country needs …nancial assistance (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 suggests that a greater amount of preferred lending may be supported as the probability of shocks rises. This suggests a positive relationship between the probability of stress periods and the amount of preferred lending. Figure 2 employs data presented in Boz (2011) regarding the probability of there being IMF lending outstanding (a signal of a negative shock/crisis) and the size of IMF lending as a percentage of GDP for the selection of emerging countries covered in that paper from 1970 to 2007. As can be seen, there is indeed a positive relationship between crisis probability and IMF lending, providing some empirical support to our arguments. 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.13 In our set up, time is discrete and runs from the current period, t, to in…nity. We further assume that, in the initial period t, the country requires assistance with probability ; but if there is no need in t, then we assume there will never be a need for such emergency lending thereafter. One interpretation of this is that the country has then “graduated” and does not need such assistance again. If, instead, there is a need for emergency lending, then with the same probability that need reoccurs in t + 1, and so forth. These assumptions simplify the analysis, allowing for a relatively simple Markovian structure. 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 3 illustrates the timing of the model. 1 3 We are agnostic regarding the motives, this could be due to an exogenous negative shock or due to another unanticipated need. 4 Figure 3: Timeline s discount factor and the (gross) risk-free interest rate are both set For the sake of simplicity, the country’ 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 it 2 is equal to C . However, by borrowing an amount L; the utility loss is reduced by aL L 2 . Thus, a is a measure of the value of emergency lending, which exhibits decreasing returns. We assume that C is large enough so that the utility during an emergency periods is never higher than the utility in non-emergency periods.14 We further assume that 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 state to 1. We denote by k the cost of repayment in the high-repayment-cost state and we assume that a > k > 1 ; that is, the marginal bene…t from borrowing is higher than its marginal cost in the high-repayment-cost state and that the expected cost of servicing the debt in the high-repayment-cost state is higher than the cost of servicing it in the low-repayment-cost’ s. Given that we want to investigate cases where the country can borrow both from the market and an IFI, it is useful to keep the model as simple as possible, ruling out a number of special cases. For example, and as we discuss further below, the country might default on the o¢ cial sector in the high repayment-cost state and then wait until a low-repayment-cost state materializes to clear the arrears and regain access to borrowing. It turns out that we can rule out that possibility assuming that the cost of servicing the debt in the high-repayment-cost state is not too elevated, that is, k < 1 + (2 1 1) . But, at the same time, it cannot be too low if we want to consider the interesting case in which borrowing from the market and defaulting in the high-repayment-cost states yields higher utility than borrowing from the o¢ cial sector at the risk-free a 1 rate and always repaying, this is the case when k > (a 1) > . To avoid abusing the reader’ s patience with too many cases and sub-cases, we thus assume that k is neither too big nor too small and that 1 a M in[a; 1 + ]>k> . (A1) j2 1j a 1 1 4 This a2 is always the case if C > 2 , which we assume holds true. 5 These inequalities are veri…ed for “reasonable”parameter values. For instance, in the numerical simulations we present below, where we assume a = 8, = :6, k = 3:25, (A1) is met for all 2 [0; 1]. 3.1 IFI lending We start our analysis by considering the case in which the country only has access to an IFI.15 IFIs are di¤erent from commercial lenders since, according to their internal rules, they normally lend at rates well below market anticipating that they will receive preferential treatment and be repaid during periods of debt distress. Indeed, some MDBs’ internal risk models essentially assume a zero probability of default on the loan principal and signi…cant adjustments are required to standard risk models applied by rating agencies to analyze MDB risks.16 While some IFIs have di¤erent facilities with di¤erent interest rates, to a …rst approximation these rates are close to the risk-free rate.17 However, as we investigate below, this means that, in equilibrium, countries should only borrow amounts that they are willing to repay under all possible circumstances. For this risk-free lending to be sustainable in equilibrium,18 we assume that, in contrast to the market, IFIs can commit to speci…c lending volumes. We also assume that if a country defaults on an IFI it is excluded from borrowing from any IFI until it fully repays the arrears. This re‡ ects IFIs’ actual rules and working practices.19 At time t, the value function for the country, assuming that, if …nancial assistance is needed, it borrows LIt from an IFI at the risk-free interest rate, and it repays both in the high- and in the low-repayment-cost state, is given by: L2 It VIt = ( C + aLI LIt ((1 )k + ) + VIt+1 ); (1) 2 where subscript I denotes IFI. Equating VIt with VIt+1 , we can rewrite the value function as L2 I VI = ( C + aLI LI ((1 )k + )): (2) 1 2 For the loan to be risk free and support the speci…cation of this value function, the country must be willing to service the loan in the high-repayment-cost state. This is the case if C VI kLI ; (3) 1 that is, when the continuation value of the o¢ cial lending relation VI , net of the repayment cost kLI , is P 1 greater than the continuation value of defaulting, which is given by (t ) C = 1 C . Also, as we =t mentioned above, we rule out the possibility for the country to default on the o¢ cial sector if the high- repayment-cost state materializes and then to clear its arrears in the next draw of a low-repayment-cost state. This is the case when 1 2 (k 1)LI (aLI L ); (4) 1 (1 ) 2 I 1 5 While we assume one IFI lender, our analysis would carry through if there were more IFIs assuming that they coordinate, which is usually the case during emergencies. 1 6 As discussed above, arrears and delays to repayment have occurred but in virtually all cases, principal and interest have eventually been repaid in full. Some MDBs do not charge interest on delayed interest. 1 7 Actually, IFIs lend slightly above the risk-free rate to cover their own operational costs. 1 8 As will become clearer, we are here referring to the case in which risk-free lending is not a market equilibrium. 1 9 For instance, the IMF’ s ability to lend to a country is (at least in principle) a multiple of the country’s IMF quota. The IBRD lending envelope to any particular country is approved by the World Bank board every 4 years in the Country Partnership Strategy and is a function of each country’ s size, needs and ability to repay. As per the no-lending into arrears clause, there is indeed a mutual understanding between IFIs that arrears to di¤erent institutions have to be cleared simultaneously. For instance, according to IMF (2013), “The Fund maintains a policy of non-toleration of arrears to o¢ cial creditors. Fund supported programs required the elimination of existing arrears and the non-accumulation of new arrears during the program period with respect to o¢ cial creditors,” (p.48). 6 where (k 1)LI is the amount the country “saves” by repaying the creditors in the low-repayment-cost states, and 1 (1 ) (aLI 1 2 2 LI ) the expected cost of the lack of access to credit. 20 When this is the case, we have that Proposition 1 The optimal amount of IFI lending is given by 8 k > < 0; I a+ (k 1) ; LI = 2(a k( 1 )); I < < bI ; (5) > : a 2k k (1 ); bI a+ (k 1)+k ; and the associated utility by 8 C > < 1 ; I; C 2k ( ( ) (1 )k ) VI = 1 + ; I < < bI ; (6) > : C ( (1 )k )2 1 + 2(1 ) ; bI : Proof : In Appendix. According to Proposition 1, if the probability of requiring emergency …nancial assistance is su¢ ciently low, I , then risk-free IFI lending is not supported in equilibrium and the country cannot improve on C in that case. The reason is that, given the low probability of requiring assistance, the borrower will default in the bad state when repayment costs are high as the value of the relationship with the o¢ cial lender is insu¢ cient to outweigh such costs. On the other hand, when the probability of requiring assistance is su¢ ciently large, bI , the lending relation is valuable enough to allow the IFI to lend the optimal unconstrained amount. For intermediate values of (bI > > I ), IFI lending is supported in equilibrium, but the participation constraint (ensuring that the IFI is repaid in the bad state) binds. This constraint then determines the amount of IFI lending. The optimal amount of IFI lending, as a function of , is illustrated in Figure 4. In Proposition 1, we have expressed the three regimes as a function of , the probability of requiring …nancial assistance. However, the critical values I and bI , also depend on the other parameters. More precisely, I and bI both increase in a and in , and decrease in k . As discussed above, a is a measure of the value of emergency lending and thus, the higher is a, the higher is the opportunity cost of defaulting. So higher values of a support larger amounts of IFI lending. Similarly, the higher is and the lower is k , the lower is the expected cost associated with servicing the debt in the high-repayment-cost state, which may be written as (1 )k , and thus the higher is the value of maintaining the relationship with the IFI and being able to borrow in the future. This, in turn, implies that higher values of , or lower values of k , also support larger volumes of IFI lending. 4 Market lending Consider now the case in which the country only borrows from private lenders, which we refer to as the market. The key di¤erences between market and IFI lenders are that private lenders are willing to extend credit even in the presence of default risks and that, being unable to commit to a maximum amount of lending, they may face a dilution problem. Private lenders are competitive and risk neutral and to break even they must charge an interest rate commensurate with the risk-free interest rate adjusted for the probability of default. Loans are short term as before. As mentioned above, we assume that if the country defaults it cannot regain access to credit from the market.21 2 0 The expected cost of the lack of access to credit is the cost of lacking access to credit in the next period should there be a need for emergency assistance (with probability ), and in the period after should there be a further need and the country again faces a high-repayment-cost state (with probability 2 (1 )) and so forth. Hence it is equal to ( + (1 ) 2 + (1 2 3 1 2 1 2 ) + :::)(aLI L ) = 1 (1 ) (aLI 2 I L ). 2 I 2 1 Had we assumed that, after a default, the borrower could borrow again from the market with a certain probability in the subsequent period, the qualitative results of the paper would remain the same. 7 Figure 4: IFI and Market Lending: Volumes and Value 8 To solve for the optimum amount of market lending, we start by assuming that the borrower always defaults in the high-repayment-cost state so that the gross interest rate is 1= . Again, we assume that in each period , loans are short term and must be repaid at the end of the period. In the initial period t, the value function for the country–assuming it borrows LM Dt from commercial lenders at the risk-adjusted L interest rate and pays the total due amount M Dt in the low-repayment-cost state, which occurs with probability , is given by L2 M Dt LM Dt C VM Dt = ( C + aLM Dt + ( + VM Dt+1 ) + (1 ) ); (7) 2 1 where superscript M D denotes market (M ) lending when repayment occurs in the low-repayment-cost state and default (D) in high-cost-repayment state. Again, 1 C is the continuation value assuming default in the bad state and no lending. Equating VM Dt with VM Dt+1 ; the value function can be written as L2 MD C VM D = ( C + aLM D LM D (1 ) ): (8) 1 2 1 For the market to be willing to o¤er loans at this interest rate, the country must be willing to repay the debt in the low-repayment-cost state. This condition can be written as LM D C VM D : (9) 1 The optimal amount of borrowing is then found by maximizing (8) subject to the constraint (9). The results are summarized in Lemma 1. Lemma 1 If the country defaults in the high-repayment-cost state, and it repays its debt in the low-repayment- cost state, the optimal amount of borrowing is given by 8 1 > < 0; M a ; 2(a 1) LM D = ; M < < bM ; (10) > : a 1; 2 bM (1+a) ; and the associated utility is given by 8 C < VM D 1 = > 1 ; M; 2(a 1) VM D = VM D 2 = 1 C+ 2 ; M < < bM ; (11) > : (a 1)2 VM D 3 = 1 C+ 2(1 ); > bM : Proof : In Appendix Thus, also in the case in which the country borrows from the market (and defaults in the high-repayment- cost state) there are three di¤erent regimes. If the probability of requiring …nancial assistance is low, M, the market cannot lend as it will not be repaid: the value of the borrowing relationship is so low that the country always …nds it in its interest to default (even in the low-repayment-cost state). On the other hand, if the probability of requiring emergency lending is high, bM , then maintaining the relation with private lenders is very valuable and the unconstrained optimal amount of market lending can be supported in equilibrium. In intermediate cases, M < < bM , the private sector is willing to lend, but the constraint that the lender must be repaid in the low-repayment-cost state binds. This repayment constraint then determines the amount of market lending. In the above, we derived the optimal amount a country can borrow from the market when there is default in the high-repayment-cost state and when the country repays in the low-repayment-cost state. For 9 this to be an equilibrium, it should indeed be the case that it is in the country’s interest to default in the high-repayment-cost state, that is, L C VN D k M D , (12) 1 where VN D is the value of borrowing from the market LM D when the market charges the risk adjusted rate, but the country never defaults. Of course, this condition is always veri…ed if bM : if the non-default constraint is binding in the low-repayment-cost state, it is a fortiori binding in the high-repayment-cost state. In the Appendix, we show that, when > bM the country has no incentives in deviating from the M D strategy if 2k c ; (13) (a + 2k 1) with c bI < . (14) c c 22 If, instead, > , and < 1 then the country will not default in any state and the market is thus willing to o¤er the very same loan the IFI o¤ers at the risk-free rate.23 Hence, it follows that c Proposition 2 If M , LM = LM D is the equilibrium level of market borrowing, and the country defaults in the high-repayment-cost state, while if > c , LM = LI is the equilibrium, the market charges the risk-free rate, and there is no default in either state. Proposition 2 con…rms the intuition that, when the need for …nancial assistance is rare, the incentives of a country to repay are lower and market lending cannot be risk free. In contrast, if there is a more frequent need for …nancial assistance and so the country would like to borrow from the market in the future, then this implies that the value of keeping the borrowing relation in good standing may be high enough that the market can mimic the o¢ cial sector and also lend risk free.24 4.1 Comparison between market and IFI lending Looking at Figure 4, which compares market and IFI lending, it is evident that, for low values of , no lending, IFI nor market, can be supported in equilibrium. When is too small, the value of the lending relationship is low so that the country will have the incentive to default, even if the cost of repayment is low. At higher values of ; > M , market lending is supported, the country will repay in the low-repayment-cost state and default in the high-repayment-cost state. At somewhat higher values of ; > I ; the IFI can lend and, as the value of the relationship is higher, it can expect to be repaid even in the high-repayment-cost state.25 At still higher values of , the market can replicate the IFI and also lend risk free. The comparison between market lending and IFI lending is most interesting for intermediate values or ; when is high enough to support both types of lending but not so high to eliminate the di¤erence between the two. We can then show that Proposition 3 For low values of , < e, the utility level associated with market lending is higher than that associated with IFI lending. For intermediate values of , 2 [e; c ], the utility associated with IFI lending is higher than that associated with market lending. For su¢ ciently high values of , > c > bI , the utility value of market and IFI lending is the same. 2 2 Notice 2k that c < 1 () > a+2 k 1 , a condition that we assume holds true to simplify the discussion of the di¤erent cases. 2 3 This follows directly from the fact that if the country has no incentive in defaulting on LM D in the high-repayment- cost state, a fortiori it will have no incentives in defaulting on the optimal amount of borrowing LI . The argument is so straightforward that we omit the formal proof. 2 4 Notice that the equilibrium characterized above, is not necessarily the only market equilibrium in the interval (e; c )–where e is the value of , such that > e () VI > VM D . There can be another equilibrium in this interval where the market believes that the country always repays creditors and thus charges the risk-free rate. However, we can show that Propositions (2), and (3) below hold true if we had selected the other equilibrium. 2 5 Condition (A1) implies that M < I < bM < bI : 10 Proof: In Appendix. Proposition 3 implies that, as shown in Figure 4, when the probability of requiring emergency …nancial assistance is low, market lending dominates IFI lending. The intuition is that, given the existence of a high-repayment-cost state, market lending de facto o¤ers a state-contingent contract. Given that …nancial assistance will only be needed again with a low probability, the costs associated with losing market access are limited, when compared with the gains associated with state-contingent repayments/defaults. Hence, for low values of , the utility associated with market lending is higher than that associated with IFI lending. When the probability of requiring …nancial assistance in the future is large, the market and IFIs o¤er the very same volume of lending, at the same price, and thus they bring the same utility levels. For intermediate values of , however, the utility associated with IFI lending is higher. It is more valuable for the country to obtain a lower rate of interest and to be assured continued access than to pay a higher rate, default and lose access. IFIs are able to o¤er this contract (and maintain preferred creditor status), as they can limit their lending to volumes that are consistent with repayment in all states. In our model, preferred creditors do not price risk, by de…nition they lend risk free. Instead, they manage risk by restricting credit volumes, if, and when, it is necessary to do so. 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 . An important assumption is that there are no cross-default clauses between IFIs and private creditors so that, if the country defaults on the market, it can continue to borrow from IFIs and vice versa. Indeed, we work under the premise that IFIs o¤er the same terms when the country is in good standing with the market as when it is in default. As we do not want to load the results in one direction or another we also assume, in symmetric fashion, that the market can o¤er the same terms whether the country defaults on IFIs or not. Assuming that the country always repays the IFIs, that the country repays the market in the low-repayment-cost state and defaults in the high-repayment-cost state, the value function can be written as VBt = VIBt + VM Bt ; (15) where LIBt 2 VIBt = ( C + aLIBt LIBt ( + (1 )k ) + VIBt+1 ); (16) 2 (LIBt + LM Bt )2 L2IBt VM Bt = (aLM Bt LM Bt + VM Bt+1 ); (17) 2 and where (16) denotes the value of the relation with the IFI, in similar vein to (1), and (17) represents the additional utility associated with borrowing LM B from the market at an interest rate of 1= . As discussed previously, IFIs di¤ers from the market in that they can commit to the amounts they lend, while there can be no such commitment from commercial lenders. It is natural therefore 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 11 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 8 > < a 1 LIB ; if 0 < LIB < L b a+1 2 ; LM B (LIB ) 2( (a LIB ) 1) b ; if L < LIB < L a 1 ; (18) > : 0; if LIB > L; and the associated utility by 8 > LIB (2a LIB 2((1 )k + ) a+LIB )2 b; > < VB 1 = (1 ) + C 2(1 ) + (1 2(1 ) ; if 0 < LIB < L VB (LIB ) = VB 2 = (1 C ) + +LIB (2a LIB 2((1 )k + ) + 2((a LIB ) 2 1) b < LIB < L; ; if L (19) > > 2(1 ) : VB 3 = C LIB (2a LIB 2((1 )k + ) (1 ) + 2(1 ) ; if LIB > L: 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 (18) can be thought of as a reaction function– how market lending responds to the chosen volume of lending by the IFI.26 Such a reaction function has a di¤erent speci…cation in each regime. In the …rst regime, the volume of IFI lending is low and the volume of market lending is unconstrained. This means 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.27 Formally: De…nition 1 LI is risk free i¤ VB (LIB ) kLIB > VM ; (20) and the set LIB where IFI lending is risk free is LIB = fLIB j VB (LIB ) kLIB > VM g: (21) Let us now start investigating under which conditions IFI lending is risk free and how the di¤erent variables a¤ect the set LIB . We begin by proving that Lemma 3 If k a a 1 > k > ( 4(1(a 1) 2) ) k b ; for a su¢ ciently high probability of requiring …nancial assistance ( > a > I ) the set LIB where o¢ cial lending is risk free is non empty. 2 6 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. See also the discussion below. 2 7 To simplify the analysis and to focus on the policy relevant cases, we rule out the possibility for the country to default on the IFI, to borrow from the market, and use the lending proceeds to repay its IFI arrears and resume IFI borrowing. 12 Figure 5: Optimal and safe lending Proof : In Appendix The blue/gray shaded area in Figure 5 depicts the set of feasible risk-free IFI lending as a function of the di¤erent parameters of the model.28 At very low values of (the probability of requiring …nancial assistance), no 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 does 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 ), such countries are able to borrow more as they have greater incentives to repay. Note that the volume of feasible IFI lending also increases with , that is, when the probability of the high-repayment-cost state declines. However, as , a and increase, at a certain point preferred lending becomes infeasible. This happens when the market becomes willing to o¤er loans on similar terms to IFIs, in which case there is very little cost29 in defaulting on the IFI and thus no risk-free IFI lending can be supported in equilibrium.30 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 (18)– computed assuming that the country defaults on the market in the high-repayment-cost state– but we also consider the case in which the market can mimic IFIs–lending the same amount risk free and charging the risk-free rate. In perhaps the most interesting cases, 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 5 also plots the optimal volume of IFI (preferred) and private (defaultable) lending. 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 low values of ; lending is infeasible then, as increases, there is a region where market lending becomes 2 8 Note that the feasible set for the IFI is a function of the volume of market lending. 2 9 To 1+ be precise, if > c , for low values of k, k < kT , 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 > kT it 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. 3 0 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 will 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 feasible and the optimum consists of solely borrowing from the market. At …rst the market is constrained by the repayment constraint in the low-repayment-cost state. In this region, the optimal amount of market lending rises with . As the probability of negative shocks rises, the value of the relationship with private lenders also rises and so does optimal market lending. As rises further, the constraint becomes irrelevant– this is the part of the red line that is horizontal, and market lending is at the optimal level and independent of . As continues to rise, risk-free IFI lending becomes feasible and becomes part of the optimal allocation. As noted above, as IFI lending rises, with higher , market lending falls in the blended optimum. To understand the interaction between the market and IFI schedules fully (the red and the green lines) it is useful to note (comparing Figure 5 with Figure 4 or considering Figure 6 below) that when both the market 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 VI and the VM B 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 , 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 able to also o¤er risk-free loans, and this undermines IFIs’ability to lend risk free and being repaid in equilibrium. Formally, we can prove that Proposition 4 If k 2 [k b ; k a ] and 2( a ; c ), LIB > 0 and 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 and the market becomes constrained– 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 which 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 6, we plot the value of the di¤erent lending relation (6a), the lending volumes (6b), 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 (6c and 6d). As discussed, for low values of ( < e), market lending is preferred. Things become more interesting in the interval [e; b ] where IFI lending is optimal but not feasible in the blended case. This is because the very presence of market lenders would induce the country to default on IFIs and thus to be able borrow (solely) from the market. 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. The existence of the market reduces welfare in this region and so, if private lending can be barred, in the interval [e; b ] the country can borrow larger amounts from IFIs and this strictly improves welfare– see Figure 6d. Note that having the possibility of blended lending adds most value (relative to just market) in the intermediate region for – see Figure 6c. 6 Optimal “capital allocation” Until now, we have assumed that IFIs always have the necessary resources to lend to any particular country as much as they want, provided the amount is compatible with maintaining PCT. However, there may well be quantitative restrictions on the total amounts IFIs can lend. Indeed, greater lending implies larger capital and overhead costs and, while the IMF and MDBs have di¤erent …nancial models, in the end lending is 14 Figure 6: IFI, market and blended limited by the amount of resources available to each entity, which, in turn, is a function of the resources given or promised to these institutions by their shareholders. As noted above, there are circumstances where IFIs should not lend at all. These include situations where it is not feasible to lend and expect to be repaid in all states, as well cases where the market can successfully mimic IFIs and thus IFIs are unable to bring anything additional to the table. These are pretty straightforward situations. But things are not always so simple, and there is a more di¢ cult question that needs to be answered. Namely, if IFIs are constrained in the amount they can lend, how should they allocate loans across a set of heterogeneous countries in which they can feasibly lend as preferred creditors and where they do add value, over and above what the market can o¤er? To answer such a question, we run numerical simulations considering a continuum of countries,31 di¤ering only with respect to the probability of requiring …nancial assistance, , which we assume to be uniformly distributed. We assume that there is a representative IFI,32 that weighs each country’ s utility equally, and that is benevolent in the sense that the IFI maximizes the sum of country utilities, net of the utility associated with optimal market lending– when IFIs refrain from o¤ering any loan. We then compare the globally unconstrained optimum against situations in which the preferred creditor’ s ability to lend is limited by increasingly tighter global lending limits. These limits may arise because of resource or capital constraints. The results are summarized in Figure 7. The green line represents the case where the preferred lender has adequate resources to fund the total amount of optimal lending, which is exactly equal to the green line in Figure 5a. When the IFI becomes constrained (when total resources, E , are less than the total amount of optimal lending), then resources 3 1 More precisely we run the numerical simulations for 20 di¤erent values of , using the same parameter values as in the previous simulations. 3 2 In our analysis, we assume that only one IFI exists. But the problem is equivalent to one in which the IFI community has to allocate its limited resources across countries. We abstract from any di¤erences in preferences among IFIs. 15 Figure 7: Optimal lending allocation should be allocated to where they are most valuable. Considering Figure 6c, preferred lending adds most value at intermediate values of where the relative advantage of IFI vis-à-vis market lending is the highest. Of course, for higher values of ( > c ), the market can mimic IFIs, and thus there is no reason for IFIs to lend in that region. These results suggest where IFIs should focus their lending …repower; the results are quite intuitive. IFI lending should target countries where the probability of large …nancial assistance needs are high– but not too high. It is in these kinds of countries that the additional value of preferred lending over market lending is greatest. For countries where the probability of requiring …nancial assistance is low, IFI lending may not be feasible. In the intermediate range, countries will in general wish to borrow from both IFIs and the market and countries bene…t from having the two types of contract– a low-cost loan that is always repaid, and a higher cost loan, which is only paid in some, but not in all states. And, as discussed previously, for high values of , the market can o¤er the same conditions as IFIs and thus replace them at no cost. 7 Interpretation and robustness 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 results, something relatively rare in the current sovereign debt literature, which tends to rely on numerical solutions. 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. We now try to answer these questions. To present the di¤erent cases, we have mostly focused on the parameter , the probability that a country requires …nancial assistance. Our 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 always default and, if is 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 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 16 value of the lending relationship.33 In addition, in the case of a high probability of requiring assistance but where such assistance had a relatively low value, then we …nd that the market could provide lending with a similar value than IFIs. This could be considered as akin to normal business-cycle lending, perhaps more common in some advanced economies. As per the intensity of the emergencies, we assumed that it is equal to a …xed parameter C . We did not vary that parameter in our analysis. Instead, we paid more attention to the parameter a, the marginal value of lending. One way to think about the parameter a is as a measure of the severity of these emergencies. Following the above discussion, the value of the lending relation should depend not only on the values of a and , but also on their correlation. In our analysis, the key parameter that di¤erentiates the value of IFI and market lending is k , the cost of repayment in the high-repayment-cost state. The higher is k , the more valuable is market lending because of the state contingency. Notice that, having normalized the cost of repayment in the low-repayment-cost state to one, k can be thought of as a “measure”of the volatility of the cost of servicing the debt, and hence as a measure of the volatility of …scal revenues or of …scal needs. With the aim of simplifying the analysis, we assumed that k could only assume two values which we can think of as high or low. In such a world, to o¤er loans at the risk-free interest rate, IFIs need to limit their lending to be repaid in both states. The market may then o¤er contracts that will be paid only in the low repayment cost state and where there is default in the high-repayment-cost state. Notice, however, that if we had a continuum of values of k , IFIs may not wish to be constrained to only lend expecting to be repaid in absolutely all states. Consider, for example, the aftermath of a major …nancial crisis, a con‡ ict, or a large natural catastrophe. Probably, in such states, the country will either enter into arrears with IFIs, or its obligations will be “evergreened.” Strictly speaking, totally risk-free lending may not exist. Hence, in a more general set-up it may be optimal for IFIs to o¤er loans that are repaid in full in almost all states, while the market will o¤er loans that are repaid less often. Our qualitative results would carry through. Countries may fall into arrears with IFIs in such states and may repay capital and interest at a later date. In our analysis, we also assumed that if a country defaulted on one type of lender (market or IFI), this would not a¤ect its ability to borrow from the other type. This, however, is generally not necessarily the case. The credit rating of a country would normally be severely a¤ected if arrears were built up with IFIs, which would then curtail the ability to borrow from the market. Had we incorporated this into the model, the value of the IFI lending relation would have increased as would the ability of IFIs to lend risk free. We solved for the optimal amount of IFI and market lending and we illustrated the parameter region where IFIs can lend and are expected to be preferred– the preferred lender feasibility set. It is interesting to note that as rises and preferred lending becomes feasible, the optimum amount of preferred lending is constrained. Optimal IFI lending is on the frontier of the preferred lender feasibility set. In this region, it might be argued that IFIs should be cautious. An error in the sense of the IFI lending a bit more than the optimum would imply straying from the feasibility set with the consequent danger that the country would not treat the IFI as preferred. In our analysis, it is assumed that all parameter values are known with certainty but in the real world this may not be the case. On the other hand, for higher values of , the IFI becomes unconstrained as the optimum is inside the feasibility set for preferred lending. At these higher values of ; straying some little way from the optimal amount would not endanger being considered as preferred. 8 Conclusion and policy discussion One of the most persistent puzzles regarding the global …nancial architecture has been in relation to the preferred status of the main IFIs. While PCT is critical to the operations of the IMF and the major MDBs, it is not generally stated in legal contracts, and it is normally described as a market custom. This suggests that it should be understood as an endogenous outcome of the relation of a country with its creditors rather than something that is imposed. And yet we know of no paper to date that provides an explanation of why 3 3 It is worth noting that in a more general model the relative weight of the two might also depend on risk aversion. 17 this may be the case. Our contribution is to provide a relatively simple model that illustrates how IFIs can lend at close to the riskless interest rate and expect to be repaid in all states of nature (as it is always in the country’ s interest to repay) and how the existence of preferred creditors, in addition to private lenders (which may su¤er default), may be valuable. Existing papers that consider sovereigns’ willingness to pay do not include seniority and those models that include seniority do not appear to consider willingness to pay. We believe that this is the …rst paper that attempts to provide a theoretical justi…cation for both the existence of preferred lenders and how they may improve welfare. From the standpoint of the country, borrowing from a private creditor is more expensive, but repayments are ex-post state contingent. In contrast, preferred lenders are in a position to o¤er cheaper more competitive …nancing but countries must be prepared to repay in all states. In our model, preferred lenders may limit the amount of …nancing that is o¤ered. The potentially binding constraint for the preferred lender is that it must be repaid in bad states of nature, where the cost of repayment is high, while the potentially binding constraint for private lenders is that they must be repaid in the good state where that cost is low. Hence, while both lenders o¤er loans with the same fair ex-ante returns, ex post outcomes may di¤er. Our results may also be considered in a more normative fashion as IFIs consider their role in sovereign lending versus that of the market. As the two types of lenders play di¤erent roles, there is no reason to think that IFIs should mirror the behavior of private lenders. Indeed, IFIs add value precisely because they behave di¤erently. If IFIs priced loans to risk, as private lenders do, then this would be tantamount to admitting that their lending is risky and that borrowers may then default. Taking this logic to the limit, IFIs would then become just one more (defaultable) lender among many, and lose their PCT. Rather, we suggest that IFIs should consider where they may add most value given that they can o¤er loans at low rates but subject to the restriction that they expect to be repaid in all states. We conclude that IFIs should focus their …repower where the probability of requiring …nancial assistance is in an intermediate zone. This result holds if preferred lenders are unconstrained in terms of capital and is strengthened if preferred lenders are constrained. Indeed, if the overall lending constraint is very tight, then preferred lenders should refrain from lending to countries with a very high probability of requiring …nancial assistance in the future, even if …scal volatility is quite high (and leave this to the market), and concentrate their activities to an even greater degree on the group of countries in an intermediate range regarding the probability of requiring …nancial assistance in the future. This would maximize the impact of IFI lending. We also discussed a number of caveats to our results given our relatively simple model. In addition to those, it is worth noting that, as it is common in the sovereign debt literature, we assumed that the market and IFIs cannot o¤er state-contingent contracts, where repayment depends on the realization of the state of nature. Were this the case, it could be possible to improve on the current allocation and countries could be able to borrow more and avoid costly defaults. There are various reasons why such contracts do not exist. Some argue that a …nance minister is generally not blamed if there is a slump in the global market for an important commodity export but that if a costly hedge is purchased and not needed then there may be an ex-post inquiry as to why resources were “wasted.”There have been various proposals for GDP-indexed debt but here there are concerns that statistics might be manipulated and/or such contracts may be di¢ cult to price. A further intriguing reason, more related to our model, is that, if a state-contingent contract takes the form of requiring lower payments in bad states but higher repayments in good states, then the willingness to repay in the good state may be threatened. In the comparison of the continuing value of the lending relationship versus the cost of repayment, this may actually restrict lending.34 We also assumed that loans should be repaid at the end of each period and hence we ruled out the possibility that countries might roll-over debt with IFIs and borrow more to avoid repayment when it is most costly to do so. This discussion is closely related to the restriction maintained by the main IFIs that they should not “evergeen” –extend new loans to repay old loans. Had we allowed this, the o¢ cial sector could lend to help countries repay market loans. However, this would go against the principle of “private 3 4 Anderson, Gilbert and Powell (1989) suggest that the World Bank may wish to guarantee such state contingent contracts. The argument is that markets can manage price risks while multilaterals may have a comparative advantage in controlling “performance risks.” This argument depends on the multilateral having some other power of persuasion on the country perhaps coming from its governance structure. 18 sector involvement”in periods of debt distress or, in other words, against the principle that the private sector should su¤er losses as, presumably, it had lent at rates precisely re‡ ecting such risks. If “evergreening” of o¢ cial loans and additional borrowing more to “bail out”private creditors were allowed, then this would add even greater value to o¢ cial lending (from the standpoint of the country) and make it easier and cheaper for the country to borrow from the market. However it is unlikely that such practices would be consistent with maintaining PCT, a AAA credit rating, and a low cost of …nancing for those multilaterals that borrow on global capital markets. A further interesting result is that, for some parameter values, it would be in a country’ s own best interest to not be able to borrow from private markets. This is an important issue that is discussed at length in IFIs and even merits an acronym, NCBP, which stands for non-concessional borrowing policy, and applies to countries that received debt relief under the Multilateral Debt Relief Initiative (MDRI). More precisely, IFIs sought to restrict the amount of commercial debt such countries could contract, both to avoid the repeat of the build-up of unsustainable levels of debt and in order to preserve PCT. IFIs have tried to implement NCBPs with the threat that future concessional resources might be curtailed if countries did not abide. But it is not easy to enforce such a rule. Countries have many ways to contract debt. For example, public companies may provide an indirect way of borrowing that is hard to monitor. Another is that investment needs in the developing world are large so that, in many instances, IFIs may be tempted to o¤er NCPBs’ waivers. Indeed, despite the NCBP, public debt in low income countries that obtained debt relief has increased in the last decade and is now close pre-MDRI levels. Still, this is an issue that deserves further thought and consideration. To conclude, our fundamental result is that creditors that expect to be paid in all states of nature are very di¤erent animals to commercial lenders. While commercial lenders price loans according to risk and should therefore expect restructuring if unfavorable states materialize, IFIs that expect loans to be risk free play by di¤erent rules. But in order to play by those rules their behavior must be consistent. Considering carefully the constraints and ensuring that preferred lending is complementary to market lending should help maximize the bang for each buck of preferred creditors’capital. 19 References [1] Aguiar, M., and Amador, M. (2014), “Sovereign debt,” in Handbook of International Economics, Vol. 4, pp. 647-687. Elsevier. [2] Anderson, R.W.; C. L. Gilbert, and A. Powell (1989), “Securitization and Commodity Contingency in International Lending,” American Journal of Agricultural Economics, Vol. 71, pp. 523–530. [3] Beers, D., and J. Mavalwalla (2017), “Database on Sovereign Debts”Bank of Canada, Technical Report #101. [4] Bolton, P. and O. Jeanne (2009) “Structuring and Restructuring Sovereign Debt: The role of seniority,” The Review of Economic Studies, Vol. 76, pp.879-902. [5] Boz, E. (2011) “Sovereign default, private sector creditors, and the IFIs,” Journal of the International Economics, Vol. 83, pp. 70–82. 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Westermann (2014) “The Role of Creditor Seniority in Europe’ Crisis,” Economic Policy, Vol. 79, pp. 495-552. 21 9 Appendix Proof of Proposition 1: From (4) a country will repay in both the low and in the high repayment cost state if (1 (1 ) )(k 1) eI . LI 2(a ) L Substituting (2) into (3), the maximum amount of o¢ cial lending that will be repaid in both states is then given by 1 LI = 2(a +( )k ). (22) e I LI > 0 () It follows that L < 1 + 1 k , which is always the case because of (A1), so that (3) 2 2 (k 1) implies (4). We thus have that k LI > 0 () > I: (23) a + (k 1) If I , no o¢ cial lending occurs. Consider the case > I. Absent default constraints, in period t, the country would choose bI L2 I L arg max C + aL ((1 )k + )LI ; (24) LI 2 that is, bI = a L (1 )k: (25) However, this ignores the default constraints. The solution will be constrained, if b I LI = 2k L (a+k (k 1) > 0 () < a+ (k 2k bI . So the optimum lending will be the con- 1) strained solution, LI = LI if < bI ; and the unconstrained one, LI = L b I if bI . Substituting LI into (2) we can then solve for the optimal value of the value function VI for each case. Proof of Lemma 1: Substituting (8) into (9), the maximum amount of lending that will be repaid in the high-repayment-cost state is given by 2( a 1) LM D = ; (26) and 1 LM D > 0 () > M: (27) a Hence, if M , no market lending occurs. Consider the case > M. Absent default constraints, should a shock occur, the country would choose bM D L2 MD L arg max C + LM D LM D ; (28) L 2 that is, bM D = a L 1: (29) However, as remarked before this ignores the default constraints. The solution will be constrained, if b M D LM D = 2 L (a+1) > 0 () < (a2 bM . So the optimum lending will be the constrained +1) solution, LM D = LM D if < bM ; and the unconstrained solution will be, LM D = L b M D ; if bM . Substituting LM D into (8), we can then solve for the optimal value of the value function VM D for each case. 22 Derivation of Condition 13: Assuming that if emergency lending is required, the country borrows Lb M D 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: b2 bM D VN D = ( C + aL b M D LM D L ((1 )k + ) + VN D ): (30) 2 Solving for VN D , and using (29), we have that ((2K (a 1)2 ) 2(a 1)(1 )k ) VN D = ; (31) 2 (1 ) and substituting this value into that condition (12), and using (29), we obtain 2k c LM D C () VN D k . (a + 2k 1) 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 VM D increases with : @ (VI VM D ) Proof: Under Assumption A1, we have that M < I < bM < bI . We show that @ is positive in all the di¤erent sub-intervals of . 2(k2 2 (i) In the interval 2 ( I < bM ], @ (VI @ VM D ) = 2 2 1) > 0, because of (A1). @ (VI VM D ) 2k 2 (a 1)2 @ (VI VM D ) (ii) In the interval 2 (bM ; bI ], @ = 2 2(1 )2 . We further have that Lim + @ = !bM (a+1)2 (k 2 1) )(a+k+(k 1) )2 2 > 0, and Lim @ (VI @ VM D ) = (k+1)(1 )(2a 1+k(1 ) 2(a+k (1+k) )2 > 0. Notice further that !bI @ (VI VM D ) @ = 0 i¤ k = 2 1a 1 . This means that there is at most one value of k > 0 in the interval for which the expression can change sign. Hence the expression is positive in the whole interval. k )2 (a 1)2 1 (a k (iii) In the interval [bI ; 1); @ (VI @ VM D ) = 2 ( (1 + )2 (1 )2 ). We further have that Lim @ (VI VM D ) @ = !bI (k+1)(1 )(2a 1+k(1 ) )(a+k+(k 1) )2 2(a+k (1+k) )2 > 0 and that Lim @ (VI @ VM D ) > 0. Notice further that @ (VI @ VM D ) =0 !1 k 1 d 2a 1 k+ (k 1) e f i¤ = a 1+(k 1) or = a(1+ ) 1 (k (k 1) . Since k < a () > 1 then there is at most one @ (VI VM D ) value of 2 (bI ; 1] for which the expression can change sign. Hence @ is positive in the interval. This, together with the fact that VI VM D is a continuous function proves the Lemma. Lemma 5 There is a e 2 [ I ; 1) , such that for > e () VI > VM D . Proof: In the interval [ M ; I ], VM > VI follows directly for the fact that LM > LI = 0. We further have )k )2 (a 1)2 that in the interval 2 (bI ; 1), VI VM D = 2 ( (1 (1 ) (1 ) , so that Lim(VI VM D ) > 0: This !1 together with the fact that VM > VI at = I , and that VI VM is increasing in in the interval 2 [ I ; 1), because of Lemma 2, proves the Lemma. Now, to prove Proposition 3, …rst, notice that, if < e, VM D > VI , and hence LM = LI cannot be an equilibrium, so that LM = LM D . For su¢ ciently high values of , > c , we have that LM = LI and thus VM = VI . It remains to prove that that the interval [e; c ] is non-empty so that the interval in which VI > VM is also non empty. Since, c > bI , it is enough to show that c f > : VM D >bM = VI >bI 23 Using (6) and (11), we have that f (a 1)2 (a k (1 ) )2 = ; (a 1)2 (a k (1 ) )2 c f and (after some algebra) a > 1 =) > . Proof of Lemma 2: For a given LIB , the additional utility associated with borrowing LM B at an interest rate 1= from the market VM Bt is given by (17). Equating VM Bt with VM Bt +1 the value of market borrowing (on top of o¢ cial borrowing) can be written as: LM B (2(a 1) LM B 2LIB ) VM B = : (32) 2(1 ) 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 LM B VM B : (33) Substituting (32) into (33) at equality, the maximum amount of lending that will be repaid in the low repayment-cost state is given by: 2( (a LIB ) 1) LM B = : (34) We further have that 1 LM B > 0 () LI < a L: Absent default constraints, in period t, the country would choose bM B L arg maxVM Bt = a 1 LIB : (35) LM B However, this ignores the default constraints. The solution will be constrained, if b M B LM B = a + 1 LI L 2 > 0 () LI < a + 1 2 b . We thus have that L 8 > < a 1 LIB ; if b; 0 < LIB < L LM B (LIB ) = 2( (a LIB ) 1) ; if b L < LIB < L; (36) > : 0; if LIB > L: Substituting these values into (32) 8 (1 a+LIB )2 b; > < 2(1 ) ; if 0 < LIB < L VM B 2( (a LIB ) 1) ; if b < LIB < L; L (37) > : 2 0; if LIB > L: We further have that the value of the relation with o¢ cial lenders in the blended case, VIBt , is given by LIBt 2 VIBt = ( C + aLIBt (1 )kLIBt LIBt + VIBt+1 ); (38) 2 and equalizing VIBt and VIBt +1 we have that 2 C + LIB (2a LIB 2((1 )k + ) VIB (LIB ) = : (39) 2(1 ) 24 Finally, the overall value function (o¢ cial and market lenders) is then given by VB = VIB (LIB ) + VM B (LIB ): Using (37), and (39), and assuming that the country is always willing to repay any LIB 2 [0; L]; we obtain (19).This proves the Lemma. Proof of Lemma 3: First notice that if I there 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 @ (VB 1 VM D3 ) @VB 1 a 2k k < Lim = Lim () > p ; LIB !0 @LIB LIB !0 @LIB 2 k + (1 )+ (1 )(4(a 1)k + (1 ) (40) and a a < 1 () k < ka . 1 It remains to verify that the market does not o¤er the risk-free loan, this is the case if p 2k (1 p)(4k (a 1) + 1 p) + 1 ap c a = p >0 p(a + 2k 1) (p 1)( (4ak 4k p + 1)) + 2kp + 1 p and a c ( (a + 1) 2) > () k > kb : 1 The fact that k a > k b completes the proof. Proof of Proposition 4: a @VB 1 From Lemma 3, we know that o¢ cial lending is feasible if > and that Lim > 0. Hence, in LIB !0 @LIB the interval k 2 [k a ; k b ] there is a level of o¢ cial lending that strictly improves welfare. 25