Serial Sovereign Defaults and Debt Restructurings

Contributor Notes

Author’s E-Mail Address: TAsonuma@imf.org,

Emerging countries that have defaulted on their debt repayment obligations in the past are more likely to default again in the future than are non-defaulters even with the same external debt-to-GDP ratio. These countries actually have repeated defaults or restructurings in short periods. This paper explains these stylized facts within a dynamic stochastic general equilibrium framework by explicitly modeling renegotiations between a defaulting country and its creditors. The quantitative analysis of the model reveals that the equilibrium probability of default for a given debt-to-GDP level is weakly increasing with the number of past defaults. The model also accords with an additional fact: lower recovery rates (high NPV haircuts) are associated with increases in spreads at renegotiation.

Abstract

Emerging countries that have defaulted on their debt repayment obligations in the past are more likely to default again in the future than are non-defaulters even with the same external debt-to-GDP ratio. These countries actually have repeated defaults or restructurings in short periods. This paper explains these stylized facts within a dynamic stochastic general equilibrium framework by explicitly modeling renegotiations between a defaulting country and its creditors. The quantitative analysis of the model reveals that the equilibrium probability of default for a given debt-to-GDP level is weakly increasing with the number of past defaults. The model also accords with an additional fact: lower recovery rates (high NPV haircuts) are associated with increases in spreads at renegotiation.

I. Introduction

Emerging countries (EM) that have defaulted on their debt repayment obligations in the past are more likely to default again in the future than are non-defaulters with the same external debt-to-GDP ratio. These countries actually have repeated defaults or restructurings in short periods. This paper explains these stylized facts within a dynamic stochastic general equilibrium framework that explicitly models renegotiations between a defaulting country and its creditors. Specifically, the model extends the existing literature by allowing the defaulter and creditors to bargain not just over recovery rates, but also over the rate of return offered on newly-issued debt. Quantitative analysis of the model reveals that the equilibrium probability of default for a given debt-to-GDP level is weakly increasing with the number of past defaults, consistent with empirical observations. The equilibrium of the model also accords with an additional observed trend: a country for which default terms require less than a 100 percent recovery rate tend to pay a higher rate of return (relative to a risk-free rate) on debt that is issued subsequently than do defaulting countries that agree to a full recovery rate. These findings are robust to extensions that allow the renegotiation outcome to be modeled more flexibly.

The empirical section of the paper presents new stylized facts on serial sovereign defaults and debt restructurings. First, we contrast characteristics between EM defaulters, which have experienced at least one default or restructuring on external private debt over 1985–2010, and non-defaulters. Through cross-sectional analysis, we find that (i) past defaulters suffer higher borrowing costs both in terms of interest spreads and yield on newly issued bonds and (ii) are more likely to default again than non-defaulters. Next, we focus specifically on serial sovereign defaults and debt restructurings using Cruces and Trebesch (2013) data, which covers 179 sovereign defaults and debt restructurings on private external debt over 1978–2010. We newly confirm that (iii) EM serial defaulters have repeated 3.7 defaults and restructurings in 1978–2010, (iv) have reached next default or restructuring quickly than the previous ones, and that (v) lower recovery rates (higher haircuts) at renegotiation are associated with larger increases in yield spreads.

The theoretical part of the paper deals with endogenous debt renegotiation after default in a standard dynamic model of defaultable debt. The renegotiation process involves Nash bargaining between the defaulting debtor and creditors over both the recovery rate and increases in rates of return on new debt. Evidence suggests that the spread between the rate of return on new debt and the risk-free rate increases after default more for defaulters that pay less than a full recovery rate than for defaulters that agree to repay all of the defaulted debt (i.e., a 100 percent recovery rate). Thus, it appears that, at least implicitly, a country that defaults negotiates with its creditors both over recovery rates and over future rates of return. This reflects a trade-off for defaulting country: the defaulted debt can be repaid in the present at a high short-run cost in return for only a small or even negligible deterioration in long-term credit condition; or the short-run benefit of repaying the debt only partially will be offset by having to pay lenders a higher rate of return on future issuances. The trade-off for creditors is symmetric: if they are not appeased by a full recovery of funds in the short term, they can attempt to recoup their losses by demanding higher rates of return for holding the country’s bonds in the future.

We seek to incorporate theoretically these trade-offs facing the debtor and creditors during renegotiations following defaults. In the model, the endogenously-determined terms of renegotiations following default present the observed pattern, i.e., lower recovery rates (higher haircuts) are associated with larger increases in yield spreads. An emerging country that defaults once therefore pays a penalty either through a large recovery rate in the short term or through higher borrowing costs in the long term. If it chooses to repay less than full recovery rates, it will face high borrowing costs, which leads to increased risks that the country will default again in the future. This mechanism drives the equilibrium serial default behavior in the model, and it is a plausible explanation of the pattern of repeat defaults observed in the data. Hence, the model is able to jointly explain both stylized facts of debt restructurings and repeat defaults.

We embed the debt renegotiation in a dynamic sovereign debt model with endogenous defaults where an emerging country is subject to exogenous income shocks. This part of the model builds on recent quantitative analysis of sovereign debt such as Aguiar and Gopinath (2006), Arellano (2008), and Tomz and Wright (2007), which is based on classical setup of Eaton and Gersovitz (1981). At the renegotiation, creditors and defaulting country bargain over increases in rate of return on new debt together with recovery rates. Outcomes of the renegotiation represent trade-offs of both defaulting country and creditors, as indicated above. Total spread between the rate of return on new debt and the risk-free rate, incorporates not only the probability of future default but also impacts on increases in rate of return on new debt agreed to buy both side at the past renegotiations.

Our paper is most closely related with Yue (2010), in which a dynamic model of defaultable debt is augmented with an endogenous treatment of debt renegotiation after default. Our model differs from her model in that we incorporate the effects of increases in rate of return on new debt. At the renegotiation, both parties bargain not only over recovery rates, but also over increases in rate of return on new debt. Therefore, its credit condition, i.e., borrowing cost of the country after re-entry to the market, depends on how much the country pays at the debt renegotiation. Increase in borrowing costs accompanied by repaying the debt only partially will lead to increase future default probability. In special cases where the country always repays in full the level of defaulted debt, increases in rate of return on new debt will be close to zero. As impacts of additional default premia are totally negligible, results will be quite similar to those in Yue (2010).

The rest of the paper is structured as follows: Section II reviews three strands of literature. Section III overviews new stylized facts on serial sovereign defaults and restructurings. We provide our theoretical model of sovereign debt and defaults in Section IV. We define recursive equilibrium of the model in Section V. Quantitative analysis of the theoretical model is discussed in Section VI. Model implications are indicated in Section VII. A short conclusion summarizes the discussion. The computation algorithm is provided in Appendix 1.

II. Literature Review

This paper is related to the literature of serial sovereign default such as Reinhart and others (2003), Reinhart and Rogoff (2005, 2009), Eichengreen and others (2003) and Catao and others (2009).1 Reinhart and others (2003) and Reinhart and Rogoff (2005, 2009) advocate the role of past credit history in debt intolerance.2 In contrast, Eichengreen and others (2003) show that countries with “original sin”, inability to issue bonds in their domestic currencies, must pay an additional risk premium when they borrow, increasing their solvency risks since the financial market knows this inability is a source of financial fragility.3 However, none provides economic models describing how weak credit history or “original sin” features are associated with serial defaults. Catao and others (2009) explain that vicious cycles in sovereigns’ credit histories arise due to output persistence coupled with asymmetric information about output shocks. This paper improves these papers by explaining theoretically how outcomes of current debt renegotiation, such as additional spread premia, lead to higher probability of the next default in future.

The other strand of literature models the sovereign default and renegotiation as a game between a sovereign debtor and its creditors (e.g., Bulow and Rogoff 1989; Benjamin and Wright 2009; Kovrijnykh and Szentes 2007; Bi 2008; Bai and Zhang 2010; D’Erasmo 2010; Yue 2010; Pitchford and Wright 2012; Arellano and Bai 2014; Hatchondo and others 2014; and Asonuma and Trebesch 2016). Yue (2010) treats debt renegotiation process using a one-round Nash bargaining game. Moreover, Bai and Zhang (2012), Benjamin and Wright (2009) and Bi (2008) presume a multi-round bargaining to analyze delay in renegotiation. Furthermore, Pitchford and Wright (2012) regard multi-creditor renegotiation process as a series of bilateral bargaining games to explain delays in renegotiation. Similarly, Kovrijnykh and Szentes (2007) also study multi-creditor renegotiation and make the time of exclusion from the financial market endogenously and potentially long. Our paper differs from this literature in that we focus on the renegotiation game where the debtor and its creditors bargain not only over recovery rates, but also over the rate of return offered on the newly issued debt.4

Lastly, our empirical finding is linked to studies analyzing the impacts of past defaults on future borrowing costs (e.g., Ozler 1992 and 1993; Cantor and Packer 1996; Lidert and Morton 1989; Catao and others 2009; Cruces and Trebesch 2013; and Benczur and Ilut 2016). Ozler (1993) finds that past defaulters had to pay a premium on the interest rate for the sovereign debt issued in the 1970s.5 Cantor and Packer (1996) also confirm that sovereign yields tend to rise as sovereign has a bad default history.6 In the similar vein, Catao and others (2009) find the existence of history-dependent “default premium” and of significant effect of output persistence and Benczur and Ilut (2016) also confirm effect of past repayment problems on current spreads on bank loans to developing countries between 1973–1981. In the recent work, using enriched sovereign debt restructuring dataset, Cruces and Trebesch (2013) show that restructurings involve higher haircuts are associated with higher subsequent bond yields. What is distinctive in our paper relative to previous work is that we analyze the deterioration of long-term borrowing on bonds, i.e., increases in spreads at the time of renegotiations for recent debt renegotiations during 1986–2010 to explain tradeoffs of both creditors and the sovereign.

III. Five New Stylized Facts on Serial Sovereign Defaults and Debt Restructurings

A. Sovereign Debt Defaulters and Non-Defaulters - EMs

We start our empirical analysis from some features differentiated by country’s history of defaults and restructurings, in particular interest spreads (yields of newly issued bonds) and default probability. Our analysis centers on emerging market (EM) countries defined by the IMF World Economic Outlook (WEO) and our EM sample consists of 83 countries. Throughout this section, we use private external debt defaults and restructurings dataset in Cruces and Trebesch (2013) which cover 179 episodes over 1978–2010.7 Cruces and Trebesch (2013) focus on distressed debt exchanges, defined as restructurings of bonds and bank loans at less favorable terms than the original bonds and bank loans. They thereby follow the definition and data provided by Standard & Poor’s (2006, 2011).

Following definition of defaults and restructurings in Cruces and Trebesch (2013), we define sovereign debt defaulters and non-defaulters as follows:

  • Sovereign debt defaulters: sovereigns which have experienced at least one default or restructuring since 1985 (1990) – 36 (34) EMs.

  • Non-defaulters: sovereigns which have experienced neither a default nor a restructuring since 1985 (1990) – 47 (49) EMs.

We set two ranges of time intervals for defaults and restructurings: (i) from 1985 (over 25 years), (ii) from 1990 (over 20 years). Our choice of two periods follow two rationales: they cover enough restructuring episodes (more than 130 and 80 cases respectively) and time intervals are consistent with finite investors’ memory, i.e., sovereigns’ credit history recovers over 25 (20) years. Among 83 EMs, there are 36 sovereign debt defaulters and 47 nondefaulters.

Figure 1 reports average Emerging Market Bond Index Global (EMBIG) spreads and credit ratings relative to public and publically guaranteed (PPG) external debt in 2005–2011. Panel A shows that past defaulters suffer higher borrowing costs at the external markets, proxied by EMBIG spreads, than non-defaulters given PPG external-to-GDP ratio. From Panel B, it is obvious that past defaulters have lower credit ratings (average of Moody’s and Standard and Poor ratings) reflecting higher default probability, given PPG external debt ratio.8

Figure 1.
Figure 1.

PPG External Debt/GDP, EMBIG Spreads, Credit Ratings, Average 2005–11

Citation: IMF Working Papers 2016, 066; 10.5089/9781513596648.001.A001

Sources: Bloomberg, Cruces and Trebesch (2013), IMF WEO, Moody’s, Standard and Poor, WB International Debt Statistics

More robust evidence appears in Table 1 which reports cross-section regression results on borrowing costs and default probability using EM sample comprised of both defaulters and non-defaulters. For borrowing costs, proxied by EMBIG spreads, our benchmark specification follows closely Eichengreen and Mody (1998) and Ardagna and others (2007). The baseline regression result (1st column) suggests that past defaulters suffer higher borrowing costs by 2.4 percentage points. If sovereigns have higher debt (PPG external debt-to-GDP ratio) and experience larger exchange rate depreciation, they have higher EMBIG spreads. This result is robust even if we include CPI inflation rates as one of controls (2nd column) and the shorter interval for past defaults starting from 1990 (3rd column). Moreover, Appendix II demonstrates that defaulters’ yields on newly issued bonds in general are higher than non-defaulters.

Table 1.

Regression Results on Borrowing Costs and Default Probability1/

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Sources: Bloomberg, Chinn and Ito (2006), Cruces and Trebesch (2013), Haver Analytics Data, IMF WEO, Moody’s, Standard and Poor, WB International Debt Statistics and author’s calculationNote: Standard errors are in parentheses. ***, **, * show significance at 1, 5, and 10 percent levels respectively.

All regression results are based on least square estimations.

Credit ratings of Moody’s and Standard and Poor are converted to numerical values using a linear scale from 0 to 20 with SD and Ca ratings corresponding to values of zero and 1 respectively, and AAA ratings being assigned a value of 20 as in Sy (2002). We take an average of ratings of Moody’s and Standard Poor on foreign-currency debt.

Change in end of period annual exchange rate from the previous level.

Capital account openness index from Chinn and Ito (2006) ranges from −1.86 and 2.44 corresponding to the lowest and highest degree of capital openness respectively.

On default probability, we use both average credit ratings of Moody’s and Standard and Poor and Credit Default Swap (CDS) spreads as proxies. Our baseline specification is in line with Kohlscheen (2009) and Dreher and Walter (2010). From our benchmark regression using credit ratings (4th column), past defaulters are more likely to default, estimated by 1.5 notches lower in credit ratings. Their default probability is higher if sovereigns accumulate higher debt (PPG external debt-to-GDP), have higher CPI inflation rates and hold lower reserves (reserves-to-GDP ratio). This is also the case with specification with the shorter interval for past defaults starting from 1990 (5th column). Regression results using CDS spreads complement our baseline results despite the limited sample of CDS spreads. Past defaulters suffer higher CDS spreads than non-defaulters by 1 percentage point (6th column). The main results remain robust with the shorter interval for past defaults starting from 1990 (7th column).

  • Stylized fact 1: Past defaulters suffer higher borrowing costs than non-defaulters. EMBIG spreads for past defaulters are higher than those for non-defaulters by 2-2.4 percentage points.

  • Stylized fact 2: Past defaulters are more likely to default again. Default probability for past defaulters are higher than those for non-defaulters, measured by lower credit ratings and higher CDS spreads.

B. Serial Sovereign Defaults and Debt Restructurings

Next we focus specifically on serial sovereign defaults and restructurings and provide three new stylized facts. Panel (A) in Table 2 shows that serial defaulters account 61 percent of sovereigns that have experienced at least one default or restructuring in 1978–2010. These serial defaulters have repeated 3.7 defaults or restructurings on average over the time period.

Table 2.

Serial Sovereign Defaults and Debt Restructurings in 1978–2010

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Source: Cruces and Trebesch (2013).

Narrowing our focus to EM sovereigns, EM serial defaulters account 58 percent of total serial defaulters and have experienced 4.1 defaults or restructurings in average as reported in Panel (B) in Table 2. In addition, periods between restructurings are 3.2 years in average.

Panel (C) in Table 3 shows that it takes less time to default or restructure debt again as serial defaulters repeat more defaults or restructurings. After sovereigns experience their first defaults, it takes 13.1 quarters to reach the second defaults or restructurings. However, since the second defaults, it takes even less time (12.0 quarters) to reach the third defaults or restructurings on average. The same pattern applies to periods to the fourth default or restructuring (11.8 quarters). This evidence suggests that serial defaulters repeat next defaults or restructurings more quickly than the previous ones.

Table 3.

Regression Results on Recovery Rates1/

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Sources: Cruces and Trebesch (2013), Datastream, PRC Group International Country Risk Guide (ICRG), IMF WEO, and author’s calculation.Note: Standard errors are in parentheses. ***, **, * show significance at 1, 5, and 10 percent levels respectively.

All regression results are based on least square estimations.

GDP deviation from the trend is a percentage deviation from the trend obtained by applying the Hodrick-Prescott (H-P) filter.

Political risk index is country composite index from ICRG is based on 100 points with zero and 100 corresponding to highest and lowest risks respectively.

London Interbank Offered Rate (LIBOR) is yearly average of monthly 1-year yields.

  • Stylized fact 3: Serial defaulters, accounting 61 percent of past defaulters have repeated 3.7 defaults or restructurings in 1978–2010.

  • Stylized fact 4: Serial defaulters repeat next defaults or restructurings more quickly than the previous ones as they experience more defaults or restructurings.

Figure 2 displays net present value (NPV) recovery rates and increases in spreads for 66 sovereign debt restructuring episodes during 1986–2010.9

Figure 2.
Figure 2.

Recovery Rates and Increases in Spreads for Recent Debt Restructurings

Citation: IMF Working Papers 2016, 066; 10.5089/9781513596648.001.A001

Sources: Cruces and Trebesch (2013), Datastream, and author’s calculation.

We define “increases in spreads” as the difference in spreads between the time of completion of the restructurings and one year before the completion.10 As most of EMBIG spreads are available from 1999, we extrapolate spread series by each country using London Inter-Bank Offered Rate (LIBOR) and International Country Risk Guide (ICRG) rating as explained in Appendix III. The fitted line is obtained by regressing recovery rates on increases in spreads controlling for GDP deviation from the trend and external debt-to-GDP ratio (1st column in Table 3). This negative relationship is robust even controlling for political risk and global factors and omitting some outlier episodes shown in the 2nd, 3rd, and 4th columns respectively.11 These results reflect that lower recovery rates (larger haircuts) at the renegotiation are associated with larger increases in yield spreads between the rates of return on new debt and the risk-free rate. This presents a trade-off for defaulting countries; if the countries recover a larger fraction of debt during renegotiations, long-term borrowing costs will be smaller. At the same time, we can interpret it as a trade-off of creditors. If the creditors receive payments for only a small fraction of defaulted debt, they can recoup their losses by demanding higher rates of return for the newly issued bonds.

  • Stylized fact 5: Lower NPV recovery rates (higher haircuts) at renegotiation are associated with larger increases in yield spreads.

IV. Model Environment

The basic structure of the model follows previous work that extends the model of sovereign default by Eaton and Gersovitz (1981) and applies its quantitative analysis. Among these studies, the closest reference to our paper is Yue (2010). The distinctive feature in our model with respect to her model is that we introduce effects of increases in rate of return on new debt after the re-entry to the market. Since both recovery rates and increases in rate of return on new debt are determined endogenously, how much the country pays at the renegotiation will affect its credit condition in the future, i.e., borrowing costs of the country after re-entry to the market, which will have an impact on default probability.12

A. General Points

The model analyzes sovereign default and negotiation in a dynamic stochastic general equilibrium framework. We consider a risk-averse country that cannot affect the world risk-free interest rate. The country’s preference is given by following utility function:

E0Σt=0βtu(ct)

where 0 < β < 1 is a discount factor, ct denotes consumption in period t and u(.) is its one-period utility function, which is continuous, strictly increasing and strictly concave and satisfies the Inada conditions. A discount factor reflects both pure time preference and the probability that the current sovereignty will survive into next period.

All the information on the country’s asset, credit history, and income realization is perfect and symmetric and only future income process remains uncertain.13 In each period, the country starts with its credit history ht, which satisfies ht ∈ H where H = [0,1,2, …, hmax]. The credit history expresses number of debt renegotiations the country has experienced in the past.14 The reason we assume multi-state credit history rather than binary credit history as in Yue (2010) is to analyze how the outcomes of past debt renegotiations associated with defaults affect the probability of next default. Moreover, we assume that the credit history reverts with exogenous probability χ conditional on that the country chooses to pay the spread returns after defaults.15 This is consistent with what we observe in the data (Cruces and Trebesch 2013).

The country receives an exogenous income shock yt. Income shock (yt) is stochastic, drawn from a compact set Y = [ymin, …., ymax] ⊂ ℝ+. µ(yt+1|yt) is the probability distribution of a shock yt+1 conditional on previous realization yt.

There is an infinite number of investors who are risk-neutral and behave competitively in the international capital market. They keep track credit history and additional spread premia agreed to by both sides at the previous debt renegotiation. We also assume that they can borrow or lend as much as needed at a constant risk-free interest rate (r) in the market. Since they are symmetric and similarly ranked, we can interpret them as “a representative investor” lending money to the country. The country borrows the money from the same representative investor through bond exchanges even after it defaults.16 As investors are able to collude at the debt renegotiation, “a representative investor” has bargaining power at the renegotiation in order to impose higher spreads on future bonds, though the bargaining power is still low compared to that of the country.17,18,19 Moreover, we assume that all the investors behave in the same manner: they all lend to the country every time the country issues bonds, and there is no sub-group of investors who behave differently from the majority of investors such as they still lend to the country even if the country defaults and refuses to negotiate with the majority of investors.20

The international capital market is incomplete. The country and foreign investors can borrow and lend only via one-period zero-coupon bonds where bt+1 denotes the amount of bonds to be repaid next period. When the country purchases bonds, bt+1 > 0, and when it issues new bonds bt+1 < 0. The set of amount of bonds is B = [bmin, …. . , bmax] ⊂ ℝ where bmin ≤ 0 ≤ bmax. The upper bound is the highest level of assets that the country can accumulate and the lower bound is the highest level of debt that the country can hold. We assume q(bt+1, ht, yt) is the price of a bond with asset position (bt+1), credit history (ht), and income level (yt). The bond price will be determined in equilibrium.

We assume that foreign investors always commit to repay their debt. However, the country is free to decide whether to repay its debt or to default. If the country chooses to repay its debt, it will preserve access to the international capital market next period.

If the country chooses not to pay its debt, it is subject to both exclusion from the international capital market and direct output cost.21, 22 When a default occurs, the country and foreign investors negotiate a reduction of unpaid debt via Nash bargaining. At the renegotiation, both recovery rates and additional spread premia on the newly issued bonds are agreed to by both parties.23, 24 The country regains access to the market after financial exclusion for short periods, but the country’s credit history records the current debt renegotiation.

In order to avoid permanent exclusion from the international capital market, the country has an incentive to negotiate over recovery rates (haircut rates) and additional default premia. From foreign investors’ point of view, they want to maximize the payment from recovered debt and spread returns on newly issued bonds after default, so they are also willing to negotiate over the reduction of unpaid debt.

B. Timing of the Model

Figure 3 summarizes the timing of decisions within each period.

Figure 3.
Figure 3.

Timing of the Model

Citation: IMF Working Papers 2016, 066; 10.5089/9781513596648.001.A001

  1. The sovereign starts current period with initial assets/debt bt, and credit history ht. We are in node (A).

  2. An income shock yt realizes. The sovereign decides whether to pay its debt or to default after observing its income.

  3. (i) In node (B) (payment node), if payment is chosen, we move to the upper branch of a tree. The sovereign chooses its consumption (ct) and level of assets/debt in next period (bt+1). Default risk is determined and creditors also choose bt+1. The price of bonds is determined in the market. With exogenous probability χ, we return to node (A) with upgraded credit history next period (ht+1 = ht − 1). Otherwise, we move back to node (A) with unchanged credit history next period (ht+1 = ht).

  4. (ii) In node (C) (default node), if default is chosen, we move on to the lower branch of a tree. The sovereign and foreign investors negotiate a debt reduction. Both recovery rates α(bt, ht, yt) and additional spread premia ϕ(bt, ht + 1, yt) are agreed to by both sides. After negotiation, the sovereign pays recovered debt α(bt, ht, yt)bt and suffers output costs λdyt. The sovereign cannot raise funds in the international capital market this period (bt+1 = 0), but will regain access to the market next period. Consumption is determined with remaining income. The sovereign’s credit history records the current debt renegotiation (ht+1 = ht + 1). We move back to node (A) with deteriorated credit history.

  5. An income shock yt+1 realizes.

V. Recursive Equilibrium

A. Sovereign Country’s Problem

In this section, we define the stationary recursive equilibrium of the model. The country’s problem is to maximize its expected lifetime utility. The country makes its default decision and determines its assets for next period (bt+1), given its current asset position (bt), credit history (ht), and income shock (yt). Let V(bt, ht, yt) be the value function of the country that starts the current period.

Given with the bond market price q(bt+1, ht, yt), debt recovery rates α(bt, ht, yt), and additional spread premia ϕ(bt, ht, yt), the country solves its optimization problem. We assume both the debt recovery rates and additional spread premia determined at current debt negotiation depend on these state variables.

For simplicity, we consider the problem with ht = 0, indicating that the country has never experienced debt renegotiation in the past. Later, we consider the problem with general cases ht ≥ 1.

For bt ≥ 0 (ht = 0), the country has savings. The country receives payments from foreign investors and determines its next-period asset position bt+1 and its consumption ct to maximize utility, given the price of bond q(bt+1, 0, yt). Thus the value function is

V(bt,0,yt)=maxct,bt+1u(ct)+βYV(bt+1,0,yt+1)dμ(yt+1,yt)s.t. ct+q(bt+1,0,yt)bt+1=yt+bt(1)

For bt < 0 (ht = 0), the country has debt. If the country decides to pay its debt, it chooses its next-period asset position bt+1 and consumption ct. On the contrary, if the country chooses to default, it suffers financial autarky for this period and its credit history deteriorates to ht+1 = 1 next period. Due to agreement in debt renegotiation, the country must pay −α(bt, 0, yt)bt in current period, and it regains access to the international capital market next period with history ht+1 = 1. With deteriorated credit history (ht+1 = 1), when the country issues new bonds, it must pay interests on newly issued bonds equal to the sum of the risk-free rate (r) and the spread premia agreed at the last renegotiation (ϕ(bt+1, 1, yt+1)). Thus, the price of bonds after default q(bt+2, 1, yt+1) incorporates the spread premia.

Given the option to default, V(bt, 0, yt) satisfies

V(bt,0,yt)=max[VR(bt,0,yt),VD(bt,0,yt;α(bt,0,yt),Φ(bt,1,yt))](2)

where VR(bt, 0, yt) is the value associated with paying debt:

VR(bt,0,yt)=maxct,bt+1u(ct)+βYV(bt+1,0,yt+1)dμ(yt+1,yt) s.t.ct+q(bt+1,0,yt)bt+1=yt+bt(3)

and VD (bt, 0, yt; α(bt, 0, yt), ϕ(bt, 1, yt)) is the value associated with default given with debt recovery schedule α(bt, 0, yt), and additional spread premia ϕ(bt, 1, yt) which will be determined at renegotiation after current default:

VD(bt,0,yt;α(bt,0,yt),ϕ(bt,1,yt))=u((1λd)yt+α(bt,0,yt)bt)+βY V(0,1,yt+1)d μ(yt+1,yt)(4)

where V(0, 1, yt+1) is value function next period with credit history ht+1 = 1 defined below in general cases with ht ≥ 1 and − α(bt, 0, yt)bt is the amount of defaulted debt which the country repays at the debt negotiation and λdyt denotes output costs which the country suffers due to current default.

Next we consider the problem with ht ≥ 1 expressing that the country has experienced the debt renegotiation at least once in the past. For bt ≥ 0 (ht ≥ 1), the country has savings. The country receives payments from foreign investors and determines its next-period asset position (bt) and its consumption (ct) to maximize utility. Thus the value function is

V(bt,ht,yt)=maxct,bt+1u(ct)+βYV(bt+1,ht,yt+1)dμ(yt+1,yt) s.t. ct+q(bt+1,ht,yt)bt+1=yt+bt(5)

Note that credit history remains unchanged in next period ht+1 = ht.

For bt < 0 (ht ≥ 1), the country has debt. The country can borrow from the foreign investors, but the country needs to pay not only the risk-free interest rate (r), but also the additional spread premia ϕ(bt, ht, yt) which was agreed to by both the country and foreign investors at the time of previous debt renegotiations. Thus, the price of bonds q(bt+1, ht, yt) is different from the one with history ht = 0, defined as q(bt+1, 0, yt), as it incorporates the effects of additional default premia associated with deteriorated credit history. As in the case of history ht = 0, the country chooses either to pay the debt or to default. The values are as before:

V(bt,ht,yt)=max[VR(bt,ht,yt),VD(bt,ht,yt;α(bt,ht,yt),ϕ(bt,ht+1,yt))](6)

where VR(bt, ht, yt) is the value associated with paying debt with history ht ≥ 1:

VR(bt,ht,yt)=maxct,bt+1u(ct)+β[(1χ)YV(bt+1,ht,yt+1)dμ(yt+1,yt)+χYV(bt+1,ht1,yt+1)dμ(yt+1,yt)]s.t. ct+q(bt+1,ht,yt)bt+1=yt+bt(7)

Note that with exogenous probability χ, the country’s credit history next period will revert due to limited memory of the investors as ht+1 = ht − 1. Otherwise, it remains constant as ht+1 = ht.

VD (bt, ht, yt; α(bt, ht, yt), ϕ(bt, ht + 1, yt)) is the value associated with default given with debt recovery schedule α(bt, ht, yt), and additional spread premia agreed after current default ϕ(bt, ht + 1, yt) which are defined:

VD(bt,ht,yt;α(bt,ht,yt),ϕ(bt,ht+1,yt))=u((1λd)yt+α(bt,ht,yt)bt)+βYV(0,ht+1,yt+1)d μ(yt+1,yt)(8)

where V(0, ht + 1, yt+1) is the value function next period with credit history ht+1 = ht + 1 and − α(bt, ht, yt)bt is amount of defaulted debt which the country recovers after negotiation.

Every time (at period t) the country defaults, its credit history records the current debt renegotiation ht+1 = ht + 1. Thus, the credit condition i.e., borrowing costs of the country after re-entry to the market depends on how much the country pays during the renegotiation. When the country issues new bonds after it defaults, it must pay returns based on the risk-free rate and the sum of additional spread premia, which are determined at the previous debt renegotiations.

The country’s default policy can be characterized by default set D(bt, ht) ⊂ Y, defined as the set of income shock y’s for which default is optimal given the debt position bt, and credit history ht.

D(bt,ht)={ytY: VR(bt,ht,yt)<VD(bt,ht,yt;α(bt,ht,yt),ϕ(bt,ht+1,yt))}(9)

Furthermore, we define an indicator of non-defaulting given initial asset position (bt < 0), credit history (ht), and income level (yt) as follows;

I(bt,ht,yt)={1ifytD(bt,ht)0ifytD(bt,ht)}

Finally, based on the policy function of asset position derived above (bt+1(bt, ht, yt)) and non-defaulting indicator I(bt, ht, yt), we define discounted value of expected amount of debt which will be paid to investors next period as:

P(bt,ht,yt)=11+rYI(bt+1(bt,ht,yt),ht,yt+1)bt+1(bt,ht,yt)dμ(yt+1,yt)(10)

Note that we use the discount factor for foreign investors (11+r), not the discount factor for the country (β).

B. Debt Renegotiation Problem

The debt renegotiation takes a form of generalized Nash bargaining game. Not only the recovery rate, but also additional spread premia are agreed to by both parties. This is because foreign investors will obtain interest returns every time the country issues new bonds after current default as long as the country does not default again. From the country’s perspective, it has to pay interests on bonds every time it issues new bonds after renegotiation, unless it chooses to remain in the financial autarky permanently.

After debt renegotiation, the country pays a fraction α(bt, ht, yt) of defaulted debt. The value of the country after the renegotiation is defined above;

VD(bt,ht,yt;α(bt,ht,yt),ϕ(bt,ht+1,yt))=u((1λd)yt+α(bt,ht,yt)bt)+βYV(0,ht+1,yt+1)d μ(yt+1,yt)

Needless to say, this value takes into account the impact of both debt reduction to −α(bt, ht, yt)bt, and additional spread premia ϕ(bt, ht + 1, yt) which will be agreed to by both sides at current debt negotiation.

Foreign investors obtain the present value of the reduced debt α(bt, ht, yt) and interests on newly issued bonds after debt negotiation. The present value of expected payment of bonds which investors receive in the future after the country’s re-entry to the market, can be defined in the following recursive form:

R(bt,ht,yt)=P(bt,ht,yt)+11+rYR(bt+1,ht,yt+1)dμ(yt+1,yt) s.t.bt+1=bt+1*(bt,ht,yt)(11)

where P(bt, ht, yt) is the discounted value of expected amount of bonds which are returned in next period defined in equation (10) and bt+1*(bt,ht,yt) is policy function of the country if it chooses not to default (ht+1 = ht).

We assume that debt negotiation takes place only once for each default event. The threat point of the bargaining game is that the country stays in financial auturky permanently and foreign investors get nothing. The country suffers output cost λdyt. The expected value of autarky for the country, VAUT( yt) is given by following expression;

VAUT(yt)=u((1λd)yt)+βYVAUT(yt+1)dμ(yt+1,yt)(12)

We consider one-round bargaining since one-round bargaining keeps the model tractable as there is no need to consider multiple rounds of bargaining or the debt arrears based on different reduction schedules.25

For any debt recovery rate at and additional spread premia spt, we denote the country’s surplus in Nash bargaining by ΔB(at, spt; bt, ht, yt), which is the difference between the value of accepting a proposal of debt recovery rate at and additional spread premia spt, and the value of rejecting it, given the country’s debt level (bt), credit history (ht), and income level (yt).

ΔB(at,spt;bt,ht,yt)=VD(bt,ht,yt;α(bt,ht,yt),ϕ(bt,ht+1,yt))VAUT(yt)(13)

The surplus to the country comes from two sources. First, the country will be able to issue bonds again from the following period, though its credit history deteriorates. Second, the country will no longer suffer output costs after negotiation.

In constrast, the surplus to investors is the present value of the sum of recovered debt and interest returns on newly issued bonds after renegotiation:

ΔL(at,spt;bt,ht,yt)=atbtR(bt,ht,yt)(14)

where interest returns are evaluated with expected payment incorporating the future default choices of the country as in equation (11).

We assume that the country has a bargaining power θ and foreign investors have a bargaining power 1 − θ. The bargaining power θ summarizes the institutional arrangement of debt negotiation. To ensure that the bargaining problem is well defined, we define the bargaining power set Θ ⊂ [0,1] such that for θ ∈ Θ, the negotiation surplus has an unique optimum for any debt (bt < 0), credit history (ht), income level (yt).

Given the country’s debt (bt < 0), credit history (ht), and income level (yt), optimal recovery rates α(bt, ht, yt) and additional spread premia ϕ(bt, ht + 1, yt) solve the following bargaining problem:

{α(bt,ht,yt)ϕ(bt,ht+1,yt)}=argmaxat,spt[(ΔB(at,spt;bt,ht,yt))θ(ΔL(at,spt;bt,ht,yt))1θ]s.t. ΔB(at,spt;bt,ht,yt)0s.t. ΔL(at,spt;bt,ht,yt)0(15)

Note that ϕ(bt, ht + 1, yt) is a function specifying state-variant contracts depending on future streams of bt and ht.26 Since the set of both debt recovery schedule and additional spread premia that maximize total negotiation surplus conditional on the country’s debt, credit history and income level, negotiation outcome provides better insurance to the country in the case of default.

C. Foreign Investors’ Problem

For the cases with ht ≥ 1, our derived bond price incorporates the effects of additional spread premia agreed at previous debt renegotiations, which are the new elements in our model. First, we consider foreign investors’ problem given the country’s credit history ht = 0.

With the country’s credit history ht = 0, taking the bond price function as given, foreign investors choose the amount of assets (bt+1) that maximizes their expected profit π(bt+1, 0, yt), given by

={π(bt+1,0,yt)q(bt+1,0,yt)bt+111+rbt+1if bt+101p(bt+1,0,yt)+p(bt+1,0,yt)γ(bt+1,0,yt)1+r(bt+1)q(bt+1,0,yt)(bt+1)otherwise}(16)

where p(bt+1, 0, yt) and γ(bt+1, 0, yt) are the expected default probability and expected recovery rates respectively for country with debt (bt+1 ≤ 0), credit history (ht = 0), income level (yt), and r is risk-free rate.

Since we assume that the market for new sovereign bonds is completely competitive, foreign investors’ expected profit is zero in equilibrium. Using the zero expected profit condition, we get

q(bt+1,0,yt)={11+rif bt+101p(bt+1,0,yt)+p(bt+1,0,yt)γ(bt+1,0,yt)1+rotherwise}(17)

When the country buys bonds from foreign investors bt+1 ≥ 0, the sovereign bond price is equal to the price of risk-free bond, 11+r. When the country issues bonds to foreign investors bt+1 ≤ 0, there is default risk, and the bond is priced to compensate foreign investors for this. Since 0p(bt+1,0,yt)1 and 0 γ(bt+1,0,yt)1 the bond price q(bt+1, 0, yt) lies in [0,11+r].

Next, we consider foreign investors’ problem for general cases with the country’s history ht ≥ 1. Note that the borrowing costs of the country is denoted by 1 + r + ϕ(bt, ht, yt) which include the additional spread premia agreed at the previous debt renegotiations. Given the borrowing costs, together with the bond price q(bt+1, ht, yt), foreign investors maximize their expected profit γ(bt+1, ht, yt), given by

={π(bt+1,ht,yt)q(bt+1,ht,yt)bt+111+rif bt+101p(bt+1,ht,yt)+p(bt+1,ht,yt)γ(bt+1,ht,yt)1+r+Φ(bt,ht,yt)(bt+1)q(bt+1,ht,yt)(bt+1)otherwise}(18)

where p(bt+1, ht, yt) and γ(bt+1, ht, yt) are as above. Using the zero profit condition, we obtain

q(bt+1,ht,yt){11+rif bt+101p(bt+1,ht,yt)+p(bt+1,ht,yt)γ(bt+1,ht,yt)1+r+Φ(bt,ht,yt)otherwise}(19)

When the country issues bonds to foreign investors, the bond price q(bt+1, ht, yt) lies in [0,11+r+Φ(bt,ht,yt)] since 0 ≤ p(bt+1, ht, yt) ≤ 1 and 0 ≤ γ(bt+1, ht, yt) ≤ 1. Thus, the bond price incorporates the additional default premia ϕ(bt, ht, yt) due to the previous debt renegotiations; the price of bonds decreases as additional spread premia increase.

Moreover, for any credit history (ht), interest rate on sovereign bonds is defined as follows; rS(bt+1,ht,yt)=1q(bt+1,ht,yt)1. It is bounded below by the risk-free rate (r). We define the country’s total spreads which is a difference between country’s interest rate and the risk-free rate:

s(bt+1,ht,yt)=1q(bt+1,ht,yt)(1+r)(20)

D. Recursive Equilibrium

We define a stationary recursive equilibrium of the model.

Definition: A recursive equilibrium is a set of functions for, (a) the country’s value function V*(bt, ht, yt) (together with VR*(bt, ht, yt) and VD*(bt, ht, yt), α(bt, ht, yt), ϕ(bt, ht + 1, yt)), asset position bt+1*(bt,ht,yt) consumption ct+1*(bt,ht,yt), default set D*(bt, ht), and discounted expected payment P*(bt, ht, yt), (b) recovery rates α*(bt, ht, yt) and additional spread premia ϕ*(bt, ht + 1, yt), (c) bond price function q*(bt+1, ht, yt), and total spreads s*(bt+1, ht, yt) such that

[1]. Given the bond price function, recovery rate and additional spread premia, the country’s value function, asset position, consumption, default set, and discounted expected payment satisfy the country’s optimization problem (1)-(10).

[2]. Given the bond price function, the country’s value function and discounted expected payment, recovery rate and additional spread premia solve debt renegotiation problem (15).

[3]. Given recovery rates and additional spread premia, the bond price fucntion and the total spreads satisfy optimal conditions of foreign investors’ problem (17) and (19).

In equilibrium, default probability p*(bt+1, ht, yt) is defined by using the country’s default decision:

p*(bt+1,ht,yt)=D*(bt,ht)du(yt+1,yt)(21)

The expected recovery rate γ*(bt+1, ht, yt) in equilibrium is given by

γ*(bt+1,ht,yt)=D*(bt,ht)α*(bt,ht,yt)du(yt+1,yt)D*(bt,ht)du(yt+1,yt)=D*(bt,ht)α*(bt,ht,yt)du(yt+1,yt)p*(bt+1,ht,yt)(22)

The numerator is expected proportion of the debt which the country will repays at renegotiation, and the denominator is default probability.

VI. Quantitative Analysis

This section provides quantitative analysis of the model. We set parameters and functional forms of the model and discuss equilibrium properties of the model. Simulation results based on equilibrium distribution of the model are presented in Section VI.C. We explore the decomposition of spreads in Section VI.D. Finally, we summarize main implications of quantitative analysis.

A. Parameters and Functional Forms

We use most of the parameters and functional forms specified in Yue (2010). There are three new elements in our model: (1) the maximum level of additional spread premia, (2) the maximum level of credit history, and (3) probability of upgrading in credit history. The rationale of the upper limits of both additional spread premia and credit history is to satisfy the stationarity of the model; if we do not set the upper limits, the country will face high borrowing costs and repeat defaults in short periods leading to higher spreads, and investors will not be able to receive spread payments. Reflecting the fact that the record of defaults remains on the country’s credit history for only a finite number of years rather than infinite periods, we assume the probability of upgrading in credit history.

We define each period as a quarter. The following constant relative risk-aversion (CRRA) utility function is used:

u(ct)=ct1σ11σ(23)

where σ expresses degree of risk aversion. We set σ equal to 2, which is a common value used in real business cycle studies. Following Arellano (2008), the risk-free rate is equal to 1.7 percent. The baseline output loss parameter λd is set to 2 percent based on Strurzeneger’s (2004) estimate.

We follow the same stochastic process for output used in Yue (2010). She models the output growth rate as AR(1) process to capture the stochastic trend in GDP of Argentina as:

log(gt)=(1ρg)log(1+ug)+ρglog(gt1)+tg

where growth rate is gt=ytyt1, growth shock is tg ~i.i.d N(0,σg2), and log (1 + µg) is expected log gross growth rate of the country’s endowment. We set μg = 0.0042, σg2=0.0253, and ρg = 0.41, and approximate this stochastic process as a discrete Markov chain of 21 equally spaced grids by using the quadrature method in Tauchen (1986).

Since a realization of the growth shock permanently affects endowment and the model economy is nonstationary, we detrend the model by dividing by the lagged endowment level yt−1. The detrended counterpart of the any variable xt is thus x̂t=xtxt1. The equilibrium value function, bond price function, recovery rate and interest spreads are evaluated based on the detrended variables.

Concerning time discount factor β and baseline country’s bargaining power θ, we set β = 0.75 and θ = 0.72, to obtain its average default frequency 2.65 percent annually or 0.66 percent quarterly and recovery rate 31.3 percent. We target default probability 2.7 percent annually and the average recovery rate 33 percent for the 2005 international debt restructuring estimated by Sturzenegger and Zettelmeyer (2006, 2008). For interest spreads, we set the maximum level of additional spread premia (ϕmax) corresponding to the evidence in Figure 2 that the increase in spreads is less than 0.01 (100 basis points). Lastly, taking into account 3 defaults of Argentina in the period from 1901–2002 indicated in Reinhart, Rogoff, and Savastano (2003), we specify the maximum level of credit history (hmax) as 3. The probability of upgrading χ, which governs the average length of time that a recent default remains on the country’s credit history is set to 0.025, reflecting that investors’ memory lasts for 10 years.27 This is also consistent with spreads dynamics in Argentina: an average of interest spreads for 2002Q1–2011Q4 is higher than one for pre-default period. Table 4 summarizes the model parameters. Our computation algorithm is shown in Appendix I.

Table 4.

Model Parameters

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B. Numerical Results on Equilibrium Properties

In this subsection, we discuss the equilibrium properties of the model. Figure 4 shows the relationship between the increase in interest spreads and recover rates unconditional on income states.28 To be consistent with Section III, we define the increase in spreads as the difference between spreads with defaults and those with non-defaults. We calculate spreads after default based on both expected recovery rates for next default and agreed additional spread premia, and spreads with non-defaults are measured with expected recovery rates for the current default. It is clear that there is a negative relationship between recovery rates and the increase in interest spreads. If the increase in spreads is high, recovery rate is low (haircut is high) and vice versa. One interpretation is that if the country repays a large fraction of its debt at the renegotiations, long-term borrowing costs will be small. In the case of Yue (2010), the slope of the contract curve is vertical as shown in Figure A2 in Appendix IV. A driving force which makes our results different from Yue (2010) is additional spread premia agreed to by both parties at the debt restructurings.

Figure 4.
Figure 4.

Relationship Between the Increase in Interest Spreads and Recovery Rates

Citation: IMF Working Papers 2016, 066; 10.5089/9781513596648.001.A001

Figure 5 illustrates the baseline default probability at the mean income level. It is apparent that the default probability is weakly increasing with the credit history. At the higher level of credit history (ht = 3), additional increase in spreads on the newly issued bonds, which is determined at the previous debt renegotiation, leads to higher borrowing costs for the country compared with non-default credit history ht = 0. The country facing higher borrowing costs is more likely to default given the debt-to-GDP ratio.

Figure 5.
Figure 5.

Default Probability under Baseline Case

Citation: IMF Working Papers 2016, 066; 10.5089/9781513596648.001.A001

Figure 6 shows that the bond price is also weakly decreasing with respect to the credit history. This is driven by the additional spread premia agreed to by both parties at the past debt renegotiations: as explained in detail in Section VI.D., these additional spread premia reduce the bond price both directly and indirectly through default probability as explained above.

Figure 6.
Figure 6.

Bond Price Schedule under Baseline Case

Citation: IMF Working Papers 2016, 066; 10.5089/9781513596648.001.A001

C. Simulation Results

We conduct 1000 rounds of simulations with 2000 periods per round and then extract 80 observations before and 25 observations after each default event in stationary distribution to compute statistics.29 Bond spreads are from the J.P. Morgan’s Emerging Markets Bond Index Global (EMBIG) for Argentina for 1997Q1–2001Q4 and 2005Q3–2011Q3. Output data are seasonally adjusted from the the Ministry of Economy and Production in Argentina (MECON) for 1980Q1–2001Q4 and 2005Q3–2011Q3. Consumption and trade balance data are also seasonally adjusted from the MECON for 1993Q1–2001Q4 and 2005Q3–2011Q3. The trade balance is calculated as ratio to nominal GDP. Argetina’s external debt data are from the IMF World Economic Outlook (WEO) for 1980–2001 and 2005–11. We compute two measures of the sovereign’s indebtness: the first measure is the average external debt/GDP ratio. We also compute the ratio of the country’s debt service (including short-term debt) to its GDP for Argentina. One advantage of our model compared with Yue (2010) or Aguiar and Gopinath (2006) is that we obtain the statistics for post-default periods.

As obvious from Table 5, the model matches the business cycle statistics in data. For pre-default periods, our model replicates volatile consumption and trade balance-to-GDP volatility, both of which are prominent features of emerging market business cycle models. In addition, it also generates the negative correlation between trade balance and output. However, a novelty of our model comes from the better match of statistics with data in post-default periods, particilarly on consumption volatility and correlation of trade balance and output.

Table 5.

Business Cycle Statistics for Argentina

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Sources: Aguiar and Gopinath (2006), author’s calculation, Datastream, IMF WEO, MECON, Yue (2010).

We move on to non-business cycle statistics of the model and data reported in Table 6. First of all, in pre-default periods, the model replicates a moderate level of debt relative to data statistics. In the data, the total debt service-to-GDP ratio and short-term debt-to-GDP ratio are 12.7 percent and 10.2 percent. Our model generates the average debt-to-GDP ratio of 9.5 percent. In addition, the model also shows the relation among bond spreads, debt-to-GDP ratio and output as in the data. Bonds spreads are possitively correlated with debt-to-GDP, but negatively correlated with output. This is because default probability is high and recovery rates are low in low income states resulting in high spreads. The average bond spreads is 3.1 percent in our simulations, lower than 7.4 percent reported in the data, but higher than in Yue (2010). The volatility of bond spreads is 1.9 percent in our simulation, close to the data (2.9 percent). The debt recovery rates are negatively correlated with default probability.

Table 6.

Model Statistics for Argentina

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Sources: Aguiar and Gopinath (2006), author’s calculation, Datastream, IMF WEO, MECON, and Yue (2010).

Data statistics before default correspond to sample of 1980Q1–2001Q1 (Output), 1990Q1–2001Q4 (trade balance and consumption), and 1997Q1–2001Q4 (spreads).

Data statistics during and after debt renegotiation correspond to samples of 2002Q1–2005Q2 and of 2005Q3–2011Q3 respectively.

Two meatures are the average total debt service (interest and amortication paid) and the average short-term debt outstanding at year end. We use the second measure (short-term debt outstanding) to calculate correlations.

More importantly, what makes our model more distinctive is that the model accounts the regularities in the post-default periods. The average debt-to-GDP ratio is 12.3 percent, close to the short-term debt-to-GDP ratio of 13.2 percent. It is clear that the model explains one prominent feature of average debt-to-GDP ratio in both pre-default and post-default periods: the average debt-to-GDP ratio is higher in post-default period (12.3 percent) than in pre-default period (9.5 percent). What drives this is the increase in borrowing costs which forces the sovereign to accumulate higher debt. Furthermore, our model provides the better match of the relation among bond spreads, debt-to-GDP ratio and output in post-default periods than in pre-default periods. Even in the same low income states, the sovereign tends to accumulate higher debt in post-default periods leading to higher spreads than in pre-default periods. This is also justified by the average bond spreads in post-default periods (3.9 percent) higher than one in pre-default periods (3.1 percent). It also shows an obvious improvement of the average spreads compared with Yue (2010). In constast, the volatility of bond spreads in post-default periods is only marginally higher than one in the pre-default periods.

Furthermore, we calculate the average time spans between defaults based on 2000 rounds of simulations by extracting the initial 200 periods of total 2000 periods per round. Table 7 reports that the average spans between defaults are weakly decreasing with respect to the number of past debt renegotiations. This pattern is robust to extensions related with the upper limits of credit history. Our model successfully replicats the observed stylized fact 3 and 4 in Section III.

Table 7.

Average Time Spans between Defaults (quarters)

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Source: author’s calculation.

D. Decomposition of Interest Spreads

In this subsection, we explain how additional spread premia agreed at past debt renegotiations lead to an increase in spreads, which distinguishes this paper from previous work. Based on equation (19) and (20), we can rewrite interest spreads for credit history ht ≥ 1 as follows.

s(bt+1,ht,yt)={0if bt+101+r+Φ(bt,ht,yt)1p(bt+1,ht,yt)+p(bt+1,ht,yt)γ(bt+1,ht,yt)(1+r)otherwise}

Given risk-free rate (r), total spreads can be decomposed into two factors:

(A) spread components based on “pure” default probability (future defaults),

(B) spread components based on impact of additional spread premia (past defaults).

The former which is simply calculated based on “pure” probability of future defaults is totally irrelevant to the credit history. It is the measure of interest spreads used in Yue (2010). The latter is how much the term ϕ(bt, ht, yt), increases total spreads both directly and indirectly through default probability as explained in Section VI.B. It can be regarded as spread components associated with the past default history.

Figure 7 displays both the total spreads and spread components measured with “pure” default probability. The spread components measured with “pure” default probability is equal to (A). The total spreads is defined by the above equation. The difference between these two corresponds to (B), which can be interpreted as spread components associated with the past default history. It is clear that total spreads deviate from spread components measured with “pure” default probability when debt-to-GDP ratio is above the threshold value 0.175 in the mean income state.

Figure 7.
Figure 7.

Total Spreads and Spreads Based on “Pure” Default Probability

Citation: IMF Working Papers 2016, 066; 10.5089/9781513596648.001.A001

E. Brief Summary of the Quantitative Analysis

Our major findings can be summarized as follows. First of all, by incorporating additional spread premia, the model accommodates the observed pattern of lower recovery rates (larger haircuts) associated with larger increases in yield spreads. Second, we show that default probability is weakly increasing with credit history, given the same debt-to-GDP ratio. Third, our model accounts both business cycle and non-business cycle regularities in the post-default periods. More importantly, we replicate that average spans between defaults are weakly decreasing as the debtor country experiences more defaults. Finally, interest spreads in our model can be decomposed into two parts: spread components of future defaults and of past default history.

VII. Model Implications

In this section, we explore the determinants of the slope of the contract curve. Moreover, we consider possible implications derived from both changes in length of creditors’ memory and size of additional spread premia.

A. Determinants of the Slope of the Contract Curve

We focus on factors which affect the value of the slope of the contract curve. Table 8 shows the values of the slope under different values for the discount factor, the maximum level of additional spread premia, output cost, risk-free rate and probability of upgrading in credit history.30 The impact of a change in one parameter, leaving all other parameters fixed is indicated.

Table 8.

Values of the Slope of the Contract Curve under Different Parameter Values

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Source: author’s calculation.

First, the slope gets steeper as the discount factor decreases. As the country is more willing to default in the future, foreign creditors opt to demand higher recovery rates at the current reneogtiation rather requesting higher spread premia, tilting the constract curve steeper. Similarly, when the maximum level of additional spread premia is reduced to 50 basis points (ϕmax = 0.005), the absolute value of the slope increases. Since foreign creditors can only demand lower spread premia, they instead request higher recovery rates at the current renegotiation resulting steeper contract curve.

In contrast, an increase in output cost leads to an increase in the absolute value of the slope. As the country is less willing to default due to higher output cost, payments on future spreads become more costly for the country. Thus, the country prefers to pay higher recovery rates at the renegotiton to reduce future spread payments.

The absolute value of slope increases as the risk-free rate increases. As the discount rate for foreign creditors (inverse of risk-free rate) decreases, receipt of future spread returns becomes less worth than one under the baseline. Instead of demanding higher spread premia, foreign creditors request higher recovery rates at the renegotiation. Lastly, probability of upgrading in credit history does not affect the value of slope.

B. Duration and Size of Additional Spread Premia

Determination of both recovery rates and additional spread premia at the debt renegotiation plays an important role in our model. The probability of upgrading in credit history and maximum level of additional spread premia are two key parameters which specify the duration and size of deterioration in long-term credit. Table 9 reports how changes in these parameter values influence the non-business cycle statistics.31

Table 9.

Statistics for Different Levels of Upgrading in Credit History and Additional Spread Premia

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Source: author’s calculation.

The increase in probability of upgrading reduces the average debt-to-GDP ratio in post-default period. As the probability of upgrading in credit history gets higher, length of deterioration in long-run credit gets shorter. The sovereign tends to accumulate lower level of debt.

On the contrary, not only the average debt-to-GDP, average bond spreads in post-default periods, but also the default probability increases as the upper limit of additional spread premia gets higher. The maximum level of additional spread premia identifies the size of deterioration in long-term credit, given the fixed duration. Associated with the increase in borrowing costs, the sovereign accumulates more debt leading to increases in both spreads and default probability.

VIII. Conclusion

This paper explores theoretically and empirically serial sovereign defaults and debt restructurings. The empirical section of our paper presents new stylized facts on serial sovereign defaults and debt restructurings. To explain observed stylized facts, we build a theoretical model of sovereign debt and defaults that explicitly models debt renegotiations between a defaulting country and its creditors. Quantitative analysis of the model reveals that the equilibrium probability of default for a given debt-to-GDP level is weakly increasing with the number of past defaults, consistent with empirical observations. The equilibrium of the model also corresponds with the observed stylized fact: lower recovery rates are associated with larger increases in yield spreads. This mechanism drives the equilibrium serial default behavior in the model, and it is a plausible explanation of the pattern of repeat defaults observed in the data.

So far, we have considered the debt renegotiation under symmetric information between the country and investors. It might be possible that some of the information concerning the country’s profile remains unrevealed to investors at the time of renegotiation, such as the country’s government type as in Hachondo and others (2009) and D’Erasmo (2010) or actual level of output costs. In constrast, degree of coordination among the creditors or creditor composition is uninformed to the country at the renegotaition. A comparison of renegotiation outcomes under two asymmetric information cases will be a potential research topic in the future.

Serial Sovereign Defaults and Debt Restructurings
Author: Mr. Tamon Asonuma