Determinants of Sovereign Risk: Macroeconomic

Fundamentals and the Pricing of Sovereign Debt1

Jens Hilscher Yves Nosbusch

Brandeis University London School of Economics

First draft: November 2004

This version: July 2008

1Contact: Jens Hilscher, International Business School, Brandeis University, 415 South Street,Waltham MA 02453, USA. Phone 781-736-2261, email hilscher@brandeis.edu. Yves Nosbusch, De-partment of Finance, London School of Economics, Houghton Street, London WC2A 2AE, UK. Phone+44-20-7955-7319, email y.nosbusch@lse.ac.uk. An earlier version of this paper was circulated underthe title “Determinants of Sovereign Risk.” We are grateful to John Campbell, N. Gregory Mankiw,Kenneth Rogoff, and Jeremy Stein for their advice and suggestions. We thank Alberto Alesina, SilviaArdagna, Gregory Connor, Darrell Duffie, Nicola Fuchs-Schündeln, Amar Gande, David Hauner, DirkJenter, David Laibson, David Lesmond, Emi Nakamura, Ricardo Reis, Andrei Shleifer, Monica Singhal,Jón Steinsson, Federico Sturzenegger, Suresh Sundaresan, Glen Taksler, Sam Thompson, and seminarparticipants at Harvard University, the Federal Reserve Board of Governors, Warwick Business School,Oxford Saïd Business School, the Bank for International Settlements, Macalester, UC Irvine, BrandeisUniversity, Barclays Global Investors, Oak Hill Platinum Partners, the 2006 MMF conference, the 2006FMA conference, the Swiss National Bank, the 2007 Moody’s and Copenhagen Business School CreditRisk Conference, the 2007 EFA meetings, the 2007 EEA meetings, the Bank of England, and the 2008ESRC/WEF Warwick Conference on Incentives and Governance in Global Finance for helpful com-ments and discussions. We also thank Timothy Callen and James Morsink at the IMF, Gonca Okurat the World Bank, Carmen Reinhart, and Alvin Ying at J.P. Morgan for providing us with data andPavel Bandarchuk for research assistance.

Abstract

This paper investigates the effects of macroeconomic fundamentals on emerg-ing market sovereign credit spreads. We pay special attention to the volatil-ity of fundamentals in addition to their levels. In reduced form regressions,the volatility of terms of trade in particular has a statistically and econom-ically significant effect on spreads. We propose an empirically tractablemodel that addresses the distinct features of sovereign risk. Our model cap-tures a significant part of the empirical variation in spreads. It fits betterfor borrowers of lower credit quality. We also estimate default probabilitiesin a hazard model and link these probabilities to observed spreads.

JEL classifications: F34, G12, G13, G15

Keywords: sovereign spreads, credit risk, bond pricing, terms of trade, de-fault probabilities.

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1 Introduction

There is tremendous variation in the interest rates emerging market governments pay

on their external debt. This is true both across countries and over time. A common

measure of a country’s borrowing cost in international capital markets is its yield spread,

which is defined as the difference between the interest rate the government pays on its

external U.S. dollar denominated debt and the rate offered by the U.S. Treasury on debt

of comparable maturity.

In this paper we consider how much of the variation in yield spreads across countries

and over time can be explained by macroeconomic fundamentals. We focus in partic-

ular on the explanatory power of the volatility of fundamentals. From a theoretical

perspective, the volatility of fundamentals should matter for the pricing of defaultable

debt, just as the level of these fundamentals does. All else equal, a country with more

volatile fundamentals is more likely to experience a severe weakening of fundamentals

which will force it into default. This risk should be reflected in a higher yield spread

on its bonds.1 While this idea is well understood in theory, it has been largely ignored

by the empirical literature on sovereign debt, which has tended to focus exclusively on

level variables.2 In contrast, the present paper includes both the level and the volatility

of macroeconomic fundamentals in its empirical analysis.

1This intuition corresponds to that of the structural bond pricing literature starting with Merton’s(1974) seminal model of risky corporate debt: an investor can view risky debt as a combination of safedebt and a short position in a put option. The value of the option depends on the volatility of theunderlying firm value; hence the value of the firm’s bonds also depends on this volatility. In the caseof a country, higher volatility of fundamentals increases the value of the default option and thereby thespread.

2Two exceptions are Edwards (1984), who includes variability of reserves and finds that it is insignif-icant, and Westphalen (2001), who finds some limited effect of changes in local stock market volatilityon changes in short term debt prices. In the corporate bond context, Campbell and Taksler (2003)find a strong empirical link between equity volatility and yield spreads.

3

There are three main parts to our analysis. In the first part we analyze sovereign

debt pricing in a reduced form regression framework. We measure yield spreads on

external U.S. dollar denominated debt using data from J.P. Morgan’s Emerging Market

Bond Index (EMBI) covering a set of 32 emerging market countries from 1994 to 2006.

We report results from reduced form regressions of these spread observations on a set of

macroeconomic fundamentals.

Motivated by previous studies (e.g. Edwards (1984, 1986)), we choose the ratio of

debt to GDP as our starting point. We then increase our set of explanatory variables,

paying particular attention to terms of trade. Terms of trade measure the price of

a country’s exports relative to its imports. Changes in the terms of trade should

therefore have a direct effect on a country’s ability to generate dollar revenue from

exports and thus make payments on its external dollar denominated debt. This point

was made by Bulow and Rogoff (1989). Mendoza (1997) presents evidence that terms

of trade volatility has negative effects on long run growth and Mendoza (1995) finds

that terms of trade volatility is important for explaining output variability at business

cycle frequencies. Another appealing feature of terms of trade is that they are plausibly

exogenous since they are calculated using world prices.

Our reduced form regression results show that spreads indeed tend to be higher for

countries that have recently experienced adverse terms of trade shocks, while countries

that have seen their terms of trade improve tend to have lower spreads. We also find that

the volatility of terms of trade has a highly significant effect on spreads, both statistically

and economically.

We also include the growth rate of GDP and the volatility of GDP growth in our

reduced form regression model and find that they are statistically and economically

4

significant and add overall explanatory power. In order to measure a country’s access to

liquid assets that can be used for debt repayment, we include the ratio of reserves to GDP

and find it to be significant. Finally, we add a measure of a country’s default history to

this set of explanatory variables. We find that, even after accounting for macroeconomic

fundamentals, spreads are higher for countries that have recently emerged from default.

This is consistent with Reinhart, Rogoff, and Savastano (2003), who argue that a key

predictor of future default is a country’s history of default.

In terms of economic significance, terms of trade turn out to be the most important

determinant of spreads, followed by the ratio of debt to GDP. Looking at explanatory

power in the cross-section and the time-series, the ratio of debt to GDP captures a large

share of the within-country time-series variation in spreads but has less explanatory

power in the cross-section. This suggests that what is important is whether a country’s

debt level is high relative to its own mean, not whether it is high relative to other

countries.

In the second part of the paper, we consider the link between debt prices and default

probabilities in the context of a structural form framework. Standard structural models

of risky corporate debt cannot be used when pricing sovereign debt. In these models,

the firm defaults and is taken over by creditors if firm asset value falls below liabilities.

In the sovereign case, there is no equivalent of firm asset value with an observable market

price. Moreover, even if one could agree on an underlying wealth measure, creditors

typically do not hold claims to a country’s assets in the event of default.

We propose an empirically tractable model in which the level and the volatility

of macroeconomic fundamentals determine the probability of default and debt prices.

The model addresses the distinct features of sovereign debt while retaining the familiar

5

intuition of structural corporate bond pricing models. In the model a country defaults if

fundamentals are too low or the debt burden is too high, i.e. if repayment becomes too

costly. Fundamentals determine both the probability of default and the recovery value

in the event of default.

Using data on country defaults and fundamentals from 1970 to 2003, we fit our model

to price bonds directly. We estimate the relative importance of fundamentals by running

a predictive regression of a default indicator on our set of explanatory variables. We

then use the estimated model implied parameters and default probabilities to predict

spreads and find that the model captures a large share of the variation in spreads.

In the third part of the paper, we estimate default probabilities in a reduced form

hazard model and use fitted probabilities to price debt. This approach effectively relaxes

the restrictions on functional form imposed by the structural model that we present

in the second part of the paper. We again use the sample period starting in 1970.

We estimate the conditional probability of default over the next period in a reduced

form logit model following the approach proposed by Shumway (2001) in the context

of predicting corporate bankruptcy. We find that the level of debt to GDP and the

volatility of terms of trade are important predictors of default, in line with their effect on

spreads. We use the reduced form default probabilities to calculate predicted spreads

and find an improvement in explanatory power relative to model implied spreads.

Both the structural model and the reduced form hazard model allow us to identify

systematic mispricing in the market, which is something reduced form spread regressions

like the ones presented in the first part of the paper cannot achieve since they fit the

overall mean of observed spreads by construction. We find that model implied and

reduced form spreads can account for 51% and 61% of the variation in observed spreads,

6

respectively.

We also group bond spread observations by their estimated default probability and

compute average levels of observed and model implied spreads for each group. We find

that model implied spreads are smaller than actual spreads for all the groups,3 but that

the proportion of the yield spread explained by our model increases significantly with the

probability of default. Huang and Huang (2003) find a similar pattern when calibrating

structural form models to U.S. corporate bond prices.

This paper adds to the large literature on the empirical determinants of sovereign

yield spreads. The literature varies widely in choice of variables and methodology. Some

papers concentrate on reduced form regressions of spreads on explanatory variables.

Examples of this line of research include Edwards (1986), Eichengreen and Mody (1998),

Min (1998), Beck (2001), and Ferrucci (2003), among others. These authors explore a

large set of macroeconomic variables to explain spreads.4 Although no clear consensus

on the determinants of spreads emerges from these studies, the level of debt to GDP is

generally found to be significant. As already mentioned, we pay special attention to

measures of volatility that are largely absent from this literature.

Duffie, Pedersen, and Singleton (2003) develop a flexible reduced form model of

sovereign yield spreads that builds on the framework of Duffie and Singleton (1999).

Their model accounts for the specific context in which a country may selectively default

3This is not surprising given that we only model the default component of the spread. Hund andLesmond (2007) provide evidence that a significant part of the spread on emerging market corporateand sovereign debt may be explained by liquidity. In related work, Chen, Lesmond, and Wei (2007)present evidence that liquidity is priced in U.S. corporate bonds. Longstaff, Mithal, and Neis (2005)find that the majority of the U.S. corporate default swap spread is explained by default risk and thatthe non-default component is time-varying and closely related to measures of liquidity.

4Some papers such as Cantor and Packer (1996), and Kamin and von Kleist (1999) instead use creditratings as a comprehensive measure.

7

on or restructure part of its debt. They estimate the model using weekly data on

Russian dollar-denominated debt and US swap yields between 1994 and 1998. Pan and

Singleton (2006) explore the term structure of credit default swap (CDS) spreads for

Mexico, Turkey, and Korea from 2001-2006 and consider the risk-neutral credit event

intensities and loss rates that best describe the CDS data. While these studies relate

spreads implied by a reduced from pricing model to political factors, foreign currency

reserves, oil prices, and measures of liquidity such as VIX, macroeconomic fundamentals

do not directly enter the estimation of the pricing model. In contrast, our focus is to

explore directly the extent to which variation in macroeconomic fundamentals determine

spreads and default probabilities across countries and over time.

There is also a large literature on predicting banking and currency crises and sov-

ereign default using macroeconomic fundamentals.5 Again, the focus of these studies

is on level variables, rather than volatility. There are some exceptions: in two recent

papers, Catão and Sutton (2002) and Catão and Kapur (2006) predict sovereign default

in a hazard model using a similar setup to the one used in the third part of this pa-

per. They identify volatility of terms of trade as an important predictor of default.

These studies on default and crisis prediction do not, however, relate the determinants

of default to the determinants of spreads.

The remainder of the paper is organized as follows. Section 2 describes the data.

Section 3 describes the results from using fundamentals to explain spreads in a reduced

form regression framework. Section 4 discusses why corporate bond pricing models

5Early contributions to this literature include Hajivassiliou (1987, 1994). Berg, Borensztein, Milesi-Ferretti, and Pattillo (1999), Kaminsky and Reinhart (1999), and Goldstein, Kaminsky, and Reinhart(2000) have concentrated on constructing what they refer to as “early warning systems.” Berg, Boren-sztein, and Pattillo (2004) provide an overview of this line of research.

8

cannot be applied in the case of sovereign debt and introduces our model of sovereign

debt. We derive the model implied probability of default and spread. In section 5 we

fit our model to the data directly, and find that it accounts for a substantial fraction

of observed spread variation. Section 6 turns to reduced form default prediction and

compares model and reduced form predicted spreads to realized spreads. This section

also relates our results to recent findings in the corporate bond literature. Section 7

concludes.

2 Choice of variables and data description

Our empirical investigation concentrates on explaining variation in sovereign external

debt prices across countries and over time. We restrict ourselves to dollar-denominated

debt instruments issued or guaranteed by emerging market governments.6 Our measure

of yield spreads over U.S. Treasuries is J.P. Morgan’s Emerging Markets Bond Index

Global (EMBI Global). This series consists of daily data starting in January of 1994

and covers a sample of 32 emerging market countries. It includes a basket of Brady

bonds, loans, and Eurobonds. The average maturity of the debt instruments included

in the index is close to 12 years. In order to be included in the index, debt instruments

need to satisfy some basic liquidity requirements such as verifiable daily prices and cash

flows. We discuss these inclusion requirements in more detail in the data appendix.

Table 1 lists the set of countries with available EMBI spread data and groups coun-

tries into regions. The largest regional group is made up of countries in Latin America

with 12 countries. The data set also includes 5 countries in Africa, 6 in Eastern Europe

6In contrast, the yield on local currency debt tends to be driven mainly by local inflation risk.

9

and a total of 9 in the Middle East and Asia. The spread data begin in 1994, but not all

countries have data going back that far. We report the first year of available spread data

for each country. In 1994 the spread data series begin for Argentina, Brazil, Mexico,

Venezuela, Nigeria, Bulgaria, Poland, China, and South Korea. By 1996, nearly half of

the eventual set of countries have available data and since 1998 J.P. Morgan has been

constructing series for close to two thirds of the countries.

There is tremendous variation in spreads across countries at any given point in time.

To illustrate this, Table 1 reports median EMBI spreads for 2003 by country. For

countries that are not in default in 2003, median daily spreads vary from 31 basis points

for Hungary to 1188 basis points for Ecuador.7 In addition to the cross-sectional

variation in spreads there is substantial variation in spreads over time, which is apparent

from Figure 1 which plots average EMBI from 1994 to 2006.8

We start our investigation of spread determinants by considering some global evi-

dence that suggests that terms of trade are an important determinant of sovereign yield

spreads. Since many emerging markets are important commodity exporters, we expect

an improvement in the terms of trade and a resulting decline in spreads when commodity

prices have increased. We plot commodity prices as measured by the CRB commodity

index9 in Figure 1 and find that commodity prices and spreads in fact exhibit a strong

negative correlation of -0.49, which is apparent from the graph.

A natural interpretation is that when commodity prices are high, commodity ex-

7The spreads can be much higher for countries that are in default. The median daily spread forArgentina in 2003 is 5441 basis points. Côte d’Ivoire, Nigeria, and Uruguay are also in default in 2003.

8We weight the individual countries’ EMBI spreads by the governments’ total outstanding externaldebt levels.

9The data appendix provides more detailed information about the index which is constructed by theCommodity Research Bureau.

10

porters are more likely to repay their external debt, which reduces the yield spread they

face in international capital markets. In particular, the well-documented narrowing of

emerging market spreads over the last few years has been accompanied by an extraordi-

nary run-up in commodity prices. We use more detailed country specific terms of trade

data rather than a single global commodity index in our empirical implementation.

We now turn to a systematic analysis of spreads across countries and over time. For

this purpose we gather annual cross-country data on macroeconomic fundamentals from

a variety of sources, details of which can be found in the data appendix. External

dollar-denominated debt issued by emerging market sovereign governments commands

a yield spread over U.S. Treasury bonds primarily to compensate investors for the risk

of default.10 In our choice of variables we therefore focus on indicators that are related

to the risk of default.

In thinking about default risk in the case of a firm, the standard approach is to

compare firm asset value to liabilities. If a measure of asset value is not available one

could calculate the present discounted value of future revenues or dividends, compare it

to the level of liabilities, and calculate a proxy for leverage. The two components of

this calculation are a measure of liabilities and a measure of repayment capabilities.

In the case of a country, the natural analogues to these two measures are debt and

GDP. The ratio of debt to GDP is indeed arguably the most important explanatory

variable identified by existing empirical work on sovereign debt pricing. We follow the

previous literature and construct a country’s external debt to GDP ratio (Debt/GDP).

Another direct determinant of a country’s ability to repay often considered in the lit-

10There are of course other components of the spread, including liquidity and taxes, but these arenot the focus of our investigation. We discuss this point further in Section 5 when comparing actualand model implied spreads.

11

erature is its access to liquid assets, commonly measured by reserves. We include the

ratio of reserves (including gold) to GDP (Reserves/GDP) in our analysis.

We then add a more explicit measure of the government’s ability to generate dollar

revenue for repayment, namely the country’s terms of trade. The terms of trade measure

the price of a country’s exports relative to its imports. To see why this measure

is relevant for the pricing of debt, consider an oil-exporting country. The country

generates dollar revenue by exporting oil and spends dollars on imports. If the price

of oil rises, the country is in a better position to generate export revenue and repay

its dollar-denominated liabilities. Another reason why terms of trade is an appealing

measure is that it is plausibly exogenous. This is because terms of trade are calculated

using prices determined in world markets. Since terms of trade is a relative price series,

we measure the country’s terms of trade by constructing the percentage change in the

terms of trade over the past five years (Change in terms of trade). A positive number

means that a country’s exports have become more expensive relative to its imports.

Bondholders, however, do not only care about recent changes in the terms of trade

but also about the risk of a large adverse shock in the future, say a large decline in the

price of oil in our example. As a result, we expect the volatility of terms of trade to

influence debt prices. More specifically, volatility should be positively correlated with

spreads. We calculate the standard deviation of the percentage change in terms of trade

(Volatility of terms of trade) over the past ten years.11 We discuss the relation between

the volatility of fundamentals and debt prices in the context of a model in Sections 4

and 5.

11When less data is available, we require as few as 6 observations; the data appendix gives furtherdetails. For the Dominican Republic there is insufficient data to calculate volatility of terms of trade.

12

Table 1 reports the median levels of debt to GDP and the volatility of terms of trade.

There is considerable variation in the median levels of these variables across countries.

The median level of external debt ranges from 14% of GDP for China to 115% for Côte

d’Ivoire. Volatility of terms of trade varies substantially cross-sectionally from less than

five percent (China, Croatia, Hungary, Lebanon, Panama, and South Korea) to annual

volatilities above twenty percent (Nigeria and Venezuela). High terms of trade volatility

is to a large extent driven by oil prices. Crude petroleum and refined petroleum products

are among the top two export categories for the three countries with the highest terms

of trade volatilities. However, excluding countries with more than 20% of their exports

concentrated in oil does not affect our empirical results.

We also expect adverse changes in a country’s output to affect debt prices and default.

If a country has recently experienced slow or negative growth, it will likely find it more

difficult to meet payments on its external debt. We add the growth rate of GDP (GDP

growth) to our set of explanatory variables. As before we also expect the volatility of

output growth to be important. We calculate the standard deviation of annual GDP

growth (Volatility of GDP growth) using a rolling ten year backward looking window.

A country’s recent default history is another predictor of default risk. We count the

years since the country’s last year in default (Years since last default). If unrestricted,

this measure can become very large for countries that continue to stay out of default.

Because we expect additional years out of default to have incrementally less importance,

we cap the variable at 10 and set it equal to 11 if a country has never defaulted. It

is set equal to zero if a country is in default. This variable is motivated by the work

of Reinhart, Rogoff, and Savastano (2003), who argue that history of default is an

important predictor of future default. These authors have constructed annual default

13

indicators for different debt categories for a large sample of countries going back to the

early nineteenth century. We use their series for default on total debt, which includes

foreign currency bonds and foreign currency bank debt. This variable is also the basis

for our investigation of determinants of country default in Sections 5 and 6.

In order to summarize default activity for the set of 32 countries, we report the

number of defaults from 1970 to 2003 in Table 1. The first thing to note is that this

was not a quiet period. There are a total of 38 sovereign default episodes. A number

of countries defaulted on multiple occasions: Peru and Uruguay each have four defaults

since 1970. On the other hand, nine countries did not go into default in the sample

period.

3 Reduced form regressions of sovereign spreads on

macroeconomic fundamentals

We now explore how much of the variation in sovereign yield spreads can be explained by

macroeconomic fundamentals in a reduced form framework. We use a linear regression

model and run panel regressions of yield spreads on explanatory variables. For each

country we construct an annual spread series to match up with the annual frequency of

our measures of fundamentals. We calculate the annual mean of the daily EMBI spread

series from J.P. Morgan. We focus on spread observations while the country is not in

default.12 For an observation to be included in the regression we require that the full

12We make this restriction because our analysis considers determinants of the risk of sovereign defaultand its impact on debt prices. Nigeria is not included since it was in default throughout the sampleperiod.

14

set of explanatory variables is available.

Our regression sample consists of 177 country-year observations covering 30 countries

from 1994 to 2003.13 We restrict the sample to be the same for different specifications.

This has the advantage of allowing us to compare point estimates, significance levels, and

R2 across specifications. Table 2 reports summary statistics for the spread regression

sample. It is apparent that there is substantial variation in spreads and all of our

explanatory variables. For some of these variables, the minimum and maximum values

may look rather extreme. In order to explore whether or not this affects our results,

we winsorize the explanatory variables at the 5th and 95th percentile levels, replacing

values above the 95th percentile of the distribution with the 95th percentile and values

below the 5th percentile with the 5th percentile of the distribution.

Table 3 reports results from running regressions of a country’s spread on different

sets of explanatory variables. To make sure that outliers are not driving some of our

results we re-estimate all the reduced form regressions on the winsorized data. Our

main results are unaffected by these changes.

We start our regression analysis by including only the level of debt to GDP, the

main explanatory variable identified by the existing literature. We find that it is highly

significant but has rather limited ability to explain spread variation at an R2 of 0.11.

We next add the change in a country’s terms of trade and the volatility of its terms of

trade in column (2). Both variables have the expected sign and are significant at the

1% level. Countries that have benefited from improvements in their terms of trade tend

to have lower spreads and countries with higher terms of trade volatilities tend to have

13Although the spread data extend to 2006, some of our explanatory variables are only available until2003.

15

higher spreads. We find a substantial effect on explanatory power of introducing these

measures: the R2 increases from 0.11 to 0.47.

In column (3) we add the remaining measures of macroeconomic fundamentals, re-

serves to GDP, GDP growth, and the volatility of GDP growth. The coefficients on

all the variables have the expected sign and are significant at the 1% level, except for

the coefficient on GDP growth, which is significant at the 10% level. This regression of

spreads on fundamentals delivers an R2 of 0.59.

In our main specification reported in column (4), we include, in addition to our

set of macroeconomic fundamentals, the variable measuring the years since a country’s

last default. We find that, all else equal, the closer a country is to its most recent

default episode, the higher its spread. The coefficient on years since last default is

significant at the 1% level. This suggests that a country’s history of default matters

above and beyond what is accounted for by macroeconomic fundamentals, consistent

with the findings of Reinhart, Rogoff, and Savastano (2003). The coefficients on the

other explanatory variables remain significant at the 1% level, with the coefficient of

GDP growth now being significant at the 5% level. Although including years since last

default adds explanatory power beyond what is captured by underlying macroeconomic

fundamentals, the incremental improvement in R2 is rather modest at 2.3 percentage

points.

In addition to being statistically significant, we find that all seven explanatory vari-

ables are also economically significant. In Panel B of Table 3, we multiply the coefficients

from our main specification with each variable’s in-sample standard deviation. The two

variables with the highest economic impact on spreads are debt to GDP and the volatility

of terms of trade. A one standard deviation increase in debt to GDP is associated with

16

an increase of 106 basis points in the spread, while a one standard deviation increase of

volatility of terms of trade implies an increase of 150 basis points. The corresponding

effects for the other explanatory variables are —51 basis points for change in terms of

trade, —74 basis points for reserves to GDP, —42 basis points for GDP growth, +76 basis

points for the volatility of GDP growth, and —73 basis points for years since last default.

We investigate regional effects in column (5) of Table 3 by including regional dummy

variables. We find that spread levels are significantly lower in Eastern Europe and

South East Asia relative to Latin America (the Latin America dummy is omitted from

the regression).

In summary, we find that spreads are high if the level of debt to GDP is high,

reserves are low, terms of trade have deteriorated, GDP growth has been slow, and if

the volatility of terms of trade or the volatility of GDP growth are high. We find that

measures of volatility, in particular volatility of terms of trade, are highly statistically

and economically significant. Including measures of the volatility of fundamentals leads

to a large improvement in explanatory power relative to the measures used in the existing

literature.

3.1 Explanatory power in the cross-section and the time-series

In this section we investigate whether the explanatory variables which we found to

be significant in the previous section are identified from cross-sectional or time-series

variation. We focus in particular on volatility of terms of trade and debt to GDP.

Figure 2a plots average EMBI spreads against average volatility of terms of trade.

Countries with higher volatility of terms of trade tend to have higher spreads. The graph

17

reflects the strong positive correlation of 0.73 between the two. This is in contrast to

the weaker correlation of 0.30 between countries’ average spread and average level of

debt to GDP. This lack of correlation is apparent in Figure 2b. It seems, therefore,

that spreads are driven mainly by terms of trade volatility and less by debt to GDP

in the cross-section. Figure 2c plots country de-meaned spreads against debt to GDP.

We see that, within countries, debt to GDP moves together with spreads. At 0.50 the

two series are highly correlated, and it seems that debt to GDP is better at explaining

time-series variation in spreads within a country rather than variation across countries.

Next we explore these effects more rigorously by running panel regressions of spreads

on explanatory variables, and including year and country fixed effects, respectively.

Results are reported in Table 4. We find that in the time-series (country fixed effects)

the coefficient on debt to GDP is about twice as large as it is in the cross-section (year

fixed effects). Debt to GDP also explains a larger share of the variation in spreads by

itself in the time-series (R2 of 0.24) than it does in the cross-section (R2 of 0.14). In

contrast, the change in terms of trade and the volatility of terms of trade add more

explanatory power in the cross-section than in the time-series. When including both

variables in the cross-section, the R2 jumps from 0.14 to 0.50, compared to a much more

modest increase from 0.24 to 0.35 in the time-series.

In summary, the change in terms of trade and the volatility of terms of trade are

more successful at explaining the cross-section, whereas debt to GDP derives most of its

explanatory power from the time-series. The latter finding is consistent with Reinhart,

Rogoff, and Savastano’s (2003) idea that some countries are more intolerant to high debt

levels. In that case it matters if a country’s debt to GDP is high relative to the country

specific mean, but it does not matter if it is high relative to other countries.

18

3.2 Robustness checks

We perform several robustness checks on our main specification (Table 3 column (4))

of the reduced form regression analysis. We first test for the significance of several

time-series variables.14 As proxies for the riskless long and short term world interest

rates, we include the 10-year and 6-month U.S. Treasury rates. We also include the U.S.

default yield spread, defined as the spread of corporate bonds with a Moody’s rating of

Baa over U.S. Treasuries. We measure liquidity as the difference between the 3-month

Eurodollar rate and the 3-month Treasury rate.

None of these variables are significant at the 10% level. The only time-series variable

that is marginally significant is the default yield spread, with a p-value of 0.107. The

fact that U.S. interest rates are insignificant is consistent with the findings of Kamin

and von Kleist (1999) who could not identify a robust relationship between a number of

industrial country interest rates and emerging market spreads.15

We also perform several other robustness checks. As mentioned earlier, we first drop

large oil exporting countries from the regression. In particular we drop countries with

more than 20% of exports concentrated in crude petroleum and petroleum products (as

listed in Table 1), which means that Columbia, Ecuador, Venezuela, Russia, and Egypt

are dropped from the regression. The results are largely unaffected indicating that

fluctuations in oil prices are only part of the reason why terms of trade fluctuations

14Diaz Weigel and Gemmill (2006) argue that global factors are more important than country specificfundamentals in explaining the Brady bond prices of Argentina, Brazil, Mexico, and Venezuela, whileJostova (2006) provides evidence of predictability resulting from local factors in these countries.15More generally, there does not seem to be a consensus with regards to the sign of the relationship in

the existing empirical literature. For instance, Min (1998) finds a positive but insignificant effect of theU.S. interest rates on sovereign credit spreads, while Eichengreen and Mody (1998) report a significantnegative effect. Uribe and Yue (2006) find that an increase in the world interest rate causes a declinein emerging market spreads in the short run followed by an overall increase in spreads in the long run.

19

impact sovereign spreads. In order to rule out the possibility that outliers might be

driving our results, we next re-estimate all our regressions, winsorizing our variables at

the 5th and 95th percentiles. Third, we replace the volatility of terms of trade with its

one year lag. We then drop observations in years preceding a default. We also cluster

standard errors by country and by year. Our results are basically unaffected by these

changes.

Finally, we check whether there is evidence of co-movement in spreads not captured

by variation in country fundamentals (reflecting, for instance, some type of contagion

effect). First, we add year dummies to our regression and find that the coefficients on

the dummies are insignificant or only significant at the 5% level. Moreover, adding the

dummies leads only to a very modest increase in R2. Second, we include the implied

volatility of the S&P500 index (VIX) and find that it is insignificant. These results

may seem surprising in light of two recent studies which use higher frequency emerging

market credit default swap (CDS) spreads: Longstaff, Pan, Pedersen, and Singleton

(2007) find that at higher frequencies there is evidence of co-movement in sovereign CDS

spreads while Pan and Singleton (2008) find that the VIX is statistically significant in

explaining CDS spreads of Mexico, Turkey, and Korea.16 However, it is important

to note that these results can be perfectly consistent with our findings. The focus of

our study is on explaining low frequency differences in spread levels, while these other

two studies use higher frequency data and focus on changes in credit spreads. Thus

it seems to be the case that at high frequencies there is co-movement in CDS spread

changes, perhaps due to changes in aggregate liquidity or short run uncertainty, while

16In related work, Berndt, Douglas, Duffie, Ferguson, and Schranz (2005) find that the VIX hassubstantial explanatory power in a high frequency data set of U.S. CDS spreads for the period 2000-2004.

20

at low frequencies cross-country variation in the level of spreads is mostly explained by

differences in macroeconomic fundamentals and their volatility.17

4 A model of fundamentals and sovereign spreads

We now propose a simple and empirically tractable model for pricing sovereign debt.

In the previous section we presented evidence that macroeconomic fundamentals, in

particular measures of debt levels and repayment capabilities, can explain sovereign

yield spreads across countries and over time. Consistent with standard option and debt

pricing intuition, we found that volatility affects debt prices. The natural next step

would be to apply standard pricing models. However, it is not clear how to apply these

models to the case of a sovereign borrower.

In standard structural corporate bond pricing models,18 firm asset value jointly de-

termines default and recovery value. If firm assets fall below liabilities, the firm defaults.

The creditors take over the firm and receive the asset value. A bond is then priced as a

combination of safe debt and a short position in a put option on the asset value of the

firm with a strike price equal to the face value of debt. In such models, leverage and

volatility determine both the probability of default and the spread.

17Another issue with comparing our results with these studies is that some of the data on countryspecific macroeconomic fundamentals, particularly on terms of trade, are not available at the higherfrequencies used by these authors. It may therefore be difficult to fully account for the effects ofcountry specific macroeconomic fundamentals in high frequency data. Furthermore, our sample periodis different from both studies; Longstaff, Pan, Pedersen, and Singleton (2007) consider the period 2000-2007; Pan and Singleton (2008) use data from 2001-2006.18Merton (1974) is arguably the first modern structural bond pricing model. Many other models

have followed. Some examples are Black and Cox (1976), Leland (1994), Longstaff and Schwartz (1995),Anderson and Sundaresan (1996), Mella-Barral and Perraudin (1997) Collin-Dufresne and Goldstein(2001). Huang and Huang (2003) provide an overview of this literature. A common feature of thesemodels is that default is related to an underlying process of asset value.

21

Pricing sovereign debt is fundamentally different. First, there is no claim on a

country’s assets that is traded or that has an observable market price. Moreover, even

if one were to construct a measure of asset value, e.g. by discounting expected future

dollar revenues from exports, asset value is not the relevant measure for pricing sovereign

debt. Creditors do not take over the country in the event of default. Country wealth

therefore does not directly determine default: a country may default even if its wealth

exceeds its liabilities. This observation is consistent with the finding that, empirically,

emerging market economies often have far lower levels of debt to GDP than developed

countries yet default much more frequently (Reinhart, Rogoff and Savastano (2003)).

The inability of creditors to claim country assets also means that a country’s wealth

level may not determine the recovery rate following default.

We propose a simple model in which macroeconomic fundamentals determine debt

prices and default. A country defaults when the cost of repayment becomes “too high.”

Intuitively, the cost of repayment is high because debt levels are high or fundamentals

are low. Our model formalizes this intuition.

We consider a discrete time setup. We denote by Ft+1 a measure of fundamentals

for a country at time t+ 1 and by D a measure of the country’s debt level, suppressing

a country specific subscript for simplicity. We assume that both of these measures are

in comparable units, a point which we discuss in further detail in Section 5. We assume

that for a currently solvent country, default occurs next period if fundamentals are too

22

low relative to the level of debt:19

Ft+1 < D : default occurs at time t+ 1. (1)

We assume that fundamentals follow a martingale and that shocks to fundamentals are

lognormally distributed:

ft+1 = ft + φt+1, where φt+1 ∼ N¡0, σ2

¢, (2)

where lower case letters denote logs and φt+1 is the shock to log fundamentals with

standard deviation σ. Given these assumptions, the probability of default is equal to:

Pt (Ft+1 < D) = Φ

µ−ft − d

σ

¶, (3)

where Φ (.) denotes the standard normal c.d.f.

Default is less likely if fundamentals are high, debt levels are low, and volatility

is low. More precisely, default is less likely if the volatility scaled difference between

fundamentals and debt levels is high. Adopting the terminology of the corporate default

literature, we refer to this scaled difference as distance to default.20

This expression already illustrates the basic intuition of our model: the probability

of default depends on the level as well as the volatility of fundamentals. As discussed

earlier, this effect motivates the inclusion of measures of volatility in our empirical ex-

19In the model we distinguish between measures of debt levels and measures of fundamentals. Fun-damentals are subject to shocks - an adverse shock to fundamentals can trigger default. Debt levelsare known at time t. We therefore suppress the time subscript on D.20Duffie, Saita and Wang (2007) for instance use distance to default to predict bankruptcy. They

refer to it as a volatility adjusted measure of leverage.

23

ploration.

In order to derive bond prices, we need to make assumptions about the payoff to

bondholders in and out of default. We assume that if the country remains solvent,

bondholders receive face value. If the country defaults, we assume that the fractional

recovery value depends on the level of fundamentals, i.e. the worse fundamentals are at

the time of default, the lower the payoff to creditors. In Section 6, we also consider an

alternative assumption of a fixed recovery rate at the time of default. The payoff to

bondholders at time t+ 1, denoted by Bt+1, is given by

solvent : Bt+1 = B (4)

default : Bt+1 = δt+1B,

where B is the face value of the bond, and δt+1 is the fractional recovery rate.

To capture the idea that recovery depends on the level of fundamentals at the time

of default, we assume that δt+1 = γ exp (ft+1 − d): recovery rates are low if the country

has low fundamentals or high debt levels. The parameter γ governs the sensitivity of

changes in the fractional recovery rate to changes in fundamentals. Intuitively, γ will

have a value that makes the recovery rate δt+1 vary between 0 and 1.21

If we assume that investors are risk neutral, we can now calculate the price and yield

spread of the bond. The yield spread on debt is defined as st = − log¡Bt

B

¢− rf , where

Bt is the price of the bond. In the appendix to this paper we show that the yield spread

21The need for this parameter is related to the fact that default depends only on the distance todefault. This means that if we scaled up fundamentals and volatility, distance to default would remainunchanged. However, if we did not adjust the recovery rate sensitivity γ appropriately, recovery valueswould change. We discuss this issue and how it influences model estimation in more detail in Section5.

24

is given by:

st = − logµγ exp

µft − d+

1

2σ2¶Φ

µ−ft − d

σ− σ

¶+ Φ

µft − d

σ

¶¶(5)

≡ g (ft, d, γ, σ) .

The first part of this expression is equal to the expected payoff to bondholders conditional

on default multiplied by the probability of default. The second part is the probability

of the country staying solvent in which case creditors receive face value. As we would

expect, the spread depends negatively on fundamentals and recovery rates, and positively

on debt levels and volatility.

One limitation of this result is that it assumes that investors are risk neutral, which

means that the correct discount rate for the bond is equal to the risk-free rate. In the

standard option pricing framework a measure of risk is not necessary since the assump-

tions of continuous trading and geometric Brownian motion allow for the construction

of a perfect hedge. The bond can then be priced using risk neutral probabilities. In

discrete time under lognormality, the no arbitrage condition implied by trading of the

underlying asset is sufficient to derive the price (Rubinstein (1976)). In our case, since

the underlying is not traded, we need a direct estimate of the riskiness of fundamentals.

Given an estimate of the covariance of the state variable with the stochastic discount

factor σfm, we can write down the spread on the bond for the case where investors are

risk averse:

st = − logµγ exp

µft − d+ σfm +

1

2σ2¶Φ

µ−ft − d+ σfm

σ− σ

¶+ Φ

µft − d+ σfm

σ

¶¶.

(6)

25

The common interpretation is that the covariance with the SDF changes the risk neutral

drift of fundamentals. The bond price is then given by the same formula, but with the

real default probabilities substituted by risk neutral default probabilities. We can see

that risk is priced in the way we would expect. If fundamentals tend to be low in bad

states of the world (from the marginal investor’s point of view), i.e. if the covariance with

the SDF is negative, the bond is more risky. Consequently, the risk neutral probability

of default is larger than the real probability of default and the spread is higher. In other

words, risk averse investors demand a higher spread if sovereign defaults tend to occur

in bad states of the world.

5 Model estimation using historical default data

In this section we take our model to the data and calculate model implied spreads.

We use historical data on defaults and explanatory variables to estimate model implied

default probabilities and parameters. The model specifies that the probability of a

country being in default in the next period is equal to the cumulative normal of a linear

combination of covariates today. Empirically we can estimate this conveniently in a

hazard model by running a probit on a set of explanatory variables.

We construct a measure of default which is equal to one in a given year if the country

is in default or goes into default over the course of the year. Specifically, we define a

default indicator variable Yi,t+1 that is equal to 1 if country i is in default in period

t+ 1, and 0 otherwise. We add to this a set of covariates. We use terms of trade as a

measure of fundamentals and repayment capabilities. Since we assume lognormality in

the model, we measure fundamentals as log terms of trade in period t relative to average

26

log terms of trade over the past ten years and denote it tti,t. Next we calculate the

volatility of log terms of trade σi,t over the past ten years. We use log debt to GDP dgi,t

to measure countries’ debt levels. To make sure that our analysis is not dominated by

extreme values, we winsorize the explanatory variables at the 5th and 95th percentile

levels.22 Since terms of trade and debt to GDP are not measured in the same units

we leave the coefficients on these variables as free parameters in the estimation. This

is in contrast to the firm case in which asset value and face value of debt are directly

comparable. We instead use model estimated parameters as measures of the relative

importance of the inputs in default prediction.

Country defaults are rare events. In order to estimate a hazard model, we need a

large enough sample with a sufficient number of defaults. We take advantage of the

fact that default data are available for a longer period than the spreads data used in the

previous section and extend the sample period to 1970. Although default data extend

back farther, terms of trade data are available from 1960. Since we are calculating

volatility over a ten year backward looking window, the sample with available covariates

begins in 1970.

Once a country enters default, economic activity does not cease and fundamentals

continue to be observable. The estimation sample therefore includes observations both

in and out of default. We include a dummy zi,t that is equal to one if the country is

currently in default because we expect that, for a given level of fundamentals, a country

is more likely to be in default next period if it is currently in default. Another reason

for including a default dummy is that it may pick up the effects of unobservable country

22This procedure is common when estimating hazard models of default and bankruptcy, e.g. Shumway(2001).

27

characteristics that are different in and out of default.23 We also include a constant term

to account for the fact that the relative magnitudes of our explanatory variables are not

directly comparable. Put differently, the fact that fundamentals lie below debt levels

does not necessarily trigger default. This is different from the case of corporate debt,

where default is conventionally triggered when asset value falls below the face value of

debt. Next, we divide through by volatility σi,t since in the model the difference between

fundamentals and debt levels is scaled by volatility. Finally, we add a country’s years

since last default denoted ytdi,t to capture the influence of recent default history on

the probability of default. The results from running a probit of default events on

explanatory variables are (z-statistics reported below the coefficients in parentheses):

P (Yi,t+1 = 1) = Φ ((−0.119 ∗ tti,t + 0.027 ∗ dgi,t + 0.119 ∗ zi,t − 0.163) /σi,t − 0.104 ∗ ytdi,t) .

(1.98) (1.67) (7.38) (2.43) (6.03)

All coefficients have the expected signs and are significant.

Before we can calculate model predicted spreads and compare those to actual spreads

we still need to scale the parameters. The reason is again related to the fact that there

are no natural units for the explanatory variables. Re-scaling both fundamentals and

the volatility of fundamentals does not affect the model implied probability of default.24

Measuring fundamentals in different units does, however, change recovery rates. We

23See, for example, De Paoli, Hoggarth, and Saporta (2006).24This feature is related to the fact that a standard probit estimation does not return an estimate of

the variance. Instead, the variance of the shock is assumed to be equal to 1.

28

can use this fact to scale the parameters. Recall that:

log (δit) = log γ + fi,t − di,t. (7)

This relation implies that recovery value moves one for one with fundamentals and debt

levels. We exploit this relation by regressing recovery values on fundamentals and

debt levels and imposing a coefficient of 1. We use spread observations in default to

calculate a measure of the market expected recovery rate. In particular, we assume that

the recovery rate is close to the current market price of the debt, i.e. δit+1 = 1

1+(sit+1+rf),

where we measure sit+1 using the country’s observed EMBI spread and rf denotes the

risk-free rate. We then re-scale the explanatory variables accordingly. From the

constant in the regression we also get an estimate of the recovery parameter γ̂. Recall

that st = g (ft, d, γ, σ) which means that we now have all the inputs necessary to calculate

model predicted spreads.25

5.1 Model implied spreads

Using the estimated model parameters we now calculate model implied spreads. Despite

a number of limitations we find that the model does surprisingly well. Figure 3 plots

actual spreads against model implied spreads. We calculate model implied spreads for

the EMBI regression sample of Tables 3 and 4. There is a strong positive relation

25Following the model in the previous section, we could, in principle, add more measures of funda-mentals and indebtedness to the analysis. Such an exercise involves estimating the relative importanceof different measures of fundamentals in predicting default. These estimates in turn affect the correctmeasure of volatility which means that the problem has to be estimated using maximum likelihood(instead of the probit setting we use here). In a previous version of the paper we discuss how toestimate such a model in more detail. One practical problem with this approach is that the maximumlikelihood surface is not concave.

29

between actual and model implied spreads which is reflected in a correlation of 71%. A

regression of actual on model implied spreads has an R2 of 51%.

In the next section we discuss the results from fitting our model to the data in more

detail. In that section, we use default probabilities estimated in a standard hazard

model to calculate reduced form spreads and compare reduced form and model implied

spreads. We also consider how well predicted spreads from both approaches can explain

variation in actual spreads.

We now turn briefly to some of the limitations we expect from this kind of an exercise.

A priori we would expect this type of model to have some difficulties matching observed

spreads closely for several reasons. First, we are only calculating the component of the

spread that is due to default risk. This means that, to the extent that there are other

spread components related to liquidity, risk aversion, and taxes (Elton, Gruber, Agrawal,

and Mann (2001), Hund and Lesmond (2007)), we expect observed spreads to be higher

on average than model implied spreads. Second, we know from the corporate bond

literature, that fitting structural form models to the data generally produces estimates

that range from less than a fraction of a basis point all the way up to unreasonably large

numbers. The reason is often that the implied default probabilities are extreme as well

(Eom, Helwege and Huang (2004), Huang and Huang (2003)). Third, unlike reduced

form models (including our analysis in Tables 3 and 4), our model estimation does not

use as inputs any of the observed spreads it is attempting to explain. This means that

there is no constraint that forces model implied and observed spreads to be broadly in

line.

Consistent with our expectations and findings in the corporate bond pricing litera-

ture, the model estimation gives some very low default probabilities. In the sample,

30

the 90th percentile of fitted distance to default is equal to 4, corresponding to a default

probability of 0.003% (the 10th percentile of the default probability distribution.) Such

low default probabilities imply low spreads and indeed the 10th percentile of the spread

distribution is equal to 0.05 bps. Since variation below 1 basis point is not really mean-

ingful, we set predicted spreads below 1 basis point equal to 1 basis point. In the figure

there is a corresponding local cluster of observations.26

We conclude that the model captures a surprisingly large share of the variation

in observed sovereign yield spreads. However, implicit nonlinearities in the assumed

functional form can lead to extreme values of predicted spreads, particularly for small

spreads.

6 Reduced form default probabilities and spreads

In this section we estimate default probabilities in a reduced form hazard model. This

effectively relaxes the functional form restriction imposed by the model in the previous

sections. We then use fitted default probabilities to calculate spreads. We compare

reduced form spreads to those predicted by our model of fundamentals and spreads.

We begin by constructing a set of explanatory variables. As in the previous spread

regression analysis we choose measures of debt levels, repayment capabilities, and volatil-

ity. We use the same set of variables as in Tables 3 and 4 measured over the extended

sample starting in 1970, again to increase power. We winsorize the data at the 5th

and 95th percentile to make sure that outliers do not drive our results. Conditional

26This feature is a result of the functional form assumed in the model. In particular, since thedifference between fundamentals and debt levels is scaled by volatility, the model can return extremevalues of distance to default if volatility is small.

31

on covariates, the sample has 587 country-year observations covering 31 countries from

1970-2002. This sample is much larger than the spread regression sample. However,

there are only 27 defaults which is less than 5% of the observations.

Table 5 presents summary statistics for our explanatory variables. We group obser-

vations into two groups: those where the country goes into default over the next year

and those observations for which it stays solvent. We calculate statistics for non-default

and default observations separately. For each of the seven explanatory variables the

mean and median of the default observations reflect noticeably less favorable conditions:

levels of debt to GDP are higher and levels of reserves are lower. Countries that are

about to default tend to have been exposed to negative terms of trade shocks and have

experienced low GDP growth. They tend to have high levels of volatility of terms of

trade and volatility of GDP growth and often have been in default more recently. The

levels of debt to GDP and volatility of terms of trade are particularly unfavorable in

years preceding default. For both measures, the mean and median of the default obser-

vation sample are about one standard deviation larger than the mean/median for the

non-default sample.

To investigate the predictive power of this set of explanatory variables more formally,

we run logit regressions of a forward looking default indicator on explanatory variables.

In particular, we estimate:

Pt (Yi,t+1 = 1) =1

1 + exp (−α− β0xi,t). (8)

The default indicator for a country is set equal to one in a given year if the country goes

into default over the course of the following year. It is set equal to zero if the country

32

is not in default the following year.

Estimation results for different specifications are reported in Table 6. We first

consider a specification that includes debt to GDP, volatility of terms of trade, and the

change in the terms of trade. We find that debt to GDP and volatility of terms of trade

are highly significant. This is consistent with the suggestive evidence from comparing

means in the summary statistics. The specification in column (1) explains variation

in default well and has a pseudo R2 of 17.3%. We also consider results from two

other specifications, one that adds the remaining variables measuring macroeconomic

fundamentals and one that also adds years since last default to measure a country’s

recent default history. Model fit improves to pseudo R2 of 20.3% and 21.4% respectively.

Debt to GDP and terms of trade volatility are significant at the 1% level in all three

specifications. However, none of the other explanatory variables are significant at the 5%

level although, with the exception of the change in terms of trade, they have the expected

signs. Reserves, GDP growth, and years since last default are significant at the 10%

level.27 We refer to the model in column (3) as our main specification. It includes the

measures of fundamentals and default history and corresponds to the main specification

in Table 3.28 We also consider economic significance of debt to GDP and volatility of

terms of trade for this specification. Both are highly economically significant. The

predicted probability of default when all explanatory variables are equal to their mean

values is equal to 4.6%. Increasing debt to GDP by one standard deviation increases the

27These results are consistent with independent work by Catão and Sutton (2002) and Catão andKapur (2006) who also investigate empirical determinants of default in a reduced form hazard modelsetting that is similar to the specification reported in Table 6.28In principle, we could consider additional explanatory variables that predict default in the sample

we consider. However, because of the sample size and the rather small number of default observations,our estimation only has a limited amount of power. For our investigation we therefore choose to usethe same set of variables as in the spread regression specifications.

33

predicted default probability to 8.4%; for a one standard deviation increase in volatility

of terms of trade the probability increases to 9.3%.

We report model forecast accuracy in Table 5 Panel B. We divide fitted default

probabilities into quintiles for the different specifications. We then count the number

of defaults in the different quintiles. A perfect model would sort all 27 defaults into the

highest quintile. If the model had no power to predict default each bin would have 5.4

defaults. We find that our best model sorts 19 of 27, or 70% of defaults, into the top

quintile, with 24 of 27 defaults in the top two quintiles. There is also an increase in

forecast accuracy across specifications which corresponds to the increase in pseudo R2.

In Panel C we report summary statistics of fitted default probabilities. Fitted prob-

abilities are comparable across the specifications. The correlations of fitted default

probabilities of specifications (1) and (2) with the best model are 90% and 96% respec-

tively. In contrast to our structural model in the previous section, the reduced form

hazard model does not return extremely low default probabilities. It does, however,

predict some very high default probabilities.29 Overall, fitted probabilities are rather

stable and similar across different specifications.

6.1 Comparing reduced form and model implied spreads

We next calculate reduced form predicted spreads using fitted probabilities from the

hazard model. We assume that recovery rates are fixed, i.e. that creditors receive

a constant fraction of face value in the event of default. We use fitted probabilities

from our main specification in column (3). We set the fractional recovery rate equal to

29The two largest fitted values are for Côte d’Ivoire in 1982 and 1999, equal to 70.2% and 76.8%respectively. In both cases default occurred over the next year.

34

0.6, which is broadly in line with the average historical experience. We then calculate

reduced form predicted spreads and use them to explain variation in actual spreads.

This means that variation in fundamentals can affect spreads only to the extent that

fundamentals affect default probabilities. Also, predicted spreads are calculated without

using actual spreads as an input. This is in contrast to the earlier methodology of

regressing spreads on explanatory variables directly.

Figure 4 plots actual against reduced form spreads. Variation in predicted spreads

matches variation in actual spreads very well. We notice a strong positive relation which

is reflected in a correlation of 78%. We can compare explanatory power of reduced form

and model implied spreads by comparing Figures 3 and 4; both plot actual against

predicted spreads for the same sample. As discussed, model implied spreads are often

extremely small. We notice that reduced form predicted spreads do not have the same

characteristic. The minimum reduced form spread is equal to 2.7 basis points, the

10th percentile is 16 basis points. These relatively larger reduced form spreads are a

result of larger predicted default probabilities. The 10th percentile reduced form default

probability is 0.4% compared to the 0.003% model implied default probability. Table

7 Panel A reports summary statistics for model implied and reduced form spreads and

default probabilities together with actual EMBI spreads. Predicted spreads are smaller

than actual spreads: median reduced form and model implied spreads are 26 and 74 basis

points compared to a 411 basis points median EMBI spread. This difference reflects

other non-default spread components and is consistent with findings in the corporate

bond literature that default risk accounts for only part of the spread (Huang and Huang

(2003) and others).

We now ask how much of the variation in spreads is explained by variation in default

35

risk. We regress actual on model implied and predicted spreads. Predicted spreads

have a large share of extreme values. This is especially true for the reduced form spreads

which reach a maximum of 4653 basis points and have an in-sample kurtosis of 67. The

large predicted spread is less surprising when considering the maximum predicted default

probability of 76.8%. If we included these large values directly into the regression they

would dominate the results. We therefore winsorize model implied and reduced form

spreads at the 10th and 90th percentiles. Model implied spreads then run from 1 to

467 basis points compared to 16 to 460 basis points for reduced from spreads. The

in-sample standard deviations are reduced to 157 basis points and 144 basis points for

model implied and reduced form spreads respectively.

Results for spread regressions are reported in Table 7 Panel B. We find that our

model explains 53% of the variation in observed spreads and that a 1 basis point increase

in model implied spreads is associated with a 1.66 basis point increase in observed

spreads. Reduced form spreads can explain 55% of the actual spread variation. The

coefficient on predicted spreads is 1.85. These R2 are similar to those reported in

Section 3. This high level of explanatory power is rather surprising, keeping in mind

that our model estimation does not use as inputs any of the observed spreads it is

attempting to explain. For comparison, our main specification in Table 3 explained

62% of the variation. The large coefficients are not surprising once we consider the data

summary statistics: predicted spreads are smaller and less variable than actual spreads.

In contrast to predicted spreads, we do not winsorize actual spreads to make results

comparable to those in Section 3. This leads to a variance reduction of the winsorized

spread data which helps explains the coefficient size. We also note that the relative

magnitude of the coefficients is consistent with the relative size of the spread standard

36

deviations.

We next consider a different approach to deal with outliers which is to run regres-

sions of log actual spreads on log predicted spreads using the unwinsorized data. This

effectively compares percentage changes of actual and predicted spreads. It also min-

imizes the risk of large outliers affecting the regression. Running log-log regressions

corresponds to the regression lines of Figures 3 and 4 which use log scales. The regres-

sion of actual on model implied spreads has a coefficient of 0.27 and an R2 of 51%. For

reduced form spreads the coefficient is 0.51 and the regression can explain 61% of the

variation. This means that a 1% relative increase in reduced form spreads implies a

0.5% relative increase in actual spreads. The larger coefficient on reduced form spreads

is again consistent with the smaller variance of log reduced form spreads. This smaller

variance is also evident from Figures 3 and 4.

Comparing means of observed and model implied spreads, we already know that a

large component of the spread is not explained by our model. In order to explore if there

is variation in the explained fraction for different levels of credit risk, we group spreads

by their estimated default probability and compare average observed and fitted spreads

across groups. We choose break points using the distribution of fitted probabilities from

the entire estimation sample (1970-2002). Figure 5 plots average realized and implied

spreads by bins. We find that fitted spreads on good credit are much smaller than

observed spreads while for poor credit, the overall size of fitted spreads is a much larger

fraction of observed spreads.

These findings are consistent with patterns in the corporate bond market. Huang

and Huang (2003) show that the fraction of observed spreads accounted for by structural

form models decreases with credit quality. In other words, model implied spreads are

37

far too low on companies of good credit quality but they are closer to realized spreads

for companies of poor credit quality. The fact that credit risk only accounts for a

small fraction of the average spread in the sovereign debt market is thus consistent with

what Huang and Huang find for corporate bonds. In order to more accurately price

sovereign debt, it will be important to increase our understanding of the other spread

components.

To summarize, we find that both model implied and reduced form spreads have sig-

nificant explanatory power for observed sovereign spreads. We find that the default

component of spreads explains variation in observed spreads surprisingly well. Elimi-

nating the specific assumption of functional form in our structural model we find that

reduced form spreads do even better in explaining observed spread variation. We also

find that our model fits better for borrowers of lower credit quality.

7 Conclusion

This paper makes three contributions to the literature on sovereign risk and sovereign

debt pricing. First, we provide evidence that variation in country fundamentals explains

a large share of the variation in emerging markets’ sovereign debt prices. We consider

a set of 32 emerging market economies over the period 1994-2006 and use J.P. Morgan’s

Emerging Markets Bond Index (EMBI) to measure a country’s spread on its external

debt.

To explain spread variation we focus on measures of liabilities and repayment ca-

pabilities. In a departure from the existing empirical literature on sovereign debt we

pay special attention to the volatility of fundamentals. We demonstrate that, consis-

38

tent with standard bond and option pricing theory, the volatility of fundamentals is

an important determinant of a country’s spread on its external debt obligations. In

particular the volatility of terms of trade is both statistically and economically signifi-

cant in explaining spread variation. In a reduced form panel regression framework, a

one standard deviation increase in the volatility of terms of trade is associated with an

increase of 150 basis points in spreads, which corresponds to nearly half of the standard

deviation of observed spreads. The debt to GDP ratio has low explanatory power for

cross-country variation in spreads. Instead it adds substantial explanatory power in the

time-series. In other words, what matters is whether a country’s debt to GDP is high

relative to its own mean, not whether it is high relative to other countries. In addition,

even after controlling for fundamentals, a country’s default history has a significant im-

pact on spreads. Overall, we obtain a good fit, both across countries and over time,

with just a few variables.

Second, we propose a model of sovereign spreads to formalize the insight that a coun-

try’s spread is higher if its fundamentals are lower or if the volatility of fundamentals is

higher. Using historical data on actual country defaults we calculate predicted spreads.

Our model can explain half of the variation in observed spreads. This level of explana-

tory power is surprisingly large given the model’s specific assumption about functional

form and the fact that our model estimation only uses data on defaults and recovery

values to calculate predicted spreads.

Third, we demonstrate empirically the explicit link between sovereign debt prices

and default probabilities. We estimate a reduced form hazard model using historical

data on measures of fundamentals and default. Again, we find that the volatility of

terms of trade is an important explanatory variable of country default. We calculate

39

reduced form spreads using only fitted probabilities of default and find that predicted

spreads explain a large share of the variation in sovereign debt prices. In the literature

on corporate debt and default, the link between default probabilities and corporate CDS

spreads has been pointed out by Berndt , Douglas, Duffie, Ferguson, and Schranz (2005)

but this point has not, to the best of our knowledge, been made in the literature on

sovereign debt pricing.30

The findings in this paper have important implications for investors and policymak-

ers. We have identified factors explaining variation in spreads both across countries

and over time. Countries with larger fluctuations in their terms of trade, possibly due

to concentrated exports in commodities with volatile prices, are more susceptible to

external shocks. They may find it beneficial to address such risk factors in order to

reduce borrowing costs as well as the probability of a crisis or default. One possiblity

of course is to reduce debt levels or increase holdings of reserves. The recent run up

in commodity prices has provided an opportunity for some countries to move to a more

favorable fiscal position and to engage in large purchases of foreign liquid assets such

as U.S. debt obligations. Over the same period, debt markets have witnessed a large

run up in prices and an associated reduction in spreads. Our results suggest a further

potential avenue for risk reduction: countries could try to explicitly hedge exposures

to macroeconomic shocks in international financial markets. Caballero (2003), Shiller

(2003), and Merton (2005) advocate the use of innovative financial contracts to share

these macroeconomic risks more effectively.

30Cantor and Packer (1996) explore the link between debt prices and sovereign credit ratings.

40

A Appendix: Data sources and construction of vari-

ables

J. P. Morgan’s EMBI index includes U.S. dollar denominated debt instruments issued

by emerging market governments. It includes Brady bonds, loans, and Eurobonds. In

order for a country to be eligible for inclusion in the index, it needs to be classified as

low or middle income by the World Bank for the last two years, or have restructured

external or local debt in the past 10 years, or have restructured external or local debt

outstanding. For a debt instrument to be eligible, it needs to be issued by a sovereign

or quasi-sovereign entity (100% owned/guaranteed by the government), its issue size

needs to be greater than or equal to U.S.$500 million, its remaining maturity needs to

be greater than 2.5 years, it needs to have verifiable daily prices and cash flows, and it

has to fall under G7 legal jurisdiction.31

In our empirical analysis we calculate the annual mean of the daily EMBI spread

series. Since not all series begin in January we also include observations for which the

mean is constructed from less than a full year of spread data. However, we require at

least a full month of data (more than 20 trading days) for the observation not to be

dropped.

The CRB commodity index series is from Global Financial Data (GFD). It is con-

structed by the Commodity Research Bureau. The series is a continuation of the older

BLS index which was discontinued in 1981. According to the CRB, the index includes

energy 18% (crude oil, heating oil, natural gas), grains and oilseed 18% (corn, soybeans,

wheat), industrials 11% (copper, cotton), livestock 11% (live cattle, live hogs), precious

31Source: Emerging Markets External Debt Handbook for 2002-2003, J.P. Morgan.

41

metals 18% (gold, platinum, silver), softs 24% (cocoa, coffee, orange juice, sugar).32

We use annual terms of trade data provided by the Development Data Group at the

World Bank.33 Terms of trade indices are constructed as the ratio of an export price

index to an import price index. The underlying price and volume indices were compiled

by the United Nations Conference on Trade and Development (UNCTAD).

When constructing volatility of terms of trade we do not always have enough data to

calculate it over a ten-year window. For some countries, e.g. Croatia, Poland, Ukraine

and Russia, data on terms of trade data start later in the sample. To make sure this does

not significantly reduce the amount of observations available for the analysis, we reduce

the window size to calculate volatility down to a minimum window of six years when

necessary. In the case of the Dominican Republic there is insufficient terms of trade

data to construct a measure of volatility, even when reducing the calculation window

(as discussed in Section 2). Spread observations for the Dominican Republic therefore

does not enter the spread regression sample of Section 3.

Our measure of government external debt is the Total Debt series from the World

Bank Global Development Finance (GDF) data set. GDP data are from the Interna-

tional Monetary Fund World Economic Outlook (WEO).34 When GDP growth data

is not available we follow the same procedure as in the case of volatility of terms of

trade: we calculate the standard deviation using a shorter window but again (as when

32Source: documentation describing CRB Commodity Index in GFD33In an earlier version of this paper we used terms of trade data from 1960 to 2002. In these data, all

series are normalized to 100 for 1995. Since we calculate the volatility of the percent change in termsof trade this normalization has no effect on the values of our variables. We have subsequently addedthe percent change in the terms of trade 2003 using an updated series.34We carefully examine the GDP data series in order to eliminate any obvious data errors. Since

WEO data is only available starting in 1970, we use data from WDI for 1960-1969 to calculate volatilityof GDP growth.

42

calculating volatility of terms of trade) require a minimum of six years of observations.

Reserves refers to the Total Reserves Including Gold series from the World Development

Indicators (WDI).

The 10-year U.S. Treasury yield, 6-month Treasury rate, and 3-month Eurodollar

rate are from the Federal Reserve Bank of St. Louis. Yields on Baa U.S. corporate

bonds are from Amit Goyal’s website. The VIX measure of volatility of the S&P500

index is provided by the Chicago Board Options Exchange.

43

B Appendix: Derivation of the model implied spread

The price of the bond in period t depends on the expected payoff to the bond and the

appropriate risk adjusted discount rate rt:

Bt = exp (−rt)Et [Bt+1]

= exp (−rt)B [Pt (Ft+1 > D) + Pt (Ft+1 < D)Et [δt+1|Ft+1 < D]]

= exp (−rt)B∙Pt (Ft+1 > D) + Pt (Ft+1 < D)Et

∙γFt+1

D|Ft+1 < D

¸¸,

since we assume that the recovery rate is given by: δt+1 = γ Ft+1D.

We assume that Ft+1 is conditionally lognormally distributed:

ft+1 = ft + φt+1

φt+1 ∼ N¡0, σ2

¢.

The conditional probability of the country defaulting next period is given by Pt (Ft+1 < D) =

Pt (ft+1 < d) , where d = log (D). Given our distributional assumption, the probability

of default is equal to:

Pt (ft+1 < d) = Φ

µd− ftσ

¶,

where Φ (.) denotes the c.d.f. of the normal distribution.

If investors are risk neutral and the risk-free rate is constant, the price of the bond

is given by:

Bt = exp (−rf)B∙Pt (Ft+1 > D) + Pt (Ft+1 < D)Et

∙γFt+1

D|Ft+1 < D

¸¸.

44

Exploiting the assumption that Ft+1 is lognormally distributed and making a change of

variable, we obtain the following expression for the price of the bond after some tedious

but straightforward calculations:

Bt = exp (−rf)B∙γ exp

µ−d+ ft +

1

2σ2¶Φ

µd− ftσ− σ

¶+ Φ

µ−d+ ft

σ

¶¸.

Bond prices are commonly quoted in yields and yield spreads. With a constant interest

rate, the bond’s yield and yield spread are given by

θt = − logµBt

B

¶, st = − log

µBt

B

¶− rf ,

where θt is the yield on the bond, and st is the spread.

With risk neutral investors, the spread is thus given by:

st = − logµγ exp

µ−d+ ft +

1

2σ2¶Φ

µd− ftσ− σ

¶+ Φ

µ−d+ ft

σ

¶¶st = g (ft, d, γ, σ) .

If investors are risk averse, we can rewrite the bond price as:

Bt = Et

∙Mt+1

½Pt (Ft+1 > D)B + Pt (Ft+1 < D)Et

∙Ft+1

DγB|Ft+1 < D

¸¾¸,

where Mt+1 is the stochastic discount factor. Then we can risk neutralize to find the

45

price:

Bt = BEt [exp (mt+1)min (exp (0) , exp (ft+1 − d) γ)]

Bt = exp (−rf)EQt [min (exp (0) , exp (ft+1 − d) γ)]

ft+1 ∼ N¡ft + σfm, σ

2¢, under Q.

With risk averse investors, the spread is given by:

st = − log

⎛⎜⎝ γ exp¡−d+ ft + σfm +

12σ2¢Φ¡d−ft−σ

σ− σ

¢+ Φ

¡−d+ft+σσ

¢⎞⎟⎠

st = g (ft; d, γ, σ, σfm) .

where σfm denotes the covariance of the willingness to pay index with the stochastic

discount factor.

46

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Latin America Argentina ARG 1994 5441 39.1 9.4 2 Crude petroleum (10%), Feeding stuff for animals (10%)Brazil BRA 1994 836 34.9 10.1 1 Aircraft (6%), Iron ore and concentrates (5%)Chile CHI 1999 126 47.9 9.4 1 Copper (27%), Base metals ores (13%)Colombia COL 1997 506 33.9 10.2 0 Crude petroleum (26%), Coffee and substitutes (8%)Dominican Rep. DMR 2001 690 29.9 . 1 Men's outwear non-knit (17%), Under garments knitted (13%)Ecuador EQU 1995 1188 70.0 13.3 2 Crude petroleum (41%), Fruit, nuts, fresh, dried (18%)El Salvador ESD 2002 338 29.5 13.8 0 Coffee and substitutes (16%), Paper and paperboard, cut (6%)Mexico MEX 1994 246 33.0 9.0 1 Passenger motor vehicles, exc. bus (10%), Crude petroleum (8%)Panama PAN 1996 367 78.2 2.3 1 Fish, fresh, chilled, frozen (20%), Fruit, nuts, fresh, dried (20%)Peru PER 1997 428 53.9 14.6 4 Gold, non-monetary (17%), Feeding stuff for animals (13%)Uruguay URU 2001 902 31.6 8.9 4 Meat, fresh, chilled, frozen (16%), Leather (10%)Venezuela VEN 1994 1004 41.4 21.6 3 Crude petroleum (59%), Petroleum products, refined (25%)

Africa Côte d'Ivoire CDI 1998 2748 115.2 20.0 2 Cocoa (28%), Petroleum products, refined (18%)Morocco MOR 1998 273 58.5 7.3 2 Women's outwear non-knit (11%), Men's outwear non-knit (8%)Nigeria NIG 1994 1004 67.2 26.8 1 Crude petroleum (99.6%)South Africa SAF 1995 175 18.2 6.9 3 Pearl, prec., semi-prec. stones (13%), Special transactions (12%)Tunisia TUN 2002 189 54.6 5.6 0 Men's outwear non-knit (17%), Women's outwear non-knit (10%)

Eastern Europe Bulgaria BUL 1994 228 75.7 7.8 1 Petroleum products, refined (11%), Copper (7%)Croatia CRO 1996 118 49.1 1.6 1 Ships, boats etc. (15%), Petroleum products, refined (8%)Hungary HUN 1999 31 58.4 3.0 0 Int. combust. piston engines (9%), Automatic data proc. eq. (7%)Poland PLD 1994 98 43.2 5.0 1 Furniture and parts thereof (7%), Ships, boats etc. (4%)Russia RUS 1998 315 47.2 13.7 1 Crude petroleum (24%), Gas, natural and manufactured (17%)Ukraine UKR 2000 359 27.0 12.9 1 Iron, steel primary forms (13%), Iron, steel shapes etc. (8%)

Southeast Asia China CHN 1994 57 13.9 2.4 0 Telecom equip., parts, acces. (5%), Automatic data proc. eq. (5%)Malaysia MAL 1996 151 39.2 7.2 0 Transistors, valves etc. (19%), Office, adp. mach. parts (12%)Philippines PHI 1998 453 64.0 7.8 1 Transistors, valves etc. (42%), Automatic data proc. eq. (13%)South Korea SKO 1994 106 34.6 4.6 0 Transistors, valves etc. (12%), Passgr. motor vehicl. exc. bus (7%)Thailand THA 1997 91 35.5 7.9 0 Office, adp. mach. parts (9%), Transistors, valves etc. (8%) Egypt EGY 2001 204 48.9 10.6 1 Petroleum products, refined (39%), Crude petroleum (10%)Lebanon LEB 1998 511 25.9 4.0 0 Gold, silver ware, jewelry (9%), Gold, non-monetary (7%)Pakistan PAK 2001 317 44.3 12.3 1 Textile articles (16%), Textile yarn (12%)Turkey TUR 1996 627 34.1 5.4 2 Outer garments knit non-elastic (6%), Under garments knitted (6%)

Top two exports (SITC group) and their percentage of total exports

EMBI refers to the median daily spread in 2003 of J.P. Morgan's Emerging Market Bond Index Global (EMBI), measured in basis points over U.S. Treasuries. We report the first year for which EMBI data is available. Debt/GDP is the median level of external debt divided by GDP. Volatility of terms of trade is the median standard deviation of the percent change in terms of trade and is calculated using annual data and a rolling ten year backward-looking window. Number of defaults is the number of times a country has gone into default between 1970 and 2003. This is also the sample for the macroeconomic explanatory variables. Export groups are for 2000-2001 (UNCTAD).

Table1: Summary statistics by country

Middle East & South Asia

Debt/ GDP

Volatility of terms of trade

Number of

defaults

Country Country code

EMBI spread

Start of EMBI series

Mean 488.9 48.9 0.5 5.7 16.7 5.3 14.4 7.3Median 411.0 47.2 -1.1 4.7 14.2 4.7 13.8 9St. Dev. 360.2 20.9 13.0 4.3 11.8 14.5 7.4 3.5

Min 30.6 11.8 -33.5 0.7 1.5 -33.9 2.0 1p5 87.5 16.7 -15.2 1.3 5.0 -20.9 5.0 1p95 1268.5 81.6 21.3 14.8 37.2 31.1 28.5 11Max 1679.1 104.7 78.8 21.8 82.4 65.4 44.5 11

Observations: 177

EMBI refers to spreads on J.P. Morgan's Emerging Market Bond Index, debt/GDP denotes US dollar denominated debt to GDP, change in terms of trade is the percent change in terms of trade over the past five years. Volatility of terms of trade is the standard deviation of the annual percent change in terms of trade. It is calculated using annual data from a ten year rolling window. Years since last default counts the number of years since the last year in which the country was in default. It is capped at 10, equal to zero if the country is in default and set equal to 11 if the country has never defaulted. It is constructed using a default indicator variable from Reinhart, Rogoff, and Savastano (2003). The sample corresponds to the regression sample used in Table 3 and Table 4. p5 and p95 refer to the 5th and 95th percentiles of the distribution respectively.

Years since last default

Table 2: Summary statistics for EMBI spread regression sample

GDP growth Volatility of GDP growth

EMBIspread

Debt/GDP

Change in terms of trade

Volatility of terms of trade

Reserves/GDP

(1) (2) (3) (4) (5)5.659 4.440 5.780 5.054 5.114

(4.61)** (4.60)** (6.23)** (5.41)** (5.66)**-4.341 -3.791 -3.893 -2.982

(2.72)** (2.69)** (2.84)** (2.22)*52.756 42.789 35.232 28.333

(10.76)** (9.41)** (6.99)** (5.62)**-8.841 -6.282 -4.659

(5.43)** (3.52)** (2.50)*-2.250 -2.923 -2.133(1.81) (2.37)* (1.79)11.205 10.304 13.036(4.45)** (4.17)** (5.16)**

-20.923 -26.323(3.15)** (3.83)**

-33.796(0.56)

-212.770(4.01)**-109.992(2.08)*19.534(0.31)

212.016 -27.448 -38.576 166.622 235.953(3.25)** (0.49) (0.66) (1.93) (2.72)**

Observations 177 177 177 177 177R-squared 0.108 0.466 0.594 0.617 0.660

Absolute value of t-statistics in parentheses* significant at 5%; ** significant at 1%

Panel B: Economic significance of coefficients in specification (4)

Debt/GDP 5.1 20.9 105.8Change in terms of trade -3.9 13.0 -50.8Volatility of terms of trade 35.2 4.3 149.8Reserves/GDP -6.3 11.8 -73.8GDP growth -2.9 14.5 -42.2Volatiliy of GDP growth 10.3 7.4 76.1Years since last default -20.9 3.5 -73.3

Regression coefficient

standard deviation

predicted change

Table 3: Regressions of sovereign spreads on fundamentals

Debt/GDP

Reserves/GDP

Change in terms of trade

Volatility of terms of trade

This table reports results from regressions of mean annual EMBI spreads for a set of 30 countries from 1994-2003 on a set of explanatory variables. We only include observations for which a country is not in default.

Panel A: EMBI spread regressions

GDP growth

Volatility of GDP growth

Constant

Years since last default

Eastern Europe

Southeast Asia

Middle East & South Asia

Africa

(1) (2) (3) (4) (5) (6) (7) (8)6.235 4.981 5.941 5.180 12.182 11.120 10.799 11.145

(5.13)** (5.28)** (6.58)** (5.61)** (6.82)** (6.45)** (6.18)** (6.40)**-3.924 -3.264 -3.281 -2.784 -2.749 -2.603(2.57)* (2.39)* (2.46)* (1.90) (2.00)* (1.91)51.054 41.514 33.938 49.313 36.324 25.899

(10.79)** (9.32)** (6.65)** (4.62)** (3.49)** (2.22)*-8.492 -6.493 -11.933 -10.150(5.25)** (3.75)** (3.81)** (3.13)**-2.133 -3.020 -1.080 -0.966(1.60) (2.25)* (0.97) (0.88)10.512 10.175 11.422 10.600(4.26)** (4.21)** (2.77)** (2.58)*

-19.456 -20.101(2.86)** (1.93)

Year fixed effects Yes Yes Yes YesCountry fixed effects Yes Yes Yes Yes

Observations 177 177 177 177 177 177 177 177R-squared 0.137 0.496 0.609 0.628 0.242 0.351 0.462 0.476

Absolute value of t-statistics in parentheses* significant at 5%; ** significant at 1%

Years since last default

Volatility of terms of trade

Reserves/GDP

GDP growth

Volatility of GDP growth

Debt/GDP

Change in terms of trade

Table 4: Determinants of spreads across countries and over timeThis table reports results from regressions of mean annual EMBI spreads on explanatory variables. Columns (1) to (4) include year fixed effects, columns (5) to (8) include country fixed effects. Coefficients are within estimators of the panel regressions. R-squared is the within R-squared. We only include observations for which a country is not in default.

cross-section time-series

Non-default observations (not in default next period):

Mean 40.8 -0.3 9.0 11.3 10.0 12.3 9.3Median 39.0 -0.8 8.0 9.5 9.8 10.6 11St. Dev. 18.8 15.6 5.5 7.4 11.8 6.0 3.1Min 12.1 -33.7 2.2 1.6 -17.7 5.0 1Max 104.3 35.6 23.9 27.6 32.3 29.8 11Observations: 560

Default observations (in default next period):

Mean 58.8 -2.1 13.9 9.2 3.1 14.8 7.4Median 59.8 -3.6 14.6 5.2 0.9 14.5 11St. Dev. 25.1 21.0 6.5 7.7 14.9 6.6 4.5Observations: 27

Table 5: Summary statistics for default prediction

Debt/GDP

Change in terms of

trade

Volatility of terms of

trade

Reserves/GDP

GDP growth

Volatility of GDP growth

Years since last

default

This table reports summary statistics for our set of 7 macroeconomic explanatory variables. We consider the sample for which all variables are available. Variables are winsorized at the 5th and 95th percentile levels. We report summary statistics of the group of observations for which the country does not enter default over the following year and for the sample where it does enter default. The sample corresponds to the sample used for logit regressions in Table 6.

GDP growth

Volatility of GDP

growth

Years since last

default

Debt/GDP

Change in terms of

trade

Volatility of terms of

trade

Reserves/GDP

Panel A: Logit regressions on fundamentals(1) (2) (3)

0.043 0.037 0.033(4.47)** (3.62)** (3.06)**0.005 0.015 0.015(0.42) (1.22) (1.19)0.135 0.128 0.132

(4.28)** (3.88)** (4.00)**-0.057 -0.066(1.75) (1.92)-0.031 -0.032(1.85) (1.85)0.029 0.020(0.87) (0.60)

-0.093(1.64)

Constant -6.672 -5.848 -4.701(8.91)** (6.73)** (4.25)**

Observations 587 587 587# of defaults 27 27 27

Pseudo R-squared 0.173 0.203 0.214Absolute value of z-statistics in parentheses* significant at 5%; ** significant at 1%

Panel B: Model forecast accuracy phat > p80 17 18 19p80 >= phat > p60 5 5 5p60 >= phat > p40 2 3 2p40 >= phat > p20 3 1 1p20 >= phat 0 0 0

Panel C: Predicted probabilities of defaultMean 4.6 4.6 4.6Median 2.3 2.2 2.0St. Dev. 7.1 8.0 8.2Min 0.3 0.2 0.1Max 69.8 77.9 76.8Observations: 587

Table 6: Reduced form default prediction

Change in terms of trade

GDP growth

Panel A reports results from logit regressions of a forward looking default indicator on explanatory variables. The default indicator is from Reinhart, Rogoff, and Savastano (2003). It is equal to one if the country goes into default during the next year and zero if it does not enter default in the following year. Summary statistics for the sample are reported in Table 5. Panel B counts the number of actual defaults for parts of the fitted default probability distribution. Panel C reports summary statistics for fitted default probabilities.

Years since last default

Volatility of GDP growth

Debt/GDP

Reserves/GDP

Volatility of terms of trade

Panel A: Summary statistics of predicted spreads and default probabilities

Mean 488.9 127.5 198.2 6.4 4.3Median 411.0 26.5 74.1 1.4 1.8St. Dev. 360.2 203.7 438.2 9.6 8.0Min 30.6 0.0 2.7 0.0 0.1Max 1679.1 864.8 4653.1 37.5 76.8Observations: 177

Panel B: Regression of realized on predicted spreads(1) (2) (3) (4)

dependent variable: EMBI EMBI log(EMBI) log(EMBI)

1.663 0.265(13.99)** (13.42)**

1.850 0.510(14.54)** (16.38)**

305.556 227.153 5.064 3.635(13.41)** (8.86)** (66.79)** (25.33)**

Observations 177 177 177 177R-squared 0.528 0.547 0.507 0.605

Absolute value of t-statistics in parentheses* significant at 5%; ** significant at 1%

Model implied probability

Constant

Table 7: Comparing actual and predicted spreadsPanel A reports summary statistics for EMBI, model implied and reduced form predicted spreads, and model implied and reduced form default probabilities. The sample corresponds to the spread regression sample of Table 3. Panel B reports estimates from regressions of actual spreads on model implied spreads and actual spreads on reduced form predicted spreads, both in levels and in logs. Model implied spreads below 1 basis point are set equal to 1 basis point. For level regressions model implied and reduced form spreads are winsorized at the 10th and 90th percentiles.

EMBI Model implied spread

Reduced form

spread

Reduced form

probability

Reduced form spread

Model implied spread

Figure 1: EMBI spreads and Commodity Prices

100

300

500

700

900

1100

1300

1500

1994

m119

94m7

1995

m119

95m7

1996

m119

96m7

1997

m119

97m7

1998

m119

98m7

1999

m119

99m7

2000

m120

00m7

2001

m120

01m7

2002

m120

02m7

2003

m120

03m7

2004

m120

04m7

2005

m120

05m7

2006

m1

date

EMB

I spr

ead

(bas

is p

oint

s ov

er U

.S. T

reas

urie

s)

180

240

300

360

CR

B C

omm

odity

pric

e in

dex

EMBI

Commodity_Index

E

MB

I spr

ead

(bas

is p

oint

s)

Figure 2a: Volatility of terms of trade in the cross sectionVolatility of terms of trade (%)

0 5 10 15 20

0

500

1000

1500

ARG

BRABUL

CDI

CHICHN

COL

CRO

EGY

EQU

ESD

HUN

LEB

MAL

MEX MOR

PAK

PAN

PER

PHI

PLD

RUS

SAF

SKOTHATUN

TUR

UKR

URU

VEN

EM

BI s

prea

d (b

asis

poi

nts)

Figure 2b: Debt/GDP in the cross-sectionDebt/GDP (%)

20 40 60 80 100

0

500

1000

1500

ARG

BRABUL

CDI

CHICHN

COL

CRO

EGY

EQU

ESD

HUN

LEB

MAL

MEX MOR

PAK

PAN

PER

PHI

PLD

RUS

SAF

SKO THATUN

TUR

UKR

URU

VEN

E

MB

I spr

ead

(bas

is p

oint

s)

Figure 2c: Debt/GDP in the time-seriesDebt/GDP (%)

-40 -20 0 20 40

-500

0

500

1000

ARG

ARG

ARG

ARG

ARG

ARGARG

BRA

BRA

BRA

BRA

BRA

BRA

BRA

BRA

BRA

BUL

BUL

BULBULBUL

BULBUL

BUL

BUL

CDICHICHI CHI CHICHI

CHNCHNCHNCHN

CHNCHNCHNCHNCHN

CHN

COL

COL

COLCOLCOL

COL

COL

CRO

CRO

CRO CRO

EGYEGY

EGYEQU

EQU

EQU

EQUEQU

EQUESD ESD

HUNHUN

HUNHUNHUN

LEB LEBLEB

LEB

LEB

LEB

MAL MAL

MAL

MAL

MAL MALMAL

MALMEX

MEX

MEX

MEX

MEXMEX

MEXMEXMEXMEX

MORMOR

MORMOR

MOR

MOR

PAK

PAK

PAK

PAN

PANPANPAN PANPAN

PANPER PER

PER

PERPER

PER

PHI

PHI

PHIPHI

PHIPHI

PLD

PLDPLD

PLD PLDPLDPLD PLD

PLD

RUS

RUS

RUS

SAF

SAFSAF

SAFSAF

SAFSAFSAF

SAFSKOSKO SKOSKO

SKO

SKOSKO THA

THA

THATHATHA

THATHA

TUN

TUN

TURTUR

TURTUR

TUR

TUR

TUR

TUR

UKR

UKR

UKR

URU

URU VEN

VEN

VEN

VENVEN

VENVEN

E

MB

I spr

ead

(bas

is p

oint

s)

Figure 3: Actual and model implied spreadsModel implied spread

EMBI Fitted_values

1 5 10 50 100 500 1000 2500

10

50

100

500

1000

2500

SAF

SAF

SAF

SAFSAF

SAF

SAF

SAFSAF

MAL

MAL

MAL

MAL

MAL

MAL

MALMAL

TUN

TUN

CHNCHNCHN

CHN

CHNCHNCHN

CHN

CHNCHN

CRO

CROCRO

CRO

HUN

HUNHUN

HUNHUN

URU

URU

SKOSKO

SKO

SKO

SKO

SKO

SKO

PANPANPANPAN

PAN

PANPAN

COL

COLCOL

COLCOL

COLCOL

THATHA

THATHA THA

THA

THAEGY

EGYEGYESDESD

LEB

LEB

LEB LEB

LEBLEB

TUR

TUR

TUR

TURTUR

TURTUR

TUR

MORMOR

MORMOR

MOR

MOR

PLD PLD

PLD

PLDPLD

PLD

PLD

PLDPLD

MEXMEX

MEXMEXMEX

MEX

MEX

MEX

MEXMEX PHI

PHI

PHIPHI

PHIPHI

CHICHICHI CHI

CHI

ARG ARG

ARG

ARGARG ARG

ARG

BRABRA

BRA

BRA

BRA

BRA

BRABRA BRA

BUL

BULBUL

BUL

BULBUL BUL

BULBUL

PERPER

PER

PERPER PER

UKR

UKR

UKR

RUS

RUS

RUSPAK

PAK

PAK

VENVENVEN

VENVEN VEN

VENEQUEQU EQUEQU

EQU

EQU

CDI

EM

BI s

prea

d (b

asis

poi

nts)

Figure 4: Actual and reduced form spreadsReduced form spread

EMBI Fitted_values

1 5 10 50 100 500 1000 2500

10

50

100

500

1000

2500

SAF

SAF

SAF

SAFSAF

SAF

SAF

SAFSAF

MAL

MAL

MAL

MAL

MAL

MAL

MALMAL

TUN

TUN

CHNCHNCHN

CHN

CHNCHNCHN

CHN

CHNCHN

CRO

CROCRO

CRO

HUN

HUNHUN

HUNHUN

URU

URU

SKOSKO

SKO

SKO

SKO

SKO

SKO

PANPANPANPAN

PAN

PANPAN

COL

COLCOL

COLCOL

COLCOL

THATHA

THATHATHA

THA

THAEGY

EGYEGYESDESD

LEB

LEB

LEBLEB

LEBLEB

TUR

TUR

TUR

TURTUR

TURTUR

TUR

MORMOR

MORMOR

MOR

MOR

PLD PLD

PLD

PLDPLD

PLD

PLD

PLDPLD

MEXMEX

MEXMEXMEX

MEX

MEX

MEX

MEXMEX PHI

PHI

PHIPHI

PHIPHI

CHICHICHI CHI

CHI

ARGARG

ARG

ARGARGARG

ARG

BRABRA

BRA

BRA

BRA

BRA

BRABRABRA

BUL

BULBUL

BUL

BUL BUL BUL

BULBUL

PERPER

PER

PERPER PER

UKR

UKR

UKR

RUS

RUS

RUSPAK

PAK

PAK

VENVENVEN

VEN VENVEN

VENEQUEQU EQUEQU

EQU

EQU

CDI

Ave

rage

spr

ead

(bas

is p

oint

s)

Figure 5: Spreads by average default probabilityAverage probability of default

0

300

600

900

(mean) EMBI (mean) Reduced_Form (mean) Model_Implied

0.4 1.1 2.0 4.1 14.1