“Rules of thumb” for sovereign debt crises

Journal of International Economics 78 (2009) 192–205

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Journal of International Economics

j ourna l homepage: www.e lsev ie r.com/ locate / j i e

“Rules of thumb” for sovereign debt crises☆

Paolo Manasse a,⁎, Nouriel Roubini b

a Economics Department, Faculty of Political Sciences, University of Bologna, Strada Maggiore, 45, 40100 Bologna, Italyb Stern School of Business, New York University, 269 Mercer Street, 7FL New York, NY 10003, USA

☆ Wewish to thank Guido Ascari, James Daniel, MarkKeller, Manmohan S. Kumar, Pier Carlo Padoan, Indira Raat seminars at the International Monetary Fund, BoccoAndy Berg and Rex Gosh provided great comments at a⁎ Corresponding author. Tel.: +39 051 209 2616; fax:

E-mail address: [email protected] (P. Manasse1 See for example Roubini and Setser (2004) for a syst

emerging market economies in the last decade, and on

0022-1996/$ – see front matter © 2009 Elsevier B.V. Adoi:10.1016/j.jinteco.2008.12.002

a b s t r a c t
a r t i c l e i n f o
Article history:Received 5 July 2005Received in revised form 10 September 2008Accepted 28 December 2008

Keywords:Sovereign debtCrisesDefault

JEL classification:F33F34F37

This paper investigates the economic and political conditions that are associated to the occurrence of a sovereigndebt crisis.Weuse anewstatistical approach (ClassificationandRegressionTree) that allowsus to derive a collectionof “rules of thumb” that help identify the typical characteristics of defaulters. We find that not all crises are equal:they differ depending onwhether the government faces insolvency, illiquidity, or variousmacroeconomic risks.Wealso characterize the set of fundamentals that canbe associatedwith a relatively “risk-free” zone. This classification isimportant for discussing appropriate policy options to prevent crises and improve response time and prediction.

© 2009 Elsevier B.V. All rights reserved.

1. Introduction

Following the debt crises of the 1980s, sovereign debt defaultshave become more frequent. Episodes of outright default includeRussia, Ecuador, and Argentina. In other cases, formal default wasavoided via a debt restructuring under a coercive threat of default as inUkraine, Pakistan, and Uruguay. Default was averted through large-scale IMF financial support in cases such as Mexico, Brazil, and Turkey.

While there has been a significant amount of research regarding debtcrises in general, and about the policy responses to these defaults, inparticular,1 the macroeconomic and structural weaknesses leading tothem are still not properly understood: there is little comparativeempirical work on the sovereign debt crises of the last decade. Manypolicymakers and analysts continue to use simple rules of thumb to judgerisks and toassessfiscal sustainability (ModyandSaravia, 2003), aswell asthe soundness of macroeconomic policies. Too often, these rules are notbased on a rigorous quantitative analysis, and may miss some coreelements that led to these sovereign debt crises.

Our aim is to provide answers to the following basic questions. Whatset of economic and political conditions is empirically associated to the

De Broeck, Bob Flood, Christianjaraman, as well as participantsni and Milan State University.n early stage of this project.+39 02 700 514 895.).ematic analysis of the crises inhow they were resolved.

ll rights reserved.

likely occurrence of a sovereign debt crisis? Can one derive thresholds forvulnerability indicators that will effectively signal the risk of a sovereigndebt crisis? Part of the motivation for the paper stems from so-calledsurveillance failures, namely cases where international financial institu-tions, such as the IMF, aswell as rating agencies, private sector agents, andacademics, were taken “by surprise” and grossly under-estimated thelikelihood of a sovereign default.

In thepaper,weuseanewstatistical approachandderivea setof “rulesof thumb” that help identify the typical characteristics of defaulters. Wefind that not all crises are equal: they differ depending on whether thegovernment faced insolvency, illiquidity, or various macroeconomicweaknesses and risks. This classification is crucial for discussingappropriate policy options for preventing crises and responding to themonce they occur. For example, it is often argued that solvent but illiquidcountrieswith large amounts of short-termdebtmayneed IMF support toavoid a liquidity run or “roll-off” crisis. Conversely, highly indebtedcountriesmay face a debt crisis, unless there is a strong and credible fiscalconsolidation. In addition, it is argued that conditionality should settargets indicating that a country's macroeconomic fundamentals areheading towards a relatively “safe” zone. In the paper these concepts ofliquidity crisis, insolvency crisis, crisis triggered by weak macro-funda-mentals, and relatively “safe zone” are made precise. Unless the diagnosisis correct, it is hard to get the policy cure right.

This empirical analysis is based on a dataset containing annualobservations for 47 emerging market economies from 1970 to 2002. Acountry is defined to be in a state of “debt crisis” if it is classified as beingin default by Standard & Poor's, or if it receives a large non-concessionalIMF loan (where “large”means in excess of 100%of IMFquota). Standard

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Table 1Countries and default episodes in the full sample.

Number of crisis Average length Years in crisis Crisis episodes (starred are added by IMF loans)

Algeria 1 6.0 6 1991–1997Argentina 3 5.0 15 1982–1994, 1995⁎,1996, 2001, 2002Bolivia 2 6.5 13 1980–1985, 1986–1994Brazil 3 5.3 16 1983–1995, 1998⁎,99⁎,2000, 2001⁎,2002⁎Chile 1 8.0 8 1983–1991China 0 … 0Colombia 0 … 0Costa Rica 1 10.0 10 1981–1991Cyprus 0 … 0Czech Republica 0 … 0Dominican Republic 1 22.0 22 1981–Ecuador 2 8.0 16 1982–1996, 1999–2001Egypt 1 1.0 1 1984–1985El Salvador 1 16.0 16 1981–1997Estoniaa 0 … 0Guatemala 1 1.0 1 1986–1987Hungarya 0 … 0India 0 … 0Indonesia 2 2.5 5 1997⁎–2001, 2002Israel 0 … 0Jamaica 3 4.7 14 1978–1980, 1981–1986, 1987–1994Jordan 1 5.0 5 1989–1994Kazakhstana 0 … 0Korea, Rep. of 2 2.0 4 1980⁎,81⁎,82, 1997⁎,98⁎,99Latviaa 0 … 0Lithuaniaa 0 … 0Malaysia 0 … 0Mexico 2 5.0 10 1982–1991, 1995⁎, 96Morocco 2 3.0 6 1983–1984, 1986–1991Oman 0 … 0Pakistan 1 2.0 2 1998–2000Panama 1 14.0 14 1983–1997Paraguay 1 7.0 7 1986–1993Peru 3 6.3 19 1976–1977, 1978, 1979⁎–1981, 1983–1998Philippines 1 10.0 10 1983–1993Polanda 0 … 0Romaniaa 0 … 0Russiaa 1 3.0 3 1998–2001Slovak Republica 0 … 0South Africa 4 1.8 7 1976⁎,77⁎,78, 1985–1988, 1989–1990, 1993–1994Thailand 2 1.0 2 1981⁎,82, 1997⁎, 98Trinidad and Tobago 1 2.0 2 1988–1990Tunisia 1 1.0 1 1991⁎, 92Turkey 2 3.5 7 1978, 1979, 1980⁎, 1981⁎, 1982, 1983, 2000⁎, 2001⁎, 2002Ukrainea 1 3.0 3 1998–2001Uruguay 3 2.0 6 1983–1986, 1987–1988, 1990–1992Venezuela 3 3.3 10 1983–1989, 1990–1991, 1995–1998Total 54 5.5 261

Sources: IMF, Standard & Poor's, World Bank, and authors' calculations. A star indicates according to IMF loan.a Transition countries are included only from 1995 onwards.

193P. Manasse, N. Roubini / Journal of International Economics 78 (2009) 192–205

& Poor's rates sovereign issuers in default when a government fails tomeetprincipal or interest paymentonanexternal obligation onduedate(including exchange offers, debt equity swaps, and buy back for cash).

We employ the Classification and Regression Tree methodology(CART) for classification and prediction.2 CART is a computer-intensive data mining technique that selects explanatory variables,their critical values, and their interactions in order to identify “safe”from “crisis-prone” types. The main conclusions of our empiricalanalysis are as follows.

First, outof 50 candidate variables,10predictor variables turnout to besufficient for classification and prediction: total external debt/GDP ratio;short-term debt reserves ratio; real GDP growth; public external debt/fiscal revenue ratio; CPI inflation; number of years to the next presidentialelection; U.S. treasury bills rate; external financial requirements (currentaccount balance plus short-term debt as a ratio of foreign reserves);exchange rate overvaluation; and exchange rate volatility.

Second, a relatively “safe” country type is described by a handful ofeconomic prerequisites: low total external debt (below 49.7% of GDP);

2 The analysis employs the data mining software CART developed by Salford Systems.

low short-term debt (below 130% of reserves); low public externaldebt (below 214% of fiscal revenue); and an exchange rate that is notexcessively over-appreciated (overvaluation below 48%).

Third, three major types of risks are identified: (i) solvency (or debtunsustainability); (ii) illiquidity; and (iii) macro-exchange rate risks. Thedebt unsustainability risk types are characterized by: external debt inexcess of 49.7% of GDP, together with monetary or fiscal imbalances, aswell as by large external financing needs that signal illiquidity as anelement of debt unsustainability. Liquidity risk types are identified bymoderate debt levels, but have short-term debt in excess of 130% ofreserves coupledwith political uncertainty and tight international capitalmarkets. Macro-exchange rate risk types arise from the combination oflow growth and relatively fixed exchange rates. Each of these risk typesdiffer in their likelihood of producing a crisis. Finally, our model hasexcellent predictive capacity in-sample, while the out-of-sample forecasthave both less false alarms and less correct predictions than the EarlyWarning Signal (EWS) literature.

The analysis has one important, albeit simple, implication forsustainability analysis. It shows thatunconditional thresholds, for examplefordebt–output ratios, areof little valueper se forassessing theprobability

194 P. Manasse, N. Roubini / Journal of International Economics 78 (2009) 192–205

of default. One country may be heavily indebted but have a negligibleprobability of default, while a second may have only moderate values ofdebt ratios while running a considerable default risk. Why? Because thejoint effects of short maturity, political uncertainty, and relatively fixedexchange ratesmake a liquidity crisis in the lattermuchmore likely than asolvency crisis in the former, particularly if the large external debt burdengoes togetherwithmonetary stability, a large current account surplus, andsound public finances.

The plan of the paper is the following. Section 2 contains a review ofthe literature. Section 3 describes the dataset. The Classification Treemethodology is reviewed in section 4, and applied to the data in section 5.Section 6 discusses an interpretation of the results. Sections 7 and 8contain standard regression analysis and a robustness check based on ageneralization of the CART procedure. The predictive power of themodel is discussed in sections 9, and 10 performs some “rolling tree”exercises in order to understand if the crises of the nineties are“structurally” different from those in the previous decades. The final

Table 2Mean of variables used in the analysis.

Current year All No cri

Next year All No cri

Total external debt over GDP 45.5 37.0Total external debt over exports 290.7 239.3Total debt service over GDPTotal debt service over reservesShort-term external debt (RM, over GDP) 10.9 9.4Short-term external debt (RM, over reserves) 1.7 1.2Interest on short-term external debt over GDP 0.5 0.5Interest on short-term external debt over reserves 0.1 0.1Debt service on short-term external debt over GDP 5.3 4.8Debt service on short-term external debt over reserves 0.8 0.7Public external debt over GDP 32.2 25.5Public external debt over revenue 1.7 1.3Consolidated central government debt 47.5 46.4Overvaluation 0.0 0.0Current account balance −2.7 −2.7Reserves growth 19.1 20.8Export growth 12.0 13.8M2 over reserves 5.6 5.3Financing requirement 1.6 1.3LIBOR 9.7 9.5U.S. treasury bill rate 6.4 6.3Inflation 54.6 17.5Nominal GDP growth 55.9 22.8Real GDP growth 4.1 4.8REER growth 121.5 124.3Import growth 10.0 12.3FDI over GDP 1.7 1.9Openness 71.2 71.3Overall balance −4.3 −4.4Primary balance 0.6 0.3Primary gap 6.6 5.7G.Gov revenue over GDP 24.3 25.4Overall Balance/GDP variability 1.92 −2.53Inflation variability 120.43 10.80Exchange rate variabilityb 57.8 56.38Real Exchange Rate Variability 2.87 1.49Terms of trade variability 2.24 2.28Index of political rights 3.52 3.63Index of civil liberties 3.77 3.85Index of freedom status 1.21 1.16Index of political constraints III 0.24 0.24Index of political constraints V 0.35 0.33Year of parliamentary elections 0.19 0.18Year of presidential elections 0.09 0.06Year of parliamentary or presidential elections 0.21 0.20Years to next parliamentary elections 2.73 2.94Years to next presidential elections 5.02 6.47Years since parliamentary elections 2.02 1.81Years since presidential elections 2.19 2.15Electoral systema 1 1

a Mode of electoral system.b Excludes Turkey. Sources: IMF, Standard & Poor's, World Bank, and authors calculations

section 11 discusses some extensions and summarizes the mainconclusions and policy implications.

2. Review of the literature

Most empirical studies consider that countries may either be unableto repay their debt, because they are insolvent or illiquid, or that theymay be unwilling to repay their debt, based on a consideration of therelative costs and benefits of default. Thus, these studies suggest proxiesfor ability and willingness to repay as the determinants of debt crises.

Different studies use different crisis definitions, depending on thespecific research question and the information available in the datasource used. A priori, there is no single empirical definition of whatshould constitute a sovereign default or a debt crisis. Some studiescompile a list of debt crisis or default episodes from case studies andanecdotal evidence (e.g., Beers and Bhatia, 1999; Beim and Calomiris,2001). Others rely on a quantitative approach. For example, Detragiache

sis No crisis Crisis Crisis No. ofobservationssis Crisis Crisis No crisis

54.7 71.4 63.7 1,051359.3 455.9 350.2 1,053

15.0 15.1 15.7 9932.9 2.9 2.2 9480.8 0.6 0.7 7540.2 0.1 0.1 7546.9 6.4 7.1 1,0501.5 1.2 0.9 1,050

36.4 53.0 46.5 1,0511.9 3.0 2.3 827

38.2 57.3 54.0 4620.0 −0.1 0.0 799

−4.3 −2.6 −1.3 1,231−5.4 17.8 22.9 1,155

4.9 6.4 7.8 1,2707.9 6.2 6.2 1,1853.0 2.4 1.4 986

10.5 10.5 9.4 1,2297.8 6.9 6.3 1,229

241.1 169.6 84.9 1,273249.4 148.6 96.0 1,276

1.8 2.1 2.2 1,276139.7 111.0 109.4 937

5.3 4.8 6.9 9021.1 1.0 1.5 1,024

64.1 72.1 72.5 903−6.3 −3.8 −4.1 1,013−0.9 2.0 1.5 61623.1 59.0 −15.0 12222.7 20.1 24.2 1,013−1.77 19.42 −1.70 824125.37 549.81 83.03 1,08245.62 39.87 159.9 1,0593.76 6.34 3.39 7532.32 2.23 1.33 1,0883.44 3.18 3.20 1,1303.75 3.44 3.65 1,1301.21 1.39 1.39 1,1300.23 0.26 0.31 1,2290.35 0.37 0.43 1,2290.24 0.23 0.20 1,2760.11 0.18 0.15 1,2760.24 0.27 0.24 1,2762.67 2.06 2.16 1,0713.15 2.18 2.39 6602.47 2.60 2.00 9012.83 2.24 1.60 4181 1 1 1,210

.

5 Recent examples of near-default avoided via a large IMF package are Mexico in1995, Brazil in 1998 and 2001, and Turkey in 2000.

6 Mainly lending via Stand By Arrangements (SBAs) and Extend Fund Facilities


and Spilimbergo (2001) define a country to be in a debt crisis if thecountry has arrears on external obligations towards commercialcreditors in excess of 5% of commercial debt outstanding, or has arescheduling or restructuring agreement with commercial creditors.This definition does not differentiate between sovereign or privatesector arrears and/or rescheduling due to data limitations. Anotherproblem of this quantitative definition is that it might exclude someincipient debt crises that were only avoided by large-scale financialsupport from official creditors (International Financial Institutions(IFIs)), and/or from bilateral creditors. A data source that provides auniformly compiled information on sovereign default is Standard andPoor's (2002) that defines a country to be in default as long as thesovereign is not current on any of its debt obligation.

Empirical studies of the determinants of debt crisis are closest innature to an Early Warning Signal model. Factors influencing theprobability of a debt crisis are identified by means of probit/logitregressions or a signal model. Most studies have focused on the debtcrisis of the 1980s, but some recent efforts have looked at crisesoccurring in the 1990s.3 Reinhart (2002) finds that in 84% of the casesin her sample, a debt crisis is preceded by a currency crisis.Detragiache and Spilimbergo (2001) find that short-term debt isendogenous to the model, as countries find it more and more difficultto borrow long term in the run-up to a debt crisis. While most studiesuse macroeconomic variables only in levels, Catão and Sutton (2002)also include measures of volatility in trade, fiscal policy, monetarypolicy and exchange rate policy. Manasse, Roubini, and Schimmelp-fennig (2003) estimate a logit model of sovereign debt crisis thatincludes a large set of emerging market economies for the 1970–2002period; thus, they include the sovereign crises of the last decade intheir sample. Their model predicts about three quarters of all crisesentries while sending few false alarms.

Taken together, the existing literature suggests several factors that areat the core of an empiricalmodel attempting to predict sovereign default:measures of solvency, such as public and external debt relative to thecapacity to pay; liquidity measures such as short-term external debt andexternal debt service, possibly as a ratio of foreign reserves or exports;political, institutional and other variables capturing a country's will-ingness to pay; macroeconomic variables such as real growth, inflation,exchange rate, etc., capturing both ability to pay and willingness to pay;measures of external volatility and volatility in economic policies. Thus,we use these variables and measures in the empirical study.

While the tree methodology that we employ has been used in alimited number of economic studies and even applied to the case ofcurrency crises (see Ghosh and Ghosh, 2002; Frankel and Wei, 2004)no previous study has used this methodology to assess thedeterminants of sovereign crises and to predict them.

3. Data and definitions

The full dataset includes annual information on 47 economies withmarket access from 1970 to 2002 (Table 1).4 A country is defined to bein a debt crisis if it is classified as being in default by Standard & Poor'sor if it receives a large non-concessional IMF loan defined as access inexcess of 100% of quota. Standard & Poor's rates sovereign issuers indefault if a government fails to meet principal or interest payment onexternal obligation on due date or within the specified grace periodcontained in the original terms of the debt issue, or when exchange

3 See for example Detragiache and Spilimbergo (2001) for a study including recentepisodes.

4 The debt crisis indicator is derived from data provided by Standard & Poor's anddata on IMF lending. Data on external debt and public debt is taken from the WorldBank's Global Development Finance database (GDF), as well as from IMF sources. Dataon public finance and other macroeconomic variables are taken from the IMF's WorldEconomic Outlook database, as well as the Government Finance Statistics database(GFS).For transition economies, the sample period is 1995–2002. Not every variable isavailable for all countries or for the full-time period.

offers contain less favorable terms than the original issue. Hence,exchange offers, debt equity swaps, and buy-backs for cash aregenerally considered as defaults. A potential problem with thisdefinition is that it may not capture episodes where near-defaults orcoercive debt restructurings were prevented only through anadjustment program and a large financial package from the IMF.5

We therefore augment the information obtained from Standard &Poor's with data on IMF non-concessional lending, as recorded byIMF's Finance Department.6 We use information on the loansapproved, approval dates and the actual disbursement of the loans.Based on the information on IMF lending, a country is classified asbeing in debt crisis if a large non-concessional loan is approved and adisbursement under this loan is actually made in the first year. Thedefinition of debt crisis thus encompasses actual defaults on debtrecorded by Standard & Poor's and “incipient” defaults that wereavoided only through a large-scale financial support from the IMF.7

Based on this definition, a country can be in a debt crisis for anextended period.We define a “large” IMF loan as being in excess of 100percent of quota; this threshold selects the top 10% of loans whenranked by the loan to quota ratio. The full list of crises in the sampleand their duration are shown in Table 1.

Our comprehensive definition identifies 54 crisis episodes in thesample period, of which 21 episodes are due to the IMF-loan criterion(these are identified by an asterisk in the table). Almost invariably,these latter episodes occur at the outset of the crisis (for example inBrazil 1998, 1999 Indonesia 1997, Korea 1980, 1981 and 1997, 1998,South Africa 1976, 1977, Thailand 1981 and 1997, Tunisia 1991, Turkey1980, 1981, 2000, 2001, see Table 1), implying that in these cases theIMF intervention only postponed the actual debt default. Thus, ourdefinition is likely to improve locating the timing of the outbreak ofthe crisis.8

4. Descriptive statistics

The explanatory variables can be grouped into three sets: (i)macroeconomic fundamentals; (ii) variability indicators (4-yearmoving window of coefficients of variation); and (iii) politicaleconomy variables. As to the former, we use various measures ofexternal debt and public debt as proxies for solvency and liquidity. Wealso employ the variables included in the IMF's Early Warning Signalsmodel of currency crises, as there is a possible link between currencycrisis and sovereign debt crisis. Finally, we employ other commonmacroeconomic indicators, such as fiscal flow-variables. Table 2 givesthe respective mean of the variables used in the analysis, distinguish-ing between means in the full sample, means for tranquil (or safe)episodes (a no crisis year followed by another no crisis), for the yearsbefore an outbreak of the crisis (a safe year followed by a crisis), forperiods “within crisis” (a crisis year followed by another crisis year),for end-of-crisis periods (a crisis year followed by a non-crisis).

In general, the path of means from tranquil times to the outbreak ofthe crisis conforms to the expectations.

The various measures of total external debt (including debtservicing) are relatively low in tranquil times. They increase in theyear before crisis outbreak, and often increase even further within the

(EFFs).7 This definition entails the possibility of a type II error of defining a crisis when a

country receive a large loan without facing insolvency problems. To our knowledge, noepisode in our sample falls into this case.

8 Our comprehensive definition adds a substantial number of crisis observations tothe sample, compared with the simple S&P criterion, and this is very useful forestimation. The drawback is that, as usual, the results inevitably depend on the choiceof the crisis definition. However, in a related paper (Manasse et al., 2003) we showthat the results of a similar (logit) exercise are robust to the choice of the criticalthreshold (here 100% of quota) for identifying a “large“ IMF loan.

10 One can explicitly set different costs from misclassifying a crisis (C1 ) and a noncrisis (C0) observation. Doing so modifies the formula for the (adjusted) posteriorprobabilities as follows:

p1 tð Þ =

C1π1Pj=0;1

CjπjN1 tð Þ=N1

Pi=0;1

CiπiPj=0;1

CjπjNi tð Þ=Ni


crisis' period. Thesemeasures fall in the year before a country exits thestate of crisis, although they are still higher than before the crisisoutbreak. The measure of public external debt follows a similarpattern, suggesting that public external debt may be a driving forcebehind total (public and private) external debt developments, as inmany countries a large fraction of external debt is indeed public.

The macroeconomic variables—including those from the IMFcurrency crisis' EWS—indicate a worsening of the macroeconomicsituation in the run-up to a crisis and within a crisis, and animprovement in the situation when exiting from crisis. For example,the current account deficit increases in the year immediately precedingthe outburst of a crisis, stabilizes within the crisis period, and improvesfurther in the year before the “exit” from the crisis. Real growth falters inthe year when the crisis outbreaks, while inflation spikes. The overallfiscal balance, as well as the primary balance, deteriorates in the run-upto crisis. It is interesting to note that both the Libor as well as the U.S.treasury bill rate increase in years preceding a crisis, suggesting thattight monetary conditions in the G-7 area may reduce capital flows toemerging market economies and thus contribute to debt servicingdifficulties (as it happened in 1982 for example).

The second set of variables contains measures of volatility. We showin Table 2 the coefficient of variation, calculated over a moving windowof 4 years, for the fiscal balance/GDP ratio, inflation, nominal and realexchange rate and the terms of trade. Interestingly, the volatilities of thereal exchange rate andof inflation rise in thewakeof a crisis, and again inthe midst of a crisis, while falling on the verge of the exit.

Finally, political economy variables are shown in the bottom part ofthe table. The indexes of political rights, civil liberties and freedomstatus, compiled by Freedom House (2002) take value on a scale fromone(most “free”) to seven(least “free”). There seems to benosignificantdifference between in and out crises episodes. The same applies to thepolitical constraint indexes (Henisz, 2002). These measure the numberof players in the political arenawith veto power, who can block reforms.They range from zero (no veto players) to one (impossible to reform thestatus quo). Again, there seems to be little difference between in and outcrisis episodes. The same applies to the typology of electoral systems.The most frequent electoral system across all cases turns out to be thenumber one, proportional representation. More action seems to stemfrom the number of years to the next presidential election: entry andstaying in crisis are on average associated with upcoming elections,possibly indicating that political uncertainty before electionsplays a rolein contributing to crises.

5. Methodology9

This section describes the Classification and Regression Treemethodology (CART).This has been applied to several fields, includingengineering, medical diagnosis, genetics, meteorology, marketing,insurance, consumer credit. Topics have included market segmenta-tion, credit risk assessment, quality control, the spread of cancer, bloodcell classification, infant mortality, wildlife management, air pollutionalerts, speech recognition, and identification of radar images for themilitary.

Developed by statisticians Breiman, Friedman, Olshen, and Stone(1984), CART searches for the characteristics that are most closelyassociated to class membership (in our case crisis vs. non-crisis).Unlike regression analysis, this computer-intensive algorithm isparticularly suited for uncovering hidden non-linear structures andvariable interactions in complex datasets. “Complexity” includes highdimensionality, a mixture of data types, nonstandard data structureand, perhaps more challenging, non-homogeneity, i.e., differentrelationships between variables may hold in different parts of themeasurement space (Breiman et al., 1984). This methodology can also

9 The next two sections draw from http://www.salford-systems.com/ and fromBreiman et al. (1984).

be useful as a data-screening device that selects relevant variables andtheir interactions, and which can be used as a preliminary explorationtool in the search for a model's specification.

CART uses a binary and recursive procedure in that parent nodes(data partitions) are split into two “more homogeneous” child nodes,and the process is repeated by treating each child node as a parent.The key elements of a CART analysis are a set of rules for: (i) splittingeach node into two child nodes; (ii) deciding when to stop growingthe tree; and (iii) assigning each terminal node to a class outcome(e.g., crisis vs. non-crisis). We discuss these issues in turn.

To split a node CARTalways asks questions that have a “yes” or “no”answer. For example, the question for assessing the likelihood of adefault on external debt might be: is the external debt–GDP ratio≤0.5? CART looks at all possible candidate splits for all variablesincluded in the analysis, and selects the one that best separatesepisodes of defaults from non-defaults. For example, in our datasetcontaining approximately 1300 observations (country–year) on 50variables, CART evaluates 1300×50=65,000 possible splits, andselects the one that generates the “purest” child nodes.

In practice, each possible split classifies observations in two groupsthat have both crises and non-crises, so the process is repeated insubsequent sub-samples. The CART algorithm computes a cost thatrises with the extent by which the actual classification departs fromthe perfect classification (all crises in one node and all non-crises inthe other) and selects the split that minimizes such cost. The lossfunction being minimized in a two-class problem is the Gini criterion:

Loss =X

t

N0 tð Þ + N1 tð Þð Þp0 tð Þp1 tð Þ ð1Þ

where N(t)=N0(t)+N1(t), is the number of observations in (terminal)node t,N0(t) is the numberof non-crises (type 0) in node t andN1(t) is thenumber of crises (type 1) in node t; p1(t) and p0(t)=1−p1(t) are theposterior probabilities that a non-crisis, respectively, crisis, observationfalls into node t. Clearly, the loss function attains a minimum whenterminal nodes (those which are not split further) contain only eithercrisis or non-crisis observations. Let π1(π0) denote the subjective priorprobability of a crisis (non-crisis), andN,N1,N0=N−N1 denote the totalnumber observations in the sample, the number of crises and non-crisesin the sample. From Bayes' rule the posterior probabilities are given by:

p1 tð Þ = π1N1 tð Þ=N1Pi=0;1

πiNi tð Þ=Ni;p0 tð Þ = 1− p1 tð Þ ð2Þ

CART allows the researcher to express its priors on the probability ofa crisis, the idea being that these priors may differ from the empiricallikelihood of a crisis, N1/N. The consequence of, say, setting a high priorprobability for a crisis π1 is to increase the posterior probability that acrisis observationwill fall in terminal node t, p1, so that it becomesmorelikely that the node will be labeled a “crisis” node (see below). Clearly,this has the drawback of raising the “type II” error that a non-crises nodet will be wrongly classified as crisis (a “false alarm,” see below).Alternatively, CART allows the researcher to weight differently the costof misclassifying crisis and non-crisis episodes:10 a higher cost ofmissing a crises raises p1(t) and similarly increases the frequency a crisis

The relative misclassification costs and prior probabilities can be used inter-changeably in order to make the crisis classification more conservative, given thesubjective preference for reducing the chance of missing crises.

http://www.salford-systems.com/


is called. The option of choosing priors andmisclassification costs at theoutset (i.e., before running the CART algorithm) influences the modelchoice (i.e., the set of indicators and thresholds). This is a key differencebetween CART and standard EWS. For example, Berg et al. (2005) use amisclassification cost function (weighting Type I and Type II errors) toidentify the probability cut-off point that would best predict crisis andnon-crisis events out-of-sample only after having estimated the probitmodel. As a result, their cost function cannot influence the choice of theindicators and coefficients in the probit model.11 Here, the choice ofpriors (and costs) shapes the model, as well as determines the cut-offpoint for labeling terminal nodes as crisis or non-crisis types (seebelow).

In order to decide when to stop the growing process, the algorithmcalculates the gain from further splitting in terms of the reduction inthe rate of misclassification from each parent to the two child nodes. Astandard approach would be to stop growing the tree when thereduction in the misclassification rate becomes lower than the changein the penalty associated with the number of terminal nodes.However, such an approach would not be capable of discoveringpossibly interesting splits further down the tree. Thus, CART initiallygrows a maximal, over-fitted, tree, and then proceeds to “pruning”branches backward. The best tree (in terms of “goodness of fit”) isdetermined by looking for the tree whose misclassification error rate(adjusted for a penalty on the number of nodes) is lowest.

Finally, the criterion to label a terminalnodeas crisis ornon-crisis-typeis quite intuitive: classify terminal node t as crisis-type if p1(t)Np0(t).Note, from Eq. (2), that when the prior distribution coincides with theempirical likelihood, π1=N1/N, then p1(t)=N1(t)/N(t) and the criterionyields the plurality rule: classify node t as type 1 if the node containsmoretype-1 observations than type 0, N1(t)NN0(t). Conversely, if priors are“agnostic” in the sense thatπ1=π0=1/2, then it is easy to see that node twill be labeled as type-1 provided the these types are relatively moreabundant in thenode than in the entire sample:N1(t)/N0(t)NN1/N0. Fromthe formulas above it descends that the posterior probability of acrisis, p1(t), is increasing in the relative cost of a crisis C1 and in theprior probability π1. Thus the larger these two parameters, the morelikely it becomes that CART will label a node as crisis-prone, and thelarger the resulting (Type II) error of false alarms.

For the classification tree presented below, we have used thefollowing specifications: (i) the criterion to be minimized is the Giniindex in Eq. (1); (ii) the a priori distribution of crises is taken to be equalto the sample distribution, πi=Ni/N; (iii) the cost of missing a crisis isset to 7 times the cost ofmissing a non-crisis (which is normalized to 1).From the expression in the previous footnote, these parameters yield aposterior probability of a crisis in node t, p1(t)=7N1(t)/[N(t)+6N1(t)].Thus, a node is labeled as crisis (p1(t)N1/2) when it contains at least12.5% of crises (that is whenN1(t)/N(t)N0.125). This cut-off point takesinto account the fact that in our sample crises episodes are possibly over-represented with respect to the “true” population (they make up 20.5%of sample observations), so thatwewant to “call” a crisis relativelymorefrequently. Ourfindings, however, are robust to this choice for the cut-offpoint for calling a node a “crisis” type (see below).

12 For each split in the tree, CART develops alternative splits (surrogates), that is,variables that produce a similar allocation of observations in child nodes. Thesevariables are used when the primary splitting variable is missing. Thus, a missing valuedoes not imply that all the observations need to be thrown away, as in regressionanalysis. The missing value is replaced by the best surrogate.13 Related to this is the criticism that the procedure is only “one-step” optimal andnot “overall” optimal. For example, suppose that the procedure produces a tree withten terminal nodes. If one could search all possible partitions of the dataset in ten

5.1. CART features

The CARTalgorithm displays a number of interesting features. First,it is well suited for discovering context dependence, interactions andheterogeneity. Unlike parametric models, which aim at uncovering asingle dominant (typically linear) structure in the data, CART isdesigned to work with data that might have multiple structures. Infact, one of our most interesting findings is exactly that not all crisesare the same. The methodology is robust to the presence of outliersamong the independent variables. These do not generally affect CART

11 See Chamon, Manasse and Prati (2007).

because splits usually occur at non-outlier values. This feature isparticularly useful when dealing with emerging markets, where,particularly in crisis times, variables such as inflation and exchangerate depreciation take extraordinary values. No specification search isnecessary. This feature is useful when theory does not preciselyidentify the “right” explanatory variable (which indicator of liquidityconstraints should we use: short-term debt over GDP, over exports,reserves, or over total debt?). Moreover, the algorithm yield the sameresults for anymonotone transformation of the variables (for example,levels or logarithms). The procedure is non-parametric, as it does notrequire specification of a functional form for the exogenous variables.Also, missing values for predictors are handled very effectively,12 so thatCART can be used also with data sets that have a fraction of missingvalues, as often is the case, for example, with fiscal data for developingcountries. Finally, the algorithm is designed to avoid “over fitting” themodel to the data, so that predictions should remain accurate whenapplied to fresh data. When data limitations do not allow for having aseparate test sample, CART proceeds by dividing the sample into 10roughly equal parts, each containing a similar distribution for thedependent variable. It takes the first nine parts of the data, constructsthe largest possible tree, and uses the remaining 1/10 of the data toobtain initial estimates of the misclassification error rate of the sub-trees. The same process is then repeated (growing the largest possibletree) on another 9/10 of the datawhile using a different 1/10 part as thetest sample. The process continues until each part of the data has beenheld in reserve one time as a test sample. The results of the tenmini-testsamples are then combined in evaluating the optimal (lowest adjustedmisclassification) tree. This procedure, called cross-validation, impliesthat the algorithm strives at finding a model that performs well oncompletely fresh data, even in the absence of an independent testsample.

CART has a few shortcomings, however. Unlike regression orprobit/logit analysis, the individual marginal contribution of eachvariable to the probability of belonging to a class cannot beascertained: CART assigns a single probability to all cases belongingto the same node. Furthermore, the procedure is not well suited foruncovering “general” relationships that hold across thewhole sample:a linear effect would show up as the same variable being selectedrepeatedly with different thresholds. Moreover, as the pattern ofdiscovery becomes progressively more localized, sample-wide infor-mation is not used.13 Third, since CART is non-parametric and freefrom assumptions on probability distributions, confidence intervalscannot be meaningfully attached to the threshold values. However,one can estimate a logit model with dummy variables correspondingto node inequalities, and test for their significance (see below). Finally,if a variable is even slightly outperformed by another as a split, it maynever appear in the final tree, even if it is more closely associated withclass membership than other variables appearing down in the tree.Thus, one may incorrectly deduct that the omitted variable is not“important.” This problem (called “masking”) is somewhat akin tohaving two significant regressors that happen to be strongly collinear:one drops out from the regression. The consequence for classificationis that the variables appearing in a tree may be sensitive to changes inthe sample, in the list of variables considered, and/or in the a prioridistribution. A possible way out is to rank each variable by looking atthe potential effect of the variable on classification. This procedure

terminal nodes for the one partition that minimizes the Loss function , the two resultmay be quite different (Breiman et al., 1984).

Fig. 1. The empirical tree. Sources: IMF; Standard & Poor's; World Bank; and authors' calculations.

198P.M

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–205

Table 3Classification table.

Column 1 2 3 4 5 6 7 8 9

Terminalnode

Rules and critical thresholds N. episodesin node

Crisislikelihoodin node

% ofcrisesin node

% of non-crisisin node

Relativesafetyof node

Classifiedcrisis (1)non-crisis (0)

Crises(entry)

A. Relatively Safe1 TotExtDebt/GDP≤49.7,

ShortTDebt/Res≤1.3,PublicExtDebt/Revenue≤2.1,GDPGrowth≤−5.5,EchROverV≤48

13 0.0 0.0 1.3 1.26 0

4 TotExtDebt/GDP≤49.7,ShortTDebt/Res≤1.3,PublicExtDebt/RevenueN2.1,Inflation≤10.7

13 0.0 0.0 1.3 1.26 0

6 TotExtDebt/GDP≤19.1,ShortTDebt/ResN1.3,YearNextPresElect≤5.5

23 0.0 0.0 2.3 1.26 0

8 TotExtDebt/GDP≤49.7,TotExtDebt/GDPN19.1,ShortTDebt/ResN1.3,YearNextPresElect≤5.5,EchRVolatilN27.9

22 0.0 0.0 2.2 1.26 0

9 TotExtDebt/GDP≤49.7,ShortTDebt/ResN1.3,YearNextPresElectN5.5,USTresBill≤9.7

51 0.0 0.0 5.0 1.26 0

11 TotExtDebt/GDPN49.7,Inflation≤10.5, ExtFinReqs/Reserve≤1.4, PublicExtDebt/Revenue≤3.1

98 2.0 0.8 9.5 1.23 0 Algeria (1991)

3 TotExtDebt/GDP≤49.7,ShortTDebt/Res≤1.3,PublicExtDebt/Revenue≤2.1,GDPGrowthN−5.5

607 2.3 5.4 58.4 1.23 0 Venezuela (1983), South Africa (1976),Russia (1998), Argentina (1995),Thailand (1981)

B. Liquidity Risk10 TotExtDebt/GDP≤49.7,

ShortTDebt/ResN1.3,YearNextPresElectN5.5,USTresBillN9.7

10 40.0 1.5 0.6 0.75 1

7 TotExtDebt/GDP≤49.7,TotExtDebt/GDPN19.1,ShortTDebt/ResN1.3,YearNextPresElect≤5.5,EchRVolatil≤27.8

130 41.5 20.7 7.5 0.73 1 Pakistan (1998), Mexico (1982, 1995),Argentina (1982, 1989, 1993), Peru (1976, 1983),Brazil (1998, 2001), Jamaica (1978) ,Turkey (1978),Korea (1997), Trinidad and Tobago (1988),Ukraine (1988), Dominican Republic (1981)

C. Solvency Risk12 TotExtDebt/GDPN49.7,

Inflation≤10.5, ExtFinReqs/Reserve≤1.4,PublicExtDebt/RevenueN3.1

10 40.0 1.5 0.6 0.75 1

13 TotExtDebt/GDPN49.7,Inflation≤10.5, ExtFinReqs/ReserveN1.4

79 46.8 14.2 4.1 0.67 1 Chile (1993), Tunisia (1991), Panama (1983),Thailand (1997), Indonesia (1997),Philippines (1983), Argentina (2001),Jordan (1989), Morocco (1986), Costa Rica (1981)

5 TotExtDebt/GDP≤49.7,ShortTDebt/Res≤1.3,PublicExtDebt/RevenueN2.1,InflationN10.6

20 55.0 4.2 0.9 0.57 1 Guatemala (1986), Paraguay (1986)

14 TotExtDebt/GDPN49.7,InflationN10.5

196 66.9 50.2 6.4 0.42 1 Jamaica (1981, 1987), Egypt (1984),Bolivia (1986), Peru (1978), Ecuador (1982, 1999),Uruguay (1987), Indonesia (2002), Bolivia (1980),Morocco (1983), Turkey (2000), South Africa (1985),Uruguay (1990), Brazil (1983), Venezuela (1990, 1995)

D. Fiscal, Exchange rate and Macrorisks2 TotExtDebt/GDP≤49.7,

ShortTDebt/Res≤1.3,PublicExtDebt/Revenue≤2.1,GDPGrowth≤−5.5,EchROverVN48

4 100.0 1.5 0.0 0.00 1 El Salvador (1981), Uruguay (1983)

Total 1276 100.0 100.0

Source: authors' calculations.


explicitly accounts for a variable's ability to classify observations ateach node, even when “masked” by the first-choice split. It yields ameasure (the Gini index of “importance”) that does not depend on thevariables actually appearing in the tree (more on this below).

The problem of robustness to the addition of new variables andobservations is rather complex, however. If a new variable isinformative enough to replace a pre-existing variable, particularly inthe top splits, there is a good chance that the branches developing


from there onwards will feature a somewhat different set of variablesand thresholds. Similarly, the introduction of additional years orcountries to the samplemay lead to substantial changes in the optimaltree. We will discuss and apply a solution based on Monte Carlosimulations proposed by Breiman (2001) in section 8 below, wherewe address the issue of the robustness of our results.

14 As explained above the posterior probability does not in general coincide with theempirical likelihood reported in the table, since it reflect the choice of priors and costweights. For example, applying the formula p1(t)=7N1(t)/[N(t)+6N1(t)] of footnote11 gives a posterior probability of crisis in node 14 of 93.4% which exceed thelikelihood (66.9%) due to the high relative cost of missing a crisis (7:1).

6. The empirical tree

CART selects the following 10 variables out of the 50 candidateslisted in Table 2: total external debt in percent of GDP; short-term debtrelative to foreign reserves; public external debt in percent of publicrevenues; real GDP growth; inflation; the U.S. treasury bill rate;exchange rate overvaluation; exchange rate volatility; the ratio ofexternal financing requirements to foreign reserves; and the numberof years before a presidential election.

The first rule splits the sample into two branches (see Fig. 1): (i)episodes with high external debt (more than 49.7% of GDP) go to theright—here the conditional crisis likelihood rises from 20.5% in theentire sample to 45.4%; and (ii) episodes with low external debt to theleft—with default likelihood of 9.7%. Episodes of high debt (more than49.7% of GDP) are further split into high/low inflation (above/below10.5%). The former incur the largest default frequency, 66.8 percent,see terminal node 14. More than half of all the crisis episodes in thesample satisfy these two simple conditions. For example, the highexternal debt plus high inflation criterionwas met 1 year ahead of thecrises in Jamaica, Egypt, Bolivia, Peru, Ecuador, Uruguay, Indonesia,Bolivia, Morocco, Turkey, South Africa, Uruguay, Brazil, and Venezuela.Terminal node 7 is second in terms of number of crisis episodes. Howdo we get there? Despite intermediate external debt levels (between49.7% and 19% of GDP), the joint effect of short-term debt (exceeding130% of reserves), political uncertainty (less than 5 years to the nextpresidential elections), and relatively rigid exchange rates (lowvolatility) conjure to raise the crisis likelihood to 41%.

By contrast, going down from the top to the left, towards terminalnode 3, one finds the circumstances that are more favorable forreducing risks: low external debt, low short-term debt to reserves on aremaining maturity basis (below 130%) and low public external debtto revenue (below 210%), coupled with the economy not being inrecession. Under these circumstances, the likelihood of being in acrisis is just 2.3%. About 58.4% of all non-crisis episodes satisfy theseconditions.

Based on the set of rules of this tree, the observations can beclassified as crisis-prone or not crisis-prone. As explained previously, aparticular final node is classified as crisis-prone (not crisis-prone), ifthe within-node posterior probability of crisis is higher (lower) than1/2. As discussed in the Methodology section, our choice ofparameters implies a cut-off share of within-node crisis frequency of12.5%, that is, below the proportion of crises in the sample, 20.5%. Ascan be seen from the figure, the largest percentage of (missed) crisesin “non-crisis” terminal node is only 2.3%, while the smallestpercentage of crises in a “crisis” node is 40%. Thus, the tree separatesthe two types quite effectively, so that any cut-off threshold forlabeling nodes, set between 2.3% and 40%, would not affect the finalclassification.

The tree has one particularly important implication for sustain-ability analysis. It shows that unconditional thresholds for debt–output ratios are of little value per se for assessing the probability ofdefault. Take terminal nodes 7 and 11. The former has only moderatevalues of debt ratio, between 49.7% and 19%, but the likelihood of acrisis is high, 41%. The latter has a debt ratio of at least 49.7%, but thecrisis probability is just 2%. Why? Clearly, other factors are at play.What makes node 7 risky is the compound effect of short maturity ofthe debt, political uncertainty and relatively fixed exchange rates.What makes node 11 safe, despite the large debt burden, is monetary

stability, a large current account surplus, and relatively large fiscalrevenues that guaranteed solvency on public debt.

6.1. Classification table

Table 3 shows some interesting informationon theclassification tree.The first column lists the terminal node's number. The second

column reports the set of inequalities satisfied by each node'sobservations: for example, row 14 identifies terminal node 14,containing all the cases (country–year) where total external debt/GDP exceeds the threshold of 49.7 percent and inflation exceeds 10.5%.Column 3 counts the number of observations that satisfy the nodecriteria, and tells us how “relevant” is a terminal node. For example,the table shows that the three most populated nodes are number 3(607 observations), 14 (196 cases) and number 7 (130 episodes).Thus, for example there are 196 observations (in node 14) that satisfythe two inequalities on debt and inflation. The fourth column reportsthe empirical likelihood of a crisis, conditional on the node'sinequalities: for example, the likelihood of a crisis next year for acountry with high debt and inflation (node 14), e.g. the proportion ofobservations satisfying the two inequalities, which had a crisis thefollowing year is 66.9%. This node is classified as a crisis node (seecolumn 8) since the crisis (posterior) probability exceeds 1/2.14 Thisallows one to calculate the Type II error. In the case of node 14, 33.1% ofthe cases displaying high debt and inflation turned out not toexperience a crisis the following year, andwere thereforemisclassifiedas crises. The fifth and sixth columns give information on howfrequent the identified characteristics are found among crises andnon-crises. For example, looking at node 14 and column 5, we see thatmore than half (50.2%) of all sovereign debt crises in the samplesatisfy the debt and inflation criteria. This number is computed as theratio of the crises in the node to the total number of crises in thesample. Similarly, the sixth column shows how frequent are thereported characteristics among non-crisis observations: for example,from the row 14, column 6, we see that only 6.4% of all non-crisisepisodes displayed large external debt and inflation. Finally, we wantto derive ameasure of “how safe” are the thresholds for fundamentals.To do so, we divide the percentage of non-crises in a node, N0(t)/N0,by the share of observations in the node, N(t)/N (for node 14 wedivide column 6 by (196/1276)). The result is shown in the seventhcolumn of the table. This “safety” index that takes value greater thanone when the node is “safer” than the overall sample, and smallerwhen it is “riskier.”

6.2. Interpretation

These calculations lend themselves to an interesting interpretation.We can regroup the terminal nodes into four blocks, which identifydifferent types of macroeconomic scenarios. Block A can be interpretedas describing the characteristics of the “(relatively) safe fundamentals”type: observations in this block are classified as non-crisis-prone. BlocksB, C, and D identify potential defaulters, which are subject to risks ofdifferent sorts. Observations therein are classified as crisis-prone.

“Relatively Safe” Fundamentals, type A. Nodes 1, 4, 6, 8, 9, 11, and 3, indescending order of “safety,” show the prerequisites for a relatively risk-free environment. Low total external debt (below 49.7%) is the commondenominator of these nodes (with the exception of partition 11). Lowshort-termdebtover reserves (below130%), lowpublic externaldebtoverrevenue (below 215%), low inflation (below 10.5%) and not too strongrecession (growth above −5.5%) also characterize many (but not all) of

Table 4Logit estimates.

Crisis Coef. Std. err. z PN |z| [95% conf. interval]

Node3 −3.746137 .2703977 −13.85 0.000 −4.276107 −3.216167Node5 .2006707 .4494666 0.45 0.655 − .6802676 1.081609Node7 − .3417493 .1779787 −1.92 0.055 − .6905811 .0070825Node10 − .4054651 .6454972 −0.63 0.530 −1.670616 .8596862Node11 −3.871201 .7144343 −5.42 0.000 −5.271466 −2.470936Node12 − .4054651 .6454972 −0.63 0.530 −1.670616 .8596862Node13 − .1267517 .2254696 −0.56 0.574 − .568664 .3151606Node14 .7008101 .1517175 4.62 0.000 .4034492 .9981709

Number of observations=1163.Log likelihood=−379.97026.


these partitions. By far the more representative partition is node 3 thatcontains 607 episodes amounting to 58% of all tranquil nodes. Node 11comes next in terms of observations. Node 11 shows that low externaldebt is by nomeans necessary for avoiding a crisis. Despite a large foreign

Table 5Variable importance and rank in Cart and Random Forest.

CART Random Forest

Variable Importance Rank Importance Rank

Tot Ext Debt/GDP 100.00 1 100.00 1Pub Ext Debt/GDP 88.35 2 94.49 4Tot Ext Debt/Exp 69.35 3 79.17 6Sh TermExtDebt/Res (rem mat) 38.87 4 79.63 5ShTermExtDebt/Res (orig mat) 34.55 5 63.09 9PubExtDebt/Res 33.71 6 94.63 3ShTermExtDebt/GDP(rem.mat) 29.85 7 42.92 11ExtFinReqs/Res 28.23 8 34.65 16GDP NominalGrowth 25.50 9 33.49 19Inflation 24.75 10 65.34 8ServExtDebt/GDP 24.40 11 38.01 12DebtServExtDebt/Res 20.89 12 35.19 15M2/Res 19.73 13 26.61 21ExchRateOverv 15.56 14 33.71 18US TreasBill Rate 15.48 15 6.94 42YearsNextPresElec 14.30 16 17.69 31IntShTermExtDebt/Res 13.33 17 99.55 2ReserveGrowth(2) 11.95 18 15.62 32DebtServExtDebt/GDP 11.61 19 22.49 27Exch Vol 11.43 20 20.61 29Inflation Vol 11.33 21 35.36 14Real GDP growth 8.56 22 23.23 26Revenue/GDP 8.35 23 22.4 28Openness 7.79 24 33.91 17PoliticalConstr III 7.00 25 27.77 20RealEchRateVol 7.57 25 67.58 7PoliticalConstr I 7.00 27 26.18 22ExpGrowth 5.98 29 13.3 35FDI/GDP 5.34 29 23.69 25LIBOR 4.45 30 9.99 38Civil Liberty Index 3.47 31 8.22 41M2 Growth 3.20 32 20.42 30PoliticalRights Index 2.95 33 9.72 39Electoral System 2.21 34 23.93 24IntShTermExtDebt/GDP 2.15 35 46.82 10GenGovBal/GDP Volat 1.33 36 15 33CurrAcc/GDP 0.97 37 10.19 37ReserveGrowth 0.34 38 25.53 23YearsSincePresElect 0.21 39 9.06 40YearsNextParlElect 0.10 40 5.08 45YearsSinceParlElect 0.00 41 4.24 46TermsofTrade Vol 0.00 42 14.65 34RealExchRateDep 0.00 43 37.07 13PublicDebt/GDP 0.00 44 6.81 43PrimBalanceAdjReq 0.00 45 1.25 47PrimaryBalance/GDP 0.00 46 10.64 36PresElectionYear 0.00 47 1.02 48Pres&ParlElectYear 0.00 48 0.15 49ParlamElectYear 0.00 49 0 50FreedomStatusIndex 0.00 50 6.64 44

Source: authors' calculations.

debt, a country may still enjoy a relatively safe environment (2% crisislikelihood), provided inflation is under control (below 10.5%), externalfinancial requirements over reserves are not too high (below 140%) andpublic external debt over revenue is not too large (below 310%). Node 3shows that lowexternal debt is bynomeans sufficient foravoidinga crisis.Despite showing relatively sound fundamentals as defined in node 3, 5.4%of theseobservationsneverthelesshada crisis the followingyear (theyarelisted in column 9).

The nature of the inequality constraints in the following “crisis-prone”nodes suggests an intuitive classification into solvency (B), liquidity (C),macro-exchange rate (D) risks.

Liquidity crisis-prone, type B is described by nodes 7 and 10. Despiterelatively low or intermediate external debt ratios, these episodesshare a ratio of short-term debt to reserves in excess of 130%. Thisfeature, coupled with political uncertainty (presidential elections inless than 5 years) and relatively fixed exchange rate (low volatility), innode 7, or with tight monetary conditions in international capitalmarkets (treasury bill rate above 9.7%), in node 10, raise the likelihoodof a crisis to about 40%. Solvency risks of the first type (node 7) makeup more than one-fifth (20.7%) of all debt crisis episodes, while only7.5% of observations with these characteristics turned out to be safe(the “false alarms,” see column 6).

Unsustainable debt path (solvency) crisis-prone, type C. Nodes 12,13, 5 and 14 belong to this type. In all these cases, either external debtexceeds 49.7% of GDP, or its public component exceeds 215% ofrevenues. In partition 14, high total external debt, together withinflation above 10.5%, raises the likelihood of a crisis from 20.5%(entire sample) to 67%. More than half of all crises episodes in thesample satisfy these characteristics (see the fifth column). Only in6.4% of the cases where debt and inflation were above thesethresholds a crisis did not occur in the following year. Note that thehigh inflation rate could be here a proxy for fiscal problems: inabilityto reduce deficit may need to monetization of them and seignoragefinancing of them. In fact, terminal node 5 is similar, but a solvencycrises (4.2% of total) are signaled by public, rather than total, externaldebt and high inflation. In node 13 (12), high external debt and highfinancing external requirement (or fiscal imbalances measured byhigh public external debt over revenue), raise the default likelihood to47% (40%). These two nodes jointly account for another 15.7% of crises.The large external financing need can be partly interpreted as anilliquidity problem: this financing need is high when the currentaccount deficit is high and/or when there is a large amount of debtcoming due; in either case, the country may be illiquid if creditors do

Table 6Prediction.

In-sample Out-of-sample

Full sample 1990s onwards(based on full sample)

1990s onwards(based on 1970–1989)

Observations 1276 556 556Number ofcrisis episodes

261 114 114

Number of crisisentry episodes

54 20 20

(In percent)Correctlycalled episodes

82.8 78.8 72.0

Correctly calleddefault episodes

93.9 89.5 57.0

Correctly callednon default episodes

79.9 76.0 76.0

Correctly called entriesinto default

88.9 85.0 35.0

Incorrectly calledentries into default

18.5 15.0 19.0

Sources: IMF, Standard & Poor's, World Bank; and authors' calculations.

17 Given the lack of good data on primary balances, our classification does not capturewell cases, such as Turkey, where the country would be deemed as insolvent based ona debt level criteria, but may be solvent as it is running a very large primary surplus


not provide new financing and/or do not rollover their debt. Thus,crisis episodes in node 13 can be interpreted as cases where a countryis not necessarily “insolvent” but rather has an unsustainable—andnon-financeable—debt path given large stocks of debt and illiquiditymeasured by large financing needs.

Exchange rate and macro-crisis-prone, type (D) A small number ofsovereign debt crises (1.5%) in node 2 appear to be driven by largeexchange rate overvaluation (above 48%) and large recession(negative growth below −5%). These are the crises of El Salvador,1981–1982, Uruguay, 1983 (the collapse of the Tablita, the forward-looking crawling peg regime of some Southern Cone economies in theearly 1980s), and Venezuela, 1984.

Finally, CART isolates a small number (13) of outliers in node 1: inthese cases, the exchange rate was not over-appreciated, values ofexternal debt were small and there were no liquidity problems, andthere were no-crises despite a strong recession.

6.3. How different are crises and how important non-linearities?

Howdifferent are the crisis types andhowimportant are the thresholdeffects found in the analysis? In order to answer these questions, we canlook at the within-node summary statistics for the selected ten crucialvariables of the tree.15 It is useful to compare the most representativenodes of liquidity (7) and the solvency crises (14 and 13) nodes. Indeed,the liquidity crisis node 7 has moderate average levels of external debt(37% of GDP), and of average public external debt (1.2% of GDP) , whileshort-term debt is very high, on average about 3 times larger thanreserves. By contrast, solvency crisis nodes 13 and14not only displayhighshort-term debt (2.7 times reserves), but also very high average levels ofexternal debt (77 and 76% of GP respectively), and public external debt(2.4 and 3.2 times revenues). This suggests that solvency problemstypically also entail liquidity difficulties, but not generally vice-versa.Solvency and liquidity crises have rather similar values for the otherfundamentals. Finally, by comparing the characteristics of the “least safe”safe node 3,with the “safest” crisis-prone nodes,10 (and 12), it is possibleto have an idea of the importance of threshold and non-linear effects.16

Nodes 3 and 10 differmainlywith respect to the ratios of short-term debtand external financial requirements to reserves: these are substantiallylower in the safe node,(0.6 against 2.1 for the average short-term debtover reserves, and0.8 against 3.3 for externalfinancing requirements overreserves). This suggests that non-linearities are not very sharp. Similarly,the safe node 3 and the risky node 12 differ substantially in the averagelevels of external debt (27 and 110% of GDP) and public debt over revenue(0.9 and 3.6%, respectively). Relative to node 10, the least safe “safe” node3 is also characterized by an exchange rate that is at the same time lessovervalued and more flexible (i.e. more volatile).

In summary, our classification of crises captures quite well most ofthe episodes of the 1990s. Korea (1997), Mexico (1995), Brazil (1998)and (2001), are in the illiquidity node 7; and indeed thesewere typicalepisodes of a liquidity crisis, not insolvency. Pakistan (1998) is also inthis node: its debt levels were not excessive but the country wasilliquid given large lumpy debt servicing payments coming due and itsloss of market access. Pakistan was then forced to restructure itsexternal sovereign debt, and it did not receive a large IMF package.Ukraine in 1998 (also in node 7) was a similar case of a solvent butilliquid country that coercively restructured its external debt byextending its maturities at below crisis level market rates. Clearinsolvency cases in node 14 are Ecuador (1999), which defaulted on itsexternal debt, Indonesia (2002), with a very large debt burden (but it

15 For reasons of space, the data for all variables (total external debt, short-term debt overreserves, public external debt over revenue, real growth, overvaluation of the exchange rate,inflation, years to the next presidential election, exchange rate volatility, US Treasury bill,external financing requirements) are available in a web appendix at the following address:http://www2.dse.unibo.it/manasse/Pdf/Web_Appendix_Within%20Node%20Summary%20statistics.pdf.16 We thank one referee for this observation.

is not illiquid given its restructuring of many external debt claims,both public and private), and Turkey (2000) with a very large debtburden. Turkey did not default thanks to an exceptional IMF program,but based on this classification was borderline insolvent.17 Russia(1998) and Argentina (1995) appear in the non-crisis node 3; hencethe tree is unable to predict these crises. In the case of Argentina, theTequila contagion from Mexico in 1994 played an important role, asother fundamentals (debt levels and deficits) were fine at that time.Russia was not insolvent based on debt levels and external flowimbalances (current account deficits) but its failure tomake flow fiscaladjustments and large capital flight led to default in 1998.18 Node 13 ofunsustainable debt path with possible illiquidity included Argentina(2001), which did default, Indonesia (1997), which defaulted onmanyprivate external debts, and Thailand (1997) that did not default onmost external debt (only on some private claims), but had severe debtservicing problems in its private financial and corporate sectors.Therefore, these are cases of outright insolvency or high illiquidity thatmade the debt path not sustainable/financeable.

7. Regression analysis

A natural question is whether the non-linear interactions andthreshold effects found in the tree are statistically significant. Weapply standard econometric techniques on our data set.19 We proceedas follows: we construct a set of dummy variables corresponding tothe inequalities that define the terminal nodes in our classificationtree (variables “node 1–14,” see Table 3), and estimate a logit modelwith our crisis indicator as dependent variables and the nodedummies as dependent variables. We report the results in Table 4.Clearly, the node dummies corresponding to a “perfect classification”(nodes 1, 3, 4, 6, 8, 9 in Fig.1) are dropped, as they perfectly predict theoutcome. Also, not surprisingly, the “small” nodes containing only ahandful of observations (nodes 5, 10, 12) are not found statisticallysignificant. Conversely, the large nodes have statistically significantcoefficients, generally with the expected sign. If a country displays“safe fundamentals,” as defined by Node 3 and Node 11 (see Table 3),the probability of experiencing a crisis next year is significantlyreduced; conversely, belonging to Node 14 of high inflation and debtsignificantly raises the probability of a crisis; the “liquidity crisis” node7 is the only dummy variable which is appears with the wrong sign,although it is only marginally significant.

8. Robustness

As we discussed in the Methodology section, robustness is a seriousissue for classification trees. Here,webriefly describe and apply a solutionrecently developed by Breiman (2001), one of CART developers. The“Random Forests” (RF) algorithm20is a generalization of CART based on acollection of hundreds (possibly thousands) of trees. The idea is to buildmany trees using different combinations of variables and data (sub)samples, in order tomake sure that the inclusion or exclusion of variablesand data-points does not affect the classification. Here is how it works. RFobtains thefinal classification (crisis vs. non-crisis) by “majority rule,” thatis, by aggregating the responses of many trees. At each run, a bootstrapprocedure estimates each tree by randomizing over two dimensions: a

(above 5% of GDP currently), that is stabilizing and reducing such high debt level.18 In principle, we may have included a variable measuring “contagion” effects fromcrises elsewhere. In practice, however, implementation in our context is problematic,since contagion typically occurs within a year, and we employ (one period lagged) dataat annual frequency.19 Ideally, one should perform such a test on a “fresh” set of data.20 We are not aware of other applications of the Random Forest algorithm tointernational macro/finance issues.

http://www2.dse.unibo.it/manasse/Pdf/Web_Appendix_Within%20Node%20Summary%20statistics.pdf

http://www2.dse.unibo.it/manasse/Pdf/Web_Appendix_Within%20Node%20Summary%20statistics.pdf

23 These results were found for out-of-sample predictions.

Fig. 2. Rolling tree variable importance. Notes: Total External Debt/GDP is replaced byTotal External Debt/Exports in 1995, and by Public External Debt/GDP in 1996–1997.Short Term Debt is Short Term Debt/GDP in 1989–1997 and 2001 and Short Tern Debt/Reserves in 1998–2000 and 2002. Public External Debt/GDP is replaced by Revenue/GDP in 1992–1993 and 1998–1999.


sub-sample of data and a (small) subset of all the variables. By picking arandom subset of the variables, any single variable is analyzed in adifferent combination with others, thus taking care of the problem of“masking” discussed in the Methodology section. Moreover, by rando-mizing simultaneously over the sub-samples, each tree analyzes only aportion of data at a time. This process, called “slow learning,” highlightsdifferent aspects of the data set and reduces the risk of possibly drawingwrong conclusions “too fast” (see Friedman, 2001) from a unique sample.If a pattern genuinely exists in the portion of data analyzed, the RFalgorithm will detect it repeatedly in different trees; conversely, it willwash out any accidental pattern in the process of averaging the results.The drawback of the algorithm is that it does not allow the researcher torecover a “single” tree with its thresholds and interactions, since it reliesupon the aggregation of the classifications that produced by manydifferent trees. For our purposes, however, Random Forest provides aninteresting benchmark for assessing the robustness of CART's selection ofvariables.21 Table 5 reports the Gini measure of the variable importancefor CART and RF22, normalized on a 0 (lowest importance)–100(highest)scale. Overall, this analysis confirms the robustness of our CART results.The solvency indicators (total external debt overGDP, public external debtover revenue), the liquidity indicator (in particular short-term debt overreserves), the exchange rate volatility and overvaluation, inflation andgrowth, all feature prominently in RF's as well as in CART's selection ofmost important variables. Interestingly, RF ranks the exchange ratevariables even higher than CART. Also, political economy variables do abetter job in the RF than in the CART tree (see the indexes of PoliticalConstraint). The proximity to presidential elections is confirmed as arelevant predictor. Overall, the coefficient of correlation between themeasures of importance in CARTand RF is 0.61, and the rank correlation is0.77.

9. Prediction

Next, we discuss the prediction accuracy of our model. Table 6reports the predictive accuracy of the tree for both crisis “states” andcrisis “entries,” being respectively defined as crises preceded by a crisis,and by a non-crisis. The purpose of this distinction is to facilitate thecomparison between our results and those obtained in the EarlyWarnings literature. Many empirical models focus only on entries, seefor example Chamon, Manasse and Prati (2007). The motivation is thatfactors that lead to a crisis may be different (or have a different impact)from factors that keep the country in the crisis state. Neglecting allwithin-crisis observations, however, does not make an efficient use ofavailable information. In fact, Manasse, Roubini, and Schimmelpfenig(2003) find that the same variables explain both crisis entry andpersistence, typically with statistically equal coefficients. In ourestimation, we have kept all crisis states information, for two additionalreasons. First, because CART treats each observation independently, sothat Argentina 1994 and Argentina 1995 are effectively different“individuals.” Second, because CART works best with large data sets.

Comparing our results with those in the EWS literature is notimmediate, since the definitions of crisis, the data frequency (monthly,yearly), the sample coverage, and the forecast horizon (one, 2 yearsahead) differ dramatically across studies. The most successful EWSmodels are able to correctly predict 60–70% of (currency) crises (forexample, Berg and Pattillo, 1999), but they differ widely in their falsealarms, and in their in and out-of-sample predictions (which typicallyperformmuchworse) . Clearly, one could easily predict as many crises as

21 Each tree in Random Forest was built by selecting 3 variables at random, and 500trees were built using of tenth of the observations at each run.22 In practice, every variable is considered at every split, in each tree, and the Giniindex provides a measure of the “purity” of the sub-nodes generated by the variablesplit, see the discussion in Section IV, and Breiman et al. (1984).

wished, simply byaccepting a very large number of false alarms (in a logitmodel one would choose a sufficiently low crisis probability threshold).BergandPattillo,1999,find that in this respect themodels theyanalyze forcurrency crises yield disappointing results: between 63 and 54% of falsealarms, with a crisis probability thresholds of 25%.23

Table 6 presents the results. The first two columns give the in-sample predictive accuracy for the model based on the full sample,both for the entire set of crises and when applied only to the post-1989 crises. The tree performs quite well when compared with thestandard EWS models. It correctly predicts 1 year ahead 82.9% of thestates, and does only slightly worse for the post 1990 period; it doesbetter with crisis states, of which it correctly predicts 93.9%, thanwithtranquil states (not shown: 79.9%). The prediction success for“entries” is comparably good (88.9 and 85% in full and post 1989samples); moreover, these results do not come at the expenses ofconsiderable false alarms: for the post 1989, only 15% of tranquil statesare incorrectly predicted as crises (and 18.5% for the entire sample).These results also compare quite favorably with those obtained byManasse, Roubini and Schimmelpfennig (2003). The logit modelestimated in this paper, for a slightly higher threshold, has fewer falsealarms (5.7%) but also correctly predicts far fewer entries (57.1%).

“Out” of sample predictions are obtained as follows. First, we build atree is built using only data only up to 1989. Here we force CART to usethe same set of 10 variables found in the optimal tree based on the entiresample.24 Predictions for thepost-1989data are thenobtainedusing thistree.

The out-of-sample prediction accuracy is considerably worse thanin-sample. About 57% of default states and 35% of post-1990 entriesare correctly predicted from the tree based on pre-1990 observations.In particular, the model fails to predict many of the important crises ofthe 1990s: the Asian crisis, Russia, Brazil and Turkey (2001) are notpredicted.25 Note however, that we are requiring our model to predictas far as 11 years ahead, quite a formidable task. Moreover, falsealarms (incorrectly called entries) are also extremely low, which

24 The resulting tree and threshold is only marginally different from the optimal onebased on the full data set. Details are available on request. Alternatively , we could havelet CART choose a potentially new set of variables in the estimation . Doing so,however, does not improve the predictive accuracy.25 The following crisis entries are missed: Indonesia (1997, 2002), Korea (1997),Thailand (1997), Argentina (1995), Brazil (1998), Mexico (1995), Russia (1998),Tunisia (1991), Turkey (2001), Ukraine (1998), Venezuela (1995). Conversely Algeria(1991), Argentina (2001), Ecuador (1999), Pakistan (1998), South Africa (1993),Uruguay (1990) and Venezuela(1990) are correctly predicted.

Fig. 3. Rolling trees' thresholds.


suggest that experimenting with different thresholds may improvethe model predictive power to some extent.26

10. Rolling trees and changes in variables and thresholds

The unsatisfactory out-of-sample performance of the model islikely to be due to the changing macroeconomic configurations ofcrisis episodes across different decades. Within our framework, thisshould be reflected either by a change in the set of explanatoryvariables and/or by a change in their critical thresholds over time. Weexamine both issues in by running “rolling trees.”

The first exercise asks the question: has the set of optimal crisis-predictors in emerging markets changed over time? We run unrest-ricted rolling trees, by letting CARTchoose the best set of predictors foreach run, starting from a 1970–1989 sample, and then adding 1 year ata time, until the full sample is covered. For each run, we calculate thevariables' “importance” measure previously discussed, and plot thenormalized values (from 0 to 100) in Fig. 2. Note that different treesoften pick different variables for very similar indicators (for example,for solvency, Total (=public+private) External Debt/GDP is some-times replaced by Total External Debt/Exports or by Public ExternalDebt/GDP).27 In the figure we pick the variable with the highestimportance measure for each indicator (see the note to the figure).

Fig. 2 shows that the size of External Debt is consistently the bestpredictor of sovereign debt crises in emerging markets. Measures ofliquidity (Short Term Debt), the second most important predictor upto the early 1990s, have become temporarily less important in the1995–1998 period, when fiscal solvency considerations (PublicExternal Debt/Revenue), political uncertainty (years to presidentialelections) and inflation have gained predictive power.28 This makessense, since in addition to the Asian crises, this period witnesses,among others, crises in Algeria 1995, 1996, Argentina 1995, Ecuador1995, Mexico 1995, Pakistan 1998, Peru 1995, 1996, 1997, Russia 1998,Ukraine 1998 and Venezuela 1995, 1996. Other indicators show asecondary and stable role.

Next we ask the question: have the critical thresholds changedover time in emerging markets? This question has no obvious answerin our tree framework, since following the top split, classification treescalculate conditional thresholds: the same variable may display adifferent thresholds, depending on the variable's place in the tree'ssequence. For this reason we adopt the following strategy: we runrolling trees as before, but this time keeping only the variables thatappear in the “final” (full sample) tree in each run, as we did in theout-of-sample exercise. For each different tree, we report the(unconditional) threshold value that each variable would havetaken, had it been selected in the top split.

26 When the estimation sample is extended to 1996, the predictive accuracy of themodel does not improve significantly, possibly confirming a sort of “structural break”in the latter crises. We have not pursued this attempt since we wanted to keep themodel parameters as closed as possible to those used in the in-sample exercise.27 Recall that a variable may score high even if it does not appear in the tree (forexample, a variable may be a “second-best” split at each stage).28 Note however that the Financial Requirement indicator (short term external debtplus current account deficit over Reserves has somewhat gained in importance).

The thresholds' evolution for the main variables are shown in Fig. 3.The critical value for the solvency indicator, Total External Debt/GDP,slowly creeps up from 0.44 to 0.5, possibly indicating more resilience tolarge debts inmore recent. episodes. By contrast, the threshold for ShortTerm Debt/Reserves slightly falls from 83 to 73% since 1994, suggestingthat although liquidity indicators may have lost some predictive powerin the late 1990s (Fig. 2), the vulnerability of emerging markets toliquidity shocksmay have risen somewhat. Interestingly, the temporaryfall in the threshold of Public External Debt/Revenue, from2 to 1.7 in thesecond half of the 1990s, confirms the larger role of public sectorvulnerability in the crises of this period. Finally, it is interesting to notethat, possibly as a reflection of larger capital market integration in morerecent years, the critical value of an over-appreciated exchange rate (notshown) falls sharply, from 100 to 34%.

In summary, the rolling tree analysis suggests that the nature ofsovereign debt crises changed somewhat in the nineties, with fiscalsolvency and political economy issues gaining more relevance, andwith emerging economies showing heightened vulnerability to(possibly less frequent) liquidity shocks and to currency misalign-ments, possibly reflecting their larger integration in the internationalcapital markets. The combination of changes in the ranking of theexplanatory variables and in their critical thresholds helps explainingwhy the more recent crises are difficult to predict on the basis of theearlier ones.

11. Conclusions

In this paper we have applied a new statistical methodology to thequestion of understanding sovereign debt crises, both in terms offundamentals that lead to a crisis, and of the factors that allow us topredict such crises. This technique allows us to derive endogenouslythe most important factors associated to vulnerability of sovereigndebt, and the thresholds that signal greater risk of a crisis.

We find that most debt crises can be classified into three types: i)episodes of insolvency (high debt and high inflation) or debtunsustainability due to high debt and illiquidity; ii) episodes ofilliquidity, where near default is driven by large stocks of short-termliabilities relative to foreign reserves; and iii) episodes of macro andexchange rate weaknesses (large overvaluation and negative growthshocks). Conversely, a relatively “risk-free” country type is describedbyahandful of economic characteristics: low total external debt relative toability to pay, low short-term debt over foreign reserves, low publicexternal debt over fiscal revenue, and an exchange rate that is notexcessively overvalued. Political instability and tight monetary condi-tions in international financial markets aggravate liquidity problems.The approach suggests that unconditional thresholds—for example,looking at debt to output ratios in isolation—are of little value per se forassessing the probability of default; it is the particular mix of differenttypes of vulnerability that may lead to a sovereign debt crisis.

The in-sample predictive power of the tree approach is quite goodwith very few crises missed; the model predictive accuracy does notsuffer when applied to the post-1990 experience. However, despitevery few false alarms, the out-of-sample predictive power is notsatisfactory: many of the crises of 1990s could not be predicted basedon previous decades information, possibly confirming the differentnature of the latter crises. The “rolling tree” analysis suggests indeedthat the nature of sovereign debt crises changed somewhat in thenineties, with fiscal solvency and political economy issues gainingmore relevance, and vulnerability to liquidity shocks and currencyover-appreciation becoming larger.

Our approach allows to derive rules of thumbwhichmay beuseful topredict crises early on (an “early warnings signal”model), and to derivepolicy adjustment paths, whichmay reduce the likelihood of a crisis forcountries that may be entering in a danger zone. Thus, ideally, this toolcan be used for surveillance, crisis prevention, and crisis resolution.


A number of possible extensions come to mind, some of which wehave tried. First, following the idea that a “history” of past defaults maybearon the credibility of a sovereign and thus affect the crisis probability(as suggested by Reinhart and others, 2003, in their “debt intolerance”hypothesis), we constructed a new variable taking on incrementalvalues each time a new default episode occurred. Our indicator of (bad)“reputation” did not affect the classification tree. Experimenting withcontagion effect is also possible. But the use of annual data precludeusing same-year information for predicting crises.

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“Rules of thumb” for sovereign debt crises

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