“Rules of Thumb” for Sovereign Debt Crises

- 3 -of short-term debt may need IMF support to avoid a liquidity run or “roll-off” crisis. Conversely, highlyindebted countries may face a debt crisis, unless there is a strong and credible fiscal consolidation. Inaddition, it is argued that conditionality should set targets indicating that a country’s macroeconomicfundamentals are heading towards a relatively “safe” zone. In the paper these concepts of liquidity crisis,insolvency crisis, crisis triggered by weak macro-fundamentals, and relatively “safe zone” are madeprecise. Unless the diagnosis is correct, it is hard to get the policy cure right.This empirical analysis is based on a dataset containing annual observations for 47 emerging marketeconomies from 1970 to 2002. A country is defined to be in a state of “debt crisis” if it is classified asbeing in default by Standard & Poor’s, or if it receives a large non-concessional IMF loan (where “large”means in excess of 100 percent of IMF quota). Standard & Poor’s rates sovereign issuers in default when agovernment fails to meet principal or interest payment on an external obligation on due date (includingexchange offers, debt equity swaps, and buy back for cash).We employ the Classification and Regression Tree methodology (CART) for classification andprediction. 3 CART is a computer-intensive data mining technique that selects explanatory variables, theircritical values, and their interactions in order to identify “safe” from “crisis-prone” types. The mainconclusions of our empirical analysis are as follows.First, out of 50 candidate variables, 10 predictor variables turn out to be sufficient for classification andprediction: total external debt/GDP ratio; short-term debt reserves ratio; real GDP growth; public externaldebt/fiscal revenue ratio; CPI inflation; number of years to the next presidential election; U.S. treasurybills rate; external financial requirements (current account balance plus short-term debt as a ratio offoreign reserves); exchange rate overvaluation; and exchange rate volatility.Second, a relatively “safe” country type is described by a handful of economic prerequisites: low totalexternal debt (below 49.7 percent of GDP); low short-term debt (below 130 percent of reserves); low3 The analysis employs the data mining software CART developed by Salford Systems.

- 4 -public external debt (below 214 percent of fiscal revenue); and an exchange rate that is not excessivelyover-appreciated (overvaluation below 48 percent).Third, three major types of risks are identified: (i) solvency (or debt unsustainability); (ii) illiquidity; and(iii) macro-exchange rate risks. The debt unsustainability risk types are characterized by: external debt inexcess of 49.7 percent of GDP, together with monetary or fiscal imbalances, as well as by large externalfinancing needs that signal illiquidity as an element of debt unsustainability. Liquidity risk types areidentified by moderate debt levels, but have short-term debt in excess of 130 percent of reserves coupledwith political uncertainty and tight international capital markets. Macro-exchange rate risk types arisefrom the combination of low growth and relatively fixed exchange rates. Each of these risk types differ intheir likelihood of producing a crisis. Finally, our model has excellent predictive capacity in sample, whilethe out-of-sample forecast have both less false alarms and less correct predictions than the Early WarningSignal (EWS) literature.The analysis has one important, albeit simple, implication for sustainability analysis. It shows thatunconditional thresholds, for example for debt-output ratios, are of little value per se for assessing theprobability of default. One country may be heavily indebted but have a negligible probability of default,while a second may have only moderate values of debt ratios while running a considerable default risk.Why? Because the joint effects of short maturity, political uncertainty, and relatively fixed exchange ratesmake a liquidity crisis in the latter much more likely than a solvency crisis in the former, particularly if thelarge external debt burden goes together with monetary stability, a large current account surplus, andsound public finances.The plan of the paper is the following. Section II contains a review of the literature. Section III describesthe dataset. The Classification Tree methodology is reviewed in Section IV, and applied to the data inSection V. Section VI discusses an interpretation of the results. Section VII and VIII contain standardregression analysis and a robustness check based on a generalization of the CART procedure. Thepredictive power of the model is discussed in Section IX, and Section X performs some “rolling tree”exercises in order to understand if the crises of the nineties are “structurally” different from those in the

- 5 -previous decades. The final Section XI discusses some extensions and summarizes the main conclusionsand policy implications.II. Review of the LiteratureMost empirical studies consider that countries may either be unable to repay their debt, because they areinsolvent or illiquid, or that they may be unwilling to repay their debt, based on a consideration of therelative costs and benefits of default. Thus, these studies suggest proxies for ability and willingness torepay as the determinants of debt crises.Different studies use different crisis definitions, depending on the specific research question and theinformation available in the data source used. A priori, there is no single empirical definition of whatshould constitute a sovereign default or a debt crisis. Some studies compile a list of debt crisis or defaultepisodes from case studies and anecdotal evidence (e.g., Beers and Bhatia, 1999; or Beim andCalomiris, 2001). Others rely on a quantitative approach. For example, Detragiache and Spilimbergo(2001) define a country to be in a debt crisis if the country has arrears on external obligations towardscommercial creditors in excess of 5 percent of commercial debt outstanding, or has a rescheduling orrestructuring agreement with commercial creditors. This definition does not differentiate betweensovereign or private sector arrears and/or rescheduling due to data limitations. Another problem of thisquantitative definition is that it might exclude some incipient debt crises that were only avoided by largescalefinancial support from official creditors (International Financial Institutions (IFIs)), and/or frombilateral creditors. A data source that provides a uniformly compiled information on sovereign default isStandard & Poor’s (2002) that defines a country to be in default as long as the sovereign is not current onany of its debt obligation.Empirical studies of the determinants of debt crisis are closest in nature to an Early Warning Signal model.Factors influencing the probability of a debt crisis are identified by means of probit /logit regressions or asignal model. Most studies have focused on the debt crisis of the 1980s, but some recent efforts have

- 6 -looked at crises occurring in the 1990s. 4 Reinhart (2002) finds that in 84 percent of the cases in hersample, a debt crisis is preceded by a currency crisis. Detragiache and Spilimbergo (2001) find that shorttermdebt is endogenous to the model, as countries find it more and more difficult to borrow long term inthe run-up to a debt crisis. While most studies use macroeconomic variables only in levels, Catão andSutton (2002) also include measures of volatility in trade, fiscal policy, monetary policy and exchangerate policy. Manasse, Roubini, and Schimmelpfenning (2003) estimate a logit model of sovereign debtcrisis that includes a large set of emerging market economies for the 1970–2002 period; thus, they includethe sovereign crises of the last decade in their sample. Their model predicts about three quarters of allcrises entries while sending few false alarms.Taken together, the existing literature suggests several factors that are at the core of an empirical modelattempting to predict sovereign default: measures of solvency, such as public and external debt relative tothe capacity to pay; liquidity measures such as short-term external debt and external debt service, possiblyas a ratio of foreign reserves or exports; political, institutional and other variables capturing a country’swillingness to pay; macroeconomic variables such as real growth, inflation, exchange rate, etc., capturingboth ability to pay and willingness to pay; measures of external volatility and volatility in economicpolicies. Thus, we use these variables and measures in the empirical study.While the tree methodology that we employ has been used in a limited number of economic studies andeven applied to the case of currency crises (see Ghosh and Ghosh, 2002, and Frankel and Wei, 2004 ) noprevious study has used this methodology to assess the determinants of sovereign crises and to predictthem.III. Data and DefinitionsThe full dataset includes annual information on 47 economies with market access from 1970 to 2002(Table 1). 5 A country is defined to be in a debt crisis if it is classified as being in default by Standard &4 See for example Detragiache and Spilimbergo (2001) for a study including recent episodes.5 The debt crisis indicator is derived from data provided by Standard & Poor’s and data on IMF lending. Data onexternal debt and public debt is taken from the World Bank’s Global Development Finance database (GDF), as wellas from IMF sources. Data on 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 is available for all countries or for the full-time period.

- 12 -weight differently the cost of misclassifying crisis and non- crisis episodes 11 : a higher cost of missing acrises raises p 1 (t) and similarly increases the frequency a crisis is called. The option of choosing priorsand misclassification costs at the outset (i.e., before running the CART algorithm) influences the modelchoice (i.e., the set of indicators and thresholds). This is a key difference between CART and standardEWS. For example, Berg, Borensztein, and Pattillo (2004) use a misclassification cost function (weightingType I and Type II errors) to identify the probability cut-off point that would best predict crisis and noncrisisevents out-of-sample only after having estimated the probit model. As a result, their cost-functioncannot influence the choice of the indicators and coefficients in the probit model 12 . Here, the choice ofpriors (and costs) shapes the model, as well as determines the cut-off point for labeling terminal nodes ascrisis or non-crisis types (see below).In order to decide when to stop the growing process, the algorithm calculates the gain from furthersplitting in terms of the reduction in the rate of misclassification from each parent to the two child nodes.A standard approach would be to stop growing the tree when the reduction in the misclassification ratebecomes lower than the change in the penalty associated with the number of terminal nodes. However,such an approach would not be capable of discovering possibly interesting splits further down the tree.Thus, CART initially grows a maximal, over-fitted, tree, and then proceeds to “pruning” branchesbackward. The best tree ( in terms of “goodness of fit”) is determined by looking for the tree whosemisclassification error rate (adjusted for a penalty on the number of nodes) is lowest.Finally, the criterion to label a terminal node as crisis or non-crisis-type is quite intuitive: classify terminalnode t as crisis-type if p 1 (t) > p 0 (t). Note, from equation (2), that when the prior distribution coincideswith the empirical likelihood, π 1 = N 1 /N , then p 1 (t)=N 1 (t)/N(t) and the criterion yields the plurality rule:11 One can explicitly set different costs from misclassifying a crisis (C1 ) and a non crisis (C 0) observation. Doing so modifies theformula for the (adjusted) posterior probabilities as follows:C1π1N1( t ) / N1∑ Cjπjj = 0 , 1p1( t ) =Ciπi∑Ni( t ) / NiC πi = 0, 1∑j = 0 , 1jjThe relative misclassification costs and prior probabilities can be used inter-changeably in order to make the crisis classificationmore conservative, given the subjective preference for reducing the chance of missing crises.

- 13 -classify node t as type 1 if the node contains more type-1 observations than type 0, N 1 (t)>N 0 (t).Conversely, if priors are “agnostic” in the sense that π 1 = π 0 = ½, then it is easy to see that node t will belabeled as type-1 provided the these types are relatively more abundant in the node than in the entiresample: N 1 (t) / N 0 (t) > N 1 / N 0 . From the formulas above it descends that the posterior probability of acrisis, p 1 (t) , is increasing in the relative cost of a crisis C 1 and in the prior probability π 1. Thus the largerthese two parameters, the more likely 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 the following specifications: (i) the criterion tobe minimized is the Gini index in equation (1); (ii) the a priori distribution of crises is taken to be equal tothe sample distribution, π i = N i / N; (iii) the cost of missing a crisis is set to 7 times the cost of missing anon-crisis (which is normalized to 1). From the expression in the previous footnote, these parameters yielda posterior probability of a crisis in node t, p 1 (t )= 7N 1 (t)/[N(t) + 6N 1 (t)]. Thus, a node is labeled as crisis(p 1 (t)>1/2 ) when it contains at least 12,5 percent of crises (that is when N 1 (t)/N(t) > 0,125). This cut-offpoint takes into account the fact that in our sample crises episodes are possibly over-represented withrespect to the “true” population (they make up 20,5 percent of sample observations), so that we want to“call” a crisis relatively more frequently. Our findings, however, are robust to this choice for the cut-offpoint for calling a node a “crisis” type (see below).CART FeaturesThe CART algorithm displays a number of interesting features. First, it is well suited for discoveringcontext dependence, interactions and heterogeneity. Unlike parametric models, which aim at uncovering asingle dominant (typically linear) structure in the data, CART is designed to work with data that mighthave multiple structures. In fact, one of our most interesting findings is exactly that not all crises are thesame. The methodology is robust to the presence of outliers among the independent variables. These donot generally affect CART because splits usually occur at non-outlier values. This feature is particularlyuseful when dealing with emerging markets, where, particularly in crisis times, variables such as inflation12 See Chamon, Manasse and Prati (2006)

- 14 -and exchange rate depreciation take extraordinary values. No specification search is necessary. Thisfeature is useful when theory does not precisely identify the “right” explanatory variable (which indicatorof liquidity constraints should we use: short-term debt over GDP, over exports, reserves, or over totaldebt?). Moreover, the algorithm yield the same results for any monotone transformation of the variables(for example, levels or logarithms). The procedure is non-parametric, as it does not require specification ofa functional form for the exogenous variables. Also, missing values for predictors are handled veryeffectively, 13 so that CART can be used also with data sets that have a fraction of missing values, as oftenis the case, for example, with fiscal data for developing countries. Finally, the algorithm is designed toavoid “over fitting” the model to the data, so that predictions should remain accurate when applied to freshdata. When data limitations do not allow for having a separate test sample, CART proceeds by dividing thesample into 10 roughly equal parts, each containing a similar distribution for the dependent variable. Ittakes the first nine parts of the data, constructs the largest possible tree, and uses the remaining 1/10 of thedata to obtain initial estimates of the misclassification error rate of the sub-trees. The same process is thenrepeated (growing the largest possible tree) on another 9/10 of the data while using a different 1/10 part asthe test sample. The process continues until each part of the data has been held in reserve one time as a testsample. The results of the ten mini-test samples are then combined in evaluating the optimal (lowestadjusted misclassification) tree. This procedure, called cross-validation, implies that the algorithm strivesat finding a model that performs well on completely fresh data, even in the absence of an independent testsample.CART has a few shortcomings, however. Unlike regression or probit/logit analysis, the individualmarginal contribution of each variable to the probability of belonging to a class cannot be ascertained:CART assigns a single probability to all cases belonging to the same node. Furthermore, the procedure isnot well suited for uncovering “general” relationships that hold across the whole sample: a linear effect13 For each split in the tree, CART develops alternative splits (surrogates), that is, variables that produce a similarallocation of observations in child nodes. These variables are used when the primary splitting variable is missing.Thus, a missing value does not imply that all the observations need to be thrown away, as in regression analysis. Themissing value is replaced by the best surrogate.

- 15 -would show up as the same variable being selected repeatedly with different thresholds. Moreover, as thepattern of discovery becomes progressively more localized, sample-wide information is not used. 14 Third,since CART is non-parametric and free from assumptions on probability distributions, confidence intervalscannot be meaningfully attached to the threshold values. However, one can estimate a logit model withdummy variables corresponding to node inequalities, and test for their significance (see below). Finally, ifa variable is even slightly outperformed by another as a split, it may never appear in the final tree, even ifit is more closely associated with class 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 to having two significant regressors that happen to be strongly collinear: one drops outfrom the regression. The consequence for classification is that the variables appearing in a tree may besensitive to changes in the sample, in the list of variables considered, and/or in the a priori distribution. Apossible way out is to rank each variable by looking at the potential effect of the variable on classification.This procedure explicitly accounts for a variable’s ability to classify observations at each node, even when“masked” by the first-choice split. It yields a measure (the Gini index of “importance”) that does notdepend on the variables actually appearing in the tree (more on this below).The problem of robustness to the addition of new variables and observations is rather complex, however.If a new variable is informative enough to replace a pre-existing variable, particularly in the top splits,there is a good chance that the branches developing from there onwards will feature a somewhat differentset of variables and thresholds. Similarly, the introduction of additional years or countries to the samplemay lead to substantial changes in the optimal tree. We will discuss and apply a solution based on MonteCarlo simulations proposed by Breiman (1992) in Section VIII below, where we address the issue of therobustness of our results.VI . The Empirical Tree14 Related to this is the criticism that the procedure is only “one-step” optimal and not “overall” optimal. For example,suppose that the procedure produces a tree with ten terminal nodes. If one could search all possible partitions of thedataset in ten terminal nodes for the one partition that minimizes the Loss function , the two result may be quitedifferent (Breiman and others, 1984).

- 16 -CART selects the following 10 variables out of the 50 candidates listed in Table 2: total external debtin percent of GDP; short-term debt relative to foreign reserves; public external debt in percent of publicrevenues; real GDP growth; inflation; the U.S. treasury bill rate; exchange rate overvaluation; exchangerate volatility; the ratio of external financing requirements to foreign reserves; and the number of yearsbefore a presidential election.The first rule splits the sample into two branches (see Figure 1) [insert Figure 1 here] : (i) episodes withhigh external debt (more than 49.7 percent of GDP) go to the right—here the conditional crisis likelihoodrises from 20.5 percent in the entire sample to 45.4 percent; and (ii) episodes with low external debt to theleft—with default likelihood of 9.7 percent. Episodes of high debt (more than 49.7 percent of GDP) arefurther split into high/low inflation (above/below 10.5 percent). The former incur the largest defaultfrequency, 66.8 percent, see terminal node 14. More than half of all the crisis episodes in the samplesatisfy these two simple conditions. For example, the high external debt plus high inflation criterion wasmet one year ahead of the crises in Jamaica, Egypt, Bolivia, Peru, Ecuador, Uruguay, Indonesia, Bolivia,Morocco, Turkey, South Africa, Uruguay, Brazil, and Venezuela. Terminal node 7 is second in terms ofnumber of crisis episodes. How do we get there? Despite intermediate external debt levels (between49.7 percent and 19 percent of GDP), the joint effect of short-term debt (exceeding 130 percent ofreserves), political uncertainty (less than five years to the next presidential elections), and relatively rigidexchange rates (low volatility) conjure to raise the crisis likelihood to 41 percent.By contrast, going down from the top to the left, towards terminal node 3, one finds the circumstancesthat are more favorable for reducing risks: low external debt, low short-term debt to reserves on aremaining maturity basis (below 130 percent) and low public external debt to revenue (below210 percent), coupled with the economy not being in recession. Under these circumstances, the likelihoodof being in a crisis is just 2.3 percent. About 58.4 percent of all non-crisis episodes satisfy theseconditions.Based on the set of rules of this tree, the observations can be classified as crisis-prone or not crisis-prone.As explained previously, a particular final node is classified as crisis-prone (not crisis-prone), if the within

- 17 -node posterior probability of crisis is higher (lower) than ½ . As discussed in the methodology section, ourchoice of parameters implies a cut-off share of within-node crisis frequency of 12,5 percent, that is, belowthe proportion of crises in the sample, 20.5 percent. As can be seen from the figure, the largest percentageof (missed) crises in “non-crisis” terminal node is only 2.3 percent, while the smallest percentage of crisesin a “crisis” node is 40 percent. Thus, the tree separates the two types quite effectively, so that any cut-offthreshold for labeling nodes, set between 2.3 percent and 40 percent, would not affect the finalclassification.The tree has one particularly important implication for sustainability analysis. It shows that unconditionalthresholds for debt output ratios are of little value per se for assessing the probability of default. Taketerminal nodes 7 and 11. The former has only moderate values of debt ratio, between 49.7percent and 19 percent, but the likelihood of a crisis is high, 41 percent. The latter has a debt ratio of atleast 49.7 percent, but the crisis probability is just 2 percent. Why? Clearly, other factors are at play. Whatmakes node 7 risky is the compound effect of short maturity of the debt, political uncertainty andrelatively fixed exchange rates. What makes node 11 safe, despite the large debt burden, is monetarystability, a large current account surplus, and relatively large fiscal revenues that guaranteed solvency onpublic debt.Classification TableTable 3 shows some interesting information on the classification tree. [insert table 3 here]The first column lists the terminal node’s number. The second column reports the set of inequalitiessatisfied by each node’s observations: for example, row 14 identifies terminal node 14, containing all thecases (country-year) where total external debt/GDP exceeds the threshold of 49.7 percent and inflationexceeds 10.5 percent. Column 3 counts the number of observations that satisfy the node criteria, and tellsus how “relevant” is a terminal node. For example, the table shows that the three most populated nodes arenumber 3 (607 observations), 14 (196 cases) and number 7 (130 episodes). Thus, for example there are196 observations (in node 14 ) that satisfy the two inequalities on debt and inflation. The fourth columnreports the empirical likelihood of a crisis, conditional on the node’s inequalities: for example, the

- 18 -likelihood of a crisis next year for a country with high debt and inflation (node 14), e.g. the proportion ofobservations satisfying the two inequalities, which had a crisis the following year is 66.9 percent. Thisnode is classified as a crisis node (see column 8) since the crisis (posterior) probability exceeds ½. 15 Thisallows one to calculate the Type II error. In the case of node 14, 33.1 percent of the cases displaying highdebt and inflation turned out not to experience a crisis the following year, and were therefore misclassifiedas crises. The fifth and sixth columns give information on how frequent the identified characteristics arefound among crises and non-crises. For example, looking at node 14 and column 5, we see that more thanhalf (50.2 percent) of all sovereign debt crises in the sample satisfy the debt and inflation criteria. Thisnumber is computed as the ratio of the crises in the node to the total number of crises in the sample.Similarly, the sixth column shows how frequent are the reported characteristics among non-crisisobservations: for example, from the row 14, column 6, we see that only 6.4 percent of all non-crisisepisodes displayed large external debt and inflation. Finally, we want to derive a measure of “how safe”are the thresholds for fundamentals. To do so, we divide the percentage of non crises in a node, N 0 (t)/N 0 ,by the share of observations in the node, N(t)/N (for node 14 we divide column 6 by (196/1276)). Theresult is shown in the seventh column of the table. This “safety” index that takes value greater than onewhen the node is “safer” than the overall sample, and smaller when it is “riskier”.InterpretationThese calculations lend themselves to an interesting interpretation. We can regroup the terminal nodes intofour blocks, which identify different types of macroeconomic scenarios. Block A can be interpreted asdescribing the characteristics of the “(relatively) safe fundamentals” type: observations in this block areclassified as non-crisis prone. Blocks B, C, and D identify potential defaulters, which are subject to risksof different sorts. Observations therein are classified as crisis prone.15 As explained above the posterior probability does not in general coincide with the empirical likelihood reported inthe table, since it reflect the choice of priors and cost weights. For example, applying the formula p 1 (t) = 7N 1 (t)/[N(t)+ 6 N 1 (t)] of footnote 11 gives a posterior probability of crisis in node 14 of 93,4 per cent which exceed the likelihood(66,9 percent) due to the high relative cost of missing a crisis (7:1).

- 19 -“Relatively Safe” Fundamentals, type A. Nodes 1, 4, 6, 8, 9, 11, and 3, in descending order of “safety,”show the prerequisites for a relatively risk-free environment. Low total external debt (below 49.7 percent)is the common denominator of these nodes (with the exception of partition 11). Low short-term debt overreserves (below 130 percent), low public external debt over revenue (below 215 percent), low inflation(below 10.5 percent) and not too strong recession (growth above -5.5 percent) also characterize many (butnot all) of these partitions. By far the more representative partition is node 3 that contains 607 episodesamounting to 58 percent of all tranquil nodes. Node 11 comes next in terms of observations. Node 11shows that low external debt is by no means necessary for avoiding a crisis. Despite a large foreign debt, acountry may still enjoy a relatively safe environment (2 percent crisis likelihood), provided inflation isunder control (below 10.5 percent), external financial requirements over reserves are not too high (below140 percent) and public external debt over revenue is not too large (below 310 percent). Node 3 shows thatlow external debt is by no means sufficient for avoiding a crisis. Despite showing relatively soundfundamentals as defined in node 3, 5.4 percent of these observations nevertheless had a crisis thefollowing year (they are listed in column 9).The nature of the inequality constraints in the following “crisis prone” nodes suggests an intuitiveclassification into solvency (B), liquidity (C), macro-exchange rate (D) risks.Liquidity Crisis-Prone, type B is described by nodes 7 and 10. Despite relatively low or intermediateexternal debt ratios, these episodes share a ratio of short-term debt to reserves in excess of 130 percent.This feature, coupled with political uncertainty (presidential elections in less than five years) and relativelyfixed exchange rate (low volatility), in node 7, or with tight monetary conditions in international capitalmarkets (treasury-bill rate above 9.7 percent), in node 10, raise the likelihood of a crisis to about40 percent. Solvency risks of the first type (node 7) make up more than one-fifth (20.7 percent) of all debtcrisis episodes, while only 7.5 percent 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. Inall these cases, either external debt exceeds 49.7 percent of GDP, or its public component exceeds

- 20 -215 percent of revenues. In partition 14, high total external debt, together with inflation above10.5 percent, raises the likelihood of a crisis from 20.5 percent (entire sample) to 67 percent. More thanhalf of all crises episodes in the sample satisfy these characteristics (see the fifth column). Only in 6.4percent of the cases where debt and inflation were above these thresholds a crisis did not occur in thefollowing year. Note that the high inflation rate could be here a proxy for fiscal problems: inability toreduce deficit may need to monetization of them and seignorage financing of them. In fact, terminal node5 is similar, but a solvency crises (4.2 percent of total) are signaled by public, rather than total, externaldebt and high inflation. In node 13 (12), high external debt and high financing external requirement (orfiscal imbalances measured by high public external debt over revenue), raise the default likelihood to47 percent (40 percent). These two nodes jointly account for another 15.7 percent of crises. The largeexternal financing need can be partly interpreted as an illiquidity problem: this financing need is highwhen the current account deficit is high and/or when there is a large amount of debt coming due; in eithercase, the country may be illiquid if creditors do not provide new financing and/or do not rollover theirdebt. Thus, crisis episodes in node 13 can be interpreted as cases where a country is not necessarily“insolvent” but rather has an unsustainable—and non-financeable—debt path given large stocks of debtand illiquidity measured by large financing needs.Exchange Rate and Macro-crisis prone, type (D) A small number of sovereign debt crises (1.5 percent) innode 2 appear to be driven by large exchange rate overvaluation (above 48 percent) and large recession(negative growth below -5 percent). These are the crises of El Salvador, 1981–82, Uruguay, 1983 (thecollapse 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: in these cases, the exchange rate was notover appreciated, values of external debt were small and there were no liquidity problems, and there wereno-crises despite a strong recession.How Different are Crises and how important Non-linearities?

- 21 -How different are the crisis types and how important are the threshold effects found in the analysis? Inorder to answer these questions, we can look at the within node summary statistics for the selected tencrucial variables of the tree. 16 It is useful to compare the most representative nodes of liquidity (7) and thesolvency crises (14 and 13) nodes. Indeed, the liquidity crisis node 7 has moderate average levels ofexternal debt ( 37 percent of GDP), and of average public external debt (1.2 percent of GDP) , whileshort-term debt is very high, on average about 3 times larger than reserves. By contrast, solvency crisisnodes 13 and 14 not only display high short-term debt (2.7 times reserves), but also very high averagelevels of external debt (77 and 76 percent of GP respectively), and public external debt (2.4 and 3.2 timesrevenues). This suggests that solvency problems typically also entail liquidity difficulties, but notgenerally vice-versa. Solvency and liquidity crises have rather similar values for the other fundamentals.Finally, by comparing the characteristics of the “least safe” safe node 3, with the “safest” crisis pronenodes, 10 (and 12), it is possible to have an idea of the importance of threshold and non linear effects 17 .Nodes 3 and 10 differ mainly with respect to the ratios of short-term debt and external financialrequirements to reserves: these are substantially lower in the safe node,(0.6 against 2.1 for the averageshort-term debt over reserves, and 0.8 against 3.3 for external financing requirements over reserves). Thissuggests that non-linearities are not very sharp. Similarly, the safe node 3 and the risky node 12 differsubstantially in the average levels of external debt ( 27 and 110 percent of GDP) and public debt overrevenue (0.9 and 3.6 percent, respectively). Relative to node 10, the least safe “safe” node 3 is alsocharacterized by an exchange rate that is at the same time less overvalued and more flexible (i.e. morevolatile).16 For reasons of space, the data for all variables (total external debt, short-term debt over reserves, publicexternal debt over revenue, real growth, overvaluation of the exchange rate, inflation, years to the nextpresidential election, exchange rate volatility, US Treasury bill, external financing requirements) areavailable in a web appendix at the following address:http://www2.dse.unibo.it/manasse/Pdf/Web_Appendix_Within%20Node%20Summary%20statistics.pdf17 We thank one referee for this observation.

- 22 -In summary, our classification of crises captures quite well most of the episodes of the 1990s. Korea(1997), Mexico (1995), Brazil (1998) and (2001), are in the illiquidity node 7; and indeed these weretypical episodes of a liquidity crisis, not insolvency. Pakistan (1998) is also in this node: its debt levelswere not excessive but the country was illiquid given large lumpy debt servicing payments coming dueand its loss of market access. Pakistan was then forced to restructure its external sovereign debt, and it didnot 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 by extending its maturities at below crisislevel market rates. Clear insolvency cases in node 14 are Ecuador (1999), which defaulted on its externaldebt, Indonesia (2002), with a very large debt burden (but it is not illiquid given its restructuring of manyexternal debt claims, both public and private), and Turkey (2000) with a very large debt burden. Turkeydid not default thanks to an exceptional IMF program, but based on this classification was borderlineinsolvent. 18 Russia (1998) and Argentina (1995) appear in the non-crisis node 3; hence the tree is unable topredict these crises. In the case of Argentina, the Tequila contagion from Mexico in 1994 played animportant role, as other fundamentals (debt levels and deficits) were fine at that time. Russia was notinsolvent based on debt levels and external flow imbalances (current account deficits) but its failure tomake flow fiscal adjustments and large capital flight led to default in 1998. 19 Node 13 of unsustainabledebt path with possible illiquidity included Argentina (2001), which did default, Indonesia (1997), whichdefaulted on many private external debts, and Thailand (1997) that did not default on most external debt(only on some private claims), but had severe debt servicing problems in its private financial and corporatesectors. Therefore, these are cases of outright insolvency or high illiquidity that made the debt path notsustainable/financeable.VII. Regression Analysis18 Given the lack of good data on primary balances, our classification does not capture well cases, such as Turkey,where the country would be deemed as insolvent based on a debt level criteria, but may be solvent as it is running avery large primary surplus (above 5 percent of GDP currently), that is stabilizing and reducing such high debt level.19 In principle, we may have included a variable measuring “contagion” effects from crises elsewhere. In practice,however, implementation in our context is problematic, since contagion typically occurs within a year, and weemploy (one period lagged) data at annual frequency.

- 23 -A natural question is whether the non-linear interactions and threshold effects found in the tree arestatistically significant. We apply standard econometric techniques on our data set. 20 We proceed asfollows: we construct a set of dummy variables corresponding to the inequalities that define the terminalnodes in our classification tree (variables “node 1-14”, see Table 3), and estimate a logit model with ourcrisis indicator as dependent variables and the node dummies as dependent variables. We report the resultsin Table 4. [insert table 4 here ] Clearly, the node dummies corresponding to a “perfect classification”(nodes 1,3,4,6,8,9 in Figure 1) are dropped, as they perfectly predict the outcome. Also, not surprisingly,the “small” nodes containing only a handful of observations (nodes 5,10,12) are not found statisticallysignificant. Conversely, the large nodes have statistically significant coefficients, generally with theexpected sign. If a country displays “safe fundamentals”, as defined by Node 3 and Node 11 (see Table3), the probability of experiencing a crisis next year is significantly reduced; conversely, belonging toNode 14 of high inflation and debt significantly 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 marginallysignificant.VIII. RobustnessAs we discussed in the Methodology section, robustness is a serious issue for classification trees. Here, webriefly describe and apply a solution recently developed by Breiman (2001), one of CART developers. The“Random Forests” (RF) algorithm 21 is a generalization of CART based on a collection of hundreds(possibly thousands) of trees. The idea is to build many trees using different combinations of variables anddata (sub) samples, in order to make sure that the inclusion or exclusion of variables and data-points doesnot affect the classification. Here is how it works. RF obtains the final classification (crisis vs. non-crisis)by “majority rule”, that is, by aggregating the responses of many trees. At each run, a bootstrap procedureestimates each tree by randomizing over two dimensions: a sub-sample of data and a (small) subset of all20 Ideally, one should perform such a test on a “fresh” set of data.21 We are not aware of other applications of the Random Forest algorithm to international macro/finance issues.

- 24 -the variables. By picking a random subset of the variables, any single variable is analyzed in a differentcombination with others, thus taking care of the problem of “masking” discussed in the Methodologysection. Moreover, by randomizing simultaneously over the sub-samples, each tree analyzes only a portionof data at a time. This process, called “slow learning,” highlights different aspects of the data set andreduces the risk of possibly drawing wrong conclusions “too fast” (see Friedman, 2001) from a uniquesample. If a pattern genuinely exists in the portion of data analyzed, the RF algorithm will detect itrepeatedly in different trees; conversely, it will wash out any accidental pattern in the process of averagingthe results. The drawback of the algorithm is that it does not allow the researcher to recover a “single” treewith its thresholds and interactions, since it relies upon the aggregation of the classifications that producedby many different trees. For our purposes, however, Random Forest provides an interesting benchmark forassessing the robustness of CART’ selection of variables. 22 Table 5 [insert Table 5 here] reports the Ginimeasure of the variable importance for CART and RF 23 , normalized on a 0 (lowest importance)-100(highest) scale. Overall, this analysis confirms the robustness of our CART results. The solvencyindicators (total external debt over GDP, public external debt over revenue), the liquidity indicator (inparticular short-term debt over reserves), the exchange rate volatility and overvaluation, inflation andgrowth, all feature prominently in RF’s as well as in CART’s selection of most important variables.Interestingly, RF ranks the exchange rate variables even higher than CART. Also, political economyvariables do a better job in the RF than in the CART tree (see the indexes of Political Constraint). Theproximity to presidential elections is confirmed as a relevant predictor. Overall, the coefficient ofcorrelation between the measures of importance in CART and RF is 0.61, and the rank correlation is 0.77.22 Each tree in Random Forest was built by selecting 3 variables at random, and 500 trees were built using of tenth ofthe observations at each run.23 In practice, every variable is considered at every split, in each tree, and the Gini index provides a measure of the“purity” of the sub-nodes generated by the variable split, see the discussion in Section IV, and Breiman et al (1984).

- 25 -IX. PredictionNext, we discuss the prediction accuracy of our model. Table 6 [insert Table 6 here] reports the predictiveaccuracy of the tree for both crisis “states” and crisis “entries”, being respectively defined as crisespreceded by a crisis, and by a non-crisis. The purpose of this distinction is to facilitate the comparisonbetween our results and those obtained in the Early Warnings literature. Many empirical models focusonly on entries, see for example Chamon, Manasse and Prati (2006). The motivation is that factors thatlead to a crisis may be different (or have a different impact) from factors that keep the country in the crisisstate. Neglecting all within-crisis observations, however, does not make an efficient use of availableinformation. In fact, Manasse, Roubini, Schimmelpfennig, (2003) find that the same variables explain bothcrisis entry and persistence, typically with statistically equal coefficients. In our estimation, we have keptall crisis states information, for two additional reasons. First, because CART treats each observationindependently, so that 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 not immediate, since the definitions of crisis, thedata frequency (monthly, yearly), the sample coverage, and the forecast horizon (one, two years ahead)differ dramatically across studies. The most successful EWS models are able to correctly predict 60-70percent of (currency) crises (for example, Berg and Patillo, 1999), but they differ widely in their falsealarms, and in their in and out-of sample predictions (which typically perform much worse) . Clearly, onecould easily predict as many crises as wished, simply by accepting a very large number of false alarms (ina logit model one would choose a sufficiently low crisis probability threshold). Berg and Patillo, 1999,find that in this respect the models they analyze for currency crises yield disappointing results: between 63and 54 percent of false alarms, with a crisis probability thresholds of 25 percent 24 .24 These results were found for out-of-sample predictions

- 26 -Table 6 presents the results. The first two columns give the in-sample predictive accuracy for the modelbased 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 the standard EWS models. It correctly predicts oneyear ahead 82.9 percent of the states, and does only slightly worse for the post 1990 period; it does betterwith crisis states, of which it correctly predicts 93.9 percent, than with tranquil states (not shown:79.9 percent). The prediction success for “entries” is comparably good (88.9 and 85 percent in full andpost 1989 samples); moreover, these results do not come at the expenses of considerable false alarms: forthe post 1989, only 15 percent of tranquil states are incorrectly predicted as crises (and 18,5 percent for theentire sample). These results also compare quite favorably with those obtained by Manasse, Roubini andSchimmelpfennig (2003). The logit model estimated in this paper, for a slightly higher threshold, hasfewer false alarms (5.7 percent) but also correctly predicts far fewer entries (57.1 percent).“Out” of sample predictions are obtained as follows. First, we build a tree is built using only data only upto 1989. Here we force CART to use the same set of 10 variables found in the optimal tree based on theentire sample 25 . Predictions for the post- 1989 data are then obtained using this tree.The out of sample prediction accuracy is considerably worse than in-sample. About 57 percent of defaultstates and 35 percent of post-1990 entries are correctly predicted from the tree based on pre-1990observations. In particular, the model fails to predict many of the important crises of the 1990’s: the Asiancrisis, Russia, Brazil and Turkey (2001) are not predicted 26 . Note however, that we are requiring ourmodel to predict as far as 11 years ahead, quite a formidable task. Moreover, false alarms (incorrectly25 The resulting tree and threshold is only marginally different from the optimal one based on the full data set. Details areavailable on request. Alternatively , we could have let CART choose a potentially new set of variables in the estimation .Doing so, however, does not improve the predictive accuracy.26 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.

- 27 -called entries) are also extremely low, which suggest that experimenting with different thresholds mayimprove the model predictive power to some extent. 27 .X. Rolling Trees and Changes in Variables and ThresholdsThe unsatisfactory out-of-sample performance of the model is likely to be due to the changingmacroeconomic configurations of crisis episodes across different decades. Within our framework, thisshould be reflected either by a change in the set of explanatory variables and/or by a change in theircritical thresholds over time. We examine both issues in by running “rolling trees”.The first exercise asks the question: has the set of optimal crisis-predictors in emerging markets changedover time? We run unrestricted rolling trees, by letting CART choose the best set of predictors for eachrun, starting from a 1970-1989 sample, and then adding one year at a time, until the full sample is covered.For each run, we calculate the variables’ “importance” measure previously discussed, and plot thenormalized values (from 0 to 100) in Figure 2. Note that different trees often pick different variables forvery similar indicators (for example, for solvency, Total (= public + private) External Debt/GDP issometimes replaced by Total External Debt/Exports or by Public External Debt/GDP). 28 In the Figure wepick the variable with the highest importance measure for each indicator (see the note to the Figure)Figure 2 shows that the size of External Debt is consistently the best predictor of sovereign debt crises inemerging markets. Measures of liquidity (Short Term Debt), the second most important predictor up to theearly 1990s, have become temporarily less important in the 1995-98 period, when fiscal solvencyconsiderations (Public External Debt/Revenue), political uncertainty (Years to Presidential elections) andinflation have gained predictive power. 29 This makes sense, since in addition to the Asian crises, this27 When the estimation sample is extended to 1996, the predictive accuracy of the model does not improvesignificantly, possibly confirming a sort of “structural break” in the latter crises We have not pursued this attemptsince we wanted to keep the model parameters as closed as possible to those used in the in-sample exercise.28 Recall that a variable may score high even if it does not appear in the tree (for example, a variable may be a“second-best” split at each stage)29 Note however that the Financial Requirement indicator (Short term external debt plus current account deficit overReserves has somewhat gained in importance) .

- 28 -period witnesses, among others, crises in Algeria 1995, 1996, Argentina 1995, Ecuador 1995, Mexico1995, Pakistan 1998 , Peru 1995, 1996 , 1997, Russia 1998, Ukraine 1998 and Venezuela 1995,1996. Other indicators show a secondary and stable role.Next we ask the question: have the critical thresholds changed over time in emerging markets? Thisquestion has no obvious answer in our tree framework, since following the top split, classification treescalculate conditional thresholds: the same variable may display a different thresholds, depending on thevariable’s place in the tree’s sequence. For this reason we adopt the following strategy: we run rollingtrees as before, but this time keeping only the variables that appear in the “final” (full sample) tree in eachrun, as we did in the out-of.-sample exercise. For each different tree, we report the (unconditional)threshold value that each variable would have taken, had it been selected in the top split.The thresholds’ evolution for the main variables s are shown in Figure 3. The critical value for thesolvency indicator, Total External Debt/GDP, slowly creeps up from 0.44 to 0.5 , possibly indicatingmore resilience to large debts in more recent. episodes. By contrast, the threshold for Short-TermDebt/Reserves slightly falls from 83 to 73 percent since 1994, suggesting that although liquidity indicatorsmay have lost some predictive power in the late 1990s (Figure 2), the vulnerability of emerging markets toliquidity shocks may have risen somewhat. Interestingly, the temporary fall in the threshold of PublicExternal Debt/Revenue, from 2 to 1.7 in the second half of the 1990s, confirms the larger role of publicsector vulnerability in the crises of this period. Finally, it is interesting to note that, possibly as a reflectionof larger capital market integration in more recent years, the critical value of an over-appreciatedexchange rate (not shown) falls sharply, from 100 to 34 percent.In summary, the rolling tree analysis suggests that the nature of sovereign debt crises changed somewhatin the nineties, with fiscal solvency and political economy issues gaining more relevance, and withemerging economies showing heightened vulnerability to (possibly less frequent) liquidity shocks and tocurrency misalignments, possibly reflecting their larger integration in the international capital markets.The combination of changes in the ranking of the explanatory variables and in their critical thresholdshelps explaining why the more recent crises are difficult to predict on the basis of the earlier ones.

- 29 -XI. ConclusionsIn this paper we have applied a new statistical methodology to the question of understanding sovereigndebt crises, both in terms of fundamentals that lead to a crisis, and of the factors that allow us to predictsuch crises. This technique allows us to derive endogenously the most important factors associated tovulnerability of sovereign debt, 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 andhigh inflation) or debt unsustainability due to high debt and illiquidity; ii) episodes of illiquidity, wherenear default is driven by large stocks of short-term liabilities relative to foreign reserves; and iii) episodesof macro and exchange rate weaknesses (large overvaluation and negative growth shocks). Conversely, arelatively “risk-free” country type is described by a handful of economic characteristics: low total externaldebt relative to ability to pay, low short-term debt over foreign reserves, low public external debt overfiscal revenue, and an exchange rate that is not excessively overvalued. Political instability and tightmonetary conditions in international financial markets aggravate liquidity problems. The approachsuggests that unconditional thresholds—for example, looking at debt to output ratios in isolation—are oflittle value per se for assessing the probability of default; it is the particular mix of different types ofvulnerability that may lead to a sovereign debt crisis.The in-sample predictive power of the tree approach is quite good with very few crises missed; the modelpredictive accuracy does not suffer when applied to the post-1990 experience. However, despite very fewfalse alarms, the out-of sample predictive power is not satisfactory: many of the crises of 1990s could notbe predicted based on previous decades information, possibly confirming the different nature of the lattercrises. The “rolling tree” analysis suggests indeed that the nature of sovereign debt crises changedsomewhat in the nineties, with fiscal solvency and political economy issues gaining more relevance, andvulnerability to liquidity shocks and currency over-appreciation becoming larger.Our approach allows to derive rules of thumb which may be useful to predict crises early on (an “earlywarnings signal” model), and to derive policy adjustment paths, which may reduce the likelihood of a

- 30 -crisis for countries that may be entering in a danger zone. Thus, ideally, this tool can be used forsurveillance, crisis prevention, and crisis resolution.A number of possible extensions come to mind, some of which we have tried. First, following the idea thata “history” of past defaults may bear on 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 newvariable taking on incremental values each time a new default episode occurred. Our indicator of (bad)“reputation” did not affect the classification tree. Experimenting with contagion effect is also possible. Butthe use of annual data preclude using same-year information for predicting crises.

- 31 -ReferencesArias, Andres F., 2004, “Comments on the paper ‘Assessing Fiscal Sustainability;’ by Enrique G.Mendoza and Pedro Marcelo Oviedo.” Available via the Internethttp://www.iadb.org/res/centralbanks/publications/cbm35_199.pptBerg, Andrew, and Catherine Pattillo, 1999, “Are Currency Crises Predictable? A Test,” StaffPapers, Vol. 46 (June), No. 2, pp. 107–38.Breiman, L. (2001). “Random Forest”, Machine Learning,http://oz.berkeley.edu/users/breiman/randomforest2001.pdfBreiman, Leo, Jerome H. Friedman, Richard A. Olshen, and Charles J. Stone, 1984, Classification andRegression Trees, (London: Chapman & Hall).Beers, David T., and Ashok Bhatia, 1999, “Sovereign Defaults: History,” in Standard & Poor’s CreditWeek, December 22.______, and John Chambers, 2002, “Sovereign Defaults: Moving Higher Again in 2003?,” Standard &Poor’s (September). Available via the Internet http://www.emta.org/keyper/sov2003.pdfBeim, David O., and Charles W. Calomiris, 2001, Emerging Financial Markets, (New York: McGraw-Hill/Irwin).Cantor, Richard, and Frank Packer, 1996, “Determinants and Impact of Sovereign Credit Ratings,”Federal Reserve Bank of New York Policy Review (October), pp. 37–52.Catão, Luis, and Bennett Sutton, 2002, “Sovereign Defaults: The Role of Volatility,” IMF Working Paper02/149 (Washington: International Monetary Fund).Corsetti, Giancarlo, Bernardo Guimarães, and Nouriel Roubini, 2003, “The Tradeoff Between anInternational Lender of Last Resort to Deal with Liquidity Crisis and Moral Hazard Distortions: AModel of the IMF’s Catalytic Finance Approach,” IMF Seminar Series Research Paper 03/149(Washington: International Monetary Fund).

- 32 -Cottarelli, Carlo, and Curzio Giannini, 2002, “Bedfellows, Hostages, or Perfect Strangers? Global CapitalMarkets and the Catalytic Effect of IMF Crisis Lending,” IMF Working Paper 02/193(Washington: International Monetary Fund).Dell’Arriccia, Giovanni, Isabel Schnabel, and Jeromin Zettelmeyer, 2002, “Moral Hazard andInternational Crisis Lending: A Test,” IMF Working Paper 02/181 (Washington: InternationalMonetary Fund).Detragiache, Enrica, and Antonio Spilimbergo, 2001, “Crises and Liquidity: Evidence and Interpretation,”IMF Working Paper 01/2 (Washington: International Monetary Fund).Eaton, Jonathan, and Raquel Fernandez, 1995, “Sovereign Debt,” NBER Working Paper 5131, Preparedfor Handbook of International Economics.Frankel, Jeffrey, and Shang-Jin Wei, 2004, “Managing Macroeconomic Crises: Policy Lessons,” NBERWorking Paper 10907, November. Available via the Internethttp://ksghome.harvard.edu/~jfrankel/Managing%20Macroeconomic%20Crises%20Policy%20Lessons.pdfGhosh, Swati, and Atish Ghosh, 2002, “Structural Vulnerabilities and Currency Crises,” IMF WorkingPaper 02/9 (Washington: International Monetary Fund).Haque, Nadeem U., Mark Nelson, and Donald J. Mathieson, 1998, “The Relative Importance of Politicaland Economic Variables in Creditworthiness Ratings,” IMF Working Paper 98/46 (Washington:International Monetary Fund).Hemming, Richard, and Nigel Chalk, 2000, “Assessing Fiscal Sustainability in Theory and Practice,” IMFWorking Paper 00/81 (Washington: International Monetary Fund).______, and Murray Petrie, 2002, “A Framework for Assessing Fiscal Vulnerability,” IMF Working Paper00/52 (Washington: International Monetary Fund).Henisz, W. J., (2002), “The Institutional Environment for Infrastructure Investment,” Industrial andCorporate Change, Vol.11, Number 2, pp. 355–89.

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- 34 -Roubini, Nouriel, and Brad Setser, 2004, Bailouts or Bail-ins? Responding to Financial Crises inEmerging Economies, (Washington: Institute for International Economics).

- 35 -Tables and FiguresTable 1. Countries and Default Episodes in the Full SampleNumber Average Yearsof Crisis Length in CrisisCrisis Episodes (starred are added byIMF loans)Algeria 1 6.0 6 1991–97Argentina 3 5.0 15 1982–94, 1995*,1996, 2001,2002Bolivia 2 6.5 13 1980–85, 1986–94Brazil 3 5.3 16 1983–95, 1998*,99*,2000, 2001*,2002*Chile 1 8.0 8 1983–91China 0 … 0Colombia 0 … 0Costa Rica 1 10. 10 1981–91Cyprus 0 … 0Czech Republic 1/ 0 … 0Dominican Republic 1 22. 22 1981–Ecuador 2 8.0 16 1982–96, 1999–01Egypt 1 1.0 1 1984–85El Salvador 1 16. 16 1981–97Estonia 1/ 0 … 0Guatemala 1 1.0 1 1986–87Hungary 1/ 0 … 0India 0 … 0Indonesia 2 2.5 5 1997*–01, 2002Israel 0 … 0Jamaica 3 4.7 14 1978–80, 1981–86, 1987–94Jordan 1 5.0 5 1989–94Kazakhstan 1/ 0 … 0Korea, Rep. of 2 2.0 4 1980*,81*,82, 1997*,98*,99Latvia 1/ 0 … 0Lithuania 1/ 0 … 0Malaysia 0 … 0Mexico 2 5.0 10 1982–91, 1995*, 96Morocco 2 3.0 6 1983–84, 1986–91Oman 0 … 0Pakistan 1 2.0 2 1998–00Panama 1 14. 14 1983–97Paraguay 1 7.0 7 1986–93Peru 3 6.3 19 1976–77, 1978,79*–81, 1983–98Philippines 1 10. 10 1983–93Poland 1/ 0 … 0Romania 1/ 0 … 0Russia 1/ 1 3.0 3 1998–01Slovak Republic 1/ 0 … 0South Africa 4 1.8 7 1976*,77*,78, 1985–88, 1989–90, 1993–Thailand 2 1.0 2 1981*,82, 1997*, 98Trinidad and Tobago 1 2.0 2 1988–90Tunisia 1 1.0 1 1991*, 92Turkey 2 3.5 7 1978,79,80*,81*,82, 83, 2000*,01*,02Ukraine 1/ 1 3.0 3 1998–01Uruguay 3 2.0 6 1983–86, 1987–88, 1990–92Venezuela 3 3.3 10 1983–89, 1990–91, 1995–98Total 54 5.5 261Sources: IMF, Standard & Poor’s, World Bank, and authors’ calculations.. A star indicates according to IMF loan

- 36 -Table 2. Mean of Variables Used in the AnalysisCurrent year All No crisis No crisis Crisis Crisis No. ofNext year All No crisis Crisis Crisis No crisis Obs.Total external debt over GDP 45.5 37.0 54.7 71.4 63.7 1,051Total external debt over exports 290.7 239.3 359.3 455.9 350.2 1,053Total debt service over GDPTotal debt service over reservesShort-term external debt (RM, over GDP) 10.9 9.4 15.0 15.1 15.7 993Short-term external debt (RM, over reserves) 1.7 1.2 2.9 2.9 2.2 948Interest on short-term external debt over GDP 0.5 0.5 0.8 0.6 0.7 754Interest on short-term external debt over reserves 0.1 0.1 0.2 0.1 0.1 754Debt service on short-term external debt over GDP 5.3 4.8 6.9 6.4 7.1 1,050Debt service on short-term external debt over reserves 0.8 0.7 1.5 1.2 0.9 1,050Public external debt over GDP 32.2 25.5 36.4 53.0 46.5 1,051Public external debt over revenue 1.7 1.3 1.9 3.0 2.3 827Consolidated central government debt 47.5 46.4 38.2 57.3 54.0 462Overvaluation 0.0 0.0 0.0 -0.1 0.0 799Current account balance -2.7 -2.7 -4.3 -2.6 -1.3 1,231Reserves growth 19.1 20.8 -5.4 17.8 22.9 1,155Export growth 12.0 13.8 4.9 6.4 7.8 1,270M2 over reserves 5.6 5.3 7.9 6.2 6.2 1,185Financing requirement 1.6 1.3 3.0 2.4 1.4 986LIBOR 9.7 9.5 10.5 10.5 9.4 1,229U.S. treasury bill rate 6.4 6.3 7.8 6.9 6.3 1,229Inflation 54.6 17.5 241.1 169.6 84.9 1,273Nominal GDP growth 55.9 22.8 249.4 148.6 96.0 1,276Real GDP growth 4.1 4.8 1.8 2.1 2.2 1,276REER growth 121.5 124.3 139.7 111.0 109.4 937Import growth 10.0 12.3 5.3 4.8 6.9 902FDI over GDP 1.7 1.9 1.1 1.0 1.5 1,024Openness 71.2 71.3 64.1 72.1 72.5 903Overall balance -4.3 -4.4 -6.3 -3.8 -4.1 1,013Primary balance 0.6 0.3 -0.9 2.0 1.5 616Primary gap 6.6 5.7 23.1 59.0 -15.0 122G.Gov revenue over GDP 24.3 25.4 22.7 20.1 24.2 1,013Overall Balance/GDP variability 1.92 -2.53 -1.77 19.42 -1.70 824Inflation variability 120.43 10.80 125.37 549.81 83.03 1,082Exchange rate variability 2/ 57.8 56.38 45.62 39.87 159.9 1,059Real Exchange Rate Variability 2.87 1.49 3.76 6.34 3.39 753Terms of trade variability 2.24 2.28 2.32 2.23 1.33 1,088Index of political rights 3.52 3.63 3.44 3.18 3.20 1,130Index of civil liberties 3.77 3.85 3.75 3.44 3.65 1,130Index of freedom status 1.21 1.16 1.21 1.39 1.39 1,130Index of political constraints III 0.24 0.24 0.23 0.26 0.31 1,229Index of political constraints V 0.35 0.33 0.35 0.37 0.43 1,229Year of parliamentary elections 0.19 0.18 0.24 0.23 0.20 1,276Year of presidential elections 0.09 0.06 0.11 0.18 0.15 1,276Year of parliamentary or presidential elections 0.21 0.20 0.24 0.27 0.24 1,276Years to next parliamentary elections 2.73 2.94 2.67 2.06 2.16 1,071Years to next presidential elections 5.02 6.47 3.15 2.18 2.39 660Years since parliamentary wlections 2.02 1.81 2.47 2.60 2.00 901Years since presidential elections 2.19 2.15 2.83 2.24 1.60 418Electoral system 1/ 1 1 1 1 1 1,2101/ Mode of electoral system.2/ Excludes Turkey. Sources: IMF, Standard & Poor’s, World Bank, and authors calculations

Table 3. Classification TableColumn 1/TerminalNode2 3 4 5 6 7 8 9Rules and Critical ThresholdsA. Relatively SafeTotExtDebt/GDP ≤ 49.7, ShortTDebt/Res ≤ 1.3,1 PublicExtDebt/Revenue ≤ 2.1, GDPGrowth ≤ -5.5,EchROverV ≤ 48N. Crisis % of % of Relative ClassifiedEpisodes Likelihood Crises NonCrisis Safety Crisis (1)CrisesIn Node In Node In Node In Node of Node NonCrisis(0) (entry)13 0.0 0.0 1.3 1.26 0468911TotExtDebt/GDP ≤ 49.7, ShortTDebt/Res ≤ 1.3,PublicExtDebt/Revenue > 2.1, Inflation ≤ 10.7TotExtDebt/GDP ≤ 19.1, ShortTDebt/Res > 1.3,YearNextPresElect ≤ 5.5TotExtDebt/GDP ≤ 49.7, TotExtDebt/GDP > 19.1,ShortTDebt/Res > 1.3, YearNextPresElect ≤ 5.5,EchRVolatil > 27.9TotExtDebt/GDP ≤ 49.7, ShortTDebt/Res > 1.3,YearNextPresElect > 5.5, USTresBill ≤ 9.7TotExtDebt/GDP > 49.7, Inflation ≤ 10.5,ExtFinReqs/Reserve ≤ 1.4,PublicExtDebt/Revenue ≤ 3.113 0.0 0.0 1.3 1.26 023 0.0 0.0 2.3 1.26 022 0.0 0.0 2.2 1.26 051 0.0 0.0 5.0 1.26 098 2.0 0.8 9.5 1.23 0 Algeria (1991)3B. Liquidity RiskTotExtDebt/GDP ≤ 49.7, ShortTDebt/Res ≤ 1.3,PublicExtDebt/Revenue ≤ 2.1, GDPGrowth > -5.5607 2.3 5.4 58.4 1.23 0Venezuela (1983), South Africa (1976), Russia (1998),Argentina (1995), Thailand (1981)- 37 -10TotExtDebt/GDP ≤ 49.7, ShortTDebt/Res > 1.3,YearNextPresElect > 5.5, USTresBill > 9.710 40.0 1.5 0.6 0.75 17TotExtDebt/GDP ≤ 49.7, TotExtDebt/GDP > 19.1,ShortTDebt/Res > 1.3, YearNextPresElect ≤ 5.5,EchRVolatil ≤ 27.8C. Solvency RiskTotExtDebt/GDP > 49.7, Inflation ≤ 10.5,12 ExtFinReqs/Reserve ≤ 1.4,PublicExtDebt/Revenue> 3.113TotExtDebt/GDP > 49.7, Inflation ≤ 10.5,ExtFinReqs/Reserve > 1.4130 41.5 20.7 7.5 0.73 110 40.0 1.5 0.6 0.75 179 46.8 14.2 4.1 0.67 1Pakistan (1998), Mexico (1982, 1995), Argentina (1982, 1989,1993), Peru (1976, 1983), Brazil (1998, 2001), Jamaica (1978),Turkey (1978), Korea (1997), Trinidad & Tobago (1988), Ukraine(1988), Dominican Republic (1981)Chile (1993), Tunisia (1991), Panama (1983), Thailand (1997),Indonesia (1997), Philippines (1983), Argentina (2001), Jordan(1989), Morocco (1986), Costa Rica (1981)5TotExtDebt/GDP ≤ 49.7, ShortTDebt/Res ≤ 1.3,PublicExtDebt/Revenue > 2.1, Inflation > 10.620 55.0 4.2 0.9 0.57 1 Guatemala (1986), Paraguay (1986)14 TotExtDebt/GDP > 49.7, Inflation > 10.5 196 66.9 50.2 6.4 0.42 1D. Fiscal, Exchange rate and MacrorisksTotExtDebt/GDP ≤ 49.7, ShortTDebt/Res ≤ 1.3,2 PublicExtDebt/Revenue ≤ 2.1, GDPGrowth ≤ -5.5,EchROverV > 48Total 1276 100.0 100.0Source: Author’s Calculations.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)4 100.0 1.5 0.0 0.00 1 El Salvador (1981), Uruguay (1983)

- 38 -Table 4. Logit estimatesNumber of obs = 1163Log likelihood = -379.97026__________________________________________________________Crisis Coef. Std. Err. z P>|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

- 39 -Table 5. Variable Importance and Rank in Cart and Random ForestCARTRandom ForestVariable Importance Rank Importance RankTot 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 44Source: Authors Calculations

- 40 -Table 6. PredictionIn SampleFull Sample1990’s Onwards (Based on FullSample)Out of Sample1990’s Onwards (Based on 1970-1989)Observations 1276 556 556Number of crisisepisodes261 114 114Number of crisis entryepisodes 54 20 20Correctly calledepisodesCorrectly called defaultepisodesCorrectly called nondefault episodes(In percent )82,8 78,8 72,093,9 89,5 57,079,9 76,0 76,0Correctly called entriesinto default88,9 85,0 35,0Incorrectly called18,5 15,0 19,0entries into defaultSources: IMF, Standard & Poor’s, World Bank; and authors’ calculation.

- 41 -

Figure 1. The Empirical TreeTotal external debt> 50 percent of GDPNoYesShort-term external debtto reserves> 1.34Inflation> 10.47 percentNo Yes No YesPublic external debt Years to nextExternal financingNode 14to revenuepresidential electionrequirementObservations: 196> 2.15> 5.5> 1.44Crises: 66.8 percentNo Yes No Yes No YesReal GDP growth Inflation Total external debtUS T-bill ratePublic external debt Node 13> -5.45 percent > 10.67 percent > 19.1 percent of GDP> 9.72 percentto revenue> 3.1Observations: 79Crises: 46.8No Yes No Yes No Yes No Yes No Yes- 42 -Overvaluation> 48Node 3 Node 4 Node 5 Node 6 Exchange rate volatility Node 9 Node 10 Node 11 Node 12Observations: 607 Observations: 13 Observations: 20 Observations: 23 > 27.88 Observations: 51 Observations: 10 Observations: 98 Observations: 10Crises: 2.3 percent Crises: 0 percent Crises: 55 percent Crises: 0 percent Crises: 0 percent Crises: 40 percent Crises: 2 percent Crises: 40 percentNo Yes No YesNode 1 Node 2 Node 7 Node 8Observations: 13 Observations: 4 Observations: 130 Observations: 22Crises: 0 percent Crises:100 percent Crises: 41.5 percent Crises: 0 percentNot crisis-prone Crisis-prone Not crisis-prone Not crisis-prone Crisis-prone Not crisis-prone Crisis-prone Not crisis-prone Not crisis-prone Crisis-prone Not crisis-prone Crisis-prone Crisis-prone Crisis-proneCrisis entries: Crisis entries: Crisis entries: Crisis entries: Crisis entries: Crisis entries: Crisis entries:El Salvador 1981 Venezuela 1983 Guatemala 1986 Pakistan 1998 Algeria 1991 Chile 1993 Jamaica 1981, 1987Uruguay 1983 South Africa 1976 Paraguay 1986 Mexico 1982, 1995 Tunisia 1991 Egypt 1984Russia 1998 Argentina 1982 Panama 1983 Bolivia 1986Argentina 1995 1989, 1993 Thailand 1997 Peru 1978Thailand 1981 1989, 1993 Indonesia 1997 Ecuador 1982,1999Peru 1976, 1983 Philippines 1983 Uruguay 1987Brazil 1998, 2001 Argentina 2001 Indonesia 2002Jamaica 1978 Jordan 1989 Bolivia 1980Turkey 1978 Morocco 1986 Morocco 1983Korea 1997Trinidad &Tobago1988Costa Rica 1981 Turkey 2000South Africa 1985Uruguay 1990Ukraine 1998 Brazil 1983Dominican Rep 1981 Venezuela 1990,1995Sources: IMF; Standard & Poor’s; World Bank; and authors’ calculations.

- 43 -Figure 2: Rolling Tree Variable Importance12010080604020External DebtShort Term DebtPubExtDebt/RevYearsNextPresElRealGrowthExchOvervInflationExtFin'lReq'tsUSTBillsExchR_volat019891990199119921993199419951996199719981999200020012002Notes: Total External debt/GDP is replaced by Total External Debt/Exports in 1995, and by Public ExternalDebt/GDP in 1996,97. Short Term Debt is Short Term Debt/ GDP in 89, 90,91,92,93,94,95,96,97,01 and Short TernDebt/Reserves in 98,99,00,02. Public External Debt/GDP is replaced by Revenue/GDP in 1992,93, 98,99Figure 3: Rolling Trees’Thresholds

- 44 -0,6002,5000,5000,4000,3000,2000,1000,00019891990199119921993199419951996up to year1997199819992000200120022,0001,5001,0000,5000,000TotExtDebt/GDPInflationRealGrowthPubExtDebt/Rev(right scale)ExtFin'Ireq's (right scale)