World Commodity Prices and Partial Default inEmerging Markets: An Empirical Analysis∗

Manoj Atolia†

Florida State UniversityShuang Feng‡

Florida State University

June 20, 2019

AbstractMost sovereign defaults are partial and commodity prices are an important determi-

nant of sovereign default. In this paper, we construct and use a novel country-specificcommodity price index with time-varying weights based on commodity exports to quan-tify the impact of commodity prices on partial default rate in a panel of 21 emergingcountries with annual observations from 1970 to 2013.

Our empirical estimates show that declines in world commodity prices have a sig-nificant, positive effect on the default rate. For the level of price index, a one-standarddeviation decrease at its 1st, 2nd, and 3rd quartile, on average, raises partial defaultrate by 9.9, 7.6, and 5.4 percentage points respectively. For the change in the priceindex, a one-standard deviation decrease at its 1st, 2nd, and 3rd quartile raises partialdefault rate by 4.8, 4.2, and 3.4 percentage points respectively. For a one-standarddeviation decrease in a composite of the level and the change of price index, the ef-fects are 12.2, 9.4, and 5.8 percentage points respectively. Our tests of endogeneity,including the use of the Bartik instrument, do not find the evidence of endogeneityof the country-specific commodity price index. Across countries, our empirical resultsimply that for a country-specific one-standard deviation decrease of the composite ofprice index, the effect on the default rate varies from insignificant to an increase of 26.5percentage points. The country-specific response of the default rate generally increasesin magnitude with the commodity exports and external indebtedness.

Keywords: Sovereign default, commodity prices, partial default, emerging countriesJEL Classification: F34; F41; H63

∗We thank Tamon Asonuma, Seungjun Baek, Paul Beaumont, Javier Cano-Urbina, Mikhail Dmitriev,Gary Fournier, Shawn Kantor, Carl Kitchens, Jonathan Kreamer, Milton Marquis, Leonardo Martinez,Anastasia Semykina, Cynthia Yang, and participants at the FSU Macro Workshop and Quant Workshopfor useful comments and suggestions. We would also like to thank Santanu Chatterjee, John Gibson, BernaKarali, and other participants at the 12th Southeastern International/Development Economics Workshopheld at the Federal Reserve Bank of Atlanta for their valuable comments. All errors remaining are ours.†Department of Economics, Florida State University, Tallahassee, FL 32306. Email: matolia@fsu.edu.‡Department of Economics, Florida State University, Tallahassee, FL 32306. Email: sf12e@my.fsu.edu.

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1 Introduction

Most sovereign defaults are partial and commodity prices are an important determinant ofsovereign default. In this paper, we construct and use a novel country-specific commodityprice index with time-varying weights based on commodity exports to quantify the impactof commodity prices on partial default rate in a panel of 21 emerging countries with annualobservations from 1970 to 2013. Methodologically, as the majority of observations of thepartial default rate in our study (besides being bounded) pile up at zero, to properly capturethis feature of data, our econometric analysis employs a fractional response model for paneldata (Papke and Wooldridge, 2008). Our estimates show that declines in world commodityprices have a significant, positive effect on the default rate—on an average 12.2, 9.4, and5.8 percentage points increase at the 1st, 2nd, and 3rd quartiles of a composite of thecommodity price index—with considerable cross-country variation. The country-specificresponse of default rate to the price index is found to generally increase in magnitude withthe commodity exports and external indebtedness. Our tests of endogeneity, including theuse of the Bartik instrument, show no evidence of the endogeneity of the country-specificcommodity price index. We carry out a few robustness tests; our main results continue tohold with no significant difference.

A number of features of our approach, combined together, allow us to provide, to ourknowledge, the first economically-significant quantitative estimates of the effect of commod-ity prices on the default rate. These features or contributions of the paper vis-a-vis theexisting literature can be summarized as follows.

The first feature relates to the construction of the country-specific commodity price indexmentioned above. Our price index simultaneously accounts for annual changes in the relativevalues of commodity exports and employs a broad-based, two-stage aggregation of variouscommodity prices using the dynamically-weighted Jevons formula (IMF, 2009). Incorporatingthe changing structure of exports in constructing our price index allows us to use a longertime period for our empirical analysis, despite a significant evolution of export structurefor many countries in our study. Also, the country-specific nature of the price index helpsus to control for common, global shocks. Our endogeneity tests, including the use of theBartik instrument, show that a country’s export structure, which is used to construct thecountry-specific commodity price index, does not cause an endogeneity problem.

Secondly, this paper focuses on the response of the partial default rate, a proxy forrealized sovereign default risk, to the fluctuations in world commodity prices. Earlier studieshave used a binary, default event, credit ratings, and/or CDS/EMBI spreads, which proxy

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anticipated default risk, as the response variables.1 The use of CDS/EMBI spreads in theexisting literature restricts the beginning of the period of analysis to the early 1990s, whereasthe use of the partial default rate allows us to do analysis using a longer time span ofdata, when combined with our country-specific price index with a similar, longer time span.Moreover, while theoretical models predict a tight relationship between spreads (capturinganticipated risk) and default variables such as default frequency (capturing realized risk),their numerical simulations fail to simultaneously match both dimensions of the data.2 Inlight of the empirical failure of this predicted theoretical relationship, it is useful to extendthe existing literature which so far focuses on spreads by using the partial default rate as aresponse variable in its own right.

Finally, the observations of the partial default rate are not only naturally bounded be-tween zero and one, but in our study, the majority of them also pile up at one of theboundaries, zero. For our econometric analysis, we use a fractional response model for paneldata introduced in Papke and Wooldridge (2008), which properly takes these features of thedata on the partial default rate into account. This method improves upon the two-limitTobit model which is the frequently-used alternative for such data.3

The fluctuations in world commodity prices are associated with sovereign default risk inemerging countries. Bulow and Rogoff (1989) note that, besides rising world interest rates,adverse shocks to terms-of-trade (which were driven by collapsing global commodity prices)precipitated the string of sovereign defaults throughout the emerging markets in the 1980s,following the commodity boom of the earlier decade. Reinhart and Rogoff (2009, Figure 5.5)observed that global commodity prices’ troughs are followed by multiple sovereign defaults.Typically, the declines in terms-of-trade are associated with economic slowdown and balanceof payments problems, which raise default risk. Economic slowdown reduces the ability ofthe government to service the (external) debt due to reduced tax revenues. Deterioration inbalance of payments results in reduced ability to muster enough foreign exchange to honorthe payments. In the case of many emerging countries, which are big commodity exporters,yet another channel operates to augment these forces as in these countries revenues from

1There is some variation in the definition of default in the literature. For example, in some cases, it in-cludes debt rescheduling with official creditors (Borensztein and Panizza, 2009; Detragiache and Spilimbergo,2001). A complementary literature on sovereign debt rescheduling/restructuring measures realized (ex post)losses or “haircuts” for the investors. See Asonuma and Trebesch (2016), Sturzenegger (2004), Sturzeneggerand Zettelmeyer (2005), and Trebesch and Zabel (2017).

2See Arellano (2008), Arellano and Ramanarayanan (2012), and Chatterjee and Eyigungor (2012).3We carry out the sensitivity analysis for the baseline regressions, by changing the methodology to the

two-limit Tobit model. Although the marginal effects of the two-limit Tobit analysis show that the significant,negative effects of commodity prices on the default rate hold without significant differences in magnitude,the two-limit Tobit model does not allow the variation of average marginal effects (AMEs) with respect tothe variation of the price index. The results for the two-limit Tobit model are available upon request.

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the sale of or the royalties on commodities are a significant part of the government revenues.Thus, declines in commodity prices also directly reduce government’s resources to servicethe external debt, increasing chances for default.

Although, early sovereign debt literature treated default as a binary event, most sovereigndefaults are partial (e.g., see Alfaro and Kanczuk, 2009). Easton and Rockerbie (1999)stressed the importance of incorporating default as a matter of degree in models of lendingto less-developed countries. Arellano, Mateos-Planas, and Rios-Rull (2013) introduced thenotion of partial default in Eaton and Gersovitz’s (1981) framework. Among other recenttheoretical studies of partial default, Aguiar, Amador, Farhi, and Gopinath (2014) studiedpartial sovereign default-by-inflation in the context of a monetary union. Alfaro and Kanczuk(2009) also mentioned the likelihood of partial default via taxation. Dubey, Geanakoplos,and Shubik (2005), in a standard general equilibrium model with incomplete markets, notethat because of the consideration of reputation, or because of collateral guarantees, thereexists at least partial repayment.

Thus, the evidence shows that most defaults are partial and commodity prices are animportant determinant of sovereign default. The existing empirical work studying the effectof macroeconomic fundamentals on sovereign default risk (sovereign yield spreads) has fo-cused more on terms-of-trade than on commodity prices. In our view, there are two reasonsfor this choice. First, compared to commodity prices, terms-of-trade are a more broad-basedmeasure of country’s ability to pay and thus deserve to be analyzed in their own right asa determinant of the sovereign default risk. Second, it is well known that, in the case ofmost emerging countries, terms-of-trade are driven, to a great extent, by trends in globalcommodity prices. Therefore, for these countries, in the absence of the availability of acountry-specific commodity price index, terms-of-trade may be considered as a useful proxyfor commodity prices.

Specifically, in the empirical literature on the determinants of sovereign risk/default, Bal-dacci, Gupta, and Mati (2011) investigated the (fiscal and political) determinants of countryrisk premium, measured by sovereign bond spreads, using a panel of 46 emerging economiesfrom 1997 to 2008. The authors concluded that the level of terms-of-trade has the expectednegative and statistically significant effect on spreads. Zinna (2013) extracted a measureof risk aversion at a daily frequency for eight of the most traded emerging markets (EM)by using a credit default swap (CDS) term-structure model and examined how global andlocal factors co-move with the EM risk premium measure at a high frequency (weekly anddaily). In particular, the author assessed the relationship between the EM risk measure andboth the level and the change of Goldman Sachs Commodity Index (GSCI). Maltritz (2012)analyzed the determinants of sovereign yield spreads of 10 European Monetary Union mem-

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bers over the period 1999–2009 and concluded that changes in terms-of-trade affect sovereignyield spreads negatively and significantly. Similarly, Aizenman, Binici, and Hutchison (2013)investigated the impact of changes in GSCI and the oil price on CDS spreads in EuropeanUnion countries using monthly data from January 2005 to August 2012. They showedthat CDS spreads consistently decrease with increase in the changes in GSCI and oil price.Hilscher and Nosbusch (2010) showed that both the change in terms-of-trade as well as itsvolatility are the determinants of yield and also important predictors of emerging marketbond index (EMBI) spreads.4

There is also an additional empirical literature that uses commodity prices, but thatfocuses on implications for other macroeconomic outcomes, not for sovereign default.5 Forexample, focusing on the structural linkage between exchange rates and commodity pricesthrough the terms-of-trade and income effects, Chen, Rogoff and Rossi (2010) investigatedthe dynamic relationship between the fluctuations in exchange rates and the movement ofcommodity prices.6 Chen and Lee (2018) examine the heterogeneity of the response of thereal effective exchange rate to world commodity price shocks in a panel of 51 commodityexporters over 1980–2010. The country-specific real commodity price index applied in thisstudy is defined as the world nominal prices of a country’s major commodity exports, whichis deflated by the price index of the manufactured exports of all industrial economies.7 Fer-nandez, Gonzalez, and Rodriguez (2018) estimate the effect of a country-specific commodityprice measure on the aggregate fluctuations in Brazil, Chile, Colombia, and Peru. The au-thors create a country-specific commodity price index using the information on prices of44 commodities and country-specific annual average (constant) export weights over the pe-riod 1999–2004. Fernandez, Schmitt-Grohe, and Uribe (2017) predict how world commodity

4There is also a strand of literature that analyzes the impact of terms-of-trade volatility on sovereignrisk premium. For example, Aizenman, Jinjarak, and Park (2016) have assessed the relative importanceof various economic fundamentals in accounting for sovereign CDS spreads in Asian and Latin Americanemerging markets during 2004–2012. They show that terms-of-trade volatility is positively associated withCDS spreads. By breaking down the aggregate volatility into its external and domestic policy componentsand by using a panel of 25 emerging markets over 1970–2001, Catao and Sutton (2002) concluded thatcountries exposed to higher terms-of-trade volatility do appear to have a higher propensity to default. Cataoand Kapur (2006) showed terms-of-trade volatility is highly significant in explaining sovereign risk, measuredby binary default events or rescheduling.

5In a work more closely related to our work, Hilscher and Nosbusch (2010) constructed country-specificcommodity export price indices with the prices of 12 individual commodities. However, they used them toeliminate the endogeneity of their terms-of-trade measure.

6The authors showed that there is a robust relationship between exchange rates and commodity prices:Exchange rates are very useful in forecasting future commodity prices. This paper focuses on the market’sown dynamics rather than the policy interventions by small commodity-exporting economies who havemarket-based floating exchange rates and are global commodity price takers.

7They find that the high degree of market power, measured by the shares in the global markets of acountry’s specific products, can reduce the exchange rate response in the long-run while an inflation target(IT) regime can amplify it in the short-run.

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price shocks explain the movements of domestic output in individual countries. They use thecyclical components of three US CPI-deflated global commodity price indices (Fuel, Agri-culture, and Metals and Minerals from the World Bank’s Pink Sheet) as the proxies forworld shocks. These price indices average the prices of representative individual commodi-ties using global weights.8 Ricci, Milesi-Ferretti, and Lee (2013) estimate the co-integratingrelationship between real exchange rates and a set of fundamentals such as productivitydifferentials, external imbalances, and commodity terms-of-trade. The commodity terms-of-trade is a weighted average of the prices of the major export commodities for a country (withcountry-specific weights), divided by a weighted average of the prices of the major importcommodities.9 In contrast to these papers, our price index uses country-specific, time-varyingweights and our study focuses on the implications on sovereign default risk.

This paper contributes to the empirical literature on sovereign default by investigatinghow the fluctuations in world commodity prices affect sovereign default rates in emergingmarkets. For this purpose, it uses a novel dataset consisting of an annual, country-specificcommodity price index and partial default rate for a panel of 21 emerging countries over theperiod 1970–2013. Following the literature surveyed above (Aizenman, Binici, and Hutchi-son, 2013; Baldacci, Gupta, and Mati, 2011; Hilscher and Nosbusch, 2010; Maltritz, 2012;and Zinna, 2013), the paper examines the effects of both the level and the change of com-modity prices on the partial default rate. Given the fact that many of the emerging countriesin our study have a large proportion of commodities in their exports and high levels of theexternal debt denominated in foreign currencies, our paper also explores how the effect ofcommodity prices on the default rate varies with a country’s dependence on commodityexports and external indebtedness. This exercise is also informed by the fact that, beinga direct source of the government revenues for these countries, the amount of commodityexports is also an important determinant of their default behavior. The significance and thedirections of the effects of other macroeconomic fundamentals on the default rate are alsoanalyzed.

In particular, this paper applies a fractional response Probit model to 21 emerging coun-tries, which are so categorized by IMF analysts and have external public debt arrears in-formation over the period 1970–2013. Those countries are located in Africa, the Americas,Asia, Eastern Europe, and the Middle East. Our results show that both the level and the

8In one of our endogeneity tests, we use the world commodity price indices (Energy, Non-energy, andPrecious Metals) as instrument.

9In Ricci, Milesi-Ferretti, and Lee (2013), the commodity price-based terms-of-trade is constructed fromthe prices of six commodity categories (Food, Fuels, Agricultural Raw Materials, Metals, Gold, and Bever-ages) and measured against the manufacturing unit value index of the WEO database. It is weighted bythe time-average (1980–2001) of export and import shares of each commodity category in the total trade(exports and imports of goods and services) defined in SITC II.

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change of world commodity prices, negatively affect the partial default rate. For the level ofthe price index, a one-standard deviation decrease at its 1st, 2nd, and 3rd quartile raises thepartial default rate, on average, by 9.9, 7.6, and 5.4 percentage points, respectively. For thechange in the price index, a one-standard deviation decrease at its 1st, 2nd, and 3rd quartileraises the partial default rate, on average, by 4.8, 4.2, and 3.4 percentage points, respectively.A one-standard deviation decrease in the composite of the level and the change of price indexat its 1st, 2nd, and 3rd quartile increases the default rate, on average, by 12.2, 9.4, and 5.8percentage points, respectively. For a country-specific one-standard deviation decrease ofthe composite, this effect varies from insignificant to an increase of 26.5 percentage points.The country-specific response of the partial default rate to the commodity price index gen-erally increases in magnitude with the commodity exports and external indebtedness. Ourtests of endogeneity, including the use of the Bartik instrument, do not find the evidence ofendogeneity of the country-specific commodity price index. We carry out a few robustnesstests and our main results continue to hold with no significant difference.

We also examine the role of other determinants of the partial default rate. Default historyis found to positively and significantly (in statistical sense) affect the partial default rate.The effect of the domestic credit-to-GDP ratio is also positive and statistically significant.Net capital transfers-to-GDP ratio and official flows and grants-to-debt service ratio, whichrepresent other international resources, negatively and significantly affect the partial defaultrate. The directions of the effects of an exchange rate peg (negative), being a member ofOPEC (positive), international reserves-to-debt service ratio (negative), the growth rate ofGDP (negative), and inflation (positive) are also as expected. Overall, these findings arefairly robust and consistent with economic intuition.

The remainder of this paper is organized as follows. The next section provides detailsof the steps for data preparation, especially for the partial default rate and the two-tier,dynamically-weighted price index. Section 3 introduces the fractional response model forpanel data and outlines other details for the model specification. Section 4 collects theestimation results for the baseline and alternative regressions. In Section 5, two endogeneitytests are conducted for the baseline regressions. Section 6 investigates the country-specific,overall response of the partial default rate to the price index and its variation with thedegree of the dependence on the commodity exports and the external indebtedness. Section7 checks the robustness of the main results. The last section concludes.

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2 Data

This paper concentrates on explaining the effects of fluctuations in world commodity priceson partial default rate across countries and time. For this purpose, we use data on publicand publicly guaranteed (PPG) external debt, world commodity prices, commodity exportstructure, interest rates, exchange rate regimes, international reserves, official flows, capitaltransfers, output (GDP), domestic credit, and inflation. Data on international reserves,official flows, GDP, domestic credit, and inflation are from World Bank Open Data, rangingfrom 1970 to 2013 annually. Data on exchange rate regimes is from Shambaugh (2004).The information of capital transfers is from IMF Balance of Payments Statistics (BOPS).More information about the data, including abbreviations, sources, and measurements aresummarized in the Appendix.10

In the next two subsections, we outline the details for the creation of the partial defaultrate and the country-specific commodity price index which are the two important variablesfor our empirical analysis.

2.1 Partial Default Rate

Easton and Rockerbie (1999) were first to stress the importance of incorporating defaultas a matter of degree in models of lending to less-developed countries. This perspective isin accordance with the fact that most sovereign defaults are partial (Alfraro and Kanczuk,2009), although, the early sovereign debt literature treated default as a binary event.

The partial default rate is defined as the ratio of the (end-of-period cumulative) debtarrears on external debt to the (beginning-of-period) debt service obligations, which consistof the previous period debt arrears and the amounts of principal and interest due:

Partial Default Rate = Debt Arrears

Debt ServiceObligations= Debt Arrears

DebtArrears+ Actual Debt Service(1)

The expression on the right hand side of the second equality sign follows from the fact that thedebt service obligations can also be written as the (end-of-period cumulative) debt arrearsand actual debt service payments (e.g., also see Arellano, Mateos-Planas, and Rios-Rull,2013).

The data on external debt (PPG), including debt arrears and service, comes from theWorld Development Indicator (WDI), part of World Bank Open Data, ranging from 1970to 2013 annually, with shorter periods for some countries (see Table 1). Being a proportion,the partial default rate is always bounded between 0 and 1.

10Appendix, Table A.1: Variables (Abbreviation), Data Source, and Measurement

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Table 1: Statistics of Partial Default Rate (1970–2013)Country Mean Std. Dev. Frequency of

Positive ArrearsMean Conditional

on Positive Arrears

Argentina 0.3435 0.3721 0.7045 0.4876Brazil 0.1348 0.2049 1.0000 0.1348Colombia 0.0161 0.0347 0.5455 0.0295Ecuador 0.1605 0.2868 0.7955 0.2018Mexico 0.0015 0.0085 0.2045 0.0074Peru 0.2613 0.3934 0.7045 0.3709Venezuela, RB 0.0635 0.1258 0.7727 0.0821China (1981–2013) 0.0000 0.0000 0.0000 0.0000India 0.0000 0.0001 0.0455 0.0003Indonesia 0.1067 0.2080 0.5000 0.2134Malaysia 0.0000 0.0000 0.2045 0.0000Pakistan 0.0084 0.0508 0.1364 0.0618Philippines 0.0298 0.0821 0.6136 0.0486Thailand 0.0004 0.0014 0.1364 0.0028Bulgaria (1981–2013) 0.1497 0.2828 0.4545 0.3294Nigeria 0.2668 0.3481 0.8636 0.3089Romania (1976–1989, 1991–2013) 0.0241 0.0522 0.3243 0.0525Russian Federation (1992–2013) 0.4115 0.3528 1.0000 0.4115South Africa (1994–2013) 0.0000 0.0000 0.1000 0.0000Turkey 0.0048 0.0197 0.2045 0.0233Ukraine (1992–2013) 0.2913 0.2121 1.0000 0.2913Total (Number of Observations: 827) 0.1001 0.2319 0.4837 0.2045

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Figure 1: Partial Default Rate (Americas)

Figure 1 to Figure 3 plot the time series of partial default rates for 21 emerging economies,as defined by the IMF and with debt arrears information available in the WDI database.11

Table 1 summarizes the essential statistics: the mean, standard deviation, positive arrearsfrequency, and positive arrears-conditional mean of the partial default rate. Figure 4 andFigure 5 display the histograms of the partial default rates and the non-zero partial defaultrates, respectively.

The following five features of default (rate) data deserve mention: (1) Sovereign defaultsare almost, always partial: the only case of nearly full default is Peru with the highestpartial default rate of 0.99; (2) The majority observations of default rates are piling up atzero, implying no default, as shown in Figure 4; (3) (Partial) default, however, is also quitefrequent: the average frequency of positive arrears is 0.48; (4) Partial default rates vary alot: the average standard deviation is 0.23, although, even for the non-zero partial defaultrates, the majority of observations are located between 0.00 and 0.20 (see Figure 5); and (5)The partial default rate is heterogeneous across countries and regions, averaging from 0.00 to0.49 during default years. Compared with emerging countries in Asia, emerging countries inthe Americas and EMA (Eastern Europe, the Middle East, and Africa) have higher averageannual default rates.

11Emerging Markets by Each Group of Analysts: https://en.wikipedia.org/wiki/Emerging markets

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Figure 2: Partial Default Rate (Asia)

Figure 3: Partial Default Rate (Eastern Europe, Middle East, and Africa)

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Figure 4: The Histogram of Partial Default Rate

Figure 5: The Histogram of Non-Zero Partial Default Rate

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2.2 Country-Specific Commodity Price Index

This paper focuses on the impact of fluctuations in world commodity prices on sovereigndefault rate. In order to capture the impact of variations in world commodity prices onindividual countries, we create a country-specific commodity price index for a country’sexports. The price index is constructed based on the methods outlined in Export andImport Price Index Manual (IMF, 2009).

Fernandez, Gonzalez, and Rodriguez (2018) create country-specific commodity price mea-sures for Brazil, Chile, Colombia, and Peru and estimate its effect on the aggregate fluctua-tions in these countries. The authors create country-specific commodity indices for 1980–2014with the information of 44 commodities’ prices. They, however, use constant weights (av-erages of 1999–2004 period) in the price index for various commodity groups, which is areasonable assumption for estimation and analysis over the period 1980–2014.

Fernandez, Schmitt-Grohe, and Uribe (2017) use data from World Bank’s Pink Sheet toconstruct three separate world commodity price indices for the cyclical components of Fuel,Agriculture, and Metal and Minerals, deflated using the US CPI. These indices are averageprices of representative individual commodities weighted by world shares, which they use topredict how world shocks explain the movements of domestic output in individual countries.

Our index advances these efforts in the following ways. Vis-a-vis Fernandez, Gonzalez,and Rodriguez (2018), we allow for time variation in the weights in the construction of thecountry-specific price index. This is necessary for our empirical study, as over the periodunder our study, 1970–2013, there has been a substantial change in the export structure ofmany emerging countries. In relation to Fernandez, Schmitt-Grohe, and Uribe (2017), weuse country-specific export weights to capture the impact of fluctuations in world commodityprices that is specific to a country.

The construction of the index involves two stages. In the first stage, price indices areestimated for dynamically-weighted elementary aggregates. In accordance with the IMFmanual, elementary aggregates are constructed by grouping individual commodities andservices into groups of relatively homogeneous commodities and services, expected to havesimilar price movements. Besides satisfying the above criteria, commodities selected for con-structing elementary aggregates in this paper satisfy the following requirements as well: theyare representative of all commodities within the elementary aggregates with large enoughglobal transaction volumes and remain on the market for some time to reduce disappearingand replacement situations. These commodities are identified with the information of globalcommodity prices in the Global Economic Monitor (GEM) commodity database, part of

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World Bank Open Data.12 The second stage averages elementary price indices to obtainhigher level indices by using as weights the country-specific dynamic relative traded (export)values for elementary aggregates.

There are various ways of aggregating individual prices in an index at both stages. TheIMF manual discusses the Carli index, the Dutot index, and the Jevons index. There aretwo approaches to select the most suitable formula to combine the elementary price indices:the axiomatic approach and the economic approach. This paper follows the axiomatic ap-proach, which requires that the method selected should satisfy certain specified axioms ortests.13,14 Based on the axiomatic approach, The Jevons index is selected and is used to yielda two-stage dynamically-weighted and chained year-to-year index formula. For individualcommodity m in the elementary aggregate n with real price pm and relative export valueweight wm, the price index for that elementary aggregate n is given by:

P tn =

∏m

(p2m

p1m

)w1m∏m

(p3m

p2m

)w2m · · ·

∏m

( ptm

pt−1m

)wt−1m (2)

where t ≥ 2 and ∑m wsm = 1, s = 1, 2, ..., t−1. In the second stage, elementary price indices

are aggregated to obtain higher level indices by using the country-specific dynamic relativeexport values for associated elementary aggregates as weights. Finally, the price index isdeflated by the US CPI as in Fernandez, Schmitt-Grohe, and Uribe (2017).

Table 2 reports the statistics, including the mean, standard deviation, and minimum andmaximum, of the original price index. The reference year for the index is 1970. The averagevalue is 90.40 with standard deviation of 89.72, implying large fluctuations in the price index.The distribution (shown in Figure 6) of the price index is highly skewed to the right, but themajority of observations are below 200. This gives a rough idea of the spread of the priceindex and how it is affected by the extreme values. These extreme values are caused by theheterogeneity of the price index across countries: a country-specific price index is not only

12Appendix, Table A.2: The Category Structure of Global Economic Monitor (GEM) CommoditiesDatabase as Presented in the Commodity Price Data (a.k.a. Pink Sheet)

13There are five basic tests of the axiomatic approach: proportionality test, changes of units of measure-ment test, time reversal test, transitivity test, and allowing for substitution test. The Carli index fails thetime reversal, transitivity, and allowing for substitution tests. The Dutot index fails changes of units ofmeasurement and allowing for substitution tests. The Jevons index, on the other hand, passes all the tests(IMF, 2009, Table 10.2).

14The economic approach requires a specific sample design involving quantities or value shares to translatea sample unweighted elementary index into an estimator of a weighted overall index and needs a checkas to whether this estimated weighted index is an appropriate target, that is, one based on the behavioralassumptions of the enterprises or households responsible for exporting or importing the commodities. In otherwords, by taking account of the interdependence between prices and quantities and by making necessarybehavioral assumptions of exporter/importer, the economic approach aims to estimate an “ideal” or “true”economic index for the elementary aggregates.

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Table 2: Price Index deflated by US CPI (1970–2013)Country Mean Std. Dev. Min. Max.

Argentina 49.51 27.39 20.70 145.1Brazil 53.68 34.57 16.60 155.2Colombia 86.72 51.51 38.40 234.7Ecuador 150.7 85.68 39.65 318.1Mexico 190.0 105.3 58.24 451.5Peru 73.26 54.89 17.11 223.0Venezuela, RB 226.4 125.3 70.74 536.1China 106.7 88.21 25.64 336.1India 51.59 45.14 14.32 196.8Indonesia 137.5 112.1 34.42 386.3Malaysia 92.67 46.29 29.93 209.4Pakistan 41.81 32.34 13.51 139.2Philippines 47.48 32.76 18.45 180.1Thailand 48.83 35.28 16.08 179.9Bulgaria 37.98 28.27 15.00 124.2Nigeria 225.3 123.9 72.66 535.9Romania 38.87 32.86 13.67 148.2Russian Federation (1992–2013) 148.7 60.51 75.36 265.0South Africa 59.57 25.12 29.05 155.6Turkey 53.87 30.45 18.66 122.6Ukraine (1992–2013) 108.0 25.13 78.21 157.7Total (Number of Observations: 880) 90.40 89.72 13.51 536.1

determined by world commodity prices, but also by the country’s own commodity exportstructure. Countries, such as Ecuador, Mexico, and Venezuela in the Americas, Indonesiain Asia, and Nigeria in EMA, have high mean and extremely high maximum values.

3 Model Specification

This section begins with the discussion of the appropriate econometric model to use in lightof the properties of the dependent variable, the partial default rate. Recall, we focus onthe response of the partial default rate to the fluctuations in world commodity prices as itis a proxy for the realized sovereign default risk. Thereafter, the section delves, into theappropriate choice for the main independent variable related to commodity prices and othercontrols.

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Figure 6: The Histogram of Price Index deflated by US CPI

3.1 The Fractional Response Model

Fractional response model (FRM) is an econometric approach that is capable of modelingbounded dependent variables (BDVs),15 which exhibit piling-up at one of the two bound-aries (or corners). The fractional response model for cross-sectional observations was firstlyintroduced by Papke and Wooldridge (1996), which was extended to panel data in Papkeand Wooldridge (2008).

The fractional response model for cross-sectional observations is an extension of the gen-eral linear model (GLM). Denote y (0 ≤ y ≤ 1) as the dependent variable, which is explainedby a 1 × K vector of explanatory variables x ≡ (x1, x2, . . . , xK) with x1 ≡ 1. The linearpopulation model is

E(y|x) ≡ β1 + β2x2 + · · ·+ βKxK = xβ

where β is a K × 1 vector, providing the description of the effect of any particular xj, j =1, 2, . . . , K. However, there are two main limitations of the linear population model. Thefirst limitation is the predicted values of the model may be outside the natural interval. Thesecond limitation is the estimated partial effects are constant and independent of the valueof the predictor. Non-linear functional forms are used for generating various partial effects.The log-odds ratio method

E[log( y

1− y )|x] = xβ

15As Gallani and Krishnan (2017) note, BDVs are variables bounded when they can only assume valueslimited by a minimum value (bounded below), or a maximum value (bounded above), or both. BDVsprimarily arise in four research situations: naturally bounded (proportions and probabilities), research designof category variables such as bond ratings, researchers’ restrictions such as top coding, and a consequenceof missing data beyond a certain limit.

16

is commonly used to deal with the first limitation of linear models, as the LHS of its expres-sion can take any value as y varies between zero and one. However, this method cannot bevalid if y equals zero and/or one.

The fractional response model for cross-sectional data provides an alternative approachto the studies of variables bounded at both extremes where observations “pile-up” at oneend of the distribution. The basic assumption is

E[yi|xi] = G (xiβ)

where {(xi, yi) : i = 1, 2, ..., N} is an independent sequence of observations, with 0 ≤ yi ≤ 1.N is the sample size. G(�) is a known function satisfying 0 < G(z) < 1 for all z ∈ R.16 Thisensures the predicted values of yi lie in the interval (0, 1). This model is well-defined even ifyi can take on 0 or 1 with positive probabilities. There is no assumption about an underlyingstructure that is used to obtain yi. yi could be a continuous variable, discrete variable, orhave both continuous and discrete characteristics.

The panel data method of the fractional response model used in this paper is proposed inPapke and Wooldridge (2008) as a nonlinear panel data model that recognizes the boundednature of the dependent variable. For an observation for cross-section i and time period t,the dependent variable is yit(0 ≤ yit ≤ 1), and a set of explanatory variables xit is a 1×Kvector.

The assumption (Assumption 1.) is

E(yit|xit, ci) = G(xitβ + ci), t = 1, . . . , T (3)

where ci is the unobserved effect. The K×1 vector β describes the directions of partial effects.By dropping the cross-sectional index i, the partial effect for continuous xjt, j = 1, . . . , K is

∂E(yt|xt, c)∂xjt

= βjg(xtβ + c) (4)

where g(�) is the probability density function. And the partial effect for discrete changes is

G(x(1)t β + c)−G(x(0)

t β + c) (5)

where x(1)t and x(0)

t are two different values of covariates.According to Papke and Wooldridge (2008), two additional assumptions are needed to

16G(�) is chosen to be a cumulative distribution function (c.d.f.), either the logistic or the standard normalc.d.f., but need not to be.

17

identify the average partial effects and β. The first additional assumption (Assumption 2.)concerns the exogeneity of {xit, t = 1, . . . , T}. Specifically, it is assumed that {xit, t = 1, . . . , T}is strictly exogenous conditional on ci:

E(yit|xi, ci) = E(yit|xit, ci), t = 1, . . . , T (6)

where xi ≡ (xi1, . . . , xiT ) is the set of covariates in all time periods. It rules out the laggeddependent variables in xit, as well as other predictors that may react to past changes in yit.

The second additional assumption (Assumption 3.) is the conditional normality as-sumption imposed on the distribution of ci. Instead, our analysis uses country dummies tocontrol for the unobserved time-invariant effect. Thus, the estimation of βj is possible up toa common scale factor, along with the consistent estimation of average partial effects. Thethree assumptions impose no additional distributional assumptions on the distribution ofdependent variable and they place no restrictions on the serial dependence in the dependentvariable across time.

By assuming G(�) = Φ(�), Bernoulli Quasi-maximum likelihood estimator (QMLE) solves

maxb

N∑i=1{yit ln Φ (xitβ + ci) + (1− yit) ln [1− Φ (xitβ + ci)]} (7)

which avoids a two-step estimation of a pooled weighted nonlinear least squares (PWNLS)estimator.17,18 The “pooled fractional probit” (PFP) estimator is consistent whenever theconditional mean is correctly specified. The assumption

V ar(yit|xi, ci) ≡ σ2Φ (xitβ + ci) [1− Φ (xitβ + ci)] (8)

where 0 ≤ σ2 ≤ 1, holds for fractional response when yit is a proportion, or the number ofBernoulli draws is not observed.

3.2 The Choice of Explanatory Variables

The existing empirical work finds both the level and the change of commodity prices (aswell as terms-of-trade) to be important determinants of default risk (Aizenman, Binici, andHutchison, 2013; Baldacci, Gupta, and Mati, 2011; Hilscher and Nosbusch, 2010; Maltritz,2012; and Zinna, 2013). This paper, accordingly, examines the effects of both the level and

17As Papke and Wooldridge (2008) note, the Probit function leads to computationally simple estimatorsin the presence of unobserved heterogeneity or endogenous explanatory variables.

18See Equation (3.1) in Papke and Wooldridge (2008) for the PWNLS estimator.

18

the change of the (log of) country-specific commodity price index on the partial default rate.For the level specification, we allow for the possibility that the default rate may respond

to commodity prices with a lag. In particular, we experiment with a fourth-order geometriclag of the commodity price index, but the specification with only the first lag is found tohave the highest likelihood.19 Thus, we present results for the level specification for the firstlag of the commodity price index. We follow a similar approach for the change specification.For a fourth-order geometric lag of the change in the commodity price index, we find thatthe specification with equal weights on all four lags has the highest likelihood.20 Thus, wepresent results for the change specification for the average four-year price change in thecommodity price index. In either case, we also allow for interaction effects as discussed laterin this subsection. We, then, consider the specification that includes both the level and thechange of price index as determinants of the default rate to capture the overall effect ofcommodity prices on the default rate.

We also include other default determinants to isolate the effect of our main independentvariable(s).

The variables that account for the foreign revenue through commodity export which weinclude are commodity export-to-GDP ratio, exchange rate regime, and whether a countryis a member of the organizations of world commodity exporting countries, i.e., the Organiza-tions of the Petroleum Exporting Countries (OPEC). The estimations include the commodityexport-to-GDP ratio, because the foreign revenue through commodity export is determinedby the movements of both price and quantity. The choice of exchange rate regime is oftenguided by international trade considerations. According to Klein and Shambaugh (2010), asmall open economy’s exchange rate, whose value is pegged to the price of the main exportcommodity, would then depreciate with a fall in that price, helping to offset the contrac-tionary effects. One of the presumed benefits of exchange rate peg is that it should expandtrade, at least with the base country. The exchange rate peg is expected to have negativeeffect on the partial default rate. OPEC dummy is included to control the potential influence

19For this, we consider a geometric distributed lag model (DLM) (ρ ∈ [0, 1]) for the level:

β∑3s=0 ρ

s

(lnPt−1 + ρ lnPt−2 + ρ2 lnPt−3 + ρ3 lnPt−4

),

and the maximization of likelihood results in ρ = 0. We do not include current commodity price index toavoid the endogeneity problem.

20For this, we consider a geometric distributed lag model (DLM) (ρ ∈ [0, 1]) for the change:

β∑3s=0 ρ

s

[ln Pt

Pt−1+ ρ ln Pt−1

Pt−2+ ρ2 ln Pt−2

Pt−3+ ρ3 ln Pt−3

Pt−4

]and the maximization of likelihood results in ρ = 1.

19

of individual countries on the world price and production of crude oil, which is one of themost important global commodities, to eliminate possible endogeneity of world prices.

We also include variables that account for the debt payment situation of individual coun-tries, namely, whether a country has debt arrears in the previous year and the externaldebt-to-GDP ratio. Being in arrears can affect the incentive to repay in the current periodceteris paribus. The external debt-to-GDP ratio directly determines the level of debt obli-gation of an economy. These two factors are expected to have positive effects on the partialdefault rate.

In the literature, a number of other variables accounting for macroeconomic fundamentalshave been found to be relevant. Accordingly, we also include as controls official flows andgrants-to-debt service ratio and net capital transfers-to-GDP ratio (both of which representother sources of foreign revenue), international reserves-to-debt service ratio, the average 3-year change in real GDP, the domestic credit-to-GDP ratio,21 and inflation, where the lattertwo reflect domestic liquidity conditions.

The empirical specification also includes country and year effects. In particular, the yeareffects are used to control for all other global shocks. We are able to do so because we developand use a country-specific measure of commodity prices. Besides using year effects to controlfor global shocks, we also specifically control for the global interest rate by interacting it withthe external debt-to-GDP ratio to reflect the cost of rolling over debt or the opportunitycost of international lenders.

Finally, we allow for the possibility that the impact of commodity prices on the defaultrate may depend on other macroeconomic fundamentals. In particular, our specificationsallow for interaction of the commodity price index with the commodity export-to-GDP ratio,exchange rate peg, as well as the external debt-to-GDP ratio.22 That is, we allow for thefact that the magnitude of the effect of world commodity prices on default rate may dependon the values of the commodity export-to-GDP ratio, the exchange rate regime, and thedebt-to-GDP ratio.

21Lopez-Espinosa, Moreno, Rubia, and Valderrama (2017) show that high expected GDP growth and lowdomestic credit-to-GDP ratios protect countries against sovereign risk especially in times of global distress.

22A few articles in the literature include interaction variables in estimations, such as Aizenman, Jinjarak,and Park (2016), which apply interactions of crisis period (pre-, crisis, and post-) with region variables andwith industrial production, and Baldacci, Gupta, and Mati (2011), which used interactions of a new index ofaggregate political risk with high volatility of political index dummy and with a previous default dummy aswell as interactions of fiscal balance with high volatility of the political index dummy and with the previousdefault dummy.

20

4 Empirical Results

We apply the pooled Bernoulli QMLE method described in the previous section to investigatehow the fluctuations in world commodity prices are associated with sovereign default.

The results are organized as follows. Firstly, we report the results of the baseline andalternative regressions with country and time effects, where with the exceptions of the ex-change rate peg dummy, the OPEC dummy, and the default history dummy variables, allother control variables are lagged. These results show the directions of the effects of theprice index and other variables on the default rate. We also calculate the average marginaleffects (AMEs) of a one-standard deviation decrease in the level and the change of the priceindex at various quartiles showing the magnitude of the effect of commodity prices on thedefault rate. Secondly, we determine the overall effect of the price index by considering boththe level and the change of the price index. While the effects of the level and the changeof the price index are, as expected, not additive, the overall effect, is still larger than eitherone alone.

4.1 Separate Regressions with Level and Change of CommodityPrice Index

Table 3-1 and Table 3-2 contain the estimates of the OLS model (1) (for the comparison ofthe direction of the effect) and the various specifications of the fractional response Probitmodel (2)− (7) for the level and the change of the price index respectively.

4.1.1 Regressions with the Level of Price Index as the Regressor

In Table 3-1, the first panel contains the main independent variable, the lagged price level,and its interactions. The second panel collects other control variables that are commonacross all specifications. Two potential variables each are available for both capital inflowsand domestic inflation. These variables are collected in the third panel of Table 3-1 andvarious specifications examine different combinations of these variables. In particular, allfour different combinations, with one potential proxy each for capital inflows and domesticinflation, are considered. A specification that includes both potential variables for capitalinflows and domestic inflation is also explored.

Starting with the control variables, as expected, the default history positively affects thepartial default rate. The commodity trade-related variable exchange rate peg negativelyaffects the partial default rate. Being an OPEC member will increase the partial defaultrate significantly. The variables related to other sources of foreign revenue, the net capital

21

transfers-to-GDP ratio, and official flows and grants-to-debt service ratio, impact the partialdefault rate negatively as expected, as does the international reserves-to-debt service ratio.The effects of domestic credit-to-GDP of (2)− (7) are positively and statistically significant,which is consistent with the conclusion in Lopez-Espinosa, Moreno, Rubia, and Valderrama(2017). Other domestic variables, the average 3-year GDP change and the CPI inflationrate have expected negative and positive effects, respectively, in specification (3) and (4). Anumber of other direction coefficients in Table 3-1 are also found to be statistically significant.

For the lagged price index, specifications (1) − (7) draw a consistent conclusion: it hasa negative effect on the default rate. The coefficient for the lagged price index is -0.062 forthe OLS model and statistically significant. In fractional response model specifications, theestimated direction coefficient ranges from -0.914 to -0.707 and are all statistically significant,especially significant at 1-percent level for estimates with net capital transfers-to-GDP ratio(specifications (3), (4), and (7)). In the last panel of Table 3-1, we report the averagemarginal effects (AMEs) for various specifications for a one-standard deviation (0.850 unit)decrease in the lagged price index at its 1st, 2nd, and 3rd quartile. A decrease in laggedprice increases the partial default rate significantly. The AMEs at all three quartiles arefairly robust and do not change much for specifications (2)− (7). The strongest AME at the1st quartile is -0.116, or -11.6 percentage points. The strongest AMEs at the 2nd and 3rdquartiles are -0.106 and -0.078, respectively.

Specification (4) is highlighted in Table 3-1 because it is selected for further analysis inSubsection 4.2 for the overall effect with both the level and the change of the price indexincluded and, in Sections 5 – 7. This specification is selected for yielding overall effects thatare in the middle of those for the 5 different specifications considered in the paper.

4.1.2 Regressions with the Change in Price Index as the Regressor

Table 3-2 summarizes the results of the estimated effects of the average 4-year change in theprice index and is organized similar to Table 3-1.

The directions of the effects of exchange rate peg, OPEC, default history, internationalreserves-to-debt service, the average 3-year GDP change, net capital transfers-to-GDP ratio,official flows and grants-to-debt service, and CPI inflation rate for specifications (2)− (7) areconsistent with the expected directions and with the directions of the effects in Table 3-1.

Specifications (1)− (7) tell the same consistent story: the change in the price index hasa statistically-significant negative effect on the partial default rate. In fractional responsemodel specifications, the estimated coefficient for the average four-year change in the priceindex is from -3.491 to -2.806 for regressions (2) to (7). The AMEs at quartiles are againfairly robust and do not change much for fractional response model specifications, except

22

perhaps (7), when all variables are included. The strongest AME at the 1st quartile is -0.049,or -4.9 percentage points. The strongest AMEs at the 2nd and 3rd quartiles are -0.044 and-0.036 respectively. Once again, specification (4) is highlighted, as it has been selected forthe analysis of the overall effect in Subsection 4.2 and further analysis in Sections 5 – 7.

4.2 Composite Regressors and the Overall Effect of World Com-modity Prices

We begin by noting that the level and the change of the price index regressors used separatelyin the previous subsection are just different transformations of the same underlying data onworld commodity prices converted to a country-specific index. Thus, it is desirable to assessthe overall impact of commodity prices on the default rate by considering both price-index-based regressors in the same regression.

The estimation results in Table 4 include results for specifications (3) − (7) from Table3-1 and Table 3-2 with both the level and the change of the price index variables included.The new regression comes to conclusions that are consistent with the level and changespecifications for the (commodity) price index: both the level and the change of worldcommodity prices have negative and statistically significant effects on the partial defaultrate, except for the change in price in specification (7). The AMEs are once again verysimilar across various specifications. We next consider specification (4) in Table 3-1 andTable 3-2 and show that the overall effect of a one-standard deviation (0.230 unit) decreaseof the composite variable (consisting of the level and the change) at its 1st, 2nd, and 3rdquartiles, the AMEs are now -0.122, -0.094 and -0.058 respectively,23 which are seen to behigher than both the level and change specifications considered earlier. More generally, theranges of our estimates for various specifications at these quartiles are -0.135 to -0.120, -0.113to -0.092, and -0.071 to -0.057 respectively.

Also, consistent with the level and the change regressions, the other fundamentals con-tinue to have statistically significant and expected impact on the partial default rate. Defaulthistory positively and significantly (in statistical sense) affects the partial default rate. Theeffect of domestic credit-to-GDP ratio is also positive and statistically significant. Net capi-tal transfers-to-GDP ratio and official flows and grants-to-debt service ratio, which representother international resources, affect the partial default rate negatively. The directions of theeffects of an exchange rate peg (negative), whether a country is a member of OPEC (posi-tive), international reserves-to-debt service ratio (negative), the average 3-year GDP change(negative), and inflation (positive) are also as expected.

23As the two regressors are correlated, the standard deviation of the shock accounts for their correlation.

23

Table 3-1: Estimates of Effects of World Commodity Prices on Partial Default Rate (Level, Alternative Specifications)

ModelOLS FRM(1) (2) (3) (4) (5) (6) (7)

Variables βj-The direction of effectlagged price level -0.062* -0.707** -0.733*** -0.749*** -0.790** -0.811** -0.914***lagged price level*commodity export/GDP -0.312 -3.577 -1.691 -1.546 -2.961 -2.818 -0.251lagged price level*commodity

export/GDP*external debt/GDP

-0.450 -0.954 -0.059 -0.054 -0.757 -0.741 0.141

lagged price level*peg 0.058 0.400 0.378 0.380 0.427 0.431 0.353commodity export/GDP 1.962 16.073 9.750 9.321 12.959 12.478 3.779external debt/GDP 0.774** -0.283 2.253 2.090 -1.002 -1.199 0.887external debt/GDP*global interest rate 0.026 0.525 0.221 0.238 0.611 0.631 0.396peg -0.226 -1.603 -1.538 -1.546 -1.732 -1.745 -1.513default history 0.048 1.184*** 1.101*** 1.048*** 1.211*** 1.152*** 1.088***OPEC 0.146*** 0.681*** 2.235*** 2.226*** 0.620*** 0.619*** 2.023***int’l reserves/debt service -0.002 -0.021 -0.026* -0.024* -0.038 -0.036 -0.047*avg. 3-year GDP change -0.983* -3.509 -1.789 -1.828 -4.502* -4.621* -3.213domestic credit/GDP 0.070 0.763*** 0.746** 0.776** 0.815** 0.855** 0.873***

net capital transfers/GDP -13.627** -13.575** -15.793***official flows & grants/debt service -0.337* -0.341* -0.535***inflation deflator 5.230E-05 -3.190E-05 -1.458E-03*inflation CPI 7.050E-05 -1.130E-05 1.327E-03**

cons. 0.333* -2.521** -2.350** -2.361** -2.018* -2.015* -1.539obs. 663 663 524 513 663 652 513R-Square/pseudo R-Square 0.5346 0.4582 0.4471 0.4487 0.4625 0.4638 0.4590

24

Table 3-1: Estimates of Effects of World Commodity Prices on Partial Default Rate (Level, Alternative Specifications) (Contd.)

Model AMEs of 1 Std. Dev. at Quartiles

Std. Dev.: 0.850 1st (25%) 2nd (50%) 3rd (75%)

OLS (1) -0.075** -0.075** -0.075**

FRM

(2) -0.112*** -0.106*** -0.078***

(3): (2) + net capital transfers/GDP + inflation deflator -0.101*** -0.077** -0.054***

(4): (2) + net capital transfers/GDP + inflation CPI -0.099*** -0.076** -0.054***

(5): (2) + official flows & grants/debt service + inflation deflator -0.116*** -0.101*** -0.072***

(6): (2) + official flows & grants/debt service + inflation CPI -0.115*** -0.100*** -0.072***

(7): all variables are included -0.098** -0.070** -0.049***

Notes:– (1) and (2) include: lagged price level · interactions of lagged price level · commodity export/GDP · external debt/GDP ·external debt/GDP *global interest rate·

peg · default history · OPEC · int’l reserves/debt service · avg. 3-year GDP change · domestic credit/GDP.– Regressions include country and year effects. Clustered standard errors at country level.– * Significant at the 10-percent level.– ** Significant at the 5-percent level.– *** Significant at the 1-percent level.

25

Table 3-2: Estimates of Effects of World Commodity Prices on Partial Default Rate (Change, Alternative Specifications)

ModelOLS FRM(1) (2) (3) (4) (5) (6) (7)

Variables βj-The direction of effectavg. 4-year price change -0.167 -3.491*** -3.138*** -3.184** -3.333*** -3.337*** -2.806**avg. 4-year price change*commodity

export/GDP

3.433** 13.197 3.569 3.497 14.397 14.305 5.217

avg. 4-year price change*commodity

export/GDP*external debt/GDP

-12.323* -15.158 1.454 2.019 -18.151 -17.634 0.371

avg. 4-year price change*peg -0.306 -1.833 -1.083 -1.103 -1.654 -1.664 -1.120commodity export/GDP -0.516 -3.068 -0.288 -0.222 -3.118 -3.063 -0.104external debt/GDP 0.741** 0.015 1.932 1.831 -0.210 -0.300 1.422external debt/GDP*global interest rate -0.021 0.365 0.120 0.128 0.394 0.402 0.196peg -0.002 -0.140 -0.204 -0.210 -0.155 -0.159 -0.239default history 0.074** 1.240*** 1.090*** 1.051*** 1.204*** 1.173*** 1.032***OPEC 0.073 0.149 1.414** 1.407** 0.176 0.181 1.344**int’l reserves/debt service -0.002 -0.020 -0.027* -0.025 -0.025 -0.024 -0.038*avg. 3-year GDP change -1.071** -3.650 -3.564 -3.574 -3.846 -3.862 -3.794domestic credit/GDP 0.099 0.751** 0.651** 0.668** 0.763** 0.780** 0.749**

net capital transfers/GDP -15.906** -15.877*** -16.504***official flows & grants/debt service -0.241 -0.242 -0.368**inflation deflator 1.249E-04 1.233E-04 -1.102E-03**inflation CPI 1.334E-04* 1.295E-04 1.103E-03***

cons. 0.249*** -3.925*** -4.420*** -4.375*** -4.039*** -4.082*** -4.421***obs. 661 661 523 512 661 650 512R-Square/pseudo R-Square 0.5361 0.4517 0.4496 0.4512 0.4547 0.4557 0.4546

26

Table 3-2: Estimates of Effects of World Commodity Prices on Partial Default Rate (Change, Alternative Specifications)(Contd.)

Model AMEs of 1 Std. Dev. at Quartiles

Std. Dev.: 0.128 1st (25%) 2nd (50%) 3rd (75%)

OLS (1) -0.020* -0.020* -0.020*

FRM

(2) -0.049** -0.044** -0.036***

(3): (2) + net capital transfers/GDP + inflation deflator -0.047** -0.041** -0.033***

(4): (2) + net capital transfers/GDP + inflation CPI -0.048** -0.042** -0.034***

(5): (2) + official flows & grants/debt service + inflation deflator -0.045** -0.040*** -0.033***

(6): (2) + official flows & grants/debt service + inflation CPI -0.045** -0.040** -0.033***

(7): all variables are included -0.039** -0.035** -0.029***

Notes:– (1) and (2) include: avg. 4-year price change · interactions of avg. 4-year price change · commodity export/GDP · external debt/GDP · external debt/GDP*

global interest rate · peg · default history · OPEC · int’l reserves/debt service · avg. 3-year GDP change · domestic credit/GDP.– Regressions include country and year effects. Clustered standard errors at country level.– Average marginal effects (AMEs) were calculated with dydx().– * Significant at the 10-percent level.– ** Significant at the 5-percent level.– *** Significant at the 1-percent level.

27

Table 4: Estimates of Overall Effects of World Commodity Prices on Partial Default Rate (Alternative Specifications)

Model (FRM)(3) (4) (5) (6) (7)

Variables βj-The direction of effectlagged price level -0.667** -0.693** -0.725** -0.753** -0.823***lagged price level*commodity export/GDP -1.236 -1.097 -2.682 -2.565 -0.244lagged price level*commodity export/GDP*external debt/GDP -0.177 -0.179 -0.648 -0.615 -0.061lagged price level*peg 0.334 0.337 0.436* 0.441* 0.320avg. 4-year price change -2.451* -2.507* -2.580** -2.631** -2.004avg. 4-year price change*commodity export/GDP -2.794 -3.159 7.864 7.778 -0.592avg. 4-year price change*commodity export/GDP*external debt/GDP 3.122 4.126 -17.562 -16.883 -0.036avg. 4-year price change*peg -0.121 -0.195 -0.849 -0.892 -0.262commodity export/GDP 7.800 7.437 11.928 11.549 3.973external debt/GDP 1.510 1.352 -0.510 -0.653 0.738external debt/GDP*global interest rate 0.228 0.241 0.463 0.472 0.345peg -1.418 -1.431 -1.811 -1.828 -1.402default history 1.155*** 1.091*** 1.226*** 1.168*** 1.108***OPEC 1.686*** 1.668*** 0.402 0.406 1.594***int’l reserves/debt service -0.027** -0.025** -0.026 -0.024 -0.040**avg. 3-year GDP change -3.637 -3.716 -4.411* -4.494* -4.109domestic credit/GDP 0.703** 0.729** 0.791** 0.820** 0.821**

net capital transfers/GDP -16.249*** -16.170*** -16.889***official flows & grants/debt service -0.250 -0.251 -0.379***inflation deflator 4.700E-05 1.810E-05 -1.101E-03inflation CPI 6.010E-05 3.030E-05 1.015E-04

cons. -1.729 -1.691 -1.621 -1.498 -1.226obs. 523 512 661 650 512pseudo R-Square 0.4590 0.4609 0.4693 0.4706 0.4654

28

Table 4: Estimates of Overall Effects of World Commodity Prices on Partial Default Rate(Alternative Specifications) (Contd.)

Model Std. Dev.AMEs of 1 Std. Dev. at Quartiles

1st (25%) 2nd (50%) 3rd (75%)

(3) 0.228 -0.120*** -0.092*** -0.057***

(4) 0.230 -0.122*** -0.094*** -0.058***

(5) 0.232 -0.134*** -0.112*** -0.070***

(6) 0.234 -0.135*** -0.113*** -0.071***

(7) 0.285 -0.128*** -0.100*** -0.062***

Notes:– Regressions include country and year effects. Clustered standard errors at country level.– Average marginal effects (AMEs) were calculated with dydx().– * Significant at the 10-percent level.– ** Significant at the 5-percent level.– *** Significant at the 1-percent level.

5 Testing for the Endogeneity of Country-Specific Com-modity Price Index

In the study of the effect of the country-specific commodity price index on default rates,it is reasonable to think that the dynamic country-specific commodity export share couldbe correlated with time-varying unobservables. In particular, endogenous supply changes inresponse to fluctuations in world commodity prices are likely to amplify the change in ourcountry-specific price index, which will likely result in a downward bias in the estimatedeffects of commodity prices on the default rate.

In order to address this potential endogeneity problem, we use a two-step control func-tion approach introduced by Papke and Wooldridge (2008), which allows for continuousendogenous variables. The conditional mean model (3) now is expressed as:

E [yit|xit1, zit, ci, υit] = E [yit|xit1, zit1, ci, υit] (9)

E [yit|xit1, zit1, ci, υit] = Φ (β1xit1 + zit1δ1 + ci + υit) (10)

where ci is the time-constant unobserved effect and υit is a time-varying omitted factorthat can be correlated with xit1. The exogenous variables are zit = (zit1, zit2), where sometime-varying, strictly exogenous variables zit2 (which include instrument variables (IVs)) areexcluded from (10).

29

To allow the instruments to be systematically correlated with time-constant omittedfactors, we include country dummies in our analysis. Specifically, we estimate a linearreduced form for xit1 (In our baseline estimates, they are the level and the change of priceindex respectively.) for each country i:

xit1 = ψi + zitδ2 + υit2 (11)

where the nature of endogeneity is through the correlation between υit and the reduced formerror υit2. Step 1 is to estimate the reduced form (11) with IVs and obtain the residuals, υit2.Additional assumptions are: υit = η1υit2 + eit1, where eit1| (zi, υit2) ∼ N (0, σ2

e1) , t =1, . . . , T .24

In Step 2, we use the pooled Probit QMLE of yit on xit1, zit1, ci, υit2:

E [yit|xit1, zit, ci, υit2] = Φ (βe1xit1 + zit1δe1 + ci + ηe1υit2) (12)

to estimate βe1, δe1, ηe1, and the country effect coefficient. The test for endogeneity of xit1 isobtained as an asymptotic t-statistics on υit2. xit1 is exogenous, if ηe1 = 0, and the methodused in Subsection 3.1 is adopted.

24See Equation (4.5) and (4.6) in Papke and Wooldridge (2008).

30

Table 5-1: Estimates of Effects of World Commodity Prices on Partial Default Rate (Bartik Instrument)

ModelLevel Change Composite

Variables βj-The direction of effectlagged price level -0.838*** -0.829**lagged price level*commodity export/GDP -1.544 -1.062lagged price level*commodity export/GDP*external debt/GDP -0.214 -0.498lagged price level*peg 0.373 0.324avg. 4-year price change -3.048* -1.958avg. 4-year price change*commodity export/GDP 3.271 -7.002avg. 4-year price change*commodity export/GDP*external debt/GDP 2.218 8.536avg. 4-year price change*peg -1.105 -0.438commodity export/GDP 9.823 -0.188 8.396external debt/GDP 1.816 1.865 0.987external debt/GDP*global interest rate 0.286 0.124 0.316peg -1.519 -0.211 -1.391default history 1.064*** 1.047*** 1.094***OPEC 2.154*** 1.424** 1.575***int’l reserves/debt service -0.023* -0.026 -0.026*avg. 3-year GDP change -1.981 -3.561 -3.872domestic credit/GDP 0.793** 0.667** 0.746**

net capital transfers/GDP -13.936*** -15.788*** -16.436***inflation CPI 6.070E-05 1.324E-04* 4.020E-05

residual (level) 0.384 0.587residual (change) -0.264 -0.753

cons. -1.884* -4.382*** -1.201obs. 513 512 512pseudo R-Square 0.4497 0.4513 0.4629

31

Table 5-1: Estimates of Effects of World Commodity Prices on Partial Default Rate (BartikInstrument) (Contd.)

Model Std. Dev.AMEs of 1 Std. Dev. at Quartiles

1st (25%) 2nd (50%) 3rd (75%)

Level 0.850 -0.111*** -0.085** -0.059***

Change 0.128 -0.046 -0.040 -0.033*

Composite 0.290 -0.133*** -0.106*** -0.065***

Notes:– Regressions include country and year effects. Clustered standard errors at country level.– Average marginal effects (AMEs) were calculated with dydx().– * Significant at the 10-percent level.– ** Significant at the 5-percent level.– *** Significant at the 1-percent level.

5.1 Bartik Instrument

In the first test of endogeneity of our price index, we use the Bartik instrument. We definethe IVs as the country-specific price index formed by using fixed country commodity exportshares for the year 1962,25 along with the world commodity prices in real 2010 US dollars.Similar to our price index, the IVs are deflated by the US CPI and transformed to leveland change specifications respectively. We estimate the reduced form in Step 1 for eachcountry (time series).26 The residuals from Step 1 for all (i, t) pairs are used in Step 2 inthe fractional response regressions. Table 5-1 shows the direction coefficients and AMEs ofthe estimate for Step 2. We reject the hypothesis that there is an endogeneity issue as theestimated coefficients of the residuals from Step 1 are insignificant in Step 2 regression. Theresults essentially remain the same in terms of the direction of the effects: countries defaultmore in years when world commodity prices drop to a low level or continuously decrease.The AMEs of the estimates with the country-specific instrument price indices are slightlyhigher but with no significant differences: a one-standard deviation (0.290 unit) decrease ofthe composite price index, the AMEs at its 1st, 2nd, and 3rd quartiles are -0.133, -0.106and -0.065 respectively. This increase in the estimates of the AMEs is consistent with ourexpectations. Recall, we anticipated a downward bias in the estimated effects of commodityprices on the default rate due to endogenous supply changes in response to fluctuations inworld commodity prices.

25We use the commodity export share of the year 1992 for Russian Federation and Ukraine, as data forthese countries starts from 1992.

26We also estimate the reduced form in Step 1 for each year (cross-section) with the Bartik instrumentand World Commodity Price Indices instrument, respectively. In those cases as well, no endogeneity issuesare observed based on the coefficients of estimated residuals in Step 2.

32

Table 5-2: Estimates of Effects of World Commodity Prices on Partial Default Rate (World Commodity Price Indices as IVs)

ModelLevel Change Composite

Variables βj-The direction of effectlagged price level -0.699** -0.731**lagged price level*commodity export/GDP -1.622 -0.885lagged price level*commodity export/GDP*external debt/GDP -0.018 -0.178lagged price level*peg 0.388 0.331avg. 4-year price change -3.724* -3.231avg. 4-year price change*commodity export/GDP 4.602 -1.681avg. 4-year price change*commodity export/GDP*external debt/GDP 2.098 3.703avg. 4-year price change*peg -1.104 -0.181commodity export/GDP 9.536 -0.307 6.442external debt/GDP 2.155 1.862 1.431external debt/GDP*global interest rate 0.226 0.119 0.227peg -1.584 -0.203 -1.400default history 1.049*** 1.055*** 1.106***OPEC 2.239*** 1.365** 1.618***int’l reserves/debt service -0.024* -0.023 -0.022**avg. 3-year GDP change -1.727 -3.640 -3.804domestic credit/GDP 0.767** 0.670** 0.730**

net capital transfers/GDP -13.488** -16.103*** -16.549***inflation CPI 8.040E-05 1.352E-04* 6.080E-05

residual (level) -0.239 -0.046residual (change) 1.351 1.848

cons. -2.517** -4.354*** -1.471obs. 513 512 512pseudo R-Square 0.4489 0.4517 0.4618

33

Table 5-2: Estimates of Effects of World Commodity Prices on Partial Default Rate (WorldCommodity Price Indices as IVs) (Contd.)

Model Std. Dev.AMEs of 1 Std. Dev. at Quartiles

1st (25%) 2nd (50%) 3rd (75%)

Level 0.850 -0.093** -0.072** -0.052**

Change 0.128 -0.056* -0.048* -0.037***

Composite 0.208 -0.132*** -0.100*** -0.058***

Notes:– Regressions include country and year effects. Clustered standard errors at country level.– Average marginal effects (AMEs) were calculated with dydx().– * Significant at the 10-percent level.– ** Significant at the 5-percent level.– *** Significant at the 1-percent level.

5.2 World Commodity Price Indices as Instruments

The IVs used in the second test of endogeneity of the price index are the three world com-modity price indices for Energy, Non-energy, and Precious Metals (measured in real 2010US dollars and constructed with weights based on 2002-2004 developing countries’ exportvalues). The IVs are deflated by the US CPI and transformed to level and change specifi-cations respectively. We estimate the reduced form in Step 1 for each country and obtainresiduals for all (i, t) pairs. As in Table 5-2, the results essentially remain the same in termsof the direction of the effects: countries tend to default more in years when world commodityprices drop to a low level or continuously decrease. The AMEs of the estimates with worldcommodity price indices are again slightly higher at the 1st quartile, but generally with nosignificant differences: for a one-standard deviation (0.208 unit) decrease of the compos-ite price index, the AMEs at its 1st, 2nd, and 3rd quartiles are -0.132, -0.100 and -0.058,respectively.

6 Country-Specific Response of the Partial Default Rate

In this section, we investigate the country-specific overall response of the partial defaultrate in the baseline specification which includes both the level and the change of the priceindex. The country-specific response of the partial default rate is different as the economicsituation facing the individual countries differ. By using emerging countries in the Amer-icas as examples, we show that the country-specific default response generally increases asthe commodity export-to-GDP ratio and the external debt-to-GDP ratio increase. Table

34

6 summarizes the AMEs of a country-specific one-standard deviation decrease of the com-posite variable of price index at the country-specific quartiles in the baseline specification(the specification (4) in Table 4). For a country-specific one-standard deviation decrease,the effect varies from insignificant to 0.265, or 26.5 percentage points increase of the partialdefault rate. The AMEs of emerging countries in the Americas and EMA are generally largerthan those of emerging countries in Asia. Countries like Argentina, Brazil, Ecuador, Peru,Nigeria, and Russian Federation have AMEs which are significantly larger than 0.100, or10.0 percentage points for one country-specific standard deviation at the 1st quartile. Forcountries, like China and India, even though the responses of the partial default rate arehighly significant, the predicted AMEs are close to zero. Malaysia and South Africa do nothave significant responses of the partial default rate at the 1st quartile to the fluctuationsin commodity prices.

6.1 Variation in Country-Specific Response with Commodity Ex-port and External Indebtedness

The commodity export and external indebtedness are two important dimensions of the eco-nomic landscape that can significantly shape the response of the default rate to the commod-ity price index. For this reason, we interacted the commodity export-to-GDP ratio and theexternal debt-to-GDP ratio with our main, price-index regressor (along with the exchangerate peg). We now show how the magnitude of the overall impact of world commodity priceson the default rate depends on the values of these variables.

Extending the results of Table 6, Table 7-1 to Table 7-3 report the AMEs of a country-specific one-standard deviation decrease at some chosen combinations of the quantiles of thecommodity export-to-GDP ratio and the external debt-to-GDP ratio for some representativecountries from the Americas, namely, Argentina, Brazil, and Peru. Figure 7-1 to Figure 7-3graphically display the results in Table 7-1 to Table 7-3, respectively. For each country, theresults are presented in three panels (upper, middle, lower) which represent different quartilesof the country-specific composite price variable. In each panel, the individual quantiles ofthe commodity export-to-GDP ratio and the external debt-to-GDP ratio represent a rowand a column respectively. The results show that the magnitude of the negative effect of theprice index on the default rate is generally increasing in commodity export-to-GDP ratioand external debt-to-GDP ratio.

35

Table 6: AMEs of 1 Standard Deviation at Quartiles by Country (Extension of the AMEsof Model (4) in Table 4)

Country Std. Dev.AMEs of 1 Std. Dev. at Quartiles

1st (25%) 2nd (50%) 3rd (75%)

Argentina 0.124 -0.109*** -0.109*** -0.104***

Brazil 0.168 -0.159*** -0.124*** -0.057***

Colombia 0.167 -0.023*** -0.013*** -0.004***

Ecuador 0.208 -0.117** -0.068*** -0.046***

Mexico 0.178 -0.013** -0.004*** -0.002***

Peru 0.226 -0.265*** -0.191*** -0.142***

Venezuela, RB 0.182 -0.109* -0.039*** -0.014*

China 0.219 -0.003*** -0.007** -2.203E-07***

India 0.250 -0.039*** -0.005*** -1.921E-07***

Indonesia 0.217 -0.095*** -0.063*** -0.022***

Malaysia 0.171 -1.439E-06 -0.041*** -0.008**

Pakistan 0.172 -0.020*** -0.014*** -0.006***

Philippines 0.153 -0.063*** -0.043*** -0.016***

Thailand 0.168 -0.010*** -0.013*** -1.919E-07***

Bulgaria 0.113 -0.040*** -0.034*** -0.030***

Nigeria 0.180 -0.197** -0.130*** -0.072***

Romania 0.137 -0.049*** -0.037*** -0.027***

Russian Federation 0.110 -0.154*** -0.127*** -0.097***

South Africa 0.110 -2.413E-05 -7.497E-06* -1.962E-06**

Turkey 0.181 -0.008*** -0.006 -0.001***

Ukraine 0.065 -0.067*** -0.061*** -0.055***

36

Table 7-1: AMEs of 1 Standard Deviation at Quantiles of Commodity Export-to-GDP Ratioand External Debt-to-GDP Ratio - Argentina (Extension of Table 6)

Argentina

Price Index 25% Commodity Export/GDP

AME: -0.109*** 10% 25% 50% 75% 90%

External Debt/GDP

10% -0.1001*** -0.1032*** -0.1069*** -0.1157*** -0.1199***

25% -0.1091*** -0.1120*** -0.1154*** -0.1236*** -0.1273***

50% -0.1199*** -0.1223*** -0.1251*** -0.1315*** -0.1344***

75% -0.1236*** -0.1254*** -0.1271*** -0.1319*** -0.1337***

90% -0.1182*** -0.1192*** -0.1201*** -0.1219*** -0.1225***

Price Index 50% Commodity Export/GDP

AME: -0.109*** 10% 25% 50% 75% 90%

External Debt/GDP

10% -0.0841*** -0.0871*** -0.0907*** -0.0998*** -0.1041***

25% -0.0950*** -0.0980*** -0.1017*** -0.1106*** -0.1149***

50% -0.1112*** -0.1140*** -0.1174*** -0.1255*** -0.1293***

75% -0.1216*** -0.1240*** -0.1269*** -0.1337*** -0.1368***

90% -0.1252*** -0.1270*** -0.1291*** -0.1337*** -0.1357***

Price Index 75%: Commodity Export/GDP

AME: -0.104*** 10% 25% 50% 75% 90%

External Debt/GDP

10% -0.0679*** -0.0705*** -0.0738*** -0.0819*** -0.0860***

25% -0.0794*** -0.0822*** -0.0856*** -0.0940*** -0.0982***

50% -0.0983*** -0.1011*** -0.1046*** -0.1131*** -0.1171***

75% -0.1134*** -0.1161*** -0.1194*** -0.1272*** -0.1310***

90% -0.1250*** -0.1273*** -0.1301*** -0.1365*** -0.1395***

37

Figure 7-1: AMEs of 1 Std. Dev. at Quantiles of Commodity Export/GDP and ExternalDebt/GDP - Argentina

38

Table 7-2: AMEs of 1 Standard Deviation at Quantiles of Commodity Export-to-GDP Ratioand External Debt-to-GDP Ratio - Brazil (Extension of Table 6)

Brazil

Price Index 25% Commodity Export/GDP

AME: -0.159*** 10% 25% 50% 75% 90%

External Debt/GDP

10% -0.1126** -0.1134** -0.1157** -0.1234** -0.1376**

25% -0.1279*** -0.1288*** -0.1312*** -0.1391*** -0.1536***

50% -0.1413*** -0.1421*** -0.1446*** -0.1525*** -0.1670***

75% -0.1547*** -0.1556*** -0.1580*** -0.1659*** -0.1801***

90% -0.1824*** -0.1832*** -0.1854*** -0.1924*** -0.2046***

Price Index 50%: Commodity Export/GDP

AME: -0.124*** 10% 25% 50% 75% 90%

External Debt/GDP

10% -0.0798** -0.0804** -0.0822** -0.0882** -0.0996**

25% -0.0939*** -0.0946*** -0.0965*** -0.1030*** -0.1152***

50% -0.1069*** -0.1076*** -0.1097*** -0.1165*** -0.1293***

75% -0.1209*** -0.1267*** -0.1238*** -0.1309*** -0.1441***

90% -0.1540*** -0.1548*** -0.1570*** -0.1642*** -0.1773***

Price Index 75%: Commodity Export/GDP

AME: -0.057*** 10% 25% 50% 75% 90%

External Debt/GDP

10% -0.0300** -0.0303** -0.0310** -0.0333** -0.0380**

25% -0.0380*** -0.0383*** -0.0392*** -0.0419*** -0.0473**

50% -0.0462*** -0.0465*** -0.0474*** -0.0506*** -0.0567***

75% -0.0559*** -0.0563*** -0.0573*** -0.0609*** -0.0677***

90% -0.0838*** -0.0843*** -0.0856*** -0.0901*** -0.0986***

39

Figure 7-2: AMEs of 1 Std. Dev. at Quantiles of Commodity Export/GDP and ExternalDebt/GDP - Brazil

40

Table 7-3: AMEs of 1 Standard Deviation at Quantiles of Commodity Export-to-GDP Ratioand External Debt-to-GDP Ratio - Peru (Extension of Table 6)

Peru

Price Index 25%: Commodity Export/GDP

AME: -0.265*** 10% 25% 50% 75% 90%

External Debt/GDP

10% -0.1532** -0.1636** -0.1727* -0.1881* -0.2479

25% -0.1787** -0.1895** -0.1991** -0.2147** -0.2737*

50% -0.2447*** -0.2549*** -0.2635*** -0.2773*** -0.3233***

75% -0.2681*** -0.2766*** -0.2837*** -0.2948*** -0.3285***

90% -0.2765*** -0.2821*** -0.2866*** -0.2933*** -0.3093***

Price Index 50%: Commodity Export/GDP

AME: -0.191*** 10% 25% 50% 75% 90%

External Debt/GDP

10% -0.0687* -0.0738* -0.0784* -0.0864 -0.1203

25% -0.0872** -0.0932** -0.0985** -0.1076** -0.1457

50% -0.1527*** -0.1606*** -0.1676*** -0.1793*** -0.2255**

75% -0.1916*** -0.2001*** -0.2076*** -0.2198*** -0.2669***

90% -0.2364*** -0.2448*** -0.2521*** -0.2640*** -0.3078***

Price Index 75%: Commodity Export/GDP

AME: -0.142*** 10% 25% 50% 75% 90%

External Debt/GDP

10% -0.0391 -0.0419 -0.0444 -0.0488 -0.0678

25% -0.0519** -0.0553** -0.0584** -0.0637** -0.0861

50% -0.1035*** -0.1088*** -0.1135*** -0.1214*** -0.1534**

75% -0.1397*** -0.1459*** -0.1513*** -0.1604*** -0.1964***

90% -0.1892*** -0.1962*** -0.2023*** -0.2124*** -0.2512***

41

Figure 7-3: AMEs of 1 Std. Dev. at Quantiles of Commodity Export/GDP and ExternalDebt/GDP - Peru

42

Table 8: Estimates of Effects of World Commodity Prices on Partial Default Rate (Default History)

ModelLevel Change Composite

Variables βj-The direction of effectlagged price level -0.839*** -0.695***lagged price level*commodity export/GDP -1.505 -1.080lagged price level*commodity export/GDP*external debt/GDP -0.078 -0.118lagged price level*peg 0.377 0.345lagged price level*default history 0.098 -0.018avg. 4-year price change -2.969** -1.311avg. 4-year price change*commodity export/GDP 3.631 -2.270avg. 4-year price change*commodity export/GDP*external debt/GDP 1.799 3.005avg. 4-year price change*peg -1.092 -0.127avg. 4-year price change*default history -0.249 -1.420commodity export/GDP 9.211 -0.245 7.206external debt/GDP 2.072 1.842 1.384external debt/GDP*global interest rate 0.242 0.125 0.228peg -1.542 -0.211 -1.470default history 0.665 1.039*** 1.100OPEC 2.218*** 1.406** 1.672***int’l reserves/debt service -0.026 -0.025 -0.023**avg. 3-year GDP change -1.770 -3.591 -3.832domestic credit/GDP 0.776** 0.668** 0.725**

net capital transfers/GDP -13.561 -15.885*** -16.226***inflation CPI 6.870E-05 1.338E-04* 6.120E-05

cons. -1.819 -4.303*** -1.603obs. 513 512 512pseudo R-Square 0.4488 0.4512 0.4611

43

Table 8: Estimates of Effects of World Commodity Prices on Partial Default Rate (DefaultHistory) (Contd.)

Model Std. Dev.AMEs of 1 Std. Dev. at Quartiles

1st (25%) 2nd (50%) 3rd (75%)

Level 0.850 -0.100*** -0.076** -0.054***

Change 0.128 -0.048** -0.042** -0.034***

Composite 0.328 -0.128*** -0.101*** -0.063***

Notes:– Regressions include country and year effects. Clustered standard errors at country level.– Average marginal effects (AMEs) were calculated with dydx().– * Significant at the 10-percent level.– ** Significant at the 5-percent level.– *** Significant at the 1-percent level.

7 Robustness Analysis

In order to gain more confidence in our results about the effect of world commodity priceson the default rate, we carry out a few tests of robustness of our results. In particular, werun additional regressions where we include: the interaction of (the level and the changeof) the price index and the default history and the interaction of (the level and the changeof) the price index and international reserves. We also analyze the baseline specificationsby dropping no/low default countries. The AMEs for the overall effect for these robustnesstests are slightly higher, but with no significant differences.

7.1 Interaction with Default History

The magnitude of the effects of world commodity prices on the partial default rate may alsobe affected by a country’s default history, because debt arrears get accumulated overtime.By including the interaction term of price index and default history to the baseline estimatesof the level, change, and composite variable of the price index for specification (4), we testwhether the AMEs of price index is significantly affected by default history. As in Table 8,the results essentially remain the same in terms of the direction of the effects. The AMEs ofthe estimates with inclusion of the interaction term of the price index and the default historyare slightly higher, but with no significant differences: for a one-standard deviation (0.328unit) decrease of the composite price index, the AMEs at its 1st, 2nd, and 3rd quartiles are-0.128, -0.101 and -0.063, respectively.

44

Table 9: Estimates of Effects of World Commodity Prices on Partial Default Rate (International Reserves)

ModelLevel Change Composite

Variables βj-The direction of effectlagged price level -0.761*** -0.709**lagged price level*commodity export/GDP -1.666 -1.405lagged price level*commodity export/GDP*external debt/GDP -0.080 -0.297lagged price level*peg 0.393 0.354lagged price level*int’l reserves/GDP 3.030E-12 4.200E-12avg. 4-year price change -3.182** -2.489*avg. 4-year price change*commodity export/GDP 3.877 -3.279avg. 4-year price change*commodity export/GDP*external debt/GDP 0.779 1.983avg. 4-year price change*peg -1.079 0.046avg. 4-year price change*int’l reserves/GDP -2.210E-11 -7.300E-11commodity export/GDP 9.584 -0.250 8.784external debt/GDP 2.935 1.820 1.684external debt/GDP*global interest rate 0.208 0.129 0.216peg -1.589 -0.210 -1.480default history 1.066*** 1.054*** 1.134***OPEC 2.269*** 1.385** 1.670***int’l reserves/debt service -0.029* -0.025 -0.034*avg. 3-year GDP change -1.809 -3.588 -3.787domestic credit/GDP 0.768** 0.665** 0.714**

net capital transfers/GDP -13.599** -15.912*** -16.330***inflation CPI 6.230E-05 1.315E-04* 3.970E-05

cons. -2.397** -4.372*** -1.579obs. 513 512 512pseudo R-Square 0.4491 0.4513 0.4617

45

Table 9: Estimates of Effects of World Commodity Prices on Partial Default Rate (Interna-tional Reserves) (Contd.)

Model Std. Dev.AMEs of 1 Std. Dev. at Quartiles

1st (25%) 2nd (50%) 3rd (75%)

Level 0.850 -0.102*** -0.092*** -0.055***

Change 0.128 -0.048** -0.042** -0.034***

Composite 0.234 -0.124*** -0.096*** -0.059***

Notes:– Regressions include country and year effects. Clustered standard errors at country level.– Average marginal effects (AMEs) were calculated with dydx().– * Significant at the 10-percent level.– ** Significant at the 5-percent level.– *** Significant at the 1-percent level.

7.2 Interaction with International Reserves

We also strengthen our analysis by testing the impact of international reserves of a countryon the effect of world commodity prices. By including the interaction term of the price indexand international reserves to the baseline estimates of the level, change, and compositespecification (4), we show the results essentially remain the same in terms of the direction ofthe effects and show that the new AMEs in Table 9 of the composite price index produce nosignificant differences: for a one-standard deviation (0.234 unit) decrease of the compositeprice index, the AMEs at its 1st, 2nd, and 3rd quartiles are -0.124, -0.096 and -0.059,respectively.

7.3 Dropping No/Low Default Countries

By dropping no/low default countries (China, India, and South Africa), we conduct anadditional regression analysis of the baseline estimates of the level, change, and compos-ite variables of the price index for specification (4). Estimation results in Table 10 showconsistent conclusions vis-a-vis earlier regressions in terms of the direction of the effectsof various regressors. Compared with the AMEs of the baseline specification of the level,change, and composite variable of the price index, the AMEs of the estimates with no/lowdefault countries dropped are higher: for a one-standard deviation (0.232 unit) decrease ofthe composite price index, the AMEs at its 1st, 2nd, and 3rd quartiles are -0.139, -0.106 and-0.062, respectively, but with no significant differences.

46

Table 10: Estimates of Effects of World Commodity Prices on Partial Default Rate (No/Low Default Countries Dropped)

ModelLevel Change Composite

Variables βj-The direction of effectlagged price level -0.749*** -0.693**lagged price level*commodity export/GDP -1.546 -1.097lagged price level*commodity export/GDP*external debt/GDP -0.054 -0.179lagged price level*peg 0.380 0.337avg. 4-year price change -3.183** -2.506*avg. 4-year price change*commodity export/GDP 3.500 -3.155avg. 4-year price change*commodity export/GDP*external debt/GDP 2.004 4.114avg. 4-year price change*peg -1.103 -0.195commodity export/GDP 9.321 -0.223 7.435external debt/GDP 2.090 1.831 1.352external debt/GDP*global interest rate 0.238 0.127 0.241peg -1.546 -0.210 -1.431default history 1.048*** 1.051*** 1.091***OPEC 2.226*** 1.407** 1.667***int’l reserves/debt service -0.024* -0.025 -0.025**avg. 3-year GDP change -1.827 -3.574 -3.716domestic credit/GDP 0.776** 0.668** 0.729**

net capital transfers/GDP -13.573** -15.876*** -16.168***inflation CPI 7.060E-05 1.334E-04* 6.010E-05

cons. -2.261** -4.357*** -1.599obs. 455 454 454pseudo R-Square 0.4258 0.4282 0.4383

47

Table 10: Estimates of Effects of World Commodity Prices on Partial Default Rate (No/LowDefault Countries Dropped) (Contd.)

Model Std. Dev.AMEs of 1 Std. Dev. at Quartiles

1st (25%) 2nd (50%) 3rd (75%)

Level 0.868 -0.115*** -0.086** -0.060***

Change 0.125 -0.053** -0.045** -0.037***

Composite 0.232 -0.139*** -0.106*** -0.062***

Notes:– Regressions include country and year effects. Clustered standard errors at country level.– Average marginal effects (AMEs) were calculated with dydx().– * Significant at the 10-percent level.– ** Significant at the 5-percent level.– *** Significant at the 1-percent level.

8 Conclusion

External sovereign lending is always exposed to default risk because of the lack of mechanismfor enforcement. This paper investigates what are the key determinants affecting the abilityof emerging countries to repay their external debt. It is commonly admitted that the fluctua-tions in world commodity prices can impact export revenues of the individual countries and,thus, affect their ability to repay sovereign debt denominated in foreign currencies. Thispaper studies how the fluctuations in world commodity prices (and other macroeconomicfundamentals) affect the the sovereign default rate. It differs from the early sovereign debtstudies that treat sovereign default as a binary event or use credit ratings and/or CDS/EMBIspreads as the proxy for anticipated default risk.

The estimates from a panel of 21 emerging countries over the period 1970–2013 show thatboth the level and the change of country-specific index of commodity prices, negatively affectthe partial default rate. For the level of the price index, a one-standard deviation decrease atits 1st, 2nd, and 3rd quartile raises the partial default rate, on average, by 9.9, 7.6, and 5.4percentage points, respectively. For the change in the price index, a one-standard deviationdecrease at its 1st, 2nd, and 3rd quartile raises the partial default rate, on average, by4.8, 4.2, and 3.4 percentage points, respectively. When considered together, a one-standarddeviation decrease in the composite of the level and the change of the price index at the 1st,2nd, and 3rd quartile increases the default rate, on average, by 12.2, 9.4 and 5.8 percentagepoints, respectively.

Our endogeneity tests, including the use of the Bartik instrument, show no evidence ofthe potential endogeneity of a country-specific commodity price index that is based on thecountry’s commodity export structure.

48

We also investigate the country-specific response of the partial default rate. For a country-specific one-standard deviation decrease of the price index, the response varies from insignif-icant to a 26.5 percentage points increase. The response for a country also varies with itsdegree of the dependence on commodity exports and external indebtedness. The country-specific response of the partial default rate to the price index generally increases in magnitudewith the commodity exports and external indebtedness.

We also conduct a few tests of robustness of our results. In particular, we run additionalregressions, where we include the interaction of (the level and the change of) the price indexand the default history and the interaction of (the level and the change of) the price indexand international reserves. We also analyze the baseline specifications by dropping no/lowdefault countries. The AMEs for the overall effect for these robustness tests are slightlyhigher, but with no significant difference.

Our results show that other fundamentals also have statistically significant and expectedimpact on the partial default rate. Default history positively and significantly (in statisticalsense) affects the partial default rate. The effect of the domestic credit-to-GDP ratio is alsopositive and statistically significant. Net capital transfers-to-GDP ratio and official flows andgrants-to-debt service ratio, which represent other international resources, negatively andsignificantly affect the partial default rate. The directions of the effects of an exchange ratepeg (negative), being a member of OPEC (positive), international reserves-to-debt serviceratio (negative), the growth rate of GDP (negative), and inflation (positive) are also asexpected. Overall, our findings are fairly robust in the sense that all results are consistentwith economic intuition. The baseline fractional response Probit model can explain abouthalf of the variation in the response of partial default rate.

Our approach to constructing the country-specific commodity price index can be usefulin many other contexts. For example, many low-income and other developing countrieshave also experienced sovereign debt crises during the past four decades. Further researchcould explore how the results of this paper extend to those countries. Moreover, our priceindex can be also used to examine how commodity prices affect the performance of theoverall macroeconomy and the conduct of monetary policy (in different frameworks, such as,managed exchange rate regimes or inflation targeting.)

49

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Appendix

Table A.1: Variables (Abbreviation), Data Source, and Measurement

Variables (Abbreviation) Data Sources MeasurementDependent VariablePartial Default Rate

(arrears/(arrears+debt service))

World Development Indicator (WDI) arrears = Interest arrears, long-term DOD

(current US$) + Principal arrears, long-term

DOD (current US$)debt service = Debt service on external debt,

public and publicly guaranteed (PPG)(TDS,

current US$)

Key Independent VariablePrice Index Observatory of Economic Complexity

(OEC)

Global Economic Monitor (GEM)

Extend the Jevons formulas (IMF, 2009).

Deflated by U.S. CPI (2010 = 100) from World

Development Indicator (WDI)

Other Independent Variables1. Country VariablesGDP World Development Indicator (WDI) Current USD

GDP at market prices (constant 2010 USD)

Commodity Export-to-GDP Ratio

(commodity export/GDP)

Observatory of Economic Complexity

(OEC)

Commodity

export-to-Exports\timesExport-to-GDP

Exchange Rate Regime (peg) Shambaugh (2004) Classification: 1 = peg, 0 = non-peg

OPEC (OPEC) Organizations of Petroleum Exporting

Countries (OPEC)

Binary panel

Positive Arrears History

(default history)

Binary panel

54

Table A.1: Variables (Abbreviation), Data Source, and Measurement (Contd.)Variables (Abbreviation) Data Sources MeasurementOther Independent Variables1. Country VariablesDebt-to-GDP Ratio

(external debt/GDP)

External debt (PPG)/GDP, current USD

Domestic Credit-to-GDP Ratio

(domestic credit/GDP)

World Development Indicator (WDI) Domestic credit/GDP, current USD

Inflation

(inflation CPI, inflation deflator)

IMF, International Financial Statistics

(IFS) data files

Inflation, consumer price index (annual %)

Inflation, GDP deflator (annual %)World Bank national accounts dataOECD National Accounts data files

International Reserves-to-Debt ServiceRatio

(int’l reserves/debt service)

World Development Indicator (WDI) Reserves and related items/Debt service on

external debt (PPG), current USD

Official Flows-to-Debt Service Ratio

(official flows & grants/debt service)

International Debt Statistics (IDS) Official Flows = Net Financial Flows (IMF

concessional) + Net Financial Flows (IMF

non-concessional) + Grants (excluding

Technology Cooperation), current USD

Net Capital Transfers-to-GDP Ratio

(net capital transfers/GDP)

IMF Balance of Payments and

International Investment Position

Statistics (BOP/IIP)

Capital transfers (credit - debit, million

USD)/GDP, current USD

2. Global Variables10-Year Treasury Constant MaturityRate

(global interest rate)

Federal Reserve Economic Data (FRED)

Federal Reserve Bank of St. Louis

55

Table A.2: The Category Structure of Global Economic Monitor (GEM) Commodities Database as Presented in the CommodityPrice Data (a.k.a. Pink Sheet)

Energy Coal AustraliaColombiaSouth Africa

Crude oil averageBrentDubaiWTI

Natural gas IndexEuropeUSLNG Japan

Non-energy

Commodities

Agriculture 1. Beverages Cocoa

Coffee ArabicaRobusta

Tea averageColombo auctionsKolkata auctionsMombasa auctions

2. Food 2.1 Fat and Oils Coconut oilCopraFishmealGroundnutsGroundnut oilPalm oilPalm kernel oilSoybean mealSoybean oilSoybeans

2.2 Grains BarleyMaizeRice Thailand 5%

Thailand 25%Thailand A1Vietnam 5%

SorghumWheat US HRW

US SRW2.3 Other Food Bananas EU

US

56

Table A.2: The Category Structure of Global Economic Monitor (GEM) Commodities Database as Presented in the CommodityPrice Data (a.k.a. Pink Sheet) (Contd.)

Non-energy

Commodities

Agriculture 2.3 Other Food Meat beef

chickensheep

Shrimp MexicoSugar EU

USWorld

3. Raw Materials 3.1 Timber Logs CameroonMalaysia

PlywoodSawn wood Cameroon

MalaysiaWood pulp

3.2 Other Raw

Materials

Cotton

Rubber RSS3TSR20

Fertilizers Diammonium

phosphate (DAP)Phosphate rockPotassium chlorideTriple

superphosphate

(TSP)Urea E. Europe

Metals and

Minerals

Aluminum

CopperIron oreLeadNickelTinZinc

Precious Metals GoldPlatinumSilver

57