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1、Predicting Debt Distress in Low-Income CountriesClemens Graf von Luckner(Stanford University)Sebastian Horn(University of Hamburg&Kiel Institute)Aart Kraay(World Bank)Rita Ramalho(World Bank)November 15,202425thJacques Polak Annual Research Conference The views expressed here are the authors and do

2、not reflect the official views of the World Bank,its Executive Directors,or the countries they represent.Motivation:general Sovereign debt crises have large economic and social costs Lower growth and productivity;higher poverty(Reinhart and Rogoff 2009,Aguiar and Amador 2021,Farah-Yacoub et al.2024a

3、)Early warning systems for“debt distress”can have large benefits if they enable preventative measures Large literature on predicting debt distress(Moreno Badia et.al.(2022)survey)Premise of WB/IMF LIC Debt Sustainability FrameworkNovember 15,2024 Graf von Luckner,Horn,Kraay and Ramalho 2Motivation:s

4、pecific WB/IMF policy application The WB/IMF DSF for Low-Income Countries Developed in mid-2000s to provide early warning of debt vulnerabilities prevent debt re-accumulation post-HIPC/MDRI Sets borrowing limits,mix of grants and loans from IDA,debt relief envelopes Last reviewed in 2017,new review

5、ongoing Core of LIC DSF is an empirical model to predict debt distress Used to derive country-specific debt thresholds reflecting countries debt carrying capacity November 15,2024 Graf von Luckner,Horn,Kraay and Ramalho 3Our contributions to literature and policy1.Refining debt distress outcome meas

6、urement to reflect the onset rather than resolution of distress2.Systematic approach to predictive model selection Evaluate 559,872 possible models based on J-K-fold cross-validated out-of-sample predictive performance3.Evaluate simple versus sophisticated prediction algorithms Best simple models st

7、rongly dominate more sophisticated alternatives such as Random Forests4.Policy implications for LIC-DSF Scope to improve predictive performance Scope to reduce overoptimism bias through k-year-ahead predictionsNovember 15,2024 Graf von Luckner,Horn,Kraay and Ramalho 41.Measuring debt distress What a

8、re we trying to predict?November 15,2024 Graf von Luckner,Horn,Kraay and Ramalho 51.1 Measuring debt distress:signalsArrears:Arrears 5%of ppg debt stock,for 3 yearsIMF Programs:Rapid disbursements 30%of quota,all program typesDebt restructuringsDefault assumed to start 1 year prior:Private creditors

9、(Cruces&Trebesch)Paris Club creditors(Das et al.)Defaults on private creditors:Data from S&P and Catao&Milesi-Ferreti,whenever availableNovember 15,2024 Graf von Luckner,Horn,Kraay and Ramalho 6LIC DSF Review 2017 reflects typical set of debt distress signals in the literature:1.1 Measuring debt dis

10、tress:signalsArrears:Arrears 5%of ppg debt stock,for 3 yearsLIC DSF Review 2017 reflects typical set of debt distress signals in the literature:Our paper:IMF Programs:Rapid disbursements 30%of quota,all program typesDebt restructuringsDefault assumed to start 1 year prior:Private creditors(Cruces&Tr

11、ebesch)Paris Club creditors(Das et al.)Defaults on private creditors:Data from S&P and Catao&Milesi-Ferreti,whenever availableArrears:Arrears 5%of ppg debt stock,for 3 yearsIMF Programs:Rapid disbursements 30%of quota,only non-concessional programs/no RFIDefaults on private creditors:New data for al

12、l LICs from Asonuma&Trebesch(2016)and Farah-Yacoub et al.(2024)no restructuring signal key timing point see next slideNovember 15,2024 Graf von Luckner,Horn,Kraay and Ramalho 71.1 Measuring debt distress:timing of arrears and restructuringsRestructurings mark conclusion rather than onset of distress

13、(Asonuma&Trebesch 2016)Long and variable lags between defaults and restructurings(median of 4 years)November 15,2024 Graf von Luckner,Horn,Kraay and Ramalho 81.2 Measuring debt distress:episodes Define distress signal=1 if any one of three distress signals is observed in country and year;=0 otherwis

14、e (1)defaults,(2)high arrears,(3)large and rapid IMF disbursement Define distress episode+1=1 if:=1=2=0:not currently/recently in distress,and+1=1:distress signal next year Define non-distress episodes+1=0 if:=1=2=0:not currently/recently in distress,and+1=0:no distress signal next yearNovember 15,2

15、024 Graf von Luckner,Horn,Kraay and Ramalho 91.4 Measuring debt distress:results Sample consists of 1,752 observations covering 80 LIC DSF-eligible countries 1970-202190 cases of debt distress represent 5.1 percent of sampleThree signals of roughly equal importance in triggering distress episodesNov

16、ember 15,2024 Graf von Luckner,Horn,Kraay and Ramalho 101.Measuring debt distress2.Predicting debt distressNovember 15,2024 Graf von Luckner,Horn,Kraay and Ramalho 112.1 Predicting debt distress:probit model Estimate predicted probability of distress using probit model:+1=1=(),+1=()Cutoff probabilit

17、y generates binary prediction+1=1 when +1 False positive rate:=1 +1+1/1 +1 False negative rate:=+11 +1/+1)Select to minimize quadratic mean squared prediction loss function:(,)=2+1 2,=0.5November 15,2024 Graf von Luckner,Horn,Kraay and Ramalho 122.2 Predicting debt distress:standard covariates from

18、literature Debt indicators PPG/GDP,PPG/Exports,NPV/GDP,NPV/Exports,TDS/Exports,TDS/Revenue,domestic debt/GDP,Interest on Public Debt/Exports Policies and institutions Country Policy and Institutional Assessment(CPIA),years since last distress,decaying average of past distress Business cycle and leve

19、l of development GDP growth,inflation rate,depreciation rate,log GDP per capita Political cycle Years in office,years until end of term External environment Current account balance,FDI inflows,remittances,change in TOT,10-year US Treasuries rate,reserves/imports,trade openness,world growth November

20、15,2024 Graf von Luckner,Horn,Kraay and Ramalho 132.3 Predicting distress:model space “Brute force”approach to model selection consider models defined by all relevant combinations of RHS variables With 28 covariates we would have 228 268 million models to study With(=10)(=10)cross-validation,26 bill

21、ion probit regressions to estimate To limit scope of task to substantively interesting models,we impose a set of restrictions on the model space:CPIA always included(for LIC DSF policy application,not very binding constraint)At least one debt variable(for LIC DSF policy application)At most one debt

22、stock-,debt service-,credit history-,political cycle-,change in value of money-variable With these restrictions,we consider 559,872 candidate prediction modelsNovember 15,2024 Graf von Luckner,Horn,Kraay and Ramalho 142.4 Predicting distress:cross-validation Evaluate models based on out-of-sample pr

23、edictive performance using J-K-fold cross-validation For each combination of variables that defines a model:Perform K-fold cross-validation for =10 exhaustive folds Estimate probit model in training sample Select that minimizes prediction loss function in test sample Repeat =10 times,retrieving mini

24、mized,and(,)Calculate mean of,and(,)across =10 replications Construct confidence interval for(,)November 15,2024 Graf von Luckner,Horn,Kraay and Ramalho 152.5 ResultsNovember 15,2024 Graf von Luckner,Horn,Kraay and Ramalho 162.6 Predicting distress:parsimony vs.performance Some tradeoffs between mod

25、el size and predictive performance Average predictive performance improves modestly with model size(red dots)Best model performance conditional on size is U-shaped in model size(lower envelope of yellow points)November 15,2024 Graf von Luckner,Horn,Kraay and Ramalho 172.7 Predicting debt distress:be

26、st models Our algorithms turn up many(many!)good models that outperform models in 2017 LIC-DSF 431K models(77%)outperform 2017 LIC-DSF mechanical predictions 395K models(71%)outperform best single probit with 2017 LIC-DSF variables To guide selection of“best models”we impose three further conditions

27、:1.No perverse incentives:02.Data availability:data on all variables in model available for at least 90%of country-year observations since 2000.3.Meaningful effect size:/0.05 (top 20 percent)November 15,2024 Graf von Luckner,Horn,Kraay and Ramalho 182.7 Predicting distress:selected best modelsNovemb

28、er 15,2024 Graf von Luckner,Horn,Kraay and Ramalho 19(1)(2)(3)(4)(5)(6)(7)CPIA-0.15*-0.10*-0.12*-0.08*-0.08*-0.06-0.11*Ext.debt service/exports0.22*0.19*0.18*0.17*0.17*0.15*Reserves/imports-0.24*-0.21*-0.17*-0.15*-0.17*GDP p.c.0.18*0.14*0.16*0.13*0.25*Inflation0.11*0.09*0.11GDP growth-0.09*-0.09*Cre

29、dit history-0.07-0.07Commodities terms of trade-0.08*-0.09US 10 year yield0.08*0.12*Openness-0.10CA balance/GDP-0.06Ext.debt stock/exports0.09Number of variables23456710Loss function0.370.310.290.270.260.270.29False positive rate0.370.320.330.210.250.190.30False negative rate0.360.300.240.320.280.34

30、0.27Data coverage since 20000.960.940.910.930.910.920.92Number of observations1,0021,0021,0021,0021,0021,0021,002Dependent variable:Incidence of external sovereign debt distress in t+1 Model with only six regressors minimizes prediction loss function(=0.26)2.7 Predicting distress:selected best model

31、s Model with only six regressors minimizes prediction loss function(=0.26)Very parsimonious model with only three predictors does almost as well(=0.31)“Best Parsimonious Model”(BPM)November 15,2024 Graf von Luckner,Horn,Kraay and Ramalho 20(1)(2)(3)(4)(5)(6)(7)CPIA-0.15*-0.10*-0.12*-0.08*-0.08*-0.06

32、-0.11*Ext.debt service/exports0.22*0.19*0.18*0.17*0.17*0.15*Reserves/imports-0.24*-0.21*-0.17*-0.15*-0.17*GDP p.c.0.18*0.14*0.16*0.13*0.25*Inflation0.11*0.09*0.11GDP growth-0.09*-0.09*Credit history-0.07-0.07Commodities terms of trade-0.08*-0.09US 10 year yield0.08*0.12*Openness-0.10CA balance/GDP-0

33、.06Ext.debt stock/exports0.09Number of variables23456710Loss function0.370.310.290.270.260.270.29False positive rate0.370.320.330.210.250.190.30False negative rate0.360.300.240.320.280.340.27Data coverage since 20000.960.940.910.930.910.920.92Number of observations1,0021,0021,0021,0021,0021,0021,002

34、Dependent variable:Incidence of external sovereign debt distress in t+12.7 Predicting distress:selected best models Model with only six regressors minimizes prediction loss function(=0.26)Very parsimonious model with only three predictors does almost as well(=0.31)“Best Parsimonious Model”(BPM)Total

35、 debt service on external debt is only debt indicator that features consistently in best models Fairly balanced FPR and FNR(due to choice of quadratic loss function)November 15,2024 Graf von Luckner,Horn,Kraay and Ramalho 21(1)(2)(3)(4)(5)(6)(7)CPIA-0.15*-0.10*-0.12*-0.08*-0.08*-0.06-0.11*Ext.debt s

36、ervice/exports0.22*0.19*0.18*0.17*0.17*0.15*Reserves/imports-0.24*-0.21*-0.17*-0.15*-0.17*GDP p.c.0.18*0.14*0.16*0.13*0.25*Inflation0.11*0.09*0.11GDP growth-0.09*-0.09*Credit history-0.07-0.07Commodities terms of trade-0.08*-0.09US 10 year yield0.08*0.12*Openness-0.10CA balance/GDP-0.06Ext.debt stoc

37、k/exports0.09Number of variables23456710Loss function0.370.310.290.270.260.270.29False positive rate0.370.320.330.210.250.190.30False negative rate0.360.300.240.320.280.340.27Data coverage since 20000.960.940.910.930.910.920.92Number of observations1,0021,0021,0021,0021,0021,0021,002Dependent variab

38、le:Incidence of external sovereign debt distress in t+12.8 Predicting distress:robustness Model selection algorithm uses common balanced sample with for so that all models are evaluated on the prediction of the same set of episodes.We re-estimate the top performing models in the largest available da

39、taset More parsimonious models appear to be more robust to increases in sample sizeNovember 15,2024 Graf von Luckner,Horn,Kraay and Ramalho 221.Measuring debt distress2.Predicting debt distress3.More sophisticated modelsNovember 15,2024 Graf von Luckner,Horn,Kraay and Ramalho 233.1 More sophisticate

40、d models:RF Probit model is very simple can more sophisticated prediction algorithms generate better out-of-sample predictions?Consider random forest(RF),apply in same sample,with same J-K-fold cross-validation Perform grid search over three key tuning parameters to find best RF model:Node purity cr

41、iterion Number of trees Depth of treesNovember 15,2024 Graf von Luckner,Horn,Kraay and Ramalho 243.2:More sophisticated models:results Best RF does significantly worse in predicting debt distress than simple linear probit models FPR=0.35(vs.0.32 in BPM)FNR=0.37 (vs.0.30 in BPM)In line with general p

42、rinciple that ML prediction algorithms adds little value in small datasets(Shmueli,2010)November 15,2024 Graf von Luckner,Horn,Kraay and Ramalho 251.Measuring debt distress2.Predicting debt distress3.More sophisticated models4.LIC DSF implicationsNovember 15,2024 Graf von Luckner,Horn,Kraay and Rama

43、lho 264.1 LIC DSF implications:better predictions Apply old LIC-DSF model to our new sample of events through 2021 New model predicts much better than mechanical predictions from LIC-DSF model Not entirely fair comparison because LIC-DSF model was trained on different sample and a different definiti

44、on of eventsNovember 15,2024 Graf von Luckner,Horn,Kraay and Ramalho 274.2 LIC-DSF implications:better predictions Re-estimate Best Parsimonious Model in 2017 LIC-DSF sample,with old dependent variable and linear loss function from previous review Pick cutoff probability to match in-sample predictiv

45、e performance Not entirely fair comparison for BPM because its predictor list was selected in a different sample,yet BPM outperforms slightly.November 15,2024 Graf von Luckner,Horn,Kraay and Ramalho 284.3 LIC-DSF implications:optimism bias LIC DSF predicts debt distress based on whether projected fu

46、ture debt ratios cross thresholds implied by probit regressions Predicting debt ratios into the future is difficult(numerator and denominator)Risk of optimism bias Instead of“predicting the predictors”of debt distress,how well can current values of predictors predict distress periods into the future

47、?Define new dependent variable+=1 if:=1=2=0:not currently/recently in distress,and max+1,+=1:distress signal any time in next =yearsNovember 15,2024 Graf von Luckner,Horn,Kraay and Ramalho 294.3 LIC-DSF implications:5-year predictions 5-year-ahead predictions are nearly as good as or even better tha

48、n one-year-ahead predictions,e.g.for 3-variable model FP=0.30(compared with 0.32 for one-year-ahead)FN=0.29(compared with 0.30 for one-year-ahead)Suggests scope to improve LIC-DSF by reducing reliance on predicted future debt ratiosNovember 15,2024 Graf von Luckner,Horn,Kraay and Ramalho 30Conclusio

49、n Improved and simplified definition of debt distress Systematic approach to model selection generates better predictions Low return to prediction model complexity probit dominates RF Five-year-ahead predictions almost as good as one-year-ahead predictions Scope to simplify prediction model to make

50、LIC-DSF more transparentNovember 15,2024 Graf von Luckner,Horn,Kraay and Ramalho 31Supplementary MaterialsExternal debt distress episodes by signalTotal number of episodes9883Of which triggered byIMF Disbursements3531Arrears3226Defaults119Restructurings22-Some combination of the above87External debt

51、 distress episodes in LICs,1970-2015Distress signalLIC DSF 2017Our paper1.5 Measuring debt distress:domestic debtUse data from IMF(2021)to capture 67 domestic debt restructurings in LICs(no data on default)Strongly correlated with external distress episodes(as expected)Yields only 4 new distress epi

52、sodes November 15,2024 Graf von Luckner,Horn,Kraay and Ramalho 341.1 External debt distress episodes and Paris Club restructurings Only 25 out of 295 Paris Club restructurings occur outside our external debt distress episodes(9 percent of cases)Most of these 25 cases are related to the HIPC initiati

53、ve and treat debts that had been contracted multiple decades ago in the 1970s and 1980s They“lag”rather than“lead”our external debt distress episodes.November 15,2024 Graf von Luckner,Horn,Kraay and Ramalho 352.2 Predicting debt distress:measurement challenges with domestic debt Domestic debt levels

54、 in LICs are on the rise,but systematic data remains scarce We construct series on total public(domestic plus external)debt to GDP by combining data from the IMF WEO,Abbas et al.(2010)and Reinhart and Rogoff(2009)Near-complete coverage of country-year observations since 1970 in 2017 LIC DSF database

55、 Two main shortcomings:Consistency of institutional coverage can not always be ascertained Limited and noisy data on domestic debt service which matters most for debt distress in short run longest available data covers only payments of interest not principalNovember 15,2024 Graf von Luckner,Horn,Kra

56、ay and Ramalho 36External debt distress episodes:RFICountryAccountArr.TypeYear DSF Risk RatingAlbaniaGRARFI2020-BangladeshGRARFI2020LowBeninGRARFI2020ModerateComorosGRARFI2020ModerateCote dIvoireGRARFI2020ModerateKyrgyz RepublicGRARFI2020ModerateLesothoGRARFI2020ModerateMyanmarGRARFI2020LowNicaragua

57、GRARFI2020ModerateNigeriaGRARFI2020-SenegalGRARFI2020ModerateSolomon IslandsGRARFI2020ModerateNone of these countries defaulted on private creditors and none accumulated significant payment arrears.They had comparatively low debt burdens in comparison to their debt servicing capacity.Including rapid

58、 disbursements under RFI as a distress signal creates 12 additional distress episodes in 2020Unconstrained top models(1)(2)(3)(4)(5)(6)(7)CPIA-0.15*-0.10*-0.10*-0.08*-0.07*-0.06*-0.06*Ext.debt service/exports0.22*0.19*0.25*0.22*0.22*0.12*0.12*Reserves/imports-0.24*-0.23*-0.20*-0.20*-0.13*-0.09*Publi

59、c debt/exports-0.10-0.11Inflation0.08GDP p.c.0.12*0.12*0.11*NPV of ext.debt/exports-0.08GDP growth-0.10*Remittances/GDP-1.74*-1.64*Post-2001 dummy-0.070.01Remittances/GDP x post-20011.62*1.54*US 10-year yield0.08*Ext.debt stock/GDP-0.03Years left in current term-0.06Number of variables23456710Loss f

60、unction0.370.310.290.270.260.250.23False positive rate0.370.320.300.250.200.250.22False negative rate0.360.300.280.280.310.240.23Number of observations1,0021,0021,0021,0021,0021,0021,002Dependent variable:Incidence of external sovereign debt distress in t+1 Loss function minimized by model with 10 p

61、redictor variables(LF=0.23)Several top models not suitable for policy application:“Wrong”coefficient signs lead to perverse policy incentivesEconomically meaningless effect sizesPredictors with low data coverage and large measurement error Remittances:data peculiarities Many LIC remittance series ex

62、hibit structural breaks in early 2000s that cannot be explained by fundamentals Likely driven by improved recording of cross-border transactions,in particular by AML and CFT regulation implemented post 9/11(Clemens&McKenzie 2018)We include remittance with post-2001 dummy and IA term to control for this pattern