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### Foreword
- Paper prepared in 2017-18 to provide options for strengthening risk analysis in low-income countries (LICs).
- Innovations proposed (including novel predictive modeling for LICs) were subsequently used to enhance the IMF’s risk analysis for countries at all income levels and informed IMF: “How to Assess Country Risk: The Vulnerability Exercise Approach Using Machine Learning” (forthcoming).
- The paper is published in only slightly altered form and does not reflect developments in LICs or progress in risk analysis in the past two to three years.

### I. Introduction and Overview — Background and Goal
- LICs improved macroeconomic stability since the early 2000s but remain prone to volatility and severe stress events; the end of the commodity price super-cycle in 2014 contributed to strains.
- Identified need: tools to predict economic stress to reduce crisis likelihood and severity and to build buffers in good times.
- Existing crisis prediction frameworks cover external sector/BoP crises, sovereign crises/debt distress, financial sector/banking crises, and growth decelerations/recessions; empirical approaches include signal extraction, logit/probit, and machine-learning techniques such as classification trees.
- Prior LIC-focused IMF efforts:
  - Dabla-Norris and Bal Gündüz (2012): Growth Decline Vulnerability Index (GDVI) using signal extraction; used in IMF Vulnerability Exercise for LICs (IMF 2014, 2015, 2016, and 2018).
  - IMF and World Bank joint debt sustainability framework for LICs (introduced 2005, recently strengthened) uses logit regressions.

### Objective and Methodological Highlights
- Proposed extension: early-warning systems for balance of payments crises, inflation crises, and financial sector crises in LICs, relying on machine-learning approaches where they outperform traditional econometrics.
- Rationale for machine learning:
  - Better at capturing non-linearities and interactions.
  - Paired with stylized-facts discussion and traditional econometrics to mitigate interpretability concerns.
- Three technical elements:
  - Crisis concepts operationalized at an intermediate severity level to capture important but not only tail events.
  - Predictions identify the unconditional likelihood that a crisis will occur in the following year (absolute risk), using "vulnerability" and "risk" synonymously.
  - Predictive performance assessed primarily via out-of-sample prediction to avoid overfitting.

### Overview of New Crisis Concepts and Country Sample
- New crisis concepts for LICs: balance of payments crises, inflation crises, and financial sector crises.
- Country sample: 73 LICs observed since 1980.

### External Sector / Balance of Payments (BoP) Crises — Concept and Stylized Facts
- Crisis definition elements (country in external crisis in a year if one or more criteria met):
  - i. Average official exchange rate depreciates against the U.S. dollar by at least 30 percent relative to the preceding year and the rate of depreciation increases by at least 10 percentage points relative to the preceding year.
  - ii. Reserve holdings, measured in U.S. dollars, drop by at least 30 percent relative to the preceding year and to a level below 1½ months of imports. Exception: if median reserve coverage in preceding 10 years is less than 1½ months of imports, the country is excluded from the reserves criterion.
  - iii. U.S. dollar value of non-oil imports falls by at least 15 percent relative to the preceding year and declines over a two-year period, plus at least one of the four additional conditions (current account shock ≥ 2 percentage points of GDP, reserves < 1½ months imports, external debt arrears grow by ≥ 3 percent of GDP, or country enters an IMF-supported program in the current or following year).
- Exclusion rule: exclude import compressions meeting criteria if reserve coverage in current and preceding year exceed 5 months of imports and reserve holdings increased by more than 5 percent in the current year (excluded 10 crisis observations in practice).
- Episode conventions:
  - Two or more consecutive years meeting definition count as a sustained crisis episode.
  - If two crises are separated by one tranquil year, that year is integrated into one crisis episode.
- Stylized facts:
  - On average, LICs moved into an external crisis once every 13 years.
  - LICs spent 16 percent of their time in crises.
  - Incidence: 1980s–1990s countries were in external crises 21 percent of the time; thereafter 9 percent.
  - Sample: 2,589 observations covering 73 countries over 1980-2016; includes 197 crisis episodes spanning 420 country-year observations.
  - Nearly two thirds of crisis episodes last only one year; most crises are over after three years.
  - Frontier markets spent limited time in external crises; fragile states and commodity/fuel exporters spent more time in crises.
- Economic impacts:
  - GDP growth typically starts falling before crisis onset.
  - Comparing GDP growth in the crisis year and the two following years with quiet times suggests that at the end of this period output is about 7 percent lower than it would have been otherwise.
  - BoP crises associated with depreciations also result in inflation spikes.
- Pre-crisis indicators:
  - High fiscal deficits, sustained credit growth, and real effective exchange rate overvaluation often precede BoP crises.
  - Both shock size and buffer strength matter: for a given shock, stronger buffers reduce crisis likelihood; for given buffers, larger shocks increase crisis likelihood.

### Inflation Crises — Definition, Drivers, Impacts, and Prediction Performance
- Definition: inflation crises/stress episodes defined as times when inflation exceeds 15 percent per year.
- Stylized facts:
  - Using the 15 percent threshold, 255 inflation crisis episodes out of 1264 country-year pairs (25 percent) during 1990−2015.
  - Incidence trend: 1990s — 37 percent of country-year pairs experienced inflation crises; since 2000 incidence dropped to 12 percent.
  - Median inflation across LICs fell during the 1990s and early 2000s; LIC inflation spiked in 2008 due mainly to higher world food prices.
- Drivers and lead indicators:
  - Fiscal crises are 10 percentage points more likely to occur three years before an inflation episode.
  - Broad money and credit to the private sector grow faster prior to inflation episodes.
  - Strong real effective exchange rates tend to precede episodes.
  - Oil and food price increases tend to precede years with inflation episodes.
- Economic impact:
  - Comparing GDP growth during the crisis year and the two following years with quiet times suggests that at the end of this period output is about 2½ percent below the level that would have prevailed otherwise.
- Early warning system comparison (out-of-sample 2008–16) — selected exact figures:
  - Naïve WEO: # early warnings 20; P(missed crises) 0.795; P(false alarms) 0.026; Loss function 2008-16: -0.345.
  - Sophisticated WEO: # early warnings 213; P(missed crises) 0.070; P(false alarms) 0.387; Cutoff probability: 16%; Loss function 2008-16: -0.809.
  - Panel Regression Model: # early warnings 278; P(missed crises) 0.053; P(false alarms) 0.542; Cutoff probability: 5%; Loss function 2008-16: -0.743.
  - Logit: # early warnings 61; P(missed crises) 0.541; P(false alarms) 0.115; Cutoff probability: 19%; Loss function 2008-16: -0.572.
  - LASSO: # early warnings 99; P(missed crises) 0.268; P(false alarms) 0.144; Cutoff probability: 8%; Loss function 2008-16: -0.771.
  - Random Forest: # early warnings 194; P(missed crises) 0.036; P(false alarms) 0.348; Cutoff probability: 29%; Loss function 2008-16: -0.846.
- Predictive takeaways:
  - Random Forest classification delivers the best tradeoff: lowest loss function (-0.846), missed crises 0.036, acceptable false alarms 0.348, and highest AUC; robustness confirmed in additional out-of-sample forecasts with missed-crises and false-alarm rates of less than 15 percent each.
  - Practical note: thresholds/cutoff probabilities determined by minimizing the loss function using data up to 2014 in the analysis; operational balance between missed crises and false alarms should reflect policy priorities.

### Financial Sector Crises and Stress Episodes — Concepts, Stylized Facts, and Predictability
- Crisis concepts:
  - Main definition follows Laeven and Valencia (2013): a banking crisis identified by significant distress (bank runs, system losses, bank liquidations) and/or significant banking policy interventions.
  - Alternative: banking sector stress episodes assessed by country teams to capture less severe stress events.
- Stylized facts:
  - Sample: 60 LICs over 1981−2015; banking crises counted in sample: 43 total; regressions capture 35 crises due to data availability.
  - Temporal clustering: 39 of the 43 LIC crises took place between 1982 and 1996.
  - Median crisis duration: two years.
  - In LICs, credit growth is depressed prior to crises (contrast with advanced-country credit booms); M2 relative to foreign exchange reserves is high prior to crises.
  - Commodity terms of trade tend to fall in lead-up; volatility of terms of trade is higher prior to crises.
  - Public debt-to-GDP ratio starts increasing prior to crises, stabilizing one year after the crisis.
- Economic impacts:
  - Large output costs of financial sector crises not documented or not apparent in the LIC sample.
  - Public debt appears to rise by several percent of GDP in the context of financial sector crises; Laeven and Valencia (2013) found debt-to-GDP ratios rose by an average of 5 percentage points in 44 LIC banking crisis episodes since the 1980s.
- Predictive performance:
  - Because of low recent frequency of banking crises, out-of-sample prediction is not meaningful.
  - In-sample RE-Mundlak logit estimator (unconditional probability of banking crisis in sample 2.2 percent based on 35 crisis events):
    - Using 2.2 percent threshold: Missed crisis rate (in-sample) 14 percent; False alarm rate (in-sample) 25 percent.
  - Using FSIs to predict less severe financial stress episodes (2016 desk survey of ten stressed countries) with signal-extraction thresholds:
    - Missed crises 40 percent; False alarms 16 percent.
  - FSIs with lowest noise-to-signal ratios (leading indicators): NPLs to total gross loans; Return on equity; Return on assets.
- Empirical logit model findings:
  - Commodity terms of trade declines and higher volatility increase banking crisis probability.
  - No evidence that credit growth predicts banking crises in LICs.
  - High public debt, reliance on short-term borrowing, low reserve coverage, and high inflation increase crisis probability.
  - Tight global monetary conditions increase crisis likelihood.
  - One-standard-deviation effects in preferred model: increase in commodity terms of trade by one standard deviation associated with about a 1 percent decline in propensity of a crisis (unconditional probability: 2.2 percent); short-term debt associated magnitude about 2.2 percent; low reserve coverage and inflation magnitudes between 1.1 percent and 1.4 percent.

### Empirical Methods — Loss Functions, ROC, and Machine Learning Techniques
- Assessing predictive performance:
  - Traditional three-step loss-function approach: estimate crisis likelihood, convert probabilities to binary predictions by threshold minimizing weighted loss of missed crises and false alarms, evaluate via loss functions.
  - Loss functions are subjective; example weights: LIC DSF weight on missed crises 0.66 (aggregation linear); VEE weight 0.5 (aggregation linear); Kaminski and Reinhart (1999) weight 0.5 (aggregation log-linear).
  - ROC curve and AUC provide objective alternative; optimal threshold where ROC tangent to loss-function indifference curve.
- Machine learning approaches:
  - Motivation: lower variance of parameter estimates across samples, improving out-of-sample stability versus traditional econometrics.
  - Regularization: Ridge (bounds sum of squared coefficients), Lasso (bounds sum of absolute coefficients), Elastic nets (combination).
  - Classification trees capture nonlinearities and interactions; ensembles (Random Forest) randomize over samples and variables to reduce overfitting and improve predictive performance.
- Implementation notes:
  - Crisis concepts set at intermediate severity; predictions are unconditional one-year-ahead crisis probabilities.
  - Out-of-sample evaluation emphasized to avoid overfitting.
  - From binary signals to three-tiered signals: options include loss-function thresholds for high risk and user-defined moderate-risk cutoffs (examples: high-risk threshold 15 percent, moderate-risk threshold 10 percent); LIC DSF stress-test approach described for debt signals.
  - Aggregation of sectoral risks options: simple average of sectoral flags; maximum of module flags; distribution-based thresholds using mean and one standard deviation.

### Machine Learning Performance — Quantitative Results and Robustness
- Machine learning provides more consistent and often better predictive performance than logit for LIC-only samples; Random Forest typically best.
- Selected cross-validated results (1990–2015) — exact reported figures:
  - Logit (limit variables): Binomial Deviance 6.77; Discrete predictions (training) Loss 0.44; Missed crises (training) 0.66; False alarms (training) 0.21; AUC 0.58. Standard deviations: (4.47) and (0.12).
  - Elastic net (limit variables): Binomial Deviance 0.55; Discrete predictions (training) Loss 0.40; Missed crises (training) 0.42; False alarms (training) 0.37; AUC 0.66. Standard deviations: (0.02) and (0.12).
  - Random Forest (limit variables): Binomial Deviance 0.55; Discrete predictions (training) Loss 0.40; Missed crises (training) 0.30; False alarms (training) 0.50; AUC 0.67. Standard deviations: (0.06) and (0.09).
  - Random Forest (full): Binomial Deviance 0.54; Discrete predictions (training) Loss 0.41; Missed crises (training) 0.24; False alarms (training) 0.57; AUC 0.67. Standard deviations: (0.03) and (0.09).
- Test-sample (training 1990–2009; test 2010–15) highlights:
  - Random Forest (limit variables) for prediction sample 2010−15: misses 25 percent of crises and generates 39 percent false alarms.
  - Random Forest (full) discrete predictions (test) Missed crises 0.32; False alarms 0.04; AUC 0.69. Standard deviations: (0.15) and (0.13).
- Pooling LICs and EMs:
  - Including EMs lowers variability and improves out-of-sample robustness; Random Forest remains top-performing.
  - Random Forest (limit variables) cross-validated: Binomial Deviance 0.50; Discrete predictions (training) Loss 0.35; Missed crises (training) 0.09; False alarms (training) 0.62; AUC 0.75. Standard deviations: (0.01) and (0.02).
  - Test-sample pooled example: Random Forest (limit variables) Discrete predictions (test) Missed crises 0.32; False alarms 0.39; AUC (test) 0.74. Standard deviations: (0.01) and (0.05).

### Policy-Relevant Implications and Recommended Approach
- For BoP crises: traditional econometric approaches struggle; Random Forest classification provides acceptable out-of-sample predictions (misses 25 percent of crises and sounds false alarms 39 percent over 2010-15 in pooled LIC+EM sample).
- For inflation crises: Random Forest recommended given lowest loss (-0.846 for 2008-16), missed crises 0.036, false alarms 0.348, highest AUC and out-of-sample stability.
- For financial sector crises: limited recent crisis frequency constrains out-of-sample prediction; in-sample RE-Mundlak logit yields missed crises 14 percent and false alarms 25 percent at threshold 2.2 percent. FSIs signal extraction predicts 2016 stress with missed crises 40 percent and false alarms 16 percent.
- General recommendations:
  - Use machine-learning methods (Random Forests) where they demonstrably outperform traditional methods, coupled with traditional econometric analysis and stylized-facts interpretation to preserve interpretability.
  - Balance thresholds between missed crises and false alarms according to policy priorities; consider three-tiered signals for operational use.
  - Pooling EM experience can improve consistency and, in some specifications, accuracy for LIC-focused prediction models.
  - Maintain emphasis on out-of-sample validation and regular robustness checks.

### Appendix I.1 — List of Low-Income Countries Included (Total 73)
- Afghanistan, Bangladesh, Benin, Bhutan, Bolivia, Burkina Faso, Burundi, Cambodia, Cameroon, Cape Verde, Central African Republic, Chad, Comoros, Republic of Congo, Democratic Republic of Congo, Côte d’Ivoire, Djibouti, Dominica, Eritrea, Ethiopia, The Gambia, Ghana, Grenada, Guinea-Bissau, Guinea, Guyana, Haiti, Honduras, Kenya, Kiribati, Kyrgyz Republic, Lao P.D.R., Lesotho, Liberia, Madagascar, Malawi, Maldives, Mali, Marshall Islands, Mauritania, Micronesia, Moldova, Mongolia, Mozambique, Myanmar, Nepal, Nicaragua, Niger, Nigeria, Papua New Guinea, Rwanda, St. Lucia, St. Vincent and the Grenadines, Samoa, São Tomé and Príncipe, Senegal, Sierra Leone, Solomon Islands, South Sudan, Sudan, Tajikistan, Tanzania, Timor Leste, Togo, Tonga, Tuvalu, Uganda, Uzbekistan, Vanuatu, Vietnam, Yemen, Zambia, and Zimbabwe.

*Source: wpiea2020289-print-pdf*

### References ________________________________________________________________55

### References

### Foreword
- Paper prepared in 2017-18 to provide options for strengthening risk analysis in low-income countries (LICs).
- Innovations proposed (including novel predictive modeling for LICs) were subsequently used to enhance the IMF’s risk analysis for countries at all income levels and informed IMF: “How to Assess Country Risk: The Vulnerability Exercise Approach Using Machine Learning” (forthcoming).
- The paper is published in only slightly altered form and does not reflect developments in LICs or progress in risk analysis in the past two to three years.

### I. Introduction and Overview — Background and Goal
- LICs have shown improved macroeconomic stability since the early 2000s but remain prone to volatility and severe stress events; the end of the commodity price super-cycle in 2014 contributed to strains on growth, fiscal balances, and external positions.
- Identified need: governments and advisers require tools to predict economic stress to reduce crisis likelihood and severity and to build buffers in good times.
- Existing crisis prediction frameworks (advanced and emerging economies): include external sector/BoP crises, sovereign crises/debt distress, financial sector/banking crises, and growth decelerations/recessions; empirical approaches include signal extraction (Kaminsky, Lizondo and Reinhart (1998)), logit/probit, and more recently machine-learning techniques such as classification trees.
- For LICs, prior IMF efforts emphasized growth decelerations and debt distress:
  - Dabla-Norris and Bal Gündüz (2012): Growth Decline Vulnerability Index (GDVI) using signal extraction; used in IMF Vulnerability Exercise for LICs (IMF 2014, 2015, 2016, and 2018).
  - IMF and World Bank joint debt sustainability framework for LICs (introduced 2005, recently strengthened) uses logit regressions.

### Objective and Methodological Highlights
- Proposed extension: early-warning systems for balance of payments crises, inflation crises, and financial sector crises in LICs, relying on machine-learning approaches where they outperform traditional econometrics.
- Rationale for machine learning:
  - Better at capturing non-linearities and interactions—key for crises that occur when multiple factors interact.
  - Machine learning methods can be less interpretable; to mitigate this, the paper pairs stylized-facts discussion and traditional econometrics with machine-learning prediction.
- Three technical elements emphasized:
  - Crisis concepts are operationalized at an intermediate level of severity to capture important but not only tail events.
  - Predictions identify the unconditional likelihood that a crisis will occur in the following year (absolute risk), using "vulnerability" and "risk" synonymously.
  - Predictive performance is assessed primarily via out-of-sample prediction to avoid overfitting.

### B. Overview of the New Crisis Concepts (summary)
- New crisis concepts for LICs: balance of payments crises, inflation crises, and financial sector crises.
- Country sample: 73 LICs observed since 1980 (see Appendix I.1); some data limitations vary by crisis concept.

### External Sector/Balance of Payments (BoP) Crises
- Crisis concept:
  - Relies on sharp nominal exchange rate depreciation, drops in reserves to a very low level, and contractions in import volumes indicating inability to maintain recent import levels.
  - Modifies existing BoP crisis definitions to address LIC-specific data quality issues; capital-account related crisis concepts are less relevant for many LICs.
- Relevance:
  - BoP crises have large output costs; GDP growth typically starts falling before crisis onset, indicating feedback between growth and BoP crises.
  - Comparison of GDP growth in the year of crisis and the two following years with quiet times suggests that at the end of this period output is about 7 percent lower than it would have been otherwise.
  - BoP crises associated with depreciations also result in inflation spikes.
- Stylized facts:
  - High fiscal deficits, sustained credit growth, and real effective exchange rate overvaluation often precede BoP crises.
  - Both shock sizes and buffer strength matter: for given shocks, stronger buffers reduce crisis likelihood; for given buffers, larger shocks increase crisis likelihood.
- Performance of early warning system:
  - Traditional econometric approaches struggle to predict BoP crises in LICs.
  - Random Forest classification technique provides acceptable out-of-sample predictions over 2010-15:
    - Misses 25 percent of crises.
    - Sounds false alarms 39 percent of the time.
    - Performance is retained reliably when the sample changes.

### Inflation Crises
- Crisis concept:
  - Inflation crises/stress episodes are defined as times when inflation exceeds 15 percent per year.
  - Level chosen because it is known to adversely affect growth and is of intermediate severity.
- Relevance:
  - High inflation adversely affects growth, income distribution, and poverty.
  - In the sample, comparing GDP growth during the year of the crisis and the two following years with quiet times suggests that at the end of this period output is about 2½ percent below the level that would have prevailed otherwise.
- Stylized facts:
  - High inflation episodes in LICs often result from both external shocks (world fuel and food price increases) and domestic policies (expansive fiscal and monetary policies); they can also result from exchange rate depreciation in external crises.
- Performance of early warning system:
  - Traditional econometric approaches failed to outperform desk forecasts.
  - Random Forests classification method delivers strong out-of-sample prediction performance:
    - Missed crises rate about 15 percent.
    - False alarm rate about 15 percent.

### Financial Sector Crises and Stress Episodes
- Crisis concept:
  - Main definition follows Laeven and Valencia (2013): a banking crisis identified by significant signs of distress (bank runs, system losses, bank liquidations) and/or significant banking policy interventions in response to losses.
  - Given limited frequency of systemic banking crises in LICs, an alternative notion of banking sector stress as assessed by country teams captures less severe stress events.
- Relevance:
  - Extensive literature documents output and fiscal costs of banking crises in advanced and emerging markets.
  - In LICs, large output costs of financial sector crises are not documented and are not apparent in the sample.
  - Public debt appears to rise by several percent of GDP in the context of financial sector crises, possibly reflecting fiscal costs of banking sector repair; Laeven and Valencia (2013) found debt-to-GDP ratios rose by an average of 5 percentage points in the 44 banking crisis episodes in LICs since the 1980s.
- Stylized facts:
  - Banking crises in LICs often follow a decline in commodity terms of trade.
  - High credit growth does not predict financial sector crises in LICs, in contrast to patterns in more developed countries.
- Performance of early warning system:
  - Using an updated sample of banking crises in LICs since the 1980s and a random effects logit estimator, (in-sample) crisis predictions are fairly accurate:
    - Missed crises: 14 percent.
    - False alarms: 25 percent.
  - Using FSIs to predict less severe financial stress episodes yields:
    - Missed crises: 40 percent.
    - False alarms: 16 percent.
    - This result would benefit from confirmation with a larger data set.

### Appendix I.1 — List of Low-Income Countries Included
- Total countries included: 73 (the 70 countries presently eligible for borrowing from the Poverty Reduction and Growth Trust (PRGT), except Somalia, plus Bolivia, Mongolia, Nigeria, and Vietnam which graduated from PRGT eligibility in 2015).
- Countries listed: Afghanistan, Bangladesh, Benin, Bhutan, Bolivia, Burkina Faso, Burundi, Cambodia, Cameroon, Cape Verde, Central African Republic, Chad, Comoros, Republic of Congo, Democratic Republic of Congo, Côte d’Ivoire, Djibouti, Dominica, Eritrea, Ethiopia, The Gambia, Ghana, Grenada, Guinea-Bissau, Guinea, Guyana, Haiti, Honduras, Kenya, Kiribati, Kyrgyz Republic, Lao P.D.R., Lesotho, Liberia, Madagascar, Malawi, Maldives, Mali, Marshall Islands, Mauritania, Micronesia, Moldova, Mongolia, Mozambique, Myanmar, Nepal, Nicaragua, Niger, Nigeria, Papua New Guinea, Rwanda, St. Lucia, St. Vincent and the Grenadines, Samoa, São Tomé and Príncipe, Senegal, Sierra Leone, Solomon Islands, South Sudan, Sudan, Tajikistan, Tanzania, Timor Leste, Togo, Tonga, Tuvalu, Uganda, Uzbekistan, Vanuatu, Vietnam, Yemen, Zambia and Zimbabwe.

*Content based solely on the provided PDF excerpt.*

### Appendix I.2. Some Explanations on Empirical Methods to Predict Stress Events

### Appendix I.2. Some Explanations on Empirical Methods to Predict Stress Events

### Assessing Predictive Performance
- Traditional three-step loss-function approach:
  - Step 1: Estimate likelihood of a crisis in the following year using probit, logit, or other approaches.
  - Step 2: Convert estimated probabilities to crisis/non-crisis predictions by choosing a threshold probability that minimizes a loss function over a weighted sum of the shares of missed crises in all crises and of false alarms in all calm times.
  - Step 3: Evaluate the empirical approach’s predictive performance using loss functions.
- Key properties of loss functions:
  - Subjective: reflect researcher preferences on Type I vs. Type II errors.
  - Different authors use different functional forms and different weights on missed crises and false alarms.
  - Example weights and aggregation methods reported: LIC DSF weight on missed crises 0.66, aggregation method linear; VEE weight 0.5, aggregation method linear; Kaminski and Reinhart (1999) weight 0.5, aggregation method log-linear.
- Receiver Operating Characteristic (ROC) curve as objective alternative:
  - Plots true positive rate (equal to 1 minus the rate of false negatives or missed crises) on y-axis vs. false positive rate (false alarms) on x-axis.
  - Random (uninformed) predictions lie on the 45-degree line between (0,0) and (1,1).
  - Greater curvature away from the 45-degree line implies larger improvement in prediction; area under the ROC curve (AUC) is a measure of predictive performance.
  - Each point on ROC corresponds to a different probability threshold. Extreme thresholds map to points (1,1) and (0,0).
- Interaction of ROC and loss-function indifference curves:
  - Functional form and weights determine indifference curve shapes; linear loss functions → linear indifference curves; noise-to-signal ratio loss → strictly convex curves.
  - Optimal threshold is where ROC is tangent to an indifference curve. Concave ROC or convex indifference curves → optimal threshold between 0 and 1. Linear indifference curves can yield corner solutions (0 or 1) if slope differs sufficiently from 1 and ROC has low concavity.
  - Corner or near-corner solutions imply little use of underlying model’s predictive potential; more balanced preferences better exploit predictive ability.
- Evaluation practice:
  - Both loss functions and ROC analyses are used to evaluate alternative empirical approaches’ predictive performance.

### Machine Learning Approaches to Prediction
- Motivation:
  - Machine learning (ML) techniques aim to lower variance of parameter estimates across samples, improving out-of-sample predictive stability compared with traditional econometric techniques that emphasize unbiased parameter identification in-sample.
  - Trade-off between bias and variance is made explicit in ML; ML can often achieve more stable predictive performance, though some approaches can be non-transparent and use implausible explanatory variables.
  - Researchers can mitigate non-transparency and implausibility by selecting suitable explanatory variables.
- “Ridge” and “Lasso”:
  - Start from logit and “shrink” coefficients toward zero by adding a constraint to the objective function:
    - Ridge: bounds the sum of squared coefficients.
    - Lasso: bounds the sum of absolute coefficients.
  - Constraint tightness governs behavior: generous constraint → coefficients close to logit; tight constraint → coefficients near zero. Regularization reduces model complexity.
  - Rationale: intermediate constraints trade off in-sample fit and robustness across samples.
  - Elastic nets: combinations of Lasso and Ridge can improve predictive quality.
- Classification Trees:
  - Sequentially split samples along the most informative criteria for future crises; do not impose linear structure and are less sensitive to outliers.
  - Can capture nonlinearities and interactions (important for crisis outbreaks).
  - Risk of overfitting as trees become complex; predictive performance improves with constraints on tree growth.
  - Simple trees can reduce to two branches (one variable) akin to signal extraction models.
  - Ensembles of trees (e.g., Random Forest) randomize over samples and variables and often outperform other methods despite severe overfitting of individual trees; ensemble diversity leverages “crowd wisdom”.

### Appendix I.3: Implementation Issues

### From Binary Early Warning Signals to Three-Tiered Signals
- Rationale: risk analysis can benefit from finer gradation than binary (high risk / not high risk).
- Options for three-tiered signals:
  - Set high-risk threshold via loss function minimization; set moderate risk threshold using a loss function with a higher weight on missed crises.
  - Set thresholds by reference to user-perceived meaningful probabilities (example: high-risk threshold 15 percent, moderate-risk threshold 10 percent), noting thresholds must be set at diverse levels for different crisis types to avoid signaling too many or too few crises.
  - Hybrid: high-risk threshold minimizes a loss function; moderate risk threshold corresponds to a set crisis probability (approach used by the VELIC).
  - LIC DSF approach with stress tests:
    - High risk if projected debt ratios exceed identified thresholds under baseline projections.
    - Moderate risk if ratios exceed thresholds under alternative stress test projections but not under baseline.
    - Applicable only for early warning systems that include stress tests.

### Aggregating Estimated Sectoral Crisis Risks
- Sectoral risks can be aggregated into an overall rating if desired, but some systems (e.g., VEA) view model collections as not lending themselves to aggregation and provide sectoral perspectives instead.
- When required, aggregation methods include:
  - Simple average of sectoral flags.
  - Maximum of the flags produced by constituent modules.
  - Overall vulnerability taken from distribution of average sectoral flags with thresholds set at the mean and one standard deviation above the mean.

### II. External Sector Crises in LICs — Concept, Definition, and Stylized Facts

### Definition and Concept for LIC External Sector Crises
- Purpose: define external sector crises for LICs using sharp drops in exchange rates, reserve levels, and imports, acknowledging data limitations and limited role of short-term capital flows in many LICs.
- Added criterion on drop of non-oil imports to capture crises not indicated by reserve movements and to account for dollarized economies, currency unions, or large deviations between official and parallel rates.
- To avoid false positives from non-crisis import declines, only consider non-oil import contractions with additional signs of significant external pressures.

- Specific crisis definition (a country is in external crisis in a year if one or more criteria is met):
  i. Average official exchange rate depreciates against the U.S. dollar by at least 30 percent relative to the preceding year and the rate of depreciation increases by at least 10 percentage points relative to the preceding year. (Adopted from Laeven and Valencia, 2013.)
  ii. Reserve holdings, measured in U.S. dollars, drop by at least 30 percent relative to the preceding year and to a level below 1½ months of imports. Exception: if median reserve coverage in preceding 10 years is less than 1½ months of imports, the country is excluded from the reserves criterion.
  iii. U.S. dollar value of non-oil imports falls by at least 15 percent relative to the preceding year and declines over a two-year period. Additionally, at least one of the following four conditions must hold:
    - Substantial negative current account shock measured as a deterioration of the current account balance net of imports by at least 2 percentage points of GDP in the current or preceding year.
    - Reserves at end of current year cover less than 1½ months of imports.
    - External debt arrears grow by at least 3 percent of GDP in the current year.
    - Country enters an IMF-supported program in the current or the following year.
- Exclusion to rule out orderly adjustments: exclude cases where import compressions meet the above criteria but reserve coverage in the current year and preceding year exceed 5 months of imports and reserve holdings increased by more than 5 percent in the current year. (In practice, this excludes 10 crisis observations.)
- Episode conventions:
  - Two or more consecutive years meeting the definition count as a sustained crisis episode rather than separate crises.
  - If two crises are separated by one tranquil year, that year is integrated into one crisis episode.

### Stylized Facts: Incidence and Duration
- Frequency and time in crisis:
  - On average, LICs moved into an external crisis once every 13 years.
  - LICs spent 16 percent of their time in crises.
  - Incidence dropped sharply around the turn of the century:
    - During the 1980s and 1990s, countries were in external crises 21 percent of the time.
    - Thereafter, countries were in crises 9 percent of the time.
  - A drop in incidence of sharp depreciations contributed most to the improvement in the 2000s, followed by fewer cases of reserve depletion.
- Sample and crisis-count statistics:
  - Sample comprises 2,589 observations, covering 73 countries over the period 1980-2016 at annual frequency.
  - Includes 197 crisis episodes, spanning 420 country-year observations.
- Cross-country heterogeneity:
  - Frontier markets spent limited time in external sector crises.
  - Fragile states experienced significantly more crises than the average LIC.
  - Commodity exporters, particularly fuel exporters, spent a larger share of time in crises than other countries (many are fragile countries).
  - Commodity exporters defined as LICs where at least 50 percent of export earnings come from commodities; fuel exporters are commodity exporters that are net fuel exporters (Bolivia, Chad, Republic of Congo, Nigeria, South Sudan, Timor-Leste, and Yemen).
- Duration:
  - Nearly two thirds of crisis episodes last only one year.
  - Most crises are over after three years.
  - Economic impacts, including recessions, typically last longer than the crisis episode itself.

*Source: Appendix I.2–I.3 and Section II (External Sector Crises in LICs) of the provided IMF content unit.*

### 10.      Using a simple linear regression to describe the behavior of macro-financial

### 10.      Using a simple linear regression to describe the behavior of macro-financial variables around external crises

### Run-up to external crises
- Expansionary policies commonly precede external crises:
  - Significant deterioration in the fiscal stance: revenue declines while spending remains broadly unchanged.
  - Current account balance weakens in line with fiscal expansion and indications of real exchange rate overvaluation.
  - Monetary and financial policies are expansive: domestic credit as a share of GDP is substantially higher than during tranquil times, and net credit to the public sector is rising.
  - Money supply grows and inflation rises.
- These expansionary policies do not lead to higher real growth; growth is below average and falling prior to crisis.

### During and after crises
- Sharp deterioration in economic performance once a crisis erupts; recovery takes several years:
  - Comparison of GDP growth during the crisis year and the two following years with growth in quiet times suggests that at the end of this period, output is about 7 percent lower than it would have been in the absence of a crisis.
  - Growth tends to slow already prior to the crisis, implying possible feedback between growth and crises.
- Fiscal and monetary dynamics:
  - Fiscal balance deteriorates sharply after crisis onset as GDP growth and fiscal revenue contract; fiscal position improves gradually thereafter with some expenditure tightening and recovering revenue and growth.
  - Monetary policy typically tightens after a crisis, with credit and money supply on a declining trend.
  - Credit to the public sector keeps rising to help finance the deteriorated fiscal balance, suggesting credit to the private sector is being squeezed.
  - Inflation spikes following crisis onset but only briefly, allowing the real exchange rate to fall and converge to equilibrium.
- External sector:
  - Current account improves gradually after crisis outbreak, initially mainly because of import compression.
  - External debt rises to a sustained higher level than before the crisis, reflecting both exchange rate depreciation and additional crisis-related borrowing.

### Differences across country groups
- Substantial heterogeneity across country groups:
  - Fuel-exporting LICs suffer the most: growth drops by 6 percentage points into negative territory, inflation jumps to high levels, and fiscal deficits more than double.
  - Countries with fixed exchange rate regimes suffer larger impacts than countries with flexible regimes.

### Triggers: shocks interacting with domestic buffers
- Crises are almost always triggered by shocks interacting with domestic macroeconomic weaknesses; weak buffers make even small shocks crisis-prone.
- Role of shock size and buffer strength (examples from sample statistics):
  - For countries with intermediate buffers: 18 percent of countries experiencing a large shock fell into crisis in the same or the next year, while only 10 percent of countries hit by a small shock did.
  - For countries hit by large shocks: those with strong buffers fell into a crisis only 6 percent of the time while countries with weak buffers did so in 33 percent of the cases.

### Predicting crises — approaches and findings
- Methods explored:
  - Traditional econometrics: simple logit model of external crisis probability with explanatory variables entering linearly without interactions; right-hand side variables lagged by at least one period and observations restricted to transitions from tranquil times into crisis.
  - Machine learning: Lasso, Ridge, and Random Forest approaches applied to the same and extended sets of explanatory variables, with parameter tuning via cross-validation and performance assessed out-of-sample.
- Key explanatory variables (logit specifications include):
  - Global variables: world real GDP growth, the VIX Index, a global liquidity indicator, ten-year U.S. interest rate, year-to-year changes in the global commodity price index.
  - Country-specific variables across real, fiscal, external, financial and institutional sectors: real GDP growth, inflation, overall fiscal balance, government grants, long-term external debt, short-term external debt service, REER misalignment, remittances, terms of trade changes, foreign exchange reserve adequacy indicators (short-term external debt/FX reserves, M2/FX reserves, FX reserves/imports), total credit to the economy, CPIA public-sector management and institutions cluster.
- Traditional econometrics results:
  - Most country-specific macroeconomic indicators significant with expected signs: weaker fiscal balance, higher inflation, higher or overvalued real exchange rate, low FX reserves, and deteriorating terms of trade are associated with higher crisis probability.
  - Among global variables, the VIX index is statistically significant across specifications with the expected sign; world real GDP growth, 10-year US interest rates, global liquidity and changes in commodity prices are not significant.
  - Adding EMs to the sample improves fit for LICs but substantially changes coefficient estimates; only the VIX and change in terms of trade remain significant when EMs are pooled with LICs.
- Predictive performance of logit models (out-of-sample):
  - Test sample period: forecasting period 2010−16 using baseline regression estimated on 1980−2009.
  - Thresholds chosen to minimize equal-weight loss on missed crises and false alarms.
  - Over 2010−16: false alarm rate was 15 percent; share of missed crises was 78 percent.
  - Adding EMs and varying loss weights improved predictions only limitedly; signal extraction methods delivered even weaker results.
- Machine learning performance:
  - Lasso and Ridge applied starting with 16 candidate explanatory variables; Random Forest also grown on same variable sets.
  - Performance assessed via shares of missed crises and false alarms, loss function, and area under the Receiver Operating Characteristic Curve (AUC).
  - Machine learning shows somewhat better and much more consistent predictive performance than traditional logit models when using LIC-only data.
  - Random Forest provides the best combination of missed crises and false alarms approaching acceptable levels: target benchmark cited as 30 percent share of missed crises and 50 percent share of false alarms.
  - Random Forest achieves highest AUC and lowest variability (stable performance across samples).
  - Sample split for robustness: training sample 1990-2009 and test sample 2010-15 (explanatory variables for predictions for 2011-16); machine learning models show robustness with test performance close to training performance, though overall performance levels remain limited.
- Benefits of pooling EM experience:
  - Drawing on EMs improves stability (lowers variability) and in some specifications improves mean prediction performance.
  - For prediction sample 2010−15 using initial limited set of 16 variables, Random Forest misses only 25 percent of crises and generates 39 percent false alarms.

### Appendix findings on interactions and robustness
- Quantification via repeated logit regressions on subsamples confirms interaction between shock size and fundamentals:
  - For weak fundamentals, both small and large shocks significantly increase crisis probability.
  - For strong fundamentals, only large shocks have a statistically significant impact on crisis probability.
- Definition and construction details (as used in the analysis):
  - Large adverse shock: meets either of five conditions over preceding 12 months — (i) terms of trade declines; (ii) global growth declines; (iii) VIX increases; (iv) tightening in global liquidity in the worst 10th decile; or (v) two or more natural disasters. Small adverse shocks: one natural disaster or unfavorable changes in other variables in bottom nine deciles.
  - Fundamentals index: for five key macro variables (growth, fiscal balance, public debt, CA balance, reserves coverage), observations classified into top quartile, bottom quartile, or middle; numerical values assigned and averaged into an index; quartiles of index define strong/medium/weak fundamentals.

*Italic source: wpiea2020289-print-pdf - 10.      Using a simple linear regression to describe the behavior of macro-financial variables around external crises*

### Appendix II.3: Machine Learning - Performance in Predicting Crises

### Appendix II.3: Machine Learning - Performance in Predicting Crises

### Machine-learning versus traditional approaches (overall findings)
- Machine learning techniques show predictive performance that is somewhat better on average and much more consistent than that of traditional approaches when using data exclusively on LICs.
- Across samples, predictive performance of logit models is weak on average and volatile; machine-learning models have somewhat better performance, with Random Forest providing the best combination of missed crises and false alarms (approaching acceptable levels described as 30 percent share of missed crises and 50 percent share of false alarms) and the highest AUC.
- Machine learning approaches achieve much more stable performance across different samples, evidenced by much lower variability of binomial deviance and the AUC compared with logit; low variability implies a high likelihood that predictive performance for a new sample will be close to those determined for past samples.

### Predictive performance for LICs only (cross-validated 1990–2015 and test 2010–15)
- Cross-validation setup: N = 20, with 5 resamples each. Standard deviations of binomial deviances and the AUC across 100 different samples are reported in parentheses.
- Selected cross-validated results (1990–2015) — key figures preserved exactly as reported:
  - Logit (limit variables): Binomial Deviance 6.77; Discrete predictions (training) Loss 0.44; Missed crises (training) 0.66; False alarms (training) 0.21; AUC 0.58. Standard deviations: (4.47) for binomial deviance and (0.12) for AUC.
  - Logit: Binomial Deviance 11.34; Discrete predictions (training) Loss 0.46; Missed crises (training) 0.69; False alarms (training) 0.23; AUC 0.55. Standard deviations: (3.04) and (0.11).
  - Elastic net (limit variables): Binomial Deviance 0.55; Discrete predictions (training) Loss 0.40; Missed crises (training) 0.42; False alarms (training) 0.37; AUC 0.66. Standard deviations: (0.02) and (0.12).
  - Elastic net: Binomial Deviance 0.55; Discrete predictions (training) Loss 0.41; Missed crises (training) 0.41; False alarms (training) 0.42; AUC 0.63. Standard deviations: (0.02) and (0.11).
  - Elastic net with interaction: Binomial Deviance 0.55; Discrete predictions (training) Loss 0.41; Missed crises (training) 0.31; False alarms (training) 0.52; AUC 0.63. Standard deviations: (0.02) and (0.11).
  - Tree: Binomial Deviance 0.56; Discrete predictions (training) Loss 0.50; Missed crises (training) 1.00; False alarms (training) 0.00; AUC 0.56. Standard deviations: (0.02) and (0.13).
  - Random Forest (limit variables): Binomial Deviance 0.55; Discrete predictions (training) Loss 0.40; Missed crises (training) 0.30; False alarms (training) 0.50; AUC 0.67. Standard deviations: (0.06) and (0.09).
  - Random Forest: Binomial Deviance 0.54; Discrete predictions (training) Loss 0.41; Missed crises (training) 0.24; False alarms (training) 0.57; AUC 0.67. Standard deviations: (0.03) and (0.09).
- Test-sample (training sample 1990–2009; test 2010–15) highlights:
  - Random Forest (limit variables) for prediction sample 2010−15: misses only 25 percent of crises and generates 39 percent of false alarms (version using a limited set of variables).
  - Random Forest (full) reported discrete predictions (test) Missed crises 0.32; False alarms 0.04; AUC 0.69. Standard deviations for binomial deviance and AUC: (0.15) and (0.13) for training/test pair reported.
- Summary interpretation: Random Forests preferred methodology for LIC-only sample due to lower mean loss, lower missed crises, lower false alarms in several specifications, and higher AUC and lower variability.

### Predictive performance when pooling LICs and EMs (training on both PRGT and EM countries)
- Including EMs as additional training data lowers variability of results and improves out-of-sample robustness; mean prediction performance improves for some specifications.
- Selected cross-validated results (1990–2015) and test-sample results:
  - Random Forest (limit variables) cross-validated: Binomial Deviance 0.50; Discrete predictions (training) Loss 0.35; Missed crises (training) 0.09; False alarms (training) 0.62; AUC 0.75. Standard deviations: (0.01) and (0.02).
  - Random Forest cross-validated: Binomial Deviance 0.50; Discrete predictions (training) Loss 0.38; Missed crises (training) 0.08; False alarms (training) 0.68; AUC 0.76. Standard deviations: (0.01) and (0.03).
  - Test-sample snapshot for pooled estimation (training 1990–2009; test 2010−15) — example figures reported:
    - Random Forest (limit variables): Discrete predictions (test) Missed crises 0.32; False alarms 0.39; AUC (test) 0.74. Standard deviations in parentheses: (0.01) for binomial deviance and (0.05) for AUC in training/test pair reported.
    - Random Forest: Discrete predictions (test) Missed crises 0.37; False alarms 0.62; AUC (test) 0.70. Standard deviations reported: (0.02) and (0.05).
- Conclusion: Drawing on EM experience improves consistency and accuracy; Random Forest remains the top-performing method.

### Inflation crises in LICs — definition, stylized facts, and drivers
- Definition: Inflation crises/episodes are defined as inflation exceeding 15 percent per year.
- Stylized facts:
  - Using the 15 percent threshold, there were 255 inflation crisis episodes out of 1264 country-year pairs (25 percent of the sample) during 1990−2015.
  - Incidence trend: 1990s — 37 percent of country-year pairs experienced inflation crises; since 2000 incidence dropped to 12 percent.
  - Median inflation across LICs fell during the 1990s and early 2000s; LIC inflation spiked in 2008 due mainly to higher world food prices.
- Drivers preceding inflation episodes (linear regression evidence):
  - Fiscal crises are 10 percentage points more likely to occur three years before an inflation episode than in other times.
  - Broad money and credit to the private sector grow faster prior to inflation episodes than in tranquil times.
  - Periods of strong real effective exchange rates (possible overvaluation) tend to precede inflation episodes.
  - Quarters with inflation crises are associated with nominal depreciations.
  - Oil and food price increases tend to precede years with inflation episodes.
- Economic impact:
  - Inflation crises are associated with a permanent output loss; a comparison suggests output is about 2½ percent below the level that would have prevailed otherwise at the end of the crisis and the following two years.

### Early warning systems for inflation crises — comparison of approaches (out-of-sample 2008–16)
- Systems compared: Naïve WEO, Sophisticated WEO, Panel Regression Model, Logit, LASSO, Random Forest.
- Overall 2008–16 performance (selected summary figures preserved exactly):
  - Naïve WEO:
    - # early warnings 20
    - P(missed crises) 0.795
    - P(false alarms) 0.026
    - Cutoff probability: n.a.
    - Loss function 2008-16: -0.345
  - Sophisticated WEO:
    - # early warnings 213
    - P(missed crises) 0.070
    - P(false alarms) 0.387
    - Cutoff probability: 16%
    - Loss function 2008-16: -0.809
  - Panel Regression Model:
    - # early warnings 278
    - P(missed crises) 0.053
    - P(false alarms) 0.542
    - Cutoff probability: 5%
    - Loss function 2008-16: -0.743
  - Logit:
    - # early warnings 61
    - P(missed crises) 0.541
    - P(false alarms) 0.115
    - Cutoff probability: 19%
    - Loss function 2008-16: -0.572
  - LASSO:
    - # early warnings 99
    - P(missed crises) 0.268
    - P(false alarms) 0.144
    - Cutoff probability: 8%
    - Loss function 2008-16: -0.771
  - Random Forest:
    - # early warnings 194
    - P(missed crises) 0.036
    - P(false alarms) 0.348
    - Cutoff probability: 29%
    - Loss function 2008-16: -0.846
- Specific system takeaways:
  - Naïve WEO (alarms when WEO forecast > 15 percent) misses most crises (79.5 percent) while sending few false alarms (2.6 percent).
  - Sophisticated WEO (assumes normal forecast error distribution; cutoff probability 16 percent) yields missed crises rate 7 percent and false alarm rate 38.7 percent; loss function -0.809.
  - Panel regression (cutoff 5 percent) yields missed crises 5.3 percent and false alarms 54.2 percent; loss function -0.743.
  - Logit (with WEO forecast included, only domestic GDP growth adds predictive power) with cutoff 19 percent yields missed crises 54.1 percent and false alarms 11.5 percent; loss function -0.572.
  - Lasso (cutoff 8 percent) yields missed crises 26.8 percent and false alarms 14.4 percent; loss function -0.771.
  - Random Forest (cutoff 29 percent) yields missed crises 3.6 percent and false alarms 34.8 percent; loss function -0.846 and highest area under the ROC curve.
- Robustness: Random Forest superior performance is apparent also in out-of-sample forecasts using data available in late summer 2009 covering 2010−17, with rates of missed crises and false alarms of less than 15 percent each.

### Policy-relevant implications and recommended approach
- For early warning of inflation crises in LICs, Random Forest classification is recommended given:
  - Lowest loss function value among compared systems (-0.846 for 2008-16).
  - Extremely low missed crises rate 0.036 (3.6 percent) over 2008–16 with an acceptable false alarm trade-off (0.348).
  - Highest AUC across methods and greater out-of-sample stability.
- Augmenting LIC-only training data with EM experience improves prediction consistency and can raise predictive accuracy; Random Forest remains preferred when pooling LICs and EMs.
- Practical notes on implementation:
  - Thresholds/cutoff probabilities are determined by minimizing the loss function using data up to 2014 in the analysis.
  - For operational early warning, balance between missed crises and false alarms should reflect policy priorities; Random Forest offers a low missed-crises profile at the cost of moderate false alarms.

*Italic: Source — Appendix II.3: Machine Learning - Performance in Predicting Crises (from wpiea2020289-print-pdf).*

### Appendix III.1. A Panel Regression-Based Model for Forecasting Inflation in LICs

### Appendix III.1. A Panel Regression-Based Model for Forecasting Inflation in LICs

### Model overview
- The model forecasts both inflation and inflation variance in the subsequent year, with inflation treated as a reduced-form function of plausible explanatory factors.
- Motivation: the Phillips curve inflation forecast model commonly used for advanced and emerging countries is not suitable for LICs because it is difficult to distinguish trend and cycle in LICs and timely data on output and unemployment gaps are often lacking.
- The specification is parsimonious, driven by theoretical considerations, data availability, and the aim to avoid overfitting; it uses data available in late summer (modifiable for other times of year).
- Estimation method: feasible generalized least squares (FGLS) for a system of two simultaneous equations:
  - Equation (2): the “level equation” providing the forecast of the inflation level.
  - Equation (3): the “conditional variance equation” providing an estimate of the inflation forecast squared error as a non-parametric function of the current level of inflation (allowing for conditional heteroscedasticity).

### Model specification — domestic factors
Preferred domestic explanatory variables:
- Current inflation carry-over (calculated from the IFS variable PCPI_IX): carry-over of inflation up to June of the present year used to forecast inflation in the next calendar year.
- Current inflation interacted with dummy for currency union: reflects expectation that inflation persistence is lessened in currency unions that maintain a peg to an anchor currency.
- Current money growth (WEO variable bmf).
- Current exchange rate depreciation and its carry-over (depreciation carry-up-to-August measures).
- Current reserve coverage (WEO variable iar_bmgs): reserve coverage measured as months of imports; low reserve coverage is a leading indicator for exchange rate depreciation and inflation increases.
- Current GDP growth (calculated from WEO variable ngdp_r): effect on inflation may be positive or negative depending on shock type.
- Interaction terms between current inflation, money growth and exchange rate depreciation to capture non-linearities; interaction coefficients are generally significant.
- Structural-break controls: dummy variables for exit from hyperinflation spells (indicator I, T_i marks end of hyperinflation spells).

### Model specification — external and structural factors
Preferred external/structural explanatory variables (included contemporaneously):
- WEO projections for world market price of food commodities in dollars (GAS variable food).
- WEO projections for world market oil prices in dollars (GAS variable crude) interacted with dummy for oil importer.
- Incidence of droughts (droughts dummy, and lagged droughts tested).
- Political instability.
- External variables treated as exogenous to a LIC’s own inflation.

### Estimation and empirical findings (inflation level and variance)
- Domestic-variable effects (preferred specification):
  - Higher next-year inflation is associated with higher current inflation, higher money growth, higher exchange rate depreciation, and lower reserve coverage.
- External/structural effects:
  - Higher next-year inflation is associated with higher global food and fuel price inflation, droughts, and political instability.
- Inflation variance:
  - Estimated inflation variance conforms to priors, with variance a monotonically rising function of inflation levels (the conditional variance equation produces an estimated inflation forecast standard error rising with inflation).

### Key numerical results and model fit (as reported)
- Number of observations (for the panel regression reported): 849
- R-squared values by column specification:
  - Column I R-squared: 0.241
  - Column II R-squared: 0.314
  - Column III R-squared (heteroscedastic preferred specification): 0.464
- Table summary of sign/statistical significance of predictors (Column III = preferred heteroscedastic model):
  - Inflation carry, up to June (t-1): +
  - Inflation carry, up to December (t-2): +
  - GDP growth (lagged): -
  - Money growth (lagged): +
  - Depreciation carry, up to August (t-1): +
  - Inflation X Depreciation: 0
  - Inflation X Money: 0
  - Depreciation X Money: -
  - Reserve coverage (months of imports): -
  - Food inflation: +
  - Fuel inflation X Importer: +
  - Droughts dummy: +
  - Droughts dummy (lagged): 0
  - Political instability: +
  - Currency union: 0

### Stylized facts on financial sector crises in LICs (context relevant to inflation and stress)
- Sample: 60 LICs over 1981−2015.
- Banking crises counted in sample: 43 total in the dataset; regressions capture 35 crises due to data availability.
- Cleaned regression sample: 1,588 observations, with an average period covered of 26.5 years per country.
- Temporal clustering: 39 of the 43 LIC crises took place between 1982 and 1996.
- Median crisis duration in the set: two years.
- Crisis-era characteristics in LICs (contrasting with advanced economies):
  - Commodity terms of trade fall in the lead-up to crises; volatility of terms of trade is higher prior to crises.
  - Credit growth is depressed prior to crises (contrast with credit booms in advanced-country crises).
  - M2 relative to foreign exchange reserves is high prior to crises—banking system liabilities not backed by international reserves is a leading indicator.
  - GDP growth is lower than in tranquil times prior to crisis events, but growth recovers fairly quickly after crisis onset.
  - Inflation is higher prior to crises than during normal times (potentially linked to devaluation following external shocks).
  - Public debt-to-GDP ratio starts increasing prior to crises, stabilizing one year after the crisis.

### Predicting crises — main econometric insights
- Estimation approach for crisis probability: logit model using the RE-Mundlak logit estimator (to avoid limiting sample to countries that experienced a crisis).
- Empirical findings:
  - Changes in commodity prices are key triggers: negative association between commodity terms-of-trade growth and likelihood of a banking crisis; positive association between volatility of commodity terms-of-trade and crisis probability.
  - No evidence that credit growth or other standard banking system variables (aside from liabilities not backed by international reserves) matter for occurrence of banking crises in LICs.
  - Crises are more likely to follow periods of high inflation, high public debt, and reliance on short-term borrowing.
  - Crises are more likely in periods of tight global monetary conditions.
  - No evidence that high net private capital inflows contribute to banking crises in the LIC sample.

*Source: Appendix III.1. A Panel Regression-Based Model for Forecasting Inflation in LICs, wpiea2020289-print-pdf*

### 18.      Given the very low number of banking crises in LICs in recent years, out-of-

### wpiea2020289-print-pdf - 18.      Given the very low number of banking crises in LICs in recent years, out-of-

### Predictive performance for banking crises
- Out-of-sample prediction covering recent years is not a meaningful option given the very low number of banking crises in LICs in recent years.
- In-sample predictive power of the empirical logit model:
  - Unconditional probability of a banking crisis in the sample: 2.2 percent (based on 35 crisis events).
  - Using 2.2 percent as a threshold for signaling a coming crisis:
    - Missed crisis rate (in-sample): 14 percent.
    - False alarm rate (in-sample): 25 percent.

### Predicting financial stress episodes (2016 desk survey)
- Desk survey (IMF (2017)) identified ten countries under financial stress in 2016: Burundi, Central African Republic, Chad, Liberia, Moldova, São Tomé and Príncipe, Sierra Leone, South Sudan, Tajikistan, and Zimbabwe.
- Focus of analysis: key financial soundness indicators (FSIs) as explanatory variables, motivated by prior evidence linking FSIs—such as NPLs and bank profitability—to banking crises.

### Differences in FSIs between stressed and non-stressed countries
- Test of means for years preceding stress designation finds robust statistical differences for:
  - Non-performing loans (higher for stressed countries).
  - Return on equity (lower for stressed countries).
  - Regulatory capital to risk weighted assets ratio (higher for stressed countries).
- Indicators with less consistent statistical differences:
  - Return on assets (lower for stressed countries).
  - Ratio of liquid assets to total assets (usually lower for stressed countries).
  - Provisioning rate (higher for stressed countries).

### Noise-to-signal ratio analysis and signal extraction
- Procedure for noise-to-signal computation for each FSI and year:
  - Construct a grid of 10,000 values between the 75th and 90th percentile of an FSI (between the 10th and 25th percentile for FSIs where lower values signal stress).
  - For each grid value compute the noise-to-signal ratio as in Kaminsky et al. (1998).
  - Choose the value that minimizes the noise-to-signal ratio as the threshold for that FSI.
- Interpretation:
  - The lower the noise-to-signal ratio, the higher the informational content; a noise-to-signal ratio of less than 1 indicates that the signal has some information.
- FSIs with the lowest noise-to-signal ratios (identified as leading indicators of financial stress):
  - Ratio of non-performing loans (NPLs) to total gross loans.
  - Return on equity.
  - Return on assets.
- Confirmation and caveat:
  - These results largely confirm the test-of-means findings, except return on assets which lacked consistent statistical significance in the test of means.
  - Results are consistent with evidence on OECD countries (Kasselaki and Tagkalakis 2014).

### Combined signal prediction quality for financial stress in 2016
- Rule: signal predicts stress if the value of at least one of the three FSIs breaches its threshold.
- Prediction performance:
  - Missed crisis rate: 40 percent.
  - False alarm rate: 16 percent.
- Note: The signal extraction approach provides acceptable prediction quality but should be used with caution given the small sample; exercise could be firmed up with additional desk surveys.

### Empirical logit model for banking crises (Appendix summary)
- Estimation approach:
  - Use RE-Mundlak logit estimator to relax no-correlation assumption between country-specific effects and covariates; coefficients capture within-country dimension.
- Key findings from baseline specifications:
  - Commodity terms of trade:
    - Negative association between growth rate of commodity terms of trade and likelihood of a banking crisis.
    - Positive association between volatility of commodity terms of trade and probability of crises.
  - Banking system variables:
    - No evidence that credit growth matters for occurrence of banking crises.
    - Banking system leverage and size do not show robust correlation with occurrence of crises.
    - Weak indications that greater bank liquidity reduces crisis likelihood (column 2).
    - High growth of banking system liabilities not backed by international reserves tends to precede crises (column 3).
  - Macroeconomic and external factors:
    - Crisis episodes more likely after periods of high inflation, high public debt, and reliance on short-term borrowing (column 3).
    - Including macroeconomic variables increases predictive power (area under the ROC curve higher than reduced model).
    - Evidence that crises are more likely in periods of tight global monetary conditions.
    - No evidence that high net private capital inflows contribute to banking crises.
- Economic magnitudes (one standard deviation effects, preferred model column 4):
  - Increase in commodity terms of trade by one standard deviation associated with about a 1 percent decline in the propensity of a crisis (sample unconditional probability: 2.2 percent).
  - High terms of trade volatility associated with an even larger increase in crisis propensity.
  - Fiscal variables:
    - Public debt: associated magnitude about 1 percent.
    - Short-term debt: associated magnitude about 2.2 percent.
  - Low reserve coverage and inflation: magnitudes range between 1.1 percent and 1.4 percent.

*Source: Appendix IV.1 and Sections D (Predicting Stress Episodes) of the supplied chapter content.*

### References for Section IV

### References for Section IV

### Early warning systems and indicators
- Anundsen, A. K., Gerdrup, K., Hansen, F., and Kragh-Sørensen, K., 2016, “Bubbles and Crises: The Role of House Prices and Credit,” Journal of Applied Econometrics, 31(7): 1291–311.  
- Bussiere, M. and Fratzscher, M., 2006, “Towards a New Early Warning System of Financial Crises,” Journal of International Money and Finance, 25(6): 953–73.  
- Caggiano, G., Calice, P., and Leonida, L., 2014, “Early Warning Systems and Systemic Banking Crises in Low Income Countries: A Multinomial Logit Approach,” Journal of Banking and Finance, 47:2 58–69. 
- Kaminsky, G. L., Lizondo, S., and Reinhart, C. M., 1998, “Leading Indicators of currency Crisis,” IMF Staff Papers, Vol 45(1): 1–48. 
- Kauko, K., 2014, “How to Foresee Banking Crises? A Survey of the Empirical Literature,” Economic Systems, 38(3): 289–308. 
- Kasselaki, M. T., and Tagkalakis, A. O., 2014, “Financial Soundness Indicators and Financial Crises Episodes,”Annals of Finance, 10: 623−69. 
- Navajas, C. M., and Thegeya, A., 2013, “Financial Soundness Indicators and Banking Crises,” IMF Working Paper 13/263 (Washington: International Monetary Fund). 

### Determinants, propagation, and costs of banking and financial crises
- Caballero, J. A., 2016, “Do Surges in International Capital Inflows Influence the Likelihood of Banking Crises?” Economic Journal, 126: 281–316. 
- Catao, L., and Milesi-Ferretti, G. M., 2014, “External Liabilities and Crises,” Journal of International Economics, 94: 18–32.  
- Cecchetti, Stephen G., Marion Kohler, and Christian Upper, 2009 “Financial Crises and Economic Activity,” NBER Working Paper 15379. 
- Dell'Ariccia, Giovanni, Detragiache Enrica, and Rajan, Raghuram, 2008, “The Real Effect of Banking Crises,” Journal of Financial Intermediation, Elsevier, vol. 17(1), pp. 89−112. 
- Demirguc-Kunt, A., and Detragiache, E., 1998, “The Determinants of Banking Crises in Developing and Developed Countries,” IMF Staff Paper, 45(1): 81–109 (Washington: International Monetary Fund). 
- Hoggarth, Glenn, Ricardo Reis, and Victoria Saporta, 2002, “Costs of Banking System Instability: Some Empirical Evidence,” Journal of Banking and Finance, 26 (5): 825−55. 
- Hutchison, Michael M., and Ilan Noy, 2005, “How Bad are Twins? Output Costs of Currency and Banking Crises,” Journal of Money, Credit and Banking, 37(4): 725−52. 
- Laeven, L., and Valencia, F., 2013, “Systemic Banking Crises Database,” IMF Economic Review, 61: 225–70 (Washington: International Monetary Fund). 
- Papi, L., Presbitero, A. F., and Zazzaro, A., 2015, “IMF Lending and Banking Crises,” IMF Economic Review, 63(3):6 44–91 (Washington: International Monetary Fund). 
- Reinhart, C. M., and Rogoff, K. S., 2013, “Banking Crises: An Equal Opportunity Menace,” Journal of Banking and Finance, 37(11): 4557–73. 
- Romer, C. D., and Romer, D. H., 2017, “New Evidence on the Aftermath of Financial Crisis in Advanced Countries,” American Economic Review, 107(10): 3072−118. 

### Credit booms, leverage cycles, and long-run perspectives
- Jorda, O., Schularick, M., and Taylor, A. M., 2011, “Financial Crises, Credit Booms, and External Imbalances: 140 Years of Lessons,” IMF Economic Review, 59(2): 340–78 (Washington: International Monetary Fund). 
- Jorda, Òscar, Moritz Schularick, and Alan M. Taylor, 2013, “When Credit Bites Back,” Journal of Money, Credit and Banking, 45 (2): 3−28. 
- Jorda, O., Schularick, M., and Taylor, A. M., 2015, “Leveraged Bubbles,” Journal of Monetary Economics, 76: S1–S20. 
- Schularick, M., and Taylor, A. M., 2012, “Credit Booms Gone Bust: Monetary Policy, Leverage Cycles, and Financial Crises, 1870−2008,” American Economic Review, 102(2): 1029–61. 
- Gourinchas, P.-O., and Obstfeld, M., 2012, “Stories of the Twentieth Century for the Twenty-First,” American Economic Journal: Macroeconomics, 4(1): 226–65. 

### Commodity prices, external shocks, and country-specific analyses
- Ciccone, A., 2018, “International commodity prices and civil war outbreak: new evidence for Sub-Saharan Africa and beyond,” Economic Working Papers 1596, Department of Economics and Business, Universitat Pompeu Fabra. 
- Gruss, B., 2014, “After the Boom-Commodity Prices and Economic Growth in Latin America and the Caribbean,” IMF Working Papers, WP/14/154 (Washington: International Monetary Fund). 

### Sentiment, textual analysis, and machine learning methods
- Correa, Ricardo, Keshav Garud, Juan M. Londono, and Nathan Mislang, 2017, “Sentiment in Central Banks’ Financial Stability Reports,” International Finance Discussion Papers 1203. 
- Kearney, C., and Liu, S., 2014, “Textual Sentiment in Finance: A survey of Methods and Models,” International Review of Financial Analysis 33, pp. 171−85. 
- Mikolov, Tomas, Ilya Sutskever, Kai Chen, Greg Corrado, and Jeffrey Dean, 2013, “Distributed Representations of Words and Phrases and their Compositionality,” Advances in Neural Information Processing Systems. arXiv:1310.4546. 

### Uncertainty, macro dynamics, and methodological contributions
- Cesa-Bianchi, A., Pesaran, H., and Rebucci, A., 2018, “Uncertainty and Economic Activity: A Multi-Country Perspective,” NBER Working Papers 24325, National Bureau of Economic Research, Inc. 
- Cerra, Valerie, and Sweta C. Saxena, 2008, “Growth Dynamics: The Myth of Economic Recovery,” American Economic Review, 98, 439–57. 
- Fernandez-Val, I., and Weidner, M., 2016, “Individual and time effects in nonlinear panel models with large N, T ,” Journal of Econometrics, vol. 192, issue1, 291-312. 

### IMF institutional publications and staff reports
- International Monetary Fund, 2009, “Staff Report for the 2009 Article IV Consultation, Third Review Under the Stand-By Arrangement, and Request for Modification of Performance Criteria,” (Washington). 
- International Monetary Fund, “Financial System Stability Assessment⸻Mongolia,” (Washington). 
- International Monetary Fund, 2017, “Macroeconomic Developments and Prospects in Low-Income Developing Countries – 2017” (Washington: International Monetary Fund). 

*Source: References for Section IV (wpiea2020289-print-pdf).*

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_Source: https://www.imf.org/-/media/files/publications/wp/2020/english/wpiea2020289-print-pdf.pdf_