## wp17282

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### Introduction and motivation
- Crises are rare but generate large economic and social costs and can afflict advanced economies (AEs) as well as emerging markets (EMs) and low-income economies (LICs); recent examples include the global financial crisis of 2008–09 and the European sovereign debt crisis of 2010–12.
- IMF Vulnerability Exercise (VE) origins and evolution:
  - VE established in 2001 to assess crisis vulnerability in EMs; IEO (2011) commended the VE for foreseeing fragile EMs before the global financial crisis but criticized lack of extension to AEs prior to that crisis.
  - Early warning models developed in 2009 for AEs (growth, fiscal, financial crises) and extended in 2013 to EMs.

### Three main messages
- Distinct crisis types
  - Growth, fiscal, and financial crises differ in intensity and affected sector; crises occur separately as well as together.
  - Separate early warning models for each crisis type are valuable.
- Model framework and drivers
  - Signal-extraction model builds on Kaminsky et al. (1998).
  - Key drivers: indicators of leveraged bubbles building and bursting; measures reflecting risk sharing, market adjustment, and policy response after shocks.
  - Models use a wide range of indicators beyond the external sector.
  - In-sample fit: sum of the percentages of missed crises and false alarms = 0.37 (overall reported metric).
- Uses and aggregation
  - Generate a “history of vulnerabilities” per country; aggregate to produce global history.
  - Global average and spread of crisis probabilities increase prior to each wave of crises.
  - For the global financial crisis:
    - AEs: vulnerabilities high because of bursting leveraged bubbles.
    - EMs: vulnerabilities from corporate and external sector weakness with credit and asset price booms.
  - Country-level behavior:
    - Upper range of predicted probabilities up to 0.50 (AEs) and up to 0.40 (EMs) in some outputs.
    - Probabilities rarely exceed 0.15 (AE cutoff cited); when they do, often a sharp spike followed by a speedy decline.

### Model design, validation, and scope
- Three key design decisions:
  - Which crises to focus on (banking/financial, growth, fiscal);
  - Estimation method: modified non-parametric signal-extraction (Kaminsky et al., 1998) rather than regressions;
  - Focus on flagging vulnerabilities (unconditional probabilities) rather than timing triggers.
- Signal-extraction procedure — key technical elements:
  - Annual country-year framework: relate variable values in year t to crisis incidence in year t+1.
  - Crisis definitions:
    - Growth crises: change in growth relative to previous five-year average in the lower 5th-percentile tail.
    - Fiscal crises: year-on-year increase in fiscal balance of 2.5 percent of GDP or higher, starting from a balance of -2.5 percent of GDP or lower.
    - Financial crises: systemic banking crises and/or currency crises per Laeven and Valencia (2012); currency crisis = nominal depreciation vis-à-vis the U.S. dollar of at least 30 percent and at least 10 percentage points higher than the prior year.
  - Loss function and threshold selection:
    - Loss = unweighted sum of percentages of missed crises and false alarms (Berg et al., 2005).
    - Threshold for each variable chosen to minimize the loss; graphical intuition = maximize vertical gap between crisis and non-crisis CDFs at threshold.
  - Flagging, weighting, grouping, aggregation:
    - Country-year receives 0/1 flag per variable.
    - Composite vulnerability index weights = (1-z)/z where z = sum of missed crisis % and false alarm %; weights normalized to sum to unity.
    - Variables grouped when correlation between 0/1 flags > 0.4; group weight set by most informative variable.
  - Composite-to-probability mapping:
    - Non-parametric mapping from composite scores to probabilities using a modified HP filter applied over score values and imposing monotonicity; mapping can have flat portions.
- Design choices to improve out-of-sample performance:
  - Limit interaction terms to household leverage and asset prices only.
  - Use the same variable set for each crisis type, allow thresholds and weights to differ.
  - For AEs restrict estimation to pre-2008 period to avoid overfitting to the global financial crisis.

### Advanced Economies (AE) — sample, methodology, and key findings
- Sample and estimation:
  - AE sample: 33 countries from 1985 onwards.
  - Estimation period ends in 2007 to avoid overfitting to the global financial crisis.
  - Financial crises data available only up to 2010 by Laeven and Valencia (2012); comparisons across crises restricted to 1985–2010 for some results.
- In-sample performance (1985–2007):
  - Average sum of the percentages of missed crises and false alarms (in-sample) = 0.30.
  - Within 1985–2007: financial crisis model performs best; growth crisis model performs worst.
  - For comparison: Berg et al. (2005) lowest in-sample sum = 0.58; lowest out-of-sample sum = 0.63.
- Out-of-sample / crisis-period behavior (2008–2010):
  - Average frequency of crises in AE sample rose from 0.03 in 1985–2007 to 0.17 during 2008–10.
  - Financial crisis model becomes uninformative during 2008–2010: financial crisis sum of errors = 0.96.
  - Fiscal crisis model’s fit remains similar to in-sample; growth crisis model performs worse during 2008–2010.
  - Interpretation: 2008–2010 financial crises may have been driven by variables not captured (e.g., banking-sector linkages).
- Back-cast history, aggregates, and sectoral contributions:
  - Back-cast time series of crisis probabilities and sectoral decompositions generated (each year’s probability based on previous year’s data).
  - Global/regional aggregates (1990–2014):
    - Mean probability elevated in early 1990s, increases before global financial crisis, jumps again in 2012 (fiscal crisis probability rises strongly).
    - Dispersion: upward spread above the median increases before and during the global crisis.
    - Median of financial crisis probabilities never changes due to clustering around a flat mapping at around 0.08.
  - Sectoral contributions (2009):
    - Household balance sheet effects primary driver (bursting asset price bubbles and household leverage).
    - Other co-equal sources in 2009: real, financial, and external sectors.
    - Public sector became especially important from 2010 onwards, driving fiscal crisis probability increases.
- Europe subset (countries receiving external assistance):
  - Crisis probabilities jumped higher than global averages; household balance-sheet vulnerabilities important, public and external sectors more important than elsewhere.
- Country-level ratings and dynamics:
  - VE AE cutoffs: L < 0.05; M 0.05–0.15; H > 0.15.
  - Although probabilities can reach 0.50, they rarely exceed 0.15; high entries typically spike then decline quickly.
  - Transition dynamics (selected transition matrices for AEs):
    - Growth transitions (rows L/M/H → cols L M H): L 0.52 0.46 0.02; M 0.21 0.65 0.15; H 0.06 0.51 0.43
    - Fiscal transitions: L 0.92 0.06 0.03; M 0.41 0.46 0.13; H 0.22 0.43 0.35
    - Financial transitions: L 0.58 0.42 0.00; M 0.14 0.80 0.05; H 0.01 0.58 0.41
  - Drivers of entering/exiting high ratings:
    - Household balance-sheet vulnerabilities more important over time among high-rated countries.
    - Exits from high ratings for growth/financial crises often due to household balance sheet improvement and reduction in external imbalances.
    - Exits from high fiscal ratings often associated with reductions in public sector vulnerabilities.

### Emerging Markets (EM) — sample, methodology, and key findings
- Sample and estimation:
  - EM sample: 53 countries from 1994 onwards.
  - Estimation period for EM models covers 1994–2010 (with some results noting 1994–2007 comparisons).
- Crisis incidence:
  - Average frequency of growth, fiscal, and financial crises rises from 0.04 during 1994–2007 to 0.07 during 2008–10 (overall).
  - Crisis incidence reached new heights in the global financial crisis; earlier waves in mid- and late 1990s.
- Relation to sudden stops:
  - Sudden stops identified using quantitative measures and IMF desk judgment (Chamon et al., 2007); overlap exists with growth, fiscal, financial crises but heterogeneity present.
  - Sudden stops show larger current account adjustment than financial crises.
- Variable set and estimation differences:
  - EM variable set includes more external-sector measures (REER appreciation, EMBI spread, oil dependence) and fewer household balance-sheet indicators due to data limitations.
  - Primary gap and public debt variables used only in fiscal crisis model.
- In-sample fit and crisis-period performance:
  - In-sample average sum of errors = 0.44 (worse than AE models but slightly better than Berg et al. (2005)).
  - Fiscal crisis model performs best; financial crisis model worst over 1994–2010.
  - Models perform better during the global crisis: average sum of errors declines from 0.46 during 1994–2007 to 0.38 during 2008–2010.
  - Average sum of errors over the out-of-sample period 2008–2010 reported elsewhere = 0.65 (comparable to Berg et al.’s out-of-sample for Kaminsky et al. (1998)).
- Back-cast history, aggregates, and sectoral contributions:
  - Global/regional aggregates (1994–2014): mean probabilities elevated in late 1990s and rise with the global financial crisis; dispersion and upward spread above median highest during these times.
  - Sector decomposition:
    - Real sector vulnerabilities declined over time as a share.
    - Household balance sheets account for a much lower share of vulnerabilities than in AEs (partly data availability).
    - 2009 global crisis: roughly equal contributions from real sector, external sector, and medium-term credit/asset price booms.
    - Public sector vulnerabilities persisted after the crisis, keeping fiscal crisis probability elevated.
- Regional example — Emerging Asia during Asian financial crisis:
  - Growth crisis probabilities rose 1994–1999 driven by corporate sector and inflation deterioration.
  - Financial crisis probabilities peaked in 1997; vulnerabilities attributed to medium-term credit/asset price growth and external imbalances; slowdown in asset price growth in 1996 may have presaged crash.
- Country-level ratings and dynamics:
  - VE EM cutoffs: L < 0.03; M 0.03–0.15; H > 0.15.
  - Upper range on probabilities up to 0.40; high ratings (> 0.15) rare and fleeting.
  - Drivers of exits from high ratings: improvements in real sector (financial/growth crises) and public/external sectors (fiscal crises).
- Transition matrices for EMs (selected blocks, rows L/M/H → cols L M H):
  - Growth transitions: L 0.79 0.20 0.01; M 0.35 0.60 0.05; H 0.08 0.49 0.42
  - Fiscal transitions: L 0.75 0.23 0.02; M 0.25 0.69 0.06; H 0.08 0.39 0.53
  - Financial transitions: L 0.72 0.27 0.00; M 0.16 0.83 0.02; H 0.07 0.36 0.57
- Selected numerical model performance metrics (preserved exactly where reported):
  - EM in-sample average sum of errors reported = 0.44.
  - Example EM sample metrics reported in tables: Growth crisis 0.42 / 0.39 / 0.53; Fiscal crisis 0.37 / 0.45 / 0.22; Financial crisis 0.52 / 0.55 / 0.39.
  - Alternate EM metrics elsewhere: Growth crisis 0.63 / 0.40 / 0.76; Fiscal crisis 0.39 / 0.34 / 0.51; Financial crisis 0.59 / 0.58 / 0.67.

### Crisis frequencies and sample-period exact values (preserved)
- AE crisis frequencies — Full sample / Estimation sample / Post-crisis sample:
  - Growth crisis: 0.08 / 0.05 / 0.30
  - Fiscal crisis: 0.03 / 0.02 / 0.06
  - Financial crisis: 0.04 / 0.02 / 0.16
- EM crisis frequencies — Full sample / Estimation sample / Post-crisis sample:
  - Growth crisis: 0.46 / 0.39 / 0.70
  - Fiscal crisis: 0.26 / 0.28 / 0.28
  - Financial crisis: 0.57 / 0.24 / 0.96
- Alternative EM frequency block (Estimation sample 1994-2010; Pre-crisis 1994-2007; Post-crisis 2008-2010):
  - Sudden stop: 0.05 / 0.04 / 0.10
  - Growth crisis: 0.04 / 0.03 / 0.11
  - Fiscal crisis: 0.04 / 0.03 / 0.06
  - Financial crisis: 0.05 / 0.05 / 0.05

### Limitations and robustness considerations
- Regime shifts and heterogeneity:
  - Estimation assumes countries within AE and EM groups follow similar stochastic processes; models do not capture within-sample regime heterogeneity.
  - Trade-off: common thresholds highlight sectoral sources of vulnerability for policy guidance; country-specific thresholds adapt to different regimes but may obscure cross-country signals.
  - Institutional evolution within countries may not be fully captured by explanatory variables (examples include exchange rate flexibility, domestic-currency debt issuance, independent central banks, euro adoption).
  - Political regime shifts can alter trigger frequency and cushioning mechanisms, changing crisis probabilities even with same vulnerabilities.
- Global risk outlook and contagion limits:
  - Global averages are unweighted (not GDP-weighted) to preserve confidentiality; models treat global developments mainly as external triggers rather than domestic vulnerabilities.
  - Model lacked precise banking-sector linkage information on eve of global crisis, limiting contagion capture; VE combines these models with banking contagion and trade contagion modules.
- Data and estimation robustness:
  - Variable selection trade-off: include enough variables to capture imbalances vs. avoid over-complexity and spurious in-sample fit.
  - Threshold estimation robust to outliers, but country crisis probabilities can be sensitive to measurement errors moving variables around thresholds.
  - Threshold values can jump between VE rounds when multiple values yield near-maximum CDF gaps; aggregation accounts for signal-to-noise but not threshold uncertainty.
  - Potential remedies: use judgmental threshold selection aligned with literature or desired missed-crises/false-alarms ratio; bootstrap thresholds to obtain standard deviations for aggregation.
  - Omitted variable bias remains possible: variable-by-variable thresholding does not eliminate bias; correlated variables may receive inflated aggregate weight.

### Conclusion and policy-relevant takeaways
- Purpose and role:
  - IMF early warning models (since 2009) assess vulnerabilities of AEs and EMs to growth, fiscal, and financial crises; crisis probabilities are comparable across countries and time and feed into the IMF’s Vulnerability Exercise.
- Key conclusions:
  - Separate models per crisis type are useful because crises do not always coincide and capture different phenomena.
  - Signal-extraction approach uses variables covering leveraged bubbles, risk sharing, market adjustment, and policy response.
  - Models can be back-cast to produce country “histories of vulnerabilities” and aggregated to produce a global history with reasonable properties.
- Stylized empirical findings:
  - Global average and spread of crisis probabilities increase prior to each crisis wave, including the global financial crisis.
  - Country probabilities mostly remain at low or medium levels and rarely enter the high category; entries into high category often spike sharply and decline quickly.
  - Models decompose sectoral drivers of vulnerability increases and identify sectors whose improvement is associated with crisis-probability declines.
- Practical use and communication:
  - Each VE round provides spreadsheets documenting country crisis-probability time series and reasons for changes since previous rounds to facilitate desk use and communication with authorities.

*Source: wp17282 - IMF working paper content provided in the source PDF.*

### References .............................................................................................................

### wp17282 - References

### Introduction and motivation
- Crises are rare but generate large economic and social costs and can afflict advanced economies (AEs) as well as emerging markets (EMs) and low-income economies (LICs); recent examples include the global financial crisis of 2008–09 and the European sovereign debt crisis of 2010–12.
- The IMF established a Vulnerability Exercise (VE) in 2001 to assess crisis vulnerability in EMs; IEO (2011) commended the VE for foreseeing which EMs were most fragile at the time of the global financial crisis but criticized the IMF for not having extended the VE to AEs before the global financial crisis.
- Early warning models developed by staff in 2009 assessed probabilities of growth, fiscal, and financial crises in AEs and were extended in 2013 to assess these same crisis types in EMs.

### Three main messages
- Distinct crisis types:
  - Growth, fiscal, and financial crises differ in intensity and affected sector; crises occur separately as well as together.
  - It is valuable to design separate early warning models for each crisis type.
- Model framework and drivers:
  - A signal-extraction model builds on Kaminsky et al. (1998).
  - Key drivers identified include indicators of leveraged bubbles building and bursting, plus measures that reflect risk sharing, market adjustment, and policy response after shocks.
  - The models use a wide range of indicators beyond the external sector (unlike sudden-stop literature).
  - In-sample fit: the sum of the percentages of missed crises and false alarms in the models is 0.37.
- Uses and aggregation:
  - Models generate a “history of vulnerabilities” for each country; these can be aggregated to produce a global history.
  - The global average and spread of crisis probabilities increase prior to each wave of crises.
  - For the global financial crisis:
    - AEs: vulnerabilities were high because of bursting leveraged bubbles.
    - EMs: vulnerabilities stemmed from corporate and external sector weakness coupled with ongoing credit and asset price booms.
  - At the individual country level:
    - The upper range of predicted probabilities goes up to 0.50.
    - Probabilities rarely exceed 0.15.
    - When high probabilities occur, they often feature a sharp upward spike followed by a speedy decline.
    - In AEs, decline typically follows bubble deflation stopping and external imbalance adjustment.
    - In EMs, decline typically accompanies recovery in corporate, public, and external sector health.

### Relation to prior work and model role within VE
- For EMs, the first VE model was based on Berg and Patillo (1999); a revised model introduced in 2007 assessed vulnerability to sudden stops (IMF, 2007).
- The crisis probability models presented are one input into the VE:
  - For AEs, they complement sector-specific modules calculated using different methodologies.
  - For EMs, they complement sector-specific scores derived from an updated EM sudden stop model.
- For LICs, separate early warning models exist for growth and financial distress.
- For a history of IMF early warning models up to 2012 see Chamon and Crowe (2013); for a comprehensive summary of the current VE see Ahuja et al. (2017).

### Model design, validation, and scope (overview)
- Framework: signal-extraction procedure applied to both AE and EM models (details in Sections III–V of the paper).
- Model outputs and diagnostics:
  - The models plot dynamics for macro-financial aggregates such as the current account, real GDP, the fiscal balance, and private sector credit.
  - Crisis incidence, overlap, macroeconomic dynamics, crisis probabilities, regional aggregations, sectoral contributions, probability and duration of ratings, sources of high ratings, and transitions between rating categories are analyzed across multiple figures and tables (listed in the source).
  - Robustness and estimation details, as well as nuances and limitations for practical application, are discussed in Section VI; conclusions in Section VII.

### Key empirical diagnostics and numerical results highlighted
- In-sample performance metric: sum of missed crises and false alarms = 0.37.
- Predicted probability bounds:
  - Upper range of predicted probabilities goes up to 0.50.
  - Probabilities rarely exceed 0.15.
- Historical crisis episodes emphasized: global financial crisis of 2008–09 and European sovereign debt crisis of 2010–12.

*Source: wp17282 - References (IMF working paper content provided in the source PDF).*

### Section II discusses the relationship between in-sample and out-of-sample fit, while sections III, IV and V describe the

### wp17282 - Section II discusses the relationship between in-sample and out-of-sample fit, while sections III, IV and V describe the

### Confidentiality and presentation constraints
- Steps taken to preserve confidentiality of the VE results:
  - (i) do not present any country-specific results;
  - (ii) present only back-cast results from the model based on the latest estimation dataset, not the ratings actually produced and/or assigned in the VE rounds;
  - (iii) present global/ regional averages only up to 2014 (so the recent post-taper-tantrum period is excluded);
  - (iv) to prevent identification of vulnerability ratings for large countries, none of the aggregate results are GDP-weighted.

### Model design — overview
- Three key design decisions:
  - which crises to focus on;
  - which estimation method to use;
  - whether to focus on flagging vulnerabilities to crises or on the timing of crises.
- Approach:
  - contributes to the second generation of early warning models (inspired by the global financial crisis) and estimates separate models for each type of crisis.
  - crises modeled: banking (financial) crises, sudden slowdowns in GDP growth, and a new fiscal crisis measure capturing episodes of sudden fiscal tightening.

### Type of crisis — characterization and rationale
- Context:
  - First-generation models: risk of speculative attacks, sudden stops, or banking distress (examples cited).
  - Second-generation models: broader vulnerabilities across AEs and EMs, including collapses in GDP and equity returns.
  - Christofides et al. (2016): different crisis dimensions (banking, balance of payments, exchange rates, growth) require different risk factors.
- Crisis types modeled:
  - Banking crises (financial crises) given the financial nature of the global crisis.
  - Growth crises capturing sudden slowdown in GDP growth from long-term trend.
  - Fiscal crises measured as episodes of sudden fiscal tightening, conjectured to reflect large negative reassessments of long-term fiscal outlook.
- Variable selection rationale:
  - Include medium-term variables capturing sustained booms in credit and asset prices.
  - Include near-term variables capturing sudden reductions in asset price growth and indicators of resilience (risk-sharing, private-sector cushioning, policy space).

### Estimation method — signal-extraction approach
- Method chosen:
  - Modified non-parametric signal-extraction approach (Kaminsky et al., 1998) rather than regression analysis.
  - Threshold for each variable flags observations as risky or safe; threshold chosen to minimize a loss combining false alarms and missed crises.
- Motivations:
  - Berg and Patillo (1999) and Berg et al. (2005) find Kaminsky et al. (1998) has reasonable out-of-sample properties.
  - Practical advantages:
    - Each variable’s threshold calculated separately, tolerating missing variables in some years.
    - Thresholds typically located mid-range, robust to poor-quality outliers.
    - Aggregation across many variables avoids multicollinearity issues in regressions.
    - Thresholds and calculation are easy to interpret and communicate to policymakers.
- Design choices to improve out-of-sample performance:
  - limit interaction terms to household leverage and asset prices only;
  - use same set of variables for each crisis type while allowing thresholds and weights to differ;
  - for AEs, restrict estimation procedure to the pre-2008 period to avoid overfitting to the global financial crisis (while still including variables revealed important by that crisis, e.g., household leverage).

### Vulnerability versus timing
- Conceptual distinction:
  - Vulnerabilities: factors increasing exposure to shocks (e.g., excessive credit growth, balance sheet mismatches).
  - Triggers: shocks (e.g., political news, bankruptcies, contagion) that interact with vulnerabilities to generate crises.
- Model task:
  - Assess vulnerabilities. Crisis probability reported is unconditional on current events and based on historical crisis frequency.
  - No attempt made to predict timing of triggers; judgment outside the model is necessary to convert unconditional probabilities into conditional probabilities given new shocks.
- Communication rationale:
  - Focus on vulnerabilities facilitates pre-emptive policy action.
  - Avoid “signal fatigue” from repeatedly flagging imminent crises when triggers do not materialize.
- Practical use:
  - Construct a “history of vulnerabilities” for each country, region, and the world to assess vulnerability even when triggers did not produce crises.

### Estimation procedure — definitions and technical steps
- Country grouping and estimation:
  - Recognize heterogeneity between AEs and EMs; select different variable sets for each group.
  - Conduct three separate estimations (one per crisis type) for each country group.
  - Use annual data: relate variable values in each year to crisis incidence in the following year.
- Crisis definitions:
  - Growth crises: occur when the change in growth relative to the previous five-year average growth rate lies in the lower 5th-percentile tail.
  - Fiscal crises: occur when there is a year-on-year increase in the fiscal balance of 2.5 percent of GDP or higher, starting from a balance of -2.5 percent of GDP or lower.
  - Financial crises: defined as systemic banking crises and/or currency crises, following Laeven and Valencia (2012). Currency crisis defined as a nominal depreciation of the currency vis-à-vis the U.S. dollar of at least 30 percent that is also at least 10 percentage points higher than the rate of depreciation in the year before.
- Loss function and threshold selection:
  - Loss function: unweighted sum of the percentages of missed crises and false alarms (following Berg et al., 2005).
  - Percentage of “missed crises”: percentage of crisis observations not flagged as vulnerable.
  - Percentage of “false alarms”: percentage of non-crisis observations incorrectly flagged as vulnerable.
  - Given crisis rarity, this loss function implies missing a crisis is substantially more costly than issuing a false alarm (example: if crises are 5 percent of the sample, then missing one crisis is as costly as issuing 19 false alarms).
  - For each explanatory variable, choose threshold to minimize the loss function.
  - Graphical intuition: maximize vertical gap between crisis and non-crisis cumulative distribution functions (CDFs) at the threshold.
- Flagging, weighting, grouping, and aggregation:
  - Each country-year observation receives a 0/1 flag per variable (1 if vulnerable side of threshold).
  - Aggregate flags into a composite vulnerability index score using weights based on signal-to-noise ratio: (1-z)/z, where z = sum of the percentages of missed crises and false alarms.
  - Weights normalized to sum to unity; weight of missing variables reallocated proportionally.
  - Variables grouped when correlations between their 0/1 flags are above 0.4; group total weight determined by the signal-to-noise ratio of the most informative variable in the group; within-group relative weights follow relative signal-to-noise ratios.
- Composite-to-probability conversion:
  - Use a non-parametric mapping:
    - Plot crisis realizations (0/1) against composite scores.
    - Generate a continuous line representing average of 0/1 crisis realizations around each composite score using a modified HP filter applied over score value (not over time).
    - Impose a monotonicity restriction on the continuous line to obtain mapping from composite scores to probabilities.
    - Mapping may have flat portions where score variation does not alter probability.

### Advanced Economies — sample and key findings
- Sample and estimation period:
  - AE sample covers 33 countries from 1985 onwards.
  - Estimation period ends in 2007 to avoid overfitting to the global financial crisis.
- Crisis incidence and impacts:
  - The global crisis had substantial impact: following a wave of financial crises in 2008, there were waves of growth crises in 2008–09 and of fiscal crises in 2009–12.
  - The average frequency of crises in the sample rose from 0.03 in 1985–2007 to 0.17 during 2008–10.
- Rationale for separate crisis models:
  - Different crisis types do not always occur together and capture different phenomena.
  - Financial crises show the most overlap, especially with growth crises.
  - Dynamics:
    - Typical growth and financial crises appear to be cushioned by an expanded fiscal deficit (distinct from the defined fiscal crisis).
    - Financial crises are followed by worsening growth performance in subsequent years.
    - Growth crises are followed by a quick recovery in activity.

*Source: wp17282 - Section II discusses the relationship between in-sample and out-of-sample fit, while sections III, IV and V describe the*

### Appendix Table A1 contains the list of countries in the AE sample.

### wp17282 - Appendix Table A1 contains the list of countries in the AE sample.

### Advanced Economies (AE) — methodology and variables
- Estimation period and crisis definition:
  - Financial crises are defined only up to 2010 by Laeven and Valencia (2012); comparisons between different types of crises are restricted to the period 1985–2010.
  - Model estimation period noted for some results as 1985–2007 (for in-sample comparisons excluding the global crisis).
- Variable set and structure:
  - Use the set of variables shown in table 2 (AE estimations).
  - Medium-term variables: capture sustained booms in credit and asset prices and relative growth in construction and financial sectors.
  - Near-term variables: include sudden reductions in asset price growth (negative readings for the “acceleration” variables), indicators of household balance-sheet dependence on asset price developments (interaction terms featuring the ratio of household liabilities to GDP), and sector-level indicators of overheating and resilience.
  - Every crisis model uses all variables in the table except primary gap and public debt variables (used only by the fiscal crisis model).

### AE — model fit, in-sample vs out-of-sample, and crisis-period behavior
- In-sample fit:
  - In-sample fit varies across the three crisis types and is on average better than the models evaluated by Berg et al. (2005).
  - Measure of in-sample fit: threshold estimation over the composite vulnerability index score and flag assignment (table 3).
  - Within 1985–2007: financial crisis model performs best, growth crisis model performs worst.
  - Average sum of the percentages of missed crises and false alarms (in-sample) is 0.30.
  - For comparison, the lowest in-sample sum of errors recorded by Berg et al. (2005) was 0.58, and the lowest out-of-sample sum of errors was 0.63.
- Out-of-sample and global financial crisis period (2008–2010):
  - Out-of-sample testing is limited; testing on 2008–2010 is inadequate because models were developed after the global financial crisis and contain conceptual information relevant to that crisis.
  - Comparing in-sample fit with the fit during 2008–2010:
    - Fiscal crisis model’s fit remains the same as the in-sample fit.
    - Growth crisis model performs worse during 2008–2010.
    - Financial crisis model becomes completely uninformative during 2008–2010: the financial crisis sum of errors is 0.96 (close to 1); if composite score is completely uninformative the sum of errors is 1.
  - Interpretation: financial crises during 2008–2010 may have been determined by variables not captured (e.g., banking-sector linkages to troubled U.S. banks).

### AE — back-casting, aggregates, sectoral contributions, and country-level dynamics
- Back-cast history of vulnerabilities:
  - Models can be back-cast to generate a time series of each crisis probability and a decomposition of each sector’s contribution to that probability (figure 6).
  - Each year’s probability is based on the data from the previous year.
- Global and regional aggregates (1990–2014):
  - Figure 7: unweighted averages of global and regional crisis probabilities, ranges, and interquartile ranges plotted for 1990–2014.
  - Mean probability of each crisis type:
    - Elevated in early 1990s,
    - Increases in run-up to global financial crisis,
    - Jumps again in 2012 (fiscal crisis probability rising especially strongly then).
  - Dispersion: upward spread above the median increases before and during the global crisis as vulnerabilities accumulate asymmetrically across countries.
  - Note: the median of financial crisis probabilities never changes because a significant fraction of countries cluster around a flat portion of the crisis probability mapping at around 0.08; mean and dispersion move similarly to other crises.
- Sectoral contribution decomposition:
  - Figure 8: relative sectoral contributions vary by crisis type and evolve over time.
  - 2009 (global crisis year): average vulnerabilities were high primarily because of household balance sheet effects (bursting asset price bubbles to which households were exposed because of their leverage).
  - Other roughly co-equal sources of vulnerability in 2009: real, financial, and external sectors.
  - Public sector became especially important from 2010 onwards, driving an increase in the fiscal crisis probability.
- Europe subset (countries receiving external assistance during global crisis and subsequent European sovereign debt crisis):
  - Figure 9: crisis probabilities jumped to higher values for these countries than globally.
  - For these countries, household balance-sheet vulnerabilities remain important, but public and external sectors were more important than for other countries in the sample.
- Country-level probabilities and categorization:
  - Model outputs analyzed over 1985–2017.
  - Probabilities categorized into L, M, and H using current VE AE cutoffs:
    - L = below 0.05
    - M = from 0.05 to 0.15
    - H = above 0.15
  - Table 4: Markov transition matrices for the three crisis types.
  - Figure 10: uses transition matrices to calculate (i) long-run probabilities of countries being in each category; (ii) long-run expected duration of each category conditional on starting there.
  - Observed dynamics: although upper range on probabilities goes up to 0.50, probabilities rarely exceed 0.15; when they do, they often show a sharp upward spike followed by a speedy decline.
  - Drivers of entering/exiting high ratings:
    - Figure 11: household balance-sheet vulnerabilities have become more important over time among countries diagnosed with high ratings (secular trends in asset prices and leverage and improved data availability).
    - Figure 12: exits from high ratings for growth and financial crises often due to improvement in household balance sheets (asset price bubble deflation stopping) and reduction in external imbalances.
    - Exiting high ratings on fiscal crises tends to be associated with reductions in public sector vulnerabilities.

### Emerging Markets (EM) — sample, crises, variables, and fit
- Sample and periods:
  - EM sample covers 53 countries from 1994 onwards.
  - Estimation period for EM models covers full period 1994–2010.
- Crisis incidence:
  - Crisis incidence reached new heights in the global financial crisis period, with earlier waves in mid- and late 1990s.
  - Average frequency of growth, fiscal, and financial crises rises from 0.04 during 1994–2007 to 0.07 during 2008–10.
- Relation to sudden stops:
  - Because of prior EM literature focus, models compared to sudden stops (sudden stops defined following Chamon et al. (2007)).
  - Sudden stops are identified via quantitative measures and IMF desk economist judgment; quantitative criteria include multiple standard-deviation and percentage-point rules (enumerated in the source).
  - Substantial overlap exists between growth, fiscal, financial crises and sudden stops, but each crisis type occurs separately and captures different phenomena; some sudden stops are heterogeneous (associated with growth collapses, fiscal tightenings, or financial crises).
  - Dynamics around crisis types (figure 15):
    - Financial crises are most similar to sudden stops, but current account adjustment is larger in sudden stops.
    - Fiscal crises: small impact on the current account; fiscal tightening occurs while other crises are cushioned by expanded fiscal deficits.
    - Sudden stops and financial crises: followed by worsening growth performance in subsequent years.
    - Growth crises: followed by quick recovery in activity.
- EM variable set and estimation differences:
  - Use the set of variables shown in table 6.
  - Data availability poorer than AEs: fewer household balance-sheet and construction/financial sector indicators.
  - Include external-sector measures: medium-term REER appreciation and sudden declines in rate of appreciation, EMBI spread, dependence on oil imports/exports.
  - Primary gap and public debt variables used only by fiscal crisis model (as in AEs).
- In-sample fit and crisis-period performance:
  - In-sample average sum of errors is 0.44 (slightly better than Berg et al. (2005), but worse than AE models).
  - Fiscal crisis model performs best, financial crisis model worst over 1994–2010.
  - Models perform better during the global crisis period: average sum of errors declines from 0.46 during 1994–2007 to 0.38 during 2008–2010.
  - Note on testing: truncating EM estimation period to end in 2007 would allow imperfect out-of-sample test over 2008–2010, acknowledging models were developed in 2013 with more information than available in 2007.

*Source: wp17282 - Appendix Table A1 contains the list of countries in the AE sample.*

### 8. It appears that the change in the sample period does not alter very much the in-sample fit of

### wp17282 - 8. It appears that the change in the sample period does not alter very much the in-sample fit of

### Model performance and back-cast vulnerabilities
- Average sum of errors over the out-of-sample period, 2008–2010, is 0.65.
- The 0.65 value is worse than in table 7 but comparable to Berg et al.’s (2005) calculated out-of-sample performance for the Kaminsky et al. (1998) model.
- Unlike in the AE case, none of the crisis models become uninformative during the global crisis.
- EM models are reported for the full sample period 1994–2010 for the remainder of the section.
- Models are used to back-cast a “history of vulnerabilities” for each country (figure 16).

### Global and regional aggregates, dispersion, and timing
- Figure 17: unweighted averages of global and regional probabilities, ranges, and interquartile ranges of country-level probabilities for the period 1994–2014.
- At global and regional levels:
  - Mean probability of each type of crisis is elevated throughout the late 1990s and increases with the global financial crisis.
  - Dispersion of country-level crisis probabilities—especially upward spread above the median—is highest during these times.
- Crises tend to affect countries in the highest tail of the vulnerability distribution; the upward spread above the median is therefore important.

### Sector decomposition of global crisis probability
- Figure 18 decomposes each sector’s contribution to the global crisis probability.
- Real sector (corporate sector health and inflation):
  - Accounts for a declining source of vulnerabilities over time, possibly due to market liberalization and inflation targeting.
- Household balance sheets:
  - Account for a much lower share of overall vulnerabilities than in the AE sample, partly because of poorer data availability for EMs.
- Global crisis year 2009:
  - Average vulnerabilities were high primarily because of roughly equal contributions from the real sector, external sector, and medium-term variables capturing credit and asset price booms.
- Public sector vulnerabilities persisted after the crisis, keeping fiscal crisis probability elevated.

### Emerging Asia during the Asian financial crisis
- Figure 19 zooms in on emerging Asia during the Asian financial crisis period:
  - Growth crisis probabilities increased steadily from 1994 to 1999 driven by deteriorating corporate sector and inflation performance.
  - Fiscal crisis probabilities were already high in 1995 because of external imbalances, reached a low in 1998, then rose again due to weakening real, financial, and public sector health.
  - Financial crisis probabilities grew from 1994 to a peak in 1997, coinciding with speculative attacks on East Asian currencies.
  - Model attributes financial vulnerabilities to excessive medium-term credit and asset price growth combined with external imbalances; it also detects a slowdown in asset price growth in 1996 that may have presaged the crash.

### Country-level dynamics, ratings, and drivers of entry/exit
- Model outputs cover 1994–2017.
- Probabilities categorized into L, M, and H ratings (VE cutoffs for EMs are):
  - L = below 0.03;
  - M = from 0.03 to 0.15;
  - H = above 0.15.
- Although the upper range on probabilities goes up to 0.40, high-probability ratings (above 0.15) are rare and fleeting.
- Drivers of high ratings and of exits from high ratings:
  - Over time, medium-term vulnerabilities related to credit and asset price booms have become more important among countries diagnosed with high ratings.
  - Improved availability of household balance sheet data is visible among those diagnosed with high ratings.
  - Prevalence of real sector vulnerabilities among high-rated countries has declined.
  - Countries exiting high ratings have done so due to improvements in:
    - Real sector (particularly for financial crisis ratings and for growth crisis ratings),
    - Public and external sectors (for fiscal crisis ratings).

### Limitations — Regime shifts
- Estimation implicitly assumes countries in the sample follow a similar underlying stochastic process (“regime”).
- AEs and EMs are separated because they follow different regimes; models do not capture regime differences within each estimation sample.
- Two dimensions of possible heterogeneity:
  - Differences in market liberalization and institutional development across countries (EM sample covers very diverse countries).
    - Choice between common thresholds and country-specific thresholds:
      - Common thresholds: identify sectoral sources of vulnerability, useful for policy guidance, but may flag vulnerabilities for countries that in practice sustain atypical levels.
      - Country-specific thresholds: suit differing regimes but may obscure cross-country policy-relevant signal on sectoral sources.
  - Evolution of economic institutions within countries over time (e.g., liberalization, inflation targeting, Eurozone creation, some countries moving from EM to AE).
    - Changes fully captured by explanatory variables do not pose a problem.
    - Problem arises if institutional changes are not fully captured by explanatory variables (examples provided for exchange rate flexibility, domestic currency debt issuance, independent central bank, and euro adoption).

- Political regime shifts:
  - Post-slowdown elections can elevate frequency of crisis triggers and remove cushioning mechanisms (e.g., bank bailouts becoming politically toxic, exchange rate depreciation ruled out), raising crisis probability for the same economic vulnerabilities.

### Limitations — Global risk outlook
- Global averages in sections IV and V reflect model output but may not be the best measure of global risks:
  - Paper does not GDP-weight averages or upper tail to preserve country confidentiality.
  - Models are based on individual-country data and treat global developments as external triggers rather than domestic vulnerabilities.
- Building a picture of global vulnerabilities requires additional indicators:
  - Macro evidence on building and bursting of global credit booms,
  - Sectoral data on bottlenecks in key financial and goods markets,
  - Assessments of correlation and transmission of shocks across countries.
- Model lacked information on precise banking-sector linkages on eve of global crisis, limiting ability to capture contagion during 2008–10; combined with other modules (banking contagion and trade contagion) in the VE.

### Limitations — Data and estimation
- Variable selection:
  - Trade-off between including enough variables to capture different manifestations of imbalances and avoiding over-complexity that yields spurious in-sample fit.
  - Aggregation procedure down-weights correlated variables.
  - Preference for variables with long time-series coverage to avoid overfitting to recent crises; downside is exclusion of recent potentially relevant series (e.g., sovereign CDS spreads).
- Data quality issues:
  - Threshold estimation is robust to outliers but each country’s crisis probability can be sensitive to measurement errors that move variables just above or below thresholds.
  - Sensitivity particularly salient for balance sheet and survey data subject to slow revision.
- Estimation robustness issues:
  - Calculated threshold values can jump between VE rounds when the distance between crisis and non-crisis CDFs is near its maximum for two different variable values.
  - Aggregation accounts for signal-to-noise but not for threshold uncertainty; same variable value may be classified differently across rounds.
  - Two approaches to address threshold uncertainty:
    - Use judgment to select threshold aligning with literature or desired missed-crises/false-alarms ratio.
    - Generate bootstrapped estimates of thresholds to obtain standard deviations that could be incorporated into aggregation.
- Correlated variables and omitted variable bias:
  - Variable-by-variable threshold estimation does not eliminate omitted variable bias, which can inflate the weight of variables correlated with true risk factors.
  - Down-weighting correlated variables helps but cannot remedy missing true risk factors.

### Conclusion and policy-relevant takeaways
- Purpose:
  - Early warning models developed at the IMF since 2009 assess vulnerabilities of AEs and EMs to growth, fiscal, and financial crises; crisis probabilities are comparable across countries and over time and are used in the IMF’s Vulnerability Exercise.
- Three main messages:
  - It is useful to have a separate model for each type of crisis because crises do not always coincide and capture different phenomena.
  - A signal-extraction approach is used to derive crisis probabilities, employing explanatory variables covering leveraged bubbles, risk sharing, market adjustment, and policy response.
  - Models can be back-cast to generate a “history of vulnerabilities” for each country and aggregated to produce a global history with reasonable properties.
- Stylized results:
  - Global average and spread of crisis probabilities increase prior to each wave of crises, including the recent global crisis.
  - At the country level, probabilities mostly remain at low or medium levels and rarely enter the high category; entries into the high category often show a sharp spike followed by a speedy decline.
  - Models help decompose which sectors historically drove large increases in vulnerabilities and which sectors typically need improvement for crisis probabilities to decline.
- Practical use:
  - Every VE round provides a spreadsheet documenting each country’s crisis-probability time series and the reasons probabilities changed since the previous round to facilitate country-desk use and communication with country authorities.

*Source: https://www.imf.org/-/media/files/publications/wp/2017/wp17282.pdf*

### References

### References

### Major cited works on early warning systems, crises, and financial vulnerability
- Abad, J., M. D’Errico, N. Killeen, V. Luz, T. Peltonen, R. Portes, and T. Urbano, 2017, “Mapping the Interconnectedness between E.U. Banks and Shadow Banking Entities,” NBER Working Paper 23280.
- Ahuja, A., K. Wiseman, and M. Syed, 2017, “Assessing Country Risk—Selected Approaches,” IMF Technical Notes and Manuals 17/08.
- Alessi, L., and C. Detken, 2017, “Identifying Excessive Credit Growth and Leverage,” Journal of Financial Stability, forthcoming.
- Babecký, J., T. Havránek, J. Matĕjů, M. Rusnák, K. Šmídková, and B. Vašíček, 2012, “Banking, Debt, and Currency Crises: Early Warning Indicators for Developed Countries,” ECB Working Paper 1485.
- Berg, A., E. Borensztein and C. Pattillo, 2005, “Assessing Early Warning Systems: How Have They Worked in Practice?” IMF Staff Papers, 52(3): 462–502.
- Berg, A., and C. Pattillo, 1999, “Are Currency Crises Predictable? A Test,” IMF Staff Papers, 46(2): 107–138.
- Blanchard, O. J., M. Das, and H. Faruqee, 2010, “The Initial Impact of the Crisis on Emerging Market Countries,” Brookings Papers on Economic Activity, 2010(1): 263–307.
- Borio, C., and P. Lowe, 2002, “Asset Prices, Financial and Monetary Stability: Exploring the Nexus,” BIS Working Paper 114.
- Calvo, G. A., 1998, “Capital Flows and Capital Market Crises: The Simple Economics of Sudden Stops,” Journal of Applied Economics, 1(1), 35–54.
- Cerutti, E., 2013, “Banks’ Foreign Credit Exposures and Borrowers’ Rollover Risks: Measurement, Evolution and Determinants,” IMF Working Paper 13/09.
- Chamon, M., and C. Crowe, 2013, “Chapter 34 - Predictive Indicators of Financial Crises,” in The Evidence and Impact of Financial Globalization.
- Chamon, M., P. Manasse, and A. Prati, 2007, “Can We Predict the Next Capital Account Crisis?” IMF Staff Papers, 54(2): 270–305.
- Christofides, C., T. S. Eicher, and C. Papageorgiou, 2016, “Did Established Early Warning Signals Predict the 2008 Crisis?” European Economic Review, 81: 103–114.
- Drehmann, M., and M. Juselius, 2014, “Evaluating Early Warning Indicators of Banking Crises: Satisfying Policy Requirements,” International Journal of Forecasting, 30(3): 759–780.
- Eichengreen, B., and A. K. Rose, 2004, “Staying Afloat When the Wind Shifts: External Factors and Emerging-Market Banking Crises,” in Money, Capital Mobility, and Trade: Essays in Honor of Robert A. Mundell.
- Eichengreen, B., A. K. Rose, and C. Wyplosz, 1995, “Exchange Market Mayhem: The Antecedents and Aftermath of Speculative Attacks,” Economic Policy, 10(21), 249–312.
- Frankel, J. A., and A. K. Rose, 1996, “Currency Crashes in Emerging Markets: An Empirical Treatment,” Journal of International Economics, 41(3-4), 351–366.
- Frankel, J. A., and G. Saravelos, 2012, “Can Leading Indicators Assess Country Vulnerability? Evidence from the 2008–09 Global Financial Crisis,” Journal of International Economics, 87(2): 216–231.
- Ghosh, A. R., J. D. Ostry, and N. Tamirisa, 2009, “Anticipating the Next Crisis—What Can Early Warning Systems be Expected to Deliver?” Finance and Development, 46(3): 35–37.
- Ghosh, S. R., and A. R. Ghosh, 2003, “Structural Vulnerabilities and Currency Crises,” IMF Staff Papers, 50(3): 481–506.
- Kaminsky, G. L., 1999, “Currency and Banking Crises: The Early Warnings of Distress,” IMF Working Paper 99/178.
- Kaminsky, G. L., S. Lizondo, and C. M. Reinhart, 1998, “Leading Indicators of Currency Crises,” IMF Staff Papers, 45(1): 1–48.
- Laeven, L., and F. Valencia, 2008, “Systemic Banking Crises: A New Database,” IMF Working Paper 08/224.
- Laeven, L., and F. Valencia, 2012, “Systemic Banking Crises Database: An Update,” IMF Working Paper 12/163.
- Lane, P. R., and G. M. Milesi-Ferretti, 2007, “The External Wealth of Nations Mark II: Revised and Extended Estimates of Foreign Assets and Liabilities, 1970–2004,” Journal of International Economics, 73(2): 223–250.
- Obstfeld, M., J. C. Shambaugh, and A. M. Taylor, 2009, “Financial Instability, Reserves, and Central Bank Swap Lines in the Panic of 2008,” The American Economic Review: Papers and Proceedings, 99(2): 480–486.
- Rey, H., 2015, “Dilemma not Trilemma: The Global Financial Cycle and Monetary Policy Independence,” NBER Working Paper 21162.
- Romer, C. D., and D. H. Romer, 2015, “New Evidence on the Impact of Financial Crises in Advanced Countries,” NBER Working Paper 21021.
- Schularick, M., and A. M. Taylor, 2012, “Credit Booms Gone Bust: Monetary Policy, Leverage Cycles, and Financial Crises, 1870–2008,” The American Economic Review, 102(2): 1029–1061.

### Datasets, IMF products, and methodological toolkits referenced
- IMF products cited: SM/07/328 “Assessing Underlying Vulnerabilities and Crisis Risks in Emerging Market Countries—A New Approach” (September 17), IMF Policy Paper “The IMF-FSB Early Warning Exercise: Design and Methodological Toolkit” (2010), World Economic Outlook chapters (2009a; 2009b).
- Databases and data sources explicitly referenced:
  - Laeven and Valencia (2012) systemic banking crisis incidence (data available only up to 2010).
  - WEO = IMF World Economic Outlook.
  - CVU = IMF Corporate Vulnerability Utility.
  - EBA = IMF External Balance Assessment.
  - WB WDI = World Bank World Development Indicators.
  - OECD EO = OECD Economic Outlook.
  - OECD HPD = OECD Housing Prices Database.
  - GPG = Global Property Guide.
  - LV = Laeven and Valencia (2012).
  - EWN = External Wealth of Nations dataset (updated Lane and Milesi-Ferretti (2007)).
  - Fitch, Bloomberg, FAD FP, CSD, INS as data sources in tables.

### Figures and notes included in the document
- Figure captions and notes:
  - Figure 1. Threshold Estimation — Source: Authors’ illustration.
  - Figure 2. Probability Mapping — Source: Authors’ illustration.
  - Figure 3. Crisis Incidence in AEs — Source: Laeven and Valencia (2012) and authors' calculations. Note: Data on financial crisis incidence is available only up to 2010.
  - Figure 4. Overlap of AE Crises, 1985–2010 — Source: Authors' calculations. Note: Crises in the same or adjacent years are regarded as coincident.
  - Figure 5. Macroeconomic Dynamics Around AE Crises, 1985–2010 — Source: Authors' calculations. Note: Date 0 is crisis year; Dates -1 and 1 are years before and after.
  - Figure 6. Crisis Probabilities at the Individual Country Level — Source: Authors’ calculations. Note: HH = Household balance sheet; MT = Medium term.
  - Figure 7. AE Crisis Probabilities at the Global and Regional Levels — a) Growth Probabilities; b) Fiscal Probabilities; c) Financial Probabilities — Source: Authors’ calculations. Note: Appendix Table A1 contains the list of countries in the AE sample and their breakdown by region.
  - Figure 8. Sectoral Contributions to Global Crisis Probabilities in AEs — Source: Authors’ calculations. Note: HH = Household balance sheet; MT = Medium term.
  - Figure 9. AEs in Distressed Europe during the Global Crisis — Source: Authors’ calculations. Note: HH = Household balance sheet; MT = Medium term.
  - Figure 10. Probability and Duration of Ratings for AEs, 1985–2017 — Source: Authors' calculations. Note: Probabilities and durations are calculated using the transition matrices in table 4.
  - Figure 11. Sources of High Ratings for AEs — Source: Authors' calculations. Note: HH = Household balance sheet; MT = Medium term.
  - Figure 12. Transition from High to Medium/Low Rating for AEs, 1985–2017 — Source: Authors' calculations. Note: HH = Household balance sheet; MT = Medium term. Date 0 is the last year with a high rating before a downgrade in rating; Dates -1 and 1 are years before and after.
  - Figures 13–23 and associated notes mirror the AE figures for EMs with corresponding sourcing: Laeven and Valencia (2012) where applicable, authors’ calculations, and notes on sample years and variable definitions (e.g., HH = Household balance sheet; MT = Medium term).
  - Figure 23. Threshold Robustness — Source: Authors’ illustration.

### Tables, sample periods, crisis frequencies, and selected numerical results (preserved exactly as in source)
- Sample periods:
  - AE full sample 1985-2010; estimation sample 1985-2007; post-crisis sample 2008-2010.
  - EM full sample 1994-2010; estimation sample 1994-2007; post-crisis sample 2008-2010.
- Crisis frequencies (AEs) — Full sample / Estimation sample / Post-crisis sample:
  - Growth crisis: 0.08 / 0.05 / 0.30
  - Fiscal crisis: 0.03 / 0.02 / 0.06
  - Financial crisis: 0.04 / 0.02 / 0.16
- Crisis frequencies (EMs) — Full sample / Estimation sample / Post-crisis sample:
  - Growth crisis: 0.46 / 0.39 / 0.70
  - Fiscal crisis: 0.26 / 0.28 / 0.28
  - Financial crisis: 0.57 / 0.24 / 0.96
- Alternative EM frequency block (presented elsewhere in tables):
  - Estimation sample 1994-2010; Pre-crisis sample 1994-2007; Post-crisis sample 2008-2010:
    - Sudden stop: 0.05 / 0.04 / 0.10
    - Growth crisis: 0.04 / 0.03 / 0.11
    - Fiscal crisis: 0.04 / 0.03 / 0.06
    - Financial crisis: 0.05 / 0.05 / 0.05
- Transition matrix excerpts for AEs (rating at t → rating at t+1):
  - Growth rating transitions (L/M/H rows): L 0.52 0.46 0.02; M 0.21 0.65 0.15; H 0.06 0.51 0.43
  - Fiscal rating transitions (L/M/H rows): L 0.92 0.06 0.03; M 0.41 0.46 0.13; H 0.22 0.43 0.35
  - Financial rating transitions (L/M/H rows): L 0.58 0.42 0.00; M 0.14 0.80 0.05; H 0.01 0.58 0.41
- Transition matrix for EMs (Table 9) — rating at t → rating at t+1 (Growth / Fiscal / Financial blocks):
  - Growth transitions (L/M/H rows): L 0.79 0.20 0.01; M 0.35 0.60 0.05; H 0.08 0.49 0.42
  - Fiscal transitions (L/M/H rows): L 0.75 0.23 0.02; M 0.25 0.69 0.06; H 0.08 0.39 0.53
  - Financial transitions (L/M/H rows): L 0.72 0.27 0.00; M 0.16 0.83 0.02; H 0.07 0.36 0.57
- Model performance and error summaries (selected reported values):
  - EM full/estimation/post-crisis sample reported example metrics: Growth crisis 0.42 / 0.39 / 0.53; Fiscal crisis 0.37 / 0.45 / 0.22; Financial crisis 0.52 / 0.55 / 0.39.
  - Additional EM metrics in a different table: Growth crisis 0.63 / 0.40 / 0.76; Fiscal crisis 0.39 / 0.34 / 0.51; Financial crisis 0.59 / 0.58 / 0.67.
- Tables of variables and sources for AE and EM crisis probability models list exact variable names and sources (examples):
  - Public sector: Real GDP (WEO); General government balance/GDP (WEO); Cyclically-adjusted primary deficit/GDP (Primary gap/GDP 3/; WEO); Public debt/GDP (WEO).
  - Financial sector: Capital adequacy ratio (Fitch / CSD); Return on bank assets (Fitch / CSD); Private sector credit growth (5-yr) (WB WDI); Non-performing loans (Fitch / CSD); Housing price growth (5-yr) (OECD HPD, GPG); Stock price growth (5-yr) (Bloomberg).
  - Household balance sheets: Housing price acceleration (OECD HPD, GPG); Stock price acceleration (Bloomberg); Household liabilities/GDP (OECD EO).
  - External and real sector variables: Current account/GDP (WEO); External debt/GDP (EWN, WEO / WEO, CSD); External debt/exports (EWN, WEO / WEO, CSD); Black-Scholes-Merton default prob. (CVU); Return on corporate assets (CVU); Price to earnings ratio (CVU); Deviation from EBA norm (EBA).
- Notes on variable usage:
  - 1/ WEO = IMF World Economic Outlook, CVU = IMF Corporate Vulnerability Utility, EBA = IMF External Balance Assessment, WB WDI = World Bank World Development Indicators, OECD EO = OECD Economic Outlook, OECD HPD = OECD Housing Prices Database, GPG = Global Property Guide, LV = Laeven and Valencia (2012), EWN = External Wealth of Nations dataset, updated version of Lane and Milesi-Ferretti (2007).
  - 2/ Nominal housing and stock prices are used in the VEA because they interact with nominal contracts held on financial sector and household balance sheets. Price acceleration is defined as the change in the annual growth rate of the price.
  - 3/ Primary gap/GDP and public debt/GDP variables are used only for the fiscal crisis modules of the VEA.
  - For EM models: 1/ WEO = IMF World Economic Outlook, CSD = IMF Common Surveillance Database, CVU = IMF Corporate Vulnerability Utility, EBA = IMF External Balance Assessment, FAD FP = FAD Fiscal Policy and Surveillance Database, INS = IMF Information Notice System, WB WDI = World Bank World Development Indicators, OECD HPD = OECD Housing Prices Database, GPG = Global Property Guide, LV = Laeven and Valencia (2012).
  - 2/ Real housing and stock prices are used in the VEE because nominal data suffer from structural breaks in inflation. Price acceleration is defined as the change in the annual growth rate of the price.
  - 3/ Primary gap/GDP and public debt/GDP variables are used only for the fiscal crisis modules of the VEE.

### Samples and country classifications
- Appendix Table A1: AE sample and assigned regions; note on "Distressed Europe" capturing European countries that received external financial assistance from the IMF, EFSF/ESM, and/or ECB SMP; SMP participation classified following ECB (2013).
- Appendix Table A2: EM sample of countries and assigned regions; country-to-region listings provided (examples include Australia — Rest of World; Austria — Non-Distressed Europe; China,P.R.:Hong Kong — Rest of World; and a comprehensive EM country list mapping to regions such as Asia, Americas, Europe, Middle East and Africa).

*Source: wp17282 - References (IMF PDF).*

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_Source: https://www.imf.org/-/media/files/publications/wp/2017/wp17282.pdf_