## 2.1  Financial Crises Classification

## Source details

**Canonical URL:** [2.1  Financial Crises Classification](https://www.imf.org/-/media/files/publications/wp/2023/english/wpiea2023157-print-pdf.pdf)

## Other formats

- [Markdown version](/-/media/files/publications/wp/2023/english/wpiea2023157-print-pdf.pdf.md)
- [Structured JSON version](/-/media/files/publications/wp/2023/english/wpiea2023157-print-pdf.pdf.json)

---

### Financial crisis definition and dataset
- Classification approach:
  - Uses Laeven and Valencia (2020) definition and dating of systemic banking crises, combining narrative and quantitative methodology.
  - Start of a banking crisis: first quarter in which (i) significant signs of financial distress in the banking system and (ii) significant policy intervention in response to banking losses are both met.
  - Laeven-Valencia database provides wide panel coverage at quarterly frequency for advanced and emerging economies.
- Sample coverage and caveats:
  - Sample spans 53 crises in total with 25 in advanced economies and 28 in emerging markets and low income countries.
  - Laeven and Valencia (2020) identifies 65 crises over the period 1995–2017; 12 of the 65 crises are not covered due to data availability for mispricing risk components.
  - LV crisis database coverage restricts sample to the end of 2017Q4.
  - Older episodes may rely more on narrative classification due to limited data availability.

### Key statistics on crisis incidence
- Unconditional probabilities (Laeven and Valencia (2020) indicator):
  - Unconditional probability of a crisis onset in any given country-quarter: 0.7%.
  - Unconditional probability at country-year level: 2.7%.
  - Unconditional probability of a crisis onset for advanced economies: 3.3%.
  - Unconditional probability in our sample for emerging markets and low income countries: 2.1%.
- Crisis clustering:
  - Crisis episodes cluster around the Mexican crisis of 1994–95, the Asian crisis of 1997–98, and the 2008 Global Financial Crisis.
  - 25 systemic banking crisis episodes occurred in 2007-09 alone.

### Credit metrics as benchmark early warning indicators
- Chosen credit-based EWIs:
  - Credit-to-GDP gap.
  - 3-year change in the (credit to the private sector)-to-GDP ratio.
  - Real credit growth.
- Motivation:
  - Inspired by Borio and Lowe (2002), Schularick and Taylor (2012), BCBS (2010), and IMF (2014).
  - Aim to (i) check replicability of Schularick and Taylor (2012)’s results and (ii) compare whether Mispricing Risk improves predictive power over credit-only metrics.
- Descriptive behavior:
  - Credit metrics tend to be elevated in the run up to a financial crisis and are followed by a significant reduction in credit growth.
  - None of the three credit metrics return to pre-crisis levels even 12 quarters after the crisis.
- Data coverage:
  - Table 2 shows good coverage for these credit metrics across advanced economies and emerging and developing countries.

### Mispricing Risk — composite indicator construction and versions
- Concept:
  - Captures potential for repricing of risk assets due to deviations of current prices from fundamentals driven by misestimation/mispricing of risk, excessive (de)leveraging, and concentration of balance-sheet exposures.
- Construction steps:
  - Combine macrofinancial variables reflecting market returns, interest rates, market volatility, and measures of loosening credit standards (speed of accumulation and concentration of balance-sheet exposures).
  - Invert indicators where crises are preceded by lower values (e.g., volatility indicators multiplied by minus one) so higher values uniformly signal higher mispricing risk.
  - Transform indicators into within-country percentiles (standardization).
  - Aggregate by taking a simple average within sectors/asset markets, then a simple average across sectors to obtain an economy-wide index.
  - Index calculated for a country-quarter iff there are at least two indicators with non-missing values.
- Three versions constructed:
  - Mispricing Risk (Unrefined): raw composite incorporating all likely risk proxies.
  - Mispricing Risk (Refined): Iossifov and Schmidt (2021)’s final specification; preferred version.
    - Based on six indicators spanning four asset markets: equity markets (real equity market returns and equity market volatility), bond markets (domestic sovereign bond yield volatility and sovereign FX risk spread), foreign exchange markets (FX market volatility), and housing markets (real house price growth).
    - Asset price volatility and risk spreads enter the linear combination with a negative sign.
  - Mispricing Risk (Volatility): incorporates only indicators of asset price volatility.
- Stylized behavior:
  - Mispricing Risk indicators are pro-cyclical and lead the credit cycle.
  - All three versions peak near one to three years ahead of a systemic banking crisis; the refined version reaches higher pre-crisis values and drops further during/after crisis onset.
  - Mispricing Risk (Volatility) confirms crises tend to be preceded by periods of exceptionally low volatility.

### ROC curve analysis — predictive performance comparison
- Methodology:
  - Binary classification following Drehmann and Juselius (2014): use indicator at time t to predict whether a crisis occurs in h quarters.
  - For indicator i and horizon h, threshold τ rule: predict crisis if indicator > τ.
  - Empirical TPR and FPR computed and ROC curve traced by varying τ; Area Under the Curve (AUC) summarizes predictive performance.
  - Horizons evaluated: h = 4, 6, 8, 10, 12 quarters.
- Main ROC findings:
  - Mispricing Risk (Unrefined) and Mispricing Risk (Refined) achieve higher AUC than the three credit metrics at all horizons.
  - Both Unrefined and Refined versions achieve best performance at a horizon of six quarters.
  - Mispricing Risk (Volatility) beats credit metrics at all but one horizon (eight quarters).
  - Mispricing Risk (Refined) performs statistically significantly better at a horizon of six quarters than at 8, 10, or 12 quarters; equality of AUC for four and six quarters cannot be rejected at the 5% significance level.
- Sectoral performance:
  - Mispricing risk indicators for the banking sector have little predictive power and are absent from the refined version.
  - Household and corporate indicators achieve slightly better AUCs but are beaten by bond and housing markets, which offer high predictive power across horizons.
  - FX market indicators have good predictive power only at a short horizon; the equity market shows the opposite pattern.
- Comparison with credit metrics:
  - credit-to-GDP gap and 3-year change in ratio of credit to private sector to GDP achieve best performance at horizon of four quarters with a mild monotone fall as horizon increases.
  - Real credit growth achieves highest AUC at a horizon of ten quarters and does not exhibit a monotone pattern across horizons.
- Sub-sample by income group:
  - Results unchanged by income group; Mispricing Risk family outperforms credit metrics for both advanced economies and emerging markets and low income countries.
- Preferred indicator:
  - Mispricing Risk (Refined) chosen due to parsimony, high predictive performance, and data availability advantages.

### Optimal thresholds and Youden’s J statistic
- Youden’s J score:
  - J_i,h = max_τ [TPR_i,h(τ) − FPR_i,h(τ)] identifies point on ROC curve with maximum distance to the 45-degree line.
- Optimal thresholds (whole sample):
  - Mispricing Risk (Refined) optimal threshold: 65.5 percentile.
  - Credit-to-GDP gap optimal threshold: 82.5 percentile.
  - 3-year change in ratio of credit to private sector to GDP optimal threshold: 77.5 percentile.
  - Real credit growth optimal threshold: 67 percentile.
- Income-group variation:
  - Mispricing Risk (Refined) optimal threshold for advanced economies: 67.5 percentile.
  - Mispricing Risk (Refined) optimal threshold for emerging markets and low income countries: 65.5 percentile.
- Rule of thumb:
  - Simple threshold proposed for Mispricing Risk (Refined): 66.7 percentile.
  - Define indicator M_high = 1 iff Mispricing Risk (Refined) exceeds 66.7.
- ROC comparison at optimal horizons:
  - Optimal horizons used: Mispricing Risk (Refined): h = 6; Credit-to-GDP gap: h = 4; 3-year change: h = 4; Real credit growth: h = 10.
  - Mispricing Risk (Refined) outperforms all three credit-based metrics along the whole ROC curve.

### Complementary linear probability model analysis
- Motivation:
  - Use linear probability models to estimate how much more likely a crisis becomes when an EWI registers high readings.
- Regression specification:
  - Crisis_{i,t+1 to t+h} = α^h_i + β^h · EWI_{i,t} + ε_{i,t+1 to t+h}
  - Crisis_{i,t+1 to t+h} = 1 if a crisis begins in any quarter between t+1 and t+h.
  - EWI_{i,t} is the early warning indicator at time t.
  - α^h_i is the country fixed effect.
  - h = 4, 6, 8, 10, 12 quarters.
  - t-statistics computed using Driscoll-Kraay (1998) standard errors with respective lags.
  - Coefficient of interest: β^h.

---

### 4.1  Credit Metric Regressions

### Predictive performance of credit-based EWIs
- Variables normalized by their sample standard deviation; βh represents change in probability of a crisis beginning within h quarters if the EWI increases by one standard deviation.

### Key regression findings
- ∆3(Credit/GDP):
  - βh positive and statistically significant in Columns 1-5 of Table 8.
  - One-standard-deviation increase associated with a 1.6 percentage point increase in probability of a crisis beginning within 4 quarters.
  - One-standard-deviation increase associated with a 3.8 percentage point increase in probability within 12 quarters.
- Credit Gap:
  - One-standard-deviation increase in credit-to-GDP gap associated with a 1.6 percentage point increase in probability within 4 quarters.
  - One-standard-deviation increase associated with a 4.2 percentage point increase in probability within 12 quarters.
- Real Credit Growth:
  - βh not statistically significant except at the 4 quarter horizon.

### Model fit and limitations
- Predictability is low despite statistical significance for some metrics.
- At a 12-quarter horizon, within-R2 values are:
  - 3.5% for ∆3(Credit/GDP)
  - 4.5% for Credit Gap

---

### 4.2  Mispricing Risk Regressions

### Mispricing Risk as an early warning indicator: main regression results
- Mispricing Risk (Refined), denoted M, normalized by sample standard deviation and 4 quarter lagged.
- Table 9 (LPM: Mispricing Risk (Refined)) — reported coefficients (in percent) and within-R2:
  - Horizon 4: M = 2.5**; R-squared (within) = 2.6
  - Horizon 6: M = 3.4**; R-squared (within) = 3.5
  - Horizon 8: M = 4.3***; R-squared (within) = 4.4
  - Horizon 10: M = 5.1***; R-squared (within) = 4.3
  - Horizon 12: M = 5.7***; R-squared (within) = 5.9
- Interpretation:
  - A one-standard-deviation increase in M is associated with a 2.5 and 5.7 percentage point increase in the probability of a crisis beginning within 4 and 12 quarters, respectively.

### High-level Mispricing Risk (threshold indicator) results
- M_high = 1 if M > 66.7th percentile.
- Table 10 (LPM: Mispricing Risk (Refined) High) — reported coefficients (in percent) and within-R2:
  - Horizon 4: M_high = 6.2***; R-squared (within) = 2.8
  - Horizon 6: M_high = 8.3***; R-squared (within) = 3.5
  - Horizon 8: M_high = 10.5***; R-squared (within) = 4.4
  - Horizon 10: M_high = 12.8***; R-squared (within) = 5.5
  - Horizon 12: M_high = 14.4***; R-squared (within) = 6.2
- Interpretation:
  - When M is above the 66.7th percentile, probability of a crisis beginning increases by 6.2 and 14.4 percentage points at 4 and 12 quarters horizons, respectively.

### Subsample heterogeneity: advanced vs EM&LICs
- Advanced Economies (Table 11, M_high):
  - Horizon 4: 8.5*; Horizon 6: 11.4**; Horizon 8: 13.8**; Horizon 10: 17.0**; Horizon 12: 19.1**
  - Within-R2 rises to 7.8 at Horizon 12.
- EMs & LICs (Table 12, M_high):
  - Horizon 4: 4.8***; Horizon 6: 6.3***; Horizon 8: 8.3***; Horizon 10: 10.1***; Horizon 12: 11.4**
  - Within-R2 at Horizon 12 = 5.2
- Conclusion:
  - Predictability using Mispricing Risk is higher for advanced economies than for emerging markets and low income countries.

### Mispricing Risk versus credit metrics (joint regressions)
- Table 13 (M continuous plus credit metrics jointly):
  - M coefficients (in percent) across horizons: 2.3**, 3.1**, 3.8**, 4.5***, 5.1***
  - Credit metrics retain positive coefficients (e.g., ∆3(Credit/GDP): 1.6* … 3.6*** across horizons).
  - Within-R2 increases with horizon (e.g., up to 8.7 at Horizon 12 in some specifications).
- Table 14 (M_high plus credit metrics jointly):
  - M_high coefficients (in percent) across horizons: 5.8**, 7.6***, 9.5***, 11.4***, 12.7***
  - Credit metrics retain positive coefficients alongside M_high.
- Interpretation:
  - Results are practically unchanged when controlling for credit-based metrics, indicating Mispricing Risk captures information additional to credit metrics.

### Robustness across income-group subsamples (joint specifications)
- Advanced Economies (Table 15, joint specs with M_high and credit metrics):
  - M_high coefficients up to 16.9% and 19.1% at longer horizons, with within-R2 up to 12.6.
- EMs & LICs (Table 16, joint specs with M_high and credit metrics):
  - M_high coefficients: 4.8***, 6.1***, 7.8***, 9.2***, 10.2** across horizons.
- Conclusion:
  - Qualitative similarity of results when regressions are limited to income group subsamples.

### Comparative predictive performance (ROC references)
- ROC analysis (Table 5 and Table 6) shows Mispricing Risk versions have higher AUC than credit metrics at several horizons.
- Table 7 reports Youden J-based optimal points for Mispricing risk (Refined): 60.5 J score and optimal point 65.5 (All countries), with income-group variations (Advanced Economies optimal point 67.5).

---

### Robustness checks (section 5)
- Robustness dimensions tested:
  - Comparison with Red-Zone indicator (Greenwood et al., 2022): Appendix C reports Mispricing Risk captures additional information not captured by Red-Zone and shows superiority of Mispricing Risk for policymakers prioritizing high true positive rate (confirmed on a smaller sample).
  - Alternative percentile computation: using within-income group and world-level percentiles instead of within-country percentiles — Mispricing Risk with alternate percentile schemes continues to outperform credit metrics.
  - Post-crisis bias test: dropping the post-crisis period (8 quarters following start of a crisis) — results unaffected.

### The policymaker’s problem (section 6)
- ROC-based thresholds address TPR and FPR trade-offs, but policymakers may care about conditional probability of crisis given a high M reading.
- Youden J maximizing threshold (66.7) differs from threshold that maximizes conditional probability; policymakers concerned with conditional probability may prefer threshold of 80.
- Table 17 (Conditional Probabilities, 12 quarters ahead) — probabilities of entering a crisis within 12 quarters (values in percent):
  - Unconditional (Whole Sample) = 6.8
  - Using threshold 66.7 (M_high = 1):
    - Whole Sample: M_high=0 => 4.4; M_high=1 => 16.69
    - Advanced Economies: M_high=0 => 5.85; M_high=1 => 23.60
    - EMDCs: M_high=0 => 3.48; M_high=1 => 12.55
  - Using threshold 80:
    - Whole Sample: M_high=0 => 6.0; M_high=1 => 22.74
    - Advanced Economies: M_high=0 => 8.08; M_high=1 => 29.11
    - EMDCs: M_high=0 => 4.68; M_high=1 => 18.34
- Interpretation:
  - Exceeding the 80th percentile raises the 12-quarter-ahead crisis probability to about 22.74% for the whole sample, compared with unconditional 6.8%.

### Key takeaways for policymakers
- Mispricing Risk (Refined) is a statistically significant predictor of future financial crises across horizons 4 to 12 quarters.
- High values of Mispricing Risk (above 66.7th and especially above 80th percentile) substantially increase the conditional probability of entering a crisis within 12 quarters (e.g., up to 22.74% at threshold 80 for whole sample).
- Mispricing Risk improves predictive performance over traditional credit-based EWIs and provides additional information even when credit metrics are controlled for.
- Predictability is stronger for advanced economies than for emerging markets and low income countries.
- Mispricing Risk is data-lite (relies purely on asset prices), enabling broader coverage including many emerging markets and low income countries.
- Policy implication: Mispricing Risk can serve as a useful data point when calibrating macroprudential policy stance and for timing policies that lean against systemic risk build-up.

### Summary statistics and model notes (selected)
- Sample: unbalanced panel from 108 countries — 34 advanced economies and 74 emerging markets and low income countries — period 1995Q1 to 2017Q4 covering 51 instances of financial crises (as reported in Table 1 notes).
- Regression framework: Linear probability model (equation 4) with country fixed effects; Driscoll and Kraay (1998) standard errors with lags of six, nine, twelve, fifteen, and eighteen quarters for prediction horizons 4, 6, 8, 10, and 12 quarters, respectively.
- Significance codes: *, **, *** denote 10%, 5%, 1% levels using Kiefer and Vogelsang (2005) corrected p-values.
- Reported coefficients and R-squared values are in percent.

---

### Appendix — comparison with Red-Zone and summary statistics

### Red-Zone summary statistics (Table 18) — selected
- Red Zone indicators (counts and descriptive stats):
  - Red-Zone 228 2.00 0.19 0.39 0.00 All
  - Red-Zone 132 1.00 0.14 0.35 0.00 AM
  - Red-Zone 96 1.00 0.25 0.43 0.00 EMDC
- Components (selected entries from Table 18; values as reported):
  - ∆3 (Credit business /GDP) 386 410.86 86.40 2.48 All
  - ∆3 (Credit household /GDP) 389 82.77 7.88 2.13 All
  - ∆3 (Real Equity Index) 557 025.79 90.01 6.74 All
  - ∆3 (Real House Price Index) 371 07.73 22.67 5.51 All
  - (Additional component rows reported by income group in source.)

### Data coverage and comparison caveats
- Coverage differences:
  - This paper covers 1995-2017 whereas Greenwood et al. (2022) cover 1950-2016.
  - This paper offers greater country coverage: 108 vs 42.
- Red-Zone computation is data-intensive and in this dataset coverage for Red-Zone computation drops to 60 countries (31 advanced economies and 29 emerging markets) over 2005Q1-2017Q3.

### ROC curve analysis: AUC by horizon (Table 19)
- Table 19 AUCs by horizon (h = 4, 6, 8, 10, 12):
  - Mispricing risk: 0.791, 0.825, 0.722, 0.767, 0.747
  - Red-Zone: 0.756, 0.746, 0.744, 0.771, 0.651
- Findings:
  - Red-Zone achieves highest AUC at horizon 10 quarters.
  - Mispricing risk achieves highest AUC at horizon 6 quarters.
  - At optimal horizon, Red-Zone narrowly beats mispricing risk when using very “strict” thresholds; for policymakers emphasizing high true positive rate, mispricing risk is superior.

### Linear probability models: Red-Zone vs Mispricing Risk (Table 20)
- Table 20 reported coefficients by horizon (4, 6, 8, 10, 12) — coefficients (percent) and standard errors in brackets:
  - M_high: -0.4 [1.9], 6.0 [4.1], 10.1** [4.8], 13.2*** [4.8], 15.6*** [4.6]
  - Red Zone: 7.6 [4.9], 10.3** [5.1], 13.6*** [4.7], 16.8*** [4.2], 20.0*** [4.0]
- Observations and groups:
  - Observations 2,282
  - Number of groups 60
  - Country FE: Yes
  - Sample: All
- R-squared (within) by horizon: 2.4, 5.4, 9.1, 12.4, 15.7
- Interpretation:
  - M_high retains predictive power when included with Red-Zone; Red-Zone is also significant, indicating both indicators capture partly distinct predictive variation.
  - Red-Zone does not incorporate asset price volatility information whereas Mispricing Risk does.

### Further summary statistics (Tables 21 and 22) — selected variables (values as reported in source)
- Table 21 (Advanced Economies) — selected entries:
  - Share of household loans in total bank claims: N=178 Mean=9.00 SD=47.27 Min=12.73 p25=14.14 p50=40.99 p75=47.43 Max=81.48
  - Stock market volatility*(-1): N=293 Mean=1.00 SD=-18.44 Min=10.30 p25=-137.49 p50=-22.09 p75=-16.06 Max=-0.68
  - Real house price growth: N=252 Mean=5.00 SD=2.63 Min=8.59 p25=-44.86 p50=-1.76 p75=2.29 Max=51.20
  - (Additional rows in source.)
- Table 22 (EMDCs) — selected entries:
  - Share of household loans in total bank claims: N=692 Mean=6.00 SD=34.48 Min=19.49 p25=0.00 p50=20.07 p75=32.60 Max=98.94
  - FX market volatility*(-1): N=11,346.00 Mean=-38.38 SD=1,623.01 Min=-1.12e+05 p25=-11.09 p50=-6.47 p75=-2.31 Max=0.00
  - Real house price growth: N=1,451.00 Mean=2.07 SD=10.08 Min=-46.06 p25=-2.91 p50=1.83 p75=6.54 Max=57.89
  - (Additional rows in source.)

### Data sources and variable definitions (Section E)
- Economy-wide variables:
  - 3-year change in credit-to-GDP ratio: IMF MFS / BIS (Percentage points change (3-year) in ratio of credit to private sector to GDP)
  - Credit-to-GDP gap: IMF MFS / BIS (one-sided HP filter using 400,000 smoothing parameter)
  - Real credit growth: IMF MFS/BIS (y-o-y growth of ratio of credit to private sector to CPI index)
- Banking sector variables: IMF IFS and IMF FSI.
- Equity, bond, and FX market variables: Bloomberg and IMF IFS (real stock returns, volatility measures, bond yields, sovereign spreads, REER).
- Housing market: BIS/GPG/Haver/WEO (real house price growth, price-to-rent, price-to-income).
- Households and corporates variables: IMF IFS, OECD/ECB, BIS-IMF-WB.
- Note: Several volatility measures are reported as *(-1) (inverse) in the source.

*Source: wpiea2023157-print-pdf — 2.1 Financial Crises Classification; 4.1–4.2 Credit Metric and Mispricing Risk Regressions; Appendix comparison with Red-Zone (Tables 18–22))*

### 2.1  Financial Crises Classification

### 2.1  Financial Crises Classification

### Financial crisis definition and dataset
- Classification approach:
  - Uses Laeven and Valencia (2020) definition and dating of systemic banking crises, combining narrative and quantitative methodology and refined over multiple editions.
  - The Laeven-Valencia database explicitly focuses on banking crises and provides wide panel coverage at quarterly frequency for advanced and emerging economies.
  - The first quarter in which (i) significant signs of financial distress in the banking system (significant bank runs, losses, and bank liquidations) and (ii) significant policy intervention in response to banking losses are both met is considered the start of the banking crisis.
- Sample coverage and caveats:
  - Our sample spans 53 crises in total with 25 in advanced economies and 28 in emerging markets and low income countries.
  - Laeven and Valencia (2020) identifies 65 crises over the period 1995–2017; due to data availability for mispricing risk components, 12 of the 65 crises are not covered in our sample.
  - The LV crisis database coverage restricts our sample to the end of 2017Q4.
  - Older episodes of financial stress may lean more on narrative classification due to limited data availability, making assessments potentially more subjective.

### Key statistics on crisis incidence
- Unconditional probabilities (Laeven and Valencia (2020) indicator):
  - Unconditional probability of a crisis onset in any given country-quarter: 0.7%.
  - Unconditional probability at country-year level: 2.7%.
  - Unconditional probability of a crisis onset for advanced economies: 3.3%.
  - Unconditional probability in our sample for emerging markets and low income countries: 2.1%.
- Crisis clustering:
  - Crisis episodes are clustered around the Mexican crisis of 1994–95, the Asian crisis of 1997–98, and the 2008 Global Financial Crisis.
  - 25 systemic banking crisis episodes occurred in 2007-09 alone.

### Credit metrics as benchmark early warning indicators
- Chosen credit-based EWIs:
  - Credit-to-GDP gap.
  - 3-year change in the (credit to the private sector)-to-GDP ratio.
  - Real credit growth.
- Motivation:
  - Inspired by Borio and Lowe (2002), Schularick and Taylor (2012), BCBS (2010), and IMF (2014) discussions on the financial cycle and macroprudential assessment.
  - Aimed to (i) check replicability of Schularick and Taylor (2012)’s results and (ii) compare whether Mispricing Risk improves predictive power over credit-only metrics.
- Descriptive behavior:
  - Credit metrics tend to be elevated in the run up to a financial crisis (relative to a country’s own history) and are followed by a significant reduction in credit growth.
  - None of the three credit metrics return to pre-crisis levels even 12 quarters after the crisis.
- Data coverage:
  - Table 2 shows good coverage for these credit metrics across both advanced economies and emerging and developing countries.

### Mispricing Risk — composite indicator construction and versions
- Concept:
  - Captures potential for repricing of risk assets due to deviations of current prices from fundamentals driven by misestimation/mispricing of risk, excessive (de)leveraging, and concentration of balance-sheet exposures.
- Construction steps:
  - Combine macrofinancial variables reflecting market returns, interest rates, market volatility, and measures of loosening credit standards (speed of accumulation and concentration of balance-sheet exposures).
  - Invert indicators where crises are preceded by lower values (e.g., volatility indicators multiplied by minus one) so higher values uniformly signal higher mispricing risk.
  - Transform indicators into within-country percentiles (standardization).
  - Aggregate by taking a simple average within sectors/asset markets, then a simple average across sectors to obtain an economy-wide index.
  - The index is calculated for a country-quarter iff there are at least two indicators with non-missing values.
- Three versions constructed:
  - Mispricing Risk (Unrefined): raw composite incorporating all likely risk proxies informed by empirical literature.
  - Mispricing Risk (Refined): Iossifov and Schmidt (2021)’s final specification; narrows constituents using empirical techniques to ensure similarity of correlation patterns over the financial (credit) cycle. Our preferred version.
    - Based on six indicators spanning four asset markets: equity markets (real equity market returns and equity market volatility), bond markets (domestic sovereign bond yield volatility and sovereign FX risk spread), foreign exchange markets (FX market volatility), and housing markets (real house price growth).
    - Asset price volatility and risk spreads enter the linear combination with a negative sign.
  - Mispricing Risk (Volatility): incorporates only indicators of asset price volatility to study volatility’s predictive power.
- Stylized behavior:
  - Mispricing Risk indicators are pro-cyclical and lead the credit cycle.
  - All three versions peak near one to three years ahead of a systemic banking crisis; the refined version reaches higher pre-crisis values and drops further during/after crisis onset.
  - The Mispricing Risk (Volatility) indicator confirms crises tend to be preceded by periods of exceptionally low volatility.

### ROC curve analysis — predictive performance comparison
- Methodology:
  - Binary classification problem following Drehmann and Juselius (2014): policymaker uses an indicator at timet to predict whether a crisis occurs in h quarters.
  - For fixed indicator i and horizon h, threshold τ rule: predict crisis if indicator > τ.
  - Compute empirical true positive rate (TPR) and false positive rate (FPR):
    - TPR_i,h(τ) = (#true positives) / (#true positives + #false negatives)
    - FPR_i,h(τ) = (#false positives) / (#false positives + #true negatives)
  - Vary τ to trace ROC curve; Area Under the Curve (AUC) summarizes predictive performance.
  - Empirical ROC computed by using every value the indicator ever takes in the dataset.
  - Horizons evaluated: h = 4, 6, 8, 10, 12 quarters.
- Main ROC findings:
  - Both Mispricing Risk (Unrefined) and Mispricing Risk (Refined) achieve higher AUC than the three credit metrics at all horizons.
  - Both Unrefined and Refined versions achieve best performance at a horizon of six quarters.
  - Mispricing Risk (Volatility) beats credit metrics at all but one horizon (eight quarters).
  - Standard errors for AUC can be computed; formal AUC equality tests:
    - Mispricing Risk (Refined) performs statistically significantly better at a horizon of six quarters than at 8, 10, or 12 quarters.
    - The hypothesis that the AUC for four and six quarters is equal cannot be rejected at the 5% significance level.
  - Sectoral performance (Figure 7):
    - Mispricing risk indicators for the banking sector have little predictive power for future financial stress (hence absence from the refined version).
    - Household and corporate indicators achieve slightly better AUCs but are beaten by bond and housing markets, which offer high predictive power across horizons.
    - FX market indicators have good predictive power only at a short horizon; the equity market shows the opposite pattern.
  - Comparison with credit metrics:
    - credit-to-GDP gap and 3-year change in ratio of credit to private sector to GDP achieve best performance at horizon of four quarters with a mild monotone fall as horizon increases.
    - Real credit growth achieves highest AUC at a horizon of ten quarters and does not exhibit a monotone pattern across horizons.
  - Sub-sample by income group:
    - Results unchanged by income group; Mispricing Risk family outperforms credit metrics for both advanced economies and emerging markets and low income countries.
- Preferred indicator choice:
  - The refined version of Mispricing Risk (six asset price variables) is chosen as the preferred version due to parsimony, high predictive performance, and data availability advantages.
  - Asset price variables are often more easily obtainable and less subject to reporting delays than credit/balance-sheet variables.

### Optimal thresholds and Youden’s J statistic
- Youden’s J score definition:
  - J_i,h = max_τ [TPR_i,h(τ) − FPR_i,h(τ)]
  - The J score identifies the point on the ROC curve with maximum distance to the 45-degree line.
- Optimal thresholds (whole sample, Table 7):
  - Mispricing Risk (Refined) optimal threshold: 65.5 percentile.
  - Credit-to-GDP gap optimal threshold: 82.5 percentile.
  - 3-year change in ratio of credit to private sector to GDP optimal threshold: 77.5 percentile.
  - Real credit growth optimal threshold: 67 percentile.
- Income-group variation:
  - Optimal threshold for Mispricing Risk (Refined) for advanced economies: 67.5 percentile.
  - Optimal threshold for Mispricing Risk (Refined) for emerging markets and low income countries: unchanged from whole sample (65.5 percentile).
- Rule of thumb:
  - Proposed simple threshold for Mispricing Risk (Refined): 66.7 percentile for ease of recall.
  - Define indicator M_high = 1 iff Mispricing Risk (Refined) exceeds 66.7.
- ROC curve comparison at optimal horizons:
  - Optimal horizons used for plotting ROC curves in Figure 9:
    - Mispricing Risk (Refined): h = 6.
    - Credit-to-GDP gap: h = 4.
    - 3-year change in ratio of credit to private sector to GDP: h = 4.
    - Real credit growth: h = 10.
  - Mispricing Risk (Refined) outperforms all three credit-based metrics along the whole ROC curve.

### Complementary linear probability model analysis
- Motivation:
  - Complement ROC curve analysis with linear probability models to estimate how much more likely a crisis becomes when an EWI registers high readings.
- Regression specification (Jordà (2005) style linear forecasting regressions):
  - Crisis_{i,t+1 to t+h} = α^h_i + β^h · EWI_{i,t} + ε_{i,t+1 to t+h}
    - Crisis_{i,t+1 to t+h} is an indicator equal to one if a crisis begins in country i in any quarter between t+1 and t+h.
    - EWI_{i,t} is the early warning indicator at time t.
    - α^h_i is the country fixed effect.
    - h = 4, 6, 8, 10, 12 quarters.
  - t-statistics computed using Driscoll-Kraay (1998) standard errors with respective lags.
  - Coefficient of interest: β^h.

*Source: wpiea2023157-print-pdf - 2.1  Financial Crises Classification*

### 4.1  Credit Metric Regressions

### 4.1  Credit Metric Regressions

### Predictive performance of credit-based EWIs
- The analysis examines three traditional credit-based early warning metrics: ∆3(Credit/GDP), Credit Gap, and Real Credit Growth.
- All three variables are normalized by their sample standard deviation; the coefficient βh represents the change in the probability of a crisis beginning within h quarters if the EWI increases by one standard deviation.

### Key regression findings
- ∆3(Credit/GDP):
  - βh is positive and statistically significant in Columns 1-5 of Table 8.
  - A one-standard-deviation increase in ∆3(Credit/GDP) is associated with a 1.6 percentage point increase in the probability of a crisis beginning within 4 quarters.
  - A one-standard-deviation increase in ∆3(Credit/GDP) is associated with a 3.8 percentage point increase in the probability of a crisis beginning within 12 quarters.
- Credit Gap:
  - Columns 6-10 show Credit Gap also serves as a good predictor with comparable magnitudes to ∆3(Credit/GDP).
  - A one-standard-deviation increase in the credit-to-GDP gap is associated with a 1.6 percentage point increase in the probability of a crisis beginning within 4 quarters.
  - A one-standard-deviation increase in the credit-to-GDP gap is associated with a 4.2 percentage point increase in the probability of a crisis beginning within 12 quarters.
- Real Credit Growth:
  - Results for Real Credit Growth (Columns 11-15) show that βh is not statistically significant except at the 4 quarter horizon.

### Model fit and limitations
- Predictability is low despite statistical significance for some metrics.
- At a 12-quarter horizon, within-R2 values are:
  - 3.5% for ∆3(Credit/GDP)
  - 4.5% for Credit Gap

*Source: 4.1  Credit Metric Regressions (wpiea2023157-print-pdf)*

### 4.2  Mispricing Risk Regressions

### 4.2  Mispricing Risk Regressions

### Mispricing Risk as an early warning indicator: main regression results
- Mispricing Risk (refined), denoted M, enters equation 4 in continuous form (normalized by sample standard deviation and 4 quarter lagged).
- Table 9 (LPM: Mispricing Risk (Refined)) — reported coefficients (in percent) and within-R2:
  - Horizon 4: M = 2.5**; R-squared (within) = 2.6
  - Horizon 6: M = 3.4**; R-squared (within) = 3.5
  - Horizon 8: M = 4.3***; R-squared (within) = 4.4
  - Horizon 10: M = 5.1***; R-squared (within) = 4.3
  - Horizon 12: M = 5.7***; R-squared (within) = 5.9
- Interpretation: a one-standard-deviation increase in M is associated with a 2.5 and 5.7 percentage point increase in the probability of a crisis beginning within 4 and 12 quarters, respectively.

### High-level Mispricing Risk (threshold indicator) results
- Mispricing Risk (Refined) high indicator, M_high, equals 1 if M > 66.7th percentile (threshold from ROC analysis).
- Table 10 (LPM: Mispricing Risk (Refined) High) — reported coefficients (in percent) and within-R2:
  - Horizon 4: M_high = 6.2***; R-squared (within) = 2.8
  - Horizon 6: M_high = 8.3***; R-squared (within) = 3.5
  - Horizon 8: M_high = 10.5***; R-squared (within) = 4.4
  - Horizon 10: M_high = 12.8***; R-squared (within) = 5.5
  - Horizon 12: M_high = 14.4***; R-squared (within) = 6.2
- Interpretation: when M is above the 66.7th percentile, probability of a crisis beginning increases by 6.2 and 14.4 percentage points at 4 and 12 quarters horizons, respectively.

### Subsample heterogeneity: advanced vs EM&LICs
- Table 11 (Advanced Economies, M_high):
  - Horizon 4: 8.5*; Horizon 6: 11.4**; Horizon 8: 13.8**; Horizon 10: 17.0**; Horizon 12: 19.1**
  - Within-R2 rises to 7.8 at Horizon 12.
- Table 12 (EMs & LICs, M_high):
  - Horizon 4: 4.8***; Horizon 6: 6.3***; Horizon 8: 8.3***; Horizon 10: 10.1***; Horizon 12: 11.4**
  - Within-R2 at Horizon 12 = 5.2
- Conclusion: degree of predictability using Mispricing Risk is higher for advanced economies than for emerging markets and low income countries.

### Mispricing Risk versus credit metrics (joint regressions)
- Table 13 (M continuous plus credit metrics jointly):
  - M coefficients (in percent) across horizons: 2.3**, 3.1**, 3.8**, 4.5***, 5.1***
  - Credit metrics retain positive coefficients (e.g., ∆3(Credit/GDP): 1.6* … 3.6*** across horizons when included).
  - Within-R2 increases with horizon (e.g., up to 8.7 at Horizon 12 in some specifications reported).
- Table 14 (M_high plus credit metrics jointly):
  - M_high coefficients (in percent) across horizons: 5.8**, 7.6***, 9.5***, 11.4***, 12.7***
  - Credit metrics retain positive coefficients alongside M_high.
- Interpretation: results are practically unchanged when controlling for credit-based metrics, indicating Mispricing Risk captures information additional to credit metrics.

### Robustness across income-group subsamples (joint specifications)
- Table 15 (Advanced Economies, joint specs with M_high and credit metrics) shows:
  - M_high coefficients up to 16.9% and 19.1% at longer horizons, with within-R2 up to 12.6.
- Table 16 (EMs & LICs, joint specs with M_high and credit metrics) shows:
  - M_high coefficients: 4.8***, 6.1***, 7.8***, 9.2***, 10.2** across horizons.
- Conclusion: qualitative similarity of results when regressions are limited to income group subsamples.

### Comparative predictive performance (ROC analysis references)
- ROC analysis (Table 5 and Table 6) shows Mispricing Risk (refined/unrefined/volatility versions) has higher AUC than credit metrics at several horizons for the whole sample and by income groups.
- Table 7 (ROC Curve Analysis: Optimal Points) reports Youden J-based optimal points for Mispricing risk (Refined): 60.5 J score and optimal point 65.5 (All countries), with variations by income group (e.g., Advanced Economies optimal point 67.5).

---

### Robustness checks (section 5)
- Robustness dimensions tested:
  - Comparison with Red-Zone indicator (Greenwood et al., 2022): Appendix C reports Mispricing Risk captures additional information not captured by Red-Zone and shows superiority of Mispricing Risk for policy makers prioritizing high true positive rate (results confirmed on a smaller sample).
  - Alternative percentile computation: using within-income group and world-level percentiles instead of within-country percentiles — Mispricing Risk computed with alternate percentile schemes continues to outperform credit metrics.
  - Post-crisis bias test: dropping the post-crisis period (8 quarters following the start of a crisis) — results are unaffected by dropping the post-crisis period.

### The policymaker’s problem (section 6)
- ROC-based thresholds answer TPR and FPR trade-offs, but policymakers may care about conditional probability of crisis given a high M reading.
- Youden J maximizing threshold (66.7) differs from threshold that maximizes conditional probability; policymakers concerned with conditional probability may prefer a threshold of 80.
- Table 17 (Conditional Probabilities, 12 quarters ahead) — probabilities of entering a crisis within 12 quarters:
  - Unconditional (Whole Sample) = 6.8
  - Using threshold 66.7 (M_high = 1):
    - Whole Sample: M_high=0 => 4.4; M_high=1 => 16.69
    - Advanced Economies: M_high=0 => 5.85; M_high=1 => 23.60
    - EMDCs: M_high=0 => 3.48; M_high=1 => 12.55
  - Using threshold 80:
    - Whole Sample: M_high=0 => 6.0; M_high=1 => 22.74
    - Advanced Economies: M_high=0 => 8.08; M_high=1 => 29.11
    - EMDCs: M_high=0 => 4.68; M_high=1 => 18.34
- Interpretation: exceeding the 80th percentile raises the 12-quarter-ahead crisis probability to about 22.7% for the whole sample, compared with unconditional 6.8%.

### Key takeaways for policymakers (drawn from regression and ROC results)
- Mispricing Risk (refined) is a statistically significant predictor of future financial crises across horizons 4 to 12 quarters.
- High values of Mispricing Risk (above 66.7th and especially above 80th percentile) substantially increase the conditional probability of entering a crisis within 12 quarters (e.g., up to 22.74% at threshold 80 for whole sample).
- Mispricing Risk improves predictive performance over traditional credit-based EWIs and provides additional information even when credit metrics are controlled for.
- Predictability is stronger for advanced economies than for emerging markets and low income countries.
- Mispricing Risk is data-lite (relies purely on asset prices), enabling broader coverage including many emerging markets and low income countries.
- Policy implication: Mispricing Risk can serve as a useful data point when calibrating macroprudential policy stance and for timing policies that lean against systemic risk build-up (such as measures curtailing credit growth).

### Summary statistics and model notes (selected)
- Sample: unbalanced panel from 108 countries — 34 advanced economies and 74 emerging markets and low income countries — over the period 1995Q1 to 2017Q4 covering 51 instances of financial crises (as reported in Table 1 notes).
- Regression framework: Linear probability model (equation 4) with country fixed effects; robust standard errors based on Driscoll and Kraay (1998) with lags of six, nine, twelve, fifteen, and eighteen quarters for prediction horizons 4, 6, 8, 10, and 12 quarters, respectively; significance codes *, **, *** denote 10%, 5%, 1% levels using Kiefer and Vogelsang (2005) corrected p-values.
- Reported coefficients and R-squared values are in percent.

*Source: wpiea2023157-print-pdf — 4.2  Mispricing Risk Regressions*

### appendix we compare mispricing risk with Red-Zone-Either. Table 18 shows summary statistics

### appendix we compare mispricing risk with Red-Zone-Either. Table 18 shows summary statistics

### Summary statistics: Red Zone Indicators and Components (Table 18)
- Credit Metrics (N Mean SD Median Sample)
  - Red Zone
    - Red-Zone 228 2.00 0.19 0.39 0.00 All
    - Red-Zone 132 1.00 0.14 0.35 0.00 AM
    - Red-Zone 96 1.00 0.25 0.43 0.00 EMDC
  - Components
    - ∆3 (Credit business /GDP) 386 410.86 86.40 2.48 All
    - ∆3 (Credit household /GDP) 389 82.77 7.88 2.13 All
    - ∆3 (Real Equity Index) 557 025.79 90.01 6.74 All
    - ∆3 (Real House Price Index) 371 07.73 22.67 5.51 All
    - ∆3 (Credit business /GDP) 144 319.98   130.79 3.05 AM
    - ∆3 (Credit household /GDP) 142 23.23 10.81 3.40 AM
    - ∆3 (Real Equity Index) 249 419.02 60.25 9.48 AM
    - ∆3 (Real House Price Index) 246 37.60 19.95 6.41 AM
    - ∆3 (Credit business /GDP) 242 15.43 40.55 2.13 EMDC
    - ∆3 (Credit household /GDP) 247 62.51 5.52 1.85 EMDC
    - ∆3 (Real Equity Index) 307 631.28   107.99 4.79 EMDC
    - ∆3 (Real House Price Index) 124 77.97 27.28 4.10 EMDC
- Notes on sample and definitions:
  - Sample: unbalanced panel from 108 countries—34 advanced economies, 73 emerging markets, and 56 low income countries—over the period 1995Q1 to 2017Q4.
  - ∆3 denotes changes over three years.
  - Red-Zone indicators are the four indicators proposed by Greenwood et al., 2022; components reported in percent by income groups.

### Data coverage and comparison caveats
- Coverage differences complicate direct comparison with Greenwood et al. (2022):
  - This paper covers 1995-2017 whereas Greenwood et al. (2022) cover 1950-2016 (coverage for many countries only starts in 1990s).
  - This paper offers greater country coverage: 108 vs 42.
- Red-Zone computation is data-intensive: requires credit and asset price data separately for households and businesses.
  - In this dataset, coverage for Red-Zone computation drops to 60 countries (31 advanced economies and 29 emerging markets) over 2005Q1-2017Q3.

### ROC curve analysis: optimal prediction horizons (Table 19)
- Table 19: Area under ROC curve (AUC) by prediction horizons measured in quarters (horizons: 4, 6, 8, 10, 12)
  - Mispricing risk: 0.791, 0.825, 0.722, 0.767, 0.747
  - Red-Zone: 0.756, 0.746, 0.744, 0.771, 0.651
- Findings:
  - Red-Zone achieves its highest AUC at a horizon of 10 quarters.
  - Mispricing risk achieves its highest AUC at a horizon of 6 quarters.
  - At the optimal horizon, Red-Zone narrowly beats mispricing risk when using very “strict” thresholds (low false positive, low true positive rates).
  - For policy makers emphasizing a high true positive rate, mispricing risk is superior.

### Linear probability models: Red-Zone vs Mispricing Risk (Table 20)
- Model setup: regressions include both Red-Zone and the binary M_high indicator; reported coefficients and R-squared are in percent; standard errors in brackets; Country FE included; sample: All.
- Table 20 reported coefficients by horizon (4, 6, 8, 10, 12):
  - M_high: -0.4 6.0 10.1** 13.2*** 15.6***
    - Standard errors: [1.9] [4.1] [4.8] [4.8] [4.6]
  - Red Zone: 7.6 10.3** 13.6*** 16.8*** 20.0***
    - Standard errors: [4.9] [5.1] [4.7] [4.2] [4.0]
- Observations and groups:
  - Observations 2,282 (for each column)
  - Number of groups 60
  - Country FE: Yes
  - Sample: All
- R-squared (within) by horizon: 2.4 5.4 9.1 12.4 15.7
- Statistical significance markers:
  - *** p<0.01, ** p<0.05, * p<0.1
- Interpretation:
  - M_high retains strong predictive power when included with Red-Zone.
  - Red-Zone is also significant, indicating both indicators capture partly distinct predictive variation.
  - Red-Zone does not incorporate asset price volatility information whereas mispricing risk does.

### Further summary statistics (Tables 21 and 22)
- Table 21: Raw data summary statistics (Advanced Economies) — selected variables (N Mean SD Min p25 p50 p75 Max)
  - Banking sector
    - Share of household loans in total bank claims: 178 9.00 47.27 12.73 14.14 40.99 47.43 54.73 81.48
    - Share of public sector claims in total bank claims: 177 5.00 13.96 9.76 0.00 7.00 11.12 18.49 48.28
    - FX share in total bank liabilities: 102 2.00 27.89 19.73 2.81 12.62 24.24 38.35 100.00
    - FX share in total bank loans: 103 8.00 29.24 24.64 0.71 11.57 22.43 35.78 100.00
    - NPLs share in total gross loans *(-1): 137 7.00 -5.18 7.57 -47.75 -5.16 -2.81 -1.05 -0.08
  - Equity market
    - Stock market volatility*(-1): 293 1.00 -18.44 10.30 -137.49 -22.09 -16.06 -11.76 -0.68
    - Real stock market returns: 280 0.00 6.54 27.51 -91.47 -9.97 8.20 20.42 279.28
  - Bond market
    - Real domestic government bond yield*(-1): 190 8.00 -3.80 2.31 -29.07 -5.02 -3.91 -2.15 0.54
    - Sovereign FX debt spread*(-1): 149 1.00 -155.01 710.89 -15747.68 -109.06 -49.45 -21.94 -1.79
    - Domestic government bond yield volatility*(-1): 266 8.00 -0.01 0.03 -1.54 -0.01 -0.01 0.00 0.00
  - FX market
    - FX market volatility*(-1): 311 0.00 -8.76 4.53 -85.33 -10.84 -8.80 -6.83 0.00
    - Growth of REER (+ = appreciation): 298 4.00 0.32 5.55 -38.95 -2.60 0.41 2.90 29.31
  - Housing market
    - Price-to-income ratio: 266 1.00 98.73 23.58 34.47 84.94 99.12 109.20 207.48
    - Price-to-rent ratio: 257 2.00 97.58 27.09 29.41 83.15 97.47 108.27 213.31
    - Real house price growth: 252 5.00 2.63 8.59 -44.86 -1.76 2.29 6.80 51.20
  - Households and Corporates (selected)
    - FX share in bank loans to households: 150 0.00 2.99 6.08 0.00 0.13 0.72 2.92 35.02
    - Real growth of bank loans to households: 166 5.00 5.59 15.98 -37.93 0.15 4.14 8.20 287.07
    - FX share in bank loans to corporates: 150 6.00 9.20 8.94 0.28 2.55 6.32 12.80 50.60
    - Real growth of bank loans to corporates: 168 6.00 2.68 12.43 -45.25 -3.13 1.82 6.73 168.19
    - Real growth of external debt of corporates: 186 7.00 7.97 54.65 -94.99 -3.51 3.49 13.11 1,334.97
- Table 22: Raw data summary statistics (EMDCs) — selected variables (N Mean SD Min p25 p50 p75 Max)
  - Banking sector
    - Share of household loans in total bank claims: 692 6.00 34.48 19.49 0.00 20.07 32.60 46.24 98.94
    - Share of public sector claims in total bank claims: 715 1.00 22.55 16.97 0.01 9.71 18.57 30.86 95.22
    - FX share in total bank liabilities: 292 1.00 34.20 25.42 0.01 13.44 27.55 51.84 100.00
    - FX share in total bank loans: 300 0.00 31.07 25.96 0.00 10.01 25.23 48.67 100.00
    - NPLs share in total gross loans *(-1): 352 8.00 -7.10 6.81 -59.76 -9.63 -4.53 -2.68 -0.51
  - Equity market
    - Stock market volatility*(-1): 370 6.00 -22.32 42.09 -633.68 -23.60 -15.87 -10.12 0.00
    - Real stock market returns: 352 8.00 9.05 39.87 -81.39 -12.16 3.30 23.93 6,17.69
  - Bond market
    - Real domestic government bond yield*(-1): 113 2.00 -7.68 3.50 -20.93 -9.70 -7.18 -4.82 -1.89
    - Sovereign FX debt spread*(-1): 349 9.00 -463.18 570.47 -6,620.90 -511.05 -307.32 -183.71 -16.26
    - Domestic government bond yield volatility*(-1): 223 5.00 -0.01 0.01 -0.16 -0.01 -0.00 0.00 0.00
  - FX market
    - FX market volatility*(-1): 11,346.00 -38.38 1,623.01 -1.12e+05 -11.09 -6.47 -2.31 0.00
    - Growth of REER (+ = appreciation): 10,961.00 1.09 11.53 -76.61 -3.37 0.68 4.96 191.49
  - Housing market
    - Price-to-income ratio: 1,571.00 117.48 59.43 54.95 93.16 101.66 121.55 662.58
    - Price-to-rent ratio: 1,245.00 116.26 111.94 42.81 83.48 99.63 107.86 1,082.73
    - Real house price growth: 1,451.00 2.07 10.08 -46.06 -2.91 1.83 6.54 57.89
  - Households and Corporates (selected)
    - FX share in bank loans to households: 3,973.00 22.78 28.31 0.00 0.54 8.46 40.53 100.00
    - Real growth of bank loans to households: 6,443.00 16.73 63.27 -99.76 1.19 8.74 19.24 1,724.86
    - FX share in bank loans to corporates: 4,548.00 35.62 28.38 0.00 9.66 31.25 56.16 100.00
    - Real growth of bank loans to corporates: 6,367.00 11.02 32.38 -98.51 -0.84 7.38 17.35 872.87
    - Real growth of external debt of corporates: 1,547.00 8.55 21.64 -65.84 -4.35 5.55 17.65 172.71

### Data sources and variable definitions (Section E)
- Economy-wide variables:
  - 3-year change in credit-to-GDP ratio: IMF MFS / BIS (Percentage points change (3-year) in ratio of credit to private sector to GDP)
  - Credit-to-GDP gap: IMF MFS / BIS (one-sided HP filter using 400,000 smoothing parameter)
  - Real credit growth: IMF MFS/BIS (y-o-y growth of ratio of credit to private sector to CPI index)
- Banking sector variables: IMF IFS and IMF FSI (definitions provided for shares, NPLs, FX shares)
- Equity, bond, and FX market variables: Bloomberg (real stock returns, volatility measures, bond yields, sovereign spreads), IMF IFS (REER)
- Housing market: BIS/GPG/Haver/WEO (real house price growth, price-to-rent, price-to-income)
- Households and corporates variables: IMF IFS, OECD/ECB, BIS-IMF-WB (loan growth, interest rate–income differentials, FX shares, external debt growth)
- Note: Several volatility measures are reported as *(-1) (inverse) in the source.

*Source: wpiea2023157-print-pdf - appendix we compare mispricing risk with Red-Zone-Either. Table 18 shows summary statistics*

---


_Source: https://www.imf.org/-/media/files/publications/wp/2023/english/wpiea2023157-print-pdf.pdf_