## _wp13263

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---

### II. FSIs and Financial Stability
- FSIs are aggregate measures of the health of a country’s financial sector and form a key part of macroprudential surveillance.
- Historical development and standards:
  - Collection of FSIs dates back to 1999 with the Financial Sector Assessment Program (FSAP).
  - Following consultations in 2000, the IMF, IASB, BIS, BCBS, and others drafted a guide on concepts, definitions, data sources, and techniques for FSI compilation.
  - A consistent set of guidelines is established in the Financial Soundness Indicators Compilation Guide published in 2006 and its amendments.
- Reporting coverage and indicator taxonomy:
  - 80 countries report FSIs on a regular basis to the IMF.
  - FSIs are split into 12 core FSIs and 28 encouraged FSIs:
    - Core FSIs: collected by all reporting countries and span deposit-taking institutions covering capital adequacy, asset quality, earnings and profitability, liquidity, and sensitivity to market risk.
    - Encouraged FSIs: collected on a country-by-country basis for deposit-taking institutions, other financial corporations, nonfinancial corporations, households, market liquidity, and real estate markets.
- Basel III implications:
  - Emphasis on common equity in regulatory capital calculations and a narrower capital base definition.
  - Introduction of a counter-cyclical buffer.
  - Introduction of two liquidity standards: the liquidity coverage ratio and the net stable funding ratio.
  - Forward-looking revisions include distribution and concentration measures to enhance FSI usefulness.
- Role and use of FSIs:
  - Indicate overall distress within a banking sector and help differentiate strong versus weak banks.
  - Should be correlated with crisis episodes or banking sector shocks; the paper examines which FSIs show highest correlation with past crises and whether some FSIs can be leading indicators.

### III. Data
- Core sample and timeline:
  - Core data set comprises 80 countries that report FSIs to the IMF between 2005 and 2012.
  - Majority of reporting countries are European; 6 percent are African.
  - First data points available in 2005; some countries begin reporting in 2008.
- FSIs used in econometric analysis:
  - Six FSIs: CAR; NPLs net of provisions to capital; NPL ratio; ROE; interest margin to gross income; non-interest expenses to gross income.
- Macroeconomic and other variables:
  - Macroeconomic indicators combined with annual FSI data: GDP growth; broad money to international reserves ratio; inflation rate; credit to the private sector; current account balance to GDP ratio; real effective exchange rate; sovereign credit default swap spreads; monetization ratio.
  - Monetization ratio defined as the ratio of broad money to GDP.
  - Data sources: IMF IFS, World Bank WDI, Bloomberg.
- Governance controls:
  - Three governance indicators used: regulatory quality, rule of law, control of corruption (World Bank’s Worldwide Governance Indicators).
  - Each governance indicator normalized to mean zero and standard deviation of one.
  - A composite governance index is the unweighted average of the three indicators for econometric analysis.
- Crisis and banking-shock definitions:
  - Dependent variable: binary outcome indicating occurrence of a banking crisis as described in Laeven and Valencia (2012): systemic crisis if 1) significant signs of distress (bank runs, losses, liquidations) and 2) significant banking policy intervention measures.
  - Banking shock defined following Boyd et al. (2009) as a significant annual decrease in gross loans outstanding, using thresholds of 10 percent and 20 percent over the period 2005–12.
  - Little overlap in systemic crisis episodes identified between the two methods.
- Extended and temporal datasets:
  - Core data set combined with additional FSI data from the IMF’s Global Financial Stability Report to create an extended data set covering 108 countries over the same period.
  - Two temporal frequencies collected: annual and quarterly data sets.
- Consolidation of FSI data:
  - Five consolidation bases per the FSI Compilation Guide: Domestically Consolidated (DC); Domestically Controlled, Cross-border, Cross Sector (DCCBS); Domestically Controlled, Cross-border (DCCB); Cross-border, cross-sector consolidation basis for all domestically incorporated entities (CBCSDI); Cross-border consolidation basis for all domestically incorporated entities (CBDI).
  - DC is the most commonly used basis (all deposit-taking entities operating within the domestic economy).
  - Recommended consolidation bases: CBCSDI and DCCBS (largest coverage across sectors and borders).
  - Use of different consolidation bases does not make FSI data incomparable across countries; countries select bases according to financial system infrastructure and exposure.

### IV. Summary Statistics
- Crisis concentration and timing:
  - Banking crises over 2000–09 were concentrated in European countries.
  - Almost three-quarters of all financial crises experienced over 2000–09 were in Europe.
  - Of these crises, 55 percent occurred within Euro area countries.
  - Three-quarters of the crisis events during the decade were concentrated in 2008.
- Comparative FSI trends (crisis vs non-crisis countries, 2005–2012):
  - Crisis countries had on average lower levels of CAR than non-crisis countries, but all countries increased regulatory capital markedly in response to the 2007 banking crisis.
  - NPLs net of provisions to capital and the NPL ratio increased more rapidly in crisis countries after the 2007 banking crisis and showed sustained increases thereafter.
  - ROA and ROE were higher in non-crisis than in crisis countries; both declined prior to the crisis onset.
  - Non-interest expenses to gross income were higher in crisis countries, with the gap widening during the crisis.
  - Crisis countries had better coverage of liquid assets to short-term liabilities (liquidity coverage ratio), although both crisis and non-crisis groups had liquidity coverage ratios below one.
- Interpretations and counterintuitive findings:
  - Higher liquidity coverage in crisis countries may reflect credit rationing: weaker banks may maintain higher liquidity coverage to withstand short-term shocks.
  - Čihák and Schaeck (2007) found regulatory capital levels higher in crisis countries within their sample (counter-intuitive finding noted).
- Country comparison (Ireland vs Chile):
  - Ireland: ROE drops precipitously and remains negative for a prolonged period beginning in 2008; NPL ratio below 1 percent prior to 2008, then jumps significantly and continues rising above 10 percent; CAR does not exhibit a significant drop prior to crisis but increases immediately following the crisis shock.
  - Chile: ROE remains relatively stable over 2005–2012; NPL ratio increases in 2008 but stabilizes below 5 percent; CAR increases immediately following the crisis shock.
- Regional and income-group patterns in core FSIs:
  - Capital adequacy levels (CAR) were lowest in high income countries over the sample period.
  - By region, CAR was lowest in Europe and highest in the MENA and Central Asia regions.
  - NPLs net of provisions to capital were highest in low and middle-income countries before the crisis, but were surpassed by levels in high-income countries after the start of the crisis.
  - Both NPLs net of provisions and the NPL ratio declined at the beginning of the crisis but subsequently increased across all regions and income groups.
  - ROE declined consistently during the crisis years, most visibly in Europe; ROE was consistently higher in low and middle-income countries between 2005 and 2012 and was highest in sub-Saharan Africa.
  - Interest margin to gross income showed an increasing trend over the sample period without clear regional patterns.
  - Non-interest expenses to gross income ratios suggest greater efficiency in low and middle-income countries than in high-income countries by this metric.
- Appendices and data notes:
  - Appendix IV provides summary statistics of the core FSI indicators by income and region.
  - WDI definitions classify countries by income; IMF regions are used for regional classification.

### V. Econometric Analysis
- Modeling framework and identification:
  - True likelihood of a financial or banking crisis y is modeled as a function of industry-specific indicators Z and economy-wide indicators X.
  - Observed likelihood is given by economy-wide indicators X and proxy variables Q when industry-specific indicators Z are unobserved.
  - If industry-specific indicators Z are unobserved and economy-wide indicators Q are used as proxy variables, the proxy variable coefficients are biased.
- Error structure and conditional expectation:
  - Model notation includes error terms e_i and asserts E(y | X,Z,Q) = E(y | X,Z).
  - Conditional on observing industry-specific indicators, economy-wide indicators carry no additional information.
- Practical implications for empirical work:
  - Importance of observing industry-specific indicators (Z) to avoid biased inference from proxy economy-wide indicators (Q).
  - Use of composite governance index and macroeconomic controls to account for cross-country institutional differences and economy-wide determinants.

### Methodology (Appendix VI and Appendix I highlights)
- Estimation approach:
  - Multivariate pooled logit model to predict banking crises where dependent variable y_it = 1 for a crisis event and 0 otherwise.
  - Explanatory variables: six core FSIs (measuring capital adequacy, asset quality, earnings and profitability) and a limited set of macroeconomic indicators; composite governance indicator included.
  - Country fixed effects excluded to avoid biased sample selection (following Demirgüç-Kunt and Detragiache (1998)).
  - Time dummies excluded because crisis episodes are concentrated around 2008 and maximum likelihood estimates are unbounded for years with no crises.
  - Two-stage estimation:
    - Stage 1: regressions of FSIs against a time trend by country; obtain residuals.
    - Stage 2: logit regressions of crisis events on FSI residuals and lagged year-on-year differences in macroeconomic indicators and the governance composite indicator.
  - Year-on-year differences in FSIs are not used due to data constraints: many countries start reporting FSIs only in the crisis year.
- Estimation issues and corrections:
  - Incidental parameters problem: maximum likelihood estimates are inconsistent for fixed effects logit with fixed time T (Chamberlain, 1980; Neyman and Scott, 1948; Hsiao, 2003).
  - Separation: variables that perfectly partition crisis and non-crisis observations (or years with no crises) produce unbounded logit coefficients and are excluded.
  - Multicollinearity: high variance inflation factors between FSIs and lagged FSIs; therefore regressions do not include FSIs and lagged FSIs simultaneously.
  - Robust standard errors clustered by country used in some specifications to correct standard errors when time dependence is present (Poirier and Ruud, 1998).
- Key empirical results — core FSI data (selected exact figures):
  - Significant contemporaneous negative correlations with crises:
    - Capital/risk weighted assets (CAR): coefficients reported as -3.147*** and -3.338*** (standard errors (1.029) and (1.153)).
    - Return on equity (banks) (ROE): coefficients reported as -0.252** and -0.255** (standard errors (0.117) and (0.114)).
  - Significant contemporaneous positive correlation:
    - Non-interest expenses to gross income: coefficients 0.220** and 0.221** (standard errors (0.105) and (0.107)).
  - Lagged indicators:
    - Return on equity (banks) (t-1): coefficients 0.435** and 0.487** (standard errors (0.180) and (0.225)) — interpreted as a leading indicator.
  - Macroeconomic controls:
    - Inflation, monetization, and broad money to international reserves are positive and significant in some specifications but none are consistently significant across all models.
    - Composite governance indicator is insignificant.
  - Model diagnostics (models I through VI):
    - N 231 231 231 231 205 205
    - Number of crises 11, 11, 11, 11, 7, 7
    - Type I Error (percent) 0.46% 0.46% 0.46% 0.46% 0.00% 0.00%
    - Type II Error (percent) 90.91% 90.91% 36.36% 36.36% 42.86% 42.86%
    - Chi-squared 16.57** 16.69* 55.87*** 56.18*** 38.78*** 39.08***
    - Akaike Information Criterion 0.3890.3970.280.2870.2650.273
    - McFadden R-squared 0.1870.1890.6320.6350.6350.64
- Key empirical results — extended FSI data (selected exact figures):
  - Extended data set: 80 IMF-reporting countries plus 28 additional GFSR countries (total coverage 108 countries; additional data may not follow consistent methodology).
  - Significant indicators (depository corporations):
    - Capital/risk weighted assets: coefficients -0.563* and -0.536* (standard errors (0.299) and (0.305)).
    - Nonperforming loans/total loans: coefficients -0.649** and -0.714*** (standard errors (0.258) and (0.268)).
    - Return on equity (banks): coefficients -0.113* and -0.136** (standard errors (0.058) and (0.063)).
  - Lagged ROE (t-1): coefficients 0.170** and 0.158** (standard errors (0.068) and (0.069)) — early warning signal.
  - Macroeconomic controls: inflation and credit to the private sector significant in some specifications; composite governance indicator insignificant across specifications.
  - Model diagnostics (models I through VI):
    - N 331 331 331 331 325 325
    - Number of crises 16, 16, 16, 16, 14, 14
    - Type I Error (percent) 0.00% 0.32% 0.64% 0.64% 0.32% 0.00%
    - Type II Error (percent) 87.50% 93.75% 81.25% 81.25% 85.71% 85.71%
    - Chi-squared 21.96*** 23.17*** 36.39*** 38.64*** 27.6*** 28.75***
    - Akaike Information Criterion 0.3750.3780.350.3490.3440.347
    - McFadden R-squared 0.1710.1810.2840.3010.2390.249
- Robustness and sensitivity:
  - Quarterly data over 2005 Q1 through 2012 Q4 for both FSI reporting countries and GFSR countries produce results in line with annual specifications.
  - Models with levels of FSIs and macroeconomic variables estimated; robust clustered standard errors used when correcting for time dependence.
  - Inclusion of duration since last crisis and number of past crises since 1970: CAR and ROE remain significant.
  - Variables dropped due to separation, insignificance, or multicollinearity include regional dummy variables, VIX, external debt to GDP, and return on assets.
  - Specific data exclusions: 1st and 99th percentiles excluded; Kazakhstan observations in 2007 dropped as FSIs were outliers in the 99.5th percentile.
- Interpretation and implications:
  - FSIs add predictive power beyond macroeconomic indicators: specifications including FSIs tend to have lower AIC and improved crisis classification accuracy relative to models without FSIs.
  - CAR and ROE show consistent negative contemporaneous correlation with crisis episodes across specifications; lagged ROE acts as a potential leading indicator.
  - Non-interest expenses to gross income positively associated with crisis likelihood in the core FSI set.
  - NPL ratio's negative sign in some specifications may reflect refinancing, transfer of poor-quality loans off balance sheet, or restructuring during distress episodes.
  - No macroeconomic control variable is consistently significant across all model specifications; composite governance indicator insignificant across specifications.
- Limitations and data needs:
  - Analysis constrained by limited historical coverage of FSIs; many countries consistently report FSIs only after 2008.
  - Results hampered by insufficient data to include a larger set of core and encouraged FSIs.
  - Policy and research would benefit from:
    - Compilation of historical FSI data for countries with gaps prior to crisis episodes.
    - Increased coverage of FSIs across countries and across various financial intermediation sectors.
    - Longer time-series of FSI data to strengthen early warning analysis.

### Appendix I — Core and Encouraged FSIs (deposit-takers and others)
- Core Set of FSIs (listed exactly as in source):
  - 1 Regulatory Capital to risk weighted assets
  - 2 Nonperforming loans net of provisions to capital
  - 3 Sectoral distribution of loans to total loans
  - 4 Return on equity
  - 5 Noninterest expenses to gross income
  - 6 Liquid assets to short-term liabilities
  - 7 Regulatory Tier 1 capital to risk weighted assets
  - 8 Nonperforming loans to total gross loans
  - 9 Return on assets
  - 10 Interest margin to gross income
  - 11 Liquid assets to total assets (liquid assets ratio)
  - 12 Net open position in foreign exchange to capital
- Encouraged Set of FSIs (listed exactly as in source):
  - Deposit-Takers:
    - 1 Capital to assets
    - 2 Geographical distribution of loans to total loans
    - 3 Gross liability position in financial derivatives to capital
    - 4 Personnel expenses to noninterest expenses
    - 5 Spread between highest and lowest interbank rate
    - 6 Foreign-currency-denominated loans to total loans
    - 7 Net open position in equities to capital
    - 8 Large exposures to capital
    - 9 Gross asset position in financial derivatives to capital
    - 10 Trading income to total income
    - 11 Spread between reference lending and deposit rates
    - 12 Customer deposits to total (non-interbank) loans
    - 13 Foreign-currency-denominated liabilities to total liabilities
  - Other Financial Corporations:
    - 14 Assets to total financial system assets
    - 15 Assets to GDP
  - Nonfinancial Corporations:
    - 16 Total debt to equity
    - 17 Return on equity
    - 18 Earnings to interest and principal expenses
    - 19 Net foreign exchange exposure to equity
    - 20 Number of applications for protection from creditors
  - Households:
    - 21 Household debt to GDP
    - 22 Household debt service and principal payments to income
  - Market Liquidity:
    - 23 Average bid-ask spread in the securities market
    - 24 Average daily turnover ratio in the securities market
  - Real estate markets:
    - 25 Residential real estate prices
    - 26 Commercial real estate prices
    - 27 Residential real estate loans to total loans
    - 28 Commercial real estate loans to total loans

*Source: _wp13263 - Section V focuses on the empirical model and presents estimation results. Finally, Section VI (IMF PDF content provided).*

### Section V focuses on the empirical model and presents estimation results. Finally, Section VI

### _wp13263 - Section V focuses on the empirical model and presents estimation results. Finally, Section VI

### II. FSIs and Financial Stability
- FSIs are aggregate measures of the health of a country’s financial sector and form a key part of macroprudential surveillance.
- Historical development and standards:
  - Collection of FSIs dates back to 1999 with the Financial Sector Assessment Program (FSAP).
  - Following consultations in 2000, the IMF, IASB, BIS, BCBS, and others drafted a guide on concepts, definitions, data sources, and techniques for FSI compilation.
  - A consistent set of guidelines is established in the Financial Soundness Indicators Compilation Guide published in 2006 and its amendments.
- Reporting coverage and indicator taxonomy:
  - 80 countries report FSIs on a regular basis to the IMF.
  - FSIs are split into 12 core FSIs and 28 encouraged FSIs:
    - Core FSIs: collected by all reporting countries and span deposit-taking institutions covering capital adequacy, asset quality, earnings and profitability, liquidity, and sensitivity to market risk.
    - Encouraged FSIs: collected on a country-by-country basis for deposit-taking institutions, other financial corporations, nonfinancial corporations, households, market liquidity, and real estate markets.
- Basel III implications:
  - Emphasis on common equity in regulatory capital calculations and a narrower capital base definition.
  - Introduction of a counter-cyclical buffer.
  - Introduction of two liquidity standards: the liquidity coverage ratio and the net stable funding ratio.
  - Forward-looking revisions include distribution and concentration measures to enhance FSI usefulness.
- Role and use of FSIs:
  - Indicate overall distress within a banking sector and help differentiate strong versus weak banks.
  - Should be correlated with crisis episodes or banking sector shocks; the paper examines which FSIs show highest correlation with past crises and whether some FSIs can be leading indicators.

### III. Data
- Core sample and timeline:
  - Core data set comprises 80 countries that report FSIs to the IMF between 2005 and 2012.
  - Majority of reporting countries are European; 6 percent are African.
  - First data points available in 2005; some countries begin reporting in 2008.
- FSIs used in econometric analysis:
  - Six FSIs: CAR; NPLs net of provisions to capital; NPL ratio; ROE; interest margin to gross income; non-interest expenses to gross income.
- Macroeconomic and other variables:
  - Macroeconomic indicators combined with annual FSI data: GDP growth; broad money to international reserves ratio; inflation rate; credit to the private sector; current account balance to GDP ratio; real effective exchange rate; sovereign credit default swap spreads; monetization ratio.
  - Monetization ratio defined as the ratio of broad money to GDP.
  - Data sources: IMF IFS, World Bank WDI, Bloomberg.
- Governance controls:
  - Three governance indicators used: regulatory quality, rule of law, control of corruption (World Bank’s Worldwide Governance Indicators).
  - Each governance indicator normalized to mean zero and standard deviation of one.
  - A composite governance index is the unweighted average of the three indicators for econometric analysis.
- Crisis and banking-shock definitions:
  - Dependent variable: binary outcome indicating occurrence of a banking crisis as described in Laeven and Valencia (2012): systemic crisis if 1) significant signs of distress (bank runs, losses, liquidations) and 2) significant banking policy intervention measures.
  - Banking shock defined following Boyd et al. (2009) as a significant annual decrease in gross loans outstanding, using thresholds of 10 percent and 20 percent over the period 2005–12.
  - Little overlap in systemic crisis episodes identified between the two methods.
- Extended and temporal datasets:
  - Core data set combined with additional FSI data from the IMF’s Global Financial Stability Report to create an extended data set covering 108 countries over the same period.
  - Two temporal frequencies collected: annual and quarterly data sets.
- Consolidation of FSI data:
  - Five consolidation bases per the FSI Compilation Guide: Domestically Consolidated (DC); Domestically Controlled, Cross-border, Cross Sector (DCCBS); Domestically Controlled, Cross-border (DCCB); Cross-border, cross-sector consolidation basis for all domestically incorporated entities (CBCSDI); Cross-border consolidation basis for all domestically incorporated entities (CBDI).
  - DC is the most commonly used basis (all deposit-taking entities operating within the domestic economy).
  - Recommended consolidation bases: CBCSDI and DCCBS (largest coverage across sectors and borders).
  - Use of different consolidation bases does not make FSI data incomparable across countries; countries select bases according to financial system infrastructure and exposure.

### IV. Summary Statistics
- Crisis concentration and timing:
  - Banking crises over 2000–09 were concentrated in European countries.
  - Almost three-quarters of all financial crises experienced over 2000–09 were in Europe.
  - Of these crises, 55 percent occurred within Euro area countries.
  - Three-quarters of the crisis events during the decade were concentrated in 2008.
- Comparative FSI trends (crisis vs non-crisis countries, 2005–2012):
  - Crisis countries had on average lower levels of CAR than non-crisis countries, but all countries increased regulatory capital markedly in response to the 2007 banking crisis.
  - NPLs net of provisions to capital and the NPL ratio increased more rapidly in crisis countries after the 2007 banking crisis and showed sustained increases thereafter.
  - ROA and ROE were higher in non-crisis than in crisis countries; both declined prior to the crisis onset.
  - Non-interest expenses to gross income were higher in crisis countries, with the gap widening during the crisis.
  - Crisis countries had better coverage of liquid assets to short-term liabilities (liquidity coverage ratio), although both crisis and non-crisis groups had liquidity coverage ratios below one.
- Interpretations and counterintuitive findings:
  - Higher liquidity coverage in crisis countries may reflect credit rationing: weaker banks may maintain higher liquidity coverage to withstand short-term shocks.
  - Čihák and Schaeck (2007) found regulatory capital levels higher in crisis countries within their sample (counter-intuitive finding noted).
- Country comparison (Ireland vs Chile):
  - Ireland: ROE drops precipitously and remains negative for a prolonged period beginning in 2008; NPL ratio below 1 percent prior to 2008, then jumps significantly and continues rising above 10 percent; CAR does not exhibit a significant drop prior to crisis but increases immediately following the crisis shock.
  - Chile: ROE remains relatively stable over 2005–2012; NPL ratio increases in 2008 but stabilizes below 5 percent; CAR increases immediately following the crisis shock.
- Regional and income-group patterns in core FSIs:
  - Capital adequacy levels (CAR) were lowest in high income countries over the sample period.
  - By region, CAR was lowest in Europe and highest in the MENA and Central Asia regions.
  - NPLs net of provisions to capital were highest in low and middle-income countries before the crisis, but were surpassed by levels in high-income countries after the start of the crisis.
  - Both NPLs net of provisions and the NPL ratio declined at the beginning of the crisis but subsequently increased across all regions and income groups.
  - ROE declined consistently during the crisis years, most visibly in Europe; ROE was consistently higher in low and middle-income countries between 2005 and 2012 and was highest in sub-Saharan Africa.
  - Interest margin to gross income showed an increasing trend over the sample period without clear regional patterns.
  - Non-interest expenses to gross income ratios suggest greater efficiency in low and middle-income countries than in high-income countries by this metric.
- Appendices and data notes:
  - Appendix IV provides summary statistics of the core FSI indicators by income and region.
  - WDI definitions classify countries by income; IMF regions are used for regional classification.

### V. Econometric Analysis
- Modeling framework and identification:
  - True likelihood of a financial or banking crisis y is modeled as a function of industry-specific indicators Z and economy-wide indicators X.
  - Observed likelihood is given by economy-wide indicators X and proxy variables Q when industry-specific indicators Z are unobserved.
  - If industry-specific indicators Z are unobserved and economy-wide indicators Q are used as proxy variables, the proxy variable coefficients are biased.
- Error structure and conditional expectation:
  - Model notation includes error terms e_i and asserts E(y | X,Z,Q) = E(y | X,Z).
  - Conditional on observing industry-specific indicators, economy-wide indicators carry no additional information.
- Practical implications for empirical work:
  - Importance of observing industry-specific indicators (Z) to avoid biased inference from proxy economy-wide indicators (Q).
  - Use of composite governance index and macroeconomic controls to account for cross-country institutional differences and economy-wide determinants.

*Source: _wp13263 - Section V focuses on the empirical model and presents estimation results. Finally, Section VI*

### Appendix VI). FSIs are industry-specific indicators that overcome the bias problem that

### _wp13263 - Appendix VI). FSIs are industry-specific indicators that overcome the bias problem that

### Methodology
- Multivariate pooled logit model to predict banking crises where dependent variable y_it = 1 for a crisis event and 0 otherwise.
- Explanatory variables: six core FSIs (measuring capital adequacy, asset quality, earnings and profitability) and a limited set of macroeconomic indicators; composite governance indicator included.
- Country fixed effects excluded to avoid biased sample selection (following Demirgüç-Kunt and Detragiache (1998)).
- Time dummies excluded because crisis episodes are concentrated around 2008 and maximum likelihood estimates are unbounded for years with no crises.
- Two-stage estimation:
  - Stage 1: regressions of FSIs against a time trend by country; obtain residuals.
  - Stage 2: logit regressions of crisis events on FSI residuals and lagged year-on-year differences in macroeconomic indicators and the governance composite indicator.
- Year-on-year differences in FSIs are not used due to data constraints: many countries start reporting FSIs only in the crisis year.

### Model specification and estimation issues
- Incidental parameters problem: maximum likelihood estimates are inconsistent for fixed effects logit with fixed time T (Chamberlain, 1980; Neyman and Scott, 1948; Hsiao, 2003).
- Separation: variables that perfectly partition crisis and non-crisis observations (or years with no crises) produce unbounded logit coefficients and are excluded.
- Multicollinearity: high variance inflation factors between FSIs and lagged FSIs; therefore regressions do not include FSIs and lagged FSIs simultaneously.
- Robust standard errors clustered by country used in some specifications to correct standard errors when time dependence is present (Poirier and Ruud, 1998).

### Key empirical results — core FSI data (Table 1)
- Significant contemporaneous negative correlations with crises:
  - Capital/risk weighted assets (CAR): coefficients reported as -3.147*** and -3.338*** (standard errors (1.029) and (1.153)).
  - Return on equity (banks) (ROE): coefficients reported as -0.252** and -0.255** (standard errors (0.117) and (0.114)).
- Significant contemporaneous positive correlation:
  - Non-interest expenses to gross income: coefficients 0.220** and 0.221** (standard errors (0.105) and (0.107)).
- Lagged indicators:
  - Return on equity (banks) (t-1): coefficients 0.435** and 0.487** (standard errors (0.180) and (0.225)) — interpreted as a leading indicator (positive lagged ROE before crises).
- Macroeconomic controls:
  - Inflation, monetization, and broad money to international reserves are positive and significant in some specifications but none are consistently significant across all models.
  - Composite governance indicator is insignificant.
- Model diagnostics and classification (models I through VI):
  - N 231 231 231 231 205 205
  - Number of crises 11, 11, 11, 11, 7, 7
  - Type I Error (percent) 0.46% 0.46% 0.46% 0.46% 0.00% 0.00%
  - Type II Error (percent) 90.91% 90.91% 36.36% 36.36% 42.86% 42.86%
  - Chi-squared 16.57** 16.69* 55.87*** 56.18*** 38.78*** 39.08***
  - Akaike Information Criterion 0.3890.3970.280.2870.2650.273
  - McFadden R-squared 0.1870.1890.6320.6350.6350.64

### Key empirical results — extended FSI data (Table 2)
- Extended data set: 80 IMF-reporting countries plus 28 additional GFSR countries (total coverage 108 countries; additional data may not follow consistent methodology).
- Significant indicators (depository corporations):
  - Capital/risk weighted assets: coefficients -0.563* and -0.536* (standard errors (0.299) and (0.305)).
  - Nonperforming loans/total loans: coefficients -0.649** and -0.714*** (standard errors (0.258) and (0.268)).
  - Return on equity (banks): coefficients -0.113* and -0.136** (standard errors (0.058) and (0.063)).
- Lagged ROE (t-1): coefficients 0.170** and 0.158** (standard errors (0.068) and (0.069)) — early warning signal.
- Macroeconomic controls: inflation and credit to the private sector significant in some specifications; composite governance indicator insignificant across specifications.
- Model diagnostics and classification (models I through VI):
  - N 331 331 331 331 325 325
  - Number of crises 16, 16, 16, 16, 14, 14
  - Type I Error (percent) 0.00% 0.32% 0.64% 0.64% 0.32% 0.00%
  - Type II Error (percent) 87.50% 93.75% 81.25% 81.25% 85.71% 85.71%
  - Chi-squared 21.96*** 23.17*** 36.39*** 38.64*** 27.6*** 28.75***
  - Akaike Information Criterion 0.3750.3780.350.3490.3440.347
  - McFadden R-squared 0.1710.1810.2840.3010.2390.249

### Comparison to Čihák and Schaeck (Table 3)
- Results comparable but with differences:
  - Contemporaneous CAR and NPL ratio, and lagged CAR and ROE for deposit-taking institutions have explanatory power.
  - Coefficient on lagged ROE is positive in this paper (consistent with prior findings), while contemporaneous NPL ratio coefficient is negative (contrasting with Čihák and Schaeck (2007) findings).
- Selected diagnostics (models II, III, V, VII, IX as presented):
  - N 256 256 256 256 198 198
  - Number of crises 16 16 16 16 7 7
  - Type I Error (percent) 0.00% 0.00% 0.42% 0.42% 0.00% 0.52%
  - Type II Error (percent) 100.00% 100.00% 100.00% 87.50% 85.71% 71.43%
  - Chi-squared 16.92*** 18.45** 29.42*** 30.83*** 24.74*** 26.62***
  - Akaike Information Criterion 0.4560.4660.4310.4410.2820.293
  - McFadden R-squared 0.1410.1540.2460.2580.4090.44

### Robustness checks
- Quarterly data over 2005 Q1 through 2012 Q4 for both FSI reporting countries and GFSR countries produce results in line with annual specifications (Tables 1 and 2).
- Models with levels of FSIs and macroeconomic variables estimated; robust clustered standard errors used when correcting for time dependence.
- Inclusion of duration since last crisis and number of past crises since 1970: CAR and ROE remain significant.
- Additional variables tested and dropped due to separation, insignificance, or multicollinearity:
  - Regional dummy variables and VIX dropped due to separation (no crisis observations in Asia and Pacific, Middle East and Central Asia, and sub-Saharan Africa in the annual core data set).
  - External debt to GDP dropped due to large coefficient and standard error (convergence problems).
  - Return on assets dropped due to strong positive correlation with return on equity.
- Specific data exclusions: 1st and 99th percentiles excluded; Kazakhstan observations in 2007 dropped as FSIs were outliers in the 99.5th percentile.

### Interpretation and implications
- FSIs add predictive power beyond macroeconomic indicators: specifications including FSIs tend to have lower AIC and improved crisis classification accuracy relative to models without FSIs.
- CAR and ROE show consistent negative contemporaneous correlation with crisis episodes across specifications; lagged ROE acts as a potential leading indicator.
- Non-interest expenses to gross income positively associated with crisis likelihood in the core FSI set.
- NPL ratio's negative sign in some specifications may reflect refinancing, transfer of poor-quality loans off balance sheet, or restructuring during distress episodes.
- No macroeconomic control variable is consistently significant across all model specifications; composite governance indicator insignificant across specifications.

### Limitations and data needs
- Analysis constrained by limited historical coverage of FSIs; many countries consistently report FSIs only after 2008.
- Results hampered by insufficient data to include a larger set of core and encouraged FSIs.
- Policy and research would benefit from:
  - Compilation of historical FSI data for countries with gaps prior to crisis episodes.
  - Increased coverage of FSIs across countries and across various financial intermediation sectors.
  - Longer time-series of FSI data to strengthen early warning analysis.

*Source: _wp13263 - Appendix VI). FSIs are industry-specific indicators that overcome the bias problem that (IMF PDF content provided).*

### Appendix I: List of Core and Encouraged FSIs for Deposit-Takers

### Appendix I: List of Core and Encouraged FSIs for Deposit-Takers

### Core Set of FSIs
- 1 Regulatory Capital to risk weighted assets
- 2 Nonperforming loans net of provisions to capital
- 3 Sectoral distribution of loans to total loans
- 4 Return on equity
- 5 Noninterest expenses to gross income
- 6 Liquid assets to short-term liabilities
- 7 Regulatory Tier 1 capital to risk weighted assets
- 8 Nonperforming loans to total gross loans
- 9 Return on assets
- 10 Interest margin to gross income
- 11 Liquid assets to total assets (liquid assets ratio)
- 12 Net open position in foreign exchange to capital

### Encouraged Set of FSIs

Deposit-Takers
- 1 Capital to assets
- 2 Geographical distribution of loans to total loans
- 3 Gross liability position in financial derivatives to capital
- 4 Personnel expenses to noninterest expenses
- 5 Spread between highest and lowest interbank rate
- 6 Foreign-currency-denominated loans to total loans
- 7 Net open position in equities to capital
- 8 Large exposures to capital
- 9 Gross asset position in financial derivatives to capital
- 10 Trading income to total income
- 11 Spread between reference lending and deposit rates
- 12 Customer deposits to total (non-interbank) loans
- 13 Foreign-currency-denominated liabilities to total liabilities

Other Financial Corporations
- 14 Assets to total financial system assets
- 15 Assets to GDP

Nonfinancial Corporations
- 16 Total debt to equity
- 17 Return on equity
- 18 Earnings to interest and principal expenses
- 19 Net foreign exchange exposure to equity
- 20 Number of applications for protection from creditors

Households
- 21 Household debt to GDP
- 22 Household debt service and principal payments to income

Market Liquidity
- 23 Average bid-ask spread in the securities market
- 24 Average daily turnover ratio in the securities market

Real estate markets
- 25 Residential real estate prices
- 26 Commercial real estate prices
- 27 Residential real estate loans to total loans
- 28 Commercial real estate loans to total loans

*Source: Appendix I, "_wp13263 - Appendix I: List of Core and Encouraged FSIs for Deposit-Takers" (IMF).*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2013/_wp13263.pdf_