## _wp12159

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### I. Introduction and Objective
- Motivating context: the financial crisis in 2007–09 and the ensuing global recession highlighted the need for a macroprudential policy framework to limit systemic financial risk.
- Objective: model and forecast the time-varying conditional probability of a systemic banking crisis (systemic risk), defined as Pr(y_{i,t}=1 | x_{i,t-h}; α_i, β), using a fixed-effect binary response model and real-time information.
- Focus: the time dimension of systemic risk and inclusion of a proxied measure of financial interconnectedness.

### Methodology and Innovations
- Model framework:
  - Dynamic binary response (logit/probit/LPM) with country fixed effects; all risk factors are known h periods in advance.
  - Estimation by maximum likelihood treating country fixed effects as parameters (no independence assumption between α_i and risk factors).
- Innovations:
  - Purely dynamic model structure so forecasts rely only on real-time information.
  - Derivation of dynamic, conditional risk-factor thresholds within the binary response framework (thresholds depend on other risk factors).
  - Pseudo out-of-sample analysis covering 2001–2010 to evaluate early-warning capability.

### Main Findings (summary)
- Predictability and key risk factors:
  - Systemic risk is predictable in real time.
  - Identified risk factors: banking sector leverage; equity price growth; credit-to-GDP gap; real effective exchange rate appreciation; changes in banks’ lending premium; bank interconnectedness proxied by non-core/core bank liabilities.
  - House price growth shows some evidence of increasing systemic risk but is not statistically significant at conventional levels in many specifications.
- Contagion:
  - A significant contagion effect: crises in economies with large financial sectors raise systemic risk forecasts in other economies.
- Credit growth interpretation:
  - Rapid credit growth associates with higher systemic risk but can be benign if linked to expected productivity gains.
  - Credit growth increases systemic risk substantially more when accompanied by high equity price growth.
- Comparative performance:
  - The binary response model outperforms the signal extraction approach on Type I and Type II errors in the crisis signaling exercise.
- Dynamic thresholds (example):
  - For the model with credit-to-GDP growth, banking sector leverage and equity price growth:
    - Optimal credit-to-GDP growth threshold ≈ 10 percent if equity prices have decreased by 10 percent and banking sector leverage ≈ 130 percent.
    - Optimal credit-to-GDP growth threshold ≈ 0 percent if equity prices have grown by 20 percent and banking sector leverage ≈ 160 percent.
  - Signal extraction static threshold (same sample): 4.9 percent (credit-to-GDP growth).
- Out-of-sample performance (2001–2010):
  - Based on in-sample calibration, around 50–80 percent of crises were correctly identified in real time without excessive false signals.
  - A monitoring model based on credit-to-GDP growth and banking sector leverage signaled early warning ahead of the U.S. subprime crisis in 2007.

### Policy-relevant Implications and Uses
- Real-time monitoring using a dynamic binary response framework is feasible and informative for policy.
- Dynamic, conditional thresholds provide nuanced policy triggers compared with static thresholds.
- Equity price information should be incorporated alongside credit growth to help distinguish benign from risky credit expansions.
- Monitoring should account for contagion effects, especially from economies with large financial sectors.

### Econometric Methodology and Model Specification
- Dependent variable:
  - Binary systemic banking crisis variable y_{i,t} ~ Bernoulli; modeled as Pr(y_{i,t}=1 | x_{i,t-h}; α_i, β) = G(α_i + x_{i,t-h}'β).
- Link functions considered:
  - Probit: G = Φ(·).
  - Logit: G = Λ(·) = e^x/(1+e^x).
  - LPM: G(x)=x (not bounded in [0,1]).
- Marginal effects:
  - ME_j = G'(α_i + x_{i,t-h}'β) · β_j.
  - Standardized marginal effect = G'(α_i + x_{i,t-h}'β) · β_j · sd(x_{j,t-h}).
  - Marginal effects depend on all risk indicators and α_i (implicit interactions).
- Estimation:
  - Maximum likelihood with country fixed effects; parameters estimated by maximizing Σ_i Σ_t [ y_{i,t} log G(α_i + x_{i,t-h}'β) + (1-y_{i,t}) log(1- G(α_i + x_{i,t-h}'β)) ].

### Data, Sample and Risk-Factor Definitions
- Sample: unbalanced annual panel of 68 advanced and emerging economies over 1970-2010.
- Crisis definition: Reinhart and Rogoff (2010) systemic banking crisis definition; only the first crisis year used.
- Key candidate risk factors and definitions (exact transformations preserved):
  - Credit-to-GDPt = (Private credit by deposit money bankst / GDPt)*100. Source: IMF IFS.
    - Credit-to-GDP Growtht (in percentage points) = (Credit-to-GDPt - Credit-to-GDPt-2)/2
    - Credit-to-GDP Gapt = Credit-to-GDPt – CtG_Trendt; CtG_Trendt from recursive HP filter with λ = 1600.
  - Banking Sector Leverage (in percent) = (Private credit by deposit money banks)/(demand, time and saving deposits in deposit money banks). Source: IMF IFS.
  - Equity Price Growtht = ln(Equity Pricet/Equity Pricet-2)/2. Source: Bloomberg.
  - House Price Growtht = ln(House Pricet/House Pricet-2)/2. Source: Bloomberg.
  - REER Growtht = ln(REERt/REERt-1). Source: IMF INS.
  - Non-core liabilities proxies:
    - Non-Core 1 = banks’ foreign liabilities + banks’ liabilities to non-banking financial sector (IFS lines).
    - Non-Core 2 = banks’ foreign liabilities + (M3 − M2).
  - Core liabilities: M2. Source: WEO.
  - Contagion variable: contagion_{i,t+1} = Σ_{j≠i} ω_{j,t} y_{j,t}, with ω_{j,t} = country j market capitalization % of world market capitalization. Source: World Bank.
  - ∆Lending Premiumt = (Lending Premiumt - Lending Premiumt-2)/2. Lending Premium = bank loan rate to prime private customers − treasury bill rate. Source: World Bank.

### Estimation Results — Single-factor and Multivariate (highlights)
- Robustness across link functions: β coefficients vary, but standardized marginal effects are consistent across logit, probit and LPM.
- Single-predictor logit standardized marginal effects (evaluated at median α_i and median risk indicator):
  - Credit-to-GDP gap:
    - Positive significant up to three years in advance.
    - A one standard deviation increase raises systemic risk by around 3.3 percent, 2.6 percent and 1.3 percent in the following three years (logit; median evaluations).
  - Credit-to-GDP growth: positive significant up to three years in advance.
  - Banking sector leverage: significant up to two years ahead; for a median risk country at a one-year horizon, one standard deviation increase raises systemic risk by 2.5 percent (logit).
  - Bank interconnectedness (non-core/core): significant at one-year horizon.
  - Equity price inflation: significant positive impact three to four years ahead.
  - House price inflation: some positive effect at two-year horizon but often not statistically significant at 5 percent.
  - REER appreciation: increases systemic risk; emerging economies more sensitive.
  - Real GDP growth: no uniform effect; emerging economies tend to have negative GDP growth before crises while advanced economies often have positive growth before crises.
- Multivariate results:
  - Implicit interactions via the binary response marginal effects allow the marginal effect of one indicator to be higher when other indicators are high (for positive βs and conditional probability < 50 percent).
  - Explicit multiplicative interaction terms were avoided due to potential perverse dynamics.

### Table and Coefficient Highlights (selected numeric entries preserved)
- McFadden's R^2 examples (percent): 32.8, 9.9, 28.9, 33.0, 25.7, 33.4, 31.8, 36.7, 16.8, 30.2, 24.1, 31.8.
- Table 8 selected coefficient patterns (examples preserved as in source):
  - Credit-to-GDP Growth (pct. points): coefficients reported across lags include 22.91***, 15.63***, -28.74***, 12.51**, 21.47***, 19.39***, 15.75***, 13.91**, 24.18*, 22.25**, 14.74*, 15.76***.
  - Banking Sector Leverage (pct.): reported significant coefficients include 15.32***, 5.92*, 4.46*, 4.95***, 1.19**.
  - Contagion effect: 6.55*** in one specification.
  - Interconnectedness Proxy 1 (pct.): 3.72* in one specification.
  - Interconnectedness Proxy 2 (pct.): 2.64*** and 2.52** in specifications.
  - REER Appreciation (pct.): selected coefficients 2.15**, -6.15*.
  - ∆Lending Premium (pct. points): 17.81** in one specification.
- Sample examples from Table 6 / Table 7:
  - Credit-to-GDP Growth models: Countries = 64; Observations = 1442.
  - Credit-to-GDP Gap models: Countries = 64; Observations = 1442; example Lag 1 Beta = 7.03*** (SE 1.59).
  - Banking Sector Leverage models: Countries = 64; Observations = 933; example Lag 1 Beta = 1.47*** (SE 0.51).
  - Equity Price Growth: Countries = 40; Observations = 862; example Lag 3 Beta = 2.31***.
  - House Price Growth: Countries = 29; Observations = 724.

### Combining Banking Leverage, Credit Gap and Equity Price Inflation
- Model performance:
  - Combining banking sector leverage, credit-to-GDP gap and equity price inflation provides a good fit for one- and two-year forecast horizons (columns (1) and (3) in source).
  - All estimated coefficients in this specification are positive and significant at the 5 percent level.
- Fixed effects vs random effects:
  - Random effects estimators can be inconsistent if α_i is correlated with risk factors; empirical results show substantial differences between fixed and random effects estimates, consistent with potential dependence and omitted variable bias.
- Asset price indicators:
  - Equity price inflation is an important positive predictor when combined with leverage and credit gap.
  - House price inflation has weaker impact in multivariate specifications and limited country coverage (29 countries).
- Contagion and interconnectedness:
  - Contagion coefficient positive and significant (column (5)).
  - Non-core to core liabilities (two definitions) positively and significantly increase systemic risk (columns (6)-(8)).
- Lending premium:
  - Coefficient on lending premium is negative and significant in some specifications: a decrease in the lending premium associates with higher systemic risk; effect loses significance when controlling for leverage and equity price growth.
- Interaction: credit-to-GDP gap & high equity growth:
  - Column (12) allows credit-to-GDP gap effect to differ if prior two-year equity inflation > 20 percent.
  - Estimated coefficients:
    - ‘Good’ credit growth coefficient = 7.44 percent.
    - ‘Bad’ credit growth coefficient = 23.78 percent (7.44 percent + 16.34 percent).
  - Interpretation: increase in systemic risk from credit-to-GDP gap is ≈ three times larger when last two years’ equity inflation exceeded 20 percent.

### V. Monitoring Systemic Risk
A. Signal Extraction Approach
- Signal: binary 1/0 if indicator crosses a threshold; no signals within two years after crisis start.
- Forecast errors:
  - Type I = no signal & crisis occurs.
  - Type II = signal & no crisis occurs.
- Optimal thresholds minimize a loss function over Type I and Type II errors (e.g., L = TypeI + TypeII or noise-to-signal = TypeII/(1−TypeI)).

B. Crisis Signals Based on Binary Response Model
- Crisis signal: ‘On’ if estimated conditional systemic risk > λ*.
- Threshold calibration: choose λ* to minimize L(TypeI,TypeII) = TypeI + TypeII (in main analysis).
- Examples of optimal thresholds:
  - λ* = 7.9 when L = TypeI + TypeII.
  - λ* = 4.9 when L = 2·TypeI + TypeII.
- Advantages vs static signal extraction:
  - More accurate crisis-probability forecasts if model approximates conditional probability well.
  - Thresholds are dynamic and conditional on other risk factors.

C. Selected signaling performance (preserved entries from Table 4)
- Binary Response Model (Logit) selected rows:
  - Credit-to-GDP Gap: Threshold 9.25; Type I 0.6% ; Type II 7.8% ; Prediction 49.4% ; NTS 15.7% ; Loss 58.4% ; Countries 68 ; Crises 87
  - Credit-to-GDP Growth: Threshold 6.63; Type I 7.9% ; Type II 18.2% ; Prediction 62.1% ; NTS 29.3% ; Loss 56.1% ; Countries 68 ; Crises 87
  - Credit-to-GDP Gap and Bank Leverage: Threshold 7.93; Type I 0.6% ; Type II 11.7% ; Prediction 69.4% ; NTS 16.9% ; Loss 42.4% ; Countries 66 ; Crises 49
  - Credit-to-GDP Growth, Bank Leverage and Equity Price Growth: Threshold 13.0; Type I 24.0% ; Type II 5.9% ; Prediction 76.0% ; NTS 7.7% ; Loss 29.9% ; Countries 38 ; Crises 25
  - CtG Growth, Bank Leverage, Equity- and House Price Growth: Threshold 9.51; Type I 4.3% ; Type II 17.9% ; Prediction 85.7% ; NTS 20.9% ; Loss 32.2% ; Countries 29 ; Crises 21
- Signal Extraction Approach selected rows:
  - Credit-to-GDP Growth (single threshold 2.84): Type I 41.4% ; Type II 21.7% ; Prediction 58.6% ; NTS 37.0% ; Loss 63.1% ; Countries 68 ; Crises 87
  - Credit-to-GDP Gap (single threshold 2.33): Type I 36.8% ; Type II 25.7% ; Prediction 63.2% ; NTS 40.6% ; Loss 62.4% ; Countries 68 ; Crises 87
  - Banking Sector Leverage (single threshold 128.3): Type I 45.1% ; Type II 27.7% ; Prediction 54.9% ; NTS 50.4% ; Loss 72.8% ; Countries 67 ; Crises 51
- Comparative example:
  - For the three-factor specification (credit-to-GDP growth, banking sector leverage and equity price growth):
    - Binary response model loss = 29.9 percent.
    - Signal extraction approach based on Credit-to-GDP gap loss = 63.1 percent.
    - Signal extraction using same sample loss = 47.0 percent.
  - Policy rule implication: If L = TypeI + TypeII, react when conditional crisis probability ≈ 13 percent (preferred three-factor specification threshold).

D. Risk Factor Thresholds (preserved expressions and numeric examples)
- Focus specification: model (1) in Table 8 — credit-to-GDP growth, banking sector leverage and equity price growth; optimal systemic risk threshold = 13.0 percent.
- Interdependence examples:
  - If equity prices have grown by 20 percent and banking sector leverage ≈ 160 percent, a crisis signal issued if credit-to-GDP growth > 0 percent.
  - If equity prices have decreased by 10 percent and banking sector leverage ≈ 130 percent, a crisis signal issued only if credit-to-GDP gap > 10 percentage points.
- Static signal extraction equivalent: credit-to-GDP growth > 4.9 percentage points triggers a signal.
- Formula for optimal threshold of risk factor j (preserving notation): t_j^* = Λ_{1/0}^{-1}(λ^*) − α − ∑ β_i x_i.
- Specific optimal credit-to-GDP growth threshold expression (numeric form preserved):
  - 39.5 − 23.2% · Bank Leverage − 7.4% · Equity Growth  (median country fixed effect used in calculation: -10.96 as noted in source).

E. Out-of-Sample Analysis (1970–2000 estimation; 2001–2010 evaluation)
- General outcome: policymaker loss generally larger out-of-sample but models still predict around 50–80 percent of crises without excessive false signals.
- Selected out-of-sample rows (preserved from Table 5):
  - Single factor examples:
    - Credit-to-GDP Gap: Threshold 6.65; Type I 0.0% ; Type II 36.9% ; Prediction 63.1% ; NTS 79.2% ; Loss 86.9% ; Countries 43 ; Observations 438
    - Credit-to-GDP Growth: Threshold 6.36; Type I 2.5% ; Type II 36.9% ; Prediction 37.5% ; NTS 98.3% ; Loss 99.4% ; Countries 43 ; Observations 438
    - Banking Sector Leverage: Threshold 6.95; Type I 0.0% ; Type II 18.7% ; Prediction 50.0% ; NTS 37.4% ; Loss 68.7% ; Countries 21 ; Observations 214
  - Two factor examples:
    - Credit-to-GDP Gap and Bank Leverage: Threshold 5.7; Type I 0.0% ; Type II 34.8% ; Prediction 100.0% ; NTS 34.8% ; Loss 34.8% ; Countries 21 ; Observations 214
    - Credit-to-GDP Growth and Bank Leverage: Threshold 7.5; Type I 25.0% ; Type II 18.1% ; Prediction 75.0% ; NTS 24.1% ; Loss 43.1% ; Countries 21 ; Observations 214
  - Three factor example:
    - Credit-to-GDP Growth, Bank Leverage and Equity Price Growth: Threshold 9.85; Type I 0.0% ; Type II 36.9% ; Prediction 50.0% ; NTS 73.8% ; Loss 86.9% ; Countries 9 ; Observations 94
- Example: United States (Figure 8 in source): systemic risk from a two-factor binary response model (credit-to-GDP growth and banking sector leverage) rises dramatically approaching 2007; out-of-sample optimal threshold shown = 7.5 (Table 5).

### VI. Concluding Remarks
- Model summary:
  - Dynamic binary response model with country fixed effects is effective for modeling time-varying conditional probability of systemic banking crises.
  - Significant predictors: banking sector leverage; credit-to-GDP growth; changes in lending premium; equity price growth; rising interconnectedness; REER appreciation.
- Policy takeaways:
  - Static thresholds (signal extraction) can misclassify benign credit expansions; binary response thresholds adapt to the economy’s state and risk-factor combinations, yielding more realistic policy triggers.
- Caveats and open questions:
  - Causality of identified risk factors remains unclear; monitoring does not require causality, but macroprudential policy interventions aimed at reducing a risk factor do.
  - Further theoretical research needed to determine whether policy should target identified risk factors.

### Appendix I — Data Sources and Description (key items)
- Crisis variable: Reinhart and Rogoff (2010) definition; annual data; first crisis year used.
- Transformations and sources (selected exact definitions preserved):
  - Credit-to-GDPt = (Private credit by deposit money bankst / GDPt)*100. Source: IMF IFS (lines 22d, 99b).
  - Credit-to-GDP Growtht = (Credit-to-GDPt - Credit-to-GDPt-2)/2.
  - Credit-to-GDP Gapt uses HP filter λ = 1600.
  - Banking Sector Leverage (pct) = Private credit by deposit money banks / (demand, time and saving deposits). Source: IMF IFS.
  - Equity Price Growtht = ln(Equity Pricet/Equity Pricet-2)/2. Source: Bloomberg.
  - House Price Growtht = ln(House Pricet/House Pricet-2)/2. Source: Bloomberg.
  - REER Growtht = ln(REERt/REERt-1). Source: IMF INS.
  - Non-core liabilities proxies: Non-Core 1 = banks foreign liabilities (line 26C) + bank liabilities to other financial institutions (line 36J); Non-Core 2 = banks foreign liabilities (26C) + (M3−M2). Core = M2. Source: IMF IFS / WEO.
  - Contagion_{i,t+1} = Σ_{j≠i} ω_{j,t} y_{j,t}, with ω_{j,t} = country j market capitalization % of world market capitalization. Source: World Bank.
  - ∆Lending Premiumt = (Lending Premiumt - Lending Premiumt-2)/2. Lending Premium = bank loan rate to prime private customers − treasury bill rate. Source: World Bank.
- Estimation sample sizes and examples:
  - Estimation period: 1970-2010; unbalanced annual panel.
  - Credit-to-GDP Growth models: Countries = 64; Observations = 1442.
  - Banking Sector Leverage models: Countries = 64; Observations = 933.
  - Equity Price Growth: Countries = 40; Observations = 862.
  - REER Appreciation: Countries = 67; Observations = 1585; example Lag 1 Beta = 0.24*.

### Appendix III — Systemic Banking Crises Dates (selected examples)
- Appendix III lists country-by-country systemic banking crises dates (Reinhart and Rogoff definition). Selected entries:
  - Algeria 1990-1992
  - Argentina 1980-1982, 1989-1990, 1995-1996 and 2001-2003
  - Australia 2008-2010
  - Brazil 1985, 1990, 1994-1997
  - Canada 1983-1985
  - China 1992-1999
  - France 1994-1995 and 2008-2010
  - Ireland 2007-2010
  - Japan 1992-2001
  - Korea, Republic of 1983, 1985-1988 and 1997-2002
  - Mexico 1981-1982 and 1994-2000
  - Spain 1977-1985 and 2008-2010
  - United States 1984-1991 and 2007-2010

*Source: _wp12159 (sections and appendices as provided in the source PDF).*

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

### _wp12159 - References .............................................................................................................

### I. Introduction and Objective
- The financial crisis in 2007–09 and the following global recession highlighted the importance of a macroprudential policy framework to limit systemic financial risk.
- The paper focuses on establishing robust methods for monitoring systemic risk in real time.
- Systemic risk is defined as the conditional probability of a systemic banking crisis; the objective is to model and forecast this potentially time-varying probability using a fixed effect binary response model.
- Focus: the time dimension of systemic risk (evolution over time due to macroeconomic changes), with inclusion of a variable proxying interconnectedness between financial institutions.

### Methodology and Innovations
- Employs a dynamic binary response model based on a panel of 68 advanced and emerging economies.
- Uses a purely dynamic model structure so systemic risk forecasts rely solely on information available in real time.
- Estimation strategy is consistent under more general conditions than random effects estimators used in some prior studies.
- Shows how to derive dynamic risk factor thresholds within the binary response framework; thresholds depend on the values of the other risk factors, in contrast to static thresholds from the signal extraction approach.
- Performs a pseudo out-of-sample analysis for the period 2001–2010 to assess early-warning capability for the recent financial crisis.

### Main Findings (numbered as in source)
1. Predictability of systemic risk:
   - Systemic risk appears to be predictable in real time.
   - Identified risk factors: banking sector leverage, equity price growth, the credit-to-GDP gap, real effective exchange rate appreciation, changes in the banks’ lending premium, and the degree of banks interconnectedness measured by the ratio of non-core to core bank liabilities.
   - Some evidence that house price growth increases systemic risk, but the effect is not statistically significant at conventional significance levels.

2. Contagion:
   - There exists a significant contagion effect between economies: when an economy with a large financial sector experiences a systemic banking crisis, systemic risk forecasts in other economies increase significantly.

3. Credit growth interpretation:
   - Rapid credit growth is often associated with higher systemic risk.
   - Credit booms can also reflect healthy market responses to expected future productivity gains (new technology, new resources, institutional improvements).
   - Empirical evidence suggests credit growth increases systemic risk considerably more when accompanied by high equity price growth.
   - Implication: equity price evolution can help distinguish healthy credit expansions from risky ones.

4. Comparative performance:
   - In a crisis signaling exercise, the binary response model approach outperforms the signal extraction approach in terms of type I and type II errors.

5. Dynamic thresholds:
   - For a model with credit-to-GDP growth, banking sector leverage and equity price growth, the optimal credit-to-GDP growth threshold is not static but depends on other risk factors.
   - Example thresholds from the model:
     - Around 10 percent if equity prices have decreased by 10 percent and banking sector leverage is around 130 percent.
     - Around 0 percent if equity prices have grown by 20 percent and banking sector leverage is 160 percent.
   - By comparison, the signal extraction method gives a static credit-to-GDP growth threshold of 4.9 percent based on the same data sample.

6. Out-of-sample performance (2001–2010):
   - Systemic risk factors generally provided informative signals in many countries.
   - Based on in-sample calibration, around 50–80 percent of the crises were correctly identified in real time without constructing too many false signals.
   - A monitoring model based on credit-to-GDP growth and banking sector leverage signaled early warning signals ahead of the U.S. subprime crisis in 2007.

### Policy-relevant Implications and Uses
- Real-time monitoring of systemic risk is feasible and can improve policy decisions when based on a dynamic binary response framework.
- Dynamic, conditional thresholds for risk factors provide a more nuanced policy trigger mechanism than static thresholds.
- Policymakers should incorporate equity price information alongside credit growth to better discern benign versus risky credit expansions.
- Monitoring models should account for contagion effects across economies, particularly when large financial sectors are affected.

*Italic: Content derived from the source PDF _wp12159 - References .............................................................................................................*

### Section III presents the econometric methodology and the model specification. Section IV

### _wp12159 - Section III presents the econometric methodology and the model specification. Section IV

### Related literature
- Two empirical approaches to systemic banking crisis analysis: (i) the signal extraction approach and (ii) the econometric approach.
- Signal extraction findings cited:
  - Kaminsky and Reinhart (1999): real exchange rate, stock prices and the ratio of public sector deficits to GDP were most useful indicators for twin crises (currency + banking).
  - Borio and Lowe (2002) and Borio and Drehmann (2009): credit-to-GDP gap is the most useful indicator of systemic risk.
- Econometric findings cited:
  - Demirgüç-Kunt and Detragiache (1998a): systemic banking distress associated with low economic growth, high inflation, high real interest rates; balance of payments crises associated with banking crises.
- This paper differentiates from prior literature by:
  - Focusing on real-time systemic risk monitoring (dynamic model with risk factors known h periods in advance) rather than causal identification.
  - Employing a fixed effect estimation approach (consistent under weaker conditions than random effects; author finds fixed and random effects estimators generate quite different parameter estimates, suggesting non-independence between risk factors and unobserved country fixed effects).
  - Deriving dynamic risk factor thresholds within a binary response model framework, allowing thresholds to depend on the state of the economy via other risk factors (contrast with static thresholds in signal-extraction approaches).

### Econometric methodology and model specification (binary response dynamic framework)
- Dependent variable:
  - Binary systemic banking crisis variable y_i,t drawn from a Bernoulli distribution.
  - Crisis probability modeled as Pr(y_i,t=1 | x_{i,t-h}; α_i, β) = G(α_i + x_{i,t-h}' β), where G is a continuous link function.
- Link functions considered:
  - Probit: G = Φ(·) (standard normal CDF).
  - Logit: G = Λ(·) = e^x / (1 + e^x).
  - Linear Probability Model (LPM): G(x)=x (drawback: probability not bounded between 0 and 1).
- Dynamic structure:
  - All risk factors are known h periods (years) in advance; crisis probability in period t is conditional on information known at t-h.
- Marginal effects:
  - Marginal effect of x_{ij,t-h} equals G'(α_i + x_{i,t-h}' β) · β_j.
  - Standardized marginal effect = G'(α_i + x_{i,t-h}' β) · β_j · sd(x_{j,t-h}), approximating the increase in systemic risk from a one standard deviation increase in the indicator.
  - Marginal effects depend on all risk indicators and the country fixed effect α_i (implicit interaction among risk indicators).
- Estimation:
  - Parameters (α, β) estimated by maximum likelihood, maximizing log likelihood Σ_i Σ_t [ y_{i,t} log G(α_i + x_{i,t-h}'β) + (1-y_{i,t}) log(1- G(α_i + x_{i,t-h}'β)) ].
  - Country fixed effects treated as parameters (no independence restriction between α_i and risk factors).

### Data, sample and risk-factor definitions
- Sample:
  - Unbalanced annual panel of 68 advanced and emerging economies over 1970-2010.
- Crisis definition:
  - Adopts Reinhart and Rogoff (2010) systemic banking crisis definition: (i) bank runs that lead to closure/merger/takeover by public sector of one or more financial institutions; or (ii) absent runs, closure/merger/takeover/large-scale government assistance of an important financial institution that marks the start of a string of similar outcomes.
- Key candidate risk factors included:
  - Private credit by deposit money banks as a percentage of GDP (credit-to-GDP measures and credit-to-GDP gap).
  - Asset prices: equity and house prices (inflation around long-run trend).
  - Banks’ lending premium (difference between bank loan rate to prime private customers and treasury bill rate).
  - Real effective exchange rate (REER).
  - Banking sector leverage: private credit by deposit money banks as a percentage of demand, time and saving deposits in deposit money banks (note: differs from standard leverage definition).
  - Bank interconnectedness proxied by ratio of non-core to core bank liabilities. Two non-core definitions adopted:
    - Non-Core 1 = Liability of banks to the foreign sector + Liability to the non-banking financial sector.
    - Non-Core 2 = Liability of banks to the foreign sector + (M3 - M2). Core liabilities measured by M2.
  - Contagion variable (for country i at time t): Σ_{j≠i} ω_{j,t} y_{j,t}, where ω_{j,t} is country j’s market capitalization as a percentage of world market capitalization.
- Credit-to-GDP gap estimation:
  - Trend estimated by backward-looking Hodrick-Prescott (HP) filter estimated recursively.
  - Smoothing parameter set to λ = 1600 (following Drehmann, Borio and Tsatsaronis (2011)); robustness checks with λ = 100 and other values showed no substantial impact.

### Estimation results (single-factor and multivariate logit/probit/LPM comparisons)
- Model specifications considered: logit, probit, and LPM; focus on logit for presentation.
- Robustness across link functions:
  - β coefficients differ across specifications, but standardized marginal effects are consistent across logit, probit and LPM.
- Single-predictor logit findings (standardized marginal effects evaluated at median country fixed effect and median risk indicator value):
  - Credit-to-GDP gap:
    - Positive significant effect on systemic risk up to three years in advance.
    - A one standard deviation increase in the credit-to-GDP gap increases systemic risk by around 3.3 percent, 2.6 percent and 1.3 percent the following three years for the logit model (evaluated at median fixed effect and median risk factor; illustrated in Figure 3).
    - Results similar across advanced and emerging economies.
  - Credit-to-GDP growth:
    - Positive significant effect up to three years in advance (consistent with Borio and Lowe (2002) and Borio and Drehmann (2009)).
  - Banking sector leverage:
    - Associated with higher systemic risk; significant up to two years in advance.
    - For a median risk country at a one year forecast horizon, a one standard deviation increase in banking leverage increases systemic risk by 2.5 percent (logit specification; see Figure 3).
  - Bank interconnectedness (non-core to core liabilities):
    - Significant impact on systemic risk at a one year forecast horizon (consistent with theory linking non-core funding to interconnectedness and systemic vulnerability).
  - Asset price inflation:
    - Equity price inflation: significant positive impact on systemic risk three to four years ahead.
    - House price inflation: appears to increase systemic risk at a two year horizon, though not statistically significant at the 5 percent level in single-predictor models.
  - Real effective exchange rate appreciation (REER):
    - Deteriorating trade competitiveness (REER appreciation) increases systemic risk; emerging economies are more sensitive to this effect.
  - Real GDP growth:
    - No clear impact on systemic risk in single-factor logit models overall.
    - Asymmetric patterns: emerging economies tend to experience negative GDP growth leading up to a systemic crisis, while advanced economies tend to experience positive GDP growth preceding crises (see Figure 4h).
- Multivariate analysis:
  - Implicit interactions among risk indicators (through binary response marginal effects) allow the marginal effect of one indicator to be higher when other indicators are high (provided other factors have positive beta coefficients and conditional probability < 50 percent for logit/probit).
  - Author avoids explicit multiplicative interaction terms (x·z) because such terms can produce perverse dynamics (e.g., sign changes in marginal effects) and are therefore not used.

### Table 2 (dynamic logit model summary highlights)
- Estimation details reported for various lags h (1–12 years) and alternative specifications; models include country fixed effects in many specifications.
- McFadden's R^2 reported in percent across specifications (examples shown in table): 32.8, 9.9, 28.9, 33.0, 25.7, 33.4, 31.8, 36.7, 16.8, 30.2, 24.1, 31.8 (values correspond to different lag/specification columns shown in Table 2).
- Coefficient estimates and standard errors in Table 2 are expressed in percent; statistical significance denoted by ***, **, * for 1 percent, 5 percent and 10 percent levels.
- Table 2 notes:
  - Sample sizes vary by specification: examples include Countries = 38, 29, 36, 29, 22, 22, 33, 23, 23, 33, 38; Observations = 399, 399, 399, 285, 940, 355, 299, 278, 525, 206, 332, 399 (these correspond to columns in Table 2).
  - Contagion variable defined as Σ_{j≠i} ω_{j,t} y_{j,t} (see above).

### Key empirical conclusions
- Credit dynamics (credit-to-GDP growth and credit-to-GDP gap) are robust leading indicators of systemic banking crises up to three years ahead.
- Banking sector leverage and non-core funding (interconnectedness proxy) are significant near-term predictors (notably at one-year horizons).
- Equity price inflation is a leading predictor several years ahead; house price inflation shows some positive association at shorter horizons.
- REER appreciation (weaker trade competitiveness) increases systemic risk, especially in emerging economies.
- Real GDP growth does not uniformly predict systemic crises; patterns differ between advanced and emerging economies.
- The dynamic binary response (logit/probit) fixed-effect framework permits computation of standardized marginal effects and dynamic risk thresholds that depend on the state of the economy and other risk factors, addressing limitations of static signal-extraction thresholds.

*Source: _wp12159 (Sections II–IV), author’s estimates and figures as provided in the source content.*

### 1. Combining banking sector leverage, credit-to-GDP gap and equity price inflation appears

### 1. Combining banking sector leverage, credit-to-GDP gap and equity price inflation appears to provide a good representation of the data for both a one and two year forecast horizon

### Model performance and key predictors
- Combining banking sector leverage, credit-to-GDP gap and equity price inflation provides a good representation of the data for both a one and two year forecast horizon (columns (1) and (3)).
- All the estimated coefficients for this specification are positive and significant at a 5 percent level.
- This finding is consistent with the theory in Allen and Gale (2000a) that asset price inflation fuelled by credit expansion can lead to systemic banking crises.

### Estimation methodology: fixed effects versus random effects
- Column (2) illustrates the effect of the fixed effect estimation methodology.
- Random effect estimators used in other studies are only consistent if the unobserved country fixed effects are independent of the risk indicators.
- The empirical results indicate the independence assumption might be violated because parameter estimates differ substantially for the random effects estimator (column (2)).
- Potential inconsistency of the random effect estimator could reflect omitted variable bias arising from dependence between country fixed effects and explanatory variables.
- Example given: if economies with a small country fixed effect (e.g., well-developed financial markets) are more likely to have a leveraged banking sector on average, an inverse relationship between country fixed effects and banking sector leverage implies the random effect estimator of the banking sector leverage coefficient will be inconsistent and have a negative asymptotic bias.

### Asset price indicators: equity and house prices
- Equity price inflation is an important positive predictor of systemic risk when combined with banking sector leverage and credit-to-GDP gap.
- House price inflation does not appear to have a large impact on systemic risk (column (4)):
  - In a single predictor model, house price inflation was only weakly related to systemic banking crisis.
  - When combined with banking sector leverage, credit-to-GDP gap and equity price inflation, the impact of house price inflation is even weaker.
  - Note: this model specification is based on only 29 countries due to data availability.

### Contagion and international linkages
- There is a significant contagion effect between economies (column (5)):
  - The estimated coefficient of the contagion variable is positive and significant.
  - If an economy with a large financial sector is experiencing a systemic banking crisis, the systemic risk forecast increases in other economies in the next period.
  - Kaminsky and Reinhart (2000) find similar results.

### Interconnectedness: non-core to core bank liabilities
- Financial institutions’ interconnectedness, approximated by non-core to core bank liabilities, has a positive significant impact on systemic risk (columns (6), (7) and (8)).
- The effect is positive and significant for both definitions of non-core bank liabilities.
- These empirical findings are consistent with the theoretical model in Hahm, Shin and Shin (2011).

### Lending premium effects
- Changes in the lending premium appear to impact the level of systemic risk (column (9)):
  - The coefficient on the lending premium is negative and significant, indicating that if the lending premium decreases in an economy, the level of systemic risk increases.
  - However, when controlling for banking sector leverage and equity price growth the effect is no longer significant (column (10)).

### Trade competitiveness
- Deteriorating trade competitiveness, as measured by a real effective exchange rate appreciation, appears to increase the level of systemic risk (illustrated in columns (6) and (8)).

### Interaction: credit-to-GDP gap and high equity price growth
- An increase in the credit-to-GDP gap increases systemic risk substantially more when accompanied by high equity price growth.
- Column (12) allows the effect of the credit-to-GDP gap to differ by adding a premium if the previous two years equity price inflation has exceeded 20 percent.
- Estimated coefficients:
  - Estimated coefficient of ‘good’ credit growth: 7.44 percent.
  - Estimated coefficient of ‘bad’ credit growth: 23.78 percent (7.44 percent + 16.34 percent).
- Implication: the increase in systemic risk following an increase in the credit-to-GDP gap is approximately three times larger if the last two years equity price inflation has exceeded 20 percent.
- Consequently, the evolution in equity prices might be useful for identifying a healthy credit expansion.

*Source: _wp12159 - 1. Combining banking sector leverage, credit-to-GDP gap and equity price inflation appears*

### 9. Finally, it should be noted that the results are not sensitive to whether one use the credit-

### V. MONITORING SYSTEMIC RISK

### A. The Signal Extraction Approach
- Method: For each period a signal is computed as 1 (“on”) or 0 (“off”); signal is “on” if one or several risk indicators cross a certain threshold and “off” otherwise.
- No signals are considered in the two years after the beginning of a crisis.
- Forecast errors:
  - Type I error: no signal issued and a crisis occurs.
  - Type II error: signal issued but no crisis occurs.
- Optimal thresholds are chosen by minimizing a loss function defined over the fraction of Type I and Type II errors, e.g., the noise-to-signal ratio: TypeII/(1−TypeI).

### B. Crisis Signals Based on Binary Response Model
- Proposal: A crisis signal is ‘On’ if the estimated level of systemic risk (from the binary response model) crosses a threshold, λ*.
- Threshold calibration: the optimal λ* minimizes a loss function over Type I and Type II errors. In the analysis the loss function is assumed to be L(TypeI,TypeII) = TypeI + TypeII.
- Trade-off: Lower thresholds reduce Type I errors but increase Type II errors; the optimal threshold depends on policymaker preferences. Examples:
  - Optimal threshold is 7.9 when L = TypeI + TypeII.
  - Optimal threshold is 4.9 when L = 2·TypeI + TypeII.
- Advantages of binary response model relative to static signal extraction:
  - If it approximates the true conditional crisis probability well, it should provide more accurate crisis-probability forecasts.
  - Thresholds are dynamic: the threshold for a single risk factor depends on values of other risk factors.

- Selected signaling performance (from Table 4; binary response model vs. signal extraction; thresholds and performance metrics preserved exactly):
  - Binary Response Model Approach (Logit) examples:
    - Credit-to-GDP Gap: Threshold 9.25; Type I 0.6% ; Type II 7.8% ; Prediction 49.4% ; NTS 15.7% ; Loss 58.4% ; Countries 68 ; Crises 87
    - Credit-to-GDP Growth: Threshold 6.63; Type I 7.9% ; Type II 18.2% ; Prediction 62.1% ; NTS 29.3% ; Loss 56.1% ; Countries 68 ; Crises 87
    - Credit-to-GDP Gap and Bank Leverage: Threshold 7.93; Type I 0.6% ; Type II 11.7% ; Prediction 69.4% ; NTS 16.9% ; Loss 42.4% ; Countries 66 ; Crises 49
    - Credit-to-GDP Growth, Bank Leverage and Equity Price Growth: Threshold 13.0; Type I 24.0% ; Type II 5.9% ; Prediction 76.0% ; NTS 7.7% ; Loss 29.9% ; Countries 38 ; Crises 25
    - CtG Growth, Bank Leverage, Equity- and House Price Growth: Threshold 9.51; Type I 4.3% ; Type II 17.9% ; Prediction 85.7% ; NTS 20.9% ; Loss 32.2% ; Countries 29 ; Crises 21
  - Signal Extraction Approach examples:
    - Credit-to-GDP Growth (single threshold 2.84): Type I 41.4% ; Type II 21.7% ; Prediction 58.6% ; NTS 37.0% ; Loss 63.1% ; Countries 68 ; Crises 87
    - Credit-to-GDP Gap (single threshold 2.33): Type I 36.8% ; Type II 25.7% ; Prediction 63.2% ; NTS 40.6% ; Loss 62.4% ; Countries 68 ; Crises 87
    - Banking Sector Leverage (single threshold 128.3): Type I 45.1% ; Type II 27.7% ; Prediction 54.9% ; NTS 50.4% ; Loss 72.8% ; Countries 67 ; Crises 51
- Key comparative result: The binary response model approach outperforms the signal extraction approach for all model specifications in Table 4. Example comparison:
  - For the model with credit-to-GDP growth, banking sector leverage and equity price growth:
    - Binary response model loss = 29.9 percent.
    - Signal extraction approach based on Credit-to-GDP gap loss = 63.1 percent.
    - Signal extraction approach using same data sample loss = 47.0 percent.
- Interpretation for policymakers:
  - If L = TypeI + TypeII, react when the conditional crisis probability reaches around 13 percent (the systemic risk threshold for the preferred three-factor specification).

### C. Risk Factor Thresholds
- Focus specification: model (1) in Table 8 — credit-to-GDP growth, banking sector leverage and equity price growth (good signaling properties).
- Policy trigger: react when conditional crisis probability ≈ 13 percent if L = TypeI + TypeII.
- Interdependence: thresholds for one indicator depend on levels of other indicators. Examples from Figure 6:
  - If equity prices have grown by 20 percent and banking sector leverage ≈ 160 percent, a crisis signal is issued if credit-to-GDP growth > 0 percent.
  - If equity prices decreased by 10 percent and banking sector leverage ≈ 130 percent, a crisis signal is issued only if the credit-to-GDP gap > 10 percentage points.
- Static signal extraction equivalent: A crisis signal is issued when credit-to-GDP growth is above 4.9 percentage points (illustrated for the signal extraction model).
- Formula for optimal threshold of risk factor j (preserving notation and structure exactly as in source):
  - t_j^* = Λ_{1/0}^{-1}(λ^*) − α − ∑ β_i x_i  (structure shown in source as equation (7), with preserved symbols x_i, α_i, β_i, Λ_{1/0}, λ^*)
- Specific derived expression for the optimal credit-to-GDP growth threshold (preserving numbers and notation exactly as in source):
  - The optimal systemic risk threshold: 13.0 percent.
  - The corresponding optimal credit-to-GDP growth threshold expression (equation (8) from the source) yields numeric results expressed in the source as:
    - 39.5 − 23.2% · Bank Leverage − 7.4% · Equity Growth  (expression as presented in the source; -10.96 denotes the median country fixed effect used in the calculation).
- Figure 7: shows how the optimal credit-to-GDP growth threshold varies with banking sector leverage and equity price growth (thresholds evaluated at the median country fixed effect; calibration uses L = Type I + Type II).

### D. Out-of-Sample Analysis
- Robustness check: estimate model parameters using data 1970-2000 and construct early-warning signals out-of-sample for 2001-2010. Thresholds calibrated on 1970-2000.
- General outcome: policymaker’s loss is generally larger out-of-sample than in-sample, but models still perform well: all models predict around 50-80 percent of systemic banking crises out-of-sample without issuing unreasonably many false signals.
- Selected out-of-sample results (Table 5; thresholds and metrics preserved exactly):
  - Single factor models:
    - Credit-to-GDP Gap: Threshold 6.65; Type I 0.0% ; Type II 36.9% ; Prediction 63.1% ; NTS 79.2% ; Loss 86.9% ; Countries 43 ; (column denotes Countries = 8? preserve as in table: 438)
    - Credit-to-GDP Growth: Threshold 6.36; Type I 2.5% ; Type II 36.9% ; Prediction 37.5% ; NTS 98.3% ; Loss 99.4% ; Countries 43 ; (438 in table)
    - Banking Sector leverage: Threshold 6.95; Type I 0.0% ; Type II 18.7% ; Prediction 50.0% ; NTS 37.4% ; Loss 68.7% ; Countries 21 ; (214 in table)
  - Two factor models:
    - Credit-to-GDP Gap and Bank Leverage: Threshold 5.7; Type I 0.0% ; Type II 34.8% ; Prediction 100.0% ; NTS 34.8% ; Loss 34.8% ; Countries 21 ; (214 in table)
    - Credit-to-GDP Growth and Bank Leverage: Threshold 7.5; Type I 25.0% ; Type II 18.1% ; Prediction 75.0% ; NTS 24.1% ; Loss 43.1% ; Countries 21 ; (214 in table)
  - Three factor models:
    - Credit-to-GDP Growth, Bank Leverage and Equity Price Growth: Threshold 9.85; Type I 0.0% ; Type II 36.9% ; Prediction 50.0% ; NTS 73.8% ; Loss 86.9% ; Countries 9 ; (94 in table)
- Example: Figure 8 (United States): systemic risk estimates based on a binary response model with credit-to-GDP growth and banking sector leverage show systemic risk rising dramatically as the subprime mortgage crisis approaches in 2007. The out-of-sample optimal threshold shown is 7.5 (see Table 5).

### VI. CONCLUDING REMARKS
- Model and findings:
  - A dynamic binary response model with country fixed effects models the time-varying conditional probability of systemic banking crisis.
  - Significant risk factors identified: banking sector leverage, credit-to-GDP growth, changes in banks’ lending premium, equity price growth, increasing interconnectedness in the financial sector and real effective exchange rate appreciation.
  - The model translates systemic risk estimates into crisis signals with accurate Type I and Type II error properties.
- Policy implications:
  - Signal extraction method uses constant thresholds independent of other indicators — this can be problematic because a credit boom may reflect benign fundamentals.
  - Binary response model thresholds adapt to the state of the economy and the combination of risk factors, providing more realistic policy triggers.
- Caution and open questions:
  - It remains unclear whether identified risk factors (e.g., credit-to-GDP growth) have causal impacts on systemic risk or are correlated with other causal variables.
  - For monitoring, causal interpretation is not necessary; for macroprudential policy aimed at reducing a risk factor, causality is required.
  - More theoretical research is needed to evaluate whether macroprudential policy should aim to reduce any of the identified risk factors.

*Source: Author’s estimates.*

### APPENDIX I. DATA SOURCES AND DESCRIPTION

### APPENDIX I. DATA SOURCES AND DESCRIPTION

### Binary Systemic Crisis Variable
- Definition adopted from Reinhart and Rogoff (2010): a banking crisis is systemic if either:
  - Bank runs that lead to closure, merger, or takeover by the public sector of one or more financial institutions.
  - Or, if there are no runs, the closure, merger, takeover, or large-scale government assistance of an important financial institution that mark the start of a string of similar outcomes for other financial institutions.
- Only the first crisis year is used in the estimation.
- All data are annual.
- Exact crisis dates are provided in Appendix III.

### Systemic Risk Factors — Definitions, Transformations, and Sources
- Credit-to-GDPt: (Private credit by deposit money bankst / GDPt)*100. Source: IMF’s International Financial Statistics (line 22d and 99b).
  - Credit-to-GDP Growtht (in percentage points) = (Credit-to-GDPt - Credit-to-GDPt-2)/2
  - Credit-to-GDP Gapt = Credit-to-GDPt – CtG_Trendt, where CtG_Trendt is computed by the Hodrick-Prescott Filter (1981) with smoothing parameter, λ=1600.
- Banking Sector Leverage (in percent): (Private credit by deposit money banks)/(demand, time and saving deposits in deposit money banks). Source: IMF’s International Financial Statistics (line 22d, line 24 and 25).
- Equity Prices: Source: Bloomberg.
  - Equity Price Growtht = ln(Equity Pricet/Equity Pricet-2)/2
- House Prices: Source: Bloomberg.
  - House Price Growtht = ln(House Pricet/House Pricet-2)/2
- REER: Real Effective Exchange Rate. Source: IMF Information Notice System (INS) database.
  - REER Growtht = ln(REERt/REERt-1)
- Non-core liabilities Proxy 1: The sum of banks foreign liabilities (line 26C) and bank liabilities to other financial institutions (line 36J). Source: IMF’s International Financial Statistics.
- Non-core liabilities Proxy 2: The sum of banks foreign liabilities (line 26C) and M3-M2. Source: IMF’s International Financial Statistics.
- Core Liabilities: Broad money, M2. Source: IMF’s World Economic Outlook.
- Real GDP (RGDP): Source: IMF’s World Economic Outlook.
  - Real GDP Growtht: ln(RGDPt/RGDPt-2)/2
- Contagion variable for country i:
  - contagion_i,t+1 = ∑_{j≠i} ω_{j,t} y_{j,t}
  - where y_{j,t} is the binary systemic banking crisis variable for country j at time t and ω_{j,t} is country j’s market capitalization, at time t, as a percentage of the world’s market capitalization. Source: World Bank.
- Change in Lending Premium:
  - Lending Premium: interest rate charged by banks on loans to prime private sector customers minus the "risk free" treasury bill interest rate.
  - ∆Lending Premiumt = (Lending Premiumt - Lending Premiumt-2)/2. Source: World Bank.

### Model Estimation: Data Coverage and Methodology
- Estimation period: 1970-2010.
- Data structure: unbalanced annual panel.
- Estimation method: maximum likelihood based on a country fixed effect model specification (logit/probit/linear probability models used).
- Dependent variable: Binary Systemic Banking Crisis Variable from Reinhart and Rogoff (2010).
- Notes on reported measures in tables:
  - Beta = risk factor parameter estimate.
  - SE = standard error.
  - McF.s R2 = McFadden's R2.
  - R2 = coefficient of determination.
  - ME LR = Marginal effect for a low risk country (20th percentile country fixed effect).
  - ME HR = Marginal effect for a high risk country (80th percentile country fixed effect).
  - Marginal effects evaluated at the median value of the risk factor.
  - Lag refers to ‘h’ in Pr(y_{i,t}=1)=G(α_i+β×x_{i,t-h}).
  - Credit-to-GDP gap uses HP-filter with λ=1600.

### Key Estimation Sample Sizes and Model Fit (selected items)
- Credit-to-GDP Growth models:
  - Countries: 64; Observations = 1442 (Table 6).
  - Reported significant coefficients: e.g., Lag 1 Beta = 11.13*** with associated statistics shown in table entries.
- Credit-to-GDP Gap models:
  - Countries: 64; Observations = 1442 (Table 6).
  - Example: Lag 1 Beta = 7.03*** (SE 1.59).
- Banking Sector Leverage models:
  - Countries: 64; Observations = 933 (Table 6).
  - Example: Lag 1 Beta = 1.47*** (SE 0.51).
- Bank Interconnectedness Proxy I:
  - Countries: 29; Observations = 382 (Table 6).
  - Example: Lag 1 Beta = 2.04* (SE 1.14).
- Equity Price Growth and House Price Growth models:
  - Equity Price Growth: Countries: 40; Observations = 862 (Table 7). Significant positive coefficients at longer lags (e.g., Lag 3 Beta = 2.31*** with reported statistics).
  - House Price Growth: Countries: 29; Observations = 724 (Table 7). Mixed coefficients across lags.
- Real GDP Growth models:
  - Countries: 68; Observations = 2306 (Table 7). Coefficients generally small and mixed in sign across lags.
- REER Appreciation (in pct.): Countries: 67; Observations = 1585 (Table 7). Example: Lag 1 Beta = 0.24* (reported as 0.24* with accompanying statistics).

### Dynamic Logit Model Highlights (Table 8)
- Models estimated for multiple lags h (columns labeled 1 through 13).
- Selected coefficient patterns:
  - Credit-to-GDP Growth (in pct. points): multiple lags significant; examples include coefficients reported as 22.91***, 15.63***, -28.74***, 12.51**, 21.47***, 19.39***, 15.75***, 13.91**, 24.18*, 22.25**, 14.74*, 15.76*** with corresponding standard errors and statistics listed in table.
  - Banking Sector Leverage (in pct.): reported significant coefficients such as 15.32*** and later lags with significance (e.g., 5.92*, 4.46*, 4.95***, 1.19**).
  - Equity Price Growth (in pct.): select coefficients reported (e.g., 1 1.70*, 0.41 1, -1.86* ... as structured in table).
  - Contagion Effect: reported significant coefficient 6.55*** in one specification.
  - Bank Interconnectedness Proxy 1 (in pct.): reported significant coefficient 3.72* in one specification.
  - Bank Interconnectedness Proxy 2 (in pct.): reported significant coefficients 2.64*** and 2.52** in specifications.
  - REER Appreciation (in pct.): reported coefficients including 2.15** and -6.15* in some specifications.
  - ∆Lending Premium (in pct. points): reported a coefficient 17.81** in one specification.
- Table-level diagnostics:
  - McFadden's R2 values across specifications reported, e.g., 32.0%, 13.1%, 31.3%, 32.5%, 26.3%, 31.4%, 27.2%, 32.6%, 16.9%, 29.3%, 24.1%, 31.7%, 19.8%.
  - Unrestricted likelihood values listed per specification (e.g., -63.5, -81.2, -64.2, -51.7, -141.8, -46.8, -49.5, -43.1, -73.3, -23.9, -44.0, -63.8, -154.29).
  - Countries and observations vary by specification (examples: Countries 38 with Observations 399; other entries include Countries 29, 22, 23, 33, 86; Observations reported per column such as 399, 285, 940, 355, 299, 278, 525, 206, 332, 399, 940).

### Appendix III — Systemic Banking Crises Dates (high-level)
- Appendix III lists country-by-country systemic banking crises dates following the Reinhart and Rogoff (2010) definition.
- Examples (as listed):
  - Algeria 1990-1992
  - Argentina 1980-1982, 1989-1990, 1995-1996 and 2001-2003
  - Australia 2008-2010
  - Brazil 1985, 1990, 1994-1997
  - Canada 1983-1985
  - China 1992-1999
  - France 1994-1995 and 2008-2010
  - Ireland 2007-2010
  - Japan 1992-2001
  - Korea, Republic of 1983, 1985-1988 and 1997-2002
  - Mexico 1981-1982 and 1994-2000
  - Spain 1977-1985 and 2008-2010
  - United States 1984-1991 and 2007-2010
- The full Appendix III table contains the complete country listing with crisis years.

*Source: APPENDIX I. DATA SOURCES AND DESCRIPTION (from the provided PDF content).*

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