## 27. Regression output is unlikely to be greatly different, as the correlation between the broad and the narrow

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---

### Credit-gap measurement, smoothing (lambda), and normalization
- Correlation between the broad and the narrow definition of credit ranges from 0.921 to 0.999 for the 18 EU countries in the BCBS dataset.
- Literature benchmarks and assumptions:
  - Arnold and others (2012): typical length of the financial cycle ranges between 16 and 20 years.
  - Under the assumption that credit cycles are four times as long as business cycles, the lambda of λ= 400,000 is calculated as 4^4 *1600 (Drehmann and others 2010; Edge and Meisenzahl 2011).
- Implications of high smoothing (large lambda):
  - A high smoothing factor can lead to continuously positive credit gaps for more than 20 years, making it difficult to distinguish cyclical developments from structural change (Detken and others 2014).
  - For countries with shorter cycles and large amplitudes (e.g., transition economies), strong smoothing may lead to implausibly large credit gaps.
- Empirical approach in this study:
  - Typical duration of the most recent credit cycle in EU countries since the 1990s was calculated to be between five and 10 years (shorter than in Drehmann and others (2010)).
  - Alternative credit gaps tested using smaller lambdas:
    - one-sided HP filter with λ=1,600 (generally recommended for quarterly data),
    - λ=25,000 as an “in-between” figure implying credit cycles are approximately twice as long as business cycles,
    - standard BCBS λ=400,000.
  - Additional normalization: credit-to-GDP gap series normalized by dividing each country’s credit gap by its credit-to-GDP ratio to address heterogeneity across countries.

### Key descriptive statistics (exact values preserved)
- Impairments (Cumulative flows of impairments and provisions during 2008–09 or 2009–10, in percent of average total assets)
  - Source: ECB
  - Mean: 2.48
  - Std.Dev.: 2.18
  - Min: 0.36
  - Max: 8.47
- GDP growth (Largest cumulative eight-quarter percentage change in real GDP during 2007–10)
  - Source: Eurostat
  - Mean: -6.03
  - Std.Dev.: 5.79
  - Min: -23.80
  - Max: 5.46
- Credit-to-GDP gap (Maximum credit-to-GDP gap, BCBS (2010) definition; alternatively, credit gap with different lambdas and normalized for credit-to-GDP levels)
  - Source: IMF / own calculations
  - λ=400,000: 12.66
  - λ=1,600: 8.59
  - Mean (additional column?): 10.61
  - Std.Dev.: 5.72
  - Min: 2.72
  - Max: 50.41
- House price growth (Compound annual growth rate of house prices during 2005–08)
  - Source: OECD
  - Mean: 17.70
  - Std.Dev.: 15.92
  - Min: 0.90
  - Max: 54.60
- Equity price growth (Compound annual growth rate of equity prices during 2005–08)
  - Source: OECD
  - Mean: 36.70
  - Std.Dev.: 17.43
  - Min: 12.00
  - Max: 80.20

### Single-stage multivariate regression results (exact equations and coefficients)
- Model estimated with robust standard errors (HC3). Multivariate setup: cumulative flow of loan impairments regressed on two-year percentage change in real GDP and normalized Basel gap (λ=1,600).
- Estimated cross-section model:
  - impairments_i = -0.513 – 0.314 gdp_growth_i + 0.128 credit_gap_normal_i + ε_i.
    - t-statistics: (-1.34) for constant, (-5.96)*** for gdp_growth, (3.28)*** for credit_gap_normal
  - Regression results: both explanatory variables are highly significant at the 1 percent level; R^2 = 0.83.
- Alternative specifications replacing credit gap:
  - With house prices:
    - impairments_i = 0.028 – 0.243 gdp_growth_i + 0.088 house_price_growth_i + ε_i.
      - t-statistics: (0.11), (-4.54)***, (3.30)***
    - House prices are highly significant after controlling for economic growth.
  - With equity prices:
    - impairments_i = -0.487 – 0.312 gdp_growth_i + 0.055 equity_price_growth_i + ε_i.
      - t-statistics: (-0.71), (-4.98)***, (1.18)
    - Equity prices are not significant.

### Correlations (exact coefficients)
- Correlation coefficients of GDP growth with drivers:
  - Credit gap, BCBS definition, λ=400,000: 0.086
  - Credit gap, normalized, λ=400,000: -0.001
  - Credit gap, normalized, λ=25,000: -0.027
  - Credit gap, normalized, λ=1,600: -0.052
  - Compound house price growth: -0.474
  - Compound equity price growth: -0.118
- Interpretation: hardly any correlation between GDP growth and credit gap measures (between 0.00 and 0.09 reported earlier); moderate negative correlation between GDP growth and house price growth.

### Two-stage regression approach and findings
- First-stage regression (impairments on GDP growth) — exact estimate:
  - impairments_i = 0.555 – 0.320 gdp_growth_i + ε_i.
    - t-statistics: (1.06), (-5.21)***
  - Fit: R^2 = 0.72.
  - Outlier: Poland (PL) identified; exclusion would improve R^2 to 0.83 and increase slope coefficient to -3.75, but authors keep the observation.
- Second-stage regression: residuals(first_stage)_i = α + β credit_gap_i + ε_i.
- Table 3 — Results of regressions of residual losses on credit gaps (exact coefficients and t-statistics)
  - Gap definition/lambda columns: λ=400,000 | λ=25,000 | λ=1,600
  - Maximum, BCBS definition:
    - λ=400,000: 0.007 (0.31)
    - λ=25,000: 0.005 (0.18)
    - λ=1,600: 0.000 (0.00)
  - Maximum, BCBS def. normalized:
    - λ=400,000: 0.077 (2.68)**
    - λ=25,000: 0.084 (3.37)***
    - λ=1,600: 0.126 (3.69)***
  - Note: Constant terms not reported; t-statistics in parentheses. ***, **, * denote significance at the 1%, 5%, 10% levels.
- Key insights from second-stage regressions:
  - The maximum gap under BCBS definition (λ=400,000) does not produce a significant outcome in this heterogeneous European sample.
  - Normalizing credit gaps for credit-to-GDP levels renders the adjusted maximum gap significant at the 5 percent level (and more so with smaller lambdas).
  - Using smaller lambdas (e.g., λ=1,600) improves regression outcomes because several transition countries have short credit cycles (five to 10 years).
  - Preferred variant: normalized maximum gap using λ=1,600 (termed gapmax1600); regression fit R^2 = 0.39.

### Mapping residual losses to the Countercyclical Capital Buffer (CCB)
- Procedure:
  - Use fitted values from second-stage regression (rather than observed residuals) to map residual losses into recommended CCB sizes.
  - Residual loan losses (expressed in percent of total assets) transformed into RWA terms because absolute RWA values were not available.
- CCB mapping parameters (exact values preserved):
  - CCB activated beyond a credit gap of 4 percent (L=4).
  - CCB increases linearly with the credit gap up to 2.5 percent of RWA corresponding to a maximum gap of 20 percent (H=20).
- Conceptual distinction:
  - Ordinary buffer: combined cushion of loan loss provisions and equity capital (serves to absorb expected losses and some unexpected losses); expressed in percent of total assets.
  - CCB: construed to cover residual losses brought about by excessive lending in the upswing phase.
- Usable ordinary buffer calculation:
  - Assumes banks must always honor minimum capital requirement.
  - Usable ordinary buffer = total buffer (expressed in RWA terms) minus minimum required buffer assumed to be 8 percent of RWA.
  - Usable ordinary buffer is intended to absorb expected losses (expressed in RWA terms); CCB covers residual losses (from first-stage regression, in RWA terms, calibrated on the maximum credit gap).

### Key empirical findings on buffers versus losses (exact country figures excerpt)
- Aggregate and categorical findings:
  - Countries identified with shortfalls in both calibrated CCBs and ordinary buffers when the downturn hit: Belgium (BE), Estonia (EE), Ireland (IE), Lithuania (LT).
  - Countries that would have profited from an extra buffer to absorb large expected losses: Ireland (IE), Latvia (LV), Estonia (EE), Lithuania (LT) (with IE and LV highlighted).
  - Nine countries (one third of the sample) show excess ordinary buffers and CCBs.
  - Four countries suffer shortfalls in both buffers.
  - Seven countries with excess ordinary buffers would not need to build CCBs under the credit gap mapping.
  - Remaining seven countries show a shortfall in the CCB and an excess in the primary buffer or vice versa; in some cases CCB shortfall is minor relative to overall buffer excess (Poland (PL), Portugal (PT), Romania (RO)).
- Representative country figures (excerpted exactly as in Table 4):
  - AT: Total Buffer/Assets 7.00; Expected Loss/RWA 2.85; Residual Loss/RWA 0.13; Usable Buffer/RWA 4.39; Excess Capital/RWA 1.54; Mapped CCB/RWA 0.25; Excess CCB/RWA 0.12.
  - BE: Total Buffer/Assets 4.11; Expected Loss/RWA 2.48; Residual Loss/RWA 1.52; Usable Buffer/RWA 2.35; Mapped CCB/RWA 0.13; Shortfall CCB/RWA 0.75; Excess CCB/RWA 0.77.
  - EE: Total Buffer/Assets 9.13; Expected Loss/RWA 9.40; Residual Loss/RWA 0.58; Usable Buffer/RWA 4.79; Excess Capital/RWA 4.61; Mapped CCB/RWA 0.50; Excess CCB/RWA 0.08.
  - IE: Total Buffer/Assets 4.52; Expected Loss/RWA 8.11; Residual Loss/RWA 1.91; Usable Buffer/RWA 1.21; Excess Capital/RWA 6.91; Mapped CCB/RWA 1.00; Shortfall CCB/RWA 0.93.
  - PL: Total Buffer/Assets 10.89; Expected Loss/RWA 0.00; Residual Loss/RWA 4.55; Usable Buffer/RWA 6.80; Excess Capital/RWA 6.80; Mapped CCB/RWA 1.50; Shortfall CCB/RWA 3.05.
  - RO: Total Buffer/Assets 10.78; Expected Loss/RWA 4.67; Residual Loss/RWA 1.91; Usable Buffer/RWA 8.14; Excess Capital/RWA 3.47; Mapped CCB/RWA 1.50; Shortfall CCB/RWA 0.41.
  - UK: Total Buffer/Assets 6.80; Expected Loss/RWA 5.18; Residual Loss/RWA 0.00; Usable Buffer/RWA 13.86; Excess Capital/RWA 8.69; Mapped CCB/RWA 0.25; Excess CCB/RWA 0.25.
- Timing observation:
  - Under the setup with L=4/H=20, the maximum gap is reached seven quarters before the economic downturn on average (median), with a standard deviation of 5.5 pp.

### Sensitivity analysis — methodology and timing issues
- Operational timing requirement:
  - BCBS (2010) and Drehmann and Juselius (2014) guidance: signal should be issued with a lead time of at least four to six quarters so banks have sufficient time to build the buffer.
  - Concern: residual loss methodology may not trigger the buildup phase in time if the largest credit gap is reached only close to or after the downturn; conversely, early triggering may lead to premature drawdown.
- Calibration approach tested:
  - Nine min-max threshold combinations examined: minimum gap at one-fifth, one-third, one-half of the maximum gap, with maximum gap amounts of 10, 15, and 20 percent.
  - Example mappings explicitly evaluated include L=2/H=10, L=3/H=15, L=4/H=20, L=3.3/H=10, L=5/H=15, L=6.6/H=20, L=5/H=10, L=7.5/H=15, L=10/H=20.
- Evaluation window(s):
  - Primary evaluation interval: eight quarters [t-4, t-11] ahead of individual GDP turning point (periods [t-0, t-3] not evaluated).
  - Additional intervals tested: [t-4, t-7] (4-quarter), [t-4, t-15] (12-quarter), [t-6, t-11] (6-quarter).
  - The analysis evaluates deviations of point-in-time buffer from required buffer; example: residual loss 0.9 percent of RWA implies buffer size at least 1 percent, with 0.25 pp increments.

### Sensitivity analysis — quantitative rankings and deviations (exact values)
- Table 5 — Ranking of Min-Max Combinations, Eight-Quarter Interval [t-4, t-11]:
  - Deviation from needed CCB size:
    - L=2/H=10: 0.444 (Rank 9)
    - L=3/H=15: 0.360 (Rank 4)
    - L=4/H=20: 0.345 (Rank 1)
    - L=3.3/H=10: 0.405 (Rank 8)
    - L=5/H=15: 0.368 (Rank 6)
    - L=6.6/H=20: 0.349 (Rank 2)
    - L=5/H=10: 0.382 (Rank 7)
    - L=7.5/H=15: 0.363 (Rank 5)
    - L=10/H=20: 0.359 (Rank 3)
  - Interpretation: under the eight-quarter evaluation, L=4/H=20 is the best (lowest deviation) and the original BCBS mapping L=2/H=10 ranks worst.
- Table 6 — Ranking Using Unequal Weights (Eight-Quarter Interval, preference parameter μ):
  - Deviation, dislike of deficit buffers (μ=0.67):
    - L=2/H=10: 0.362 (Rank 3)
    - L=3/H=15: 0.355 (Rank 2)
    - L=4/H=20: 0.384 (Rank 5)
    - L=3.3/H=10: 0.353 (Rank 1)
    - L=5/H=15: 0.401 (Rank 6)
    - L=6.6/H=20: 0.421 (Rank 7)
    - L=5/H=10: 0.362 (Rank 3)
    - L=7.5/H=15: 0.425 (Rank 8)
    - L=10/H=20: 0.463 (Rank 9)
  - Deviation, dislike of excess buffers (μ=0.333):
    - L=2/H=10: 0.527 (Rank 9)
    - L=3/H=15: 0.365 (Rank 6)
    - L=4/H=20: 0.307 (Rank 4)
    - L=3.3/H=10: 0.457 (Rank 8)
    - L=5/H=15: 0.334 (Rank 5)
    - L=6.6/H=20: 0.278 (Rank 2)
    - L=5/H=10: 0.402 (Rank 7)
    - L=7.5/H=15: 0.301 (Rank 3)
    - L=10/H=20: 0.256 (Rank 1)
  - Interpretation: policymaker preferences matter — a dislike of insufficient buffers favors lower minimum thresholds; a dislike of excessive buffers favors higher minimum thresholds.
- Table 7 — Ranking, Different Evaluation Intervals:
  - Deviation; 4-qtr. interval [t-4, t-7]:
    - L=2/H=10: 0.430 (Rank 9)
    - L=3/H=15: 0.348 (Rank 5)
    - L=4/H=20: 0.330 (Rank 1)
    - L=3.3/H=10: 0.392 (Rank 8)
    - L=5/H=15: 0.353 (Rank 6)
    - L=6.6/H=20: 0.331 (Rank 2)
    - L=5/H=10: 0.371 (Rank 7)
    - L=7.5/H=15: 0.345 (Rank 4)
    - L=10/H=20: 0.339 (Rank 3)
  - Deviation, 12-qtr. interval [t-4, t-15]:
    - L=2/H=10: 0.657 (Rank 9)
    - L=3/H=15: 0.556 (Rank 3)
    - L=4/H=20: 0.544 (Rank 1)
    - L=3.3/H=10: 0.608 (Rank 8)
    - L=5/H=15: 0.569 (Rank 6)
    - L=6.6/H=20: 0.550 (Rank 2)
    - L=5/H=10: 0.582 (Rank 7)
    - L=7.5/H=15: 0.564 (Rank 4)
    - L=10/H=20: 0.567 (Rank 5)
  - Deviation, 6-qtr. interval [t-6, t-11]:
    - L=2/H=10: 0.333 (Rank 9)
    - L=3/H=15: 0.300 (Rank 5)
    - L=4/H=20: 0.298 (Rank 3)
    - L=3.3/H=10: 0.313 (Rank 8)
    - L=5/H=15: 0.300 (Rank 5)
    - L=6.6/H=20: 0.294 (Rank 1)
    - L=5/H=10: 0.304 (Rank 7)
    - L=7.5/H=15: 0.299 (Rank 4)
    - L=10/H=20: 0.295 (Rank 2)
  - Interpretation:
    - High upper threshold combinations (H=20) generally perform better across intervals.
    - BCBS mapping L=2/H=10 consistently ranks lowest under these setups.
    - The six-quarter interval [t-6, t-11] yields the lowest deviations overall and smaller differences across mappings; L=6.6/H=20 performs best for that interval (Deviation 0.294, Rank 1).
- Table 8 — Ranking, Strongly Unequal Weights (six-quarter interval implied):
  - Deviation, strong dislike of deficits (μ=0.8):
    - L=2/H=10: 0.302 (Rank 1)
    - L=3/H=15: 0.349 (Rank 4)
    - L=4/H=20: 0.364 (Rank 6)
    - L=3.3/H=10: 0.311 (Rank 2)
    - L=5/H=15: 0.354 (Rank 5)
    - L=6.6/H=20: 0.389 (Rank 8)
    - L=5/H=10: 0.327 (Rank 3)
    - L=7.5/H=15: 0.383 (Rank 7)
    - L=10/H=20: 0.411 (Rank 9)
  - Deviation, strong dislike of surpluses (μ=0.2):
    - L=2/H=10: 0.365 (Rank 9)
    - L=3/H=15: 0.252 (Rank 6)
    - L=4/H=20: 0.232 (Rank 4)
    - L=3.3/H=10: 0.316 (Rank 8)
    - L=5/H=15: 0.247 (Rank 5)
    - L=6.6/H=20: 0.200 (Rank 2)
    - L=5/H=10: 0.280 (Rank 7)
    - L=7.5/H=15: 0.215 (Rank 3)
    - L=10/H=20: 0.179 (Rank 1)
  - Interpretation: a policymaker strongly averse to deficits would favor low-threshold combinations (e.g., L=2/H=10); one strongly averse to surpluses would favor high-threshold combinations (e.g., L=10/H=20).

### Policy implications and recommendations
- Timing and lead time:
  - Ensure CCB buildup occurs well in advance of crises; aim for signal issuance with at least four to six quarters lead time consistent with BCBS (2010) and Drehmann and Juselius (2014).
- Mapping calibration choices:
  - The BCBS credit gap mapping L=2/H=10 tends to produce higher excess buffers under some setups and often ranks poorly for minimizing deviations from required CCB size in the sample of EU-27 countries analyzed.
  - Higher maximum gap thresholds (H=20) and adjusted minimum thresholds (e.g., L=4 or L=6.6) improve alignment with needed CCB sizes in many tested intervals.
  - Choice of min-max mapping is policy-preference dependent:
    - Policymakers prioritizing avoidance of insufficient buffers (dislike of deficits) should favor lower minimum thresholds (e.g., L=2/H=10, L=3.3/H=10).
    - Policymakers prioritizing avoidance of excessive buffers (dislike of surpluses) should favor higher minimum thresholds (e.g., L=10/H=20).
- Indicator design and country heterogeneity:
  - For heterogeneous samples including transition economies with short financial cycles and low financial deepening, modifying the BCBS approach (lower smoothing factor; normalize credit gap to credit-to-GDP level) improves explanatory power for residual losses.
  - Consider complementing the credit gap with other indicators (e.g., house price growth) or combinations of indicators, and use stress testing and other tools — the BCBS buffer guide should be an input, not an automatism.
- Operational guidance:
  - Evaluate CCB calibration over an appropriate evaluation interval; the six-quarter interval [t-6, t-11] showed lower deviations on average and may serve as a relatively reliable buffer guide in this sample.
  - Incorporate policymakers’ objectives and risk tolerance explicitly (parameter μ) when selecting min-max thresholds to balance missed crises versus false alarms.

*Source: wpiea2019086 - 27. Regression output is unlikely to be greatly different, as the correlation between the broad and the narrow*

### 27. Regression output is unlikely to be greatly different, as the correlation between the broad and the narrow

### wpiea2019086 - 27. Regression output is unlikely to be greatly different, as the correlation between the broad and the narrow

### Credit-gap measurement, smoothing (lambda), and normalization
- Correlation between the broad and the narrow definition of credit ranges from 0.921 to 0.999 for the 18 EU countries in the BCBS dataset.
- Literature benchmarks and assumptions:
  - Arnold and others (2012): typical length of the financial cycle ranges between 16 and 20 years.
  - Under the assumption that credit cycles are four times as long as business cycles, the lambda of λ= 400,000 is calculated as 4^4 *1600 (Drehmann and others 2010; Edge and Meisenzahl 2011).
- Implications of high smoothing (large lambda):
  - A high smoothing factor can lead to continuously positive credit gaps for more than 20 years, making it difficult to distinguish cyclical developments from structural change (Detken and others 2014).
  - For countries with shorter cycles and large amplitudes (e.g., transition economies), strong smoothing may lead to implausibly large credit gaps.
- Empirical approach in this study:
  - Typical duration of the most recent credit cycle in EU countries since the 1990s was calculated to be between five and 10 years (shorter than in Drehmann and others (2010)).
  - Alternative credit gaps tested using smaller lambdas:
    - one-sided HP filter with λ=1,600 (generally recommended for quarterly data),
    - λ=25,000 as an “in-between” figure implying credit cycles are approximately twice as long as business cycles,
    - standard BCBS λ=400,000.
  - Additional normalization: credit-to-GDP gap series normalized by dividing each country’s credit gap by its credit-to-GDP ratio to address heterogeneity across countries.

### Key descriptive statistics (Table 1) — exact values preserved
- Impairments (Cumulative flows of impairments and provisions during 2008–09 or 2009–10, in percent of average total assets)
  - Source: ECB
  - Mean: 2.48
  - Std.Dev.: 2.18
  - Min: 0.36
  - Max: 8.47
- GDP growth (Largest cumulative eight-quarter percentage change in real GDP during 2007–10)
  - Source: Eurostat
  - Mean: -6.03
  - Std.Dev.: 5.79
  - Min: -23.80
  - Max: 5.46
- Credit-to-GDP gap (Maximum credit-to-GDP gap, BCBS (2010) definition; alternatively, credit gap with different lambdas and normalized for credit-to-GDP levels)
  - Source: IMF / own calculations
  - λ=400,000: 12.66
  - λ=1,600: 8.59
  - Mean (additional column?): 10.61
  - Std.Dev.: 5.72
  - Min: 2.72
  - Max: 50.41
- House price growth (Compound annual growth rate of house prices during 2005–08)
  - Source: OECD
  - Mean: 17.70
  - Std.Dev.: 15.92
  - Min: 0.90
  - Max: 54.60
- Equity price growth (Compound annual growth rate of equity prices during 2005–08)
  - Source: OECD
  - Mean: 36.70
  - Std.Dev.: 17.43
  - Min: 12.00
  - Max: 80.20

### Single-stage multivariate regression results (exact equations and coefficients)
- Model estimated with robust standard errors (HC3). Multivariate setup: cumulative flow of loan impairments regressed on two-year percentage change in real GDP and normalized Basel gap (λ=1,600).
- Estimated cross-section model:
  - impairments_i = -0.513 – 0.314 gdp_growth_i + 0.128 credit_gap_normal_i + ε_i.
    - t-statistics: (-1.34) for constant, (-5.96)*** for gdp_growth, (3.28)*** for credit_gap_normal
  - Regression results: both explanatory variables are highly significant at the 1 percent level; R^2 = 0.83.
- Alternative specifications replacing credit gap:
  - With house prices:
    - impairments_i = 0.028 – 0.243 gdp_growth_i + 0.088 house_price_growth_i + ε_i.
      - t-statistics: (0.11), (-4.54)***, (3.30)***
    - House prices are highly significant after controlling for economic growth.
  - With equity prices:
    - impairments_i = -0.487 – 0.312 gdp_growth_i + 0.055 equity_price_growth_i + ε_i.
      - t-statistics: (-0.71), (-4.98)***, (1.18)
    - Equity prices are not significant.

### Correlations (Table 2) — exact coefficients
- Correlation coefficients of GDP growth with drivers:
  - Credit gap, BCBS definition, λ=400,000: 0.086
  - Credit gap, normalized, λ=400,000: -0.001
  - Credit gap, normalized, λ=25,000: -0.027
  - Credit gap, normalized, λ=1,600: -0.052
  - Compound house price growth: -0.474
  - Compound equity price growth: -0.118
- Interpretation: hardly any correlation between GDP growth and credit gap measures (between 0.00 and 0.09 reported earlier); moderate negative correlation between GDP growth and house price growth.

### Two-stage regression approach and findings
- First-stage regression (impairments on GDP growth) — exact estimate:
  - impairments_i = 0.555 – 0.320 gdp_growth_i + ε_i.
    - t-statistics: (1.06), (-5.21)***
  - Fit: R^2 = 0.72.
  - Outlier: Poland (PL) identified; exclusion would improve R^2 to 0.83 and increase slope coefficient to -3.75, but authors keep the observation.
- Second-stage regression: residuals(first_stage)_i = α + β credit_gap_i + ε_i.
- Table 3 — Results of regressions of residual losses on credit gaps (exact coefficients and t-statistics)
  - Gap definition/lambda columns: λ=400,000 | λ=25,000 | λ=1,600
  - Maximum, BCBS definition:
    - λ=400,000: 0.007 (0.31)
    - λ=25,000: 0.005 (0.18)
    - λ=1,600: 0.000 (0.00)
  - Maximum, BCBS def. normalized:
    - λ=400,000: 0.077 (2.68)**
    - λ=25,000: 0.084 (3.37)***
    - λ=1,600: 0.126 (3.69)***
  - Note: Constant terms not reported; t-statistics in parentheses. ***, **, * denote significance at the 1%, 5%, 10% levels.
- Key insights from second-stage regressions:
  - The maximum gap under BCBS definition (λ=400,000) does not produce a significant outcome in this heterogeneous European sample.
  - Normalizing credit gaps for credit-to-GDP levels renders the adjusted maximum gap significant at the 5 percent level (and more so with smaller lambdas).
  - Using smaller lambdas (e.g., λ=1,600) improves regression outcomes because several transition countries have short credit cycles (five to 10 years).
  - Preferred variant: normalized maximum gap using λ=1,600 (termed gapmax1600); regression fit R^2 = 0.39.

### Mapping residual losses to the Countercyclical Capital Buffer (CCB)
- Procedure:
  - Use fitted values from second-stage regression (rather than observed residuals) to map residual losses into recommended CCB sizes.
  - Residual loan losses (expressed in percent of total assets) transformed into RWA terms because absolute RWA values were not available.
- CCB mapping parameters (exact values preserved):
  - CCB activated beyond a credit gap of 4 percent (L=4).
  - CCB increases linearly with the credit gap up to 2.5 percent of RWA corresponding to a maximum gap of 20 percent (H=20).
- Conceptual distinction:
  - Ordinary buffer: combined cushion of loan loss provisions and equity capital (serves to absorb expected losses and some unexpected losses); expressed in percent of total assets.
  - CCB: construed to cover residual losses brought about by excessive lending in the upswing phase.
- Usable ordinary buffer calculation:
  - Assumes banks must always honor minimum capital requirement.
  - Usable ordinary buffer = total buffer (expressed in RWA terms) minus minimum required buffer assumed to be 8 percent of RWA.
  - Usable ordinary buffer is intended to absorb expected losses (expressed in RWA terms); CCB covers residual losses (from first-stage regression, in RWA terms, calibrated on the maximum credit gap).

*Source: wpiea2019086 - 27. Regression output is unlikely to be greatly different, as the correlation between the broad and the narrow*

### 0.25 pp increments, third column in from the right. As a result, countries can have a surplus

### wpiea2019086 - 0.25 pp increments, third column in from the right. As a result, countries can have a surplus

### Key empirical findings on buffers versus losses
- Table 4 (buffers versus losses, CCBs based on normalized credit gap) findings:
  - Countries identified with shortfalls in both calibrated CCBs and ordinary buffers when the downturn hit: Belgium (BE), Estonia (EE), Ireland (IE), Lithuania (LT).
  - Countries that would have profited from an extra buffer to absorb large expected losses: Ireland (IE), Latvia (LV), Estonia (EE), Lithuania (LT) (with IE and LV highlighted).
  - Nine countries (one third of the sample) show excess ordinary buffers and CCBs.
  - Four countries suffer shortfalls in both buffers.
  - Seven countries with excess ordinary buffers would not need to build CCBs under the credit gap mapping.
  - Remaining seven countries show a shortfall in the CCB and an excess in the primary buffer or vice versa; in some cases CCB shortfall is minor relative to overall buffer excess (Poland (PL), Portugal (PT), Romania (RO)).

- Representative country figures (excerpted exactly as in Table 4):
  - AT: Total Buffer/Assets 7.00; Expected Loss/RWA 2.85; Residual Loss/RWA 0.13; Usable Buffer/RWA 4.39; Excess Capital/RWA 1.54; Mapped CCB/RWA 0.25; Excess CCB/RWA 0.12.
  - BE: Total Buffer/Assets 4.11; Expected Loss/RWA 2.48; Residual Loss/RWA 1.52; Usable Buffer/RWA 2.35; Mapped CCB/RWA 0.13; Shortfall CCB/RWA 0.75; Excess CCB/RWA 0.77.
  - EE: Total Buffer/Assets 9.13; Expected Loss/RWA 9.40; Residual Loss/RWA 0.58; Usable Buffer/RWA 4.79; Excess Capital/RWA 4.61; Mapped CCB/RWA 0.50; Excess CCB/RWA 0.08.
  - IE: Total Buffer/Assets 4.52; Expected Loss/RWA 8.11; Residual Loss/RWA 1.91; Usable Buffer/RWA 1.21; Excess Capital/RWA 6.91; Mapped CCB/RWA 1.00; Shortfall CCB/RWA 0.93.
  - PL: Total Buffer/Assets 10.89; Expected Loss/RWA 0.00; Residual Loss/RWA 4.55; Usable Buffer/RWA 6.80; Excess Capital/RWA 6.80; Mapped CCB/RWA 1.50; Shortfall CCB/RWA 3.05.
  - RO: Total Buffer/Assets 10.78; Expected Loss/RWA 4.67; Residual Loss/RWA 1.91; Usable Buffer/RWA 8.14; Excess Capital/RWA 3.47; Mapped CCB/RWA 1.50; Shortfall CCB/RWA 0.41.
  - UK: Total Buffer/Assets 6.80; Expected Loss/RWA 5.18; Residual Loss/RWA 0.00; Usable Buffer/RWA 13.86; Excess Capital/RWA 8.69; Mapped CCB/RWA 0.25; Excess CCB/RWA 0.25.
  - (Other country entries appear in Table 4 with the exact numeric fields reported in the source.)

- Timing observation:
  - Under the setup with L=4/H=20, the maximum gap is reached seven quarters before the economic downturn on average (median), with a standard deviation of 5.5 pp.

### Sensitivity analysis — methodology and timing issues
- Operational timing requirement:
  - BCBS (2010) and Drehmann and Juselius (2014) guidance: signal should be issued with a lead time of at least four to six quarters so banks have sufficient time to build the buffer.
  - Concern: residual loss methodology may not trigger the buildup phase in time if the largest credit gap is reached only close to or after the downturn; conversely, early triggering may lead to premature drawdown.

- Calibration approach tested:
  - Nine min-max threshold combinations examined: minimum gap at one-fifth, one-third, one-half of the maximum gap, with maximum gap amounts of 10, 15, and 20 percent.
  - Example mappings explicitly evaluated include L=2/H=10, L=3/H=15, L=4/H=20, L=3.3/H=10, L=5/H=15, L=6.6/H=20, L=5/H=10, L=7.5/H=15, L=10/H=20.

- Evaluation window(s):
  - Primary evaluation interval: eight quarters [t-4, t-11] ahead of individual GDP turning point (periods [t-0, t-3] not evaluated).
  - Additional intervals tested: [t-4, t-7] (4-quarter), [t-4, t-15] (12-quarter), [t-6, t-11] (6-quarter).
  - The analysis evaluates deviations of point-in-time buffer from required buffer; example: residual loss 0.9 percent of RWA implies buffer size at least 1 percent, with 0.25 pp increments.

### Sensitivity analysis — quantitative rankings and deviations
- Table 5 — Ranking of Min-Max Combinations, Eight-Quarter Interval [t-4, t-11]:
  - Deviation from needed CCB size:
    - L=2/H=10: 0.444 (Rank 9)
    - L=3/H=15: 0.360 (Rank 4)
    - L=4/H=20: 0.345 (Rank 1)
    - L=3.3/H=10: 0.405 (Rank 8)
    - L=5/H=15: 0.368 (Rank 6)
    - L=6.6/H=20: 0.349 (Rank 2)
    - L=5/H=10: 0.382 (Rank 7)
    - L=7.5/H=15: 0.363 (Rank 5)
    - L=10/H=20: 0.359 (Rank 3)

  - Interpretation: under the eight-quarter evaluation, L=4/H=20 is the best (lowest deviation) and the original BCBS mapping L=2/H=10 ranks worst.

- Table 6 — Ranking Using Unequal Weights (Eight-Quarter Interval, preference parameter μ):
  - Deviation, dislike of deficit buffers (μ=0.67):
    - L=2/H=10: 0.362 (Rank 3)
    - L=3/H=15: 0.355 (Rank 2)
    - L=4/H=20: 0.384 (Rank 5)
    - L=3.3/H=10: 0.353 (Rank 1)
    - L=5/H=15: 0.401 (Rank 6)
    - L=6.6/H=20: 0.421 (Rank 7)
    - L=5/H=10: 0.362 (Rank 3)
    - L=7.5/H=15: 0.425 (Rank 8)
    - L=10/H=20: 0.463 (Rank 9)

  - Deviation, dislike of excess buffers (μ=0.333):
    - L=2/H=10: 0.527 (Rank 9)
    - L=3/H=15: 0.365 (Rank 6)
    - L=4/H=20: 0.307 (Rank 4)
    - L=3.3/H=10: 0.457 (Rank 8)
    - L=5/H=15: 0.334 (Rank 5)
    - L=6.6/H=20: 0.278 (Rank 2)
    - L=5/H=10: 0.402 (Rank 7)
    - L=7.5/H=15: 0.301 (Rank 3)
    - L=10/H=20: 0.256 (Rank 1)

  - Interpretation: policymaker preferences matter — a dislike of insufficient buffers favors lower minimum thresholds; a dislike of excessive buffers favors higher minimum thresholds.

- Table 7 — Ranking, Different Evaluation Intervals:
  - Deviation; 4-qtr. interval [t-4, t-7]:
    - L=2/H=10: 0.430 (Rank 9)
    - L=3/H=15: 0.348 (Rank 5)
    - L=4/H=20: 0.330 (Rank 1)
    - L=3.3/H=10: 0.392 (Rank 8)
    - L=5/H=15: 0.353 (Rank 6)
    - L=6.6/H=20: 0.331 (Rank 2)
    - L=5/H=10: 0.371 (Rank 7)
    - L=7.5/H=15: 0.345 (Rank 4)
    - L=10/H=20: 0.339 (Rank 3)

  - Deviation, 12-qtr. interval [t-4, t-15]:
    - L=2/H=10: 0.657 (Rank 9)
    - L=3/H=15: 0.556 (Rank 3)
    - L=4/H=20: 0.544 (Rank 1)
    - L=3.3/H=10: 0.608 (Rank 8)
    - L=5/H=15: 0.569 (Rank 6)
    - L=6.6/H=20: 0.550 (Rank 2)
    - L=5/H=10: 0.582 (Rank 7)
    - L=7.5/H=15: 0.564 (Rank 4)
    - L=10/H=20: 0.567 (Rank 5)

  - Deviation, 6-qtr. interval [t-6, t-11]:
    - L=2/H=10: 0.333 (Rank 9)
    - L=3/H=15: 0.300 (Rank 5)
    - L=4/H=20: 0.298 (Rank 3)
    - L=3.3/H=10: 0.313 (Rank 8)
    - L=5/H=15: 0.300 (Rank 5)
    - L=6.6/H=20: 0.294 (Rank 1)
    - L=5/H=10: 0.304 (Rank 7)
    - L=7.5/H=15: 0.299 (Rank 4)
    - L=10/H=20: 0.295 (Rank 2)

  - Interpretation:
    - High upper threshold combinations (H=20) generally perform better across intervals.
    - BCBS mapping L=2/H=10 consistently ranks lowest under these setups.
    - The six-quarter interval [t-6, t-11] yields the lowest deviations overall and smaller differences across mappings; L=6.6/H=20 performs best for that interval (Deviation 0.294, Rank 1).

- Table 8 — Ranking, Strongly Unequal Weights (six-quarter interval implied):
  - Deviation, strong dislike of deficits (μ=0.8):
    - L=2/H=10: 0.302 (Rank 1)
    - L=3/H=15: 0.349 (Rank 4)
    - L=4/H=20: 0.364 (Rank 6)
    - L=3.3/H=10: 0.311 (Rank 2)
    - L=5/H=15: 0.354 (Rank 5)
    - L=6.6/H=20: 0.389 (Rank 8)
    - L=5/H=10: 0.327 (Rank 3)
    - L=7.5/H=15: 0.383 (Rank 7)
    - L=10/H=20: 0.411 (Rank 9)

  - Deviation, strong dislike of surpluses (μ=0.2):
    - L=2/H=10: 0.365 (Rank 9)
    - L=3/H=15: 0.252 (Rank 6)
    - L=4/H=20: 0.232 (Rank 4)
    - L=3.3/H=10: 0.316 (Rank 8)
    - L=5/H=15: 0.247 (Rank 5)
    - L=6.6/H=20: 0.200 (Rank 2)
    - L=5/H=10: 0.280 (Rank 7)
    - L=7.5/H=15: 0.215 (Rank 3)
    - L=10/H=20: 0.179 (Rank 1)

  - Interpretation: a policymaker strongly averse to deficits would favor low-threshold combinations (e.g., L=2/H=10); one strongly averse to surpluses would favor high-threshold combinations (e.g., L=10/H=20).

### Policy implications and recommendations
- Timing and lead time:
  - Ensure CCB buildup occurs well in advance of crises; aim for signal issuance with at least four to six quarters lead time consistent with BCBS (2010) and Drehmann and Juselius (2014).

- Mapping calibration choices:
  - The BCBS credit gap mapping L=2/H=10 tends to produce higher excess buffers under some setups and often ranks poorly for minimizing deviations from required CCB size in the sample of EU-27 countries analyzed.
  - Higher maximum gap thresholds (H=20) and adjusted minimum thresholds (e.g., L=4 or L=6.6) improve alignment with needed CCB sizes in many tested intervals.
  - Choice of min-max mapping is policy-preference dependent:
    - Policymakers prioritizing avoidance of insufficient buffers (dislike of deficits) should favor lower minimum thresholds (e.g., L=2/H=10, L=3.3/H=10).
    - Policymakers prioritizing avoidance of excessive buffers (dislike of surpluses) should favor higher minimum thresholds (e.g., L=10/H=20).

- Indicator design and country heterogeneity:
  - For heterogeneous samples including transition economies with short financial cycles and low financial deepening, modifying the BCBS approach (lower smoothing factor; normalize credit gap to credit-to-GDP level) improves explanatory power for residual losses.
  - Consider complementing the credit gap with other indicators (e.g., house price growth) or combinations of indicators, and use stress testing and other tools — the BCBS buffer guide should be an input, not an automatism.

- Operational guidance:
  - Evaluate CCB calibration over an appropriate evaluation interval; the six-quarter interval [t-6, t-11] showed lower deviations on average and may serve as a relatively reliable buffer guide in this sample.
  - Incorporate policymakers’ objectives and risk tolerance explicitly (parameter μ) when selecting min-max thresholds to balance missed crises versus false alarms.

*Source: Author’s calculations (content unit: wpiea2019086 - 0.25 pp increments, third column in from the right. As a result, countries can have a surplus).*

### REFERENCES

### REFERENCES

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*References compiled from the source PDF "wpiea2019086 - REFERENCES".*

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_Source: https://www.imf.org/-/media/files/publications/wp/2019/wpiea2019086.pdf_