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---

### The Basel Credit Gap (BCG): definition and operational guidance
- Definition:
  - BCG = difference between aggregate credit-to-GDP ratio and its long-term Hodrick-Prescott (HP) filtered trend.
  - Credit: total credit to the non-financial private sector, including credit extended by nonbanks and foreign entities.
  - HP filtering specifics used by BCBS: one-sided HP filter with smoothing parameter (lambda) of 400,000 applied to quarterly data (assumption: credit cycles range about 30 years).
- CCyB guidance based on BCG:
  - Activate CCyB when BCG is above a top threshold (i.e., 2 percentage points).
  - Continue increasing until a maximum is reached; release when BCG falls below a bottom threshold.

### Key weaknesses of the BCG (enumerated findings)
- Excessive credit vs. financial deepening:
  - Credit growth exceeding GDP growth can reflect benign financial deepening (policy-driven financial liberalization, dismantling of capital controls) rather than excessive risk taking.
  - Need for supplementary indicators: lending practices and standards, household and corporate balance sheets, housing and other asset prices, bank funding profile.
- Countercyclicality:
  - Credit-to-GDP ratio can increase during downturns because credit (a stock) adjusts more slowly than GDP (a flow), producing a positive BCG in recessions.
  - Implication: BCG could signal tightening in downturns, potentially propagating negative shocks.
  - Empirical note: Drehmann and Tsatsaronis (2014) find a negative correlation between credit gap and real GDP growth (panel of 53 countries, 1980-2013), but correlation degree is small.
  - Possible remedy: scale credit with a more stable denominator than GDP (example: population).
- Large credit booms in the past:
  - In pronounced boom-bust cycles, the HP trend may track the boom with a lag, leaving BCG large and negative for an extended period after the bust even as credit normalizes.
  - Consequence: BCG may fail to identify renewed excesses after a prolonged boom-bust.
- General problems with HP filters:
  - End-point problem: one-sided (real-time) HP filter estimates are strongly influenced by the end-point of the sample; revisions reflect end-point problem more than data revisions (Edge and Meisenzahl 2011).
  - Sensitivity to length of time series and choice of lambda:
    - No consensus on credit cycle duration to guide lambda choice (Ravn and Uhlig 2002).
    - Studies report heterogeneous cycle lengths; some find credit cycles similar to GDP cycles (shorter than 30 years).
    - Empirical examples: reducing lambda from 400,000 to 25,000 improved early warning performance for Spain (Galán 2019); Kauko and Tölö (2019) find optimal lambda much smaller than 400,000.
- Lack of sectoral detail:
  - BCG uses broad credit aggregate which may mask sectoral imbalances (e.g., residential mortgage market).
  - Some studies find narrower aggregates (e.g., bank credit) can perform better for signaling crises.
  - BCG credit data do not consolidate intra-company loans.

### Methodological strands in the literature on credit gaps
- Two main strands:
  1. Purely statistical approaches (univariate and multivariate filters).
  2. Structural/model-based approaches (regress credit on fundamentals; use residuals as gap).
- Statistical approaches:
  - Filters: HP; bandpass methods (Baxter-King (BK) 1999, Christiano-Fitzgerald (CF) 2003).
    - BK and CF extract frequencies within predetermined ranges; sensitive to assumed cycle length.
  - Hamilton (2017) linear projection alternative:
    - For standard macro quarterly series: recommends h=8 and x=4 (preceding 8,7,6,5 quarters).
    - For credit cycles (long-lasting): recommends h=20 and x=4 (preceding 20,19,18,17 quarters).
    - Strength: overcomes HP end-point problem; weakness: produces volatile gaps with frequent sign changes and may perform poorly as early-warning indicator (Drehmann and Yetman 2018).
  - Multivariate statistical models:
    - Kalman filter applied to unobserved components models for GDP, credit, house prices.
    - Advantage: can estimate cycle length from data; drawback: lack structural theory and estimation complexity as variables increase.
- Structural/model approaches:
  - Regress credit on fundamentals (e.g., GDP, real long-run interest rates, real house prices) and take residuals as credit gaps.
  - Examples: VEC models, ADL on per-capita private debt, regressions controlling for institutions, equilibrium real interest rate, demographics.
  - Advantages: capture determinants of credit trend (income, reforms, real rates, demographics); allow separation of long-run and short-run effects.
  - Limitations: residual sensitivity to model specification, sample composition, omitted fundamentals; treating housing prices as exogenous problematic.

### Two complementary approaches proposed to address BCG weaknesses (overview)
- Common design choice: use real credit or real credit per capita to avoid dividing a stock variable (credit) by a flow variable (GDP).
- Approach A: Multivariate Filtering (MVF) — jointly estimate cyclical component of credit and macro variables within a structural model.
- Approach B: Fundamentals-based empirical models — estimate long-term credit trend from fundamentals and use deviations (residuals) as prima facie credit gaps.

### Multivariate Filtering Approach (MVF): model structure and intuition
- Model lineage: Krznar and Matheson (2017) variant of Carabenciov et al. (2008); related to Benes et al. (2010), Andrle et al. (2014), Maria (2016); inspired by Laxton and Tetlow (1992).
- Key model components:
  - Output (IS-type), Inflation (Phillips-curve), Policy interest rate (Taylor rule), Real interest rate (Fisher), Real exchange rate.
  - Credit-gap equation (conceptual): c_t = θ_y y_(t−1) + θ_c c_(t−1) + θ_r r_(t−1) + ε^c_t.
    - Intuition: new credit flows respond to lagged economic activity and real rates; stock of credit adjusts slowly via repayments.
  - Feedback from credit gap to aggregate demand through a credit shock ε^c_t in the output-gap equation.
- Model variants: tailored for economies in a currency union and for economies with floating exchange rates.
- Estimation approach: country-by-country Bayesian estimation with quarterly data; Kalman filter used for one-sided (real-time) filtering.

### MVF: strengths and limitations
- Advantages:
  - Explicitly models linkages between credit gaps and macro variables; identifies drivers of unobserved credit gaps.
  - Produces more stable estimates of unobserved components compared to univariate filters.
  - Does not require prior assumption on credit cycle length (data-driven cycle length).
- Disadvantages:
  - End-point bias not fully resolved by MVF, though MVF reduces the problem considerably.
  - Requires empirical validation of assumed macroeconomic relationships and sensitivity checks to parametrization.

### MVF: empirical implementation and quantitative results
- Countries estimated: Germany and Spain (euro area); Poland and Sweden (independent monetary policy).
- Samples for MVF estimation:
  - Spain and Germany: 1995:Q1-2018:Q3.
  - Sweden: 1993:Q1-2018:Q3.
  - Poland: 2001:Q1-2018:Q3.
- Samples for HP filter comparison:
  - Sweden and Spain: 1980:Q1-2018:Q3.
  - Germany: 1970:Q1-2018:Q3.
  - Poland: 1995:Q4-2018:Q3.
- Empirical findings:
  - MVF real credit gaps have on average lower volatility and a shorter cycle than HP gaps.
  - MVF-implied cycle typically less than 15 years (equivalent to a smoothing factor roughly below 25,000 in the HP filter).
  - Turning points often similar between MVF and HP, but MVF cycle amplitudes are smaller; MVF real credit gap is less volatile than credit-to-GDP gap.
  - MVF using real credit avoids the countercyclicality problem (notably during 2009 recession).
  - Real-time MVF estimates (data up to end-2007) show widening positive gaps ahead of the Global Financial Crisis.
  - Revision properties: MVF has better revision properties than HP; MVF reduces large negative post-bust gaps observed with BCG (e.g., Spain and Sweden).
  - Country-specific: in Germany the negative credit gap closed before the GFC according to MVF.
- Real-time revision metric:
  - MAE of MVF typically much smaller than MAE for the HP, reducing MAE by as much as 80 percent in some cases.
  - Credit gap MAEs are larger relative to output gap MAEs.

### Fundamentals-based approach: panel error-correction (EC) model — specification and data
- Approach:
  - Error-correction model estimated on an unbalanced panel of 40 European countries (annual data, 1970-2017).
  - Dependent variable: change in log credit per capita (credit defined as total credit to private sector including bank loans, debt securities, credit by nonbanks and foreign entities).
  - Residuals from the long-run EC relation interpreted as prima facie credit gaps; examined alongside vulnerability indicators.
- Fundamentals included:
  - GDP per capita (log), Total bank deposits per capita (log), Real interest rate, Old-age dependency ratio (log).
  - Country fixed effects included.
- Panel composition:
  - 40 countries: Albania, Austria, Belgium, Bosnia and Herzegovina, Bulgaria, Croatia, Cyprus, Czech Republic, Estonia, Finland, France, Germany, Hungary, Iceland, Ireland, Israel, Italy, Kosovo, Latvia, Lithuania, Luxembourg, Macedonia, Malta, Moldova, Montenegro, Netherlands, Norway, Poland, Portugal, Romania, Russia, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey, Ukraine, United Kingdom.
  - Series length ranges between 5 and 47 years; data expressed per capita in 2010 U.S. PPP; variables in logs except interest rates.

### Estimation methods and dynamic estimators
- Techniques used:
  - Dynamic fixed effect estimation (DFE) of Pesaran et al. (1997): assumes common coefficients across panels for long-run and short-run equations.
  - Pooled-mean group (PMG) estimator: allows country-specific short-term dynamics while restricting long-run elasticities to be equal across panels.
- Country fixed effects included in all specifications.
- Hausman test: does not reject the use of the restrictions employed by the DFE relative to the PMG in the reported estimations.

### Regression results — long-run, short-run, and adjustment dynamics (selected quantitative estimates)
- Error-correction term (speed of adjustment; standard errors in parentheses):
  - Fixed effects: -0.136*** (0.023)
  - DFE All: -0.127*** (0.029)
  - DFE Emerging: -0.199*** (0.051)
  - PMG All: -0.205*** (0.033)
  - PMG Advanced: -0.201*** (0.038)
  - PMG Emerging: -0.194*** (0.063)
- Long-run relation (selected coefficients; standard errors in parentheses):
  - GDP per capita (log):
    - Fixed effects: 1.010*** (0.308)
    - DFE All: 0.789** (0.399)
    - DFE Emerging: 1.984** (0.887)
    - PMG All: 0.738*** (0.085)
    - PMG Advanced: 0.725*** (0.086)
    - PMG Emerging: 2.648*** (0.374)
  - Deposit per capita (log):
    - Fixed effects: 0.429** (0.215)
    - DFE All: 0.549* (0.291)
    - DFE Emerging: 0.086 (0.450)
    - PMG All: 0.458*** (0.048)
    - PMG Advanced: 0.456*** (0.049)
    - PMG Emerging: 0.250 (0.182)
  - Real interest rate:
    - Fixed effects: 0.008 (1.190)
    - DFE Advanced: -1.810 (1.815)
    - DFE Emerging: 0.306 (1.343)
    - PMG All: -0.592** (0.257)
    - PMG Advanced: -0.716*** (0.290)
    - PMG Emerging: -0.840** (0.386)
  - Old age dependency (log):
    - Fixed effects: -0.068 (0.443)
    - DFE Advanced: -0.242 (0.424)
    - DFE Emerging: -0.415 (1.010)
    - PMG All: -1.212*** (0.151)
    - PMG Advanced: -1.139*** (0.155)
    - PMG Emerging: -5.253*** (0.862)
- Short-run (Δ) coefficients (selected; standard errors in parentheses):
  - Δ Lagged credit per capita (log): 0.238*** (0.029) in Fixed effects.
  - Δ GDP per capita (log): 0.704*** (0.107) in Fixed effects; PMG Advanced: 0.771** (0.331); PMG Emerging: 0.866* (0.444); PMG All: 0.229 (0.195).
  - Δ Deposit per capita (log): 0.370*** (0.049) in Fixed effects; PMG All: 0.477*** (0.134).
  - Δ Real interest rate: 0.086 (0.105) in Fixed effects; PMG Advanced: 0.318* (0.182); PMG Emerging: 0.334 (0.248); PMG All: -0.001 (0.057).
  - Δ Old age dependency (log): -0.691** (0.324) in Fixed effects; PMG All: -2.453*** (0.800); PMG Emerging: 1.476** (0.593).
- Interpretation of adjustment:
  - Estimated speed of adjustment: between around 13 and 20 percent per year for deviations of credit from its long-term equilibrium.
  - Implied duration: roughly 5-8 years for credit to return to its long-term equilibrium.
  - Advanced economies adjust more slowly: 12 percent per year.
  - Emerging economies adjust faster: 20 percent per year.
- Sample and fit (selected):
  - Maximum time span shown: 1980-2017 and 1994-2017 for some specifications.
  - Number of observations by column as reported: 894, 907, 705, 189, 881, 705, 176.
  - Number of countries by column as reported: 40, 40, 27, 13, 38, 27, 11.
  - R-squared (Fixed effects): 0.299.
- Statistical notation: Standard errors clustered by country in parentheses. *** p<0.01, ** p<0.05, * p<0.1.

### Interpreting EC-model residuals as credit gaps and use of supplementary indicators
- Residuals from the long-run EC model serve as prima facie credit gap measures.
- Empirical behavior and country illustrations:
  - Spain: EC residuals show large and prolonged boom and bust; positive credit gap closing and around zero at end of sample (contrasts with BCG showing large negative credit gaps for Spain in 2018).
  - France: negative gaps in late 1990s and early 2000s, positive in recent years (growth in corporate non-financial sector debt).
  - Sweden: gap positive around past financial crises; recent credit upswing has not yet translated into positive gaps.
  - Czech Republic: illustrated among country examples.
- Limitations:
  - Real-time signaling not tested due to data limitations; regression residuals for 2018 are out-of-sample estimates in the illustrations.
  - Residuals can reflect estimation errors and omitted variables; therefore should be examined alongside supplementary indicators.
- Example supplementary indicators used (Spain):
  - House price-to-rent ratio, Real house price, Share of high-yield corporate bonds in total corporate bond issuance (HY share), Gross value added of construction sector.
  - Positive residuals coinciding with high values of such indicators signal excessive credit and vulnerability buildup.
  - Data sources: OECD housing database (price-to-rent and real house price), Kirti (2018) (HY share), EU and World KLEMS and Dell’Ariccia et. al (2019) (construction GVA).

### Decomposing credit growth with the EC model
- EC model decomposes credit growth into:
  1. Adjustments to the long-term level (error-correction term).
  2. Contemporaneous developments in fundamentals (changes in GDP, deposits, demography, interest rates).
- Illustration for Spain:
  - After excess credit, equilibrium credit growth was subdued to allow adjustment to long-term level.
  - As credit gap closed and GDP and deposit growth picked up, equilibrium credit growth accelerated in recent years.
- Figures for Spain, France, Sweden, Czech Republic show decomposition; 2018 data are out-of-sample estimates.

### Appendix I (MVF) — model details, estimation priors, and data
- Domestic economy structure highlights:
  - Output gap, potential output growth, and output-gap law of motion specified with lead–lag dynamics and dependence on real rate gap, credit shock ε^c_t, foreign output gap, real exchange rate gap.
  - Inflation modeled with Phillips-curve specifications (euro-area and non-euro alternatives).
  - Credit gap defined as c_t ≡ 100 * ln(CRED_t / coreCPI_t) − c*_t, with credit gap law c_t = θ_y y_(t−1) + θ_c c_(t−1) + θ_r r_(t−1) + ε^c_t.
  - Unemployment and NAIRU dynamics included (Okun-type relationship).
- Foreign economy and interest-rate specifications:
  - Foreign output gap and Phillips curve specified; foreign nominal rate follows forward-looking Taylor-type rule.
  - Domestic non-currency-union and currency-union variants specified, including country risk premium φ_t and real rate gap definitions.
- Exchange-rate dynamics:
  - Currency-union and non-currency-union definitions and dynamics provided (real exchange rate, gap dynamics, interest-parity relation).
- Estimation approach and priors:
  - MVF uses calibration and Bayesian estimation; “system priors” applied; prior penalizes estimated business cycle length longer than 40 quarters.
  - Real-time revision properties: MVF MAE typically much smaller than HP MAE; example MAE table labels include ESP21.25.4, DEU6.31.7, SWE6.71.4, POL8.14.1 as reported in source table header.
- Data used for MVF (quarterly, sources noted):
  - Domestic: Real GDP; Credit to private nonfinancial sector; Headline inflation; Unemployment rate; 10-year government bond yield; Nominal Exchange Rate; 3-Month nominal rate (Federal Reserve Bank of St. Louis).
  - Euro area: Real GDP; Headline inflation; 10-year benchmark yield; 3-Month nominal rate (Euro Area Wide Model Database).
  - Fundamentals-based approach sources: World Economic Outlook (GDP, PPP, Population); International Finance Statistics, BIS (Credit); IFS, ECB, Eurostat, OECD (interest rates, deposits, GDP deflator).

### Conclusions and policy-relevant takeaways
- Measuring credit gaps correctly is crucial for assessing macro-financial vulnerabilities and guiding macroprudential policy.
- Limitations of the BCG:
  - Tends to become persistently negative after a pronounced boom deflates, implying credit should return to its cyclical peak and raising questions about usefulness over full cycles.
- Complementary methods proposed and tested:
  1. Model-based Multivariate Filter (MVF): identifies cyclical conditions of credit and macroeconomy jointly; useful where instability builds when credit growth coincides with macroeconomic overheating.
  2. Fundamentals-based EC model: identifies long-term determinants of credit; residuals examined with vulnerability indicators to assess policy relevance.
- Advantages of the two methods:
  - Do not impose an exogenous specific duration to credit cycle.
  - Produce sensible credit-gap estimates in countries with large booms and busts.
- Caveats:
  - End-point bias remains an issue for MVF, though smaller than for the BCG.
  - EC-model coefficients sensitive to country selection and time-series length.
  - Using multiple methods helps identify a range of plausible assessments; large ranges warrant deeper analysis for policy decisions.
- Policy implication:
  - The two methods show promise in complementing the BCG and guiding policymakers’ judgment in assessing the credit cycle position and calibrating macroprudential stance.

*Italic source: Excerpt from IMF working paper (wpiea2020006-print-pdf), Sections II–IV.*

### Section III provides a brief literature survey on measuring credit gaps. Section IV describes

### wpiea2020006-print-pdf - Section III provides a brief literature survey on measuring credit gaps. Section IV describes

### The Basel Credit Gap (BCG): definition and intended use
- BCG defined as the difference between the aggregate credit-to-GDP ratio and its long-term Hodrick-Prescott (HP) filtered trend.
- Credit definition: total credit to the non-financial private sector, including credit extended by nonbanks and foreign entities.
- HP filtering specifics used by BCBS: one-sided HP filter with smoothing parameter (lambda) of 400,000 applied to quarterly data (assumption: credit cycles range about 30 years).
- CCyB guidance based on BCG:
  - Activate CCyB when BCG is above a top threshold (i.e., 2 percentage points).
  - Continue increasing until a maximum is reached; release when BCG falls below a bottom threshold.

### Key weaknesses of the BCG (enumerated findings)
- Excessive credit vs. financial deepening:
  - Periods where credit growth exceeds GDP growth can reflect benign financial deepening (policy-driven financial liberalization, dismantling of capital controls) rather than excessive risk taking.
  - Need for supplementary indicators: lending practices and standards, household and corporate balance sheets, housing and other asset prices, bank funding profile.
- Countercyclicality:
  - Credit-to-GDP ratio can increase during downturns because credit (a stock) adjusts more slowly than GDP (a flow), producing a positive BCG in recessions.
  - Implication: BCG could signal tightening in downturns, potentially propagating negative shocks.
  - Empirical note: Drehmann and Tsatsaronis (2014) find a negative correlation between credit gap and real GDP growth (panel of 53 countries, 1980-2013), but correlation degree is small.
  - Possible remedy: scale credit with a more stable denominator than GDP (example: population).
- Large credit booms in the past:
  - In pronounced boom-bust cycles, the HP trend may track the boom with a lag, leaving BCG large and negative for an extended period after the bust even as credit normalizes.
  - Consequence: BCG may fail to identify renewed excesses after a prolonged boom-bust.
- General problems with HP filters:
  - End-point problem: one-sided (real-time) HP filter estimates are strongly influenced by the end-point of the sample; revisions reflect end-point problem more than data revisions (Edge and Meisenzahl 2011).
  - Sensitivity to length of time series and choice of lambda:
    - No consensus on credit cycle duration to guide lambda choice (Ravn and Uhlig 2002).
    - Studies report heterogeneous cycle lengths; some find credit cycles similar to GDP cycles (shorter than 30 years).
    - Empirical examples: reducing lambda from 400,000 to 25,000 improved early warning performance for Spain (Galán 2019); Kauko and Tölö (2019) find optimal lambda much smaller than 400,000.
- Lack of sectoral detail:
  - BCG uses broad credit aggregate which may mask sectoral imbalances (e.g., residential mortgage market).
  - Some studies find narrower aggregates (e.g., bank credit) can perform better for signaling crises.
  - BCG credit data do not consolidate intra-company loans.

### Brief literature review on credit gaps: methodological strands
- Two main strands:
  1. Purely statistical approaches (univariate and multivariate filters).
  2. Structural/model-based approaches (regress credit on fundamentals; use residuals as gap).
- Statistical approaches:
  - Filters: HP, bandpass methods (Baxter-King (BK) 1999, Christiano-Fitzgerald (CF) 2003).
    - BK and CF extract frequencies within predetermined ranges; more flexible than HP but still sensitive to assumed cycle length.
  - Hamilton (2017) linear projection alternative:
    - Defines trend at t+h as the value forecasted at t using past x realizations.
    - Recommendations: for standard macro quarterly series, h=8 and x=4 (preceding 8,7,6,5 quarters); for credit cycles (long-lasting), h=20 and x=4 (preceding 20,19,18,17 quarters).
    - Strength: overcomes HP end-point problem; weakness: produces volatile gaps with frequent sign changes, performs poorly as early-warning indicator in some findings (Drehmann and Yetman 2018).
  - Multivariate statistical models:
    - Kalman filter applied to unobserved components models for GDP, credit, house prices.
    - Advantage: can estimate cycle length from data; drawback: lack structural theory and estimation complexity as variables increase.
- Structural/model approaches:
  - Regress credit on fundamentals (e.g., GDP, real long-run interest rates, real house prices) and take residuals as credit gaps.
  - Examples: VEC models (Galán and Mencía 2018), ADL on per-capita private debt (IMF 2015), regressions controlling for institutions, equilibrium real interest rate, demographics (Lang and Welz 2017).
  - Advantages: capture determinants of credit trend (income, reforms, real rates, demographics); allow separation of long-run and short-run effects.
  - Limitations: residual sensitivity to model specification, sample composition, omitted fundamentals; treating housing prices as exogenous problematic.

### Two approaches proposed to complement the BCG (overview)
- Common design choice: use real credit or real credit per capita to avoid dividing a stock variable (credit) by a flow variable (GDP).
- Approach A: Multivariate Filtering (MVF) based on economic theory — jointly estimate cyclical component of credit and macro variables.
- Approach B: Empirical models of credit consistent with fundamentals — estimate long-term credit trend from fundamentals and use deviations as prima facie credit gap.

### Multivariate Filtering Approach (MVF): model structure and intuition
- Model lineage: Krznar and Matheson (2017) variant of Carabenciov et al. (2008); similar to Benes et al. (2010), Andrle et al. (2014), Maria (2016); Laxton and Tetlow (1992) inspiration.
- Model components include equations for:
  - Output (IS curve),
  - Inflation (Phillips curve),
  - Policy interest rate (Taylor rule),
  - Real interest rate (Fisher equation),
  - Real exchange rate.
- Credit-gap equation (conceptual description from text):
  - Credit gap (ct) affected by lagged output gap (yt−1), its own lag (ct−1), and deviation of real interest rate from trend (rt−1).
  - Intuition: new credit flows respond to economic activity and prevailing interest rate; stock of credit adjusts slowly via loan repayments.
- Feedback from credit gap to aggregate demand included via a credit shock in output gap equation:
  - Output gap affected by lead and lag of output gap, real rate gap, credit shocks (changes in lending behavior εc t), foreign output gap, and real exchange rate gap.
  - Consistent with evidence that credit and output can grow without immediate inflationary pressure.
- Two model variants developed: for economies in a currency union and for economies with floating exchange rates (different interest rate and exchange-rate modeling).
- Estimation approach: country-by-country Bayesian estimation with quarterly data; Kalman filter used for one-sided filtering.

### MVF: strengths and limitations
- Advantages:
  - Explicitly models linkages between credit gaps and macro variables; identifies drivers of unobserved credit gaps.
  - Produces more stable estimates of unobserved components compared to univariate filters.
  - Does not require prior assumption on credit cycle length (data-driven cycle length).
- Disadvantages:
  - End-point bias not fully resolved by MVF (like other filters), though MVF reduces the problem considerably (referenced Appendix IV).
  - Requires empirical validation of assumed macroeconomic relationships and sensitivity checks to parametrization.

### MVF: empirical implementation and key quantitative results
- Countries estimated: two inside the euro area (Germany and Spain) and two with independent monetary policy (Poland and Sweden).
- Comparison metrics:
  - MVF real credit gaps (red lines) estimated with Kalman filter (one-sided) vs. one-sided HP filter with smoothing value of 400,000 (blue lines); Kalman smoother pseudo real-time using data up to end-2007 (black lines).
- Samples used for MVF estimation:
  - Spain and Germany: 1995:Q1-2018:Q3.
  - Sweden: 1993:Q1-2018:Q3.
  - Poland: 2001:Q1-2018:Q3.
- Samples used for HP filter:
  - Sweden and Spain: 1980:Q1-2018:Q3.
  - Germany: 1970:Q1-2018:Q3.
  - Poland: 1995:Q4-2018:Q3.
- Empirical findings:
  - MVF-estimated credit gaps have on average lower volatility and a shorter cycle than HP gaps.
  - MVF-implied cycle typically less than 15 years (equivalent to a smoothing factor roughly below 25,000 in the HP filter).
  - Turning points often similar between MVF and HP, but cycle amplitudes differ; MVF real credit gap is less volatile than credit-to-GDP gap.
  - MVF using real credit avoids the countercyclicality problem (notably during 2009 recession).
  - Real-time MVF estimates (data up to end-2007) show widening positive gaps ahead of the Global Financial Crisis.
  - Revision properties: MVF has better revision properties than HP filter (Appendix IV); MVF reduces large negative post-bust gaps observed with BCG, shown for Spain and Sweden.
  - Country-specific note: in Germany the negative credit gap closed before the GFC according to MVF.

### Empirical models of credit consistent with fundamentals (panel error-correction model)
- Approach summary:
  - Estimate an error-correction (EC) model on an unbalanced panel of 40 European countries (annual data, 1970-2017).
  - Dependent variable: change in log credit per capita (credit defined as total credit to private sector including bank loans, debt securities, credit by nonbanks and foreign entities).
  - EC specification separates long-run equilibrium from short-run dynamics; residuals used to assess deviations from fundamentals.
- Model elements and fundamentals included:
  - GDP per capita (opportunities/capacity to borrow; log specification).
  - Total bank deposits per capita (capture financial deepening).
  - Real interest rate (negative effect on credit supply, positive on demand).
  - Old-age dependency ratio (expected negative effect on credit demand).
  - Country fixed effects included.
  - Statistical tests support cointegrating relationships.
- Data specifics:
  - Unbalanced panel of 40 countries: Albania, Austria, Belgium, Bosnia and Herzegovina, Bulgaria, Croatia, Cyprus, Czech Republic, Estonia, Finland, France, Germany, Hungary, Iceland, Ireland, Israel, Italy, Kosovo, Latvia, Lithuania, Luxembourg, Macedonia, Malta, Moldova, Montenegro, Netherlands, Norway, Poland, Portugal, Romania, Russia, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey, Ukraine, United Kingdom.
  - Time coverage varies across countries: series length ranges between 5 and 47 years.
  - Credit, GDP, and bank deposits expressed per capita in 2010 U.S. PPP terms; all variables (except interest rates) in logarithms.
- Advantages and limitations:
  - Advantage: separates long-term and short-term effects; panel estimation can isolate steady-state relationships.
  - Limitation: assuming identical coefficients across countries and over time may be strong if cycles are heterogeneous; results sensitive to country choice and time-series length.

*Italic source: Excerpt from IMF working paper (wpiea2020006-print-pdf), Sections II–IV.*

### Appendix II.

### Appendix II.

### Estimation methods
- Techniques used:
  - Dynamic fixed effect estimation (DFE) of Pesaran et al. (1997): assumes common coefficients across all panels for long-run and short-run equations, including the error-correction term.
  - Pooled-mean group (PMG) estimator: allows country-specific short-term dynamics while restricting long-run elasticities to be equal across panels (short-term coefficients reported are the mean value of country-by-country coefficients).
- Country fixed effects are included in all specifications to capture time-invariant country characteristics, such as institutional quality and the steady-state level of per capita credit.
- Hausman test: does not reject the use of the restrictions employed by the DFE relative to the PMG in the reported estimations.

### Regression results — long-run and short-run findings
- General:
  - Most fundamental variables have expected signs in both long-run and short-run equations across estimators.
  - DFE standard errors are clustered within panel and are heteroscedasticity robust.
- GDP per capita and deposits per capita:
  - Coefficients on GDP per capita and per capita deposits are generally statistically and economically significant with expected signs for both DFE and PMG.
- Real interest rate and old-age dependency ratio:
  - Statistically and economically significant for the PMG estimator but not always for the DFE estimator.
  - Signs are generally consistent with theoretical priors.
  - The coefficient on the old-age dependency ratio is larger for emerging markets economies than for advanced economies (possible explanation: faster aging in European emerging markets driven by emigration of the working-age population).
- PMG versus DFE:
  - PMG yields smaller standard errors for long-run coefficients than DFE.
  - PMG results in smaller elasticities for GDP per capita except for emerging economies.
  - Magnitudes of coefficients for real interest rate and old-age dependency become larger with PMG and become statistically significant.
  - Note: Some PMG coefficients for emerging markets are implausibly large, possibly due to relatively short sample periods.
- Error-correction term and speed of adjustment:
  - Estimated speed of adjustment: between around 13 and 20 percent per year for deviations of credit from its long-term equilibrium.
  - Interpretation: takes roughly 5-8 years for credit to return to its long-term equilibrium.
  - Advanced economies adjust more slowly: 12 percent per year.
  - Emerging economies adjust faster: 20 percent per year.
- Short-run dynamics:
  - Credit grows more rapidly with higher GDP growth, higher deposit growth, and slower aging.
  - The coefficient on the change in real interest rates is generally positive across specifications, possibly suggesting credit supply factors dominate credit demand in the short run.
  - Results broadly hold across country groupings and estimators, though magnitudes vary.

### Key numerical estimates from Table 1 (selected coefficients and statistics)
- Error correction term:
  - Fixed effects: -0.136*** (0.023)
  - DFE All: -0.127*** (0.029)
  - DFE Emerging: -0.199*** (0.051)
  - PMG All: -0.205*** (0.033)
  - PMG Advanced: -0.201*** (0.038)
  - PMG Emerging: -0.194*** (0.063)
- Long-run relation (selected):
  - GDP per capita (log):
    - Fixed effects: 1.010*** (0.308)
    - DFE All: 0.789** (0.399)
    - DFE Emerging: 1.984** (0.887)
    - PMG All: 0.738*** (0.085)
    - PMG Advanced: 0.725*** (0.086)
    - PMG Emerging: 2.648*** (0.374)
  - Deposit per capita (log):
    - Fixed effects: 0.429** (0.215)
    - DFE All: 0.549* (0.291)
    - DFE Emerging: 0.086 (0.450)
    - PMG All: 0.458*** (0.048)
    - PMG Advanced: 0.456*** (0.049)
    - PMG Emerging: 0.250 (0.182)
  - Real interest rate:
    - Fixed effects: 0.008 (1.190)
    - DFE Advanced: -1.810 (1.815)
    - DFE Emerging: 0.306 (1.343)
    - PMG All: -0.592** (0.257)
    - PMG Advanced: -0.716*** (0.290)
    - PMG Emerging: -0.840** (0.386)
  - Old age dependency (log):
    - Fixed effects: -0.068 (0.443)
    - DFE Advanced: -0.242 (0.424)
    - DFE Emerging: -0.415 (1.010)
    - PMG All: -1.212*** (0.151)
    - PMG Advanced: -1.139*** (0.155)
    - PMG Emerging: -5.253*** (0.862)
- Short-run (Δ) coefficients (selected):
  - Δ Lagged credit per capita (log): 0.238*** (0.029) in Fixed effects; other estimates reported in table.
  - Δ GDP per capita (log): 0.704*** (0.107) in Fixed effects; PMG Advanced: 0.771** (0.331); PMG Emerging: 0.866* (0.444); PMG All: 0.229 (0.195).
  - Δ Deposit per capita (log): 0.370*** (0.049) in Fixed effects; PMG All: 0.477*** (0.134).
  - Δ Real interest rate: 0.086 (0.105) in Fixed effects; PMG Advanced: 0.318* (0.182); PMG Emerging: 0.334 (0.248); PMG All: -0.001 (0.057).
  - Δ Old age dependency (log): -0.691** (0.324) in Fixed effects; PMG All: -2.453*** (0.800); PMG Emerging: 1.476** (0.593).
- Sample and fit:
  - Maximum time span shown: 1980-2017 and 1994-2017 for some specifications.
  - Num of observations: 894, 907, 705, 189, 881, 705, 176 (by column as reported).
  - Num of countries: 40, 40, 27, 13, 38, 27, 11 (by column as reported).
  - R-squared (Fixed effects): 0.299
- Notes: Standard errors clustered by country in parentheses. *** p<0.01, ** p<0.05, * p<0.1.

### Interpreting regression residuals as credit gaps
- Regression residuals from the long-term (EC) model correspond to the error-correction term and can be interpreted as prima facie measures of the credit gap.
- Empirical behavior:
  - Credit gap signals financial crises reasonably well in general.
  - Spain: large and prolonged credit boom and bust; positive credit gap closing and around zero at end of sample (contrasts with the BCG which shows large negative credit gaps for Spain in 2018).
  - France: negative gaps in late 1990s and early 2000s, positive in recent years—reflecting growth in corporate non-financial sector debt.
  - Sweden: gap was positive around past financial crises; recent credit upswing has not yet translated into positive gaps.
  - Czech Republic: shown in figures as part of country illustrations.
- Real-time limitations:
  - Real-time signaling property of this approach is not tested due to data limitations.
  - Regression residuals for 2018 are out-of-sample estimates in the illustrations.

### Using supplementary indicators to assess vulnerabilities
- Residuals can be driven by estimation errors and omitted variables; therefore, residuals should be examined alongside supplementary indicators of systemic vulnerabilities.
- Example (Spain):
  - Plots compare estimated credit gaps with:
    - House price-to-rent ratio,
    - Real house price,
    - Share of high-yield corporate bonds in total corporate bond issuance (HY share),
    - Gross value added of the construction sector.
  - If positive credit gaps coincide with high values (relative to historical mean) of such indicators, this signals excessive credit and vulnerability buildups.
  - Spain in mid-2000s: positive credit gaps accompanied by high and rising LTD ratio, increasing housing prices, and construction-sector activity.
- Data sources used in examples:
  - Price-to-rent ratio and real house price: OECD housing database.
  - High-yield share: Kirti (2018).
  - Gross value added of construction sector: EU and World KLEMS and Dell’Ariccia et. al (2019).

### Decomposing credit growth with the EC model
- The EC model decomposes credit growth into:
  1. Adjustments to the long-term level (error-correction term).
  2. Contemporaneous developments in fundamental variables: GDP, deposit, demography, interest rates (as changes in log terms).
- Illustration (Spain):
  - After excess credit, equilibrium credit growth was subdued to allow adjustment to long-term level.
  - As credit gap closed and GDP and deposit growth picked up, equilibrium credit growth accelerated in recent years.
- Figures for Spain, France, Sweden, and Czech Republic show the decomposition time series; 2018 data are out-of-sample estimates.

### Conclusions (policy-relevant takeaways)
- Measuring credit gaps properly is important to assess macro-financial vulnerabilities and guide macroprudential policy.
- The Basel Committee’s credit-to-GDP gap (BCG) has weaknesses:
  - Tends to become persistently negative after a pronounced boom deflates, implying credit should return to its cyclical peak—raising questions about its usefulness over full cycles.
- Two complementary approaches proposed and applied to selected European countries:
  1. Model-based multivariate filter: identifies cyclical conditions of credit and macroeconomy jointly; useful for macroprudential policy where instability builds when credit growth occurs during macroeconomic overheating.
  2. Fundamentals-based EC model: identifies long-term determinants of credit; regression residuals examined with vulnerability indicators to assess whether they are policy-relevant gaps.
- Advantages of the two methods:
  - Do not impose exogenous specific duration to credit cycle.
  - Produce sensible estimates of credit gaps in countries with large booms and busts.
- Disadvantages and caveats:
  - End-point bias remains an issue for the model-based multivariate filter, though smaller than for the BCG.
  - Coefficients in the fundamentals-based EC model are sensitive to country selection and time-series length.
  - Using multiple methods helps identify a range of plausible assessments; large ranges require deeper analysis for policy decisions.
- Policy implication:
  - Methods show promise in complementing the BCG and guiding policymakers’ judgment in assessing position in the credit cycle and calibrating macroprudential stance.

### Annex I — BCBS Operational Guidance for the Countercyclical Capital Buffer (CCyB) (selected principles)
- Primary aim: use capital buffer to protect the banking sector from periods of excess aggregate credit growth associated with system-wide risk; may also help lean against the buildup phase.
- Common reference guide: aggregate private sector credit-to-GDP gap (credit gap guide) is useful but does not work well in all jurisdictions; judgment and communication are integral.
- Authorities expected to apply judgment anchored to principles:
  - Principle 1 (Objectives): buffer decisions guided by objective to protect banking system when excess credit growth is associated with increased system-wide risk.
  - Principle 2 (Common reference guide): credit gap guide is a useful reference but need not be dominant; authorities should explain information used and how considered.
  - Principle 3 (Risk of misleading signals): assessments should be mindful of factors that can lead guides to give misleading signals.
  - Principle 4 (Prompt release): promptly releasing the buffer in times of stress can help reduce risk of credit supply being constrained by regulatory capital requirements.
  - Principle 5 (Other macroprudential tools): CCyB is part of a suite of tools; authorities should deploy CCyB possibly in tandem with other tools when excess aggregate credit growth is judged to be associated with system-wide risk buildup.

### Annex II — Indicators used by country authorities to guide CCyB decisions (selected facts)
- BCBS member practices:
  - European members tend to use a wider set of indicators—the median number of indicators of nine—than non-European counterparts.
  - This holds for both advanced and emerging market economies.
- Frequency of indicator use:
  - Credit-related indicators: about 80 percent of BCBS members use at least one credit-related indicator; 100 percent of European BCBS members do so.
  - Financial health of households: about 2/3 of BCBS members use related indicators.
  - Health of banking sector: used by 1/2 of members.
  - Financial health of businesses, market risks, macroeconomics: used by about 1/3 of members.
  - None of the non-European members use indicators on market risks (as reported).
- Subcomponents of credit:
  - All members that use credit-related indicators use the BCG most commonly.
  - About 80 percent of BCBS members—100 percent of European BCBS members—use at least one credit-related indicator (reiterated).
  - About 1/3 of BCBS members look at growth of total private credit and indicators on household credit or business credit.
  - Emerging market economies (e.g., Brazil and Russia) also look at currency-adjusted credit measures.

*Source: IMF Staff estimations.*

### Appendix I . Detailed Overview of the Multivariate Filter

### Appendix I . Detailed Overview of the Multivariate Filter

### A. Domestic Economy — Model structure and key relationships
- Output:
  - Output gap definition: *t y = X_t − x*_t* where X_t ≡ 100 * ln(Y_t/GDP).
  - Potential output dynamics: *y*_t = y*_(t−1) + g*_t /4 + ε^y_t* (equation (0.2) form).
  - Potential growth convergence: *g*_t = (1 − ρ_g) g_ss + ρ_g g*_(t−1) + ε^g_t* (equation (0.3) specification).
  - Output gap law of motion (equation (0.4)): output gap t y depends on y_(t+1), y_(t−1), real rate gap t r, credit shock ε^c_t, foreign output gap e_t y, and real exchange rate gap t z with coefficients β lead, β lag, β r, β c, β e, β z as shown in the model text.

- Inflation:
  - Phillips-curve specification for euro area model (equation (0.5)): current headline inflation t π linked to π_(t+1), π_(t−1), the domestic output gap t y, and the difference between euro area annual inflation A_t^e π and domestic annual inflation A_t π, with lead–lag and λ coefficients as specified.
  - Annual inflation definition (equation (0.6)): A_t π = (π_t + π_(t−1) + π_(t−2) + π_(t−3))/4.
  - Non-euro-area alternative (equation (0.7)): inflation dynamics substitute the inflation differential with change in real exchange rate z.

- Credit:
  - Credit gap equation (equation (0.8)): c_t = θ_y y_(t−1) + θ_c c_(t−1) + θ_r r_(t−1) + ε^c_t (with lead/lag placement as in text).
  - Credit gap definition (equation (0.9)): c_t ≡ 100 * ln(CRED_t / coreCPI_t) − c*_t where CRED is credit to private non-financial sector scaled by core CPI.
  - Trend credit dynamics (equations (0.10)–(0.11)): c*_t evolves with growth and shocks; trend credit growth g*_c converges toward steady state g_ss^c with autoregressive dynamics as specified.

- Unemployment:
  - Okun’s-law type dynamics (equation (0.12)): u_t = α_1 u_(t−1) + α_2 y_t + ε^u_t (text specifies lead/lag structure).
  - Unemployment gap definition (equation (0.13)): u_t ≡ U_t − u*_t where U_t is actual quarterly unemployment and u*_t is NAIRU.
  - NAIRU and its growth dynamics (equations (0.14)–(0.15)): u*_t and its growth g*_u follow autoregressive convergence toward steady state u_ss with parameters α_3, α_4 and shock terms.

### B. Foreign Economy — Model structure and linkages
- Output:
  - Foreign output gap: e_t y = Y^e_t − y*^e_t with Y^e_t ≡ 100 * ln(Y^e_t/GDP) (equation (0.16) definition).
  - Foreign potential output dynamics (equations (0.17)–(0.18)): y*^e_t evolves with growth g^e_t and shocks; g^e_t converges toward steady-state e_ss g with autoregressive form.
  - Foreign output gap law of motion (equation (0.19)): e_t y depends on e_(t+1) y, e_(t−1) y, foreign real rate gap e_t r and exogenous shocks; for Germany the domestic output gap is allowed to affect the euro area output gap (equation (0.20)).

- Inflation:
  - Foreign Phillips curve (equation (0.21)): e_t π depends on π^e_(t+1), π^e_(t−1), foreign output gap e_t y and shocks with λ coefficients as specified.

### C. Interest Rates — Policy rules and real rate gaps
- Domestic economy outside a currency union:
  - Nominal interest rate rule (equation (0.22)): forward-looking Taylor-type rule with response to expected annual inflation 4 A_t π_(t+1), inflation target π^tar_(t+1), output gap t y, equilibrium real rate *t r, and shock term; coefficients γ_π, γ_y, etc., as indicated.
  - Inflation target dynamics (equation (0.23)): π^tar_t converges toward steady state π_ss^tar with autoregressive form.
  - Real rate definition (equation (0.24)): R_t = i_t − π_(t+1).
  - Real rate gap (equation (0.25)): r_t = R_t − r*_t + φ_t where φ_t is a risk premium.
  - Trend real rate convergence (equation (0.26)): r*_t converges toward r_ss with autoregressive form.
  - Risk premium dynamics (equation (0.27)): φ_t follows an AR(1) around φ_ss with persistence ρ_φ and shocks; model treats risk premium as exogenous.

- Foreign economy interest rate rule:
  - Foreign nominal rate follows analogous forward-looking Taylor-type rule (equation (0.28)) with foreign inflation target π^tar,e_t (equation (0.29)).
  - Foreign real rate (equation (0.30)): R^e_t = i^e_t − π^e_(t+1).
  - Foreign real rate gap (equation (0.31)): e_t r = R^e_t − r*^e_t with trend convergence (equation (0.32)) toward e_ss r.

- Domestic economy in a currency union:
  - Nominal interest rate equals common nominal rate plus country risk premium (equation (0.33)): i_t = i^e_t + φ_t.
  - Country real rate gap measured relative to currency-union common trend real rate r*^e_t (equations (0.34)–(0.35)).

### D. Exchange Rates — Definitions and dynamics
- Currency union case:
  - Real exchange rate definition (text): Z_t ≡ 100 * (log Z_t − log CP I_t) with nominal rates irrevocably fixed.
  - Real exchange rate gap: z_t = Z_t − z*_t (equation (0.36)).
  - Gap dynamics (equation (0.37)): z_t = z_(t−1) + ρ_z (z_(t−1) − z_ss) + ε^z_t form implied; trend dynamics (equation (0.38)): z*_t converges toward z_ss with autoregressive form.

- Non-currency-union case:
  - Real exchange rate defined as Z_t ≡ 100 * (log(s_t * CPI^*_t / CPI_t)) where s is nominal exchange rate.
  - Interest parity condition (equation (0.39)): z_(t+1) = z_t + r_t − r^e_t /4 + ε^z_t (structure given in text).
  - Rational expectations allowance (equation (0.40)): z_t follows forward-looking AR structure with δ and θ parameters.
  - Equilibrium risk premium (equation (0.41)): ρ^*_t = z^*_t + (r_t − r^e_t)/4 + ... (as specified).

### E. Estimation approach, priors, and revision properties
- Estimation strategy:
  - MVF uses a mixture of calibration (to ensure robust impulse response functions and 8 quarters step-ahead projection quality) and Bayesian estimation for model shocks.
  - “System priors” (Andrle and Plasil 2016) are used to aid identification; an imposed prior penalizes estimated business cycle length longer than 40 quarters.
  - Estimated coefficients and shocks are reported country-by-country (Germany, Spain, Sweden, Poland) in the Appendix tables.

- Real-time revision properties:
  - Revision metric: mean absolute error (MAE) between nowcasts and final estimates.
  - Empirical finding summarized in text: The MAE of the MVF is typically much smaller than the MAE for the HP, reducing the MAE by as much as 80 percent in some cases.
  - Credit gap MAEs are larger relative to output gap MAEs, suggesting potential refinements to MVF using different data or cycle specifications are warranted for future research.
  - Table note: Real-time properties for four countries reported; example numeric MAE labels in table header include values formatted as: ESP21.25.4, DEU6.31.7, SWE6.71.4, POL8.14.1 (presented in the source table format).

### F. Data used for the MVF and fundamentals-based approach
- Multivariate Filter (Quarterly Data) — Domestic economy data sources (all from Federal Reserve Bank of St. Louis):
  - Real GDP
  - Credit to the private nonfinancial sector
  - Headline inflation
  - Unemployment rate
  - 10-year government bond yield
  - Nominal Exchange Rate
  - 3-Month nominal rate

- Euro area data sources (Euro Area Wide Model Database):
  - Real GDP
  - Headline inflation
  - 10-year benchmark yield
  - 3-Month nominal rate

- Fundamentals-Based Approach sources:
  - GDP, PPP Exchange Rate vs USD, Population — World Economic Outlook
  - Credit to the private nonfinancial sector — International Finance Statistics, BIS
  - GDP deflator, Deposits — International Finance Statistics
  - Interest Rates — ECB, Eurostat, OECD, IFS

*Appendix I . Detailed Overview of the Multivariate Filter — source: wpiea2020006-print-pdf (Appendix I)

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_Source: https://www.imf.org/-/media/files/publications/wp/2020/english/wpiea2020006-print-pdf.pdf_