## Annex I. Main Features of the Euro Area Model

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### Model purpose and conceptual integration
- Combines macro-financial linkages (credit cycle) and New-Keynesian (NK) policy analysis to:
  - identify an unobserved credit cycle distinct from but correlated with the business cycle;
  - analyze propagation of financial and macroeconomic shocks where banks generate frictions and shocks;
  - study effects of a countercyclical macroprudential rule (CCyB) responding to credit dynamics.
- Extends the multivariate filter model in Baba et al. (2020) to explicitly model credit demand and supply with microfoundations from Dib (2010) and de Resende et al. (2016), and incorporates a macroprudential policy rule.
- Applied to Luxembourg as a small open economy with a large banking sector and an active countercyclical macroprudential framework.

### Core structure and key channels
- Retains canonical NK elements: aggregate demand block (dynamic IS), New Keynesian Phillips Curve, and monetary policy block representing exogenous European Central Bank (ECB) policy (set externally to Luxembourg).
- Deviations from canonical NK:
  - explicit credit markets, active banking sector, and a regulator that sets a countercyclical capital buffer (CCyB);
  - loan demand derived from households’ consumption–savings optimization (deposits as savings vehicles; credit for consumption smoothing and risk-sharing);
  - loan supply from monopolistically competitive banks: banks collect deposits, raise capital to “produce” loans, and set lending rates as a mark-up over marginal cost;
  - minimum capital requirement affects banks’ marginal cost, prompting capital increases (at increasing cost), loan cuts, or both.
- Financial accelerator mechanisms:
  - BGG-inspired linkage between output, borrowers' net worth, loan supply risk, and lending rates;
  - Kiyotaki–Moore (KM) style borrowing constraints that loosen or tighten with collateral values (e.g., house prices).
- CCyB channel: changes in CCyB alter loan supply marginal costs, equilibrium credit volumes and interest rates, and thus both business and credit cycles.

### Shocks and propagation
- Shocks increasing banks' marginal costs of loan supply → reduced loan volumes, higher lending rates → dampened aggregate demand and output.
- Shocks to household preferences raising aggregate demand → higher loan demand, increased loan volumes, higher market interest rates.
- Exogenous loan demand shocks (household preferences) and loan supply shocks (cost-push and riskiness shocks) change equilibrium in credit markets.
- Nominal interest rate rigidity ensures sluggish adjustment of lending rates and credit supply to shocks and policy changes.

### Calibration, estimation, and data mapping
- Model mapped to Luxembourg quarterly data from 2010-2020 using a mix of calibration and Bayesian estimation.
- Simulated data generated from many bootstrapped samples with the same size as the calibration/estimation sample.
- Forecasts and validation use data up to 2022Q2 for scenario and projection exercises.
- Estimation sample for Bayesian estimation: 2003Q1–2019Q4 (COVID excluded) with 500,000 simulated paths for posterior; acceptance ratio ≈ 20%.
- Example calibration targets and estimated parameters (posterior modes highlighted in source):
  - A 1 percentage point increase in the countercyclical capital buffer reduces the credit gap by about 0.5 percentage points over 5 quarters.
  - ψ_1 = 0.8 (persistence of minimum capital requirements).
  - ψ_5 = 0.2 (sensitivity of bank capital buffer to minimum capital requirements).
  - β_r = 0.075
  - β_c = 0.028
  - θ_2 = 0.83 (credit persistence)
  - δ_2 = 0.83 (interbank rate importance for lending rates)
  - ψ_1 = 0.8 (policy persistence)

### Empirical validation and forecasting performance
- Simulated data replicate well the first and second moments of key macro and financial variables.
- One- to six-quarter ahead pseudo and true out-of-sample conditional forecasts produce unbiased forecast errors for most variables and capture turning points and general dynamics of most indicators.
  - Exception: short-lived downward-biased forecast of the nominal lending rate (in the near term).
- Diebold-Mariano tests indicate model forecasts are more accurate than simple benchmarks (VAR and ARMA).
- Forecast performance vs reduced-form benchmarks:
  - Model outperforms VAR for most variables and horizons.
  - Average ratio of RMSEs below 0.7 for output growth, lending rate, and credit growth.
  - Inflation: model RMSE ratio > 1; accuracy not statistically different from ARMA benchmark.
- Moment-matching via bootstrap: 10,000 simulated paths for 2010Q1–2020Q4; real credit growth variance higher in model (higher rejection rate 16%).

### Key empirical findings for Luxembourg
- Banking sector contributes about 10 percent of GDP.
- Domestically oriented banks (DOBs) provide 88 percent of credit to resident non-financial private customers as of end-2022.
- Captive financial institutions (mainly special-purpose entities) account for roughly 20 percent of total credit extended by DOBs to non-bank resident customers; these are excluded from the model’s credit measure because they primarily transact with non-residents.
- Credit to the resident non-financial private sector grew, but slowed in 2022 reflecting tighter financial conditions and credit standards; credit growth to resident non-financial sector: 4.4 percent in end-2022.
- CCyB history:
  - initially introduced at zero;
  - increased to 0.25 percent in late 2018 (effective January 2020);
  - increased to 0.5 percent in March 2020 (effective January 2021);
  - has remained unchanged since then.
- Luxembourg entered a cyclical downturn in mid-2022, primarily reflecting unfavorable demand shocks.
- Post-COVID rise in inflation driven by expectations, cost-push shocks (possibly international food and energy price spikes), and robust domestic demand.
- Credit gap dynamics:
  - credit gap narrowed significantly after remaining positive under low-for-long interest rates and was almost closed in early 2022 (≈ 1 percent above long-term trend).
  - tightening of ECB’s monetary policy and bank capital buffers are driving lending rates up toward estimated neutral level.

### Policy experiments, macroprudential insights, and scenarios
- Minimum capital requirement shock (unexpected one-off 1 percentage point increase; endogenous regulator deactivated to show "pure" effect):
  - Banks increase capital-ratio holdings only partially (≈ 0.2 percentage points at peak).
  - Lending rates increase by 0.16 pp at peak.
  - Credit gap turns negative, reaching −0.5 percent after five quarters.
  - Output gap peak deviation ≈ −0.25 percent.
  - Unemployment deviates by 0.04 percentage points at the peak.
  - Inflation almost unchanged due to low sensitivity (α_Y = 0.005).
- Policy stances considered:
  - Dovish: low responsiveness to financial cycle (ψ = ψ_low).
  - Hawkish: high responsiveness to financial cycle (ψ = ψ_high).
  - Counterfactual: macroprudential policy inactive (ψ = 0).
- Responses to shocks:
  - 1-percent positive aggregate demand shock: inflation ~ 0.01 percent; credit gap ~ +0.7 percent at quarter 2.
  - Hawkish macroprudential response raises minimum capital requirements (peak +0.45 pp under Hawkish) and accelerates convergence of credit to trend.
  - Aggregate supply (cost-push) shock: output and credit contract; macroprudential authority eases policy (cuts minimum capital requirements).
  - Credit demand shock: Hawkish stance can raise minimum capital requirements up to 0.5 pp at peak; shortens stabilization time by about two quarters relative to Dovish and four quarters relative to inactive policy.
  - Credit supply shock: macroprudential authority cuts minimum capital requirements to allow use of buffers and support credit and output recovery.
- Robustness checks with three macroprudential rule variations (less to more aggressive):
  - faster convergence to equilibrium with more aggressive responses;
  - overall macroeconomic impact remains mild across scenarios.
- Use of credit-to-GDP gap in rule:
  - reacting to credit-to-GDP gap can produce procyclical responses because credit-to-GDP can move opposite to credit gap initially, introducing undesirable volatility.
- Quantitative trade-off:
  - Tightening macroprudential stance produces rapid contraction of credit volumes and increase in lending rates, but quantitative impact on real economy is relatively modest under model parameterization — suggesting a favorable trade-off for Luxembourg.

### Baseline projections and policy-rule implications (2023–2027; conditional on data up to 2022Q2 and WEO October 2022 vintage)
- Baseline projects Luxembourg business and credit cycles to deteriorate in the near term; output gap negative until end-2024 and gradually closes over the medium term.
- Given credit gap as of 2022Q2, the model suggests keeping macroprudential stance unchanged initially.
- Under baseline assumptions and most aggressive policy stance:
  - macroprudential authorities would loosen the macroprudential policy stance, reducing the minimum capital requirements by up to 5 percentage points.
- Lending rate and credit path:
  - the lending rate gap is projected to decline relatively quickly, turning negative by early 2025.
  - lower lending rates help support credit demand and lead to sustained credit growth over the medium term; the credit cycle would fully recover only over the medium term due to strong persistence.
- Policy-rule design implications:
  - a policy rule assigning equal weights to credit and housing indicators can induce a procyclical and unstable policy response (given house price gap large at 15 percent as of 2022Q2 while credit gap was almost closed).
  - adopting a positive neutral CCyB is recommended to:
    - soften the impact of adverse shocks on credit and economic activity;
    - reduce sensitivity of the macroprudential rule to short-run assessments of credit and asset price gaps;
    - avoid unnecessary volatility in minimum capital requirements and the credit cycle.
  - focusing the rule on the credit indicator and assigning different weights to credit and asset prices (house prices) can avoid undue volatility of macroprudential policy responses.

### Model technical structure and selected parameterization (preserved exactly)
- Core blocks: aggregate demand (dynamic IS), New Keynesian Phillips Curve, monetary policy (exogenous ECB), banking/credit sector, macroprudential regulator.
- Notation and setup: quarterly frequency; trend superscript *; (e) foreign economy; (ss) steady-state; (e) and (ss) used as in source.
- Selected calibrated parameters and steady-state values (preserved exactly):
  - Persistence of the trend output growth: 0.950
  - Sensitivity of inflation to output gap: 0.005
  - Persistence of the trend credit growth: 0.700
  - Persistence of the trend lending rate: 0.980
  - Persistence of the asset price gap: 0.800
  - Sensitivity of credit demand to real lending rate: 1.800
  - Persistence of real lending rate: 0.005
  - Sensitivity of the real lending rate to bank capital buffer: 0.195
  - Persistence of the minimum capital requirements: 0.800
  - Sensitivity of the macroprudential rule to credit gap: [0.000, 0.150]
  - Sensitivity of the macroprudential rule to credit growth: [0.000, 0.100]
  - Sensitivity of the macroprudential rule to house price gap: [0.000, 0.150]
  - Sensitivity of bank capital buffer to minimum capital requirements: 0.200
  - Persistence of the trend bank capital: 0.950
  - Persistence of the unemployment gap: 0.800
  - Persistence of the real interbank rate's trend: 0.900
  - Persistence of the risk premium: 0.800
- Steady state:
  - Trend output growth: 2.500
  - Trend aggregate credit growth: 2.500
  - Non-financial private sector's risk premium: 1.500
  - Trend bank capital ratio: 25.000
  - Long-term bank capital buffer: 14.000
  - Long-term unemployment rate: 5.800
  - Long-term risk premium: 0.000
  - Long-term Euro Area interbank rate: 0.000
- Selected shocks (standard deviations preserved exactly):
  - Standard deviation of the shock to potential output: 0.001
  - Standard deviation of the shock to potential growth: 0.001
  - Standard deviation of the shock to the equilibrium unemployment rate: 0.001
  - Standard deviation of the shock to trend credit: 0.001
  - Standard deviation of the shock to trend credit growth: 0.009
  - Standard deviation of the shock to trend bank capital: 0.200
  - Standard deviation of the asset price shock: 0.020
- Euro area model key steady states and parameters (preserved exactly):
  - Forward-looking expectations on output gap (훽_lead_e): 0.500
  - Persistence of output gap (훽_lag_e): 0.550
  - Persistence of the real interbank rate’s trend (⁡휌_r_e*): 0.050
  - Sensitivity of inflation to output gap (훼_y_e): 0.050
  - Trend output growth (푔_ss_e): 1.200
  - Long-term euro area inflation target (휋_ss_e_target): 1.800
  - Long-term euro area interbank rate (푟_ss_e*): 0.000

### Key quantitative illustrative results (impulse-response summary)
- Minimum capital requirement shock (one-off +1 percentage point, regulator deactivated):
  - Bank capital-ratio holdings increase ≈ 0.2 percentage points at peak.
  - Lending rates increase by 0.16 pp at peak.
  - Credit gap reaches −0.5 percent after five quarters.
  - Output gap peak deviation ≈ −0.25 percent.
  - Unemployment deviates by 0.04 percentage points at peak.
  - Inflation effect negligible given α_Y = 0.005.
- Aggregate demand shock (1 percent):
  - Inflation response: 0.01 percent.
  - Credit gap response: ~ +0.7 percent at quarter 2.
- Hawkish vs Dovish macroprudential responses:
  - Hawkish: peak increase in minimum capital requirements +0.45 pp for an aggregate demand shock; faster credit convergence.
  - Hawkish shortens credit stabilization by about two quarters versus Dovish and four quarters versus inactive policy in response to positive credit demand shocks.

*Source: Annex I. Main Features of the Euro Area Model, IMF Working Paper "A Semi-Structural Model for Credit Cycle and Policy Analysis" (content unit provided).*

### Annex I. Main Features of the Euro Area Model ..........................................................................

### Annex I. Main Features of the Euro Area Model

### Model purpose and conceptual integration
- Combines two literature strands: macro-financial linkages (credit cycle) and New-Keynesian (NK) policy analysis to:
  - identify an unobserved credit cycle distinct from but correlated with the business cycle;
  - analyze propagation of financial and macroeconomic shocks where banks generate frictions and shocks;
  - study effects of a countercyclical macroprudential rule (CCyB) responding to credit dynamics.
- Extends the multivariate filter model in Baba et al. (2020) to explicitly model credit demand and supply with microfoundations from Dib (2010) and de Resende et al. (2016), and incorporates a macroprudential policy rule.
- Applied to Luxembourg as a small open economy with a large banking sector and an active countercyclical macroprudential framework.

### Core structure and key channels
- Retains canonical NK elements: aggregate demand block, NK Phillips Curve, and monetary policy block representing exogenous European Central Bank (ECB) policy (set externally to Luxembourg).
- Deviations from canonical NK:
  - explicit credit markets, active banking sector, and a regulator that sets a countercyclical capital buffer (CCyB);
  - loan demand derived from households’ consumption–savings optimization (deposits as savings vehicles; credit for consumption smoothing and risk-sharing);
  - loan supply from monopolistically competitive banks: banks collect deposits, raise capital to “produce” loans, and set lending rates as a mark-up over marginal cost;
  - minimum capital requirement affects banks’ marginal cost, prompting capital increases (at increasing cost), loan cuts, or both.
- Financial accelerator mechanisms included:
  - BGG-inspired linkage between output, borrowers' net worth, loan supply risk, and lending rates;
  - Kiyotaki–Moore (KM) style borrowing constraints that loosen or tighten with collateral values (e.g., house prices) driven by the business cycle.
- CCyB channel: changes in CCyB alter loan supply marginal costs, equilibrium credit volumes and interest rates, and thus both business and credit cycles.

### Shocks and propagation
- Shocks increasing banks' marginal costs of loan supply → reduced loan volumes, higher lending rates → dampened aggregate demand and output.
- Shocks to household preferences raising aggregate demand → higher loan demand, increased loan volumes, higher market interest rates.
- Exogenous loan demand shocks (household preferences) and loan supply shocks (cost-push and riskiness shocks) change equilibrium in credit markets.

### Calibration, estimation, and data mapping
- Model mapped to Luxembourg quarterly data from 2010-2020 using a mix of calibration and Bayesian estimation.
- Simulated data generated from many bootstrapped samples with the same size as the calibration/estimation sample.
- Forecasts and validation use data up to 2022Q2 for scenario and projection exercises.

### Empirical validation and forecasting performance
- Simulated data replicate well the first and second moments of key macro and financial variables.
- One- to six-quarter ahead pseudo and true out-of-sample conditional forecasts produce unbiased forecast errors for most variables and capture turning points and general dynamics of most indicators.
  - Exception: short-lived downward-biased forecast of the nominal lending rate (in the near term).
- Diebold-Mariano tests indicate model forecasts are more accurate than simple benchmarks (VAR and ARMA).
- RMSEs and confidence intervals assessed (figures and tables referenced in source).

### Key empirical findings for Luxembourg
- Banking sector contributes about 10 percent of GDP.
- Domestically oriented banks (DOBs) provide 88 percent of credit to resident non-financial private customers as of end-2022.
- Captive financial institutions (mainly special-purpose entities) account for roughly 20 percent of total credit extended by DOBs to non-bank resident customers; these are excluded from the model’s credit measure because they primarily transact with non-residents.
- Credit to the resident non-financial private sector grew, but slowed in 2022 reflecting tighter financial conditions and credit standards; credit growth to resident non-financial sector: 4.4 percent in end-2022.
- CCyB history and magnitudes:
  - initially introduced at zero;
  - increased to 0.25 percent in late 2018 (effective January 2020);
  - increased to 0.5 percent in March 2020 (effective January 2021);
  - has remained unchanged since then.
- Luxembourg entered a cyclical downturn in mid-2022, primarily reflecting unfavorable demand shocks.
- Post-COVID rise in inflation driven by expectations, cost-push shocks (possibly international food and energy price spikes), and robust domestic demand.
- Credit gap dynamics:
  - credit gap narrowed significantly after remaining positive under low-for-long interest rates and was almost closed in early 2022.
  - tightening of ECB’s monetary policy and bank capital buffers are driving lending rates up toward estimated neutral level.

### Policy experiment results and macroprudential insights
- Tightening macroprudential stance (higher CCyB) produces:
  - rapid contraction of credit volumes and increase in lending rates;
  - partial increase in bank capital-to-loan ratios, deleveraging via loan cuts, and higher lending rates.
- Quantitative impact of macroprudential tightening on real economy is relatively modest under model parameterization — suggesting a favorable trade-off for Luxembourg.
- Response of macroprudential policy:
  - positive credit demand shocks (boost credit growth and market lending rates) prompt swift tightening of macroprudential policy;
  - adverse credit supply shocks (higher lending rates and reduced credit supply) lead to relaxation of macroprudential stance.
- Robustness checks with three macroprudential rule variations (less to more aggressive) show:
  - faster convergence to equilibrium with more aggressive responses;
  - overall macroeconomic impact remains mild across scenarios.
- Forecast baseline (data up to 2022Q2):
  - with increasing policy and lending rates, short-term economic slack is predicted, mainly from weak external demand;
  - negative output gap and above-trend unemployment prevailing until late 2024;
  - demand for credit will fall and further narrow the positive credit gap, triggering a prescribed reduction in minimum capital requirements to reduce lending rate gaps and support credit demand.
- Macroprudential rule design implication:
  - focusing on the credit indicator and assigning different weights to credit and asset prices (house prices) can avoid undue volatility of macroprudential policy responses.

### Model features and technical notes
- Nominal interest rate rigidity ensures sluggish adjustment of lending rates and credit supply to shocks and policy changes.
- Core model consists of five main building blocks (aggregate demand, NK Phillips Curve, monetary policy, banking/credit sector, macroprudential regulator); see source for detailed block descriptions.
- Monetary policy is exogenous to the small open economy context and set by the regional central bank (ECB); Annex I contains details on euro-area mapping.

*Source: Annex I. Main Features of the Euro Area Model, IMF Working Paper "A Semi-Structural Model for Credit Cycle and Policy Analysis" (content unit provided).*

### 1. Output (dynamic IS curve),

### 1. Output (dynamic IS curve),

### Output (dynamic IS curve) — model assumption on expectations
- Expectations are rational, i.e., the model assumes that economic agents, including banks, know the dynamics of the economy and the behavior of key macroeconomic variables (model-consistent expectations).

### Inflation (New Keynesian Philips curve)
- Model incorporates a New Keynesian Philips curve for inflation dynamics.

### Macroprudential policy rule
- The model includes a macroprudential policy rule as a mechanism for affecting credit and financial stability.

### Empirical illustrations and chart annotations (as presented)
- Chart: Contribution to Credit Growth
  - Label: Contribution to Credit Growth
  - Specification: (YoY change, in percent, non-bank resident customers, DoBs)
  - Series labels shown: NFCs; HHs; Non-bank FIs; Captive Financial Institutions; Government; Total (RHS)
  - Vertical axis ticks (percent): -25, -20, -15, -10, -5, 0, 5, 10, 15
  - Horizontal axis years: 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019, 2020
  - Sources: BCL; and IMF staff calculation

- Chart: Evolution of Mortgages and Interest Rates
  - Title: Evolution of Mortgages and Interest Rates
  - Units: (In million EUR (LHS), in percent (RHS))
  - Series labels shown: New mortgages (SA); Interest rates, weighted average (RHS)
  - Left axis ticks (million EUR): 0, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000
  - Right axis ticks (percent): 0, 0.5, 1, 1.5, 2, 2.5, 3, 3.5
  - Horizontal axis years: 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019, 2020, 2021, 2022
  - Sources: BCL and IMF staff calculations

### Key methodological points (from the source fragment)
- The model is semi-structural and designed for credit cycle and policy analysis.
- Core blocks include:
  - Output: dynamic IS curve
  - Inflation: New Keynesian Philips curve
  - Policy tools: macroprudential policy rule

*IMF WORKING PAPERS A Semi-Structural Model for Credit Cycle and Policy Analysis — INTERNATIONAL MONETARY FUND*

### 5. Exogenous monetary policy (set by the ECB).

### 5. Exogenous monetary policy (set by the ECB)

### Notation and model setup
- Variables: trend component denoted by superscript * (lower-case letter with *), cyclical component denoted by lower-case letter without *; x = X − x*.
- Frequency: quarterly; growth rates are quarter-over-quarter, annualized and seasonally adjusted.
- (e) denotes foreign economy; (ss) denotes steady-state variables.
- All variables except inflation and interest rates are in natural log terms so changes ≡ growth rates and deviations from trends measured in percentage points.
- Foreign/domestic real exchange dynamics: Zt = 100*(log CPI^e_t − log CPI_t), real exchange rate gap z_t = Z_t − z_t^* with z_t = ρ_z z_{t−1} + ε^z_t and z_t^* = z_{t−1}^* + ε^{z*}_t.

### A. Output and inflation (demand and supply blocks)
- Open-economy IS (aggregate demand) equation (quarterly, gaps):
  - y_t = β_lead y_{t+1} + β_lag y_{t−1} + β_y y_t^e + β_z z_t − β_r r_t^L + β_c c_t − β_π ε_t^π + ε_t^y
  - Credit channel included via real lending rate r_t^L and volume of credit c_t.
  - Foreign demand enters via euro area output gap y_t^e and real exchange rate gap z_t.
  - Persistence via y_{t−1} and forward-looking y_{t+1}.
- New Keynesian Phillips Curve (open economy):
  - π_t = (1−α_lag) π_{t+1} + α_lag π_{t−1} + α_y y_t + α_z (π_t^{eA} − π_t^A) + ε_t^π
  - Annualized real exchange rate change ∆z_t^A = π_t^{eA} − π_t^A enters inflation dynamics.
- Definitions:
  - Output gap: y_t = Y_t − y_t^* where Y_t ≡ 100*ln(GDP).
  - Potential output evolves: y_t^* = y_{t−1}^* + (1/4) g_t + ε_t^{y*}; g_t reverts to g_ss with shock ε_t^g.
  - Annual inflation π_t^A = (∑_{i=0}^3 π_{t−i})/4.

### B. Credit market and banking sector (credit demand, lending rate, bank capital)
- Credit demand (real, gap form):
  - c_t = θ_1 y_{t−1} + θ_2 c_{t−1} − θ_3 r_t^L + ε_t^{CD}
  - Credit gap defined as real credit C_t ≡ 100*ln(CRED/DEF) minus trend c_t^*; trend evolves c_t^* = c_{t−1}^* + (1/4) g_t^c + ε_t^{c*}.
- Lending rate gap (banks' supply of credit):
  - r_t^L = δ_0 r_{t−1}^L − δ_1 (k_{t−1}^{act} − k_{t−1}^{reg} − k_{ss}^{buff}) + δ_2 r_t + δ_3 lev_{t−1} − δ_4 p_{t−1}^h + ε_t^{rL}
  - Real interbank rate gap r_t = R_t − r_t^* with R_t = i_t − π_{t+1}^e and r_t^* = r_t^{e*} − ∅_t.
  - Bank capital buffer defined as (k_t^{act} − k_t^*); trend k_t^* follows AR(1).
- Bank capital dynamics (capital buffer):
  - k_t^{act} − k_t^* = ψ_5 (k_t^{reg} − k_t^*) + (1 − ρ_{kact}) k_{ss}^{buff} + ρ_{kact} (k_{t−1}^{act} − k_{t−1}^*) + ψ_6 (g_{t−1}^c − g_{t−1}^{c*}) + ψ_7 D_{2008} + ψ_8 D_{2014} + ε_t^{kact}
  - Persistence captured by ρ_{kact}; ψ_5 < 1 so changes in minimum capital requirements implemented partially in current period.
  - Dummies D_{2008} and D_{2014} capture phasing-in of Basel II and III capital requirements.
- Leverage and house prices:
  - lev_t = c_t − A_t where A_t (assets available) follows AR(1) and depends on y_{t−1} and p_{t−1}^h.
  - House price gap p_t^h = ρ_h p_{t−1}^h − σ_3 u_{t−1} + ε_t^{p_h}; unemployment gap u_t linked to y_t via Okun’s law.

### C. Macroprudential policy rule (minimum capital requirements)
- Policy rule for regulatory minimum capital requirement (gap form):
  - k_t^{reg} − k_t^* = ψ_1 (k_{t−1}^{reg} − k_{t−1}^*) + ψ_2 c_{t−1} + ψ_3 (g_{t−1}^c − g_{t−1}^{c*}) + ψ_4 p_{t−1}^h + ε_t^{kreg}
  - ψ_2, ψ_3, ψ_4 capture responsiveness to credit level, credit growth, and house price gap respectively.
  - ψ_1 captures persistence in decision making (higher ψ_1 → less effective countercyclical response).
  - When credit and house price gaps are zero and credit grows at trend g_t^{c*}, k_t^{reg} = k_t^* (neutral level).
- Comment: rule focuses on financial cycle indicators; interactions with business cycle via output and unemployment effects on credit and houses and via lending rate → output channel.

### V. Data, calibration, Bayesian estimation, and model validation
- Data:
  - Quarterly Luxembourg and euro area series, 2003Q1–2019Q4 for estimation (COVID excluded).
  - Luxembourg variables: real GDP, GDP deflator, HICP, unemployment rate, aggregate credit, nominal bank lending rate, bank balance sheet indicators, capital ratios, minimum capital requirements; euro area macro indicators included.
- Calibration and estimation:
  - Mixture of calibration and Bayesian estimation; calibrated shocks' dynamics and steady-state parameters; calibrated responses guided by literature and data.
  - Example calibration targets:
    - A 1 percentage point increase in the countercyclical capital buffer reduces the credit gap by about 0.5 percentage points over 5 quarters.
    - ψ_1 = 0.8 (persistence of minimum capital requirements).
    - ψ_5 = 0.2 (see Annex III).
  - Bayesian estimation: sample 2003Q1–2019Q4, priors imposed, 500,000 simulated paths for posterior, acceptance ratio ≈ 20%.
- Key estimated parameters (posterior modes highlighted in text):
  - β_r = 0.075
  - β_c = 0.028
  - θ_2 = 0.83 (credit persistence)
  - δ_2 = 0.83 (interbank rate importance for lending rates)
  - ψ_1 = 0.8 (policy persistence)
- Model validation and fit:
  - Moment-matching via bootstrap: 10,000 simulated paths for 2010Q1–2020Q4; means and variances of simulated moments close to data; real credit growth variance higher in model (higher rejection rate 16%).
  - Pseudo out-of-sample forecasts: recursive 1- to 6-quarter forecasts over 2016Q1–2020Q4 using data up to 2019Q4; forecasts conditional on exogenous supervisory changes and WEO euro area trajectories (October 2022 vintage).
  - Forecast performance vs reduced-form benchmarks (VAR/ARMA):
    - Model outperforms VAR for most variables and horizons.
    - Average ratio of RMSEs below 0.7 for output growth, lending rate, and credit growth.
    - Inflation: model RMSE ratio > 1; accuracy not statistically different from ARMA benchmark.

### VI. Model properties — impulse responses and transmission
- Minimum capital requirement shock (unexpected one-off 1 percentage point increase in minimum capital requirements; endogenous regulator deactivated to show "pure" effect):
  - Banks increase capital-ratio holdings only partially (≈ 0.2 percentage points at peak).
  - Lending rates increase by 0.16 pp at peak.
  - Credit gap turns negative, reaching −0.5 percent after five quarters.
  - Credit growth (qoq annualized) declines (figures show negative credit growth responses).
  - Output gap peak deviation ≈ −0.25 percent.
  - Unemployment deviates by 0.04 percentage points at the peak.
  - Inflation almost unchanged due to low sensitivity (α_Y = 0.005).
  - Persistence: ψ_1 = 0.8 and ρ_{kact} = 0.3 contribute to gradual fade-out.
- Structural shocks (all shocks simulated are 1 percent, unexpected): two policy stances considered for macroprudential authority
  - Dovish: low responsiveness to financial cycle (ψ = ψ_low).
  - Hawkish: high responsiveness to financial cycle (ψ = ψ_high).
  - Counterfactual: macroprudential policy inactive (ψ = 0).
- Responses to aggregate demand shock:
  - 1-percent positive demand shock: small impact on inflation (0.01 percent), credit gap ~ +0.7 percent at quarter 2.
  - Hawkish macroprudential response raises minimum capital requirements (peak +0.45 pp under Hawkish), increases lending rates and accelerates convergence of credit to trend.
- Responses to aggregate supply (cost-push) shock:
  - Output and credit contract; macroprudential authority eases policy (cuts minimum capital requirements) to restore equilibrium; milder response than to demand shock.
- Use of credit-to-GDP gap in rule:
  - If policy reacts to credit-to-GDP gap instead of credit gap, procyclical responses can emerge because credit-to-GDP can move opposite to credit gap initially (output responses dominate), introducing undesirable volatility.
- Credit demand shock:
  - Positive credit demand shock triggers tightening of macroprudential stance; under Hawkish stance minimum capital requirements can rise up to 0.5 pp at peak.
  - Higher lending rates and lower credit growth follow; Hawkish stance shortens time to stabilize credit by about two quarters relative to Dovish and four quarters relative to inactive policy.
  - Limited real economy impact due to low sensitivity of output to credit and rates.
- Credit supply shock:
  - Adverse credit supply shock raises lending rates exogenously and lowers credit; macroprudential authority cuts minimum capital requirements to allow banks to use buffers, supporting credit and output recovery.

### Interpretation of historical developments (filtration and shock decomposition)
- Estimation via Kalman filter for 2008–2022:
  - Output gap:
    - Persistent positive output gap during 2015–2019.
    - Large temporary negative output gap in 2020 driven by external euro area contraction and domestic supply shocks (COVID).
    - Post-COVID expansion yielded positive output gap through 2021; mid-2022 the output gap turned slightly negative due to unfavorable demand shocks.
  - Inflation since 2021:
    - Driven primarily by supply shocks (food/energy prices), inflation expectations, and to lesser extent aggregate demand.
    - Supply shocks and expectations have abated more recently.
  - Credit cycle:
    - Positive credit gap persisted for an extended period due to low lending rates and high credit persistence; narrowed since early 2021 and nearly closed in early 2022 (≈ 1 percent above long-term trend).
    - Real lending rate gap near neutral level by mid-2022 as policy rate tightening and changes in banks’ buffers offset previous accommodative influences.
  - Lending rate gap drivers:
    - Bank capital buffers and policy rate are important drivers; lending rate evolved below equilibrium in 2012–2020 due to ECB accommodation and large capital buffers.
    - Mid-2022 lending rate gap almost closed.

### VII. Out-of-sample forecasts and macroprudential policy implications (2023–2027)
- Baseline assumptions for euro area:
  - Uses WEO October 2022 vintage.
  - Euro area: weak growth and high inflation short term; output gap negative until mid-2024; monetary policy normalization with ECB policy rate reaching neutral by early 2023 (as assumed in WEO vintage).
- Model projections (Luxembourg, baseline 2023–2027):
  - Under baseline, Luxembourg business and credit cycles deteriorate in near term.
  - Given credit gap as of 2022Q2, the model suggests keeping macroprudential stance unchanged initially.
  - Output gap remains negative until end-2024 and gradually closes over medium term.
  - Labor market cools with unemployment gap turning positive by early (projection period).

*Source: IMF Working Paper — “A Semi-Structural Model for Credit Cycle and Policy Analysis”, chapter 5 (Exogenous monetary policy set by the ECB), wpiea2024140-print-pdf.*

### 2024. Weaker economic activity and increasing lending rates (driven by higher ECB policy rates) would reduce

### 2024. Weaker economic activity and increasing lending rates (driven by higher ECB policy rates) would reduce

### Baseline forecasts and dynamics (2023–2027)
- Conditional on (i) the information set available up to 2022Q2; (ii) the October 2022 WEO projections for the Euro area; (iii) the calibration of the MPP rule; and (iv) the materialization of the projected tightening in financial conditions, the macroprudential authorities would loosen the macroprudential policy stance, reducing the minimum capital requirements by up to 5 percentage points under the most aggressive policy stance.
- Lending rates decline, and credit recovers, although at a slower pace:
  - The lending rate gap is projected to decline relatively quickly, turning negative by early 2025.
  - Lower lending rates help support credit demand and lead to sustained credit growth over the medium term.
  - Given the strong persistence of credit, the credit cycle would fully recover only over the medium term.
- The model projects Luxembourg's business and credit cycles to deteriorate until late 2024.

### Policy rule behavior and volatility
- A policy rule that assigns equal weights to credit and housing market indicators initially projects a procyclical policy response (higher minimum capital requirements), followed by some loosening of the policy stance.
  - As of 2022Q2, the house price gap was large (estimated at 15 percent), while the credit gap was almost closed.
  - A rule giving identical weights to the house price and credit gaps would imply tightening the macroprudential stance early, further deteriorating the credit cycle, and then loosening later as gaps narrow—creating instability in the macroprudential response.
- The instability of the macroprudential policy response is undesirable because it exacerbates fluctuations in the credit cycle and potentially heightens economic volatility.
- Adopting a positive neutral CCyB could soften the adverse shocks’ impact on credit and economic activity and make the macroprudential policy rule less sensitive to assessments of the credit and asset price gaps, avoiding unnecessary volatility in the rule.

### Model structure, shocks, and key mechanisms
- The paper incorporates macro-financial linkages and an active banking sector into a canonical semi-structural New-Keynesian model, extending the multivariate filter approach of Baba et al. (2020) and incorporating:
  - Supply and demand for bank loans derived from micro-foundations in Dib (2010).
  - Financial accelerator mechanisms inspired by BGG and KM.
  - A countercyclical macroprudential policy rule.
- Shocks affecting banks' marginal costs of loan supply and household preferences propagate to aggregate demand, output, interest rates, and credit volumes.
- Changes in the countercyclical macroprudential rule have meaningful effects on credit market equilibrium, interest rates, and both business and credit cycles.
- Quantitatively, tightening the macroprudential stance in Luxembourg prompts a contraction in credit volumes and an increase in lending rates, but only a relatively modest impact on the real economy (output, unemployment, and inflation), indicating a favorable trade-off for such policies for Luxembourg.

### Selected calibrated parameters and steady-state values (preserved exactly)
- Persistence of the trend output growth: 0.950
- Sensitivity of inflation to output gap: 0.005
- Persistence of the trend credit growth: 0.700
- Persistence of the trend lending rate: 0.980
- Persistence of the asset price gap: 0.800
- Sensitivity of credit demand to real lending rate: 1.800
- Persistence of real lending rate: 0.005
- Sensitivity of the real lending rate to bank capital buffer: 0.195
- Persistence of the minimum capital requirements: 0.800
- Sensitivity of the macroprudential rule to credit gap: [0.000, 0.150]
- Sensitivity of the macroprudential rule to credit growth: [0.000, 0.100]
- Sensitivity of the macroprudential rule to house price gap: [0.000, 0.150]
- Sensitivity of bank capital buffer to minimum capital requirements: 0.200
- Persistence of the trend bank capital: 0.950
- Persistence of the unemployment gap: 0.800
- Persistence of the real interbank rate's trend: 0.900
- Persistence of the risk premium: 0.800

Steady state
- Trend output growth: 2.500
- Trend aggregate credit growth: 2.500
- Non-financial private sector's risk premium: 1.500
- Trend bank capital ratio: 25.000
- Long-term bank capital buffer: 14.000
- Long-term unemployment rate: 5.800
- Long-term risk premium: 0.000
- Long-term Euro Area interbank rate: 0.000

Shocks (selected standard deviations)
- Standard deviation of the shock to potential output: 0.001
- Standard deviation of the shock to potential growth: 0.001
- Standard deviation of the shock to the equilibrium unemployment rate: 0.001
- Standard deviation of the shock to trend credit: 0.001
- Standard deviation of the shock to trend credit growth: 0.009
- Standard deviation of the shock to trend bank capital: 0.200
- Standard deviation of the asset price shock: 0.020

Euro area model key steady states and parameters
- Forward-looking expectations on output gap (훽_lead_e): 0.500
- Persistence of output gap (훽_lag_e): 0.550
- Persistence of the real interbank rate’s trend (⁡휌_r_e*): 0.050
- Sensitivity of inflation to output gap (훼_y_e): 0.050
- Trend output growth (푔_ss_e): 1.200
- Long-term euro area inflation target (휋_ss_e_target): 1.800
- Long-term euro area interbank rate (푟_ss_e*): 0.000

### Policy implications and recommendations
- Macroprudential authorities should design the policy rule to avoid undue volatility in the macroprudential response; equal weighting of credit and housing gaps can lead to procyclical and unstable outcomes.
- Consideration of a positive neutral CCyB is recommended to:
  - Soften the impact of adverse shocks on credit and economic activity.
  - Reduce sensitivity of the macroprudential rule to short-run assessments of credit and asset price gaps.
  - Avoid unnecessary volatility in minimum capital requirements and the credit cycle.

*Source: IMF Working Paper — A Semi-Structural Model for Credit Cycle and Policy Analysis (selected excerpts).*

### References

### wpiea2024140-print-pdf - References

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### Bank capital, macroprudential policy, and countercyclical measures
- Van den Heuvel, S. (2008). “The welfare cost of bank capital requirements,” Journal of Monetary Economics 55, p. 298-320.
- Valencia, O., and Ortiz Bolaños, A. (2018). “Bank Capital Buffers Around the World: Cyclical Patterns and the Effect of Market Power’, Journal of Financial Stability, vol. 38, pp. 119-131.
- Jiménez, G., Ongena, S., Peydró, J., and Saurina, J. (2017). “Macroprudential Policy, Countercyclical Bank Capital Buffers, and Credit Supply: Evidence from the Spanish Dynamic Provisioning Experiments,” Journal of Political Economy, vol. 125, no. 6.
- ECB (2023). “A Positive Neutral Rate for the Countercyclical Capital Buffer – State of Play in the Banking Union”, Macroprudential Bulletin No. 21.
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### Models, model-based analysis, and projection frameworks
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- Karam, P., Pranovich, M., and Vlcek, J. (2021). “An Extended Quarterly Projection Model: Credit Cycle, Macrofinancial Linkages and Macroprudential Measures: The Case of the Philippines,” IMF Working Paper 21/256, International Monetary Fund, Washington, DC.
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- Carabenciov, I., Ermolaev, I., Freedman, C., Juillard, M., Kaminek, O., Korshunov, D., and Laxton, D. (2008). “A Small Quarterly Projection Model of the U.S. Economy.” IMF Working Paper 08/278, International Monetary Fund, Washington, DC. 

### Financial cycles, potential output, and related BIS work
- Borio, C, Disyatat, P., and Juselius, M. (2013). “Rethinking potential output: embedding information about the financial cycle”, BIS Working Papers, no. 404, February. 
- Borio, C, Disyatat, P., and Juselius, M. (2014). “A parsimonious approach to incorporating economic information in measures of potential output’, BIS Working Papers, no. 442, February. 
- Galati, G., and Moessner, R. (2011).  “Macroprudential Policy - a Literature Review. BIS Working Papers No 337. 
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### Country and regional studies, housing, lending rates, and tax treatment
- International Monetary Fund (2018). “Housing Market: Assessment and Policy Recommendations,” Luxembourg Selected Issues Paper, IMF Country Report, 18/97, International Monetary Fund, Washington, DC.
- International Monetary Fund (2021). Staff Report for the 2021 Article IV Consultation for Luxembourg, IMF Country Report, 21/93, International Monetary Fund, Washington, DC.
- International Monetary Fund (2023). “Restoring Price Stability and Securing Strong and Green Growth,” Regional Economic Outlook for Europe, November 2023, International Monetary Fund, Washington, DC.
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- Karmelavičius, J., Mikaliūnaitė-Jouvanceau, J., and Buteikis, A. (2023). “What drove the rise in bank lending rates in Lithuania during the low-rate era?”, Baltic Journal of Economics, Vol. 23, no. 2., pp. 162-199.
- Marcucci, J., and Quagliariello, M. (2009). “Asymmetric effects of the business cycle on bank credit risk,” Journal of Banking & Finance, Volume 33, Issue 9. 

### Empirical evidence on credit supply, spreads, and market power
- Jiménez, G., Ongena, S., Peydró, J., and Saurina, J. (2017). “Macroprudential Policy, Countercyclical Bank Capital Buffers, and Credit Supply: Evidence from the Spanish Dynamic Provisioning Experiments,” Journal of Political Economy, vol. 125, no. 6.
- Valencia, O., and Ortiz Bolaños, A. (2018). “Bank Capital Buffers Around the World: Cyclical Patterns and the Effect of Market Power’, Journal of Financial Stability, vol. 38, pp. 119-131. 
- Kiyotaki, N., and Moore, J. (1997). “Credit Cycles,” Journal of Political Economy, 105 (2), pp. 211-48. 

*Content extracted from the References section of wpiea2024140-print-pdf*

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_Source: https://www.imf.org/-/media/files/publications/wp/2024/english/wpiea2024140-print-pdf.pdf_