## 1. Korea: Macroprudential Model Simulations, 2002–2010

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### Introduction: definition, motivation, and scope
- Macroprudential policies (MaPPs) are a set of financial policies aimed at limiting, mitigating or reducing systemic financial risk.
- Paper focus:
  - Time-series dimension of systemic risk.
  - Stylized model for MaPPs that targets system-wide banking aggregates.
- Rationale for MaPPs:
  - Monetary policy is a blunt tool for some financial risks; MaPPs can more precisely target sectoral or balance-sheet vulnerabilities.
  - In an open economy, cross-border linkages and excess external liquidity can fuel domestic credit growth beyond the control of monetary policy.
  - MaPPs can complement macroeconomic policy to prevent leverage from increasing beyond cyclical norms.

### Korea’s experience motivating the model
- Key empirical points:
  - Loan-to-deposit ratios rose above 140 percent in the period leading up to the global crisis.
  - Credit growth hovered around 20 percent per annum while bank deposits remained stable.
  - Non-core liabilities (defined as non-deposit liabilities in this paper) and bank credit moved beyond the cycle; deposits remained very stable.
  - Currently, about 70 percent of non-core liabilities of the Korean banking system are external.
- Policy responses (post-crisis and since November 2009):
  - A 100 percent loan-to-deposit ratio limit.
  - A macroprudential levy on short-term debt and other measures.
- Details of the levy:
  - The levy is less than 0.5 percent and is determined by remaining maturity of non-core liabilities:
    - 0.2 percent for maturities of less than one year;
    - 0.1 percent for maturities of one to three years;
    - 0.05 percent for maturities of three to five years;
    - 0.02 percent for maturities over five years.
  - For a period of rapid capital inflows, the government has discretion to impose a maximum surcharge of 0.5 percent that varies depending on net capital inflows.
  - The overall levy cannot exceed 1.0 percent, and the surcharge cannot be imposed for more than six months.

### Need for a coherent MaPP framework
- Observed shortcomings of Korea’s measures:
  - Effective in limiting wholesale funding and short-term external debt but viewed as targeted/ad hoc.
  - Policy framework lacked clarity on circumstances for abolition or adjustment of the levy.
  - No clear triggers (e.g., thresholds of short-term debt or GDP growth) specified.
- Proposed approach:
  - Stylized, model-based building block: simple tax rates on systemic risk indicators that respond smoothly to deviations from thresholds over the business cycle.
- Advantages of model-based MaPP tax rates:
  - Respond to the macroeconomic cycle for smooth and timely responses to buildup of vulnerabilities.
  - Apply to system-wide aggregates, leaving bank-specific supervision to microprudential policies.
- Limitations:
  - Partial equilibrium model; takes macroeconomic policy as given.
  - Does not assess optimality of thresholds themselves.
  - Alternative models (e.g., countercyclical capital requirements) not compared here.

### Stylized partial equilibrium model: objectives, instruments, and objective function
- Focus:
  - Mitigate excessive buildup of leverage over the economic cycle.
  - Emphasis on non-core liabilities and assets relative to non-core liabilities.
- Policy instruments:
  - Taxes on the entire banking system proportional to quadratic deviations from set thresholds for:
    - non-core liabilities to GDP; and
    - assets to non-core liabilities.
  - Quadratic form captures increasing sensitivity to larger deviations and higher volatility as system size increases.
- Objective function:
  - Macroprudential policy maker (MPM) minimizes a quadratic loss function depending on deviations of banking system ratios from desired thresholds adjusted for the economic cycle.
  - Numeric simulations based on MPM’s relative preferences for different financial ratios.

### Model structure: two-stage game and comparative statics
- Stage 1 — Banking system:
  - Representative bank maximizes economic value added (EVA): revenue net of financing costs and MaPP taxes.
  - Assumptions:
    - Operating costs, cost of core liabilities and cost of capital are fixed.
    - Capital and deposits initially assumed fixed; expanding assets by $1 requires increasing non-core liabilities by $1.
    - MaPP taxes imposed on quadratic ratios of non-core liabilities to GDP and assets to non-core liabilities.
  - Taxed ratios interpretation:
    - Non-core liabilities capture unstable portion of bank leverage.
    - Assets to non-core liabilities capture leverage of the non-financial private sector relative to bank leverage.
  - First-order conditions imply higher tax rates on the targeted ratios reduce assets/GDP, non-core liabilities/GDP, and assets/non-core liabilities.
- Stage 2 — Macroprudential policy maker (MPM):
  - MPM sets tax rates to minimize quadratic loss function taking banking reaction as given.
  - Targets are state-contingent:
    - Target for non-core liabilities to GDP parameterized as alpha(1) adjusted by alpha(2) times the output gap and alpha(3) times growth of GDP relative to potential.
    - Target for assets to non-core liabilities parameterized as beta(1) adjusted by beta(2) times the output gap and beta(3) times growth of GDP relative to potential.
  - Cycle adjustments interpretation:
    - When output is at potential (output gap = 0) and growing at potential (g = 0), thresholds are alpha(1) and beta(1).
    - If output is above potential or growing above potential, MPM thresholds decrease (policy leans against the wind).

### MPM optimization and capital constraint variants
- MPM chooses tax rates on non-core liabilities and on assets to non-core liabilities by substituting banking first-order conditions into MPM’s objective.
- Special case (no upper bound on τ1 and τ2):
  - First-order conditions (FOCs) presented in the source (preserved verbatim).
  - Closed-form solutions for τ1* and τ2* provided in the source (expressions preserved there).
- General case with upper bounds on τ1 and τ2 solved numerically.
- Regulatory capital adequacy constraint:
  - To achieve capital adequacy of k_min, MPM should set β1 = 1/(1−λ) (expression in source) to ensure compliance with minimum capital adequacy ratio requirement.

### Model with direct capital constraint (variable capital as ratio of RWA)
- Banking system holds capital K ≥ θ·RWA and in equilibrium keeps minimum regulatory capital ratio k_min = K/RWA.
- Define λ ≡ k_min·w and use balance sheet identity to express liabilities as a function of assets: L = (1−λ)^{-1} D_A^* (as in text).
- MaPP reduces to a single tax rate τ on assets to GDP (τ on A/Y).
- Banking FOC and optimal assets:
  - FOC presented as equation (6) in the source.
  - Optimal A*/Y expression given as equation (7) in the source.
- Comparative statics (from equation (7) and text):
  - Optimal A increases with return on assets, r_a.
  - Optimal A decreases with higher cost of non-core funding, c_nc, including cost of capital, c_k, and as taxes τ increase.
  - r_a, c_nc and c_k are market-determined; λ determined by banks’ balance sheets.
  - A lower λ raises funding costs c_nc and c_k; partial equilibrium model assumes this possibility away.
- Effectiveness of τ in controlling A/Y:
  - ∂(A*/Y)/∂τ given by equation (8) in the source.
  - Imposing τ becomes more effective in containing A/Y under higher leverage ratio and/or higher risk premium.
- MPM solves constrained minimization:
  - min_τ [ (A/Y − α1)^2 + (α2·y − g)^2 + ... ] subject to (7) and 0 ≤ τ ≤ τ_max (problem statement preserved).
  - FOC leads to closed-form τ* given in equation (9) in the source.
- Policy implication:
  - When setting τ, regulatory authority should consider r_a, c_nc, c_k (market-determined) and λ (banks’ balance-sheet determined).

### Simulations calibrated to Korea (2002–2010)
- Calibration details:
  - Model calibrated to Korean data for 2002–2010.
  - Return on assets and unit cost of non-core liabilities held constant at their actual averages of the last 10 quarters of the sample.
  - α1 and β1 set to long-term averages of non-core liabilities to GDP and assets to non-core liabilities in Korea.
  - α2, β2, α3, β3 set at arbitrary levels in the baseline; sensitivity analysis conducted in alternative scenarios.
- Baseline parameter values (as given in Table 1 line):
  - α1 α2 α3 β1 β2 β3
  - 0.6 3.0 3.0 1.9 1.0 1.0
- Scenarios simulated:
  - Baseline (bold solid black): MaPPs respond to both GDP level and growth. Policy rule raises τ1 and τ2 when GDP is above potential and growing above potential; lowers them when GDP is below potential and growing below potential.
  - Scenario 2 (solid blue): MaPPs care only about the output gap (α2=0, α3=0, β2=0, β3=0). Optimal τ paths follow output gap more closely.
  - Scenario 3 (dotted red): MaPPs care only about growth relative to potential (α2=0, β2=0, α3≠0, β3≠0). Optimal τ paths follow GDP growth (net of potential) more closely.
- Figure and series notes (preserved from source):
  - tau1 (tax rate on Non-core Liabilities/GDP; percent) plotted with values around 0.72–0.80 for 02Q1–10Q3.
  - tau2 (tax rate on Assets/Non-core Liabilities; percent) plotted with values around 1.92–2.08 for 02Q1–10Q3.
  - Real GDP Growth Minus Potential Growth (percent) scale shown −6 to 4.
  - Output Gap (percent) scale shown −5 to 3.
  - Assets/GDP, Non-core Liabilities/GDP, Assets/Non-core Liabilities time series plotted for 02Q1–10Q3 and 12/1/2001–12/1/2010.
  - Unit cost of capital, return on assets, and unit cost of non-core liabilities plotted in Figure 3.

### Simulation findings and quantitative results
- MaPPs on assets and non-core liabilities substantially contain systemic risk indicators:
  - Simulated non-core liabilities/GDP, assets/non-core liabilities and assets/GDP are more dampened over the cycle than actual trends, while preserving similar trends.
- Model with variable capital yields similar simulation results to the baseline: τ1 on Assets/GDP is set in line with the economic cycle.
- Time span used in calibration: 2002–2010.
- Return and cost assumptions: constant at their actual averages of the last 10 quarters of the sample (as stated).

### Main conclusions and policy recommendations
- MaPPs that set tax rates on assets/non-core liabilities and non-core liabilities/GDP can act as a second lever to dampen credit growth and banking-system leverage beyond cyclical norms.
- MaPPs should be set in line with the economic cycle:
  - Raise tax rates when GDP is above potential and growing above potential.
  - Reduce tax rates when GDP is below potential and growing below potential.
- Regulatory authorities, when setting MaPP tax rates, should consider market-determined variables r_a, c_nc, c_k and banks’ balance-sheet variable λ.
- Implementation guidance:
  - Actual implementation of such taxes—including the macroprudential stability levy in Korea—should be transparent and predictable.
  - Avoid frequent adjustments even if the model indicates incremental changes, analogous to monetary policy under inflation targeting.

*Source: IMF staff paper excerpt — “1. Korea: Macroprudential Model Simulations, 2002–2010”*

### 1. Korea: Macroprudential Model Simulations, 2002–2010 ..............................................15

### 1. Korea: Macroprudential Model Simulations, 2002–2010

### Introduction: definition, motivation, and scope
- Macroprudential policies (MaPPs) are a set of financial policies aimed at limiting, mitigating or reducing systemic financial risk.
- The paper focuses on the time-series dimension of systemic risk and develops a stylized model for MaPPs that targets system-wide banking aggregates.
- Rationale for MaPPs:
  - Monetary policy is a blunt tool for some financial risks; MaPPs can more precisely target sectoral or balance-sheet vulnerabilities.
  - In an open economy, cross-border linkages and excess external liquidity can fuel domestic credit growth beyond the control of monetary policy.
  - MaPPs can complement macroeconomic policy to prevent leverage from increasing beyond cyclical norms.

### Korea’s experience motivating the model
- Key empirical points:
  - Korean banks’ loan-to-deposit ratios rose above 140 percent in the period leading up to the global crisis.
  - Credit growth hovered around 20 percent per annum while bank deposits remained stable.
  - Non-core liabilities (defined as non-deposit liabilities in this paper) and bank credit moved beyond the cycle; deposits remained very stable.
  - Currently, about 70 percent of non-core liabilities of the Korean banking system are external.
- Policy responses in Korea (post-crisis and since November 2009) included:
  - A 100 percent loan-to-deposit ratio limit.
  - A macroprudential levy on short-term debt and other measures.
- Details of the actual levy (as described in the source):
  - The levy is less than 0.5 percent and is determined by remaining maturity of non-core liabilities:
    - 0.2 percent for maturities of less than one year;
    - 0.1 percent for maturities of one to three years;
    - 0.05 percent for maturities of three to five years;
    - 0.02 percent for maturities over five years.
  - For a period of rapid capital inflows, the government has discretion to impose a maximum surcharge of 0.5 percent that varies depending on net capital inflows.
  - The overall levy cannot exceed 1.0 percent, and the surcharge cannot be imposed for more than six months.

### Need for a coherent MaPP framework
- The Korean measures were effective in limiting wholesale funding and short-term external debt but were viewed as targeted/ad hoc; the policy framework lacked clarity on:
  - Under what circumstances the levy would be abolished or adjusted.
  - Whether thresholds of short-term debt or GDP growth would trigger changes.
- The paper proposes a stylized, model-based building block for MaPPs: simple tax rates on systemic risk indicators that respond smoothly to deviations from thresholds over the business cycle.
- Advantages of the model-based MaPP tax rates:
  - Respond to the macroeconomic cycle for smooth and timely responses to buildup of vulnerabilities.
  - Apply to system-wide aggregates, leaving bank-specific supervision to microprudential policies.
- Limitations acknowledged:
  - The model is partial equilibrium and does not set macroeconomic policy; it takes macroeconomic policy as given.
  - The model does not assess the optimality of the thresholds themselves.
  - Alternative models (e.g., countercyclical capital requirements) could deliver similar outcomes but are not compared here.

### Stylized partial equilibrium model: objectives and scope
- Focus:
  - MaPPs mitigate excessive buildup of leverage over the economic cycle.
  - Main emphasis on non-core liabilities because these were central in Korea’s crises of 1997 and 2008.
  - The model also targets assets in relation to non-core liabilities.
- Policy instruments:
  - Taxes on the entire banking system proportional to quadratic deviations from set thresholds for:
    - non-core liabilities to GDP; and
    - assets to non-core liabilities.
  - The quadratic form captures increasing sensitivity to larger deviations and higher volatility as system size increases.
- Objective function:
  - The macroprudential policy maker (MPM) minimizes a quadratic loss function that depends on deviations of the banking system’s ratios from desired thresholds adjusted for the economic cycle.
  - The model uses numeric simulations based on the MPM’s relative preferences for different financial ratios.

### Model structure: two-stage game
- Stage 1 — Banking system:
  - The banking system is modeled as a single representative bank that maximizes economic value added (EVA): revenue net of financing costs and MaPP taxes.
  - Assumptions in the banking problem:
    - Operating costs, cost of core liabilities and cost of capital are all fixed.
    - Capital and deposits are initially assumed fixed; an expansion of assets by one dollar requires increasing non-core liabilities by one dollar.
    - MaPP taxes are imposed on quadratic ratios of non-core liabilities to GDP and assets to non-core liabilities.
  - Interpretation of taxed ratios:
    - Non-core liabilities capture the unstable portion of bank leverage.
    - Assets to non-core liabilities capture leverage of the non-financial private sector relative to bank leverage.
  - First-order conditions imply:
    - Higher tax rates on non-core liabilities to GDP and on assets to non-core liabilities result in lower assets/GDP, lower non-core liabilities/GDP, and lower assets/non-core liabilities.
- Stage 2 — Macroprudential policy maker (MPM):
  - The MPM sets tax rates to minimize a quadratic loss function based on deviations of system-wide ratios from targets, taking the banking system’s reaction function as given.
  - Targets are state-contingent and depend on the economic cycle:
    - The target for non-core liabilities to GDP is parameterized as alpha(1) adjusted by alpha(2) times the output gap and alpha(3) times the growth of GDP relative to potential.
    - The target for assets to non-core liabilities is parameterized as beta(1) adjusted by beta(2) times the output gap and beta(3) times the growth of GDP relative to potential.
  - Interpretation of cycle adjustments:
    - When output is at potential (output gap = 0) and growing at potential (g = 0), the MPM imposes thresholds alpha(1) and beta(1).
    - If output is above potential or growing above potential, MPM thresholds decrease (policy leans against the wind).

*Source: IMF staff paper excerpt — “1. Korea: Macroprudential Model Simulations, 2002–2010”*

### 10.      Accordingly, the MPM decides optimal values of the tax rates on non-core

### _wp1227 - 10.      Accordingly, the MPM decides optimal values of the tax rates on non-core

### MPM optimization: objective and first-order conditions
- MPM chooses tax rates on non-core liabilities and on assets to non-core liabilities by solving a minimization problem that substitutes equations (4) and (5) into the MPM’s objective.
- For the special case with no upper bound on τ1 and τ2, FOCs reduce to:
  - 1 τ1 (1 τ2) (r_a)^ψ φ(α1, α2, α3) = 0
  - r_a τ2 φ(β1, β2, β3) = 0
  (as presented in the text; FOC labels and functional forms are preserved verbatim from the source).
- Closed-form solutions in that special case:
  - τ1* = 1/2 β(β1 β2 β3 r_a) ψ φ(α1 α2 α3)
  - τ2* = ... (solution expression given in source)
- For the general case with upper bounds on τ1 and τ2, the model is solved numerically.

- Regulatory capital adequacy constraint:
  - To achieve capital adequacy of k_min, MPM should set β1 = 1/(1−λ) (expression in source) to ensure banks comply with the minimum capital adequacy ratio requirement.

### Model with direct capital constraint (variable capital as ratio of RWA)
- Banking system holds capital K at least as much as risk-weighted assets: K ≥ θ·RWA, and in equilibrium banks keep minimum regulatory capital ratio k_min = K/RWA.
- Define λ ≡ k_min·w (leverage ratio) and use balance sheet identity to express liabilities as a function of assets: L = (1−λ)^{-1} D_A^* (as in text).
- MaPP reduces to a single tax rate τ imposed on assets to GDP (τ on A/Y).
- Banking system’s problem (objective and constraint) yields FOC (equation (6)):
  - FOC: ∂/∂A [ ... ] = 0  (preserved as equation (6) in source)
- Optimal level of assets from FOC (equation (7)):
  - A*/Y = expression as given in the source (equation (7))
- Comparative statics (equation (7) and following text):
  - The banking system increases optimal A as return on assets, r_a, increases.
  - The banking system lowers A with higher cost of non-core funding, c_nc, including the cost of capital, c_k, and as taxes τ increase.
  - r_a, c_nc and c_k are determined by market conditions; λ is determined by banks’ balance sheets.
  - A lower λ raises funding costs c_nc and c_k, but the partial equilibrium model assumes this possibility away.

- Effectiveness of τ in controlling A/Y (equation (8)):
  - ∂(A*/Y)/∂τ = expression given in equation (8).
  - Imposing τ becomes more effective in containing A/Y under higher leverage ratio and/or higher risk premium.

### MPM’s problem under direct capital constraint and solution
- MPM solves:
  - min_τ [ (A/Y − α1)^2 + (α2·y − g)^2 + ... ] s.t. (7); 0 ≤ τ ≤ τ_max  (problem statement preserved)
- FOC for τ is given in the text and leads to closed-form expression (equation (9)):
  - τ* = expression reproduced in the source (equation (9)).
- Policy implication from equation (9):
  - When regulatory authority sets τ, it should consider r_a, c_nc, c_k (market-determined) and λ (banks’ balance-sheet determined).

### Simulations calibrated to Korea (2002–2010)
- Calibration details:
  - Model calibrated to Korean data for 2002-2010.
  - Return on assets and unit cost of non-core liabilities are held constant at their actual averages of the last 10 quarters of the sample.
  - α1 and β1 are set to long-term averages of non-core liabilities to GDP and assets to non-core liabilities in Korea.
  - α2, β2, α3, β3 set at arbitrary levels in the baseline; sensitivity analysis conducted in alternative scenarios.
- Scenarios simulated:
  - Baseline (bold solid black): MaPPs respond to both GDP level and growth. Policy rule raises τ1 and τ2 when GDP is above potential and growing above potential; lowers them when GDP is below potential and growing below potential.
  - Scenario 2 (solid blue): MaPPs care only about the output gap (α2=0, α3=0, β2=0, β3=0). Optimal τ paths follow output gap more closely.
  - Scenario 3 (dotted red): MaPPs care only about growth relative to potential (α2=0, β2=0, α3≠0, β3≠0). Optimal τ paths follow GDP growth (net of potential) more closely.
- Simulation findings:
  - MaPPs on assets and non-core liabilities substantially contain systemic risk indicators: simulated non-core liabilities/GDP, assets/non-core liabilities and assets/GDP are more dampened over the cycle than actual trends, while preserving similar trends.
  - Model with variable capital yields similar simulation results to the baseline (Figure 3): τ1 on Assets/GDP is set in line with the economic cycle.

### Key quantitative and parameter values preserved from the source
- Time span used in calibration: 2002–2010.
- Return and cost assumptions: constant at their actual averages of the last 10 quarters of the sample (as stated).
- Baseline parameter values (as given in Table 1 line):
  - α1 α2 α3 β1 β2 β3
  - 0.6 3.0 3.0 1.9 1.0 1.0
- Figure labels and ranges (preserved as in source figures):
  - tau1 (tax rate on Non-core Liabilities/GDP; percent) plotted with values around 0.72–0.80 for 02Q1–10Q3.
  - tau2 (tax rate on Assets/Non-core Liabilities; percent) plotted with values around 1.92–2.08 for 02Q1–10Q3.
  - Real GDP Growth Minus Potential Growth (percent) scale shown −6 to 4.
  - Output Gap (percent) scale shown −5 to 3.
  - Assets/GDP, Non-core Liabilities/GDP, Assets/Non-core Liabilities time series plotted for 02Q1–10Q3 and 12/1/2001–12/1/2010 as in Figures 1–3.
  - Unit cost of capital, return on assets, and unit cost of non-core liabilities plotted in Figure 3.

### Main conclusions and policy recommendations
- MaPPs that set tax rates on assets/non-core liabilities and non-core liabilities/GDP can act as a second lever to dampen credit growth and banking-system leverage beyond cyclical norms.
- MaPPs should be set in line with the economic cycle: raise tax rates when GDP is above potential and growing above potential; reduce them when GDP is below potential and growing below potential.
- Regulatory authorities, when setting MaPP tax rates, should consider market-determined variables (r_a, c_nc, c_k) and banks’ balance-sheet variables (λ).
- Implementation guidance:
  - Actual implementation of such taxes—including the macroprudential stability levy in Korea—should be transparent and predictable.
  - Avoid frequent adjustments even if the model indicates incremental changes, analogous to monetary policy under inflation targeting.

*Source: Authors' simulations.*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2012/_wp1227.pdf_