## wpiea2020072-print-pdf

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### Stress simulation algorithm: scope and flexibility
- The algorithm is flexible and can accommodate different types of bank lending behavior.
- It can be used to compute:
  - “quasi-static” solutions where all banks behave quasi-statically;
  - “dynamic” solutions where all banks behave dynamically;
  - “mixed” runs where some banks behave dynamically while others follow quasi-static behavior.
- Mixed runs can measure individual bank contributions to systemic risk.
- In country-specific applications, four types of simulations are conducted.

### Simulation types and model consistency
- Dynamic
  - Model‐based (iterated/consistent)? Yes
  - Bank Behavior: Dynamic for all banks
- Quasi‐static
  - Model‐based (iterated/consistent)? Yes
  - Bank Behavior: Quasi‐static for all banks
- Initial
  - Model‐based (iterated/consistent)? No
  - Bank Behavior: Quasi‐static for all banks
- Mixed (Bi‐QS)
  - Model‐based (iterated/consistent)? Yes
  - Bank Behavior: Quasi‐static for bank i; Dynamic for all other banks

### Characteristics and implications of the “Initial” scenario
- Replicates sequential and quasi-static stress testing approach commonly used in policy institutions.
- Procedure: construct multi-year scenario and perform bank stress tests based on these scenarios.
- Main drawbacks:
  - Ex-post outcomes for banks, once aggregated, do not coincide with assumptions made at the scenario design stage.
  - Ex-post inconsistency between banks’ desired lending responses and availability of credit assumed under the initial adverse scenario.
  - Does not account for macro-financial loops.
- Use:
  - “Initial” scenario can be used to kick-start iterated simulations that exhibit ex-post consistency under the model.
  - Paths for aggregate lending and lending rates are included in the “initial” scenarios shown in Section IV to highlight inconsistencies.

### Dynamic, Quasi-static, and Mixed (Bi‐QS) simulations: outcomes and uses
- Dynamic and Quasi-static simulations:
  - Macroeconomic and bank-specific results are outcomes of the analysis.
  - Ex-post consistency between aggregate and bottom-up lending behavior is ensured by model iteration.
  - All banks exhibit dynamic or quasi-static behavior respectively.
- Mixed (Bi‐QS) simulations:
  - Bank i behaves quasi-statically while all other banks behave dynamically.
  - Permit assessment of individual bank contributions to systemic risk.

### Country application: Indonesia — data and sample
- Quarterly macroeconomic data series:
  - Obtained from various sources.
  - Span from 1990:Q1 to 2018:Q2, covering both the Asian and the global financial crises.
- Banking data:
  - Obtained from Fitch (Bankscope).
- Dynamic panel regressions:
  - Cover the entire banking system (118 banks).
  - Performed using quarterly data from Q1:2001 to Q1:2015.
- Stress simulation analysis:
  - Performed on 12 small and large banks that jointly account for 70 percent of the banking system’s assets.

### Baseline and “Initial Adverse” annual paths (Table 4)
- Real GDP growth (percent):
  - Baseline: 2017 5.1; 2018 5.3; 2019 5.5; 2020 5.6; 2021 5.6; 2022 5.6
  - Initial adverse: 2017 5.1; 2018 4.6; 2019 0.6; 2020 1.8; 2021 5.6; 2022 7.8
- Inflation, y-o-y change (percent):
  - Baseline: 2017 3.8; 2018 3.4; 2019 3.7; 2020 3.7; 2021 3.6; 2022 3.6
  - Initial adverse: 2017 3.8; 2018 4.0; 2019 9.6; 2020 12.8; 2021 3.4; 2022 -1.0
- Real effective exchange rate index (2014=100):
  - Baseline: 2017 100.0; 2018 94.2; 2019 94.0; 2020 94.0; 2021 94.0; 2022 94.0
  - Initial Adverse: 2017 100.0; 2018 92.1; 2019 77.2; 2020 78.5; 2021 88.6; 2022 94.0
- Nominal effective exchange rate, y-o-y change (percent):
  - Baseline: 2017 -0.4; 2018 -6.7; 2019 -1.1; 2020 -1.2; 2021 -1.4; 2022 -1.5
  - Initial adverse: 2017 -0.4; 2018 -10.1; 2019 -23.7; 2020 -9.6; 2021 11.4; 2022 9.2
- Nominal interest rate (BI policy rate), percent per annum:
  - Baseline: 2017 4.5; 2018 5.0; 2019 5.3; 2020 5.3; 2021 5.3; 2022 5.3
  - Initial adverse: 2017 4.5; 2018 5.7; 2019 11.6; 2020 12.4; 2021 5.7; 2022 2.2
- International interest rate (Fed Funds Rate), percent:
  - Baseline: 2017 1.0; 2018 2.0; 2019 3.1; 2020 3.7; 2021 3.2; 2022 2.9
  - Initial adverse: 2017 1.0; 2018 2.3; 2019 4.7; 2020 5.6; 2021 4.7; 2022 3.8
- Trading partners' growth (percent):
  - Baseline: 2017 8.4; 2018 4.9; 2019 5.8; 2020 5.7; 2021 5.7; 2022 5.7
  - Initial adverse: 2017 8.4; 2018 3.6; 2019 1.8; 2020 6.5; 2021 6.4; 2022 6.0
- Commodity prices (2007=100):
  - Baseline: 2017 113.5; 2018 130.5; 2019 131.5; 2020 131.5; 2021 131.5; 2022 131.5
  - Initial adverse: 2017 113.5; 2018 114.6; 2019 71.5; 2020 90.0; 2021 108.2; 2022 118.7
- Real bank credit to the private sector growth (percent):
  - Baseline: 2017 3.7; 2018 5.2; 2019 5.0; 2020 5.3; 2021 5.3; 2022 5.3
  - Initial adverse: 2017 3.7; 2018 3.0; 2019 -9.5; 2020 -22.7; 2021 -20.6; 2022 12.3
- Nominal bank credit to the private sector growth (percent):
  - Baseline: 2017 7.5; 2018 8.5; 2019 8.6; 2020 9.0; 2021 8.9; 2022 8.9
  - Initial adverse: 2017 7.5; 2018 7.0; 2019 0.1; 2020 -9.8; 2021 -17.2; 2022 11.3
- Bank lending rate (percent):
  - Baseline: 2017 11.1; 2018 10.5; 2019 10.5; 2020 10.5; 2021 10.5; 2022 10.5
  - Initial adverse: 2017 11.1; 2018 10.8; 2019 13.1; 2020 13.8; 2021 11.1; 2022 8.7

### VAR impulse-response and yields calibration
- VAR includes aggregate credit (R_L) and the lending rate (L_i); impulses are one standard deviation (positive) structural shocks applied for one quarter with endogenous dynamic responses spanning 20 quarters and confidence bands corresponding to (.16,.84) intervals.
- Key impulse-response findings:
  - Shock to trading partners' real GDP (U.S., China, EU) => increase commodity prices, boost domestic real GDP, rupiah appreciation, lower inflation, policy interest rate adjusts downward.
  - Positive shock to commodity prices => boosts domestic real GDP (Indonesia is a commodity exporter).
  - Positive shock to U.S. federal funds rate => reduces Indonesian real GDP via capital outflows and rupiah depreciation.
  - Positive shock to domestic real GDP => raises inflation and the policy interest rate.
  - Positive shock to lending rate => declines in real bank credit and GDP (adverse credit supply shock).
  - Positive shock to real bank credit => raises lending rate (credit demand shock).
- Government and corporate yields:
  - SVAR for domestic policy rate (i_0) and 10-year government bond yield (ir,40G_Y) estimated using quarterly data for 2004:Q1 to 2018:Q3 with two lags, a constant and linear trend.
  - Corporate yields assumed to follow government yields amplified by 30 percent (100 basis point shift in government yields => 130 basis point shift in corporate yields); amplification adjustable for robustness.
  - Iteration algorithm relies on impulse responses of 10-year government yields and short- and 10-year corporate yields to policy rate shocks; corporate rates imposed as 1.3 times corresponding government bond responses.

### Dynamic Panel Estimates — Credit risk and lending blocks
- Credit risk block (logit transform of i_NPLR), regression with bank fixed effects:
  - Lagged dependent variable: sum of coefficients 1 to 20 = 0.85
  - Real GDP growth (lags 2 to 5): sum = -12.33; F-statistic 14.08; marginal significance 0.000
  - Real GDP growth squared (lags 2 to 5): sum = 105.05; F-statistic 2.20; marginal significance 0.066
  - Change in the nominal policy interest rate (lags 2 to 5): sum = 3.52; F-statistic 5.38; marginal significance 0.000
  - Capital adequacy ratio (lags 4-): sum = -0.16; F-statistic -2.04; marginal significance 0.041
  - R-squared 0.85; Number of observations 5,497
- Selected long-run elasticities (Table 6(b)) reported examples:
  - Real GDP growth long-run elasticities (examples as reported): when initial 0.01 RGDPΔ = 0.02 and 0.00 RGDPΔ = 0.05: -1.3 (-0.3) and -3.2 (-0.8); table also reports -1.6 (-0.4) and -3.9 (-1.0) in other entries.
  - Change in nominal policy interest rate long-run elasticity: 0.46 (0.11) and 1.11 (0.28)
- Bank lending block (Augmented ARDL panel; unbalanced quarterly panel 2001:Q1–2015:Q1; 118 banks; Number of observations 5,863):
  - Short-run dynamic effects (sums and reported p-values in table formatting):
    - Lagged dependent variable (lags 1 to 40): sum 0.302; p-value 12.9 (0.00) and 57.8 (0.00) as reported
    - Change in non-performing loan ratio (lags 1 to 5): sum -0.667; exclusion p-value -4.5 (0.00); sum significance 8.5 (0.00)
    - Change in liquid assets ratio (1 to 5): sum -0.024; exclusion p-value -1.0 (0.32); sum significance 0.3 (0.93)
    - Change in capital ratio distance (1 to 5): sum -0.437; exclusion p-value -3.6 (0.00); sum significance 5.4 (0.00)
    - Change in policy rate (0 to 4): sum -0.690; exclusion p-value -1.8 (0.07); sum significance 5.3 (0.00)
    - Change in real GDP growth (0 to 4): sum -6.833; exclusion p-value -2.2 (0.03); sum significance 16.8 (0.00)
    - Change in inflation rate (0 to 4): sum -2.918; exclusion p-value -3.4 (0.00); sum significance 14.6 (0.00)
  - Long-run effects (coefficients and p-values reported):
    - Non-performing loan ratio (long-run): -0.076; significance -2.3 (0.02)
    - Liquid assets ratio (long-run): 0.033; significance 34.8 (0.00)
    - Capital ratio distance (long-run): 0.193; significance 37.0 (0.00)
    - Capital ratio distance squared: -0.082; significance -4.3 (0.00)
    - Real GDP growth (long-run, common): 5.266; significance 65.3 (0.00)
  - Adjusted R-squared 0.152; Standard error 0.113

### CREAM application to Indonesia — macrofinancial feedback loops, stress simulations, and externalities
- Simulation taxonomy and definitions:
  - “Initial” simulation: one-way impact of initial adverse macro scenario on banks; bank balance sheets grow in line with nominal GDP (no deleveraging); ex-post inconsistency between bottom-up and aggregate credit paths.
  - “Quasi-static” simulation: aggregate credit paths consistent with individual bank lending behaviour but banks do not deleverage dynamically (full consistency between macro and aggregated bottom-up conditions).
  - “Dynamic” simulation: aggregate credit paths consistent with individual bank lending behaviour accounting for macro-financial feedback loops and heterogeneous deleveraging; includes iterative revision until consistency achieved.
- Comparative outcomes:
  - Deleveraging in “Dynamic” amplifies impact of weaker trading partners’ activity, adverse terms of trade shocks, and higher world interest rates on the domestic economy: real GDP and stock of loans are lower in “Dynamic” than in “Quasi-static”.
  - Deleveraging cushions interest-rate channels: lending and policy rates, and corporate and government yields are lower in “Dynamic” than in “Quasi-static”.
  - Lending rates adjust gradually in “Dynamic” reflecting loan portfolio maturity structure; delayed and persistent responses transmitted to policy rate and bond yields.
- Aggregate bank balance-sheet and profit dynamics:
  - In “Dynamic”, loans, cash balances, and deposits and other debt are significantly lower than in “Initial” and “Quasi-static”.
  - Market losses on securities portfolios larger in “Quasi-static” than in “Dynamic”; “Initial” shows large market losses in first 2 years and sharp market gains in last three years.
  - Deleveraging reduces interest income on loans and interest expense on deposits; mitigates rise in total loan losses.
  - Valuations of securities portfolios decline first 2–3 years and increase last 2–3 years as yields decline.
  - CARs initially cushioned by deleveraging but second-round effects reduce activity and feed back into bank losses; CARs lower in “Quasi-static” than in “Dynamic”.
- Bank-specific heterogeneity and rankings:
  - Some banks perform better in “Dynamic” than “Initial”; others worse.
  - “Quasi-static” results are always dominated by “Dynamic” results (all points above 45-degree line in relevant panels).
  - Accounting for macro-financial feedback loops can change relative ordering of vulnerabilities across banks.
  - Increasing severity of initial adverse scenario makes all banks worse-off but does not change relative bank vulnerability ranking.
- Externalities and mixed-run findings:
  - Mixed runs (Bi_QS−) where bank i behaves quasi-statically and others dynamic used to assess systemic importance.
  - Systemic importance depends on size, lending rate relative to system average, exposures, sensitivities to shocks, buffers, and behavioral responses in credit quantity and price.
  - Examples:
    - Bank 1: large, lends at rates well above system average; its credit expansion raises aggregate lending but also increases aggregate lending rate substantially; cross-bank externalities and macro feedback offset expansionary output effects.
    - Bank 2: lending rate near system average; credit expansion produces less upward pressure on interest rates and larger output effect than Bank 1.
    - Bank 4: smaller but lends at rates well below average; despite size, its lending decisions have larger GDP impact than Bank 1.
  - Contribution measure for bank i’s deleveraging to total GDP decline over 5 years: B / (A+B) where A and B are areas described in Figure 10 (area interpretation preserved verbatim).
  - Cross-bank externalities illustrated for Bank 3:
    - Under dynamic simulation, Bank 3’s loans decline by more than 30 percent (real) and CAR declines 7 percentage points.
    - If Bank 3 behaves quasi-statically (B3_QS−), lending expands 25 percent (real) and CAR declines 10 percentage points.
    - Quasi-static behavior by Bank 1 (B1_QS−) generates negative externality on Bank 3: CAR falls 9 percentage points and real lending declines almost 40 percent.
  - Collective dynamics:
    - Declines in individual banks’ CARs due to stress are smaller when all banks exhibit dynamic lending behavior versus collective quasi-static behavior.
    - A single bank can mitigate its CAR impact by deleveraging individually when others are quasi-static; deleveraging by other banks mitigates stress on individual banks via lower interest rates and bond yields.
    - Complementarity among banks’ decisions can generate perverse dynamics where deleveraging by some encourages deleveraging by others.
- Policy experiment — system-wide capital injections:
  - All banks receive capital injections equivalent to 3 percentage points of CAR over a two-year period (equally spread across 8 quarters).
  - Effects:
    - Effect on aggregate credit is significant but takes time to materialize.
    - Impact on other macro variables (e.g., output) is modest and meaningful only with a significant time lag.

### Key methodological and calibration details
- CREAM framework integrates a disaggregated banking sector into a macro SVAR to evaluate macro-financial feedback loops and time-dimension contributions to systemic risk.
- Loss decomposition separates credit (loan portfolios), market (securities portfolios), and net interest income losses; vary across banks.
- Bank-specific calibration notes:
  - Pass-through of government bond yield changes to lending rates: set at 0.6 for all banks.
  - Pass-through of cost of funding spread to lending rates: set at 0.6 for all banks.
  - Loss given default (LGD): set constant at 0.5 for all banks.
  - Dividend distribution ratio: set constant and equal to 0.3 for all banks.
  - Cash-to-debt ratio, durations, repricing fractions, risk weights, and other parameters calibrated from Fitch (Bankscope) and matched to last observations where indicated.
- SVAR for government yields: quarterly data 2004:Q1–2018:Q3, two lags, deterministic constant and linear trend.
- Panel estimation sample and coverage:
  - Credit risk dynamic panel: Number of observations 5,497.
  - Lending block ARDL panel: unbalanced quarterly panel 2001:Q1–2015:Q1 for 118 banks; number of observations 5,863.

### APPENDIX I — Equations of the model: key blocks and identities
- Estimated blocks:
  - Macro block (SVAR): estimated equation (1) for macro variables z̃.
  - Macro block (ir): estimated equation (2) for interest-related macro dynamics.
  - Bank credit risk block: estimated equation (3) with ln() transformations and lagged LLR, LLRΔ, etc.
  - Bank lending block: estimated equation (4) / (12) for lending behavior, using Δln and levels; R_it = L_it / L_it-1 defined in (4).
  - Bank funding cost block: estimated equation (5) for spr_it with additive shocks ν and ζ (notation sprμ_it = (,) spr_it ν ζ zx).
- Profit and loss block (equations 10–19):
  - Total profit Π_it defined in (10): Π_it = II_it + EL_it + LLR_it − RR_it − OO_it + GC_it + LD_it
  - Interest income on loans: IIL_it given by (11): IIL_it-1 = 0.25 · LL_i,t-1 · NPL_i,t-1 · i
  - Interest expense on deposits and debt: IED_it given by (14): IED_it-1 = 0.25 · DD_i,t-1 · i
  - Loan losses and provisions: LL_it = LLLR_it-1 (17); PR_it = PR_it-1 + LL_it (23)
  - Securities return: RBB_it-1 = h_it-1 (18)
- Balance sheet dynamics (equations 20–31):
  - Balance sheet identity (20): ALPR_it = M_it − BBOA_it + K_it + D_it = A_it + L_it + P_it + R_it + O_it
  - Aggregation of securities: B_it = HTM_it + MTM_it (21)
  - NPL dynamics: NPL_it = NPL_it-1 + LL_it · LGD_i (22)
  - Cash balances: M_it = m_i · D_it (24)
  - Capital dynamics (30): K_it = K_it-1 + Π_it · (1 − div_it) − kir · RWA_it + ...
  - Risk-weighted assets (31): RWA_it expression includes LG, GCC, ORWA, RWAL, NPL, PR, BB terms and multiplicative Θ and ρ factors
- Aggregation (32–33):
  - Aggregate lending: L_t = Σ_{i=1}^I L_it
  - Aggregate lending interest rate: i^LL_it = Σ_i i_it · ω_it with ω_it = (LNPL_it− LNPL_it−1) / Σ_i (LNPL_it− LNPL_it−1)
- Initial conditions and predetermined paths (34–43):
  - Macroeconomic historical series z_{-12},...,z_0; L_{-12},...,L_0; ir_{-12},...,ir_0; P_{-12},...,P_0 (34)
  - Bank-specific initial conditions LLR_{i,-12},...,LLR_{i,0} (35); x_{i,-12}, x_{i,-1}, x_{i,0},... (36)
  - HTM/MTM initial splits: B_{h,i0} = HTM_{h,i0} + MTM_{h,i0} for h ∈ {GC, h} (39)
  - Predetermined shock paths (43): shocks z_t^ε, ir_t^μ, kir_it, spr_it μ_it given for all t = 1,2,... with relation 1z_{t-1} = B · ε · μ

*Source: Appendix II, Appendix III, and Appendix I excerpts from wpiea2020072-print-pdf*

### Appendix II describes the stress simulation algorithm. The algorithm is flexible and can

### wpiea2020072-print-pdf - Appendix II describes the stress simulation algorithm. The algorithm is flexible and can

### Stress simulation algorithm: scope and flexibility
- The algorithm is flexible and can accommodate different types of bank lending behavior.
- It can be used to compute:
  - “quasi-static” solutions where all banks behave quasi-statically;
  - “dynamic” solutions where all banks behave dynamically;
  - “mixed” runs where some banks behave dynamically while others follow quasi-static behavior.
- Particular cases of mixed runs can be used to measure individual bank contributions to systemic risk.
- In country-specific applications, four types of simulations are conducted.

### Simulation types and model consistency (from the Table)
- Simulation: Dynamic
  - Model‐based (iterated/consistent)? Yes
  - Bank Behavior: Dynamic for all banks
- Simulation: Quasi‐static
  - Model‐based (iterated/consistent)? Yes
  - Bank Behavior: Quasi‐static for all banks
- Simulation: Initial
  - Model‐based (iterated/consistent)? No
  - Bank Behavior: Quasi‐static for all banks
- Simulation: Mixed (Bi‐QS)
  - Model‐based (iterated/consistent)? Yes
  - Bank Behavior: Quasi‐static for bank i; Dynamic for all other banks

### Characteristics and implications of the “Initial” scenario
- The “Initial” simulation replicates the sequential and quasi-static stress testing approach commonly used in policy institutions.
- It involves constructing a multi-year scenario and then performing bank stress tests based on these scenarios.
- A significant drawback: ex-post outcomes for banks, once aggregated, do not coincide with assumptions made at the scenario design stage.
- There is an ex-post inconsistency between banks’ desired lending responses and the availability of credit assumed under the initial adverse scenario.
- The “Initial” simulation does not account for macro-financial loops.
- To highlight these inconsistencies, paths for aggregate lending and lending rates are included in the “initial” scenarios shown in Section IV.
- The “Initial” scenario can be used to kick-start iterated simulations that exhibit ex-post consistency under the model.

### Dynamic, Quasi-static, and Mixed (Bi‐QS) simulations: outcomes and uses
- In the “Dynamic” and “Quasi static” simulations:
  - Macroeconomic and bank-specific results are outcomes of the analysis.
  - Ex-post consistency between aggregate and bottom-up lending behavior is ensured by application of the model.
  - All banks exhibit dynamic or quasi-static behavior respectively.
- In mixed simulations labeled Bi‐QS:
  - An individual bank i is the only bank that behaves quasi-statically, while all other banks exhibit dynamic lending behavior.
  - These mixed runs permit assessment of individual bank contributions to systemic risk.

### Country application: Indonesia — data and sample
- Quarterly macroeconomic data series:
  - Obtained from various sources.
  - Span from 1990:Q1 to 2018:Q2, covering both the Asian and the global financial crises.
- Banking data:
  - Obtained from Fitch (Bankscope).
- Dynamic panel regressions:
  - Cover the entire banking system (118 banks).
  - Performed using quarterly data from Q1:2001 to Q1:2015.
- Stress simulation analysis:
  - Performed on 12 small and large banks that jointly account for 70 percent of the banking system’s assets.

*Source: Appendix II and Section IV excerpts from the provided content unit.*

### Appendix III.

### Appendix III

### A. Baseline and “Initial Adverse Scenarios” — Impulse Responses and Scenario Construction
- VAR model includes aggregate credit (R_L) and the lending rate (L_i); impulses are one standard deviation (positive) structural shocks applied for one quarter with endogenous dynamic responses spanning 20 quarters and confidence bands corresponding to (.16,.84) intervals.
- Key impulse-response observations:
  - A shock to real GDP of Indonesia’s main trading partners (U.S., China, and the EU) triggers an increase in commodity prices, boosts domestic real GDP, and appreciates the rupiah in real terms; inflation declines and the policy interest rate adjusts downward.
  - A positive shock to commodity prices boosts domestic real GDP (Indonesia is a commodity exporter).
  - A positive shock to the U.S. federal funds rate reduces Indonesian real GDP via capital outflows and rupiah depreciation.
  - A positive shock to domestic real GDP raises inflation and the policy interest rate.
  - Banking sector transmission: real GDP expansion from stronger export demand is fueled by bank lending—at a much faster rate than real GDP—and reduced lending rates.
  - A positive shock to the lending rate causes declines in real bank credit and GDP (interpreted as adverse credit supply shock); a positive shock to real bank credit raises the lending rate (consistent with credit demand shock).
- Government and corporate yields:
  - Separate two-equation SVAR estimated for the domestic policy rate (i_0) and 10-year government bond yield (ir,40G_Y) using quarterly data for 2004:Q1 to 2018:Q3 with two lags, a constant and linear trend.
  - Due to short government bond yield series and lack of corporate bond data for Indonesia, corporate yields are assumed to follow government yields amplified by 30 percent (i.e., a 100 basis point shift in government yields => 130 basis point shift in corporate yields). The amplification parameter is adjustable for robustness.
- Scenario construction:
  - Table 3 shows structural shocks used to generate combined responses in Figure 5; these responses produce the “initial adverse scenario” in Table 4 alongside the baseline.
  - Iteration algorithm (Appendix II) relies on impulse responses of 10-year government yields and short- and 10-year corporate yields to policy rate shocks; responses of corporate rates are imposed as 1.3 times corresponding government bond responses.

### Baseline and “Initial Adverse” annual paths (Table 4)
- Real GDP growth (percent):
  - Baseline: 2017 5.1; 2018 5.3; 2019 5.5; 2020 5.6; 2021 5.6; 2022 5.6
  - Initial adverse: 2017 5.1; 2018 4.6; 2019 0.6; 2020 1.8; 2021 5.6; 2022 7.8
- Inflation, y-o-y change (percent):
  - Baseline: 2017 3.8; 2018 3.4; 2019 3.7; 2020 3.7; 2021 3.6; 2022 3.6
  - Initial adverse: 2017 3.8; 2018 4.0; 2019 9.6; 2020 12.8; 2021 3.4; 2022 -1.0
- Real effective exchange rate index (2014=100):
  - Baseline: 2017 100.0; 2018 94.2; 2019 94.0; 2020 94.0; 2021 94.0; 2022 94.0
  - Initial Adverse: 2017 100.0; 2018 92.1; 2019 77.2; 2020 78.5; 2021 88.6; 2022 94.0
- Nominal effective exchange rate, y-o-y change (percent):
  - Baseline: 2017 -0.4; 2018 -6.7; 2019 -1.1; 2020 -1.2; 2021 -1.4; 2022 -1.5
  - Initial adverse: 2017 -0.4; 2018 -10.1; 2019 -23.7; 2020 -9.6; 2021 11.4; 2022 9.2
- Nominal interest rate (BI policy rate), percent per annum:
  - Baseline: 2017 4.5; 2018 5.0; 2019 5.3; 2020 5.3; 2021 5.3; 2022 5.3
  - Initial adverse: 2017 4.5; 2018 5.7; 2019 11.6; 2020 12.4; 2021 5.7; 2022 2.2
- International interest rate (Fed Funds Rate), percent:
  - Baseline: 2017 1.0; 2018 2.0; 2019 3.1; 2020 3.7; 2021 3.2; 2022 2.9
  - Initial adverse: 2017 1.0; 2018 2.3; 2019 4.7; 2020 5.6; 2021 4.7; 2022 3.8
- Trading partners' growth (percent):
  - Baseline: 2017 8.4; 2018 4.9; 2019 5.8; 2020 5.7; 2021 5.7; 2022 5.7
  - Initial adverse: 2017 8.4; 2018 3.6; 2019 1.8; 2020 6.5; 2021 6.4; 2022 6.0
- Commodity prices (2007=100):
  - Baseline: 2017 113.5; 2018 130.5; 2019 131.5; 2020 131.5; 2021 131.5; 2022 131.5
  - Initial adverse: 2017 113.5; 2018 114.6; 2019 71.5; 2020 90.0; 2021 108.2; 2022 118.7
- Real bank credit to the private sector growth (percent):
  - Baseline: 2017 3.7; 2018 5.2; 2019 5.0; 2020 5.3; 2021 5.3; 2022 5.3
  - Initial adverse: 2017 3.7; 2018 3.0; 2019 -9.5; 2020 -22.7; 2021 -20.6; 2022 12.3
- Nominal bank credit to the private sector growth (percent):
  - Baseline: 2017 7.5; 2018 8.5; 2019 8.6; 2020 9.0; 2021 8.9; 2022 8.9
  - Initial adverse: 2017 7.5; 2018 7.0; 2019 0.1; 2020 -9.8; 2021 -17.2; 2022 11.3
- Bank lending rate (percent):
  - Baseline: 2017 11.1; 2018 10.5; 2019 10.5; 2020 10.5; 2021 10.5; 2022 10.5
  - Initial adverse: 2017 11.1; 2018 10.8; 2019 13.1; 2020 13.8; 2021 11.1; 2022 8.7

### B. Dynamic Panel Estimates — Bank Credit Risk and Lending Blocks
- Credit risk block (Table 6(a)):
  - Dependent variable: logistic transformation of bank non-performing loan ratio (i_NPLR) regressed on lags of dependent variable, macro variables, and bank-specific capital ratios. Lagged coefficients are summed for interpretation.
  - Regression summary (with bank-specific fixed effects):
    - Lagged dependent variable: sum of coefficients 1 to 20 = 0.85
    - Real GDP growth (lags 2 to 5): sum = -12.33; F-statistic 14.08; marginal significance 0.000
    - Real GDP growth squared (lags 2 to 5): sum = 105.05; F-statistic 2.20; marginal significance 0.066
    - Change in the nominal policy interest rate (lags 2 to 5): sum = 3.52; F-statistic 5.38; marginal significance 0.000
    - Capital adequacy ratio (lags 4-): sum = -0.16; F-statistic -2.04; marginal significance 0.041
    - R-squared 0.85; Number of observations 5,497
  - Interpretation:
    - Slower real GDP growth or increases in the policy interest rate lead to higher i_NPLR.
    - Higher bank-specific capital ratios (i_CAR) associate with lower i_NPLR.
    - Model non-linear due to logit transform and quadratic RGDP term; elasticities vary with initial conditions.
  - Selected long-run elasticities (Table 6(b)):
    - For 0.01 RGDPΔ = 0.02 and 0.00 RGDPΔ = 0.05 (contextual presentation in table):
      - Real GDP growth long-run elasticities (examples reported in table):
        - when initial 0.020.05: -1.3 (-0.3) and -3.2 (-0.8)
        - when initial 0.00.02? table reports values including -1.6 (-0.4) and -3.9 (-1.0) (retain table formatting/values as reported)
      - Change in nominal policy interest rate long-run elasticity: 0.46 (0.11) and 1.11 (0.28)
- Bank lending block (Table 7):
  - Augmented ARDL panel (fixed effects) for real loan growth using unbalanced quarterly panel 2001:Q1–2015:Q1 for 118 banks; contemporaneous and lagged regressors included.
  - Short-run dynamic effects (sum of coefficients; p-values in parentheses):
    - Lagged dependent variable (real loan growth lags 1 to 40): sum 0.302; p-value 12.9 (0.00) and 57.8 (0.00) as reported in table formatting.
    - Change in non-performing loan ratio (lags 1 to 5): sum -0.667; exclusion p-value -4.5 (0.00); sum significance 8.5 (0.00)
    - Change in liquid assets ratio (1 to 5): sum -0.024; exclusion p-value -1.0 (0.32); sum significance 0.3 (0.93)
    - Change in capital ratio distance (1 to 5): sum -0.437; exclusion p-value -3.6 (0.00); sum significance 5.4 (0.00)
    - Change in policy rate (0 to 4): sum -0.690; exclusion p-value -1.8 (0.07); sum significance 5.3 (0.00)
    - Change in real GDP growth (0 to 4): sum -6.833; exclusion p-value -2.2 (0.03); sum significance 16.8 (0.00)
    - Change in inflation rate (0 to 4): sum -2.918; exclusion p-value -3.4 (0.00); sum significance 14.6 (0.00)
  - Long-run effects (coefficients and p-values reported):
    - Non-performing loan ratio (long-run): -0.076; significance -2.3 (0.02)
    - Liquid assets ratio (long-run): 0.033; significance 34.8 (0.00)
    - Capital ratio distance (long-run): 0.193; significance 37.0 (0.00)
    - Capital ratio distance squared: -0.082; significance -4.3 (0.00)
    - Real GDP growth (long-run, common): 5.266; significance 65.3 (0.00)
  - Adjusted R-squared 0.152; Standard error 0.113; Number of observations 5,863

### C. Accounting for Macrofinancial Feedback Loops — CREAM Application to Indonesia, Stress Simulations, and Externalities
- Simulation types:
  - “Initial” simulation: one-way impact of initial adverse macro scenario on banks; bank balance sheets grow in line with nominal GDP (no deleveraging). Ex-post inconsistency between bottom-up and aggregate credit paths because nominal GDP growth outpaces nominal credit growth projected under the scenario.
  - “Quasi-static” simulation: aggregate credit paths consistent with individual bank lending behaviour but banks do not deleverage dynamically (full consistency between macro and aggregated bottom-up conditions).
  - “Dynamic” simulation: aggregate credit paths consistent with individual bank lending behaviour accounting for macro-financial feedback loops and heterogeneous deleveraging; includes iterative revision until consistency between bottom-up aggregation and adverse macro scenario is achieved.
- Main comparative outcomes (Figures 6–8 summary):
  - Deleveraging in the “Dynamic” simulation amplifies the impact of weaker trading partners’ activity, adverse terms of trade shocks, and higher world interest rates on domestic economy: real GDP and stock of loans are lower in “Dynamic” than in “Quasi-static”.
  - Deleveraging cushions interest-rate channels: lending and policy rates, and corporate and government yields are lower in “Dynamic” than in “Quasi-static”.
  - Lending rates adjust gradually in the “Dynamic” simulation reflecting loan portfolio maturity structure; delayed and persistent responses of real lending and lending rate are transmitted to policy rate and bond yields.
- Aggregate bank balance-sheet and profit dynamics (Figure 7 summary):
  - In the “Dynamic” simulation, loans, cash balances, and deposits and other debt are significantly lower than in “Initial” and “Quasi-static”.
  - Market losses on securities portfolios are larger in “Quasi-static” than in “Dynamic”; “Initial” shows large market losses in first 2 years and sharp market gains in last three years.
  - Deleveraging reduces interest income on loans and interest expense on deposits; it mitigates the rise in total loan losses.
  - Valuations of securities portfolios decline first 2–3 years and increase last 2–3 years as yields decline.
  - Capital adequacy ratios (CAR) are initially cushioned by deleveraging but second-round effects of widespread deleveraging reduce activity and feed back into bank losses; CARs are lower in “Quasi-static” than in “Dynamic” because quasi-static implies additional credit provision and higher risk-weighted assets.
- Bank-specific heterogeneity and rankings (Figure 9):
  - Comparing CAR changes between simulations:
    - Some banks perform better in “Dynamic” than “Initial”; others worse.
    - “Quasi-static” results are always dominated by “Dynamic” results (all points above 45-degree line in relevant panels).
  - Accounting for macro-financial feedback loops can change the relative ordering (rankings) of vulnerabilities across banks (examples provided: rank shifts between simulations).
  - Increasing severity of initial adverse scenario (larger structural shocks) makes all banks worse-off but does not change relative bank vulnerability ranking—hence severity scaling is not a substitute for macro-financial stress analysis with heterogeneous deleveraging.
- Externalities analysis (Figures 10–12):
  - Simulation of mixed runs (Bi_QS−: bank i behaves quasi-statically while others dynamic) for three large banks (1, 2, 4) demonstrates that systemic importance depends on size, lending rate relative to system average, exposures, sensitivities to shocks, buffers, and behavioral responses in credit quantity and price.
    - Bank 1: large, lends at rates well above system average; its credit expansion raises aggregate lending but also increases aggregate lending rate substantially; cross-bank externalities and macro feedback offset expansionary output effects.
    - Bank 2: lending rate near system average; credit expansion produces less upward pressure on interest rates and larger output effect than Bank 1.
    - Bank 4: smaller but lends at rates well below average; despite size, its lending decisions have larger GDP impact than Bank 1.
  - Contribution measure for bank i’s deleveraging to total GDP decline over 5 years: B / (A+B) where A and B are areas described in Figure 10 (area interpretation preserved verbatim).
  - Cross-bank externalities illustrated for Bank 3 (Figure 11):
    - Under dynamic simulation, Bank 3’s loans decline by more than 30 percent (real) and CAR declines 7 percentage points.
    - If Bank 3 behaves quasi-statically (B3_QS−), lending expands 25 percent (real) and CAR declines 10 percentage points.
    - Quasi-static behavior by Bank 1 (B1_QS−) generates negative externality on Bank 3: CAR falls 9 percentage points and real lending declines almost 40 percent.
  - Collective dynamics (Figure 12):
    - Declines in individual banks’ CARs due to stress are smaller when all banks exhibit dynamic lending behavior versus collective quasi-static behavior.
    - A single bank can mitigate its CAR impact by deleveraging individually when others are quasi-static; deleveraging by other banks mitigates stress on individual banks via lower interest rates and bond yields.
    - Complementarity among banks’ decisions can generate perverse dynamics where deleveraging by some encourages deleveraging by others.
- Policy experiment — system-wide capital injections (Figure 13):
  - All banks receive capital injections equivalent to 3 percentage points of CAR over a two-year period (equally spread across 8 quarters).
  - Effects:
    - The effect on aggregate credit is significant but takes time to materialize.
    - Impact on other macro variables (e.g., output) is modest and meaningful only with a significant time lag.

### Key methodological and calibration details
- CREAM framework integrates a disaggregated banking sector into a standard macro SVAR to evaluate macro-financial feedback loops and time-dimension contributions to systemic risk.
- Loss decomposition: separate estimates for credit (loan portfolios), market (securities portfolios), and net interest income losses; these vary across banks.
- Bank-specific parameter calibration (Table 2 notes):
  - Pass-through of government bond yield changes to lending rates: set at 0.6 for all banks.
  - Pass-through of cost of funding spread to lending rates: set at 0.6 for all banks.
  - Loss given default (LGD): set constant at 0.5 for all banks.
  - Dividend distribution ratio: set constant and equal to 0.3 for all banks.
  - Cash-to-debt ratio, durations, repricing fractions, risk weights, and other parameters are calibrated from Fitch (Bankscope) and matched to last observations where indicated.
- SVAR for government yields: quarterly data 2004:Q1–2018:Q3, two lags, deterministic constant and linear trend.
- Panel estimation sample and coverage:
  - Credit risk dynamic panel: Number of observations 5,497.
  - Lending block ARDL panel: unbalanced quarterly panel 2001:Q1–2015:Q1 for 118 banks; number of observations 5,863.

### Main conclusions and implications
- The banking sector is central to shock transmission: heterogeneous bank lending responses and deleveraging materially influence macroeconomic outcomes and stress-test results.
- Accounting explicitly for macro-financial feedback loops and heterogeneous bank behavior:
  - Can lower aggregate activity further via deleveraging but can also reduce interest rates and yields, cushioning some effects.
  - Changes the cross-sectional pattern of stress-test outcomes and can reorder bank vulnerability rankings.
  - Is critical for assessing systemic importance, which depends on bank size, exposures, sensitivities, buffers, and behavioral responses in both credit quantity and pricing.
- Policy experiments (e.g., CAR injections of 3 percentage points over two years) expand aggregate credit but have modest and lagged effects on output, underscoring the complex transmission of capital policy through macro-financial channels.

*Source: Appendix III, wpiea2020072-print-pdf*

### APPENDIX I. EQUATIONS OF THE MODEL

### APPENDIX I. EQUATIONS OF THE MODEL

### A) Estimated Blocks (SVAR, interest, credit risk, lending, funding)
- Macro block (SVAR): estimated equation (1) governing macro variables z̃ with lag/interaction structure as presented in equation (1).
- Macro block (ir): estimated equation (2) for interest-related macro dynamics.
- Bank credit risk block: estimated equation (3) for loan-related risk dynamics, including ln() transformations and lagged LLR, LLRΔ, and other terms.
- Bank lending block: estimated equation (4) / (12) for lending behavior, using Δln and levels; where R_it = L_it / L_it-1 is defined in (4).
- Bank funding cost block: estimated equation (5) for spr_it with additive shocks ν and ζ (notation sprμ_it = (,) spr_it ν ζ zx).

Key variable transformations and definitions related to estimated blocks:
- Transformation mapping: ttt LL→̃ z̃ (6).
- Vector z̃' = [RGDP, PiRGDP, REER, INF, i, COMMUS] with INF = 1/ln(INFPP_t-1) ln (7).
- Bank-level vector z̃^f: RL' = [Li_t, ...] and definitions in (8).
- Bank internal variables x = [CAR, LATA, LLR, ...] as in (8).
- Ratio definition K_it = CAR_it / RWA_it and LAMBB/LATA relations in (9).

### B) Bank Profit and Loss Block (equations 10–19)
- Total profit (Π_it) defined in (10):
  - Π_it = II_it + EL_it + LLR_it − RR_it − OO_it + GC_it + LD_it (notation preserved as in (10)).
- Interest income on loans:
  - IIL_it given by (11): IIL_it-1 = 0.25 · LL_i,t-1 · NPL_i,t-1 · i (exact functional form as in (11)).
  - Loan pricing and related components via equations (12) and (13), including π terms and spr adjustments.
- Interest expense on deposits and debt:
  - IED_it given by (14): IED_it-1 = 0.25 · DD_i,t-1 · i (as in (14)).
  - Deposit pricing dynamics in (15) and (16) with π and spr terms.
- Loan losses and provisions:
  - Loan losses: LL_it = LLLR_it-1 (17) (dynamics as specified).
  - Provisions: PR_it = PR_it-1 + LL_it (23) (provision accumulation; see cross-reference in Block C).
- Securities return:
  - RBB_it-1 = h_it-1 (18) for h ∈ {GC, h} as specified.
- Other net income:
  - OA_it = Ξ_it · 0 (19) (notation preserved).

### C) Bank Balance Sheet Dynamics (equations 20–31)
- Balance sheet identity (20):
  - ALPR_it = M_it − BBOA_it + K_it + D_it = A_it + L_it + P_it + R_it + O_it (preserve original symbols and ordering from (20)).
- Aggregation of securities portfolios and holdings:
  - B_it = HTM_it + MTM_it (21) for h ∈ {GC, h}.
  - HTM and MTM dynamics in (25) and (26) with 10.25 and 0.25 coefficients and duration (dur) adjustments; see (26) detailed expression.
- Dynamics of non-performing loans:
  - NPL_it = NPL_it-1 + LL_it · LGD_i (22) (LGD multiplicative update).
- Dynamics of provisions:
  - PR_it = PR_it-1 + LL_it (23).
- Cash balances:
  - M_it = m_i · D_it (24).
- Other assets:
  - OA_it = OA_it-0 (29).
- Dynamics of capital (30):
  - K_it = K_it-1 + Π_it · (1 − div_it) − kir · RWA_it + ... (preserve exact functional form as in (30)).
- Risk-weighted assets (31):
  - RWA_it expression includes LG, GCC, ORWA, RWAL, NPL, PR, BB terms and multiplicative Θ and ρ factors as in (31).

### D) Aggregation (equations 32–33)
- Aggregate lending (32):
  - L_t = Σ_{i=1}^I L_it.
- Aggregate lending interest rate (33):
  - i^LL_it aggregated via ω weights: i^LL_it = Σ_i i_it · ω_it.
  - Weight definition: ω_it = (LNPL_it− LNPL_it−1) / Σ_i (LNPL_it− LNPL_it−1) (preserve original expression and ordering from (33)).

### E) Initial conditions and variables with predetermined paths (equations 34–43)
- Macroeconomic initial series given as historical data:
  - z_{-12},...,z_0; L_{-12},...,L_0; ir_{-12},...,ir_0; P_{-12},...,P_0 (34).
- Bank-specific initial conditions:
  - LLR_{i,-12},...,LLR_{i,0} (35).
  - x_{i,-12}, x_{i,-1}, x_{i,0},... (36).
  - Full vector of initial bank-level items across groups GC and C as listed in (37) and identity in (38): ALPR_i0 = M_i0 − BBOA_i0 + K_i0 + D_i0 (38).
  - HTM/MTM initial splits in (39): B_{h,i0} = HTM_{h,i0} + MTM_{h,i0} for h ∈ {GC, h}.
  - Initial NPL, NL, L, D entries as in (40)–(41).
  - Initial spr μ_i,-1 and spr μ_i,0 as in (42).
- Predetermined shock paths (43):
  - Shocks z_t^ε, ir_t^μ, kir_it, spr_it μ_it given for all t = 1,2,... with relation 1z_{t-1} = B · ε · μ (exact notation preserved from (43)).

*Source: APPENDIX I. EQUATIONS OF THE MODEL, wpiea2020072-print-pdf*

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_Source: https://www.imf.org/-/media/files/publications/wp/2020/english/wpiea2020072-print-pdf.pdf_