## _wp1456 - References

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### I. Introduction and purpose
- MAPMOD: a new IMF model to support macrofinancial and macroprudential policy analysis; companion paper (Benes, Kumhof, and Laxton,2014) discusses theoretical structure; this paper presents simulation properties.
- Design purpose:
  - Study vulnerabilities associated with excessive credit expansions and asset price bubbles, and consequences of different macroprudential policies.
  - Highlight critical macroprudential tradeoff: reducing risks of very costly financial crises versus minimizing costs of macroprudential policies during normal times.
- Key modeling emphasis:
  - Revamp of conventional linear DSGE models to incorporate the special role played by banks, bank balance sheets, and nonlinear feedbacks between bank balance sheets, borrower balance sheets and the real economy.

### II. MAPMOD key features and nonlinear mechanisms
- Banks and balance sheets:
  - Banks maintain net worth buffers to absorb loan losses because of Basel-style minimum capital adequacy regulation, frictions in acquiring new net worth, and non-diversifiable aggregate lending risk.
  - Loan price and quantity, and maintenance of capital buffers above minimum requirements, arise as an optimal equilibrium phenomenon from loan contracts, endogenous loan losses and regulation.
  - Bank lending creates matching liabilities (bank deposits) and expands balance sheets; banks are limited by perceived profitability and risk absorption capacity of capital.
  - Banks respond to shocks via higher spreads and non-price credit rationing; rapid credit shrinkage during distress cuts households and firms from financing.
- Two highlighted nonlinear feedbacks:
  - Lending losses erode bank capital adequacy, triggering rapid contraction in lending and higher spreads as banks rebuild equity buffers.
  - Declines in borrowers’ asset values raise loan-to-value ratios, further reducing lending volumes and increasing spreads.
- Policy implication: macroprudential policy should encourage more countercyclical bank behavior to mitigate severe crisis amplification.

### III. Scenario summaries and quantitative findings
- Presentation format:
  - Four columns of charts: (1) GDP and demand components; (2) price variables (wage and CPI inflation, policy rate, real exchange rate); (3) nonbank financial variables (net foreign assets/GDP, physical capital stock, real asset prices, real value of capital stock); (4) bank variables (real bank credit, pre-default lending spread, loan default rate, post-default Basel capital adequacy ratio).
  - Blue box encloses five key banking system variables.

A. Revisions in views about trend productivity growth (Figure 1)
- Experiment setup:
  - Agents expect higher trend productivity growth in export sector over subsequent 10 years → expected long-run output rise by approximately 10 percent; expectations improve gradually and linearly over first four quarters shown.
- Good credit expansion (if expectations realized):
  - Output ultimately grows by 10 percent.
  - Investment increases; by year three almost 12 percent above initial level.
  - Headline inflation falls by around 1.2 percentage points in year 5.
  - Policy rate stays essentially constant first two years, then drops.
  - Trade balance deterioration: almost 2 percent of GDP in second year.
  - Net foreign assets deteriorate by about 3.5 percent of GDP at end of third year, and by almost 4.5 percent of GDP after five years.
  - Bank capital adequacy ratio starts at 11.4 percent (buffer of 3.4 percent above minimum 8 percent) and banks reduce buffer to 3.1 percent.
  - Real bank credit increases by almost 8 percent after three years, and by well over 20 percent in the long run.
  - Short-run reduction in spreads small: less than 50 basis points.
- Bad credit expansion (expectations revised back at beginning of fourth year):
  - Real asset prices drop over 6 percent; real output contracts around 4 percent.
  - Loan losses equal around 0.5 percent of the value of all loans.
  - Spreads rise by more than one percentage point (~120 basis points on impact).
  - Average capital adequacy ratio deteriorates roughly 0.5 percentage point to around 10.7 percent.
  - Instantaneous reduction in lending around 3 percent on impact.
  - Policy rate reduction around 2.3 percentage points two years into crisis mitigates but cannot offset balance-sheet dislocations fully.

B. Underpricing of lending risk by banks (“NINJA Loans” shock) (Figure 2)
- Setup:
  - Banks revise down perceived standard deviation of borrower idiosyncratic risk by 5 percent by end of third year; actual standard deviation unchanged.
- NINJA1 (permanent underpricing):
  - Real bank credit increases by around 1.5 percent by end of third year.
  - Lending spreads drop by around 15 basis points.
  - Capital-adequacy ratio allowed to drop by almost 0.5 percentage points in the long run.
  - Investment reaches 2 percent increase by end of third year; real asset prices increase roughly 0.5 percent.
  - Consumption increases over 1.5 percent by end of third year.
  - GDP increases by around 1 percent by end of third year.
  - Inflation increases by 0.6 percentage points by end of third year; policy rate rises accordingly.
  - Net foreign assets position reduced to just under 4 percent of GDP.
  - Long-run: spreads permanently lower by around 5 basis points; credit permanently higher by around 1.5 percent.
- NINJA2 (expectations revert to true risk over about three years):
  - Rapid contraction of lending back to original level; immediate 20 basis points increase in lending spreads.
  - Sudden tightening leads to roughly 2 percent drop in real asset prices.
  - Bank lending losses around 0.1 percent of loan book value.
  - GDP drops by 1.75 percent; real exchange rate depreciates; trade balance improves; inflation falls faster than in NINJA1.

C. Asset price bubble—excessive credit expansion (Figure 3)
- Setup:
  - Expected returns on physical capital include exogenous non-fundamental shocks peaking end of year three. Actual bubble component: 10 percent at end of third year; observed real asset price increase ~18 percent over first three years due to endogenous feedback.
- Boom phase (first three years):
  - Real bank credit increases by 9 percent after three years.
  - Spreads fall by less than 50 basis points.
  - Equity buffer declines from 11.4 percent to 10.8 percent.
  - Investment increases by around 24 percent by end of third year.
  - Consumption increases by almost 3 percent; GDP over 5 percent.
  - Net foreign assets deteriorate by almost 3 percent of GDP by end of third year.
  - Inflation increases by around 0.7 percentage points over first three years; policy rate increases.
- Crash at end of third year:
  - Asset prices collapse by over 25 percent; undershoot long-run values by around 8 percent initially.
  - Loan losses roughly 1.5 percent of total loans.
  - Average capital adequacy ratio deteriorates from 10.8 percent to 9.5 percent.
  - Banks raise spreads around 150 basis points and implement instantaneous 8 percent contraction in lending, destroying roughly equal-sized purchasing power.
  - Investment collapses around 15 percent within less than a year and over 25 percent eventually.
  - Consumption drops by about 5 percent within less than one year; GDP drops around 5 percent.
  - Wage inflation surges by over 100 basis points following collapse.

### IV. Nonlinear amplification, comparison with linearized models
A. Financial sector vulnerabilities and crisis amplification (Figure 4)
- Combined shocks (productivity and borrower riskiness) produce:
  - Pre-crisis (first three years) roughly additive effects:
    - Real bank credit grows around 9 percent (7.5 percent and 1.5 percent).
    - Investment grows by 14 percent (12 percent and 2 percent).
    - Consumption grows by 5.5 percent (4 percent and 1.5 percent).
    - GDP grows by 5 percent (4 percent and 1 percent).
  - Upon reversal at end of third year: nonlinear amplification much larger than sum of individual shocks:
    - Asset prices collapse 12 percent (versus 6 percent and 2 percent).
    - Lending losses 2 percent of asset value (versus 0.5 percent and <0.1 percent).
    - Bank capital adequacy declines by 1.5 percentage points (versus 0.4 and 0.1).
    - Lending spreads increase over 300 basis points (versus 110 and 20).
    - Real bank credit drops more than 5 percent (versus <3 percent and <1 percent).
    - Investment drops 15 percent over first two quarters (versus 9 percent and 2 percent).
    - Consumption drops 8 percent (versus 4 percent and 1.5 percent).
    - GDP drops 6 percent (versus 3.5 percent and 1 percent).
- Conclusion: large balance-sheet vulnerabilities lead to crisis amplification exceeding linear aggregation.

B. Nonlinear versus linear simulations (Figure 5)
- Identical shocks in nonlinear model generate much more severe downturns than linearized version:
  - Asset prices drop 12 percent (nonlinear) versus 6 percent (linearized).
  - Loan losses equal 2 percent of loans (nonlinear) versus 0.25 percent (linearized).
  - Pre-default lending spreads increase over 300 basis points (nonlinear) versus around 80 basis points (linearized).
  - Bank credit decreases 5 percent on impact (nonlinear) versus <3 percent (linearized).
  - GDP declines 7 percent peak-to-trough (nonlinear) versus a little over 4 percent (linearized); contraction is faster in nonlinear simulation.
- Lesson: linearized models fail to capture crisis-time nonlinearities originating in balance-sheet dynamics; nonlinear simulations are imperative for crisis policy analysis.

### V. Macroprudential policy experiments and outcomes
A. Countercyclical Minimum Capital Adequacy Ratio (MCAR) (Figure 6)
- Baseline: constant MCAR of 8 percent.
- Countercyclical MCAR design:
  - Time-varying, asymmetric and countercyclical: never below 8 percent on downside; raised on upside in response to positive year-on-year loan growth (exact path in Table 6).
  - Policy inertia allows gradual compliance and accumulation of additional capital buffer when lending increases.
- Effects during boom (first three years):
  - Actual capital adequacy ratio increases by around 0.2 percentage points by end of third year.
  - Spreads higher under countercyclical MCAR by ~30 basis points by end of third year.
  - Boom-phase increases in physical capital stock and real asset prices ~half as large as under constant MCAR.
  - Investment boom smaller by almost two thirds.
  - GDP growth little over 3 percent by end of third year versus 5 percent under constant MCAR.
  - Inflation declines immediately under countercyclical MCAR; policy rate follows.
- Crisis-phase benefits:
  - MCAR immediately lowered by a full 1.5 percentage points to minimum of 8 percent following expectations revision, permitting less drastic bank measures.
  - Resulting crisis dynamics under countercyclical MCAR:
    - Asset prices drop by around 2 percent compared to 12 percent under constant MCAR.
    - Amplitudes of investment and consumption fluctuations are around one third and one half (respectively) of those under constant MCAR.
    - GDP contracts around 2 percent peak-to-trough versus around 7 percent under constant MCAR.
    - Inflation "barely affected"; policy rate does not exhibit major reversal.
- Policy trade-off and guidance:
  - Countercyclical MCAR imposes costs during correct-fundamentals booms (slower growth, lower investment).
  - Given uncertainty about reversal risk and large nonlinear crisis costs, even modest probability of getting it wrong argues for countercyclical macroprudential approach.

B. Contractionary shock to bank capital (exogenous 20 percent regulatory bank equity loss) (Figure 7)
- Shock specifics:
  - Exogenous 20 percent loss of regulatory bank equity in a single period.
  - Capital adequacy ratio immediately reduced by 2.4 percentage points, from 11.4 percent to 9.0 percent; MCAR remains at 8 percent.
- Scenario 1: recapitalize only from retained earnings (≥E = 1)
  - Immediate reduction in loans: 2.2 percent.
  - Immediate increase in spreads: 2.1 percentage points.
  - Real effects by end of first year: GDP drops more than 2 percent; consumption almost 3 percent; investment almost 5 percent.
  - CPI inflation drops around 0.6 percentage points; policy rate drops around 1 percentage point.
  - Asset prices drop over 5 percent on impact.
  - Capital stock reduced by 0.8 percent after three years.
  - Banks experience spike in loan losses ≈ 0.2 percent of portfolio value at shock time.
- Scenario 2: banks access equity markets (≥E = 0.5)
  - Immediate reduction in loans: 0.9 percent.
  - Immediate increase in spreads: 1.0 percentage point.
  - GDP trough: drops 0.8 percent (vs 2.2 percent in Scenario 1).
  - Inflation declines by 0.2 percent instead of 0.6 percent.
- Mechanism and implication:
  - Access to equity markets allows less reliance on lending reductions and spread increases; policies that reassure potential equity investors during crisis can disproportionately reduce nonlinearities.

C. Permanent increase in MCAR from 8 percent → 10 percent (Figure 8)
- Experiment design:
  - Three implementation speeds (no equity market access; equity via earnings only):
    - Immediate jump.
    - Gradual raise over four years, most in first two years.
    - Announced future increase with gradual implementation after two years.
- Long-run effects (identical across scenarios):
  - Spreads rise by about 30 basis points in very long run.
  - Banks’ loan and deposit levels decline by approximately 2 percent.
  - Potential output (capital stock) drops by around 0.8 percent.
- Short-run effects by scenario:
  - Immediate increase:
    - Loan volume reduced by over 3 percent immediately.
    - Spreads increase around 2 percentage points on impact.
    - Real asset prices decline by around 8 percent on impact.
    - Lending losses ≈ 0.4 percent of asset value on impact.
    - Actual capital adequacy ratio initially reduced by around 0.2 percent.
    - GDP contracts by almost 3 percent toward end of first year.
    - Inflation drops almost 0.7 percentage points; policy rate drops 1.7 percentage points.
    - Banks rebuild equity buffer above new MCAR after around 5 years.
  - Unanticipated gradual increase:
    - Spreads rise just over 40 basis points initially and remain 30 basis points above previous level thereafter.
    - Real asset prices decline by around 4 percent.
    - GDP trough around 1.75 percent (vs almost 3 percent immediate).
    - Investment amplitude similar; consumption contraction markedly shallower.
  - Anticipated gradual increase:
    - Spreads increase by less than 10 basis points over initial two-year period prior to MCAR increases, then rise subsequently.
    - Banks’ loan book declines by 2 percent prior to end of second year.
    - Real asset prices decline by less than 1 percent on impact.
    - Consumption barely affected over first two years; GDP smoothly declines toward new long-run level (~0.8 percent lower).
- Policy lesson: implementation speed and communication matter; gradual and well-communicated increases reduce short-run disruption.

D. Shocks to the cost of borrowing in international financial markets (foreign financing boom-bust) (Figure 9)
- Setup:
  - Two economies: resilient (0% forex lending; black solid) and vulnerable (50% forex lending; red dashed).
  - Sequence: three-year boom with cost of foreign financing dropping by 200 basis points (misperceived as permanent); unanticipated reversal at end of third year: cost increases by 300 basis points to 100 basis points above original level, then gradually declines.
- Common initial effects:
  - Real exchange rate appreciation ≈ 5 percent on impact.
  - Domestic lending increases by 4 to 5 percent by end of third year.
  - By end of year three: real GDP expands ≈ 3 percent; consumption just under 2 percent; investment almost 15 percent.
  - Spreads decrease initially; stronger impact in vulnerable economy.
- Post-reversal: resilient economy (domestic-currency lending)
  - Domestic real rate rises gradually; immediate drop in investment and output; real bank credit declines with GDP.
  - Lending spreads increase to around 20 basis points above initial at reversal, then decline.
  - Small borrower defaults and bank losses; real asset prices decline by less than 2 percent.
  - Banks’ capital adequacy remains almost unchanged; GDP declines smoothly without large negative output gaps; inflation returns to target aided by depreciation.
- Post-reversal: vulnerable economy (50% forex lending)
  - Real depreciation increases domestic-currency value of foreign-currency loans, impairing borrowers’ net worth.
  - Banks make large loan losses ≈ 0.8 percent of loan book value; capital adequacy deteriorates by similar amount.
  - Banks reduce lending immediately by almost 4 percent and increase spreads by almost 2 percentage points.
  - Vicious cycle: deeper demand contraction, larger depreciation, asset prices drop over 8 percent.
  - GDP drops by almost 5 percent within a year of reversal; inflation continues falling for another year; policy rate declines to contain downturn.
- Policy implication:
  - Foreign currency exposure amplifies nonlinear costs during reversals.
  - Macroprudential options: tighten during booms and relax during reversals; prudential regulation of currency mismatches is an additional tool.

### VI. Appendices, calibration, and key parameter values
- Model calibrated to a typical emerging market economy: high shares of exports and imports in GDP, flexible access to international financial markets, autonomous monetary policy with floating exchange rate.
- Baseline assumption: 50% dollarization (financial dollarization 0.5) of bank loans held by non-financial agents; banks assumed hedged to avoid direct currency mismatch exposure.
- Credit-risk calibration produces troughs in GDP and domestic demand ranging roughly between 5 and 10 % relative to pre-event levels.
- Selected Table 1 baseline parameter values (selected entries preserved exactly):
  - ØDiscount parameter 0.966
  - Ø0 Reduced discount parameter 0.955
  - ∏Loss given default 0.9
  - &Total credit risk 0.21
  - ˆ&Prediction of total credit risk 0.21
  - %Cross-correlation of exposures 0.21
  - ¡C Financing of consumption 1.46
  - ¡I Financing of investment 1.46
  - ¡K Financing of physical capital 0.1
  - ÆDomestic labor in exports 0.3
  - ¥Inverse elasticity of labor supply 0
  - ±Depreciation of physical capital 0.025
  - ∞N Labor share of domestic production 0.4
  - ∞M Import share of domestic production 0.2
  - μMonopoly power 1.2
  - ∑Location parameter for stochatic default threshold 0.74
  - !Direct import in final demand 0
  - ∫Local ownership of banks 0
  - 'Minimum capital adequacy ratio 0.08
  - ¿Regulatory penalty 0.06
  - ºInflation target 0
  - μ1 Monetary policy smoothing 0.8
  - μ2 Monetary policy reaction to inflation 4
  - ∂Non-price lending conditions response 0.2
  - ªE Bank capital adjustment cost 1
  - ¬Consumption habit 0.85
  - ªC Current income dependence 0.5
  - ªW Wage adjustment cost 300
  - ªP Price adjustment cost 300
  - ªY Input factor adjustment cost 30
  - ªX Export adjustment cost 30
  - ªI Investment adjustment cost 5
  - oFinancial dollarization 0.5
- Table 2 selected steady-state characteristics (selected entries preserved exactly):
  - Capital adequacy ratio 11.41 %
  - Capital buffers 3.41 %
  - Capital-to-assets ratio (not adjusted) 10.98 %
  - Lending spread 2.37 %
  - Individual risk component of lending spread 1.22 %
  - Regulatory component of lending spread 1.13 %
  - Bank-deposits-to-GDP-ratio 56 %
  - Total-consumption-to-GDP ratio 79 %
  - Business-investment-to-GDP ratio 19 %
  - Export-to-GDP ratio 62 %
  - Share of value added in exports 30 %
  - Net-exports-to-GDP ratio 2 %
  - Foreign-debt-to-GDP ratio 20 %
  - Note: "All steady-states rates of interest and flows-to-stock ratios are annualized."

### VII. Model capabilities, caveats, and final lessons
- Capabilities:
  - MAPMOD simulates shocks to productivity, borrower riskiness, asset-price deviations, bank equity, and foreign interest rates; it also simulates macroprudential policy changes (MCAR levels and countercyclicality).
  - Global nonlinear version captures pre-crisis and crisis phases of financial cycles and endogenous bank-borrower-real economy feedbacks.
- Caveats:
  - MAPMOD is a prototype calibrated to basic facts of financial cycles; parameterization is illustrative.
  - Estimation of nonlinear models requires large samples; success of macroprudential policy in preventing crises limits available observations, implying continued reliance on judgment informed by cross-country empirical evidence.
- Core policy takeaways:
  - Nonlinear balance-sheet feedbacks can produce crisis amplifications far larger than implied by linear models; nonlinear simulations are essential for policy evaluation.
  - Countercyclical macroprudential policies can substantially reduce crisis amplitudes but impose costs during benign booms; uncertainty about reversals often justifies countercyclical approaches.
  - Access to external equity and well-communicated, gradual regulatory changes reduce short-run disruption.
  - Foreign currency exposure on domestic balance sheets amplifies reversal costs; direct prudential limits on currency mismatches are an important supplement to macroprudential toolkits.

*Source: _wp1456 - References . . . . . . . . . . . . . . . . . . . . . . . . . 37*

### References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .37

### _wp1456 - References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .37

### Appendices
- A.   Parameterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .38
- B.   Numerical Assumptions for Simulations . . . . . . . . . . . . . . . . . . . . . . . . .42
- C.   Figures with Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .45

### Tables
- 1.   Baseline Parameter Values  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .40
- 2.   Selected Steady-State Characteristics . . . . . . . . . . . . . . . . . . . . . . . .41
- 3.   Revisions in Views About Trend Productivity Growth – Assumptions  . . . . . .42
- 4.   Underpricing of Lending Risk by Banks (“NINJA Loans” Shock) – Assumptions . .43
- 5.   Excessive Credit Expansion Caused by an Asset Price Bubble – Assumptions . .43
- 6.   Countercyclical Macroprudential Policy – Assumptions . . . . . . . . . . . . . . .44
- 7.   Permanent Increase in Minimum Capital Adequacy Ratio – Assumptions  . . . .44
- 8.   Shocks to the Cost of Borrowing in International Financial Markets – Assumptions44

### Figures
- 1.   Revisions in Views About Trend Productivity Growth . . . . . . . . . . . . . . .46
- 2.   Underpricing of Lending Risk by Banks (“NINJA Loans” Shock)  . . . . . . . .47
- 3.   Excessive Credit Expansion Caused by an Asset Price Bubble . . . . . . . . . .48
- 4.   Financial Sector Vulnerabilities and Financial Crises . . . . . . . . . . . . . . .49
- 5.   Nonlinear versus Linear Simulations . . . . . . . . . . . . . . . . . . . . . . . . .50
- 6.   Countercyclical Macroprudential Policy . . . . . . . . . . . . . . . . . . . . . . . .51
- 7.   Contractionary Shock to Bank Capital  . . . . . . . . . . . . . . . . . . . . . . .52
- 8.   Permanent Increase in Minimum Capital Adequacy Ratio . . . . . . . . . . . . . .53

*Source: _wp1456 - References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .37*

### 9.   Shocks to the Cost of Borrowing in International Financial Markets . . . . . . . . .54

### 9.   Shocks to the Cost of Borrowing in International Financial Markets . . . . . . . . .54

### I. Introduction
- MAPMOD: a new IMF model to support macrofinancial and macroprudential policy analysis; companion paper (Benes, Kumhof, and Laxton,2014) discusses theoretical structure; this paper presents simulation properties.
- Design purpose: study vulnerabilities associated with excessive credit expansions and asset price bubbles, and consequences of different macroprudential policies.
- Critical macroprudential tradeoff: reducing the risks of very costly financial crises versus minimizing costs of macroprudential policies during normal times.
- Key modeling emphasis: revamp of conventional linear DSGE models to incorporate the special role played by banks, especially bank balance sheets and nonlinear feedbacks between bank balance sheets, borrower balance sheets and the real economy.
- MAPMOD features:
  - Banks and bank balance sheets that absorb lending losses via net worth.
  - Bank loans create purchasing power (bank deposits) and expand balance sheets.
  - Globally nonlinear version captures pre-crisis and crisis phases of financial cycles.

### II. Modeling philosophy and key design features of MAPMOD
- Rationale:
  - Large distress events generate inherently nonlinear economic mechanisms (Milne(2009); Borio,2012).
  - Vicious interactions between asset prices, bank lending conditions and the real economy magnify effects.
  - Conventional linearized DSGE models fail to capture nonlinearities and the special role of banks.
- Key differences in MAPMOD’s treatment of banks (partial list):
  - Banks maintain a stock of net worth to absorb loan losses because of Basel-style minimum capital adequacy regulation, frictions in acquiring new net worth, and non-diversifiable aggregate lending risk.
  - Determination of loan price and quantity, and maintenance of capital buffers above minimum requirements, arise as an optimal equilibrium phenomenon from loan contracts, endogenous loan losses and regulation.
  - In making new loans, commercial banks create matching liabilities (bank deposits) for borrowers, thereby expanding their balance sheets; banks are limited by perceived profitability and risk absorption capacity of capital.
  - Banks respond to financial shocks through higher spreads and non-price credit rationing; rapid credit shrinkage during distress cuts households and firms from financing.
  - Severe crises feature vicious and highly nonlinear feedbacks between borrower balance sheets, banks’ balance sheets, and the real economy.
- Two nonlinear feedback effects highlighted:
  - Lending losses erode bank capital adequacy, triggering rapid contraction in lending and higher spreads as banks rebuild equity buffers.
  - Declines in borrowers’ asset values increase loan-to-value ratios, further reducing lending volumes and increasing spreads.
- Policy implication: macroprudential policy should encourage more countercyclical bank behavior.

### III. Examples of good and bad credit expansions
- Presentation format for scenarios: four columns of charts showing (1) GDP and aggregate demand components, (2) price variables (wage and CPI inflation, policy interest rate, real exchange rate), (3) nonbank financial variables (net foreign assets relative to GDP, physical capital stock, real asset prices, real value of capital stock), and (4) bank-specific variables (real bank credit, pre-default lending spread, loan default rate, post-default Basel capital adequacy ratio). A blue box encloses the five key banking system variables.
- Initial simulation assumption approach: deliberately exclude countercyclical macroprudential response to highlight vulnerabilities to revisions in beliefs.

A. Revisions in views about trend productivity growth (Figure1)
- Experiment setup:
  - Agents initially expect higher trend productivity growth rates in the export sector over the subsequent 10 years, leading to expected long-run output rise by approximately 10 percent;
  - Expectations improve gradually and linearly over the first four quarters shown.
- Good credit expansion (black solid lines):
  - If expectations remain correct, output ultimately grows by 10 percent.
  - Investment increases particularly fast, by year three almost 12 percent above initial level.
  - Headline inflation eventually falls by around 1.2 percentage points in year 5.
  - Policy rate stays essentially constant over first two years, then drops with forecast lower headline inflation.
  - Real appreciation: very strong and highly persistent.
  - Trade balance deterioration: almost 2 percent of GDP in the second year.
  - Net foreign assets position deteriorates by about 3.5 percent of GDP at end of third year, and by almost 4.5 percent of GDP after five years.
  - Bank responses: quantity of lending dominates; reduction in spreads in short run is small at less than 50 basis points; bank capital adequacy ratio starts at 11.4 percent (buffer of 3.4 percent above minimum 8 percent) and banks reduce buffer to 3.1 percent as lending grows.
  - Real bank credit increases by almost 8 percent after three years, and by well over 20 percent in the long run.
- Bad credit expansion (red dashed lines):
  - Expectations and realizations revised back to baseline at beginning of fourth year (less than a third of initially expected long-term potential output increase realized).
  - Immediate steep drop in real asset prices of over 6 percent, and real output contraction of around 4 percent.
  - Loan losses equal around 0.5 percent of the value of all loans.
  - Immediate rise in spreads by more than one percentage point (~120 basis points on impact); initial deterioration in average capital adequacy ratio of roughly 0.5 percentage point to around 10.7 percent.
  - Instantaneous discontinuous reduction in lending volume around 3 percent; lending spreads rise about 120 basis points on impact.
  - Policy rate reduction around 2.3 percentage points two years into crisis mitigates but cannot offset balance sheet dislocations fully.

B. Underpricing of lending risk by banks (“NINJA Loans” shock) (Figure2)
- Setup:
  - Banks revise down perceived standard deviation of borrower idiosyncratic risk by 5 percent by end of third year; actual standard deviation unchanged.
- Two scenarios:
  - NINJA1 (black solid lines): banks permanently maintain reduced perceived risk.
    - Real bank credit increases by around 1.5 percent by end of third year.
    - Lending spreads drop by around 15 basis points over same period.
    - Capital-adequacy ratio allowed to drop by almost 0.5 percentage points in the long run.
    - Investment reaches 2 percent increase by end of third year; real asset prices increase roughly 0.5 percent.
    - Consumption increases over 1.5 percent by end of third year.
    - GDP increases by around 1 percent by end of third year.
    - Inflation increases by 0.6 percentage points by end of third year; policy rate rises accordingly.
    - Net foreign assets position reduced to just under 4 percent of GDP.
    - Long-run: spreads permanently lower by around 5 basis points; credit permanently higher by around 1.5 percent.
  - NINJA2 (red dashed lines): banks’ expectations return to true borrower risk over about three years.
    - Rapid contraction of lending back to original level; immediate 20 basis points increase in lending spreads; average spreads thereafter around 5 basis points higher than initially.
    - Sudden tightening leads to roughly 2 percent drop in real asset prices.
    - Bank lending losses around 0.1 percent of the value of the loan book.
    - GDP drops by 1.75 percent; real exchange rate depreciates; trade balance improves; inflation falls faster than in NINJA1.

C. Excessive credit expansion caused by an asset price bubble (Figure3)
- Setup:
  - Over first three years, expected future returns on physical capital equal fundamentals plus exogenous non-fundamental shocks that peak end of year three.
  - Actual bubble component: 10 percent at end of third year; observed real asset price increase ~18 percent over first three years due to endogenous feedback.
- Boom phase:
  - Real bank credit increases by 9 percent after three years.
  - Spreads fall by less than 50 basis points over same period.
  - Equity buffer declines from 11.4 percent to 10.8 percent.
  - Investment increases by around 24 percent by end of third year.
  - Consumption increases by almost 3 percent; GDP over 5 percent.
  - Net foreign assets deteriorate by almost 3 percent of GDP by end of third year.
  - Inflation increases by around 0.7 percentage points over first three years; policy rate increases.
- Crash at end of third year:
  - Asset prices collapse by over 25 percent, initially undershooting long-run values by around 8 percent.
  - Loan losses roughly equal to 1.5 percent of total value of loans.
  - Average capital adequacy ratio deteriorates from 10.8 percent to 9.5 percent.
  - Banks raise spreads around 150 basis points and implement an instantaneous 8 percent contraction in lending, destroying roughly equal-sized purchasing power.
  - Investment collapses around 15 percent within less than a year and over 25 percent eventually.
  - Consumption drops by about 5 percent within less than one year; GDP drops around 5 percent.
  - Wage inflation surges by over 100 basis points following collapse.

### IV. Nonlinearities, leverage, and macroprudential policy
A. Financial sector vulnerabilities and financial crises (Figure4)
- Combined shocks (productivity shocks of Figure1 and borrower riskiness shocks of Figure2) produce:
  - Pre-crisis (first three years): combined effects roughly additive:
    - Real bank credit grows around 9 percent (7.5 percent and 1.5 percent in Figures1 and 2).
    - Spreads roughly unchanged by end of third year (approximately +10 basis points and -10 basis points in Figures1 and 2).
    - Investment grows by 14 percent by end of third year (12 percent and 2 percent).
    - Consumption grows by 5.5 percent (4 percent and 1.5 percent).
    - GDP grows by 5 percent (4 percent and 1 percent).
  - Upon reversal at end of third year: nonlinear amplification produces far larger effects than sum of individual shocks:
    - Asset prices collapse 12 percent (versus 6 percent and 2 percent in Figures1 and 2).
    - Lending losses 2 percent of value of assets (versus 0.5 percent and <0.1 percent).
    - Bank capital adequacy declines by 1.5 percentage points (versus 0.4 percentage points and 0.1 percentage points).
    - Lending spreads increase over 300 basis points (versus 110 basis points and 20 basis points).
    - Real bank credit drops more than 5 percent (versus <3 percent and <1 percent).
    - Investment drops 15 percent over first two quarters (versus 9 percent and 2 percent).
    - Consumption drops 8 percent (versus 4 percent and 1.5 percent).
    - GDP drops 6 percent (versus 3.5 percent and 1 percent).
- Conclusion: large balance sheet vulnerabilities lead to nonlinear crisis amplification; combined effects exceed sum of individual shock effects.

B. Nonlinear versus linear simulations (Figure5)
- Comparison of identical shocks simulated in nonlinear model versus linearized version:
  - Nonlinear simulation (black solid lines in Figure5 identical to red dashed lines in Figure4) generates much more severe downturn in financial and real variables than linearized simulation.
  - Asset prices drop 12 percent in nonlinear simulation versus 6 percent in linearized simulation.
  - Loan losses equal 2 percent of value of loans in nonlinear simulation versus 0.25 percent in linearized simulation.
  - Pre-default lending spreads increase over 300 basis points in nonlinear simulation versus around 80 basis points in linearized simulation.
  - Bank credit decreases 5 percent on impact in nonlinear simulation versus <3 percent in linearized simulation.
  - GDP declines 7 percent peak-to-trough in nonlinear simulation versus a little over 4 percent in linearized simulation; contraction also happens faster in nonlinear simulation.
- Lesson: linearized models fail to capture crisis-time nonlinearities originating in balance-sheet dynamics; nonlinear simulations are imperative for policy analysis of crises and macroprudential measures.

C. Countercyclical macroprudential policy (Figure6)
- Baseline (constant MCAR scenario):
  - All prior scenarios assume constant minimum capital adequacy ratio (MCAR) of 8 percent.
- Countercyclical MCAR scenario:
  - MCAR is time-varying, asymmetric and countercyclical: never allowed to drop below 8 percent on downside; on the upside it is raised in response to positive year-on-year loan growth (exact numerical path reported in Table6).
  - If banks increase lending, they must accumulate additional capital buffer; policy inertia allows gradual compliance.
- Effects during boom (initial three years):
  - Countercyclical MCAR forces banks to maintain or slightly increase capital adequacy ratio; actual capital adequacy ratio increases by around 0.2 percentage points by end of third year.
  - Difference in spreads between scenarios ~30 basis points by end of third year (spreads higher under countercyclical MCAR).
  - Boom-phase increases in physical capital stock and real asset prices ~half as large as under constant MCAR.
  - Investment boom smaller by almost two thirds; GDP growth little over 3 percent by end of third year versus 5 percent under constant MCAR.
  - Real appreciation and trade balance deterioration less pronounced.
  - Inflation declines immediately under countercyclical MCAR; policy rate follows.
- Trade-off:
  - Countercyclical MCAR imposes costs during correct-fundamentals booms (slower growth and lower investment).
  - Benefits in crisis: because of nonlinearities and asymmetries, crisis-phase gains (smaller drops) can be far larger than boom-phase costs.
- Crisis-phase adjustment under countercyclical MCAR:
  - MCAR immediately lowered substantially following expectations revision by a full 1.5 percentage points to minimum of 8 percent, permitting banks to take less drastic measures while satisfying regulations.
  - Banks still incur lending losses, but their capital adequacy ratio only dropping by around

*Source: IMF working paper chapter content (MAPMOD simulation and analysis).*

### 0.25 percentage points. The reason is that lending losses are themselves a function of the

### _wp1456 - 0.25 percentage points. The reason is that lending losses are themselves a function of the

### Countercyclical MCAR and lending dynamics
- Countercyclical policy response permits smaller increases in spreads and a smaller contraction in lending, directly feeding into smaller effects on future earnings of borrowers.
- Under countercyclical MCAR:
  - Asset prices drop by around 2 percent, compared to 12 percent under constant MCAR.
  - Amplitudes of fluctuations in investment and consumption are at around one third and one half (respectively) of those under constant MCAR.
  - GDP contracts by around 2 percent from peak to trough, compared to around 7 percent under constant MCAR.
  - Inflation is "barely affected" by onset of recession; policy rate does not exhibit a major reversal.
- Policy trade-off:
  - If lending boom is based on sound fundamentals, raising capital adequacy requirements imposes significant costs while benefits (which occur during downturns) are unlikely.
  - Where policymakers are uncertain about reversal risk, even modest probability of getting it wrong argues for a countercyclical macroprudential approach because of large costs from nonlinearities and asymmetries on balance sheets.

### A. Contractionary shock to bank capital (exogenous 20 percent regulatory bank equity loss)
- Shock specifics:
  - Exogenous 20 percent loss of regulatory bank equity in a single period.
  - Banking system’s capital adequacy ratio immediately reduced by 2.4 percentage points, from 11.4 percent to 9.0 percent; MCAR assumed to remain at 8 percent.
- Two recapitalization scenarios:
  - Scenario 1 (banks recapitalize only from retained earnings; corresponds to ≥E = 1):
    - Immediate reduction in loans equals 2.2 percent.
    - Immediate increase in spreads equals 2.1 percentage points.
    - Real effects: GDP drops by more than 2 percent by end of first year; consumption by almost 3 percent; investment by almost 5 percent.
    - CPI inflation drops by around 0.6 percentage points by end of first year; policy rate drops by around 1 percentage point.
    - Asset prices drop by over 5 percent on impact.
    - Capital stock reduced by 0.8 percent after three years.
    - Banks experience a spike in loan losses equal to around 0.2 percent of portfolio value at time of shock.
  - Scenario 2 (banks can access equity markets, parameterized by ≥E = 0.5):
    - Immediate reduction in loans equals 0.9 percent.
    - Immediate increase in spreads equals 1.0 percentage point.
    - Real effects: GDP drops by 0.8 percent at the lowest point (vs 2.2 percent when recapitalization via retained earnings only).
    - Inflation declines by 0.2 percent instead of 0.6 percent.
- Mechanism and implication:
  - Access to equity markets allows banks to rebuild capital adequacy with less reliance on lending reductions and spread increases.
  - Macroprudential policies that reassure potential bank equity investors during a crisis can disproportionately reduce nonlinearities and yield large benefits.

### B. Permanent increase in Minimum Capital Adequacy Ratio (MCAR: 8 percent → 10 percent)
- Experiment design:
  - Permanent increase in MCAR from 8 percent to 10 percent.
  - Three implementation speed scenarios (banks have no access to equity markets; equity changes via earnings only):
    - Immediate jump (black solid line).
    - Gradual raise over four years, most in first two years (red dashed line).
    - Announced future increase starting after two years, then same path as gradual scenario (blue dash-dotted line).
  - Exact numerical MCAR paths reported in Table 7 (table content not reproduced here).
- Long-run effects (identical across scenarios):
  - Spreads rise by about 30 basis points in the very long run.
  - Banks’ loan and deposit levels decline by approximately 2 percent.
  - Potential output (capital stock) drops by around 0.8 percent.
- Short-run effects by scenario:
  - Immediate increase scenario:
    - Banks immediately reduce loan volume by over 3 percent.
    - Spreads increase around 2 percentage points on impact.
    - Real asset prices decline by around 8 percent on impact.
    - Banks make lending losses equal to around 0.4 percent of asset value on impact.
    - Actual capital adequacy ratio initially reduced by around 0.2 percent.
    - GDP contracts by almost 3 percent towards the end of the first year.
    - Inflation drops by almost 0.7 percentage points; policy rate drops by 1.7 percentage points.
    - Banks rebuild equity buffer above new MCAR after around 5 years.
  - Unanticipated but gradual increase:
    - Spreads rise by just over 40 basis points initially and remain 30 basis points above previous level thereafter.
    - Real asset prices decline by around 4 percent (about half of the immediate scenario).
    - GDP contracts by around 1.75 percent at the lowest point (vs almost 3 percent under immediate change).
    - Investment fluctuation amplitude similar to immediate scenario; consumption contraction markedly shallower.
  - Anticipated gradual increase:
    - Spreads increase by less than 10 basis points over the initial two-year period prior to MCAR increases, then rise subsequently.
    - Banks’ loan book declines by 2 percent prior to end of second year (main strategy is balance-sheet reduction rather than immediate spread spike).
    - Real asset prices decline by less than 1 percent on impact.
    - Consumption barely affected over first two years; GDP smoothly declines toward new long-run level (around 0.8 percent lower).
    - Inflation downward pressure far smaller in short term.
- Policy lesson:
  - Implementation speed and communication matter: gradual and well-communicated increases in MCAR reduce short-run disruption and avoid turning regulation into an unexpected shock.

### C. Shocks to the cost of borrowing in international financial markets (boom-bust driven by foreign financing cost)
- Setup:
  - Two scenarios: resilient economy (all lending in domestic currency; black solid line) vs vulnerable economy (50 percent of lending in foreign currency; red dashed line).
  - Sequence of foreign financing cost shocks:
    - Initial three-year boom: cost of foreign financing drops by 200 basis points (misperceived as permanent).
    - Unanticipated reversal at end of third year: cost increases by 300 basis points to 100 basis points above original level, then gradually declines back to original.
- Common initial effects:
  - Real exchange rate appreciation of approximately 5 percent on impact.
  - Domestic lending increases by 4 to 5 percent by end of third year.
  - By end of year three: real GDP expands by about 3 percent; consumption by just under 2 percent; investment by almost 15 percent.
  - Spreads decrease initially; impact stronger in vulnerable economy.
- Post-reversal: resilient economy (domestic-currency lending)
  - Foreign real interest rate rises suddenly; domestic real rate rises more gradually.
  - Immediate drop in investment demand and output; real bank credit declines with GDP.
  - Lending spreads had increased to around 20 basis points above initial value by reversal, then decline as banks cut funding to riskier borrowers.
  - Small increase in borrower defaults and bank losses; real asset prices decline by less than 2 percent.
  - Banks’ capital adequacy ratio remains almost unchanged; no large forced lending cuts or spread spikes.
  - GDP declines smoothly without large negative output gaps; inflation returns to target, aided by depreciation.
- Post-reversal: vulnerable economy (50 percent foreign-currency lending)
  - Real depreciation increases domestic-currency value of foreign currency loans, severely impairing borrowers’ net worth.
  - Banks make large loan losses equal to around 0.8 percent of loan book value; capital adequacy ratio deteriorates by a similar amount.
  - Banks respond by reducing lending immediately by almost 4 percent and increasing spreads by almost 2 percentage points.
  - This triggers a vicious cycle: deeper contraction in demand, larger real depreciation, asset prices drop over 8 percent.
  - Result: GDP drops by almost 5 percent within a year of the reversal; inflation continues falling for another year; policy rate declines to contain downturn.
- Policy implication:
  - Foreign currency exposure on domestic balance sheets amplifies nonlinear costs during reversals.
  - Macroprudential responses can include tightening during booms and relaxing during reversals, and direct prudential regulation of currency mismatches is an additional policy tool to consider.

### Conclusion and model features
- MAPMOD highlights banks as active agents in macro transmission, creating deposits when making loans and rapidly expanding or contracting balance sheets when adequately capitalized.
- Key nonlinear mechanism: when optimistic lending assessments reverse, severe cutbacks in lending (not only spread increases) drive deep and sudden recessions via balance-sheet feedbacks.
- The model can simulate shocks to productivity, borrower riskiness, asset price deviations, bank equity, and foreign interest rates, and simulate macroprudential policy changes (MCAR levels and countercyclicality).
- Calibration and estimation caveats:
  - MAPMOD is a prototype calibrated to basic facts of financial cycles.
  - Estimation of nonlinear models requires large samples; macroprudential success in preventing crises may limit available observations, implying continued reliance on judgment informed by cross-country empirical evidence.

*Italic line: Source: Excerpt from the provided IMF PDF content unit.*

### REFERENCES

### _wp1456 - REFERENCES

### References
- Benes, Jaromir, and Michael Kumhof, 2011, “Risky Bank Lending and Optimal Capital Adequacy Regulation,” IMF Working Paper, 11/130.
- Benes, Jaromir, Michael Kumhof, and Douglas Laxton, 2014, “Financial Crises in DSGE Models: A Prototype Model,” IMF Working Paper.
- Blanchard, Olivier J., Jean-Paul L’Huillier, and Guido Lorenzoni, 2013, “News, Noise, and Fluctuations: An Empirical Exploration,” American Economic Review, Vol. 103, No. 7, pp. 3045–3070.
- Boissay, Frederic, Fabrice Collard, and Frank Smets, 2013, “Booms and Systemic Banking Crises,” ECB Working Paper, 1514.
- Borio, Claudio, 2012, “The financial cycle and macroeconomics: What have we learnt?” BIS Working Paper, 395.
- ———, 2014, “The financial cycle and macroeconomics: What have we learnt?” Journal of Banking and Finance (In Press).
- Christiano, Lawrence J., Cosmin L. Ilut, Roberto Motto, and Massimo Rostagno, 2010, “Monetary Policy and Stock Market Booms,” NBER Working Paper, 16402.
- Claessens, Stijn, M. Ayhan, and Macro Terrones, 2011, “How Do Business and Financial Cycles Interact?” IMF Working Paper, 11/88.
- Committee on the Global Financial System, 2010, “Macroprudential instruments and frameworks: a stocktaking of issues and experiences,” CGFS Paper, 38.
- Hansen, Lars P., 2012, “Challenges in Identifying and Measuring Systemic Risk,” NBER Working Paper, 18505.
- Jaimovich, Nir, and Sergio Rebelo, 2009, “Can News about the Future Drive the Business Cycle?” American Economic Review, Vol. 99, No. 4, pp. 1097–1118.
- Juillard, Michael, Ondra Kamenik, Michael Kumhof, and Douglas Laxton, 2008, “Optimal price setting and inflation inertia in a rational expectations model,” Journal of Economic Dynamics and Control, Vol. 32, No. 8, pp. 2584–2621.
- Macroeconomic Assessment Group, 2010, “Assessing the macroeconomic impact of the transition to stronger capital and liquidity requirements,” Macroeconomic Assessment Group Final Report, Basel Committe on Banking Supervision.
- Milne, Alistair, 2009, “Macroprudential policy: what can it achieve?” Oxford Review of Economic Policy, Vol. 25, No. 4, pp. 608–629.
- Yang, Jing, and Kostas Tsatsaronis, 2012, “Bank stock returns, leverage and the Business Cycle,” BIS Quarterly Review, March 2012, pp. 45–59.

### Appendix A. Parameterization — Key points
- Model calibrated to a typical emerging market economy: high shares of exports and imports in GDP, flexible access to international financial markets, autonomous monetary policy with a floating exchange rate.
- Baseline assumption: 50% dollarization of financial liabilities (bank loans) held by non-financial agents (households); banks remain unexposed to direct currency mismatches via hedging strategies.
- Credit risk characteristics calibrated to produce troughs in real economic activity (GDP and domestic demand) ranging roughly between 5 and 10 % relative to the level preceding the adverse event.
- Individual parameter values used for simulation experiments are listed in Table 1; selected steady-state characteristics are in Table 2.
- Authors caution: parameterization is illustrative; results should not be used for direct quantitative inference due to large uncertainties, including Knightian uncertainty.

### Table 1. Baseline Parameter Values (selected entries)
- Parameters Affecting Steady State
  - ØDiscount parameter 0.966
  - Ø0 Reduced discount parameter 0.955
  - ∏Loss given default 0.9
  - &Total credit risk 0.21
  - ˆ&Prediction of total credit risk 0.21
  - %Cross-correlation of exposures 0.21
  - ¡C Financing of consumption 1.46
  - ¡I Financing of investment 1.46
  - ¡K Financing of physical capital 0.1
  - ÆDomestic labor in exports 0.3
  - ¥Inverse elasticity of labor supply 0
  - ±Depreciation of physical capital 0.025
  - ∞N Labor share of domestic production 0.4
  - ∞M Import share of domestic production 0.2
  - μMonopoly power 1.2
  - ∑Location parameter for stochatic default threshold 0.74
  - !Direct import in final demand 0
  - ∫Local ownership of banks 0
- Policy parameters
  - 'Minimum capital adequacy ratio 0.08
  - ¿Regulatory penalty 0.06
  - ºInflation target 0
  - μ1 Monetary policy smoothing 0.8
  - μ2 Monetary policy reaction to inflation 4
- Other Parameters
  - ∂Non-price lending conditions response 0.2
  - ªE Bank capital adjustment cost 1
  - ¬Consumption habit 0.85
  - ªC Current income dependence 0.5
  - ªW Wage adjustment cost 300
  - ªP Price adjustment cost 300
  - ªY Input factor adjustment cost 30
  - ªX Export adjustment cost 30
  - ªI Investment adjustment cost 5
  - oFinancial dollarization 0.5

### Table 2. Selected Steady-State Characteristics (selected entries)
- Banking
  - Capital adequacy ratio 11.41 %
  - Capital buffers 3.41 %
  - Capital-to-assets ratio (not adjusted) 10.98 %
  - Lending spread 2.37 %
  - Individual risk component of lending spread 1.22 %
  - Regulatory component of lending spread 1.13 %
  - Bank-deposits-to-GDP-ratio 56 %
- Real economy
  - Total-consumption-to-GDP ratio 79 %
  - Business-investment-to-GDP ratio 19 %
  - Export-to-GDP ratio 62 %
  - Share of value added in exports 30 %
  - Net-exports-to-GDP ratio 2 %
  - Foreign-debt-to-GDP ratio 20 %
- Note: "All steady-states rates of interest and flows-to-stock ratios are annualized."

### Appendix B. Numerical Assumptions for Simulations — Tables and scenario assumptions
- Table 3. Revisions in Views About Trend Productivity Growth – Assumptions
  - Provides quarterly series for five variant sequences (labelled (1) through (5)) across quarters 0–24 with explicit numbers (e.g., series (1): 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.7 1.9 2.1 2.3 ... up to quarter 24 value 8.0).
  - Notes define levels as "100 log (A_X,t/A_X,0)" for different expectation scenarios and actual realizations.
- Table 4. Underpricing of Lending Risk by Banks (“NINJA Loans” Shock) – Assumptions
  - Quarterly series of standard deviation assumptions (100 b&t and 100 &t) for scenarios labelled (1)–(4) across quarters 0–24 (e.g., many entries equal 21.0, others decline to 20.0).
  - Notes define each series as standard deviation of the log return on collateralizing assets in "NINJA1" and "NINJA2" scenarios.
- Table 5. Excessive Credit Expansion Caused by an Asset Price Bubble – Assumptions
  - Two series across quarters 0–12 and beyond, e.g., series (1): 0 0.4 1.1 1.8 2.6 3.5 4.4 5.3 6.2 7.1 8.0 9.0 9.9; series (2): 0 0.4 0.8 1.2 1.7 2.1 2.5 2.9 3.3 3.8 4.2 4.6 5.0.
  - Notes: (1) Asset price bubble, 100 log (B_t/B_0). (2) Unanticipated shocks to the bubble process, 100 ≤ B,t.
- Table 6. Countercyclical Macroprudential Policy – Assumptions
  - Series for constant minimum capital adequacy ratios and countercyclical minimum capital adequacy ratios across quarters 0–24, e.g., constant series (1) equals 8.0 for many quarters; countercyclical series (2) rises from 8.0 to 9.5 in some quarters.
  - Notes: (1) Constant minimum capital adequacy ratios, 100 g_t. (2) Countercyclical minimum capital adequacy ratios, 100 g_t.
- Table 7. Permanent Increase in Minimum Capital Adequacy Ratio – Assumptions
  - Three series across quarters 0–24 representing unanticipated immediate, unanticipated gradual, and anticipated gradual increases, with explicit quarterly values (e.g., series (1) starts 8.0 then 10.0 from quarter 1 onward).
  - Notes label each series accordingly.
- Table 8. Shocks to the Cost of Borrowing in International Financial Markets – Assumptions
  - Series for quarter 0–12 and 13–24, e.g., series (1) shows 0 -2.00 -2.00 ... -2.00 for quarters 1–12, then quarters 13–24 show gradual reductions (1.00 0.50 0.25 0.12 0.06 0.03 0.02 0.01 0.00 0.00 0.0000).
  - Note: "Cost of world finance (non-resident bank liabilities), 100 h°R§t ± R§0¢ 4°1 i."

### Appendix C. Figures with Simulation Results — Themes and scenarios illustrated
- Figures 1–9 present impulse responses (Real GDP, Wage Inflation, Net Foreign Assets to GDP, Real Bank Credit, Consumption, CPI Inflation, Physical Capital Stock, Lending Spread, Investment, Policy Rate, Real Asset Prices, Portfolio Default Rate, Trade Balance to GDP, Real Exchange Rate, Real Value of Capital Stock, Post-Default Capital Adequacy Ratio) across 0–40 quarters for multiple scenarios. Key scenario annotations include:
  - Figure 1: "Revisions in Views About Trend Productivity Growth" — scenarios: "High productivity growth for 10 years" and "Productivity optimism for 3 years, then revised down."
  - Figure 2: "Underpricing of Lending Risk by Banks (“NINJA Loans” Shock)" — scenarios: "Underpriced risk builds up in the first 3 years, then lasts forever" and "Underpriced risk builds up in the first 3 years, then comes back."
  - Figure 3: "Excessive Credit Expansion Caused by an Asset Price Bubble" — displays dynamics of bubble-driven credit expansion.
  - Figure 4: "Financial Sector Vulnerabilities and Financial Crises" — scenarios: "Lasts for 10 years" and "Lasts for 3 years and then risk and productivity growth revised back to baseline."
  - Figure 5: "Nonlinear versus Linear Simulations" — compares Nonlinear and Linearized simulations for a lead simulation with revisions.
  - Figure 6: "Countercyclical Macroprudential Policy" — compares baseline scenario with a countercyclical macroprudential reaction; caption notes "Productivity growth and underpriced risk for 3 years then both revised back to baseline" and "Countercyclical capital requirements."
  - Figure 7: "Contractionary Shock to Bank Capital" — compares "Retained Earnings Only" and "External Capital Flows" cases.
  - Figure 8: "Permanent Increase in Minimum Capital Adequacy Ratio" — compares "Unanticipated Immediate Increase in Capital Requirements," "Unanticipated Gradual Increase in Capital Requirements," and "Anticipated Gradual Increase in Capital Requirements."
  - Figure 9: "Shocks to the Cost of Borrowing in International Financial Markets" — compares "Resilient Economy (0% Forex Lending)" and "Vulnerable Economy (50% Forex Lending)."

- Each figure displays quarter-by-quarter deviations (pct level deviations, pp deviations, pct ratio) across a 0–40 quarter horizon with explicit axis tick marks reflected in the visuals.

*Source: _wp1456 - REFERENCES (PDF chapter/section).*

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