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### Introduction: purpose and scope
- Most models used by central banks prior to the international financial crisis were in the New-Keynesian style and implicitly assumed perfect and complete financial markets.
- Financial frictions arising from information asymmetry and non-convex transaction costs were missing; models featured a single risk-free interest rate and aggregated non-monetary assets into government bonds.
- The paper surveys the state of development of DSGE models with financial frictions in use by central banks and reviews main approaches to introducing financial frictions into such models.
- The paper offers priorities for future development of such models for monetary policy and financial stability analysis.
- Plan of the paper:
  - Section II: overview of DSGE models with financial features in use by central banks prior to the crisis and developments since the crisis.
  - Section III: weaknesses in existing models and priorities for development for forecasting and policy analysis.
  - Appendix: principal approaches to introducing financial frictions and modeling of banking sectors in DSGE models.

### Key findings on pre-crisis modeling (Sections I–II)
- Prior to the crisis, standard macroeconomic models used by most advanced country central banks modeled inter-linkages between the financial system and real activity in a very simplified manner.
- Central bank policy interest rate and exchange rate were treated as the financial variables of over-riding importance linking policy with economic activity.
- Implicit assumptions: perfect and complete financial markets (frictionless, fully competitive, without barriers to entry or exit) and absence of asymmetric information and non-convex transaction costs.
- Institutional and practical barriers limited integration of macroeconomic forecasting and financial stability analysis:
  - Financial stability analysis often located in different departments or outside central banks.
  - Data frequency mismatches: macro forecasting is typically quarterly; many financial stability data sources are lower frequency.
  - Financial stability analyses were often "snapshot" focused rather than dynamic and forward-looking for integration into forecasting.
- The lack of integrated macrofinancial models likely contributed to insufficient early warning of systemic vulnerabilities prior to the crisis.
- In response to the crisis, central banks and financial stability authorities are prioritizing incorporation of financial intermediation processes and frictions into forecasting and policy frameworks.

### Models in use before and after the crisis (Section II.A and II.B)
- General observation:
  - Prior to the financial crisis, main forecasting and policy analysis models—including DSGE models—used by most central banks almost all lacked financial frictions and credit channels and the scope for analyzing macrofinancial interactions and shocks.
  - Development of DSGE forecasting models with embedded financial frictions is "very much a work in progress."
- Adoption and coverage:
  - As of end–2010, the ECB, the U.S. Federal Reserve, and the Reserve Bank of New Zealand appear to have introduced such features into their main forecasting models.
  - Around "half a dozen countries have DSGE models with financial features in operation" based on consultations and a survey of working papers published through to end–2010.
- Representative model features (preserving source phrasing):
  - Bank of England — BEQM — "Housing as a financial asset with wealth effects on consumption. However, there are no financial imperfections."
  - Bank of Japan — JEM — "Housing as a financial asset with wealth effects on consumption and a financial intermediary. However, there are no financial imperfections."
  - US Federal Reserve — EDO (pre-crisis) — "Residential capital providing housing services. However, there are no financial imperfections per-se."
  - CMR (Christiano, et al. (2010)) — "The financial accelerator and financial intermediaries. Financial assets with different degrees of liquidity."
  - Reserve Bank of New Zealand — KITT (Lees (2009)) — "Households borrowing against housing; collateral constraints on foreign borrowing."
- Typical post-crisis modeling strategies:
  - Financial imperfections introduced mostly via the financial accelerator or collateral constraint frameworks, together with an explicit banking sector.
  - Models aim to capture the credit channel of transmission and frictions related to the banking sector.
  - Many such models remain developmental or research-oriented and may be used alongside main forecasting models during a break-in period.

### Published central bank DSGE models with financial frictions — features and banking representation
- Common features across surveyed models:
  - Financial accelerator frameworks, collateral constraints tied to housing, explicit banking sectors, bank capital requirements, and imperfect competition in banking.
- Selected model summaries (preserving original phrasing and balance-sheet descriptions):
  - Bank of Canada — Beaton, Lalonde, and Snudden (2010)
    - "Multi-country model with international financial flows. Each country features a heterogeneous banking sector following Dib (2010b). The credit channel is introduced via the financial accelerator framework"
    - Banking structure: "Monopolistic deposit and lending banks exchange resources in an interbank market. No cross-border interbank borrowing; international financial flows introduced via cross-border loans."
    - Banks balance sheets: Deposit banks: Assets: Net interbank position and government bonds. Liabilities: deposits. Lending banks: Assets: Loans. Liabilities: Net interbank position and bank capital.
  - Dib (2010a,b)
    - "The financial accelerator framework along with a heterogeneous banking sector. Lending banks face capital requirements."
    - Banking structure: "Two types of banks—deposit and lending banks. Resources are exchanged via an interbank market. Banks have monopolistic power to set interest rates on deposits and loans; and they can default on interbank borrowing and capital returns. Capital accumulated by the lending banks facing penalty costs whenever they deviate from the required level."
    - Banks balance sheets: Deposit banks: Assets: Net interbank position and government bonds. Liabilities: deposits. Lending banks: Assets: Loans and government bonds. Liabilities: Net interbank position, bank capital, and central banks injections.
  - Meh and Moran (2008)
    - "A double moral hazard framework—an agency problem between banks and their creditors (lenders); and between banks and entrepreneurs (borrowers). Capital position of banks determines their ability to obtain funds—the bank capital channel."
    - Banks balance sheets: Assets: Loans. Liabilities: Deposits and bank capital.
  - Bank of England — Markovic (2006)
    - "The financial accelerator framework with an external financing premium enriched by banks capital costs. The banking sector faces adjustment costs in capital accumulation—the capital channel."
    - Banks balance sheets: Assets: Loans. Liabilities: Deposits and bank capital.
  - Banco de España — Andres and Arce (2009)
    - "The collateral constraints framework, tied to house prices; An explicit banking sector collecting deposits and issuing loans. Assumption of imperfect competition in the banking sector."
    - Banks balance sheets: Assets: Loans to entrepreneurs. Liabilities: Deposits.
  - Banque de France — Dellas, et al. (2010)
    - "An assumption that households need to hold deposits to purchase consumption goods; Firms finance their production via bank loans. A time-varying default rate on loans."
    - Banks balance sheets: Assets: Loans to firms and reserves. Liabilities: Deposits, banks capital and risk-free securities.
  - Bank of Italy — Gerali et al. (2010)
    - "The collateral constraints framework; Costly accumulation of banking capital shifting interest rate margins; Banks are subject to capital requirements."
    - Banks balance sheets: Assets: Loans to households and entrepreneurs. Liabilities: Deposits and banks capital.
  - ECB — Angeloni and Faia (2009)
    - "Banks are exposed to runs with probability increasing with banks’ leverage ratio—the bank capital channel."
    - Banks balance sheets: Assets: Loans. Liabilities: Deposits and banks capital.
  - Christiano et al. (2010)
    - "The financial accelerator enriched by an explicit banking sector providing liquidity services."
    - Banks balance sheets: Assets: Reserves and loans. Liabilities: Deposits and securities.
- Cross-border aspects:
  - Most models assume only domestic banks and domestic currency funding; cross-border borrowing generally not allowed except in multi-country setups such as Beaton, et al. (2010).

### Identified weaknesses in existing models
- Limited endogenous modeling of financial frictions in many forecasting models.
- Many models lack a fully integrated banking sector and explicit credit channels.
- Institutional separation between macroeconomic forecasting and financial stability analysis impeded integrated model development and use.
- Data frequency and data availability constraints complicate embedding detailed financial sector features in quarterly forecasting models.
- Balance-sheet composition and portfolio riskiness often exogenous rather than endogenously optimized.
- Liability-side endogeneity largely absent, limiting analysis of funding composition effects (domestic vs foreign; retail vs wholesale).
- Liquidity and contagion risks receive much less attention than market and credit risks in existing DSGE frameworks.

### Priorities for future development (policy and modeling recommendations)
- Incorporate financial frictions (financial accelerator, collateral constraints, banking frictions) into DSGE models used for forecasting and policy analysis.
- Develop models that capture both credit channels and banking-sector-specific frictions including:
  - bank capital dynamics;
  - liquidity provision;
  - interbank markets.
- Improve collaboration and integration between macroeconomic forecasting units and financial stability units within central banks.
- Use a mix of approaches:
  - modify existing forecasting (often semi-structural) models to include key financial features for expediency;
  - develop new DSGE models incorporating banking and financial intermediation where appropriate.
- Address data and frequency issues to enable dynamic, forward-looking incorporation of financial sector information into macro forecasts.
- For macroprudential analysis:
  - Top priority: incorporate key elements of Basel III reforms into model frameworks.
  - Models must, at minimum, take into account impacts of changes in bank capital and liquidity requirements, imposition of leverage ratios and net stable funding ratios.
- Pragmatic modeling advice:
  - Keep incorporation parsimonious and focused on most important transmission mechanisms.
  - Consider a modeling "architecture" of multiple linked models: a core forecasting model with satellite models for detailed stress-testing and non-linear events.
  - Ensure satellite models are well integrated with core models and organizational procedures to enable iterative forecasting and scenario analysis.

### Modeling architecture and handling non-linearities
- Recommendation: develop several model versions with basic financial features as a common denominator; more complex versions for macroprudential analysis and stress-testing.
- Semi-structural core models may be extended with financial features more expediently than building DSGE models from scratch.
- Satellite models:
  - Useful for detailed, disaggregated stress-testing and to handle non-linearities and interbank activity.
  - Help manage technical solution and simulation difficulties—especially for non-linearities and interbank activity.
- Occasionally-binding constraints (OBC):
  - Important for modeling crisis episodes (e.g., sudden stops) where constraints bind only after sequences of adverse shocks.
  - OBC methods are currently research-focused but could be incorporated for constraints that are sufficiently likely to bind and sufficiently well-defined (e.g., regulatory requirements).
  - Less suitable to model rarely binding or heterogeneous constraints within the core; such cases better handled in satellite models.

### Approaches to embedding financial frictions (Appendix A)
- Three principal approaches:
  - The financial accelerator framework.
  - The collateral constraints framework.
  - Explicit modeling of financial intermediaries (costly intermediation, imperfect competition, bank capital channels).
- Two model changes required:
  - Replace representative agent framework with heterogeneous agents to motivate borrowing and lending.
  - Introduce information asymmetries between agents (adverse selection and agency costs), generating an external financing premium.
- No consensus "workhorse" approach; many variants remain under investigation.

### The financial accelerator (core mechanics and relevance)
- Source: ex-post information asymmetry → external finance premium inversely related to borrower net worth.
- Transmission: countercyclical premium amplifies and propagates output and investment responses to shocks.
- Sensitivities:
  - Stronger amplification for financial shocks affecting asset prices; moderate for supply shocks.
  - Debt contract specification (nominal vs indexed) matters for amplifier strength.
- Implementation: requires equations for external financing premium, entrepreneurs’ consumption, and wealth accumulation.

### The collateral constraints framework (core mechanics and relevance)
- Source: limited contract enforcement; borrowing quantity constrained by collateral value (housing, capital).
- Transmission: asset price–collateral feedback amplifies shocks.
- Empirical fit: models with housing as collateral can match co-movement of aggregate demand and housing prices.
- Sensitivities:
  - Amplification moderate for non-financial shocks.
  - Amplification increases with ratio of collateral to output, share of constrained agents, and productivity differentials.
- Implementation: heterogeneity with impatient, credit-constrained agents and durable collateral.

### Modeling financial intermediaries and bank capital
- Rationale: intermediaries enable modeling of intermediation costs, spreads, bank capital channels, and risk management behavior.
- Costly intermediation framework:
  - Representative bank; intermediation costs create positive loan spreads.
  - If costs rise with volume, spreads are procyclical—often combined with accelerator or collateral frameworks to match evidence.
- Imperfect competition and stickiness:
  - Monopolistic competition in retail banking can produce non-zero steady-state margins and incomplete pass-through of policy rates.
  - Modeling of interest-rate re-optimization frequency used to represent maturity mismatch between deposits and loans.
- Bank capital:
  - Banks use capital with deposits to extend loans; capital often increases via retained earnings in models (imperfect equity markets).
  - Motivations for capital: agency problems (double moral hazard), regulatory penalties for deviations from capital targets.
  - Effects of capital requirements on real variables vary across specifications and assumptions about bank behavior.
- Bank risk management and risk-taking:
  - Modeling risk-taking channel requires assets with different risk/return and endogenous portfolio shares; largely missing from standard models.
  - Some models introduce portfolios of risky loans and risk-free securities, but often with exogenous portfolio shares.

### Interbank markets, liquidity, and contagion risks
- Interbank markets largely omitted in many models; exceptions include Dib (2010) and multi-bank frameworks.
- Inclusion of interbank markets is important to:
  - Assess amplification through interbank linkages and runs.
  - Analyze implications of Basel III liquidity and net stable funding ratio requirements.
  - Provide macro-consistent inputs to satellite stress-testing frameworks.
- Liquidity risk modeling examples:
  - Angeloni and Faia (2009): runs on deposits increasing with leverage.
  - Dib (2010a,b): lending banks choose between loans and government securities; capital signals creditworthiness in interbank markets.
  - Christiano, et al. (2010): excess liquidity as production factor for transaction services.
  - Roger and Vlcek (2011): liquidity requirements as exogenous share of banks’ assets in government bonds.
- Contagion risks and default interactions:
  - Endogenous defaults and interbank spillovers modeled in de Walque, et al. (2009), Dib (2010a,b), and related work; interconnectedness can amplify shocks while higher capital buffers mitigate effects.

### Open-economy, exchange-rate, and denomination issues
- External financing premium becomes a country risk premium when agents can borrow abroad; evolves with balance sheets and asset prices.
- Currency denomination of assets/liabilities critically affects balance-sheet consequences of exchange rate movements.
- Liability dollarization can worsen balance sheets upon depreciation, potentially overpowering standard substitution effects and influencing monetary policy.

### Non-linearities, occasionally-binding constraints, and solution methods
- Many DSGE models linearized around steady state; linearization may miss crucial non-linear dynamics near critical points.
- Occasionally-binding constraints (used in Mendoza (2006, 2008)) can produce sudden stops and spirals in asset prices, requiring cardinal utility and non-linear global solution methods.
- Recommendation: model OBCs for constraints that are likely to bind and well-defined; handle rare or highly disaggregated non-linearities in satellite models.

### Prioritization and practical steps for central banks
- Immediate priorities:
  - Model implications of forthcoming Basel III decisions (capital, liquidity regulation).
  - Integrate financial stability concerns into monetary policy analysis.
- Practical modeling architecture:
  - Use core forecasting models extended with key financial features for macrofinancial monitoring and forecasting.
  - Use linked satellite models for stress-testing, detailed interbank and non-linear/crisis analysis.
  - Ensure institutional procedures and collaboration to iterate forecasts and scenario inputs between forecasting and financial stability teams.

*Italic source-attribution: _wp1221 - References (excerpt) from the source PDF content provided.*

### References .............................................................................................................

### _wp1221 - References

### Introduction: purpose and scope
- Most models used by central banks prior to the international financial crisis were in the New-Keynesian style and implicitly assumed perfect and complete financial markets.
- Financial frictions arising from information asymmetry and non-convex transaction costs were missing; models featured a single risk-free interest rate and aggregated non-monetary assets into government bonds.
- The paper surveys the state of development of DSGE models with financial frictions in use by central banks and reviews main approaches to introducing financial frictions into such models.
- The paper offers priorities for future development of such models for monetary policy and financial stability analysis.
- Plan of the paper:
  - Section II: overview of DSGE models with financial features in use by central banks prior to the crisis and developments since the crisis.
  - Section III: weaknesses in existing models and priorities for development for forecasting and policy analysis.
  - Appendix: principal approaches to introducing financial frictions and modeling of banking sectors in DSGE models.

### Key findings on pre-crisis modeling (Sections I–II)
- Prior to the crisis, standard macroeconomic models used by most advanced country central banks modeled inter-linkages between the financial system and real activity in a very simplified manner.
- Central bank policy interest rate and exchange rate were treated as the financial variables of over-riding importance linking policy with economic activity.
- Implicit assumptions: perfect and complete financial markets (frictionless, fully competitive, without barriers to entry or exit) and absence of asymmetric information and non-convex transaction costs.
- The assumptions aided tractability and computational feasibility of DSGE models.
- Institutional and practical barriers limited integration of macroeconomic forecasting and financial stability analysis:
  - Financial stability analysis often located in different departments or outside central banks.
  - Data frequency mismatches: macro forecasting is typically quarterly; many financial stability data sources are lower frequency.
  - Financial stability analyses were often "snapshot" focused rather than dynamic and forward-looking for integration into forecasting.
- The lack of integrated macrofinancial models likely contributed to insufficient early warning of systemic vulnerabilities prior to the crisis.
- In response to the crisis, central banks and financial stability authorities are prioritizing incorporation of financial intermediation processes and frictions into forecasting and policy frameworks.

### Models in use before the crisis (Section II.A) — specific model features
- General observation:
  - Prior to the financial crisis, main forecasting and policy analysis models—including DSGE models—used by most central banks almost all lacked financial frictions and credit channels and the scope for analyzing macrofinancial interactions and shocks.
- Exceptions and partial features (Table 1 entries preserved as presented):
  - Bank of Canada — ToTEM (Murchison and Rennison (2006)) — --
  - Bank of England — BEQM (Harrison et al. (2005)) — "Housing as a financial asset with wealth effects on consumption. However, there are no financial imperfections."
  - Bank of Japan — JEM (Fujiwara et al. (2004)) — "Housing as a financial asset with wealth effects on consumption and a financial intermediary. However, there are no financial imperfections."
  - European Central Bank — AWM (Fagan et al. (2005)) — --
  - US Federal Reserve — EDO (Edge et al. (2007)) — "Residential capital providing housing services. However, there are no financial imperfections per-se."
  - SIGMA (Erceg et al. (2006)) — --
  - Sveriges Riksbank — RAMSES (Adolfson et al. (2007)) — --
  - Christiano et al. (2007) — "The financial accelerator framework."
- Note: Some central banks used satellite models (stress-testing, partial-equilibrium financial models) and expert judgment to inform macro forecasting despite main models lacking embedded financial frictions.

### Model development since the crisis (Section II.B) — progress and examples
- Development status:
  - The development of DSGE forecasting models with embedded financial frictions is "very much a work in progress."
  - As of end–2010, the ECB, the U.S. Federal Reserve, and the Reserve Bank of New Zealand appear to have introduced such features into their main forecasting models (Table 2).
  - Around "half a dozen countries have DSGE models with financial features in operation" based on consultations and a survey of working papers published through to end–2010.
  - Several other central banks (e.g., Czech Republic, Singapore, and Switzerland) are developing or modifying models to incorporate financial frictions, but unpublished details are excluded from the survey.
- Representative post-crisis model features (Table 2 entries preserved as presented):
  - European Central Bank — NAWM (Christoffel, et al. (2008)) — --
  - CMR (Christiano, et al. (2010)) — "The financial accelerator and financial intermediaries. Financial assets with different degrees of liquidity."
  - US Federal Reserve — EDO (Chung et al. (2010)) — "Residential capital providing housing services, exogenous risk premium, and financial shocks. However, there are no endogenous financial imperfections per se."
  - Reserve Bank of New Zealand — KITT (Lees (2009)) — "Households borrowing against housing; collateral constraints on foreign borrowing."
- Typical modeling strategies since the crisis:
  - Financial imperfections are introduced mostly via the financial accelerator or collateral constraint frameworks, together with an explicit banking sector.
  - Models aim to capture the credit channel of transmission and frictions related to the banking sector.
  - Many such models remain developmental or research-oriented and may be used alongside main forecasting models during a break-in period.

### Published central bank DSGE models with financial frictions — features and banking sector representation (Table 3 highlights)
- General observation:
  - Around a half dozen published central bank DSGE models incorporate financial frictions; features often include financial accelerator frameworks, collateral constraints tied to housing, explicit banking sectors, bank capital requirements, and imperfect competition in banking.
- Selected central bank model entries (preserving original phrasing and table structure):
  - Bank of Canada — Beaton, Lalonde, and Snudden (2010)
    - "Multi-country model with international financial flows. Each country features a heterogeneous banking sector following Dib (2010b). The credit channel is introduced via the financial accelerator framework"
    - Banking structure: "Monopolistic deposit and lending banks exchange resources in an interbank market. No cross-border interbank borrowing; international financial flows introduced via cross-border loans."
    - Banks balance sheets (as listed): Deposit banks: Assets: Net interbank position and government bonds. Liabilities: deposits. Lending banks: Assets: Loans. Liabilities: Net interbank position and bank capital.
  - Dib (2010a,b)
    - "The financial accelerator framework along with a heterogeneous banking sector. Lending banks face capital requirements."
    - Banking structure: "Two types of banks—deposit and lending banks. Resources are exchanged via an interbank market. Banks have monopolistic power to set interest rates on deposits and loans; and they can default on interbank borrowing and capital returns. Capital accumulated by the lending banks facing penalty costs whenever they deviate from the required level."
    - Banks balance sheets: Deposit banks: Assets: Net interbank position and government bonds. Liabilities: deposits. Lending banks: Assets: Loans and government bonds. Liabilities: Net interbank position, bank capital, and central banks injections.
  - Meh and Moran (2008)
    - "A double moral hazard framework—an agency problem between banks and their creditors (lenders); and between banks and entrepreneurs (borrowers). Capital position of banks determines their ability to obtain funds—the bank capital channel."
    - Banks balance sheets: Assets: Loans. Liabilities: Deposits and bank capital.
  - Bank of England — Markovic (2006)
    - "The financial accelerator framework with an external financing premium enriched by banks capital costs. The banking sector faces adjustment costs in capital accumulation—the capital channel."
    - Banking: "A representative bank facing non-zero costs of raising new capital. Costs of bank liabilities (capital and deposits) affect the external finance premium."
    - Banks balance sheets: Assets: Loans. Liabilities: Deposits and bank capital.
  - Banco de España — Andres and Arce (2009)
    - "The collateral constraints framework, tied to house prices; An explicit banking sector collecting deposits and issuing loans. Assumption of imperfect competition in the banking sector."
    - "Imperfectly competitive banks introduced assuming Salop’s circular-city model. Steady-state lending spreads depend negatively on banks’ market shares—the degree of banks’ competitiveness."
    - Banks balance sheets: Assets: Loans to entrepreneurs. Liabilities: Deposits.
  - Banque de France — Dellas, et al. (2010)
    - "An assumption that households need to hold deposits to purchase consumption goods; Firms finance their production via bank loans. A time-varying default rate on loans."
    - Banking: "An explicit banking sector exhibiting monopolistic competition. Banks accumulate capital retaining profits and smoothing dividend policy. Banks face costs issuing equities and securing their portfolios through risk-free government bonds. Banks hold reserve to manage liquidity of deposits."
    - Banks balance sheets: Assets: Loans to firms and reserves. Liabilities: Deposits, banks capital and risk-free securities.
  - Bank of Italy — Gerali et al. (2010)
    - "The collateral constraints framework; Costly accumulation of banking capital shifting interest rate margins; Banks are subject to capital requirements."
    - Banking: "A wholesale bank and monopolistic competition of retail branches. Bank profits are used to accumulate capital assuming fixed dividend policy. A capital to loans ratio has to be followed by banks, otherwise they face penalty costs."
    - Banks balance sheets: Assets: Loans to households and entrepreneurs. Liabilities: Deposits and banks capital.
  - Croatian National Bank — Bokan et al. (2009)
    - "Costly banking, sticky interest rates on loans and deposits, and foreign currency borrowing."
    - Banking: "Wholesale banks have to follow loan to deposits ratio otherwise they face penalty costs. Wholesale banks and monopolistic competition of retail branches."
    - Banks balance sheets: Assets: Loans to households and entrepreneurs. Liabilities: Deposits and foreign borrowing.
  - ECB — Angeloni and Faia (2009)
    - "Banks are exposed to runs with probability increasing with banks’ leverage ratio—the bank capital channel."
    - "Heterogeneous banks assuming relationship banking. Holding of capital endogenously motivated by liquidity risks arising from runs on banks."
    - Banks balance sheets: Assets: Loans. Liabilities: Deposits and banks capital.
  - Christiano et al. (2010)
    - "The financial accelerator enriched by an explicit banking sector providing liquidity services."
    - Banking: "Representative banks using capital, labor and reserves to provide liquidity services—deposits. A bank production function is used to capture non-zero interest rate spreads in steady state."
    - Banks balance sheets: Assets: Reserves and loans. Liabilities: Deposits and securities.
  - Reserve Bank of New Zealand — Lees (2009)
    - "Households borrow against housing; collateral constraints on foreign borrowing."
    - Banks balance sheets: -- (not specified in table)
  - Sveriges Riksbank — Christiano et al. (2007)
    - "The financial accelerator framework."
    - Banks balance sheets: -- (not specified in table)

### Identified weaknesses and priorities for development (summary from Section III plan and discussion)
- Weaknesses in existing models:
  - Limited endogenous modeling of financial frictions in many forecasting models.
  - Many models still lack a fully integrated banking sector and explicit credit channels.
  - Institutional separation between macroeconomic forecasting and financial stability analysis impeded integrated model development and use.
  - Data frequency and data availability constraints complicate embedding detailed financial sector features in quarterly forecasting models.
- Priorities for future development:
  - Incorporate financial frictions (financial accelerator, collateral constraints, banking frictions) into DSGE models used for forecasting and policy analysis.
  - Develop models that capture both credit channels and banking-sector-specific frictions including bank capital dynamics, liquidity provision, and interbank markets.
  - Improve collaboration and integration between macroeconomic forecasting units and financial stability units within central banks.
  - Use a mix of approaches: modify existing forecasting models to include key financial features, and develop new DSGE models incorporating banking and financial intermediation where appropriate.
  - Address data and frequency issues to enable dynamic, forward-looking incorporation of financial sector information into macro forecasts.

*Italic source-attribution: _wp1221 - References (excerpt) from the source PDF content provided.*

### 16.      The models surveyed in Table 3 are fully structural. A number of central banks may

### _wp1221 - 16.      The models surveyed in Table 3 are fully structural. A number of central banks may

### Overview of current modeling practice
- The models surveyed in Table 3 are fully structural; some central banks employ semi-structural macroeconomic models with important elements of financial transmission (example: Norges Bank includes house prices, credit, and equities, allowing house prices affect real economic activity).8
- Relatively few central banks have core models incorporating financial frictions due to:
  - Absence of a generally agreed “workhorse” model akin to the New-Keynesian setup.
  - Current modeling approaches are unable to characterize financial channels and risks comprehensively (see Appendix I).9
  - Uncertainty about the relative importance of different sources of financial frictions and transmission channels.
  - Substantial increase in complexity when introducing financial frictions, including the need to abandon representative agent assumptions and to introduce heterogeneity, non-linearities, and occasionally binding constraints.

### Nature and examples of financial frictions
- Financial frictions stem from information asymmetries between lenders and borrowers or from difficulties in enforcing contracts (fuller discussion in Appendix I).
- Common modeling approaches:
  - Financial accelerator: borrowers (usually firms) face a risk premium that is decreasing in their net worth.10
  - Collateral constraint: borrowing is quantity constrained by availability of suitable collateral—typically housing for households, physical capital for firms.11
- These frictions enable procyclical interactions among asset prices, balance sheet positions, and real activity via changes in access to borrowing.

### Modeling the banking sector
- Models introducing an explicit banking sector broadly seek to capture:
  - (i) a bank capital channel of macrofinancial interaction (role of bank capital in shaping the business cycle);
  - (ii) role of interest rate spreads in transmission and business cycle dynamics;
  - (iii) transmission effects of interbank borrowing and related risks.
- Most surveyed models concentrate on the bank capital channel, partly reflecting interest in macroeconomic implications of Basel III regulatory changes.
- Modeling bank capital channel requires:
  - Demand for capital linked to bank lending, and capital being costly to obtain in the short term.
  - Limited short-term access to equity markets implies capital increases via retained earnings (cuts in dividends or increases in revenues).
  - Regulatory requirements or agency problems or liquidity-mitigation motives are used to motivate costly capital holdings (examples: Gerali, et al. (2010); Dellas, et al. (2010); Dib (2010); Meh and Moran (2008); Angeloni and Faia (2009)).
- Deposit and lending spreads modeling typically:
  - Assumes a specific “technology” transforming deposits and factor inputs into loans.
  - Uses monopolistically competitive banking sectors with non-zero steady-state margins and lagged transmission of policy rates into loan and deposit rates (examples: Andres and Arce (2009)).12
  - Incorporates stickiness in average interest rates to reflect maturity structure of bank balance sheets.
- Balance sheets are stylized:
  - Liabilities: bank deposits and capital; Assets: loans.
  - Composition and riskiness of portfolios generally exogenous rather than the result of bank optimization.
  - Some exceptions allow richer structure (Christiano, et al. (2010); Angeloni and Faia (2009); Dib (2009)).
- Cross-border aspects:
  - Most models assume only domestic banks and domestic currency funding; cross-border borrowing is generally not allowed.
  - Exception: Beaton, et al. (2010) use a multi-country framework with a constant share of cross-border borrowing on firms’ loans.

### Challenges and priorities for model development (Section III)
- Incorporation of financial structure and behavior into DSGE models is at an early stage; recent additions improve earlier models but many limitations remain:
  - Focus on a small number of frictions; limited range of financial assets; simplified representation of intermediaries; limited heterogeneity.
- Adding financial frictions increases model complexity, reduces tractability and user understanding—important for policy formulation and communication.
- Need to keep incorporation parsimonious and focused on most important transmission mechanisms, but no consensus yet on minimum financial sector representation.
- Models must allow analysis of macroeconomic effects of macroprudential tools and implications for monetary policy (need to incorporate key elements of Basel III).

### Key issues to be addressed in current models
Representation of non-financial agents and their behavior
- Households and firms both borrow and save to manage liquidity risk; current models do not capture this behavior well and should incorporate it to reflect responses to shocks affecting perceived income risks.
- Financial accelerator frameworks presuppose default risks, but realizations and losses do not create distress in financial institutions; explicit representation of default probabilities and associated losses—linked to macro developments—should be incorporated to connect macrofinancial models to stress testing frameworks.14
- Financial balance sheet of the public sector is typically omitted; models would benefit from more complete representation of public sector financial positions and linking these to the sovereign risk premium.

Representation of financial agents and markets
- Financial sector comprises diverse institutions, but current models mostly use a representative monopolistically competitive “bank”; more explicit differentiation among banks, shadow banks, and non-bank financial institutions will be needed.
- Realistic heterogeneity is challenging; it will be important to determine which institution types belong in core models versus satellite models.
- Interbank market omission is important; current models largely exclude interbank markets except Dib (2010). Incorporation is important because the interbank market amplified the crisis; Gertler and Kiyotaki (2009) framework may offer a way forward.
- Inclusion of wholesale or interbank markets is needed to assess Basel III reforms (liquidity requirements, net stable funding ratio requirements) and to complement financial stability models and stress testing.
- Maturity transformation role of financial sector requires introducing deposit and loan contracts of different maturities (multi-period contracts or differing inertia in interest rates) to address liquidity risk, liquidity requirements, and stable funding implications.
- Greater differentiation in maturity structures adds complexity but is essential; maturity mismatching will influence cyclical behavior of lending spreads and could reverse procyclicality found in many current models.
- Valuation of financial assets is central:
  - In collateral constraints, housing price responses determine collateral value and amplification through housing market.
  - In financial accelerator, firm net worth valuation governs amplification.
  - Valuation of liquid assets underpins liquidity “spirals” in interbank markets.
- Most current models are closed-economy or restrict domestic currency borrowing; need to add open economy aspects including foreign-currency borrowing, currency risks, and sudden stops.
- Decision-making and optimization processes of banks are simplified; many choice variables are exogenized (e.g., methods of adjusting capital adequacy ratios are not endogenously determined).
- Endogenizing behavior with varied asset/liability riskiness and maturities will be difficult; pragmatic approach may impose a minimal set of optimization criteria and treat other behaviors as alternative scenarios.

### Prioritization, timing, and modeling architecture
- The list of improvements is extensive and beyond what can be achieved in the next year or two, but there is an urgent need to model implications of forthcoming Basel III decisions and to integrate financial stability concerns into monetary policy analysis.
- Two important considerations to move forward:
  - Purposes for which models are used (influences priority of features).
  - Modeling “architecture”: organization and relationship between different models.
- Model objectives can differ; three purposes distinguished:
  - Macrofinancial analysis and forecasting:
    - Objective is not to forecast crises but to enrich transmission mechanisms and allow financial shocks.
    - Adding credit frictions via collateral constraints or financial accelerator and assets such as housing may suffice.
    - Models should provide forecast-consistent paths for lending spreads, housing prices, and bank lending to facilitate macrofinancial monitoring.
  - Macroprudential analysis:
    - Important to examine impacts of changes in macroprudential instruments and regulations on the macroeconomy.
    - Top priority: incorporate key elements of Basel III reforms into model frameworks.
    - Practically, models must, at minimum, take into account impacts of changes in bank capital and liquidity requirements, imposition of leverage ratios and net stable funding ratios.

*Source: _wp1221 - 16.*

### introduction of an explicit banking sector with financial liabilities and assets with

### _wp1221 - introduction of an explicit banking sector with financial liabilities and assets with

### Introduction: motives for introducing explicit banking sector and interbank markets
- Purpose: introduce an explicit banking sector with financial liabilities and assets with differing degrees of liquidity or maturity, and introduce interbank markets, together with the regulatory constraints and the behavior of banks in observing those constraints.
- Usefulness:
  - Assess how the conduct of monetary policy should change in response to the use of macroprudential instruments.
  - Determine whether the use of some instruments, such as countercyclical capital requirements, should be incorporated into the main macrofinancial forecasting model (acknowledged as uncertain ex ante).
- Stress-testing requirement:
  - The macroeconomic model must be able to provide inputs to “satellite” models that represent the financial system at a more disaggregated level and which can allow for crises.
  - It may be especially important to have the interbank market represented in the macroeconomic model, together with model-consistent determination of asset prices.

### Modeling architecture: multiple models, core vs. satellite
- Recommendation: instead of a single all-purpose DSGE model, central banks and financial stability authorities might consider developing several versions of a model with at least some basic financial features and frictions as a common denominator (paragraph 31).
  - More complex versions would probably be needed for macroprudential analysis and stress-testing (paragraph 31).
- Current practice and expediency (paragraph 32):
  - Most central banks still use semi-structural models as their core model in forecasting and policy analysis.
  - Extending existing semi-structural models to incorporate financial features and frictions may be more expedient than developing DSGE models from scratch.
  - Expansion can borrow from existing DSGE models to guide specification and calibration of modified semi-structural models.
- Satellite models (paragraphs 33–35):
  - Even where DSGE models are used, it may be more efficient to conduct some aspects of analysis in satellite models linked to the core model to avoid increasing size and complexity of the core.
  - For stress-testing, conducting stress-testing in a disaggregated, detailed framework linked to, but largely outside, the core forecasting macroeconomic model may be most sensible (paragraph 34).
  - Satellite approaches help manage technical solution and simulation difficulties (paragraph 35), especially for non-linearities and interbank activity.

### Non-linearities and occasionally-binding constraints (OBC)
- Criticism: most DSGE and other macroeconomic models do not incorporate non-linearities that may play a major role in triggering or defining financial crises (paragraph 36).
  - Most DSGE models are linearized around the steady state; linearization is reasonable for small disturbances unless the system is near a critical point where non-linear effects matter (paragraph 36).
- Approaches to handle non-linearities:
  - Incorporate non-linearities explicitly into the main framework by modeling the existence of occasionally-binding constraints (OBC) (paragraph 37).
    - OBC approach currently used only in research models but could be incorporated into policy/forecasting models.
    - Likely most useful for constraints that are (i) sufficiently likely to bind to warrant modeling complications; and (ii) sufficiently well-defined to model at an aggregate level (e.g., regulatory requirements) (paragraph 37).
    - Less suitable for rarely binding constraints or where constraints bind heterogeneously across the financial system (paragraph 37).
  - Leave infrequent or highly disaggregated non-linearities outside the core model and address them in detailed, partial-equilibrium satellite models (paragraph 38).
    - Advantage: keeps regular analysis and forecasting simpler analytically and computationally.
    - Requirement: financial satellite models must be well integrated into forecasting and analysis frameworks, often entailing modifications to models and to institutional relationships and procedures (paragraph 38).

### Interbank market modeling: core vs. satellite trade-offs
- Uncertainty about incorporating an explicit interbank market into workhorse forecasting models (paragraph 39):
  - Feasible to include, but it adds complexity and heterogeneity which may be unnecessary for most occasions.
  - When shocks to the interbank market are important, it may be preferable to model the interbank market outside the core model while ensuring necessary linkages to incorporate interbank developments into the core as needed (paragraph 39).
  - Before deciding, determine whether frictions within the interbank market alter the transmission mechanism enough to require full incorporation into the core model (paragraph 39).
- Effective satellite use requires procedures and corporate culture of close integration between macroeconomic analysis/forecasting teams and financial stability analysis teams (paragraph 39).
  - The appropriate form of collaboration and procedures should depend on the focus of the analysis (paragraph 39).

### Collaboration and procedures: integrating financial stability into forecasting and stress-testing
- For macroeconomic forecasting (paragraph 40):
  - Financial stability considerations would normally feed into macroeconomic forecasts iteratively or shape particular scenarios.
  - Iterative approach or scenario-shaping approach is the typical integration method.
- For stress-testing (paragraph 40):
  - Alternative macroeconomic scenarios would be used to feed into detailed financial stability analysis models.
  - Procedures will differ between forecasting and stress-testing but both require higher degrees of collaboration than often practiced historically.

*Source: _wp1221 - introduction of an explicit banking sector with financial liabilities and assets with (PDF).*

### 1.      This appendix reviews the incorporation of various financial frictions, transmission

### This appendix reviews the incorporation of various financial frictions, transmission

### A. Approaches to Embedding Financial Frictions
- Three basic approaches extensively used to embed financial frictions into DSGE models:
  - The financial accelerator framework.
  - The collateral constraints framework.
  - Explicit modeling of financial intermediaries.
- Two crucial model changes required to introduce financial frictions:
  - Replace the representative agent framework with heterogeneous agents to motivate borrowing and lending as agents differ in consumption preferences, productivities, or financing constraints.
  - Introduce information asymmetries between agents: ex-ante asymmetries induce adverse selection; ex-post asymmetries imply agency costs for assessing creditworthiness and monitoring costs, leading to an external financing premium.
- No consensus approach has emerged; many variants on each approach continue to be investigated.

### The financial accelerator framework
- Core features:
  - Assumes an ex-post information asymmetry giving rise to an external finance premium reflecting the difference between the costs of externally borrowed and internally generated funds.
  - The external borrowing premium varies inversely with borrower net worth and limits agents’ borrowing. (Borrowers’ net worth defined as the value of assets minus outstanding obligations.)
  - Premium is countercyclical: higher net worth in good times lowers the premium; lower net worth in bad times raises it.
- Typical modeling assumptions:
  - Focuses on lending between households and entrepreneurs.
  - Entrepreneurs: possess production technologies, undertake risky projects, are assumed risk neutral, experience idiosyncratic shocks to project outcomes, observe outcomes costlessly.
  - Lenders (households) face monitoring and auditing costs, producing a costly state verification problem for lenders.
  - Optimal incentive-compatible contracts characterized by a non-negative external financing premium induced by monitoring costs and uncertainty about project returns.
- Mechanism and empirical relevance:
  - Countercyclical external finance premium amplifies and propagates real output and investment responses to shocks (e.g., technology shocks: asset prices up → borrower net worth up → premium down → spending up).
  - Helps explain large swings in investment and hump-shaped output responses to moderate interest rate changes.
  - Empirical evidence noted from Bernanke, et al. (1996); Christiano, et al. (2004); Christensen and Dib (2008).
- Sensitivities:
  - Strength of accelerator varies with the nature of shocks: strong for financial shocks affecting asset prices; moderate for supply shocks (productivity or price mark-up shocks).
  - Specification of debt contracts matters: nominal (non-indexed) debt contracts can dampen the accelerator for productivity and price markup shocks because unexpected productivity increases lower consumer prices, raising the real cost of nominal debt repayments.
- Implementation in DSGE:
  - Embedding the framework with investment and capital accumulation requires adding equations for an external financing premium, entrepreneurs’ consumption, and wealth accumulation, given conditions in Bernanke, et al. (1999).

### The collateral constraints framework
- Core features:
  - Borrower net wealth directly affects borrowing limits through limited contract enforceability—lenders cannot fully force repayment, so contracts are secured by collateral (durable assets: land, housing, capital).
  - Groups of impatient agents (lower discount factor) motivated to borrow; credit limits determined by collateral value and assumed binding (scarcity of collateral).
- Mechanism:
  - Interaction between credit limits and asset prices amplifies shocks: negative asset price shock lowers collateral value → credit limits tighten → spending by impatient agents falls → asset prices fall further.
- Empirical relevance:
  - Models with housing as collateral (Iacoviello (2005); Iacoviello and Neri (2007)) match co-movement of aggregate demand and housing prices under asset price shocks.
  - Liu, et al. (2010) find the collateral framework with asset price shocks helps account for empirical business cycle features.
- Sensitivities:
  - Amplification is moderate for non-financial shocks with limited effects on asset prices.
  - Collateral framework characterized by weak amplification of supply shocks, particularly when debt contracts are nominal and not indexed.
  - Importance of amplification increases with:
    - Ratio of collateral to output.
    - Share of output produced by credit-constrained agents.
    - Productivity differential between constrained and unconstrained agents.
  - Cordoba and Ripoll (2004) argue amplification is very weak unless unorthodox assumptions (e.g., intertemporal elasticity of substitution significantly below one and a large ratio of collateral to GDP) are made.
- Implementation in DSGE:
  - Requires heterogeneity of agents including a group of impatient, credit-constrained agents; binding credit constraint; durable goods as collateral.

### Modeling of financial intermediaries
- Rationale:
  - Original financial accelerator and collateral frameworks assumed direct lending between borrowers and lenders without intermediaries.
  - Introducing a banking sector allows modeling frictions linked to costs of intermediation, intermediaries’ balance sheets, and banks’ risk management behavior.
  - Modeled institutions may include banks or non-banks performing intermediation functions.
- Typical modeling focuses:
  - Endogenous determination of interest rate spreads over the business cycle and a non-zero spread in steady state.
  - A bank capital channel so financial intermediary balance sheets and regulatory constraints influence transmission in addition to nonbank balance sheets.
  - Bank risk management behavior.
- Approaches to banking:
  - Costly intermediation (neoclassical banking) framework: representative bank in perfect competition providing deposits and loans; intermediation is a costly activity using resources to create and maintain debt contracts; balance sheets stylized with deposits (liabilities) and loans (assets).
  - Costly intermediation gives rise to a positive premium on loans (interest rate spread). If intermediation costs are positively related to volume, costs and spreads are procyclical—contradicting empirical evidence—so costly intermediation is often combined with accelerator or collateral frameworks.
  - Imperfect competition in retail banking introduced to match incomplete pass-through from policy rates to deposit and loan rates in the short-run and observed propagation of monetary policy shocks. Motivations for stickiness in interest rates include monopolistic bank power, entry costs, or relationship borrowing.
  - Stickiness of interest rates can represent maturity mismatch between deposits and loans: probability of interest rate renewal considered duration of financial contacts (high re-optimization probability → short duration of deposit contracts; lower frequency of loan rate re-optimization → longer loan maturities).
- Table comparison (summarized):
  - The financial accelerator: source is ex-post information asymmetry; key variable external finance premium; transmission via net worth affecting external financing costs; amplifies asset price shocks; no explicit financial intermediary.
  - The collateral constraints: source is limited contract enforcement; key variables credit limits and spreads; transmission via asset prices affecting collateral value; amplifies asset price shocks; no explicit financial intermediary.
  - The costly banking framework: source is non-convex production technologies (increasing intermediation costs); key variable interest rate spreads; transmission via spreads reflecting amount of lending; tends to dampen transmission due to procyclical spreads unless combined with sticky interest rates or other frictions; includes explicit banking sector.

### The costly banking framework
- Key points:
  - Representative bank in neoclassical framework; costly activity of intermediation creates spreads (Edwards and Vegh (1997)).
  - If intermediation costs rise with volume, spreads become procyclical—empirically at odds—motivating combination with other frameworks.
  - Introducing imperfect competition in retail banking can generate sticky deposit and loan rates consistent with incomplete pass-through of policy rates.
  - Relationship between interest rate re-optimization frequency and contract duration used to model maturity mismatches.

### Bank capital
- Focus:
  - Modeling bank balance sheets and bank capital to analyze financial stability and prudential regulatory measures (capital, liquidity, reserve, leverage requirements).
- Common assumptions:
  - Banks use capital together with deposits to extend loans.
  - Monopolistic banks earn profits that are retained to build capital or distributed as dividends.
  - Frequent assumption: banks cannot raise capital via new equity issues, so capital increases only via retained earnings (imperfect equity market).
- Motivations for holding capital:
  - Market incentives: banks subject to credit constraints due to agency problem between banks and their creditors (double moral hazard). Bank capital mitigates agency problem and constrains credit extension.
  - Regulatory incentives: penalty costs for deviations from regulatory capital targets (penalty cost function usually exogenous; calibration reflects empirically observed speed of elimination of deviations). Endogenous penalty functions can be derived via agency problems or by introducing uncertainty into financial contracts and defining payout schemes.
  - Market-based and exogenous regulatory requirements are quantitatively equivalent in this respect.
- Implications:
  - Effects of capital requirements on real variables vary across models depending on bank behavior assumptions.
  - Meh and Moran (2010): bank capital channel amplifies and propagates effects of supply shocks on real activity; amplification moderate for demand shocks—reflects countercyclical lending spreads from bank agency problems.
  - If penalty costs for deviations of capital from required targets are procyclical, then interest rate spreads will be procyclical, dampening cyclical impact of both supply and demand shocks.

### Bank risk management
- Modeling banks’ risk management behavior provides an additional channel for transmission through risk taking and responses to asset return changes (risk taking channel referenced earlier in appendix overview).
- Incorporating risk management links intermediaries’ behavior to market risks, exchange rate risk, credit/default risk, and liquidity risk (these kinds of risk are the focus of the third part of the appendix).

*Source: IMF Staff.*

### 27.      Finally, there is a strand of banking sector modeling that focuses on embedding bank

### _wp1221 - 27.      Finally, there is a strand of banking sector modeling that focuses on embedding bank

### Banking sector modeling that embeds bank risk management
- Approaches introduce uncertainty and defaults into financial contracts and define bank incentives and payout schemes.
- Most approaches incorporate into the DSGE framework partial equilibrium setups originally developed in the theory of corporate finance.
- Example: Angeloni and Faia (2009)
  - Banks face two kinds of risk:
    - Lending-side: losses on loans for projects with uncertain returns; losses when loans are recalled early forcing termination of projects.
    - Deposit-side: exposure to bank runs arising from a payout scheme where depositors are served sequentially (first come first served).
  - Depositors cannot observe lending portfolio risk directly and rely on observed ratio of bank capital to loans—the leverage ratio—to estimate the risk the bank will be unable to pay deposits.
  - Risk of a bank run is increasing in the leverage ratio; runs that force loan recalls create losses from project termination.
  - Banks face an endogenous trade-off: choose leverage to balance higher returns on capital from high leverage (“greed”) against increased likelihood of runs and capital losses from early project termination (“fear”).

### Occasionally binding constraints
- Most models employing credit frictions assume constraints are always binding.
- Mendoza (2006) and Mendoza (2008) introduce occasionally binding constraints to explain sudden stops (sharp reversals of international capital flows).
  - In these models credit constraints become binding only after a sequence of adverse shocks and induce spiraling collapse of asset prices, further dampening real activity.
  - To allow occasionally binding constraints, these papers assume a cardinal utility function for agents and require numerical solution using a non-linear global approximation method.

### Transmission Channels
- Main modeling focus: credit channels—balance sheet and bank lending channels.
- Balance sheet channel:
  - Works through net wealth of borrowers; described by financial accelerator and collateral constraints frameworks.
  - Borrowers' net wealth, determined by asset price behavior, affects either an external finance premium or credit limits.
  - Monetary policy influences demand via traditional interest rate channels and via effects on collateral values and net worth, affecting private sector access to credit.
- Bank lending channel:
  - Introduction of banks and bank balance sheets modifies transmission of macro developments and monetary policy.
  - Bank capital is a key additional constraint on intermediation.
    - Intermediation and capital accumulation modeled as costly activities; non-zero capital motivated by regulatory requirements or an agency problem.
    - With costly capital accumulation and constrained equity financing, lending spreads play a key role in adjusting bank capital in response to shocks or regulatory requirements.
    - Incorporation of bank capital is important for analyzing interaction of monetary policy with regulatory requirements, including proposed countercyclical capital requirements under Basel III.
  - Modeling shortcomings:
    - Riskiness of bank loan portfolios and share of non-performing loans often treated as exogenous and unaffected by bank leverage, limiting analysis of financial stability implications of changing capital requirements.
    - Exception: Angeloni, et al. (2010) links probability of bank runs to degree of bank leverage.
- Risk-taking channel (largely missing from standard models):
  - Mechanism: in low interest rate environments intermediaries increase portfolio risk and leverage to raise return on capital.
  - Addressing this requires models with assets of different risk/return characteristics and endogenous portfolio shares.
  - Roger and Vlcek (2011) introduce portfolios with risky private loans and risk-free government bonds, but relative sizes are exogenous and overall portfolio risk is constant.
- Liability-side endogeneity absent in most models:
  - Limits analysis of effects of funding choices (domestic vs foreign currency funding; retail deposits vs wholesale interbank funding).
  - Dib (2010a,b) and Meh and Moran (2010) allow interbank funding but not choice between retail and interbank funding.

### Risks

- Overall focus of DSGE models with financial frictions: market and credit risks; much less attention to liquidity and contagion risks.

Interest rate and asset price risks
- Market risks related to interest rates:
  - Described relatively well by models with financial frictions.
  - Depending on debt contract nature, interest rate movement costs borne by borrowers or lenders.
  - Fully indexed and state-contingent debt contracts (as in original financial accelerator) imply borrower bears all interest rate risks.
  - When contracts are non-indexed, supply shocks (e.g., price markup or productivity shocks) give rise to real redistribution effects; because borrowers generally have higher propensity to consume, these redistributions likely amplify demand effects.
- Introducing market risks to bank balance sheets requires embedding either maturity transformation or a difference between ex-ante and ex-post loan returns.
  - Zhang (2009) modifies the financial accelerator by introducing an explicit banking sector sharing aggregate risks with entrepreneurs; unexpected aggregate shocks to project outcomes affect both firms' and banks' balance sheets.
- Asset price risks:
  - Modeled by shocks directly affecting asset prices or collateral values.
  - DSGE models, reflecting the transversality condition, do not allow endogenous asset price bubbles; deviations from fundamentals are modeled as standard high-persistence shocks or via learning/confidence shocks.
  - Bernanke and Gertler (1999) suggest an asset price bubble as a temporary deviation with stochastic duration and amplitude and assess implications for monetary policy.

Exchange rate risk
- In open economy models, the external financing premium becomes a country risk premium when agents can borrow abroad; it evolves endogenously with agents' balance sheets and asset prices.
  - Choi and Cook (2004) apply external financing premium to banks rather than entrepreneurs.
  - Iacoviello and Minetti (2006) embed collateral constraint framework into a two-country model enabling entrepreneurs to borrow from domestic or foreign households.
- Currency denomination of assets and liabilities crucially influences wealth and cash flow consequences of exchange rate movements, analogous to contract indexation.
  - Liability dollarization implies exchange rate depreciation raises debt service costs and worsens borrowers' balance sheets—potentially overshadowing usual substitution effects and affecting monetary policy conduct.
  - Cespedes, et al. (2004) and Elekdag and Tchakarov (2007) discuss effects of liability dollarization and credit constraints under different exchange rate regimes; both introduce credit frictions via the financial accelerator and assume full dollarization of liabilities.

Default risk
- Financial accelerator framework is the only one allowing endogenous defaults of debt contracts via stochastic project outcomes; original setup had default costs borne by entrepreneurs so lenders could not go bankrupt.
- Collateral framework rules out endogenous defaults because borrowers do not face idiosyncratic project outcome risks.
- Introducing endogenous default probabilities:
  - de Walque, et al. (2009): defaulters remain in market but face higher costs to obtain loans reflecting bad reputations; firms choose repayment considering higher future borrowing costs and disutility from reputation loss; firm defaults can lead to banks defaulting on interbank debts.
  - Dib (2010a,b): similar interbank market setup; interconnectedness can amplify shocks while higher capital buffers mitigate shock effects.
  - Alternative approach: link likelihood of project failure and loan default to the business cycle so default rates rise in busts and fall in booms.
  - Goodhart, et al. (2009): heterogeneous agents and banks produce equilibrium defaults that affect borrowing costs.
  - Zhang (2009): bank default rate on liabilities is a negative function of their capital; low capital raises funding costs and adversely affects credit supply.
- Reiteration: Mendoza (2006) and Mendoza (2008) model occasionally binding constraints to explain sudden stops, requiring cardinal utility and non-linear global approximation methods.

Liquidity risk
- Liquidity risks were not a priority in central bank DSGE models until recently; the financial crisis highlighted liquidity constraints and their role in contagion.
- Modeling examples:
  - Angeloni and Faia (2009): capture liquidity risk via runs on deposits increasing with leverage; banks must hold non-zero capital to dampen liquidity risk.
  - Dib (2010a,b): lending banks choose between lending to entrepreneurs and holding risk-free government securities; capital held to satisfy regulatory requirements and to signal creditworthiness in interbank market.
  - Christiano, et al. (2010): excess liquidity modeled as a production factor in supply of financial transaction services.
  - Roger and Vlcek (2011): introduce liquidity requirements as an exogenously determined share of banks’ assets to be held in government bonds.

*Italic: Content derived from the supplied IMF PDF chapter/section.*

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