## _wp0818

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---

### Introduction and research question
- How should changes in financial sector soundness affect monetary policy?
- Two simplifications addressed relative to standard DSGE:
  - (i) the omission of a financial system, and
  - (ii) the omission of forward-looking variables in the policy (Taylor) rule.
- Assumption: the central bank has privileged information about the health of the financial system.

### Core findings (simulation results)
- If the central bank responds to a deterioration in the credit risk faced by the financial system by monetary easing using an augmented rule, such a “preemptive strike” stabilizes inflation and output better in the short run than the simple Taylor rule.
- Well-informed, forward-looking discretionary policymaking that takes into account the default rate of financial intermediaries’ lending projects and its impact on future output is preferable to simple backward-looking rules.
- The central bank following the augmented policy rule trades off more output and inflation instability today for a faster return to the trend path tomorrow.
- Long-run consumption volatility remains practically identical under both the augmented and simple rules.

### Positive and normative implications
- Positive implications:
  - Provides model justification for central banks intervening against financial shocks; the simple rule underestimates actual policy changes.
- Normative implications / limits:
  - The size and duration of the financial shock constrain effectiveness of monetary policy.
  - Central bank appears capable only of a faster reaction to the financial instability shock, keeping the nature of monetary policy unchanged.
  - Monetary easing is unlikely to work in economies with either fixed exchange rates or a strong exchange rate channel of monetary transmission.

### Model innovations and mechanism
- Innovations relative to Galí (2002):
  - Financial intermediaries supply external financing to some firms.
  - Firms sensitive to loan supply and interest rates are linked to other firms through a productivity nexus.
- Stylized facts captured:
  - Credit channel via subset of firms dependent on external finance.
  - Small/start-up firms perish easily without external financing; large firms rely on small firms for technology improvements.
  - Higher lending rates increase riskiness of marginal loan and overall lending portfolio (loan concentration effect).
  - Central bank observes financial-system health one period before the public.
- Key mechanism:
  - Higher policy rates → higher lending rates → loan portfolio concentrates on riskier firms (higher ω_t) → greater probability of failures → lower endogenous technology and output.

### Model structure (concise technical points and equations preserved)
- Households:
  - Consumption aggregator: c_t = [∫ c(i)_t^{(ε-1)/ε} di]^{ε/(ε-1)} with elasticity ε.
  - Utility: U(c,n) with nominal budget constraint; deposits pay nominal rate tr.
- Goods firms:
  - Technology: y_t(j) = a_t n_t(j).
  - Calvo price stickiness with adjustment probability θ−1.
- Innovative firms:
  - Two-period firms: s_{t+1}(j) = s_t(j) + χ_t(j).
  - Constant fraction γ survive with probability one; returns log-normal with μ and σ.
- Financial intermediaries:
  - Lend at lending rate t z; opportunity cost policy rate ti.
  - Loans per borrowing firm: l_t = d_t/(1−ω_t).
  - Equilibrium loan rate: (1+ i_t) = E_t[(1+ l_t) ~ ] (equation (3) preserved).
- Technology aggregation:
  - a_t = (a^s_t)^{1−α} (a^i_t)^α with exogenous a^s_t AR(1): a^s_t = ρ_a a^s_{t−1} + ε^a_t and ρ_a = 0.95.
- Central bank policy rules:
  - Benchmarked Taylor rule (equation (4)): i_t = φ_π π_t + φ_x x_t with φ_π > 1.
  - Augmented rule (equation (5)): central bank conditions on private signal about δ_t; paper notes specification including an indicator when conditional expectation of δ_t crosses thresholds.

### Calibration and parameterization (preserve exact values)
- Time unit: one quarter.
- Calvo price-adjust probability: θ−1 = 0.25.
- Discount factor: β = 0.99.
- Technology AR(1) serial correlation: a_ρ = 0.95.
- Parameter values:
  - δ (annual rate of business failure) = 0.03.
  - γ (share of firms that survive for sure) = 0.2.
    - quarterly steady-state spread between loan and deposit rates = 0.76 percent.
    - annual loan rate = 7.28 percent.
  - σ_a (variance of technological shock) = 0.01.
  - σ_δ (variance of probability-of-survival shocks) = 0.0025.
  - α = 0.05.
  - τ = 4/3.
  - Distribution of innovative-firm returns: lognormal with μ = 0.05 and σ = 1.0.
- Policy-rule parameterization:
  - Benchmark Taylor rule: π_φ = 1.5 and x_φ = 0.5.
  - Alternative augmented rule: 5.0−=δφ (paper notes qualitative results invariant to 25.0−=δφ or 75.0−=δφ and stresses requirement 0<δφ).

### Simulations — shocks analyzed
- Shocks:
  - Pure technological shock to a^s_t (one standard deviation ε_a).
  - Shock to probability of survival δ_t (one standard deviation ε_δ).

### Simulation results — exogenous technology shock (one standard deviation of the technology shock, a_ε)
- General:
  - In model with innovative sector, responses differ from benchmark and are more pronounced though numerical differences across policy rules are small.
  - From period 2 onward qualitative responses identical across the three scenarios (two Taylor-rule specifications and benchmark).
- Dynamics:
  - Labor and output gap: positive in period 1, become negative from period 2 onward due to initial monetary loosening based on central bank private information.
  - Endogenous technology increases with lag (full impact in period 2), raising expectations for period 2 output and boosting period 1 consumption and labor.
  - Financial instability is not generated by this shock: ∀ t, E_{t−1} δ_t = 0, so central bank reaction identical across rule specifications.
- Nonmonotonicities:
  - Paths for labor, output gap, and i_t^a can be nonmonotonic because innovative firms live two periods and lending conditions affect endogenous technology with lags.

### Simulation results — shock to default probability (one standard deviation of δ_ε)
- Shock properties:
  - Negative shock to survival probability δ_t of one standard deviation; less persistent than technology shock, dying out in approximately 4 quarters.
- Under traditional Taylor rule (equation (4)):
  - Period 1: output declines; fewer firms survive next period → less endogenous technology → output falls; inflation increases and output gap negative.
  - Central bank fails to react in period 1 to δ_{t+2} even though it possesses the information; reacts from period 2 onward, widening output gap and increasing inflation before tightening.
  - Period 2: depressed endogenous technology can paradoxically cause labor and output gap to increase above steady state.
- Under augmented Taylor rule (equation (5)):
  - Central bank knows δ_{t+2} at beginning of period 1 and decreases policy rate in period 1, lowering loan rate and expected deposit rate, stimulating aggregate demand.
  - Lower policy rate reduces 1ω, generates positive expectations, stimulates deposits, and boosts endogenous technology in period 2 more than the negative δ_{t+2} effect.
  - Deposit and loan rates decrease in period 1 and increase gradually thereafter.
- Information role:
  - Monetary policy useful for financial-stability shocks only to extent private agents’ signal extraction is limited; only central bank has information on δ_{t+1} at beginning of period t.

### Welfare calculations (Lucas (1987) measure; preserve exact reported numbers)
- Method: compare variance of consumption under alternative rules; simulations for 300 periods with simultaneous technology and default probability shocks; repeated 100 times.
- Results (standard deviations of consumption):
  - For δ_φ = –0.5:
    - Traditional rule consumption standard deviation = 0.05915.
    - Augmented rule consumption standard deviation = 0.05947.
  - For δ_φ = –0.1:
    - Traditional rule consumption standard deviation = 0.05899.
    - Augmented rule consumption standard deviation = 0.05892.
- Interpretation:
  - Standard deviations of consumption are practically identical for both rules and robust to δ_φ.
  - Augmented rule stabilizes the economy faster but produces more volatile output and consumption initially; long-run consumption virtually unaffected.

### Practical issues and extensions
- Nonlinear and asymmetric real-world policy responses; central banks focus on shocks with systemic implications.
- Long-term fiscal effects: liquidity provision vs. institution closure may delay adjustment and increase fiscal cleanup costs.
- If financial system faces credibility crisis, lower policy rates may not calm depositors.
- Monetary easing cannot substitute for prudential regulation; supervisory/regulatory measures often take longer to implement.
- External sector and exchange-rate considerations:
  - Introducing external sector limits scope for monetary easing in regimes with exchange rate anchors or strong exchange-rate transmission and increases risk of currency runs.
  - Less scope for easing in countries with significant capital flows.
- Privileged information and transparency:
  - Central banks often have privileged supervisory/payment-system information; public disclosure is a policy choice constrained by legal and crisis-provocation considerations.
  - Gaps exist between published financial-stability reports and “good practice”; disclosure extent merits further research.

### Conclusions
- Financial instability imposes significant macroeconomic costs and is largely ignored in standard monetary policy rules.
- The paper enriches the new Keynesian model with a financial system and firms requiring external financing and introduces a forward-looking element into the Taylor rule.
- Main implications:
  - A central bank lowering its policy rate in response to financial-sector instability yields different short-term outcomes in output and inflation compared with the traditional Taylor rule.
  - For short-lived and reasonably sized financial-instability shocks, a forward-looking central bank can limit short-term falls in output and consumption by monetary easing.
  - The central bank’s trade-off—more instability today for a faster return to trend tomorrow—leaves long-run consumption largely unaffected.

*Source: _wp0818 - References*

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

### _wp0818 - References

### Introduction and research question
- How should changes in financial sector soundness affect monetary policy?
- The paper addresses two simplifications in the standard monetary dynamic stochastic general equilibrium (DSGE) model:
  - (i) the omission of a financial system, and
  - (ii) the omission of forward-looking variables in the policy (Taylor) rule.
- Assumption: the central bank has privileged information about the health of the financial system (justified by central bank involvement in financial sector supervision and access to payment system data).

### Core findings (simulation results)
- If the central bank responds to a deterioration in the credit risk faced by the financial system by monetary easing using an augmented rule, such a “preemptive strike” stabilizes inflation and output better in the short run than the simple Taylor rule usually assumed in the DSGE model.
- Well-informed, forward-looking discretionary policymaking that takes into account the default rate of financial intermediaries’ lending projects and its impact on future output developments is preferable to simple backward-looking rules.
- The central bank following the augmented policy rule trades off more output and inflation instability today for a faster return to the trend path tomorrow.
- Long-run consumption volatility remains practically identical under both the augmented and simple rules.

### Positive and normative implications
- Positive: Provides model justification for existing central bank practice of intervening against a background of financial shocks; the simple rule is an inaccurate description of central bank behavior and generally underestimates actual policy changes.
- Normative: Suggests limits to the use of monetary policy instruments for financial system stabilization:
  - The size and duration of the financial shock constrain effectiveness.
  - The central bank appears capable only of a faster reaction to the financial instability shock, keeping the nature of monetary policy unchanged.
  - Monetary easing is unlikely to work in economies with either fixed exchange rates or a strong exchange rate channel of monetary transmission.

### Relevant quoted benchmarks
- “[A] reaction function in which the real funds rate changes by roughly equal amounts in response to deviations of inflation from a target of 2 percent and to deviations of actual from potential output describes reasonably well what this committee has done since 1986.” — Janet Yellen at the January 1995 FOMC
- “[S]imple instrument rules at most explain two-thirds of the empirical variance of interest rate changes.” — Lars E.O. Svensson (2003)

### Paper scope and structure
- Section II: reviews the recent literature on the link between monetary policy and financial sector instability.
- Section III: builds a DSGE model with financial intermediaries and an augmented policy rule.
- Section IV: calibrates the model on U.S. data and presents simulations from the model for a range of policy-relevant shocks.
- Figures included in the source (enumerated): Figures 1–9 covering distributions of returns of innovative firms; shocks to exogenous technology and to probability of default; and responses of output, output gap, inflation, labor, policy rate, real interest rate, loan rate, effective deposit rate, endogenous technology, and total technology.

*Source: _wp0818 - References*

### Section V, we discuss possible extensions of the model. Section VI concludes.

### _wp0818 - Section V, we discuss possible extensions of the model. Section VI concludes.

### How central banks actually set policy under financial instability (summary of Section II)
- The “Taylor rule” links the policy rate to contemporaneous deviations of inflation and output from targets but can explain only up to two-thirds of the empirical variance of policy rate changes.
- Standard monetary DSGE models typically omit the financial sector and therefore ignore the health of banks when modeling monetary policy, despite many central banks having financial stability as an explicit objective.
- Two broad views on whether financial-sector concerns should influence monetary policy:
  - Price-stability-first view: vigorously pursue price stability; financial stability follows (Schwartz, 1995).
  - Financial-stability-aware view: central banks should intervene because financial systems are inherently fragile; interventions can be proactive (“pricking the bubbles”) or reactive (adjusting stance in response to stress) (Bernanke and Gertler, 1999; Cecchetti and others, 2000).
- Central banks may react to financial problems for non-monetary reasons (prudential supervision role), potentially intertwining regulatory and monetary objectives (Quintyn, 2007).

### Empirical evidence on central bank responses to financial instability (summary of Section II.B)
- Empirical findings indicate central bank reactions to financial instability are:
  - asymmetric,
  - nonlinear,
  - conditional on the nature of the shock.
- Key empirical results cited:
  - Borio and Lowe (2004): central banks “either do not respond much to financial imbalances or, to the extent that they do, they respond asymmetrically,” with policy loosened during unwinding but not tightened during buildup (financial instability measured by credit and equity-price gaps).
  - Bordo and Jeanne (2002): reactive liquidity injections ex post can be more costly in output losses than proactive policies in some historical episodes.
  - Cecchetti and Li (2005): policymakers react to banking-system balance-sheet stress, setting lower interest rates when financial stress is higher during downturns; critique: reaction conditioned on business cycle only and capital adequacy is a weak instability measure.
  - Bulíř and Čihák (2007): in a quarterly panel of 28 countries, financial instability is associated with short-term interest rates below those implied by a simple Taylor rule; a one standard deviation increase in the “probability of crisis” is associated with rates about 0.2 percentage points below otherwise in a freely floating exchange-rate country.
- DSGE literature largely neglects financial intermediaries; notable attempts:
  - Williamson (1987): banks from asymmetric information and monitoring costs create business cycles via credit supply effects, but model lacks nominal rigidities and monetary policy role.
  - Bernanke, Gertler and Gilchrist (1998): introduce a financial accelerator in a new Keynesian setup; banks intermediate between depositors and entrepreneurs; no explicit financial instability concept and complete diversification of idiosyncratic shocks.
  - Brousseau and Detken (2001): use sunspot equilibria to model central bank tradeoffs between short-term inflation target deviations and financial stability; model lacks explicit financial-sector modeling and clear propagation mechanism.

### Model innovations and key mechanisms (summary of Section III)
- Two main innovations relative to Galí (2002) DSGE:
  - Financial intermediaries supply external financing to some firms.
  - Firms sensitive to loan supply and interest rates are linked to other firms through a productivity nexus.
- Stylized facts captured:
  - The credit channel operates via a subset of firms dependent on external finance.
  - Small- and medium-sized firms depend more on banks than large firms.
  - Small/start-up firms perish easily without external financing.
  - Large firms rely on small firms for technology and productivity improvements.
  - Higher lending rates increase riskiness of marginal loan and overall lending portfolio.
  - Central bank observes financial-system health one period before the public.
  - Monetary policy actions do not generate moral-hazard behavior by banks.
- Agents in the economy: households; monopolistic-competition goods-producing firms (do not need external finance); competitive innovative firms (need external finance; live two periods); freely competitive financial intermediaries; central bank.

### Model structure — concise technical points (from Sections III.A–F)
- Households:
  - Utility: U(cn, ot) with budget constraint given in nominal terms; deposits pay nominal rate tr for one-period deposits.
  - Consumption aggregator: c_t = [∫ c(i)_t^{(ε-1)/ε} di]^{ε/(ε-1)} with ε elasticity of substitution.
- Goods firms (no external financing):
  - Technology y_t(j) = a_t n_t(j).
  - Price stickiness via Calvo: probability of adjusting price each period is θ−1.
- Innovative firms (need external financing):
  - Two-period firms. Period t investment s_t(j); period t+1 return χ_t(j) so that s_{t+1}(j) = s_t(j) + χ_t(j) (equation (1) notation).
  - Constant fraction γ survive with probability one; remaining firms die with probability 1+t δ (stochastic).
  - Returns distributed log-normally with parameters μ and σ; firms indexed by cumulative distribution proportion j.
  - Example parameterization: 05.0=μ, 1.0=σ, and 2.0=γ — firms with returns higher than 9664.0)(=γχ are risky (may die).
- Financial intermediaries:
  - Receive deposits and lend at lending rate tz; opportunity cost is central bank bill paying policy rate ti.
  - Banks cannot distinguish firms; marginal firm ω_t satisfies t z = χ_t(ω).
  - Loans per borrowing firm: l_t = d_t/(1−ω_t) (loans equally split among borrowing firms), implying higher lending rates concentrate the loan portfolio and increase risk.
  - Equilibrium loan rate set so expected returns from loans equal policy rate: (1+ i_t) = E_t[(1+ l_t) ~ ], equation (3).
  - No moral hazard; banks monitor existence at zero cost but cannot distinguish firm types.
- Technology:
  - Total technology a_t has exogenous AR(1): a^s_t = ρ_a a^s_{t−1} + ε^a_t with ρ_a = 0.95.
  - Endogenous component from surviving innovative firms enters via a Cobb-Douglas aggregate: a_t = (a^s_t)^{1−α} (a^i_t)^α, where α is contribution of innovative firms.
- Central bank:
  - Benchmarked Taylor rule (equation (4)): i_t = φ_π π_t + φ_x x_t with requirement φ_π > 1 for uniqueness.
  - Augmented rule with private financial information (equation (5)): central bank conditions on private signal about δ_t and may include sensitivity parameter δ_φ and shock δ_ν; paper uses specification including an indicator for when conditional expectation of δ_t crosses thresholds.
  - Central bank timing: at beginning of period, after δ_t and a^s_t realized, total technology a_t is observed; central bank may observe δ_t one period before public and set i_t accordingly.
  - Empirical motivation: supervisory/on-site information can improve predictions of financial stability (cited studies).

### Calibration and simulation setup (start of Section IV)
- Time unit: one quarter.
- Household utility: U(c,n) = [c^{1−σ}/(1−σ)] − φ n^{1+φ}/(1+φ) with 1==φσ (as stated).
- Calibrated parameters:
  - Calvo price-adjust probability θ−1 = 0.25 (implies average price duration of one year).
  - Discount factor β = 0.99.
  - Technology AR(1) serial correlation a_ρ = 0.95.
- Process for small-firm survival probability δ_t:
  - δ_t = δ_ρ δ_{t−1} + ε^δ_t (where ε^δ_t is i.i.d.).
  - Given average post-war U.S. recession duration of 11 months, δ_ρ chosen accordingly (text breaks off before numerical value).
- Policy-rule parameterization for simulations:
  - Benchmark Taylor rule: π_φ = 1.5 and x_φ = 0.5 (values from Taylor (1993)).
  - Alternative augmented rule: 5.0−=δφ (expressed in text as "5.0 −= δ φ"); paper notes qualitative results invariant to choice of, e.g., 25.0−=δφ or 75.0−=δφ and stresses requirement 0<δφ for qualitative implications.
- Shocks analyzed in simulations:
  - Pure technological shock (to a^s_t).
  - Shock to the probability of survival of firms (δ_t).

### Key analytical implications highlighted
- Incorporating financial intermediaries and forward-looking policy rules enables analysis of:
  - How the credit channel and firm survival affect aggregate productivity and output.
  - How central bank private information on financial health could alter policy setting compared with a standard Taylor rule.
- The model generates a mechanism whereby higher lending rates make loan portfolios more concentrated and risky, linking policy rates to financial stability via endogenous portfolio risk.
- Empirical literature suggests central banks holding supervisory information may achieve better stabilization outcomes by using that private information in policy decisions.

*Source: _wp0818 - Section V, we discuss possible extensions of the model. Section VI concludes.*

### 0.25 and the annual rate of business failure,

### 0.25 and the annual rate of business failure,

### Model parameterization
- δ (annual rate of business failure) = 0.03.
- γ (share of firms that survive for sure) = 0.2, which implies:
  - quarterly steady-state spread between loan and deposit rates = 0.76 percent.
  - annual loan rate = 7.28 percent.
- Variances:
  - σ_a (variance of technological shock) = 0.01.
  - σ_δ (variance of probability-of-survival shocks) = 0.0025.
- Other parameters:
  - α (participation of i_t^a in creation of technology) = 0.05.
  - τ (elasticity of substitution between projects j and j’) = 4/3.
- Distribution of returns to innovative firms for simulations:
  - lognormal with μ = 0.05 and σ = 1.0.
- Robustness: simulations conducted with a range of distributions; general results do not vary substantially.

### Simulation results — exogenous technology shock
- Shock specification:
  - positive shock in s_t^a equal to its one standard deviation (ε_a).
- Key dynamics and comparative results:
  - In an economy with sticky prices, imperfect competition, and no innovative sector, a positive exogenous technology shock generates lower employment, higher output, and opening of the output gap.
  - In the model with an innovative sector:
    - Responses differ from the benchmark model and are more pronounced.
    - From period 2 on the qualitative response of all variables is identical across all three scenarios (two Taylor-rule specifications and benchmark).
    - Labor and output gap: positive in period 1, become negative from period 2 onward due to initial monetary loosening based on central bank private information.
    - Paths may be nonmonotonic and less smooth for variables such as labor and output gap because lending conditions affect endogenous technology.
  - Endogenous technology creation depends on loan applicants (1−ω_{t−1}) and deposits (1−d_{t−1}). The effect of 1−ω_{t−1} on i_t^a is a priori indeterminate.
  - Mechanism on impact:
    - Policy rate decrease (due to negative response of inflation) causes loan applications to decrease on impact and deposits to increase.
    - Full impact on endogenous technology is positive but occurs in period 2, raising expectations for period 2 output and boosting period 1 consumption and labor.
    - From period 2 onward, higher endogenous technology amplifies responses to the initial shock.
  - As technology shock dies out:
    - tω (loan applications) increases and 1−t d (deposits) decreases toward steady state.
    - i_t^a path is not monotonic because i_t^a has no memory (innovative firms live for two periods only).
  - Financial instability is not generated by technology shock: ∀ t, E_{t−1} δ_t = 0, so central bank reaction identical across rule specifications.
  - With α = 0.05 the model departs visibly (but slightly) from the benchmark without innovative sector; numerical differences between Taylor-rule specifications are small.

### Simulation results — shock to default probability
- Shock specification:
  - negative shock to probability of survival tδ of one standard deviation (εδ).
  - This shock is less persistent than the technology shock, dying out in approximately 4 quarters.
- Dynamics under traditional Taylor rule (equation (4)):
  - Negative default shock in period t leads to a decline in output in period 1.
  - Fewer firms survive next period → less endogenous technology generation in period 1 → output falls.
  - Inflation increases and aggregate demand decreases less than natural output fall → output gap is negative.
  - In period 1: current and future output weakness reduces deposits and increases 1ω, further depressing endogenous technology in period 2.
  - Paradoxically, depressed endogenous technology in period 2 causes labor and the output gap to increase even above steady state.
  - From period 2 onward, dynamics resemble those in the benchmark model for a negative technology shock.
  - Central bank following the traditional Taylor rule fails to react in period 1 to δ_{t+2} even though it possesses the information; it reacts from period 2 onward after the shock has affected the economy, widening the output gap and increasing inflation before tightening policy.
- Dynamics under augmented Taylor rule (equation (5)):
  - Central bank knows δ_{t+2} at beginning of period 1 and can decrease policy rate in period 1, lowering loan rate.
  - Expected deposit rate change mimics policy rate, stimulating aggregate demand.
  - Lower policy rate reduces 1ω and generates positive expectations, stimulating deposits.
  - These effects have positive impact on endogenous technology in period 2, more than offsetting negative effect of δ_{t+2}.
  - Deposit and loan rates decrease in period 1 and increase gradually in subsequent periods.
- Information and signal extraction:
  - Monetary policy is useful for financial stability shocks only to the extent private agents’ signal extraction is limited.
  - Only the central bank has information on δ_{t+1} at the beginning of period t; households decide with information on t_a and t_δ due to reporting lags.
- Policy implication from simulations:
  - A central bank responding to financial sector instability can trade off marginally higher beginning-of-period inflation for more stable output and inflation in subsequent periods.
  - Ignoring information about δ under the traditional Taylor rule leads to longer-lasting output declines and higher inflation.

### Welfare calculations
- Method:
  - Lucas (1987) measure of welfare: compare variance of consumption under alternative rules.
  - Welfare differential = ½ × risk aversion coefficient (σ) × difference in variance of CES consumption simulated for 300 periods with simultaneous technology and default probability shocks; repeated 100 times.
- Results:
  - Standard deviations of consumption are practically identical for both rules and robust to δ_φ (weight of financial instability in policy rule).
  - Examples:
    - For δ_φ = –0.5:
      - Traditional rule consumption standard deviation = 0.05915.
      - Augmented rule consumption standard deviation = 0.05947.
    - For δ_φ = –0.1:
      - Traditional rule consumption standard deviation = 0.05899.
      - Augmented rule consumption standard deviation = 0.05892.
  - Interpretation:
    - Differences are not substantial; augmented rule does not extend into more stable long-run consumption.
    - Economy stabilizes faster under the augmented rule, but output and consumption paths are more volatile initially.
    - Central bank trades off more instability today for faster return to trend tomorrow.
    - Introduction of financial sector shocks in the DSGE model accelerates policy reaction to signs of financial instability but does not change the nature of monetary policy.

### Practical issues and possible extensions
- Practical limitations of embedding financial instability in a policy rule:
  - Central bank response in reality is likely highly nonlinear; central banks focus more on shocks with systemic implications.
  - Long-term fiscal effects: providing liquidity instead of closing weak institutions may delay adjustment and increase fiscal cleanup costs.
  - If the financial system faces a credibility crisis, lower policy rates may not calm depositors.
  - Monetary easing cannot substitute for prudential regulation.
- External sector and exchange rate considerations:
  - Introducing external sector requires distinguishing residents and nonresidents and introduces exchange rate regime considerations.
  - Scope for monetary easing is more limited in regimes with exchange rate anchors or strong exchange rate transmission; easing can trigger currency runs and unwind external positions.
  - Less enthusiasm for monetary easing in countries with significant capital flows.
- Other policy instruments and central bank roles:
  - Central banks may react to instability because they have prudential supervision roles and responsibility for payment systems, creating incentives to lower rates to alleviate instability.
  - Supervisory/regulatory measures (limits on financial ratios, corrective actions) exist but often take longer to implement than interest-rate changes.
- Privileged information and transparency:
  - Central banks often have privileged information about systemic financial health due to roles in payment systems and supervision.
  - Public release of privileged information is a policy choice; greater transparency can improve private signal extraction but may be legally or practically constrained.
  - Banking confidentiality laws and risk of provoking crises can limit disclosure.
  - There are substantial gaps between published financial stability reports and “good practice”; extent of disclosure is an area for further research.

### Conclusions
- Financial instability has significant macroeconomic costs and has largely been ignored in standard monetary policy rules.
- This paper:
  - Enriches the standard new Keynesian model with a financial system and firms requiring external financing.
  - Introduces a forward-looking element into the Taylor rule so the central bank responds to deterioration in the financial system balance sheet with instant monetary loosening.
  - Is the first to model central bank response to financial instability in a general equilibrium context (within the scope of this paper).
- Main findings:
  - A policy rule where the central bank lowers its policy rate in response to financial sector instability yields different short-term outcomes in output and inflation compared with the traditional Taylor rule.
  - For short-lived and reasonably sized financial instability shocks, a forward-looking central bank can limit short-term falls in output and consumption by monetary easing.
  - The central bank trading off more output and inflation instability today for a faster return to trend tomorrow leaves long-run consumption largely unaffected.

*Source: _wp0818 - 0.25 and the annual rate of business failure,*

### REFERENCES

### _wp0818 - REFERENCES

### References (selected by topic)
- Bank performance and market vs supervisory assessments: Berger, Allen; Sally Davies; Mark Flannery, 2001, “Comparing Market and Supervisory Assessments of Bank Performance: Who Knows What and When?” Journal of Money Credit and Banking, 32, pp. 641–667.
- Monetary policy and asset-price/financial stability interactions: Bernanke, Ben, and Mark Gertler, 1999, “Monetary policy and asset price volatility”, Economic Review (FRB of Kansas City), 4th quarter, pp. 17–51; Borio, Claudio, 2006, “Monetary and Prudential Policies at a Crossroads? New Challenges in the New Century,” BIS Working Papers No. 216; Borio, Claudio, and Philip Lowe, 2004, “Securing Sustainable Price Stability: Should Credit Come Back from the Wilderness?” BIS Working Papers No. 157.
- Financial accelerator and business cycle modeling: Bernanke, Ben; Mark Gertler; Simon Gilchrist, 1998, “The Financial Accelerator in a Quantitative Business Cycle Framework,” NBER Working Paper No. 6455.
- Market indicators of bank fragility and capital adequacy: Bongini, Paola; Luc Laeven; Giovanni Majnoni, 2002; Cecchetti, Stephen, and Lianfa Li, 2005, “Do Capital Adequacy Requirements Matter for Monetary Policy?” NBER Working Paper No. 11830.
- Financial crisis management and East Asia experience: Boorman, Jack et al., 2000, “Managing Financial Crises: The Experience in East Asia,” Carnegie-Rochester Conference Series on Public Policy, Vol. 53, pp. 1-67.
- Central bank policy, Taylor rules, and judgment: Svensson, Lars E. O., 2003, “What Is Wrong with Taylor Rules? Using Judgment in Monetary Policy through Targeting Rules,” Journal of Economic Literature, Vol. 41; Taylor, John B., 1993, “Discretion Versus Policy Rules in Practice,” Carnegie-Rochester Conference Series on Public Policy, Vol. 39.
- Financial supervision, independence, and accountability: Quintyn, Marc; Silvia Ramirez; Michael W. Taylor, 2007, “The Fear of Freedom: Politicians and the Independence and Accountability of Financial Sector Supervisors,” IMF Working Paper 07/25.
- Additional theoretical and methodological references: Calvo, Guillermo A., 1983; Galí, Jordi, 2002; Lucas, Robert, 1987; Monacelli, Tommaso, 2004; Crockett, Andrew, 1997; others listed.

### Appendix — Model structure and key equations

Households
- Consumption aggregator and isoelastic demand:
  - Aggregate consumption basket: integral expression with parameter ε as in the source.
  - Isoelastic demand of good i (Equation (A1)):
    - ic = (Pt/Pt(i))^ε  (as presented: t t t c P iP ic ε− ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ = )( )(  )
  - Aggregate price index definition: Pt = [∫ P_t(i)^{1−ε} di]^{1/(1−ε)} (preserved as in source).
- Household optimization problem:
  - First-order conditions summarized:
    - wt = −σ c_t n_t  (household labor condition)
    - Intertemporal condition (A2): expression with β, σ, expectations and price terms preserved exactly as in the source.
  - Log-linear forms:
    - w_t + σ c_t = −φ n_t  (as in text: ttt wcn ))) =+ σφ )
    - ˆcr + E_{t+1}ˆc_{t+1} − ... = −σ π_t (preserved as in source text: )ˆ( 111+++ −−=− ttttt crEc ))) σπσ )

Goods firms (sticky prices)
- Aggregate price index evolution (A3):
  - P_t^{1−ε} = θ P_{t}^{1−ε} + (1−θ) P_t^{new (1−ε)}  (preserved structure: [] ε ε θθ − − − −+ 1 1 1 1 )1( new ttt PPP )
- Firm’s price-setting problem: firm j resets price taking into account probability θ^{-1} of being able to reset in the future; first-order conditions lead to Euler-type summations (preserved as in source).
- Log-linearized optimality condition (A4):
  - κ(·) relation: ttt cmE ))) θ βθθ πβ π )1)(1( 1 −− += +  (as in source)

Aggregate production and efficiency
- Aggregate production: y_t = a_t + n_t  (Equation (A5))
- Log-linear: ˆy_t = ˆa_t + ˆn_t  (Equation (A6))
- Cost-minimization and marginal cost condition (A7): m c_t = ν a_t
- Relation combining household FOCs and cost conditions (A8, A9):
  - ν c_t = −σ φ n_t (A8)
  - Log-linear combination (A9): ˆa_t + ... = ˆm c_t (preserved structure: ttt aycm ))) += ( )1()(φφσ+−+= )

Flexible-price allocation and natural output
- Under flexible prices:
  - Real marginal cost constant: ε/(ε−1) (source states ε ε1− = mc)
  - Natural output (A10):
    - y_t^* = (φ + σ)^{-1} φ σ ... (source gives: tt ay )) φσ φ + + = 1 *  — preserve as in text: tt ay )) φσ φ + + = 1 *
- Output gap definition and forward-looking Phillips Curve:
  - Output gap: x_t = y_t − y_t^* (Equation (A11): *()( )() ttt t mcyyxσφσφ=+ − =+ )))
  - Phillips Curve (A12):
    - π_t = β E_{t+1} π_{t+1} + κ x_t  (preserved exact form: 1ttt t Exπβπ κ + =+ )) )

Computation of tω and t z (loan/firm risk structure)
- Define t z and t ω relationship: t z = ω_t χ (source: First remember that tt z = )(ωχ.)
- Two cases for marginal firm ω_t relative to γ:
  - Case ω_t > γ:
    - Use equation (3) in text and lognormal cdf: ω_t computed as cdf of a lognormal distribution with parameters μ and σ for (1+ 1/(1+ t E_i δ_t )) (preserve exact phrasing and parentheses from source).
  - Case ω_t < γ:
    - ω_t computed by numerical root-finding; define A_t^z (loan rate when ω_t < γ) and B_t^z (when ω_t > γ) and note B_t^z < A_t^z.
- Expressions preserved as in the source for the piecewise algebra determining ω_t and the inequality chain leading to B_t z < A_t z.

Steady state
- Steady-state relations (preserve exact equalities and statements):
  - β^{-1} = R (From equation (A2): β 1 = R)
  - wy = +σφ (household condition: wy= +σφ)
  - To attain efficient allocation: ν = ε/(ε−1) (source: 1− = ε ε υ . Also, ε ε1− = mc.)
  - In steady state: 1 = P (assumption)
  - Budget constraint in steady state: Td + Rn w d c − Π + ... preserved as in the source text.
  - Assumption on f_T: chosen such that ε 1 0 =⇒=Π f_T (preserve exact phrasing)
  - Deposits in steady state: d = 0 )1( 1)1( 1 1 > − −− − = εε εε R d (preserve the source’s exact numeric/formula expression and inequalities)

Computation of deposits (d_t)
- Period-by-period budget constraint and Euler equation combined (A13):
  - Full equation preserved as in source (complex expression with P_{t+1}/P_t terms, r_t, d_t, taxes, Π_t, σ, β).
- Iteration and transversality condition leading to (A14):
  - d_t expressed as infinite sum (preserved structure).
- Log-linearization and simplification under parameterization (σ = 1, WNC = 1, Π = 0, constant taxes) yields:
  - Rewritten form: )() ˆˆ ( ˆ )1()( 1+ ++ − − = ttttt sVEnwcTsVβ  (preserve exact algebraic layout from source).
- Solve for sV_t by value function iteration; then extract d_t̂ using the stated expressions:
  - Final log-linear deposit expression: d_t̂ = ( ) ( ˆ )1( ˆ ˆ 1 ttttt sV cRD nw D d + − + + =  (preserve source structure and notation).

Fundamental equations of the model
- The model’s fundamental equations are:
  - Equations (A6), (A7) in log-linear terms;
  - Equation (A11) (relation linking marginal cost, output, natural output);
  - Equation (A12) (forward-looking Phillips Curve);
  - Two first-order conditions for households;
  - Two first-order conditions for innovative firms and financial intermediaries;
  - Expression for deposits.
- These together constitute the system to be solved numerically, as indicated in the text.

### Figures (captions and shocks described)
- Figure 1: Distribution of Returns of Innovative Firms
- Figure 2: Shock to Exogenous Technology (One standard deviation of the technology shock, a_ε)
- Figure 3: Shock to Exogenous Technology: Response of Output, Output Gap, Inflation, and Labor (One standard deviation of the technology shock, a_ε)
- Figure 4: Shock to Exogenous Technology: Response of Policy Rate, Real Interest Rate, Loan Rate, and Effective Deposit Rate (One standard deviation of the technology shock, a_ε)
- Figure 5: Shock to Exogenous Technology: Response of tω, Endogenous Technology and Total Technology (One standard deviation of the technology shock, a_ε)
- Figure 6: Shock to Probability of Default (One standard deviation of the shock to the default probability, δ_ε)
- Figure 7: Shock to Probability of Default: Response of Output, Output Gap, Inflation, and Labor (One standard deviation of the shock to the default probability, δ_ε)
- Figure 8: Shock to Probability of Default: Response of Policy Rate, Real Interest Rate, Loan Rate, and Effective Deposit Rate (One standard deviation of the shock to the default probability, δ_ε)
- Figure 9: Shock to Probability of Default: Response of tω, Endogenous Technology and Total Technology (One standard deviation of the technology shock, a_ε)

*Source: _wp0818 - REFERENCES (IMF PDF content provided).*

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