## 3. Optimal Weight on Nominal Credit in the Macroprudential Rule ## Source details **Canonical URL:** [3. Optimal Weight on Nominal Credit in the Macroprudential Rule](https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2009/_wp09251.pdf) ## Other formats - [Markdown version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2009/_wp09251.pdf.md) - [Structured JSON version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2009/_wp09251.pdf.json) --- ### Introduction - Empirical links: future asset price busts associated with credit, share of residential investment in GDP, and current account balances. - Key policy questions: - What are the potential gains from reacting to signs of emerging financial vulnerability? - Is monetary policy the appropriate tool, or should other policies be used? - What are the trade-offs between stabilizing output and CPI inflation versus reducing asset price crash risk? - Approach: - Simulations with a two-sector New Keynesian model extended for housing, borrower/saver heterogeneity, and lending spreads dependent on loan-to-value, bank markups, and a macroprudential instrument. - Main messages: - Stronger monetary reactions to overheating or credit/asset price bubbles can help counter credit accelerator mechanisms. - A macroprudential instrument designed to dampen credit cycles is useful and often more efficient for financial shocks. - Correct identification of shock origins is crucial; invariant and rigid policy responses raise the risk of policy errors — discretion is required. ### Model (features and structure) - Core features: - Two-sector general equilibrium model (durables and non-durables) with monopolistic competition and Calvo price stickiness. - Housing provides services and is the principal vehicle for wealth accumulation. - Heterogeneous households: savers (fraction ) and borrowers (fraction 1) with borrowers more impatient ( B < ). - Borrowers finance housing with loans; lending rate R^L_t is a spread over the policy rate R_t: - R^L_t = _t R_t + F(B^B_t = P_D_t D^B_t) + _t (equation (18) form). - Financial intermediaries set spreads that depend on: - _t: financial shock (AR(1) in logs, persistence set to 0.95). - F(.): increasing, convex function of borrowers’ net worth; F(1)=0 ( interpretable as down-payment rate / 1 minus loan-to-value). - _t: macroprudential instrument affecting lending spreads. - Household and producer features: - Savers: external habit parameter " and durable weight (1 ). - Borrowers: discount factor B, borrowing constraints; Euler equations (8), (16). - Producers: final and intermediate goods, Calvo pricing with fractions 1_i resetting prices; real marginal cost MC_x_t = W_x_t / (P_x_t A_x_t), x = C, D. - Market clearing: - Non-durable output equals aggregate consumption (equation (25)). - Durable output equals aggregate residential investment (equation (26)). - Deposit/lending market clearing:  B_t + (1) B^B_t = 0 (equation (30)). ### Policy Regimes (in experiments) - Instruments available: - Policy rate R_t (monetary policy). - Macroprudential instrument _t responding to lagged nominal credit growth and affecting lending spreads (equation (33)). - Four regimes evaluated: 1. Baseline Taylor rule: - Taylor weights: 1.5 on CPI inflation, 0.5 on output gap; interest rate inertia included (equation (31)). 2. Augmented Taylor rule: - Adds reaction to lagged nominal credit growth (B^B_{t-1}/B^B_{t-2}) (P_{t-1}/P_{t-2}) with weight b; example weight b = 0.5 (equation (32)). 3. Augmented Taylor + macroprudential: - Monetary reaction to credit plus macroprudential rule _t = (lagged nominal credit growth); example macroprudential weight = 0.5 (equation (33)). 4. Optimized augmented Taylor + macroprudential: - Weights on inflation, output gap, credit, and  optimized to minimize variation in output gap and inflation. ### Calibration - Parameter choices: - Most taste and technology parameters set to standard literature values. - All shock persistence coefficients set to 0.95. - Key steady-state values: - Steady-state loan-to-value ratio: 80 percent. - Share of residential investment in GDP: 10 percent. - Selected parameter values (from Table 1): - Discount factor savers: 0.99 - Discount factor borrowers: 0.98 - Depreciation rate: 0.025 - Share of savers: 1/2 - Down payment rate (1 minus LTV): 0.2 - Average markup (ζ=(ζ̄−1)): 1.1 - Labor disutility of switching sectors (χL): 1 - Inverse Frisch elasticity of labor supply: 1 - Habit formation: 0.75 - Adjustment cost residential investment: 0.5 - Elasticity of spread with respect to net worth: 0.5 - Share of nondurables in GDP: 0.9 - Calvo lottery nondurable (θc): 0.75 - Calvo lottery durable (θd): 0.66 - Backward looking behavior nondurable (φc): 1 - Backward looking behavior durable (φd): 1 ### Simulation Results — Overview - Shock types: - Financial shock: relaxation in lending standards (_t) that immediately reduces lending rates by 100 basis points in the baseline Taylor regime (Figure 1 normalization). - Productivity shock: positive productivity in the nondurable sector yielding an immediate 1 percent increase in output under the Taylor rule (Figure 2 normalization). - Objective: evaluate which policy regimes better stabilize against housing-market-driven pressures and reduce financial vulnerability risk. ### A. Responses to Financial Shocks - Baseline Taylor rule: - Financial shock → immediate rise in residential investment and house prices; credit accelerator amplifies borrowing and CPI inflation. - After normalization, residential investment and house prices undershoot → temporary recession and higher volatility. - Augmented Taylor rule (b = 0.5 example): - Reacting to nominal credit growth reduces volatility of residential investment, GDP, output gap, house price inflation, and CPI inflation. - Interest rate volatility is lower despite a more aggressive rule due to forward-looking expectational effects. - Augmented Taylor + macroprudential (example ξ = 0.5): - Further improves macro stabilization by directly countering easing lending conditions. - Optimized augmented Taylor + macroprudential (financial-shock optimization): - Minimizes output gap and inflation variance; comes close to efficient reaction (no output gap). - Optimized monetary policy is very aggressive: weights on output gap and inflation are multiples of standard Taylor values; optimized interest rate smoothing r = 0.01 (≈ zero). - Optimal weight on nominal credit in the monetary policy rule b = 0.0. - Optimal weight on nominal credit in the macroprudential rule ξ = 0.8 in baseline optimization. - Performance metrics (Table 3, reaction to financial shocks): - Taylor: Std.dev. CPI inflation 0.51, Std.dev. output gap 20.62, Loss 0.65, Rank 4 - Augmented Taylor: Std.dev. CPI inflation 0.11, Std.dev. output gap 0.076, Loss 0.018, Rank 3 - Augmented Taylor + macroprudential: Std.dev. CPI inflation 0.09, Std.dev. output gap 0.061, Loss 0.012, Rank 2 - Optimized augmented Taylor + macroprudential: Std.dev. CPI inflation 0.01, Std.dev. output gap 0.04, Loss 0.002, Rank 1 - Interpretation: - Macroprudential policy is more efficient for addressing financial shocks than aggressive use of policy rates because it targets lending conditions directly. - Including nominal credit in the monetary rule is not optimal when monetary policy can be very aggressive and a macroprudential tool is available. ### B. Responses to Productivity Shocks - Productivity shock in nondurable sector → immediate 1 percent increase in output under baseline Taylor rule. - Effects: - Residential investment, house prices, and demand for credit rise, but consumption goods prices fall (CPI down). - Policy implications: - Best policy is accommodation by the central bank rather than suppressing credit. - Augmented Taylor and macroprudential rules calibrated for financial shocks can worsen outcomes: acting to suppress credit accentuates downward CPI pressure and raises volatility of output gap and inflation. - Standard Taylor rule performs best among the three non-optimized regimes. - Performance metrics (Table 5, reaction to productivity shocks): - Taylor: Std.dev. CPI inflation 0.199, Std.dev. output gap 0.162, Loss 0.066, Rank 2 - Augmented Taylor: Std.dev. CPI inflation 0.184, Std.dev. output gap 0.220, Loss 0.082, Rank 3 - Augmented Taylor + macroprudential: Std.dev. CPI inflation 0.233, Std.dev. output gap 0.276, Loss 0.130, Rank 4 - Optimized augmented Taylor + macroprudential: Std.dev. CPI inflation 0.072, Std.dev. output gap 0.080, Loss 0.011, Rank 1 - Conclusion: rigid use of indicators like nominal credit and automatic macroprudential tightening can generate policy errors when shocks are productivity-driven; discretion is required. ### C. Multiple-Shock Environment and Optimal Weights - Optimization exercise: - Vary the ratio of financial shock variance to productivity shock variance (productivity variance fixed at 1, covariance = 0); re-optimize augmented Taylor + macroprudential weights. - Result: - Optimal weight on nominal credit in the macroprudential rule increases as financial shocks become relatively more important. - When no financial shocks → no need for macroprudential tool. - When only financial shocks → optimal macroprudential weight on nominal credit = 0.8 (baseline). - Policy implication: - Policymakers need discretion and ability to judge shock composition, rather than rigid fixed rules. ### Robustness - Re-optimized augmented Taylor + macroprudential for five alternative calibrations (one-parameter changes): - Variation 1: θd = 0 and φd = 0 (eliminate nominal house price rigidities). - Variation 2: reduce lending rate elasticity κ from 0.5 to 0.1. - Variation 3: increase lending rate elasticity κ to 2. - Variation 4: raise Frisch elasticity of labor supply φ from 1 to 2. - Variation 5: remove labor reallocation costs χL = 0. - Optimized parameters to financial shocks (Table 6) — (r, π, y, b, ξ): - Original calibration: 0.01, 3.2, 3.2, 0.0, 0.8 - Flexible house prices (θd = 0, φd = 0): 0.01, 4.3, 1.6, 0.0, 0.75 - Lower lending rate elasticity (κ = 0.1): 0.09, 9.1, 0.8, 0.0, 0.85 - Higher lending rate elasticity (κ = 2): 0.01, 8.0, 2.4, 0.0, 0.55 - Higher labor elasticity (φ = 2): 0.01, 5.9, 0.0, 0.0, 0.90 - No labor reallocation costs (χL = 0): 0.01, 1.8, 4.0, 0.0, 1.00 - Optimized parameters to productivity shocks (Table 7) — (r, π, y, b, ξ): - Original calibration: 0.03, 3.5, 12.0, 0.3, 0.0 - Flexible house prices (θd = 0, φd = 0): 0.01, 1.8, 21.6, 0.0, 0.60 - Lower lending rate elasticity (κ = 0.1): 0.05, 5.5, 20.8, 0.5, 0.00 - Higher lending rate elasticity (κ = 2): 0.03, 3.1, 8.0, 0.3, 0.00 - Higher labor elasticity (φ = 2): 0.02, 2.7, 7.8, 0.0, 0.00 - No labor reallocation costs (χL = 0): 0.02, 2.2, 4.4, 0.2, 0.00 - Robustness findings: - Optimal weight on nominal credit in the macroprudential rule lies within 0.5 to 1 across calibrations when optimized for the financial shock. - Weight on nominal credit in the monetary policy rule remains uniformly 0.0 across these calibrations. - Weights on inflation are consistently higher than 1.5 in the optimized solutions. - When optimized for the productivity shock, macroprudential policy is generally not used, except in the flexible house price calibration. ### Conclusions and Policy Recommendations - Benefits and tools: - There are potential benefits from aggressive monetary reactions to financial shocks and from deploying macroprudential tools to counter loose credit conditions and credit-asset price accelerator mechanisms. - Macroprudential tools can reduce the need for aggressive monetary tightening and may be less disruptive to the macroeconomy than using policy rates to address credit accelerations. - Crucial caveats: - Identifying the source of asset price booms is difficult; distinguishing financial shocks from productivity shocks is essential. - Fixed, invariant policy responses to indicators such as nominal credit flows risk policy errors; judgment and discretion are required. - Practical design and management of macroprudential tools are complex; the paper’s representation is simple and further research on operational details is required. - Institutional implications: - Consider expanding central bank mandates to include explicit concern for financial vulnerabilities, but be mindful of practical and communication challenges. - Monetary and macroprudential policies need coordination, more information exchange, and consultation between monetary and supervisory authorities. *Source: IMF working paper section "3. Optimal Weight on Nominal Credit in the Macroprudential Rule" (excerpt provided).* ### References ............................................................................................................. ### _wp09251 - References ### Tables - 1. Parameter Values .......................................................................................................... 24 - 2. Parameters of Policy Rules in Reaction to Financial Shocks ....................................... 25 - 3. Performance of Policy Rules in Reaction to Financial Shocks ..................................... 26 - 4. Parameters of Policy Rules in Reaction to Productivity Shocks .................................. 27 - 5. Performance of Policy Rules in Reaction to Productivity Shocks ................................ 28 - 6. Sensitivity of Parameters of Policy Rules Optimized to Financial Shocks to Changes in Key Parameters ............................................................................. 29 - 7. Sensitivity of Parameters of Policy Rules Optimized to Productivity Shocks to Changes in Key Parameters ............................................................................. 30 ### Figures - 1. Effect of a Financial Shock ........................................................................................... 31 - 2. Effect of a Productivity Shock ...................................................................................... 32 *Source: _wp09251 - References* ### 3. Optimal Weight on Nominal Credit in the Macroprudential Rule ............................... 33 ### 3. Optimal Weight on Nominal Credit in the Macroprudential Rule ### Introduction - Empirical work links future asset price busts to variables such as credit, the share of residential investment in GDP, and current account balances. - Key policy questions addressed: - What are the potential gains from reacting to signs of emerging financial vulnerability? - Is monetary policy the appropriate tool, or should other policies be used? - What are the trade-offs between stabilizing output and CPI inflation versus reducing asset price crash risk? - Approach: simulations using a two-sector New Keynesian model extended for housing, borrowing/lending heterogeneity, and lending spreads that depend on loan-to-value ratios, bank markups, and a macroprudential instrument. - Main message: - Stronger monetary reactions to signs of overheating or credit/asset price bubbles can help counter credit accelerator mechanisms. - A macroprudential instrument designed to dampen credit cycles is also useful. - Correct identification of shock origins is crucial; invariant and rigid policy responses raise the risk of policy errors — discretion is required. ### Model (features and structure) - Core features: - Two-sector general equilibrium model (durables and non-durables) with monopolistic competition and Calvo price stickiness. - Housing provides services and is the principal vehicle for wealth accumulation. - Heterogeneous households: savers (fraction ) and borrowers (fraction 1) with borrowers more impatient ( B < ). - Borrowers finance housing with loans; lending rate R^L_t is a spread over the policy rate R_t: - R^L_t = _t R_t + F(B^B_t = P_D_t D^B_t) + _t (equation (18) form). - Financial intermediaries set spreads that depend on: - _t: financial shock (AR(1) in logs). - F(.): increasing, convex function of borrowers’ net worth; F(1)=0 ( interpretable as down-payment rate / 1 minus loan-to-value). - _t: macroprudential instrument affecting lending spreads. - Households: - Savers utility: includes external habit in consumption (parameter ") and durable consumption weight (1 ). - Borrowers utility: similar with discount factor B and borrowing constraints; Euler equations (8), (16). - Producers and pricing: - Final and intermediate goods producers in each sector; Calvo pricing with fraction 1_i resetting prices and fraction ' i indexing to last period’s sectoral inflation. - Real marginal cost MC_x_t = W_x_t / (P_x_t A_x_t), x = C, D. - Market clearing: - Non-durable output equals aggregate consumption (equation (25)). - Durable output equals aggregate residential investment (equation (26)). - Deposit/lending market clearing:  B_t + (1) B^B_t = 0 (equation (30)). ### Policy Regimes (in experiments) - Instruments available: - Policy rate R_t (monetary policy). - Macroprudential instrument _t that responds to lagged nominal credit growth and affects lending spreads (equation (33)). - Four regimes evaluated: 1. Baseline Taylor rule: - R_t = _R [ (P_C_{t-1}/P_C_{t-2}) / _C ]^{?} * [ Y_{t-1} / Y^*_ {t-1} ]^{?} * (1R(R_{t-1}))/R (equation (31) — Taylor weights: 1.5 on CPI inflation, 0.5 on output gap; interest rate inertia included). 2. Augmented Taylor rule: - Adds a reaction to lagged nominal credit growth: (B^B_{t-1}/B^B_{t-2}) (P_{t-1}/P_{t-2}) with weight b (equation (32)); example weight used in illustrations: b = 0.5. 3. Augmented Taylor plus macroprudential: - Monetary reaction to credit plus macroprudential rule _t = (lagged nominal credit growth) (equation (33)); example weight in macroprudential rule: 0.5. 4. Optimized augmented Taylor plus macroprudential: - Weights on inflation, output gap, credit, and  are optimized to minimize variation in output gap and inflation. ### Calibration - Parameters: - Most taste and technology parameters set to standard literature values. - All shock persistence coefficients set to 0.95. - Key steady-state values: - Steady-state loan-to-value ratio: 80 percent. - Share of residential investment in GDP: 10 percent. - These shares make housing important for aggregate fluctuations in the model. ### Simulation Results — Overview - Shock types considered: - Financial shock: relaxation in lending standards (_t) that immediately reduces lending rates by 100 basis points in the baseline Taylor regime. - Productivity shock: positive productivity in the nondurable sector yielding an immediate 1 percent increase in output under the Taylor rule. - Objective: evaluate which policy regimes better stabilize the economy against housing-market-driven pressures and reduce risk of financial vulnerabilities. ### A. Responses to Financial Shocks - Baseline Taylor rule (dotted line in figures): - Financial shock → immediate rise in residential investment and house prices. - Credit accelerator: higher house prices raise collateral values → lower lending rates → more borrowing → higher residential investment and CPI inflation. - After normalization of financial conditions, residential investment and house prices undershoot, causing temporary recession and higher volatility. - Augmented Taylor rule (example weight on nominal credit = 0.5): - Reacting to nominal credit growth reduces volatility of residential investment, GDP, output gap, house price inflation, and CPI inflation. - Interest rate volatility is lower despite more aggressive rule due to strong forward-looking expectational effects. - Augmented Taylor + macroprudential (macroprudential weight on nominal credit = 0.5 in illustration): - Further improves macroeconomic stabilization by directly countering easing lending conditions. - Optimized augmented Taylor + macroprudential: - Optimized rules (minimizing output gap and inflation variance) deliver the best stabilization; come close to efficient reaction (no output gap). - Optimized monetary policy is very aggressive: weights on output gap and inflation are multiples of standard Taylor values; optimized interest rate smoothing = 0. - Optimal weight on nominal credit in the monetary policy rule = zero. - Optimal weight on nominal credit in the macroprudential rule ≠ zero; in baseline optimization it equals 0.8. - Key interpretations: - Macroprudential policy is more efficient for addressing financial shocks than aggressive use of policy rates because it targets lending conditions directly. - Inclusion of nominal credit in the monetary rule is not optimal when monetary policy can be very aggressive and a macroprudential tool is available. ### B. Responses to Productivity Shocks - Productivity shock in nondurable sector → immediate 1 percent increase in output under baseline Taylor rule. - Effects resemble a housing boom: residential investment, house prices, and demand for credit rise, but consumption goods prices fall (CPI down). - Policy implications: - Best policy is accommodation by the central bank rather than suppressing credit. - Augmented Taylor and macroprudential rules with the same parameter values used for financial shocks can worsen outcomes: acting to suppress credit accentuates downward pressure on CPI and raises volatility of output gap and inflation. - In this case, standard Taylor rule performs best among the three non-optimized regimes. - Conclusion: rigid use of indicators like nominal credit and automatic macroprudential tightening can generate policy errors when shocks are productivity-driven; discretion is required. ### C. Multiple-Shock Environment and Optimal Weights - Optimal policy must balance responses across shock types according to relative shock importance. - Exercise: vary the ratio of financial shock variance to productivity shock variance (keeping productivity shock variance = 1 and covariance = 0), re-optimize augmented Taylor + macroprudential weights. - Result: optimal weight on nominal credit in the macroprudential rule increases as financial shocks become relatively more important. - When no financial shocks → no need for macroprudential tool. - When only financial shocks → optimal macroprudential weight on nominal credit = 0.8 (as in baseline). - Policy implication: policymakers need discretion and ability to judge shock composition, rather than rigid fixed rules. ### Robustness - Re-optimized augmented Taylor + macroprudential regime for five alternative calibrations (changing one parameter each time): - Variation 1: eliminate nominal house price rigidities (set _d and _d to zero). - Variation 2: reduce elasticity of lending rate to housing collateral from baseline  = 0.5 to  = 0.1. - Variation 3: increase elasticity to  = 2. - Variation 4: raise Frisch elasticity of labor supply  from 1 to 2. - Variation 5: remove labor reallocation costs (_L = 0). - Robustness findings: - Optimal weight on nominal credit in the macroprudential rule lies within the range 0.5 to 1 across calibrations when optimized for the financial shock. - The weight on nominal credit in the monetary policy rule remains uniformly zero across these calibrations. - Weights on inflation are consistently higher than 1.5 (the standard Taylor inflation weight) in the optimized solutions. - When optimized for the productivity shock, macroprudential policy is generally not used, except in the calibration with fully flexible house prices. - Interpretation: the role of the macroprudential instrument in addressing financial shocks is robust to reasonable parameter variations; rigid macroprudential rules can, however, be counterproductive for productivity shocks. ### Conclusions and Policy Recommendations - There are potential benefits from aggressive monetary reactions to financial shocks and from deploying macroprudential tools to counter loose credit conditions and credit-asset price accelerator mechanisms. - Macroprudential tools can reduce the need for aggressive monetary tightening and may be less disruptive to the macroeconomy than using policy rates to address credit accelerations. - Crucial caveats: - Identifying the source of asset price booms is difficult; distinguishing financial shocks from productivity shocks is essential. - Fixed, invariant policy responses to indicators such as nominal credit flows risk policy errors; judgment and discretion are required. - Practical design and management of macroprudential tools are complex and the paper's representation is simple; further research on operational details is required. - Institutional implications: - Consider expanding central bank mandates to include explicit concern for financial vulnerabilities, but be mindful of practical and communication challenges. - Monetary and macroprudential policies need coordination, more information exchange, and consultation between monetary and supervisory authorities. *Source: IMF working paper section "3. Optimal Weight on Nominal Credit in the Macroprudential Rule" (excerpt provided).* ### References ### _wp09251 - References ### Key literature cited - Aoki, Kosuke; James Proudman; Gertjan Vlieghe, 2004, “House Prices, Consumption, and Monetary Policy: A Financial Accelerator Approach,” Journal of Financial Intermediation, Vol. 13, No. 4, pp. 414–35. - Bernanke, Ben; Mark Gertler; Simon Gilchrist, 1998, “The Financial Accelerator in a Quantitative Business Cycle Framework,” NBER Working Paper No. 6455. - Bernanke, Ben; Mark Gertler, 2001, “Should Central Banks Respond to Movements in Asset Prices?” American Economic Review Vol. 91, No. 2, pp. 253–257. - Borio, Claudio; Philip Lowe, 2004, “Securing Sustainable Price Stability: Should Credit Come Back from the Wilderness?” BIS Working Paper No. 157. - Calvo, Guillermo, 1983, “Staggered Prices in a Utility-maximizing Framework,” Journal of Monetary Economics, Vol. 12, Issue 3, pp. 383-398. - Cecchetti, Stephen G.; Hans Genberg; John Lipsky; Sushil Wadhwani, 2000, Asset Prices and Central Bank Policy, Geneva Reports on the World Economy 2. - Christiano, Lawrence; Martin Eichenbaum; Charles Evans, 2005, “Nominal Rigidities and the Dynamic Effects of a Shock to Monetary Policy,” Journal of Political Economy, Vol. 113, Issue 1, pp. 1-45. - Cúrdia, Vasco; Michael Woodford, 2009, “Credit Spreads and Monetary policy," NBER Working Paper 15289. - Galí, Jordi, 2009, Monetary Policy, Inflation, and the Business Cycle, Princeton University Press. - Iacoviello, Matteo, 2005, “House Prices, Borrowing Constraints, and Monetary policy in the Business Cycle,” American Economic Review, Vol. 95, No. 3, pp. 739–64. - Monacelli, Tommaso, 2009, “New Keynesian Models, Durable Goods, and Collateral,” Journal of Monetary Economics, Vol. 56, pp. 242–54. - Woodford, Michael, 2001, “The Taylor Rule and Optimal Monetary Policy” (unpublished). ### Model calibration — Table 1 (Parameter values) - Discount factor savers: 0.99 - Discount factor borrowers: 0.98 - Depreciation rate: 0.025 - Share of savers: 1/2 - Down payment rate (1 minus LTV): 0.2 - Average markup (ζ=(ζ̄−1)): 1.1 - Labor disutility of switching sectors (χL): 1 - Inverse Frisch elasticity of labor supply: 1 - Habit formation: 0.75 - Adjustment cost residential investment: 0.5 - Elasticity of spread with respect to net worth: 0.5 - Share of nondurables in GDP: 0.9 - Calvo lottery nondurable (θc): 0.75 - Calvo lottery durable (θd): 0.66 - Backward looking behavior nondurable (φc): 1 - Backward looking behavior durable (φd): 1 ### Policy-rule parameterizations — Tables 2 and 4 (Parameters of policy rules) - Taylor rule: r: 0.7, π: 1.5, y: 0.5, b: __ - Augmented Taylor: r: 0.7, π: 1.5, y: 0.5, b: 0.5, 𐄁 - Augmented Taylor + macroprudential: r: 0.7, π: 1.5, y: 0.5, b: 0.5, 0.5 - Optimized augmented Taylor + macroprudential (financial shocks): r: 0.01, π: 3.2, y: 3.2, b: 0.0, 0.8 - Optimized augmented Taylor + macroprudential (productivity shocks): r: 0.03, π: 3.5, y: 12.0, b: 0.3, 0.0 (Note: Tables present parameter vectors for r, π, y, b, ξ under different calibrations and optimizations.) ### Policy-rule performance — Tables 3 and 5 (Performance metrics) - Performance metric definition: Loss equals sum of the variances of CPI inflation and output gap. - In reaction to financial shocks (Table 3): - Taylor: Std.dev. CPI inflation 0.51, Std.dev. output gap 20.62, Loss 0.65, Rank 4 - Augmented Taylor: Std.dev. CPI inflation 0.11, Std.dev. output gap 0.076, Loss 0.018, Rank 3 - Augmented Taylor + macroprudential: Std.dev. CPI inflation 0.09, Std.dev. output gap 0.061, Loss 0.012, Rank 2 - Optimized augmented Taylor + macroprudential: Std.dev. CPI inflation 0.01, Std.dev. output gap 0.04, Loss 0.002, Rank 1 - In reaction to productivity shocks (Table 5): - Taylor: Std.dev. CPI inflation 0.199, Std.dev. output gap 0.162, Loss 0.066, Rank 2 - Augmented Taylor: Std.dev. CPI inflation 0.184, Std.dev. output gap 0.220, Loss 0.082, Rank 3 - Augmented Taylor + macroprudential: Std.dev. CPI inflation 0.233, Std.dev. output gap 0.276, Loss 0.130, Rank 4 - Optimized augmented Taylor + macroprudential: Std.dev. CPI inflation 0.072, Std.dev. output gap 0.080, Loss 0.011, Rank 1 ### Sensitivity analysis — Tables 6 and 7 (Optimized parameters under alternative calibrations) - Optimized parameters to financial shocks (Table 6), reporting (r, π, y, b, ξ): - Original calibration: 0.01, 3.2, 3.2, 0.0, 0.8 - Flexible house prices (θd = 0, φd = 0): 0.01, 4.3, 1.6, 0.0, 0.75 - Lower lending rate elasticity (κ = 0.1): 0.09, 9.1, 0.8, 0.0, 0.85 - Higher lending rate elasticity (κ = 2): 0.01, 8.0, 2.4, 0.0, 0.55 - Higher labor elasticity (φ = 2): 0.01, 5.9, 0.0, 0.0, 0.90 - No labor reallocation costs (χL = 0): 0.01, 1.8, 4.0, 0.0, 1.00 - Optimized parameters to productivity shocks (Table 7), reporting (r, π, y, b, ξ): - Original calibration: 0.03, 3.5, 12.0, 0.3, 0.0 - Flexible house prices (θd = 0, φd = 0): 0.01, 1.8, 21.6, 0.0, 0.60 - Lower lending rate elasticity (κ = 0.1): 0.05, 5.5, 20.8, 0.5, 0.00 - Higher lending rate elasticity (κ = 2): 0.03, 3.1, 8.0, 0.3, 0.00 - Higher labor elasticity (φ = 2): 0.02, 2.7, 7.8, 0.0, 0.00 - No labor reallocation costs (χL = 0): 0.02, 2.2, 4.4, 0.2, 0.00 ### Impulse-response illustrations — Figures 1 and 2 (Effects of shocks) - Figure 1: Effect of a Financial Shock (Deviation from steady state; quarters on x-axis) - The impulse response is to an unanticipated financial shock in the first quarter, normalized such that it leads to a 1 percent decline of the lending rate on impact under the Taylor rule. - Variables shown: Consumption (percent), Residential Investment (percent), GDP (percent), Consumer Price Index Inflation (percentage points), Nominal House Price Inflation (percentage points), Policy Rate (percentage points), Lending Rate (percentage points), Nominal Debt Growth (percent), Output Gap (percent). - Paths denote different policy regimes: Taylor; Augmented Taylor; Augmented Taylor + macroprudential; Optimized Augmented Taylor + macroprudential. - Figure 2: Effect of a Productivity Shock (Deviation from steady state; quarters on x-axis) - The impulse response is to an unanticipated productivity shock in the first quarter, normalized such that it leads to a 1 percent increase in real GDP on impact under the Taylor rule. - Variables shown: same set as Figure 1; paths denote the same policy regimes. ### Macroprudential instrument usefulness — Figure 3 - Figure 3: Optimal Weight on Nominal Credit in the Macroprudential Rule - Message: "As the importance of financial shocks increases, the macroprudential tool becomes more useful." - Axes: Weight on changes in nominal credit in the macroprudential rule; Relative standard deviation of financial shocks with respect to productivity shocks. - Statement: Source: IMF staff calculations. ### Appendix: Linearized conditions (model structure and key equations) - Notation: Lower case variables denote log-linear deviations from steady-state values. Q_t = P^D_t / P^C_t is the relative price of durables in terms of non-durables. !^i_t denotes deviations from the real wage from steady-state values, defined as nominal wage W^i_t divided by aggregate price level P_t, for i = C, D. - Representative first-order conditions and blocks (selected equations as presented): - Optimal decisions by savers: - q_t − c_t − " c_{t−1} 1−" + ψ (i_t − i_{t−1}) = μ_t + β ψ (E_t i_{t+1} − i_t) (equation 34) - (1−β)(d_t − d_{t}) = μ_t − β(1−β) E_t μ_{t+1} (equation 35) - " c_t = E_t " c_{t+1} − (1−")(r_t − E_t p^C_{t+1}) (equation 36) - Consumption-labor-price relations for savers: equations 37–38. - Corresponding conditions for borrowers: equations 39–43. - Borrowers' budget constraint (log-linear deviation form): equation 44. - Effective interest rate for borrowers (spread over riskless rate), including macroprudential rule substitution: - r^L_t = r_t + κ(b^B_t − d^B_t − ϕ q_t − υ_t) + ξ(b^B_{t−1} − b^B_{t−2} + p_t−1) (equation 45) - Comment: As long as ξ = 0 this instrument is not operational; otherwise it raises the costs of lending in proportion to nominal credit growth. - Price and relative price definitions: - p_t = ρ p^C_t + (1−ρ) p^D_t (equation 46) - q_t = q_{t−1} + p^D_t − p^C_t (equation 47) - Production functions: - y^C_t = a^C_t + l^C;tot_t (equation 48) - y^D_t = a^D_t + l^D;tot_t (equation 49) - Pricing equations (Calvo-style with inflation persistence and markup terms): equations 50–51 with definitions of Λ_C and Λ_D. - Market clearing for nondurables and investment goods: equations 52–53. - Housing law of motion: - d_t = (1−δ) d_{t−1} + δ i_t (equation 54) - d^B_t = (1−δ) d^B_{t−1} + δ i^B_t (equation 55) - Labor aggregation across sectors: equations 56–57. - Monetary policy Taylor rule (log-linear): - r_t = R r_{t−1} + (1−R)(α p^C_{t−1} + y(y_{t−1} − ȳ_{t−1}) + d p^D_{t−1} + b(b^B_{t−1} − b^B_{t−2} + p_{t−1})) (equation 58) - Aggregate real GDP: - y_t = β y^C_t + (1−β) y^D_t (equation 59) - Shock processes (autoregressive forms): - a^C_t = ρ^a_C a^C_{t−1} + ε^{a;C}_t - a^D_t = ρ^a_D a^D_{t−1} + ε^{a;D}_t - υ_t = ρ^υ υ_{t−1} + ε^υ_t - Practical focus: TFP shocks in the nondurable sector (a^C_t) and the financial shock (υ_t). *Source: _wp09251 - References* --- _Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2009/_wp09251.pdf_