Credit Frictions and Optimal Monetary Policy

Credit Frictions and Optimal Monetary Policy Vasco Cúrdia FRB New York Michael Woodford Columbia University Conference on Monetary Policy and Financial Frictions Cúrdia and Woodford () Credit Frictions Halloween 2008 1 / 40

Motivation New Keynesian monetary models often abstract entirely from financial intermediation and hence from financial frictions Cúrdia and Woodford () Credit Frictions Halloween 2008 2 / 40

Motivation New Keynesian monetary models often abstract entirely from financial intermediation and hence from financial frictions Representative household Complete (frictionless) financial markets Single interest rate (which is also the policy rate) relevant for all decisions Cúrdia and Woodford () Credit Frictions Halloween 2008 2 / 40

Motivation New Keynesian monetary models often abstract entirely from financial intermediation and hence from financial frictions Representative household Complete (frictionless) financial markets Single interest rate (which is also the policy rate) relevant for all decisions But in actual economies (even financially sophisticated), there are different interest rates, that do not move perfectly together Cúrdia and Woodford () Credit Frictions Halloween 2008 2 / 40

3.50 3.00 2.50 2.00 1.50 1.00 0.50 0.00 Spreads (Sources: FRB, IMF/IFS) Q3:1986 Q1:1987 Q3:1987 Q1:1988 Q3:1988 Q1:1989 Q3:1989 Q1:1990 Q3:1990 Q1:1991 Q3:1991 Q1:1992 Q3:1992 Q1:1993 Q3:1993 Q1:1994 Q3:1994 Q1:1995 Q3:1995 Q1:1996 Q3:1996 Q1:1997 Q3:1997 Q1:1998 Q3:1998 Q1:1999 Q3:1999 Q1:2000 Q3:2000 Q1:2001 Q3:2001 Q1:2002 Q3:2002 Q1:2003 Q3:2003 Q1:2004 Q3:2004 Q1:2005 Q3:2005 Q1:2006 Q3:2006 Q1:2007 Q3:2007 Q1:2008 Prime Spread to FF C&I Spread to FF

380 360 340 320 300 280 260 240 220 200 180 160 140 120 100 80 60 40 20 0 USD LIBOR-OIS Spreads (Source: Bloomberg) 01/04/05 03/04/05 05/04/05 07/04/05 09/04/05 11/04/05 01/04/06 03/04/06 05/04/06 07/04/06 09/04/06 11/04/06 01/04/07 03/04/07 05/04/07 07/04/07 09/04/07 11/04/07 01/04/08 03/04/08 05/04/08 07/04/08 09/04/08 basis points 1M 3M 6M

7 6 5 4 3 2 1 0 LIBOR 1m vs FFR target (source: Bloomberg and Federal Reserve Board) 1/2/2007 2/2/2007 3/2/2007 4/2/2007 5/2/2007 6/2/2007 7/2/2007 8/2/2007 9/2/2007 10/2/2007 11/2/2007 12/2/2007 1/2/2008 2/2/2008 3/2/2008 4/2/2008 5/2/2008 6/2/2008 7/2/2008 8/2/2008 9/2/2008 10/2/2008 % LIBOR 1m FFR target

Motivation Questions: How much is monetary policy analysis changed by recognizing existence of spreads between different interest rates? How should policy respond to financial shocks that disrupt financial intermediation, dramatically widening spreads? Cúrdia and Woodford () Credit Frictions Halloween 2008 3 / 40

Motivation John Taylor (Feb. 2008) has proposed that Taylor rule for policy might reasonably be adjusted, lowering ff rate target by amount of increase in LIBOR-OIS spread Essentially, Taylor rule would specify operating target for LIBOR rate rather than ff rate Would imply automatic adjustment of ff rate in response to spread variations, as under current SNB policy Cúrdia and Woodford () Credit Frictions Halloween 2008 4 / 40

3.500 3.000 2.500 2.000 1.500 1.000 0.500 0.000 SNB Interest rates (source: SNB) 1/3/2007 2/3/2007 3/3/2007 4/3/2007 5/3/2007 6/3/2007 7/3/2007 8/3/2007 9/3/2007 10/3/2007 11/3/2007 12/3/2007 1/3/2008 2/3/2008 3/3/2008 4/3/2008 5/3/2008 6/3/2008 7/3/2008 Repo O/N Index Libor 3m Libor Target Lower Bound Libor Target Upper Bound

Motivation John Taylor (Feb. 2008) has proposed that Taylor rule for policy might reasonably be adjusted, lowering ff rate target by amount of increase in LIBOR-OIS spread Essentially, Taylor rule would specify operating target for LIBOR rate rather than ff rate Would imply automatic adjustment of ff rate in response to spread variations, as under current SNB policy Is a systematic response of that kind desirable? Cúrdia and Woodford () Credit Frictions Halloween 2008 5 / 40

The Model Generalizes basic (representative household) NK model to include Cúrdia and Woodford () Credit Frictions Halloween 2008 6 / 40

The Model Generalizes basic (representative household) NK model to include heterogeneity in spending opportunities costly financial intermediation Cúrdia and Woodford () Credit Frictions Halloween 2008 6 / 40

The Model Generalizes basic (representative household) NK model to include heterogeneity in spending opportunities costly financial intermediation Each household has a type τ t (i) {b, s}, determining preferences 1 ] E 0 β [u t τt(i) (c t (i); ξ t ) v τt(i) (h t (j; i) ; ξ t ) dj, t=0 0 Cúrdia and Woodford () Credit Frictions Halloween 2008 6 / 40

The Model Generalizes basic (representative household) NK model to include heterogeneity in spending opportunities costly financial intermediation Each household has a type τ t (i) {b, s}, determining preferences 1 ] E 0 β [u t τt(i) (c t (i); ξ t ) v τt(i) (h t (j; i) ; ξ t ) dj, t=0 0 Each period type remains same with probability δ < 1; when draw new type, always probability π τ of becoming type τ Cúrdia and Woodford () Credit Frictions Halloween 2008 6 / 40

The Model 5 4 3 λ b 2 λ s u b c (c) 1 u s c (c) 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 c c s b Marginal utilities of the two types Cúrdia and Woodford () Credit Frictions Halloween 2008 7 / 40

The Model Aggregation simplified by assuming intermittent access to an insurance agency Cúrdia and Woodford () Credit Frictions Halloween 2008 8 / 40

The Model Aggregation simplified by assuming intermittent access to an insurance agency State-contingent contracts enforceable only on those occasions Other times, can borrow or lend only through intermediaries, at a one-period, riskless nominal rate, different for savers and borrowers Consequence: long-run marginal utility of income same for all households, regardless of history of spending opportunities Cúrdia and Woodford () Credit Frictions Halloween 2008 8 / 40

The Model Aggregation simplified by assuming intermittent access to an insurance agency State-contingent contracts enforceable only on those occasions Other times, can borrow or lend only through intermediaries, at a one-period, riskless nominal rate, different for savers and borrowers Consequence: long-run marginal utility of income same for all households, regardless of history of spending opportunities MUI and expenditure same each period for all households of a given type: hence only increase state variables from 1 to 2 Cúrdia and Woodford () Credit Frictions Halloween 2008 8 / 40

The Model Euler equation for each type τ {b, s}: { 1 + i λt τ τ } = βe t t [δλt+1 τ + (1 δ)λ t+1 ] Π t+1 where λ t π b λ b t + π s λ s t Cúrdia and Woodford () Credit Frictions Halloween 2008 9 / 40

The Model Euler equation for each type τ {b, s}: { 1 + i λt τ τ } = βe t t [δλt+1 τ + (1 δ)λ t+1 ] Π t+1 where λ t π b λ b t + π s λ s t Aggregate demand relation: Y t = π τ c τ (λt τ ; ξ t ) + G t + Ξ t τ where Ξ t denotes resources used in intermediation Cúrdia and Woodford () Credit Frictions Halloween 2008 9 / 40

Log-Linear Equations Intertemporal IS relation: Ŷ t = E t Ŷ t+1 σ[î avg t π t+1 ] E t [ g t+1 + ˆΞ t+1 ] where σs Ω ˆΩ t + σ(s Ω + ψ Ω )E t ˆΩ t+1, î avg t π b î b t + π s î d t, ˆΩ t ˆλ b t ˆλ s t, g t is a composite exogenous disturbance to expenditure of type b, type s, and government, σ π b s b σ b + π s s s σ s > 0, and s Ω, ψ Ω depend on asymmetry Cúrdia and Woodford () Credit Frictions Halloween 2008 10 / 40

Log-Linear Equations Determination of the marginal-utility gap: where ˆδ < 1 and ˆΩ t = ˆω t + ˆδE t ˆΩ t+1, ˆω t î b t î d t measures deviation of the credit spread from its steady-state value Cúrdia and Woodford () Credit Frictions Halloween 2008 11 / 40

The Model Financial intermediation technology: in order to supply loans in (real) quantity b t, must obtain (real) deposits d t = b t + Ξ t (b t ), where Ξ t (0) = 0, Ξ t (b) 0, Ξ t(b) 0, Ξ t (b) 0 for all b 0, each date t. Competitive banking sector would then imply equilibrium credit spread ω t (b t ) = Ξ bt (b t ) Cúrdia and Woodford () Credit Frictions Halloween 2008 12 / 40

The Model Financial intermediation technology: in order to supply loans in (real) quantity b t, must obtain (real) deposits d t = b t + Ξ t (b t ), where Ξ t (0) = 0, Ξ t (b) 0, Ξ t(b) 0, Ξ t (b) 0 for all b 0, each date t. Competitive banking sector would then imply equilibrium credit spread ω t (b t ) = Ξ bt (b t ) More generally, we allow 1 + ω t (b t ) = µ b t (b t )(1 + Ξ bt (b t )), where {µ b t } is a markup in the banking sector (perhaps a risk premium) Cúrdia and Woodford () Credit Frictions Halloween 2008 12 / 40

Log-Linear Equations Monetary policy: central bank can effectively control deposit rate i d t, which in the present model is equivalent to the policy rate (interbank funding rate) Lending rate then determined by the ω t (b t ): in log-linear approximation, î b t = î d t + ˆω t Cúrdia and Woodford () Credit Frictions Halloween 2008 13 / 40

Log-Linear Equations Monetary policy: central bank can effectively control deposit rate i d t, which in the present model is equivalent to the policy rate (interbank funding rate) Lending rate then determined by the ω t (b t ): in log-linear approximation, î b t = î d t + ˆω t Hence the rate î avg t that appears in IS relation is determined by î avg t = î d t + π b ˆω t Cúrdia and Woodford () Credit Frictions Halloween 2008 13 / 40

The Model Supply side of model: same as in basic NK model, except must aggregate labor supply of two types Cúrdia and Woodford () Credit Frictions Halloween 2008 14 / 40

The Model Supply side of model: same as in basic NK model, except must aggregate labor supply of two types Labor only variable factor of production for each differentiated good Cúrdia and Woodford () Credit Frictions Halloween 2008 14 / 40

The Model Supply side of model: same as in basic NK model, except must aggregate labor supply of two types Labor only variable factor of production for each differentiated good Firms wage-takers in labor market Competitive labor supply, except wage demand may be increased by exogenous wage markup process {µ w t } Dixit-Stiglitz monopolistic competition Cúrdia and Woodford () Credit Frictions Halloween 2008 14 / 40

The Model Supply side of model: same as in basic NK model, except must aggregate labor supply of two types Labor only variable factor of production for each differentiated good Firms wage-takers in labor market Competitive labor supply, except wage demand may be increased by exogenous wage markup process {µ w t } Dixit-Stiglitz monopolistic competition Calvo staggering of adjustment of individual prices Cúrdia and Woodford () Credit Frictions Halloween 2008 14 / 40

The Model Supply side of model: same as in basic NK model, except must aggregate labor supply of two types Labor only variable factor of production for each differentiated good Firms wage-takers in labor market Competitive labor supply, except wage demand may be increased by exogenous wage markup process {µ w t } Dixit-Stiglitz monopolistic competition Calvo staggering of adjustment of individual prices Only difference: labor supply depends on both MUI: λ b t, λ s t, or alternatively on Ω t as well as λ t Cúrdia and Woodford () Credit Frictions Halloween 2008 14 / 40

Log-Linear Equations Log-linear AS relation: generalizes NKPC: π t = κ(ŷ t Ŷt n ) + u t + ξ(s Ω + π b γ b ) ˆΩ t ξ σ 1 ˆΞ t +βe t π t+1 where ( λ γ b b ) 1/ν π b λ depends on Ω Cúrdia and Woodford () Credit Frictions Halloween 2008 15 / 40

Log-Linear Equations Log-linear AS relation: generalizes NKPC: π t = κ(ŷ t Ŷt n ) + u t + ξ(s Ω + π b γ b ) ˆΩ t ξ σ 1 ˆΞ t +βe t π t+1 where ( λ γ b b ) 1/ν π b λ depends on Ω other coefficients, and disturbance terms Ŷ n t, u t, defined as in basic NK model, using σ in place of the rep hh s elasticity Cúrdia and Woodford () Credit Frictions Halloween 2008 15 / 40

What Difference Do Frictions Make? A simple special case: credit spread {ω t } evolves exogenously, and intermediation uses no resources (i.e., spread is a pure markup) Cúrdia and Woodford () Credit Frictions Halloween 2008 16 / 40

What Difference Do Frictions Make? A simple special case: credit spread {ω t } evolves exogenously, and intermediation uses no resources (i.e., spread is a pure markup) Then ˆΞ t terms vanish, and { ˆω t } exogenous implies { ˆΩ t } exogenous The usual 3-equation model suffices to determine paths of {Ŷ t, π t, î avg t }: AS relation IS relation MP relation (written in terms of implication for î avg t, given exogenous spread) Cúrdia and Woodford () Credit Frictions Halloween 2008 16 / 40

What Difference Do Frictions Make? The difference made by the credit frictions: The interest rate in this system is î avg t, not same as policy rate Additional disturbance terms in each of the 3 equations Responses of output, inflation, interest rates to non-financial shocks (under a given monetary policy rule, e.g. Taylor rule) are identical to those predicted by basic NK model hence no change in conclusions about desirability of a given rule, from standpoint of stabilizing in response to those disturbances Cúrdia and Woodford () Credit Frictions Halloween 2008 17 / 40

What Difference Do Frictions Make? The difference made by the credit frictions: The interest rate in this system is î avg t, not same as policy rate Additional disturbance terms in each of the 3 equations Responses of output, inflation, interest rates to non-financial shocks (under a given monetary policy rule, e.g. Taylor rule) are identical to those predicted by basic NK model hence no change in conclusions about desirability of a given rule, from standpoint of stabilizing in response to those disturbances Responses to financial shocks: equivalent to responses (in basic NK model) to a simultaneous monetary policy shock, cost-push shock, and shift in natural rate of interest. Cúrdia and Woodford () Credit Frictions Halloween 2008 17 / 40

Optimal Policy Natural objective for stabilization policy: average expected utility: where E 0 t=0 βu(y t, λ b t, λ s t, t ; ξ t ) U(Y t, λ b t, λ s t, t ; ξ t ) π b u b (c b (λ b t ; ξ t ); ξ t ) + π s u s (c s (λ s t; ξ t ); ξ t ) 1 ( ) 1+ν ( ) λ ν 1+ω t H t 1 + ν Λ Yt t, t and λ t / Λ t is a decreasing function of λ b t /λ s t, so that total disutility of producing given output is increasing function of the MU gap A t Cúrdia and Woodford () Credit Frictions Halloween 2008 18 / 40

Optimal Policy: LQ Approximation Compute a quadratic approximation to this welfare measure, in the case of small fluctuations around the optimal steady state Cúrdia and Woodford () Credit Frictions Halloween 2008 19 / 40

Optimal Policy: LQ Approximation Compute a quadratic approximation to this welfare measure, in the case of small fluctuations around the optimal steady state Results especially simple in special case: No steady-state distortion to level of output (P = MC, W/P = MRS)(Rotemberg-Woodford, 1997) No steady-state credit frictions: ω = Ξ = Ξ b = 0 Cúrdia and Woodford () Credit Frictions Halloween 2008 19 / 40

Optimal Policy: LQ Approximation Compute a quadratic approximation to this welfare measure, in the case of small fluctuations around the optimal steady state Results especially simple in special case: No steady-state distortion to level of output (P = MC, W/P = MRS)(Rotemberg-Woodford, 1997) No steady-state credit frictions: ω = Ξ = Ξ b = 0 Note, however, that we do allow for shocks to the size of credit frictions Cúrdia and Woodford () Credit Frictions Halloween 2008 19 / 40

Optimal Policy: LQ Approximation Approximate objective: max of expected utility equivalent (to 2d order) to minimization of quadratic loss function β t [πt 2 + λ y (Ŷ t Ŷt n ) 2 + λ Ω ˆΩ 2 t + λ Ξ Ξ bt ˆb t ] t=0 Weight λ y > 0, definition of natural rate Ŷt n NK model New weights λ Ω, λ Ξ > 0 same as in basic LQ problem: minimize loss function subject to log-linear constraints: AS relation, IS relation, law of motion for ˆb t, relation between ˆΩ t and expected credit spreads Cúrdia and Woodford () Credit Frictions Halloween 2008 20 / 40

Optimal Policy: LQ Approximation Consider special case: No resources used in intermediation (Ξ t (b) = 0) Financial markup {µ b t } an exogenous process Cúrdia and Woodford () Credit Frictions Halloween 2008 21 / 40

Optimal Policy: LQ Approximation Consider special case: No resources used in intermediation (Ξ t (b) = 0) Financial markup {µ b t } an exogenous process Result: optimal policy is characterized by the same target criterion as in basic NK model: π t + (λ y /κ)(x t x t 1 ) = 0 ( flexible inflation targeting ) Cúrdia and Woodford () Credit Frictions Halloween 2008 21 / 40

Optimal Policy: LQ Approximation Consider special case: No resources used in intermediation (Ξ t (b) = 0) Financial markup {µ b t } an exogenous process Result: optimal policy is characterized by the same target criterion as in basic NK model: π t + (λ y /κ)(x t x t 1 ) = 0 ( flexible inflation targeting ) However, state-contingent path of policy rate required to implement the target criterion is not the same Cúrdia and Woodford () Credit Frictions Halloween 2008 21 / 40

Implementing Optimal Policy: Interest-Rate Rule Instrument rule to implement the above target criterion: Given lagged variables, current exogenous shocks, and observed current expectations of future inflation and output, solve the AS and IS relations for target it d that would imply values of π t and x t projected to satisfy the target relation What Evans-Honkapohja (2003) call expectations-based rule for implementation of optimal policy Desirable properties: ensures that there are no REE other than those in which the target criterion holds hence ensures determinacy of REE in this example, also implies E-stability of REE, hence convergence of least-squares learning dynamics to REE Cúrdia and Woodford () Credit Frictions Halloween 2008 22 / 40

Implementing Optimal Policy: Interest-Rate Rule i d t = r n t + φ u u t + [1 + βφ u ]E t π t+1 + σ 1 E t x t+1 φ x x t 1 [π b + δ 1 s Ω ] ˆω t + [(δ 1 1) + φ u ξ]s Ω ˆΩ t where φ u κ σ(κ 2 +λ y ) > 0, φ x λ y σ(κ 2 +λ y ) > 0 Cúrdia and Woodford () Credit Frictions Halloween 2008 23 / 40

Implementing Optimal Policy: Interest-Rate Rule i d t = r n t + φ u u t + [1 + βφ u ]E t π t+1 + σ 1 E t x t+1 φ x x t 1 [π b + δ 1 s Ω ] ˆω t + [(δ 1 1) + φ u ξ]s Ω ˆΩ t where φ u κ σ(κ 2 +λ y ) > 0, φ x λ y σ(κ 2 +λ y ) > 0 a forward-looking Taylor rule, with adjustments proportional to both the credit spread and the marginal-utility gap Cúrdia and Woodford () Credit Frictions Halloween 2008 23 / 40

Implementing Optimal Policy: Interest-Rate Rule Note that if s b σ b >> s s σ s, then s Ω π s, so that if in addition δ 1, the rule becomes approximately i d t =... ˆω t + φ Ω ˆΩ t Cúrdia and Woodford () Credit Frictions Halloween 2008 24 / 40

Implementing Optimal Policy: Interest-Rate Rule Note that if s b σ b >> s s σ s, then s Ω π s, so that if in addition δ 1, the rule becomes approximately i d t =... ˆω t + φ Ω ˆΩ t Since for our calibration, φ Ω is also quite small (.03), this implies that a 100 percent spread adjustment would be close to optimal, except in the case of very persistent fluctuations in the credit spread Cúrdia and Woodford () Credit Frictions Halloween 2008 24 / 40

Implementing Optimal Policy: Interest-Rate Rule Essentially, in the case that s b σ b >> s s σ s, it is really only i b t that matters much to the economy, and the simple intuition for the spread adjustment is reasonably accurate. But for other parameterizations that would not be true. For example, if s b σ b = s s σ s, the optimal rule is i d t =... π b ˆω t which is effectively an instrument rule in terms of it avg than either it d or it b rather Cúrdia and Woodford () Credit Frictions Halloween 2008 25 / 40

Optimal Policy: Numerical Results Above target criterion no longer an exact characterization of optimal policy, in more general case in which ω t and/or Ξ t depend on the evolution of b t Cúrdia and Woodford () Credit Frictions Halloween 2008 26 / 40

Optimal Policy: Numerical Results Above target criterion no longer an exact characterization of optimal policy, in more general case in which ω t and/or Ξ t depend on the evolution of b t But numerical results suggest still a fairly good approximation to optimal policy Cúrdia and Woodford () Credit Frictions Halloween 2008 26 / 40

Calibrated Model Calibration of preference heterogeneity: assume equal probability of two types, π b = π s = 0.5, and δ = 0.975 (average time that type persists = 10 years) Cúrdia and Woodford () Credit Frictions Halloween 2008 27 / 40

Calibrated Model Calibration of preference heterogeneity: assume equal probability of two types, π b = π s = 0.5, and δ = 0.975 (average time that type persists = 10 years) Assume C b /C s = 1.27 in steady state (given G /Y = 0.3, this implies C s /Y 0.62, C b /Y 0.78) implied steady-state debt: b/ȳ = 0.8 years (avg non-fin, non-gov t, non-mortgage debt/gdp) Cúrdia and Woodford () Credit Frictions Halloween 2008 27 / 40

Calibrated Model Calibration of preference heterogeneity: assume equal probability of two types, π b = π s = 0.5, and δ = 0.975 (average time that type persists = 10 years) Assume C b /C s = 1.27 in steady state (given G /Y = 0.3, this implies C s /Y 0.62, C b /Y 0.78) implied steady-state debt: b/ȳ = 0.8 years (avg non-fin, non-gov t, non-mortgage debt/gdp) Assume relative disutility of labor for two types so that in steady state H b /H s = 1 Cúrdia and Woodford () Credit Frictions Halloween 2008 27 / 40

Calibrated Model Assume σ b /σ s = 5 implies credit contracts in response to monetary policy tightening (consistent with VAR evidence [esp. credit to households]) Cúrdia and Woodford () Credit Frictions Halloween 2008 28 / 40

Calibrated Model Calibration of financial frictions: Resource costs Ξ t (b) = Ξ t b η, exogenous markup µ b t Cúrdia and Woodford () Credit Frictions Halloween 2008 29 / 40

Calibrated Model Calibration of financial frictions: Resource costs Ξ t (b) = Ξ t b η, exogenous markup µ b t Zero steady-state markup; resource costs imply steady-state credit spread ω = 2.0 percent per annum (follows Mehra, Piguillem, Prescott) implies λ b / λ s = 1.22 Cúrdia and Woodford () Credit Frictions Halloween 2008 29 / 40

Calibrated Model Calibration of financial frictions: Resource costs Ξ t (b) = Ξ t b η, exogenous markup µ b t Zero steady-state markup; resource costs imply steady-state credit spread ω = 2.0 percent per annum (follows Mehra, Piguillem, Prescott) implies λ b / λ s = 1.22 Calibrate η in convex-technology case so that 1 percent increase in volume of bank credit raises credit spread by 1 percent (ann.) implies η 52 Cúrdia and Woodford () Credit Frictions Halloween 2008 29 / 40

Numerical Results: Alternative Policy Rules Compute responses to shocks under optimal (i.e., Ramsey) policy, compare to responses under 3 simple rules: Cúrdia and Woodford () Credit Frictions Halloween 2008 30 / 40

Numerical Results: Alternative Policy Rules Compute responses to shocks under optimal (i.e., Ramsey) policy, compare to responses under 3 simple rules: simple Taylor rule: î d t = φ π π t + φ y Ŷ t + ɛ m t Cúrdia and Woodford () Credit Frictions Halloween 2008 30 / 40

Numerical Results: Alternative Policy Rules Compute responses to shocks under optimal (i.e., Ramsey) policy, compare to responses under 3 simple rules: simple Taylor rule: î d t = φ π π t + φ y Ŷ t + ɛ m t strict inflation targeting: π t = 0 flexible inflation targeting: π t + (λ y /κ)(x t x t 1 ) = 0 Cúrdia and Woodford () Credit Frictions Halloween 2008 30 / 40

Numerical Results: Optimal Policy Y 0 2 0.2 1 0.4 π 0 0 4 8 12 16 0.6 0 4 8 12 16 0 i d 0 i b 0.2 0.4 0.6 0.2 0.4 0 4 8 12 16 0 4 8 12 16 0.15 0.1 0.05 0 0 4 8 12 16 b Optimal PiStab Taylor FlexTarget Responses to technology shock, under 4 monetary policies Cúrdia and Woodford () Credit Frictions Halloween 2008 31 / 40

Numerical Results: Optimal Policy 0 0.5 1 1.5 0 4 8 12 16 0.4 0.3 0.2 0.1 Y i d 0 0 4 8 12 16 0.4 0.3 0.2 0.1 0 0.3 0.2 0.1 π 0 4 8 12 16 i b 0 0 4 8 12 16 b 0 0.05 Optimal PiStab Taylor FlexTarget 0.1 0 4 8 12 16 Responses to wage markup shock, under 4 monetary policies Cúrdia and Woodford () Credit Frictions Halloween 2008 32 / 40

Numerical Results: Optimal Policy 0.3 0.2 0.1 Y 0 0 4 8 12 16 0.2 0.15 0.1 0.05 i d 0 0 4 8 12 16 0 0.01 0.02 0.03 0 4 8 12 16 0.15 0.1 0.05 0 0 4 8 12 16 π i b b 0 0.02 0.04 Optimal PiStab Taylor FlexTarget 0 4 8 12 16 Responses to shock to government purchases, under 4 monetary policies Cúrdia and Woodford () Credit Frictions Halloween 2008 33 / 40

Numerical Results: Optimal Policy 0.1 Y 0.01 0.005 π 0.05 0 0 4 8 12 16 0 0.005 0.01 0 4 8 12 16 0.1 i d 0.06 i b 0.05 0.04 0.02 0 0.01 0 0.01 0.02 0.03 0 4 8 12 16 0.04 0 4 8 12 16 b 0 0 4 8 12 16 Optimal PiStab Taylor FlexTarget Responses to shock to demand of savers, under 4 monetary policies Cúrdia and Woodford () Credit Frictions Halloween 2008 34 / 40

Numerical Results: Optimal Policy 0.1 0.05 Y 0 0 4 8 12 16 π 0.01 0.005 0 0.005 0.01 0 4 8 12 16 0.04 0.02 0 0.02 0.01 0 i d 0 4 8 12 16 b 0.04 0.02 0 i b 0 4 8 12 16 Optimal PiStab Taylor FlexTarget 0.01 0 4 8 12 16 Responses to shock to demand of borrowers, under 4 monetary policies Cúrdia and Woodford () Credit Frictions Halloween 2008 35 / 40

Numerical Results: Optimal Policy Y 0 0.1 0.2 0.3 0.4 0 4 8 12 16 i d 0 0.2 0.4 0.6 0 4 8 12 16 0 0.02 0.04 0.06 0 4 8 12 16 0.2 0.15 0.1 0.05 0 π i b 0 4 8 12 16 0 0.1 0.2 0.3 b 0 4 8 12 16 Optimal PiStab Taylor FlexTarget Responses to financial shock, under 4 monetary policies Cúrdia and Woodford () Credit Frictions Halloween 2008 36 / 40

Provisional Conclusions Time-varying credit spreads do not require fundamental modification of one s view of monetary transmission mechanism Cúrdia and Woodford () Credit Frictions Halloween 2008 37 / 40

Provisional Conclusions Time-varying credit spreads do not require fundamental modification of one s view of monetary transmission mechanism In a special case: the same 3-equation model continues to apply, simply with additional disturbance terms More generally, a generalization of basic NK model that retains many qualitative features of that model of the transmission mechanism Cúrdia and Woodford () Credit Frictions Halloween 2008 37 / 40

Provisional Conclusions Time-varying credit spreads do not require fundamental modification of one s view of monetary transmission mechanism In a special case: the same 3-equation model continues to apply, simply with additional disturbance terms More generally, a generalization of basic NK model that retains many qualitative features of that model of the transmission mechanism Quantitatively, basic NK model remains a good approximation, esp. if little endogeneity of credit spreads Cúrdia and Woodford () Credit Frictions Halloween 2008 37 / 40

Provisional Conclusions Recognizing importance of credit frictions does not require reconsideration of the de-emphasis of monetary aggregates in NK models Cúrdia and Woodford () Credit Frictions Halloween 2008 38 / 40

Provisional Conclusions Recognizing importance of credit frictions does not require reconsideration of the de-emphasis of monetary aggregates in NK models Here, a model with credit frictions in which no reference to money whatsoever Credit a more important state variable than money Cúrdia and Woodford () Credit Frictions Halloween 2008 38 / 40

Provisional Conclusions Recognizing importance of credit frictions does not require reconsideration of the de-emphasis of monetary aggregates in NK models Here, a model with credit frictions in which no reference to money whatsoever Credit a more important state variable than money However, interest-rate spreads really what matter more than variations in quantity of credit Cúrdia and Woodford () Credit Frictions Halloween 2008 38 / 40

Provisional Conclusions Spread-adjusted Taylor rule can improve upon standard Taylor rule under some circumstances Cúrdia and Woodford () Credit Frictions Halloween 2008 39 / 40

Provisional Conclusions Spread-adjusted Taylor rule can improve upon standard Taylor rule under some circumstances However, full adjustment to spread increase not generally optimal, and optimal degree of adjustment depends on expected persistence of disturbance to spread And desirability of spread adjustment depends on change in deposit rate being passed through to lending rates Cúrdia and Woodford () Credit Frictions Halloween 2008 39 / 40

Provisional Conclusions Spread-adjusted Taylor rule can improve upon standard Taylor rule under some circumstances However, full adjustment to spread increase not generally optimal, and optimal degree of adjustment depends on expected persistence of disturbance to spread And desirability of spread adjustment depends on change in deposit rate being passed through to lending rates General principle can be expressed more robustly in terms of a target criterion Cúrdia and Woodford () Credit Frictions Halloween 2008 39 / 40

Provisional Conclusions Simple guideline for policy: base policy decisions on a target criterion relating inflation to output gap (optimal in absence of credit frictions) Take account of credit frictions only in model used to determine policy action required to fulfill target criterion Cúrdia and Woodford () Credit Frictions Halloween 2008 40 / 40