Credit Frictions and Optimal Monetary Policy

Transcription

1 Vasco Cúrdia FRB of New York 1 Michael Woodford Columbia University National Bank of Belgium, October 28 1 The views expressed in this paper are those of the author and do not necessarily re ect the position of the Federal Reserve Bank of New York or the Federal Reserve System.

2 Motivation "New Keynesian" monetary models often abstract entirely from nancial intermediation and nancial frictions

3 Motivation "New Keynesian" monetary models often abstract entirely from nancial intermediation and nancial frictions Representative household Complete (frictionless) nancial markets Single interest rate (also the policy rate) relevant for all decisions

4 Motivation "New Keynesian" monetary models often abstract entirely from nancial intermediation and nancial frictions Representative household Complete (frictionless) nancial markets Single interest rate (also the policy rate) relevant for all decisions But in actual economies (even nancially sophisticated)

5 Motivation "New Keynesian" monetary models often abstract entirely from nancial intermediation and nancial frictions Representative household Complete (frictionless) nancial markets Single interest rate (also the policy rate) relevant for all decisions But in actual economies (even nancially sophisticated) di erent interest rates rates do not move perfectly together

6 Spreads change over time Spreads (Sources: FRB, IMF/IFS) Q3:1986 Q1:1987 Q3:1987 Q1:1988 Q3:1988 Q1:1989 Q3:1989 Q1:199 Q3:199 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 Q1:2 Q3:2 Q1:21 Q3:21 Q1:22 Q3:22 Q1:23 Q3:23 Q1:24 Q3:24 Q1:25 Q3:25 Q1:26 Q3:26 Q1:27 Q3:27 Q1:28 Prime Spread to FF C&I Spread to FF

7 Spreads volatility USD LIBOR-OIS Spreads (Source: Bloomberg) basis points /4/5 3/4/5 5/4/5 7/4/5 9/4/5 11/4/5 1/4/6 3/4/6 5/4/6 7/4/6 9/4/6 11/4/6 1/4/7 3/4/7 5/4/7 7/4/7 9/4/7 11/4/7 1/4/8 3/4/8 5/4/8 7/4/8 9/4/8 1M 3M 6M

8 Policy and lending rates LIBOR 1m vs FFR target (source: Bloomberg and Federal Reserve Board) /2/27 2/2/27 3/2/27 4/2/27 5/2/27 6/2/27 7/2/27 8/2/27 9/2/27 1/2/27 11/2/27 12/2/27 1/2/28 2/2/28 3/2/28 4/2/28 5/2/28 6/2/28 7/2/28 8/2/28 9/2/28 1/2/28 % LIBOR 1m FFR target

9 Questions How much is monetary policy analysis changed by recognizing existence of spreads between di erent interest rates? How should policy respond to " nancial shocks" that disrupt nancial intermediation, dramatically widening spreads?

10 Systematic response to spreads? John Taylor (Feb. 28) Proposed "Taylor rule" adjustment: FF rate target lowered by amount of increase in LIBOR-OIS spread

11 Systematic response to spreads? John Taylor (Feb. 28) Proposed "Taylor rule" adjustment: FF rate target lowered by amount of increase in LIBOR-OIS spread Taylor rule would set operating target for LIBOR rate, not the FFR

12 Systematic response to spreads? John Taylor (Feb. 28) Proposed "Taylor rule" adjustment: FF rate target lowered by amount of increase in LIBOR-OIS spread Taylor rule would set operating target for LIBOR rate, not the FFR Would imply automatic adjustement of FFR in response to spread variations

13 Systematic response to spreads? John Taylor (Feb. 28) Proposed "Taylor rule" adjustment: FF rate target lowered by amount of increase in LIBOR-OIS spread Taylor rule would set operating target for LIBOR rate, not the FFR Would imply automatic adjustement of FFR in response to spread variations Current Swiss National Bank policy

14 Systematic response to spreads? SNB Interest rates (source: SNB) /3/27 2/3/27 3/3/27 4/3/27 5/3/27 6/3/27 7/3/27 8/3/27 9/3/27 1/3/27 11/3/27 12/3/27 1/3/28 2/3/28 3/3/28 4/3/28 5/3/28 6/3/28 7/3/28 Repo O/N Index Libor 3m Libor Target Lower Bound Libor Target Upper Bound

15 Systematic response to spreads? John Taylor (Feb. 28) Proposed "Taylor rule" adjustment: FF rate target lowered by amount of increase in LIBOR-OIS spread Taylor rule would set operating target for LIBOR rate, not the FFR Would imply automatic adjustement of FFR in response to spread variations Current Swiss National Bank policy Question: Is a systematic response of that kind desirable?

16 Model: A generalization of the NK model Generalizes basic (representative household) NK model:

17 Model: A generalization of the NK model Generalizes basic (representative household) NK model: heterogeneity in spending opportunities costly nancial intermediation

18 Model: A generalization of the NK model Generalizes basic (representative household) NK model: heterogeneity in spending opportunities costly nancial intermediation Each household has type τ t (i) 2 fb, sg, determining preferences E β u t τ t (i) (c t (i) ; ξ t ) t=1 Z 1 v (h t (j; i) ; ξ t ) dj

19 Model: A generalization of the NK model Generalizes basic (representative household) NK model: heterogeneity in spending opportunities costly nancial intermediation Each household has type τ t (i) 2 fb, sg, determining preferences E β u t τ t (i) (c t (i) ; ξ t ) t=1 Z 1 v (h t (j; i) ; ξ t ) dj each period type remains same with probability δ < 1 when draw new type, always probability π τ of becoming type τ

20 Model: Marginal utilities of two types λ 2 b λ s u b c (c) 1 u s c (c) c c s b

21 Model: Incomplete markets Aggregation simpli ed by assuming intermittent access to an "insurance agency"

22 Model: Incomplete markets Aggregation simpli ed by assuming intermittent access to an "insurance agency" State-contingent contracts enforceable only on those occasions

23 Model: Incomplete markets Aggregation simpli ed by assuming intermittent access to an "insurance agency" State-contingent contracts enforceable only on those occasions Other times: - households borrow or lend only through intermediaries - one-period contracts - riskless nominal rate di erent for savers and borrowers

24 Model: Incomplete markets Aggregation simpli ed by assuming intermittent access to an "insurance agency" State-contingent contracts enforceable only on those occasions Other times: - households borrow or lend only through intermediaries - one-period contracts - riskless nominal rate di erent for savers and borrowers Consequence: long-run marginal utility of income same for all households (regardless of history of spending opportunities)

25 Model: Incomplete markets Aggregation simpli ed by assuming intermittent access to an "insurance agency" State-contingent contracts enforceable only on those occasions Other times: - households borrow or lend only through intermediaries - one-period contracts - riskless nominal rate di erent 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 households of a given type

26 Model: Aggregate demand Euler equation for each type τ 2 fb, sg: 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

27 Model: Aggregate demand Euler equation for each type τ 2 fb, sg: 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 = c τ (λt τ ; ξ t ) + G t + Ξ t τ where Ξ t denotes resources used in intermediation

28 Model: Log-linear IS Intertemporal IS relation: where Ŷ t = E t+1 Ŷ t+1 σ [î avg t π t+1 ] E t g t+1 E t ˆΞ t+1 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 composite exogenous disturbance to expenditure σ π b s b σ b + π s s s σ s > s Ω π b π s s b σ b s s σ s σ

29 Model: Marginal utility gap and spreads Determination of the marginal utility gap: where ˆΩ t = ˆω t + ˆδE t ˆΩ t+1 ˆω t î b t î d t ˆδ < 1

30 Model: Financial intermediation Financial intermediation technology: d t = b t + Ξ t (b t ) where Ξ t (b t ) is positive and convex

31 Model: Financial intermediation Financial intermediation technology: d t = b t + Ξ t (b t ) where Ξ t (b t ) is positive and convex Competitive banking sector would imply equilibrium credit spread ω t (b t ) = Ξ bt (b t )

32 Model: Financial intermediation Financial intermediation technology: d t = b t + Ξ t (b t ) where Ξ t (b t ) is positive and convex Competitive banking sector would imply equilibrium credit spread ω t (b t ) = Ξ bt (b t ) More generally, 1 + ω t (b t ) = µ b t (b t) (1 + Ξ bt (b t )) where µ b t is markup in banking sector

33 Model: Interest rates Monetary policy: CB can e ectively control deposit rate, i d t

34 Model: Interest rates Monetary policy: CB can e ectively control deposit rate, i d t in model is equivalent to policy rate (interbank funding rate)

35 Model: Interest rates Monetary policy: CB can e ectively control deposit rate, i d t in model is equivalent to policy rate (interbank funding rate) Lending rate determined by spread ω t (b t ): î b t = î d t + ˆω t

36 Model: Interest rates Monetary policy: CB can e ectively control deposit rate, i d t in model is equivalent to policy rate (interbank funding rate) Lending rate determined by spread ω t (b t ): î b t = î d t + ˆω t Rate that matters for the IS relation: î avg t = î d t + π b ˆω t

37 Model: Supply side Same as in basic NK model

38 Model: Supply side Same as in basic NK model... but must aggregate labor supply of two types

39 Model: Supply side Same as in basic NK model... but must aggregate labor supply of two types Labor only variable factor of production for each di erentiated good

40 Model: Supply side Same as in basic NK model... but must aggregate labor supply of two types Labor only variable factor of production for each di erentiated good Firms wage-takers in labor market

41 Model: Supply side Same as in basic NK model... but must aggregate labor supply of two types Labor only variable factor of production for each di erentiated good Firms wage-takers in labor market Competitive labor supply

42 Model: Supply side Same as in basic NK model... but must aggregate labor supply of two types Labor only variable factor of production for each di erentiated good Firms wage-takers in labor market Competitive labor supply... except for exogenous wage markup process, µ w t

43 Model: Supply side Same as in basic NK model... but must aggregate labor supply of two types Labor only variable factor of production for each di erentiated good Firms wage-takers in labor market Competitive labor supply... except for exogenous wage markup process, µ w t Dixit-Stiglitz monopolistic competition

44 Model: Supply side Same as in basic NK model... but must aggregate labor supply of two types Labor only variable factor of production for each di erentiated good Firms wage-takers in labor market Competitive labor supply... except for exogenous wage markup process, µ w t Dixit-Stiglitz monopolistic competition Calvo staggering of adjustment of individual prices

45 Model: Supply side Same as in basic NK model... but must aggregate labor supply of two types Labor only variable factor of production for each di erentiated good Firms wage-takers in labor market Competitive labor supply... except for exogenous wage markup process, µ w t Dixit-Stiglitz monopolistic competition Calvo staggering of adjustment of individual prices Only di erence: labor supply depends on both MUI: λ b t and λ s t

46 Model: AS relation Log-linear AS generalizes NK Phillips curve: π t = βe t π t+1 + κ Ŷ t Ŷt n + ut + ξ (s Ω + π b γ b ) ˆΩ t ξ σ 1 ˆΞ t where Ŷ n t, u t, κ, ξ de ned exactly as in basic NK σ is average of elasticity of two types γ b π b λ b / λ 1/ν, with λ an average of MUI of two types

47 What di erence do frictions make? A simple special case: credit spread ω t evolves exogenously intermediation uses no resources (i.e., spread is pure markup)

48 What di erence do frictions make? A simple special case: credit spread ω t evolves exogenously intermediation uses no resources (i.e., spread is pure markup) Then ˆΞ t terms vanish ˆω t exogenous ) ˆΩ t exogenous

49 What di erence do frictions make? A simple special case: credit spread ω t evolves exogenously intermediation uses no resources (i.e., spread is pure markup) Then ˆΞ t terms vanish ˆω t exogenous ) ˆΩ t exogenous Usual 3-equation model su ces to determine paths of Ŷ t, π t, î avg t AS relation IS relation MP relation (written in terms of î avg t, given exogenous spread)

50 What di erence do frictions make? Di erence made by credit frictions: The interest rate in this system is î avg t (not same the policy rate) Additional disturbance terms in each of the 3 equations

51 What di erence do frictions make? Di erence made by credit frictions: The interest rate in this system is î avg t (not same the policy rate) Additional disturbance terms in each of the 3 equations Responses of Ŷ t, π t, î avg t to non- nancial shocks (under a given monetary policy rule, e.g. Taylor rule) identical to those predicted by basic NK model

52 What di erence do frictions make? Di erence made by credit frictions: The interest rate in this system is î avg t (not same the policy rate) Additional disturbance terms in each of the 3 equations Responses of Ŷ t, π t, î avg t to non- nancial shocks (under a given monetary policy rule, e.g. Taylor rule) identical to those predicted by basic NK model no change in conclusions about desirability of a given rule, from standpoint of stabilizing in response to those disturbances

53 What di erence do frictions make? Di erence made by credit frictions: The interest rate in this system is î avg t (not same the policy rate) Additional disturbance terms in each of the 3 equations Responses of Ŷ t, π t, î avg t to non- nancial shocks (under a given monetary policy rule, e.g. Taylor rule) identical to those predicted by basic NK model no change in conclusions about desirability of a given rule, from standpoint of stabilizing in response to those disturbances Responses to nancial shocks equivalent to responses to 3 shocks in simultaneous: monetary policy shock "cost-push" shock shift in natural rate of interest

54 What di erence do frictions make? General case Ξ t and/or ω t depend on volume of lending b t

55 What di erence do frictions make? General case Ξ t and/or ω t depend on volume of lending b t Need to include law of motion for private debt b t

56 What di erence do frictions make? General case Ξ t and/or ω t depend on volume of lending b t Need to include law of motion for private debt b t Resort to numerical solution of calibrated examples see how much di erence the credit frictions make

57 Calibration Preferences heterogeneity: assume equal probability of two types, π b = π s =.5 δ =.975 (average time that type persists = 1 years)

58 Calibration Preferences heterogeneity: assume equal probability of two types, π b = π s =.5 δ =.975 (average time that type persists = 1 years) Assume C b /C s = 3.67 in steady state given s c =.7, this implies s b = 1.1 and s s =.3 implied steady-state debt: b/ȳ.65

59 Calibration Preferences heterogeneity: assume equal probability of two types, π b = π s =.5 δ =.975 (average time that type persists = 1 years) Assume C b /C s = 3.67 in steady state given s c =.7, this implies s b = 1.1 and s s =.3 implied steady-state debt: b/ȳ.65 Assume σ b /σ s = 5 implies credit contracts in response to monetary policy tightening (consistent with VAR evidence)

60 Calibration Financial frictions: Resource costs: Ξ t (b) = Ξ t b η t Exogenous markup: µ b t (no steady state markup: µb = 1)

61 Calibration Financial frictions: Resource costs: Ξ t (b) = Ξ t b η t Exogenous markup: µ b t (no steady state markup: µb = 1) Resource costs imply steady-state credit spread ω = 2. percent per annum (median spread between FRB C&I loan rate and FF rate) λ b / λ s = 1.22

62 Calibration Financial frictions: Resource costs: Ξ t (b) = Ξ t b η t Exogenous markup: µ b t (no steady state markup: µb = 1) Resource costs imply steady-state credit spread ω = 2. percent per annum (median spread between FRB C&I loan rate and FF rate) λ b / λ s = 1.22 Calibrate η 1% increase in credit raises spread by.1% (per annum) (relative VAR responses of credit, spread) requires η = 6.6

63 Numerical results: Taylor rule Monetary policy rule: with φ π = 2 and φ y =.75/4 î d t = φ π π t + φ y Ŷ t + ε m t

64 Numerical results: Taylor rule Monetary policy rule: with φ π = 2 and φ y =.75/4 î d t = φ π π t + φ y Ŷ t + ε m t Compare 3 model speci cations: FF model: model with heterogeneity and credit frictions No FF model: same heterogeneity, but ω t = Ξ t =, 8t RepHH model: representative household w/ intertemporal elasticity σ

65 Numerical results: Taylor rule Y π b i d i b FF NoFF RepHH Responses to monetary policy shock

66 Numerical results: Taylor rule Y π b i d i b FF NoFF RepHH Responses to technology shock

67 Numerical results: Taylor rule Y π b i d i b FF NoFF RepHH Responses to wage markup shock

68 Numerical results: Taylor rule Y π b i d i b FF NoFF RepHH Responses to shock to government purchases

69 Numerical results: Taylor rule Y π b i d i b FF NoFF RepHH Responses to shock to government debt

70 Numerical results: Taylor rule Y π.1.3 b i d i b FF NoFF RepHH Responses to shock to demand of savers

71 Optimal policy Natural objective for stabilization policy: average expected utility E βu Y t, λ b t, λ s t, t ; ξ t t= where U Y t, λ b t, λ s t, t ; ξ t and 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+ν 1 λ ν t 1 + ν Λ t H ν t Yt A t 1+ωy t λ t / Λ t is decreasing function of λ b t /λ s t total disutility of producing is increasing function of MU gap

72 Optimal policy: LQ approximation Compute a quadratic approximation to welfare measure in the case of small uctuations around optimal steady state

73 Optimal policy: LQ approximation Compute a quadratic approximation to welfare measure in the case of small uctuations around 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 = Allow for shocks to the size of credit frictions

74 Optimal policy: LQ approximation Approximate objective for the special case: max expected utility, min quadratic loss function (to 2 nd order)

75 Optimal policy: LQ approximation Approximate objective for the special case: max expected utility, min quadratic loss function (to 2 nd order) t= h β t π 2 t + λ y Ŷ t Ŷt n i 2 + λω ˆΩ 2 t + λ Ξ ˆΞ bt ˆb t λ y > and Ŷ n t same as in basic NK model New weights: λ Ω, λ Ξ >

76 Optimal policy: LQ approximation Approximate objective for the special case: max expected utility, min quadratic loss function (to 2 nd order) t= h β t π 2 t + λ y Ŷ t Ŷt n i 2 + λω ˆΩ 2 t + λ Ξ ˆΞ bt ˆb t λ y > and Ŷ n t same as in basic NK model New weights: λ Ω, λ Ξ > 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

77 Optimal policy: LQ approximation Consider special case: No resources used in intermediation (Ξ t (b) = ) Financial markup µ b t exogenous

78 Optimal policy: LQ approximation Consider special case: Result: No resources used in intermediation (Ξ t (b) = ) Financial markup µ b t exogenous optimal policy characterized by same target criterion as in basic NK model π t + λ y κ (x t x t 1 ) = " exible in ation targeting"

79 Optimal policy: LQ approximation Consider special case: Result: No resources used in intermediation (Ξ t (b) = ) Financial markup µ b t exogenous optimal policy characterized by same target criterion as in basic NK model π t + λ y κ (x t x t 1 ) = " exible in ation targeting" but, state-contingent path of policy rate required to implement target criterion not the same

80 Implementing optimal policy: Interest rate rule Instrument rule to implement the above target criterion: Given lagged variables current exogenous shocks observed current expectations of future in ation and output solve AS and IS relations for target i d t s.t. fπ t, x t g satisfy target relation

81 Implementing optimal policy: Interest rate rule Instrument rule to implement the above target criterion: Given lagged variables current exogenous shocks observed current expectations of future in ation and output solve AS and IS relations for target i d t s.t. fπ t, x t g satisfy target relation What Evans-Honkapohja (23) call "expectations-based" rule for implementation of optimal policy

82 Implementing optimal policy: Interest rate rule Instrument rule to implement the above target criterion: Given lagged variables current exogenous shocks observed current expectations of future in ation and output solve AS and IS relations for target i d t s.t. fπ t, x t g satisfy target relation What Evans-Honkapohja (23) call "expectations-based" rule for implementation of optimal policy Desirable properties: there are no REE other than those in which target criterion holds ) ensures determinacy of REE

83 Implementing optimal policy: Interest rate rule Instrument rule to implement the above target criterion: Given lagged variables current exogenous shocks observed current expectations of future in ation and output solve AS and IS relations for target i d t s.t. fπ t, x t g satisfy target relation What Evans-Honkapohja (23) call "expectations-based" rule for implementation of optimal policy Desirable properties: there are no REE other than those in which target criterion holds ) ensures determinacy of REE in this example, also implies "E-stability" of REE ) convergence of least-squares learning dynamics to REE

84 Implementing optimal policy: Interest rate rule Implementable rule: where î d t = ˆr n t + φ u u t + (1 + βφ u ) E t π t+1 + σ 1 E t x t+1 φ y x t 1 π b + δ 1 s Ω ˆωt + δ φ u ξ s Ω ˆΩ t φ u κ σ 1 λ y + κ 2 φ y λ y σ 1 λ y + κ 2

85 Implementing optimal policy: Interest rate rule Implementable rule: where î d t = ˆr n t + φ u u t + (1 + βφ u ) E t π t+1 + σ 1 E t x t+1 φ y x t 1 π b + δ 1 s Ω ˆωt + δ φ u ξ s Ω ˆΩ t φ u κ σ 1 λ y + κ 2 φ y λ y σ 1 λ y + κ 2 This is a forward-looking Taylor rule, w/ adjustments proportional to the credit spread the marginal-utility gap

86 Implementing optimal policy: Interest rate rule Note that if s b σ b >> s s σ s ) s Ω π s δ 1

87 Implementing optimal policy: Interest rate rule Note that if s b σ b >> s s σ s ) s Ω π s δ 1 then rule becomes approximately î d t =... ˆω t + φ Ω ˆΩ t

88 Implementing optimal policy: Interest rate rule Note that if s b σ b >> s s σ s ) s Ω π s δ 1 then rule becomes approximately î d t =... ˆω t + φ Ω ˆΩ t In calibration φ Ω is also quite small (.4)

89 Implementing optimal policy: Interest rate rule Note that if s b σ b >> s s σ s ) s Ω π s δ 1 then rule becomes approximately î d t =... ˆω t + φ Ω ˆΩ t In calibration φ Ω is also quite small (.4) 1 percent spread adjustment close to optimal

90 Implementing optimal policy: Interest rate rule Note that if s b σ b >> s s σ s ) s Ω π s δ 1 then rule becomes approximately î d t =... ˆω t + φ Ω ˆΩ t In calibration φ Ω is also quite small (.4) 1 percent spread adjustment close to optimal... except in case of very persistent uctuations in credit spread

91 Implementing optimal policy: Interest rate rule Note that if s b σ b >> s s σ s ) s Ω π s δ 1 then rule becomes approximately î d t =... ˆω t + φ Ω ˆΩ t In calibration φ Ω is also quite small (.4) 1 percent spread adjustment close to optimal... except in case of very persistent uctuations in credit spread In this scenario it is really only it b that matters much to economy simple intuition for spread adjustment is reasonably accurate

92 Implementing optimal policy: Interest rate rule For other parameterizations 1 percent spread adjustment not optimal

93 Implementing optimal policy: Interest rate rule For other parameterizations 1 percent spread adjustment not optimal For example if s b σ b = s s σ s, optimal rule is î d t =... π b ˆω t

94 Implementing optimal policy: Interest rate rule For other parameterizations 1 percent spread adjustment not optimal For example if s b σ b = s s σ s, optimal rule is î d t =... π b ˆω t e ectively an instrument rule in terms of î avg t, rather than î d t or î b t

95 Numerical results: Optimal policy General case ω t and/or Ξ t depend on b t

96 Numerical results: Optimal policy General case ω t and/or Ξ t depend on b t target criterion no longer exact characterization of optimal policy

97 Numerical results: Optimal policy General case ω t and/or Ξ t depend on b t target criterion no longer exact characterization of optimal policy Numerical results suggest target criterion still fairly good approximation to optimal policy

98 Numerical results: Optimal policy Y π b i d i b Optimal PiStab Taylor FlexTarget Responses to technology shock

99 Numerical results: Optimal policy Y π b i d i b Optimal PiStab Taylor FlexTarget Responses to wage markup shock

100 Numerical results: Optimal policy Y π b i d.15 i b Optimal PiStab Taylor FlexTarget Responses to shock to government purchases

101 Numerical results: Optimal policy Y π b i d i b Optimal PiStab Taylor FlexTarget Responses to shock to demand of savers

102 Numerical results: Optimal policy Y π b i d.1 i b Optimal PiStab Taylor FlexTarget Responses to nancial shock

103 Spread-adjusted Taylor rule Rule of thumb suggested by various authors: (McCulley and Toloui, 28; Taylor, 28) adjust intercept of Taylor rule in proportion to changes in spreads î d t = φ π π t + φ y Ŷ t φ ω ˆω t

104 Spread-adjusted Taylor rule Rule of thumb suggested by various authors: (McCulley and Toloui, 28; Taylor, 28) adjust intercept of Taylor rule in proportion to changes in spreads î d t = φ π π t + φ y Ŷ t φ ω ˆω t McCulley-Toloui, Taylor suggest 1 percent adjustment, φ ω = 1

105 Spread-adjusted Taylor rule Rule of thumb suggested by various authors: (McCulley and Toloui, 28; Taylor, 28) adjust intercept of Taylor rule in proportion to changes in spreads î d t = φ π π t + φ y Ŷ t φ ω ˆω t McCulley-Toloui, Taylor suggest 1 percent adjustment, φ ω = 1 Equivalent to having a Taylor rule for the borrowing rate, rather than the interbank funding rate

106 Spread-adjusted Taylor rule Rule of thumb suggested by various authors: (McCulley and Toloui, 28; Taylor, 28) adjust intercept of Taylor rule in proportion to changes in spreads î d t = φ π π t + φ y Ŷ t φ ω ˆω t McCulley-Toloui, Taylor suggest 1 percent adjustment, φ ω = 1 Equivalent to having a Taylor rule for the borrowing rate, rather than the interbank funding rate We allow for other possible values of φ ω

107 Numerical results: Spread-adjusted Taylor rule Y π b i d i b Optimal Taylor Taylor+25 Taylor+5 Taylor+75 Taylor Responses to nancial shock

108 Numerical results: Spread-adjusted Taylor rule Y π b i d.1 i b Optimal Taylor Taylor+25 Taylor+5 Taylor+75 Taylor+1 Responses to a shock to government debt

109 Numerical results: Spread-adjusted Taylor rule Y π.1.3 b i d i b Optimal Taylor Taylor+25 Taylor+5 Taylor+75 Taylor+1 Responses to a shock to the demand of savers

110 Numerical results: Spread-adjusted Taylor rule Y π b i d.15 i b Optimal Taylor Taylor+25 Taylor+5 Taylor+75 Taylor Responses to a shock to government purchases

111 Numerical results: Spread-adjusted Taylor rule Y π b i d i b Optimal Taylor Taylor+25 Taylor+5 Taylor+75 Taylor+1 Responses to a shock to the demand of borrowers

112 Numerical results: Spread-adjusted Taylor rule Y π b i d i b Optimal Taylor Taylor+25 Taylor+5 Taylor+75 Taylor+1 Responses to a technology shock

113 Responding to credit It is often suggested that: credit frictions make it desirable for monetary policy to respond to variation in aggregate credit

114 Responding to credit It is often suggested that: credit frictions make it desirable for monetary policy to respond to variation in aggregate credit Christiano et al. (27) suggest modi ed Taylor rule with φ b > î d t = φ π π t + φ y Ŷ t + φ b ˆb t

115 Responding to credit It is often suggested that: credit frictions make it desirable for monetary policy to respond to variation in aggregate credit Christiano et al. (27) suggest modi ed Taylor rule with φ b > î d t = φ π π t + φ y Ŷ t + φ b ˆb t We consider this family of rules, allowing also for φ b <

116 Numerical results: Responding to credit Y π b i d i b Optimal Taylor 5 Taylor 25 Taylor Taylor+25 Taylor Responses to nancial shock

117 Numerical results: Responding to credit Y π b i d i b Optimal Taylor 5 Taylor 25 Taylor Taylor+25 Taylor+5 Responses to a shock to government purchases

118 Numerical results: Responding to credit Y π b i d i b Optimal Taylor 5 Taylor 25 Taylor Taylor+25 Taylor+5 Responses to a technology shock

119 Provisional Conclusions Time-varying credit spreads do not require fundamental modi cation of one s view of monetary transmission mechanism

120 Provisional Conclusions Time-varying credit spreads do not require fundamental modi cation of one s view of monetary transmission mechanism In a special case: same "3-equation model" continues to apply simply with additional disturbance terms

121 Provisional Conclusions Time-varying credit spreads do not require fundamental modi cation of one s view of monetary transmission mechanism In a special case: 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

122 Provisional Conclusions Time-varying credit spreads do not require fundamental modi cation of one s view of monetary transmission mechanism In a special case: 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 especially if little endogeneity of credit spreads

123 Provisional Conclusions Recognizing importance of credit frictions does not require reconsideration of de-emphasis of monetary aggregates in NK models

124 Provisional Conclusions Recognizing importance of credit frictions does not require reconsideration of de-emphasis of monetary aggregates in NK models Here: model w/ credit frictions, no reference to money whatsoever

125 Provisional Conclusions Recognizing importance of credit frictions does not require reconsideration of de-emphasis of monetary aggregates in NK models Here: model w/ credit frictions, no reference to money whatsoever Credit more important state variable than money

126 Provisional Conclusions Recognizing importance of credit frictions does not require reconsideration of de-emphasis of monetary aggregates in NK models Here: model w/ credit frictions, no reference to money whatsoever Credit more important state variable than money However, interest-rate spreads really what matter more than variations in quantity of credit

127 Provisional Conclusions Spread-adjusted Taylor rule can improve upon standard Taylor rule under some circumstances

128 Provisional Conclusions Spread-adjusted Taylor rule can improve upon standard Taylor rule under some circumstances However, optimal degree of adjustment not same for all shocks

129 Provisional Conclusions Spread-adjusted Taylor rule can improve upon standard Taylor rule under some circumstances However, optimal degree of adjustment not same for all shocks Such a rule is inferior to commitment to a target criterion

130 Provisional Conclusions Spread-adjusted Taylor rule can improve upon standard Taylor rule under some circumstances However, optimal degree of adjustment not same for all shocks Such a rule is inferior to commitment to a target criterion Guideline for policy:

131 Provisional Conclusions Spread-adjusted Taylor rule can improve upon standard Taylor rule under some circumstances However, optimal degree of adjustment not same for all shocks Such a rule is inferior to commitment to a target criterion Guideline for policy: base policy decisions on target criterion relating in ation to output gap (optimal in absence of credit frictions)

132 Provisional Conclusions Spread-adjusted Taylor rule can improve upon standard Taylor rule under some circumstances However, optimal degree of adjustment not same for all shocks Such a rule is inferior to commitment to a target criterion Guideline for policy: base policy decisions on target criterion relating in ation to output gap (optimal in absence of credit frictions) Take account of credit frictions only in model used to determine policy action required to ful ll target criterion