The Risky Steady State and the Interest Rate Lower Bound

Transcription

1 The Risky Steady State and the Interest Rate Lower Bound Timothy Hills Taisuke Nakata Sebastian Schmidt New York University Federal Reserve Board European Central Bank 1 September The views expressed in this presentation are not necessarily those of the Federal Reserve Board of Governors, the Federal Reserve System, or European Central Bank.

2 Question What are the implications of the effective lower bound (ELB) risk after liftoff? The federal funds rate is currently above the ELB. In the 2016 July Survey of Primary Dealers, a median respondent sees 25 percent chance that the federal funds rate will return to the ELB in

3 Background One implication of the ELB risk: Deflationary bias The possibility of returning to the ELB leads price-setters to lower prices via expectations. Adam and Billi (2007) and Nakov (2008) made this observation in stylized models. Is the deflationary bias quantitatively important in empirically realistic models?

4 What We Do We characterize the risky steady state in an empirically rich sticky-price model with an occasionally binding ELB constraint. The risky steady state is a point where the economy eventually converges to when all exogenous shocks dissipate (Coeurdacier, Rey, and Winant (2011)). By comparing the deterministic and risky steady states, we quantify the effects of the ELB risk on allocations and prices at the steady state. The model is calibrated to match key features of the U.S. economy.

5 Main Results Inflation and the policy rate are nontrivially lower at the risky steady state than at the deterministic steady state Inflation falls below the target rate of inflation in the policy rule at the risky steady state. i.e. the central bank systematically undershoots its inflation objective. The ELB risk reduces inflation by about basis points below the target rate.

6 The undershooting result Figure: The Effect of the ELB Risk on Projections 4 Policy Rate (Annualized %) 2.5 Inflation (Annualized %) Quarter Quarter 3 Output Gap (%) 0 3 With ELB risk Without ELB risk Quarter

7 Why We Care (I) The risky steady state inflation = private sector s long-run inflation expectations. U.S. policymakers project that inflation will eventually return to the target rate of 2 percent (Summary of Economic Projections). This projection is based on the assumption that long-run inflation expectations are anchored at 2 percent (Yellen (2016), various FOMC Minutes). Long-run inflation expectations are unobserved and this assumption could turn out to be wrong.

8 Why We Care (II) Many measures of long-run inflation expectations have declined last few years and are currently at the low ends of their historical ranges (Michigan Survey, SPF, expectations inferred from financial markets). Our model endogenously generates long-run inflation expectations that are below 2 percent. Our analysis thus provides a cautionary tale for policymakers.

9 ELB Literature Many papers assume an absorbing state or perfect-foresight (no ELB risk by construction). Most papers examine the implications of the ELB constraint for the economy when the ELB is binding. Adam and Billi (2007) and Nakov (2008) have commented on the implications of the ELB constraint when the ELB is not binding, but only in stylized models. Our paper examines the implications of the ELB constraint for the economy when the ELB is not binding in an empirically serious model.

10 Outline of the Talk Stylized Model Empirical Model

11 A Stylized Model A standard New Keynesian model: Discrete Time, Infinite Horizon. Discount factor shocks: {δ t } t=1. δ t 1 = ρ(δ t 1 1) + ɛ t, ɛ t N(0, σ 2 ɛ). A representative household. A final good producer. A continuum of intermediate-good producers, indexed by i [0, 1]. subject to quadratic price-adjustment costs. The government.

12 An Equilibrium Given any P 0 and a stochastic process for {δ t } t=1, an equilibrium can be characterized by {C t, N t, Y t, w t, Π t, R t } t=1 {d t} t=1 satisfying where Π t C χc t w t = Nt χn Y t Ct χc = βδ t R t E t C χc t+1 Π 1 t+1 (1) C χc t [ ϕ( Π t Π 1)Π t Π (1 θ) θw t Y t+1 = βδ t E t ϕ( Π t+1 C χc t+1 Π 1)Π t+1 Π (3) Y t = C t + ϕ [Π t 2 Π 1] 2 Yt (4) Y t = N t R t = max Pt P t 1 [ 1, 1 β ( Πt Π and w t = Wt P t. ) φπ ] ] (2) (5) (6)

13 The Risky Steady State Generically Defined Γ t : a vector of endogenous variables in the model under investigation. X t : a vector of exogenous variables. Let X SS denote the steady state of X t. f (, ): a vector of policy functions mapping (i) endogenous variables in the previous period and (ii) today s realizations of exogenous variables into (iii) endogenous variables today. The risky steady state, Γ RSS, is a fixed point of the economy: Γ RSS = f (Γ RSS, X SS )

14 Table: Parameterization for the Stylized Model Parameter Description Value 1 β Discount rate χ c Inverse intertemporal elasticity of substitution for C t 1.0 χ n Inverse labor supply elasticity 1 θ Elasticity of substitution among intermediate goods 11 ϕ Price adjustment cost ( Π 1) (Annualized) target rate of inflation 2.0 φ π Coefficient on inflation in the Taylor rule 1.5 φ y Coefficient on the output gap in the Taylor rule 0 ρ AR(1) coefficient for the discount factor shock σ ɛ The standard deviation of shocks to the discount factor 100 *The implied prob. that the policy rate is at the lower bound 10% *The implied deterministic steady-state policy rate is 3.75 percent.

15 Annualized % Nominal Interest Rate Annualized % Inflation % Deviation from the Det. Steady State Output δ δ δ 1 Real Wage 3 Exp. Real Rate Annualized % Annualized % With uncertainty Without uncertainty Deterministic St.St. Risky St.St δ δ

16 Mechanism π t = κw t + βe t π t+1 π t = κ k=0 βk E t w t+k The distribution of real wage (w t+1 ) when δ t = and 400(R t 1) = Median: 1.15 Mean:

17 Table: The Risky Steady State in the Stylized Model Inflation Output gap Policy rate Deterministic steady state Risky steady state (Wedge) ( 0.29) (0.03) ( 0.43) Risky steady state w/o the ELB (Wedge) ( 0.01) ( 0.02) ( 0.03)

18 Outline of the Talk Stylized Model Empirical Model

19 Our empirical model adds four features common in the DSGE literature to the stylized model: Consumption Habits Sticky Wages Interest-Rate Smoothing Non-stationary TFP

20 Table: Parameter Values for the Empirical Model Parameter Description Parameter Value β Discount rate a Trend growth rate of productivity 400 χ c Inverse intertemporal elasticity of substitution for C t 1.0 ζ Degree of consumption habits 0.5 χ n Inverse labor supply elasticity 0.5 θ p Elasticity of substitution among intermediate goods 11 θ w Elasticity of substitution among intermediate labor 4 ϕ p Price adjustment cost 1000* ϕ w Wage adjustment cost 300* Interest-rate feedback rule 400( Π 1) (Annualized) target rate of inflation 2.0 ρ R Interest-rate smoothing parameter in the Taylor rule 0.8 φ π Coefficient for inflation in the Taylor rule 3 φ y Coefficient for the output gap in the Taylor rule (R ELB 1) (Annualized) effective lower bound 0.13 Shock ρ d AR(1) coefficient for the discount factor shock σ ɛ,d The standard deviation of shocks to the discount factor 100 *The corresponding Calvo parameters are 0.85 and 0.85.

21 Table: Key Moments Moment Variable Model St.Dev.( ) E[X R t = R ELB ] ELB Data (1995Q3 2015Q2) Output gap Inflation Policy rate Output gap Inflation Policy rate Frequency 13.8% 32.5% Expected/Actual Duration 8.6 quarters 26 quarters

22 Table: The Risky Steady State in the Empirical Model Inflation Output gap Policy rate Deterministic steady state Risky steady state (Wedge) ( 0.26) (0.30) ( 0.49) Risky steady state w/o the ELB (Wedge) ( 0.08) (0.05) ( 0.19)

23 Long-Run Interest Rates Substantial uncertainty regarding the level of long-run equilibrium interest rates (Hamilton et al. (2015)). We vary the deterministic steady-state policy rate by varying the trend productivity growth parameter. Motivated by the recent attention given to uncertainty regarding the long-run growth (Fernald (2014) and Gordon (2014)).

24 26 Probability of being at the ELB 2 RSS Inflation With ELB Constraint Without ELB Constraint DSS Policy Rate DSS Policy Rate 0.7 RSS Output Gap 4.5 RSS Policy Rate DSS Policy Rate DSS Policy Rate DSS stands for Deterministic Steady State and RSS stands for Risky Steady State

25 Other Sensitivity Analyses Parameters in the policy rule. Adding other shocks (MP and TFP shocks). Price and wage indexation.

26 Summary The ELB constraint can adversely affect the economy even after liftoff via expectations. The ELB risk reduces the steady state inflation by basis points.

27 Thoughts In linear models, the following three objects coincide: The inflation-target parameter in the policy rule. RSS inflation. Unconditional average of inflation. As a result, modelers can simply assign the central bank s inflation objective to the inflation-target parameter in the policy rule and no complication arises. In stochastic nonlinear models, they do not. It becomes important for modelers to understand the differences between the three objects and how they relate to the central bank s inflation objective. The Risk-Adjusted Monetary Policy Rule (Nakata and Schmidt (2016)) for more details.

28 Extra slides

29 Households max {C t,n t,b t} t=1 subject to E 1 β t 1[ t 1 t=1 s=0 ][ C 1 χ c t δ s ] N1+χn t 1 χ c 1 + χ n P t C t + Rt 1 B t W t N t + B t 1 + P t Φ t where B 0 = 0 and δ 1 is given. βδ t is the relative weight the agent puts on the future utility flows at time t: βδ 0 U(C 1, N 1, G 1 ) + β 2 δ 0 δ 1 U(C 2, N 2, G 2 ) + β 3 δ 0 δ 1 δ 2 U(C 3, N 3, G 3 ) +...

30 Firms A final-good firm aggregates intermediate goods by CES technology. Intermediate-good firms: max {P i,t } t=1 subject to E 1 β t 1[ t 1 t=1 s=0 δ s ] λ t [ ϕ P i,t Y i,t W t N i,t P t 2 [ P i,t ΠP i,t 1 1 ] 2 Yt ] Y i,t = [ P i,t P t ] θyt & Y i,t = N i,t P i,0 = P 0 for some given constant P 0 > 0

31 Government s Policy The supply of the government bond is zero. The nominal interest rate is set according to a truncated Taylor rule. R t = max [ 1, 1 β ( Πt Π ) φπ ]

32 Risk-Adjusted Fisher Relation Standard Fisher Relation: R DSS = Π DSS β

33 Risk-Adjusted Fisher Relation Standard Fisher Relation: R DSS = Π DSS β Risk-Adjusted Fisher Relation: R RSS = Π RSS β 1 [ ( ) χc C E RSS ΠRSS ] RSS C t+1 Π t+1 where E RSS [ ] := E[ δ t = 1]

34 Risk-Adjusted Fisher Relation Standard Fisher Relation: R DSS = Π DSS β Risk-Adjusted Fisher Relation: R RSS = Π RSS β 1 [ ( ) χc C E RSS ΠRSS ] RSS C t+1 Π t+1 where E RSS [ ] := E[ δ t = 1] and 1 [ ( ) χc C E RSS ΠRSS ] < 1, RSS C t+1 Π t+1 if the distributions of C and Π are negatively skewed.

35 Risk-Adjusted Fisher Relation R t DSS Standard Fisher Relation RSS Risk Adjusted Fisher Relation Taylor Rule 1 Π t

36 5 Output Gap (%) 3 Inflation (Annualized %) Policy Rate (Annualized %) Year Year Year The output gap measure is from FRB/US model. Inflation rate is computed as the annualized quarterly percentage change (log difference) in core PCE price index. The annualized federal funds rate is used as the measure for the policy rate.

37 Policy Implications Can the central bank do something to mitigate the deflationary bias? Recall that the policy rule is given by where R t = max [R ELB, R t ] Rt R ( R ) ρr ( = t 1 Π p ) (1 ρr )φπ t R Π p ) (1 ρr )φ y (Ỹt Ȳ

38 Policy Implications (I) 2 RSS Inflation (Left Axis) ZLB Frequency (Right Axis) RSS Inflation Prob[R t =R ELB ] Inflation Coefficient (φ π )

39 Policy Implications (II) 2 RSS Inflation ZLB Frequency RSS Inflation Prob[R t =R ELB ] Output Gap Coefficient (φ y ) 0

40 Policy Implications (III) 2 RSS Inflation ZLB Frequency RSS Inflation Prob[R t =R ELB ] Interest Rate Smoothing Parameter (ρ r )

41 Policy Implications (IV) 3 RSS Inflation ZLB Frequency RSS Inflation 2 10 Prob[R t =R ELB ] Inflation Target ( Π p )

42 Policy Implications (V) 2 RSS Inflation ZLB Frequency RSS Inflation Prob[R t =R ELB ] Effective Lower Bound (R ELB )

43 Related Literature Risky Steady State: Coeurdacier et al. (2011), Devereux and Sutherland (2011), and de Groot (2013). These papers study, and develop computational techniques to solve, differentiable economies. We analyze a non-differentiable economy.