TFP Persistence and Monetary Policy Roberto Pancrazi Toulouse School of Economics Marija Vukotić Banque de France NBS, April 27, 2012 NBS, April 27, 2012 1 / 44
Motivation 1 Well Known Facts about the Evolution of Macroeconomic Volatility: Evidence 1: Large reduction in the last 30 years [Great Moderation: Kim and Nelson (1999), Stock and Watson (2003)] 2 Our Findings about the Evolution of Macroeconomic Volatility Evidence 2: Uneven decline of the volatility across frequencies Evidence 3: ncreased persistence NBS, April 27, 2012 2 / 44
Macroeconomic Variables are Trending Real Per Capita Consumption (US) NBS, April 27, 2012 3 / 44
We Need to solate the Trend Real Per Capita Consumption (US) and its Trend NBS, April 27, 2012 4 / 44
Motivation Business Cycle Frequencies (2q-32q) component US real per capita Consumption (red-dashed) and Output (blue-solid): 1950:1-2010:4 NBS, April 27, 2012 5 / 44
Motivation High-Frequencies (2q-16q) components US real per capita Consumption (red-dashed) and Output (blue-solid): 1950:1-2010:4 Band-Pass lters: Christiano and Fitzgerald 2003. NBS, April 27, 2012 6 / 44
Motivation Total Factor Productivity What drives the real variables dynamics? A possible candidate is TFP. Stationary component of U.S. TFP with varying capacity utilization (blue-solid) and constant utilization (red-dashed): 1950:1-2010:4 NBS, April 27, 2012 7 / 44
Normalized Spectrum of the TFP NBS, April 27, 2012 8 / 44
Motivation Equilibrium dynamics of a model: y t = g (x t ; Θ, Φ) x t+1 = h (x t ; Θ, Φ) Θ = structural parameters h i Φ = ϱ Σ laws of motion parameters A change in the autocorrelations structure of an exogenous process has rst-order e ect in the equilibrium: y t ' g Θ, ϱ x t x t+1 ' h Θ, ϱ x t Policy-makers maximize some objective functions to determine their policy, taking into account the equilibrium dynamics. A changed autocorrelation structure modi es the policy functions, thus altering the optimal policy NBS, April 27, 2012 9 / 44
n this paper: 1 Provide evidence of a change in the autocorrelation structure of TFP Split Sample, Rolling Windows, Recursive Regressions, TVP-SV Estimates 2 Analyze the analytical relationship between TFP persistence and monetary policy Classical Monetary Model (provide intuition) New-Keynesian Model (workhorse for monetary economics) Medium Scale DSGE Model (numerical methods) 3 Derive the optimal monetary policy as a function of the TFP persistence NBS, April 27, 2012 10 / 44
Road-map 1 Provide evidence of a change in the autocorrelation structure of TFP Split sample, Rolling Windows, Recursive Regressions, TVP-SV Estimates 2 Analyze the analytical relationship between TFP persistence and monetary policy Classical Monetary Model (provide intuition) New-Keynesian Model (workhorse for monetary economics) Medium Scale DSGE Model (numerical methods) 3 Characterize the optimal monetary policy as a function of the TFP persistence NBS, April 27, 2012 11 / 44
Total Factor Productivity Constructing the data Y t and L t = non-farm business hours and output (BLS). K t = Capital (BLS). U t =capacity utilization manufacturing (FED Board) TFP t = L 1 t Y t α (U t K t ) α Stationary component TFP t follows an autoregressive process: (1 B (L)) TFP t = σ ε ε t ε t iid N (0, 1). NBS, April 27, 2012 12 / 44
Split Sample Statistics Split Sample at the early eighties (GM break) Varying utilization 0.74 [0.06] Constant utilization 0.83 [0.05] Sample 1: 1950:1-1982:4 Sample 2: 1983:1-2009:4 Largest Root Std. Dev. nnovations Largest Root Std. Dev. nnovations AR(1) 0.78 [0.05] 1.03 [0.06] 0.95 [0.04] 0.91 [0.04] 0.61 [0.04] 0.63 [0.04] AR(4) Varying utilization 0.60 0.77 0.84 0.60 Constant utilization 0.63 1.00 0.92 0.59 spectrum NBS, April 27, 2012 13 / 44
Rolling Windows Statistics Assume an AR (1) process for TFP t : compute ˆρ t (blue-solid) and ˆσ ε,t (green-dashed) TFP t TFP t ˆρ t = ˆρ ˆσ j=t k ε,t = ˆσ ε for t = k + 1,..., T j=t k k = 80 NBS, April 27, 2012 14 / 44
Recursive Regression Estimates Assume an AR (1) process for TFP t : compute ˆρ RE t TFP ˆρ RE t t = ˆρ for t = k + 1,..., T k NBS, April 27, 2012 15 / 44
TVP-SV Model Evidence suggests that ˆρ and ˆσ ε are time-varying: TFP t = ρtfp t 1 + σ ε ε t ε t iid N (0, 1) We formally estimate a Time-Varying-Parameter with Stochastic Volatility: TFP t = ρ t TFP t 1 + ε t ε t N 0, σ 2 t ρ t+1 = ρ t + u t u t N 0, σ 2 u σ 2 t = γ exp (h t ) h t+1 = φh t + η t η t N 0, σ 2 η. Use 1 million repetitions with MCMC methods. NBS, April 27, 2012 16 / 44
TVP-SW Model Posterior mean estimate for α t : Posterior mean estimate for σ 2 t : NBS, April 27, 2012 17 / 44
Road-map 1 Provide evidence of a change in the autocorrelation structure of TFP Split sample, Rolling Windows, Recursive Regressions, TVP-SV Estimates 2 Analyze the analytical relationship between TFP persistence and monetary policy Classical Monetary Model (provide intuition) New-Keynesian Model (workhorse for monetary economics) Medium Scale DSGE Model (numerical methods) 3 Derive the optimal monetary policy as a function of the TFP-persistence NBS, April 27, 2012 18 / 44
Classical Monetary Model (Cooley-Hansen 1989) Money is neutral. Example to illustrate in ation dynamics. Perfect competition, exible prices. Agents trade one-period nominally risk-less bonds Monetary authority sets the nominal interest rate: i t = ρ + φ π π t Fisherian equation: i t = E t π t+1 + r t NBS, April 27, 2012 19 / 44
Simple Monetary Model Real interest rate dynamics: Exogenous TFP: Equilibrium in ation dynamics: r t = ρ + σψe t f a t+1 g a t = ρ a a t 1 + σ a ε t ε t iid N (0, 1) π t = φ (k+1) π E t (r t+k ρ), k=0 1 π t = δ a a t δ a = σψ ρ a σ 2 a σ 2 π = δ 2 a (1 ρ 2 a ) φ π ρ a NBS, April 27, 2012 20 / 44
n ation Variance and TFP Persistence n ation variance as a function of TFP persistence and monetary policy parameter: NBS, April 27, 2012 21 / 44
E ectiveness of Monetary Policy and TFP Persistence E ectiveness of Monetary Policy on the instantaneous response of in ation to a technology shock: δ 1 a = σψ ρ a φ 2. π φ π ρ a NBS, April 27, 2012 22 / 44
E ectiveness of Monetary Policy and TFP Persistence Proposition: f we consider a simple monetary model just described, then we can show that the variance of in ation is non-monotone in ρ a and the value of the monetary policy response to in ation φ π that maximizes the variance of in ation in is given by: φ π = 1 + ρ a ρ 2 a NBS, April 27, 2012 23 / 44
Road-map 1 Provide evidence of a change in the autocorrelation structure of TFP Split sample, Rolling Windows, Recursive Regressions, TVP-SV Estimates 2 Analyze the analytical relationship between TFP persistence and monetary policy Classical Monetary Model (provide intuition) New-Keynesian Model (workhorse for monetary economics) Medium Scale DSGE Model (numerical methods) 3 Derive the optimal monetary policy as a function of the TFP-persistence NBS, April 27, 2012 24 / 44
Standard New-Keynesian Model ntroducing features to obtain non-neutrality of money Staggered price setting and imperfect competition Agents trade one-period nominally risk-less bonds Monetary authority sets the nominal interest rate: i t = ρ + φ π π t + φ y ỹ t + v t Exogenous TFP and monetary shocks a t = ρ a a t 1 + σ a ε a t, where ε a t N (0, 1) v t = ρ v v t 1 + σ v ε v t, where ε v t N (0, 1) NBS, April 27, 2012 25 / 44
Equilibrium: rst order approximation Output Gap ỹ t = Λ v φ π, φ y, ρ v, Θ v t + Λ a φ π, φ y, ρ a, Θ (1 βρ Λ v φ π, φ y, ρ v, Θ = v ) (1 βρ v ) σ (1 ρ v ) + φ y + κ (φ π ρ v ) Λ a φ π, φ y, ρ a, Θ = 1 β ρ a σ ψσ 1 ρ a 1 β ρ a 1 ρ a + φ y + κ φ π ρ a a t NBS, April 27, 2012 26 / 44
Equilibrium: rst order approximation n ation Λ π v Λ π a π t = Λv π φ π, φ y, ρ v, Θ v t + Λa π φ π, φ y, ρ a, Θ a t κ φ π, φ y, ρ v, Θ = (1 βρ v ) σ (1 ρ v ) + φ y + κ (φ π ρ v ) ψσ 1 ρ a κ φ π, φ y, ρ a, Θ = 1 β ρ a σ 1 ρ a + φ y + κ φ π ρ a NBS, April 27, 2012 27 / 44
Standard Calibration: Discount factor:β = 0.99 nverse of intertemporal elast. of substitution: σ = 1 Labor share in the production function: 1 α = 2 3 Elasticity of subs among di erentiated goods: ε = 6 Price stickiness parameter: θ = 2 3 nverse of the Frish elast. of labor supply: ϕ = 1 Monetary response to output gap: φ y = 0.125 NBS, April 27, 2012 28 / 44
Equilibrium: Response of Output Gap to a Technology Shock Monotone relationship between TFP persistence and output gap response to technology (Λ a ) NBS, April 27, 2012 29 / 44
Equilibrium: Variance of Output Gap NBS, April 27, 2012 30 / 44
ntuition: r n t = ρ + σψe t f a t+1 g = ρ + σψ (1 ρ a ) a t When ρ a! 1, then r n t constant, as well as r t. The output gap in this model results from the current and anticipated deviations of the real interest rate from its natural level: Marginal cost: ỹ t = 1 σ (r t+k rt+k n ) k=0 fmc t ỹ t n ation results from the price-setting decisions by rms that adjust their price considering present and current cost conditions: π t = λ k=0 β k E t f fmc t+k g NBS, April 27, 2012 31 / 44
Equilibrium: Response of n ation to a technology shock Non-Monotone relationship between TFP persistence and in ation response to technology (Λ π a ) NBS, April 27, 2012 32 / 44
Equilibrium: Variance of n ation NBS, April 27, 2012 33 / 44
Proposition: Assume that ρ a 2 ( 1, 1), β < 1, φ y > 0, θ < 1, α < 1, σ > 0, ε > 0, ζ > 0, and φ π > 1. Then and Λ a φ π, φ y, ρ a, Θ > 0 φ π Λ a φ π, φ y, ρ a, Θ > 0 ρ a for any structural parameter vector Θ.Moreover, there exists a value φ π π that maximizes instantaneous response Λa π φ π, φ y, ρ a, Θ. This value is: φ π π = κ + βσ (1 ρ a )2 (1 β) φ y κ for any structural parameter vector Θ NBS, April 27, 2012 34 / 44
Road-map 1 Provide evidence of a change in the autocorrelation structure of TFP Split sample, Rolling Windows, Recursive Regressions, TVP-SV Estimates 2 Analyze the analytical relationship between TFP persistence and monetary policy Classical Monetary Model (provide intuition) New-Keynesian Model (workhorse for monetary economics) Medium Scale DSGE Model (numerical methods) 3 Derive the optimal monetary policy as a function of the TFP-persistence NBS, April 27, 2012 35 / 44
DSGE Model More features are considered (add capital, real rigidities - habit persistence, investment adjustment cost, variable capacity utilization) Smets and Wouters (2007) Nonlinear relationship among technology persistence, monetary policy response to in ation and variances of output gap and in ation NBS, April 27, 2012 36 / 44
DSGE Model Variance of Output Gap and n ation NBS, April 27, 2012 37 / 44
Road-map 1 Provide evidence of a change in the autocorrelation structure of TFP Split sample, Rolling Windows, Recursive Regressions, TVP-SV Estimates 2 Analyze the analytical relationship between TFP persistence and monetary policy Classical Monetary Model (provide intuition) New-Keynesian Model (workhorse for monetary economics) Medium Scale DSGE Model (numerical methods) 3 Derive the optimal monetary policy as a function of the TFP-persistence NBS, April 27, 2012 38 / 44
Welfare Average Welfare Loss: Rotemberg and Woodford (1999) Second order approximation to the consumer utility loss due to deviations from e cient allocation: AWL = 1 2 σ + ϕ + α var (ỹ t ) + ε 1 α λ var (π t). Calibrated parameters: σ a = 0.45%, σ v = 0.24%, ρ v = 0.15. The ratio of variance of v t shock and α t shock is kept constant at 3% as estimated by Smets and Wouters (2007) solate the e ect of the increasing persistence by keeping constant the unconditional variance of a t when varying ρ a NBS, April 27, 2012 39 / 44
Welfare Average Welfare Loss No Trade-o : respond to in ation arbitrarily strong (devine coincidence) nteresting dynamics driven by ρ a NBS, April 27, 2012 40 / 44
Welfare NBS, April 27, 2012 41 / 44
Optimal Monetary Policy with Trade-o Without cost-push shocks, the monetary authority does not face trade o between stabilizing output variance and in ation variance and it is optimal to respond to in ation as strongly as possible Add cost-push shocks and then characterize optimal Taylor rule under commitment (φ π, φ y ) by minimizing expected welfare loss: E (WL) = E ( (1 β) t=0 β t h π 2 t + λ y (ỹ t y ) 2 + λ i (i t i ) 2i) Optimal φ π and φ y depend on the persistence of productivity: optimal response is to increase both φ π and φ y as a response to higher persistence of TFP NBS, April 27, 2012 42 / 44
Optimal Monetary Policy Parameters as a Function of the Persistence of Technology Higher TFP response calls for a higher response of monetary policy, implying a lower ability of monetary policy to smooth the volatility of macroeconomic variables NBS, April 27, 2012 43 / 44
Conclusions Statistical evidences for increasing TFP persistence Analyze the relationship between TFP persistence and monetary policy in the equilibrium dynamics of monetary models Study the e ects of increased TFP persistence on the optimal monetary policy nvestigation of the productivity in the di erent sectors of the economy [Ongoing Research] NBS, April 27, 2012 44 / 44