Monetary Policy and Unemployment: A New Keynesian Perspective Jordi Galí CREI, UPF and Barcelona GSE May 218 Jordi Galí (CREI, UPF and Barcelona GSE) Monetary Policy and Unemployment May 218 1 / 18
Introducing Unemployment in the Standard NK Model Recent literature: labor market frictions + nominal rigidities Walsh, Trigari, Blanchard-Galí, Thomas, Gertler-Sala-Trigari, Faia, Ravenna-Walsh, Christiano-Eichenbaum-Trabandt Alternative approach developed in my Zeuthen lectures [1] - reformulation of the standard NK model ) unemployment Applications: - An empirical model of wage in ation and unemployment dynamics [2] - Unemployment and the measurement of the output gap (ch. 2 in [1]) - Unemployment and the design of monetary policy (ch.3 in [1]) - Revisiting the sources of uctuations in the Smets-Wouters model [3] - A structural interpretation of slow recoveries [4] - European unemployment [5], [6] Jordi Galí (CREI, UPF and Barcelona GSE) Monetary Policy and Unemployment May 218 2 / 18
References [1] Unemployment Fluctuations and Stabilization Policies: A New Keynesian Perspective (211, MIT Press) [2] "The Return of the Wage Phillips Curve" Journal of the European Economic Association, 211. [3] "An Estimated New Keynesian Model with Unemployment," (with F. Smets and R. Wouters), NBER Macroeconomics Annual 211 [4] "Slow Recoveries: A Structural Interpretation," (with F. Smets and R. Wouters), Journal of Money, Credit and Banking, 212. [5] "Hysteresis and the European Unemployment Problem Revisited," Proceedings of the ECB Forum on Central Banking, 215, [6] "Insider-Outsider Labor Markets, Hysteresis, and Monetary Policy," unpublished manuscript. Jordi Galí (CREI, UPF and Barcelona GSE) Monetary Policy and Unemployment May 218 3 / 18
A New Keynesian Model with Unemployment Households Representative household with a continuum of members, indexed by (j, s) 2 [, 1] [, 1] Continuum of di erentiated labor services, indexed by j 2 [, 1] Disutility from (indivisible) labor: χs ϕ, for s 2 [, 1], where ϕ Full consumption risk sharing within the household Household utility: E t= β t U(C t, fn t (j)g; Z t ) U(C t, fn t (j)g; Z t ) where C t = C 1 R 1 C t(i) 1 1 ɛp ɛp 1 ɛp di σ t 1 1 σ C 1 σ t 1 1 σ Z 1 χ χ Z 1 Z Nt (j) N t (j) 1+ϕ 1 + ϕ dj s ϕ dsdj Z t Z t Jordi Galí (CREI, UPF and Barcelona GSE) Monetary Policy and Unemployment May 218 4 / 18
Budget constraint Z 1 Z 1 P t (i)c t (i)di + Q t B t B t 1 + W t (j)n t (j)dj + D t Two optimality conditions where P t Pt (i) ɛp C t (i) = C t P t R 1 1 P t(i) 1 ɛ 1 p di ɛp, implying R 1 P t(i)c t (i)di = P t C t. ( Ct+1 σ Zt+1 Pt Q t = βe t C t Z t P t+1 ) Jordi Galí (CREI, UPF and Barcelona GSE) Monetary Policy and Unemployment May 218 5 / 18
Wage Setting Nominal wage for each labor type reset with probability 1 period Average wage dynamics θ w each Optimal wage setting rule w t = µ w + (1 βθ w ) ɛ w ɛ w w t = θ w w t 1 + (1 θ w )w t k= (βθ w ) k E t mrst+kjt + p t+k where µ w log 1 and mrs t+kjt σc t+k + ϕn t+kjt + ξ Wage in ation equation π w t = βe t fπ w t+1g λ w (µ w t µ w ) where π w t w t w t 1, µ w t w t p t mrs t, mrs t σc t + ϕn t + ξ, and λ w (1 θ w )(1 βθ w ) θ w (1+ɛ w ϕ). Jordi Galí (CREI, UPF and Barcelona GSE) Monetary Policy and Unemployment May 218 6 / 18
Introducing Unemployment Participation condition for an individual (j, s): W t (j) P t χc σ t s ϕ Marginal participant, L t (j), given by: W t (j) P t = χc σ t L t (j) ϕ Taking logs and integrating over i, w t p t = σc t + ϕl t + ξ where w t ' R 1 w t(j)dj and l t R 1 l t(j)dj is the model s implied (log) aggregate labor force. Jordi Galí (CREI, UPF and Barcelona GSE) Monetary Policy and Unemployment May 218 7 / 18
Introducing Unemployment Unemployment rate u t l t n t Average wage markup and unemployment µ w t = (w t p t ) (σc t + ϕn t + ξ) = ϕu t Jordi Galí (CREI, UPF and Barcelona GSE) Monetary Policy and Unemployment May 218 8 / 18
Introducing Unemployment Unemployment rate u t l t n t Average wage markup and unemployment µ w t = (w t p t ) (σc t + ϕn t + ξ) = ϕu t Under exible wages: µ w = ϕu n ) u n : natural rate of unemployment A New Keynesian Wage Phillips Curve π w t = βe t fπ w t+1g λ w ϕ(u t u n ) Jordi Galí (CREI, UPF and Barcelona GSE) Monetary Policy and Unemployment May 218 9 / 18
Figure 7.1 The Wage Markup and the Unemployment Rate Wage Labor demand Labor supply u t wt p t w µ t nt lt Employment Labor force
Firms and Price Setting Continuum of rms, i 2 [, 1], each producing a di erentiated good. Technology Y t (i) = A t N t (i) 1 R ɛw 1 where N t (i) N t(i, j) 1 1 ɛw 1 ɛw di Price of each good reset with a probability 1 Average price dynamics Opimal price setting rule p t = θ p p t 1 + (1 θ p )p t α θ p each period where p t = µ p + (1 βθ p ) k= (βθ p ) k E t fψ t+kjt g ψ t+kjt w t (a t αn t+kjt + log(1 α)) Jordi Galí (CREI, UPF and Barcelona GSE) Monetary Policy and Unemployment May 218 1 / 18
Firms and Price Setting Implied price in ation equation π p t = βe t fπ p t+1 g λ p(µ p t µ p ) where µ p t p t ψ t ψ t w t (a t αn t + log(1 α)) and λ p (1 θ p)(1 βθ p ) θ p 1 α 1 α + αɛ p. Jordi Galí (CREI, UPF and Barcelona GSE) Monetary Policy and Unemployment May 218 11 / 18
Equilibrium Non-Policy block ey t = 1 σ (i t E t fπ p t+1 g r n t ) + E t fey t+1 g π p t = βe t fπ p t+1 g + { pey t + λ p eω t π w t = βe t fπ w t+1g λ w ϕbu t eω t eω t 1 + π w t π p t ω n t ϕbu t = bµ w t = eω t (σec t + ϕen t ) = eω t σ + ϕ 1 α ey t Jordi Galí (CREI, UPF and Barcelona GSE) Monetary Policy and Unemployment May 218 12 / 18
Policy block Example: i t = ρ + φ p π p t + φ y by t + v t Natural equilibrium by n t = ψ ya a t with ψ ya r n t = ρ σ(1 ρ a )ψ ya a t + (1 ρ z )z t bω n t = ψ wa a t 1+ϕ σ(1 α)+ϕ+α and ψ wa 1 αψ ya 1 α >. Exogenous AR(1) processes for fa t g, fz t g, and fv t g Jordi Galí (CREI, UPF and Barcelona GSE) Monetary Policy and Unemployment May 218 13 / 18
Calibration Baseline calibration Description Value Target ϕ Curvature of labor disutility 5 Frisch elasticity.2 α Index of decrasing returns to labor 1/4 ɛ w Elasticity of substitution (labor) 4.52 u n =.5 ɛ p Elasticity of substitution (goods) 9 S = 1 α ɛ p /(ɛ p 1) = 2/3 θ p Calvo index of price rigidities 3/4 avg. duration = 4 θ w Calvo index of wage rigidities 3/4 avg. duration = 4 φ p In ation coe cient in policy rule 1.5 Taylor (1993) φ y Output coe cient in policy rule.125 Taylor (1993) β Discount factor.99 ρ a Persistence: technology shocks.9 ρ z Persistence: demand shocks.5 ρ v Persistence: monetary shocks.5 Jordi Galí (CREI, UPF and Barcelona GSE) Monetary Policy and Unemployment May 218 14 / 18
The E ects of Monetary Policy Shocks on Unemployment - Impulse responses - Volatility, Persistence and Cyclicality Jordi Galí (CREI, UPF and Barcelona GSE) Monetary Policy and Unemployment May 218 15 / 18
Figure 7.2 Response of Labor Market Variables to a Monetary Policy Shock.6.1.5.4 -.1.3 -.2.2 -.3.1 -.4 -.5 -.1 2 4 6 8 1 12 14 16 unemployment rate -.6 2 4 6 8 1 12 14 16 employment.4.2 -.5 -.1 -.2 -.15 -.4 2 4 6 8 1 12 14 16 labor force -.2 2 4 6 8 1 12 14 16 real wage
Source: Galí (215, ch. 7)
The E ects of Monetary Policy Shocks on Unemployment - Impulse responses - Volatility, Persistence and Cyclicality Optimal Monetary Policy Problem min 1 2 E β t σ + ϕ + α ey t 2 + ɛ p (π p t ) 2 + ɛ w (1 α) (π w t ) 2 t= 1 α λ p λ w subject to: π p t = βe t fπ p t+1 g + { pey t + λ p eω t π w t = βe t fπ w t+1g + { w ey t λ w eω t eω t eω t 1 + π w t π p t ω n t Jordi Galí (CREI, UPF and Barcelona GSE) Monetary Policy and Unemployment May 218 16 / 18
Optimality conditions σ + ϕ + α ey t + { p ζ 1 α 1,t + { w ζ 2,t = (1) ɛ p π p t ζ λ 1,t + ζ 3,t = (2) p ɛ w (1 α) λ w π w t ζ 2,t ζ 3,t = (3) λ p ζ 1,t λ w ζ 2,t + ζ 3,t βe t fζ 3,t+1 g = (4) Impulse responses: Optimal policy vs. Taylor rule Jordi Galí (CREI, UPF and Barcelona GSE) Monetary Policy and Unemployment May 218 17 / 18
Figure 7.3 Optimal Policy vs. Taylor Rule: Technology Shocks 1 taylor rule optimal 1.5.5 2 4 6 8 1 12 14 16 output -.5 2 4 6 8 1 12 14 16 unemployment.5.2.1 -.5 -.1-1 2 4 6 8 1 12 14 16 employment -.2 2 4 6 8 1 12 14 16 labor force.4.5.3.2.1 -.5 2 4 6 8 1 12 14 16 real wage -1 2 4 6 8 1 12 14 16 price inflation
Figure 7.4 Optimal Policy vs. Taylor Rule: Demand Shocks 1.5 taylor rule optimal.5 -.5-1 -.5 2 4 6 8 1 12 14 16 output -1.5 2 4 6 8 1 12 14 16 unemployment 1.5.5 1.5 -.5 -.1 -.5 2 4 6 8 1 12 14 16 employment -.15 2 4 6 8 1 12 14 16 labor force.3.6.2.4.1 -.1 2 4 6 8 1 12 14 16 real wage.2 2 4 6 8 1 12 14 16 price inflation
Optimality conditions σ + ϕ + α ey t + { p ζ 1 α 1,t + { w ζ 2,t = (5) ɛ p π p t ζ λ 1,t + ζ 3,t = (6) p ɛ w (1 α) λ w π w t ζ 2,t ζ 3,t = (7) λ p ζ 1,t λ w ζ 2,t + ζ 3,t βe t fζ 3,t+1 g = (8) Impulse responses: Optimal policy vs. Taylor rule A simple rule with unemployment: i t =.1 + 1.5π p t.5bu t (9) Jordi Galí (CREI, UPF and Barcelona GSE) Monetary Policy and Unemployment May 218 18 / 18
Figure 7.5 Optimal Policy vs. Simple Rule: Technology Shocks 1.5 simple taylor optimal 1.5 2 4 6 8 1 12 14 16 output -.5 2 4 6 8 1 12 14 16 unemployment.5.2.1 -.5 -.1-1 2 4 6 8 1 12 14 16 employment -.2 2 4 6 8 1 12 14 16 labor force.4.5.3.2.1 -.5 2 4 6 8 1 12 14 16 real wage -1 2 4 6 8 1 12 14 16 price inflation
Figure 7.6 Optimal Policy vs. Simple Rule: Demand Shocks 1.5 simple taylor optimal.5 -.5-1 -.5 2 4 6 8 1 12 14 16 output -1.5 2 4 6 8 1 12 14 16 unemployment 1.5.5 1.5 -.5 -.1 -.5 2 4 6 8 1 12 14 16 employment -.15 2 4 6 8 1 12 14 16 labor force.3.6.2.4.1.2 -.1 2 4 6 8 1 12 14 16 real wage 2 4 6 8 1 12 14 16 price inflation