Monetary Policy and Unemployment: A New Keynesian Perspective Jordi Galí CREI, UPF and Barcelona GSE April 215 Jordi Galí (CREI, UPF and Barcelona GSE) Monetary Policy and Unemployment April 215 1 / 16
Introducing unemployment in the Standard NK model New approach developed in my Zeuthen lectures [1] - reformulation of the standard NK model unemployment Alternative to recent literature: labor market frictions + nominal rigidities Walsh, Trigari, Blanchard-Galí, Thomas, Gertler-Sala-Trigari, Faia, Ravenna-Walsh,... Applications: - An empirical model of wage inflation 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 fluctuations in the Smets-Wouters model [3] - A structural interpretation of slow recoveries [4] Jordi Galí (CREI, UPF and Barcelona GSE) Monetary Policy and Unemployment April 215 2 / 16
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. Jordi Galí (CREI, UPF and Barcelona GSE) Monetary Policy and Unemployment April 215 3 / 16
A Model of Unemployment and Inflation Fluctuations Households Representative household with a continuum of members, indexed by (j, s) [, 1] [, 1] Continuum of differentiated labor services, indexed by j [, 1] Disutility from (indivisible) labor: χs ϕ, for s [, 1], where ϕ Full consumption risk sharing within the household Household utility: E t= β t U(C t, {N t (j)}; Z t ) U(C t, {N t (j)}; Z t ) where C t = ( ) 1 C t(i) 1 ɛp 1 ɛp ɛp 1 di ( C 1 σ t 1 1 σ 1 χ ( C 1 σ t 1 χ 1 σ 1 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 April 215 4 / 16
Budget constraint 1 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 ( ) 1 1 P t(i) 1 ɛ p di 1 ɛp, implying 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 April 215 5 / 16
Wage Setting Nominal wage for each labor type reset with probability 1 θ w each period Average wage dynamics Optimal wage setting rule w t = µ w + (1 βθ w ) w t = θ w w t 1 + (1 θ w )w t k= (βθ w ) k E t { mrst+k t + p t+k } where µ w log ɛ w ɛ w 1 and mrs t+k t σc t+k + ϕn t+k t + ξ Wage inflation equation π w t = βe t {π w t+1} 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, 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 April 215 6 / 16
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 1 w t(j)dj and l t 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 April 215 7 / 16
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 flexible wages: µ w = ϕu n u n : natural rate of unemployment The nature of unemployment and its fluctuations A New Keynesian Wage Phillips Curve π w t = βe t {π w t+1} λ w ϕ(u t u n ) Jordi Galí (CREI, UPF and Barcelona GSE) Monetary Policy and Unemployment April 215 8 / 16
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 firms, i [, 1], each producing a differentiated good. Technology Y t (i) = A t N t (i) 1 α ( ) 1 where N t (i) N t(i, j) 1 ɛw 1 ɛw ɛw 1 di The price of each good reset with a probability 1 θ p each period Average price dynamics Opimal price setting rule p t = θ p p t 1 + (1 θ p )p t p t = µ p + (1 βθ p ) k= (βθ p ) k E t {ψ t+k t } Jordi Galí (CREI, UPF and Barcelona GSE) Monetary Policy and Unemployment April 215 9 / 16
Firms and Price Setting Implied price inflation equation π p t = βe t {π p t+1 } λ p(µ p t µp ) 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 April 215 1 / 16
Equilibrium Non-Policy block ỹ t = 1 σ (i t E t {π p t+1 } r n t ) + E t {ỹ t+1 } π p t = βe t {π p t+1 } + κ pỹ t + λ p ω t π w t = βe t {π w t+1} λ w ϕû t ω t ω t 1 + π w t π p t ω n t ϕû t = µ w t = ω t (σ c t + ϕñ t ) ( = ω t σ + ϕ 1 α ) ỹ t Jordi Galí (CREI, UPF and Barcelona GSE) Monetary Policy and Unemployment April 215 11 / 16
Policy block Example: i t = ρ + φ p π p t + φ y ŷ t + v t Natural equilibrium ŷ n t = ψ ya a t r n t = ρ σ(1 ρ a )ψ ya a t + (1 ρ z )z t with ψ ya ω 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 {a t }, {z t }, and {v t } Jordi Galí (CREI, UPF and Barcelona GSE) Monetary Policy and Unemployment April 215 12 / 16
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 Inflation coeffi cient in policy rule 1.5 Taylor (1993) φ y Output coeffi 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 April 215 13 / 16
Dynamic Effects of Monetary Policy Shocks on Labor Markets - Impulse responses - Wage rigidities and the volatility and persistence of unemployment Jordi Galí (CREI, UPF and Barcelona GSE) Monetary Policy and Unemployment April 215 14 / 16
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)
Optimal Monetary Policy Problem min 1 2 E (( β t σ + ϕ + α ) ỹt 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 {π p t+1 } + κ pỹ t + λ p ω t π w t = βe t {π w t+1} + κ w ỹ t λ w ω t ω t ω t 1 + π w t π p t ω n t Jordi Galí (CREI, UPF and Barcelona GSE) Monetary Policy and Unemployment April 215 15 / 16
Optimality conditions ( σ + ϕ + α ) ỹ t + κ p ζ 1 α 1,t + κ 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 {ζ 3,t+1 } = (4) Impulse responses: Optimal vs. Taylor A simple rule with unemployment (vs. optimal policy) i t =.1 + 1.5π p t.5û t (5) Jordi Galí (CREI, UPF and Barcelona GSE) Monetary Policy and Unemployment April 215 16 / 16
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
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