The Return of the Wage Phillips Curve Jordi Galí CREI, UPF and Barcelona GSE March 2010 Jordi Galí (CREI, UPF and Barcelona GSE) The Return of the Wage Phillips Curve March 2010 1 / 15
Introduction Two shortcomings of the standard New Keynesian model - no financial frictions - no reference to unemployment Recent literature: labor market frictions + nominal rigidities Walsh, Trigari, Blanchard-Galí, Thomas, Gertler-Sala-Trigari,... My approach: reformulation of the standard NK model unemployment Application in the present paper: understanding joint dynamics of wage inflation and unemployment. Jordi Galí (CREI, UPF and Barcelona GSE) The Return of the Wage Phillips Curve March 2010 2 / 15
Outline Reformulation of the wage-setting block of the standard New Keynesian model (Erceg-Henderson-Levin) - indivisible labor - introduction of unemployment (non-frictional) - well defined natural rate of unemployment - structural relation between wage inflation and unemployment New Keynesian Wage Phillips Curve (NKWPC) Empirical assessment: How well can the NKWPC account for observed wage inflation fluctuations? - empirical evidence based on postwar U.S. data - maintained assumption: constant natural rate of unemployment Jordi Galí (CREI, UPF and Barcelona GSE) The Return of the Wage Phillips Curve March 2010 3 / 15
Staggered Wage Setting and Wage Inflation Dynamics Representative household with a continuum of members, indexed by (i, j) [0, 1] [0, 1] Continuum of differentiated labor services, i [0, 1] Indivisible labor. Disutility from work: χ t j ϕ, j [0, 1] Full consumption risk sharing Household utility: E 0 t=0 β t U(C t, {N t (i)}, χ t ) U t (C t, {N t (i)}, χ t ) log C t χ t 1 = log C t χ t 1 0 0 Nt (i) 0 j ϕ djdi N t (i) 1+ϕ 1 + ϕ di and χ t exp{ξ t } is a preference shifter ("labor supply shock") Jordi Galí (CREI, UPF and Barcelona GSE) The Return of the Wage Phillips Curve March 2010 4 / 15
Wage Setting Nominal wage for each labor type reset with probability 1 θ w each period No indexation to price inflation (relaxed later) 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 (1) k=0 (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 c t+k + ϕn t+k t + ξ t+k Wage inflation equation (2) π w t = βe t {π w t+1} λ w (µ w t µ w ) (3) where µ w t (w t p t ) (c t + ϕn t + ξ t ) and λ w (1 θ w )(1 βθ w ) θ w (1+ɛ w ϕ). Jordi Galí (CREI, UPF and Barcelona GSE) The Return of the Wage Phillips Curve March 2010 5 / 15
Introducing Unemployment Participation condition for an individual (i, j): ( ) ( ) 1 Wt (i) χ t j ϕ C t Marginal participant in market for type-i labor, L t (i): P t W t (i) P t = χ t C t L t (i) ϕ Taking logs and integrating over i, w t p t = c t + ϕl t + ξ t where l t 1 0 l t(i) di is the model s implied (log) aggregate participation rate. Jordi Galí (CREI, UPF and Barcelona GSE) The Return of the Wage Phillips Curve March 2010 6 / 15
Introducing Unemployment Unemployment rate u t l t n t Average wage markup and unemployment µ w t = (w t p t ) (c t + ϕn t + ξ t ) = (w t p t ) (c t + ϕl t + ξ t ) + ϕ(l t n t ) = ϕu t Under flexible wages: µ w = ϕu n u n : natural rate of unemployment 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) The Return of the Wage Phillips Curve March 2010 7 / 15
Figure 1. The Wage Markup and the Unemployment Rate Wage wt p t u t Labor supply mrs ) ( t w t Labor demand p ( mpn ) t t n t l t Employment Labor force
Allowing for Wage Indexation Indexation rule w t+k t = w t+k 1 t + γπ p t+k 1 + (1 γ)πp + g Implied wage inflation equation π w t = α + γπ p t 1 + βe t{π w t+1 γπ p t } λ w (µ w t µ w ) Implied New Keynesian Wage Phillips Curve π w t = α + γπ p t 1 + βe t{π w t+1 γπ p t } λ w ϕ(u t u n ) Jordi Galí (CREI, UPF and Barcelona GSE) The Return of the Wage Phillips Curve March 2010 8 / 15
Two Extensions (Galí-Smets-Wouters) Time-varying desired wage markups {µ w t } π w t = α + γπ p t 1 + βe t{π w t+1 γπ p t } λ w ϕu t + λ w µ w t overcomes the identification problem raised by Chari et al. (2009) Preferences with limited short-run wealth effects (Jaimovich-Rebelo) w t p t = z t + ϕl t + ξ t where z t = ϑz t 1 + (1 ϑ)c t unchanged specification of the NKWPC Jordi Galí (CREI, UPF and Barcelona GSE) The Return of the Wage Phillips Curve March 2010 9 / 15
A Reduced Form Representation of the NKWPC Unemployment process Implied NKWPC where λ w ϕ ψ 0 1 β(φ 1 + βφ 2 ) or, equivalently, û t = φ 1 û t 1 + φ 2 û t 2 + ε t π w t = α + γπ p t 1 + ψ 0ût + ψ 1 û t 1 (4) λ w ϕβφ ; ψ 1 2 1 β(φ 1 + βφ 2 ) π w t = α + γπ p t 1 δû t ψ 1 u t (5) where δ (ψ 0 + ψ 1 ) In the data: φ 1 > 1, 1 < φ 2 < 0 ψ 0 < 0, ψ 1 > 0, and δ > 0 Relation to empirical wage inflation equations Jordi Galí (CREI, UPF and Barcelona GSE) The Return of the Wage Phillips Curve March 2010 10 / 15
Data Postwar quarterly U.S. data Civilian unemployment rate Wage inflation: two alternative measures: - earnings ("establishment survey") - compensation ("productivity and costs") CPI inflation: two alternative indexing variables π p t 1 = πp t 1 π p t 1 = (1/4)(πp t 1 + πp t 2 + πp t 3 + πp t 4 ) Jordi Galí (CREI, UPF and Barcelona GSE) The Return of the Wage Phillips Curve March 2010 11 / 15
Figure 1. Two Measures of WageInflation
Empirical Evidence A quick glance at the data Reduced form estimates Estimated AR(2) process for unemployment u t = 0.22 + 1.66 u t 1 0.70 u t 2 + ε t (0.08) (0.08) (0.08) Jordi Galí (CREI, UPF and Barcelona GSE) The Return of the Wage Phillips Curve March 2010 12 / 15
Figure 2. Wage Inflation and Unemployment
Figure 3. Wage Inflation and Unemployment over Time
Figure4 4. Wage Inflation and Unemployment during the Great Moderation
Late 60s Figure 5. The Wage Phillips Curve over Time
Figure 5. The Wage Phillips Curve over Time Early 70s Late 60s
Figure 5. The Wage Phillips Curve over Time Early 70s Late 70s Late 60s
Figure 5. The Wage Phillips Curve over Time Early 70s Late 70s Late 60s Early 80s
Figure 5. The Wage Phillips Curve over Time Early 70s Late 70s Late 60s Great Moderation Early 80s
Fundamental vs. Actual Wage Inflation "Fundamental" wage inflation: π w t (Θ) γπ p t 1 λ w ϕ k=0 β k E {u t+k z t } = γπ p t 1 λ w ϕe 1(I βa) 1 z t where Θ [γ, θ w, β, ɛ w, ϕ] z t = [u t, π w t γπ p t 1,..., u t q, π w t q γπ p t 1 q ] z t = A z t 1 + ε t If the model is "true": π w t (Θ) = π w t Jordi Galí (CREI, UPF and Barcelona GSE) The Return of the Wage Phillips Curve March 2010 13 / 15
Fundamental vs. Actual Wage Inflation Calibration: β = 0.99 ϕ = 1 or 5 ɛ w set to imply u n = 0.05, given ϕ Estimation of θ w and γ, by minimizing T t=0(π w t π w t (Θ)) 2 Jordi Galí (CREI, UPF and Barcelona GSE) The Return of the Wage Phillips Curve March 2010 14 / 15
Figure 6. Actual vs. Fitted Wage Inflation 1964Q1 2007Q4
Figure 7. Actual vs. Fundamental Wage Inflation
Figure 8. Wage Inflation and its Cyclical Component
Concluding remarks Microfounded model of the relation between wage inflation and unemployment = New Keynesian Wage Phillips Curve Good performance in accounting for patterns wage inflation (given unemployment), even under the maintained assumption of a constant natural rate Other applications of the same approach: - accounting for the volatility and persistence of unemployment - unemployment, the output gap and the costs of fluctuations - unemployment and monetary policy design - estimation of a medium-scale DSGE model with unemployment (with Smets and Wouters). Jordi Galí (CREI, UPF and Barcelona GSE) The Return of the Wage Phillips Curve March 2010 15 / 15