The Vanishing Procyclicality of Labor Productivity
and the Great Moderation
Jordi Galí
Thijs van Rens
CREI and UPF
September 2008
Jordi Galí, Thijs van Rens (CREI and UPF)
Vanishing Procyclicality
September 2008
1 / 16
Motivation
Changes in U.S. labor market dynamics: Three observations
The procyclicality of labor productivity has vanished
Jordi Galí, Thijs van Rens (CREI and UPF)
Vanishing Procyclicality
September 2008
2 / 16
Motivation
Changes in U.S. labor market dynamics: Three observations
The procyclicality of labor productivity has vanished
The relative volatility of (measured) labor input has increased
Jordi Galí, Thijs van Rens (CREI and UPF)
Vanishing Procyclicality
September 2008
2 / 16
Motivation
Changes in U.S. labor market dynamics: Three observations
The procyclicality of labor productivity has vanished
The relative volatility of (measured) labor input has increased
The volatility of the real wage has increased
Jordi Galí, Thijs van Rens (CREI and UPF)
Vanishing Procyclicality
September 2008
2 / 16
Motivation
Changes in U.S. labor market dynamics: Three observations
The procyclicality of labor productivity has vanished
The relative volatility of (measured) labor input has increased
The volatility of the real wage has increased
Our goals:
To document the previous three observations
Jordi Galí, Thijs van Rens (CREI and UPF)
Vanishing Procyclicality
September 2008
3 / 16
Motivation
Changes in U.S. labor market dynamics: Three observations
The procyclicality of labor productivity has vanished
The relative volatility of (measured) labor input has increased
The volatility of the real wage has increased
Our goals:
To document the previous three observations
To assess the hypothesis of a possible common source: A decline in labor
market frictions
Jordi Galí, Thijs van Rens (CREI and UPF)
Vanishing Procyclicality
September 2008
3 / 16
Motivation
Changes in U.S. labor market dynamics: Three observations
The procyclicality of labor productivity has vanished
The relative volatility of (measured) labor input has increased
The volatility of the real wage has increased
Our goals:
To document the previous three observations
To assess the hypothesis of a possible common source: A decline in labor
market frictions
To understand their connection (if any) to the Great Moderation
Jordi Galí, Thijs van Rens (CREI and UPF)
Vanishing Procyclicality
September 2008
3 / 16
The Potential Role of Declining Labor Market Frictions:
Some Intuition
Assume two margins of adjustment of e¤ective labor input: (observed)
employment/hours vs. (unobserved) e¤ort
yt = (1
yt
Jordi Galí, Thijs van Rens (CREI and UPF)
nt =
α) (nt + θ et ) + at
α nt + (1
Vanishing Procyclicality
α ) θ et + a t
September 2008
4 / 16
The Potential Role of Declining Labor Market Frictions:
Some Intuition
Assume two margins of adjustment of e¤ective labor input: (observed)
employment/hours vs. (unobserved) e¤ort
yt = (1
yt
nt =
α) (nt + θ et ) + at
α nt + (1
α ) θ et + a t
E¤ects of labor market frictions (large costs of adjusting nt ):
) smaller ‡uctuations in employment, larger ‡uctuations in e¤ort
) low volatility of employment relative to output
) procyclical labor productivity conditional on non-technology shocks
) room for wage rigidity =) more volatility in response to technology
shocks
Jordi Galí, Thijs van Rens (CREI and UPF)
Vanishing Procyclicality
September 2008
5 / 16
Observation #1: The Procyclicality of Labor Productivity has Vanished
See also: Barnichon (2007), Stiroh (2008), Galí-Gambetti (2008)
Time-Varying Response of Labor Productivity
to Non-Technology Shocks
Source: Galí and Gambetti (2008)
Observation #2 : The Relative Volatility of (Measured) Labor Input has Risen
See also: Hall (2007), Galí-Gambetti (2009)
Observation #3: The Volatility of the Real Wage has Risen
A Stylized Model of Economic Fluctuations with Labor
Market Frictions
Households
Preferences
∞
E0
∑ βt
U (Ct , Nt , fEit g, Zt )
t =0
where
U (Ct , Nt , fEit g)
Zt log Ct
Constraints
Ct =
Z Nt
0
Nt = ( 1
0
where Ut
1
(1
δ ) Nt
Jordi Galí, Thijs van Rens (CREI and UPF)
Z Nt
0
1+ ϕ
E
b + it
1+ϕ
!
di
Wit di + Πt
δ ) Nt
1
Nt
1
+ xt Ut
1.
Vanishing Procyclicality
September 2008
6 / 16
Firms
Objective
∞
max E0
∑ Q0,t
(Yjt
Wjt Njt
Gt Hjt )
t =0
where Q0,t = Q0,1 Q1,2 ...Qt
1,t
β CCt +t 1 ZZt +t 1 .
and Qt,t +1
Cost per hire Gt taken as given.
Constraints:
Yjt = At
Njt = (1
Jordi Galí, Thijs van Rens (CREI and UPF)
Z N jt
0
1 α
Ejitθ di
δ) Nj ,t
1
Vanishing Procyclicality
+ Hjt
September 2008
7 / 16
Labor Market Frictions
Cost per hire:
Gt = ΓAt xt
η
where
xt
Jordi Galí, Thijs van Rens (CREI and UPF)
Ht
2 [0, 1]
Ut
Vanishing Procyclicality
September 2008
8 / 16
The Firm-Worker Relationship
Once employed, individual e¤ort chosen e¢ ciently:
Ct
ϕ
Ejit = (1
Zt
α)θ
Yjt
E
Njt Ejtθ jit
(1 θ )
Symmetric equilibrium:
1+ ϕ
Ejt
= (1
Yjt = At
α)θ
Yjt Zt
Njt Ct
1 α
Njt Ejtθ
implying:
Ejt =
Jordi Galí, Thijs van Rens (CREI and UPF)
(1
α)θ At Njt
α
Zt
Ct
Vanishing Procyclicality
1
1 θ (1 α)+ ϕ
September 2008
9 / 16
Marginal Product of Labor :
dYjt
dNjt
where 1
Θ = (1
α) 1
∂Yjt
∂Yjt ∂Ejt
+
∂Njt
∂Ejt ∂Njt
Yjt
= (1 Θ )
Njt
=
αθ
1 θ (1 α)+ ϕ
Optimal hiring policy:
Gt = (1
Θ)
Yjt
Njt
Wjt + (1
δ) Et fQt,t +1 Gt +1 g
Firm surplus from marginal worker employed: StF = Gt
Jordi Galí, Thijs van Rens (CREI and UPF)
Vanishing Procyclicality
September 2008
10 / 16
Household surplus from marginal worker employed:
VtN
= Wt
Ct
b
Zt
+Et fQt,t +1
(1 α)θ Yt
1 + ϕ Nt
[(1 δ(1 xt +1 )) VtN+1 + δ(1
VtU = Et fQt,t +1 [(1
Letting StH
VtN
StH = Wt
Ct
b
Zt
xt +1 ) VtU+1 ]g
xt +1 ) VtN+1 + xt +1 VtU+1 ]g
VtU ,
(1 α)θ Yt
+ (1
1 + ϕ Nt
Jordi Galí, Thijs van Rens (CREI and UPF)
δ) Et fQt,t +1 (1
Vanishing Procyclicality
xt +1 ) StH+1 g
September 2008
11 / 16
Bargaining Set
Wt 2 [WtL , WtU ]
where
WtL =
Ct
(1 α)θ Yt
b+
Zt
1 + ϕ Nt
Θ)
WtU = (1
(1
δ) Et fQt,t +1 (1
Yt
+ (1
Nt
xt +1 ) StH+1 g
δ) Et fQt,t +1 Gt +1 g
Nash Bargaining
ξ StH = (1
ξ ) StF
Nash Wage
Wt = ξ WtL + (1
ξ ) WtU
Wt = ξ W L + ( 1
ξ) W U
Rigid Wage
Size of bargaining set:
∆t = WtU
Jordi Galí, Thijs van Rens (CREI and UPF)
WtL =
Vanishing Procyclicality
1
Gt
ξ
September 2008
12 / 16
The Bargaining Set and the Rigid Wage
0.75
0.7
0.65
0.6
0.55
0.5
0.45
0.4
0
10
20
30
40
50
60
70
80
90
100
The Frictionless Case (Γ = 0 =) Gt = 0, all t)
Φ)
(1
Yt
Ct
=
b
Nt
Zt
Yt = Ct
implying
Nt =
1+ ϕ
Et
= (1
α)θ
Φ
1
b
Zt
Yt Zt
(1 α)θb
=
Nt Ct
1 Φ
In logs:
nt = zt
yt = (1
wt = yt
Jordi Galí, Thijs van Rens (CREI and UPF)
α) zt + at
nt =
α zt + at
Vanishing Procyclicality
September 2008
13 / 16
Implications:
cov (yt
nt , yt ) =
cov (yt
α (1
nt , nt ) =
α) var (zt ) + var (at )
α var (zt )
var (yt ) = (1
α)2 var (zt ) + var (at )
var (nt )
=
var (yt )
(1
var (zt )
α)2 var (zt ) + var (at )
var (wt )
α2 var (zt ) + var (at )
=
var (yt )
(1 α)2 var (zt ) + var (at )
Question: How do frictions a¤ect the above statistics?
Jordi Galí, Thijs van Rens (CREI and UPF)
Vanishing Procyclicality
September 2008
14 / 16
Calibration
Preferences: β = 0.99
;
ϕ=1
Technology: α = 1/3
Frictions: η = 2
SS.
;
Γ so that hiring costs equal 0.1% of output in
Bargaining: ξ = 0.5
(δ, b ) to match x = 0.7 and u = 5.5% in SS
Wage rigidity:
γ=1
Driving forces:
at = ρa at 1 + εat
zt = ρz zt
1
+ εzt
where ρa = ρz = 0.9 and (σa , σz ) chosen to match σ(n) and σ(y ) in the
post-84 period using the frictionless model.
Simulations
Jordi Galí, Thijs van Rens (CREI and UPF)
Vanishing Procyclicality
September 2008
15 / 16
To Do List
Analysis of the role of di¤erent parameters, more careful calibration
Endogenize degree of wage rigidity
Additional shocks
Nominal rigidities, changes in monetary policy rule
More direct evidence on declining frictions...
Jordi Galí, Thijs van Rens (CREI and UPF)
Vanishing Procyclicality
September 2008
16 / 16
The Rising Share of Temp Workers
Source: Estevao and Lach (1999)
Source: Estevao and Lach (1999)
Decline in unionization rates
Source: Farber and Western (2002)
Changes in “effective” unionization: NLRB elections
Source: Farber and Western (2001)