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Unemployment in the Smets-Wouters Model:The GSW Model
Jordi Galí
April 2016
Jordi Galí () Unemployment in the Smets-Wouters Model: The GSW Model April 2016 1 / 11
Introduction
Medium-scale New Keynesian DSGE models (SW, CEE)
- good empirical fit- useful for forecasting and policy analysis- basis for in-house models at policy institutions
Shortcoming: no reference to unemployment
GSW: estimation of the "reformulated" Smets-Wouters model usingunemployment data
Issues:
- role of wage markup shocks in fluctuations- new measures of the output gap- sources of unemployment fluctuations
Jordi Galí () Unemployment in the Smets-Wouters Model: The GSW Model April 2016 2 / 11
A Reformulation of the Standard NK Model
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 and heterogeneity in work disutility, indexed by j
Individual utility: E0 ∑∞t=0 βt
(log C̃t (i , j)− 1t (i , j)χtΘt j ϕ
)where
C̃t (i , j) ≡ Ct (i , j)− hC t−1
Θt ≡Zt
C t − hC t−1; Zt = Z 1−υ
t−1 (C t − hC t−1)υ
Remark: υ parametrizes short-term wealth effects. Limiting cases: KPR(υ = 1) and GHH (υ = 0)
Jordi Galí () Unemployment in the Smets-Wouters Model: The GSW Model April 2016 3 / 11
A Reformulation of the Standard NK Model
Risk sharing withing the household: C̃t (i , j) = C̃t
Household utility:
E0∞
∑t=0
βtUt (Ct , {Nt (i)}) ≡ E0∞
∑t=0
βt(log C̃t − χtΘt
∫ 1
0
∫ Nt (i )
0j ϕdjdi
)= E0
∞
∑t=0
βt(log C̃t − χtΘt
∫ 1
0
Nt (i)1+ϕ
1+ ϕdi)
where Nt (i) : employment rate for type-i labor.
Jordi Galí () Unemployment in the Smets-Wouters Model: The GSW Model April 2016 4 / 11
A Reformulation of the Standard NK Model
Marginal rate of substitution for type-i labor:
−Un(i ),tUc ,t
= χtΘt C̃tNt (i)ϕ
= χtZtNt (i)ϕ
Average marginal rate of substitution (in logs)
mrst = zt + ϕnt + ξt
where ξt ≡ log χt .
Average wage markup
µw ,t ≡ (wt − pt )− (zt + ϕnt + ξt )
Jordi Galí () Unemployment in the Smets-Wouters Model: The GSW Model April 2016 5 / 11
Introducing Unemployment
Participation condition for individual (i , j):(1
C̃t
)(Wt (i)Pt
)≥ χtΘt j ϕ
Marginal participant in market for type-i labor, Lt (i):(1
C̃t
)(Wt (i)Pt
)= χtΘtLt (i)ϕ
Evaluating at a symmetric equilibrium (C̃tΘt = Zt), taking logs andintegrating over i ,
wt − pt = zt + ϕlt + ξt
where lt ≡∫ 10 lt (i) di is aggregate participation ("labor force").
Jordi Galí () Unemployment in the Smets-Wouters Model: The GSW Model April 2016 6 / 11
Introducing Unemployment
Unemployment rateut ≡ lt − nt
Average wage markup and unemployment
µw ,t ≡ (wt − pt )− (zt + ϕnt + ξt )
= (wt − pt )− (zt + ϕlt + ξt ) + ϕ(lt − nt )= ϕut
Under flexible wages:µnw ,t = ϕunt
⇒ unt : natural rate of unemployment
Jordi Galí () Unemployment in the Smets-Wouters Model: The GSW Model April 2016 7 / 11
The Identification Problem in Smets-Wouters
Calvo nominal wage setting (no indexation, standard preferences)
πwt = βEt{πwt+1} − λw (µw ,t − µnw ,t )
where µw ,t ≡ (wt − pt )− (ct + ϕnt + ξt )
The basic identification problem:
πwt = βEt{πwt+1} − λw [(wt − pt )− (ct + ϕnt )] + λw (ξt + µnw ,t )
Unemployment-based specification:
πwt = βEt{πwt+1} − λw ϕut + λwµnw ,t
Jordi Galí () Unemployment in the Smets-Wouters Model: The GSW Model April 2016 8 / 11
The Smets-Wouters Model: Remaining Ingredients
Capital accumulation, with investment adjustment costs
Calvo price and wage-setting, with partial indexation
Taylor-type interest rate rule
Multiple shocks:
- neutral and investment-specific technology- risk premium- government spending- monetary policy- price and wage markups- labor supply
Jordi Galí () Unemployment in the Smets-Wouters Model: The GSW Model April 2016 9 / 11
Data
U.S. quarterly data
Sample period: 1966Q1-2007Q4 (estimation baseline)
Observables:
- GDP- consumption- investment- GDP deflator- federal funds rate- employment (vs. hours)- compensation and earnings- unemployment rate
Jordi Galí () Unemployment in the Smets-Wouters Model: The GSW Model April 2016 10 / 11
Galí-Smets-Wouters (2011): Main Findings
Much smaller role for wage markup shocks as a source of outputfluctuations
Jaimovich-Rebelo preferences ⇒ small wealth effects on laborsupply/wage setting
Sources of unemployment fluctuations:
business cycle frequencies: "demand" shocks dominantmedium-term: wage markup shocks dominant
Unemployment during the Great Recession
Jordi Galí () Unemployment in the Smets-Wouters Model: The GSW Model April 2016 11 / 11
Figure 3. Dynamic Responses to Demand Shocks
0 10 20-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6Output
Risk Premium Investment Monetary Policy Exogenous spending
0 10 20
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05Unemployment Rate
0 10 20-0.05
0
0.05
0.1
0.15
0.2
0.25
Employment
0 10 20-0.05
0
0.05
0.1
0.15
0.2
0.25
Labor Force
0 10 20-0.01
0
0.01
0.02
0.03
0.04
0.05
0.06Inflation
0 10 20-0.05
0
0.05
0.1
0.15Real Wage
0 10 20-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6Output Gap
0 10 20-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15Interest Rate
Figure 4. Dynamic Responses to Labor Market Shocks
0 10 20-0.5
-0.4
-0.3
-0.2
-0.1
0Output
Wage Markup Labor Supply
0 10 20-0.2
-0.1
0
0.1
0.2
0.3Unemployment Rate
0 10 20
-0.2
-0.1
0
0.1
0.2Employment
0 10 20
-0.2
-0.1
0
0.1
0.2Labor Force
0 10 200
0.02
0.04
0.06
0.08
0.1
0.12
0.14Inflation
0 10 200
0.05
0.1
0.15
0.2Real Wage
0 10 200
0.02
0.04
0.06
0.08
0.1Interest Rate
0 10 20-0.6
-0.4
-0.2
0
0.2
0.4Output Gap
0 10 200
0.2
0.4
0.6
0.8
1Output
Productivity Price Markup
0 10 20
-0.1
-0.05
0
0.05
0.1
0.15
Unemployment Rate
0 10 20-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
Employment
0 10 20-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
Labor Force
0 10 20-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1Inflation
0 10 200
0.1
0.2
0.3
0.4Real Wage
0 10 20-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2Output Gap
0 10 20-0.15
-0.1
-0.05
0
0.05Interest Rate
Figure 5. Dynamic Responses to Supply Shocks
0 5 10 15 20
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
Unemployment Rate
0 5 10 15 20-0.1
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3Employment
0 5 10 15 20-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2Labor Force
Baseline model KPR-preferences
Figure 6. Monetary Policy Shocks and the Role of Wealth Effects
Figure 7. Two Measures of the Output Gap
1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
-10
-8
-6
-4
-2
0
2
4
6
8
10
Outputgap with UR Outputgap without UR
Figure 8. The Output Gap and the Unemployment Rate
1965 1970 1975 1980 1985 1990 1995 2000 2005 2010-8
-6
-4
-2
0
2
4
6
Outputgap
Unemployment Rate
correlation = -0.95
1965 1970 1975 1980 1985 1990 1995 2000 2005 2010-10
-8
-6
-4
-2
0
2
4
6
hp
bk
qt
cbo
model
Figure 9. The Output Gap vs. Detrended GDP
Figure 10. The Natural Rate of Unemployment
1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
-4
-2
0
2
4
6
8
10
12
observed UR natural UR UR gap
Figure 11. Sources of Unemployment Rate Fluctuations
1965 1970 1975 1980 1985 1990 1995 2000 2005 20102
3
4
5
6
7
8
9
10
11Unemployment Rate decomposition
historical UR
supply shocks
demand shocks
1965 1970 1975 1980 1985 1990 1995 2000 2005 20102
3
4
5
6
7
8
9
10
11
historical UR
labor supply
wage mark-up
Figure 12. Unemployment during the Great Recession
3.5
4.5
5.5
6.5
7.5
8.5
9.5
10.5
11.5
-1.0
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
2007
Q1
2007
Q2
2007
Q3
2007
Q4
2008
Q1
2008
Q2
2008
Q3
2008
Q4
2009
Q1
2009
Q2
2009
Q3
2009
Q4
2010
Q1
2010
Q2
2010
Q3
2010
Q4
productivity risk premium exo.spendinginvestment mon.pol. price markupwage markup labor preference Unemployment (right hand scale)