Introduction
The Model
Steady State
Aggregate Shocks
Employment
Conclusion
The Employment and Output Effects of
Short-Time Work in Germany
Russell Cooper1
1 Penn.
State
2 The
Moritz Meyer
World Bank
2
Immo Schott
3 Université
AFiD-Nutzerkonferenz
March 30th, 2017
de Montréal
3
Appendix
Introduction
The Model
Steady State
Aggregate Shocks
Employment
Conclusion
Motivation
2008 recession in Germany entailed:
Large negative effect on GDP & total hours worked
Small effect on unemployment
Stark contrast with other OECD economies
‘German Labor Market Miracle’
One Leading Explanation: Short-Time Work (STW)
Our question:
Can STW save jobs?
And if yes, at what cost?
Appendix
Introduction
The Model
Steady State
Aggregate Shocks
Employment
Conclusion
−10
GDP growth
−5
0
5
GDP Growth (year-to-year)
1995q1
2000q1
2005q1
Time
DEU
OECD
ESP
Micro Data
Hours Change
2010q1
USA
AUT
FRA
2015q1
Appendix
Introduction
The Model
Steady State
Aggregate Shocks
Employment
Conclusion
50
100
2005q1 = 100
150
200
250
Unemployment Rate
1995q1
2000q1
2005q1
Time
DEU
OECD
ESP
Micro Data
2010q1
USA
AUT
FRA
2015q1
Appendix
Introduction
The Model
Steady State
Aggregate Shocks
Employment
Conclusion
Appendix
What is Short-Time Work (STW)?
Labor market policy instrument
Goal: Mitigating cyclical shocks
Change labor demand via intensive margin (hours vs. workers)
UI compensates workers for lost income (60-67%)
Absent STW, unilateral reductions in hours worked are illegal
Use of STW is subject to strict set of legal requirements Details
The ‘STW policy’: 2009 - 2010
Gov’t dramatically reduced eligibility criteria & burden of proof
Maximum duration increased from six to 18, and then 24
months
June 2009: Around 60,000 establishments and 1,500,000
workers Graph
Introduction
The Model
Steady State
Aggregate Shocks
Employment
Summary of Results
Can STW save jobs?
Economic press, Government, Unions
→ We find a positive effect on employment
What are the costs?
Reduced form vs. structural model
‘Reallocation channel’
→ STW prevents reallocation of labor
→ adverse effect on GDP
Conclusion
Appendix
Introduction
The Model
Steady State
Aggregate Shocks
Employment
Conclusion
Appendix
Literature
Work Sharing: Burdett & Wright (1989), Hunt (1998,
1999), Marimon & Zilibotti (2000), Kudoh & Sasaki (2011)
German Labor Market: Krause & Uhlig (2011), Burda &
Hunt (2011), Cahuc & Carcillo (2011), Balleer et al. (2016)
Factor allocation: Hsieh & Klenow (2007), Bartelsman et. al
(2013)
Multi-worker firms: Cooper, Haltiwanger, & Willis (2007),
Elsby & Michaels (2013), Stole & Zwiebel (1996)
Introduction
The Model
Steady State
Aggregate Shocks
Employment
Conclusion
Data
Afid-Panel Indusriebetriebe from German Statistical Office
Universe of manufacturing plants, annual panel 1995-2010
Up to 68,000 observations, use ≈ 39,000
Variables: Revenue, Employment, Hours Worked, . . .
Advantages
Sumstats
June 2009: 80.4% (41%) of workers (firms) using STW were
located in manufacturing
Heavy concentrating of employment in Mittelstand
No sampling bias
Disadvantages
No direct information on STW
Appendix
Introduction
The Model
Steady State
Aggregate Shocks
Employment
Conclusion
Appendix
Employment
Hours per Employee
2010
2009
2008
2007
2006
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
−.1
−.05
0
.05
Changes in Total Hours: Extensive and Intensive Margins
Introduction
The Model
Steady State
Aggregate Shocks
Employment
Conclusion
0
5
Frequency
10
15
Distribution of changes in annual hours per worker:
1995-2008
Appendix
x>.3
.2>x>.3
.1>x>.2
.05<x<.1
.025<x<.05
.01<x<.025
inactive
−.025<x<−.01
−.05<x<−.025
−.1<x<−.05
−.2<x<−.1%
−.3<x<.2
<−.3
Introduction
The Model
Steady State
Aggregate Shocks
Employment
Conclusion
0
5
Frequency
10
15
20
Distribution of changes in annual hours per worker:
1995-2009
x>.3
.2>x>.3
2009
.1>x>.2
.05<x<.1
.025<x<.05
.01<x<.025
inactive
−.025<x<−.01
−.05<x<−.025
−.1<x<−.05
−.2<x<−.1%
−.3<x<.2
<−.3
1995−2008
Appendix
Introduction
The Model
Steady State
Aggregate Shocks
Employment
Conclusion
0
5
Frequency
10
15
20
Distribution of changes in annual hours per worker:
1995-2010
x>.3
.2>x>.3
2009
.1>x>.2
.05<x<.1
.025<x<.05
.01<x<.025
inactive
−.025<x<−.01
−.05<x<−.025
−.1<x<−.05
−.2<x<−.1%
−.3<x<.2
<−.3
1995−2008
2010
Appendix
Introduction
The Model
Steady State
Aggregate Shocks
Model - Overview
Basic Model
Hours Contraints & STW
Aggregate Shocks
Quantitative Results: Counterfactuals
Employment
Conclusion
Appendix
Introduction
The Model
Steady State
Aggregate Shocks
Employment
Model - Ingredients
Workers and multi-worker Firms
Firms face idiosyncratic productivity shocks ε
Decreasing returns to scale in production
Total labor input L = h · n
Frictional labor market produces rents
Nash-Bargaining
Matching Function M = m(U, V ), CRS
Labor Market Tightness θ = VU
Vacancy-filling probability q = M
V
Distribution of firms over (ε, n)
Conclusion
Appendix
Introduction
The Model
Steady State
Aggregate Shocks
Employment
Conclusion
Model - Timing
Firm enters period with n−1 workers and productivity ε
Choose n workers and average hours h
Negotiate wage with n workers
Produce output
Appendix
Introduction
The Model
Steady State
Aggregate Shocks
Employment
Conclusion
Model - Firm’s Problem
V (ε, n−1 ) = max εF (h · n) − ω(h, n, ε) · h · n −
h,n
Z
cv
(n − n−1 )1+ + β V (ε0 , n)dG (ε0 |ε) ,
q
ω(·) is a wage schedule
cv is a linear vacancy creation cost
1+ is an indicator for when a firm is hiring
q is the vacancy filling rate, determined in equilibrium
Appendix
Introduction
The Model
Steady State
Aggregate Shocks
Employment
Model - Firm’s Problem
FOC Hours
εFL (h · n) − ω(h, n, ε) − ωh (h, n, ε) · h = 0
Conclusion
Appendix
Introduction
The Model
Steady State
Aggregate Shocks
Employment
Conclusion
Appendix
Model - Firm’s Problem
FOC Hours
εFL (h · n) − ω(h, n, ε) − ωh (h, n, ε) · h = 0
FOC Employment (if ∆n 6= 0)
εhFL (h·n)−ω(h, n, ε)·h−ωn (h, n, ε)·nh−
where D(ε, n) ≡
R
Vn (ε0 , n)dG (ε0 |ε)
cv +
1 +βD(ε, n) = 0,
q
Introduction
The Model
Steady State
Aggregate Shocks
Employment
Conclusion
Appendix
Model - Worker’s Problem
W e (ε, n) = ω(h, ε, n)·h −ξ(h)+βEε0 |ε sW u + (1 − s)W e (ε0 , n0 ) .
W u = b + βE(ε0 ,n0 ) (1 − φ)W u + φW e (ε0 , n0 ) .
value of employment conditional on the state of a firm: used
for negotiation
s endogenous separation rate
Introduction
The Model
Steady State
Aggregate Shocks
Employment
Conclusion
Appendix
Model - Wages
Workers and Firm share surplus of match
Decreasing return to scale → surplus changes for each worker
Nash bargaining over marginal surplus (Stole & Zwiebel
(1996))
Firm’s marginal surplus for matching with a worker:
S(ε, n) = εhFL (h · n) − ω(h, n, ε)h − ωn (h, n, ε)hn + βD(ε, n)
Surplus is shared according to
W e (ε, n) − W u =
η
S(ε, n).
1−η
Introduction
The Model
Steady State
Aggregate Shocks
Employment
Conclusion
Appendix
Model - Wages
Appendix B: Wage solves differential equation
ω(h, ε, n) · h = (1 − η) [b + ξ(h)] +
cv
η εhFL (h · n) + φ − ωn (h, n, ε) · h · n
q
Assume F (L) = Lα = (n · h)α
εαhα nα−1
cv
ω(h, ε, n) · h = (1 − η) [b + ξ(h)] + η
+φ
1 − η(1 − α)
q
Alternative Interpretation of Bargain:
Negotiated at t = 0
Covers many workers/firm pairs
Introduction
The Model
Steady State
Aggregate Shocks
Employment
Conclusion
Model - Optimal Labor Demand
Combine wage with FOCs to get H(ε, n) and N (ε, n−1 ).
The optimal hours choice:
1
1−α
εαnα−1
H(ε, n) = 0
ξ (h) (1 − η(1 − α))
The optimal employment choice:

−1

ψv (ε) if ε > ψv (n−1 ),
N (ε, n−1 ) = n−1
if ε ∈ [ψ(n−1 ), ψv (n−1 )] ,

 −1
ψ (ε) if ε < ψ(n−1 ),
Graph
Appendix
Introduction
The Model
Steady State
Aggregate Shocks
Employment
Conclusion
Introducing Hours Constraint and STW
Standard hours = h. Generally, firm cannot set h < h
STW
Ξ ∈ [0, h]
Constraint changes to h − Ξ
Workers compensated for income loss
STW use has to be approved by gov’t
The optimal hours policy function becomes
H(ε, n) = max h − Ξ,
εαnα−1
0
ξ (h) (1 − η(1 − α))
extensive margin
impacts firm demand for workers
equilibrium effect on vacancy filing rate
NO effects on wage function
1 1−α
.
Appendix
Introduction
The Model
Steady State
Aggregate Shocks
Employment
Conclusion
Appendix
Model - Calibration (Ξ = 0)
Parameter
Meaning
Value
Reason
β
γ
µ
α
ε̄
b
ξ0
η
Discount factor
Matching elasticity
Matching efficiency
F (L) = Lα
Mean of ε
Unemployment benefit
Disutility of work (scale)
Worker bargaining power
.9967
.6
.1622
.65
1
.024
.124
.413
Annual r = 4%
Petrongolo & Pissarides (2001)
θ = 0.091
Cooper et al. (2007)
Normalization
Average employment = 98.5
Average hours = 1
Labor share 0.76
Table: Calibrated Parameters
Introduction
The Model
Steady State
Aggregate Shocks
Employment
Model - Estimation (Ξ = 0)
Moment
δ
= φ+δ
∆h < |5%| (annual)
∆n < |5%| (annual)
cv (n)/cv (h)
Distance L(Θ)
L−N
L
Data
.09
.538
.476
5.63
-
Model
.09
.542
.440
5.66
0.001382
Table: Moments for Estimation
Conclusion
Appendix
Introduction
The Model
Steady State
Aggregate Shocks
Employment
Parameter
Meaning
Value
ξ1
cv
ρε
σε
Disutility of work
Vacancy cost
Persistence of ε
Std. dev. of ε
4.42
.065
.983
.037
Table: Estimated Parameters
Conclusion
Appendix
Introduction
The Model
Steady State
Aggregate Shocks
Employment
Conclusion
Steady state results - no policy
Match inactivity regions of
Hours
and
Employment
changes
Match the relative variability of hours and employment
Value of leisure = 13.24% of average wages
Firms spend on average 1.07% of monthly wage bill on
recruiting costs
Labor market tightness θ = VU = 0.091
Monthly job-finding rate of 6.22%
US ≈ 30% (Hall (2006))
Appendix
Introduction
The Model
Steady State
Aggregate Shocks
Employment
Steady state results - Hourly wage
0.17
Wage
0.165
0.16
0.155
0.15
0.145
80
100
120
1.5
1.4
Employment
1.3
1.2
1.1
1
Hours
Wage is decreasing in n and h
Effect via marginal product of labor & disutility
More productive firms are large
Positive relationship between size and wages
Conclusion
Appendix
Introduction
The Model
Steady State
Aggregate Shocks
Employment
Conclusion
Steady state results - The Hours Constraint h = 1
Empirical CDF of Hours
1
0.9
0.8
0.7
F(x)
0.6
0.5
0.4
0.3
0.2
0.1
no STW
STW
0
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
Average Hours
Constraint can be binding in steady state
h prevents hours reductions, firms use extensive margin
Appendix
Introduction
The Model
Steady State
Aggregate Shocks
Employment
Conclusion
Appendix
Aggregate Shocks
Ahigh
Ahigh
Π=
Alow
AΞ

Alow
ρ
1−ρ
 1−ρ
ρ
1−ρ ρ−π
AΞ

0
0 
π
Average duration of STW is six months: π
Solve similarly to Krusell & Smith (1998)
Firms need to forecast q 0 which depends on the cross-sectional
distribution
summarized by inclusion of lagged q
Introduction
The Model
Steady State
Aggregate Shocks
Employment
Effect of STW
Simulation of economy
Let STW policy become active in period t = 200
no negative productivity shocks
Conclusion
Appendix
Introduction
The Model
Steady State
Aggregate Shocks
Employment
Conclusion
IRF - Effect of STW
Aggregate Productivity
2
Output
1.01
1.5
1
1
0.99
0.5
0.98
0
50
100
150
200
250
300
350
Employment
50
100
150
200
250
300
350
300
350
300
350
Total Hours Worked
1.01
1.06
1.04
1
1.02
0.99
1
0.98
0.98
0.97
0.96
50
100
150
200
250
300
350
50
Average Hours
100
150
200
250
Vacancy-filling probability
0.68
1
0.66
0.98
0.64
0.96
0.62
50
100
150
200
250
300
350
Hourly Wages
50
100
150
200
250
Fraction of Firms using STW
0.5
1.015
0.4
1.01
1.005
0.3
1
0.2
0.1
0.995
0.99
0
50
100
150
200
250
300
350
50
100
150
200
250
300
350
Appendix
Introduction
The Model
Steady State
Aggregate Shocks
Employment
Effect of STW
Simulation of economy
Let STW policy become active in period t = 200
no negative productivity shocks
Partial Equilibrium: Keep q fixed
Conclusion
Appendix
Introduction
The Model
Steady State
Aggregate Shocks
Employment
Conclusion
IRF - Effect of STW - PE
Aggregate Productivity
2
Output
1.01
1.005
1.5
1
0.995
1
0.99
GE
PE
0.5
0.985
0.98
0
50
100
150
200
250
300
350
Employment
50
100
150
200
250
300
350
300
350
300
350
300
350
Total Hours Worked
1.01
1.1
1
1.05
0.99
0.98
1
0.97
0.95
50
100
150
200
250
300
350
Average Hours
50
100
150
200
250
Vacancy-filling probability
0.69
1
0.68
0.67
0.98
0.66
0.65
0.96
0.64
0.94
0.63
50
100
150
200
250
300
350
Hourly Wages
50
100
150
200
250
Fraction of Firms using STW
0.6
0.5
1.01
0.4
1.005
0.3
1
0.2
0.995
0.1
0.99
0
50
100
150
200
250
300
350
50
100
150
200
250
Appendix
Introduction
The Model
Steady State
Aggregate Shocks
Employment
Conclusion
Appendix
Effect of STW
STW increases employment but has a negative effect on
output.
Key: endogeneity of q
Positive employment response more than twice as large in PE
Output falls by almost 1%
Heterogeneous effect on firms
Introduction
The Model
Steady State
Aggregate Shocks
Employment
Conclusion
IRF - Recession without STW
1.01
Aggregate Productivity
Output
1
0.99
1
0.98
0.99
0.97
5
1.1
10
15
20
25
Unemployment Rate
1.05
5
1
10
15
20
25
Total Labor Input L
0.99
1
0.98
5
10
15
20
25
Average Hours
1
5
10
0.995
15
20
25
20
25
q
1.03
1.02
0.99
1.01
0.985
1
5
10
15
20
25
Hourly Wages
1
5
10
15
Fraction of Firms using STW
1
no STW
0.999
0.5
0.998
0
0.997
5
10
15
20
25
5
10
15
20
25
Appendix
Introduction
The Model
Steady State
Aggregate Shocks
Employment
Conclusion
IRF - Recession with STW
1.01
Aggregate Productivity
Output
1
1
0.98
0.99
0.96
5
1.1
10
15
20
25
Unemployment Rate
5
1
10
15
20
25
Total Labor Input L
0.98
1.05
0.96
1
0.94
5
10
15
20
25
Average Hours
1
5
10
0.98
15
20
25
20
25
q
1.03
1.02
0.96
1.01
0.94
1
5
10
15
20
25
Hourly Wages
1.005
5
0.6
10
15
Fraction of Firms using STW
no STW
STW
0.4
1
0.2
0.995
0
5
10
15
20
25
5
10
15
20
25
Appendix
Introduction
The Model
Steady State
Aggregate Shocks
Employment
Productivity Effects
Correlation of Employment and Productivity
1.014
no STW
STW
1.012
1.01
1.008
1.006
1.004
1.002
1
0.998
0.996
5
10
15
20
25
30
Conclusion
Appendix
Introduction
The Model
Steady State
Aggregate Shocks
Employment
Employment Effects for firms with ∆ε < 0
Average Employment Change
-7.8
-8
-8.2
-8.4
-8.6
-8.8
-9
-9.2
-9.4
5
10
15
20
25
Average Hours
1.02
1
0.98
0.96
0.94
0.92
no STW
STW
0.9
0.88
5
10
15
20
25
Conclusion
Appendix
Introduction
The Model
Steady State
Aggregate Shocks
Average Hours in Firms with ∆ε < 0
1.02
1
Conclusion
Average Hours in Firms with ∆ε > 0
1.155
GE
PE
Employment
1.15
1.145
0.98
1.14
0.96
1.135
0.94
1.13
0.92
1.125
0.9
1.12
0
100
200
300
400
Average Employment Growth in Firms with ∆ε < 0
-3.5
0
100
200
300
400
Average Employment Growth in Firms with ∆ε > 0
8.5
-4
8
-4.5
-5
7.5
-5.5
-6
7
-6.5
6.5
-7
-7.5
6
-8
-8.5
5.5
0
100
200
300
400
0
Figure: Average Hours and Employment Change by ∆ε.
100
200
300
400
Appendix
Introduction
The Model
Steady State
Aggregate Shocks
Employment
Job Creation and Job Destruction
Job Destruction
0.8
no STW
STW
0.6
0.4
0.2
0
-0.2
5
10
15
20
25
20
25
Job Creation
0.06
0.05
0.04
0.03
0.02
0.01
0
-0.01
-0.02
5
10
15
Conclusion
Appendix
Introduction
The Model
Steady State
Aggregate Shocks
Robustness
Role of parameters (see paper)
Role of labor market institutions
Flexibility, h < 1
Alternative: Hiring Credits
cheaper, but less effective
Large initial effect on U via JD
Employment
Conclusion
Appendix
Introduction
The Model
Steady State
Aggregate Shocks
Employment
Model Predictions
Germany 2009:
labor productivity per worker -4.9%
labor productivity per hour -2.2%
Less job creation in sectors with more STW
in line with model prediction
Graph
Conclusion
Appendix
Introduction
The Model
Steady State
Aggregate Shocks
Employment
Conclusion
Can STW save jobs?
Economic press, Government, Unions
→ We find a positive effect on employment
What are the costs?
Reduced form vs. structural model
‘Reallocation channel’
→ STW prevents reallocation of labor
→ negative effect on GDP of around 1%
Conclusion
Appendix
Introduction
The Model
Steady State
Aggregate Shocks
Employment
Conclusion
Appendix
Employment Policy
Employment Policy Function for levels of productivity
8
7
Log Employment Tomorrow
6
5
4
3
2
1
0
0
1
2
3
4
5
6
7
8
Log Employment Today
Figure: Firm’s Employment Policy N (ε, n−1 ) as a function of productivity.
back
Introduction
The Model
Steady State
Aggregate Shocks
Employment
Conclusion
−6
Total Hours growth, %
−4
−2
0
2
4
Change in Total Hours Worked
1995
2000
2005
Time
DEU
OECD
ESP
back
2010
USA
AUT
FRA
2015
Appendix
Introduction
The Model
Steady State
Aggregate Shocks
Employment
Conclusion
Summary Statistics
N
H
H/N
PY
Count
Mean
SD
IQR
p10
p50
p90
38,839
33,617
34,303
39,180
98.5
156,300
135.8
1,531,785
142.6
20,576
35.7
3,106,538
73.8
11,694
31.6
1,116,285
19.4
3,578
104.5
101,242
48.2
8,366
134.0
474,343
228.0
35,107
167.9
3,766,944
Table: Summary Statistics
Note: Summary statistics for Employment N, Hours H, Hours per Employee
H/N, and Revenues PY . The table shows average values over all years.
Revenues are deflated to 2005 Euros.
back
Appendix
Introduction
The Model
Steady State
Aggregate Shocks
Employment
Conclusion
Appendix
Rules for STW
1
Hours reduction must not be preventable (overtime, holidays)
2
The firm must be unable to compensate the work stoppage
with permissible variations in intra-firm working hours
3
At least a third of the firm’s workforce must suffer an earnings
loss of at least 10%.
4
Reduction in working time must be temporary. The maximum
duration of STW is six months. After this time full-time
employment should be restored.
Hours worked will be paid as usual
Remanence costs for the firm
The gov’t will compensate workers for 60% (67%) of earnings
loss
back
Introduction
The Model
Steady State
Aggregate Shocks
Employment
Conclusion
2008m1
0
0
20
500
Firms
Workers
40
1000
60
1500
STW use by Workers and Firms
2010m1
2012m1
Time
Firms
back
2014m1
Workers
2016m1
Appendix
Introduction
The Model
Steady State
Aggregate Shocks
Employment
Hours Change Distribution
0.6
Data
Model
0.5
0.4
0.3
0.2
0.1
0
<-.20
back
-.20--.10
-.10--.05
Inactive
.05-.10
.10-.20
>.20
Conclusion
Appendix
Introduction
The Model
Steady State
Aggregate Shocks
Employment
Employment Change Distribution
0.5
Data
Model
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
<-.20
back
-.20--.10
-.10--.05
Inactive
.05-.10
.10-.20
>.20
Conclusion
Appendix
Introduction
The Model
Steady State
Aggregate Shocks
Employment
Conclusion
Appendix
.98
Log Job Creation (2004 = 1)
.99
1
1.01
1.02
1.03
Job Creation
2005
2010
year
Manufacturing
2015
Services
Figure: Job Creation, in logs, normalized to 2004 values. Source: German
Employment Agency.
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