1. The European Unemployment Puzzle: implications from population aging
Krzysztof Makarski1,3 Joanna Tyrowicz2,3 Sylwia Radomska2,3
1SGH Warsaw School of Economics
2University of Warsaw
3FAME|GRAPE
The European Unemployment Problem: Past Trajectory, Present Dilemmas and Future Policies, Zurich, 5-6 June 2023
1 / 37

2. Motivation

3. Eurozone (EZ) ages fast, faster than the US
ˆ Share of young workers shrinks fast.
ˆ Share of elderly workers grows fast.
Shares in working age population
1970 (in %) ∆ :1970→2010 (in pp)
20-30 31-54 55-64 20-30 31-54 55-64
EZ 28.9 52.9 18.2 −10.0 +0.2 +8.8
US 29.8 52.7 17.5 −4.4 −2.3 +2.0
2 / 37

4. Demographics and unemployment: empirical regularities
ˆ We estimate : unemploymenti,t = αi + αt + βy %pop15−24 + βo%pop50−64 + i,t
ˆ ↓ 15-24 share by 10 pp, unemployment rate ↓ by approx 3 pp, ceteris paribus.
ˆ ↑ 50-64 share by 10 pp, unemployment rate ↓ by approx 2 pp, ceteris paribus.
Eurostat World Bank
all EU 28
(all years)
EZ
(all years)
(1) (2) (3) (4)
βy 0.35*** 0.33*** 0.42*** 0.053
(0.10) (0.08) (0.09) (0.10)
βo -0.29** -0.056 -0.16* -0.34**
(0.10) (0.08) (0.10) (0.10)
Observations 804 1383 1015 622
R-squared 0.71 0.74 0.55 0.55
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5. Labor market ows in EZ: job nding rate (left) and separation rate (right)
4 / 37

6. In this paper
ˆ Major question: how does aging aect labor market, and conduct of monetary policy?
ˆ Our tool: build a large scale NK OLG-DSGE model w/ search matching frictions [⇐NEW!]
ˆ Our analysis: look into
ˆ long-term trends
ˆ decompose the role of demographics and changes in the labor market features
= Can there be a reversal of European-US unemployment gap?
ˆ local stochastic properties
ˆ Model can account for many aspects = we welcome all the comments about which direction to go.
5 / 37

7. Preview of the results
ˆ Aging lowers unemployment levels.
ˆ Decomposition of the role of demographics and changes in the labor market features in progress.
ˆ Aging shifts Beveridge curve to left.
ˆ Aging reduces the cost of stabilizing ination in terms of unemployment volatility.
ˆ The eects in the EZ larger than in the US.
6 / 37

8. Model

9. Model structure: overview
ˆ Add search matching frictions to a large scale NK-OLG-DSGE model (Bielecki, Brzoza-Brzezina and
Kolasa, 2022).
ˆ 80 cohorts of overlapping generations of households (age 20-99)
ˆ Age-specic asset structure: bonds and real assets
ˆ ... with nominal real frictions...
ˆ sticky prices, external habits, investment adjustment costs
ˆ ... with labor market frictions...
ˆ search and matching frictions
ˆ wages set in Nash bargaining with wage norm.
ˆ ... with scal and monetary policy.
7 / 37

10. Labor market: set up
ˆ Two-state model: employed or unemployed.
ˆ Workers value of employment and unemployment (I{j¯
j−1} indicator for retired tomorrow)
Wj,t = zj wj,t + I{j¯
j−1}Et
πt+1
Rt+1
ωj ((1 − ρj )Wj+1,t+1 + ρj Υj+1,t+1)
(1)
Υj,t = χt + I{j¯
j−1}Et
πt+1
Rt+1
ωj (sj,t Wj+1,ι,t+1 + (1 − sj,t )Υj+1,t+1)
(2)
ˆ Job brokering agency needs to post vacancy to hire (search is not directed towards age groups)
c(Vt ) = κVt (3)
receives payment from rms Ωt zj and pays workers wj,t , with value of worker
Jj,t = Ωt zj − wj,t zj + I{j¯
j−1}Et [
πt+1
Rt+1
ωj (1 − ρj )Jj+1,t+1] (4)
8 / 37

11. Labor market: search and matching
ˆ New matches are created according to
Mj,t = mj (Uj,t , Vt ) = σj,m(
Nrel
j,t
Nrel
t
)1−φj
U
φj
j,t V
1−φj
t (5)
which implies following vacancy lling and job nding probability
qj,t = Nrel
j,t σj,m(
1
Nrel
t
)1−φj
ϑ
−φj
j,t
sj,t = σj,m(
1
Nrel
t
)1−φj
ϑ
1−φj
j,t
ˆ Wages are determined in Nash bargaining with wage norm
wj,t = (1 − ζw ) wnorm
j,t + ζw wj,t−1
with wnorm
j,t = argmaxJ1−η
j,t (Wj,t − Υj,t )η
9 / 37

12. We use this model to
ˆ Deterministic simulations of transition across model parameters.
ˆ Population structure
ˆ Labor market parameters [IN PROGRESS]
ˆ Stochastic simulations around local steady state for a given population structure.
Shocks to: preferences, technology (TFP) and monetary policy
ˆ Beveridge curve
ˆ Monetary policy frontier
10 / 37

13. Derivation of monetary policy frontier
ˆ We minimize the standard central bank loss function within Taylor rule dierent populations (younger
from 1980 and older from 2020) by solving the following problems for all λ ∈ [0, 1]
min
(γy ,γπ)
λ · Var(π̃t ) + (1 − λ) · Var(ỹt )
subject to equilibrium conditions of the model, with the following Taylor rule
Rt
R̄
=
Rt
R̄
γR
πt
π̄
γπ yt
ȳ
γy
1−γR
(6)
11 / 37

14. Calibration

15. Calibration
ˆ Demographic data: Eurostat and EUROPOP,
ˆ Standard structural parameters: taken from literature or to match data moments
ˆ Vacancy data from the OECD (averaged to eurozone by population + for US)
ˆ Life-cycle features calibrated from individual level data:
ˆ Age-specic productivity: HFCS and PSID
ˆ Age-specic labor market ows: EU LFS (ndings and separations) + ACS (separations)
ˆ Age-specic asset holdings HFCS
ˆ The main calibration was made on the pre-covid data from 2010s.
12 / 37

16. Calibration: Labor market
variable
EZ US
description
model data model data
u 11.0% 11% 6.4% 6.7% total unemployment rate
u20−30 21.8% 21.9% 12.1% 11.5% unemployment rate 20-30
u31−54 8.2% 9.1% 4.8% 4.6% unemployment rate 31-54
u55−64 7.2% 7.2% 4.1% 4.0% unemployment rate 55-64
s20−30 35% 35% 53% - job nding rate 20-30
s31−54 40% 43% 66% - job nding rate 31-54
s55−64 33% 34% 79% - job nding rate 55-64
s 66% 58% job nding rate all
ϑ 0.16 0.13 0.39 0.39 market tightness
ρ20−30 6% 6% 7.4% 7.4% separation rate 20-30
ρ31−54 3% 3% 2.9% 2.9% separation rate 31-54
ρ55−64 2% 2% 2.5% 2.5% separation rate 55-64
Note: the unemployment data for Europe includes NEETs.
13 / 37

17. Results

18. Three sets of results
1. Trend (deterministic) eects of aging for unemployment
2. Local (stochastic) implications for Beveridge curve
3. Local (stochastic) implications for monetary policy frontier (MPF)
14 / 37

19. Aging in EZ: unemployment ↓ by approx. 1pp.
variable EZ
1970 1980 2010 2020 2030
u 12 11.9 11 10.8 10.9
u20−30 22.1 22 21.8 22 22.3
u31−54 8.4 8.3 8.2 8.3 8.4
u55−64 7.2 7.2 7.2 7.3 7.5
s20−30 35 35 35 34 34
s31−54 40 40 40 39 39
s55−64 33 33 33 32 32
JVR 1.8 1.8 1.9 1.9 1.9
15 / 37

20. The eects are negligible in the US (less aging)
variable EZ US
1970 1980 2010 2020 2030 1970 1980 2010 2020 2030
u 12 11.9 11 10.8 10.9 6.7 7.1 6.4 6.5 6.6
u20−30 22.1 22 21.8 22 22.3 12.0 12.0 12.1 12.2 12.3
u31−54 8.4 8.3 8.2 8.3 8.4 4.8 5.0 4.8 4.9 5.0
u55−64 7.2 7.2 7.2 7.3 7.5 4.1 4.1 4.1 4.2 4.3
s20−30 35 35 35 34 34 56 56 56 55 54
s31−54 40 40 40 39 39 69 69 69 68 66
s55−64 33 33 33 32 32 80 80 79 78 77
JVR 1.8 1.8 1.9 1.9 1.9 2.46 2.51 2.48 2.52 2.54
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21. Aging shifts Beveridge curve to the left
0
.01
.02
.03
.04
vacancy
rate
.09 .1 .11 .12 .13 .14
unemployment rate
1980 2000 2020
EZ
0
.01
.02
.03
.04
vacancy
rate
.05 .06 .07 .08 .09
unemployment rate
1980 2000 2020
USA
17 / 37

22. Aging lowers costs of stabilizing ination of OUTPUT volatility
0 0.5 1 1.5 2 2.5 3
Standard deviation of GDP
0
0.5
1
1.5
2
2.5
3
3.5
Standard
deviation
of
inflation
1980 demography
2020 demography
(a) Monetary policy frontier in EZ
0 0.5 1 1.5 2 2.5 3
Standard deviation of GDP
0
0.5
1
1.5
2
2.5
3
3.5
Standard
deviation
of
inflation
1980 demography
2020 demography
(b) Monetary policy frontier in US
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23. Aging lowers costs of stabilizing ination of UNEMPLOYMENT volatility
5 5.5 6 6.5 7 7.5 8 8.5
Standard deviation of unemployment
0
0.5
1
1.5
2
2.5
3
3.5
Standard
deviation
of
inflation
1980 demography
2020 demography
(a) Trade-o at monetary policy frontier in EZ
5 5.5 6 6.5 7 7.5
Standard deviation of unemployment
0
0.5
1
1.5
2
2.5
3
3.5
Standard
deviation
of
inflation
1980 demography
2020 demography
(b) Trade-o at monetary policy frontier in US
19 / 37

24. EZ: zoom in on trade-os gap between the young and elderly
0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2
Standard deviation of unemployment of young
0
0.5
1
1.5
2
2.5
3
3.5
Standard
deviation
of
inflation
1980 demography
2020 demography
0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2
Standard deviation of unemployment of elderly
0
0.5
1
1.5
2
2.5
3
Standard
deviation
of
inflation
1980 demography
2020 demography
20 / 37

25. Implications for optimal monetary policy
ˆ Elderly more sensitive to ination than young
ˆ Both young and elderly more sensitive to ination after demographic change.
ˆ Optimal monetary policy becomes more restrictive:
ˆ All age groups become more hawkish (or less dovish)
ˆ Share of young declines and share of elderly rises
21 / 37

26. Still to do
ˆ improve the US calibration
ˆ simulations of the trend unemployment: demographics, labor market changes, and both
[to disentangle contribution of demography and labor market characteristics]
ˆ we also welcome all suggestions
22 / 37

27. Conclusions

28. Conclusions
ˆ Aging has several implications for the EZ labor market. It
ˆ ... lowers unemployment.
ˆ ... shifts the Beveridge curve to the left.
ˆ ... weakens the response of unemployment to monetary policy shocks
ˆ ... and raises the sacrice ratio.
ˆ Demographics more favorable in the US → smaller labor market eects
23 / 37

29. Thank you for your attention
w: grape.org.pl
t: grape_org
f: grape.org
e: kmakarski@grape.org.pl
24 / 37

30. Additional slides

31. Households
ˆ Maximize expected lifetime utility with external habit formation
Uj,t =
1
1 − σ
(cj,t − %c̄j,t−1)1−σ
+ βωj Et Uj+1,t+1
subject to
cj,t + aj,t = (1 − τt )wt zj Nj,t + χj,t Uj,t +
Ra
j,t
πt
aj−1,t−1 + beqj,t
25 / 37

32. Labor market: set up
ˆ Two state unemployment model (employed or unemployed).
ˆ Workers value of employment and unemployment
Wj,t = zj wj,t + I{j¯
j−1}Et
πt+1
Rt+1
ωj ((1 − ρj )Wj+1,t+1 + ρj Υj+1,t+1)
(7)
Υj,t = χt + I{j¯
j−1}Et
πt+1
Rt+1
ωj (sj,t Wj+1,ι,t+1 + (1 − sι,t )Υj+1,t+1)
(8)
ˆ Job brokering agency needs to post vacancy to hire
c(Vt ) = κVt (9)
receives payment from rms Ωt and pays workers wj,t , with value of worker
Jj,t = Ωt zj − wj,t zj + I{j¯
j−1}Et [
πt+1
Rt+1
ωj (1 − ρj )Jj+1,t+1] (10)
26 / 37

33. Labor market: search and matching
ˆ New matches are created according to
Mj,t = mj (Uj,t , Vt ) = σj,m(
Nrel
j,t
Nrel
t
)1−φj
U
φj
j,t V
1−φj
t (11)
which implies following vacancy lling and job nding probability
qj,t = Nrel
j,t σj,m(
1
Nrel
t
)1−φj
ϑ
−φj
j,t
sj,t = σj,m(
1
Nrel
t
)1−φj
ϑ
1−φj
j,t
ˆ Wages are determined in Nash bargaining with wage norm
max
wnorm
j,t
J1−η
j,t (Wj,t − Υj,t )η
wj,t = (1 − ζw ) wnorm
j,t + ζw wj,t−1
27 / 37

34. Producers
ˆ Final goods aggregated from dierentiated intermediate products
ct + it + gt =
Z
yt (i)
1
µ di
µ
ˆ Intermediate goods rms face Calvo-type price stickiness and produce
yt (i) = kt (i)α
ht (i)1−α
− Ψ
ˆ Capital producers are subject to investment adjustment cost
kt+1 = (1 − δ)kt +
1 − Sk
it
it−1
it
28 / 37

35. Government and monetary policy
ˆ Government runs a balanced budget
Rt
πt
bt + gt = (1 + n) bt+1 +
X
j
τt wj,t Lj,t (12)
ˆ Monetary policy follows the Taylor rule
Rt
R̄
=
Rt
R̄
γR
πt
π̄
γπ yt
ȳ
γy
1−γR
(13)
29 / 37

36. Calibration: parameters
Parameter Value Description
EZ US
A. Households
β 0.9835 0.9834 Discount factor
% 0.754
0.754
Habit persistence
B. Firms
δ 0.12 0.675 Capital depreciation rate
α 0.25 0.315 Capital share in output
SK 4 4 Investment adjustment cost curvature
µ 1.2 1.2 Steady state product markup
θ 0.664
0.664
Calvo probability (prices)
Φ 0.04 0.04 Intermediate goods producers xed cost
D. Government and central bank
π 1.02 1.02 Ination target
γR 0.41 0.41 interest rate smoothing
γπ 1.97 1.97 reaction to ination
γy 0.42 0.42 reaction to GDP growth
30 / 37

37. Calibration: parameters cont'd
which implies
qj,t = Nrel
j,t σj,m(
1
Nrel
t
)1−φj
ϑ
−φj
j,t
sj,t = σj,m(
1
Nrel
t
)1−φj
ϑ
1−φj
j,t
Parameter Value Description
EZ US
C. Labor market
gy 0.2 0.2 Share of government purchases in GDP
κ 0.24 0.75 cost of posting the vacancy
ρyoung 0.06 0.074 separation rate for young
ρprime 0.03 0.029 separation rate for prime
ρold 0.02 0.025 separation rate for old
σyoung 0.53 0.92 scaling parameter in the matching function
σprime 0.45 0.87 scaling parameter in the matching function
σelderly 0.39 0.97 scaling parameter in the matching function
φj 0.72 0.72 elasticity of matching function 31 / 37

38. Calibration: stochastic shocks
Table 1: Calibrated stochastic shocks
Parameter Value Description
A. Persistence
ρz 0.954
Productivity shock - autocorrelation
ρc 0.994
Preference shock - autocorrelation
B. Standard deviations
σz
√
1 + 0.952 + 0.954 + 0.956 · 0.007 Productivity shock - standard deviation
σc
√
1 + 0.992 + 0.994 + 0.996 · 0.013 Preference shock - standard deviation
σR
√
1 + 0.82 + 0.84 + 0.86 · 0.0013 Monetary shock - standard deviation
32 / 37

39. Calibration: Macroeconomic variables
variable
EZ US
description
model data model data
r 0.79% 0.8% 2.22% 2.24% real interest rate
bg
/y 53% 53% 51% 51% government debt to GDP ratio
i
y
23.7% 24% 24% 24% investment rate
k
y
1.95 1.97 3.51 3.54 capital to GDP ratio
33 / 37

40. Model EZ data t
Standard Deviations Correlation with output
Variable data model model model data model model model
(1980) (2010) (2030) (1980) (2010) (2030)
in percent
output 1.89 1.84 1.83 1 1 1
consumption 2.01 2.03 2.04 0.78 0.77 0.76
investments 4.37 4.29 4.27 0.79 0.78 0.78
ination 1.09 1.06 1.06 −0.94 −0.94 −0.94
interest rate 1.34 1.31 1.30 −0.89 −0.89 −0.89
wages 0.56 0.55 0.55 0.49 0.50 0.50
unemployment 6.22 6.06 5.78 −0.77 −0.76 −0.76
in percentage points
unemployment young 1.03 0.97 0.96 −0.77 −0.76 −0.76
unemployment prime 0.67 0.62 0.62 −0.77 −0.76 −0.76
unemployment old 0.54 0.51 0.44 −0.77 −0.76 −0.76
34 / 37

41. Unemployment rate of age groups vs ination trade-o on the policy frontier
0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2
Standard deviation of unemployment of young
0
0.5
1
1.5
2
2.5
3
3.5
Standard
deviation
of
inflation
1980 demography
2020 demography
0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2
Standard deviation of unemployment of prime age
0
0.5
1
1.5
2
2.5
3
3.5
Standard
deviation
of
inflation
1980 demography
2020 demography
0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2
Standard deviation of unemployment of elderly
0
0.5
1
1.5
2
2.5
3
Standard
deviation
of
inflation
1980 demography
2020 demography
35 / 37

42. Unemployment response is weaker after monetary policy shock
10 20 30 40
-0.04
-0.03
-0.02
-0.01
0
logy
10 20 30 40
-0.04
-0.03
-0.02
-0.01
0
logpi
10 20 30 40
-0.01
0
0.01
0.02
logU
10 20 30 40
-0.1
-0.08
-0.06
-0.04
-0.02
0
logc_young
10 20 30 40
-0.1
-0.08
-0.06
-0.04
-0.02
0
logc_prime
10 20 30 40
-0.06
-0.04
-0.02
0
0.02
0.04
logc_elderly
10 20 30 40
-1
0
1
2
3
4
10-3 u_young_dev
10 20 30 40
-1
0
1
2
10-3 u_prime_dev
10 20 30 40
-5
0
5
10
15
10-4 u_elderly_dev
1980
2030
36 / 37

43. Unemployment response is weaker after technology shock
10 20 30 40
-0.2
0
0.2
0.4
0.6
0.8
logy
10 20 30 40
-0.4
-0.3
-0.2
-0.1
0
logpi
10 20 30 40
-2
-1.5
-1
-0.5
0
0.5
logU
10 20 30 40
0
0.2
0.4
0.6
0.8
1
logc_young
10 20 30 40
0
0.2
0.4
0.6
0.8
1
logc_prime
10 20 30 40
-0.2
0
0.2
0.4
0.6
0.8
logc_elderly
10 20 30 40
-0.4
-0.3
-0.2
-0.1
0
0.1
u_young_dev
10 20 30 40
-0.2
-0.1
0
0.1
u_prime_dev
10 20 30 40
-0.2
-0.15
-0.1
-0.05
0
0.05
u_elderly_dev
1980
2030
37 / 37