The European Unemployment Puzzle: implications from population aging

We study the link between the evolving age structure of the working population and unemployment. We build a large new Keynesian OLG model with a realistic age structure, labor market frictions, sticky prices, and aggregate shocks. Once calibrated to the European economy, we quantify the extent to which demographic changes over the last three decades have contributed to the decline of the unemployment rate. Our findings yield important implications for the future evolution of unemployment given the anticipated further aging of the working population in Europe. We also quantify the implications for optimal monetary policy: lowering inflation volatility becomes less costly in terms of GDP and unemployment volatility, which hints that optimal monetary policy may be more hawkish in an aging society. Finally, our results also propose a partial reversal of the European-US unemployment puzzle due to the fact that the share of young workers is expected to remain robust in the US.

1. The European Unemployment Puzzle: implications from population aging
Krzysztof Makarski
1,3
Joanna Tyrowicz
2,3
Sylwia Radomska
4,3
1
SGH Warsaw School of Economics
2
University of Warsaw
3
FAME|GRAPE
4
Institute of Economics, Polish Academy of Sciences
WeLaR conference, May 2024
1 / 40

2. Motivation

3. Unemployment in EZ higher than in the US
•The European unemployment rates are persistently above the levels observed in the US
(Blanchard and Summers, 1986; Gal, 2015)
2 / 40

4. EZ labor force ages fast, much faster than the US
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
•Share of young workers shrinks fast.
•Share of elderly workers grows fast.
3 / 40

5. Demographics and unemployment: empirical regularities
•Age population structure and unemployment rate
4 / 40

6. Demographics and unemployment: empirical regularities
We estimate
unemploymentc,t=αc+αt+βypopulation share
15−24
c,t
+βopopulation share
50−64
c,t
+ϵi,t
Eurostat World Bank
data all years same years as Eurostat EU 28 (all years) EU15 (all years)
ˆ
βy−
ˆ
β0 -0.33***-0.20*** -0.34*** -0.32*** -0.18*
(0.07) (0.05) (0.07) (0.06) (0.1)
Observations 800 1389 800 1012 620
R
2
0.71 0.74 0.69 0.55 0.56
•↓15-24 share by 10 pp, unemployment rate↓by approx 4 pp,ceteris paribus
•↑50-64 share by 10 pp, unemployment rate↓by approx 3 pp,ceteris paribus
5 / 40

7. In this paper
•Major question: how does aging affect labor market, and conduct of monetary policy?
•Our tool: build a large scale NK OLG-DSGE model w/ search & matching frictions
population structure⇐NEW!
•Our analysis: look into
•long-term trends
•decompose the role of demographics and changes in the labor market features
⇒Can there be a reversal of European-US unemployment gap?
•local stochastic properties
6 / 40

8. Preview of the results
•Aging lowers unemployment levels.
•Aging reduces the cost of stabilizing inflation in terms of unemployment volatility.
•The effects in the EZ larger than in the US.
•Pitch demographics vs changes in labor market
•Model can account for many aspects => we welcome all the comments about which direction to go.
7 / 40

9. Preview of the results
•Aging lowers unemployment levels.
•Aging reduces the cost of stabilizing inflation in terms of unemployment volatility.
•The effects in the EZ larger than in the US. •Pitch demographics vs changes in labor market
•Model can account for many aspects => we welcome all the comments about which direction to go.
7 / 40

10. Preview of the results
•Aging lowers unemployment levels.
•Aging reduces the cost of stabilizing inflation in terms of unemployment volatility.
•The effects in the EZ larger than in the US. •Pitch demographics vs changes in labor market•Model can account for many aspects => we welcome all the comments about which direction to go.
7 / 40

11. Preview of the results
•Aging lowers unemployment levels.
•Aging reduces the cost of stabilizing inflation in terms of unemployment volatility.
•The effects in the EZ larger than in the US. •Pitch demographics vs changes in labor market•Model can account for many aspects => we welcome all the comments about which direction to go.
7 / 40

12. Labor market flows in EZ: job finding rate (left) and separation rate (right)
8 / 40

13. Model

14. Model structure: overview
Add search & matching frictions to a large scale NK-OLG-DSGE model
(Bielecki, Brzoza-Brzezina and Kolasa, 2022)
•80 cohorts of overlapping generations of households (age 20-99)
•Age-specific asset structure: bonds and real assets
•... with nominal & real frictions...
•sticky prices, external habits, investment adjustment costs
•... with labor market frictions...
•search and matching frictions
•wages set in staggered Nash bargaining
•... with fiscal and monetary policy...
•realistic population structure and population growth.
9 / 40

15. Labor market: set up
Two-state model:
•Employed
Wj,t( ˜wj,t) =zj˜wj,t+I
{j<¯J−1}
Et
»
πt+1
Rt+1
ωj((1−ρj)(θwWj+1,t+1(
πt−1
πt
˜wj,t)
+ (1−θw)Wj+1,t+1( ˜wj+1,t+1)) +ρjΥj+1,t+1)
–
(1)
•or unemployed
Υj,t=χt+I
{j<¯J−1}
Et
»
πt+1
Rt+1
ωj(sj,tWj+1,t+1(wj+1,t+1) + (1−sj,t)Υj+1,t+1)
–
(2)
(I
{j<¯j−1}is an indicator for retired tomorrow)
10 / 40

16. Labor market: search and matching
•New matches are created according to
Mj,t=mj(Uj,t,Vt) =e
ϵ
M,t
σj,m
“
Nj,t
Nt
”
1−ϕj
U
ϕj
j,t
V
1−ϕj
t (3)
withϵM,tdenoting shocks to matching technology.
•Vacancy filling and job finding probability
qj,t=e
ϵ
M,t
σj,m
“
Nj,t
Nt
”
ϑ
−ϕj
j,t
andsj,t=e
ϵ
M,t
σj,mϑ
1−ϕj
j,t
withϑj,t=
VtNt
uj,t
denoting the tightness anduj,tdenoting unemployment.
•This yields labor market flows
nj,t= (1−ρj−1)nj−1,t−1+sj−1,t−1uj−1,t−1 (4)
uj,t=1−nj,t+ρjnj,t (5)
11 / 40

17. Labor market: search and matching
•New matches are created according to
Mj,t=mj(Uj,t,Vt) =e
ϵ
M,t
σj,m
“
Nj,t
Nt
”
1−ϕj
U
ϕj
j,t
V
1−ϕj
t (3)
withϵM,tdenoting shocks to matching technology.
•Vacancy filling and job finding probability
qj,t=e
ϵ
M,t
σj,m
“
Nj,t
Nt
”
ϑ
−ϕj
j,t
andsj,t=e
ϵ
M,t
σj,mϑ
1−ϕj
j,t
withϑj,t=
VtNt
uj,t
denoting the tightness anduj,tdenoting unemployment.
•This yields labor market flows
nj,t= (1−ρj−1)nj−1,t−1+sj−1,t−1uj−1,t−1 (4)
uj,t=1−nj,t+ρjnj,t (5)
11 / 40

18. Labor market: search and matching
•New matches are created according to
Mj,t=mj(Uj,t,Vt) =e
ϵ
M,t
σj,m
“
Nj,t
Nt
”
1−ϕj
U
ϕj
j,t
V
1−ϕj
t (3)
withϵM,tdenoting shocks to matching technology.
•Vacancy filling and job finding probability
qj,t=e
ϵ
M,t
σj,m
“
Nj,t
Nt
”
ϑ
−ϕj
j,t
andsj,t=e
ϵ
M,t
σj,mϑ
1−ϕj
j,t
withϑj,t=
VtNt
uj,t
denoting the tightness anduj,tdenoting unemployment.
•This yields labor market flows
nj,t= (1−ρj−1)nj−1,t−1+sj−1,t−1uj−1,t−1 (4)
uj,t=1−nj,t+ρjnj,t (5)
11 / 40

19. Job brokers sell labor services to intermediate good producers at priceΩt
•Job brokering agency needs to post vacancy to hirec(Vt) =
κ
2
P¯J−1
j=1
q
2
j,tV
2
t→search is not directed
•The agency receives payment from firmsΩtzjand pays workers˜wj,t
•... with the value of worker
Jj,t( ˜wj,t) = Ωι(j),tzj−˜wj,tzj
+ωj(1−ρj)I
{j<
¯
J−1}
Et[
πt+1
Rt+1
(θwJj+1,t+1(
πt−1
πt
˜wj,t) + (1−θw)Jj+1,t+1( ˜wj+1,t+1))](6)
12 / 40

20. Job brokers sell labor services to intermediate good producers at priceΩt
•Job brokering agency needs to post vacancy to hirec(Vt) =
κ
2
P¯J−1
j=1
q
2
j,tV
2
t→search is not directed
•The agency receives payment from firmsΩtzjand pays workers˜wj,t
•... with the value of worker
Jj,t( ˜wj,t) = Ωι(j),tzj−˜wj,tzj
+ωj(1−ρj)I
{j<¯J−1}
Et[
πt+1
Rt+1
(θwJj+1,t+1(
πt−1
πt
˜wj,t) + (1−θw)Jj+1,t+1( ˜wj+1,t+1))](6)
12 / 40

21. Labor supply
•Labor services in periodt
ℓt=
»
X
ι∈{y,p,e}
`
ℓι,t
´
σ
L
−1
σ
L
–
σ
L
σ
L
−1
(7)
where
ℓy,t=
P
j=1,...,10
ℓj,t→young,
ℓp,t=
P
j=11,...,35
ℓj,t→prime-age,
andℓe,t=
P
j=36,...,¯J−1
ℓj,t→elderly.
•Effective labor supply per capita of cohortjin periodtis
ℓj,t=
z
j
Nj,t
Nt
(8)
13 / 40

22. Wages
Wages are determined in in staggered Nash bargaining - are either re-optimzed or indexed to past inflation
(Gertler and Trigari, 2009)
wj,t= (1−θw) ˜wj,t+θw
πt−1
πt
wj,t−1
14 / 40

23. We use this model to
•Deterministic simulations of transition across model parameters.
•Population structure
•Labor market parameters
•Stochastic simulations around local steady state for a given population structure.
Shocks to: preferences, technology (TFP) and monetary policy
•Impulse response functions
•Monetary policy frontier
see detailes
15 / 40

24. Calibration

25. Calibration
•Demographic data: Eurostat and EUROPOP,
•Standard structural parameters: taken from literature or to match data moments
•Vacancy data from the OECD (averaged to eurozone by population + for US)
•Life-cycle features calibrated from individual level data:
•Age-specific productivity: HFCS and PSID
•Age-specific labor market flows: EU LFS (findings and separations) + ACS (separations)
•Age-specific asset holdings HFCS
•The main calibration was made on the pre-covid data from 2010s.
16 / 40

26. Calibration EZ: Labor market
Table 1:Target statistics in the data and the model for EZ
variable 1990s 2010s description
model data model data
uyoung 30.9%30.8%19.1%19.2%unemployment rate for young (includes NEETs)
uprime age7.3% 7.3% 7.3% 7.5% unemployment rate for prime age individuals
uelderly6.3% 6.4% 6.1% 6.3% unemployment rate for elderly
utotal13.4%13.7%9.6% 8.8% total unemployment rate
syoung 23% 25% 34% 36% job finding rate for young
sprime age38% 36% 36% 43% job finding rate for prime age individuals
selderly25% 23% 27% 34% job finding rate for elderly
ϑ 0.13 - 0 .22 0.13 labor market tightness
Note: the unemployment data for Europe includes NEETs.
17 / 40

27. Calibration US: Labor market
Table 2:Target statistics in the data and the model US
variable 1990s 2010s description
model data model data
uyoung 9.2%9.1%11.76%11.48%unemployment rate for young (includes NEETs)
uprime age4.8%4.6%4.82% 4.6% unemployment rate for prime age individuals
uelderly4.3%4.2%4.11% 3.96% unemployment rate for elderly
utotal 6.0%6.3%6.40% 6.65% total unemployment rate
syoung 74% - 63 % - job finding rate for young
sprime age78% - 62 % - job finding rate for prime age individuals
selderly76% - 59 % - job finding rate for elderly
ϑ 0.44 - 0 .41 0 .43 labor market tightness
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28. Performance of our model1990 1995 2000 2005 2010 2015
0
2
4
6
8
10
12
14
16
18
20
model
data - HP filtered
data
19 / 40

29. Results

30. Three sets of results
1.
ut=ωy,tuy,t+ωp,tup,t+ωo,tuo,t,
ut−u0
= (ωy,t−ωy,0)uy,t+ (ωp,t−ωp,0)up,t+ (ωo,t−ωo,0)uo,t
| {z }
composition
+ωy,0(uy,t−uy,0) +ωp,0(up,t−up,0) +ωo,0(uo,t−uo,0).
| {z }
behavioral
2.
Impulse response functions (stochastic, around steady state)
3.
Local implications for monetary policy frontier (stochastic, around steady state)
20 / 40

31. Three sets of results
1.
ut=ωy,tuy,t+ωp,tup,t+ωo,tuo,t,
ut−u0= (ωy,t−ωy,0)uy,t+ (ωp,t−ωp,0)up,t+ (ωo,t−ωo,0)uo,t
| {z }
composition
+ωy,0(uy,t−uy,0) +ωp,0(up,t−up,0) +ωo,0(uo,t−uo,0).
| {z }
behavioral
2.
Impulse response functions (stochastic, around steady state)
3.
Local implications for monetary policy frontier (stochastic, around steady state)
20 / 40

32. Three sets of results
1.
ut=ωy,tuy,t+ωp,tup,t+ωo,tuo,t,
ut−u0= (ωy,t−ωy,0)uy,t+ (ωp,t−ωp,0)up,t+ (ωo,t−ωo,0)uo,t
| {z }
composition
+ωy,0(uy,t−uy,0) +ωp,0(up,t−up,0) +ωo,0(uo,t−uo,0).
| {z }
behavioral
2.
3.
20 / 40

33. Aging in EZ: unemployment↓by approx. 3.5 pp.Unemployment rate
1990 1995 2000 2005 2010 2015
-5
-4
-3
-2
-1
0
1
Youth unemployment rate
1990 1995 2000 2005 2010 2015
-15
-10
-5
0
Prime-age unemployment rate
1990 1995 2000 2005 2010 2015
-3
-2
-1
0
1
2
3
Elderly unemployment rate
1990 1995 2000 2005 2010 2015
-3
-2
-1
0
1
2
3
Labor market change: total effect
Demographic change: behavioral effect
Demographic change: composition effect
Demographic & labor market change
21 / 40

34. Aging in US: unemployment≈Unemployment rate
1990 1995 2000 2005 2010 2015
-2
-1
0
1
2
3
4
Youth unemployment rate
1990 1995 2000 2005 2010 2015
-2
-1
0
1
2
3
4
Prime-age unemployment rate
1990 1995 2000 2005 2010 2015
-2
-1
0
1
2
3
4
Elderly unemployment rate
1990 1995 2000 2005 2010 2015
-2
-1
0
1
2
3
4
Labor market change: total effect
Demographic change: behavioral effect
Demographic change: composition effect
Demographic & labor market change
22 / 40

35. IRFs of monetary policy shock with 1990 and 2020 population for the Euro zone0 10 20 30 40
-0.4
-0.3
-0.2
-0.1
0
Output
0 10 20 30 40
-0.2
-0.15
-0.1
-0.05
0
0.05
Inflation
0 10 20 30 40
0
0.2
0.4
0.6
0.8
Interest rate
2020 population
1990 population
0 10 20 30 40
-0.6
-0.4
-0.2
0
Consumption
0 10 20 30 40
-3
-2
-1
0
Vacancies
0 10 20 30 40
0
0.2
0.4
0.6
Unemployment rate
0 10 20 30 40
0
0.2
0.4
0.6
0.8
Youth unemployment rate
0 10 20 30 40
0
0.1
0.2
0.3
0.4
Prime-age unemployment rate
0 10 20 30 40
0
0.1
0.2
0.3
Elderly unemployment rate
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36. Aging lowers costs of stabilizing inflation of OUTPUT volatility (EZ)0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
Standard deviation of GDP
0
0.5
1
1.5
2
2.5
Standard deviation of inflation
1990 population
2020 population
24 / 40

37. Aging lowers costs of stabilizing inflation in terms of UNEMPLOYMENT volatility0 5 10 15 20 25
Standard deviation of youth unemployment
0
0.5
1
1.5
2
2.5
Standard deviation of inflation
1990 population
2020 population
6 7 8 9 10 11 12 13 14
Standard deviation of prime-age unemployment
0
0.5
1
1.5
2
2.5
Standard deviation of inflation
1990 population
2020 population
6 7 8 9 10 11 12
Standard deviation of elderly unemployment
0
0.5
1
1.5
2
2.5
Standard deviation of inflation
1990 population
2020 population
25 / 40

38. Implications for optimal monetary policy
•Elderly less sensitive to inflation than young
•Both young and elderly less sensitive to inflation after demographic change.
•Optimal monetary policy becomes more restrictive:
•All age groups become more hawkish (or less dovish)
•Share of young declines and share of elderly rises
26 / 40

39. Conclusions

40. Conclusions
•Aging has several implications for the EZ labor market. It
•... lowers unemployment.
•... shortens (but strengthens) the response of unemployment to monetary policy shocks
•... and lowers the sacrifice ratio.
•Demographics more favorable in the US→smaller labor market effects
27 / 40

41. Thank you for your attention
w: grape.org.pl
t: grape_org
f: grape.org
e: [email protected]
28 / 40

42. Additional slides

43. Households
•Maximize expected lifetime utility with external habit formation
Uj,t=
1
1−σ
e
εc,t
(cj,t−ϱ¯cj.t−1)
1−σ
+βω
j
Uj+1,t+1
subject to
cj,t+aj,t= (1−τt)wj,tzjnj,t+χj,tuj,t+
R
a
j,t
πt
aj−1,t−1−Tt+beqj,t
29 / 40

44. Producers
•Final goods aggregated from differentiated intermediate products
ct+it+gt=
»Z
yt(i)
1
µdi
–
µ
•Intermediate goods firms face Calvo-type price stickiness and produce
yt(i) =e
At
kt(i)
α
ℓt(i)
1−α
−Φ
•Capital producers are subject to investment adjustment cost
(1+νt+1)kt+1= (1−δ)kt+
"
1−
Sk
2
„
it
it−1
−1
«
2
#
it
30 / 40

45. Job broker
•Job brokers sell labor services to intermediate good producers in the perfectly competitive market for the
price ofΩt.
•Labor services in periodtare given by the following formula
ℓt=
»
X
ι∈{y,p,e}
`
ℓι,t
´
σ
L
−1
σ
L
–
σ
L
σ
L
−1
(9)
whereℓy,t=
P
j=1,...,10
ℓj,tdenotes young,ℓp,t=
P
j=11,...,35
ℓj,tprime-age, andℓe,t=
P
j=36,...,¯J−1
ℓj,t
elderly.
•and effective labor supply per capita of cohortjin periodtis
ℓj,t=
z
j
Nj,t
Nt
(10)
31 / 40

46. Government and monetary policy
•Government runs a balanced budget
Rt
πt
bt+gt= (1+νt+1)bt+1+
X
j
τtwj,tLj,t+
X
j
Nj,tTt (11)
•Monetary policy follows the Taylor rule
Rt
¯
R
=
“
Rt
¯
R
”
γ
R
“
`πt
¯π
´
γπ
`yt
¯y
´
γy
”
1−γ
R
(12)
32 / 40

47. Calibration EZ: parameters
Parameter Value Description
1990s 2010s
A. Households
β 0.9833 0 .9833 Discount factor
ϱ 0.75
4
0.75
4
Habit persistence
B. Firms
δ 0.12 0 .12 Capital depreciation rate
α 0.25 0 .25 Capital share in output
SK 4 4 Investment adjustment cost curvature
µ 1.2 1 .2 Steady state product markup
θ 0.75
4
0.75
4
Calvo probability (prices)
∗
ζπ 0.25 0 .25 Weight of past inflation in prices indexation
∗
Φ 0.04 0 .04 Intermediate goods producers fixed cost
D. Government and central bank
¯π 1.02 1 .02 Steady state inflation
γR 0.8
4
0.8
4
interest rate smoothing
γπ 1.97 1 .97 reaction to inflation
γy 0.41 0 .41 reaction to GDP growth
γb 0.42 0 .42 fiscal rule parameter
∗
Note: Parametersθ,ζπ, andγnare set to 0 in the deterministic simulations.
33 / 40

48. Calibration EZ: parameters cont’d
These parameters implyqj,t=N
rel
j,tσj,m
„
1
N
rel
t
«
1−ϕj
ϑ
−ϕj
j,t
andsj,t=σj,m(
1
N
rel
t
)
1−ϕj
ϑ
1−ϕj
j,t
Parameter Value Description
1990s 2010s
C. Labor market
κ 15 15 .3 cost of posting the vacancy
N
first 0.62 0 .73 number of employed young entering the market
ρyoung 0.07 0 .06 separation rate for the young
ρprime 0.02 0 .03 separation rate for the prime age
ρ
elderly 0.02 0 .02 separation rate for the elderly
σyoung 0.55 0 .92 scaling parameter in the matching function
σprime 0.58 0 .8 scaling parameter in the matching function
σ
elderly 0.38 0 .56 scaling parameter in the matching function
ϕj 0.72 0 .72 elasticity of matching function
η 0.72 0 .72 parameter in the Nash bargaining process
θw 0.85
4
0.85
4
nominal wage stickiness
χ 0.64 0 .64 unemployment benefit
γn 2 2 responsiveness of labor market entrants employment to GDP
34 / 40

49. Calibration US: parameters
Parameter Value Description
1990s 2010s
A. Households
β 0.983 0 .983 Discount factor
ϱ 0.75
4
0.75
4
Habit persistence
B. Firms
δ 0.05 0 .05 Capital depreciation rate
α 0.24 0 .24 Capital share in output
SK 4 4 Investment adjustment cost curvature
µ 1.2 1 .2 Steady state product markup
θ 0.75
4
0.75
4
Calvo probability (prices)
ζπ 0.25 0 .25 Weight of past inflation in prices indexation
Φ 0.04 0 .04 Intermediate goods producers fixed cost
D. Government and central bank
¯π 1.02 1 .02 Steady state inflation
γR 0.8
4
0.8
4
interest rate smoothing
γπ 1.97 1 .97 reaction to inflation
γy 0.41 0 .41 reaction to GDP growth
γb 0.42 0 .42 fiscal rule parameter
∗
Note: Parametersθ,ζπ, andγnare set to 0 in the deterministic simulations.
35 / 40

50. Calibration US: parameters cont’d
These parameters implyqj,t=N
rel
j,tσj,m
„
1
N
rel
t
«
1−ϕj
ϑ
−ϕj
j,t
andsj,t=σj,m(
1
N
rel
t
)
1−ϕj
ϑ
1−ϕj
j,t
Parameter Value Description
1990s 2010s
C. Labor market
κ 8.9 13 .8 cost of posting the vacancy
N
first 1 0 .93 number of employed young entering the market
ρyoung 0.0725 0 .074 separation rate for young
ρprime 0.0368 0 .0294 separation rate for prime
ρ
old 0.0332 0 .0246 separation rate for old
σyoung 1.11 1 .01 scaling parameter in the matching function
σprime 0.97 0 .78 scaling parameter in the matching function
σ
elderly 0.92 0 .71 scaling parameter in the matching function
ϕj 0.72 0 .72 elasticity of matching function
η 0.72 0 .72 parameter in the Nash bargaining process
θw 0.85
4
0.85
4
nominal wage stickiness
χ 0.52 0 .52 unemployment benefit
36 / 40

51. Calibration: Stochastic shocks obtained in moment matching procedure for the EZ economy
Table 3:Calibrated stochastic shocks
Parameter Value Description
A. Persistence
ρ
A 0.999 Productivity shock - autocorrelation
ρc 0.999 Preference shock - autocorrelation
ρg 0.714 Gov. expenditure shock - autocorrelation
B. Standard deviations
σ
A 0.00093763 Productivity shock - standard deviation
σc 0.22125 Preference shock - standard deviation
σg 0.0013589 Gov. expenditure shock - standard deviation
σ
R 0.00007336 Monetary shock - standard deviation
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52. Calibration: macroeconomic variables of the Eurozone economy
variable
EZ US
description
model data model data
1990s 2010s 2010s 1990s 2010s 2010s
r 1.54% 0.8% 0.8% 2.77% 2.14% 2.11% real interest rate
b
g
/y 53% 53% 53% 55% 55% 55% government debt to GDP ratio
i
y
24% 24% 24% 23% 24% 24% investment rate
k
y
1.85 1 .95 1 .97 3.1 3 .36 3 .56 capital to GDP ratio
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53. Model EZ data fit: selected moments of the Eurozone economy
Standard Deviations Correlation with output Autocorrelation
Variable data model data model data model
in percent
output 1.75 2 .03 1 1 0 .56 0 .99
consumption 1.36 2 .38 0 .90 0 .59 0 .79 0 .99
interest rate 1.67 1 .60 0 .59 −0.80 0 .89 0 .99
gov. expenditure 0.98 0 .98 0 .23 0 .03 0 .77 0 .71
inflation 1.12 1 .18 0 .65 −0.91 0 .51 0 .99
unemployment 10.65 10 .37 −0.88 −0.98 0 .73 0 .99
variables not used in moment matching
investment 4.65 6 .78 0 .96 0 .76 0 .67 0 .99
unemployment young 8.25 12 .38 −0.84 −0.99 0 .68 0 .99
unemployment prime 11.01 9 .08 −0.89 −0.96 0 .72 0 .99
unemployment old 9.64 8 .35 −0.84 −0.95 0 .69 0 .99
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54. Derivation of monetary policy frontier
•We minimize the standard central bank loss function within Taylor rule different populations (younger
from 1990s and older from 2010s) by solving the following problems for allλ∈[0,1]
min
(γy,γπ)
λ·Var(˜πt) + (1−λ)·Var(˜yt)
subject to equilibrium conditions of the model, with the following Taylor rule
Rt
¯
R
=
“
Rt
¯
R
”
γ
R
“
`πt
¯π
´
γπ
`yt
¯y
´
γy
”
1−γ
R
(13)
Go back
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