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 economies, we use this model to provide comparative statics across past and contemporaneous age structures of the working population. Thus, we quantify the extent to which the response of labor markets to adverse TFP shocks and monetary policy shocks becomes muted with the aging of the working population. Our findings have important policy implications for European labor markets and beyond. For example, the working population is expected to further age in Europe, whereas the share of young workers will remain robust in the US. Our results suggest a partial reversal of the European-US unemployment puzzle. Furthermore, with the aging population, lowering inflation volatility is less costly in terms of higher unemployment volatility. It suggests that optimal monetary policy should be more hawkish in the older society.

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
Annual Lithuanian Conference on Economic Research, December 2023
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
We estimate
unemploymentc,t = αc + αt + βy population share15−24
c,t + βopopulation share50−64
c,t + ϵi,t
Eurostat World Bank
data all years same years as Eurostat EU 28 (all years) EU15 (all years)
β̂y − β̂0 -0.32*** -0.20*** -0.31*** -0.32*** -0.19*
(0.07) (0.05) (0.07) (0.06) (0.1)
Observations 804 1383 804 1006 615
R2
0.71 0.74 0.70 0.55 0.55
• ↓ 15-24 share by 10 pp, unemployment rate ↓ by approx 3 pp, ceteris paribus
• ↑ 50-64 share by 10 pp, unemployment rate ↓ by approx 2 pp, ceteris paribus
4 / 40

6. 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 ⇐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
5 / 40

7. 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.
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.
6 / 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.
6 / 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.
6 / 40

11. Labor market flows in EZ: job finding rate (left) and separation rate (right)
7 / 40

12. Model

13. 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 Nash bargaining with wage norm.
• ... with fiscal and monetary policy.
8 / 40

14. Labor market: set up
Two-state model:
• Employed
Wj,t = zj wj,t + I{j<j̄−1}Et
h
πt+1
Rt+1
ωj ((1 − ρj )Wj+1,t+1 + ρj Υj+1,t+1)
i
(1)
• or unemployed
Υj,t = χt + I{j<j̄−1}Et
h
πt+1
Rt+1
ωj (sj,t Wj+1,ι,t+1 + (1 − sj,t )Υj+1,t+1)
i
(2)
(I{j<j̄−1} is an indicator for retired tomorrow)
9 / 40

15. Labor market: search and matching
• New matches are created according to
Mj,t = mj (Uj,t , Vt ) = eϵM,t
σj,m
Nj,t
Nt
1−ϕj
U
ϕj
j,t V
1−ϕj
t (3)
with ϵM,t denoting shocks to matching technology.
• Vacancy filling and job finding probability
qj,t = eϵM,t
σj,m
Nj,t
Nt
ϑ
−ϕj
j,t and sj,t = eϵM,t
σj,mϑ
1−ϕj
j,t
with ϑj,t = Vt Nt
uj,t
denoting the tightness and uj,t denoting 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 − uj,t + ρj nj,t (5)
10 / 40

16. Labor market: search and matching
• New matches are created according to
Mj,t = mj (Uj,t , Vt ) = eϵM,t
σj,m
Nj,t
Nt
1−ϕj
U
ϕj
j,t V
1−ϕj
t (3)
with ϵM,t denoting shocks to matching technology.
• Vacancy filling and job finding probability
qj,t = eϵM,t
σj,m
Nj,t
Nt
ϑ
−ϕj
j,t and sj,t = eϵM,t
σj,mϑ
1−ϕj
j,t
with ϑj,t = Vt Nt
uj,t
denoting the tightness and uj,t denoting 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 − uj,t + ρj nj,t (5)
10 / 40

17. Labor market: search and matching
• New matches are created according to
Mj,t = mj (Uj,t , Vt ) = eϵM,t
σj,m
Nj,t
Nt
1−ϕj
U
ϕj
j,t V
1−ϕj
t (3)
with ϵM,t denoting shocks to matching technology.
• Vacancy filling and job finding probability
qj,t = eϵM,t
σj,m
Nj,t
Nt
ϑ
−ϕj
j,t and sj,t = eϵM,t
σj,mϑ
1−ϕj
j,t
with ϑj,t = Vt Nt
uj,t
denoting the tightness and uj,t denoting 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 − uj,t + ρj nj,t (5)
10 / 40

18. Job brokers sell labor services to intermediate good producers at price Ωt
• Job brokering agency needs to post vacancy to hire c(Vt ) = κVt → search is not directed
• The agency receives payment from firms Ωt zj and pays workers wj,t
• ... with the value of worker
Jj,t = Ωt zj − wj,t zj + I{jj̄−1}Et
h
πt+1
Rt+1
ωj (1 − ρj )Jj+1,t+1
i
(6)
11 / 40

19. Job brokers sell labor services to intermediate good producers at price Ωt
• Job brokering agency needs to post vacancy to hire c(Vt ) = κVt → search is not directed
• The agency receives payment from firms Ωt zj and pays workers wj,t
• ... with the value of worker
Jj,t = Ωt zj − wj,t zj + I{jj̄−1}Et
h
πt+1
Rt+1
ωj (1 − ρj )Jj+1,t+1
i
(6)
11 / 40

20. Labor supply
• Labor services in period t
ℓt =
X
ι∈{y,p,e}
ℓι,t
σL−1
σL
σL
σL−1
(7)
where
ℓy,t =
P
j=1,...,10
ℓj,t → young,
ℓp,t =
P
j=11,...,35
ℓj,t →prime-age,
and ℓe,t =
P
j=36,...,J̄−1
ℓj,t → elderly.
• Effective labor supply per capita of cohort j in period t is
ℓj,t =
zj
Nj,t
Nt
(8)
12 / 40

21. Wages
Wages are determined in Nash bargaining with wage norm
wj,t = (1 − ζw ) wnorm
j,t + ζw wj,t−1 with wnorm
j,t = argmax J1−η
j,t (Wj,t − Υj,t )η
13 / 40

22. 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
14 / 40

23. Calibration

24. 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.
15 / 40

25. Calibration EZ: Labor market
Table 1: Target statistics in the data and the model for EU
variable 1990s 2010s description
model data model data
uyoung 31.9% 31.8% 21.2% 21.1% unemployment rate for young (includes NEETs)
uprime age 8.0% 7.6% 8.5% 8.8% unemployment rate for prime age individuals
uelderly 6.9% 6.7% 6.7% 7.2% unemployment rate for elderly
utotal 14.14% 14.35% 11.9% 12.1% total unemployment rate
syoung 24% 26% 34% 34% job finding rate for young
sprime age 39% 34% 36% 41% job finding rate for prime age individuals
selderly 23.5% 20% 27% 31% job finding rate for elderly
ϑ 0.18 - 0.22 0.13 market tightness
Note: the unemployment data for Europe includes NEETs.
16 / 40

26. Calibration US: Labor market
Table 2: Target statistics in the data and the model US
variable 1990s 2010s description
model data model data
uyoung 9.3% 9.1% 11.8% 11.5% unemployment rate for young (includes NEETs)
uprime age 4.8% 4.6% 4.8% 4.6% unemployment rate for prime age individuals
uelderly 4.3% 4.2% 4.0% 4.0% unemployment rate for elderly
utotal 6.3% 6.3% 6.3% 6.7% total unemployment rate
syoung 74% - 62% - job finding rate for young
sprime age 77% - 62% - job finding rate for prime age individuals
selderly 76% - 61% - job finding rate for elderly
ϑ 0.42 - 0.44 0.43 market tightness
17 / 40

27. Performance of our model
1990 1995 2000 2005 2010 2015 2020
7
8
9
10
11
12
13
14
15
16
17
Model
Data raw
Data hp
18 / 40

28. Results

29. Three sets of results
1. Trend effects of aging for unemployment (deterministic)
ut = ωy,t uy,t + ωp,t up,t + ωo,t uo,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)
19 / 40

30. Three sets of results
1. Trend effects of aging for unemployment (deterministic)
ut = ωy,t uy,t + ωp,t up,t + ωo,t uo,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)
19 / 40

31. Three sets of results
1. Trend effects of aging for unemployment (deterministic)
ut = ωy,t uy,t + ωp,t up,t + ωo,t uo,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)
19 / 40

32. Aging in EZ: unemployment ↓ by approx. 3pp.
Unemployment rate
1990 1995 2000 2005 2010 2015 2020
-6
-5
-4
-3
-2
-1
0
1
Labor market change
Composition effect
Behavioral effect
Demographic labor market change
Youth unemployment rate
1990 1995 2000 2005 2010 2015 2020
-14
-12
-10
-8
-6
-4
-2
0
2
Prime-age unemployment rate
1990 1995 2000 2005 2010 2015 2020
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
Elderly unemployment rate
1990 1995 2000 2005 2010 2015 2020
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
20 / 40

33. Aging in US: unemployment ≈
Unemployment rate
1990 2000 2010 2020
-1
-0.5
0
0.5
1
Labor market change
Composition effect
Behavioral effect
Demographic labor market change
Youth unemployment rate
1990 2000 2010 2020
-0.5
0
0.5
1
1.5
2
2.5
3
3.5
Prime-age unemployment rate
1990 2000 2010 2020
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
Elderly unemployment rate
1990 2000 2010 2020
-0.8
-0.6
-0.4
-0.2
0
0.2
21 / 40

34. IRFs of monetary policy shock with 1990 and 2020 population for the Euro zone
0 10 20 30 40
-0.1
-0.08
-0.06
-0.04
-0.02
0
Output
0 10 20 30 40
-0.08
-0.06
-0.04
-0.02
0
0.02
Inflation
0 10 20 30 40
-0.05
0
0.05
0.1
0.15
Interest rate
2020 population
1990 population
0 10 20 30 40
-0.15
-0.1
-0.05
0
Consumption
0 10 20 30 40
-2.5
-2
-1.5
-1
-0.5
10-4 Wages
0 10 20 30 40
-0.01
0
0.01
0.02
0.03
0.04
Unemployment rate
0 10 20 30 40
0
0.01
0.02
0.03
Youth unemployment rate
0 10 20 30 40
-0.01
0
0.01
0.02
0.03
0.04
Prime-age unemployment rate
0 10 20 30 40
0
0.01
0.02
0.03
Elderly unemployment rate
22 / 40

35. Aging lowers costs of stabilizing inflation of OUTPUT volatility (EZ)
0 0.5 1 1.5 2 2.5 3 3.5
Standard deviation of GDP
0
0.5
1
1.5
2
2.5
3
3.5
Standard
deviation
of
inflation
1990 population
2020 population
23 / 40

36. Aging lowers costs of stabilizing inflation in terms of UNEMPLOYMENT volatility (EZ)
6 6.5 7 7.5 8 8.5 9 9.5
Standard deviation of unemployment rate
0
0.5
1
1.5
2
2.5
3
3.5
Standard
deviation
of
inflation
1990 population
2020 population
24 / 40

37. Aging lowers costs of stabilizing inflation in terms of UNEMPLOYMENT volatility
4 4.5 5 5.5 6 6.5
Standard deviation of youth unemployment
0
0.5
1
1.5
2
2.5
3
3.5
Standard
deviation
of
inflation
1990 population
2020 population
8 8.5 9 9.5 10 10.5 11 11.5 12
Standard deviation of prime-age unemployment
0
0.5
1
1.5
2
2.5
3
3.5
Standard
deviation
of
inflation
1990 population
2020 population
7.5 8 8.5 9 9.5 10 10.5 11
Standard deviation of elderly unemployment
0
0.5
1
1.5
2
2.5
3
3.5
Standard
deviation
of
inflation
1990 population
2020 population
25 / 40

38. Implications for optimal monetary policy
• Elderly more sensitive to inflation than young
• Both young and elderly more 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.
• ... weakens the response of unemployment to monetary policy shocks
• ... and raises 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: j.tyrowicz@grape.org.pl
28 / 40

42. Additional slides

43. Households
• Maximize expected lifetime utility with external habit formation
Uj,t = log(cj,t − ϱc̄j,t−1) + 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
29 / 40

44. Producers
• Final goods aggregated from differentiated intermediate products
ct + it + gt =
Z
yt (i)
1
µ di
µ
• Intermediate goods firms face Calvo-type price stickiness and produce
yt (i) = kt (i)α
ht (i)1−α
− Ψ
• Capital producers are subject to investment adjustment cost
(1 + νt+1)kt+1 = (1 − δ)kt +
1 − Sk
it
it−1
it
30 / 40

45. Job broker
• Job brokers sell labor services to intermediate good producers in the perfectly competitive market for the
price of Ωt .
• Labor services in period t are given by the following formula
ℓt =
X
ι∈{y,p,e}
ℓι,t
σL−1
σL
σL
σL−1
(9)
where ℓy,t =
P
j=1,...,10
ℓj,t denotes young, ℓp,t =
P
j=11,...,35
ℓj,t prime-age, and ℓe,t =
P
j=36,...,J̄−1
ℓj,t
elderly.
• and effective labor supply per capita of cohort j in period t is
ℓj,t =
zj
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
τt wj,t Lj,t (11)
• Monetary policy follows the Taylor rule
Rt
R̄
=
Rt
R̄
γR
πt
π̄
γπ yt
ȳ
γy
1−γR
(12)
32 / 40

47. Calibration EZ: parameters
Parameter Value Description
1990s 2010s
A. Households
β 0.9837 0.9837 Discount factor
ϱ 0.754
0.754
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 0.664
0.664
Calvo probability (prices)
ζπ 0.24 0.24 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 Inflation target
γR 0.41 0.41 interest rate smoothing
γπ 1.97 1.97 reaction to inflation
γy 0.42 0.42 reaction to GDP growth
γb 0.42 0.42 fiscal rule parameter
33 / 40

48. Calibration EZ: parameters cont’d
These parameters imply qj,t = Nrel
j,t σj,m
1
N rel
t
1−ϕj
ϑ
−ϕj
j,t and sj,t = σj,m( 1
N rel
t
)1−ϕj
ϑ
1−ϕj
j,t
Parameter Value Description
1990s 2010s
C. Labor market
κ 0.95 0.95 cost of posting the vacancy
Nfirst 0.57 0.74 number of employed young entering the market
ρyoung 0.07 0.067 separation rate for young
ρprime 0.0251 0.0295 separation rate for prime
ρold 0.0204 0.0192 separation rate for old
σyoung 0.52 0.67 scaling parameter in the matching function
σprime 0.56 0.55 scaling parameter in the matching function
σelderly 0.33 0.39 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
ζw 0.99 0.99 real wage rigidity
χ 0.5 0.5 unemployment benefit
34 / 40

49. Calibration US: parameters
Parameter Value Description
1990s 2010s
A. Households
β 0.9853 0.9853 Discount factor
ϱ 0.754
0.754
Habit persistence
B. Firms
δ 0.055 0.055 Capital depreciation rate
α 0.277 0.277 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)
ζπ 0.24 0.24 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 Inflation target
γR 0.41 0.41 interest rate smoothing
γπ 1.97 1.97 reaction to inflation
γy 0.42 0.42 reaction to GDP growth
γb 0.42 0.42 fiscal rule parameter
35 / 40

50. Calibration US: parameters cont’d
These parameters imply qj,t = Nrel
j,t σj,m
1
N rel
t
1−ϕj
ϑ
−ϕj
j,t and sj,t = σj,m( 1
N rel
t
)1−ϕj
ϑ
1−ϕj
j,t
Parameter Value Description
1990s 2010s
C. Labor market
κ 0.8 0.8 cost of posting the vacancy
Nfirst 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
ρold 0.0332 0.0246 separation rate for old
σyoung 1.12 0.99 scaling parameter in the matching function
σprime 0.98 0.77 scaling parameter in the matching function
σelderly 0.93 0.72 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
ζw 0.99 0.99 real wage rigidity
χ 0.41 0.41 unemployment benefit
36 / 40

51. Calibration: stochastic shocks
Table 3: Calibrated stochastic shocks
Parameter Value Description
A. Persistence
ρz 0.954
Productivity shock - autocorrelation
ρc 0.994
Preference shock - autocorrelation
B. Standard deviations
σz
p
1 + 0.952 + 0.954 + 0.956 · 0.007 Productivity shock - standard deviation
σc
p
1 + 0.992 + 0.994 + 0.996 · 0.013 Preference shock - standard deviation
σR
p
1 + 0.82 + 0.84 + 0.86 · 0.0013 Monetary shock - standard deviation
37 / 40

52. Calibration: macroeconomic variables of the Eurozone economy
variable
EZ US
description
model data model data
1990s 2010s 2010s 1990s 2010s 2010s
r 1.41% 0.8% 0.8% 2.59% 2.22% 2.24% real interest rate
bg
/y 53% 53% 53% 55% 55% 51% government debt to GDP ratio
i
y
23.5% 24% 24% 23% 24% 24% investment rate
k
y
1.9 1.96 1.97 3.44 3.59 3.54 capital to GDP ratio
38 / 40

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 1.73 2.02 0.56 1 0.56 0.95
consumption 1.45 2.00 0.90 0.74 0.81 0.93
inflation 1.12 1.12 0.51 −0.95 0.53 0.92
interest rate 1.67 1.34 0.35 −0.92 0.89 0.95
unemployment 10.65 7.95 −0.91 −0.84 0.72 0.98
in percentage points
unemployment young - 5.52 - −0.86 - 0.98
unemployment prime - 9.88 - −0.84 - 0.99
unemployment old - 9.23 - −0.83 - 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 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
(13)
Go back
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