![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
(7)
Go back
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![Job brokers sell labor services to intermediate good producers at price Ωt
• Job brokering agency needs to post vacancy to hire c(Vt ) = κ
2
PJ̄−1
j=1
q2
j,t V 2
t → search is not directed
• The agency receives payment from firms Ωt zj and pays workers w̃j,t
• ... with the value of worker
Jj,t (w̃j,t ) = Ωι(j),t zj − w̃j,t zj
+ ωj (1 − ρj )I{jJ̄−1}Et [
πt+1
Rt+1
(θw Jj+1,t+1(
πt−1
πt
w̃j,t ) + (1 − θw )Jj+1,t+1(w̃j+1,t+1))] (13)
back
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Population aging DSGE OLG NK model Euro area
- 1. Population aging through the lens of DSGE-OLG-NK model: implications for unemployment and monetary policy in the Euro area Krzysztof Makarski1,3 Sylwia Radomska4,3 Joanna Tyrowicz2,3 1SGH Warsaw School of Economics 2University of Warsaw 3FAME|GRAPE 4Institute of Economics, Polish Academy of Sciences 21th International Conference on Pensions, Insurance, and Savings, May 2024 1 / 42
- 2. Motivation
- 3. Aging populations tend to have lower unemployment rate 2 / 42
- 4. 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 -0.33*** -0.20*** -0.34*** -0.32*** -0.18* (0.07) (0.05) (0.07) (0.06) (0.1) Observations 800 1389 800 1012 620 R2 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 3 / 42
- 5. 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. 4 / 42
- 6. In this paper we ask: how does aging affect labor market? Our tool: build a large scale NK OLG-DSGE model with: • search & matching frictions • and realistic population structure We look into: • long-term trends • decompose the role of demographics and changes in the labor market features • local stochastic properties & the conduct of monetary policy Preview of the results • Aging lowers unemployment levels. • Aging reduces the cost of stabilizing inflation in terms of unemployment volatility. • Model can account for many aspects => we welcome all the comments about which direction to go. 5 / 42
- 7. In this paper we ask: how does aging affect labor market? Our tool: build a large scale NK OLG-DSGE model with: • search & matching frictions • and realistic population structure We look into: • long-term trends • decompose the role of demographics and changes in the labor market features • local stochastic properties & the conduct of monetary policy Preview of the results • Aging lowers unemployment levels. • Aging reduces the cost of stabilizing inflation in terms of unemployment volatility. • Model can account for many aspects => we welcome all the comments about which direction to go. 5 / 42
- 8. In this paper we ask: how does aging affect labor market? Our tool: build a large scale NK OLG-DSGE model with: • search & matching frictions • and realistic population structure We look into: • long-term trends • decompose the role of demographics and changes in the labor market features • local stochastic properties & the conduct of monetary policy Preview of the results • Aging lowers unemployment levels. • Aging reduces the cost of stabilizing inflation in terms of unemployment volatility. • Model can account for many aspects => we welcome all the comments about which direction to go. 5 / 42
- 9. In this paper we ask: how does aging affect labor market? Our tool: build a large scale NK OLG-DSGE model with: • search & matching frictions • and realistic population structure We look into: • long-term trends • decompose the role of demographics and changes in the labor market features • local stochastic properties & the conduct of monetary policy Preview of the results • Aging lowers unemployment levels. • Aging reduces the cost of stabilizing inflation in terms of unemployment volatility. • Model can account for many aspects => we welcome all the comments about which direction to go. 5 / 42
- 10. Labor market flows in EZ: job finding rate (left) and separation rate (right) 6 / 42
- 11. Model
- 12. Model structure: overview A large scale DSGE-OLG NK model with search & matching frictions (Bielecki, Brzoza-Brzezina and Kolasa, 2022) • 80 cohorts of overlapping generations of households (age 20-99) • Age-specific asset structure: bonds and real assets • Age-specific labor dynamics • ... with nominal & real frictions... • sticky prices, investment adjustment costs see detailes • ... with labor market frictions... • two-state model (employed & unemployed) see detailes • search and matching frictions see detailes • wages set in staggered Nash bargaining (Gertler and Trigari, 2009) see detailes • job brokers see detailes • ... with fiscal and monetary policy... see detailes • realistic population structure and population growth. 7 / 42
- 13. Demographics and Population Structure • Agents live for J = 80 periods (corresponds to age 20 - 99) • Labor market participation until retirement age J̄ = 45 (corresponds to 65) • young workers aged 20-30 • prime-age workers 31-55 • elderly workers 56-64 • Population size Nt = PJ j=1 Nj,t ; νt = Nt Nt−1 − 1 • Utility function (with habit formation): Uj,t = 1 1 − σ eεc,t (cj,t − ϱc̄j,t−1)1−σ + βωj Uj+1,t+1 • The function captures habit persistence ϱ, risk aversion σ, preference shocks eεc,t , and mortality risk ωj 8 / 42
- 14. Household budget constraint Household budget constraint: cj,t + aj,t = (1 − τt )wj,t zj nj,t + χj,t uj,t + Ra j,t πt aj−1,t−1 − Tt + beqj,t • aj,t - total asset holdings (riskless bonds with Rb t + risky assets Rk t ) • Ra j,t - weighted return on household’s portfolio: Ra j,t = ωb j Rb t + (1 − ωb j )Rk t • Portfolio weights ωb j vary by age (Bielecki et al., 2022) • Unintended bequests beqj,t shared by agents with j < J̄ − 10 • Households expected income is a weighted share of earned labor income and unemployment benefit. 9 / 42
- 15. Labor supply • Labor services in period t ℓt = X ι∈{y,p,e} ℓι,t σL−1 σL σL σL−1 (1) 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 (2) 10 / 42
- 16. 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 11 / 42
- 17. Calibration
- 18. 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) • Life-cycle features calibrated from individual level data: • Age-specific productivity: HFCS and PSID • Age-specific labor market flows: EU LFS (findings and separations) • Age-specific asset holdings HFCS • The main calibration was made on the pre-covid data from 2015s. 12 / 42
- 19. Calibration: Labor market Table 1: Target statistics in the data and the model for EZ variable 1995s 2015s description model data model data uyoung 18% 18% 16.8% 16.8% unemployment rate for young uprime age 8.7% 8.7% 8.6% 8.7% unemployment rate for prime age individuals uelderly 8% 8% 7% 7% unemployment rate for elderly syoung 41% 41% 41% 40% job finding rate for young sprime age 35% 36% 38% 41% job finding rate for prime age individuals selderly 24% 24% 32% 32% job finding rate for elderly ϑ 0.1 - 0.1 0.1 labor market tightness Note: the unemployment data for Europe includes NEETs. 13 / 42
- 20. Performance of our model 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 0 2 4 6 8 10 12 model data - HP filtered data 14 / 42
- 21. Results
- 22. 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) 15 / 42
- 23. 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) 15 / 42
- 24. 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) 15 / 42
- 25. Aging in EZ: unemployment ↓ by approx. 3.5 pp. Unemployment rate 1995 2000 2005 2010 2015 -2 -1.5 -1 -0.5 0 0.5 1 Youth unemployment rate 1995 2000 2005 2010 2015 -4 -3 -2 -1 0 1 Prime-age unemployment rate 1995 2000 2005 2010 2015 -3 -2 -1 0 1 2 3 Elderly unemployment rate 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 16 / 42
- 26. IRFs of monetary policy shock with 1990 and 2020 population 0 10 20 30 40 -0.2 -0.15 -0.1 -0.05 0 Output 0 10 20 30 40 -0.1 -0.08 -0.06 -0.04 -0.02 0 Inflation 0 10 20 30 40 0 0.1 0.2 0.3 Interest rate 2015 population 1995 population 0 10 20 30 40 -0.3 -0.2 -0.1 0 Consumption 0 10 20 30 40 -2 -1.5 -1 -0.5 0 Vacancies 0 10 20 30 40 0 0.05 0.1 0.15 0.2 0.25 Unemployment rate 0 10 20 30 40 0 0.1 0.2 0.3 0.4 Youth unemployment rate 0 10 20 30 40 0 0.05 0.1 0.15 0.2 Prime-age unemployment rate 0 10 20 30 40 0 0.05 0.1 0.15 0.2 Elderly unemployment rate 17 / 42
- 27. Aging lowers costs of stabilizing inflation of OUTPUT volatility 0 0.5 1 1.5 2 2.5 3 3.5 4 Standard deviation of GDP 0 0.5 1 1.5 2 2.5 3 Standard deviation of inflation 1995 population 2015 population 18 / 42
- 28. Aging lowers costs of stabilizing inflation in terms of UNEMPLOYMENT volatility 2 4 6 8 10 12 14 16 Standard deviation of youth unemployment 0 0.5 1 1.5 2 2.5 3 Standard deviation of inflation 1995 population 2015 population 5.5 6 6.5 7 7.5 8 8.5 9 9.5 Standard deviation of prime-age unemployment 0 0.5 1 1.5 2 2.5 3 Standard deviation of inflation 1995 population 2015 population 6 6.5 7 7.5 8 8.5 9 9.5 Standard deviation of elderly unemployment 0 0.5 1 1.5 2 2.5 3 Standard deviation of inflation 1995 population 2015 population 19 / 42
- 29. 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 20 / 42
- 30. Conclusions
- 31. 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. 21 / 42
- 32. Thank you for your attention w: grape.org.pl t: grape_org f: grape.org e: [email protected] 22 / 42
- 34. 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) = eAt 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 23 / 42
- 35. 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 (3) 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 (4) 24 / 42
- 36. 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 + X j Nj,t Tt (5) • Monetary policy follows the Taylor rule Rt R̄ = Rt R̄ γR πt π̄ γπ yt ȳ γy 1−γR (6) 25 / 42
- 37. Calibration EZ: parameters Parameter Value Description 1995s 2015s A. Households β 0.982 0.982 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 0.754 0.754 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 π̄ 1.02 1.02 Steady state inflation γR 0.84 0.84 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 Ψ 0.85 1−0.85 0.85 1−0.85 capacity utilization costs ∗ Note: Parameters θ, ζπ, and γn are set to 0 in the deterministic simulations. 26 / 42
- 38. 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 1995s 2015s C. Labor market κ 13.3 15.4 cost of posting the vacancy Nfirst 0.71 0.73 number of employed young entering the market ρyoung 0.058 0.056 separation rate for the young ρprime 0.030 0.034 separation rate for the prime age ρelderly 0.020 0.022 separation rate for the elderly σyoung 0.89 0.93 scaling parameter in the matching function σprime 0.64 0.73 scaling parameter in the matching function σelderly 0.43 0.58 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 0.854 0.854 nominal wage stickiness χ 0.64 0.64 unemployment benefit σL 5 5 substitutability of workers γn 2 2 responsiveness of labor market entrants employment to GDP 27 / 42
- 39. Calibration: Stochastic shocks obtained in moment matching procedure for the EZ economy Table 2: Calibrated stochastic shocks Parameter Value Description A. Persistence ρA 0.999 Productivity shock - autocorrelation ρc 0.999 Preference shock - autocorrelation ρg 0.714 Gov. expenditure shock - autocorrelation B. Standard deviations σA 0.00093763 Productivity shock - standard deviation σc 0.22125 Preference shock - standard deviation σg 0.0013589 Gov. expenditure shock - standard deviation σR 0.00007336 Monetary shock - standard deviation 28 / 42
- 40. 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 29 / 42
- 41. 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 (7) Go back 30 / 42
- 42. Labor market: set up Two-state model: • Employed Wj,t (w̃j,t ) = zj w̃j,t + I{jJ̄−1}Et h πt+1 Rt+1 ωj ((1 − ρj )(θw Wj+1,t+1( πt−1 πt w̃j,t ) + (1 − θw )Wj+1,t+1(w̃j+1,t+1)) + ρj Υj+1,t+1) i (8) • or unemployed Υj,t = χt + I{jJ̄−1}Et h πt+1 Rt+1 ωj (sj,t Wj+1,t+1(wj+1,t+1) + (1 − sj,t )Υj+1,t+1) i (9) (I{jj̄−1} is an indicator for retired tomorrow) back 31 / 42
- 43. 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 (10) 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 (11) uj,t = 1 − nj,t + ρj nj,t (12) back 32 / 42
- 44. Monetary Policy Rule • Central bank sets nominal interest rate via Taylor rule: Rt R̄ = Rt−1 R̄ γR πt π̄ γπ yt ȳ γy 1−γR εR,t • Policy parameters: γR , γπ, γy back 33 / 42
- 45. Wage Setting: Nash Bargaining • Wages are determined in staggered Nash bargaining - are either re-optimzed or indexed to past inflation (Gertler and Trigari, 2009) wj,t = (1 − θw )w̃j,t + θw πt−1 πt wj,t−1 • Reflects wage rigidity and cohort-specific re-negotiation. back 34 / 42
- 46. Job brokers sell labor services to intermediate good producers at price Ωt • Job brokering agency needs to post vacancy to hire c(Vt ) = κ 2 PJ̄−1 j=1 q2 j,t V 2 t → search is not directed • The agency receives payment from firms Ωt zj and pays workers w̃j,t • ... with the value of worker Jj,t (w̃j,t ) = Ωι(j),t zj − w̃j,t zj + ωj (1 − ρj )I{jJ̄−1}Et [ πt+1 Rt+1 (θw Jj+1,t+1( πt−1 πt w̃j,t ) + (1 − θw )Jj+1,t+1(w̃j+1,t+1))] (13) back 35 / 42
- 47. Key Transmission Mechanisms • Composition effect: Fewer young workers ⇒ lower average unemployment. • Behavioral effect: Firms adjust vacancies ⇒ improved job finding for young. • Policy implication: Aging society ⇒ lower sacrifice ratio ⇒ more hawkish optimal monetary policy. 36 / 42
- 48. Overview of Firm Sector Structure • The model distinguishes three types of producers: • Final good producers (perfect competition) see detailes • Intermediate good producers (monopolistic competition) see detailes • Capital good producers (perfect competition) see detailes • This separation allows us to model price stickiness, markups, and investment frictions in a tractable way. back 37 / 42
- 49. Final Good Producers • Operate under perfect competition • Produce a homogeneous final good using a CES aggregator: yt = 1 υ Z υ 0 yt (i) 1 µ di µ • Demand function for each intermediate good: yt (i) = Pt (i) Pt µ 1−µ yt • Zero profits in steady state back 38 / 42
- 50. Intermediate Good Producers • Monopolistically competitive firms producing differentiated goods • Cobb-Douglas production: yt (i) = eAt (ks t (i))α ℓt (i)1−α − Φ • Price setting with Calvo rigidity: • Firms can reset prices with probability 1 − θ • Otherwise, prices indexed to past inflation (ζπ) • Profit: Pt (i) Pt yt (i) − Ωt ℓt (i) − rk,t ks t (i) back 39 / 42
- 51. Capital Good Producers • Operate in perfect competition • Transform final goods into capital, subject to adjustment costs: (1 + νt+1)kt+1 = (1 − δ)kt + 1 − Sk 2 it it−1 − 1 2 # it • Adjustment costs smooth investment responses to shocks back 40 / 42
- 52. Why This Structure? • Captures key macroeconomic mechanisms: • Price stickiness ⇒ non-neutral monetary policy • Investment frictions ⇒ realistic capital dynamics • Markups and firm heterogeneity in price setting • Ensures consistency with observed business cycle behavior 41 / 42
- 53. Our Contribution to the Literature Youth Unemployment and Age Heterogeneity • Youth unemployment exceeds overall unemployment and is more cyclical (e.g., Bloom et al. 1988; Bell Blanchflower, 2011) • Young workers face higher entry frictions and are imperfect substitutes for older cohorts Demographic Unemployment • Limited empirical work on demographic structure and unemployment (e.g., Aaronson et al., 2015; Fallick Foote, 2022) • Demographics as key driver of secular unemployment trends. Demographics Monetary Policy: • Demographic trends influence natural interest rate and monetary transmission (Bielecki et al., 2020, 2022) • Age-specific labor frictions affect macroeconomic policy trade-offs (Cheron et al., 2011, 2013; Hairault et al., 2019) 42 / 42