The Sooner The Better - The Welfare Effects of the Retirement Age Increase Under Various Pension Schemes
The Sooner The Better - The Welfare Effects of the RetirementAge Increase Under Various Pension Schemes
(with Marcin Bielecki, Jan Hagemejer and Joanna Tyrowicz)
Karolina GorausFaculty of Economics, University of Warsaw
ISCEF 201411 April 2014
The Sooner The Better - The Welfare Effects of the Retirement Age Increase Under Various Pension Schemes
Table of contents
1 Motivation and insights from literature
2 Model setup
3 Calibration
4 Baseline and reform scenarios
5 ResultsBasic scenarioRobustness checks
The Sooner The Better - The Welfare Effects of the Retirement Age Increase Under Various Pension Schemes
Motivation and insights from literature
Motivation
Current problems with pension systems:
increasing old-age dependency ratio
majority of pension systems fails to assure actuarial fairness
in most countries people tend to retire as early as legally allowed
Typical reform proposals
switching to individual accounts’ systems
raising the social security contributions per worker
introducing general fiscal contraction
increasing the retirement age!
The Sooner The Better - The Welfare Effects of the Retirement Age Increase Under Various Pension Schemes
Motivation and insights from literature
Literature review
Two streams of literature:
1 Answering the question about optimal retirement age (Gruber and Wise(2007), Galasso (2008), Heijdra and Romp (2009))
2 Comparing different pensions system reforms: increasing retirement agevs. cut in benefits/privatization of the system/... (Auerbach et al. (1989),Hviding and Marette (1998), Fehr (2000), Boersch-Supan and Ludwig(2010), Vogel et al. (2012))
Fehr(2000)
Macroeconomic effects of retirement age increase may depend on the existingrelation between contributions and benefits!
Remaining gaps in the literature
We increase retirement age...
how the macroeconomic effects differ between various pension systems?
what happens to the welfare of different generations?
The Sooner The Better - The Welfare Effects of the Retirement Age Increase Under Various Pension Schemes
Motivation and insights from literature
Goals and expectations
Goal
Analyse macroeconomic and welfare implications of retirement age increaseunder DB (defined benefit), NDC (notional defined contribution), and FDC(funded defined contribution) systems
Tool
OLG models with first steady states calibrated to result in the samereplacement rate (Auerbach and Kotlikoff, 1987)
Expectations
under DB: leisure ↓, taxes ↓, welfare?
under NDC: leisure ↓, pensions ↑, welfare?
under FDC: leisure ↓, pensions ↑, welfare?
What else makes the results less predictable? → Labor supply adjustments,general equilibrium effects...
The Sooner The Better - The Welfare Effects of the Retirement Age Increase Under Various Pension Schemes
Model setup
Model structure - consumer I
is ”born” at age J = 20 and lives up to J = 100
optimizes lifetime utility derived from leisure and consumption:
U0 =J∑
j=1
δj−1πj,t−1+juj(cj,t−1+j , lj,t−1+j) (1)
where δ is the time discounting factor and πj,t denotes the unconditionalprobability of a household of having survived from birth to age j at timeperiod t (accidental bequests are spreaded equally to all cohorts).
The instantaneous utility function takes the theGreenwood-Hercowitz-Huffman (GHH) form:
u (cj,t , lj,t) =1
1− θ
(cj,t − ψt
l1+ξj,t
1 + ξ
)1−θ
− 1
, (2)
The Sooner The Better - The Welfare Effects of the Retirement Age Increase Under Various Pension Schemes
Model setup
Model structure - consumer II
is paid a market clearing wage for labour supplied and receives marketclearing interest on private savings
is free to choose how much to work, but only until retirement age J̄(forced to retire)
The budget constraint of agent j in period t is given by:
(1 + τc,t)cj,t + sj,t + Υt = (1− τ ιj,t − τl,t)wj,t lj,t ← labor income (3)
+ (1 + rt(1− τk,t))sj,t−1 ← capital income
+ (1− τl,t)pj,t + bj,t ← pensions and bequests
The Sooner The Better - The Welfare Effects of the Retirement Age Increase Under Various Pension Schemes
Model setup
Model structure - producer
Firms solve the following problem:
max(Yt ,Kt ,Lt )
Yt − wtLt − (r kt + d)Kt (4)
s.t. Yt = Kαt (ztLt)
1−α
Standard firm optimization implies:
the average market wage wt = (1− α)Kαt (ztLt)
−α (there might beheterogeneity between cohorts if age-specific productivity is assumed)
interest rate r kt = αKα−1t (ztLt)
1−α − d , where d stands for depreciation
The Sooner The Better - The Welfare Effects of the Retirement Age Increase Under Various Pension Schemes
Model setup
Model structure - government
collects social security contributions and pays out pensions of DB andNDC system
subsidyt = τt · wtLt −J∑
j=J̄
pj,tπj,tNt−j (5)
collects taxes on earnings, interest and consumption + spends GDP fixed amountof money on unproductive (but necessary) stuff + servicing debt
Tt = τl,t
(wtLt +
J∑j=J̄
pj,tπj,tNt−j
)+(τc,tct + τk,t rtsj,t−1
) J∑j=1
πj,tNt−j (6)
Γt = Gt + (1 + rgt )Dt−1 − Dt + subsidyt (7)
wants to maintain long run debt/GDP ratio fixed
The Sooner The Better - The Welfare Effects of the Retirement Age Increase Under Various Pension Schemes
Calibration
Calibration of technology and preference parameters
Parameters ω – flat ω – Deaton (1997)
Technologyα capital share of income 0.31 0.31d depreciation rate 0.055 0.055
Preferencesδ discounting factor 0.99175 1.00693θ relative risk aversion 1 1ξ Frisch elasticity (inverse) 3.846 4.101ψ labour disutility 7.59 4.64
Target statisticsr interest rate 0.0625 0.0625
∆k/y investment rate 0.23 0.23
The Sooner The Better - The Welfare Effects of the Retirement Age Increase Under Various Pension Schemes
Calibration
AWG’s projection of productivity growth
The Sooner The Better - The Welfare Effects of the Retirement Age Increase Under Various Pension Schemes
Calibration
Calibration of tax rates and pension system parameters
Parameters ω – flat ω – Deaton (1997)
Taxes and governmentτ c consumption tax 0.11 0.11τ l labor income tax 0.11 0.11τ k capital income tax 0.19 0.19γG government spending / GDP 0.2 0.2Pension systemsρ exogenous replacement rate 0.25 0.15τ ι contribution rate 0.61 0.61
Target statisticsbudget deficit (as % of GDP) 0.03 0.03aggregate benefits (as % of GDP) 0.05 0.05subsidyDB (as % of GDP) 0.015 0.015
The Sooner The Better - The Welfare Effects of the Retirement Age Increase Under Various Pension Schemes
Baseline and reform scenarios
Pension systems
Defined Benefit → constructed by imposing a mandatory exogenouscontribution rate τ and an exogenous replacement rate ρ
pDBj,t =
{ρtwj−1,t−1, for j = J̄t
κDBt · pDB
j−1,t−1, for j > J̄t(8)
Defined Contribution → constructed by imposing a mandatory exogenouscontribution rate τ and actuarially fair individual accounts
Notional
pNDCj,t =
∑J̄t−1
i=1
[Πis=1(1+r It−i+s−1)
]τNDCJ̄t−i,t−i
wJ̄t−i,t−i lJ̄t−i,t−i∏Js=J̄t
πs,t, for j = J̄t
(1 + r It )pNDCj−1,t−1, for j > J̄t
(9)Funded
pFDCj,t =
∑J̄t−1
i=1
[Πis=1(1+rt−i+s−1)
]τFDCJ̄t−i,t−i
wJ̄t−i,t−i lJ̄t−i,t−i∏Js=J̄t
πs,t, for j = J̄t
(1 + rt)pFDCj−1,t−1, for j > J̄t
(10)
The Sooner The Better - The Welfare Effects of the Retirement Age Increase Under Various Pension Schemes
Baseline and reform scenarios
Reform of the systems
Three experiments:
1 DB with flat retirement age → DB with increasing retirement age
2 NDC with flat retirement age → NDC with increasing retirement age
3 FDC with flat retirement age → FDC with increasing retirement age
What is flat and what is increasing retirement age?
flat: 60 years old increasing:
The Sooner The Better - The Welfare Effects of the Retirement Age Increase Under Various Pension Schemes
Baseline and reform scenarios
Welfare analysis - like Nishiyama & Smetters (2007)
What happens within each experiment?
1 Run the no policy change scenario ⇒ baseline
2 Run the policy change scenario ⇒ reform
3 For each cohort compare utility, compensate the losers from the winners
4 If net effect positive ⇒ reform efficient
Basic scenario
demographic profile includes both decreasing mortality and fertility rates
flat age-productivity profile
Robustness checks
alternative demographic scenario (stable fertility)
alternative age-productivity pattern (Deaton, 1997)
The Sooner The Better - The Welfare Effects of the Retirement Age Increase Under Various Pension Schemes
Baseline and reform scenarios
Demographics: unconditional survival probability from birth to retirement
The Sooner The Better - The Welfare Effects of the Retirement Age Increase Under Various Pension Schemes
Baseline and reform scenarios
Demographic scenarios
Total 20-year-olds
The Sooner The Better - The Welfare Effects of the Retirement Age Increase Under Various Pension Schemes
Baseline and reform scenarios
Age-productivity profiles (Deaton, 1997)
The Sooner The Better - The Welfare Effects of the Retirement Age Increase Under Various Pension Schemes
Results
Basic scenario
Baseline levels
Labour supply Capital Interest rate
Subsidy (% of GDP) Benefits (% of GDP) Labour tax
The Sooner The Better - The Welfare Effects of the Retirement Age Increase Under Various Pension Schemes
Results
Basic scenario
Aggregate labour supply
The Sooner The Better - The Welfare Effects of the Retirement Age Increase Under Various Pension Schemes
Results
Basic scenario
Capital
The Sooner The Better - The Welfare Effects of the Retirement Age Increase Under Various Pension Schemes
Results
Basic scenario
Interest rate
The Sooner The Better - The Welfare Effects of the Retirement Age Increase Under Various Pension Schemes
Results
Basic scenario
Subsidy as % of GDP
The Sooner The Better - The Welfare Effects of the Retirement Age Increase Under Various Pension Schemes
Results
Basic scenario
Aggregate benefits as % of GDP
The Sooner The Better - The Welfare Effects of the Retirement Age Increase Under Various Pension Schemes
Results
Basic scenario
Labour tax
The Sooner The Better - The Welfare Effects of the Retirement Age Increase Under Various Pension Schemes
Results
Basic scenario
Welfare effects of the reform, in consumption equivalent terms
Consumption equivalent effect of the increase in retirement age under thebaseline assumptions on demographics and productivity is calculated at almost27% of lifetime consumption in the case of FDC and 21% and 18% for DB andNDC respectively.
DB NDC FDC
The Sooner The Better - The Welfare Effects of the Retirement Age Increase Under Various Pension Schemes
Results
Basic scenario
Effects of retirement age increase (relative to the baseline)
Labour supply Capital Interest rate(ratio) (ratio) (p.p. difference)
Subsidy as % of GDP Benefits as % of GDP Labour tax(p.p. difference) (p.p. difference) (p.p. difference)
The Sooner The Better - The Welfare Effects of the Retirement Age Increase Under Various Pension Schemes
Results
Basic scenario
Aggregate labour supply (ratio)
The Sooner The Better - The Welfare Effects of the Retirement Age Increase Under Various Pension Schemes
Results
Basic scenario
Capital (ratio)
The Sooner The Better - The Welfare Effects of the Retirement Age Increase Under Various Pension Schemes
Results
Basic scenario
Interest rate (p.p. difference)
The Sooner The Better - The Welfare Effects of the Retirement Age Increase Under Various Pension Schemes
Results
Basic scenario
Subsidy as % of GDP (p.p. difference)
The Sooner The Better - The Welfare Effects of the Retirement Age Increase Under Various Pension Schemes
Results
Basic scenario
Aggregate benefits as % of GDP (p.p. difference)
The Sooner The Better - The Welfare Effects of the Retirement Age Increase Under Various Pension Schemes
Results
Basic scenario
Labour tax (p.p. difference)
The Sooner The Better - The Welfare Effects of the Retirement Age Increase Under Various Pension Schemes
Results
Basic scenario
Labor supply effects of the reform - decomposition
Baseline Reform scenariooverall j < 60 j ≥ 60 TotalLFP LFP baseline=100 LFP baseline=100
DB 57.9% 58.1% 100.2% 58.1% 117.3%NDC 58.8% 58.2% 99.0% 58.2% 115.9%FDC 59.8% 58.9% 98.4% 58.9% 115.2%
The Sooner The Better - The Welfare Effects of the Retirement Age Increase Under Various Pension Schemes
Results
Robustness checks
Alternative scenarios
Table: Consumption equivalents as % of permanent consumption
Productivity Demographics DB NDC FDCFlat Baseline 19.9% 20.0% 24.7%Flat Stable fertility 20.0% 20.5% 25.2%
Deaton Baseline 33.5% 33.5% 36.4%Deaton Stable fertility 33.61% 33.8% 36.8%
The Sooner The Better - The Welfare Effects of the Retirement Age Increase Under Various Pension Schemes
Results
Robustness checks
Conclusions
extending the retirement age is universally welfare improving
this effect is strongly enhanced if productivity is increasing in age
agents adjust downwards the average labor supply, but theaggregated supply increases
lower savings imply decrease in per capita capital and output
The Sooner The Better - The Welfare Effects of the Retirement Age Increase Under Various Pension Schemes
Results
Robustness checks
Questions or suggestions?
Thank you!
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