This document summarizes a study that analyzes the macroeconomic and welfare effects of increasing the retirement age under different pension systems (defined benefit, notional defined contribution, and funded defined contribution). It finds that increasing the retirement age is universally welfare improving. Specifically, it leads to a decrease in average labor supply but an increase in aggregate labor supply. Capital and output per capita decrease due to lower savings. The positive welfare effects are enhanced when productivity increases with age.

1. Old vs young. Aging under different pension schemes.
Old vs young. Aging under different pension schemes.
(with Marcin Bielecki, Jan Hagemejer and Joanna Tyrowicz)
Karolina Goraus
PhD Candidate
Faculty of Economics
University of Warsaw
31 March 2013

2. Old vs young. Aging under different pension schemes.
Table of contents
1 Motivation and insights from literature
2 Model setup
3 Baseline and reform scenarios
4 Results
Basic scenario
Robustness checks

3. Old vs young. Aging under different 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!

4. Old vs young. Aging under different pension schemes.
Motivation and insights from literature
Literature review
Two streams of literature:
1 Answering the question about optimal retirement age
2 Comparing different pensions system reforms: increasing retirement age
vs. cut in benefits/privatization of the system/...
Fehr(2000)
Macroeconomic effects of retirement age increase may depend on the existing
relation 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?

5. Old vs young. Aging under different pension schemes.
Motivation and insights from literature
Goals and expectations
Goal
Analyse macroeconomic and welfare implications of retirement age increase
under 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 same
replacement rate
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...

6. Old vs young. Aging under different 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−1
πj,t−1+j uj (cj,t−1+j , lj,t−1+j ) (1)
where δ is the time discounting factor and πj,t denotes the unconditional
probability of a household of having survived from birth to age j at time
period t (accidental bequests are spreaded equally to all cohorts).
The instantaneous utility function takes the the
Greenwood-Hercowitz-Huffman (GHH) form:
u (cj,t , lj,t ) =
1
1 − θ

 cj,t − ψt
l1+ξ
j,t
1 + ξ
1−θ
− 1

 , (2)

7. Old vs young. Aging under different pension schemes.
Model setup
Model structure - consumer II
is paid a market clearing wage for labour supplied and receives market
clearing interest on private savings
is free to choose how much to work, but only until retirement age ¯J
(forced to retire)
The budget constraint of agent j in period t is given by:
(1 + τc,t )cj,t + sj,t + Υt = (1 − τι
j,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

8. Old vs young. Aging under different pension schemes.
Model setup
Model structure - producer
Firms solve the following problem:
max
(Yt ,Kt ,Lt )
Yt − wt Lt − (rk
t + d)Kt (4)
s.t. Yt = Kα
t (zt Lt )1−α
Standard firm optimization implies:
the average market wage wt = (1 − α) Kα
t (zt Lt )−α
(there might be
heterogeneity between cohorts if age-specific productivity is assumed)
interest rate rk
t = αKα−1
t (zt Lt )1−α
− d, where d stands for depreciation

9. Old vs young. Aging under different pension schemes.
Model setup
Model structure - government
collects social security contributions and pays out pensions of DB and
NDC system
subsidyt = τt · wt Lt −
J
j=¯J
pj,t πj,t Nt−j (5)
collects taxes on earnings, interest and consumption + spends GDP fixed amount
of money on unproductive (but necessary) stuff + servicing debt
Tt = τl,t wt Lt +
J
j=¯J
pj,t πj,t Nt−j + τc,t ct + τk,t rt sj,t−1
J
j=1
πj,t Nt−j (6)
Γt = Gt + (1 + rg
t )Dt−1 − Dt + subsidyt (7)
wants to maintain long run debt/GDP ratio fixed

10. Old vs young. Aging under different pension schemes.
Baseline and reform scenarios
Pension systems
Defined Benefit → constructed by imposing a mandatory exogenous
contribution rate τ and an exogenous replacement rate ρ
pDB
j,t =
ρt wj−1,t−1, for j = ¯Jt
κDB
t · pDB
j−1,t−1, for j > ¯Jt
(8)
Defined Contribution → constructed by imposing a mandatory exogenous
contribution rate τ and actuarially fair individual accounts
Notional
pNDC
j,t =



¯Jt −1
i=1
Πi
s=1(1+rI
t−i+s−1) τNDC
¯Jt −i,t−i
w¯Jt −i,t−i l¯Jt −i,t−i
J
s=¯Jt
πs,t
, for j = ¯Jt
(1 + rI
t )pNDC
j−1,t−1, for j > ¯Jt
(9)
Funded
pFDC
j,t =



¯Jt −1
i=1
Πi
s=1(1+rt−i+s−1) τFDC
¯Jt −i,t−i
w¯Jt −i,t−i l¯Jt −i,t−i
J
s=¯Jt
πs,t
, for j = ¯Jt
(1 + rt )pFDC
j−1,t−1, for j > ¯Jt
(10)

11. Old vs young. Aging under different 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:

12. Old vs young. Aging under different 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 projection
alternative age-productivity pattern

13. Old vs young. Aging under different pension schemes.
Results
Basic scenario
Baseline levels
Capital Aggregate labour supply Benefits
Subsidy as % of GDP Interest rate Labour tax

14. Old vs young. Aging under different pension schemes.
Results
Basic scenario
Effects of retirement age increase (relative to the baseline)
Capital Aggregate labour supply Benefits
(ratio) (ratio) (ratio)
Subsidy as % of GDP Interest rate Labour tax
(p.p. difference) (p.p. difference) (p.p. difference)

15. Old vs young. Aging under different pension schemes.
Results
Basic scenario
Welfare effects
Welfare effects: Consumption equivalent Table: Individual labor supply effects
Baseline Reform
DB 58.1% 58.0%
NDC 58.7% 58.2%
FDC 59.8% 58.8%

16. Old vs young. Aging under different pension schemes.
Results
Robustness checks
Alternative scenarios
Table: Consumption equivalents as % of permanent consumption
Productivity Demographics DB NDC FDC
Flat Baseline 20.5% 18.3% 26.8%
Flat Stable fertility 20.7% 18.8% 27.3%
Deaton Baseline 35.0% 29.5% 42.1%
Deaton Stable fertility 35.1% 29.9% 42.6%

17. Old vs young. Aging under different 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 the
aggregated supply increases
lower savings imply decrease in per capita capital and output

18. Old vs young. Aging under different pension schemes.
Results
Robustness checks
Questions or suggestions?
Thank you!