We search for Pareto optimal transition path between pay-as-you-go pension system and privatised one.

1. In the search for the optimal path to establish a funded pension system
In the search for the optimal path to establish a funded
pension system
Joanna Tyrowicz
with Marcin Bielecki, Krzysztof Makarski, Marcin Waniek and Jan Woznica
National Bank of Poland
University of Warsaw
Warsaw School of Economics
Group for Research in Applied Economics
ISCEF 2016 – April 2016

2. In the search for the optimal path to establish a funded pension system
Motivation
Background
Reform: two (or more!) dimensions
The way pensions (or implicit debt) is computed: DB → DC
Privatizing: PAYG → F or no system at all
Plus: changing parameters such as retirement age, contribution rates,
eligibility rules, etc.
What is an optimal reform?
Hicks optimality: welfare gains exceed welfare loss (after discounting) ⇒
lump-sum redistribution authority
Pareto optimality: reform such that nobody looses
Why relevant?

3. In the search for the optimal path to establish a funded pension system
Motivation
Literature
Breyer (1989): transition from PAYG to FF system implies loss on at least
one cohort
Economy with no pension system can be achieved with Pareto optimal
paths
Kotlikoff (1996), Kotlikof et al (1999), Hirte and Weber (1997), Belan and
Pestieu (1999), Gy´arf´as and Marquardt (2001), McGrattan and Prescott
(2014)
Typically, adjustment in contribution rates or pensions to keep pension
system fiscally neutral
Economy with a pension system (FF)
???, Roberts (2013) needs endogenous growth and specific parametrizations

4. In the search for the optimal path to establish a funded pension system
Motivation
Our contribution
Pareto-improving privatization of social security
Politically feasible
Credible
Features
OLG model with no adjustments in contributions / pensions
realistic demographics
Start: DC PAYG
End: DC partially funded

5. In the search for the optimal path to establish a funded pension system
Motivation
1 Motivation
2 Model Setup
Production
Consumers
Pension system and the government
Optimal reform
3 Calibration
4 Results
Robustness
5 Conclusions

6. In the search for the optimal path to establish a funded pension system
Model Setup
Production
Production
Perfectly competitive representative firm
Standard Cobb-Douglas production function
Yt = Kα
t (zt Lt )1−α
Profit maximization implies
wt = z1−α
t (1 − α)Kα
t L−α
t
rt = αKα−1
t (zt Lt )1−α
− d

7. In the search for the optimal path to establish a funded pension system
Model Setup
Consumers
Consumers
”born” at age 20 (j = 1) and live up to 100 years (J = 80)
subject to time and cohort dependent survival probability π
choose labor supply l endogenously until exogenous retirement age ¯J
(forced to retire)

8. In the search for the optimal path to establish a funded pension system
Model Setup
Consumers
Consumers
”born” at age 20 (j = 1) and live up to 100 years (J = 80)
subject to time and cohort dependent survival probability π
choose labor supply l endogenously until exogenous retirement age ¯J
(forced to retire)
optimize remaining lifetime utility derived from leisure 1 − l
and consumption c
Uj,t =
J−j
s=0
βs πj+s,t+s
πj,t
u(cj+s,t+s , lj+s,t+s )
with
u(c, l) = cj,t (1 − lj,t )φ

9. In the search for the optimal path to establish a funded pension system
Model Setup
Consumers
Consumers’ choice
receive market clearing wage for labor
receive market clearing interest rate on private savings
receive pension income + unintentional bequests
pay taxes

10. In the search for the optimal path to establish a funded pension system
Model Setup
Consumers
Consumers’ choice
receive market clearing wage for labor
receive market clearing interest rate on private savings
receive pension income + unintentional bequests
pay taxes
Subject to the budget constraint
(1 + τc
t )cj,t + sj,t = (1 − τl
t )(1 − τs
t )wj,t lj,t ← labor income
+ (1 + (1 − τk
t )rt )sj−1,t−1 ← capital income
+ (1 − τl
t )bι
j,t ← pension income
+ beqj,t ← bequests

11. In the search for the optimal path to establish a funded pension system
Model Setup
Pension system and the government
Government
collects taxes on earnings, interest and consumption (sum up to T)
spends a fixed share of GDP on government consumption G
collects social security contributions and pays out pensions
of the NDC and FDC systems
subsidyt = τι
¯J−1
j=1
wj,t lj,t −
J
j= ¯J
pj,t Nj,t
services debt D and targets a fixed long-run debt/GDP ratio
Gt + subsidyt + rt Dt−1 = Tt + (Dt − Dt−1)

12. In the search for the optimal path to establish a funded pension system
Model Setup
Pension system and the government
Pension system
Initial steady state: defined contribution PAYG (NDC)
bNDC
¯J,t =
¯J−1
s=1 Πs
i=1(1 + rNDC
t− ¯J+i−1) τt− ¯J+s−1wt− ¯J+s−1ls,t− ¯J+s−1
J
s= ¯J πs,t
rNDC
= payroll growth

13. In the search for the optimal path to establish a funded pension system
Model Setup
Pension system and the government
Pension system
Initial steady state: defined contribution PAYG (NDC)
bNDC
¯J,t =
¯J−1
s=1 Πs
i=1(1 + rNDC
t− ¯J+i−1) τt− ¯J+s−1wt− ¯J+s−1ls,t− ¯J+s−1
J
s= ¯J πs,t
rNDC
= payroll growth
Final steady state: NDC + funded defined contribution (FDC)
bFDC
¯J,t =
¯J−1
s=1 Πs
i=1(1 + rFDC
t− ¯J+i−1) τFDC
t− ¯J+s−1wt− ¯J+s−1ls,t− ¯J+s−1
J
s= ¯J πs,t
with τ = τNDC
+ τFDC

14. In the search for the optimal path to establish a funded pension system
Model Setup
Pension system and the government
Pension system
Initial steady state: defined contribution PAYG (NDC)
bNDC
¯J,t =
¯J−1
s=1 Πs
i=1(1 + rNDC
t− ¯J+i−1) τt− ¯J+s−1wt− ¯J+s−1ls,t− ¯J+s−1
J
s= ¯J πs,t
rNDC
= payroll growth
Final steady state: NDC + funded defined contribution (FDC)
bFDC
¯J,t =
¯J−1
s=1 Πs
i=1(1 + rFDC
t− ¯J+i−1) τFDC
t− ¯J+s−1wt− ¯J+s−1ls,t− ¯J+s−1
J
s= ¯J πs,t
with τ = τNDC
+ τFDC
and rFDC
> rNDC

15. In the search for the optimal path to establish a funded pension system
Model Setup
Pension system and the government
Pension system
Initial steady state: defined contribution PAYG (NDC)
bNDC
¯J,t =
¯J−1
s=1 Πs
i=1(1 + rNDC
t− ¯J+i−1) τt− ¯J+s−1wt− ¯J+s−1ls,t− ¯J+s−1
J
s= ¯J πs,t
rNDC
= payroll growth
Final steady state: NDC + funded defined contribution (FDC)
bFDC
¯J,t =
¯J−1
s=1 Πs
i=1(1 + rFDC
t− ¯J+i−1) τFDC
t− ¯J+s−1wt− ¯J+s−1ls,t− ¯J+s−1
J
s= ¯J πs,t
with τ = τNDC
+ τFDC
and rFDC
> rNDC
and rFDC
is tax free

16. In the search for the optimal path to establish a funded pension system
Model Setup
Optimal reform
Forming the funded pillar
Policy instrument
Transition cohorts receive an indexation of pension in excess of rNDC
:
rNDC
t = rNDC
t + generosity(rFDC
t − rNDC
t )
Politically feasible (unlike LSRA)
Generosity: year specific or cohort specific
Year specific : easily enacted
Cohort specific : similar to the LSRA but not a lump-sum transfer
Policy instrument = algorithm for optimization

17. In the search for the optimal path to establish a funded pension system
Model Setup
Optimal reform
Algorithm
Search values of generosityt that :
maximizes the number of cohorts that benefited from the reform
minimize loss to the cohort which suffers most due to the reform, thus
reducing differences between welfare of transition cohorts
allow compensations for a limited time (180 periods)

18. In the search for the optimal path to establish a funded pension system
Model Setup
Optimal reform
Algorithm
Search values of generosityt that :
maximizes the number of cohorts that benefited from the reform
minimize loss to the cohort which suffers most due to the reform, thus
reducing differences between welfare of transition cohorts
allow compensations for a limited time (180 periods)
Computations
1 generate periodically constant paths
2 calculate welfare effects
3 genetic algorithm: take the best paths and combines them to test if any
combination results in beter outcomes
4 some slight randomization of combined paths improves efficiency of search
5 two approaches: pure generosity or generosity + τNDC
t

19. In the search for the optimal path to establish a funded pension system
Calibration
Calibration
Replicates micro- and macroeconomic features of the Polish economy
in 1999
Demographics based on projection by EU’s Economic Policy Committee
Working Group on Aging Populations and Sustainability

20. In the search for the optimal path to establish a funded pension system
Calibration
Demographics
Total population size (left) and Total Factor Productivity (right) projections
Source: AWG demographic forecast.

21. In the search for the optimal path to establish a funded pension system
Calibration
Calibrated parameters
Parameters
α capital share of income 0.33
d depreciation rate 0.05
β discounting factor 0.9735
φ preference for leisure 0.825
γg share of govt expenditure in GDP 20%
D/Y share of public debt to GDP 45%
τk
capital income tax 19%
τc
consumption tax 11%
τι
effective social security contribution 6.2%
Outcome values (initial steady state)
(dk)/y share of investment in GDP 21%
b/y share of pensions in GDP 5.0%
r interest rate 7.2%
labor force participation rate 56.9%
τl
labor income tax 17.4%

22. In the search for the optimal path to establish a funded pension system
Results
Year specific generosity

23. In the search for the optimal path to establish a funded pension system
Results
Year specific generosity
349 cohorts out of 399 benefit from reform

24. In the search for the optimal path to establish a funded pension system
Results
Cohort specific generosity

25. In the search for the optimal path to establish a funded pension system
Results
Cohort specific generosity
200 cohorts out of 399 benefit from reform, but losses small

26. In the search for the optimal path to establish a funded pension system
Results
Robustness
Robustness checks (year specific)

27. In the search for the optimal path to establish a funded pension system
Results
Robustness
Robustness checks (year specific)

28. In the search for the optimal path to establish a funded pension system
Results
Robustness
Robustness checks (cohort specific)

29. In the search for the optimal path to establish a funded pension system
Conclusions
Main findings
We seek Pareto-improving pension system reform

30. In the search for the optimal path to establish a funded pension system
Conclusions
Main findings
We seek Pareto-improving pension system reform
We propose a politically feasible instrument of redistribution
Compensation via higher indexation costs nothing (unlike debt)
Results prove robust to parametrization

31. In the search for the optimal path to establish a funded pension system
Conclusions
Main findings
We seek Pareto-improving pension system reform
We propose a politically feasible instrument of redistribution
Compensation via higher indexation costs nothing (unlike debt)
Results prove robust to parametrization
Still, no ful Pareto-optimality

32. In the search for the optimal path to establish a funded pension system
Conclusions
Thank you for your attention!