Jan Woźnica, Marcin Bielecki, Krzysztof Makarski and Joanna Tyrowicz Group for Research in APplied Economics (GRAPE) 15th International Pension Workshop Paris, May 2017

1. On the optimal introduction of a funded pension pillar
On the optimal introduction of a funded pension pillar
Jan Woznica
with Marcin Bielecki, Krzysztof Makarski and Joanna Tyrowicz
National Bank of Poland
University of Warsaw
Warsaw School of Economics
Group for Research in Applied Economics
ICPIS – May 2017

2. On the optimal introduction of a funded pension pillar
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. On the optimal introduction of a funded pension pillar
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. On the optimal introduction of a funded pension pillar
Motivation
Our contribution
Pareto-improving privatization of social security
Politically feasible
Credible

5. On the optimal introduction of a funded pension pillar
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
Compare different algorithms

6. On the optimal introduction of a funded pension pillar
Motivation
1 Motivation
2 Model Setup
Production
Consumers
Pension system and the government
Optimal reform
3 Calibration
4 Results
Robustness
5 Conclusions

7. On the optimal introduction of a funded pension pillar
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

8. On the optimal introduction of a funded pension pillar
Model Setup
Consumers
Consumers
”born” at age j = 1 and live up to J = 80
subject to time and cohort dependent survival probability π
choose labor supply l until retirement at ¯J

9. On the optimal introduction of a funded pension pillar
Model Setup
Consumers
Consumers
”born” at age j = 1 and live up to J = 80
subject to time and cohort dependent survival probability π
choose labor supply l until retirement at ¯J
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

10. On the optimal introduction of a funded pension pillar
Model Setup
Consumers
Consumers’ choice
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. On the optimal introduction of a funded pension pillar
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
τι
¯J−1
j=1
wj,t lj,t −
J
j= ¯J
pj,t Nj,t = subsidyt
services debt D and targets a fixed long-run debt/GDP ratio
Gt + subsidyt + rt Dt−1 = Tt + (Dt − Dt−1)

12. On the optimal introduction of a funded pension pillar
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. On the optimal introduction of a funded pension pillar
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. On the optimal introduction of a funded pension pillar
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. On the optimal introduction of a funded pension pillar
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. On the optimal introduction of a funded pension pillar
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 + ϕ(rFDC
t − rNDC
t )
ϕ > 0: premium on standard indexation
Policy instrument = algorithm for optimization

17. On the optimal introduction of a funded pension pillar
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 + ϕ(rFDC
t − rNDC
t )
ϕ > 0: premium on standard indexation
Policy instrument = algorithm for optimization
Politically feasible (unlike LSRA)

18. On the optimal introduction of a funded pension pillar
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 + ϕ(rFDC
t − rNDC
t )
ϕ > 0: premium on standard indexation
Policy instrument = algorithm for optimization
Politically feasible (unlike LSRA)
Year specific ϕ: easily enacted
Cohort specific ϕ: similar to the LSRA but not a lump-sum transfer

19. On the optimal introduction of a funded pension pillar
Model Setup
Optimal reform
Algorithm I: minimizer
minimax criterion
minimize the loss of the biggest loser
1 find most losing cohort (year)
2 adjust incrementally indexation
3 adjust τFDC
4 repeat until threshold is hit

20. On the optimal introduction of a funded pension pillar
Model Setup
Optimal reform
Algorithm II: genetic
criterion based on number of losing cohorts
starts by generating periodically constant paths of indexation and τFDC
1 find two best paths among already calculated
2 combine them with random mutation
3 if better, return to start
4 elsewise move to next paths

21. On the optimal introduction of a funded pension pillar
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

22. On the optimal introduction of a funded pension pillar
Calibration
Demographics
Total population size (left) and Total Factor Productivity (right) projections
Source: AWG demographic forecast.

23. On the optimal introduction of a funded pension pillar
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%

24. On the optimal introduction of a funded pension pillar
Results
Best found paths
results from 10 000 iterations for minimizer and 20 000 for genetic algorithm

25. On the optimal introduction of a funded pension pillar
Results
Genetic algorithm paths

26. On the optimal introduction of a funded pension pillar
Results
Minimizer paths

27. On the optimal introduction of a funded pension pillar
Results
Robustness
Robustness checks (minimizer, year specific)

28. On the optimal introduction of a funded pension pillar
Results
Robustness
Robustness checks (minimizer, cohort specific)

29. On the optimal introduction of a funded pension pillar
Results
Robustness
Robustness checks (genetic, year specific)

30. On the optimal introduction of a funded pension pillar
Results
Robustness
Robustness checks (genetic, cohort specific)

31. On the optimal introduction of a funded pension pillar
Conclusions
Main findings
We seek Pareto-improving pension system reform

32. On the optimal introduction of a funded pension pillar
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

33. On the optimal introduction of a funded pension pillar
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
Effectively Pareto-optimal transition found

34. On the optimal introduction of a funded pension pillar
Conclusions
Thank you for your attention!