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

In the search for the optimal path to establish a fundedpension system

Joanna Tyrowiczwith Marcin Bielecki, Krzysztof Makarski, Marcin Waniek and Jan Woznica

National Bank of PolandUniversity of Warsaw

Warsaw School of EconomicsGroup for Research in Applied Economics

ISCEF 2016 – April 2016


Motivation

Background

Reform: two (or more!) dimensionsThe way pensions (or implicit debt) is computed: DB → DCPrivatizing: PAYG → F or no system at allPlus: 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 authorityPareto optimality: reform such that nobody looses

Why relevant?


Motivation

Literature

Breyer (1989): transition from PAYG to FF system implies loss on at leastone cohort

Economy with no pension system can be achieved with Pareto optimalpaths

Kotlikoff (1996), Kotlikof et al (1999), Hirte and Weber (1997), Belan andPestieu (1999), Gyarfas and Marquardt (2001), McGrattan and Prescott(2014)Typically, adjustment in contribution rates or pensions to keep pensionsystem fiscally neutral

Economy with a pension system (FF)???, Roberts (2013) needs endogenous growth and specific parametrizations


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


Motivation

1 Motivation

2 Model SetupProductionConsumersPension system and the governmentOptimal reform

3 Calibration

4 ResultsRobustness

5 Conclusions


Model Setup

Production

Production

Perfectly competitive representative firm

Standard Cobb-Douglas production function

Yt = Kαt (ztLt)

1−α

Profit maximization implies

wt = z1−αt (1− α)Kα

t L−αt

rt = αKα−1t (ztLt)

1−α − d


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− land consumption c

Uj,t =

J−j∑s=0

[βs πj+s,t+s

πj,tu(cj+s,t+s , lj+s,t+s)

]with

u(c, l) = cj,t(1− lj,t)φ


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− land consumption c

Uj,t =

J−j∑s=0

[βs πj+s,t+s

πj,tu(cj+s,t+s , lj+s,t+s)

]with

u(c, l) = cj,t(1− lj,t)φ


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 + τ ct )cj,t + sj,t = (1− τ lt )(1− τ st )wj,t lj,t ← labor income

+ (1 + (1− τ kt )rt)sj−1,t−1 ← capital income

+ (1− τ lt )bιj,t ← pension income

+ beqj,t ← bequests


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 + τ ct )cj,t + sj,t = (1− τ lt )(1− τ st )wj,t lj,t ← labor income

+ (1 + (1− τ kt )rt)sj−1,t−1 ← capital income

+ (1− τ lt )bιj,t ← pension income

+ beqj,t ← bequests


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 pensionsof the NDC and FDC systems

subsidyt = τ ιJ−1∑j=1

wj,t lj,t −J∑

j=J

pj,tNj,t

services debt D and targets a fixed long-run debt/GDP ratio

Gt + subsidyt + rtDt−1 = Tt + (Dt − Dt−1)


Model Setup


Pension system

Initial steady state: defined contribution PAYG (NDC)

bNDCJ,t =

∑J−1s=1

[Πs

i=1(1 + rNDCt−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)

bFDCJ,t =

∑J−1s=1

[Πs

i=1(1 + rFDCt−J+i−1)

]τFDCt−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


Model Setup


Pension system


bNDCJ,t =

∑J−1s=1

[Πs



s=J πs,t



bFDCJ,t =

∑J−1s=1

[Πs



s=J πs,t

with τ = τNDC + τFDC

and rFDC > rNDC and rFDC is tax free


Model Setup


Pension system


bNDCJ,t =

∑J−1s=1

[Πs



s=J πs,t



bFDCJ,t =

∑J−1s=1

[Πs



s=J πs,t

with τ = τNDC + τFDC and rFDC > rNDC

and rFDC is tax free


Model Setup


Pension system


bNDCJ,t =

∑J−1s=1

[Πs



s=J πs,t



bFDCJ,t =

∑J−1s=1

[Πs



s=J πs,t

with τ = τNDC + τFDC and rFDC > rNDC and rFDC is tax free


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(rFDCt − 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


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, thusreducing 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 anycombination results in beter outcomes

4 some slight randomization of combined paths improves efficiency of search

5 two approaches: pure generosity or generosity + τNDCt


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, thusreducing 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 anycombination results in beter outcomes

4 some slight randomization of combined paths improves efficiency of search

5 two approaches: pure generosity or generosity + τNDCt


Calibration

Calibration

Replicates micro- and macroeconomic features of the Polish economyin 1999

Demographics based on projection by EU’s Economic Policy CommitteeWorking Group on Aging Populations and Sustainability


Calibration

Demographics

Total population size (left) and Total Factor Productivity (right) projections

Source: AWG demographic forecast.


Calibration

Calibrated parameters

Parametersα capital share of income 0.33d depreciation rate 0.05β discounting factor 0.9735φ preference for leisure 0.825γg share of govt expenditure in GDP 20%

D/Y share of public debt to GDP 45%τ k capital income tax 19%τ c consumption tax 11%τ ι 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%τ l labor income tax 17.4%


Results

Year specific generosity

349 cohorts out of 399 benefit from reform


Results

Year specific generosity

349 cohorts out of 399 benefit from reform


Results

Cohort specific generosity

200 cohorts out of 399 benefit from reform, but losses small


Results

Cohort specific generosity

200 cohorts out of 399 benefit from reform, but losses small


Results

Robustness

Robustness checks (year specific)


Results

Robustness

Robustness checks (year specific)


Results

Robustness

Robustness checks (cohort specific)


Conclusions

Main findings

We seek Pareto-improving pension system reform

We propose a politically feasible instrument of redistributionCompensation via higher indexation costs nothing (unlike debt)Results prove robust to parametrization

Still, no ful Pareto-optimality


Conclusions

Main findings





Conclusions

Main findings





Conclusions

Thank you for your attention!

Economy & Finance

In the search for the optimal path to establish a funded pension system