in the search for the optimal path to establish a funded pension system
TRANSCRIPT
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
In the search for the optimal path to establish a funded pension system
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?
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 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
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
In the search for the optimal path to establish a funded pension system
Motivation
1 Motivation
2 Model SetupProductionConsumersPension system and the governmentOptimal reform
3 Calibration
4 ResultsRobustness
5 Conclusions
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 = Kαt (ztLt)
1−α
Profit maximization implies
wt = z1−αt (1− α)Kα
t L−αt
rt = αKα−1t (ztLt)
1−α − d
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− 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
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− 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
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 + 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
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 + 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
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 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)
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)
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
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)
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
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)
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
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)
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
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(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
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, 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
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, 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
In the search for the optimal path to establish a funded pension system
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
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.
In the search for the optimal path to establish a funded pension system
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%
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
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
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
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
In the search for the optimal path to establish a funded pension system
Results
Robustness
Robustness checks (year specific)
In the search for the optimal path to establish a funded pension system
Results
Robustness
Robustness checks (year specific)
In the search for the optimal path to establish a funded pension system
Results
Robustness
Robustness checks (cohort specific)
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 redistributionCompensation via higher indexation costs nothing (unlike debt)Results prove robust to parametrization
Still, no ful Pareto-optimality
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 redistributionCompensation via higher indexation costs nothing (unlike debt)Results prove robust to parametrization
Still, no ful Pareto-optimality
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 redistributionCompensation via higher indexation costs nothing (unlike debt)Results prove robust to parametrization
Still, no ful Pareto-optimality
In the search for the optimal path to establish a funded pension system
Conclusions
Thank you for your attention!