Inequality in an OLG economy with heterogeneous cohorts and pension systems
Inequality in an OLG economywith heterogeneous cohorts and pension systems
Marcin Bielecki, Krzysztof Makarski and Joanna Tyrowicz
FAME | GRAPE& University of Warsaw & National Bank of Poland
International Economic Association Meeting, Mexico, 2017
Inequality in an OLG economy with heterogeneous cohorts and pension systems
Motivation
Motivation
Wealth inequality increases due to:Demographic transitionPension reform: de�ned bene�t → de�ned contribution
E�ects for consumption inequality: unclear
Can policy instruments help?minimum pensions: ↑ pensions; ↓ labor supply incentivescontribution caps : obligatory savings replaced with private savings
Intuition insu�cient
Inequality in an OLG economy with heterogeneous cohorts and pension systems
Motivation
Motivation
Wealth inequality increases due to:Demographic transitionPension reform: de�ned bene�t → de�ned contribution
E�ects for consumption inequality: unclear
Can policy instruments help?minimum pensions: ↑ pensions; ↓ labor supply incentivescontribution caps : obligatory savings replaced with private savings
Intuition insu�cient
Inequality in an OLG economy with heterogeneous cohorts and pension systems
Motivation
Literature review
Distributional e�ects of pension systems: OLG models with ex postheterogeneity:
Castaneda et al. (2003, JPE); Fehr et al. (2008, RED); Song (2011, RED);Bucciol (2011, MD); Cremer and Pestieau (2011, EER); Kumru andThanopoulos (2011, JPubE); Fehr and Uhde (2014, EM); St-Amant andGaron (2014, ITPF)
Ex ante + ex post heterogeneity: education a�ects mortality ratesHairault and Langot (2008, JEDC):McGrattan and Prescott (2013, NBER)Kindermann and Krueger (2014, NBER)
Inequality in an OLG economy with heterogeneous cohorts and pension systems
Motivation
Literature review
Distributional e�ects of pension systems: OLG models with ex postheterogeneity:
Castaneda et al. (2003, JPE); Fehr et al. (2008, RED); Song (2011, RED);Bucciol (2011, MD); Cremer and Pestieau (2011, EER); Kumru andThanopoulos (2011, JPubE); Fehr and Uhde (2014, EM); St-Amant andGaron (2014, ITPF)
Ex ante + ex post heterogeneity: education a�ects mortality ratesHairault and Langot (2008, JEDC):McGrattan and Prescott (2013, NBER)Kindermann and Krueger (2014, NBER)
Inequality in an OLG economy with heterogeneous cohorts and pension systems
Motivation
Our approach
Question 1: distributional e�ects of a pension system reform
Question 2: are standard instruments e�ective in reducing the increase ininequality
Ex ante heterogeneous agents: age + within cohort
endowments + preferences ← not a stand
separate endowments from preferences
most countries: no data on mortality by education / income groups
Inequality in an OLG economy with heterogeneous cohorts and pension systems
Motivation
Our approach
Question 1: distributional e�ects of a pension system reform
Question 2: are standard instruments e�ective in reducing the increase ininequality
Ex ante heterogeneous agents: age + within cohort
endowments + preferences ← not a stand
separate endowments from preferences
most countries: no data on mortality by education / income groups
Inequality in an OLG economy with heterogeneous cohorts and pension systems
Motivation
Results preview
DB → DC reform: both wealth and consumption inequalities ↑
Demographic transition → inequalities ↑, more than due to reform
Minimum pensions:reduce inequality from the reform by 40-50%work on the endowments margin, but not on preferences
E�ects of the contribution cap: negligible
Inequality in an OLG economy with heterogeneous cohorts and pension systems
Motivation
Results preview
DB → DC reform: both wealth and consumption inequalities ↑Demographic transition → inequalities ↑, more than due to reform
Minimum pensions:reduce inequality from the reform by 40-50%work on the endowments margin, but not on preferences
E�ects of the contribution cap: negligible
Inequality in an OLG economy with heterogeneous cohorts and pension systems
Motivation
Results preview
DB → DC reform: both wealth and consumption inequalities ↑Demographic transition → inequalities ↑, more than due to reform
Minimum pensions:reduce inequality from the reform by 40-50%work on the endowments margin, but not on preferences
E�ects of the contribution cap: negligible
Inequality in an OLG economy with heterogeneous cohorts and pension systems
Motivation
Outline
1 Motivation
2 Model
3 Calibration
4 Results
Inequality in an OLG economy with heterogeneous cohorts and pension systems
Model
Method
ModelDeterministicOLGex ante heterogeneity: endowments + preferences
Calibrate to Poland in 1999
Solved by Gauss-Seidel algorithm (iterative convergence on a problem withclosed form solution)
Inequality in an OLG economy with heterogeneous cohorts and pension systems
Model
Method
ModelDeterministicOLGex ante heterogeneity: endowments + preferences
Calibrate to Poland in 1999
Solved by Gauss-Seidel algorithm (iterative convergence on a problem withclosed form solution)
Inequality in an OLG economy with heterogeneous cohorts and pension systems
Model
Method
ModelDeterministicOLGex ante heterogeneity: endowments + preferences
Calibrate to Poland in 1999
Solved by Gauss-Seidel algorithm (iterative convergence on a problem withclosed form solution)
Inequality in an OLG economy with heterogeneous cohorts and pension systems
Model
Households I
�Born� at age 20 (j = 1) and live up to 100 years (J = 80)
Subject to time and cohort dependent survival probability π
Belong to a type k:productivity level ωtime discounting δrelative leisure preference φ
Choose labor supply l endogenously
Maximize remaining lifetime utility derived from consumption c and leisure1− l:
Uj,k,t =
J−j∑s=0
[δskπj+s,t+sπj,t
[cφkj+s,k,t+s (1− lj+s,k,t+s)1−φk
]]
Inequality in an OLG economy with heterogeneous cohorts and pension systems
Model
Households II
Subject to the budget constraint
(1 + τ ct )cj,k,t + sj,k,t = (1− τ lt )(1− τ)wtωklj,k,t ← labor income
+ (1 + (1− τkt )rt)sj−1,k,t−1 ← capital income
+ (1− τ lt )bj,k,t ← pension income
+ beqj,k,t ← bequests
−Υt ← lump-sum tax
There exists a closed-form solution to this problem
Inequality in an OLG economy with heterogeneous cohorts and pension systems
Model
Producers
Perfectly competitive representative �rm
Standard Cobb-Douglas production function
Yt = Kαt (ztLt)
1−α
Pro�t maximization implies
wt = zt(1− α)k̂αt
rt = αk̂α−1t − d
where d is the capital depreciation rateand k̂ is capital per e�ective unit of labor
Inequality in an OLG economy with heterogeneous cohorts and pension systems
Model
Government
Spends a �xed share of GDP (g) on government consumption
Collects taxes T
Closes the gap between pension system contributions and bene�ts
Can take on debt D
Tt +Dt = (1 + rt)Dt−1 + gYt + subsidyt
We �x debt at constant 45% debt to GDP ratio.Consumption tax varies to satisfy the government constraint.
Inequality in an OLG economy with heterogeneous cohorts and pension systems
Model
Pension System
Pay As You Go De�ned Bene�t (PAYG DB)
bJ̄,k,t = ρ · gross wageJ̄−1,k,t−1
Pay As You Go De�ned Contribution (PAYG DC)
bJ̄,k,t =accumulated sum of contributionsJ̄,k,t
expected remaining lifetimeJ̄,t
Pensions indexed by the rate of annual payroll growth
Inequality in an OLG economy with heterogeneous cohorts and pension systems
Model
Instrument 1: minimum pensions
De�nitionbj,k,t ≥ ρmin · gross average waget
We set ρmin = 0.2 → 4% coverage (consistent with the data)
ExpectationsDirectly a�ects only the left tail of income distributionIncreases lifetime incomes of targeted group → consumption inequalityshould decreaseLower incentives to work → possible reduction in hours workedLower incentives for private savings → possible increase in consumption
Inequality in an OLG economy with heterogeneous cohorts and pension systems
Model
Instrument 1: minimum pensions
De�nitionbj,k,t ≥ ρmin · gross average waget
We set ρmin = 0.2 → 4% coverage (consistent with the data)
ExpectationsDirectly a�ects only the left tail of income distributionIncreases lifetime incomes of targeted group → consumption inequalityshould decreaseLower incentives to work → possible reduction in hours workedLower incentives for private savings → possible increase in consumption
Inequality in an OLG economy with heterogeneous cohorts and pension systems
Model
Instrument 2: contribution cap
De�nition:
τ e�j,k,t = min
{τ,τcap · gross average waget
wtωklj,k,t
}To replicate 2% coverage, τcap = 1.7 (lower than de iure 2.5)
ExpectationsA�ects directly only the right tail of income distributionLower contributions of targeted group → higher voluntary saving rates →wealth inequalities ↑Matters because market interest rates and social security indexation di�er
Inequality in an OLG economy with heterogeneous cohorts and pension systems
Model
Instrument 2: contribution cap
De�nition:
τ e�j,k,t = min
{τ,τcap · gross average waget
wtωklj,k,t
}To replicate 2% coverage, τcap = 1.7 (lower than de iure 2.5)
ExpectationsA�ects directly only the right tail of income distributionLower contributions of targeted group → higher voluntary saving rates →wealth inequalities ↑Matters because market interest rates and social security indexation di�er
Inequality in an OLG economy with heterogeneous cohorts and pension systems
Calibration
1 Motivation
2 Model
3 Calibration
4 Results
Inequality in an OLG economy with heterogeneous cohorts and pension systems
Calibration
Exogenous assumptions
Projections for Poland provided by the European Commission
Population Size TFP Growth
Kept constant across scenarios, don't a�ect results
Inequality in an OLG economy with heterogeneous cohorts and pension systems
Calibration
Exogenous assumptions
Projections for Poland provided by the European Commission
Population Size TFP Growth
Kept constant across scenarios, don't a�ect results
Inequality in an OLG economy with heterogeneous cohorts and pension systems
Calibration
Within cohort heterogeneity - endowments
Structure of Earnings Survey, 1998, Poland
Productivity ω
Resulting: 10 values for ω
Inequality in an OLG economy with heterogeneous cohorts and pension systems
Calibration
Within cohort heterogeneity - leisure preference
Structure of Earnings Survey, 1998, Poland
Leisure Preference φ
Resulting: 4 values for φ
Inequality in an OLG economy with heterogeneous cohorts and pension systems
Calibration
Within cohort heterogeneity - time preference
No data on mortality rates or wealth by income or education groups
Calibrate the central value of δ to match the investment rate
Split population ad hoc to 3 groups:to match the wealth inequality Gini (HFCN)discount factors are (0.98δ, δ, 1.02δ)
Inequality in an OLG economy with heterogeneous cohorts and pension systems
Calibration
Within cohort heterogeneity � summary outcomes in initial SS � I
In total we have 120 types within each cohort
The resulting consumption Gini index in the initial steady state is 25.5,consistent with Brzezinski (2011)
Inequality in an OLG economy with heterogeneous cohorts and pension systems
Calibration
Within cohort heterogeneity � summary outcomes in initial SS � II
02
46
0 20 40 60 80age
Lowest omega multiplierStandard omega multiplierHighest omega multiplier
Inequality in an OLG economy with heterogeneous cohorts and pension systems
Calibration
Within cohort heterogeneity - summary outcomes III
−5
05
10
0 20 40 60 80age
Lowest delta multiplierHighest delta multiplierStandard multipliersLowest phi multiplierHighest phi multiplier
Inequality in an OLG economy with heterogeneous cohorts and pension systems
Results
1 Motivation
2 Model
3 Calibration
4 Results
Inequality in an OLG economy with heterogeneous cohorts and pension systems
Results
Minimum pensions coverage (longevity vs �xed retirement age)
0.2
.4.6
.81
2000 2050 2100 2150 2200 2250year
Defined Benefit with minimum pensionsDefined Contribution with minimum pensions
Inequality in an OLG economy with heterogeneous cohorts and pension systems
Results
Consumption Gini index
Inequality in an OLG economy with heterogeneous cohorts and pension systems
Results
Wealth Gini index
Inequality in an OLG economy with heterogeneous cohorts and pension systems
Results
Wealth Gini index at retirement I
Inequality in an OLG economy with heterogeneous cohorts and pension systems
Results
Wealth Gini index at retirement II
Inequality in an OLG economy with heterogeneous cohorts and pension systems
Results
Inequality decomposition � endowments vs preferences
Social justice: instruments should reduce inequality stemming fromendowments (luck) but not from preferences
To isolate the e�ects of the two sources:Shut down each channel separatelyKeep prices constant from the full model to avoid GE e�ectsSolve for decisions of households in partial equilibrium
Inequality in an OLG economy with heterogeneous cohorts and pension systems
Results
Consumption inequality decomposition - minimum pensions
DB DC
Inequality in an OLG economy with heterogeneous cohorts and pension systems
Results
Wealth inequality decomposition - minimum pensions
DB DC
Inequality in an OLG economy with heterogeneous cohorts and pension systems
Results
Wealth inequality decomposition - minimum pensions
DB DC
Inequality in an OLG economy with heterogeneous cohorts and pension systems
Results
Welfare e�ects minuscule
Inequality in an OLG economy with heterogeneous cohorts and pension systems
Results
Conclusions
Consumption inequality increase due toaging processesDB→DC reform
Minimum pensionse�ective in reducing consumption inequality resulting from the DB→DCreform by 40-50%with 80% coverage minimum pension costs appox 1 pp higher consumptiontax (transfer of about 0.9% GDP)wealth inequality increases
Contribution cap has virtually no e�ects
Inequality in an OLG economy with heterogeneous cohorts and pension systems
Results
Questions?
Thank you for your attention!
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