Inequality in an OLG economy with heterogeneous cohorts ...€¦ · Inequality in an OLG economy...

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


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


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)


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


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


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


Motivation

Outline

1 Motivation

2 Model

3 Calibration

4 Results


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)


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

]]


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


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


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.


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


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


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


Calibration

1 Motivation

2 Model

3 Calibration

4 Results


Calibration

Exogenous assumptions

Projections for Poland provided by the European Commission

Population Size TFP Growth

Kept constant across scenarios, don't a�ect results


Calibration

Within cohort heterogeneity - endowments

Structure of Earnings Survey, 1998, Poland

Productivity ω

Resulting: 10 values for ω


Calibration

Within cohort heterogeneity - leisure preference

Structure of Earnings Survey, 1998, Poland

Leisure Preference φ

Resulting: 4 values for φ


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)


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)


Calibration

Within cohort heterogeneity � summary outcomes in initial SS � II

02

46

0 20 40 60 80age

Lowest omega multiplierStandard omega multiplierHighest omega multiplier


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


Results

1 Motivation

2 Model

3 Calibration

4 Results


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


Results

Consumption Gini index


Results

Wealth Gini index


Results

Wealth Gini index at retirement I


Results

Wealth Gini index at retirement II


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


Results

Consumption inequality decomposition - minimum pensions

DB DC


Results

Wealth inequality decomposition - minimum pensions

DB DC


Results

Welfare e�ects minuscule


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


Results

Questions?

Thank you for your attention!

w: grape.org.plt: grape_orgf: grape.orge: [email protected]

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