inequality in an olg economy with heterogeneous cohorts and pension systems

Inequality in an OLG economy with heterogeneous cohorts and pension systems

Inequality in an OLG economywith heterogeneous cohorts and pension systems

(with help from Marcin Bielecki and Marcin Waniek)

Joanna Tyrowicz and Krzysztof Makarski

GRAPE|FAME & University of Warsaw & National Bank of Poland

Inequality and Fairness of Political Reforms, Mannheim, 2016


Motivation

Motivation

Wealth inequality increases due to:Demographic transitionPension reform: defined benefit → defined contribution

Effects for consumption inequality: unclear

Can policy instruments help?minimum pensions: ↑ pensions; ↓ labor supply incentivescontribution caps : obligatory savings replaced with private savings

Intuition insufficient


Motivation

Literature review

Distributional effects 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 affects mortality ratesHairault and Langot (2008, JEDC):McGrattan and Prescott (2013, NBER)Kindermann and Krueger (2014, NBER)


Motivation

Our approach

Question 1: distributional effects of a pension system reform

Question 2: are standard instruments effective 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

Effects 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

Effects of the contribution cap: negligible


Motivation

Outline


Model

Method

ModelDeterministicOLGex ante heterogeneity: endowments + preferences

Calibrate to Poland in 1999


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 πBelong 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 firm

Standard Cobb-Douglas production function

Yt = Kαt (ztLt)

1−α

Profit maximization implies

wt = zt(1− α)kαt

rt = αkα−1t − d

where d is the capital depreciation rateand k is capital per effective unit of labor


Model

Government

Spends a fixed share of GDP (g) on government consumption

Collects taxes T

Closes the gap between pension system contributions and benefits

Can take on debt D

Tt +Dt = (1 + rt)Dt−1 + gYt + subsidyt

We fix debt at constant 45% debt to GDP ratio.Consumption tax varies to satisfy the government constraint.


Model

Pension System

Pay As You Go Defined Benefit (PAYG DB)

bJ,k,t = ρ · gross wageJ−1,k,t−1

Pay As You Go Defined Contribution (PAYG DC)

bJ,k,t =accumulated sum of contributionsJ,k,t

expected remaining lifetimeJ,t

Pensions indexed by the rate of annual payroll growth


Model

Instrument 1: minimum pensions

Definitionbj,k,t ρmin · gross average waget

We set ρmin = 0.2 → 4% coverage (consistent with the data)

ExpectationsDirectly affects 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 1: contribution cap

Definition:

τ effj,k,t = min

τ,τcap · gross average waget

wtωklj,k,t

To replicate 2% coverage, τcap = 1.7 (lower than de iure 2.5)

ExpectationsAffects 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 differ


Model

Solution procedure

Gauss-Seidel iterative algorithmSteady states (initial and final)

1 Guess an initial value for k2 Use it to compute the prices3 Have households of each type and age solve their problem given prices4 Aggregate individual labor supply and savings to get new values

for L and K5 If the new value for k satisfies predefined norm, finish,

else update k and return to point (2)


Calibration


Calibration

Exogenous assumptions

Projections for Poland provided by the European Commission

Population Size TFP Growth

Kept constant across scenarios, don’t affect 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

Again: no data on mortality rates or wealth by income or education groups

Calibrate the central value of δ to match the investment rateSplit 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 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 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


Results

Minimum pensions coverage

0.2

.4.6

.81

2000 2050 2100 2150 2200 2250year

Defined Benefit with minimum pensionsDefined Contribution with minimum pensions


Results

Macroeconomic effects

No instrument Minimum pension Contribution capDB DC (to DB) DB DC DB DC

Capital 52.6% 60.4% 52.7% 60.3% 52.6% 60.5%Tax rate

initial 11.00 11.00 11.00 11.00 11.00 11.00final 15.44 10.95 15.43 11.99 15.46 10.95diff. (in pp) 4.44 - 0.05 4.43 0.99 4.46 - 0.05

Pension system deficitinitial 1.46 1.56 1.46final 3.95 0.00 4.02 0.87 3.97 0.00diff (in pp) 2.49 2.46 -0.69 2.51


Results

Consumption Gini


Results

Wealth Gini


Results

Wealth Gini at retirement I


Results

Wealth Gini at retirement II


Results

Inequality decomposition – endowments vs preferences

Instruments should reduce inequality stemming from endowments (luck)but not from preferencesTo isolate the effects of the two sources:

Shut down each channel separatelyKeep prices constant from the full model to avoid GE effectsSolve for decisions of households in partial equilibrium


Results

Consumption inequality decomposition - minimum pensions

DB DC


Results

Wealth inequality decomposition - minimum pensions

DB DC


Results

Wealth Gini at retirement

DB DC


Results

Welfare effects

Defined Benefit Defined Contribution


Results

Conclusions

Consumption inequality increase due toaging processesDB→DC reform

Minimum pensionseffective in reducing consumption inequality resulting from the DB→DCreform by 40-50%with 80% coverage minimum pension costs 1 pp higher consumption tax(transfer of about 0.9% GDP)wealth inequality increases

Contribution cap has virtually no effects


Results

Thank you for your attention!


Appendix

Household Sector Closed Form Solution I

For j < J (working):

cj,t =Ωj,t + Γj,t

(1 + τ ct )[∑J−j−1

s=0

((1 + φ) δs πj+s,t+s

πj,t

)+∑J−j

s=J−j

(δsπj+s,t+sπj,t

)]lj,t = 1− φ(1 + τ ct )cj,t

(1− τ lt )(1− τ)wt

sj,t = (1− τ lt )(1− τ)wtlj,t + (1 + (1− τkt )rt)sj−1,t−1 − (1 + τ ct )cj,t,

with

Ωj,t =J−j−1∑s=0

(1− τ lt+s)(1− τ)wt+s + beqj+s,t+s −Υt+s∏s

i=1(1 + (1− τkt+i)rt+i)

Γj,t =J−j∑s=J−j

(1− τ lt+s)bj+s,t+s + beqj+s,t+s −Υt+s∏s

i=1(1 + (1− τkt+i)rt+i).


Appendix

Household Sector Closed Form Solution II

For j J (retired):

cj,t =Γj,t

(1 + τ ct )[∑J−j

s=J−j

(δsπj+s,t+sπj,t

)]lj,t = 0

sj,t = (1− τ lt )bιj,t + (1 + (1− τkt )rt)sj−1,t−1 − (1 + τ ct )cj,t,

with

Γj,t =J−j∑s=0

(1− τ lt+s)bj+s,t+s + beqj+s,t+s −Υt+s∏s

i=1(1 + (1− τkt+i)rt+i).

inequality in an olg economy with heterogeneous cohorts and pension systems

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