Inequalities in an OLG economy with heterogeneity within cohorts and an obligatory pension systems

Motivation Model Calibration Results

Inequalities in an OLG economywith heterogeneous cohorts and pension systems

(with Joanna Tyrowicz, Krzysztof Makarski and Marcin Waniek)

Marcin Bielecki

Faculty of Economics, University of Warsaw

19th ICMAIF28-30 May 2015

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Outline

1 Motivation

2 Model

3 Calibration

4 Results

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Motivation

Domeij and Klein (2002, RED) find private savings for largefraction of Swedish population reduced to zero due to the pensionsystem, increasing wealth inequalitiesCastaneda et al. (2003, JPE) find necessary to model the pensionsystem to account for the US inequality distributionAging of the developed countries’ population induces thegovernments to either change the parameters of existing pensionsystems or switch from defined benefit to defined contributionsystems, which will likely increase inequality, see Hairault andLangot (2008, JEDC)Thus, it is important to know whether commonly used ‘tweaks’ –minimum pensions and contribution caps – are effective inreducing inequality

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Literature Review

There exists a large body of literature analyzing the distributionaleffects of pension systems in incomplete market economies:

Castaneda et al. (2003, JPE)Nishiyama and Smetters (2007, QJE)Fehr et al. (2008, RED)Hairault and Langot (2008, JEDC)Song (2011, RED)Bucciol (2011, MD)Cremer and Pestieau (2011, EER)Kumru and Thanopoulos (2011, JPubE)Fehr and Uhde (2014, EM)St-Amant and Garon (2014, ITPF)Kindermann and Krueger (2014, NBER)

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Our Approach

While the approach of ex ante homogeneous and ex postheterogeneous agents is useful (and maybe methodologically‘cleaner’), it necessarily confounds the effects of differences in‘luck’ (endowments) and in preferencesWe adopt a ‘microsimulation’ approach, in the vein of Gruber andWise (2004) and Bourguignon and Spadaro (2006, JEI)We allow individuals to vary in their ex ante productivity, similar toHenin and Weitzenblum (2005, JPEF) and McGrattan andPrescott (2013, NBER).We also vary individual preference parametersThus, we are able to distinguish whether pension system ‘tweaks’address inequalities due to endowments or due to preferences

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Methodology & Results Preview

We employ a deterministic heterogeneous agent OLG modelwith within cohort heterogeneityWe calibrate the model to match closely the Polish economyin 1999, as that was the year of the enacted pension system reform

We find that due to the changing demographic structure,inequalities increase along the demographic transitionUnder both systems the contribution cap has an insignificantimpact on welfare, macroeconomic variables, and inequalityMinimum pensions have an insignificant impact under the definedbenefit system but significant impact under the definedcontribution systemMinimum pensions alleviate inequalities from endowments, but notfrom preferences

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Households I

Are “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 which determines their productivity level ωand preference parameters δ and φChoose labor supply l endogenously until they reach exogenousretirement age J̄Maximize remaining lifetime utility derived from consumption cand leisure 1− 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

]]

Subject to the budget constraint (next slide)

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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

with the following kinds of taxation:consumption tax τ c

labor & pension income tax τ l

social security contribution τcapital income tax τk

There exists a closed-form solution to this problem

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Producers

Perfectly competitive representative firmStandard Cobb-Douglas production function

Yt = Kαt (ztLt)1−α,

where K is the aggregate capital stock, L is the aggregate laborsupply, and z denotes labor-augmenting exogenous technologicalprogressProfit maximization implies

wt = (1− α)Kαt zt(ztLt)−α

rt = αKα−1(ztLt)1−α − d

where d is the capital depreciation rate

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Government

Closes the gap between pension system contributions and benefitsSpends a fixed share of GDP on (useless) government consumptionCollects taxesCan take on debt

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

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Pension System

Pay As You Go Defined Benefit (PAYG DB)

bJ̄ ,k,t = ρ · wt−1ωklJ̄−1,k,t−1

Pay As You Go Defined Contribution (PAYG DC)

bJ̄ ,k,t = accumulated sum of contributionsexpected remaining lifetime

Under both system pensions are subsequently indexed by the rateof annual payroll growthMinimum pensions

bj,k,t ≥ ρmin · gross average wagetContribution cap

τ effj,k,t = τ ·min

{1, τcap · gross average waget

wtωklj,k,t

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Solution Procedure

Gauss-Seidel iterative algorithmSteady states (initial and final)

1 Guess an initial value for K/L2 Use it to compute the prices3 Have households solve their problem given prices4 Aggregate individual labor supply and savings to get new values forL and K

5 If the new value for K/L satisfies predefined norm, finish, elseupdate K/L and return to point (2)

Transition path1 Basing on the initial and final steady state values for K/L guess an

initial path between the terminal points2 The rest of the procedure is analogous

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Individual Productivity and Leisure Preference

Individual Productivity Leisure Preference

Based on Structure of Earnings Survey, 1998, Poland

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Within Cohort Heterogeneity

Parameter Central Value MultipliersProductivity ω 1 0.60

0.700.800.900.951.001.051.101.151.20

Consumption-leisure 0.5 0.50preference φ 1.00

1.502.00

Impatience δ 0.975 0.981.001.02

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Inequalities – Initial Steady State

Lifecycle wealth profilesDifferences in productivity Differences in preferences

02

46

0 20 40 60 80age

Lowest omega multiplierStandard omega multiplierHighest omega multiplier

−5

05

10

0 20 40 60 80age

Lowest delta multiplierHighest delta multiplierStandard multipliersLowest phi multiplierHighest phi multiplier

Consumption inequality 25.5, consistent with Brzezinski (2011)

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Inequalities – Transition Path, PAYG DB

Consumption Gini Wealth Gini

.26

.27

.28

.29

.3

2000 2050 2100 2150 2200year

No instrumentsMinimum benefitsContributions cap

.94

.96

.98

11.

02

2000 2050 2100 2150 2200year

No instrumentsMinimum benefitsContributions cap

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Inequalities – Transition Path, PAYG DC

Consumption Gini Wealth Gini

.24

.26

.28

.3

2000 2050 2100 2150 2200year

DB: No instrumentsDC: No instrumentsDC: Minimum benefitsDC: Contributions cap

.85

.9.9

51

1.05

2000 2050 2100 2150 2200year

DB: No instrumentsDC: No instrumentsDC: Minimum benefitsDC: Contributions cap

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Instruments Coverage

Contribution cap Minimum pension

0.0

1.0

2.0

3

2000 2050 2100 2150 2200 2250year

Defined Benefit with capDefined Contribution with cap

0.2

.4.6

.81

2000 2050 2100 2150 2200 2250year

Defined Benefit with minimum pensionsDefined Contribution with minimum pensions

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Welfare Effects

Defined benefit Defined contribution

−.0

004

−.0

002

0.0

002

Wei

ghte

d M

ean

Com

pens

atin

g V

aria

tion

2000 2050 2100 2150 2200 2250Year of birth

Minimum benefitsContributions cap

−.0

03−

.002

−.0

010

Wei

ghte

d M

ean

Com

pens

atin

g V

aria

tion

2000 2050 2100 2150 2200Year of birth

Minimum benefitsContributions cap

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Macroeconomic Effects

No instrument Minimum pension Contribution capDB DC DB DC DB DC

Capital 52.6% 60.4% 52.7% 60.3% 52.6% 60.5%Tax rate (τ c)

initial 11.00 11.00 11.00 11.00 11.00 11.00final 15.44 10.95 15.43 11.99 15.46 10.95

Pension system deficitinitial 1.46 1.56 1.46final 3.95 0.00 4.02 0.87 3.97 0.00

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Decomposing inequalities to endowments and preferences

Differing preferences Differing endowments

.05

.1.1

5.2

.25

.3

2000 2050 2100 2150 2200year

Fixed endowments, no instrumentsFixed endowments, minimum benefitsFixed endowments, contributions cap

.05

.1.1

5.2

.25

.3

2000 2050 2100 2150 2200year

Fixed preferences, no instrumentsFixed preferences, minimum benefitsFixed preferences, contributions cap

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Conclusions

Inequalities increase due to the aging processesContribution cap’s effects are negligibleMinimum pensions are effective in reducing consumptioninequalities resulting from the DB→DC reformProvision of the minimum pension guarantee covering the majorityof the populace costs about 1 pp higher VAT tax and requires atransfer of about 0.9% GDP (under DC)Due to the minimum pensions

Consumption inequalities decreaseWealth inequalities increase (Piketty?)Both aggregate welfare and macroeconomic effects are negligibleThe influence of inequality in endowments is moderated, theinfluence of inequality in preferences is unchanged

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Thank you for your attention

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Economy & Finance

Inequalities in an OLG economy with heterogeneity within cohorts and an obligatory pension systems