Inequality in an OLG economy with heterogeneous cohorts and pension systems

Inequality in an OLG economy with heterogeneous cohorts and pension systems

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  Inequality in anOLG economy with heterogeneous cohorts and pension systems Inequality in an OLG economy with 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
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  Inequality in anOLG economy with heterogeneous cohorts and pension systems Motivation Motivation Wealth inequality increases due to: Demographic transition Pension reform: defined benefit → defined contribution Effects for consumption inequality: unclear
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  Inequality in anOLG economy with heterogeneous cohorts and pension systems Motivation Motivation Wealth inequality increases due to: Demographic transition Pension reform: defined benefit → defined contribution Effects for consumption inequality: unclear Can policy instruments help? minimum pensions: ↑ pensions; ↓ labor supply incentives contribution caps : obligatory savings replaced with private savings Intuition insufficient
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  Inequality in anOLG economy with heterogeneous cohorts and pension systems Motivation Literature review Distributional effects of pension systems: OLG models with ex post heterogeneity: Castaneda et al. (2003, JPE); Fehr et al. (2008, RED); 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)
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  Inequality in anOLG economy with heterogeneous cohorts and pension systems Motivation Literature review Distributional effects of pension systems: OLG models with ex post heterogeneity: Castaneda et al. (2003, JPE); Fehr et al. (2008, RED); 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) Ex ante + ex post heterogeneity: education affects mortality rates Hairault and Langot (2008, JEDC): McGrattan and Prescott (2013, NBER) Kindermann and Krueger (2014, NBER)
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  Inequality in anOLG economy with heterogeneous cohorts and pension systems Motivation Our approach Question 1: distributional effects of a pension system reform Question 2: are standard instruments effective in reducing the increase in inequality
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  Inequality in anOLG economy with heterogeneous cohorts and pension systems Motivation Our approach Question 1: distributional effects of a pension system reform Question 2: are standard instruments effective in reducing the increase in inequality 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
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  Inequality in anOLG economy with heterogeneous cohorts and pension systems Motivation Results preview DB → DC reform: both wealth and consumption inequalities ↑
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  Inequality in anOLG 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
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  Inequality in anOLG 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 Effects of the contribution cap: negligible
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  Inequality in anOLG economy with heterogeneous cohorts and pension systems Motivation Outline
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  Inequality in anOLG economy with heterogeneous cohorts and pension systems Model Method Model Deterministic OLG ex ante heterogeneity: endowments + preferences
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  Inequality in anOLG economy with heterogeneous cohorts and pension systems Model Method Model Deterministic OLG ex ante heterogeneity: endowments + preferences Calibrate to Poland in 1999
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  Inequality in anOLG 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 ω time discounting δ relative leisure preference φ Choose labor supply l endogenously Maximize remaining lifetime utility derived from consumption c and leisure 1 − l: Uj,k,t = J−j s=0 δs k πj+s,t+s πj,t c φk j+s,k,t+s (1 − lj+s,k,t+s)1−φk
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  Inequality in anOLG economy with heterogeneous cohorts and pension systems Model Households II Subject to the budget constraint (1 + τc t )cj,k,t + sj,k,t = (1 − τl t )(1 − τ)wtωklj,k,t ← labor income + (1 + (1 − τk t )rt)sj−1,k,t−1 ← capital income + (1 − τl t )bj,k,t ← pension income + beqj,k,t ← bequests − Υt ← lump-sum tax There exists a closed-form solution to this problem
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  Inequality in anOLG economy with heterogeneous cohorts and pension systems Model Producers Perfectly competitive representative firm Standard Cobb-Douglas production function Yt = Kα t (ztLt)1−α Profit maximization implies wt = zt(1 − α)ˆkα t rt = αˆkα−1 t − d where d is the capital depreciation rate and ˆk is capital per effective unit of labor
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  Inequality in anOLG economy with heterogeneous cohorts and pension systems 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.
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  Inequality in anOLG economy with heterogeneous cohorts and pension systems Model Pension System Pay As You Go Defined Benefit (PAYG DB) b ¯J,k,t = ρ · gross wage ¯J−1,k,t−1 Pay As You Go Defined Contribution (PAYG DC) b ¯J,k,t = accumulated sum of contributions ¯J,k,t expected remaining lifetime ¯J,t Pensions indexed by the rate of annual payroll growth
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  Inequality in anOLG economy with heterogeneous cohorts and pension systems Model Instrument 1: minimum pensions Definition bj,k,t ρmin · gross average waget We set ρmin = 0.2 → 4% coverage (consistent with the data)
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  Inequality in anOLG economy with heterogeneous cohorts and pension systems Model Instrument 1: minimum pensions Definition bj,k,t ρmin · gross average waget We set ρmin = 0.2 → 4% coverage (consistent with the data) Expectations Directly affects only the left tail of income distribution Increases lifetime incomes of targeted group → consumption inequality should decrease Lower incentives to work → possible reduction in hours worked Lower incentives for private savings → possible increase in consumption
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  Inequality in anOLG economy with heterogeneous cohorts and pension systems Model Instrument 1: contribution cap Definition: τeff 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)
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  Inequality in anOLG economy with heterogeneous cohorts and pension systems Model Instrument 1: contribution cap Definition: τeff 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) Expectations Affects directly only the right tail of income distribution Lower contributions of targeted group → higher voluntary saving rates → wealth inequalities ↑ Matters because market interest rates and social security indexation differ
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  Inequality in anOLG economy with heterogeneous cohorts and pension systems Model Solution procedure Gauss-Seidel iterative algorithm Steady states (initial and final) 1 Guess an initial value for ˆk 2 Use it to compute the prices 3 Have households of each type and age solve their problem given prices 4 Aggregate individual labor supply and savings to get new values for L and K 5 If the new value for ˆk satisfies predefined norm, finish, else update ˆk and return to point (2)
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  Inequality in anOLG economy with heterogeneous cohorts and pension systems Calibration
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  Inequality in anOLG economy with heterogeneous cohorts and pension systems Calibration Exogenous assumptions Projections for Poland provided by the European Commission Population Size TFP Growth
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  Inequality in anOLG 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 affect results
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  Inequality in anOLG 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
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  Inequality in anOLG 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
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  Inequality in anOLG economy with heterogeneous cohorts and pension systems 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 rate Split population ad hoc to 3 groups: to match the wealth inequality Gini (HFCN) discount factors are (0.98δ, δ, 1.02δ)
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  Inequality in anOLG economy with heterogeneous cohorts and pension systems 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)
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  Inequality in anOLG economy with heterogeneous cohorts and pension systems Calibration Within cohort heterogeneity - summary outcomes II 0246 0 20 40 60 80 age Lowest omega multiplier Standard omega multiplier Highest omega multiplier
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  Inequality in anOLG economy with heterogeneous cohorts and pension systems Calibration Within cohort heterogeneity - summary outcomes III −50510 0 20 40 60 80 age Lowest delta multiplier Highest delta multiplier Standard multipliers Lowest phi multiplier Highest phi multiplier
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  Inequality in anOLG economy with heterogeneous cohorts and pension systems Results
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  Inequality in anOLG economy with heterogeneous cohorts and pension systems Results Minimum pensions coverage 0.2.4.6.81 2000 2050 2100 2150 2200 2250 year Defined Benefit with minimum pensions Defined Contribution with minimum pensions
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  Inequality in anOLG economy with heterogeneous cohorts and pension systems Results Macroeconomic effects No instrument Minimum pension Contribution cap DB 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 11.00 final 15.44 10.95 15.43 11.99 15.46 10.95 diff. (in pp) 4.44 - 0.05 4.43 0.99 4.46 - 0.05 Pension system deficit initial 1.46 1.56 1.46 final 3.95 0.00 4.02 0.87 3.97 0.00 diff (in pp) 2.49 2.46 -0.69 2.51
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  Inequality in anOLG economy with heterogeneous cohorts and pension systems Results Consumption Gini
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  Inequality in anOLG economy with heterogeneous cohorts and pension systems Results Wealth Gini
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  Inequality in anOLG economy with heterogeneous cohorts and pension systems Results Wealth Gini at retirement I
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  Inequality in anOLG economy with heterogeneous cohorts and pension systems Results Wealth Gini at retirement II
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  Inequality in anOLG economy with heterogeneous cohorts and pension systems Results Inequality decomposition – endowments vs preferences Instruments should reduce inequality stemming from endowments (luck) but not from preferences To isolate the effects of the two sources: Shut down each channel separately Keep prices constant from the full model to avoid GE effects Solve for decisions of households in partial equilibrium
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  Inequality in anOLG economy with heterogeneous cohorts and pension systems Results Consumption inequality decomposition - minimum pensions DB DC
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  Inequality in anOLG economy with heterogeneous cohorts and pension systems Results Wealth inequality decomposition - minimum pensions DB DC
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  Inequality in anOLG economy with heterogeneous cohorts and pension systems Results Wealth inequality decomposition - minimum pensions DB DC
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  Inequality in anOLG economy with heterogeneous cohorts and pension systems Results Wealth Gini at retirement DB DC
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  Inequality in anOLG economy with heterogeneous cohorts and pension systems Results Welfare effects Defined Benefit Defined Contribution
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  Inequality in anOLG economy with heterogeneous cohorts and pension systems Results Conclusions Consumption inequality increase due to aging processes DB→DC reform Minimum pensions effective in reducing consumption inequality resulting from the DB→DC reform 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
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  Inequality in anOLG economy with heterogeneous cohorts and pension systems Results Thank you for your attention!
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  Inequality in anOLG economy with heterogeneous cohorts and pension systems Appendix Household Sector Closed Form Solution I For j < ¯J (working): cj,t = Ωj,t + Γj,t (1 + τc t ) ¯J−j−1 s=0 (1 + φ) δs πj+s,t+s πj,t + J−j s= ¯J−j δs πj+s,t+s πj,t lj,t = 1 − φ(1 + τc t )cj,t (1 − τl t )(1 − τ)wt sj,t = (1 − τl t )(1 − τ)wtlj,t + (1 + (1 − τk t )rt)sj−1,t−1 − (1 + τc t )cj,t, with Ωj,t = ¯J−j−1 s=0 (1 − τl t+s)(1 − τ)wt+s + beqj+s,t+s − Υt+s s i=1 (1 + (1 − τk t+i)rt+i) Γj,t = J−j s= ¯J−j (1 − τl t+s)bj+s,t+s + beqj+s,t+s − Υt+s s i=1 (1 + (1 − τk t+i)rt+i) .
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  Inequality in anOLG economy with heterogeneous cohorts and pension systems Appendix Household Sector Closed Form Solution II For j ¯J (retired): cj,t = Γj,t (1 + τc t ) J−j s= ¯J−j δs πj+s,t+s πj,t lj,t = 0 sj,t = (1 − τl t )bι j,t + (1 + (1 − τk t )rt)sj−1,t−1 − (1 + τc t )cj,t, with Γj,t = J−j s=0 (1 − τl t+s)bj+s,t+s + beqj+s,t+s − Υt+s s i=1 (1 + (1 − τk t+i)rt+i) .