Inequalities in an OLG economy with heterogeneous cohorts and pension systems
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1) A pension system reform from defined benefit to defined contribution in Poland would likely increase consumption inequalities but decrease wealth inequalities. 2) The demographic transition alone would increase consumption inequalities more than the pension reform. 3) Minimum pensions could reduce the rise in consumption inequality from the pension reform by around 40% by targeting those with lower incomes, but would slightly increase consumption by reducing savings incentives. The effects of contribution caps would be negligible.
Inequalities in an OLG economy with heterogeneous cohorts and pension systems
- 1. Motivation Model Calibration Results Appendix Inequalities in an OLG economy with heterogeneous cohorts and pension systems (with Joanna Tyrowicz, Krzysztof Makarski and Marcin Waniek) Marcin Bielecki Faculty of Economics, University of Warsaw 4th NBP Summer Workshop 22-24 June 2015 1 / 33
- 2. Motivation Model Calibration Results Appendix Motivation Consumption inequality increases due to: Demographic transition Pension reform: defined benefit → defined contribution Effects for wealth inequality: unclear 2 / 33
- 3. Motivation Model Calibration Results Appendix Motivation Consumption inequality increases due to: Demographic transition Pension reform: defined benefit → defined contribution Effects for wealth inequality: unclear Can policy instruments help? minimum pensions: pensions ↑, labor supply incentives ↓ contribution caps: mandatory savings replaced with private Intuition insufficient – need quantitative answers 2 / 33
- 4. Motivation Model Calibration Results Appendix 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) 3 / 33
- 5. Motivation Model Calibration Results Appendix 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 (2014, NBER) Kindermann and Krueger (2014, NBER) 3 / 33
- 6. Motivation Model Calibration Results Appendix Our approach Question 1: distributional effects of a pension system reform Question 2: are standard instruments effective in reducing the increase in inequality 4 / 33
- 7. Motivation Model Calibration Results Appendix 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 isolate the role of each separately most countries: no data on mortality by education or income groups 4 / 33
- 8. Motivation Model Calibration Results Appendix Results preview DB→DC reform: consumption inequalities ↑, wealth inequalities ↓ 5 / 33
- 9. Motivation Model Calibration Results Appendix Results preview DB→DC reform: consumption inequalities ↑, wealth inequalities ↓ Demographic transition: consumption inequalities ↑ – effect larger than reform 5 / 33
- 10. Motivation Model Calibration Results Appendix Results preview DB→DC reform: consumption inequalities ↑, wealth inequalities ↓ Demographic transition: consumption inequalities ↑ – effect larger than reform Minimum pensions: reduce consumption inequality from the reform by approx. 40% work on the endowments margin, but not on preferences Effects of the contribution cap: unnoticeable 5 / 33
- 11. Motivation Model Calibration Results Appendix Method Model deterministic general equilibrium overlapping generations ex ante heterogeneity: endowments + preferences Calibrate to Poland in 1999 6 / 33
- 12. Motivation Model Calibration Results Appendix 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 until retirement 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 cφk j+s,k,t+s (1 − lj+s,k,t+s)1−φk 7 / 33
- 13. Motivation Model Calibration Results Appendix 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 8 / 33
- 14. Motivation Model Calibration Results Appendix 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 9 / 33
- 15. Motivation Model Calibration Results Appendix 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. 10 / 33
- 16. Motivation Model Calibration Results Appendix 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 11 / 33
- 17. Motivation Model Calibration Results Appendix Instrument 1: minimum pensions Definition bj,k,t ≥ ρmin · gross average waget We set ρmin = 0.2 → 4% coverage (consistent with the data) 12 / 33
- 18. Motivation Model Calibration Results Appendix Instrument 1: minimum pensions Definition bj,k,t ≥ ρmin · gross average waget We set ρmin = 0.2 → 4% coverage (consistent with the data) Expected effects Affects directly only the left tail of income distribution Increases lifetime incomes of targeted group: consumption inequality should decrease Lower incentives for private savings: possible increase in consumption Lower incentives to work: possible reduction in hours worked 12 / 33
- 19. Motivation Model Calibration Results Appendix Instrument 2: 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) 13 / 33
- 20. Motivation Model Calibration Results Appendix Instrument 2: 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) Expected effects Affects directly only the right tail of income distribution Lower contributions of targeted group: higher voluntary saving rates → wealth inequalities ↑, capital accumulation ↑ Matters because market interest rates and social security indexation differ 13 / 33
- 21. Motivation Model Calibration Results Appendix 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 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) Transition path 1 Basing on the initial and final steady state values for ˆk guess an initial path between the terminal points ... 14 / 33
- 22. Motivation Model Calibration Results Appendix Exogenous assumptions Projections for Poland provided by the European Commission Population Size TFP Growth 15 / 33
- 23. Motivation Model Calibration Results Appendix Exogenous assumptions Projections for Poland provided by the European Commission Population Size TFP Growth Kept constant across scenarios, don’t affect results 15 / 33
- 24. Motivation Model Calibration Results Appendix Within cohort heterogeneity: endowments Structure of Earnings Survey, 1998, Poland Productivity ω Resulting: 10 values for ω 16 / 33
- 25. Motivation Model Calibration Results Appendix Within cohort heterogeneity: leisure preference Structure of Earnings Survey, 1998, Poland Leisure Preference φ Resulting: 4 values for φ 17 / 33
- 26. Motivation Model Calibration Results Appendix 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 interest rate Split population ad hoc to 3 groups: discount factors are (0.98δ, δ, 1.02δ) 18 / 33
- 27. Motivation Model Calibration Results Appendix Within cohort heterogeneity: summary outcomes I Productivity values and leisure preference parameters matched to replicate data Discount factors differentiated ad hoc 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) 19 / 33
- 28. Motivation Model Calibration Results Appendix Within cohort heterogeneity: summary outcomes II 0246 0 20 40 60 80 age Lowest omega multiplier Standard omega multiplier Highest omega multiplier 20 / 33
- 29. Motivation Model Calibration Results Appendix 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 21 / 33
- 30. Motivation Model Calibration Results Appendix Minimum pensions coverage (demographic transition) 0.2.4.6.81 2000 2050 2100 2150 2200 2250 year Defined Benefit with minimum pensions Defined Contribution with minimum pensions 22 / 33
- 31. Motivation Model Calibration Results Appendix Consumption Gini .24.26.28.3 2000 2050 2100 2150 2200 year DB: No instruments DC: No instruments DC: Minimum benefits 23 / 33
- 32. Motivation Model Calibration Results Appendix Wealth Gini .85.9.9511.05 2000 2050 2100 2150 2200 year DB: No instruments DC: No instruments DC: Minimum benefits 24 / 33
- 33. Motivation Model Calibration Results Appendix Inequality decomposition – endowments vs preferences Clear arguments for reducing inequality stemming from endowments (luck), not so much 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 25 / 33
- 34. Motivation Model Calibration Results Appendix Consumption inequality decomposition Fixed endowments Fixed preferences Differing preferences Differing endowments .05.1.15.2.25.3 2000 2050 2100 2150 2200 year DB: Fixed endowments, no instruments DC: Fixed endowments, no instruments DC: Fixed endowments, minimum benefits .05.1.15.2.25.3 2000 2050 2100 2150 2200 year DB: Fixed preferences, no instruments DC: Fixed preferences, no instruments DC: Fixed preferences, minimum benefits 26 / 33
- 35. Motivation Model Calibration Results Appendix Wealth inequality decomposition Fixed endowments Fixed preferences Differing preferences Differing endowments 0.2.4.6.81 2000 2050 2100 2150 2200 year DB: Fixed endowments, no instruments DC: Fixed endowments, no instruments DC: Fixed endowments, minimum benefits 0.2.4.6 2000 2050 2100 2150 2200 year DB: Fixed preferences, no instruments DC: Fixed preferences, no instruments DC: Fixed preferences, minimum benefits 27 / 33
- 36. Motivation Model Calibration Results Appendix Macroeconomic effects No instrument Minimum pension Contribution cap DB DC DB DC DB DC Capital 52.6% 60.4% 52.7% 60.3% 52.6% 60.5% Consumption tax rate (τc ) 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 Pension system deficit initial 1.46 1.56 1.46 final 3.95 0.00 4.02 0.87 3.97 0.00 28 / 33
- 37. Motivation Model Calibration Results Appendix Welfare effects Defined Benefit Defined Contribution −.0004−.00020.0002 WeightedMeanCompensatingVariation 2000 2050 2100 2150 2200 2250 Year of birth Minimum benefits Contributions cap −.003−.002−.0010 WeightedMeanCompensatingVariation 2000 2050 2100 2150 2200 Year of birth Minimum benefits Contributions cap 29 / 33
- 38. Motivation Model Calibration Results Appendix Conclusions Consumption inequalities increase due to demographic transition DB → DC reform Minimum pensions effective in reducing consumption inequality resulting from the DB → DC reform by approx. 40% 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 30 / 33
- 39. Motivation Model Calibration Results Appendix Thank you for your attention 31 / 33
- 40. Motivation Model Calibration Results 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) . 32 / 33
- 41. Motivation Model Calibration Results 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) . 33 / 33