Effciency versus insurance: The role for fiscal policy in social security privatization

1. Eﬃciency versus insurance: The role for ﬁscal policy in social security privatization Oliwia Komada (WSE and GRAPE) Krzysztof Makarski (NBP, WSE and GRAPE) Joanna Tyrowicz (GRAPE, IAAEU, UW and IZA) International Pension Workshop – Leiden – 2019 1 / 37

2. Motivation • Longevity hazards DB viability: deﬁcit ↑ 1.4% of GDP → reforms Feldstein, BEA, SSA 2 / 37

3. Motivation • Longevity hazards DB viability: deﬁcit ↑ 1.4% of GDP → reforms Feldstein, BEA, SSA • (Any) Reform of social security necessitates redistribution • between: from current generations to future ones • within: loss of insurance built in DB 2 / 37

4. Motivation • Longevity hazards DB viability: deficit ↑ 1.4% of GDP → reforms Feldstein, BEA, SSA • (Any) Reform of social security necessitates redistribution • between: from current generations to future ones • within: loss of insurance built in DB • Deterministic setup: horse-race between • efficiency (+) • fiscal cost of the transition period (–) 2 / 37

5. Motivation • Longevity hazards DB viability: deficit ↑ 1.4% of GDP → reforms Feldstein, BEA, SSA • (Any) Reform of social security necessitates redistribution • between: from current generations to future ones • within: loss of insurance built in DB • Deterministic setup: horse-race between • efficiency (+) • fiscal cost of the transition period (–) • Stochastic setup: insurance (–) Nishiyama & Smetters (2007, QJE) and subsequent literature 2 / 37

6. Motivation • Longevity hazards DB viability: deficit ↑ 1.4% of GDP → reforms Feldstein, BEA, SSA • (Any) Reform of social security necessitates redistribution • between: from current generations to future ones • within: loss of insurance built in DB • Deterministic setup: horse-race between • efficiency (+) • fiscal cost of the transition period (–) • Stochastic setup: insurance (–) Nishiyama & Smetters (2007, QJE) and subsequent literature 2 / 37

7. Motivation → contribution Fiscal policy around the pension reform matters: • counteracts / reinforces redistribution • aﬀects eﬃciency (scope of distortions) 3 / 37

8. Motivation → contribution Fiscal policy around the pension reform matters: • counteracts / reinforces redistribution • affects efficiency (scope of distortions) Literature “low profile” on fiscal policy (accompanying the reform) • compare variants of fiscal closures • introduce new fiscal closures 3 / 37

9. Literature diﬀers in terms of ﬁnancing the reform • Financing within pension system • contribution rates (20 papers) Kumru & Thanopoulos (2011, JPE), Bruce & Turnovsky (2013, JPE) • replacement rate (8 papers) Boersch-Supan et al. (2014, AER), Kitao (2014, RED) 4 / 37

10. Literature differs in terms of financing the reform • Financing within pension system • contribution rates (20 papers) Kumru & Thanopoulos (2011, JPE), Bruce & Turnovsky (2013, JPE) • replacement rate (8 papers) Boersch-Supan et al. (2014, AER), Kitao (2014, RED) • Financing via fiscal policy • labor tax (3 papers) Bouzahzah et al. (2002, JEDC) • consumption tax (10 papers) Nishiyama & Smetters (2007, QJE), Diaz-Gimenez & Diaz-Saavedra (2009, RED) • debt (5 papers ) Song, et al. (2015, AEJ) Lindbeck & Persson (2003, JEL) 4 / 37

11. Literature differs in terms of financing the reform • Financing within pension system • contribution rates (20 papers) Kumru & Thanopoulos (2011, JPE), Bruce & Turnovsky (2013, JPE) • replacement rate (8 papers) Boersch-Supan et al. (2014, AER), Kitao (2014, RED) • Financing via fiscal policy • labor tax (3 papers) Bouzahzah et al. (2002, JEDC) • consumption tax (10 papers) Nishiyama & Smetters (2007, QJE), Diaz-Gimenez & Diaz-Saavedra (2009, RED) • debt (5 papers ) Song, et al. (2015, AEJ) Lindbeck & Persson (2003, JEL) No comparisons across fiscal closures 4 / 37

12. What we do: focus on fiscal policy for a given reform • Scrutinize links between fiscal policy and pension system reform • Propose new ways of financing the pensions system reform • insurance → labor tax progression • efficiency → capital income gains tax • timing → smoothing reform cost with public debt 5 / 37

13. What we do: focus on fiscal policy for a given reform • Scrutinize links between fiscal policy and pension system reform • Propose new ways of financing the pensions system reform • insurance → labor tax progression • efficiency → capital income gains tax • timing → smoothing reform cost with public debt Findings: • Nishiyama & Smetters is NOT universal → welfare ↑ in stochastic setup • Labor tax progression mitigates insurance loss • Capital income gains tax boost efficiency 5 / 37

14. What we do: focus on fiscal policy for a given reform • Scrutinize links between fiscal policy and pension system reform • Propose new ways of financing the pensions system reform • insurance → labor tax progression • efficiency → capital income gains tax • timing → smoothing reform cost with public debt Findings: • Nishiyama & Smetters is NOT universal → welfare ↑ in stochastic setup • Labor tax progression mitigates insurance loss • Capital income gains tax boost efficiency • Welfare gains and political support only sometimes overlap • Public debt often “buys” political support 5 / 37

15. OLG model with income shocks, US Procedure Baseline: Redistributing PAYG DB system with aging → deﬁcit Reform: Non-redistributing DC, 50% funded 6 / 37

16. OLG model with income shocks, US Procedure Baseline: Redistributing PAYG DB system with aging → deficit Reform: Non-redistributing DC, 50% funded • 9 fiscal policies • 2 pension system adjustments: contribution or benefits • 7 fiscal closures: tax on labor (with/without debt adjustment), consumption (with/without debt adjustment), tax on capital income (with/without debt adjustment), progressive income tax 6 / 37

17. OLG model with income shocks, US Procedure Baseline: Redistributing PAYG DB system with aging → deficit Reform: Non-redistributing DC, 50% funded • 9 fiscal policies • 2 pension system adjustments: contribution or benefits • 7 fiscal closures: tax on labor (with/without debt adjustment), consumption (with/without debt adjustment), tax on capital income (with/without debt adjustment), progressive income tax • government may behave differently in baseline and reform → 81 combinations 6 / 37

18. OLG model with income shocks, US Procedure Baseline: Redistributing PAYG DB system with aging → deficit Reform: Non-redistributing DC, 50% funded • 9 fiscal policies • 2 pension system adjustments: contribution or benefits • 7 fiscal closures: tax on labor (with/without debt adjustment), consumption (with/without debt adjustment), tax on capital income (with/without debt adjustment), progressive income tax • government may behave differently in baseline and reform → 81 combinations • compare welfare effect and political support 6 / 37

19. OLG model with income shocks, US Procedure Baseline: Redistributing PAYG DB system with aging → deficit Reform: Non-redistributing DC, 50% funded • 9 fiscal policies • 2 pension system adjustments: contribution or benefits • 7 fiscal closures: tax on labor (with/without debt adjustment), consumption (with/without debt adjustment), tax on capital income (with/without debt adjustment), progressive income tax • government may behave differently in baseline and reform → 81 combinations • compare welfare effect and political support • decompose welfare change into insurance and efficiency 6 / 37

20. Model Consumers • uncertain lifetimes: live for 16 periods, with survival rate πj,t < 1 unintended bequest redistributed within a cohort 7 / 37

21. Model Consumers • uncertain lifetimes: live for 16 periods, with survival rate πj,t < 1 unintended bequest redistributed within a cohort • uninsurable earnings risk: endogenous labor supply + income shocks process that follows AR(1) approximated by Markov chain 7 / 37

22. Model Consumers • uncertain lifetimes: live for 16 periods, with survival rate πj,t < 1 unintended bequest redistributed within a cohort • uninsurable earnings risk: endogenous labor supply + income shocks process that follows AR(1) approximated by Markov chain • pay taxes (labor, consumption, capital gains) & contribute to pensions 7 / 37

23. Model Consumers • uncertain lifetimes: live for 16 periods, with survival rate πj,t < 1 unintended bequest redistributed within a cohort • uninsurable earnings risk: endogenous labor supply + income shocks process that follows AR(1) approximated by Markov chain • pay taxes (labor, consumption, capital gains) & contribute to pensions • no annuity ﬁnancial markets with (risk free) interest rate 7 / 37

24. Model Consumers • uncertain lifetimes: live for 16 periods, with survival rate πj,t < 1 unintended bequest redistributed within a cohort • uninsurable earnings risk: endogenous labor supply + income shocks process that follows AR(1) approximated by Markov chain • pay taxes (labor, consumption, capital gains) & contribute to pensions • no annuity ﬁnancial markets with (risk free) interest rate Competitive producers • Cobb-Douglas production function • capital depreciation rate d 7 / 37

25. Pension system Baseline scenario PAYG DB • equal beneﬁt for whole cohort (provides insurance) b ¯J,t = ρ · wavg,t 8 / 37

26. Pension system Baseline scenario PAYG DB • equal beneﬁt for whole cohort (provides insurance) b ¯J,t = ρ · wavg,t • indexed with payroll growth rate (GE labor ↑ ⇒ beneﬁts ↑) 8 / 37

27. Pension system Baseline scenario PAYG DB • equal benefit for whole cohort (provides insurance) b ¯J,t = ρ · wavg,t • indexed with payroll growth rate (GE labor ↑ ⇒ benefits ↑) • longevity ↑ creates deficit (no balancing mechanism in a system) 8 / 37

28. Pension system Baseline scenario PAYG DB • equal benefit for whole cohort (provides insurance) b ¯J,t = ρ · wavg,t • indexed with payroll growth rate (GE labor ↑ ⇒ benefits ↑) • longevity ↑ creates deficit (no balancing mechanism in a system) Reform scenario partially funded DC • contributions go into PAYG and funded pillar: τt = τI t + τII t 8 / 37

29. Pension system Baseline scenario PAYG DB • equal benefit for whole cohort (provides insurance) b ¯J,t = ρ · wavg,t • indexed with payroll growth rate (GE labor ↑ ⇒ benefits ↑) • longevity ↑ creates deficit (no balancing mechanism in a system) Reform scenario partially funded DC • contributions go into PAYG and funded pillar: τt = τI t + τII t • individual pension accounts indexed with payroll growth rate ⇒ insurance ↓ b ¯J,t = accrued ‘savings’ life expectancyt + accrued savings life expectancyt 8 / 37

30. Pension system Baseline scenario PAYG DB • equal benefit for whole cohort (provides insurance) b ¯J,t = ρ · wavg,t • indexed with payroll growth rate (GE labor ↑ ⇒ benefits ↑) • longevity ↑ creates deficit (no balancing mechanism in a system) Reform scenario partially funded DC • contributions go into PAYG and funded pillar: τt = τI t + τII t • individual pension accounts indexed with payroll growth rate ⇒ insurance ↓ b ¯J,t = accrued ‘savings’ life expectancyt + accrued savings life expectancyt • Reform generates a deficit in the pension system ⇒ need for fiscal closure. 8 / 37

31. Government • Collects taxes Tt = τl,t(1 − τt)wtLt + τk,trtAt + τc,tCt + Υt J j=1 Nj,t • Finances government spending Gt = gzt J j=1 Nj,t, • Balances pension system subsidyt • Services debt ∆Dt = Dt − Dt−1 Gt + subsidyt + rtDt = Tt + ∆Dt 9 / 37

32. Fiscal policy accompanying the reform • Three new closures details • progressive labor tax → labor supply • capital income gain tax (+ debt) → capital accumulation 10 / 37

33. Fiscal policy accompanying the reform • Three new closures details • progressive labor tax → labor supply • capital income gain tax (+ debt) → capital accumulation • Two closures within pension system details • contributions → labor supply • pensions ⇒→ consumption (of retirees) 10 / 37

34. Fiscal policy accompanying the reform • Three new closures details • progressive labor tax → labor supply • capital income gain tax (+ debt) → capital accumulation • Two closures within pension system details • contributions → labor supply • pensions ⇒→ consumption (of retirees) • Four closures outside pension system details • consumption tax (+ debt) → consumption • labor tax (+ debt) → labor supply 10 / 37

35. Fiscal policy accompanying the reform • Three new closures details • progressive labor tax → labor supply • capital income gain tax (+ debt) → capital accumulation • Two closures within pension system details • contributions → labor supply • pensions ⇒→ consumption (of retirees) • Four closures outside pension system details • consumption tax (+ debt) → consumption • labor tax (+ debt) → labor supply • In total: 9 closures (and a 81 combinations) 10 / 37

36. Calibration

37. Calibration to replicate US economy (2015) Preferences • Preference for leisure φ matches average hours 33% • Discounting rate δ matches interest rate 4% 11 / 37

38. Calibration to replicate US economy (2015) Preferences • Preference for leisure φ matches average hours 33% • Discounting rate δ matches interest rate 4% Idiosyncratic productivity shock based on Kruger and Ludwig (2013): • Persistence η = 0.95 • Variance ση = 0.375 11 / 37

39. Calibration to replicate US economy (2015) Preferences • Preference for leisure φ matches average hours 33% • Discounting rate δ matches interest rate 4% Idiosyncratic productivity shock based on Kruger and Ludwig (2013): • Persistence η = 0.95 • Variance ση = 0.375 Pension system • Replacement rate ρ matches beneﬁts as % of GDP 5.2% • Contribution rate balances pension system in the initial steady state • Pension eligibility age at 65 11 / 37

40. Calibration to replicate US economy (2015) Preferences • Preference for leisure φ matches average hours 33% • Discounting rate δ matches interest rate 4% Idiosyncratic productivity shock based on Kruger and Ludwig (2013): • Persistence η = 0.95 • Variance ση = 0.375 Pension system • Replacement rate ρ matches beneﬁts as % of GDP 5.2% • Contribution rate balances pension system in the initial steady state • Pension eligibility age at 65 Taxes {τc, τl, τk} match revenue as % of GDP {9.2%, 3.8%, 3.6%} Depreciation rate d matches investment rate of 25% 11 / 37

41. Calibration to replicate US economy (2015) Demography is based on UN projections. number of 20-year-olds mortality rates 12 / 37

42. Results

43. No reform: deficit ↑ Adjustment in pension parameters contribution rate ↑ from 7.8% to 9% tax on pensions ↑ from 0.0% to 17.3% Adjustment in fiscal parameters pension system deficit ↑ by 1pp of GDP 13 / 37

44. Funding the reform requires 2% of GDP (temporarily) capital labor Pension system deﬁcit temporary ↑ from 0% to 2% of GDP 14 / 37

45. Major effects of the reforming Pensions linked to contributions 1. reduced labor supply distortion (efficiency ↑) 2. income shocks carry over to retirement ( insurance ↓ ) Intuition: fiscal policy can reinforce or attenuate these effects 15 / 37

46. Major effects of the reforming Pensions linked to contributions 1. reduced labor supply distortion (efficiency ↑) 2. income shocks carry over to retirement ( insurance ↓ ) Intuition: fiscal policy can reinforce or attenuate these effects Eventually taxes decline (relative to baseline scenario of permanent pension system deficit) Intuition: long run effects are surely positive 15 / 37

47. Result 1: insurance is small & eﬃciency is large capital tax: the highest welfare gain due to eﬃciency progression: the smallest welfare loss due to insurance 16 / 37

48. Result 2: loss of insurance important but not decisive τk has larger gain than τc → positive overall welfare eﬀect 17 / 37

49. Result 3: public debt helps gaining political support Welfare eﬀect – τk 18 / 37

50. Result 3: public debt helps gaining political support Welfare eﬀect - τk & debt + τk 19 / 37

51. Result 3: public debt helps gaining political support Welfare eﬀect - transition - τk & debt + τk actual adjustments 20 / 37

52. Aggregate welfare eﬀects and political support Fiscal closure Baseline τk d + τk prog. τ τb τc d + τc τl d + τl Reform τk 0.57 0.56 1.01 0.59 0.50 0.65 0.65 0.65 0.66 d + τk 0.54 0.54 0.99 0.56 0.47 0.63 0.63 0.63 0.64 prog. -0.45 -0.45 0.02 -0.13 -0.07 -0.35 -0.35 -0.36 -0.34 τ -0.13 -0.12 0.35 0.09 0.14 -0.03 -0.02 -0.03 -0.01 τb -0.15 -0.14 0.33 0.07 0.13 -0.05 -0.04 -0.05 -0.03 τc -0.14 -0.14 0.33 0.11 0.17 -0.04 -0.03 -0.05 -0.03 d + τc -0.16 -0.16 0.31 0.09 0.15 -0.07 -0.06 -0.07 -0.05 τl -0.46 -0.46 0.01 -0.11 -0.03 -0.36 -0.35 -0.37 -0.35 d + τl -0.45 -0.45 0.01 -0.1 -0.02 -0.36 -0.35 -0.36 -0.35 % of consumption in the reform scenario which you are willing to give up to ensure that the reform take place, green cells refer suﬃcient to political support • τk is always a good idea 21 / 37

53. Aggregate welfare eﬀects and political support Fiscal closure Baseline τk d + τk prog. τ τb τc d + τc τl d + τl Reform τk 0.57 0.56 1.01 0.59 0.50 0.65 0.65 0.65 0.66 d + τk 0.54 0.54 0.99 0.56 0.47 0.63 0.63 0.63 0.64 prog. -0.45 -0.45 0.02 -0.13 -0.07 -0.35 -0.35 -0.36 -0.34 τ -0.13 -0.12 0.35 0.09 0.14 -0.03 -0.02 -0.03 -0.01 τb -0.15 -0.14 0.33 0.07 0.13 -0.05 -0.04 -0.05 -0.03 τc -0.14 -0.14 0.33 0.11 0.17 -0.04 -0.03 -0.05 -0.03 d + τc -0.16 -0.16 0.31 0.09 0.15 -0.07 -0.06 -0.07 -0.05 τl -0.46 -0.46 0.01 -0.11 -0.03 -0.36 -0.35 -0.37 -0.35 d + τl -0.45 -0.45 0.01 -0.1 -0.02 -0.36 -0.35 -0.36 -0.35 % of consumption in the reform scenario which you are willing to give up to ensure that the reform take place, green cells refer suﬃcient to political support • τk is always a good idea • prog. (almost) always better then τl in the reform 21 / 37

54. Aggregate welfare effects and political support Fiscal closure Baseline τk d + τk prog. τ τb τc d + τc τl d + τl Reform τk 0.57 0.56 1.01 0.59 0.50 0.65 0.65 0.65 0.66 d + τk 0.54 0.54 0.99 0.56 0.47 0.63 0.63 0.63 0.64 prog. -0.45 -0.45 0.02 -0.13 -0.07 -0.35 -0.35 -0.36 -0.34 τ -0.13 -0.12 0.35 0.09 0.14 -0.03 -0.02 -0.03 -0.01 τb -0.15 -0.14 0.33 0.07 0.13 -0.05 -0.04 -0.05 -0.03 τc -0.14 -0.14 0.33 0.11 0.17 -0.04 -0.03 -0.05 -0.03 d + τc -0.16 -0.16 0.31 0.09 0.15 -0.07 -0.06 -0.07 -0.05 τl -0.46 -0.46 0.01 -0.11 -0.03 -0.36 -0.35 -0.37 -0.35 d + τl -0.45 -0.45 0.01 -0.1 -0.02 -0.36 -0.35 -0.36 -0.35 % of consumption in the reform scenario which you are willing to give up to ensure that the reform take place, green cells refer sufficient to political support • τk is always a good idea • prog. (almost) always better then τl in the reform • little effect of debt on welfare 21 / 37

55. Aggregate welfare effects and political support Fiscal closure Baseline τk d + τk prog. τ τb τc d + τc τl d + τl Reform τk 0.57 0.56 1.01 0.59 0.50 0.65 0.65 0.65 0.66 d + τk 0.54 0.54 0.99 0.56 0.47 0.63 0.63 0.63 0.64 prog. -0.45 -0.45 0.02 -0.13 -0.07 -0.35 -0.35 -0.36 -0.34 τ -0.13 -0.12 0.35 0.09 0.14 -0.03 -0.02 -0.03 -0.01 τb -0.15 -0.14 0.33 0.07 0.13 -0.05 -0.04 -0.05 -0.03 τc -0.14 -0.14 0.33 0.11 0.17 -0.04 -0.03 -0.05 -0.03 d + τc -0.16 -0.16 0.31 0.09 0.15 -0.07 -0.06 -0.07 -0.05 τl -0.46 -0.46 0.01 -0.11 -0.03 -0.36 -0.35 -0.37 -0.35 d + τl -0.45 -0.45 0.01 -0.1 -0.02 -0.36 -0.35 -0.36 -0.35 % of consumption in the reform scenario which you are willing to give up to ensure that the reform take place, green cells refer sufficient to political support • τk is always a good idea • prog. (almost) always better then τl in the reform • little effect of debt on welfare • debt ’buys’ support (for good and bad reforms) 21 / 37

56. Conclusions The same reform gets different effects depending on fiscal policy • efficiency effects of fiscal policy can be big • insurance loss can be substituted and not very large 22 / 37

57. Conclusions The same reform gets different effects depending on fiscal policy • efficiency effects of fiscal policy can be big • insurance loss can be substituted and not very large Preferred policy options • Smoothing by debt buys political support • Taxes decline, so tax biggest efficiency driver (capital in our economy) 22 / 37

58. Conclusions The same reform gets different effects depending on fiscal policy • efficiency effects of fiscal policy can be big • insurance loss can be substituted and not very large Preferred policy options • Smoothing by debt buys political support • Taxes decline, so tax biggest efficiency driver (capital in our economy) Features of this literature • Labor response to reduced distortion enormous if people “understand” the link between contributions and pensions • Savings react greatly if people “understand” longevity and risk of old-age poverty 22 / 37

59. Thank you and I am happy to take questions! w: grape.org.pl t: grape org f: grape.org e: k.makarski@grape.org.pl 23 / 37

60. New fiscal closures: capital income gain tax GO BACK • capital income gain tax, τk,t Tt = τl,t(1 − τt)wtLt + τk,trtAt + τc,tCt + Υt J j=1 Nj,t Gt + subsidyt + rtDt = Tt + ∆Dt • smoothing tax adjustments with public debt • part of the costs of the reform shifted to the future generations • fiscal rule τk,t = (1 − )τfinal k + τk,t−1 + D Dt Yt − D Y final • debt in the final steady state the same as in the initial steady state

61. New ﬁscal closures: labor tax progression GO BACK • tr1 the lowest income threshold • trn is the highest income threshold • n is the number of income brackets • m is a tax multiplier such that τi l,t = τ0 l,t ∗ mi

62. New ﬁscal closures: labor tax progression GO BACK • tr1 the lowest income threshold • trn is the highest income threshold • n is the number of income brackets • m is a tax multiplier such that τi l,t = τ0 l,t ∗ mi • Income threshold is multiple of average labor income, (1 − τt)wt ¯lt. • In the initial steady state m = 1 • In the transition path m = 1.15 and n = 4

63. New ﬁscal closures: labor tax progression Total gross labor income (1 − τt)wtLt is a sum of n + 1 components: earnings taxed by one of n + 1 tax rate. L0 t = ¯J j=1 Nj,t Ω min(ωj,t(sj,t)lj,t(sj,t), tr1)dPj,t Li t = ¯J j=1 Nj,t Ω max(min(ωj,t(sj,t)lj,t(sj,t − tr1), tri − tri−1), 0)dPj,t∀i = 1, ..., n τ0 l,t = Gt + subsidyt + ∆Dt − Υ1 J j=1 Nj,t − τc,1Ct − τk,1rtAt − n i=0 Li tτi l n i=0 Li t τi l,1 = mi ∗ τ0 l,1

64. Fiscal closures within pension system, subsidyt = 0 GO BACK To keep pension system balanced government may adjust: • contribution rate τ • beneﬁts bj (as a tax on beneﬁts) J j= ¯Jt Nj,t(1 − τb,t)bj,t = τt ¯wtLt and subsidyt = 0

65. Fiscal closures outside pension system, subsidyt = 0 GO BACK • consumption tax, τc,t • labor tax, τl,t Tt = τl,t(1 − τt)wtLt + τk,trtAt + τc,tCt + Υt J j=1 Nj,t Gt + subsidyt + rtDt = Tt + ∆Dt • smoothing tax adjustments with public debt via a ﬁscal rule: ∀tax ∈ {l, c} τtax,t = (1 − )τfinal tax + τtax,t−1 + D (D/Y )t − (D/Y ) final • public debt in the ﬁnal steady state = the initial steady state

66. Proﬁle of average consumption for τk closure other closures GO BACK in line with Gourinchas & Parker (2002, Econometrica)

67. Proﬁle of average savings for τk closure other closures GO BACK

68. Proﬁle of average labor for τk closure other closures GO BACK

69. GO BACK τk debt + τk progression τ τl debt + τl τb τc debt + τc

70. GO BACK τk debt + τk progression τ τl debt + τl τb τc debt +τc

71. GO BACK τk debt + τk progression τ τl debt + τl τb τc debt +τc

72. Capital GO BACK

73. Labor GO BACK

74. Model solving GO BACK • Gauss-Seidel iterative algorithm • Guess an initial value for k = K/(zL) and compute prices • Solve individual problem and aggregate it to ﬁnd new K and L , thus k • iterate until convergence

75. Model solving GO BACK • Gauss-Seidel iterative algorithm • Guess an initial value for k = K/(zL) and compute prices • Solve individual problem and aggregate it to ﬁnd new K and L , thus k • iterate until convergence • Consumer problem (backward policy function iterations)

76. Model solving GO BACK • Gauss-Seidel iterative algorithm • Guess an initial value for k = K/(zL) and compute prices • Solve individual problem and aggregate it to ﬁnd new K and L , thus k • iterate until convergence • Consumer problem (backward policy function iterations) • implicit tax to reduce state space, Butler (2002) • policy function iterations with picewise linear interpolation • within period problem solved with Newton-Raphson • given initial distribution at age j = 1, transition matrix for idiosyncratic productivity and the policy functions compute the distribution in any successive age j. • aggregation done with Gaussian quadrature

77. Model solving GO BACK • Gauss-Seidel iterative algorithm • Guess an initial value for k = K/(zL) and compute prices • Solve individual problem and aggregate it to ﬁnd new K and L , thus k • iterate until convergence • Consumer problem (backward policy function iterations) • implicit tax to reduce state space, Butler (2002) • policy function iterations with picewise linear interpolation • within period problem solved with Newton-Raphson • given initial distribution at age j = 1, transition matrix for idiosyncratic productivity and the policy functions compute the distribution in any successive age j. • aggregation done with Gaussian quadrature • Transition path, goes between the initial and ﬁnal steady state

Effciency versus insurance: The role for fiscal policy in social security privatization

Effciency versus insurance: The role for fiscal policy in social security privatization

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Effciency versus insurance: The role for fiscal policy in social security privatization