(with Marcin Bielecki, Krzysztof Makarski and Marcin Waniek) Joanna Tyrowicz. University of Warsaw and National Bank of Poland

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1 Outline Inequality in an OLG economy with heterogeneous cohorts and pension systems (with Marcin Bielecki, Krzysztof Makarski and Marcin Waniek) Joanna Tyrowicz University of Warsaw and National Bank of Poland MoPAct Workshop, ETLA, Helsinki, / 40

2 Motivation Wealth inequality increases due to: Demographic transition Pension reform: defined benefit defined contribution Effects for consumption inequality: unclear 2 / 40

3 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 2 / 40

4 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 / 40

5 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 / 40

6 Our approach Question 1: distributional effects of a pension system reform Question 2: are standard instruments effective in reducing the increase in inequality 4 / 40

7 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 4 / 40

8 Results preview DB DC reform: both wealth and consumption inequalities 5 / 40

9 Results preview DB DC reform: both wealth and consumption inequalities Demographic transition inequalities, more than due to reform 5 / 40

10 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 5 / 40

11 Outline 1 Motivation 2 Model 3 Calibration 4 Results 5 Appendix 6 / 40

12 Method Model Deterministic ( we are working on it!) OLG ex ante heterogeneity: endowments + preferences 7 / 40

13 Method Model Deterministic ( we are working on it!) OLG ex ante heterogeneity: endowments + preferences Calibrate to Poland in / 40

14 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: U j,k,t = J j s=0 [ δ s k π [ ] ] j+s,t+s c φ k j+s,k,t+s π (1 l j+s,k,t+s) 1 φ k j,t 8 / 40

15 Households II Subject to the budget constraint (1 + τt c )c j,k,t + s j,k,t = (1 τt)(1 l τ)w t ω k l j,k,t labor income + (1 + (1 τt k )r t )s j 1,k,t 1 capital income + (1 τt)b l j,k,t pension income + beq j,k,t bequests Υ t lump-sum tax There exists a closed-form solution to this problem 9 / 40

16 Producers Perfectly competitive representative firm Standard Cobb-Douglas production function Y t = Kt α (z t L t ) 1 α Profit maximization implies w t = z t (1 α)ˆk α t r t = αˆk α 1 t d where d is the capital depreciation rate and ˆk is capital per effective unit of labor 10 / 40

17 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 T t + D t = (1 + r t )D t 1 + gy t + subsidy t We fix debt at constant 45% debt to GDP ratio. Consumption tax varies to satisfy the government constraint. 11 / 40

18 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 12 / 40

19 Instrument 1: minimum pensions Definition b j,k,t ρ min gross average wage t We set ρ min = 0.2 4% coverage (consistent with the data) 13 / 40

20 Instrument 1: minimum pensions Definition b j,k,t ρ min gross average wage t We set ρ min = 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 13 / 40

21 Instrument 1: contribution cap Definition: τ eff j,k,t = min { τ, τ cap gross average wage t w t ω k l j,k,t } To replicate 2% coverage, τ cap = 1.7 (lower than de iure 2.5) 14 / 40

22 Instrument 1: contribution cap Definition: τ eff j,k,t = min { τ, τ cap gross average wage t w t ω k l j,k,t } To replicate 2% coverage, τ cap = 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 14 / 40

23 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) 15 / 40

24 1 Motivation 2 Model 3 Calibration 4 Results 5 Appendix 16 / 40

25 Exogenous assumptions Projections for Poland provided by the European Commission Population Size TFP Growth 17 / 40

26 Exogenous assumptions Projections for Poland provided by the European Commission Population Size TFP Growth Kept constant across scenarios, don t affect results 17 / 40

27 Within cohort heterogeneity - endowments Structure of Earnings Survey, 1998, Poland Productivity ω Resulting: 10 values for ω 18 / 40

28 Within cohort heterogeneity - leisure preference Structure of Earnings Survey, 1998, Poland Leisure Preference φ Resulting: 4 values for φ 19 / 40

29 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: discount factors are (0.98δ, δ, 1.02δ) 20 / 40

30 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) 21 / 40

31 Within cohort heterogeneity - summary outcomes II age Lowest omega multiplier Standard omega multiplier Highest omega multiplier 22 / 40

32 Within cohort heterogeneity - summary outcomes III age Lowest delta multiplier Highest delta multiplier Standard multipliers Lowest phi multiplier Highest phi multiplier 23 / 40

33 1 Motivation 2 Model 3 Calibration 4 Results 5 Appendix 24 / 40

34 Minimum pensions coverage year Defined Benefit with minimum pensions Defined Contribution with minimum pensions 25 / 40

35 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 final diff. (in pp) Pension system deficit initial final diff (in pp) / 40

36 Consumption Gini 27 / 40

37 Wealth Gini 28 / 40

38 Wealth Gini at retirement I 29 / 40

39 Wealth Gini at retirement II 30 / 40

40 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 31 / 40

41 Consumption inequality decomposition - minimum pensions DB DC 32 / 40

42 Wealth inequality decomposition - minimum pensions DB DC 33 / 40

43 Wealth inequality decomposition - minimum pensions DB DC 34 / 40

44 Wealth Gini at retirement DB DC 35 / 40

45 Welfare effects Defined Benefit Defined Contribution 36 / 40

46 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 37 / 40

47 Thank you for your attention 38 / 40

48 Household Sector Closed Form Solution I For j < J (working): c j,t = Ω j,t + Γ j,t [ ( (1 + τt c) J j 1 s=0 (1 + φ) δ s π ) j+s,t+s π j,t + ( J j s= J j δ s π )] j+s,t+s π j,t l j,t = 1 φ(1 + τ c t )c j,t (1 τ l t )(1 τ)w t s j,t = (1 τ l t)(1 τ)w t l j,t + (1 + (1 τ k t )r t )s j 1,t 1 (1 + τ c t )c j,t, with Ω j,t = Γ j,t = J j 1 s=0 J j s= J j (1 τ l t+s)(1 τ)w t+s + beq j+s,t+s Υ t+s si=1 (1 + (1 τ k t+i )r t+i) (1 τt+s)b l j+s,t+s + beq j+s,t+s Υ t+s si=1 (1 + (1 τt+i k )r. t+i) 39 / 40

49 Household Sector Closed Form Solution II For j J (retired): with c j,t = Γ [ j,t (1 + τt c) J j ( s= J j δ s π )] j+s,t+s π j,t l j,t = 0 s j,t = (1 τ l t)b ι j,t + (1 + (1 τ k t )r t )s j 1,t 1 (1 + τ c t )c j,t, Γ j,t = J j s=0 (1 τt+s)b l j+s,t+s + beq j+s,t+s Υ t+s si=1 (1 + (1 τt+i k )r. t+i) 40 / 40

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