Most reforms of the pension systems imply substantial redistribution between cohorts and within a cohort. Fiscal policy, which accompanies these changes may counteract or reinforce this redistribution. Moreover, the literature has argued that the insurance motive implicit in some pension systems plays a major role in determining the welfare eects of the reform: reforms otherwise improving welfare become detrimental to welfare once insurance motive is internalized. We show that this result is not universal, i.e. there exists a variety of scal closures which yield welfare gains and political support for a pension system reform. In an OLG model with uncertainty, we analyze two sets of fiscal adjustments: fiscally neutral adjustments in the pension system (via contribution rate or replacement rate) and balancing pension system by a combination of taxes and/or public debt. We find that fiscally neutral pension system reforms are more likely to yield welfare gains. Many adjustments obtain sufficient political support despite yielding aggregate welfare losses and vice versa. Furthermore, we point to fiscal closures which attenuate and reinforce the relevance of the insurance motive in determining the welfare effects.

1. Motivation Model Calibration Results
Welfare effects of fiscal policy
in reforming the pension system
Olivia Komada
(with Joanna Tyrowicz and Krzysztof Makarski)
Group for Research in APplied Economics (GRAPE)
XXII WORKSHOP ON DYNAMIC MACROECONOMICS
Vigo, 2017
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2. Motivation Model Calibration Results
Motivation
Longevity ⇑
Pay-As-You-Go Defined Benefits (PAYG DB) ⇒ fiscally unstable if not reformed
(Feldstein: deficit + 1.4% of GDP share) ⇒ reform needed
Defined Contribution (DC) immune to longevity risk (fiscal side)
(Partial) funding fosters accumulation of capital
Reform : PAYG DB =⇒ partially funded DC
⇒ part of contribution goes to funded pillar ⇒ deficit ⇑ in the short run ⇒ financing?
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3. Motivation Model Calibration Results
Motivation
Pension system reform
in deterministic setting horse-race between
efficiency
fiscal cost for cohorts paying for the reform
efficiency prevails - reform welfare improving
in stochastic setting: loss of insurance
Nishiyama & Smetters (2007, QJE) and subsequent papers: negative welfare effects of
the reform
But:
government may counteract or reinforce between and within cohort redistribution
affecting also economic efficiency (scope of distortions)
Is Nishiyama & Smetters (2007) result universal?
compare variants of fiscal closures (accompanying the reform)
consider new fiscal closures
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4. Motivation Model Calibration Results
Literature differs in terms of fiscal closures
Pension system parameters
contribution rates (20 papers)
e.g. Kumru & Thanopoulos (2011, JPE ), Bruce & Turnovsky (2013, JPE)
replacement rate (8 papers)
e.g. Boersch-Supan et al. (2014, AER), Kitao (2014, RED)
Fiscal closure
debt (5 papers )
e.g. Song, et al. (2015, AEJ) Lindbeck & Persson (2003, JEL)
labor tax (3 papers)
e.g. Bouzahzah et al. (2002, JEDC)
consumption tax (10 papers)
e.g. Nishiyama & Smetters (2007, QJE), Diaz-Gimenez & Diaz-Saavedra (2009, RED)
⇒ Studies do not compare across fiscal closures (except for within pension system)
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5. Motivation Model Calibration Results
What we do
Challenge the view that in stochastic framework pension system privatization is welfare
deteriorating
Provide a systematic overview of the interaction between the pension system reform
and fiscal closure
Consider new ways of financing the pensions system reform
tax on capital income
labor tax progression
public spending
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6. Motivation Model Calibration Results
Preview of the results
Nishiyama & Smetters (2007) result is NOT universal ⇔ fiscal closure matters for the
welfare effects of the pension system reform
(Even in stochastic framework) Depending on the fiscal closure:
welfare effect of the same reform can be positive or negative
political support is sufficient or not
Welfare gains and political support only sometimes overlap
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7. Motivation Model Calibration Results
Contents
1 Motivation
2 Model
3 Calibration
4 Results
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8. Motivation Model Calibration Results
Consumers I
live for j = 1, 2, ..., 16 periods
face survival πj,t < 1
choose labor supply endogenously
Instantaneous utility
u(cj,t, 1 − lj,t, gt) = log(cj,t) ← private consumption
+φl log(1 − lj,t) ← leisure
+φg log(gt) ← public goods consumption
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9. Motivation Model Calibration Results
Consumers II
Income is composed of
net labor income wj,tlj,t = (1 − τl,t)(1 − τt)ωj,twtlj,t
and productivity changes randomly: ωj,t = eηj,t
where ηj,t follows AR(1) process approximated by 3 stages Markov chain
after-tax capital income (1 − τk)rtaj,t
unintended bequests Γj,t
pension benefits bj,t
and is used to finance
consumption (1 + τc,t)cj,t
savings aj+1,t+1 − (1 + rt) aj,t
lump sum tax / transfer Υt (to ”close” the initial steady state)
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10. Motivation Model Calibration Results
Consumers III
Solve the following optimization problem
Vj,t(sj,t) = max
cj,t,lj,t,aj+1,t+1
u(cj,t, lj,t, gt) + δ
πj+1,t+1
πj,t
E Vj+1,t+1(sj+1,t+1) | sj,t
BC : aj+1,t+1 + (1 + τc,t)cj,t + Υt = wj,tlj,t + bj,t + (1 + (1 − τk)rt) aj,t + Γj,t
where sj,t = (aj,t, ηj,t, fj,t) and aj,t denotes private assets, ηj,t productivity and fj,t
pension assets
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11. Motivation Model Calibration Results
Producers
Perfectly competitive representative firm with Cobb-Douglas production function
Yt = Kα
t (ztLt)1−α
Lt =
¯J−1
j=1 Nj,t St
ωj,t(sj,t)lj,t(sj,t)dX(sj,t)
Profit maximization implies
wt = (1 − α)Kα
t zt(ztLt)−α
rt = αKα−1
(ztLt)1−α
− d
where d is the capital depreciation rate
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12. Motivation Model Calibration Results
Government
Collects taxes
Tt = τl,t(1 − τt)wtLt + τk,trtAt + τc,tCt + Υt
J
j=1
Nj,t
Finances spending on public goods and service Gt = gt
J
j=1 Nj,t,
Balances pension system subsidyt
Services debt ∆Dt = (1 + rt)Dt−1 − Dt
Tt = Gt + subsidyt + ∆Dt
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13. Motivation Model Calibration Results
Pension system- baseline scenario PAYG DB
equal benefits for everybody within a cohort (provide insurance)
b ¯J,t = ρ · wavg,t
indexed by payroll growth rate (labor ↑ ⇒ benefits ↑)
bj,t = (1 + rI
t )bj−1,t−1
longevity ↑ ⇒ deficit occurs
subsidyt =
J
j= ¯J
Nj,tbj,t − τtwtLt,
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14. Motivation Model Calibration Results
Pension System - reform scenario partially funded DC
contributions go into PAYG and funded pillar: τt = τI
t + τII
t
individual pension accounts fj,t = {fI
j,t, fII
j,t} ⇒ no insurance
fI
j,t = (1 + rI
t )fI
j−1,t−1 + τI
t wj,tlj,t
fII
j,t = (1 + rt)fII
j−1,t−1 + τII
t wj,tlj,t
benefits are actuarially fair
b ¯J,t =
accrued ‘savings’
life expectancyt
+
accrued savings
life expectancyt
indexed by payroll growth rate and capital rate respectively
bI
j,t = (1 + rI
t )bI
j−1,t−1 and bII
j,t = (1 + rt)bII
j−1,t−1
Introducing such reform generates a gap in the pension system because of fII
j,t ⇒ need
for fiscal closure.
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15. Motivation Model Calibration Results
Fiscal closures within pension system
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 subsityt = 0
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16. Motivation Model Calibration Results
Fiscal closures (outside pension system, subsidyt = 0 )
Tt = τl,t(1 − τt)wtLt + τk,trtAt + τc,tCt + Υt
J
j=1
Nj,t
Tt = gt
J
j=1
Nj,t + subsidyt + (1 + rt)Dt−1 − Dt
capital tax, τk,t
consumption tax, τc,t
public spending closure, gt
labor tax, τl,t
labor tax progressivity, (τH
l,t, τL
l,t)
τH
l,t = 2τL
l,t
τH
l,t on earnings above 150% of average labor income
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17. Motivation Model Calibration Results
Fiscal closures (outside pension system, subsidyt = 0)
smoothing tax adjustments with public debt
part of the costs of the reform shifted to the future generations
fiscal rule ∀tax ∈ l, c, k
τtax,t = (1 − )τfinal
tax + τtax,t−1 + D
D
Y t
−
D
Y
final
in the final steady state debt level converges to the same levels (= initial steady state)
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18. Motivation Model Calibration Results
Fiscal closures – summary
Two closures within pension system
contributions ⇒ working cohorts ⇒ labor supply
pensions ⇒ on retirees ⇒ consumption
Eight closures outside pension system
public spending (enters utility)
consumption tax (+ debt) ⇒ all cohorts ⇒ consumption
labor tax (+ debt) ⇒ working cohorts ⇒ labor supply
progressive labor tax ⇒ working cohorts with favorable shocks ⇒ labor supply
capital tax (+ debt) ⇒ cohorts with more wealth ⇒ savings & investment
In total: ten closures (and a 100 possible combinations of fiscal policy in baseline and
reform)
Model Solving
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19. Motivation Model Calibration Results
Contents
1 Motivation
2 Model
3 Calibration
4 Results
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20. Motivation Model Calibration Results
Calibration to replicate 2015 US economy
Preferences
Preference for leisure φl matches average hours 33%
Preference for public consumption φg optimal p.c value in the initial steady state
Discounting rate δ matches interest rate 4%
Idiosyncratic productivity shock based on Kruger& 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
Retirement age equal 65 ( ¯J = 9)
Taxes {τc, τl, τk} match revenue as % of GDP {9.2%, 3.8%, 3.6%}
Depreciation rate d matches investment rate 25%
Demographyis based on the projection by The United Nations Graphs
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21. Motivation Model Calibration Results
Baseline: PAYG DB with aging and thus deficit
Adjustment in pension parameters Adjustment in fiscal parameters
contribution rate ↑ from 7.8% to 9% pension system deficit ↑ from 0% to 1% of GDP
replacement rate ↓ from 21.1% to 17.8%
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22. Motivation Model Calibration Results
Reform: gradually replace PAYG DB ...
... with a partially funded define contribution (DC)
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23. Motivation Model Calibration Results
Contents
1 Motivation
2 Model
3 Calibration
4 Results
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24. Motivation Model Calibration Results
Welfare analysis - like Nishiyama and Smetters (2007)
What happens within each experiment?
1 Run the no policy reform scenario ⇒ baseline
2 Run the policy reform scenario ⇒ reform
3 For each cohort compare utility, compensate the losers from the winners
4 If net effect positive ⇒ reform efficient
consumption labor savings
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25. Motivation Model Calibration Results
Welfare effect - final steady state
Fiscal
Baseline
closure τ τb τc τl τk prog. dτc dτl dτk gt
Reform
τ 0.70 0.53 0.52 0.52 0.44 1.02 0.52 0.52 0.44 0.55
τb 0.70 0.53 0.52 0.52 0.44 1.02 0.52 0.52 0.44 0.55
τc 0.63 0.48 0.39 0.39 0.41 0.89 0.39 0.39 0.41 0.42
τl 0.55 0.42 0.25 0.24 0.31 0.75 0.25 0.24 0.31 0.27
τk 1.07 0.84 1.00 1.00 0.93 1.50 1.00 1.00 0.93 1.03
prog. 0.51 0.35 0.26 0.26 0.34 0.76 0.26 0.26 0.34 1.04
dτc 0.63 0.48 0.39 0.39 0.41 0.89 0.39 0.39 0.41 0.42
dτl 0.55 0.42 0.25 0.24 0.31 0.75 0.25 0.24 0.41 0.27
dτk 1.07 0.84 1.00 1.00 0.93 1.50 1.00 1.00 0.93 1.03
gt 0.48 0.38 0.05 0.04 0.12 0.55 0.05 0.04 0.12 0.08
% of consumption in reform scenario which you are willing to give up to ensure that the
reform take place
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26. Motivation Model Calibration Results
Welfare effect - transition
Fiscal
Baseline
closure τ τb τc τl τk prog. dτc dτl dτk gt
Reform
τ 0.07 0.13 -0.04 -0.03 -0.15 0.53 -0.05 -0.02 -0.12 0.02
τb 0.06 0.11 -0.06 -0.05 -0.17 0.51 -0.06 -0.04 -0.14 0.00
τc 0.09 0.15 -0.06 -0.05 -0.16 0.51 -0.06 -0.05 -0.14 0.00
τl -0.12 -0.04 -0.38 -0.37 -0.43 0.18 -0.38 -0.37 -0.46 -0.32
τk 0.57 0.48 0.64 0.64 0.55 1.17 0.63 0.64 0.56 0.68
prog. -0.23 -0.18 -0.43 -0.42 -0.48 0.13 -0.43 -0.42 -0.43 -0.19
dτc 0.07 0.13 -0.08 -0.07 -0.18 0.49 -0.09 -0.07 -0.16 -0.02
dτl -0.11 -0.04 -0.38 -0.37 -0.43 0.19 -0.38 -0.37 -0.45 -0.32
dτk 0.56 0.47 0.63 0.63 0.54 1.15 0.63 0.64 0.54 0.65
gt -0.04 0.07 -0.39 -0.38 -0.49 0.19 -0.40 -0.38 -0.40 -0.33
% of consumption in reform scenario which you are willing to give up to ensure that the
reform take place
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27. Motivation Model Calibration Results
Welfare effect - transition - τc
Why debt may help with political support?
It helps pensioners (who gain anyway)
Young always against
With debt we sway working who remain in the old system
They give us majority
other closures
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28. Motivation Model Calibration Results
Welfare effect - transition - τc
other closures
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29. Motivation Model Calibration Results
Welfare effect - transition - τc & debtτc
other closures
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30. Motivation Model Calibration Results
Welfare effect - transition - τc & debtτc
other closures
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31. Motivation Model Calibration Results
Political support
Fiscal closure
Baseline
τ τb τc τl τk prog. debtτc debtτl debtτk gt
Reform
τ 0.07 0.13 -0.04 -0.03 -0.15 0.53 -0.05 -0.02 -0.12 0.02
τb 0.06 0.11 -0.06 -0.05 -0.17 0.51 -0.06 -0.04 -0.14 0.00
τc 0.09 0.15 -0.06 -0.05 -0.16 0.51 -0.06 -0.05 -0.14 0.00
τl 0.12 -0.04 -0.38 -0.37 -0.43 0.18 -0.38 -0.37 -0.46 -0.32
τk 0.57 0.48 0.64 0.64 0.55 1.17 0.63 0.64 0.56 0.68
prog. -0.23 -0.18 -0.43 -0.42 -0.48 0.13 -0.43 -0.42 -0.43 -0.19
debtτc 0.07 0.13 -0.08 -0.07 -0.18 0.49 -0.09 -0.07 -0.16 -0.02
debtτl -0.11 -0.04 -0.38 -0.37 -0.43 0.19 -0.38 -0.37 -0.45 -0.32
debtτk 0.56 0.47 0.63 0.63 0.54 1.15 0.63 0.64 0.54 0.65
gt -0.04 0.07 -0.39 -0.38 -0.49 0.19 -0.40 -0.38 -0.40 -0.33
% of consumption in reform scenario which you are willing to give up to ensure that the
reform take place
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32. Motivation Model Calibration Results
Nishiyama & Smetters, 2007: stochastic vs deterministic?
Compare the effects of pension system reform in a stochastic and deterministic framework
large role for the insurance motive per se
but there are closures with positive outcomes despite stochastic setup
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33. Motivation Model Calibration Results
Nishiyama & Smetters, 2007: stochastic vs deterministic?
τc τ
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34. Motivation Model Calibration Results
Conclusions
Social Security reform requires fiscal adjustment
Fiscal closures redistribute, therefore matter a lot (unnoticed in earlier literature)
Insurance motive large but not decisive for evaluation of (partial) privatization
Preferred policy options
Debt closures: yield some welfare gains and obtain political support
Tax on capital income
Good but never favored policy options
Adjustment in pensions
Labor tax progression
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35. Motivation Model Calibration Results
Questions or suggestions?
Thank you!
w: grape.org.pl
t: grape org
f: grape.org
e: okomada@grape.org.pl
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36. 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 S(ηj,t|ηj−1,t−1) 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
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37. Calibration to replicate 2015 US economy
GO BACK Demography is based on the projection by The United Nations.
number of 20-year-olds mortality rates
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38. Profile of average consumption for τc closure
GO BACK
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39. Profile of average labor for τc closure
GO BACK
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40. Profile of average savings for τc closure
GO BACK
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41. GO BACK
τ τb gt
τl progression τk
debtτl debtτc debtτk
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42. GO BACK
τ τb gt
τl progression τk
debtτl debtτc debtτk
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43. GO BACK
τ τb gt
τl progression τk
debtτl debtτc debtτk
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44. GO BACK
τ τb gt
τl τc τk
debtτl debtτc progression
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