Welfare effects of fiscal policy in reforming the pension system

Motivation Model Calibration Results
Welfare eﬀects of ﬁscal policy in reforming the pension system
Krzysztof Makarski
(with Oliwia Komada and Joanna Tyrowicz )
FAME|GRAPE, NBP, University of Warsaw & Warsaw School of Economics
6th NBP Summer Workshop, 2017
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Motivation
Longevity ⇑
Pay-As-You-Go Defined Benefits (PAYG DB) ⇒ fiscally unstable if not
reformed (Feldstein: deficit +1.4pp of GDP share )
2 / 46

Motivation
Longevity ⇑
reformed (Feldstein: deﬁcit +1.4pp of GDP share ) ⇒ reform needed
2 / 46

Motivation
Longevity ⇑
Deﬁned Contribution (DC) immune to longevity risk (ﬁscal side)
(Partial) funding fosters accumulation of capital
2 / 46

Motivation
Longevity ⇑
Literature
Reform : PAYG DB =⇒ (partially) funded DC
2 / 46

Motivation
Longevity ⇑
Literature
Reform : PAYG DB =⇒ (partially) funded DC
shift of contributions to funded pillar ⇒ short run ﬁnancing?
2 / 46

Motivation
in deterministic setting horse-race between
efficiency
fiscal cost for cohorts paying for the reform
efficiency prevails - reform welfare improving
3 / 46

Motivation
eﬃciency
in stochastic setting: loss of insurance
Nishiyama & Smetters (2007, QJE) and subsequent papers: negative welfare
eﬀects of the reform
3 / 46

Motivation
efficiency
But:
fiscal policy counteracts / reinforces between and within cohort redistribution
affecting also economic efficiency (scope of distortions)
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Motivation
efficiency
But:
fiscal policy counteracts / reinforces 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)
introduce new fiscal closures
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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)
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Fiscal closure
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)
debt (5 papers )
e.g. Song, et al. (2015, AEJ) Lindbeck & Persson (2003, JEL)
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Fiscal closure
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)
debt (5 papers )
e.g. Song, et al. (2015, AEJ) Lindbeck & Persson (2003, JEL)
⇒ Studies do not compare across ﬁscal closures (except for within pension system)
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What we do
Challenge the view that in stochastic framework pension system privatization
is welfare deteriorating
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What we do
Provide a systematic overview of the interaction between the pension system
reform and ﬁscal closure
5 / 46

What we do
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
5 / 46

Preview of the results
Nishiyama & Smetters (2007) result is NOT universal ⇔ fiscal closure matters
Depending on the fiscal closure in stochastic framework:
welfare effect of the same reform can be positive or negative
with political support or not
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Preview of the results
Nishiyama & Smetters (2007) result is NOT universal ⇔ fiscal closure matters
Depending on the fiscal closure in stochastic framework:
welfare effect of the same reform can be positive or negative
with political support or not
Welfare gains and political support only sometimes overlap
there are many combinations of fiscal policy that make pension system reform
welfare improving
public debt often “buys” political support for the reform (both improving and
deteriorating)
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Contents
1 Motivation
2 Model
3 Calibration
4 Results
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Consumers
live for j = 1, 2, ..., 16 periods
stochastic survival πj,t < 1
choose labor supply endogenously until retirement age ¯j
labor income wj,tlj,t = ωj,twtlj,t
where ωj,t = eηj,t
and ηj,t follows AR(1) process approximated by 3 stages
Markov chain
state of the agent sj,t = (aj,t, ηj,t, fj,t)
instantaneous utility:
u(cj,t, 1 − lj,t, gt) = log(cj,t) + φl log(1 − lj,t) + φg log(gt)
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Consumer: Recursive 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
subject to
aj+1,t+1 + (1 + τc,t)cj,t + Υt =(1 − τl,t)(1 − τt)wj,tlj,t + bj,t
+ (1 + (1 − τk,t)rt) aj,t + Γj,t (1)
9 / 46

Producers
Perfectly competitive representative ﬁrm with Cobb-Douglas production function
Yt = Kα
t (ztLt)1−α
Lt =
¯j
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
10 / 46

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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Pension system- baseline scenario PAYG DB
equal beneﬁts for everybody within a cohort (provides insurance)
bj,t =
ρ · wavg,t, for j = ¯j
(1 + rI
t )bj−1,t−1, for j > ¯j
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bj,t =
(1 + rI
t )bj−1,t−1, for j > ¯j
i.e. pensions are indexed payroll growth rate 1 + rI
t = wtLt/wt−1Lt−1
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bj,t =
(1 + rI
t )bj−1,t−1, for j > ¯j
i.e. pensions are indexed payroll growth rate 1 + rI
t = wtLt/wt−1Lt−1
longevity ↑ creates deﬁcit (no balancing mechanism in a system)
subsidyt =
J
j= ¯J
Nj,tbj,t − τtwtLt,
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Pension System - reform scenario partially funded DC
contributions go into PAYG and funded pillar: τt = τI
t + τII
t
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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/(πj,t/πj−1,t−1) + τI
t wj,tlj,t
fII
j,t = (1 + rt)fII
j−1,t−1/(πj,t/πj−1,t−1) + τII
t wj,tlj,t
beneﬁts are ’actuarially fair’, bj,t = bI
j,t + bII
j,t, where
bI
j,t =
fI
j,t/life expectancyt, for j = ¯j
(1 + rI
t )bI
j−1,t−1, for j > ¯j
bII
j,t =
fII
(1 + rt)bII
j−1,t−1, for j > ¯j
13 / 46

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/(πj,t/πj−1,t−1) + τI
t wj,tlj,t
fII
j,t = (1 + rt)fII
j−1,t−1/(πj,t/πj−1,t−1) + τII
t wj,tlj,t
benefits are ’actuarially fair’, bj,t = bI
j,t + bII
j,t, where
bI
j,t =
fI
(1 + rI
t )bI
j−1,t−1, for j > ¯j
bII
j,t =
fII
(1 + rt)bII
j−1,t−1, for j > ¯j
Introducing such reform generates a deficit in the pension system ⇒ need for
fiscal closure.
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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
14 / 46

Fiscal closures (outside pension system, subsidyt = 0 )
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
15 / 46

Fiscal closures (outside pension system, subsidyt = 0 )
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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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)
16 / 46

Fiscal closures – summary
Two closures within pension system
contributions ⇒ working cohorts ⇒ labor supply
pensions ⇒ on retirees ⇒ consumption
17 / 46

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
17 / 46

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)
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Model solving
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
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Model solving
Consumer problem (backward policy function iterations)
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Model solving
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
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Model solving
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
18 / 46

Contents
1 Motivation
2 Model
3 Calibration
4 Results
19 / 46

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%
20 / 46

Preferences
state
Idiosyncratic productivity shock based on Kruger and Ludwig (2013):
Persistence η = 0.95
Variance ση = 0.375
20 / 46

Preferences
state
Pension system
Replacement rate ρ matches beneﬁts as % of GDP 5.2%
Contribution rate balances pension system
Retirement age equal 65 (¯j = 9)
20 / 46

Preferences
state
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 of 25%
20 / 46

Demography is based on the projection by The United Nations.
number of 20-year-olds mortality rates
21 / 46

Reform: gradually replace PAYG DB ...
... with a partially funded deﬁne contribution (DC)
22 / 46

Proﬁle of average consumption for τc closure
other closures
in line with Gourinchas & Parker (2002, Econometrica)
23 / 46

Proﬁle of average labor for τc closure
other closures
24 / 46

Proﬁle of average savings for τc closure
other closures
25 / 46

Contents
1 Motivation
2 Model
3 Calibration
4 Results
26 / 46

Baseline: PAYG DB with aging and thus deficit
Adjustment in pension parameters
contribution rate ↑ from 7.8% to 9%
replacement rate ↓ from 21.1% to 17.8%
Adjustment in fiscal parameters
pension system deficit ↑ by 1pp of GDP
27 / 46

Reform: partially funded DC
Adjustment in ﬁscal parameters
pension system deﬁcit ↑ from 0% to 2% of GDP (and eventually back to 0%)
28 / 46

Capital and labor
Capital Labor
29 / 46

Welfare analysis - like Nishiyama & 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
30 / 46

Compare two diﬀerent tax closures, τc and τk
τk has larger gain towards the end, → positive overall welfare eﬀect
31 / 46

Welfare eﬀect - ﬁnal steady state
Fiscal
Baseline
closure τ τb τc τl τk prog. dτc dτl dτk gt
Reform
τ 0.70
τb 0.53
τc 0.39
τl 0.24
τk 0.93
prog. 0.76
dτc 0.39
dτl 0.24
dτk 0.93
gt 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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Welfare eﬀect - ﬁnal steady state
Fiscal
Baseline
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
32 / 46

Welfare eﬀect - transition
Fiscal
Baseline
Reform
τ 0.07
τb 0.11
τc -0.06
τl -0.37
τk 0.55
prog. 0.13
dτc -0.09
dτl -0.37
dτk 0.54
gt -0.33
33 / 46

Welfare eﬀect - transition
Fiscal
Baseline
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
33 / 46

Welfare eﬀects: why public debt can help gaining political support?
It helps pensioners (who gain anyway)
Young always loose (→ are againsr the reform)
With debt we sway some working who remain in the old system → majority
34 / 46

Welfare eﬀect – τc
Why debt can help gain political support
35 / 46

Welfare eﬀect - transition - τc & debt + τc
36 / 46

Welfare eﬀect - transition - τc & debt + τc
37 / 46

Political support
lime area denotes political support, green font denotes welfare gain
Fiscal
Baseline
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
38 / 46

Nishiyama & Smetters, 2007: stochastic vs deterministic?
Compare the eﬀects of pension system reform in a stochastic and deterministic
framework
39 / 46

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
39 / 46

τc
40 / 46

τc τ
40 / 46

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 (puzzling)
41 / 46

Questions or suggestions?
Thank you!
w: grape.org.pl
t: grape org
f: grape.org
e: kmakarski@grape.org.pl
42 / 46

GO BACK
τ τb gt
τl progression τk
debtτl debtτc debtτk
43 / 46

GO BACK
τ τb gt
τl progression τk
44 / 46

GO BACK
τ τb gt
τl progression τk
45 / 46

GO BACK
τ τb gt
τl τc τk
debtτl debtτc progression
46 / 46

Welfare effects of fiscal policy in reforming the pension system

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