Efficiency versus insurance: The role for capital income taxation in social security privatization

Eﬃciency versus insurance:
The role for capital income taxation in social security privatization
Joanna Tyrowicz (GRAPE, IAAEU, UW and IZA)
Oliwia Komada (GRAPE and WSE)
Krzysztof Makarski (GRAPE and WSE)
RCEA
Waterloo, September, 2019
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Motivation – pension systems
Longevity hazards DB viability: deﬁcit ↑ 1.4% of GDP → reforms
Feldstein, BEA, SSA
• between generations −→ timing of costs vs gains
• within generations −→ insurance
• aggregate change in the economy −→ eﬃciency
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Motivation – pension systems
Longevity hazards DB viability: deficit ↑ 1.4% of GDP → reforms
Feldstein, BEA, SSA
• between generations −→ timing of costs vs gains
• within generations −→ insurance
• aggregate change in the economy −→ efficiency
• Consensus:
• Deterministic setup: efficiency wins over the loosers
• Stochastic setup: insurance drags efficiency boost down
Nishiyama & Smetters (2007, QJE) and subsequent literature
2 / 35

Motivation – capital (income gains) taxation
τk > 0 is eﬃcient in an OLG economy
Garriga (2001), Findeisen & Sachs (2017), Krueger & Ludwig (2018)
• Is taxing capital a good idea for pension system reform?
• longevity −→ saving less elastic on price
• privatized pensions −→ precautionary savings
• pension system balanced −→ taxation decline
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Our contribution
Q1: Is it ok to raise τk?
3 / 35

Our contribution
Q1: Is it ok to raise τk? ←− Transitory
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Our contribution
Q2: Is it ok to reduce τk?
3 / 35

Our contribution
Q2: Is it ok to reduce τk? ←− Permanent
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Our contribution
Q3: Does it matter for pension systems if we close with τk?
3 / 35

Our contribution
Q3: Does it matter for pension systems if we close with τk? Yes!
3 / 35

What we do
OLG model with idiosyncratic income shocks, US
Baseline: Stylized US system: AIME and caps
with longevity → deﬁcit
4 / 35

What we do
Reform: Individual DC, 50% funded
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What we do
• tax on capital income gains
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What we do
• compare it with the literature
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What we do
• 2 pension system adjustments: contribution or beneﬁts
4 / 35

What we do
• 2 alternative tax closures: tax on labor income, consumption (with or without
debt)
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What we do
debt)
• study welfare eﬀect and political support
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What we do
debt)
• study welfare eﬀect and political support
• decompose welfare change into insurance and eﬃciency
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Preview of ﬁndings
• Nishiyama & Smetters is NOT universal: reform + τk −→ welfare ↑
5 / 35

• boost eﬃciency more
5 / 35

• low elasticity of response to taxation
5 / 35

• insurance motive actually rather small
5 / 35

• Public debt often “buys” political support
5 / 35

• Public debt often “buys” political support
• Welfare gains and political support only sometimes overlap
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Contents
The model
The government
Calibration
Results
Summary
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The model
Consumers
• uncertain lifetimes: live for 16 periods, with survival rate πj,t < 1
7 / 35

The model
Consumers
• uninsurable earnings risk: endogenous labor supply + income shocks
AR(1) process approximated by Markov chain
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The model
Consumers
• pay taxes (progressive on labor, linear on consumption and capital gains)
7 / 35

The model
Consumers
• contribute to pensions
7 / 35

The model
Consumers
• no annuity ﬁnancial markets with (risk free) interest rate
7 / 35

The model
Consumers
• no annuity ﬁnancial markets with (risk free) interest rate
Competitive producers
• Cobb-Douglas production function, with capital depreciation rate d
• Proﬁt maximization implies
wt = (1 − α)Kα
t zt(ztLt)−α
and rt = αKα−1
(ztLt)1−α
− d
7 / 35

The pension system
Baseline scenario: PAYG DB with progressivity
• AIME: regressive replacement rate on life-time contributions ⇒ insurance
8 / 35

The pension system
• b ¯J,t = ρ · ¯wt
8 / 35

The pension system
• b ¯J,t = ρ · ¯wt
• longevity ↑ −→ deﬁcit ↑ ⇒ permanent ﬁscal closure
8 / 35

The pension system
• b ¯J,t = ρ · ¯wt
• pensions remain high
8 / 35

The pension system
• b ¯J,t = ρ · ¯wt
Reform scenario: partially funded DC (τ = τP AY G
+ τF
)
• individual pension accounts ⇒ no insurance
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The pension system
• b ¯J,t = ρ · ¯wt
+ τF
)
• b ¯J,t = bP AY G
+ bF
= accrued ‘savings’
life expectancyt
+ accrued savings
life expectancyt
8 / 35

The pension system
• b ¯J,t = ρ · ¯wt
+ τF
)
+ bF
life expectancyt
+ accrued savings
life expectancyt
• longevity ↑ −→ pensions ↓ ⇒ private voluntary savings ↑
8 / 35

The pension system
• b ¯J,t = ρ · ¯wt
+ τF
)
+ bF
life expectancyt
+ accrued savings
life expectancyt
• longevity ↑ −→ pensions ↓ ⇒ private voluntary savings ↑
• funding generates deﬁcit ⇒ transitory ﬁscal closure
8 / 35

Contents
The model
The government
Calibration
Results
Summary
9 / 35

Government
• Finances government spending Gt = gzt
J
j=1 Nj,t,
10 / 35

Government
J
j=1 Nj,t,
• Balances pension system: subsidyt
10 / 35

Government
J
j=1 Nj,t,
• Services debt: ∆Dt = Dt − Dt−1
10 / 35

Government
J
j=1 Nj,t,
• Collects taxes
Tt = ∆Dt + Gt + subsidyt + rtDt
Tt = τk,trtAt + Taxl,t + τc,tCt + Υ
J
j=1
Nj,t
10 / 35

Government
J
j=1 Nj,t,
• Collects taxes
Tt = ∆Dt + Gt + subsidyt + rtDt
Tt = τk,trtAt + Taxl,t + τc,tCt + Υ
J
j=1
Nj,t
−→ which taxes to adjust?
10 / 35

The literature diﬀers in terms of ﬁnancing the reform
11 / 35

• 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)
12 / 35

• 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)
12 / 35

• 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 papers with comparisons across ﬁscal closures
12 / 35

Fiscal policy: capital income taxation
• capital income gain tax, τk,t
τk,t =
1
rtAt
· τl(1 − τ)wtLt + τcCt + Υ
J
j=1
Nj,t − Gt − subsidyt − rtDt + ∆Dt
13 / 35

τk,t =
1
rtAt
J
j=1
• smoothing tax adjustments with public debt, with a ﬁscal rule
τk,t = (1 − )τfinal
k + τk,t−1 + D
Dt
Yt
−
D
Y
final
• debt in the ﬁnal SS = debt in the initial SS
13 / 35

τk,t =
1
rtAt
J
j=1
k + τk,t−1 + D
Dt
Yt
−
D
Y
final
Baseline: ﬁnance permanent gap (∀t : subsidyt > 0)
13 / 35

τk,t =
1
rtAt
J
j=1
k + τk,t−1 + D
Dt
Yt
−
D
Y
final
Baseline: ﬁnance permanent gap (∀t : subsidyt > 0)
Reform: ﬁnance transitory gap (t → T : subsidyt = 0)
13 / 35

For comparison: other ﬁscal policy accompanying the reform
• Two closures within pension system details
• contributions → labor supply
• pensions → consumption (of retirees)
14 / 35

For comparison: other ﬁscal policy accompanying the reform
• Two closures within pension system details
• contributions → labor supply
• pensions → consumption (of retirees)
• Two closures outside pension system details
• consumption tax (+ debt) → consumption (of all cohorts)
14 / 35

Contents
The model
The government
Calibration
Results
Summary
15 / 35

Calibration to replicate US economy (2015)
Preferences
• Preference for leisure φ matches average hours 33%
• Discounting rate δ matches interest rate 5.5%
16 / 35

Preferences
Idiosyncratic productivity shock based on Kruger and Ludwig (2013):
• Persistence η = 0.95
• Variance ση = 0.375
16 / 35

Preferences
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 (¯j = 9)
16 / 35

Preferences
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 (¯j = 9)
Taxes {τc, τk, τl} match revenue as % of GDP {2.8%, 5.4%, 9.2%}
Depreciation rate d matches investment rate of 22%
16 / 35

Demography is based on UN projections.
number of 20-year-olds mortality rates
17 / 35

Contents
The model
The government
Calibration
Results
Summary
18 / 35

No reform: if longevity ↑, economy adjusts K/L
capital labor supply
19 / 35

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
20 / 35

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
20 / 35

The ﬁscal needs: baseline vs reform
baseline reform
21 / 35

The welfare eﬀects: τk vs Nishiyama & Smetters
τc τk
22 / 35

Welfare effects of the pension system reform
Fiscal closure
Reform to DC Reform to DC with partial funding
fixed longevity growing longevity fixed longevity growing longevity
(1) (2) (3) (4)
τk 0.83 0.89 0.47 0.06
23 / 35

Welfare effects of the pension system reform
Fiscal closure
Reform to DC Reform to DC with partial funding
fixed longevity growing longevity fixed longevity growing longevity
(1) (2) (3) (4)
τk 0.83 0.89 0.47 0.06
τc 0.72 0.57 0.13 -0.04
23 / 35

Insurance is small & eﬃciency is large(er)
τc
24 / 35

Insurance is small & eﬃciency is large(er)
τc τk
24 / 35

Reform: the capital grows more with the reform
capital labor supply
25 / 35

Public debt helps gaining political support (not just for τk)
26 / 35

Welfare eﬀect - τk & debt + τk
27 / 35

Welfare eﬀect - transition - τk & debt + τk
28 / 35

Capital really is becoming less elastic
29 / 35

Contents
The model
The government
Calibration
Results
Summary
30 / 35

Welfare effects of reform depend on fiscal policy
1. efficiency effects of fiscal policy can be big
2. smoothing by public debt buys political support
31 / 35

Features of this literature
• Labor has a roughly 10% reaction to reduced distortions
• Savings have a roughly 10% reaction to longevity
31 / 35

Features of this literature
• Labor has a roughly 10% reaction to reduced distortions
• Savings have a roughly 10% reaction to longevity
Why is capital tax so nice? −→ relatively less responsive to the tax hikes
capital accumulation ↑ with longevity + funding + less insurance
Under longevity: capital tax better than consumption tax
Without longevity: funding and DC reduce welfare regardless of ﬁscal closure
31 / 35

Thank you and
I am happy to take questions!
w: grape.org.pl
t: grape org
f: grape.org
e: j.tyrowicz@grape.org.pl
32 / 35

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

Fiscal closures outside pension system, subsidyt = 0
GO BACK
• consumption tax, τc,t
Tt = Taxl,t + 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: the ﬁnal SS = the initial SS

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

Model solving
• Consumer problem (backward policy function iterations)

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 for idiosyncratic
productivity and the policy functions compute the distribution in any successive
age j.
• aggregation done with Gaussian quadrature

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 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

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