Progressing towards efficiency: the role for labor tax progression in reforming social security

Progressing into efficiency:
the role for labor tax progression in privatizing social security
Oliwia Komada (FAME|GRAPE)
Krzysztof Makarski (FAME|GRAPE and Warsaw School of Economics)
Joanna Tyrowicz (FAME|GRAPE, University of Regensburg, and IZA)
Baltic Economic Conference
Riga | Latvia | 2023
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Motivation
Social security is essentially about insurance:
• old age (between cohorts) & mortality (annuitized)
Benartzi et al. 2011, Bruce & Turnovsky 2013, Reichling & Smetters 2015, Caliendo et al. 2017
• low income (within cohort redistribution)
Cooley & Soares 1996, Tabellini 2000
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Motivation
Prevailing consensus:
• privatization of social security brings efficiency gains,
• but reduces (within cohort) redistribution
• the insurance loss outweighs efficiency gains
e.g. Nishiyama & Smetters (2007)
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Motivation
Our approach: replace redistribution in social security with labor tax progression
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Motivation
Our approach: replace redistribution in social security with labor tax progression
Bottom line: shift insurance from retirement to working period →
improve efficiency of social security → raise welfare.
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Table of contents
Motivation
Stylized theoretical model
Quantitative model
Results
Conclusions
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Stylized theoretical model
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Stylized theoretical model: partial equilibrium OLG model
Two types of households:
• measure one, θ ∈ {θL, θH } with ωθ ∈ {ωL, ωH }, and ωH > ωL,
• income y(θ) = ωθwt ℓt (θ),
• wage wt grows at the constant rate γ, wt = (1 + γ)t
• wlog: interest rate r = γ and 1 + r = δ−1
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Two types of households:
• measure one, θ ∈ {θL, θH } with ωθ ∈ {ωL, ωH }, and ωH > ωL,
• income y(θ) = ωθwt ℓt (θ),
• wage wt grows at the constant rate γ, wt = (1 + γ)t
• wlog: interest rate r = γ and 1 + r = δ−1
• GHH preferences: Frisch elasticity + risk aversion
U(θ) =
1
1 − σ
(c1,t (θ) −
ϕ(1 + γ)t
1 + 1
η
ℓ1,t (θ)
1+ 1
η )1−σ
+ β
1
1 − σ
c2,t+1(θ)1−σ
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Households: live for 2 periods, population is constant
• choose labor, consumption and assets
first period: c1,t (θ) + a1,t+1(θ) = (1 − τ)ωθwt ℓt (θ) − τℓ(1 − τ)ωθwt ℓt (θ) + µt
second period: c2,t+1(θ) = (1 + r)a1,t+1(θ) + b2,t+1(θ)
• lifetime budget constraint (allows to see the main result)
c1,t (θ) +
c2,t+1(θ)
1 + r
= RHSt (θ) = (1 − τ)ωθwt ℓ1,t (θ) − τℓ(1 − τ)wt ωθℓ1,t (θ) + µt +
b2,t+1(θ)
1 + r
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Government:
• needs to finance exogenous level of expenditure g̃ = gt /(1 + γ)t
= constant,
• collects progressive income tax with fixed marginal rate and lump-sum grants
τℓ · (1 − τ)ωθwt ℓt (θ) − µt
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Government:
• needs to finance exogenous level of expenditure g̃ = gt /(1 + γ)t
= constant,
• collects progressive income tax with fixed marginal rate and lump-sum grants
τℓ · (1 − τ)ωθwt ℓt (θ) − µt
• The government budget constraint is
gt + 2 · µt =
X
θ∈{θL,θH }
τℓ · (1 − τ)ωθwt ℓt (θ),
whatever funds are left after covering government expenditures are spent on lump-sum grants µt .
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Social security
Beveridge (full redistribution): bBEV
2,t+1(θ) = τ (1 + γ) wt
1
2
X
θ∈{L,H}
ωθℓ1,t+1(θ)
Bismarck (no redistribution): bBIS
2,t+1(θ) = τ (1 + γ) wt ωθℓ1,t (θ)
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Social security
Beveridge (full redistribution): bBEV
2,t+1(θ) = τ (1 + γ) wt
1
2
X
θ∈{L,H}
ωθℓ1,t+1(θ)
Bismarck (no redistribution): bBIS
2,t+1(θ) = τ (1 + γ) wt ωθℓ1,t (θ)
RHS of lifetime budget
Beveridge: RHSt (θ) = (1 − τ)wt ωθℓ1,t (θ) − τℓ(1 − τ)wt ωθℓ1,t (θ) + µt + τwt
1
2
X
θ∈{L,H}
ωθℓ1,t+1(θ)
Bismarck: RHSt (θ) = (1 − τ)wt ωθℓ1,t (θ) − τℓ(1 − τ)wt ωθℓ1,t (θ) + µt + τwt ωθℓ1,t (θ)
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Basic intuitions
Reform and lifetime budget for type θ
RHSBIS
t (θ) − RHSBEV
t (θ) =
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Basic intuitions
RHSBIS
t (θ) − RHSBEV
t (θ) =
ωθwt (ℓBIS
1,t (θ) − ℓBEV
1,t (θ))
| {z }
efficiency gain
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Basic intuitions
RHSBIS
t (θ) − RHSBEV
t (θ) =
ωθwt (ℓBIS
1,t (θ) − ℓBEV
1,t (θ))
| {z }
efficiency gain
W (θH ) ↑ W (θL) ↑
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Basic intuitions
RHSBIS
t (θ) − RHSBEV
t (θ) =
ωθwt (ℓBIS
1,t (θ) − ℓBEV
1,t (θ))
| {z }
efficiency gain
W (θH ) ↑ W (θL) ↑
−
1
2
τwt (ωLℓBEV
1,t (θL) − ωH ℓBEV
1,t (θH ))
| {z }
social security redistribution
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Basic intuitions
RHSBIS
t (θ) − RHSBEV
t (θ) =
ωθwt (ℓBIS
1,t (θ) − ℓBEV
1,t (θ))
| {z }
efficiency gain
W (θH ) ↑ W (θL) ↑
−
1
2
τwt (ωLℓBEV
1,t (θH ))
| {z }
W (θH ) ↑ W (θL) ↓
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Basic intuitions
RHSBIS
t (θ) − RHSBEV
t (θ) =
ωθwt (ℓBIS
1,t (θ) − ℓBEV
1,t (θ))
| {z }
efficiency gain
W (θH ) ↑ W (θL) ↑
−
1
2
τwt (ωLℓBEV
1,t (θH ))
| {z }
W (θH ) ↑ W (θL) ↓
+ (µBIS
t − µBEV
t − τℓ(1 − τ)ωLwt (ℓBIS
1,t (θL) − ℓBEV
1,t (θL))
| {z }
⇑ NEW tax system redistribution
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Basic intuitions
RHSBIS
t (θ) − RHSBEV
t (θ) =
ωθwt (ℓBIS
1,t (θ) − ℓBEV
1,t (θ))
| {z }
efficiency gain
W (θH ) ↑ W (θL) ↑
−
1
2
τwt (ωLℓBEV
1,t (θH ))
| {z }
W (θH ) ↑ W (θL) ↓
+ (µBIS
t − µBEV
t − τℓ(1 − τ)ωLwt (ℓBIS
1,t (θL) − ℓBEV
1,t (θL))
| {z }
⇑ NEW tax system redistribution
W (θH ) ↓ W (θL) ↑
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The three effects
1. Efficiency effect (Beveridge → Bismarck, reduces distortions)
ℓBIS
1,t (θ) > ℓBEV
1,t (θ) > 0
Welfare ∀θ W (θ) ↑ follows from the envelope theorem.
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The three effects
ℓBIS
1,t (θ) > ℓBEV
1,t (θ) > 0
2. Redistribution effect (PV Pen
t (θ) =
b2,t+1(θ)
1+r
− τwt ωθℓ1,t (θ))
W (θH ) gains
W (θL) looses
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The three effects
ℓBIS
1,t (θ) > ℓBEV
1,t (θ) > 0
2. Redistribution effect (PV Pen
t (θ) =
b2,t+1(θ)
1+r
− τwt ωθℓ1,t (θ))
W (θH ) gains
W (θL) looses
3. Additional redistribution through the tax system
Can it compensate?
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Redistribution through tax system
1. % ∆ in labor supply is equal for both productivity types and increases with η
ℓBIS
(θ) − ℓBEV
(θ)
ℓBEV (θ)
=

(1 − τℓ(1 − τ))
(1 − τ − τℓ(1 − τ))
η
− 1 ≡ ξη
− 1
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ℓBIS
(θ) − ℓBEV
(θ)
ℓBEV (θ)
=

(1 − τℓ(1 − τ))
(1 − τ − τℓ(1 − τ))
η
− 1 ≡ ξη
− 1
2. % ∆ in government revenue R increases with η (Frisch elasticity) ⇒ pool for µt ↑
RBIS
− RBEV
RBEV
≡ ξη
− 1
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ℓBIS
(θ) − ℓBEV
(θ)
ℓBEV (θ)
=

(1 − τℓ(1 − τ))
(1 − τ − τℓ(1 − τ))
η
− 1 ≡ ξη
− 1
RBIS
− RBEV
RBEV
≡ ξη
− 1
3. The change in net tax transfer for θL positive and for θH negative
∆µt − τℓ(1 − τ)ωLwt ∆ℓt (θL) 0 and ∆µt − τℓ(1 − τ)ωH wt ∆ℓt (θH ) 0
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ℓBIS
(θ) − ℓBEV
(θ)
ℓBEV (θ)
=

(1 − τℓ(1 − τ))
(1 − τ − τℓ(1 − τ))
η
− 1 ≡ ξη
− 1
RBIS
− RBEV
RBEV
≡ ξη
− 1
Reform + lump sum transfers bundle =⇒ positive (increasing in η) transfers from θH -type households to
the θL-type households through the tax system.
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ℓBIS
(θ) − ℓBEV
(θ)
ℓBEV (θ)
=

(1 − τℓ(1 − τ))
(1 − τ − τℓ(1 − τ))
η
− 1 ≡ ξη
− 1
RBIS
− RBEV
RBEV
≡ ξη
− 1
Reform + lump sum transfers bundle =⇒ positive (increasing in η) transfers from θH -type households to
the θL-type households through the tax system.
Is it big enough?
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Key results: Reform social security and extra government revenue → lump-sum grants µ
1 θH under BIS work more, have strictly higher pension benefits and pay higher taxes
(efficiency ↑ social security benefits ↑ tax liability ↑)
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2 θL under BIS work more, have (most likely) lower pension benefits and pay lower taxes
(efficiency ↑ social security benefits ↓ tax liability ↓)
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3 ∃ η̃ s.t. for θL HHs redistribution lost in pension system is fully compensated by tax system
∆PV Pen
(θL) = ∆Tax(θL)
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∆PV Pen
(θL) = ∆Tax(θL)
4 ∃ η ∈ (0, η̃) s.t. for η η reform with µ is a Pareto-improving (by continuity of the utility function)
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∆PV Pen
(θL) = ∆Tax(θL)
4 ∃ η ∈ (0, η̃) s.t. for η η reform with µ is a Pareto-improving (by continuity of the utility function)
5 ∃ η ∈ (0, η) s.t. for η η reform with µ is a Hicks-improving (by the same token)
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Quantitative model
Consumers
• uncertain lifetimes: live for 16 periods, with survival πj 1
• ex ante heterogeneous productivity + uninsurable productivity risk
• consume, work and save based on CRRA instantaneous utility function 1
1−σ
c1−σ
− ϕ
1+1/η
ℓ1+1/η
• pay taxes (progressive on labor, linear on consumption and capital gains)
• contribute to social security, face natural borrowing constraint
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Quantitative model
Consumers
• uncertain lifetimes: live for 16 periods, with survival πj 1
• ex ante heterogeneous productivity + uninsurable productivity risk
• consume, work and save based on CRRA instantaneous utility function 1
1−σ
c1−σ
− ϕ
1+1/η
ℓ1+1/η
• pay taxes (progressive on labor, linear on consumption and capital gains)
• contribute to social security, face natural borrowing constraint
Firms and markets
• Cobb-Douglas production function, capital depreciates at rate d
• no annuity, financial markets with (risk free) interest rate
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Quantitative model
Government
• Finances government spending Gt , constant between scenarios,
• Balances pension system: subsidyt
• Services debt: rt Dt ,
• Collects taxes on capital, consumption, labor, and covers lump-sum grant
(progressive labor tax given by Benabou form)
Gt + subsidyt + rt Dt + Mt = τk,t rt At + τc,t Ct + Taxℓ,t + ∆Dt
where ∆Dt = Dt − Dt−1
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Policy experiment: comparative statics
Status quo: current US social security
• benefits redistributive, with high replacement rate for low income individuals
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• distortion, households do not see the link between labor supply and pension benefits
aj+1,t+1 + (1 + τc,t )cj,t = (1 + (1 − τk )rt )aj,t + (1 − τ)yj,t − Tt ((1 − τ)yj,t ) + Γj,t + 0 · τwt ωj,t ℓj,t + 0
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Alternative: fully individualized social security and lump-sum grants
• benefits proportional to contribution, no redistribution through social security
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• no distortion, households see the link between labor supply and pension benefits
aj+1,t+1 + (1 + τc,t )cj,t = (1 + (1 − τk )rt )aj,t + (1 − τ)yj,t − Tt ((1 − τ)yj,t ) + Γj,t + υR
j,t · τwt ωj,t ℓj,t + µt ,
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• no distortion, households see the link between labor supply and pension benefits
aj+1,t+1 + (1 + τc,t )cj,t = (1 + (1 − τk )rt )aj,t + (1 − τ)yj,t − Tt ((1 − τ)yj,t ) + Γj,t + υR
j,t · τwt ωj,t ℓj,t + µt ,
• additional tax revenue (from increased efficiency) goes into lump-sum grants
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Calibration to replicate US economy (2015)
Preferences: instantaneous utility function take CRRA form with
• Risk aversion σ is equal to 2
• Disutility form work ϕ matches average hours 33%
• Frisch elasticity η is equal to 0.8
• Discounting rate δ matches interest K/Y ratio 2.9
Productivity risk and age profiles shock based on Borella et. al (2018):
Pension system
• Replacement rate ρ matches benefits as % of GDP 5.0%
• Contribution rate balances pension system in the initial steady state
• Pension eligibility age at 65
Taxes {τc , τk , τℓ} match revenue as % of GDP {2.8%, 5.4%, 9.2%}
Depreciation rate d based on Kehoe Ruhl (2010) equal to 0.06
Population survival probabilities based on UN forecast
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Distortion for η = 0.8
labor wedge formula
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Labor supply reaction for η = 0.8
Average ∆ℓ ↑ 2.6% for HHs below median and 3.0% above median
Heathcote et al. (2008) argue for ↑ for high-productivity and ↓ for low-productivity.
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Taxes and pensions changes
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Distribution of welfare effects for η = 0.8
Under the veil of ignorance consumption equivalent increases by 0.3%
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Distribution of welfare effects for η = 0.8
Under the veil of ignorance consumption equivalent increases by 0.3%
Ex post almost universal gains (90%).
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Welfare effect across η
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Macroeconomic adjustment across η
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Fiscal adjustment across η
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Longevity makes the reform beneficial for even less responsive labor markets
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Half-internalizing the reform is sufficient to deliver welfare gains (η = 0.8)
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Conclusions
1. Progression in the tax system can effectively substitute for progression in social security ...
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Conclusions
2. ... generating welfare gains
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Conclusions
3. With rising longevity, the potential welfare gains are higher.
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Conclusions
3. With rising longevity, the potential welfare gains are higher.
4. Important role for response of labor to the features of the pension system
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Questions or suggestions?
Thank you!
w: grape.org.pl
t: grape org
f: grape.org
e: j.tyrowicz@grape.org.pl
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Labor wedge as measure of distortion
With marginal labor income tax denoted as T ′
(yj,t (sj,t ))
ϕℓj,t (sj,t )
1
η =
cj,t (sj,t )−σ
1 + τc

1 − (1 − τ)T ′
(yj,t (sj,t )) − τ(1 − υj,t )

wt ωj,t (sj,t ),
Which gives the formula for wedge:
ϑj,t (sj,t ) =
(1 − τ)T ′
(yj,t (sj,t )) + τ(1 − υj,t ) − 1
1 + τc
+ 1.
Chari et al (2007), Berger et al (2019) and Boar and Midrigan (2020), Cociuba and Ueberfeldt (2020)
back to results
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Progressing towards efficiency: the role for labor tax progression in reforming social security

Progressing towards efficiency: the role for labor tax progression in reforming social security

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Progressing towards efficiency: the role for labor tax progression in reforming social security