Progressing towards efficiency: the role for labor tax progression ...

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Progressing into efficiency:
the role for labor tax progression in privatizing social security
Oliwia Komada (FAME|GRAPE)
...

Motivation
2 / 34

Motivation
Social security is essentially about insurance:
• old age (between cohorts) & mortality (annuitized)
Benartzi e...

Motivation
Social security is essentially about insurance:
• old age (between cohorts) & mortality (annuitized)
Benartzi e...

Motivation
Social security is essentially about insurance:
• old age (between cohorts) & mortality (annuitized)
Benartzi e...

Motivation
Social security is essentially about insurance:
• old age (between cohorts) & mortality (annuitized)
Benartzi e...

Table of contents
Motivation
Stylized theoretical model
Quantitative model
Results
Conclusions
4 / 34

Stylized theoretical model
5 / 34

Stylized theoretical model: partial equilibrium OLG model
Incomes:
• wage wt grows at the constant rate γ, wt = (1 + γ)t
,...

Stylized theoretical model: partial equilibrium OLG model
Incomes:
• wage wt grows at the constant rate γ, wt = (1 + γ)t
,...

Stylized theoretical model: partial equilibrium OLG model
Incomes:
• wage wt grows at the constant rate γ, wt = (1 + γ)t
,...

Stylized theoretical model: partial equilibrium OLG model
Government:
• needs to finance exogenous level of expenditure g̃...

Stylized theoretical model: partial equilibrium OLG model
Government:
• needs to finance exogenous level of expenditure g̃...

Stylized theoretical model: partial equilibrium OLG model
Social security
Beveridge (full redistribution): bBEV
2,t+1(θ) =...

Stylized theoretical model: partial equilibrium OLG model
Social security
Beveridge (full redistribution): bBEV
2,t+1(θ) =...

Stylized theoretical model: partial equilibrium OLG model
Social security
Beveridge (full redistribution): bBEV
2,t+1(θ) =...

Basic intuitions
Reform and lifetime budget for type θ
RHSBIS
t (θ) − RHSBEV
t (θ) =
9 / 34

Basic intuitions
Reform and lifetime budget for type θ
RHSBIS
t (θ) − RHSBEV
t (θ) =
ωθwt (ℓBIS
1,t (θ) − ℓBEV
1,t (θ))
| ...

Basic intuitions
Reform and lifetime budget for type θ
RHSBIS
t (θ) − RHSBEV
t (θ) =
ωθwt (ℓBIS
1,t (θ) − ℓBEV
1,t (θ))
| ...

Basic intuitions
Reform and lifetime budget for type θ
RHSBIS
t (θ) − RHSBEV
t (θ) =
ωθwt (ℓBIS
1,t (θ) − ℓBEV
1,t (θ))
| ...

Basic intuitions
Reform and lifetime budget for type θ
RHSBIS
t (θ) − RHSBEV
t (θ) =
ωθwt (ℓBIS
1,t (θ) − ℓBEV
1,t (θ))
| ...

Basic intuitions
Reform and lifetime budget for type θ
RHSBIS
t (θ) − RHSBEV
t (θ) =
ωθwt (ℓBIS
1,t (θ) − ℓBEV
1,t (θ))
| ...

Basic intuitions
Reform and lifetime budget for type θ
RHSBIS
t (θ) − RHSBEV
t (θ) =
ωθwt (ℓBIS
1,t (θ) − ℓBEV
1,t (θ))
| ...

Efficiency effect
Beveridge (full redistribution)
ℓBIS
1,t (θ) = [
1
ϕ
(1 − τℓ(1 − τ))ωθ]η
.
10 / 34

Efficiency effect
Beveridge (full redistribution)
ℓBIS
1,t (θ) = [
1
ϕ
(1 − τℓ(1 − τ))ωθ]η
.
Bismarck (no redistribution)
...

Efficiency effect
Beveridge (full redistribution)
ℓBIS
1,t (θ) = [
1
ϕ
(1 − τℓ(1 − τ))ωθ]η
.
Bismarck (no redistribution)
...

Redistribution through social security
Denote: PV Pen
t (θ) =
b2,t+1(θ)
1 + r
− τwt ωθℓ1,t (θ), then:
11 / 34

Redistribution through social security
Denote: PV Pen
t (θ) =
b2,t+1(θ)
1 + r
− τwt ωθℓ1,t (θ), then:
θH gains from less r...

Redistribution through social security
Denote: PV Pen
t (θ) =
b2,t+1(θ)
1 + r
− τwt ωθℓ1,t (θ), then:
θH gains from less r...

Redistribution through social security
Denote: PV Pen
t (θ) =
b2,t+1(θ)
1 + r
− τwt ωθℓ1,t (θ), then:
θH gains from less r...

Redistribution through social security
Denote: PV Pen
t (θ) =
b2,t+1(θ)
1 + r
− τwt ωθℓ1,t (θ), then:
θH gains from less r...

Redistribution through tax system
1. % ∆ in labor supply is equal for both productivity types and increases with η
ℓBIS
(θ...

Redistribution through tax system
1. % ∆ in labor supply is equal for both productivity types and increases with η
ℓBIS
(θ...

Redistribution through tax system
1. % ∆ in labor supply is equal for both productivity types and increases with η
ℓBIS
(θ...

Redistribution through tax system
1. % ∆ in labor supply is equal for both productivity types and increases with η
ℓBIS
(θ...

Redistribution through tax system
1. % ∆ in labor supply is equal for both productivity types and increases with η
ℓBIS
(θ...

Redistribution through tax system
1. % ∆ in labor supply is equal for both productivity types and increases with η
ℓBIS
(θ...

Redistribution through tax system
1. % ∆ in labor supply is equal for both productivity types and increases with η
ℓBIS
(θ...

Key results: Reform social security and extra government revenue → lump-sum grants µ
1 θH under BIS work more, have strict...

Key results: Reform social security and extra government revenue → lump-sum grants µ
1 θH under BIS work more, have strict...

Key results: Reform social security and extra government revenue → lump-sum grants µ
1 θH under BIS work more, have strict...

Key results: Reform social security and extra government revenue → lump-sum grants µ
1 θH under BIS work more, have strict...

Key results: Reform social security and extra government revenue → lump-sum grants µ
1 θH under BIS work more, have strict...

Key results: Reform social security and extra government revenue → lump-sum grants µ
1 θH under BIS work more, have strict...

Key results: Reform social security and extra government revenue → lump-sum grants µ
1 θH under BIS work more, have strict...

Key results: Reform social security and extra government revenue → lump-sum grants µ
1 θH under BIS work more, have strict...

Quantitative model
14 / 34

Quantitative model
Consumers
• uncertain lifetimes: live for 16 periods, with survival πj 1
• ex ante heterogeneous produ...

Quantitative model
Consumers
• uncertain lifetimes: live for 16 periods, with survival πj 1
• ex ante heterogeneous produ...

Quantitative model
Government
• Finances government spending Gt , constant between scenarios,
• Balances pension system: s...

Policy experiment: comparative statics
Status quo: current US social security
• benefits redistributive, with high replace...

Policy experiment: comparative statics
Status quo: current US social security
• benefits redistributive, with high replace...

Policy experiment: comparative statics
Status quo: current US social security
• benefits redistributive, with high replace...

Policy experiment: comparative statics
Status quo: current US social security
• benefits redistributive, with high replace...

Policy experiment: comparative statics
Status quo: current US social security
• benefits redistributive, with high replace...

Policy experiment: comparative statics
Status quo: current US social security
• benefits redistributive, with high replace...

Calibration to replicate US economy (2015)
Preferences: instantaneous utility function take CRRA form with
• Risk aversion...

Results
19 / 34

Distortion for η = 0.8
labor wedge formula
20 / 34

Distortion for η = 0.8
21 / 34

Distortion for η = 0.8
22 / 34

Labor supply reaction for η = 0.8
Average ∆ℓ ↑ 2.6% for HHs below median and 3.0% above median
Heathcote et al. (2008) arg...

Taxes and pensions changes
24 / 34

Distribution of welfare effects for η = 0.8
Under the veil of ignorance consumption equivalent increases by 0.3%
25 / 34

Distribution of welfare effects for η = 0.8
Under the veil of ignorance consumption equivalent increases by 0.3%
Ex post a...

Welfare effect across η
26 / 34

Macroeconomic adjustment across η
27 / 34

Fiscal adjustment across η
28 / 34

Longevity makes the reform beneficial for even less responsive labor markets
29 / 34

Half-internalizing the reform is sufficient to deliver welfare gains (η = 0.8)
30 / 34

Conclusions
31 / 34

Conclusions
1. Progression in the tax system can effectively substitute for progression in social security ...
32 / 34

Conclusions
1. Progression in the tax system can effectively substitute for progression in social security ...
2. ... gene...

Conclusions
1. Progression in the tax system can effectively substitute for progression in social security ...
2. ... gene...

Conclusions
1. Progression in the tax system can effectively substitute for progression in social security ...
2. ... gene...

Questions or suggestions?
Thank you!
w: grape.org.pl
t: grape org
f: grape.org
e: j.tyrowicz@grape.org.pl
33 / 34

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...

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