We study interactions between progressive labor taxation and social security reform. Increasing longevity puts fiscal strain that necessitates the social security reform. The current social security is redistributive, thus providing (at least partial) insurance against idiosyncratic income shocks, but at the expense of labor supply distortions. A reform which links pensions to individual incomes reduces distortions associated with social security contributions, but incurs insurance loss. We show that the progressive labor tax can partially substitute for the redistribution in social security, thus reducing the insurance loss.

1. 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)
IIPF, Linz, 2022
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2. Motivation

3. 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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4. 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
Prevailing consensus:
• privatization of social security brings efficiency gains,
• but reduces (within cohort) redistribution
e.g. Diamond 1977 + large and diverse subsequent literature
• this insurance loss reduces overall welfare effect of such reforms
e.g. Nishiyama & Smetters (2007)
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5. 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
Prevailing consensus:
• privatization of social security brings efficiency gains,
• but reduces (within cohort) redistribution
e.g. Diamond 1977 + large and diverse subsequent literature
• this insurance loss reduces overall welfare effect of such reforms
e.g. Nishiyama & Smetters (2007)
Our approach: replace redistribution in social security with tax progression
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6. 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
Prevailing consensus:
• privatization of social security brings efficiency gains,
• but reduces (within cohort) redistribution
e.g. Diamond 1977 + large and diverse subsequent literature
• this insurance loss reduces overall welfare effect of such reforms
e.g. Nishiyama & Smetters (2007)
Our approach: replace redistribution in social security with tax progression
Bottom line: shift insurance from retirement to working period →
improve efficiency of social security → raise welfare.
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7. Table of contents
Motivation
Stylized theoretical model
Quantitative model
Results
Conclusions
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8. Stylized theoretical model

9. Stylized theoretical model: partial equilibrium OLG model
Incomes:
• wage wt grows at the constant rate γ, wt = (1 + γ)t
, interest rate r = γ.
• two types θ ∈ {θL, θH } of measure one
• income y(θ) = ωθwt `t (θ), ωθ ∈ {ωL, ωH }, ωH > ωL,
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10. Stylized theoretical model: partial equilibrium OLG model
Households: live for 2 periods, population is constant
• choose labor, consumption and assets
first period: c1,t (θ) + a1,t+1(θ) = (1 − τ)yt (θ) − Tt ((1 − τ)yt (θ)), Tt (yt ) = τ`yt − µt
second period: c2,t+1(θ) = (1 + r)a1,t+1(θ) + b2,t+1(θ)
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11. Stylized theoretical model: partial equilibrium OLG model
Households: live for 2 periods, population is constant
• choose labor, consumption and assets
first period: c1,t (θ) + a1,t+1(θ) = (1 − τ)yt (θ) − Tt ((1 − τ)yt (θ)), Tt (yt ) = τ`yt − µt
second period: c2,t+1(θ) = (1 + r)a1,t+1(θ) + b2,t+1(θ)
• GHH preferences: Frisch elasticity + risk aversion
U(θ) =
1
1 − σ
(c1,t (θ) −
φ
1 + 1
η
zt `1,t (θ)
1+ 1
η + βc2,t+1(θ))1−σ
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12. Stylized theoretical model: partial equilibrium OLG model
Households: live for 2 periods, population is constant
• choose labor, consumption and assets
first period: c1,t (θ) + a1,t+1(θ) = (1 − τ)yt (θ) − Tt ((1 − τ)yt (θ)), Tt (yt ) = τ`yt − µt
second period: c2,t+1(θ) = (1 + r)a1,t+1(θ) + b2,t+1(θ)
• GHH preferences: Frisch elasticity + risk aversion
U(θ) =
1
1 − σ
(c1,t (θ) −
φ
1 + 1
η
zt `1,t (θ)
1+ 1
η + βc2,t+1(θ))1−σ
• In this setup c1 and c2 perfect substitutes + β−1
= 1 + r, so:
c2,t+1(θ) = 0
a1,t+1 = −
b2,t+1(θ)
(1+r(=γ))
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13. Stylized theoretical model: partial equilibrium OLG model
Households: live for 2 periods, population is constant
• choose labor, consumption and assets
first period: c1,t (θ) + a1,t+1(θ) = (1 − τ)yt (θ) − Tt ((1 − τ)yt (θ)), Tt (yt ) = τ`yt − µt
second period: c2,t+1(θ) = (1 + r)a1,t+1(θ) + b2,t+1(θ)
• GHH preferences: Frisch elasticity + risk aversion
U(θ) =
1
1 − σ
(c1,t (θ) −
φ
1 + 1
η
zt `1,t (θ)
1+ 1
η + βc2,t+1(θ))1−σ
• In this setup c1 and c2 perfect substitutes + β−1
= 1 + r, so:
c2,t+1(θ) = 0
a1,t+1 = −
b2,t+1(θ)
(1+r(=γ))
c1,t (θ) = (1 − τ)yt (θ) − Tt (y(θ)) + b2,t+1/(1 + γ)
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14. Stylized theoretical model: partial equilibrium OLG model
Social security
Beveridge (full redistribution): bBEV
2,t+1(θ) = τ
1
2
wt+1
X
θ∈{L,H}
ωθ`1,t+1(θ)
Bismarck (no redistribution): bBIS
2,t+1(θ) = τ (1 + γ) wt ωθ`1,t (θ)
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15. Stylized theoretical model: partial equilibrium OLG model
Social security
Beveridge (full redistribution): bBEV
2,t+1(θ) = τ
1
2
wt+1
X
θ∈{L,H}
ωθ`1,t+1(θ)
Bismarck (no redistribution): bBIS
2,t+1(θ) = τ (1 + γ) wt ωθ`1,t (θ)
Lifetime consumption
Beveridge: c1,t (θ) = (1 − τ)wt ωθ`1,t (θ) − Tt (y(θ)) + τ
1
2
wt
X
θ∈{L,H}
ωθ`1,t+1(θ)
Bismarck: c1,t (θ) = (1 − τ)wt ωθ`1,t (θ) − Tt (y(θ)) + τwt ωθ`1,t (θ)
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16. Stylized theoretical model: partial equilibrium OLG model
Government:
• needs to finance exogenous expenditure g̃ = gt /(1 + γ)t
= constant
• collects progressive income tax with marginal rate and lump-sum grants
T(ỹ(θ)) = τ` · (1 − τ)ỹ(θ) − µ̃
where ˜
yt = yt /(1 + γ)t
and µ̃t = µt /(1 + γ)t
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17. Stylized theoretical model: partial equilibrium OLG model
Government:
• needs to finance exogenous expenditure g̃ = gt /(1 + γ)t
= constant
• collects progressive income tax with marginal rate and lump-sum grants
T(ỹ(θ)) = τ` · (1 − τ)ỹ(θ) − µ̃
where ˜
yt = yt /(1 + γ)t
and µ̃t = µt /(1 + γ)t
• The government budget constraint:
g̃ +
X
θ∈{θL,θH }
µ̃t =
X
θ∈{θL,θH }
τ` · (1 − τ)ỹ(θ),
Lump-sum grants µt are a fiscal closure.
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18. Efficiency effect (result established in the literature)
Beveridge (full redistribution)
`BIS
1,t (θ) = [
1
φ
(1 − τ`(1 − τ)ωθ]η
.
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19. Efficiency effect (result established in the literature)
Beveridge (full redistribution)
`BIS
1,t (θ) = [
1
φ
(1 − τ`(1 − τ)ωθ]η
.
Bismarck (no redistribution)
`BEV
1,t (θ) = [
1
φ
(1 − τ`(1 − τ) + τ)ωθ]η
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20. Efficiency effect (result established in the literature)
Beveridge (full redistribution)
`BIS
1,t (θ) = [
1
φ
(1 − τ`(1 − τ)ωθ]η
.
Bismarck (no redistribution)
`BEV
1,t (θ) = [
1
φ
(1 − τ`(1 − τ) + τ)ωθ]η
Result: Reform (= Beveridge → Bismarck) reduces distortions: `BIS
1,t (θ) > `BEV
1,t (θ)
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21. Efficiency effect (result established in the literature)
Beveridge (full redistribution)
`BIS
1,t (θ) = [
1
φ
(1 − τ`(1 − τ)ωθ]η
.
Bismarck (no redistribution)
`BEV
1,t (θ) = [
1
φ
(1 − τ`(1 − τ) + τ)ωθ]η
Result: Reform (= Beveridge → Bismarck) reduces distortions: `BIS
1,t (θ) > `BEV
1,t (θ)
Efficiency effect −→ labor wedge ↓, both types: `(θ) ↑ and W (θ) ↑,
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22. Efficiency effect (result established in the literature)
Beveridge (full redistribution)
`BIS
1,t (θ) = [
1
φ
(1 − τ`(1 − τ)ωθ]η
.
Bismarck (no redistribution)
`BEV
1,t (θ) = [
1
φ
(1 − τ`(1 − τ) + τ)ωθ]η
Result: Reform (= Beveridge → Bismarck) reduces distortions: `BIS
1,t (θ) > `BEV
1,t (θ)
Efficiency effect −→ labor wedge ↓, both types: `(θ) ↑ and W (θ) ↑,
but what about redistribution?
1 through social security
2 through labor taxation
8 / 28

23. Redistribution through social security (result established in the literature)
High type gains from lower redistribution
bBIS
t (θH ) − bBEV
t (θH ) =
τwt
2
[ωH (`BIS
1 (θH ) − `BEV
1 (θH ))
| {z }
efficiency effect >0
+ (ωH `BIS
(θH ) − ωL`BEV
1 (θL)
| {z }
redistribution effect>0
]
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24. Redistribution through social security (result established in the literature)
High type gains from lower redistribution
bBIS
t (θH ) − bBEV
t (θH ) =
τwt
2
[ωH (`BIS
1 (θH ) − `BEV
1 (θH ))
| {z }
efficiency effect >0
+ (ωH `BIS
(θH ) − ωL`BEV
1 (θL)
| {z }
redistribution effect>0
]
Low type loses from lower redistribution
bBIS
(θL) − bBEV
(θL) =
τwt
2
[ωL(`BIS
(θL) − `BEV
(θL))
| {z }
efficiency effect >0
+ (ωL`BIS
(θL) − ωH `BEV
(θH )
| {z }
redistribution effect<0
]
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25. Redistribution through social security (result established in the literature)
High type gains from lower redistribution
bBIS
t (θH ) − bBEV
t (θH ) =
τwt
2
[ωH (`BIS
1 (θH ) − `BEV
1 (θH ))
| {z }
efficiency effect >0
+ (ωH `BIS
(θH ) − ωL`BEV
1 (θL)
| {z }
redistribution effect>0
]
Low type loses from lower redistribution
bBIS
(θL) − bBEV
(θL) =
τwt
2
[ωL(`BIS
(θL) − `BEV
(θL))
| {z }
efficiency effect >0
+ (ωL`BIS
(θL) − ωH `BEV
(θH )
| {z }
redistribution effect<0
]
Social security redistribution effect −→ benefits θH , harms: θL,
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26. Redistribution through social security (result established in the literature)
High type gains from lower redistribution
bBIS
t (θH ) − bBEV
t (θH ) =
τwt
2
[ωH (`BIS
1 (θH ) − `BEV
1 (θH ))
| {z }
efficiency effect >0
+ (ωH `BIS
(θH ) − ωL`BEV
1 (θL)
| {z }
redistribution effect>0
]
Low type loses from lower redistribution
bBIS
(θL) − bBEV
(θL) =
τwt
2
[ωL(`BIS
(θL) − `BEV
(θL))
| {z }
efficiency effect >0
+ (ωL`BIS
(θL) − ωH `BEV
(θH )
| {z }
redistribution effect<0
]
Social security redistribution effect −→ benefits θH , harms: θL, can θL be compensated?
9 / 28

27. Redistribution through tax system (new results)
1 % ∆ in labor supply is equal for both productivity types and increases with η
10 / 28

28. Redistribution through tax system (new results)
1 % ∆ in labor supply is equal for both productivity types and increases with η
10 / 28

29. Redistribution through tax system (new results)
1 % ∆ in labor supply is equal for both productivity types and increases with η
`BIS
(θ) − `BEV
(θ)
`BEV (θ)
=
(1 − τ`(1 − τ))
(1 − τ − τ`(1 − τ))
η
− 1 ≡ ξη
− 1
2 % ∆ in government revenue is exactly proportional → ∆µt ↑
RBIS
− RBEV
RBEV
≡ ξη
− 1
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30. Redistribution through tax system (new results)
1 % ∆ in labor supply is equal for both productivity types and increases with η
`BIS
(θ) − `BEV
(θ)
`BEV (θ)
=
(1 − τ`(1 − τ))
(1 − τ − τ`(1 − τ))
η
− 1 ≡ ξη
− 1
2 % ∆ in government revenue is exactly proportional → ∆µt ↑
RBIS
− RBEV
RBEV
≡ ξη
− 1
3 The change in net tax transfer for θL positive and for θH negative
10 / 28

31. Redistribution through tax system (new results)
1 % ∆ in labor supply is equal for both productivity types and increases with η
`BIS
(θ) − `BEV
(θ)
`BEV (θ)
=
(1 − τ`(1 − τ))
(1 − τ − τ`(1 − τ))
η
− 1 ≡ ξη
− 1
2 % ∆ in government revenue is exactly proportional → ∆µt ↑
RBIS
− RBEV
RBEV
≡ ξη
− 1
3 The change in net tax transfer for θL positive and for θH negative
10 / 28

32. Redistribution through tax system (new results)
1 % ∆ in labor supply is equal for both productivity types and increases with η
`BIS
(θ) − `BEV
(θ)
`BEV (θ)
=
(1 − τ`(1 − τ))
(1 − τ − τ`(1 − τ))
η
− 1 ≡ ξη
− 1
2 % ∆ in government revenue is exactly proportional → ∆µt ↑
RBIS
− RBEV
RBEV
≡ ξη
− 1
3 The change in net tax transfer for θL positive and for θH negative
∆µt − τ`(1 − τ)ωLwt ∆`t (θL) 0 and ∆µt − τ`(1 − τ)ωH wt ∆`t (θH ) 0
10 / 28

33. Redistribution through tax system (new results)
1 % ∆ in labor supply is equal for both productivity types and increases with η
`BIS
(θ) − `BEV
(θ)
`BEV (θ)
=
(1 − τ`(1 − τ))
(1 − τ − τ`(1 − τ))
η
− 1 ≡ ξη
− 1
2 % ∆ in government revenue is exactly proportional → ∆µt ↑
RBIS
− RBEV
RBEV
≡ ξη
− 1
3 The change in net tax transfer for θL positive and for θH negative
∆µt − τ`(1 − τ)ωLwt ∆`t (θL) 0 and ∆µt − τ`(1 − τ)ωH wt ∆`t (θH ) 0
Tax system redistribution effect −→ benefits θL at the expense of θH
10 / 28

34. Summary of intuitions
Reform and lifetime consumption
cBIS
t (θ) − cBEV
t (θ) =
Reform: bundle change in social security with lump sum transfers:
=⇒ raises efficiency reduces redistribution in social security
=⇒ transfers from θH -type to the θL-type through tax system are positive increasing in η.
11 / 28

35. Summary of intuitions
Reform and lifetime consumption
cBIS
t (θ) − cBEV
t (θ) = ωθwt (`BIS
1,t (θ) − `BEV
1,t (θ))
| {z }
efficiency gain
Reform: bundle change in social security with lump sum transfers:
=⇒ raises efficiency reduces redistribution in social security
=⇒ transfers from θH -type to the θL-type through tax system are positive increasing in η.
11 / 28

36. Summary of intuitions
Reform and lifetime consumption
cBIS
t (θ) − cBEV
t (θ) = ωθwt (`BIS
1,t (θ) − `BEV
1,t (θ))
| {z }
efficiency gain
W (θH ) ↑ W (θL) ↑
Reform: bundle change in social security with lump sum transfers:
=⇒ raises efficiency reduces redistribution in social security
=⇒ transfers from θH -type to the θL-type through tax system are positive increasing in η.
11 / 28

37. Summary of intuitions
Reform and lifetime consumption
cBIS
t (θ) − cBEV
t (θ) = ωθwt (`BIS
1,t (θ) − `BEV
1,t (θ))
| {z }
efficiency gain
W (θH ) ↑ W (θL) ↑
−
1
2
τwt (ωθ`BEV
1,t (θ) − ω−θ`BEV
1,t (−θ))
| {z }
social security redistribution
Reform: bundle change in social security with lump sum transfers:
=⇒ raises efficiency reduces redistribution in social security
=⇒ transfers from θH -type to the θL-type through tax system are positive increasing in η.
11 / 28

38. Summary of intuitions
Reform and lifetime consumption
cBIS
t (θ) − cBEV
t (θ) = ωθwt (`BIS
1,t (θ) − `BEV
1,t (θ))
| {z }
efficiency gain
W (θH ) ↑ W (θL) ↑
−
1
2
τwt (ωθ`BEV
1,t (θ) − ω−θ`BEV
1,t (−θ))
| {z }
social security redistribution
W (θH ) ↑ W (θL) ↓
Reform: bundle change in social security with lump sum transfers:
=⇒ raises efficiency reduces redistribution in social security
=⇒ transfers from θH -type to the θL-type through tax system are positive increasing in η.
11 / 28

39. Summary of intuitions
Reform and lifetime consumption
cBIS
t (θ) − cBEV
t (θ) = ωθwt (`BIS
1,t (θ) − `BEV
1,t (θ))
| {z }
efficiency gain
W (θH ) ↑ W (θL) ↑
−
1
2
τwt (ωθ`BEV
1,t (θ) − ω−θ`BEV
1,t (−θ))
| {z }
social security redistribution
W (θH ) ↑ W (θL) ↓
+ (µBIS
t − µBEV
t − τ`(1 − τ)ωθwt (`BIS
1,t (θ) − `BEV
1,t (θ))
| {z }
⇑ NEW tax system redistribution
Reform: bundle change in social security with lump sum transfers:
=⇒ raises efficiency reduces redistribution in social security
=⇒ transfers from θH -type to the θL-type through tax system are positive increasing in η.
11 / 28

40. Summary of intuitions
Reform and lifetime consumption
cBIS
t (θ) − cBEV
t (θ) = ωθwt (`BIS
1,t (θ) − `BEV
1,t (θ))
| {z }
efficiency gain
W (θH ) ↑ W (θL) ↑
−
1
2
τwt (ωθ`BEV
1,t (θ) − ω−θ`BEV
1,t (−θ))
| {z }
social security redistribution
W (θH ) ↑ W (θL) ↓
+ (µBIS
t − µBEV
t − τ`(1 − τ)ωθwt (`BIS
1,t (θ) − `BEV
1,t (θ))
| {z }
⇑ NEW tax system redistribution
W (θH ) ↓ W (θL) ↑
Reform: bundle change in social security with lump sum transfers:
=⇒ raises efficiency reduces redistribution in social security
=⇒ transfers from θH -type to the θL-type through tax system are positive increasing in η.
11 / 28

41. Key results
1 ∃ η̃ such that for θL HHs redistribution lost in social security is fully compensated by tax system
∆b(θL) = ∆Tax(θL) and it is given by ξη̃
− 1 =
τ
τ`(1 − τ)
12 / 28

42. Key results
1 ∃ η̃ such that for θL HHs redistribution lost in social security is fully compensated by tax system
∆b(θL) = ∆Tax(θL) and it is given by ξη̃
− 1 =
τ
τ`(1 − τ)
12 / 28

43. Key results
1 ∃ η̃ such that for θL HHs redistribution lost in social security is fully compensated by tax system
∆b(θL) = ∆Tax(θL) and it is given by ξη̃
− 1 =
τ
τ`(1 − τ)
(and then, by continuity of the utility function)
2 ∃ η ∈ (0, η̃) such that for η η reform with µ is a Pareto-improvement
12 / 28

44. Key results
1 ∃ η̃ such that for θL HHs redistribution lost in social security is fully compensated by tax system
∆b(θL) = ∆Tax(θL) and it is given by ξη̃
− 1 =
τ
τ`(1 − τ)
(and then, by continuity of the utility function)
2 ∃ η ∈ (0, η̃) such that for η η reform with µ is a Pareto-improvement
12 / 28

45. Key results
1 ∃ η̃ such that for θL HHs redistribution lost in social security is fully compensated by tax system
∆b(θL) = ∆Tax(θL) and it is given by ξη̃
− 1 =
τ
τ`(1 − τ)
(and then, by continuity of the utility function)
2 ∃ η ∈ (0, η̃) such that for η η reform with µ is a Pareto-improvement
3 ∃ η ∈ (0, η) such that for η η reform with µ is a Hicks-improvement
12 / 28

46. Quantitative model

47. 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
`1+1/η
• pay taxes (progressive on labor, linear on consumption and capital gains)
• contribute to social security, face natural borrowing constraint
13 / 28

48. 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
`1+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
13 / 28

49. 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 given by Benabou form)
Gt + subsidyt + rt Dt + Mt = τk,t rt At + τc,t Ct + Tax`,t + ∆Dt
where ∆Dt = Dt − Dt−1
14 / 28

50. Policy experiment: comparative statics
Status quo: current US social security
• benefits redistributive, with high replacement rate for low income individuals
15 / 28

51. Policy experiment: comparative statics
Status quo: current US social security
• benefits redistributive, with high replacement rate for low income individuals
• distortion, households do not perceive labor supply and pension benefits link
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 `j,t + 0
15 / 28

52. Policy experiment: comparative statics
Status quo: current US social security
• benefits redistributive, with high replacement rate for low income individuals
• distortion, households do not perceive labor supply and pension benefits link
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 `j,t + 0
15 / 28

53. Policy experiment: comparative statics
Status quo: current US social security
• benefits redistributive, with high replacement rate for low income individuals
• distortion, households do not perceive labor supply and pension benefits link
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 `j,t + 0
Alternative: fully individualized social security and lump-sum grants
• benefits proportional to contribution, no redistribution through social security
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54. Policy experiment: comparative statics
Status quo: current US social security
• benefits redistributive, with high replacement rate for low income individuals
• distortion, households do not perceive labor supply and pension benefits link
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 `j,t + 0
Alternative: fully individualized social security and lump-sum grants
• benefits proportional to contribution, no redistribution through social security
• no distortion, households perceive labor supply and pension benefit link,
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 `j,t + µt ,
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55. Policy experiment: comparative statics
Status quo: current US social security
• benefits redistributive, with high replacement rate for low income individuals
• distortion, households do not perceive labor supply and pension benefits link
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 `j,t + 0
Alternative: fully individualized social security and lump-sum grants
• benefits proportional to contribution, no redistribution through social security
• no distortion, households perceive labor supply and pension benefit link,
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 `j,t + µt ,
• additional tax revenue (from increased efficiency) goes into lump-sum grants
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56. 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 , τ`} 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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57. Results

58. Distortion for η = 0.8
labor wedge formula 17 / 28

59. Distortion for η = 0.8
labor wedge formula 18 / 28

60. Labor supply reaction for η = 0.8
Average ∆` ↑ 2.6% for HHs below median and 3.0% above median
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61. Changes in taxes (left) and pensions (right)
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62. Changes in taxes (left) and pensions (right)
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63. Distribution of welfare effects for η = 0.8
Under the veil of ignorance consumption equivalent ↑ by 0.3%
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64. Distribution of welfare effects for η = 0.8
Under the veil of ignorance consumption equivalent ↑ by 0.3%
Ex post almost universal gains (90%).
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65. Welfare effect across η
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66. Macroeconomic adjustment across η
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67. Fiscal adjustment across η
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68. Longevity makes the reform beneficial for even less responsive labor markets
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69. Conclusions

70. Conclusions
1 Progression in the tax system can effectively substitute for progression in social security ...
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71. Conclusions
1 Progression in the tax system can effectively substitute for progression in social security ...
2 ... generating welfare gains, potentially: a Pareto-improvement
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72. Conclusions
1 Progression in the tax system can effectively substitute for progression in social security ...
2 ... generating welfare gains, potentially: a Pareto-improvement
3 With rising longevity, the potential welfare gains are higher.
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73. Conclusions
1 Progression in the tax system can effectively substitute for progression in social security ...
2 ... generating welfare gains, potentially: a Pareto-improvement
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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74. Questions or suggestions?
Thank you!
w: grape.org.pl
t: grape org
f: grape.org
e: jtyrowicz@grape.org.pl
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75. Labor wedge as measure of distortion
With marginal labor income tax denoted as T 0
(yj,t (sj,t ))
φ`j,t (sj,t )
1
η =
cj,t (sj,t )−σ
1 + τc
1 − (1 − τ)T 0
(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 0
(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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