We show that labor tax progression can effectively substitute for the insurance implicit in redistributive social security. The existing view in the literature is that linking pensions to individual incomes wages reduces distortions associated with social security, but removes insurance. The net outcome of efficiency gain and insurance loss was found to be negative in an economy with idiosyncratic income shocks. Our study shows that privatizing social security can deliver aggregate welfare gains if alternative channels of providing insurance are implemented.

1. Progressing into efficiency:
the role for labor tax progression in privatizing social security
Oliwia Komada (GRAPE and WSE)
Krzysztof Makarski (GRAPE and WSE)
Joanna Tyrowicz (GRAPE, UW, and IZA)
1

2. Motivation

3. Motivation
Social security is essentially about insurance:
• mortality (annuitized)
Benartzi et al. 2011, Bruce & Turnovsky 2013, Reichling & Smetters 2015, Caliendo et al. 2017
• low income (redistribution)
Cooley & Soares 1996, Tabellini 2000
2

4. Motivation
Social security is essentially about insurance:
• mortality (annuitized)
Benartzi et al. 2011, Bruce & Turnovsky 2013, Reichling & Smetters 2015, Caliendo et al. 2017
• low income (redistribution)
Cooley & Soares 1996, Tabellini 2000
Prevailing consensus:
• redistribution is costly (distorts incentives)
e.g. Diamond 1977 + large and diverse subsequent literature
• but provides insurance against low income, so some is desirable
Davidoff et al. 2005, Nishiyama & Smetters 2007, Fehr et al. 2008
2

5. Motivation
Social security is essentially about insurance:
• mortality (annuitized)
Benartzi et al. 2011, Bruce & Turnovsky 2013, Reichling & Smetters 2015, Caliendo et al. 2017
• low income (redistribution)
Cooley & Soares 1996, Tabellini 2000
Prevailing consensus:
• redistribution is costly (distorts incentives)
e.g. Diamond 1977 + large and diverse subsequent literature
• but provides insurance against low income, so some is desirable
Davidoff et al. 2005, Nishiyama & Smetters 2007, Fehr et al. 2008
Our approach: replace redistribution in social security with tax progression
2

6. Motivation
Social security is essentially about insurance:
• mortality (annuitized)
Benartzi et al. 2011, Bruce & Turnovsky 2013, Reichling & Smetters 2015, Caliendo et al. 2017
• low income (redistribution)
Cooley & Soares 1996, Tabellini 2000
Prevailing consensus:
• redistribution is costly (distorts incentives)
e.g. Diamond 1977 + large and diverse subsequent literature
• but provides insurance against low income, so some is desirable
Davidoff et al. 2005, Nishiyama & Smetters 2007, Fehr et al. 2008
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.
2

7. Table of contents
Motivation
Theoretical model
Quantitative model
Results
Conclusions
3

8. Theoretical model

9. (Stylized) theoretical model: partial equilibrium OLG model
Incomes:
• wage wt grows at the constant rate γ, zt = (1 + γ)t
, interest rate r is constant
• two types θ ∈ {θH , θL}, with productivities ωθ ∈ {ωL, ωH }, and ωH > ωL
denote y(θ) = (1 − τ)wt ωθ`t (θ) (and ỹ(θ) = (1 − τ)w̃ωθ`t (θ), w̃ = wt /zt )
4

10. (Stylized) theoretical model: partial equilibrium OLG model
Incomes:
• wage wt grows at the constant rate γ, zt = (1 + γ)t
, interest rate r is constant
• two types θ ∈ {θH , θL}, with productivities ωθ ∈ {ωL, ωH }, and ωH > ωL
denote y(θ) = (1 − τ)wt ωθ`t (θ) (and ỹ(θ) = (1 − τ)w̃ωθ`t (θ), w̃ = wt /zt )
Households:
• Live for 2 periods, population is constant,
• choose labor, consumption and assets
first period: c1,t (θ) + a1,t+1(θ) = (1 − τ)wt ωθ`t (θ) − zt T(ỹ(θ))
second period: c2,t+1(θ) = (1 + r)a1,t+1(θ) + b2,t+1(θ)
T(y(θ)) is the progressive income tax and τ is social security contribution
4

11. (Stylized) theoretical model: partial equilibrium OLG model
Incomes:
• wage wt grows at the constant rate γ, zt = (1 + γ)t
, interest rate r is constant
• two types θ ∈ {θH , θL}, with productivities ωθ ∈ {ωL, ωH }, and ωH > ωL
denote y(θ) = (1 − τ)wt ωθ`t (θ) (and ỹ(θ) = (1 − τ)w̃ωθ`t (θ), w̃ = wt /zt )
Households:
• Live for 2 periods, population is constant,
• choose labor, consumption and assets
first period: c1,t (θ) + a1,t+1(θ) = (1 − τ)wt ωθ`t (θ) − zt T(ỹ(θ))
second period: c2,t+1(θ) = (1 + r)a1,t+1(θ) + b2,t+1(θ)
T(y(θ)) is the progressive income tax and τ is social security contribution
• GHH preferences: Frisch elasticity + risk aversion
U(θ) =
1
1 − σ
(c1,t (θ) −
φ
1 + η
zt `1,t (θ)1+η
+ βc2,t+1(θ))1−σ
4

12. (Stylized) theoretical model: partial equilibrium OLG model
Government:
• needs to collect exogenously given level of revenue R̃ = Rt /zt = constant,
• with progressive income taxation:
T(ỹ) = τ` · ỹ − µ̃
5

13. (Stylized) theoretical model: partial equilibrium OLG model
Government:
• needs to collect exogenously given level of revenue R̃ = Rt /zt = constant,
• with progressive income taxation:
T(ỹ) = τ` · ỹ − µ̃
The implied government budget constraint is then
R̃ =
X
θ∈{θL,θH }
T(ỹt (θ)),
whatever funds are left are spent on lump-sum grants µt .
5

14. (Stylized) theoretical model: partial equilibrium OLG model
Social security
Beveridge (full redistribution)
bBEV
2,t+1(θ) = τ wt+1
1
2
X
θ∈{L,H}
ωθ`1,t+1(θ).
6

15. (Stylized) theoretical model: partial equilibrium OLG model
Social security
Beveridge (full redistribution)
bBEV
2,t+1(θ) = τ wt+1
1
2
X
θ∈{L,H}
ωθ`1,t+1(θ).
Bismarck (no redistribution)
bBIS
2,t+1(θ) = τ wt (1 + γ) ωθ`1,t (θ)
6

16. (Stylized) theoretical model: partial equilibrium OLG model
Social security
Beveridge (full redistribution)
bBEV
2,t+1(θ) = τ wt+1
1
2
X
θ∈{L,H}
ωθ`1,t+1(θ).
Bismarck (no redistribution)
bBIS
2,t+1(θ) = τ wt (1 + γ) ωθ`1,t (θ)
In stationary equilibrium:
`BIS
1 (θ) > `BEV
1 (θ)
→ both types have efficiency gain, what about redistribution?
In BEV social security transfers from θH to θL are strictly positive.
They are zero in BIS.
6

17. Basic intuitions
With β = 1
1+r
, discounted lifetime consumption becomes
cBIS
t (θ) − cBEV
t (θ) =
7

18. Basic intuitions
With β = 1
1+r
, discounted lifetime consumption becomes
cBIS
t (θ) − cBEV
t (θ) = (1 − τ`(1 − τ))ωθwt (`BIS
1 (θ) − `BEV
1 (θ))
| {z }
efficiency gain
7

19. Basic intuitions
With β = 1
1+r
, discounted lifetime consumption becomes
cBIS
t (θ) − cBEV
t (θ) = (1 − τ`(1 − τ))ωθwt (`BIS
1 (θ) − `BEV
1 (θ))
| {z }
efficiency gain
W (θH ) ↑ & W (θL) ↑
7

20. Basic intuitions
With β = 1
1+r
, discounted lifetime consumption becomes
cBIS
t (θ) − cBEV
t (θ) = (1 − τ`(1 − τ))ωθwt (`BIS
1 (θ) − `BEV
1 (θ))
| {z }
efficiency gain
W (θH ) ↑ & W (θL) ↑
−
1
2
τwt (ωθ`BEV
1,t (θ) − ω−θ`BEV
1,t (−θ))
| {z }
pension system redistribution
7

21. Basic intuitions
With β = 1
1+r
, discounted lifetime consumption becomes
cBIS
t (θ) − cBEV
t (θ) = (1 − τ`(1 − τ))ωθwt (`BIS
1 (θ) − `BEV
1 (θ))
| {z }
efficiency gain
W (θH ) ↑ & W (θL) ↑
−
1
2
τwt (ωθ`BEV
1,t (θ) − ω−θ`BEV
1,t (−θ))
| {z }
pension system redistribution
W (θH ) ↑ & W (θL) ↓
7

22. Basic intuitions
With β = 1
1+r
, discounted lifetime consumption becomes
cBIS
t (θ) − cBEV
t (θ) = (1 − τ`(1 − τ))ωθwt (`BIS
1 (θ) − `BEV
1 (θ))
| {z }
efficiency gain
W (θH ) ↑ & W (θL) ↑
−
1
2
τwt (ωθ`BEV
1,t (θ) − ω−θ`BEV
1,t (−θ))
| {z }
pension system redistribution
W (θH ) ↑ & W (θL) ↓
+ (µBIS
t (θ) − µBEV
t (θ)
| {z }
tax system redistribution
7

23. Basic intuitions
With β = 1
1+r
, discounted lifetime consumption becomes
cBIS
t (θ) − cBEV
t (θ) = (1 − τ`(1 − τ))ωθwt (`BIS
1 (θ) − `BEV
1 (θ))
| {z }
efficiency gain
W (θH ) ↑ & W (θL) ↑
−
1
2
τwt (ωθ`BEV
1,t (θ) − ω−θ`BEV
1,t (−θ))
| {z }
pension system redistribution
W (θH ) ↑ & W (θL) ↓
+ (µBIS
t (θ) − µBEV
t (θ)
| {z }
tax system redistribution
redistribution
7

24. Basic intuitions
With β = 1
1+r
, discounted lifetime consumption becomes
cBIS
t (θ) − cBEV
t (θ) = (1 − τ`(1 − τ))ωθwt (`BIS
1 (θ) − `BEV
1 (θ))
| {z }
efficiency gain
W (θH ) ↑ & W (θL) ↑
−
1
2
τwt (ωθ`BEV
1,t (θ) − ω−θ`BEV
1,t (−θ))
| {z }
pension system redistribution
W (θH ) ↑ & W (θL) ↓
+ (µBIS
t (θ) − µBEV
t (θ)
| {z }
tax system redistribution
redistribution ⇐ NEW
7

25. Effect on labor supply and government revenue
1. θH workers work more in both BIS and BEV than θL,
8

26. Effect on labor supply and government revenue
1. θH workers work more in both BIS and BEV than θL,
8

27. Effect on labor supply and government revenue
1. θH workers work more in both BIS and BEV than θL, and ratio is constant
`BEV
(θH )
`BEV (θL)
=
`BIS
(θH )
`BIS (θL)
=
ωH
ωL
≡ $1/η
> 1
2. % ∆ in labor supply depends on η
(the smaller η, the larger ∆ )
`BIS
(θ) − `BEV
(θ)
`BEV (θ)
=
(1 − τ`(1 − τ))
(1 − τ − τ`(1 − τ))
1/η
− 1 ≡ ξ1/η
− 1
8

28. Effect on labor supply and government revenue
1. θH workers work more in both BIS and BEV than θL, and ratio is constant
`BEV
(θH )
`BEV (θL)
=
`BIS
(θH )
`BIS (θL)
=
ωH
ωL
≡ $1/η
1
2. % ∆ in labor supply depends on η
(the smaller η, the larger ∆ )
`BIS
(θ) − `BEV
(θ)
`BEV (θ)
=
(1 − τ`(1 − τ))
(1 − τ − τ`(1 − τ))
1/η
− 1 ≡ ξ1/η
− 1
3. % ∆ in gov’nt revenue depends on η (Frisch elasticity)
RBIS
− RBEV
RBEV
≡ ξ1/η
− 1
8

29. Key results
1 θH have strictly higher benefits under BIS than under BEV
(efficiency ↑ redistribution ↑)
9

30. Key results
1 θH have strictly higher benefits under BIS than under BEV
(efficiency ↑ redistribution ↑)
2 θL may have lower benefits under BIS than under BEV
(efficiency ↑ but redistribution ↓)
9

31. Key results
1 θH have strictly higher benefits under BIS than under BEV
(efficiency ↑ redistribution ↑)
2 θL may have lower benefits under BIS than under BEV
(efficiency ↑ but redistribution ↓)
9

32. Key results
1 θH have strictly higher benefits under BIS than under BEV
(efficiency ↑ redistribution ↑)
2 θL may have lower benefits under BIS than under BEV
(efficiency ↑ but redistribution ↓)
−→ reform social security and distribute extra government revenue as lump-sum
grants µ
3 ∃ η 1 such that reform is a Pareto-improvement.
9

33. Key results
1 θH have strictly higher benefits under BIS than under BEV
(efficiency ↑ redistribution ↑)
2 θL may have lower benefits under BIS than under BEV
(efficiency ↑ but redistribution ↓)
−→ reform social security and distribute extra government revenue as lump-sum
grants µ
3 ∃ η 1 such that reform is a Pareto-improvement.
9

34. Key results
1 θH have strictly higher benefits under BIS than under BEV
(efficiency ↑ redistribution ↑)
2 θL may have lower benefits under BIS than under BEV
(efficiency ↑ but redistribution ↓)
−→ reform social security and distribute extra government revenue as lump-sum
grants µ
3 ∃ η 1 such that reform is a Pareto-improvement.
4 ∃ η η such that ∀ 1 η η̄ reform reform raises social welfare function
W =
X
θ∈{θL,θH }
U(θ)
9

35. Quantitative model

36. Consumers
• uncertain lifetimes: live for 16 periods, with survival πj 1
• uninsurable productivity risk + endogenous labor supply
• CRRA utility function
• pay taxes (progressive on labor, linear on consumption and capital gains)
• contribute to social security, face natural borrowing constraint
10

37. Consumers
• uncertain lifetimes: live for 16 periods, with survival πj 1
• uninsurable productivity risk + endogenous labor supply
• CRRA utility function
• 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
10

38. Government
• Finances government spending Gt , constant as a share of GDP,
• Balances pension system: subsidyt
• Services debt: rt Dt ,
• Collects taxes on capital, consumption, labor
(progressive given by Benabou form)
Gt + subsidyt + rt Dt = τk,t rt At + τc,t Ct + Tax`,t + ∆Dt
where ∆Dt = Dt − Dt−1
11

39. Policy experiment
Status quo: current US social security
• redistribution through AIME
12

40. Policy experiment
Status quo: current US social security
• redistribution through AIME
• high distortion (no link between LS and future pension benefits)
aj+1,t+1 + c̃j,t + Υt = (1 − τ)wt ωj,t lj,t − T ((1 − τ)wt ωj,t lj,t ) + (1 + r̃t )aj,t + Γj,t
12

41. Policy experiment
Status quo: current US social security
• redistribution through AIME
• high distortion (no link between LS and future pension benefits)
aj+1,t+1 + c̃j,t + Υt = (1 − τ)wt ωj,t lj,t − T ((1 − τ)wt ωj,t lj,t ) + (1 + r̃t )aj,t + Γj,t
12

42. Policy experiment
Status quo: current US social security
• redistribution through AIME
• high distortion (no link between LS and future pension benefits)
aj+1,t+1 + c̃j,t + Υt = (1 − τ)wt ωj,t lj,t − T ((1 − τ)wt ωj,t lj,t ) + (1 + r̃t )aj,t + Γj,t
Alternative: fully individualized social security and lump-sum grants
• no redistribution through social security
12

43. Policy experiment
Status quo: current US social security
• redistribution through AIME
• high distortion (no link between LS and future pension benefits)
aj+1,t+1 + c̃j,t + Υt = (1 − τ)wt ωj,t lj,t − T ((1 − τ)wt ωj,t lj,t ) + (1 + r̃t )aj,t + Γj,t
Alternative: fully individualized social security and lump-sum grants
• no redistribution through social security
• no distortion
aj+1,t+1 + c̃j,t + Υt = (1 − τ)wt ωj,t lj,t − T ((1 − τ)wt ωj,t lj,t ) + (1 + r̃t )aj,t + Γj,t
+ ξj,t
|{z}
implicit tax: PV of ∆b due to contribution
·τwt ωj,t lj,t
12

44. Results

45. Welfare effect and η
13

46. Welfare effect and “understanding” the reform (for η = 0.8)
14

47. Fiscal adjustment
15

48. Conclusions

49. Conclusions
1. Progression in tax system can effectively substitute for progression in social security ...
16

50. Conclusions
1. Progression in tax system can effectively substitute for progression in social security ...
2. ... generating welfare gains [potentially: Pareto improvement]
16

51. Conclusions
1. Progression in tax system can effectively substitute for progression in social security ...
2. ... generating welfare gains [potentially: Pareto improvement]
3. Important role for response of labor to the features of the pension system
16

52. Questions or suggestions?
Thank you!
w: grape.org.pl
t: grape org
f: grape.org
e: j.tyrowicz@grape.org.pl
17