The paper studies the interaction between capital (income) taxation and pension system reform in the context of rising longevity. In an economy with idiosyncratic income shocks and uncertainty about life duration, defined benefit pension plans with redistribution (similar to the current US pension system) provide some insurance against these risks. The existing view in the literature states that the current pension system in the US introduces distortions to labor supply decisions and reduces capital accumulation, but reducing this distortion by the means of introducing (partially) funded defined contribution system involves loss of insurance and transitory fiscal gap, which dominate the benefits of reform. Prior financed the transitory costs of the reform by taxing consumption. We show that in the context of longevity, capital income taxation provides a superior alternative: welfare gains are sufficient to outweigh the loss of insurance and transitory funding costs. Our approach builds on optimal taxation literature: taxes should be levied on the least responsive tax base, and growing life expectancy raises incentives for capital accumulation. Further, higher risk exposure amplifies incentives for precautionary savings. These two mechanisms -- the rising longevity and the stronger precautionary motive -- make capital accumulation relatively less responsive to the tax hikes, thus reducing the dead-weight loss from increased taxation. In the long run, privatizing social security permits lower taxation, thus boosting capital income gains, accelerating capital accumulation, and economic progress. We reconcile our results with the earlier literature. We also study the political economy context and show that political support for capital income taxation is feasible.

1. Efficiency versus insurance:
capital income taxation and privatizing social
security
Oliwia Komada (WSE and GRAPE)
Krzysztof Makarski (NBP, WSE and GRAPE)
Joanna Tyrowicz (GRAPE, IOS, UW, and IZA)
European Economic Association – 2020
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2. Motivation

3. Motivation – pension systems
Problem: Longevity hazards pension system viability:
for US deficit ↑ 1.4% of GDP
Feldstein, BEA, SSA
Solution: Privatization of pension system
(redistributive) Defined Benefit ⇒ Defined Contribution
• within generations redistribution −→ insurance ↓
• aggregate change in the economy −→ efficiency ↑
Consensus:
• Deterministic setup: efficiency wins over the looses
• Stochastic setup: insurance drags efficiency boost down
Nishiyama & Smetters (2007, QJE) and subsequent literature
• Reform ⇒ fiscal adjustments, elasticity of response to taxation is crucial
for welfare Diamond and Spinnewijn 2011, Golosov et al. 2013, Straub and Werning 2020
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4. Motivation – capital (income gains) taxation
Why is taxing capital a good idea for pension privatization?
Q1: Is it ok to raise τk? ←− in the short run Yes!
Households have to save more, low elasticity of savings with respect to τk:
• longevity ↑ ⇒ assets ↑
• redistribution ↓ ⇒ precautionary savings ↑
Q2: Is it ok to reduce τk? ←− in the long run Yes!
We can do it!
• system immune to longevity ⇒ tax ↓ in the long run
Our contribution
1: Insights on τk in the context of longevity and pension privatization.
2: Quantification of the role of the insurance motive in terms of welfare.
3: Comparison of welfare and macro effects along with different fiscal tools.
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5. What we do
OLG model with idiosyncratic income shocks and longevity, US
Baseline: US pension system = DB + redistribution
Reform: gradual shift to (partially funded) DC
• tax on capital income gains (with or without temporal debt adjustment)
• compare it with the literature
• consumption tax closure (with or without temporal debt adjustment)
• 2 pension system adjustments: contributions or benefits
• study welfare effect and political support
• decompose welfare change into insurance and efficiency
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6. Results in a nutshell
1. Privatization of social security + τk → welfare ↑:
• in the short run: low elasticity of response to τk
• in the long run: τk boosts efficiency more then other closures, e.g. τc
• insurance motive actually rather small
−→ Nishiyama & Smetters is NOT universal
2. Public debt often “buys” political support
3. Welfare gains and political support only sometimes overlap
Results robust to
• secular stagnation
• more rapid reform implementation
• different values of risk aversion
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7. Model

8. Consumers
• uncertain lifetimes: live for 16 periods, with survival rate πj,t < 1
• uninsurable productivity risk: + endogenous labor supply
AR(1) process approximated by Markov chain
• CRRA utility function
• pay taxes (progressive on labor, linear on consumption and capital gains)
• contribute to pensions, face natural borrowing constraint
Firms and markets
• Producers with Cobb-Douglas production function, with capital
depreciation rate d
• no annuity, financial markets with (risk free) interest rate
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9. Government
• Finances government spending Gt, constant as a share of GDP,
• Balances pension system: paying subsidyt,
• Services debt: ∆Dt + rtDt = Dt − Dt−1 + rtDt,
• Collects taxes on capital, consumption, labor (progressive given by
Benabou form),
Gt + subsidyt + ∆Dt + rtDt
= τk,trtAt + τc,tCt + Taxl,t
−→ Which taxes to adjust? The elasticity of response to taxation important!
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10. Pension system
Baseline scenario: AIME = PAYG DB with progressivity
• redistribution within a cohort ⇒ insurance but high labor distortion
• defined benefit → longevity ⇒ long run deficit
Reform scenario: (partially funded) DC
• individual defined contribution ⇒ less insurance but less labor distortion
• self balancing ⇒ no long run deficit
• if partially funded ⇒ short run deficit but since r > g higher pensions
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11. Results

12. Major effects of the reform
Calibration
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 the baseline scenario of permanent pension system deficit)
Intuition: long run effects are surely positive, but elasticity matter for the size
of these effects
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13. Pension system subsidy and taxes
pension subsidy τk tax rate
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14. Pension system subsidy and taxes
pension subsidy τk tax rate
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15. Pension system subsidy and taxes
pension subsidy τk tax rate
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16. Pension system subsidy and taxes
pension subsidy τk tax rate
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17. Pension system subsidy and taxes
pension subsidy τk tax rate
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18. Pension system subsidy and taxes
pension subsidy τktax rate
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19. Why does τk work so nicely with longevity and funding?
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20. Response of k to τk over transition - smaller in a short run
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21. Response of k to τk over transition - bigger in the long run
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22. Welfare effects of the pension system reform
Reform scenario to DC to DC with partial funding
Life expectancy constant rising constant rising
Fiscal closure
τk 1.25 1.37 -0.28 0.60
1. DC:
• no fiscal cost
• the only cost of the reform is insurance loss
• drop in labor market distortion generates sufficient efficiency gain
2. DC with partial funding
• insurance loss + fiscal cost >> efficiency gain due to ↓ labor distortion
• welfare ↓ without longevity, with longevity ↑, additional efficiency gain due
to lower capital tax in the long run
• without rising longevity little or no merit in pension system privatization
Replication of N& S results
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23. Welfare across generations
Reform: DC with partial funding
τk τc
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24. Welfare decomposition: insurance loss efficiency gain
Reform: DC with partial funding
τk τc
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25. Debt smoothing helps with political support (not just for τk)
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26. Debt smoothing helps with political support (not just for τk)
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27. Debt smoothing helps with political support (not just for τk)
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28. Sensitivity of the results
1. Capital income taxation vs. other fiscal closures details
• in long run welfare ↑ for all closures
• only τk + debt ⇒ aggregate welfare ↑ + political support
2. Declining rate of exogenous technological progress details
• r >> g more long run benefits due to funding
3. Does it matter how fast the reform is implemented? details
• so far: only future cohorts join the reformed P.S.
• more rapid reform (45+ join new P.S.) ⇒ the key results the same
4. What is quantitative role for redistribution? details
• high levels of risk aversion ⇒ insurance loss dominant,
• the key argument: τk works better than τc is still valid
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29. Conclusion

30. Summary
1. Fiscal cost + insurance loss efficiency gain if reform accompanied by
complementary closure.
2. Distribution of fiscal cost and gains makes capital tax attractive closure.
Why is capital tax so nice?
−→ relatively less responsive to the tax hikes
capital accumulation ↑ with longevity + funding + less insurance
Without longevity: funding and DC make little sense
Features of this literature
• Savings have a roughly 10% reaction to longevity
do people really “understand” the risk of old-age poverty
• Labor has a roughly 10% reaction to reduced distortions
do people really “understand” the link between contributions and pensions
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31. Questions or suggestions?
Thank you!
w: grape.org.pl
t: grape org
f: grape.org
e: okomada@grape.org.pl
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32. Calibration to replicate US economy (2015)
Preferences: instantaneous utility function take CRRA form with
• Risk aversion in equal to 2
• Preference for leisure φ matches average hours 33%
• Discounting rate δ matches interest rate 4.5%
Idiosyncratic productivity shock based on Kruger and Ludwig (2013):
• Persistence η = 0.95
• Variance ση = 0.375
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%
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33. Welfare effects of the pension system reform
Reform scenario to DC to DC with partial funding N&S
Life expectancy constant rising constant rising constant constant rising
(1) (1a) (2) (2a) (2b) (3) (3a)
Fiscal closure
τc 1.18 0.94 0.14 -0.06 -0.41 -0.52 -0.57
τk 1.25 1.37 -0.28 0.60 0.06 -0.24 0.09
1. DC:
• no fiscal cost
• the only cost of the reform is insurance loss
• drop in labor market distortion generates sufficientefficiency gain
2. DC with partial funding
• insurance loss + fiscal cost >>efficiency gain due to ↓ labor distortion
• welfare ↓ without longevity, with longevity ↑, additionalefficiency gain due
to lower capital tax in the long run
3. N&S
• privatization = pension reduction, there is a fiscal cost of the reform
• higher interest rate environment - future gains matter less 29 / 33

34. Capital income taxation vs. other fiscal closures
Reform: DC + partial funding
Fiscal closure Welfare effects Political support (in %)
long run aggregate initial steady state
capital income tax τk 1.93 0.60 42.60
capital income tax smoothed debt + τk 1.93 0.55 90.62
consumption tax τc 0.93 -0.06 35.16
consumption tax smoothed debt + τc 0.93 -0.07 74.20
raising contributions τ 1.21 -0.01 58.13
reducing pensions τb 0.07 0.11 9.85
• only capital income tax (with debt) and pension reduction yields to
increase in welfare
• but only capital income tax with debt gain political support
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35. Secular stagnation
In our main calibration, we assume a constant g = 2%. In robustness check,
we assume a gradual decline in the rate of technological progress to 1.5%.
Relatively high technological progress in our central scenario favors the current
pension system in the US. With declining technological progress, its even
easier to implement privatization and obtain welfare improvement and political
support.
Fiscal closure Welfare effects Political support
final steady state aggregate initial steady s
reducing pensions τb 0.12 0.11 9.85
raising contributions τ 1.76 0.05 58.13
capital income tax τk 2.05 0.39 42.60
capital income tax smoothed debt + τk 2.12 0.38 90.62
consumption tax τc 1.46 0.05 35.16
consumption tax smoothed debt + τc 1.46 0.06 74.21
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36. Does it matter how fast the reform is implemented?
In our main scenario, only newborns enter the privatized pension system.
Faster implementation (workers older that 45 enter new pension) of the
reform yields to higher pension deficit and, thus, the fiscal cost in the short
run. Still, capital income taxation with debt smoothing generates welfare
increase and political support.
Fiscal closure Welfare effects Political support
final steady state aggregate initial steady s
reducing pensions τb 0.07 0.11 9.85
raising contributions τ 1.21 0.03 58.13
capital income tax τk 1.93 0.67 42.60
capital income tax smoothed debt + τk 1.93 0.55 90.62
consumption tax τc 0.93 0.00 42.60
consumption tax smoothed debt + τc 0.93 -0.07 74.21
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37. What is a quantitative role for redistribution?
• the main results: CRRA utility function with θ = 2
• with high levels of risk aversion (θ ≥ 3), the insurance channel becomes
quantitatively dominant
• but the key argument: τk works better than τc is still valid
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