Welfare and Generational Equity in Sustainable Unfunded Pension

Systems

Alan J. Auerbach

Ronald Lee

UC Berkeley

Overview

• Need to reform existing PAYGO public pension schemes, due to lack of stability and transparency

• Shift to funded systems confronts economic and political problems of transition

• An alternative: Notional Defined Contribution (NDC) plans; PAYGO systems, but with some potential advantages (transparency, stability)

NDC Systems

• Two phases: accumulation and retirement• Accumulation phase – accumulate an

imaginary stock of Notional Pension Wealth (NPW) based on annual contributions

• Retirement phase: annuitize NPW using same assumed rate of return, based on life table

NDC Systems

• How is assumed rate of return determined?

• This is the key decision with respect to potential stability

• Sweden bases return on wage growth (g) adjusted for annual mortality probability

• Could base return on growth of covered wages (n+g)

Previous Auerbach-Lee Paper

• Studied the Swedish NDC plan, in terms of stability

• With stochastic wages, interest rates, birth rates and mortality (based on US data), how likely is debt to explode over time?

• Swedish system is stable downward (no excessive debt build-up), but only because it also includes a “balancing mechanism” that reduces rate of return when trouble near; but doesn’t avoid asset accumulation

Previous Auerbach-Lee Paper

• Could avoid accumulation of assets (and pay a higher average rate of return) by making balance mechanism symmetric, also raising growth rate of accounts and benefits when system assets too high

• Could make Swedish system more stable by basing growth rate of accounts and annuities on growth rate of wage bill (n+g) rather than growth rate of wage rate (g)

This Paper

• Look at risk-sharing and welfare properties of different types of fiscally stable systems– Actual Swedish system and symmetric variants of

it from our earlier paper– New German system– Versions of the US system forced to be stable by

annual tax or benefit adjustments

The Systems

• All systems based on simplified US OASI system for a representative individual per cohort– 10.6 percent payroll tax– work until age 67, with retirement at 67

• US system variants, all PAYGO, with tax profiles based on US data, and benefit profiles generated by simplified version of benefit formula assuming retirement at 67

The Systems

• Three US system variants:– “Benefit Adjust” – raise or lower benefits each

year so that taxes = benefits– “Tax Adjust” – raise or lower taxes each year so

that taxes = benefits; scale so that average tax rate = 10.6 percent (since actual US system not viable)

– “50-50 Adjust” – divide annual adjustment equally between taxes and benefits

The Systems

• Swedish system variants:– All with tax rate fixed at 10.6 percent– Actual Swedish system

• Notional Pension Wealth accumulates at rate g and is annuitized at age 67, with annuity rate of return also based on g

• Brake mechanism that temporarily lowers benefits by setting gross return to (1+g)b when a measure of assets/liabilities, b, falls below 1

The Systems

• Three Swedish system variants:– All with symmetric brake– Two based on g, one based on n+g– One with full brake, reducing gross rate of return

by a factor (1- b); two with dampened brake, reducing gross rate of return by a factor 0.5*(1-b)

The Systems

• German system:– Strictly PAYGO– Benefits the same for all cohorts at a given time– Benefits grow according to:

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– Taxes adjusted as a residual to ensure balance– System scaled so that taxes average 10.6 percent

Evaluation Criteria

• Internal Rate of Return (IRR)

• Net Present Value relative to PV of earnings (NPV)

• Expected Utility Approximation (EU)

• Horizontal Equity (HE)

• Social Welfare Function, taking transition generations into account (SWF)

Social Welfare Measures

US - Tax

Adjust

US – Ben.

Adjust

US –50-50

Adjust

NDC Sweden

NDC(g)

Symm. BrakeA=.5

NDC(g)

Symm.BrakeA=1

NDC(n+g)

Symm. BrakeA=.5

German

Unadjusted

= 0 0.00140 0.00140 0.00140 -0.00878 0.00189 0.00186 0.00181 0.00140

Adjusted  

= 0 0.00186 0.00186 0.00186 -0.00878 0.00186 0.00186 0.00186 0.00186

 

= 3 -0.00360 -0.00262 -0.00227 -0.01175 -0.00229 -0.00226 -0.00248 -0.00241

 

= 5 -0.02063 -0.01877 -0.01844 -0.02645 -0.01796 -0.01788 -0.01835 -0.01875

Social Welfare Measures

US - Tax

Adjust

US – Ben.

Adjust

US –50-50

Adjust

NDC Sweden

NDC(g)

Symm. BrakeA=.5

NDC(g)

Symm.BrakeA=1

NDC(n+g)

Symm. BrakeA=.5

German

Unadjusted

= 0 0.00140 0.00140 0.00140 -0.00878 0.00189 0.00186 0.00181 0.00140

Adjusted  

= 0 0.00186 0.00186 0.00186 -0.00878 0.00186 0.00186 0.00186 0.00186

 

= 3 -0.00360 -0.00262 -0.00227 -0.01175 -0.00229 -0.00226 -0.00248 -0.00241

 

= 5 -0.02063 -0.01877 -0.01844 -0.02645 -0.01796 -0.01788 -0.01835 -0.01875

Social Welfare Measures

US - Tax

Adjust

US – Ben.

Adjust

US –50-50

Adjust

NDC Sweden

NDC(g)

Symm. BrakeA=.5

NDC(g)

Symm.BrakeA=1

NDC(n+g)

Symm. BrakeA=.5

German

Unadjusted

= 0 0.00140 0.00140 0.00140 -0.00878 0.00189 0.00186 0.00181 0.00140

Adjusted  

= 0 0.00186 0.00186 0.00186 -0.00878 0.00186 0.00186 0.00186 0.00186

 

= 3 -0.00360 -0.00262 -0.00227 -0.01175 -0.00229 -0.00226 -0.00248 -0.00241

 

= 5 -0.02063 -0.01877 -0.01844 -0.02645 -0.01796 -0.01788 -0.01835 -0.01875

Social Welfare Measures

US - Tax

Adjust

US – Ben.

Adjust

US –50-50

Adjust

NDC Sweden

NDC(g)

Symm. BrakeA=.5

NDC(g)

Symm.BrakeA=1

NDC(n+g)

Symm. BrakeA=.5

German

Unadjusted

= 0 0.00140 0.00140 0.00140 -0.00878 0.00189 0.00186 0.00181 0.00140

Adjusted  

= 0 0.00186 0.00186 0.00186 -0.00878 0.00186 0.00186 0.00186 0.00186

 

= 3 -0.00360 -0.00262 -0.00227 -0.01175 -0.00229 -0.00226 -0.00248 -0.00241

 

= 5 -0.02063 -0.01877 -0.01844 -0.02645 -0.01796 -0.01788 -0.01835 -0.01875

Conclusions

• Swedish system provides most stability, but generally not as good as other systems under welfare measures– This is particularly so when transition is taken into account,

because the stability is provided by a buffer stock accumulated at the expense of early generations

• Basing NDC plan on g rather than n+g may be better for welfare, even if not for stability– Smaller fluctuations when brake is not in effects seem to

outweigh more frequent application of the brake (with associated fluctuations)

• Systems that spread risk broadly over generations (US 50-50, NDC) do best