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:
 OAt 1  OAt 2 
AGWt 1 (1  CRt 1 ) 

Bt  Bt 1 *
* 1   * 
AGWt 2 (1  CRt 2 ) 
OAt 2


– 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 –
NDC
NDC
50-50 Sweden
(g)
Adjust
Symm.
Brake
A=.5
NDC
(g)
Symm.
Brake
A=1
NDC German
(n+g)
Symm.
Brake
A=.5
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 –
NDC
NDC
50-50 Sweden
(g)
Adjust
Symm.
Brake
A=.5
NDC
(g)
Symm.
Brake
A=1
NDC German
(n+g)
Symm.
Brake
A=.5
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 –
NDC
NDC
50-50 Sweden
(g)
Adjust
Symm.
Brake
A=.5
NDC
(g)
Symm.
Brake
A=1
NDC German
(n+g)
Symm.
Brake
A=.5
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 –
NDC
NDC
50-50 Sweden
(g)
Adjust
Symm.
Brake
A=.5
NDC
(g)
Symm.
Brake
A=1
NDC German
(n+g)
Symm.
Brake
A=.5
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