Notional Defined Contribution
Pension Systems in a
Stochastic Context:
Design and Stability
Alan J. Auerbach and Ronald Lee
University of California, Berkeley
What are NDC plans?
• Motivation: can one obtain some of the
benefits of a defined contribution scheme
without confronting the difficult funding
transition?
– property rights
– transparency
– solvency in the face of demographic shifts
• Answer: possibly, if use “biological” rate of
return instead of the market rate of return
Example: Sweden’s NDC Plan
• Two phases: pre-retirement and retirement
• Pre-retirement: each year’s payroll taxes
added to stock of “notional pension
wealth” (NPW); NPW compounded
annually using growth rate of average
wage
• Retirement: level real annuity based on
trend wage growth rate, but adjusted up or
down if actual growth rate faster or slower
Example: Sweden’s NDC Plan
• No guarantee that NDC plan as used in
Sweden will be stable, in terms of
evolution of debt-payroll ratio
• This is recognized in Sweden, so an
additional “brake” mechanism is included
• Construct a balance ratio, b, meant to
approximate ratio of system assets to
liabilities
• If b < 1, then multiply by b the rate of
return called for by the basic formula
Potential Problems with the Brake
• Asymmetry (applies only when b < 1)
means potential asset accumulation
• Applying brake to net return
– Imposes lower bound of 0 on adjusted return
– Has other anomalous properties
– An alternative that eliminates these problems
is a brake applied to gross return
• Either the gross brake or the net brake can
be applied symmetrically (for b > 1)
The Model
• Stochastic population projections
– Eliminate drift term in mortality process to
generate quasi-stationary equilibrium
• Stationary stochastic interest rate and
wage growth rate processes
• Estimate distribution of outcomes using
1000 paths followed for 500 years
• Implement NDC system based on US
OASI system parameters
Simulation Results
• Consider versions of NDC system that
vary by
– Rate of return used: wage rate growth (g) vs.
wage bill growth (n+g)
– Type of brake (none/asymmetric/symmetric;
net/gross)
• To evaluate stability, look at distribution of
assets-payroll paths
Figure 2. Assets/ Payroll
(r=g, no brake)
Figure 2. Assets/ Payroll
(r=g, no brake)
Figure 3. Assets/Payroll
(r=g, asymmetric brake, net)
Figure 4. Assets/Payroll
(r=g, asymmetric brake, gross)
Figure 5. Assets/Payroll
(r=g, symmetric brake, gross)
Figure 6. Assets/Payroll
(r=n+g, no brake)
Figure 6.a. Assets/Payroll (r=n+g,
no brake); constant i,g
Conclusions
• Swedish-style NDC system not stable,
even with brake
• System can be made stable, using brake
that is stronger and symmetric
• Using growth rate of wage bill rather than
of wage rate is inherently more stable
• A considerable share of instability is
attributable to economic, as opposed to
demographic, fluctuations