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