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