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 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