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Notional Defined Contribution Pension Systems in a Stochastic Context: Design and StabilityPowerPoint Presentation

Notional Defined Contribution Pension Systems in a Stochastic Context: Design and Stability

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### 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? Stochastic Context:

- 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 Stochastic Context:

- 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 Stochastic Context:

- 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 Stochastic Context:

- 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 Context:

- 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 Stochastic Context:

- 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 Stochastic Context:(r=g, no brake)

Figure 2. Assets/ Payroll Stochastic Context:(r=g, no brake)

Figure 3. Assets/Payroll Stochastic Context:(r=g, asymmetric brake, net)

Figure 4. Assets/Payroll Stochastic Context:(r=g, asymmetric brake, gross)

Figure 5. Assets/Payroll Stochastic Context:(r=g, symmetric brake, gross)

Figure 6. Assets/Payroll Stochastic Context:(r=n+g, no brake)

Figure 6.a Stochastic Context:. Assets/Payroll (r=n+g, no brake); constant i,g

Conclusions Stochastic Context:

- 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

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