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

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?.

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

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  1. Notional Defined Contribution Pension Systems in a Stochastic Context:Design and Stability Alan J. Auerbach and Ronald Lee University of California, Berkeley

  2. 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

  3. 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

  4. 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

  5. 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)

  6. 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

  7. 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

  8. Figure 2. Assets/ Payroll(r=g, no brake)

  9. Figure 2. Assets/ Payroll(r=g, no brake)

  10. Figure 3. Assets/Payroll(r=g, asymmetric brake, net)

  11. Figure 4. Assets/Payroll(r=g, asymmetric brake, gross)

  12. Figure 5. Assets/Payroll(r=g, symmetric brake, gross)

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

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

  15. 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

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