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?.

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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
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
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 plan1
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
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
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
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 r g no brake
Figure 2. Assets/ Payroll Stochastic Context:(r=g, no brake)


Figure 2 assets payroll r g no brake1
Figure 2. Assets/ Payroll Stochastic Context:(r=g, no brake)


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


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


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


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


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


Conclusions
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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