1、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 fundin
2、g 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: Swedens NDC Plan,Two phases: pre-retirement and retirement Pre-retirement: each years payroll taxes added to stock
3、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: Swedens NDC Plan,No guarantee that NDC plan as used in Sweden will be
4、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,Pote
5、ntial Problems with the Brake,Asymmetry (applies only when 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 10
6、00 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, loo
7、k 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.
8、 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,
