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

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

401 Views

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

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -

**Notional Defined Contribution Pension Systems in a**Stochastic Context: Design and Stability Alan Auerbach Ronald Lee NBER Center for Retirement Research October 19-22, 2006 The Woodstock Inn Erin Metcalf and Anne Moore provided excellent research assistance.**Problems with PAYGO public pensions**• In many countries, the ratio of elderly to workers will double or more by 2050. • Consequently, unfunded (PAYGO) pension plans are not sustainable without major increases in taxes and/or reductions in benefits • Other problems • Below market implicit rate of return • May reduce saving rates and aggregate capital formation • Distort labor supply incentives, e.g cause early retirement • Inevitable uncertainty about rates of return, as in any system • Political risk; no individual control**Privatization?**• Some propose privatizing, replacing PAYGO with Defined Contribution accounts. • These might solve those problems, but… • Difficulties of transition to funded system • Huge implicit debts must be repaid • Can be 1, 2, 3 or 4 times GDP • Transitional generations suffer heavy burden**Another idea – unfunded individual accounts**• Notional Defined Contribution plans, or Non-Financial Defined Contribution (NDC) • Mimic regular Defined Contribution plans, but only minimal assets. • A different flavor of PAYGO.**NDC might solve some problems**• Might be fiscally stable, depending on details. • Individual accounts (but not bequeathable) • Actuarially fair at the NDC rate of return, so less distortion of labor incentives (contributions not viewed as taxes?) • Deals fairly with tradeoffs between benefit levels and age at retirement • Solvency in the face of longevity shifts; automatically indexed to life expectancy through annuity. • No transition cost, because implicit debt is rolled over • Transparency through explicit rules vs political risk**NDC doesn’t solve other problems**• Pays below market rate of return • For a generation, IRR should equal growth rate of wage level (g) plus growth rate of labor force (n), that is growth rate of covered wage bill (real) (n+g) • Still probably displaces savings and capital**Sweden instituted their NDC system in mid 1990s**• Italy and Latvia have also adopted NDC. • French and German systems have elements of NDC**Strategy of this study**• Construct stochastic economic and demographic environment by modifying existing stochastic forecasting model for US Social Security (Lee-Tuljapurkar) • Study the performance of a pension system in this stochastic environment. • Relatively new approach, although see Juha Alho (2006).**Questions addressed**• Can NDC deliver a reasonably consistent and equitable implicit rate of return (IRR) across generations? • Can NDC achieve fiscal stability through appropriate choice of IRR and annuitized benefits sensitive to life expectancy? • How should system be structured to perform well on these measures?**Preview of results**• Swedish style system does not automatically stay on the tracks fiscally; about 30% of the time it collapses. • We suggest some modifications • The implicit rates of return are quite variable from generation to generation.**Plan of rest of talk**• More detail on the Swedish NDC system • Background on constructing stochastic simulations • Results • Conclusions**Closer look at Swedish NDC system, tested in this study**• Two phases: pre-retirement and retirement • Pre-retirement: • each year’s payroll taxes are added to stock of “notional pension wealth” (NPW); • NPW is compounded annually using growth rate of average wage, g (they do not use n+g) • Rate of return earned by surviving individual is higher than cohort rate of return, because survivors inherit account of those in cohort who die. • ri is individual rate of return; r is cohort rate of return**Retirement and beyond**• Worker decides when to retire, above minimum. • Receives a level real annuity based on trend wage growth rate, g = .016 • Subsequently the rate of return is adjusted up or down if actual growth rate of wage is faster or slower then .016. • Annuity is based on level of mortality at time the generation reaches a specified age, such as 65. • This achieves automatic indexing of benefit levels to life expectancy – if annuity benefit is adjusted for post retirement changes in mortality, too.**Initial Comments**• Might wish to use growth rate of wage bill, rather than wage rate, in computing rate of return on NPW and for annuity (n+g vs. g) • n+g is the steady state implicit rate of return, not g • Even if average growth rate of labor force is zero, there are fluctuations • Most demog variation comes from fertility, not mortality, and using g ignores this.**Fiscal stability?**• No guarantee that NDC plan as used in Sweden will be stable, in terms of evolution of debt-payroll ratio. • If fertility goes below replacement level and pop growth becomes negative, then rate of return g will not be sustainable. • This is recognized in Sweden, so an additional “brake” mechanism is included • Brake will control for demography through the back door by reducing rate of return.**Fiscal status is assessed without using projections**• Rules are specified in terms of observable quantities, so no projections involved. • This further insulates the system from political pressures. • Steady state approximations replace projections for present value of future tax receipts, C, in the balance equation. • Downside: calculations of fiscal health may be less accurate.**How the Brake Works**• Start with the balance ratio: All can be estimated from base period data, no projection. where: F = financial assets C = a “contribution” asset P = an approximation of pension commitments to current retirees NPW = notional pension wealth**How the Swedish Brake Works**• If bt < 1, then multiply the rate of return the basic formula calls for by bt. • If bt+1 is still <1.0 then • So when b<1, the rate of return is adjusted only when b is falling or rising. • If b gets close to zero, then the ratio can go wild.**The Brake is asymmetric**• When the ratio of assets to obligations is falling, the rate of return is reduced. • Applies when b < 1, but not when b > 1 • Helps avoid deficits, but allows surpluses to accumulate without limit**Potential Problems with the Brake**• Is the brake strong enough to head off fiscal disaster? • Asymmetry means potential for unneeded asset accumulation, depressing rate of return.**We design our own brake**where A is a scaling factor, which provides another degree of freedom • A=1 gives • The brake can be applied symmetrically (that is, also for b > 1)**Now briefly consider the stochastic simulation model**• Starting point is stochastic forecasting model for Social Security finances, developed by Lee and Tuljapurkar. • This model is rooted in historical context • Baby boom, baby bust • We construct a model purged of historical context and of trends: • quasi-stationary • Rationale: aim for more general results**The Basic Model**• Stochastic population projections (Lee and Tuljapurkar) based on mortality and fertility models of Lee and co-authors; immigration held constant • Eliminate drift term in mortality process to generate quasi-stationary equilibrium • Below replacement fertility plus constant immigration inflow implies stationary equilibrium. • Stochastic interest rates and covered wage growth rates as well, modeled as stationary stochastic processes using VAR • No economic feedbacks; based on stochastic trend extrapolations.**Stochastic simulations**• Set initial population age distribution based on expected values of fertility, mortality, immigration. • Generate stochastic sample paths for fertility, mortality (derive population age distribution), productivity growth, and interest rates. • Use these to generate stochastic outcomes of interest. • Each sample path is 600 years long. • Throw out first 100 years to permit convergence to stochastic steady state.**Spain 2050, UN Low Proj**Current US**Incorporating an NDC System centered on US Soc Sec**parameters • As under Soc Sec (OASI), assume 10.6 percent payroll tax rate, applied to fraction of total wages below payroll tax earnings cap. • Long-run covered wage growth of 1.1 percent; base system rate of return on realized wage growth (g) or wage bill growth (n+g) • Accumulate NPW until age 67; then annuitize; in simulations shown, update annuities after 67 to reflect changes in rate of return and mortality (not a big deal)**Simulation Results**• We consider versions of the NDC system that vary by • the rate of return used (g vs. n+g) • the type of brake (none/asymmetric/symmetric; Swedish or revised) • To evaluate stability, look at distribution of ratio of financial assets to payroll • Look at summary measures of distributions of implicit rates of return across paths and cohorts**Table 1. Average Internal Rates of Return**Asymm brake reduces rate of return Asymm brake reduces rate of return Source: Calculated from stochastic simulations described in text.**Table 1. Average Internal Rates of Return**Making brake symmetric raises the rate of return Source: Calculated from stochastic simulations described in text.**Now consider fiscal stability**• Following slides look at ratio of financial asset, F, to payroll. • For less stable systems, we look at first 100 years only, since the probability distributions explode.**Financial Assets/Payroll in an NDC(g) system with no brake**– solely for reference purposes Range at 100 years = 56 Range at 100 years = 56**Financial Assets/Payroll in the Swedish System: NDC(g) with**asymmetric brake Range = 28**Now look at systems with rate of return = n + g**• These should be more stable, because the rate of return they pay reflects demography as well as wage growth.**Range = 8.8 after 100 years; asymmetric brake helps**slightly.**Range = 2.0 after 500 years; symmetric brake makes highly**stable.**Conclusions**• Swedish-style NDC system not stable, even with brake (30% failure over 500 yrs) • System can be made stable, using brake that is stronger and symmetric. • Using growth rate of wage bill (n+g) rather than of wage rate (g) for IRR is inherently more stable • A considerable share of instability is attributable to economic, as opposed to demographic, fluctuations.**Conclusions**• Next step is to evaluate a stable version of an NDC plan against a stable version of traditional social security (with benefit or tax adjustments providing stability) in terms of intergenerational risk sharing**Outcome measures for generations**• Measures • IRR (variance) • NPV (variance) • Expected Utility (assuming only income for workers is net wages, and for retirees is pension benefits). • Evaluates entire distribution of outcomes**Compare NDC outcomes to balanced budget Soc Sec**• Tax-adjust system achieves continuous balance by adjusting taxes to benefit costs. • Benefit-adjust system adjusts benefits to tax revenues. • 50-50 adjust system combines these.**Variance of IRR**• The Swedish NDC(g) system: lowest IRR variance of any plan—but not fiscally stable. • The US 50-50 adjust has the lowest IRR variance of any stable plan. • Others have similarly high variance.**Expected Utility with risk aversion**• NDC(n+g) with symmetric brake has highest EU. • Swedish system next best, but not fiscally stable. • US Benefit adjust is the second best fiscally stable program.**Expected utility without risk aversion**• NDC(g) and NDC(n+g) with symmetric brakes are the best.**Conclusion on variability of outcomes**• Rank ordering depends on summary measure used; none dominates on all measures. • The NDC(n+g) with symmetric brake looks best on Expected Utility measures.