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 Auerbach Ronald Lee NBER Center for Retirement Research October 19-22, 2006 The Woodstock Inn Erin Metcalf and Anne Moore provided excellent research assistance.

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Notional defined contribution pension systems in a stochastic context design and stability l.jpg

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 l.jpg
Problems with PAYGO public pensions Stochastic Context: Design and Stability

  • 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 l.jpg
Privatization? Stochastic Context: Design and Stability

  • 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 l.jpg
Another idea – unfunded individual accounts Stochastic Context: Design and Stability

  • 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 l.jpg
NDC might solve some problems Stochastic Context: Design and Stability

  • 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 l.jpg
NDC doesn’t solve other problems Stochastic Context: Design and Stability

  • 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 l.jpg
Sweden instituted their NDC system in mid 1990s Stochastic Context: Design and Stability

  • Italy and Latvia have also adopted NDC.

  • French and German systems have elements of NDC


Strategy of this study l.jpg
Strategy of this study Stochastic Context: Design and Stability

  • 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 l.jpg
Questions addressed Stochastic Context: Design and Stability

  • 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 l.jpg
Preview of results Stochastic Context: Design and Stability

  • 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 l.jpg
Plan of rest of talk Stochastic Context: Design and Stability

  • More detail on the Swedish NDC system

  • Background on constructing stochastic simulations

  • Results

  • Conclusions


Closer look at swedish ndc system tested in this study l.jpg
Closer look at Swedish NDC system, tested in this study Stochastic Context: Design and Stability

  • 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 l.jpg
Retirement and beyond Stochastic Context: Design and Stability

  • 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 l.jpg
Initial Comments Stochastic Context: Design and Stability

  • 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 l.jpg
Fiscal stability? Stochastic Context: Design and 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 l.jpg
Fiscal status is assessed without using projections Stochastic Context: Design and Stability

  • 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 l.jpg
How the Brake Works Stochastic Context: Design and Stability

  • 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 l.jpg
How the Swedish Brake Works Stochastic Context: Design and Stability

  • 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 l.jpg
The Brake is asymmetric Stochastic Context: Design and Stability

  • 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 l.jpg
Potential Problems with the Brake Stochastic Context: Design and Stability

  • 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 l.jpg
We design our own brake Stochastic Context: Design and Stability

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 l.jpg
Now briefly consider the stochastic simulation model Stochastic Context: Design and Stability

  • 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 l.jpg
The Basic Model Stochastic Context: Design and Stability

  • 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 l.jpg
Stochastic simulations Stochastic Context: Design and Stability

  • 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.


Slide25 l.jpg

Spain 2050, UN Low Proj Stochastic Context: Design and Stability

Current US


Incorporating an ndc system centered on us soc sec parameters l.jpg
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 l.jpg
Simulation Results parameters

  • 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


Slide28 l.jpg

Table 1. Average Internal Rates of Return parameters

Asymm brake reduces rate of return

Asymm brake reduces rate of return

Source: Calculated from stochastic simulations described in text.


Slide29 l.jpg

Table 1. Average Internal Rates of Return parameters

Making brake symmetric raises the rate of return

Source: Calculated from stochastic simulations described in text.


Now consider fiscal stability l.jpg
Now consider fiscal stability parameters

  • 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.


Slide31 l.jpg

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




Slide34 l.jpg

Range = 2.4 after asymmetric brake 500 years; highly stable


Now look at systems with rate of return n g l.jpg
Now look at systems with rate of return = n + g asymmetric brake

  • These should be more stable, because the rate of return they pay reflects demography as well as wage growth.




Slide38 l.jpg

Range = 2.0 after slightly.500 years; symmetric brake makes highly stable.


Conclusions l.jpg
Conclusions slightly.

  • 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.


Conclusions40 l.jpg
Conclusions slightly.

  • 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 l.jpg
Outcome measures for generations slightly.

  • 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 l.jpg
Compare NDC outcomes to balanced budget Soc Sec slightly.

  • 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 l.jpg
Variance of IRR slightly.

  • 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 l.jpg
Expected Utility with risk aversion slightly.

  • 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 l.jpg
Expected utility without risk aversion slightly.

  • NDC(g) and NDC(n+g) with symmetric brakes are the best.


Conclusion on variability of outcomes l.jpg
Conclusion on variability of outcomes slightly.

  • 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.


Slide48 l.jpg

END slightly.


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