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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.

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.

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.

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