Changing Progressivity as a Means of Risk Protection in Investment-Based Social Security Andrew Samwick Dartmouth College and NBER October 21, 2006

2 That’s Quite a Mouthful What Does It Mean?  Some proposals to restore solvency combine a scaled-back traditional benefit with a personal retirement account (PRA) invested in financial assets.  Financial assets, particularly equities, introduce financial risk.  To make reform more feasible, PRAs can be designed to minimize financial risk or mitigate its consequences.

3 Mechanisms To Minimize Financial Risk  Don’t Invest in Equities At the cost of lower expected returns and higher required PRA contributions.  Follow Life Cycle Investment Strategies Reduce exposure to equity risk as retirement approaches, by shifting steadily into bonds.  Offer a Third-Party Guarantee Specify a minimum rate of return (hard) or a minimum benefit level (easier) that will be achieved by the PRA portfolio.  Use Options To Protect Against Low Outcomes Either a put or a put plus a written call

4 Really, All of These Are Just a Version of “Don’t Invest in Equities.”  Life Cycle funds shift to bonds with age. The more interesting question is whether the timing adds value, conditional on the average allocation to equities.  With Guarantees: The guarantor funds the guaranteed benefits with bonds, then lets the investor have the maximum of the bonds or the portfolio.  With No-Loss Strategies: The investor earmarks a portion of the contributions for bonds to return the nominal (or real) principal.  With Pension Collars: The portfolio is (dynamically) equivalent to specified fractional ownership levels in the stock, a bond at the lower limit, and a bond at the higher limit.

5 What If Portfolio Restrictions Are Not Feasible or Desirable?  Social Security already provides a benefit floor, and it would continue to do so to some degree in (almost) any reformed system.  If Social Security were made more progressive, that benefit floor would increase (in relative terms).  This, in turn, would allow us to be less concerned about exposure to equity in the PRAs and to allow them to be less tightly regulated.  The paper quantifies how much equity risk we can shed based on how progressive we make the scaled-back traditional benefit.

6 Varying the Progressivity in the Scaled-Back Traditional Benefit  Proportional: Reduce all benefits by 40% across the board.  Floors at the 10 th or 25 th percentile: First move all benefits below the specified percentile up to that percentile’s benefit. Then scale all benefits down by whatever amount is needed to achieve a 40% aggregate reduction.  Progressive: First reduce the AIME-to-PIA replacement rates down from {90, 32, 15} to {67.5, 16, 8} Then scale all benefits to achieve a 40% aggregate reduction.  Uniform at Mean: Set all benefits equal to 40% of the original mean benefit.

7 Preview of Key Results  Greater progressivity can substitute for higher equity allocations. Compared to a proportional cut in the traditional benefits: A commonly proposed progressive cut to the traditional benefit allows the worker to shed half the equity risk. A maximally progressive cut to a uniform benefit allows the worker to shed two thirds of the equity risk. Progressivity is more important when the investor is risk averse or the equity premium is lower.  But progressivity does not change the desire to invest in equities much. We would observe similar amounts of financial risk in PRA portfolios regardless of how traditional benefits were cut.

8 Details of the Simulation Model One Cohort of Workers  Start with the age-specific mean and quartiles of covered earnings in Kunkel (1996) for the years from 1980 –  Scale them up to 2003 levels by the growth in the national average wage relative to the base year.  Impute a lognormal cross-sectional distribution: Median = exp() Mean = exp( +  2 /2)  Draw a 10,000 observation sample of wages for 30-year olds based on that distribution.

9 Details of the Simulation Method Time-Series Earnings Process  A deterministic component that mimics the low-education income profile from HSZ (1995).  An AR(1) stochastic component to log earnings with  = 0.95 and  drawn from a uniform distribution on [0.05, 0.20]  Backcast to 21 and forecast to 67.  Even for a single cohort, this is a very stylized model.

10 Details of the Simulation Method PRA Investment Returns  For each observation, at each age, assign a randomly drawn “year” from the Ibbotson (2006) data of asset returns from 1926 –  Make a few additional assumptions: Equity is large vs small stocks Govt bonds are equally long-, medium-, and short-term Parameter that varies is share in bonds (assumed corporate-government) relative to equity.  Keep the variation, but reset the means: Follow SSA’s assumptions when it scores plans: 6.2% equity, 3.2% corp bonds, 2.7% govt bonds (net of 30 basis points in administrative costs) Consider alternative equity means of 5.2% and 4.2%

11 Details of the Simulation Model Benefit Calculations  Traditional Benefit Project the national average wage based on the average wage growth for this cohort over its working career. Use this series and the highest 35 years of earnings to compute the AIME. Use this series to update the bendpoints in the PIA-to- AIME formula and compute benefits. Modify as appropriate to increase progressivity.  PRA Benefit Accumulate a 2- or 3-percent contribution on each year of covered earnings. Convert accumulations to a real annuity benefit based on the period life table for  Combine 40% of the first with all of the second.

12 Figure 1: Changing Progressivity These differences are very important. These differences are relatively unimportant.

13 Figure 2: Shifting from Bonds to Equity With SSA’s equity premium, high equity allocations aren’t the problem.

14 And with 2% off the equity premium Even these differences are not particularly large.

15 Cut by 40% Increase Progressivity, Decreasing Variation Decrease Bond Share Increasing Equity Share Raising Expected Benefits Raising Variation

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17 How Much Equity Risk Can Be Avoided? (56 – 10)/90 = 51% (72 – 10)/90 = 69%

18 With less risk aversion, the all-equity portfolio dominates, and greater progressivity would not enable investors to shed much equity risk.

19 With more risk aversion, the optimal equity portfolio shares fall from 90% to 80% or 70% as progressivity increases, and greater progressivity could enable investors to shed all or almost all equity risk.

20 Knocking 100 basis points off the equity premium has analogous effects as increasing risk aversion: slightly lower equity allocations are optimal, and all or almost all equity risk could be shed with higher progressivity.

21 With larger PRAs, optimal equity allocations fall from 90% to 80%, and greater progressivity facilitates shedding about the same proportions of equity risk (half and two thirds).

22 Life Cycle Strategies  Start with low bond allocations at young ages, shifting over time to high bond allocations. 5 to 95 in increments of 2% per year 27.5 to 72.5 increments of 1% per year.  Compared to a uniform 50% allocation in bonds, these strategies have lower return and lower risk. The average PRA balance grows with age, so equity allocations above 50 multiply smaller balances.  In general, these strategies don’t outperform uniform portfolio allocations. With 200 basis points off the equity premium, the second strategy can (mildly) dominate the uniform portfolio, which was previously optimal.

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24 Conclusions  Higher progressivity, in this framework, makes workers better off.  It also allows them to maintain expected utility with lower exposure to equity risk. In the baseline, half to two-thirds of this risk can be eliminated. More at higher risk aversion or lower equity premiums, despite lower optimal equity allocations.  However, greater progressivity does not reduce their desire to invest in equities much.  Life Cycle strategies are of some, but limited, use in improving welfare.

25 Possibilities for Further Research  Simulating the portfolio returns Should I be assigning everyone the same sequence of “years” and bootstrapping the results?  More sensitivity tests More variety in (deterministic) wage profiles Couples versus single households Multiple cohorts Actual versus hypothetical workers