1. Discussion of Changing Progressivity as a Means of Risk Protection in Investment-Based Social Security Michael Hurd RAND and NBER

2. Can risk of low rates of return from Private Retirement Accounts be partially offset by increased progressivity in (reduced) Social Security program? Interesting alternative to pure insurance against bad outcomes on rates of return

3. Done through simulation Here are the steps

4. Simulation of lifetime earnings Cohort born in 1973 age 30 in 2003 Take distribution of earnings from cross- section estimate of log normal First order Markov with high persistence

5. Age 30 Age 67 Forecast and back-cast earnings from age 30 in 20003 Low earning person in 2003 Range of wage outcomes

6. Age 30 Age 67 Forecast and back-cast earnings from age 30 in 20003

7. Age 30 Age 67 Forecast and back-cast earnings from age 30 in 20003

8. At each age save 2% of earnings into PRA in bond-stock portfolio augment PRA by random draw from historical rates of return

9. Calculate Social Security benefits for each path based on current law Repeat many times

10. Distribution of Social Security Benefits Scheduled: E(B) = $21.8k

11. But current law not sustainable, so reduce benefits by 40%

12. Reduced Distribution of Social Security Benefits to close actuarial gap Reduced by 40%: E(B) = $13.1k Scheduled: E(B) = $21.8k

13. Redistribute to increase progressivity…example E(B) = $13.1k Topped up at, say, 25 th percentile and then reduced

14. Then add in private investment account : Distribution of Social Security Benefits + PRA E(B) = $13.1k 2% annual earnings invested in ½ stocks and ½ bonds, annuitized plus Soc. Sec.

15. Calculate E(U)

16. Repeat for other investment programs 2% annual earnings invested in ½ stocks and ½ bonds, annuitized plus Soc. Sec. 2% annual earnings invested in bonds, annuitized plus Soc. Sec. Calculate expected utility for these and variants

17. Compare utilities (certainty equivalents) for variation in Risk aversion Rates of return on equities Fraction of earnings in Private Retirement Accounts

18. My main question: Whose utility? Thought experiment: Draw a worker from population. Calculate wage path Calculate saving path with stochastic rates of return Calculate utility Repeat and average

19. Whose utility Stochastic elements: wage level w, wage growth (u), rates of return (v) What is calculated:

20. Thus average (over workers) of individual expected utility Not utility of any individual Is this quantity a desirable social objective?

21. Alternative…utility of individuals Begin with a worker (w) Calculate wage and saving path Utility for that worker Replicates for that worker E(U)

22. Utility of individuals Repeat for many workers Study distribution of E(U) –E.g. How many workers have their E(U) improved and how many reduced under each alternative –Effects on workers in lower part of wage distribution compared with workers in upper part.

23. Additional advantage Workers indexed by initial wage Use more realistic life-cycle wage paths

25. Question about utility calculation Consumption in retirement equals Social Security plus annuitized Private Retirement Account But most have other resources Variation in marginal utility from earnings uncertainty and investment returns will vary with other resources Other resources positively correlated with initial wage and therefore position in Social Security benefit distribution

26. Conclusion Package of increasing progressivity in Social Security along with PRAs can lead to higher resources along with some protection for low wage or unlucky workers. Moves in direction of some European public pension systems –Politically feasible somewhere in world Excellent contribution to debate

27. Conclusions (cont.) But reservations about utility calculation Ex ante random worker –Interest in distribution of E(U) No accounting for differing rates of growth in earnings No accounting for other resources