Discussion of

Changing Progressivity as a Means of Risk Protection in

Investment-Based Social Security

Michael Hurd

RAND and NBER

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

Done through simulation

Here are the steps

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

Age 30 Age 67

Forecast and back-cast earnings from age 30 in 20003

Low earning person in 2003

Range of wage outcomes

Age 30 Age 67

Forecast and back-cast earnings from age 30 in 20003

Age 30 Age 67

Forecast and back-cast earnings from age 30 in 20003

At each age

• save 2% of earnings

• into PRA in bond-stock portfolio

• augment PRA by random draw from historical rates of return

Calculate Social Security benefits for each path based on current law

Repeat many times

Distribution of Social Security Benefits

Scheduled: E(B) = $21.8k

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

Reduced Distribution of Social Security Benefits to close actuarial gap

Reduced by 40%: E(B) = $13.1k

Scheduled: E(B) = $21.8k

Redistribute to increase progressivity…example

E(B) = $13.1k

E(B) = $13.1k

Topped up at, say, 25th percentile and then reduced

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.

Calculate E(U)

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

Compare utilities (certainty equivalents) for variation in

• Risk aversion

• Rates of return on equities

• Fraction of earnings in Private Retirement Accounts

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

Whose utility

Stochastic elements: wage level w, wage growth (u), rates of return (v)

What is calculated:

, , , |( ) (( ) | )w u v u v w wU c dP U c w dP dP

Thus average (over workers) of individual expected utility

• Not utility of any individual• Is this quantity a desirable social

objective?

, , , |( ) (( ) | )w u v u v w wU c dP U c w dP dP

Alternative…utility of individuals

• Begin with a worker (w)

• Calculate wage and saving path

• Utility for that worker

• Replicates for that worker

• E(U)

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.

Additional advantage

• Workers indexed by initial wage

• Use more realistic life-cycle wage paths

Real earnings of cohort born in 1940-45

0

200

400

600

800

1000

1200

1400

25-29 35-39 45-49

Age

16+ years education

9-12 years education

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

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

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