Valuing the Longevity Insurance Acquired by Delayed Claiming of Social Security

1. Valuing the Longevity Insurance Acquired by Delayed Claiming of Social Security Wei Sun and Anthony Webb Center for Retirement Research at Boston College Fifth International Longevity Risk and Capital Markets Solutions ConferenceSt. John's University, New York September 25 - 26, 2009

2. What is the optimal age to claim Social Security benefits? • How much do households lose by claiming at sub-optimal ages? • How much does the optimal age vary with socio-economic status?Calculate Social Security Equivalent Income –factor by which Social Security benefits of a household claiming at sub-optimal ages must be multiplied so that it is indifferent between claiming at those ages and the optimal combination of ages. 1

3. The United States Social Security Program Retired worker benefit Can be claimed at any age between 62 and 70. Full Retirement Age 66. 25% reduction if claimed at 62. 32% increase if claimed at 70. Reductions and increases approximately actuarially fair. 40% replacement rate if claimed at age 66. 2

4. The United States Social Security Program • Spousal Benefit • If claimed at age 66, equals 50% of spouse’s retired worker if claimed at his/her Full Retirement Age. • Payable to the extent it exceeds own retired worker benefit. • Must be at least age 62. • Spouse must have claimed his/her own retired worker benefit. • 30% reduction if claimed at age 62. • No increase if claimed after age 66. • Most claimants are women. 3

5. The United States Social Security Program Survivor benefit • 100% of husband’s benefit if wife is aged 66 or older when husband dies — subject to a floor of 82.5% of husband’s Primary Insurance Amount (PIA) (benefit husband would get if he claimed at 66). • Reduction if wife is less than 66 when husband dies — minimum benefit payable at age 60 equals 71.5% of husband’s Primary Insurance Amount. 4

6. The Social Security Program — tradeoffs If husband delays claiming his retired worker benefit > increase in wife’s survivor benefit. But also delays wife’s receipt of spousal benefit. 5

7. Option to delay is equivalent to purchase of an annuity Example: Single earner couple — $1,000 benefits payable at age 66, both aged 62. Can claim at age 62 • get $750 retired worker benefit • $350 spousal benefit • $1,100 total benefit Can claim at age 63 • get $800 retired worker benefit • $375 spousal benefit • $1,175 total benefit Buys $75 a month inflation protected joint life annuity ($900 a year) for $13,200 ($1,100 x 12). Better terms than those available from insurance companies. 6

8. Previous Research–Munnell and Soto (2005) Claim Ages at Which Expected Present Value of Social Security Benefits is Maximized (Husband, Wife) Note: Age difference equals number of years the husband is older than the wife. Source: Munnell and Soto (2005). Earnings 7

9. Previous research continued • Costs of claiming at sub-optimal ages typically small – • Sass, Sun, and Webb (2007). 8

10. But above analyses ignore value of additionallongevity insurance acquired by delay • Follow existing annuitization literature: • Assume CRRA utility— • Endow households with an amount of financial wealth equal to the expected present value of Social Security income. • Each period husband and wife each choose whether to claim benefits. • Household chooses how much to consume. • Solved using numerical optimization. 9

11. Assumptions • Base case — single earner couple, same age, born 1946, CRRA utility, time preference=real interest rate=3%. • Alternatives — wife one to six years younger • -Impatient households. • -Households in high/low mortality socio economic groups. 10

12. Social Security Equivalent Income Single Men and Women 11

13. Social Security Equivalent Income Single Earner Couple – Money’s Worths Female Claim Age Male Claim Age Note: Both the same age. 12

14. Social Security Equivalent Income Single Earner Couple – CRRA = 5 Female Claim Age Male Claim Age 70 62 65 63 66 67 68 64 69 Note: Both the same age. 13

15. Results — Single Earner Couples Later claimers enjoy higher initial consumption Monthly Consumption Age 14

16. Social Security Equivalent Income Wife Five Years Younger – CRRA = 5 Female Claim Age Male Claim Age 15

17. Social Security Equivalent Income Two Earner Couple – CRRA = 5 Female Claim Age Male Claim Age Note: Both the same age, wife’s PIA 50% of husband’s. 16

18. Social Security Equivalent Income Five Percent Rate of Time Preference – CRRA = 5 Female Claim Age Male Claim Age Note: Both the same age. 17

19. Black – Less than High School – CRRA = 5 Social Security Equivalent Income Female Claim Age Male Claim Age 69 62 64 67 70 63 66 68 65 Note: Both the same age. 18

20. Social Security Equivalent Income White – College Educated – CRRA = 5 Female Claim Age Male Claim Age 62 64 65 63 67 69 70 68 66 Note: Both the same age. 19

21. Why do households claim benefits so early? • Many households can’t afford to delay. • Desire for liquidity – medical costs. • Another manifestation of annuity puzzle. 20