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 Conference St. John's University, New York September 25 - 26, 2009

2. What is the optimal age to claim Social Security benefits? 1 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.

3. The United States Social Security Program 2 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.

4. The United States Social Security Program 3 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.

5. The United States Social Security Program 4 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.

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

7. 6 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.

8. Earnings 7 Previous Research–Munnell and Soto (2005) Claim Ages at Which Expected Present Value of Social Security Benefits is Maximized (Husband, Wife) Wife's PIA of as a Percent of Husband's PIA Age Difference0-3030-4040-100 066,6667,6669,62 167,66 69,62 268,6668,6569,62 368,6569,62 468,6469,62 568,6269,62 668,6269,62 Percent of Households32%11%47% Note: Age difference equals number of years the husband is older than the wife. Source: Munnell and Soto (2005).

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

10. But above analyses ignore value of additional longevity insurance acquired by delay 9 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.

11. Assumptions 10 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.

12. Social Security Equivalent Income 11 Single MenSingle Women Claim Age Money's WorthCRRA = 2CRRA = 5 Money's WorthCRRA = 2CRRA = 5 621.0001.1131.1581.0291.1501.190 631.0071.0961.1361.0281.1301.166 641.0011.0651.0981.0131.0941.125 651.0031.0431.0701.0061.0681.094 661.0121.0291.0501.0061.0491.070 671.0161.0101.0241.0001.0241.040 681.0291.0001.0071.0021.0081.019 691.0491.000 1.0101.0001.005 701.0771.0131.0041.0251.0011.000 Single Men and Women

13. Social Security Equivalent Income 12 626364656667686970 621.0271.0311.0271.0261.0281.0511.0731.0951.116 63 1.0351.0311.0301.0321.0551.0781.0991.121 64 1.0181.0171.0191.0421.0631.0851.105 65 1.0051.0071.0291.0501.0711.091 66 1.0001.0211.0421.0631.083 67 1.0101.0301.0501.069 68 1.0241.0431.062 69 1.0411.060 70 1.063 Single Earner Couple – Money’s Worths Female Claim Age Male Claim Age Note: Both the same age.

14. 13 621.1111.1101.1021.0961.0941.1131.1321.1511.170 63 1.1021.0941.0891.0871.1061.1251.1441.162 64 1.0671.0621.0601.0791.0971.1151.133 65 1.0351.0331.0511.0681.0851.102 66 1.0121.0291.0461.0631.079 67 1.0041.0201.0351.051 68 1.0001.0151.031 69 1.0011.016 70 1.008 Female Claim Age Male Claim Age Single Earner Couple – CRRA = 5 Note: Both the same age. Social Security Equivalent Income 62 63 64 65 666768 69 70

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

16. Social Security Equivalent Income 15 626364656667686970 621.168 1.17 01.1641.1621.1631.1801.1961.2121.228 631.163 1.16 51.1601.159 1.1761.1921.2081.223 641.135 1.13 71.1321.1311.1321.1471.1631.1781.192 651.107 1.10 81.1031.102 1.1171.1321.1461.160 661.086 1.0821.0801.0811.0951.1091.1231.136 671.056 1.05 71.0521.0501.0511.0641.0771.0901.103 68 1.03 41.0301.028 1.0411.0541.0661.078 69 1.0131.011 1.0241.0361.0491.060 70 1.000 1.0131.0251.0371.049 Wife Five Years Younger – CRRA = 5 Female Claim Age Male Claim Age

17. 16 626364656667686970 621.154 1.152 1.1541.156 1.16 01.166 1.17 5 631.1461.1471.145 1.1481.149 1.15 41.160 1.16 9 641.1181.1191.117 1.1201.122 1.12 61.132 1.14 1 651.0901.0911.089 1.0921.093 1.09 71.1031.111 661.0691.0701.067 1.0701.071 1.07 51.080 1.08 8 671.0431.0441.042 1.0431.045 1.04 81.053 1.06 1 681.0241.0251.022 1.0241.025 1.02 81.033 1.04 0 691.0101.0111.009 1.0101.011 1.01 41.019 1.02 6 701.0021.0031.000 1.0021.003 1.00 61.010 1.01 7 Female Claim Age Male Claim Age Note: Both the same age, wife’s PIA 50% of husband’s. Two Earner Couple – CRRA = 5 Social Security Equivalent Income

18. 17 626364656667686970 621.1051.1041.0951.0901.0881.1071.1271.1461.165 63 1.0961.0881.0831.0811.1011.1201.1391.157 64 1.0621.0571.0551.0741.0921.1111.128 65 1.0311.0291.0471.0651.0821.099 66 1.0091.0261.0441.0601.077 67 1.0021.0181.0341.051 68 1.0001.0161.032 69 1.0041.019 70 1.014 Female Claim Age Male Claim Age Note: Both the same age. Five Percent Rate of Time Preference – CRRA = 5

19. Black – Less than High School – CRRA = 5 18 621.0981.1001.0951.0921.0931.1121.1311.1491.166 63 1.0941.0891.0871.0881.1071.1261.1441.161 64 1.0621.0611.0621.0801.0981.1151.131 65 1.0331.0341.0511.0681.0841.100 66 1.0121.0291.0451.0611.077 67 1.0031.0191.0341.049 68 1.0001.0151.029 69 1.0021.016 70 1.009 Female Claim Age Male Claim Age Note: Both the same age. Social Security Equivalent Income 62 63 64 65 66 67 68 69 70

20. Social Security Equivalent Income 19 621.1151.1141.1041.0971.0941.1131.1321.1521.171 63 1.1051.0951.0891.086 1.10 51.1241.1431.162 64 1.0681.0621.059 1.07 81.0961.1141.132 65 1.0361.033 1.05 11.0681.0851.103 66 1.012 1.02 91.0461.0631.080 67 1.00 31.0201.0361.052 68 1.0001.0161.031 69 1.0011.017 70 1.008 Female Claim Age Male Claim Age White – College Educated – CRRA = 5 Note: Both the same age. 62 63 6465 66 67 68 6970

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