valuing the longevity insurance acquired by delayed claiming of social security

Valuing the Longevity Insurance Acquired

by Delayed Claiming of Social SecurityWei 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

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.

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.


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.


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.

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.

6

Option to delay is equivalent to purchase of an annuityExample: 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 benefitCan 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.

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 Difference 0-30 30-40 40-100

0 66,66 67,66 69,62

1 67,66 67,66 69,62

2 68,66 68,65 69,62

3 68,65 69,62 69,62

4 68,64 69,62 69,62

5 68,62 69,62 69,62

6 68,62 69,62 69,62

Percent of Households 32% 11% 47%

Note: Age difference equals number of years the husband is older than the wife.Source: Munnell and Soto (2005).

Previous research continued

8

•Costs of claiming at sub-optimal ages typically small –

Sass, Sun, and Webb (2007).

But above analyses ignore value of additionallongevity 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.

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.

Social Security Equivalent Income

11

Single Men Single Women

Claim Age

Money's Worth

CRRA = 2 CRRA = 5

Money's Worth

CRRA = 2 CRRA = 5

62 1.000 1.113 1.158 1.029 1.150 1.190

63 1.007 1.096 1.136 1.028 1.130 1.166

64 1.001 1.065 1.098 1.013 1.094 1.125

65 1.003 1.043 1.070 1.006 1.068 1.094

66 1.012 1.029 1.050 1.006 1.049 1.070

67 1.016 1.010 1.024 1.000 1.024 1.040

68 1.029 1.000 1.007 1.002 1.008 1.019

69 1.049 1.000 1.000 1.010 1.000 1.005

70 1.077 1.013 1.004 1.025 1.001 1.000

Single Men and Women


12

62 63 64 65 66 67 68 69 70

621.02

71.03

11.02

71.02

61.02

81.05

11.07

31.09

51.11

6

63 1.03

51.03

11.03

01.03

21.05

51.07

81.09

91.12

1

64 1.01

81.01

71.01

91.04

21.06

31.08

51.10

5

65 1.00

51.00

71.02

91.05

01.07

11.09

1

66 1.00

01.02

11.04

21.06

31.08

3

67 1.01

01.03

01.05

01.06

9

68 1.02

41.04

31.06

2

69 1.04

11.06

0

70 1.06

3

Single Earner Couple – Money’s Worths

Female Claim Age Male Claim Age

Note: Both the same age.

13

621.11

11.11

0 1.102 1.096 1.094 1.113 1.132 1.151 1.170

63 1.10

2 1.094 1.089 1.087 1.106 1.125 1.144 1.162

64 1.067 1.062 1.060 1.079 1.097 1.115 1.133

65 1.035 1.033 1.051 1.068 1.085 1.102

66 1.012 1.029 1.046 1.063 1.079

67 1.004 1.020 1.035 1.051

68 1.000 1.015 1.031

69 1.001 1.016

70 1.008

Female Claim Age Male Claim Age

Single Earner Couple – CRRA = 5



62

63 64

65 66

67

68 6970

Results — Single Earner Couples

14

500

700

900

1100

1300

1500

62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94 96 98 100

62

66

Optimal

70Month

ly C

onsu

mpti

on

Later claimers enjoy higher initial consumption

Age


15

62 63 64 65 66 67 68 69 70

62 1.1681.17

0 1.164 1.162 1.163 1.1801.19

6 1.212 1.228

63 1.1631.16

5 1.160 1.159 1.159 1.1761.19

2 1.208 1.223

64 1.1351.13

7 1.132 1.131 1.132 1.1471.16

3 1.178 1.192

65 1.1071.10

8 1.103 1.102 1.102 1.1171.13

2 1.146 1.160

66 1.0861.08

6 1.082 1.080 1.081 1.0951.10

9 1.123 1.136

67 1.0561.05

7 1.052 1.050 1.051 1.0641.07

7 1.090 1.103

68 1.03

4 1.030 1.028 1.028 1.0411.05

4 1.066 1.078

69 1.013 1.011 1.011 1.0241.03

6 1.049 1.060

70 1.0001.000 1.013

1.025 1.037 1.049

Wife Five Years Younger – CRRA = 5

Female Claim AgeMale Claim Age

16

62 63 64 65 66 67 68 69 70

62 1.1541.15

4 1.152 1.1521.15

4 1.1561.16

0 1.1661.17

5

63 1.1461.14

7 1.145 1.1451.14

8 1.1491.15

4 1.1601.16

9

64 1.1181.11

9 1.117 1.1171.12

0 1.1221.12

6 1.1321.14

1

65 1.0901.09

1 1.089 1.0891.09

2 1.0931.09

7 1.1031.11

1

66 1.0691.07

0 1.067 1.0671.07

0 1.0711.07

5 1.0801.08

8

67 1.0431.04

4 1.042 1.0421.04

3 1.0451.04

8 1.0531.06

1

68 1.0241.02

5 1.022 1.0221.02

4 1.0251.02

8 1.0331.04

0

69 1.0101.01

1 1.009 1.0091.01

0 1.0111.01

4 1.0191.02

6

70 1.0021.00

31.000

1.000

1.002 1.003

1.006 1.010

1.017


Note: Both the same age, wife’s PIA 50% of husband’s.

Two Earner Couple – CRRA = 5



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62 63 64 65 66 67 68 69 70

621.10

51.10

41.09

5 1.090 1.088 1.107 1.1271.14

61.16

5

63 1.09

61.08

8 1.083 1.081 1.101 1.1201.13

91.15

7

64 1.06

2 1.057 1.055 1.074 1.0921.11

11.12

8

65 1.031 1.029 1.047 1.0651.08

21.09

9

66 1.009 1.026 1.0441.06

01.07

7

67 1.002 1.0181.03

41.05

1

68 1.00

01.01

61.03

2

69 1.00

41.01

9

70 1.01

4



Five Percent Rate of Time Preference – CRRA = 5

Black – Less than High School – CRRA = 5

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62 1.098 1.1001.09

5 1.092 1.093 1.112 1.1311.14

9 1.166

63 1.0941.08

9 1.087 1.088 1.107 1.1261.14

4 1.161

64 1.06

2 1.061 1.062 1.080 1.0981.11

5 1.131

65 1.033 1.034 1.051 1.0681.08

4 1.100

66 1.012 1.029 1.0451.06

1 1.077

67 1.003 1.0191.03

4 1.049

68 1.0001.01

5 1.029

69 1.00

2 1.016

70 1.009




62

63

64 65 66 67 68 69 70


19

62 1.115 1.114 1.104 1.097 1.0941.11

3 1.1321.15

21.17

1

63 1.105 1.095 1.089 1.0861.10

5 1.1241.14

31.16

2

64 1.068 1.062 1.0591.07

8 1.0961.11

41.13

2

65 1.036 1.0331.05

1 1.0681.08

51.10

3

66 1.0121.02

9 1.0461.06

31.08

0

67 1.00

3 1.0201.03

61.05

2

68 1.00

01.01

61.03

1

69 1.00

11.01

7

70 1.00

8


White – College Educated – CRRA = 5


62 63 64 65 66 67 68 69 70

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.

valuing the longevity insurance acquired by delayed claiming of social security

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