Valuing the Longevity Insurance Acquired by Delayed Claiming of Social Security

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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

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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.

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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.

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The United States Social Security Program

• Spousal Benefit
• If claimed at age 66, equals 50 of spouses
  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.

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The United States Social Security Program

• Survivor benefit
• 100 of husbands benefit if wife is aged 66 or
  older when husband dies subject to a floor of
  82.5 of husbands 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 husbands Primary Insurance Amount.

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The Social Security Program tradeoffs

• If husband delays claiming his retired worker
  benefit gt increase in wifes survivor benefit.
• But also delays wifes receipt of spousal benefit.

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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.

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Previous ResearchMunnell 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
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Previous research continued

• Costs of claiming at sub-optimal ages typically
  small
• Sass, Sun, and Webb (2007).

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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.

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Assumptions

• Base case single earner couple, same age, born
  1946, CRRA utility, time preferencereal interest
  rate3.
• Alternatives wife one to six years younger
• -Impatient households.
• -Households in high/low mortality socio economic
  groups.

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Social Security Equivalent Income
Single Men and Women
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Social Security Equivalent Income
Single Earner Couple Moneys Worths
Female Claim Age Male Claim Age
Note Both the same age.
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Social Security Equivalent Income
Single Earner Couple CRRA 5
Female Claim Age Male Claim Age
62
65
70
63
66
67
68
64
69
Note Both the same age.
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Results Single Earner Couples
Later claimers enjoy higher initial consumption
Monthly Consumption
Age
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Social Security Equivalent Income
Wife Five Years Younger CRRA 5
Female Claim Age Male Claim Age

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Social Security Equivalent Income
Two Earner Couple CRRA 5
Female Claim Age Male Claim Age
Note Both the same age, wifes PIA 50 of
husbands.
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Social Security Equivalent Income

Five Percent Rate of Time Preference CRRA 5
Female Claim Age Male Claim Age
Note Both the same age.
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Black Less than High School CRRA 5
Social Security Equivalent Income

Female Claim Age Male Claim Age
69
62
63
64
66
67
68
70
65
Note Both the same age.
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Social Security Equivalent Income
White College Educated CRRA 5
Female Claim Age Male Claim Age
62
64
65
63
67
68
69
70
66
Note Both the same age.
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Why do households claim benefits so early?

• Many households cant afford to delay.
• Desire for liquidity medical costs.
• Another manifestation of annuity puzzle.

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