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How Long Will You Collect Social Security Survivor Benefits?

In the last two weeks, a common question about the Open Social Security calculator has been why it uses mortality tables (to calculate a probability of being alive in each given year) rather than simply assuming the user will die precisely at their life expectancy. The answer has to do with survivor benefits for married couples.

Specifically, assuming that each person will die at their expected date often results in an underestimation of the total amount of survivor benefits that are likely to be received — and that could cause the calculator to suggest a suboptimal strategy.

As one quick example, consider a husband and wife, each born 4/15/1960. The husband has PIA of $1,800, and the wife has PIA of $1,000. And let’s assume that they are in average health.

The calculator as it’s written now suggests that the husband files at 70 and the wife files at 62 and 3 months. The total present value of this strategy (i.e., the total amount of spending it can be expected to fund over their lifetimes) is $549,164, of which $102,742 comes from survivor benefits.

Now what if we instead do the analysis using fixed “death date” assumptions?

Well, if we look at the SSA 2015 period life table to find their life expectancies at age 62, we see that:

  • The husband has a life expectancy of age 82, and
  • The wife has a life expectancy of age 84.81.

If we used those as the fixed “death dates,” the calculator would be calculating for 2.81 years of survivor benefits.

If filing at 70 the husband has a retirement benefit of $2,232 per month. If filing at 62 and 3 months the wife has a retirement benefit of $712 per month. The difference between $2,232 and $712 is $1,520, which tells us that if the wife outlives the husband, she’ll get a survivor benefit of $1,520 per month — or $18,240 per year.

Multiply $18,240 by the “expected” 2.81 years, and we get a total survivor benefit of $51,254, before discounting for time value of money.

When we discount that back to age 62 with the 0.89% real rate the calculator is currently using, we get a PV of $42,399.

In other words, with this particular set of inputs, by assuming fixed dates of death, the calculator would only assign about 41% of the value ($42,399 rather than $102,742) to survivor benefits that it really should.

In some cases (depending on difference in ages, PIAs, etc) this might not matter much in terms of the suggested strategy. But in other cases it will be important. Accepting and accounting for uncertainty in death dates is, in general, useful.

Why Is There Such a Difference?

Even though each approach (year-by-year mortality, or fixed death date assumption) is using the same “expected” date at death, the year-by-year mortality approach accounts for scenarios in which there’s a long length of time where survivor benefits are relevant. For example, it accounts for a scenario in which the husband dies at 71 and the wife lives until 84. And a scenario in which the husband dies at 72 and the wife lives until 83. And a scenario in which the husband dies at 82 and the wife lives until 96, etc.

Each such scenario is unlikely, but when taken together they add up to a nontrivial probability. And in such scenarios, the payout for strategies that maximized survivor benefits is quite a bit higher than for strategies that did not do so. It would usually be a mistake not to take that into account.

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