## Monday, July 22, 2013

### Gender Breakdown of Widows

Here is a quick post with an interesting result I get from playing around with mortality data.

These results are based on a Gompertz distribution function using parameters that Moshe Milevsky determined are optimistic/reasonable. They probably apply better to my readers than to the overall population, who will likely live longer than average on account of higher education, income, and an interest in retirement planning.

As a purely technical note, here are the parameters:

mm=88.18;dm=10.5; % Milevsky (2006) reasonable assumptions
mf=92.63; df=8.78;

Now to the interesting results.

Consider a 65-year old couple with one male and one female (I point out the gender, because since males and females have different life expectancies, the results will be different for same-sex couples). The calculations are made assuming each spouse's lifespan is independent of the other, i.e. that one does not die from a broken heart, etc.

This table shows, by age, the probability that both spouses are still alive, the probability that neither is alive, and the probability that only one of the two spouses is still alive. These three columns add up to 100%.  Then I further provided the gender breakdown among those couples in which only one member is still alive. In other words, the percentage of widows which are male and the percentage which are female.

For instance, at age 85, with 36.6% of couples, both are still alive. For another 14.6% of couples, both have passed away. Strikingly, for 48.8% of the couples (almost half), one member carries on as a widow. Among these widows, 34.3% are male and 65.7% are female. What is striking is that across the age range, there is consistency that about a 1/3 of widows are male and 2/3 are female. If one spouse tends to take care of the family finances, it is certainly clear that a game plan must be in place to ensure that financial matters remain secure for the surviving spouse in the event of widowhood.

1. According to this chart, there is a15% chance that one of the spouses will be alive at age 100. As a physician, I find that hard to believe.

1. Even with the 2009 Period Life Table from the Social Security Administration, if you calculate out for a 65 year old couple, there is about a 4.3% chance that at least one is still alive at 100, and about a 15% chance that at least one is still alive at 96. So we are just talking about increasing lifespans by a few more years over the next 30-35 years for today's 65 year olds, and also these assumptions are meant to apply more to a subsection of the population can expect to live longer than the general population.

Youn and Shemyakin how reasonably conclusively that there is an excess mortality related to death of a spouse - surviving spouses tend to die sooner once they're predeceased.

www.soa.org/library/research/actuarial-research...1/arch01v19.pdf

I imagine that incorporating the excess mortality rates into your calculations would yield a higher expected joint mortality.

http://www.soa.org/library/research/actuarial-research-clearing-house/2000-09/2001/arch-1/arch01v19.pdf

2. Jason,

Thanks for sharing. I haven't checked it yet, but I imagine that this is a result which still holds after factoring out things like car accidents or house fires that get both spouses at the same time.

Any thoughts on why the consistency of 1/3::2/3 ratio of male to female survivorship over all ages. It would seem to me that as males and females continue to seek parity in work and family that the ratio would narrow. I know this calculation only captures a moment in time but the anomaly seems significant.

1. Mitchell,

This is simulated data from something like a normal distribution. That ratio could be a bit less constant in the real world, but it should still be something like that, and it is essentially happening as a result of women living longer.

2. Yes, but aren't women taking on many of the behaviors that men have and aren't men beginning to adopt female roles in the home as well, thus beginning to close the mortality gap that has existed in the past between the sexes. From what I have read women are now suffering from the same set of physical and psychological aliments that men have and vice versa. Shouldn't we see that show up in statistical work like this. Are there any studies which have addressed this perhaps looking at a narrowing of the mortality gap?