STUMP » Articles » Mortality with Meep: Cohort vs. Period Mortality Tables » 7 February 2019, 17:28

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Mortality with Meep: Cohort vs. Period Mortality Tables  


7 February 2019, 17:28

I’ve mentioned this in prior posts, but when you hear that “life expectancy dropped this year!” they are talking about a number that has no meaning for individuals, but does have meaning for society — they are using the changes in calendar year mortality. In this prior post, I looked at what happened with mortality between two separate calendar-year tables.

Here is my video:

The Social Security tables I mention are at this link. So let’s do some comparisons!


Let’s do some comparisons – what’s the life expectancy for a specific cohort minus the life expectancy for a specific period? So, I’ll take the mortality table for calendar year 1900, say, calculate the life expectancy based on that table, and then take the cohort table for 1900 – those born that year – and calculate the life expectancy based on that.

Haha, I don’t have to calculate a damn thing – the actuaries at the Social Security Administration have already done this for me.

Here are life expectancies at various ages for specific calendar years, and here are life expectancies for specific cohorts.

Let’s first look at difference in life expectancy from birth:

Let me walk you through what we’re looking at here. In general, because mortality in general has been improving, the cohort life expectancy will be higher than the calendar year life expectancy for the same year. This has not always been true throughout history (think of the Black Death).

We see an anomaly in 1918 – in which the life expectancy difference spikes. And that’s because that year, a bunch of young adults died from the Spanish flu… but the kids born in 1918 were not disproportionately affected. If you have a pandemic that affects relatively young people — or a mortality trend (like opioid overdoses) that affects people at young-ish ages — that will have a disproportionate effect on that calendar year life expectancy.

The rule of thumb is that the more rapid the mortality improvement over a projected lifetime, the larger the difference between the cohort and period life expectancy.

Now, notice that the difference between the life expectancy of cohort and period decreases over time. Some of that is built on an assumption that mortality improvement is slowing (not necessarily true, but let’s go with that for now). Some of the interesting patterns in males vs. females is primarily driven by historical trends of when male & female smoking rates peaked in the U.S. Men’s smoking rates peaked in the mid-1940s (approximately), and women’s smoking rates peaked in the mid-1970s (approximately) — and the male peak was higher than the female peak. That has led to different patterns in mortality improvement for males and females.

But that’s from birth — what if we pick higher ages to calculate life expectancies from. Say, you make it to age 30 — what’s your life expectancy from there?


We see here a less severe spike in 1918, but the general shape is about the same.

So what’s the difference between this graph and the prior one?

This one looks at all the people who made it to age 30 — so it excludes any mortality improvement for people under age 30 — all improvements in infant mortality, child mortality, teen mortality — none of that is in there. But for most of the graph, people are living to age 30, at least. So you’re going to get the same general shape.

So let’s push it out to age 65.


This one is interesting.

This shows the improvement in elderly mortality — so early in the 20th century, there wasn’t a lot of mortality improvement for elderly men… but there was a lot for elderly women. That’s interesting.

But for men, the elderly mortality improved at a faster clip, up until about 1980, and has been coming down since then.

But you’ve got to realize — we are comparing 65-year-olds born in 1980 (… and they’ve not gotten there yet) versus 65-year-olds who were 65 years old in 1980. Obviously, we’re getting to a lot of assumptions once we hit cohort year 1950, forget about projecting to 1980.

In any case, this is generally how I like to look at mortality trends (generally not by life expectancy, but looking at ratios between q_x’s) — by sex and over time at different age ranges. Mortality improvement is rarely even over an entire population, especially by cause of death: the trend for improvement of cancer mortality vs. heart disease mortality vs. accidental cause mortality hits different ages very differently.

When I worked at TIAA, we looked at general population as well as our particular customer mortality improvement, and it definitely made a huge difference whether the improvement was in middle age (say age 40-60), or in senior years (60 – 80) — those had vastly different effects on retirement income annuities.

By the way, I want to highlight how much of mortality improvement we’re talking here, as you keep hearing talk re: “But everybody was dead at age 65 when Social Security was created!” (okay, I exaggerate… and it’s false).

There has been improvement — let’s pick 1950 in specific (to pick on Boomers).

In 1950, men age 65 could expect to live 12.81 more years (so to age 77.81 years).

Men born in 1950, who turned 65 in 2015, could expect to live 17.62 more years (to age 82.62)

So that’s a life expectancy increase of about 5 years between that year and that cohort. You could say about a 5 year improvement over that 65-year period.

For men, the peak improvement in this graph is for 1968 — almost 6 years improvement between those age 65 in 1968 and those who were born in 1968 (and who, obviously, aren’t even 65 yet).

Now, elderly women haven’t seen such improvement as the men, but weep not for us ladies.

The trough seems to be in 1992 — so 65-year-old women in 1992 had a life expectancy of about 3 years less than women born in 1992… who aren’t even 30 years old yet. So, obviously, this is dependent on the assumptions of how that cohort of Millennials are going to develop with mortality. This number is, basically, bogus. It’s assumption-driven.

But let’s just look at the calendar year life expectancy for women age 65 in 1992 … it was 19.25 years.

Compare that to men age 65 in 1992: 15.28 years.

Almost 4 year difference.

But the difference between male and female mortality… is for another time.

Underlying spreadsheet is here.

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