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The strange career of period life expectancy

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Breaking: Joe Biden is now 81 years old.

A few years ago, I asked a very eminent government scientist, whose work was intimately related to questions of mortality risk in general and life expectancy in particular, the following question. If life expectancy in the USA in 1900 was 47, but age adjusted mortality rates fell a lot over the course of the 20th century, didn’t that necessarily mean that people born in America in 1900 ended up living quite a bit longer than 47 years, on average? And how much longer? Had anybody calculated this?

The scientist didn’t know the answer to this question, and seemed amused that I considered it interesting. Which, at a meta-level, I also found interesting. Dr. X’s work regarding mortality risk had at times generated some fairly heated public controversy, so I would have thought this was the sort of question that Dr. X — an extremely prominent and distinguished epidemiologist — would also have considered interesting and important.

The point of this windup is this: Even among experts in related fields, there’s sometimes surprisingly little knowledge regarding what, exactly, the concept of “life expectancy” actually means and entails. So like Aaron Rodgers I had to do my own research, and I discovered the following:

What is almost exclusively referred to as “life expectancy,” or more precisely “life expectancy at birth,” is just one statistical construct, and what turns out to be a rather misleading one for the purposes of public policy debate. That construct is period life expectancy. Period life expectancy isn’t a prediction, it’s a statement of a statistical fact. That fact is, if age adjusted mortality rates were to remain constant over the course of a cohort’s lifetime, what would be the average age to which people in the cohort lived? But the concept itself doesn’t include any assumption that mortality rates will remain constant.

In fact, as a historical matter, age adjusted mortality rates in the USA almost always fall, subject to certain notable exceptions. The result is that people live to be quite a bit older, on average, than what is described as their “life expectancy,” since “life expectancy” is almost exclusively used tor refer to period life expectancy.

Take Joe Biden. When Biden was born in 1942, the period life expectancy for American males at birth was 62.6 years. 81 years later, it’s possible to estimate within an extremely high degree of accuracy how long American men born in 1942 will end up living, on average. The answer is 71.1 years, i.e., 14% longer than than their period life expectancy at birth. This alternative definition of life expectancy — how long people actually live — is called cohort life expectancy.

The gap between period life expectancy and cohort life expectancy was at one point nearly 20% — it turns out that people born in the USA in 1900 lived to be on average 56 rather than 47. The gap has been closing, as the massive improvements in medicine and public health that marked the past century have slowed down, but it’s still quite significant.

For instance, the Social Security Administration, which for obvious reasons has to be focused on cohort rather than period life expectancy, currently estimates that boys born in the USA this year will live to an average age of 82.3 years, and girls will live to an average of 86.7 years. By contrast, period life expectancy in 2021 was 73.5 and 79.3 years for boys and girls born in that year. Cohort life expectancy for infants is of course a pure statistical extrapolation from existing trends, but the trends have continued over many decades to produce cohort life expectancy figures that are a lot higher than period life expectancy. (The two and a half year decline in period life expectancy at birth in the USA between 2020 and 2021 has been largely a product of Covid, which probably has almost no relevance to the cohort life expectancy of young people in America today. In addition, it seems likely that about half of that decline will be erased by the 2022 period life expectancy figures, and most of the rest by the 2023 figures. Back of the enveloping suggests that period life expectancy at birth in the USA in 2023 will be around six to nine months less than it was in 2019).

It’s a cultural curiosity of some practical significance that period life expectancy — which is a statistical construct rather than a prediction, and indeed a very inaccurate number if treated as a prediction — is nevertheless almost always interpreted by the media and even many otherwise well-informed people as a prediction.

There’s a lot more to say about this general topic, which I’ll save for another post.

In the meantime, happy birthday Joe Biden, who statisticians predict will be approximately one year older than he is today on election day 2024, which is very old — a fact which the American media have somehow completely overlooked to this point.

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