Occasional reflections on Life, the World, and Mathematics


I was commenting on how people like to turn age-structured information into longitudinal stories: If 80-year-olds buy more big-band recordings, and 20-year-olds more rap, we describe how people’s tastes shift as they age, from the hard rhythms of rap to the gentle lilt of swing. And I noted that the Obama campaign got itself into trouble last year trying to turn its age-specific policies into a longitudinal fable, called “The Life of Julia”. Looking at the pictures of Julia at different agesobama-julia-infographic

I had the impression that Julia is shrinking as she moves into her forties.

More careful inspection of the pictures revealed that she is not shrinking (or not much); the main height change came when she stopped wearing high heels at age 37. But  that got me wondering: should she have been shrinking? Or would that again have been confusing the cross section with the individual life course — the period with the cohort effect, in demographer jargon?

It’s certainly true that cohorts in America (and in many other prosperous countries) have been getting taller. US Civil war soldiers in 1863-4 averaged 5′ 7 1/2″. 50 years later the average height of young men had not changed significantly, but by 1955 the average height of young men was up to 5′ 9 1/2″ (and they were attaining their maximum height several years earlier). It’s not clear to what extent the trend has continued in the US — according to recent data, the average height of young male adults in the US is still about 5′ 9 1/2″ — though it clearly has in other countries that have seen a substantial improvement in children’s average nutritional welfare, such as Portugal, or the Netherlands, Italy, and Japan.

There is also a tendency for individuals to shrink as they age, from compression of the spine, particularly pronounced after age 60, and more extreme in women than in men. A sketch from this paper is included below. So, in fact, the hypothetical Julia should probably have been drawn about 2 inches shorter at age 67 than when she was 20. That’s about 3% — hard to tell from the silhouettes, with the changing hairstyle and all…

It’s funny, because I have seen height used as a paradigm example of where cross-sectional measures are misleading if you interpret them as cohort effects — narrating the changes within individual lives — but at least for the latter half of the 20th century in the US, the cross sectional data seem to give the right picture.

Longitudinal change of height with age

Longitudinal change of height with age

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