A misuse of life expectancy

Jared Diamond is going back and forth with Acemoglu and Robinson over his review of their new book, Why Nations Fail. The exchange is interesting in and of itself, but I wanted to highlight one passage from Diamond’s response:

The first point of their four-point letter is that tropical medicine and agricultural science aren’t major factors shaping national differences in prosperity. But the reasons why those are indeed major factors are obvious and well known. Tropical diseases cause a skilled worker, who completes professional training by age thirty, to look forward to, on the average, just ten years of economic productivity in Zambia before dying at an average life span of around forty, but to be economically productive for thirty-five years until retiring at age sixty-five in the US, Europe, and Japan (average life span around eighty). Even while they are still alive, workers in the tropics are often sick and unable to work. Women in the tropics face big obstacles in entering the workforce, because of having to care for their sick babies, or being pregnant with or nursing babies to replace previous babies likely to die or already dead. That’s why economists other than Acemoglu and Robinson do find a significant effect of geographic factors on prosperity today, after properly controlling for the effect of institutions.

I’ve added the bolding to highlight an interpretation of what life expectancy means that is wrong, but all too common.

It’s analagous to something you may have heard about ancient Rome: since life expectancy was somewhere in the 30s, the Romans who lived to be 40 or 50 or 60 were incredibly rare and extraordinary. The problem is that life expectancy — by which we typically mean life expectancy at birth — is heavily skewed by infant mortality, or deaths under one year of age. Once you get to age five you’re generally out of the woods — compared to the super-high mortality rates common for infants (less than one year old) and children (less than five years old). While it’s true that there were fewer old folks in ancient Roman society, or — to use Diamond’s example — modern Zambian society, the difference isn’t nearly as pronounced as you might think given the differences in life expectancy.

Does this matter? And if so, why? One area where it’s clearly important is Diamond’s usage in the passage above: examining the impact of changes in life expectancy on economic productivity. Despite the life expectancy at birth of 38 years, a Zambian male who reaches the age of thirty does not just have eight years of life expectancy left — it’s actually 23 years!

Here it’s helpful to look at life tables, which show mortality and life expectancy at different intervals throughout the lifespan. This WHO paper by Alan Lopez et al. (PDF) examining mortality between 1990-9 in 191 countries provides some nice data: page 253 is a life table for Zambia in 1999. We see that males have a life expectancy at birth of just 38.01 years, versus 38.96 for females (this was one of the lowest in the world at that time). If you look at that single number you might conclude, like Diamond, that a 30-year old worker only has ~10 years of life left. But the life expectancy for those males remaining alive at age 30 (64.2% of the original birth cohort remains alive at this age) is actually 22.65 years. Similarly, the 18% of Zambians who reach age 65, retirement age in the US, can expect to live an additional 11.8 years, despite already having lived 27 years past the life expectancy at birth.

These numbers are still, of course, dreadful — there’s room for decreasing mortality at all stages of the lifespan. Diamond’s correct in the sense that low life expectancy results in a much smaller economically active population. But he’s incorrect when he estimates much more drastic reductions in the economically productive years that workers can expect once they reach their economically productive 20s, 30s, and 40s.


[Some notes: 1. The figures might be different if you limit it to “skilled workers” who aren’t fully trained until age 30, as Diamond does; 2. I’m also assumed that Diamond is working from general life expectancy, which was similar to 40 years total, rather than a particular study that showed 10 years of life expectancy at age 30 for some subset of skilled workers, possibly due to high HIV prevalence — that seems possible but unlikely; 3. In these Zambia estimates, about 10% of males die before reaching one year of age, or over 17% before reaching five years of age. By contrast, between the ages of 15-20 only 0.6% of surviving males die, and you don’t see mortality rates higher than the under-5 ones until above age 85!; and 4. Zambia is an unusual case because much of the poor life expectancy there is due to very high HIV/AIDS prevalence and mortality — which actually does affect adult mortality rates and not just infant and child mortality rates. Despite this caveat, it’s still true that Diamond’s interpretation is off. ]

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  1. Michael Wironen #

    I read the exchange in the NYRB and reacted similarly. This misconception is common.

    To build further on your point, the impact of different tropical diseases varies tremendously, in terms of the cohort affected, mortality rates, and the persistence of morbidity. Malaria significantly increases infant mortality, lowering average life expectancy in countries with highly rates of malaria. Mortality rates among adults are lower, although chronic morbidity has been argued to impact worker productivity. HIV/AIDS, as you rightly point out, causes high mortality rates among productive workers.

    The second point by Diamond, arguing that certain resources are more prone to causing ‘resource curse’ than others, also merits a more nuanced response.

  2. 2

    FYI, I’ve written the editor of the New York Review of Books noting the error and requesting a correction.

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