The most widely used indicator of the level of mortality in any population is the life expectancy at birth. This is entirely appropriate as the measure is usually an excellent reflection of the overall mortality conditions of a given year or other period. Similar calculations can be made for life expectancy any age, but the value at birth is by far the most commonly encountered in general discussion of health and mortality.

The term is also venerable; life expectancy or the related terms “life expectation” or “expectation of life” can be found in scholarly publications back into the 18^{th} century. Google’s Ngram suggests that the earliest use of one of these terms (in fact, expectation of life) is as early as 1738, though the earliest correct calculation is found in Milne (1815). The precise meaning of ‘life expectancy’, however, is easily misunderstood. The interpretation usually given is as a hypothetical indication of “how long a new born baby would live if experiencing the mortality of the population in the year in question”. This readily becomes “how long a baby will live …” in the non-specialist media. And even publications from the statistical offices that calculate life expectancy sometimes fail to make clear the distinction. I believe that the term itself increases the likelihood such misinterpretation. Indeed, the way in which the term life expectancy is used (and often misused) today is a classic example of reification – the tendency to create an abstract measure of a phenomenon and then to treat this abstraction as if it was a “real thing” (Wilson and Oeppen 2003).

Expectation of life was first used by scholars interested in actuarial calculations. For insurers to know how to value financial instruments such as annuities or life insurance, it is essential to have a good idea of how many years any individual is likely to live. Thus the “predictive” dimension of the term seems appropriate. This was especially so when the term was first employed, as mortality was generally thought to be relatively unchanging and thus that it would be possible to find “laws” of mortality that were widely applicable. In a context of broadly constant mortality, the predictive aspect of the term seems appropriate. However, in more recent times, when mortality has improved substantially, the hypothetical interpretation is questionable. At present, life expectancy is rising, often rapidly, in most of the world. In the United Kingdom, for example, male life expectancy is probably rising as fast as at any time in statistically documented history. Thus new born infants will live much longer than the current life expectancy. In fact, the period life expectancy does not indicate how much more life anyone in the population can actually expect to have.

It is my assertion here that the term “life expectancy” itself is something of an invitation to misinterpretation. If we consider how the life expectancy is calculated, then an alternative terminology which does not encourage the predictive interpretation of the measure seems to be worth considering. As anyone who has learned demographic techniques knows, the life expectancy is one of the results that emerge from a life table. The first step is the calculation of age-specific death rates (D_{x}) based on the observed data for a country (or some other clearly defined population) in a year or other period. From these observed death rates it is possible, using simple equations, to calculate the probability of either dying (q_{x}) or surviving (p_{x}) between any two ages. The probabilities of survival define the number of years lived in the life table at each age, given an arbitrary initial number of births, usually a round number such as 1,000 or 10,000. Summing these years-lived for all ages yields a value of life expectancy at birth (e_{0}) or from any other age x (e_{x}).

An alternative viewpoint is that the life expectancy calculated for the population in question is equivalent to the average age at death in the population during a given period, adjusted to take into account the fact that the size of the various age groups differs, reflecting the varying history of fertility and migration in that population. Given this, rather than offer an easily misunderstood hypothetical interpretation, why do we not simply call the e_{0} what it actually is? Perhaps “Standardised mean age at death” or “Adjusted mean age at death” or some similar term would be suitable? This would be much easier for non-specialists to understand, would avoid the implicitly predictive aspects of the term, and could thus help avoid the misleading interpretations. Overturning more than 250 years of accepted usage is not something to be entered into lightly. But it seems to me to be worth considering.

Joshua Milne (1815) A treatise on the valuation of annuities and assurances on lives and survivors”. In David P. Smith and Nathan Keyfitz (2013) *Mathematical Demography: Selected Papers*. Second, revised edition, edited by Kenneth W Wachter and Hervé Le Bras. Berlin and Heidelberg: Springer Verlag

Chris Wilson and Jim Oeppen. 2003. “On reification in demography” In Jochen Fleishhacker, Henk de Gans and Thomas K .Burch (eds.) *Populations, Projections and Politics: Critical and Historical Essays on Early 20 ^{th} Century Population Forecasting*. Amsterdam: Rozenberg Publishers, 113-29.

As a scholar interested in actuarial calculations (or perhaps better an actuary interested in scholarly calculations) I share Chris’ frustration about the use and misuse of the term ‘expectation of life’ but am less convinced that any alternative would be better. The average reader of the popular press would find terms such as standardised mean age at death unintelligible or would respond “oh, you mean life expectancy!” My preference would be a term such as ‘average life span’. Additional confusion comes in when faced with presenting period or cohort measures of life expectancy. But just because something is hard does not mean it is not worth trying.

Dermot

You raise some interesting points. I’d guess that all demographers deal regularly with misinterpretation of e0. I once had a lawyer (born in 1946) ask why his life expectancy was so much higher than that of his business partner (born in 1944). He didn’t quite believe that WW2 was the explanation.

As you point out, there are two fundamental sources of misunderstanding about e0 (1) it summarizes the present rather than predicting the future, and (2) it’s the mean of random distribution — ‘your results may vary’.

To address both problems without using any jargon, how about ‘current average lifetime’ ?