Why life expectancy over-predicts crude death rate

Life expectancy is widely used and reported; for example, the UN Human Development Index uses life expectancy as a key component. But many users of period life expectancy do not understand and interpret life expectancy as demographers do. In particular, period life expectancy almost always over-predicts the crude death rate. Indeed, in most observed populations, the annual deaths recorded are always less than one may expect in the corresponding stationary population. To explain this over-prediction, in this paper we analyze how deviations from stationarity affect the crude death rate. We use theory to show that small deviations from the stationary age structure (as high as 20% at each age) always lead to over-prediction. Then we examine global data to show that over-prediction is widespread, occurring even in populations where the deviation from stationarity is large. Finally, we show that populations around the world and over many decades have age structures that are almost always far from stationary (or indeed, stability). But we also show that the deviation is often due to the demographic transition, with population bulges at the middle ages where mortality is low.