Changes in numerators and denominators of death rates and their contributions to changes in life expectancy

Demographers use ratios, proportions, and rates-all calculated as counts in numerators divided by counts in denominators-as key research inputs. For age-specific death rates, the numerator is observed deaths and the denominator is person-years lived. Life expectancy summarizes those rates into one measure, and its changes convey messages of changing mortality across time. We examine the contributions from the two components of life expectancy change: the population growth rate (relative changes in person-years in the denominator) and growth rate of deaths (relative changes in number of deaths in the numerator). We name this the numerator-denominator decomposition method. Applying the method to high-longevity countries during 2009-19 shows increases in life expectancy driven by high population growth at older ages without comparable increases in deaths. The United States experienced little life expectancy increase, and subnational comparisons show stark differences between urban and rural areas.