Research Article: Probabilistic population aging

Date Published: June 21, 2017

Publisher: Public Library of Science

Author(s): Warren C. Sanderson, Sergei Scherbov, Patrick Gerland, Hafiz T.A. Khan.


We merge two methodologies, prospective measures of population aging and probabilistic population forecasts. We compare the speed of change and variability in forecasts of the old age dependency ratio and the prospective old age dependency ratio as well as the same comparison for the median age and the prospective median age. While conventional measures of population aging are computed on the basis of the number of years people have already lived, prospective measures are computed also taking account of the expected number of years they have left to live. Those remaining life expectancies change over time and differ from place to place. We compare the probabilistic distributions of the conventional and prospective measures using examples from China, Germany, Iran, and the United States. The changes over time and the variability of the prospective indicators are smaller than those that are observed in the conventional ones. A wide variety of new results emerge from the combination of methodologies. For example, for Germany, Iran, and the United States the likelihood that the prospective median age of the population in 2098 will be lower than it is today is close to 100 percent.

Partial Text

Population aging poses widely discussed policy challenges [1–4]. The United Nations publishes probabilistic forecasts of three measures of population aging, the old-age dependency ratio, the total dependency ratio, and the potential support ratio [5]. These provide information about the likely extent and uncertainty of population aging on the national level and so provide the basis for policy and academic analyses.

We drew for each country a systematic subsample of one thousand random trajectories from the 10,000 that were the basis of the UN’s 2015 probabilistic population projections. Each trajectory included the age structure of the population at 5 year intervals starting in 2015 and abridged life tables for five year intervals from 2015–2020 to 2095–2100 combining data for both sexes. Conventional measures were computed at the midpoint of the 5 year intervals and prospective measures were computed applying the corresponding life tables to those populations.

Figs 2–5 present measures of population aging for four countries, China, Germany, Iran, and the US. Each figure has six panels. The panels on the left-hand side show three measures of aging that are based on chronological ages. The topmost shows the probabilistic distribution of the proportion of the population who are 65+ years old. The middle graph presents the distribution of the old age dependency ratio (OADR), defined as the ratio of people 65+ years old to those 20–64 years old. The bottom graph shows the distribution of the median age of the population.

Each of the trajectories that we use is computed using assumptions about the paths of fertility and mortality rates. In the four countries that we are considering infant and child mortality rates are already quite low at our starting date in 2013, so most of the increase in life expectancy arises because of future increases in survival at upper ages. Some probabilistic trajectories will tend to have higher life expectancies and other lower ones. The life expectancies are auto-correlated, so that a trajectory with a higher than average life expectancy in one year has a greater probability of having a higher than average life expectancy in the following year. On trajectories that, on average, have higher life expectancies, the number of people aged 65+ is higher and therefore, so is the proportion of the population 65+ and the old age dependency ratio.