# Demographic Conditions Responsible for Population Aging

**Citation:** *Preston, Samuel H., Himes, Eggers (1989) Demographic Conditions Responsible for Population Aging. Demography (RSS)*

**Tagged:** uw-madison (RSS), wisconsin (RSS), sociology (RSS), demography (RSS), prelim (RSS), qual (RSS), WisconsinDemographyPrelimAugust2009 (RSS)

**Summary:**

This article develops and applies 2 expressions for the rate of change of a population's mean age. In one, equation (1), aging is shown to be negatively related to contemporary birth rates and death rates. [Where Ap is mean age of pop, AD is mean age at death, b is birth rate, d is death rate, dAp/dt is derivative of mean age of pop with respect to time.] This equation shows the time derivative of the mean age to be a function of contemporary birth and death rates and the mean ages of people living and dying. In a general sense, aging occurs when vital rates are too low/not intense enough, as illustrated through applications to the US, the Netherlands, and Japan. Comparing the US and Japan, for example, Japan has a substantially lower death rate and the US has higher in-migration and slightly higher birth rates. The other expression, equation (4), relates the rate of aging to a population's demographic history, in particular to changes in mortality, migration, and the annual number of births. [Where r(a,t) is growth rate of pop aged a at time t, and c(a,t) is proportion of pop aged a at time t.] This equation shows the derivative to be a function of age-specific growth rates, which can in turn be traced to the history of change in births and in mortality and migration rates. Applications to the US and Sweden show that the dominant factor in current aging in these countries is a history of declining mortality. Migration also contributes significantly but in the opposite directions in the 2 countries keeping the US younger and helping to age Sweden. The 2 approaches are integrated after recognizing that the rate of change in the mean age is equal to the covariance between age and age-specific growth rates. A decomposition of this covariance shows that the 2 seemingly unrelated expressions contain exactly the same information about the age pattern of growth rates. A population's history appears in equation (1) in both the Ap and AD terms and in the rates of birth and death, which are affected by age distribution. Contemporary rates of birth and death figure into equation (4) through the r(a,t) function, which reflects all differences between past and present rates of mortality and migration as well as the growth rates of births up to and including the present. In conclusion, the rate of change of a population's mean age is equal to the covariance between age and age-specific growth rates. Since the age-specific growth rate can be expressed in terms of either 3 additive elements reflecting the population's demographic history, or 2 additive elements representing contemporary conditions, the rate of aging can also be expressed in 2 different ways as the sum of covariance terms. Through these equations, we can conclude that populations are aging when birth rates and death rates are sufficiently low that a positive correlation exists between age and age-specific growth rates