The size of momentum effects

The amount of momentum resulting from a population's age structure can be estimated from knowledge of the initial (stable) conditions of the population. Keyfitz (1971) showed that the final population size is approximately equal to:

N s = N 0 × C B R ⋅ e 0 r ⋅ μ f ⋅ N R R − 1 N R R

where:

Ns = the stationary population size
N0 = the population size at the time of the fertility transition
r = the stable population growth rate
uf = the mean age at childbearing in the stable population

 

Frauenthal (1975) demonstrated that this formula could be simplified without much loss of accuracy:

N s = N 0 × C B R ⋅ e 0 N R R

These expressions demonstrate that greater population momentum is associated with high pre-transition birth rates and high life expectancy (offset to some extent by the positive association between each of these two indicators and the NRR).