PAPP103 - S08: Population dynamics and momentum

Replacement level fertility

Population momentum is a theoretical concept - a thought experiment - that quantifies the relative increase of the total population following an instantaneous decline in fertility to replacement level. Replacement level fertility rates are those fertility rates that under the current mortality conditions ensure that newborn girls will bear on average about 2.05 children during their lifetime. We say 2.05 children because we assume a male to female sex ratio at birth of 1.05. In other words 1/2.05 babies are female and these conditions thus guarantee that each generation of women will bear just enough children to replace itself, hence the name replacement level fertility. It is worth noting that the population growth due to momentum is not the result of high or excessive fertility rates because these are, by definition, set to replacement level.

For most practical applications replacement level fertility rates () can be obtained by dividing age-specific fertility rates () by the Net Reproduction Rate (NRR):

$${\tilde{f}}_x=\frac{f_x}{NRR}$$

These new age-specific fertility rates will produce a new, replacement-level Net Reproduction Rate,

$$N\tilde{R}R={{\displaystyle \sum }}^{\text{}}{\tilde{f}}_x{}_{n}L{}_x={{\displaystyle \sum }}^{\text{}}\frac{f_x}{NRR}{}_n{}^{}L{}_x=\frac{1}{NRR}{{\displaystyle \sum }}^{\text{}}{f}_x{}_n{}^{}L{}_x=\frac{NRR}{NRR}=1$$

The practice of proportionally scaling up or down the age-specific fertility rates to obtain replacement level fertility rates is not necessarily a good representation of real fertility transitions because the latter are usually associated with considerable shifts in the age distributions of births. However, the error introduced by this simplifying assumption is marginal and often ignored.