The time response in averted births

Abstract A calculation of the timing of births that are averted may seem a curious exercise, when not only do the births in question not occur, but the corresponding conceptions may never have existed. However, such a calculation may have considerable use. In order to assess the likely direct impact of a contraceptive programme on birth rates it is useful to estimate the number of births that would, in the absence of the programme, have occurred among the couples who accept it. Moreover, some time would necessarily elapse before a new 'steady state' in fertility could be reached, even if the programme and the potentially fertile population did not change in any way; and it is worth while to seek to find the times (for a few years after the start of a programme) when the (averted) births would have occurred in its absence, and to examine any inherent oscillations produced in birth rates by it. This question is considered below only for groups of women aged 20 at marriage (a state which is taken to be the start of regular exposure to the risk of conception), but the same methods are applicable to other ages, (possibly allowing for mortality) and appropriate combinations of age groups and cohorts in the fertile range may be used to estimate changes in fertility and reproduction rates expected from a programme, subject to given conditions, for several years after its start. The methods can also be generalised, by means of convolution, to contraceptive programmes that change with time, but these are not considered further.