Another tempo distortion: analyzing controlled fertility by age-specific marital fertility rate

The rise in marital fertility in East Asian societies with very low fertility has been reported through analyses using the age-specific marital fertility rate (AMFR). Though the measure is often considered related to the average number of children married women have (CMF), we demonstrated that such an interpretation is often erroneous (AMFR problem) and valid only under limited conditions in more or less controlled fertility, a fact that has been known by some researchers. We conducted numerical simulations based on a simple mathematical model. Holding completed marital fertility (CMF) constant, tempo changes in the age-specific marriage rate and in the duration-specific marital fertility produce a parallel and opposite change in the AMFR, respectively. Note that the former is in the opposite direction of demographic translation. This means that a change in the AMFR caused by such tempo changes may cancel the change in the CMF thus leading to an erroneous interpretation. We should be careful in using the AMFR when the age at marriage or the tempo in duration-specific marital fertility changes or differs notably. Hence, the observed rise in the AMFR should be interpreted after subtracting the enormous effect by such tempo changes so as to avoid exaggeration of the marriage rate decline and negligence of marital fertility decline. This problem may even apply to some developing countries or Western societies.