How to analyze fertility decline?: Drawback in age-specific marital fertility rate

The view that marital fertility decline accounts for nothing of the decline in total fertility rate since 1970's has become most influential in Japan. We criticize the view and the component analysis using age-specific marital fertility rate, AMFR that yields the view. We observed the results of the component analyses decomposing the decline in TFR using period age-specific proportion married and period age-specific marital fertility rate, AMFR that were produced by the four simulations with cohort inputs of different levels or timings of first marriage rates and duration-specific marital fertility rates. We found that the decomposition produces the valid results only when cohort first marriage schedule is stable and that if the cohort marriage schedule is delaying, the decline in TFR is accounted for exclusively by the decline in the age-specific proportion married and the AMFR has the positive influence although cohort marital fertility for input is held stable, which may yield a misunderstanding. The issue can be stated more generally as the issue when analyzing behavior one using age-specific rate for those who have experienced behavior two when behavior one is conditional to behavior two.