This paper presents detailed description of a newly developed fertility projection system, which was used in Population Projections for Japan, and Population Projections by Prefectures, officially announced in September and November 1992 respectively. The system is based on a model of age-specific fertility rate by birth order, and it converts parameters, which convey behavioral traits of cohort fertility into age-specific fertility rates of future years.
In this paper, first, I compared several nuptiality models regarding applicability to cohort age-specific fertility rates by birth order. The comparison was made among models based on log-gamma distribution as extensions of Coale-McNail Nuptiality model, model proposed by Hernes (1972), log-logistic model, and model based on gamma distribution. They were examined in goodness of fit and predictability of cohort fertility characteristics (completed fertility level, mean age at birth, and spread of age at birth). As a result, 4-parameter log-gamma distribution model indicated good overall applicability and predictability especially to higher birth order, and seemed more suitable for the projection system.
Using the log-gamma model with empirical adjustment, fertility rates were projected in future up to 2025. First, parameters of the model were estimated by the maximum likelihood method for cohorts who have completed substantial parts of their fertility process, and then time trends of the parameters were projected toward targets for cohorts who are in early stages of the process, or not yet in the process at all. Second, the estimated and projected parameter values were converted into cohort age-specific fertility rates by the model. Next, the cohort fertility rates were reconstructed into period age-specific fertility rates. The projected period fertility was compared with actual statistics for years in which both data and projection were available, indicating good correspondence. Finally, the system provided the projected future fertility rates with a minor adjustment for most immediate years.
Some major problems, reduction of the model, introduction of socioeconomic factors into the system via parametric regression method in event history technique, and treatment of period effects were briefly discussed.