Methods for projecting fertility

Applying the Statistical Technique of Principal Components Analysis to the schedules of Age-Specific Fertility Rates (ASFR) in Five year age groups for 74 countries around 1960, for 68 countries around 1970, and for 53 countries around 1980, Sivamurthy found that the First Two Principal Components accounted for about 90 percent of the total variation in observed ASFR, and the First Three Components accounted for 96–97 percent . Based on this analysis, Sivamurthy suggested a Two parameter Principal Components Model ( Sivamurthy’s PC Model) for representing ASFR schedule, which is shown to be useful in fertility estimation and projection. Since fertility situations have changed greatly in most of the countries in recent decades, Sivamurthy and Chetna applied the same PC Analysis to the ASFR schedules of 88 countries for the years around 2001, and found that the First Three Principal Components accounted for 92 percent of the total variation in ASFR. Based on this analysis Sivamurthy and Chetna suggested Revised Sivamurthy’s PC Model for ASFR schedule, which can be used for projecting ASFR. A simple procedure is suggested for estimating the three parameters of the Model. The procedure is applied to the Indian data for illustration.

Establishing a link between fertility prospects and aggregate fertility is a widespread concern, with most of the literature dating from the 1970s-80s. Long time-series on fertility preferences are however scarce, and first attempts are made here of looking at the correlation between cohort aggregate preferences and actual cohort completed fertility on a series of definitions of fertility prospects (intended number of children, ideal and societal ideal family size). We use a set of French surveys: past surveys on demographic situation (Ined), more recent surveys on family (Ined/Insee/Inserm), and a yearly time-series of ideal family size (CREDOC). Mean “societal” ideals are found the closest to completed cohort fertility in terms of level. We use the only consistent time-series on ideals (CREDOC) in order to model the link more precisely. In terms of trends, it appears that completed fertility and ideal family size are quite linked together, while ideals do not predict accurately period total fertility rate.

Recently, the United Nations Population Division adopted a new method for projecting total fertility (TF) for all countries. The new projection method was well received but raised discussion about the model assumption that in the long run, the TF will oscillate around the approximate replacement level of 2.1 for all countries. In this paper, we investigate a modified TF projection model, whereby the ultimate fertility levels are country-specific and estimated using a Bayesian hierarchical model. Expert opinion is incorporated into the model by setting the upper bound on the ultimate fertility level to 2.1. Under the proposed model, ultimate fertility levels are smaller though within 0.25 child of the current UN projection for most low fertility countries, and 1.9 (80% projection interval 1.6-2.3) for countries that have not yet completed the fertility transition, compared to 2.1 (1.8-2.4) for the existing method.

In a cohort approach, the extrapolation may refer either to the incomplete fertility of a cohort or to the time series of the parameters of the model. By "forecasting" or "extrapolation" we mean here the capacity of a method to both complete the childbearing period of cohorts of women who have not yet reached its end and forecast the entire set of fertility rates for future cohorts, using the parameters of the model. Various methods have been proposed in the literature but, to our knowledge, there is no study in the international literature which investigates the performances of the various models for the extrapolation of cohort fertility, especially on both perspectives. Yet, this is of particular relevance for projections, especially for those with a long time horizon. This study intends to fill in this gap, comparing the pros and cons of the models listed above using Japan as case study. In addition, given the relevance which is acknowledged in the cohort fertility to the parity, the analysis will be carried out by birth order, in fact a further test on the capability of the methods to adapt to various fertility patterns.

The United Nations Population Division releases country fertility estimates and projections every two years, currently using the model of Alkema et al (2011, Demography) for total fertility rate (TFR). This Bayesian hierarchical model produces a predictive distribution of TFR for each country. We extend this model to allow probabilistic projection of the TFR for any set of countries, such as a region or trading bloc. We model the correlation between country TFRs that is not captured by the original model as a linear function of time invariant covariates, namely whether the countries are contiguous, whether they had a common colonizer after 1945, and whether they are in the same UN region. This correlation structure is incorporated into the original model's error distribution and is shown to improve the calibration of predictive intervals for the future TFR of regions.