Good forecasts for future fertility developments are of high importance in political planning, especially regarding measures in social insurance. Fertility is the main driver of demographic change, since small fertility rates lead to a shrinking population and together with decreasing mortality rates to an aging of the population structure. Which means an increasing stock of elder people, who have to be financed by less people in the working ages. Parametric time series models based on a quasi-three principal component model are fitted to the age- and sex-specific fertility rates (ASSFR). Age-specific migration, represented by a migration index derived from a previous principal component analysis (PCA), is used as a predictor variable to take into account its impact on fertility. Simulations of Wiener processes are used for estimating the future distributions of each ASSFR as well as the Total Fertility Rate (TFR). The forecast shows, ceteris paribus, a further increase in the TFR, with increases in the ASSFR for older women and decreasing ones for younger females. A test based on squared residuals shows that the model gives better forecast accuracy than the most commonly used methods in Germany. The modeling approach performs better than common projection and forecast methods in Germany while integrating the often discussed link between migration and fertility into a forecasting model. Next to the detailed and stochastic quantification of age-specific fertility it includes the gender of newborns, which allows for easy implementation into regular population updating through a stochastic cohort-component model.
Statistical Demography Forecasting Fertility and International Migration Principal Component Analysis Time Series Analysis