Predictive intervals for age-specific fertility

A multivariate ARIMA model is combined with a Gamma curve to predict confidence intervals for age-specific birth rates by 1-year age groups. The method is applied to observed age-specific births in Norway between 1900 and 1995, and predictive intervals are computed for each year up to 2050. The predicted two-thirds confidence intervals for Total Fertility (TF) around 2010 agree well with TF errors in old population forecasts made by Statistics Norway. The method gives useful predictions for age-specific fertility up to the years 2020-30. For later years, the intervals become too wide. Methods that do not take into account estimation errors in the ARIMA model coefficients underestimate the uncertainty for future TF values. The findings suggest that the margin between high and low fertility variants in official population forecasts for many Western countries are too narrow.