Synergy in fertility forecasting: improving forecast accuracy through model averaging

Abstract

Accuracy in fertility forecasting has proved challenging and warrants renewed attention. One way to improve accuracy is to combine the strengths of a set of existing models through model averaging. The model-averaged forecast is derived using empirical model weights that optimise forecast accuracy at each forecast horizon based on historical data. We apply model averaging to fertility forecasting for the first time, using data for 17 countries and six models. Four model-averaging methods are compared: frequentist, Bayesian, model confidence set, and equal weights. We compute individual-model and model-averaged point and interval forecasts at horizons of one to 20 years. We demonstrate gains in average accuracy of 4–23% for point forecasts and 3–24% for interval forecasts, with greater gains from the frequentist and equal weights approaches at longer horizons. Data for England and Wales are used to illustrate model averaging in forecasting age-specific fertility to 2036. The advantages and further potential of model averaging for fertility forecasting are discussed. As the accuracy of model-averaged forecasts depends on the accuracy of the individual models, there is ongoing need to develop better models of fertility for use in forecasting and model averaging. We conclude that model averaging holds considerable promise for the improvement of fertility forecasting in a systematic way using existing models and warrants further investigation.

A brief guide to producing a national population projection

“…Some fertility projections are produced from extrapolative models, some from explanatory models linked to variables such as unemployment rates, some projections are created by trending from recent fertility to a long-run target, while others are based on expert opinions. An overview of fertility projection methods used in practice can be found in Gleditsch and Syse (2020), while reviews of the academic literature are included in Booth (2006), Shang and Booth (2020), Hilton et al (2019), andBohk-Ewald et al (2018) ,though this last paper focuses largely on cohort fertility projections. In practice, fertility assumptions are often created by drawing on a variety of models and approaches.…”

Pandemic babies? Fertility in the aftermath of the first COVID-19 wave across European regions

“…Whatever the methodological approach, the expected value based on prior birth rate trends remains an approximation. Moreover, no consensus exists in the literature on how to best estimate an 'expected' birth rate, although recent advances suggest model averaging as the most accurate approach (Shang & Booth, 2020).…”

Methods for Small Area Population Forecasts: State-of-the-Art and Research Needs

“…Unfortunately, existing cohort-component projection models for countries and large subnational regions, and accompanying fertility, mortality, and migration forecasting methods (e.g. Li & Lee, 2005 ; Raymer et al, 2006 ; Shang & Booth, 2020 ), are often unsuitable for small areas. Difficulties include less detailed and poorer quality demographic data (due to geocoding inaccuracy, imputation, data adjustment/suppression, among others), short time series of datasets due to boundary changes, often erratic demographic trends, zero cell counts, and random noise in the data which mask underlying patterns.…”