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.
Highlights
Fertility forecasts are a vital element of population and labour force forecasts, and accurate fertility forecasting is essential for government policy, planning and decision-making regarding the allocation of resources to multiple sectors, including maternal and child health, childcare, education and housing
This paper aims to empirically assess the extent to which forecast accuracy can be improved through model averaging in the context of age-specific fertility forecasting
The model averaging methods based on the Bayesian approach and Model confidence set (MCS) do not perform well
Summary
Fertility forecasts are a vital element of population and labour force forecasts, and accurate fertility forecasting is essential for government policy, planning and decision-making regarding the allocation of resources to multiple sectors, including maternal and child health, childcare, education and housing. Parametric models used in forecasting include the beta, gamma, double exponential and Hadwiger functions (see, e.g., Thompson et al (1989); Congdon (1990); Congdon (1993); Knudsen et al (1993); Keilman and Pham (2000)), while semi-parametric models include the Coale-Trussell and Relational Gompertz models (see, e.g., Coale and Trussell (1974); Brass (1981); Murphy (1982); Booth (1984); Zeng et al (2000)) The use of these models is variously limited by parameter un-interpretability, over-parameterization and the need for vector autoregression. Structural change limits their utility, especially where vector autoregression is involved (Booth 2006)
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