Abstract
Coherent models were developed recently to forecast the mortality of two or more sub-populations simultaneously and to ensure long-term non-divergent mortality forecasts of sub-populations. This paper evaluates the forecast accuracy of two recently-published coherent mortality models, the Poisson common factor and the product-ratio functional models. These models are compared to each other and the corresponding independent models, as well as the original Lee–Carter model. All models are applied to age-gender-specific mortality data for Australia and Malaysia and age-gender-ethnicity-specific data for Malaysia. The out-of-sample forecast error of log death rates, male-to-female death rate ratios and life expectancy at birth from each model are compared and examined across groups. The results show that, in terms of overall accuracy, the forecasts of both coherent models are consistently more accurate than those of the independent models for Australia and for Malaysia, but the relative performance differs by forecast horizon. Although the product-ratio functional model outperforms the Poisson common factor model for Australia, the Poisson common factor is more accurate for Malaysia. For the ethnic groups application, ethnic-coherence gives better results than gender-coherence. The results provide evidence that coherent models are preferable to independent models for forecasting sub-populations’ mortality.
Highlights
The widely-used Lee–Carter [1] model is an extrapolative mortality forecasting model that uses a single time-varying index of the mortality level
All five models were applied to age- and gender-specific mortality rates from Australia and Malaysia in which gender-coherence was employed for coherent models
The out-of-sample log death rate forecast errors of different models showed that both coherent models outperformed independent models for three out of the four sub-populations: Australian males and females and Malaysian females
Summary
The widely-used Lee–Carter [1] model is an extrapolative mortality forecasting model that uses a single time-varying index of the mortality level. The Lee–Carter model and its earlier extensions are independent models [11] and, as such, forecast sub-populations (such as males and females) separately, failing to account for any relationship between groups [12]. Such independent models may produce divergent forecasts between two or more sub-populations, which may poorly represent the smaller populations within the same larger region or country [13]. Coherent models were developed to forecast the mortality of two or more sub-populations simultaneously and to ensure long-term non-divergent forecasts of sub-populations [11,12,13].
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