Tags: mortality rate, forecasting, life expectancy, longevity, developing country, IRFRC
More from: Pintao Lyu, Hong Li, Yang Lu

The past decades have witnessed a drastic increase of life expectancy in the less developed countries around the world. According to the 2017 revision of the World Population Prospects, life expectancy at birth in the less developed countries has increased by 27.4 years (from 41.7 to 69.1) between 1950 and 2015, against the 13.6 years gain in the more developed countries (64.8 to 78.4). Meanwhile, the total population in the less developed countries reached 6.13 billion in 2015, which was about 5 times that of the more developed ones (1.25 billion). This fast mortality improvement in the less developed countries would have huge impacts on the worldwide population aging process, and thus spells a critical need for reliable mortality projection tools.

Although the life expectancy at birth in the less developed countries has been extensively studied. Much less attention has been paid to the age-specific mortality rates. Yet the latter are important on their own right, since they contain much richer information than the life expectancy at birth, and are the necessary inputs to generate other useful demographic indicators, such as the population structure, the dependency ratio, and the life expectancy at age, say, 65.

So far, the best-known approach to stochastically forecasting the age-specific mortality rates is the Lee-Carter model. In this model, the logarithms of the age-specific mortality rates are decomposed into a time-varying factor (the period effect) and a set of age-specific sensitivity parameters with respect to this factor (the age effect). Mortality projections are then obtained by extrapolating linearly the period effect. The two major assumptions of the Lee-Carter model are the linearity of the period effect and the time-invariance of the age effect. The first assumption implies that the trend in the aggregate decline of the logarithm mortality is linear, while the latter implies that the relative improvement rates of the age-specific mortality are constant, i.e., ages with faster historical mortality declines are forced to maintain their faster decline rate in the projection phase. Though there exists an extensive literature confirming the compatibility of these two assumptions with the post-war mortality data in the industrialized countries, very few studies have examined their suitability for the less developed world.

In the less developed world, the mortality rate dropped much faster among the young and the working ages in these countries, in particular, mortality rates between ages 15 to 55, i.e., the majority of the working ages, became lower in China than the US in 2015 (for statistical details, we refer the readers to the paper). On the other hand, the reductions of mortality differential among the elders were much milder. As a result, mortality projections for these four less developed countries by the Lee-Carter model would, firstly, decrease at faster speeds than the US at the aggregate level and, secondly, have increasingly large proportional difference to their US counterparts for most ages.

Prior studies largely attribute the recent mortality improvements in the less developed countries to factors such as modernization, improved health care coverage, better nutrition, and prevention of infectious diseases. While such socioeconomic transitions have led to fast aggregate mortality declines, especially for infants, the young and the working age population, they are unlikely to last for very long periods. In fact, chronic diseases have already replaced infectious diseases in recent years and become the major causes of death in many low- and middle-income countries. In other words, the mortality patterns of many less developed countries are becoming closer to those of the industrialized countries, where mortality declines have been slowing down at younger ages, and at the same time accelerating among the elders. This phenomenon can be explained by factors including healthier lifestyle, e.g., smoking reduction, and medical advances in the treatment of chronic diseases including cardiovascular diseases. Hence, when it comes to mortality projections for the less developed countries, one should account for the possibility that the mortality patterns of these countries will gradually converge to those of the more developed countries, rather than sticking to their own historical trends.

In the existing literature, the Li-Lee (2005) model is a popular approach to accounting for the future changes of mortality patterns and to generate coherent mortality projections for multiple countries. In this model, a set of common age and period effects are first estimated using the mortality data of a group of more developed countries. These parameters are then set as the benchmark and the less developed countries are assumed to follow the benchmark in the projection phase. As a result, the historical mortality patterns of the less developed countries do not affect their long-term mortality trends, and coherent mortality projections between the modeled and the benchmark countries are automatically ensured. While having the desirable coherence property, the Li and Lee model has also some potential limitations. First, mortality patterns in the less developed countries are assumed to immediately follow the benchmark patterns in the projection phase. Such abrupt changes will cause an artificial structural break in the projected mortality of the less developed countries, and are thus rather unlikely in reality. In addition, mortality projection is unfeasible for a population if its historical mortality pattern significantly diverges from the benchmark. This regularly happens, as long as the residual effects of the modeled population exhibit non-stationarity after the benchmark age and period effects are imposed.

This paper proposes an innovative mortality rotation method to derive long-term coherent mortality forecasts for the less developed countries. Specifically, we use the historical mortality patterns of a collection of more developed countries as the benchmark, and allow the mortality patterns of a less developed country to gradually rotate to the latter. In contrast to the Li-Lee model, we do not impose instant convergence in the projection phase. Instead, for a less developed country, we let its projected mortality patterns be weighted averages of their own historical patterns and the benchmark values, with time-varying weights determined by the projected life expectancy. The weight of the benchmark values gradually increases from 0 to 1 in the projection phase, and stays there in the long run. In this way, coherent mortality projections are assured between the modeled and the benchmark countries. Moreover, the coherence will be achieved precisely when the life expectancy gap between these two (sets of) countries becomes smaller than a certain threshold. This latter is country-specific, and is determined by a logistic regression of the life expectancy gap on the current life expectancy level of the modeled country. Finally, our method is applicable to countries with different past mortality patterns, even for those significantly different from the benchmark values.

In the empirical analysis, we illustrate the proposed algorithm with three less developed countries: China, Brazil, and Nigeria, which are the most populous countries on their respective continent. A set of 10 more developed countries is used as the benchmark. We show that our algorithm works for countries that exhibit significant mortality divergence with the benchmark (Brazil and Nigeria). Moreover, we show that the rotation algorithm produces more intuitive projections for the age-specific mortality rates and the life expectancy than the independent forecasts using the Lee-Carter model.

The complete paper is available for download at:
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3209392.