Coherent Mortality Forecasting for Less Developed Countries †
Abstract
:1. Introduction
2. The Mortality Models
3. The Rotation Algorithm
3.1. Rotating the Age and Period Effects for Mortality Projections
3.2. Determining the Weight Parameter
4. Empirical Analysis
4.1. Mortality Data
4.2. Empirical Results
4.2.1. China
4.2.2. Brazil
4.2.3. Nigeria
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Abbreviations
Variables of the Lee–Carter model: | |
Log central mortality rate at age x in year t | |
The average mortality level at each age x | |
The mortality index at time t | |
The age-specific sensitivity of to changes in | |
The normal error term in the process | |
The normal error term in the process | |
Additional variables of the Li–Lee models | |
Age effect of the common factor | |
Period effect of the common factor | |
The normal error term in the common factor | |
The age-specific sensitivity of log central mortality rate to the population-specific index |
Appendix A. Optimal Logistic Function
AIC | ||
Country | Single logistic | Double logistic |
China | −21.32 | −16.23 |
Brazil | 40.68 | −13.75 |
Nigeria | 154.14 | 140.36 |
BIC | ||
Country | Single logistic | Double logistic |
China | −13.22 | |
Brazil | 48.79 | 0.43 |
Nigeria | 162.24 | 154.54 |
Appendix B. The Weight Parameter of the Rotation Algorithm
Appendix C. The Projected Life Expectancy at Birth
1 | The United Nations defines the less developed countries/regions as all regions of Africa, Asia (except Japan), Latin America and the Caribbean plus Melanesia, Micronesia and Polynesia, and the more developed countries/regions as all regions in Europe, Northern America, Australia, New Zealand, and Japan. For ease of exposition, we will use the word “country” to refer to any country or region. |
2 | The age-specific death rates are calculated using data from the 2017 revision of the World Population Prospects by the United Nations. The ranking is based on population statistics as of 1 June 2018. Source: https://www.census.gov/popclock/print.php?component=counter (accessed on 14 August 2021). |
3 | Besides these two models, there are many other linear extrapolation models consistent with our rotation algorithm, such as Cairns et al. (2006) and Hyndman and Ullah (2007), as well as Li et al. (2021) for a single population and Dowd et al. (2011), Hyndman et al. (2013), Li et al. (2019), Li and Lu (2018, 2019) for multiple populations. For summaries of linear extrapolation models, we refer to Booth et al. (2002), Cairns et al. (2011), and Li and Hardy (2011). |
4 | When convergence is achieved, the improvement rates of the logarithm of the age-specific mortality rates are the same between the modeled country and the benchmark countries. However, this does not necessarily lead to the same improvement rate of the life expectancy, due to Jensen’s inequality. |
5 | The data were collected from the 2017 revision of the World Population Prospects. We excluded 9 less developed countries/regions with life expectancy higher than 80 in 2010–2015, such as Hong Kong, Macao, and Singapore. The benchmark life expectancy was calculated using 10 more developed countries: Germany, Denmark, Finland, France, The Netherlands, Switzerland, Sweden, the UK, the US, and Japan. |
6 | The United Nations uses a simplified version of Equation (14) where is set to 0. |
7 | Source: http://www.mortality.org/ (accessed on 14 August 2021). |
8 | UN Source: http://www.un.org/en/development/desa/population/ (accessed on 14 August 2021). WHO Source: http://apps.who.int/gho/data/view.main.60340?lang=en (accessed on 14 August 2021). |
9 | Source: http://www.mortality.org/ (accessed on 14 August 2021). |
10 | UN Source: http://www.un.org/en/development/desa/population/ (accessed on 14 August 2021). WHO Source: http://apps.who.int/gho/data/view.main.60340?lang=en (accessed on 14 August 2021). |
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Li, H.; Lu, Y.; Lyu, P. Coherent Mortality Forecasting for Less Developed Countries. Risks 2021, 9, 151. https://doi.org/10.3390/risks9090151
Li H, Lu Y, Lyu P. Coherent Mortality Forecasting for Less Developed Countries. Risks. 2021; 9(9):151. https://doi.org/10.3390/risks9090151
Chicago/Turabian StyleLi, Hong, Yang Lu, and Pintao Lyu. 2021. "Coherent Mortality Forecasting for Less Developed Countries" Risks 9, no. 9: 151. https://doi.org/10.3390/risks9090151