×

Improving HMD mortality estimates with HFD fertility data. (English) Zbl 1460.91211

Summary: This article aims to improve mortality estimates using fertility data. Estimating the population exposed to risk, such as in the human mortality database (HMD), can suffer from errors for cohorts born in years in which births fluctuate unevenly over the year. When comparing period and cohort mortality tables, we highlight the presence of anomalies in the period tables in the form of isolated cohort effects. Our investigation of the HMD methodology shows that it assumes a uniform distribution of births that is specific to the period tables, which is likely to lead to an asymmetry with the cohort tables. Building on the “phantoms never die” study of A. J. G. Cairns et al. [“Phantoms never die: living with unreliable population data”, J. R. Stat. Soc. Ser. A 179, No. 4, 975–1005 (2016; doi:10.1111/rssa.12159)] regarding the construction of a “data quality indicator”, we utilize the human fertility database (HFD), which is the perfect counterpart to the HMD in terms of fertility. The indicator is then used to construct corrected period mortality tables for several countries, which are then analyzed from both historical and prospective points of view. The analysis has implications for the reduction of volatility of mortality improvement rates, the use of cohort parameters in stochastic mortality models, and the improved fit of corrected tables by classical mortality models.

MSC:

91G05 Actuarial mathematics
91D20 Mathematical geography and demography
PDF BibTeX XML Cite
Full Text: DOI HAL

References:

[1] Arnold, S.; Boumezoued, A.; Labit Hardy, H.; El Karoui., N., Cause-of-death mortality: What can be learned from population dynamics?, Insurance: Mathematics and Economics (2015) · Zbl 1400.91242
[2] Boumezoued, A., Macroscopic behavior of heterogenous populations with fast random life histories (2015), HAL preprint Id
[3] Boumezoued, A. (2016)
[4] Cairns, A. J. G.; Blake, D.; Dowd., K., A two-factor model for stochastic mortality with parameter uncertainty: Theory and calibration, Journal of Risk and Insurance, 73, 4, 687-718 (2006)
[5] Cairns, A. J. G.; Blake, D.; Dowd, K.; Coughlan, G. D.; Epstein, D.; Ong, A.; Balevich., I., A quantitative comparison of stochastic mortality models using data from England and Wales and the United States, North American Actuarial Journal, 13, 1, 1-35 (2009)
[6] Cairns, A. J. G.; Blake, D.; Dowd, K.; Kessler., A. R., Phantoms never die: Living with unreliable population data, Journal of the Royal Statistical Society - Series A: Statistics in Society, 179, 4, 975-1005 (2016)
[7] Human Fertility Database (2009)
[8] Human Mortality Database (2002)
[9] Keiding, N., Statistical inference in the Lexis diagram, Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 332, 1627, 487-509 (1990) · Zbl 0714.62102
[10] Lee, R. D.; Carter., L. R., Modeling and forecasting U.S. mortality, Journal of the American Statistical Association, 87, 419, 659-71 (1992) · Zbl 1351.62186
[11] Lexis, W.; Smith, D.; Keytz, N., Mathematical demography, Einleitung in die theorie der bevolkerungsstatistik (1977), Berlin: Springer, Berlin
[12] McKendrick, A. G., Application of mathematics to medical problems, 54, 98-130 (1926) · JFM 52.0542.04
[13] Richards, S. J., Detecting year-of-birth mortality patterns with limited data, Journal of the Royal Statistical Society - Series A: Statistics in Society, 171, 1, 279-98 (2008)
[14] Von Foerster, H., The kinetics of cellular proliferation (1959), Grune & Stratton
[15] Willets, R. C., The cohort effect: insights and explanations (2004), Cambridge University Press
[16] Wilmoth, J. R.; Andreev, K.; Jdanov, D.; Glei, D. A. (2007)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.