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Identifiability, cointegration and the gravity model

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  • Hunt, Andrew
  • Blake, David

Abstract

The gravity model of Dowd et al. (2011) was introduced in order to achieve coherent projections of mortality between two related populations. However, this model as originally formulated is not well-identified since it gives projections which depend on the arbitrary identifiability constraints imposed on the underlying mortality model when fitting it to data. In this paper, we discuss how the gravity model can be modified to give well-identified projections of mortality rates and how this result can be generalised to more complicated mortality models.

Suggested Citation

  • Hunt, Andrew & Blake, David, 2018. "Identifiability, cointegration and the gravity model," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 360-368.
    • Handle: RePEc:eee:insuma:v:78:y:2018:i:c:p:360-368
    DOI: 10.1016/j.insmatheco.2017.09.014
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    References listed on IDEAS

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    1. Kevin Dowd & Andrew Cairns & David Blake & Guy Coughlan & Marwa Khalaf-Allah, 2011. "A Gravity Model of Mortality Rates for Two Related Populations," North American Actuarial Journal, Taylor & Francis Journals, vol. 15(2), pages 334-356.
    2. Andrew Cairns & David Blake & Kevin Dowd & Guy Coughlan & David Epstein & Alen Ong & Igor Balevich, 2009. "A Quantitative Comparison of Stochastic Mortality Models Using Data From England and Wales and the United States," North American Actuarial Journal, Taylor & Francis Journals, vol. 13(1), pages 1-35.
    3. Plat, Richard, 2009. "On stochastic mortality modeling," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 393-404, December.
    4. Rob Hyndman & Heather Booth & Farah Yasmeen, 2013. "Coherent Mortality Forecasting: The Product-Ratio Method With Functional Time Series Models," Demography, Springer;Population Association of America (PAA), vol. 50(1), pages 261-283, February.
    5. Wolfgang Reichmuth & Samad Sarferaz, 2008. "Bayesian Demographic Modeling and Forecasting: An Application to U.S. Mortality," SFB 649 Discussion Papers SFB649DP2008-052, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    6. Coughlan, Guy & Khalaf-Allah, Marwa & Ye, Yijing & Kumar, Sumit & Cairns, Andrew & Blake, David & Dowd, Kevin, 2011. "Longevity hedging 101: A framework for longevity basis risk analysis and hedge effectiveness," MPRA Paper 35743, University Library of Munich, Germany.
    7. French, Declan, 2014. "International mortality modelling—An economic perspective," Economics Letters, Elsevier, vol. 122(2), pages 182-186.
    8. Cairns, Andrew J.G. & Blake, David & Dowd, Kevin, 2006. "Pricing Death: Frameworks for the Valuation and Securitization of Mortality Risk," ASTIN Bulletin, Cambridge University Press, vol. 36(1), pages 79-120, May.
    9. Yang, Sharon S. & Wang, Chou-Wen, 2013. "Pricing and securitization of multi-country longevity risk with mortality dependence," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 157-169.
    10. Carter, Lawrence R. & Lee, Ronald D., 1992. "Modeling and forecasting US sex differentials in mortality," International Journal of Forecasting, Elsevier, vol. 8(3), pages 393-411, November.
    11. Cairns, Andrew J.G. & Blake, David & Dowd, Kevin & Coughlan, Guy D. & Khalaf-Allah, Marwa, 2011. "Bayesian Stochastic Mortality Modelling for Two Populations," ASTIN Bulletin, Cambridge University Press, vol. 41(1), pages 29-59, May.
    12. Johnny Li & Mary Hardy, 2011. "Measuring Basis Risk in Longevity Hedges," North American Actuarial Journal, Taylor & Francis Journals, vol. 15(2), pages 177-200.
    13. Jarner, Søren Fiig & Kryger, Esben Masotti, 2011. "Modelling Adult Mortality in Small Populations: The Saint Model," ASTIN Bulletin, Cambridge University Press, vol. 41(2), pages 377-418, November.
    14. Hunt, Andrew & Blake, David, 2015. "Modelling longevity bonds: Analysing the Swiss Re Kortis bond," Insurance: Mathematics and Economics, Elsevier, vol. 63(C), pages 12-29.
    15. Nan Li & Ronald Lee, 2005. "Coherent mortality forecasts for a group of populations: An extension of the lee-carter method," Demography, Springer;Population Association of America (PAA), vol. 42(3), pages 575-594, August.
    16. Rui Zhou & Yujiao Wang & Kai Kaufhold & Johnny Li & Ken Tan, 2014. "Modeling Period Effects in Multi-Population Mortality Models: Applications to Solvency II," North American Actuarial Journal, Taylor & Francis Journals, vol. 18(1), pages 150-167.
    17. Andrés Villegas & Steven Haberman, 2014. "On the Modeling and Forecasting of Socioeconomic Mortality Differentials: An Application to Deprivation and Mortality in England," North American Actuarial Journal, Taylor & Francis Journals, vol. 18(1), pages 168-193.
    18. Guy Coughlan & Marwa Khalaf-Allah & Yijing Ye & Sumit Kumar & Andrew Cairns & David Blake & Kevin Dowd, 2011. "Longevity Hedging 101," North American Actuarial Journal, Taylor & Francis Journals, vol. 15(2), pages 150-176.
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    Cited by:

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    3. Li, Johnny Siu-Hang & Liu, Yanxin, 2021. "Recent declines in life expectancy: Implication on longevity risk hedging," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 376-394.
    4. Thilini Dulanjali Kularatne & Jackie Li & Yanlin Shi, 2022. "Forecasting Mortality Rates with a Two-Step LASSO Based Vector Autoregressive Model," Risks, MDPI, vol. 10(11), pages 1-23, November.
    5. Hong Li & Yanlin Shi, 2021. "Mortality Forecasting with an Age-Coherent Sparse VAR Model," Risks, MDPI, vol. 9(2), pages 1-19, February.
    6. Li, Hong & Shi, Yanlin, 2021. "Forecasting mortality with international linkages: A global vector-autoregression approach," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 59-75.
    7. Börger, Matthias & Freimann, Arne & Ruß, Jochen, 2021. "A combined analysis of hedge effectiveness and capital efficiency in longevity hedging," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 309-326.

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    More about this item

    Keywords

    Mortality modelling; Age/period/cohort models; Multi-population modelling; Coherent mortality projection; Gravity model;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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