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Evaluating the goodness of fit of stochastic mortality models

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Author Info

  • Dowd, Kevin
  • Cairns, Andrew J.G.
  • Blake, David
  • Coughlan, Guy D.
  • Epstein, David
  • Khalaf-Allah, Marwa

Abstract

This study sets out a framework to evaluate the goodness of fit of stochastic mortality models and applies it to six different models estimated using English & Welsh male mortality data over ages 64-89 and years 1961-2007. The methodology exploits the structure of each model to obtain various residual series that are predicted to be iid standard normal under the null hypothesis of model adequacy. Goodness of fit can then be assessed using conventional tests of the predictions of iid standard normality. The models considered are: Lee and Carter's (1992) one-factor model, a version of Renshaw and Haberman's (2006) extension of the Lee-Carter model to allow for a cohort-effect, the age-period-cohort model, which is a simplified version of the Renshaw-Haberman model, the 2006 Cairns-Blake-Dowd two-factor model and two generalized versions of the latter that allow for a cohort-effect. For the data set considered, there are some notable differences amongst the different models, but none of the models performs well in all tests and no model clearly dominates the others.

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Bibliographic Info

Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

Volume (Year): 47 (2010)
Issue (Month): 3 (December)
Pages: 255-265

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Handle: RePEc:eee:insuma:v:47:y:2010:i:3:p:255-265

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Web page: http://www.elsevier.com/locate/inca/505554

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Keywords: Goodness of fit Mortality models Standard normality;

References

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  1. Katja Hanewald, 2009. "Mortality modeling: Lee-Carter and the macroeconomy," SFB 649 Discussion Papers SFB649DP2009-008, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  2. Heather Booth & Rob Hyndman & Leonie Tickle & Piet de Jong, 2006. "Lee-Carter mortality forecasting: a multi-country comparison of variants and extensions," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 15(9), pages 289-310, October.
  3. 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.
  4. Yang, Sharon S. & Yue, Jack C. & Huang, Hong-Chih, 2010. "Modeling longevity risks using a principal component approach: A comparison with existing stochastic mortality models," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 254-270, February.
  5. Andrew W. Lo & A. Craig MacKinlay, 1988. "The Size and Power of the Variance Ratio Test in Finite Samples: A Monte Carlo Investigation," NBER Technical Working Papers 0066, National Bureau of Economic Research, Inc.
  6. Jarque, Carlos M. & Bera, Anil K., 1980. "Efficient tests for normality, homoscedasticity and serial independence of regression residuals," Economics Letters, Elsevier, vol. 6(3), pages 255-259.
  7. Andrew W. Lo, A. Craig MacKinlay, 1988. "Stock Market Prices do not Follow Random Walks: Evidence from a Simple Specification Test," Review of Financial Studies, Society for Financial Studies, vol. 1(1), pages 41-66.
  8. Rob J. Hyndman & Md. Shahid Ullah, 2005. "Robust forecasting of mortality and fertility rates: a functional data approach," Monash Econometrics and Business Statistics Working Papers 2/05, Monash University, Department of Econometrics and Business Statistics.
  9. Huang Hong-Chih & Yue Jack C. & Yang Sharon S., 2008. "An Empirical Study of Mortality Models in Taiwan," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 3(1), pages 1-16, September.
  10. Brouhns, Natacha & Denuit, Michel & Vermunt, Jeroen K., 2002. "A Poisson log-bilinear regression approach to the construction of projected lifetables," Insurance: Mathematics and Economics, Elsevier, vol. 31(3), pages 373-393, December.
  11. Cochrane, John H, 1988. "How Big Is the Random Walk in GNP?," Journal of Political Economy, University of Chicago Press, vol. 96(5), pages 893-920, October.
  12. Andrew J. G. Cairns & David Blake & Kevin Dowd, 2006. "A Two-Factor Model for Stochastic Mortality with Parameter Uncertainty: Theory and Calibration," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 73(4), pages 687-718.
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Citations

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Cited by:
  1. Cairns, Andrew & Dowd, Kevin & Blake, David & Coughlan, Guy, 2011. "Longevity hedge effectiveness: a decomposition," MPRA Paper 34236, University Library of Munich, Germany.
  2. Biffis, Enrico & Blake, David & Pitotti, Lorenzo & Sun, Ariel, 2011. "The cost of counterparty risk and collateralization in longevity swaps," MPRA Paper 35740, University Library of Munich, Germany.
  3. Li, J.S.H. & Ng, A.C.Y. & Chan, W.S., 2013. "Stochastic life table forecasting: A time-simultaneous fan chart application," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 93(C), pages 98-107.
  4. De Waegenaere, A.M.B. & Melenberg, B. & Stevens, R., 2010. "Longevity risk," Open Access publications from Tilburg University urn:nbn:nl:ui:12-4578387, Tilburg University.
    • Anja De Waegenaere & Bertrand Melenberg & Ralph Stevens, 2010. "Longevity Risk," De Economist, Springer, vol. 158(2), pages 151-192, June.
  5. Haberman, Steven & Renshaw, Arthur, 2012. "Parametric mortality improvement rate modelling and projecting," Insurance: Mathematics and Economics, Elsevier, vol. 50(3), pages 309-333.
  6. O’Hare, Colin & Li, Youwei, 2012. "Explaining young mortality," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 12-25.
  7. Cairns, Andrew J.G. & Blake, David & Dowd, Kevin & Coughlan, Guy D. & Epstein, David & Khalaf-Allah, Marwa, 2011. "Mortality density forecasts: An analysis of six stochastic mortality models," Insurance: Mathematics and Economics, Elsevier, vol. 48(3), pages 355-367, May.

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