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Bayesian Demographic Modeling and Forecasting: An Application to U.S. Mortality

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  • Wolfgang Reichmuth
  • Samad Sarferaz

Abstract

We present a new way to model age-specific demographic variables with the example of age-specific mortality in the U.S., building on the Lee-Carter approach and extending it in several dimensions. We incorporate covariates and model their dynamics jointly with the latent variables underlying mortality of all age classes. In contrast to previous models, a similar development of adjacent age groups is assured allowing for consistent forecasts. We develop an appropriate Markov Chain Monte Carlo algorithm to estimate the parameters and the latent variables in an efficient one-step procedure. Via the Bayesian approach we are able to asses uncertainty intuitively by constructing error bands for the forecasts. We observe that in particular parameter uncertainty is important for long-run forecasts. This implies that hitherto existing forecasting methods, which ignore certain sources of uncertainty, may yield misleadingly sure predictions. To test the forecast ability of our model we perform in-sample and out-of-sample forecasts up to 2050, revealing that covariates can help to improve the forecasts for particular age classes. A structural analysis of the relationship between age-specific mortality and covariates is conducted in a companion paper.

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Bibliographic Info

Paper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2008-052.

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Length: 35 pages
Date of creation: Jul 2008
Date of revision:
Handle: RePEc:hum:wpaper:sfb649dp2008-052

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Related research

Keywords: Demography; Age-specific; Mortality; Lee-Carter; Stochastic; Bayesian; State Space Models; Forecasts;

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References

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  1. Ben S. Bernanke & Jean Boivin & Piotr Eliasz, 2004. "Measuring the Effects of Monetary Policy: A Factor-Augmented Vector Autoregressive (FAVAR) Approach," NBER Working Papers 10220, National Bureau of Economic Research, Inc.
  2. Piet De Jong & Leonie Tickle, 2006. "Extending Lee-Carter Mortality Forecasting," Mathematical Population Studies, Taylor & Francis Journals, vol. 13(1), pages 1-18.
  3. Robert McNown & Andrei Rogers, 1989. "Forecasting Mortality: A Parameterized Time Series Approach," Demography, Springer, Springer, vol. 26(4), pages 645-660, November.
  4. Sims, Christopher A & Zha, Tao, 1998. "Bayesian Methods for Dynamic Multivariate Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 949-68, November.
  5. Marco Del Negro & Frank Schorfheide, 2004. "Priors from General Equilibrium Models for VARS," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 45(2), pages 643-673, 05.
  6. 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.
  7. John Geweke & Guofu Zhou, 1996. "Measuring the Pricing Error of the Arbitrage Pricing Theory," CEMA Working Papers, China Economics and Management Academy, Central University of Finance and Economics 276, China Economics and Management Academy, Central University of Finance and Economics.
  8. Renshaw, A.E. & Haberman, S., 2006. "A cohort-based extension to the Lee-Carter model for mortality reduction factors," Insurance: Mathematics and Economics, Elsevier, vol. 38(3), pages 556-570, June.
  9. Booth, Heather, 2006. "Demographic forecasting: 1980 to 2005 in review," International Journal of Forecasting, Elsevier, Elsevier, vol. 22(3), pages 547-581.
  10. Chang-Jin Kim & Charles R. Nelson, 1999. "State-Space Models with Regime Switching: Classical and Gibbs-Sampling Approaches with Applications," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262112388, December.
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Cited by:
  1. Hendrik Hansen, 2013. "The forecasting performance of mortality models," AStA Advances in Statistical Analysis, Springer, Springer, vol. 97(1), pages 11-31, January.
  2. Samir Soneji & Gary King, 2012. "Statistical Security for Social Security," Demography, Springer, Springer, vol. 49(3), pages 1037-1060, August.
  3. Kogure, Atsuyuki & Kurachi, Yoshiyuki, 2010. "A Bayesian approach to pricing longevity risk based on risk-neutral predictive distributions," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 162-172, February.
  4. Cairns, Andrew & Dowd, Kevin & Blake, David & Coughlan, Guy, 2011. "Longevity hedge effectiveness: a decomposition," MPRA Paper 34236, University Library of Munich, Germany.

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