Negative binomial version of the Lee–Carter model for mortality forecasting

Negative binomial version of the Lee–Carter model for mortality forecasting

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Article ID: iaor20082862
Country: United Kingdom
Volume: 23
Issue: 5
Start Page Number: 385
End Page Number: 401
Publication Date: Sep 2007
Journal: Applied Stochastic Models in Business and Industry
Authors: , ,
Keywords: health services, statistics: distributions, statistics: regression
Abstract:

Mortality improvements pose a challenge for the planning of public retirement systems as well as for the private life annuities business. For public policy, as well as for the management of financial institutions, it is important to forecast future mortality rates. Standard models for mortality forecasting assume that the force of mortality at age x in calendar year t is of the form exp(αx + βxκt). The log of the time series of age-specific death rates is thus expressed as the sum of an age-specific component αx that is independent of time and another component that is the product of a time-varying parameter κt reflecting the general level of mortality, and an age-specific component βx that represents how rapidly or slowly mortality at each age varies when the general level of mortality changes. The parameters are usually estimated via singular value decomposition or via maximum likelihood in a binomial or Poisson regression model. This paper demonstrates that it is possible to take into account the overdispersion present in the mortality data by estimating the parameter in a negative binomial regression model.

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