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Negative binomial version of the Lee–Carter model for mortality forecasting
Author(s) -
Delwarde Antoine,
Denuit Michel,
Partrat Christian
Publication year - 2007
Publication title -
applied stochastic models in business and industry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.413
H-Index - 40
eISSN - 1526-4025
pISSN - 1524-1904
DOI - 10.1002/asmb.679
Subject(s) - overdispersion , poisson regression , negative binomial distribution , poisson distribution , econometrics , statistics , mortality rate , mathematics , component (thermodynamics) , regression analysis , logistic regression , demography , economics , population , physics , sociology , thermodynamics
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(α x + β x κ t ). The log of the time series of age‐specific death rates is thus expressed as the sum of an age‐specific component α x that is independent of time and another component that is the product of a time‐varying parameter κ t reflecting the general level of mortality, and an age‐specific component β x 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. Copyright © 2007 John Wiley & Sons, Ltd.