A geostatistical approach for dynamic life tables: The effect of mortality on remaining lifetime and annuities
Dynamic life tables arise as an alternative to the standard (static) life table, with the aim of incorporating the evolution of mortality over time. The parametric model introduced by Lee and Carter in 1992 for projected mortality rates in the US is one of the most outstanding and has been used a great deal since then. Different versions of the model have been developed but all of them, together with other parametric models, consider the observed mortality rates as independent observations. This is a difficult hypothesis to justify when looking at the graph of the residuals obtained with any of these methods. Methods of adjustment and prediction based on geostatistical techniques which exploit the dependence structure existing among the residuals are an alternative to classical methods. Dynamic life tables can be considered as two-way tables on a grid equally spaced in either the vertical (age) or horizontal (year) direction, and the data can be decomposed into a deterministic large-scale variation (trend) plus a stochastic small-scale variation (residuals). Our contribution consists of applying geostatistical techniques for estimating the dependence structure of the mortality data and for prediction purposes, also including the influence of the year of birth (cohort). We compare the performance of this new approach with different versions of the Lee-Carter model. Additionally, we obtain bootstrap confidence intervals for predicted qxt resulting from applying both methodologies, and we study their influence on the predictions of e65t and a65t.
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