Lee-Carter mortality projection with «Limit Life Table»

Abstract

The Lee-Carter Model and extensions have been used for decades by official Statistic Bureaus has the standard framework for projecting future mortality rates in population projections. Intrinsically, the model assumes that the dynamics of death rates over time are driven by a single time-varying parameter and that mortality forecasts rely on the extrapolation of this index using appropriate statistical timeseries methods. Despite its simplicity and appealing features, the asymptotic behaviour of mortality rates projected by LC model cannot be considered satisfactory. Empirical studies conducted using LC model show a decreasing pattern for the time index parameter kt, combined with positive finite parameters αx and βx. In this scenario, it can easily be shown that the extrapolation of past time index trends into the future will invariably lead to zero mortality rates at all ages. In this paper we develop a new variant of the so called Poisson Lee-Carter model in which mortality projections are bounded by a limit life table to which future mortality improvements converge over time. This model explicitly assumes that over a fixed time range there are lower bounds to mortality rates. We assume that these limit rates are exogenously determined, either by expert subjective judgements on the limits to human longevity, or by considering that the limit table resembles that of a more advanced population in terms of socio-economic conditions (target life table), or by admitting that the limit table can be expressed by a parametric mortality law that conveys information on the main trends in population mortality.