by Carlo Maccheroni and Tiziana Barugola; CeRP WP N. 97/10
Abstract
Longevity is one of the most recent striking phenomena of the developed world where the main factor in determining this result has been the rapid decline in mortality in old age. This silent revolution that has completely remodelled the previous mortality patterns offers everyone or almost everyone the possibility of a longer life – deaths are concentrated in elderly or old age groups – so that future evolution will be conditioned by the progress in a more successful ageing. In this field, however, general optimism is to be found in most of international literature, which suggests that further positive surprises are expected.
To formulate the forecast, we have based ourselves on literature to assume the limit characteristics of mortality by making a survival table and inserting this scenario in a timeframe – presumably about the year 2100 for males and females – passing from the current mortality to the limit mortality pattern. The scenario is constructed considering a Weibull model in order to describe endogenous mortality and the recent trend of the causes of death in a group of developed countries for exogenous or accidental causes. The synthetic characteristics of this mortality model are e0 = 108,8 and a life span of about 130 years.
In order to establish a timeframe for the scenario we used a procedure based on the logit model that has linked the mortality database used (1975 – 2005), with the scenario. More precisely the link was established by extrapolating the historical series of the logit relationship parameters in order to find the convergence of the database to the scenario.
The decreasing evolution gap between current mortality and the limit situation will be bridged with a conventional exponential model and on the historical series thus obtained we applied the Lee Carter model from which the stochastic forecast was derived by estimating the time-varying parameter.
The passage from the forecast of mortality by fictitious cohorts to that by birth cohorts was very fast. As the results of the former cover a period of time which is about as long as the life span of the birth cohorts considered, all the data necessary to describe their future process of mortality are available in the age/time matrix of the results of the forecast by fictitious cohorts, so that the corresponding life tables can be easily obtained.
The ongoing growth in life expectancy with good health has important implications and opens a good deal of debate in several fields regarding elderly people.
Published: March 2010