The maximum entropy mortality model: forecasting mortality using statistical moments

Abstract

The age-at-death distribution is a representation of the mortality experience in a population. Although it proves to be highly informative, it is often neglected when it comes to the practice of past or future mortality assessment. We propose an innovative method to mortality modeling and forecasting by making use of the location and shape measures of a density function, i.e. statistical moments. Time series methods for extrapolating a limited number of moments are used and then the reconstruction of the future age-at-death distribution is performed. The predictive power of the method seems to be net superior when compared to the results obtained using classical approaches to extrapolating age-specific-death rates, and the accuracy of the point forecast (MASE) is improved on average by 33% respective to the state-of-the-art, the Lee-Carter model. The method is tested using data from the Human Mortality Database and implemented in a publicly available R package.

Variability Matters

“…Depending on the kind of inequality and the period that he studies, four or five of such quantiles are deemed sufficient to grasp the main elements of economic inequality and its evolution. In their approach of forecasting statistical moments of the age-at-death distribution, Pascariu et al [ 29 ] found that using seven statistical moments tends to strike a good balance between simplicity and computational tractability. Standard statistical courses often teach the first four moments (mean, variance, skew, kurtosis), all of which can be explained intelligibly with pictures, which becomes increasingly difficult for higher moments.…”

Alternative Forecasts of Danish Life Expectancy

“…The final period model is the maximum entropy method (MEM). The MEM makes use of the statistical properties of a probability density function in order to estimate the distribution of deaths of a population in the future (Pascariu et al 2019). Time series methods for forecasting a limited number of central statistical moments are used and then a reconstruction of the future distribution of deaths using the predicted moments is performed.…”

An age-at-death distribution approach to forecast cohort mortality

“…Rather than modelling mortality rates (the standard approach in mortality forecasting, as in, for example, the Lee and Carter model and its variants), our model is based on the distribution of deaths. Ageat-death distributions have recently received increasing attention in mortality forecasting (Oeppen, 2008;Bergeron-Boucher et al, 2017;Basellini and Camarda, 2019;Pascariu et al, 2019), as they provide a different and rather unexplored perspective on mortality developments that can be leveraged by forecasters. For this reason, we extend a newly introduced methodology to model and forecast adult age-at-death distributions (Basellini and Camarda, 2019) with the aim of analyzing and forecasting mortality developments across cohorts.…”