Mathematical and Actuarial Demography
At a Glance
Mortality Modeling, Forecasting Mortality, and Evaluating Mortality Forecasts
Conducted by Roland Rau; Marcus Ebeling, Christina Bohk-Ewald, James W. Vaupel; in Collaboration with Frederik Peters (University of Rostock, Germany), Fernando Colchero (Max-Planck Odense Center on the Biodemography of Aging / University of Southern Denmark, Odense, Denmark), Carl Schmertmann (Florida State University, Tallahassee, USA), Joel E. Cohen (Rockefeller University, New York / Columbia University, New York, USA), Felix zur Nieden (Federal Statistical Office, Wiesbaden, Germany), Marc Luy (Vienna Institute of Demography, Austria)
Demography affects almost all areas of public policy. Any planning requires knowledge about the current structure of the population and its (potential) development in the future. Among the three core parameters that affect the size and structure of population, the research group Mathematical and Actuarial Demography (MAD) focuses on mortality. The goals of this project are three-fold: 1. To estimate mortality for small areas. 2. To develop new models to forecast mortality. 3. To devise new methods to evaluate the accuracy and plausibility of mortality forecasts.
As to the first goal, age-specific mortality and, as a summary measure, life expectancy are not only the cornerstones of any mortality forecast. They are also often used as indicators for the well-being of a population. Estimating mortality and life expectancy can become difficult if age-specific mortality suffers from large random fluctuations. This can be the result of very deaths at young ages or the result of very few people at older ages. Germany's Federal Statistical Office worked together with the group to apply modern statistical methods to obtain the official census life-tables for Germany and its 16 states. Currently, the group cooperates with Prof. Carl Schmertmann, Florida State University, to develop new models based on the TOPALS approach of Joop de Beer and modern Bayesian methods. Preliminary ideas have already been applied to Brazilian data and are currently adapted to take the nested structure of Germany's administrative units (country, states, counties) into account.
As regards the second goal, the group is modeling and forecasting mortality. Jointly with a member of the Laboratory of Population Health, a model was developed to forecast mortality that is being refined in an on-going process. Two key characteristics are: 1. The model does not model age-specific death rates, as most other models do. Rather, it models their time-derivative. We coined the term ROMI – Rates of Mortality Improvements – for our unit of observation when the original model was developed. 2. Following the seminal paper by Nan Li and Ron Lee in 2005, we allow for forecasting several populations at the same time. This can be used, for instance, if the recent trend in the population of interest is rather irregular, and it is expected that the population will follow the trends in populations in close geographical and/or socio-cultural proximity.
In terms of our third goal, research during the past few years has shown that there is a very close (log-) linear relationship between the mean age at death and the variability of ages at death. One paper that illustrates this finding and in which the MAD group was involved has won the best paper award at PNAS for behavioral and social sciences in 2016. In the journal Demography, the MAD group suggests in a paper that this empirical relationship can be used to evaluate mortality forecasts for their plausibility. Alternatively, it can be used as a model constraint for future (Bayesian) mortality forecasting models.
Ageing, Mortality and Longevity, Projections and Forecasting, Statistics and Mathematics