Gompertz Law Revisited: Forecasting Mortality with a Multi-factor Exponential Model

Abstract

This paper provides a flexible multi-factor framework to address some ongoing challenges in mortality modeling, with a special focus on the mortality curvature and possible mortality plateau for extremely old ages. We extend the Gompertz law Gompertz (1825) by proposing a multi-factor exponential model. The proposed framework is based on the Laguerre approximating functions, and is able to capture flexible mortality patterns, and allows for a convenient estimation and prediction algorithm. An extensive empirical analysis is conducted using the proposed framework with a merged mortality database containing a large number of countries and regions with credible old-age mortality data. We find that the proposed exponential model leads to superior goodness-of-fit to historical data, and better out-of-sample forecast performance. Moreover, the exponential model predicts more balanced mortality improvements across ages, and thus leads to higher projected remaining life expectancy for the old ages than existing Gompertz-based mortality models. Finally, the modeling capacity of the proposed exponential model is further demonstrated by a multi-population extension, and an illustrative example of estimation and forecast is provided.