Location–Scale Models in Demography: A Useful Re-parameterization of Mortality Models

Several parametric mortality models have been proposed to describe the age pattern of mortality since Gompertz introduced his “law of mortality” almost two centuries ago. However, very few attempts have been made to reconcile most of these models within a single framework. In this article, we show that many mortality models used in the demographic and actuarial literature can be re-parameterized in terms of a general and flexible family of models, the family of location–scale (LS) models. These models are characterized by two parameters that have a direct demographic interpretation: the location and scale parameters, which capture the shifting and compression dynamics of mortality changes, respectively. Re-parameterizing a model in terms of the LS family has several advantages over its classic formulation. In addition to aiding parameter interpretability and comparability, the statistical estimation of the LS parameters is facilitated due to their significantly lower correlation. The latter, in turn, further improves parameter interpretability and reduces estimation bias. We show the advantages of the LS family over the typical parameterization of mortality models with two illustrations using the Human Mortality Database.