Markov mortality models: implications of quasistationarity and varying initial distributions

This paper explains some implications of Markov-process theory for models of mortality. We show that an important qualitative feature common to empirical mortality data, and which has been found in certain models-the convergence to a "mortality plateau"-is, in fact, a generic consequence of the models' convergence to a "quasistationary distribution". This phenomenon has been explored extensively in the mathematical literature. Not only does this generalization free important results from specifics of the models, it also suggests a new explanation for the convergence to constant mortality. At the same time that we show that the late behavior of these models-convergence to a finite asymptote-is almost logically immutable, we also point out that the early behavior of the mortality rates can be more flexible than has been generally acknowledged. We show, in particular, that an appropriate choice of initial conditions enables one popular model to approximate any reasonable hazard-rate data. This illustrates how precarious it can be to read a model's vindication from its consilience with a favored hazard-rate function, such as the Gompertz exponential.