R Programming for Actuarial Science

19 The Lee-Carter Model

Peter McQuire

library(demography)

19.1 Introduction

In Chapters 16 and 17 we developed parametric models to analyse age-dependent mortality rates at a point in time. An example of the model is shown earlier in Figure 17.2. Such a model may be adequate if we are concerned with mortality rates in the immediate future, for example pricing one-year term assurance policies.

However, a major issue with these models is that they make no allowance for changes in the level of mortality rates with time. Mortality rates may change significantly in the future due to, for example, medical advances or increases in national obesity; by not projecting these rates we are implicitly assuming they will remain constant in the future.

Mortality rates in the developed world have generally been decreasing since population data records started to be collected (see Figure 19.1). In the 19th century UK life expectancy was around 40 years; currently UK life expectancy is in excess of 80 years. The improvements have been evident even in recent times, with UK infant mortality rates falling from 0.94% to 0.39% since the mid-80s (Source: HMD).

Figure 19.1 Changes in UK mortality from 1922 to 2018 : Source – the Human Mortality Database.

It is therefore vital to understand these trends and construct suitable models such that reasonable forecasts can be made about future mortality ...