Prediction of the modal age at death by means of Lee – Carter model. Application to Slovak data

Karol Pastor, Comenius University in Bratislava

The modal age at death is the mode of random variable, which indicates the length of life of an individual and is estimated from the life tables. It belongs among the most important indicators of longevity, particularly in the low-mortality populations (see Horiuchi et al. 2013, Canudas-Romo 2008). In these populations, if the life expectancy at birth is growing, the modal age at death usually growths, as well. However, temporal exceptions are possible, for example in the case of non-uniform decrease in age specific death rates. One of those exceptions poses the population of Slovak males in early 1990’s. Here, as a suitable model for non-uniform changes, the Lee-Carter model (1992) is suggested. In the presented paper, the time development of the (adult) modal age at death during the recent decades in Slovakia and Czech Republic is examined. Then, by means of the Lee-Carter model, predictions of the mortality rates, life expectancy, and modal age at death are calculated. The results indicate that, despite of many common features, this development differs to a certain extent between counties, and similarly between men and women. While the life expectancy stepwise increases in all of the examined datasets, for the modal age at death the same needn’t be true. The anomalies occurring at Slovak men at the end of the twentieth century will persist in the predicted development, as well. It is also shown that the calculation of the modal age at death is very sensitive especially to the quality of input data, the smoothing procedure at the end of the table (i.e. for higher ages), and the calculation method for the mode. The paper is an extended version of a paper presented at the international conference RELIK 2015 in Prague.