Hierarchical Lee-Carter model estimation through data cloning applied to demographically linked countries

Some groups of countries are connected not only economically, but also social and even demographically. This last fact can be exploited when trying to forecast the death rates of their populations. In this paper we propose a hierarchical specification of the Lee-Carter model and we assume that there is a common latent mortality factor for all of them. We introduce an estimation procedure for this kind of structures by means of a data cloning methodology. To our knowledge, this is the first time that this methodology is used in the actuarial field. It allows approximating the maximum likelihood estimates, which are not affected by the prior distributions assumed for the calculus. Finally, we apply the methodology to some France, Italy, Portugal and Spain data. The forecasts obtained using this methodology can be considered as very satisfactory.