Multiple mortality modeling in Poisson Lee–Carter framework

The academic literature in longevity field has recently focused on models for detecting multiple population trends (D'Amato et al., 2012b D'Amato, V., Haberman, S., Piscopo, G., Russolillo, M., Trapani, L. (2012b). Detecting longevity common trends by a multiple population approach. Presented at Eight International Longevity Risk and Capital Market Solutions Conference, Waterloo, Ontario (Canada). [Google Scholar]; Njenga and Sherris, 2011 Njenga, C., Sherris, M. (2011). Longevity risk and the econometric analysis of mortality trends and volatility. Asia-Pac. J. Risk Insurance 5:2. [Google Scholar]; Russolillo et al., 2011, etc.). In particular, increasing interest has been shown about “related” population dynamics or “parent” populations characterized by similar socioeconomic conditions and eventually also by geographical proximity. These studies suggest dependence across multiple populations and common long-run relationships between countries (for instance, see Lazar et al., 2009). In order to investigate cross-country longevity common trends, we adopt a multiple population approach. The algorithm we propose retains the parametric structure of the Lee–Carter model, extending the basic framework to include some cross-dependence in the error term. As far as time dependence is concerned, we allow for all idiosyncratic components (both in the common stochastic trend and in the error term) to follow a linear process, thus considering a highly flexible specification for the serial dependence structure of our data. We also relax the assumption of normality, which is typical of early studies on mortality (Lee and Carter, 1992 Lee, R.D., Carter, L.R. (1992). Modelling and forecasting U.S. mortality. J. Am. Stat. Assoc. 87:659–671.[Taylor & Francis Online], [Web of Science ®], [Google Scholar]) and on factor models (see e.g., the textbook by Anderson, 1984 Anderson, T.W. (1984). An Introduction to Multivariate Statistical Analysis (2nd ed.). New York: Wiley. [Google Scholar]). The empirical results show that the multiple Lee–Carter approach works well in the presence of dependence