Detecting Common Longevity Trends by a Multiple Population Approach

Abstract

Abstract.Recently the interest in the development of country and longevity risk models (Njienga and Sherris. 2011) has been growing. The investigation of long-run equilibrium relationships could provide valuable information about the factors driving changes in mortality, in particular across ages and across countries. In order to investigate cross-country common longevity trends, tools to quantify, compare and model the strength of dependence become essential. On one hand, it is necessary to take into account either the dependence for adjacent age groups, or the dependence structure across time in a single population setting: a sort of intradependence structure (D'Amato et al. 2012b). On the other hand, the dependence across multiple populations, which we describe as inter-dependence, can be explored for capturing common long run relationships between countries. The objective of our work is to produce longevity projections by taking into account the presence of various forms of cross-sectional and temporal dependencies in the error processes of multiple populations, considering mortality data from different countries. The algorithm that we propose combines model-based predictions in the Lee Carter (LC) framework (1992) with a bootstrap procedure for dependent data, and so both the historical parametric structure and the intra-group error correlation structure are preserved. We modify the model presented by D' Amato et al. (2012b), which applies a sieve bootstrap to the residuals of the LC model and is able to reproduce, in the sampling, the dependence structure of the data under consideration. In the current paper, the algorithm that we build is applied to a pool of populations by using ideas from panel data; we refer to this new algorithm as the Multiple Lee Carter Panel Sieve (MLCPS). We are interested in estimating the relationship between populations of similar socioeconomic conditions. The empirical results show that the MLCPS approach works well in the presence of dependence.

The dependency premium based on a multifactor model for dependent mortality data

“…The structure of the dependence present in mortality data cannot be ignored, in order to obtain reliable projections as demonstrated by D'Amato et al (2012D'Amato et al ( , 2014aD'Amato et al ( . 2014bD'Amato et al ( , 2016.…”

Modeling Longevity Risk With Generalized Dynamic Factor Models and Vine-Copulae

“…Cointegration in multiple times series is generally based on tests constructed on the VAR representation of the system (Johansen, 1988;Stock and Watson, 1988). Indeed, this econometric machinery of unit roots pretesting procedures, cointegration tests, VAR and VEC models has recently been put to use in the actuarial literature, specifically to perform the task of estimating and forecasting mortality rates (Gaille and Sherris, 2011;Njenga and Sherris, 2011;Torri, 2011;D'Amato et al, 2014). The aforementioned studies present evidence in favor of cointegration, using few variables.…”

Mortality Projections for Small Populations: An Application to the Maltese Elderly

“…• Li and Lee (2005), who applied the Lee-Carter model, with the introduction of common factors, for a group of given population, in order to predict single mortality evolution; • Cairns et al (2011a), who introduced a Bayesian framework to jointly model two populations, referring to one of them as sub-population of the other one; • Dowd et al (2011), who proposed the gravity model for two populations in order to obtain coherent mortality forecasts; • Jarner and Kryger (2011), who proposed a model for the Danish mortality (the Spread Adjusted InterNational Trend (SAINT) model) combining the mortality deterministic evolution of a basket of population with the stochastic evolution of the spread; • D Amato et al (2014), who extended the Lee-Carter model in order to take into account the existence of dependence in mortality data across multiple populations; • Villegas and Haberman (2014), who applied a relative modeling approach where the death rates of a subpopulation are modeled in relation to the death rates of a reference population; they considered different multiple population extensions of the Lee-Carter model and applied their approach in order to study and forecast socioeconomic mortality differentials across deprivation subgroups in England;…”