A Gravity Model of Mortality Rates for Two Related Populations

By Kevin Dowd, Andrew J. G. Cairns, David P. Blake, Guy D. Coughlan, M. Khalaf-Allah. 2011

166 citations recorded by the source corpus.

Abstract The mortality rate dynamics between two related but different-sized populations are modeled consistently using a new stochastic mortality model that we call the gravity model. The larger population is modeled independently, and the smaller population is modeled in terms of spreads (or deviations) relative to the evolution of the former, but the spreads in the period and cohort effects between the larger and smaller populations depend on gravity or spread reversion parameters for the two effects. The larger the two gravity parameters, the more strongly the smaller population’s mortality rates move in line with those of the larger population in the long run. This is important where it is believed that the mortality rates between related populations should not diverge over time on grounds of biological reasonableness. The model is illustrated using an extension of the Age-Period-Cohort model and mortality rate data for English and Welsh males representing a large population and the Continuous Mortality Investigation assured male lives representing a smaller related population.

Subfields: Demography, General Health Professions, Health

View Paper: https://www.semanticscholar.org/paper/9172d00a443701abe0363ba838638fa7c5650405

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Citations in the corpus

Multi-population mortality models: A factor copula approach (2015, unknown): “…Sun Literature Two-population mortality model Li and Lee (2005): augmented common factor model Li and Hardy (2011): cointegrated Lee-Carter model Dowd et al. (2011): gravity model (see also Jarnerand Kryger 2011) Carins et al. (2011): framework for two-population models Zhou et al.…”
The New Life Market (2013, unknown): “…other longevity-linked products (e.g., Blake et al., 2006a; Bauer, 2006; Bauer and Ruβ, 2006; Denuit et al., 2007; Barbarin, 2008; Bauer et al., 2010b; Chen and Cummins, 2010; Kogure and Kurachi, 2010; Dowd et al., 2011a; Lane, 2011; Li and Ng, 2011; Mayhew and Smith, 2011; and Zhou et al., 2011).”
Pricing Standardized Mortality Securitizations: A Two‐Population Model with Transitory Jump Effects (2013, unknown): “Li and Lee (2005) and Li and Hardy (2011) proposed the augmented common factor model and the co-integrated LeeCarter model, respectively.”
Modelling and management of longevity risk: Approximations to survivor functions and dynamic hedging (2011, background): “…recently become possible to hedge the plan’s exposure to longevity risk through the use of customised longevity swaps and index-based hedging instruments such as q-forwards (see, for example, Blake et al., 2006, Dahl et al., 2008, Cairns et al., 2008, 2011b, Li and Hardy, 2011, Dowd et al., 2011b).”
A step-by-step guide to building two-population stochastic mortality models (2015, background): “The gravity process, proposed by Dowd et al. (2011), can be expressed as follows: ∆γ(i,1)c = µ (i,1) + φ(i,1)∆γ (i,1) c−1 + Z (i,1) c , ∆γ(i,2)c = µ (i,2) + α(i,2)(γ (i,1) c−1 − γ (i,2) c−1 ) + φ (i,2)∆γ (i,2) c−1 + Z (i,2) c , where c = t − x denotes the year of birth, µ(i,1), µ(i,2), φ(i,1) and…”
Modeling Period Effects in Multi-Population Mortality Models: Applications to Solvency II (2014, methodology): “For instance, we may also use VAR and VECM to model the time-varying factors in the model structures that are documented in Cairns et al. (2009) and Dowd et al. (2011).”