Uncertainty in Mortality Forecasting: An Extension to the Classical Lee-Carter Approach

Abstract

Traditionally, actuaries have modeled mortality improvement using deterministic reduction factors, with little consideration of the associated uncertainty. As mortality improvement has become an increasingly significant source of financial risk, it has become important to measure the uncertainty in the forecasts. Probabilistic confidence intervals provided by the widely accepted Lee-Carter model are known to be excessively narrow, due primarily to the rigid structure of the model. In this paper, we relax the model structure by considering individual differences (heterogeneity) in each age-period cell. The proposed extension not only provides a better goodness-of-fit based on standard model selection criteria, but also ensures more conservative interval forecasts of central death rates and hence can better reflect the uncertainty entailed. We illustrate the results using US and Canadian mortality data.

Longevity Risk

“…The Lee and Carter (1992)-model implicitly assumes that there is no heterogeneity in the measurement error terms x,t , see (14). Li et al (2006) propose a way to incorporate heterogeneity into the Brouhns et al (2002a)variant of the Lee and Carter (1992)-model. Alternatively, suggest to use the Negative Binomial distribution to allow for more heterogeneity.…”

Bayesian mortality forecasting with overdispersion

“…Renshaw and Haberman (2005) introduced a single dispersion parameter into the quasi-Poisson likelihood to increase the flexibility of their model specification, but made no attempt to assess the impact of this parameter on the prediction intervals. Their approach also suffers from the issue that the relationship between the expectation, variance and probability function of death data under the model are internally inconsistent (see Li et al (2009)). Delwarde et al (2007) then proposed a direct extension of the Poisson LC model to form the negative binomial LC model (again, they did not consider the construction of prediction intervals).…”

“…Delwarde et al (2007) then proposed a direct extension of the Poisson LC model to form the negative binomial LC model (again, they did not consider the construction of prediction intervals). In addition, Li et al (2009) attempted to account for mortality variations by introducing an age-specific latent variable that accounts for heterogeneity of individuals, which upon marginalisation, leads to the negative binomial LC model as well. They also extended the parametric bootstrap approach in Brouhns et al (2002) for the generation of prediction intervals.…”

Future Life Expectancy in GCC Countries: Projections with an Extended Lee-Carter Approach

“…This is because the model has several attractive advantages: the number of parameters is small compared to other stochastic models, the model parameters can be straightforwardly understood and interpreted, and the model's organization offers a steady age pattern of mortality in its projections (Li et al, 2009). Li et al (2004) modified the original Lee and Carter approach to tackle situations in which mortality data is available for limited observations with unequal age-specific intervals.…”