A Bayesian Comparison of Models for Changing Mortalities toward Evaluating Longevity Risk in Japan

We present a Bayesian approach to compare models for forecasting mortality rates under the framework of the Lee-Carter methodology. We consider the original normal log-bilinear formulation of the methodology as well as the recently proposed Poisson log-bilinear formulation. For each formulation, we compare three models: the deterministic trend model, the stochastic trend model and the stationary (no trend) model, each of which represents a different future scenario for changing mortalities. Markov-chain Monte Carlo methods are used to sample the predictive distributions from each model and to calculate the marginal likelihoods for the model selection. The approach is applied to Japanese male mortality rates from 1970 to 2003. The results show that the stochastic trend model is most appropriate for forecasting mortality rates both for the normal and the Poisson formulation. We then use the selected model to evaluate longevity risk in Japan by calculating the posterior predictive distributions of the life annuities for the population at age 65.