A particle Markov chain Monte Carlo approach for the estimation of CBD-type models

The current literature on mortality has mainly focused on model specification, giving less regard to parameter estimation. Indeed, over the last three decades, multiple mortality models have been introduced, most being extensions of the well-known Lee-Carter model or the Cairns-Black-Dowd (CBD) model. However, the estimation of these models has been somewhat overlooked; most papers focus on frequentist methods, such as the (two-stage) maximum likelihood estimation method that estimates the mortality parameters first and then the parameters of the mortality improvement dynamics second. In this report, we present a new Bayesian-based estimation procedure for CBD-type models that relies on the particle Markov chain Monte Carlo (pMCMC) method of Andrieu et al. (2010). This methodology captures the dynamic nature of the mortality improvement factors (and their underlying parameters) consistently, unlike most two-stage estimation methods used in the literature.