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In mortality modelling, cohort effects are often taken into consideration asthey add insights about variations in mortality across different generations.Statistically speaking, models such as the Renshaw-Haberman model may provide abetter fit to historical data compared to their counterparts that incorporateno cohort effects. However, when such models are estimated using an iterativemaximum likelihood method in which parameters are updated one at a time,convergence is typically slow and may not even be reached within a reasonablyestablished maximum number of iterations. Among others, the slow convergenceproblem hinders the study of parameter uncertainty through bootstrappingmethods.  In this paper, we propose an intuitive estimation method that minimizes thesum of squared errors between actual and fitted log central death rates. Thecomplications arising from the incorporation of cohort effects are overcome byformulating part of the optimization as a principal component analysis withmissing values. We also show how the proposed method can be generalized tovariants of the Renshaw-Haberman model with further computational improvement,either with a simplified model structure or an additional constraint. Usingmortality data from the Human Mortality Database (HMD), we demonstrate that ourproposed method produces satisfactory estimation results and is significantlymore efficient compared to the traditional likelihood-based approach.

Fast Estimation of the Renshaw-Haberman Model and Its Variants