Modeling Mortality Rates Using Heligman-Pollard and Lee-Carter in Nigeria

Abstract

In recent years the need for accurate mortality statistics has been emphasized by researchers in planning, analyzing, monitoring and projection of health situations in the country. It helps the government and other health agencies initiate various programs that can improve life expectancy especially in developing countries like Nigeria. Given the impact of mortality rates on the population size, structure, social security system, life insurance and pension (from actuarial point of view) there is need to understand how mortality patterns change with time. According to past studies the Heligman-Pollard (Henceforth HP) model and Lee-Carter (Henceforth LC) model have been widely accepted and use by researchers in forecasting future mortality. In this study both models were applied to Nigerian data with the objective to investigate the accuracy of their performances by comparing their assumptions. The LC model parameters were estimated based on the singular value decomposition technique (SVD), while HP model parameters were estimated using nonlinear least squares method. Autoregressive Integrated Moving Average (ARIMA) procedure was applied to acquire to forecasted parameters for both models. To investigate the accuracy of the estimation, the forecasted results were compared based on the mean absolute percentage error (MAPE). The results indicate that both models provide better results for female population. However, for the elderly female population, HP model seems to overestimate to the mortality rates while LC model seems to underestimate to the mortality rates. Although the HP model does not seem to follow the pattern of the actual mortality rates, after further analysis was carried out it was discovered that the HP model gave a better forecast than the Lee-Carter model. Based on the HP model the forecasted probabilities of death were used to construct an abridged life table for males and females and the life expectancy at e 0 and e 75 were obtained. From our results we see that males experience higher life expectancy than females due to the mortality rates experienced by both sexes. Given the level of mortality rate especially in developing countries like Nigeria, the study therefore recommends the need for a vital registration system that could continuously and reliably collect information because it is well known that incomplete data affect the performance of a model to forecast. To ascertain level and pattern of mortality rate especially in adult, parameterization model especially the HP model should be considered because of it lesser errors, with the view of achieving a robust forecasting model that could improve the understanding of the pattern of general mortality rate and how it affects life expectancy level in the country.