Forecasting Mortality Trend of Indonesian Old Aged Population with Bayesian Method

From around the nineteenth until the beginning of the twenty-first century, mortality rates show a declining trend. However, recent data on the United States population shows that the rate of decline started to slow down in the 2010s. Insurance companies need to be prepared in both ways: either mortality rates continue to decline, or there will be a turning point, and mortality rates start to increase. In this paper, we aim to get the whole picture of the mortality trend of Indonesian males, detect the possibility of a turning point in the mortality rates, and forecast mortality rates in the future. To reach this aim, we propose adjustments to the Makeham mortality model by including period and cohort information of the population via quadratic function. We also propose using the Bayesian method to estimate the parameters for the Indonesian old-aged males' population, where some adjustments were made in determining the priors, and the estimates were sampled from the posterior distribution using the Gibbs sampling algorithm. We found that our forecasting accuracy is satisfactory by considering the mean absolute percentage error values and coefficient of determination (R2). We found that mortality rates are declining in the long term, but the probability of a turning point in the future is statistically significant. We identified two risks, longevity risk because of more centenarians in the future and mortality risk before their children complete compulsory education