The increasing life expectancy, although a symptom of social progress, raises a challenge for governments, private pension plans and life insurers, due to its impact on health and pension costs.
Spain, like most industrialized countries, faces a demographic future with low birth rates. Moreover, it is one of the countries with a higher life expectancy, therefore, for economic, social and political purposes is important to project and forecast mortality and fertility rates. To forecast mortality rates, we used the R software for two purposes: first, based on generalized nonlinear models we defined the age-cohort model family (GAPC) and replicate such models of stochastic mortality considered in the study by Villegas et al. (2016) and second, adapting the model to data from the Spanish population using the bootstrapping technique, we incorporated the parameter based on uncertainty when estimating the general age-cohort mortality model.
On the other hand, the Bayesian model proposed by Alkema et al. (2011) for fertility projection and on which the R package 'bayesTFR' is based, uses 5-year estimates of the total fertility rate from several periods and is based on the observation that the evolution of TFR (Total Fertility Rate) includes three broad phases. Such a model has been used to project fertility rates in Spain.
Simulations conclude that a three-parameter model can capture most of the variation in the fertility and mortality patterns observed. Models with more parameters, for most purposes, are not necessary and they may experience difficulties adapting such models to a small or data number.
