A small stochastic model of a pension fund with endogenous saving

We live in an uncertain world, yet a lot of research into the sustainability of welfare states is done in the context of certainty. There are good reasons why the analysis is mostly confined to a model of a certain world. A full analysis of the sustainability of welfare states which includes all relevant economic interactions is already intricate in a certain world because it requires the use of complex dynamic general equilibrium models. Even without stochastics, understanding all the mechanisms and its results is sometimes difficult. In addition, when building stochastics into these type of models one may run into the limitations of computer capacity. In this paper we investigate whether uncertainty on the real rate of return on capital and productivity growth (labelled as economic uncertainty) is more or less important than mortality and fertility uncertainty (labelled as demographic uncertainty) for a consumer facing a decision how much to save. Furthermore we look at the errors that are made when uncertainty is neglected in consumer behaviour. The results indicate that economic uncertainty is far more important than demographic uncertainty. The welfare costs of neglecting uncertainty in consumer behaviour seem to be small.