Before revision:  Possible by-directional relations between the economic series have been considered and the model is designed to provide long-term forecasts that should find application in long-term modelling for both pension funds and life insurance companies .
After revision:  Possible by-directional relations between the economic series have been considered , the parameters and their confidence intervals have been estimated recursively to examine their stability and the model validation has been tested. The model is designed to provide long-term forecasts that should find application in long-term modelling for both pension funds and life insurance companies .