Balanced-growth-consistent recursive utility

Koopmans's 'recursive utility' has proven useful in a number of dynamic modelling contexts. Nonetheless, recursive utility has not made significant inroads into what one would expect to be a natural haven - models of balanced growth, whether 'exogenous' or 'endogenous'. Mainly, this is due to the dearth of interesting recursive utilities which are consistent with balanced growth. In this paper I provide conditions on the aggregator which guarantee the existence of a recursive utility function which is consistent with balanced growth. The result in turn shows how a family of such utility functions may be constructed. I also provide a generalization of Jones and Manuelli's theorem on the existence of optimal endogenous growth.