Hyperbolical discounting and endogenous growth

This paper provides the exact analytical solution for the standard model of endogenous growth when consumers have present-biased preferences and make time-inconsistent savings plans, which they revise continuously. It is shown that long-run growth is not necessarily lower under present-biased preferences. In fact, an equivalence result holds. If hyperbolical discounting provides the same present value of a constant infinite income stream as standard exponential discounting, then the equilibrium rate of economic growth is also the same under both discounting methods. In this sense present-bias and the entailed time-inconsistency of savings plans are harmless for economic growth. The result is robust to the introduction of non-homothetic utility and a variable elasticity of intertemporal substitution in consumption.