Savings, investment and the real interest rate in an endogenous growth model

Abstract

This paper proposes a framework for comparing the predictions of representative household modelswith those of models of overlapping generations, in the context of a class of endogenous growththeories with investment adjustment costs. In the model used in this paper, savings and investmentare co-determined through adjustments in the real interest rate, and the equilibrium investment ratedetermines the long-run growth rate. The two classes of models have similar predictions regardingthe effects of technological and preference shocks, but the overlapping generations model predictslower savings and investment, higher interest rates and lower growth rates that the correspondingrepresentative household model. We calibrate the two models using similar parameter values andthe results suggest that the differences between the two models are not quantitatively large. Forplausible parameter values, the differences in growth rates, savings rates and investment rates are ofthe order of 0.1 to 0.2 of a percentage point per annum, which accumulated over twenty five yearsis at most 5% of aggregate output. The differences for real interest rates are even smaller. Overallthe results suggest that the relative simplicity of the representative household model does not lead toresults that would be too far off quantitatively, even if the real world is characterized by overlappinggenerations.