Savings, Investment and the Real Interest Rate in an Endogenous Growth Model

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