The Dynamic IS Curve when there is both Investment and Savings

The dynamic IS curve of New-Keynesian models captures the dependence of aggregate demand on future interest rates, but only in the case where there is no investment and the interest rate channel only originates in the savings decisions of households. The paper derives the dynamic IS curve analytically in a model with investment, where the interest rate channel originates both in the the savings decisions of households and the investment decisions of firms. This generalized dynamic IS curve sheds light on several new factors that shape the dependence of aggregate demand on interest rates. In particular, interest rates are discounted in investment and aggregate demand if and only if the intertemporal elasticity of substitution in consumption (IES) is low enough, and compounded if it is higher. The addition of household heterogeneity can generate discounting in aggregate consumption as well, in a new way that does not rely on precautionary savings. Instead, household heterogeneity creates discounting by making consumption respond to interest rates primarily as a ripple effect of the response of investment, not through intertemporal substitution