What happens behind the New Keynesian IS?

The aim of these notes is to point out and address a few technical problems concerning the so-called «IS» equation in the New Keynesian macroeconomic model. First, in the basic NK model with sole consumption, the consumption function is not properly derived from first principles (the intertemporal budget constraint is missing), and when it is, the IS as locus of aggregate demand-supply equality may not exist. Second, when investment is introduced, and the investment-saving equalization mechanism is properly worked out, the resulting IS locus is different from the NK one, with different dynamic properties and different implications for interest-rate control. In particular, the paper shows that a simple linear feed-back rule with respect to output gaps is necessary and sufficient to drive the economy to the «zero-gaps» steady state. Yet the dynamic path of output becomes (endogenously) oscillatory. It is also shown that the same implications arise for inflation control too