Is the new keynesian is curve forward looking?

This paper analyzes the solutions of the canonical and hybrid New Keynesian IS curve difference equation. It shows that the usual forward solution is ruled out because it is at odds with the underlying economic theory. This implies that current and expected future real interest rates do not matter for the determination of the current output gap. Indeed, the new Keynesian IS curve has multiple backward solutions and determines not the level of the output gap, as does the traditional IS curve, but its expected rate of change. The paper also shows that the hybrid IS has (multiple) backward solutions regardless the size of the forward coefficient.