Determinacy in New Keynesian Models: a role for money after all?

The New-Keynesian Taylor-Rule model of inflation determination with no role for money is incomplete. As Cochrane (2007a, b) argues, it has no credible mechanism for ruling out bubbles (or deal with the non-uniqueness problem that arises when the Taylor principle is violated) and as a result fails to provide a reason for private agents to pick a unique stable path. We propose a way forward. Our proposal is in effect that the New-Keynesian model should be formulated with a money demand and money supply function. It should also embody a terminal condition for money supply behaviour. If indeterminacy of stable (or unstable paths) occurred the central bank would switch to a money supply rule explicitly designed to stop it via the terminal condition. This would be therefore a `threat/trigger strategy' complementing the Taylor Rule --- only to be invoked if inflation misbehaved. Thus we answer the criticisms levelled at the Taylor Rule that it has no credible mechanism for dealing with these issues. However it does imply that money cannot be avoided in the new Keynesian set-up, contrary to Woodford (2008).