Can money matter for interest rate policy?

In this paper it is shown that money can matter for macroeconomic stability under interest rate policy when transactions frictions are non-negligible. We develop a sticky price model with a shopping time function, which induces the marginal utility of consumption to depend on the (predetermined) stock of money held at the beginning of the period. Equilibrium stability and uniqueness are then ensured by a passive interest rate policy, whereas activeness is associated with an explosive equilibrium. By reacting to changes in beginning-of-period real balances, the central bank can restore stability. Interest rates further depend on lagged real balances even if the central bank acts in an entirely forward-looking way, as under discretionary optimization. If the model is revised such that end-of-period money provides transaction services, money can in principle be neglected for a stabilizing interest rate policy. Discretionary monetary policy is, however, likely to be associated with equilibrium indeterminacy, which can be avoided if interest rates are set contingent on beginning-of-period real balances.