Can Money Matter for Interest Rate Policy?

In this paper it is shown that money can matter for macroeconomic stability under interest rate policy, if transactions frictions are specified in a consistent way. We develop a sticky price model with a shopping time specification, which induces the marginal utility of consumption to depend on the (predetermined) stock of money held at the beginning of the period. Saddle path stability is then ensured by a passive interest rate policy, whereas activeness is associated with an explosive equilibrium path unless the central bank reacts to changes in beginning-of-period real balances. When the central bank aims at minimizing macroeconomic distortions, real balances enter the interest rate feedback rule under discretionary optimization. If it is alternatively assumed that end-of-period money provides transaction services, money can be neglected for interest rate policy in order to implement the optimal plan. However, the equilibrium under the targeting rule is likely to be indetermined, allowing for endogenous fluctuations, which can be avoided by the central bank implementing the optimal plan with an interest rate feedback rule featuring beginning-of-period real balances.