The Taylor rule and dynamic stability in a small macroeconomic model

In this paper we embed the Taylor interest rate rule in a simple macroeconomic model with Calvo contracts. We contrast this with the case in which the interest rate is determined by the conventional LM curve along with a fixed value for the monetary aggregate. We derive conditions under which the adjustment of the economy is characterised by a unique saddle-path and show that the conditions required for this to be the case are more stringent when the authorities adopt the Taylor rule. In both cases the possible failure of the saddle-path condition arises when there are debt-deflation effects in the IS curve. If interest rates are set according to the Taylor rule, then debt-deflation is always enough to cause the failure of the saddle-path condition. However, when interest rates are determined by the LM curve then it is possible that the real balance effect from the LM curve may offset the debt-deflation effect and produce a saddle-path.