Interest Rate Policy in Continuous Time with Discrete Delays

We study the design of monetary policy in a continuous-time framework with delays. More explicitly, we consider a linear, flexible-price model where inflation and nominal interest rates change continuously, but where nominal rates are set by the Central Bank in response to a lagged inflation measure, and where the measure of inflation can be constructed as a flexible distributed delay. Therefore, the Central Bank has, in addition to the choice of an "active" or "passive" response to inflation, two additional parameters to select: the lag of the inflation measure, and the coefficient for the distributed delay to construct the inflation measure. The pure continuous-time and discrete-time frameworks emerge as special cases of our differential-delay system. This richer framework also allows us to reconcile results on the local uniqueness and multiplicity of equilibria that are obtained in the two pure cases, to uncover special assumptions embedded in the pure cases, and to prescribe effective policy options to avoid the problem of local indeterminacy and its unintended consequences.