On the Rationality of Discontinuous Monetary Policy

Traditionally, in the Federal Reserve's Open Market statements, the planned Federal Funds rate is set to be contained within well defined bands and not a given single value, so that the funds rate is able to vary freely within that range without interference.This paper provides an explanation of this phenomenon as a specific type of optimization that draws on (s,S) inventory theory. The driver of the observed discontinuity is an "announcement effect " (signal) that produces a fixed cost of implementation. Given that within short periods, such as a week, the target variables money and ultimately, income, are not observed, the fixed cost is expressed as an addition to the variance of the target variable, whenever the policy instrument rises above or falls below a certain threshold level indicated by (s,S). An optimal combination policy, given by a schedule of the interest rate and money, is one that refrains from changing the policy instrument within certain optimally derived bands, exactly as observed