We investigate the derivation of optimal interest rate rules in a simple stochastic framework. The monetary authority chooses to minimise an asymmetric loss function made up of the sum of squared components, where the monetary authority places positive weight on squared negative (positive) deviations of output (inflation) and zero weight on squared positive (negative) deviations. Recent approaches to monetary policy under asymmetric preferences have emphasised the adoption of a linear exponential (linex) preference structure. This paper presents a new and different analytic methodology that is based on the explicit calculation of semi-variances. This approach can be used to derive precise coefficients of the optimal interest rate rules. We derive optimal interest rate rules based on two different informational assumptions. In the first case, which we call a fixed interest rate rule, the monetary authority knows only the structure of the economy and the variance of sectoral shocks so that interest rates must take a constant value. In the second case, which we call a flexible interest rate rule, the monetary also has access to additional information in that it can observe the contemporaneous inflation rate. In this second case, we restrict our analysis to the class of linear interest rate rules. The more standard approach in the literature derives optimal monetary policy rules using symmetric loss functions, where monetary policy is designed to minimise the sum of squared components. We also compare optimal interest rate rules under both symmetric and asymmetric loss functions.
