Optimal Interest Rate Rules Under One-Sided Output and Inflation Targets

We investigate the derivation of optimal interest rate rules in a simple stochastic framework. The monetary authority chooses to minimise an asymmetric loss function, where the monetary authority places positive weight on negative (positive) deviations of output (inflation) and zero weight on positive (negative) deviations. Our focus is on deriving optimal interest rate rules in a series of special cases where shocks come from only one sector. We show that whether or not the optimal rules derived under asymmetric loss functions will be different than the optimal rules derived under symmetric loss functions is crucially dependent on the interest rate rule chosen. Under a fixed interest rate rule, the optimal rules differ. However, under a more flexible linear interest rate rule that incorporates additional information about contemporaneous shocks, the optimal rules are the same. The approach adopted here could be used, in conjunction with computational techniques, to calculate the precise coefficients of optimal interest rate rules derived from asymmetric preferences.