Piecewise Linear Feedback Rules in a Non Linear Model of the Phillips Curve: Evidence from the US and the UK

Optimal nominal interest rates rule are usually set assuming that the underlying world is linear. Our work relaxes this assumption and examines the performance of optimal rules when non-linearities are present. In particular if the inflation-output trade off exhibits non linearities (convexities) this will impart a bias to inflation when a linear rule is used. To correct this bias we propose a piecewise linear rule, which can be thought of as an approximation to the non- linear rule of Schaling (1999). We show that this reduces the bias, but at the expense of an increase in the volatility of the nominal interest rate. Finally we examine how the zero floor on nominal interest rate affects output and inflation when both rules are adopted. With a linear feedback rule the output variability increases since nominal interest rate cannot be further reduced in presence of adverse shocks. The adoption of a piecewise rule with a zero floor on interest rates successfully reduces output volatility. Significant differences in the transmission mechanism of monetary policy, between the USA and the UK, show up both in the form of the optimal feedback rule and in the distribution of outcomes when there is a zero floor to nominal interest rates and non-linearities in the Phillips curve.