Optimal nominal interest rate rules are usually set assuming that the underlying world is linear. In this paper, we consider the performance of 'optimal' rules when the underlying relationship between in ation and the output gap may be nonlinear. In particular if the in ation-output trade-o exhibits nonlinearities this will impart a bias to in ation when a linear rule is used. By deriving some analytical results for the higher moments and in particular the skewness of the distribution of output and in ation, we show that the sign of the skewness of the distribution of in ation and output depends upon the nature of the nonlinearity. For the convex modiΓΏed hyperbolic function used by Chadha et al. (IMF Sta Papers 39(2) (1992) 395) and Schaling (Bank of England Working Paper Series, 1999) in ation is positively and output negatively skewed. Whereas, if a concave-convex form is used the skewness of in ation and output is reversed. To correct this bias we propose a piecewise linear rule, which can be thought of as an approximation to the nonlinear rule of . In order to evaluate the relevance of these results, we turn to some illustrative empirical results for the US and the UK. We show that this reduces the bias, but at the expense of an increase in the volatility of the nominal interest rate.