We study monetary policy in a New Keynesian model with heterogeneity in expectations. Agents may choose from a continuum of forecasting rules and adjust their expectations based on relative past performance. The extent to which expectations are anchored to the fundamentals of the economy turns out to be crucial in determining whether the central bank (CB) can stabilize the economy. When expectations are strongly anchored, little is required of the CB for local stability. Only when expectations are unanchored, the Taylor principle becomes a necessary condition. More aggressive policy may however be required to prevent coordination on almost self-fulfilling optimism or pessimism. When the zero lower bound on the nominal interest rate (ZLB) is accounted for, the inflation target must furthermore be high enough, in order to prevent coordination on self-fulfilling liquidity traps and deflationary spirals. Joint with Cars Hommes.