There is a near-consensus that central bankers should focus their attention on the control of inflation, and should accordingly not pay attention to movements in stock markets. This view is reinforced by the continuing influence of the Efficient Markets Hypothesis (EMH), which maintains that financial markets correctly price firms at all times. The authors assert that this general view is incorrect. There are strong reasons, both in principle and in practice, to doubt the applicability of the EMH to the valuation of the stock market as a whole. Indicators of stock market value, such as q, show the market to have been severely overvalued at the end of the twentieth century. Previous episodes of overvaluation have been succeeded, both in the US and Japan, by severe recessions. Such recessions raise the risk of central banks losing control of inflation, due to liquidity traps; they also impose costs, in terms of output and inflation, which central bankers should take into account. Finally, central bankers already do in any case take these into account, but asymmetrically: only when markets fall, not when they rise.