This article argues that an independent central bank is not in itself sufficient to ensure the long-term success and stability of the economy. While there are strong academic arguments for making the central bank independent, these arguments are often developed in a closed economy setting. Where trade is important and the economy is open, making the central bank independent can lead to a strategic interaction between the bank and the fiscal authorities which can produce serious imbalances in the economy over time. In particular, the analysis below suggests that there could be excess demand in the non tradable sector combined with a recession in the sectors of the economy open to trade. Our contention is that the UK economy exhibits all the signs that we would expect to see if this argument were relevant.