BEFORE the financial crisis, central bankers were backroom technocrats: unelected, unexciting men in grey suits, who adjusted interest rates to keep prices stable on the basis of widely agreed rules. There were a few stars (such as Alan Greenspan) and a few controversies (whether to prick asset bubbles). But most central bankers operated below the public’s radar and above the political fray. Politicians seldom questioned how they did their job, and virtually never challenged the wisdom of their independence.

The suits are the same these days, but not much else is. Central bankers have become the most powerful and daring players in the global economy. By providing massive liquidity to the financial system, they saved the world from economic collapse in 2008. They have propped up the recovery since, not least by buying boatloads of government bonds; and they have rewritten the rules of global banking. All this has brought rock-star status: witness the excitement over this week’s appointment of Mark Carney, the head of Canada’s central bank, to run the Bank of England (see article). But it also brings big risks. More power for central bankers means less for politicians. Hardly surprising, then, that a backlash is starting.

Central-bank independence is a big issue in Japan’s election campaign. Shinzo Abe, the leading opposition candidate, has attacked the Bank of Japan for acting too timidly against deflation. He wants to force it to adopt a higher inflation target and has flirted with the idea of making it buy more government bonds. Some German lawmakers are furious that the European Central Bank has promised “unlimited” purchases of government bonds from the euro zone’s peripheral economies. In America Republicans gripe that the Federal Reserve’s programme of quantitative easing—buying Treasury bonds—is a recipe for high inflation. The squalls will get worse when central bankers start selling the bonds on their balance-sheets or tightening lending rules to prevent a new housing bubble. That is why central bankers’ autonomy needs rethinking.

Who will guard the guardians of the printing press?

Societies give unelected technocrats power over monetary policy because they think they will do a better job than politicians with an eye on the next election. Some countries with memories of painful inflation (notably Germany) reached that conclusion decades ago. But in many places it is a more recent idea. Generally, politicians set the goal (usually an inflation target). Central bankers have wide latitude in how to achieve it, but the toolkit is well known and has been well tested.

The sharp lines of that bargain have blurred since the financial crisis. Price stability is now widely considered insufficient to ensure overall economic stability. Central bankers have also been told to preserve “financial stability” (ie, make sure there is not another crisis). Inflation is no longer seen by all as the best target for monetary policy: many wonks argue that stabilising nominal GDP growth would be better.

Setting the central banks’ goals is the politicians’ job. It is therefore reasonable for Mr Abe to argue that the Bank of Japan should have a higher inflation target. The decision over whether central banks should target inflation or nominal GDP should be made by politicians, not central bankers alone. It is not good enough for politicians to call vaguely for “financial stability”: they need to give central bankers more concrete guidance, defined in terms of avoiding asset bubbles, excessive borrowing and large concentrations of risk.

But setting clear goals does not solve all the problems, because some of the tools that central bankers are using are experimental. Plenty of clever people fret that quantitative easing does more harm than good for instance (see article).

Politicians should leave central bankers to choose their tools: it is, after all, what the bankers are good at. So Mr Abe would be wrong to exhort the Bank of Japan to buy specific bonds, and America’s Republicans are wrong to carp at quantitative easing when the Fed has, as instructed, kept inflation close to its target. Politicians can intervene by changing either those goals or the central bankers themselves (when their terms are up for renewal).

For their part, central bankers need to become more open—to explain to investors, politicians and voters the logic behind their actions and the trade-offs between their goals. Transparency will help protect them from political meddling.

Maintaining central-bank independence was a lot easier when monetary policy was simpler. But that doesn’t mean the effort should be abandoned. The more important central banks become, the more important it is for politicians to keep their noses out of the bankers’ business.