The race is on between the U.S. and British central banks to be the first major economy to raise interest rates after a long period of unprecedented monetary generosity.

It won't happen immediately but both Janet Yellen, who chairs the U.S. Federal Reserve, and Bank of England Gov. Mark Carney signaled in the past week that higher rates are close.

Not everything in the world economy, however, is as sanguine as the U.S. and British economies would appear to be.

In the eurozone, European Central Bank President Mario Draghi has promised rock-bottom interest rates for the foreseeable future and pledged to see through the bank's monthly 60 billion euro asset purchases until September next year.

In Asia, China's policymakers are struggling to contain stock market mayhem that could still undermine attempts to reverse a growth slowdown. The central bank is now set to pump $48 billion into the country's biggest lender.

Elsewhere, countries as diverse as Sweden, South Korea, Guatemala and Azerbaijan have cut rates over the past three to four weeks. Canada, Washington's closest developed trading partner, surprised by easing rates last week.

In all, 37 central banks around the world have eased monetary policy so far this year to boost growth, fight deflation or both.

Influential though they are, the Fed and Bank of England are outliers.

So are Yellen and Carney right to be signaling at least an end to near-universal easing?

Clearly they believe that domestic growth, job creation and inflation are on trend to warrant it. But their views are couched in caution.

Carney, for example, has said that interest rates will rise only gradually from their record low of 0.5 percent. Meanwhile, Yellen told Congress that risks remain, notably from spillover from the Greek and Chinese crises. But she added: "The importance of the initial step to raise the federal funds rate target should not be overemphasized."