BASEL, Switzerland—Every two months, more than a dozen bankers meet here on Sunday evenings to talk and dine on the 18th floor of a cylindrical building looking out on the Rhine.

The dinner discussions on money and economics are more than academic. At the table are the chiefs of the world's biggest central banks, representing countries that annually produce more than $51 trillion of gross domestic product, three-quarters of the world's economic output.

Of...