An experimental bond-trading program being run at the Federal Reserve Bank of New York could fundamentally change the way the central bank sets interest rates.

Fed officials see the program, known as a "reverse repo" facility, as a potentially critical tool when they want to raise short-term rates in the future to fend off broader threats to the economy. Of particular concern for the Fed is finding a way to contain inflation once the trillions of dollars it has sent into the financial system get put to use as loans....