The president probably wasn’t pleased when the Fed raised interest rates. But when the press asked Dwight Eisenhower to comment in 1956, he said: “The Federal Reserve Board is set up as a separate agency of government. . . . It would be a mistake to make it definitely and directly responsible to the political head of state.”

In the 1990s, President Clinton’s economic advisers, led by Bob Rubin, initiated a rule that the White House would make no comment on Fed policy, even anonymously. That rule held until last week, when...