Republicans have warned since the outset that the Fed was losing control of inflation. During the 2012 campaign, Rick Perry, then the governor of Texas and a Republican presidential candidate, called the Fed’s policies “treasonous” and warned that if Ben S. Bernanke, then the Fed chairman, came to Texas, “we would treat him pretty ugly.” The party added a plank to its platform calling for a commission “to investigate possible ways to set a fixed value for the dollar,” reviving language last seen in 1984.

Instead, four years later, inflation remains unusually sluggish. Some economists and Fed officials argue the economy would benefit from a little more. But the language of the Fed’s critics remains heated.

“Instead of adjusting monetary policy according to whims and getting it wrong over and over again and causing booms and busts, what the Fed should be doing is, No. 1, keeping our money tied to a stable level of gold,” Mr. Cruz said last month during a Republican presidential debate.

Senator Rand Paul, Republican of Kentucky, agreed that the Fed “destroys the value of the currency” by allowing too much inflation. Ben Carson and Mike Huckabee, former Arkansas governor, both agreed that the value of the dollar should be tied to something.

Image The front page of The Daily News of New York on March 4, 1933. President Franklin D. Roosevelt later did just that. Credit... The Daily News, via Getty Images

“If it’s not going to be gold, make it the commodity basket,” Mr. Huckabee said.

Economists generally regard a gold standard as a crude and outdated method of inflation control. There is nothing inherently stable about the value of gold. It fluctuates, like the value of everything else, as more is extracted from the ground and as demand waxes and wanes.