Congratulations are in order for Senator Ted Cruz for his questioning of the Federal Reserve’s chairman, Janet Yellen, at this week’s hearing of the Joint Economic Committee. The Texan had not been on the Committee’s list for the hearing, understandable given the pressures of his presidential campaign. That he made a point of being there signals an instinct to lead on one of the most strategic economic issues facing the country — the soundness of the American dollar.

The key question Mr. Cruz asked is whether Mrs. Yellen agrees with her predecessor Paul Volcker that the absence of a cooperatively managed rules-based monetary system has not been a great success. Mr. Volcker offered that assessment in a speech to the Bretton Woods Committee in May 2014; it was first reported in a Wall Street Journal op-ed piece by the editor of the Sun and, given Mr. Volcker’s stature, was an important moment in the debate over monetary reform.

Mr. Cruz sketched the economic turmoil since we abandoned the Bretton Woods system for fiat money. He also pressed Mrs. Yellen about a view — of Nobel laureate Robert Mundell, among others — that the central bank’s tightening early in 2008 precipitated the crisis that became the Great Recession. Mrs. Yellen seemed startled, even confused, by the question, at least according to some, and in any event dodged Mr. Cruz’s query with classic Fed-speak.

Although she agreed that there had been a large number of damaging crises, Mrs. Yellen resisted the idea that the Fed might shoulder some blame. It was important, she averred, to have taken steps to have a stronger financial system. She suggested — correctly, in our interpretation — that Mr. Volcker hadn’t intended to endorse a mathematical rule to guide the Fed. She said that most central banks today are public about their “inflation objective.” She boasted of the Fed’s transparency.

A plug for central bank independence was also made by Mrs. Yellen. But not once did she address what is bothering Congress, namely a growing sense that fiat money has turned out to be more of a cause than a cure for the sluggishness of our recovery. She’s loathe to acknowledge that Congress is losing faith in a system that relies only on a band of Ph.D.-bureaucrats to set, in interest rates, the most important price in the economy. Witness the Fed Oversight Reform and Modernization Act.

That is the bill that was passed last month by the House and is now before the Senate. It would set up a system for a regular audit of the Fed, giving Congress a look at how it sets monetary policy; it would establish a Centennial Monetary Commission to review the successes and failures of the Federal Reserve Act as the central bank begins, as it does this year, its second century of operations; and it would require the Fed to establish a rule to guide its formation of monetary policy and let the Congress know what it is.

This is a serious moment for the Federal Reserve. It is no small thing that the FORM Act has passed the House. It is dismaying to see a Fed chairman fail to lead on reform and play, as Mrs. Yellen is playing, such a defensive game. She resists engaging with the reformers on how the Federal Reserve notes issued by our central bank have shed more than 98% of their value. It is not enough to state the Fed’s goals without noting that one of them — 2% inflation — would have horrified the Founders.

Congress is pressing more fundamental questions. What is the Fed doing overseas? Should it have a dual mandate to manage the employment rate as well as the interest rate? Should there be within its governance more representation of regional banks? How closely should Congress — which holds the only grant of monetary powers made in the Constitution — be involved in the formation of policy? How independent should a central bank be from its creator?

America has experienced but one presidential election that focused on the monetary system. That was in 1896, when William Jennings Bryan, the Democrat, ran on an inflation platform against the Republican’s William McKinley. The winner, McKinley (subject of a brilliant new book by Karl Rove) went on to sign the Gold Standard Act of 1900, which set the stage for the great advances in the first three generations of the 20th Century. That’s the long game that Senator Cruz is now leading.