What is Janet Yellen afraid of? That question will be percolating in Congress next week when the Senate Banking Committee starts considering proposals for reforming the Federal Reserve that she chairs.

Yellen dug in her heels Tuesday, when she appeared before the committee and was asked about Sen. Rand Paul’s Federal Reserve Transparency Act. She said she wanted to be “completely clear” that she “strongly” opposes the measure.

Paul’s bill is known as “Audit the Fed.” At one point Yellen waved a copy of the central bank’s regular financial statement, which is prepared by its certified accountant, and declared that the Fed is already audited. But that was a disingenuous flourish.

What Paul is talking about (and she knows it) isn’t a financial audit of the Fed’s books. He’s eying a much broader look at how the Fed makes monetary policy and what it is doing with foreign banks.

Such matters, which would be routine at any other bank, are off-limits to the Fed’s auditors as a matter of law passed in the 1970s.

So Congress is looking at overriding that law. A few months ago, the House passed the measure by a vote of 333 to 92.

The audit the House wants would be done by the Government Accountability Office (which dubs itself “the taxpayer’s friend”). Yellen’s line before the Senate was that opening up the Fed to an audit would “politicize monetary policy.”

She should take that up with George Washington, James Madison, Alexander Hamilton and the boys. After all, the Constitution they wrote specifically granted the monetary powers to Congress, the most political branch of the government.

The question is whether Yellen’s warning about politics is a smokescreen for more substantive concerns. As she was testifying against Fed transparency, The Wall Street Journal was uncorking on its Page One a whale of a banking scoop.

It turns out that the Justice Department is investigating trading by “at least 10 major banks” for rigging the market in precious metals. Among the banks named by the Journal are HSBC, Goldman Sachs, JP Morgan Chase, Barclays and several others.

The Fed is a major regulator of most of these banks. So, if the Justice Department comes up with something, the question will be, “Where was the Fed when all this was going on?”

Meantime, Congress is wondering what rules the Fed follows as it makes monetary policy — that is, as it fundamentally decides what our paper dollars will be worth.

Should the Congress be let in on the question of whether there is a rule?

This question was put to Yellen by the banking committee chairman, Sen. Richard Shelby (R-Ala.).

Next week, he will start Fed reform hearings with testimony from a Stanford professor, John Taylor, who is the leading advocate of a system of rules.

Yet Yellen took a hard line, saying she is “not a proponent” of “chaining” the Fed “to any rule whatsoever.”

Yellen also bridled when asked about the idea of opening up the Fed’s key committee to greater representation from the regional banks — a move that, ironically, many believe would make the Fed less political.

She basically said that she likes the way things work now. Marie Antoinette, telephonez votre bureau.

Not everyone agrees that the current system, or lack thereof, is working so well. In May, no less distinguished a figure than former Fed chief Paul Volcker gave a speech in Washington with a warning.

“By now,” he said, “I think we can agree that the absence of an official, rules-based, cooperatively managed monetary system has not been a great success.”

It’s no small thing when Volcker, by all accounts our era’s greatest central banker, condemns the non-system that Yellen defends.

Particularly because Volcker is no supporter of “Audit the Fed.” He thinks the idea is “dangerous,” he told me when I phoned him this week.

It may be that Yellen is sensing the ground is shifting in Congress.

In her testifimony before the House this week, she disclosed that, after meeting with a number of liberal groups, she’d agreed to a meeting with conservative critics of the Fed.

That will take place Friday at the Fed, where she is likely to hear support (from the American Principles Project, among others) for a Monetary Commission to review the future of the Fed as it begins its second century.

She will hear conservatives concerned that American workers are hurting for jobs and gasping for wage gains six years into the Great Recession — a circumstance in which surely Congress should audit something.