Through a spokeswoman, Mr. Geithner declined to elaborate on his testimony.

Hal S. Scott, a professor at Harvard Law School and the author of “The Global Financial Crisis,” says the bottom line is, “Solvent is pretty much whatever the Fed says it is.” He added: “I have a lot of sympathy for what Geithner was trying to say. It’s difficult in the middle of a run or a panic to determine whether something is insolvent, because you don’t know how to value the assets. At the end of the day, it’s an art, not science. The issue of how does a lender of last resort determine whether an institution is, or isn’t, solvent has been one of the most difficult problems for a very long time.”

Marvin Goodfriend, a professor at the Carnegie Mellon Tepper School of Business who spent 12 years as a policy adviser at the Federal Reserve Bank of Richmond, agreed. “It’s hard to define insolvency in a financial crisis, since it depends on the behavior of the entire financial system,” he said. “Solvency is only well defined when a particular firm is in trouble but the rest of the economy is O.K. When you come to a systemic problem, where the Fed’s very action has a bearing on whether those firms are solvent or not, you have a Catch-22 problem that can’t be solved.”

The Fed seems to have been well aware of the issue. In a legal memo from 1999 produced at the A.I.G. trial, a lawyer at the New York Fed, Joseph H. Sommer, cautioned that the Fed’s emergency lending “must be an exercise in on-the-fly policy making.” And he posed two questions that, in light of the financial crisis, seem prescient: “Does the lending bank have enough time to make a reasoned decision?” and “Does the lending bank understand the procedural consequences of its actions?”

After the financial crisis, and facing persistent questions as to why some firms were bailed out and others weren’t, Congress sought to clarify the Fed’s emergency lending powers as part of the Dodd-Frank Act. The Federal Reserve Act was amended to make it explicit that only solvent firms qualified for loans, and the act further defined “insolvent” to mean “in bankruptcy” or other insolvency proceeding at the time of the loan request. But that definition is so broad as to be all but meaningless. “It’s a huge loophole,” Professor Goodfriend said. By that standard, Lehman Brothers was plainly solvent, since it wasn’t in bankruptcy proceedings when it sought the Fed’s support.

A spokeswoman for the Federal Reserve in Washington and a spokesman for the New York Fed declined to comment.