America’s central bank, the Federal Reserve, is engaged in a bailout of European banks. Surprisingly, its operation is largely unnoticed here.

The Fed is using what is termed a “temporary U.S. dollar liquidity swap arrangement” with the European Central Bank (ECB). There are similar arrangements with the central banks of Canada, England, Switzerland and Japan. Simply put, the Fed trades or “swaps” dollars for euros. The Fed is compensated by payment of an interest rate (currently 50 basis points, or one-half of 1%) above the overnight index swap rate. The ECB, which guarantees to return the dollars at an exchange rate fixed at the time the original swap is made, then lends the dollars to European banks of its choosing.

Why are the Fed and the ECB doing this? The Fed could, after all, lend directly to U.S. branches of foreign banks. It did a great deal of lending to foreign banks under various special credit facilities in the aftermath of Lehman’s collapse in the fall of 2008. Or, the ECB could lend euros to banks and they could purchase dollars in foreign-exchange markets. The world is, after all, awash in dollars.

The two central banks are engaging in this roundabout procedure because each needs a fig leaf. The Fed was embarrassed by the revelations of its prior largess with foreign banks. It does not want the debt of foreign banks on its books. A currency swap with the ECB is not technically a loan.

The ECB is entangled in an even bigger legal and political mess. What the heads of many European governments want is for the ECB to bail them out. The central bank and some European governments say that it cannot constitutionally do that. The ECB would also prefer not to create boatloads of new euros, since it wants to keep its reputation as an inflation-fighter intact. To mitigate its euro lending, it borrows dollars to lend them to its banks. That keeps the supply of new euros down. This lending replaces dollar funding from U.S. banks and money-market institutions that are curtailing their lending to European banks — which need the dollars to finance trade, among other activities. Meanwhile, European governments pressure the banks to purchase still more sovereign debt.

The Fed’s support is in addition to the ECB’s €489 billion ($638 billion) low-interest loans to 523 euro-zone banks last week. And if 2008 is any guide, the dollar swaps will again balloon to supplement the ECB’s euro lending.

This Byzantine financial arrangement could hardly be better designed to confuse observers, and it has largely succeeded on this side of the Atlantic, where press coverage has been light. Reporting in Europe is on the mark. On Dec. 21 the Frankfurter Allgemeine Zeitung noted on its website that European banks took three-month credits worth $33 billion, which was financed by a swap between the ECB and the Fed. When it first came out in 2009 that the Greek government was much more heavily indebted than previously known, currency swaps reportedly arranged by Goldman Sachs were one subterfuge employed to hide its debts.

The Fed had more than $600 billion of currency swaps on its books in the fall of 2008. Those draws were largely paid down by January 2010. As recently as a few weeks ago, the amount under the swap renewal agreement announced last summer was $2.4 billion. For the week ending Dec. 14, however, the amount jumped to $54 billion. For the week ending Dec. 21, the total went up by a little more than $8 billion. The aforementioned $33 billion three-month loan was not picked up because it was only booked by the ECB on Dec. 22, falling outside the Fed’s reporting week. Notably, the Bank of Japan drew almost $5 billion in the most recent week. Could a bailout of Japanese banks be afoot? (All data come from the Federal Reserve Board H.4.1. release, the New York Fed’s Swap Operations report, and the ECB website.)

No matter the legalistic interpretation, the Fed is, working through the ECB, bailing out European banks and, indirectly, spendthrift European governments. It is difficult to count the number of things wrong with this arrangement.

First, the Fed has no authority for a bailout of Europe. My source for that judgment? Fed Chairman Ben Bernanke met with Republican senators on Dec. 14 to brief them on the European situation. After the meeting, Sen. Lindsey Graham told reporters that Mr. Bernanke himself said the Fed did not have “the intention or the authority” to bail out Europe. The week Mr. Bernanke promised no bailout, however, the size of the swap lines to the ECB ballooned by around $52 billion.

Second, these Federal Reserve swap arrangements foster the moral hazards and distortions that government credit allocation entails. Allowing the ECB to do the initial credit allocation — to favored banks and then, some hope, through further lending to spendthrift EU governments — does not make the problem better.

Third, the nontransparency of the swap arrangements is troublesome in a democracy. To his credit, Mr. Bernanke has promised more openness and better communication of the Fed’s monetary policy goals. The swap arrangements are at odds with his promise. It is time for the Fed chairman to provide an honest accounting to Congress of what is going on.