German Chancellor Angela Merkel and French President Nicolas Sarkozy are in a terrible bind. They don’t want financially distressed European governments to default. But they can’t afford to keep them solvent.

Collectively, the governments in question -- Greece, Ireland, Portugal, Spain and Italy -- owe more than 3 trillion euros ($4.1 trillion), much of it short term, and are still borrowing at a rapid clip. The market isn’t buying their fiscal pledges or their risky paper, forcing the European Financial Stability Facility and the European Central Bank to step in. But the EFSF has its limits, and the ECB doesn’t want to keep buying indefinitely.

There’s a big rub, though. European banks hold large quantities of sovereign debt, so if the governments don’t pay the banks, the banks might not be able to pay their depositors. Since depositors are paid on a first-come, first-served basis, widespread government defaults -- or even the expectation of them -- could produce a colossal bank run.

Financially strapped governments are in no position to borrow to bail out their banks. And if other governments do so, their own creditworthiness could be threatened. Indeed, investors are showing increased concern about Belgium, which together with France just committed to bail out Dexia SA (whose balance sheet is larger than Belgium’s annual economic output). France and even Germany face a potential downgrade of their credit ratings, or so says the market. Default insurance on AAA rated French and German government bonds now costs roughly thrice and twice as much, respectively, as insuring AA+ U.S. Treasuries.

Bank Run

To some extent, the feared bank run is already under way. U.S. lenders and money-market funds are moving their money out of European banks, which are balking at lending to one another. This is exactly what happened before the bankruptcy of Lehman Brothers Holdings Inc. in 2008.

In this quiet run, the ECB is again left holding the bag. It’s printing fresh euros to replace those fleeing the banks. But ECB President Jean-Claude Trichet doesn’t want to go far beyond this, as signaled by his reluctance to provide financing to bolster the EFSF.

Merkel and Sarkozy are pledging to recapitalize Europe’s banks, but doing so without fundamental banking reform will, over time, prove impossible. Governments can sell bonds to their banks knowing that Merkel and Sarkozy, in backing all European banks, are effectively guaranteeing the returns on these and other risky investments. Indeed, financial institutions could end up holding all the outstanding debt of distressed sovereigns as governments take advantage of free access to this guarantee. This “no fail” policy would create immense moral hazard -- or, rather, immoral certainty -- because it suggests that all bank creditors, not just depositors, will never lose a penny.

Plan Unclear

What specifically the two leaders have in mind remains unclear. Meanwhile, every day the crisis festers is another day a major run can spontaneously erupt. Just imagine how the media would react to long lines of desperate people trying to get their money out of every bank in every city, town and village in Europe.

Reporters might start asking whether the U.S. banking system is exposed to Europe and could also suffer a run. According to the Office of the Comptroller of the Currency, federally insured banks had sold more than $7 trillion in credit protection as of June 30. An unknown share of that insures European sovereign debt.

Insured Deposits

The Federal Deposit Insurance Corporation is supposed to stand ready to protect all insured deposits. But some muckraker -- say, Rush Limbaugh -- might point out that the FDIC has only about $4 billion in net assets with which to meet $6.5 trillion in deposit guarantees. And Limbaugh’s avid followers might decide to get their money quick and use it to buy something real before the Federal Reserve starts printing the missing trillions. The Empty Wall Street movement would be a lot scarier than Occupy Wall Street.

Last month, I wrote about the impending global Greek tragedy. I’m getting more concerned and more convinced that the only safe way out is Europe’s immediate switch to limited-purpose banking -- that is, transforming all European lenders into non-leveraged mutual funds. Once that happens, Merkel and Sarkozy can go back to their regular jobs and let the financial system run itself.

So what’s the cost and way to get to limited-purpose banking? First, the ECB would inject 300 billion euros into the banks in exchange for shares, thereby making them solvent. Next, the European Union would require each bank to reorganize itself immediately as a 100 percent equity-financed mutual-fund holding company by following some simple steps.

1. Stop borrowing in any form, including checking and savings accounts.

2. Transform investment banking into a no-risk consulting business, and trading into a no-risk matching business.

3. Open cash mutual-fund accounts for all checking customers, and very strongly encourage them to put their money in the new accounts. This will transfer the banks’ reserves to the mutual funds, which will automatically be backed to the buck because they will hold only cash. They will also constitute a perfectly safe, fully reliable payment system because funds can be accessed using checks, debit cards, and ATMs.

4. Very strongly encourage other short-term creditors to transfer their accounts to short-term money-market mutual funds. Have these mutual funds purchase the short-term assets held by the banks.

5. Very strongly encourage long-term bank creditors to swap their holdings for shares of mutual funds that specialize in long-term bonds, stocks or real estate. These mutual funds would then purchase those assets from the banks. In the case of real estate, the mutual funds would be closed-end funds, which don’t provide for immediate redemptions but have shares that trade in secondary markets.

Such a banking system can’t fail because it has no debt on which to default, and its assets always cover its liabilities. The transition can be done quickly, and the 300 billion-euro cost is small compared with eliminating the risk of financial collapse. Merkel and Sarkozy could even provide the protesters occupying Wall Street with a concrete goal for their movement: adopting a system that limits bankers to their sole legitimate purpose, which is boring, low-paying, safe financial intermediation.

(Laurence Kotlikoff, a professor of economics at Boston University, is a Bloomberg View columnist. The opinions expressed are his own.)

To contact the writer of this article: Laurence Kotlikoff at kotlikoff@gmail.com

To contact the editor responsible for this article: Mark Whitehouse at mwhitehouse1@bloomberg.net