The year-2000 problem is causing making bank customers more than a little nervous.

For the first time since before the Federal Deposit Insurance Corp. was established in 1934, customers genuinely fear they will not be able to withdraw funds on demand.

Before the creation of the FDIC, there was always fear of bank failure. Banks would advertise their strength with gold-leaf signs in the window telling their capital position at the last reporting period. Even so there were fears that some event, or just a rumor, would lead to a run on banks.

To prove that they had enough cash to cover any requests, whether they really did or not, bankers would make a show of the physical availability of funds.

Employees would walk through the lobby with bags marked "Federal Reserve System" that might or might not be filled with currency. Some banks would stack piles of one-dollar bills at teller stations, with a twenty or fifty on the top.

"If you don't have it I want it, but if you do I don't" is just human nature.

Even after the FDIC was established, many depositors, especially immigrants, would come into their banks every statement day to make sure their money was still there. They would withdraw it all, look at it, and then redeposit it.

Banks made it their business to handle this "out and in" business as fast as possible, because long lines in the lobby would fuel rumors of trouble, and the lines would grow. That is why First of Chicago-a bank with a lot of immigrant customers-was the first to install an IBM on-line savings system to speed lobby transactions.

Fear that the bank could not meet demands is evident even today in the desire of some depositors for a passbook instead of a statement savings account. The passbook gave the holder the feeling that the money was there.

Most depositors whose accounts are under the FDIC limit do not fear for their deposits. But this is not always the case.

I have had some people ask me if the FDIC has enough resources to cover withdrawals if depositors all wanted their money at once. My response was that the FDIC would ask the Federal Reserve to create more money.

But bankers I've talked to at recent conventions are reporting that customers fear not only for the soundness of their banks, but also for the soundness of the FDIC as the century turns!

What can banks do about this?

The answer, of course, is to reinforce public confidence in banks.

One approach that some community bankers are contemplating is announcing early and often that they will be open 24 hours a day the last week of December and in early January to meet requests for funds and handle other business.

And the faith that open doors on New Year's Day could instill could be buttressed by the old practice of stacking up currency in tellers' cages and having armored cars arrive with currency bags often and conspicuously- just as in the early 1930s.

Though not all banks may want to take such drastic steps, one thing is certain: Much of the public does not share bankers' confidence that the Y2K problem will be solved.

Anything banks can do to boost customer confidence will help make the turn of the century the non-event for banks that many hope and feel it will be. Mr. Nadler, an American Banker contributing editor, is a professor of finance at Rutgers University Graduate School of Management.

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