A new study, which was published on Monday by the National Bureau of Economic Research, suggests that the Federal Reserve’s policy of using ultra-low interest rates in order to encourage lending, might be doing the opposite.

This is, of course, not what Federal Reserve chairman Ben Bernanke has maintained. Ever since the financial crisis, and even a little before it, Bernanke has pushed the Fed to do whatever it can — quantitative easing, Operation Twist, making promises — to keep rates low. Bernanke has said that low interest rates would make it cheaper for people and companies to borrow, and so they will.

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But that’s not what’s happened. Long after the official end of the recession, credit remained tight. Bank lending has finally been rising recently, but it’s a small increase. It’s still down from before the financial crisis. And, at least by one key measure, lending is not only weak by recent standards, it’s historically weak.

At the end of 2012, banks had lent out just under 70% of their deposits, which was a multi-decade low. Back before the financial crisis, that figure was 93%.

Bernanke has responded by doubling down. Last summer he announced an expansion of the Fed’s bond buying program to drive down interest rates further. And he has since said the Fed won’t stop buying bonds until the unemployment rate hits 6.5%, which, with Washington going from stimulus to austerity, might take a while.

Traditionally, low interest rates have boosted lending. The question is why it hasn’t this time around. The NBER study, provocatively titled
Banks Exposure to Interest Rate Risk and The Transmission of Monetary Policy
, suggests that the reason might not just be a long hangover from the financial crisis, but instead it’s from a shift in the banking industry.

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Banks traditionally fund their loans using deposits and short-term debt. So when the Fed lowers short-term interest rates, that means they can lend money out cheaper. And for the majority of banks that’s probably still how it works. Lower interest rates equals more loans.

The exception, though, appears to be the nation’s biggest banks.

Citigroup (C), for instance, had $601 billion in loans outstanding at the end of 2012, according to FDIC data. That’s down from $604 billion a year earlier. At Bank of America (BAC), lending shrunk 2% in 2012 to $912 billion. By comparison, lending at Apple Bank for Savings, which is the 100th largest bank in the U.S., rose 32% in 2012 to $5.8 billion.

As the big banks have gone from large to mega in the past two decades, they have tended to do more of their borrowing through long-term debt, meaning more of their funding costs are locked in. As a result, the big banks don’t see the same drop in their expenses when interest rates fall that they once did, at least not immediately. Indeed, the study, which is co-authored by three economists – one from Bernanke’s own Princeton, where the Fed chair is tenured, says that for 12 of the 16 largest banks in the U.S. lower interest rates make it more expensive to lend.

The bad news is that the four largest banks in the country account for about 40% of all loans. So while low rates will cause most banks to lend more, the affect of low rates is more muted than it used to be.

“Low interest rates benefit lending, but it’s less than people think,” says David Thesmar, who teaches at HEC Paris and is a co-author of the study. “And it’s a significant effect.”

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The authors suggest the best way to boost lending at large banks, therefore, could be to boost interest rates. Bernanke, though, is unlikely to do that anytime soon.

Low-interest rates have other positives, namely boosting the stock market. And low-interest rates may still encourage borrowing, even if it doesn’t encourage big banks to lend. Companies, for example, have borrowed a lot of money in the past few years. They’ve just done it from the bond market, and not from banks directly.

So don’t expect the bank lending spigot to open widely anytime soon. But there is something even more bothersome. Besides the too big to fail problem of the mega banks, which we talk about all the time, there is another issue. The really large banks also make it tougher for the Fed to manufacture swift economic recoveries.

The good news: When Jamie Dimon of JPMorgan Chase (JPM) says his bank will do just fine when rates rise, the NBER study suggests he’s telling the truth. (There are reasons he’s richer than you are.) As a result, the drop off in lending that some fear when Bernanke eventually takes his foot off the pedal might not be as bad as some fear.