According to American folklore, the famously long-legged Abraham Lincoln was once asked: "Abe, how long should a man's legs be?" Lincoln is reported to have answered: "Long enough to reach the ground."

If Abe was still with us, we might want to ask him "How large should a bank be?"  This is a perennial worry for community bankers, for whom smallness is an advertised virtue. When do scale economies from growing bigger run out for community banks?  And will the pursuit of these savings result in community banks losing touch with their business model and their customers?

At the other end of the industry, this question worries bank policymakers. Do our largest banks need to do trillions of dollars of business to remain on a competitive footing with their international rivals?  And if so, are the cost savings captured by this hugeness large enough to justify the systemic risks posed by these banks?

Banking economists (including me, for a time) have been hard at work for several decades estimating complex econometric models of bank scale economies. They still haven't reached a conclusion. 

Some researchers argue that even the largest banks have access to scale economies. A recently published study by economists at Clemson University and the St. Louis Fed finds that banks of all sizes — community banks, regional banks, and nationwide banks — can reduce their costs of production by growing larger. Using a different measurement technique, a recent Rutgers University-Philadephia Fed study similarly concludes that U.S. bank holding companies of all sizes have access to increasing scale economies.

But other researchers disagree. A pair of Bank of England economists have recently found that large international banks exhibit constant returns to scale — that is, their costs per unit neither increase nor decrease as they grow larger. And a new study by a team of researchers at Rice University, the Federal Reserve Board and the OCC also finds no evidence of scale economies for the largest 50 U.S. banks. 

The stark disagreement among world-class researchers is testimony to the difficulty of their task — trying to capture in numbers the bank production process amid ever-changing technological, regulatory and market conditions.  An easier approach is to simply sit back and wait for the marketplace to reveal which banks are too big or too small. This is the so-called "survivor analysis" of Nobel laureate George Stigler, which recognizes that competition will drive inefficient banks — those that are either too small or too large — out of the industry. 

In 1980, state and federal regulation protected most banks from out-of-market competition — but as these protections faded away, banks faced increased competitive pressures. By the onset of the financial crisis in 2007, the number of commercial banks with less than $500 million of assets (in today's dollars) fell from over 14,000 to less than 7,000. In contrast, banks with between $500 million and $1 billion increased in number from 422 to 560, while banks with assets greater than $1 billion did not change, remaining constant at about 525 banks.

By the logic of survivor analysis, scale economies are important for small banks with less than $500 million of assets, but relatively unimportant for banks above $1 billion. 

Of course, we are mixing apples with oranges by lumping all of the $1 billion-plus banks into the same category. Business models and production processes at the very largest U.S. banking companies are quite different than those at large community banks. So let's take a separate look at the survivability of the largest banks.

During the financial crisis, four of the largest ten U.S. depository institutions, Citibank (C), Bank of America (BAC), Wachovia and Washington Mutual, either failed or had to be bailed out. This 40% failure rate exceeds by far the failure rate in the rest of the industry — as of year-end 2011, only about 6% of smaller banks had failed due to the financial crisis.

This is consistent with something that bank researchers (including me) have been observing for about a decade now: the business models and financial activities of the largest banking companies are simply riskier than those of smaller, more traditional banks. Risk usually means increased costs — the banks' ex ante costs of managing risk, or society's ex post costs of cleaning up the mess. Indeed, capturing these costs of risk in their models is one of the challenges facing scale economy researchers.

So how big should a community bank be? According to both the simple numbers and the complex models, if you have less than $500 million or so in assets — and don't have a special strategic niche — then you can add un-exploited scale savings to your list of challenges.

And how big should we allow large banks to get? There is no consensus among bank researchers that restricting large bank size will either reduce or enhance their cost competitiveness. The ideal policy would replace the expectation of bailouts with the demonstrated ability of regulators to seize and wind-down insolvent banks of all sizes. This would allow successful banks to grow to whatever is truly their most efficient (but un-subsidized) size.

Bob DeYoung is the Capitol Federal Professor in Financial Markets and Institutions at the University of Kansas School of Business. He was previously an FDIC official and senior economist at the Federal Reserve and the OCC.