by Tony Lima
February 2, 2010
Updated April 26, 2010 to correct a
mistake pointed out by David Spitzley.

Copyright 2010 Tony Lima.  All rights reserved.

“Indeed, policymakers will have to consider the loss of scale benefits when they determine the net benefits of breaking up firms in the first place.”[1]

TBTF: Too Big To Fail.

Huge numbers of economists, politicians, and people in the street are all calling for one policy: make the biggest banks smaller.  A common refrain is, “If it’s too big to fail then it’s too big period.”  Overlooked in the hue and cry is the issue of cost.  It’s quite likely that shrinking the biggest banks will drastically  increase the price of banking services to the public.

The quotation that begins this entry is excerpted from a short, cogent piece by Ron Feldman and Gary Stern in The Region published by the Minneapolis Fed.  The point they are making is well known among economists: there are economies of scale in banking.

Economies of scale is conventionally defined as decreases in average variable cost caused by increases in the size of the production operation.  In studies of banking, economies of scale are often confabulated with increasing returns to scale.  Since banks’ inputs and outputs are various forms of money and monetary instruments, it’s silly to quibble about the difference between the two.

Let’s look at two recent papers that study this subject.  Using very different methodologies (including different samples, statistical methodology, and time periods), these papers reach the same conclusion: there are increasing returns to scale in U.S. banking.  That means larger banks are generally more efficient than smaller banks.  Therefore, before policymakers rush to break up those banks, they should include potential costs as well as benefits.

A fascinating (but mathematically challenging) paper by David C. Wheelock and Paul W. Wilson has a title that asks a simple question: “Are U.S. Banks too Large?”[2] Using state-of-the-art methodology and a sample that includes every bank in the U.S., they conclude that there are increasing returns to scale in U.S. banking.  Unfortunately, their methodology does not lend itself to easily getting a quantitative estimate of the degree of increasing returns.

Can we make a guess at the size of those costs?  Of course, but it’s only a guess.  Guoha Feng and Apostolos Serletis studied economies of scale in U.S. banks with more than $1 billion in assets.[3] Their estimate of the returns to scale coefficient is in the neighborhood of 1.045.[4] That means for a ten percent increase in bank size we expect average variable cost to fall by about 0.45%.  Conversely, for a ten percent decrease in bank size average variable cost would rise by about 0.45%.

How does that number translate into the real world?  The seven largest bank holding companies as of Sept. 30, 2009 are shown in Table 1.[5] On that date, total assets of U.S. commercial banks were $11,666,582,800,000.[6] The total assets of these seven banks were $9,598,327,759,000.  Those banks contain 82 percent of all assets of U.S. commercial banks.  As of the same date, there were 6,829 commercial banks.[7] The average bank size was $1,708,388,168.  Suppose we require each of the seven largest banks to split itself into a number of banks each equal to the current average size.  Thus, for example, Bank of America would be split into $2,252,813,550,000/$1,708,388,168 or about 1,318 banks.  How much would this increase cost?

Table 1

If a 10 percent increase in bank size reduces average variable cost by 0.45 percent then a 13,186.8 percent decrease in bank size should increase average variable cost by (0.45%)x(1,318.68) = 593.406%, about 6 times.  I won’t claim any degree of accuracy for this figure because I’m projecting outside the range of the observed data.  It’s safe, however, to say that costs will rise quite a bit, perhaps by as much as a factor of 5 or 10.  To be conservative, let’s say unit costs rise by a factor of 6.  The implications are staggering.

Every three or four years the U.S. Federal Reserve surveys households to determine various financial details.  For example, in the 2007 survey,[8] the mean transaction balance held by the group in the 40th through 59.9th percentile of income was $10,400.  That sounds like a lot until you realize the Fed includes checkable deposits, savings deposits, money market accounts, and call or cash accounts at brokerages.  The  interest rate paid on these deposits was about 0.16 percent per year,[9] implying median interest payments of $16.64 per year.  However, that is more than offset by fees charged by banks.

There are several sources for estimates of bank fees.[10] Until 2003 the Fed submitted an annual report to Congress titled Annual Report to the Congress on Retail Fees and Services of Depository Institutions.[11] Monthly fees range from about $2.70 on savings accounts to $8.71 on NOW accounts charging a monthly fee with no per-check charge.[12] A second source is a paper by Joanna Stavins of the Boston Fed.[13] Using her sample, the mean monthly fee was $7.06.  Picking a number out of this range, let’s say the monthly fee is $6.00.  Subtract $1.39 for the interest paid.  The net cost is $4.61 per month.  If the banks’ costs rise by a factor of 6, that implies a monthly fee of $4.61.  Putting this another way, if the bank’s average yield on its asset portfolio is 5 percent, the monthly average balance requirement to cover costs of $4.61 per month is $571.44.

So here’s the summary.

• Free checking?  Forget it unless you can carry a minimum balance upwards of $500.
• Interest on savings deposits?  Banks will stop offering savings accounts without a large minimum balance, probably over $10,000.
• Certificates of deposit?  None offered under $100,000.
• And interest rates will rise on all categories of loans, including auto loans, mortgages, and credit card debt.  An increase of 400 basis points would not be out of the question.

If policymakers want to break up the large banks, they should be prepared for the consequences.  Consumers are angry at banks today.  How will they feel about regulatory actions that reduce access to some long-cherished benefits of the U.S. financial system?

[2] Wheelock, David C. and Paul W. Wilson, “Are U.S. Banks too Large?” Working Paper 2009-054B, Federal Reserve Bank of St. Louis, December, 2009.  Available at http://research.stlouisfed.org/wp/2009/2009-054.pdf.  Accessed February 2, 2010.

[3] Feng, Guoha and Apostolos Serletis, “Efficiency, technical change, and returns to scale in large US banks: Panel data evidence from an output distance function satisfying theoretical regularity.” Journal of Banking & Finance 34 (2010) 127–138.

[4] Ibid, Table 9, p. 135.

[5] Source: Board of Governors of the Federal Reserve System, Washington, D.C.  Available at http://www.ffiec.gov/nicpubweb/nicweb/Top50Form.aspx.  Accessed February 2, 2010.

[6] Source: Board of Governors of the Federal Reserve System, Washington, D.C.  Available at http://federalreserve.gov/datadownload/Choose.aspx?rel=H.8.  Accessed February 2, 2010.

[7] Source: Federal Deposit Insurance Corporation, Washington, D.C.  Available at http://www2.fdic.gov/idasp/KeyStatistics.asp?tdate=1/28/2010&pDate=1/27/2010. Accessed February 2, 2010.

[8] Board of Governors of the Federal Reserve System, Washington, D.C.  Available at http://federalreserve.gov/pubs/oss/oss2/2007/scf2007home.html.  Accessed February 5, 2010.

[9] Board of Governors of the Federal Reserve System, Washington, D.C.  Available at http://federalreserve.gov/releases/h15/current/h15.htm.  Accessed February 5, 2010.

[10] ”Bank fees” include everything from monthly service charges to additional fees for bounced checks, ATM use (own-bank and foreign-bank), stop-payment fees, and bounced checks deposited into the deposit-holder’s account.  For an analysis of these fees individually, see Timothy H. Hannan, “Retail deposit fees and multimarket banking,” Journal of Banking and Finance, 30 (2006), pages2561-2578.

[11] Available at http://www.federalreserve.gov/boarddocs/rptcongress/2003fees.pdf.  Accessed February 5, 2010.  I was unable to find any reference to this document on the Fed’s web site after 2003.

[12] Annual Report to the Congress on Retail Fees and Services of Depository Institutions, pages 3-4.  Board of Governors of the Federal Reserve System, Washington, D.C.  June, 2003.

[13] Stavins, Joanna, “Checking accounts: What do banks offer and what do consumers value?”  New England Economic Review, March/April, 1999, pages 3-14.  Federal Reserve Bank of Boston, Boston, MA.