The Size Distribution of US Banks and Credit Unions

Abstract

This study examines the firm size distribution of US banks and credit unions. A truncated lognormal distribution describes the size distribution, measured using assets data, of a large population of small, community-based commercial banks. The size distribution of a smaller but increasingly dominant cohort of large banks, which operate a high-volume low-cost retail banking model, exhibits power-law behaviour. There is a progressive increase in skewness over time, and Zipf’s Law is rejected as a descriptor of the size distribution in the upper tail. By contrast, the asset size distribution of the population of credit unions conforms closely to the lognormal distribution.

Key Words:

• Firm Size distribution
• Zipf’s Law
• Gibrat’s Law
• Banks
• Credit Unions

JEL classifications:

• G21
• L10
• L16

Notes

The authors gratefully acknowledge the helpful comments of two anonymous referees on an earlier draft of this paper. The usual disclaimer applies.

1. These include: proportional growth subject to a reflecting lower barrier (a minimum size threshold beneath which no firm can fall); and proportional growth with deaths at a rate that is inversely proportional to size, and births at a constant size (Gabaix, 2009).

2. See also Stanley et al. (1995) and Growiec, Pammolli, Riccaboni, and Eugene (2008). For empirical evidence on the size distribution of cities, regions and countries, see Gabaix (1999a), Gabaix (1999b), Eeckhout (2004), Rose (2006) and Luttmer (2007).

3. For example, the McFadden Act of 1927, which prohibited interstate branch banking, was repealed by the Riegle-Neal Interstate Banking and Branching Efficiency Act of 1994; and the Glass-Steagall Act of 1933, which prohibited commercial banks from transacting other financial services including investment banking and insurance, was repealed by the Gramm-Leach-Bliley Financial Services Modernization Act of 1999. Berger, Kashyap, and Scalise (1995) and DeYoung (2010) describe the evolution of the US banking industry.

4. According to DeYoung (2010), around 350 commercial banks were acquired each year during the 1980s, around 500 each year during the 1990s, and around 300 each year during the first half of the 2000s. More than 10,000 bank charters were terminated owing to acquisitions (excluding acquisitions enforced by the Federal Deposit Insurance Corporation owing to severe financial distress) between 1980 and 2005, and acquisitions accounted for more than 80% of all bank charters that terminated during this period.

5. A number of publications routinely monitor changes in the size distribution and performance of commercial banks. For example, the FDIC Quarterly Banking Profile provides a summary of financial results for all FDIC-insured commercial banks. The Federal Reserve annual publication Profits and Balance Sheet Developments at US Commercial Banks examines banks, and not BHC. Several recent analyses of the effects of the financial crisis on industry structure focus upon the bank and not the BHC (see, for example, Wheelock, 2011). In antitrust cases, policy makers concerned with issues of product and geographic market definition normally consider banks, and not BHCs, to be the appropriate unit of analysis (Gilbert and Zaretsky, 2003).

6. See JP, 312–314. The credit equivalent is a weighted sum of the following OBS items: financial standby letters of credit (weighting = 1.00); performance and standby letters of credit (0.50); commercial standby letters of credit (0.25); risk participations in bankers’ acceptances (1.00); securities lent (1.00); retained recourse on small business obligations (1.00); recourse and direct credit substitutes (1.00); other financial assets sold with recourse (1.00); other OBS liabilities (1.00); and unused loan commitments with maturity greater than one year (0.50). Items below the line are usually recorded in notes to the accounts, in supervisory reports, within banks’ internal reporting systems, or in some cases not at all. Credit unions typically do not report OBS items.

7. Commercial banks’ call reports include a variable which reports (if applicable) the parent BHC code number.

8. Banks that form part of a BHC are subject to bank supervision and regulation. For example, they raise insured deposits, are subject to risk-based capital regulation and prompt corrective action, and have access to lender of last resort facilities via the Federal Reserve discount window.

9. The maximised value of the pseudo-log-likelihood function (not reported in Table 1) for (ii) is substantially larger than the corresponding value for (i) in every case.

10. In Figure 3, both the maximum likelihood estimate of the Pareto upper tail, and the Zipf’s Law upper tail, commence from the maximum likelihood estimate of the cut-off threshold.

11. To avoid a proliferation of similar results, for the loans size measure Table 3 only reports the results without the addition of OBS credit equivalents.

12. The finding that the upper tail of the log size distribution can be represented by a Pareto distribution reflects skewness and kurtosis coefficients for the log size distribution that are persistently higher than the values (of zero and three respectively) associated with the normal distribution. This approach, however, leaves open the possibility that the entire log size distribution could be represented by some other probability distribution that allows for excess kurtosis. The Student-t distribution allows flexibility in modelling excess kurtosis through variation in the degrees of freedom parameter. Experimentation with use of the Student-t distribution as an alternative to the normal distribution produced similar results for all four log size measures. As before, the formulation representing the upper tail of the log size population using the Pareto distribution and the rest of the population using a truncated Student-t distribution was preferred to the formulation representing the entire population using a Student t-distribution in every case. However, the threshold values of k that locate the switch between the truncated Student-t and Pareto distributions were persistently smaller than the corresponding threshold values obtained using the normal and Pareto distributions, as reported in Tables23. This pattern seems plausible: the Student-t distribution describes accurately a somewhat larger proportion of the upper tail than the normal distribution; but neither of these distributions adequately represents the upper tail in its entirety.

13. The Gramm-Leach-Bliley Act in 1999 removed many restrictions previously imposed on the activities of banks.

14. Walter (2006) and Goddard, McKillop, and Wilson (2009) describe the evolution of the US credit union sector. Wheelock and Wilson (2011) present evidence that credit unions are, on average, too small to benefit from economies of scale.

15. The largest credit union, Navy Federal with assets of USD 44.2 billion in 2010, would have ranked 36th in the distribution of commercial banks by asset size in the same year.