The financial crisis, the collapse of bank entry, and changes in the size distribution of banks.
McCord, Roisin ; Prescott, Edward Simpson
The recent financial crisis has had an enormous impact on the
banking industry. There were numerous bank failures, bank bailouts, and
bank mergers. One of the more striking effects was the decline in the
number of banks. At the end of 2007, as the recent financial crisis was
developing, there were 6,153 commercial banks in the United States. At
the end of 2013, as the direct effects of the crisis were wearing off,
the number of banks had dropped 14 percent, reaching 5,317. (1)
The purpose of this article is to document the size and scope of
these recent changes to the size distribution of banks, particularly
among the smaller banks, and explain the sources of these recent
changes. In doing so, we also update the work of Janicki and Prescott
(2006), who studied the size distribution in the banking industry from
1960-2005.
Our most significant finding is that the recent decline in the
number of banks is not due to exit from banking. Despite the financial
crisis, the exit rate--the percentage of active banks that disappeared
due to failure or merger with another bank--over the period 2008-2013 is
not that different from 2002-2007. There are significant differences in
how banks exited--in the earlier period virtually all of the exit was
due to acquisitions and mergers, while in the later period there were
also many failures--but mechanically it is the number of exits, not the
reason for them, that matters for calculating the total number of banks.
Instead, nearly two-thirds of the recent decline is due to the
collapse of entry into commercial banking. Very few new banks have
started since 2008 and most of these are thrifts or credit unions
changing their charter or, in a smaller number of cases, banks that were
spun out of multi-bank holding companies. Entry by newly created banks,
commonly called de novo banks, has been minimal and was actually zero in
2012. This is unprecedented over the last 50 years. Even during the
previous banking crisis of the late 1980s and early 1990s when large
numbers of banks failed or merged, there was still substantial entry.
The recent lack of entry has large implications for the number of
banks and bank size distribution. Most new banks start small, so without
that flow into banking, the number of small banks will decline. Indeed,
we find that the biggest drop is in the smallest size class, those with
less than $100 million in assets, and that two-thirds of this decline
can be attributed to the lack of entry. This drop is of potential
concern because small banks are considered to have a comparative
advantage in small business, relationship-type lending (Berger and Udell
2002). For better or worse, a drastic change in the bank size
distribution could have an impact on the allocation of credit to
different sectors in the economy. (2)
To demonstrate the importance of entry for the future number of
banks, we provide forecasts of the number of banks based on different
assumptions about entry rates and show how these depend on the degree to
which entry recovers to historical rates. Finally, we discuss various
reasons for why entry has been so low.
1. DATA
Historically, in the United States there have been many legal and
regulatory limits on bank size. For example, in the 1960s banks could
not branch across state lines, and in some states banks were required to
be unit banks, that is, they could not even have a branch. These limits
were removed gradually starting in the 1970s, more rapidly in the 1980s,
and mostly eliminated in the 1990s with the Riegle-Neal Interstate
Banking and Branching Efficiency Act of 1994. This law allowed bank
holding companies to acquire banks in different states and allowed
interstate bank mergers. (3)
A bank holding company is a company that directly or indirectly
owns at least 25 percent of a bank's stock, controls the election
of a majority of a bank's directors, or is deemed to exert
controlling influence over a bank's policy by the Federal Reserve
(Spong 2000). Often, a bank holding company will have multiple banks--or
even another bank holding company--under its control. Historically, this
structure was used to avoid some of the restrictions on bank branching
(Mengle 1990) while still allowing the bank holding company to jointly
manage many activities. For this reason, we follow Berger, Kashyap, and
Scalise (1995) and treat all banks and bank holding companies under a
bank holding company as a single banking entity. For convenience, we
will call one of these entities a bank.
Bank structure and bank size data are measured at the end of each
year from 1960-2013. Data on bank structure are taken from the Federal
Reserve's National Information Center bank structure database. We
only include commercial banks and exclude savings and loans, savings
banks, and credit card banks.
Bank size data comes from the Reports on Condition and Income (the
"Call Report"), which is collected by federal bank regulators.
Bank size is measured by assets, though in a few places we use
additional size measures. For the analysis, assets are also adjusted by
off-balance sheet items starting in 1983. Starting in that period,
banks, and larger banks in particular, began to undertake numerous
activities like providing lines of credit, supporting securitizations,
and issuing derivatives that expose a bank to risk but are not reported
on a traditional balance sheet. These adjustments significantly increase
the size of the largest banks. The Appendix contains more information on
these adjustments.
To facilitate comparison of bank size across years, we report size
measures relative to 2010 dollars. Data in other years are scaled by the
change in total bank assets between those years and 2010. The resulting
number is essentially a market share number, but scaled by the size of
the commercial banking industry in 2010. For example, total bank assets
in 2000 were 50.5 percent of total bank assets in 2010. Consequently, we
roughly double the size of a bank in 2000 to make it comparable to a
bank in 2010. (4)
[FIGURE 1 OMITTED]
2. CHANGES IN BANK SIZE DISTRIBUTION
Figure 1 shows the number of banks from 1960 through 2013. Several
distinct periods are apparent in the graph. From 1960 to 1980, the
number of banks is relatively stable. There is a drop in the early
1970s, which overlaps with the sharp recession of 1973-1975, but
compared with future changes this drop is proportionally small. The most
dramatic changes start in 1980 and last through the late 1990s. This is
the era when many regulatory restrictions were removed from bank
branching and interstate banking, and there was a commercial banking
crisis in the 1980s and early 1990s when many banks failed. These
factors led to a large amount of consolidation through both merger and
failure. Starting in the late 1990s, however, the decline continues, but
the rate of decline slows down. This trend lasts until about 2005,
before the crisis, and then the numbers begin to rapidly decline again.
[FIGURE 2 OMITTED]
A second phenomenon associated with the latter period of bank
consolidation is an increase in concentration, particularly for the
largest banks. Figure 2 shows the market share of the 10 largest banks
for four different measures of firm size. Interestingly, the big
increase in concentration starts around 1990 and continues until the
financial crisis, at which point it levels off.
Like many industries, the size distribution of banks consists of a
large number of small firms and a small number of large ones. One class
of distributions that is often used to fit the size distribution of
firms is one that is based on a power law, that is, it satisfies the
relation
f(x) = c[x.sup.-[alpha]],
where c > 0. Power laws also describe a large number of other
empirical phenomena in economics as well as in the natural sciences. (5)
[FIGURE 3 OMITTED]
In this article, we will look at the data with a Zipf plot, or
rank-frequency plot. In our context, this means we rank banks by size
and then plot the log of the rank versus the log of the size of the
bank. If this relationship is linear, then it satisfies a power law
because
[y.sub.r] = c[r.sup.-[alpha]],
where r is the rank of a bank measured by size and [y.sub.r] is the
size of the rth largest bank. Furthermore, when [alpha] = 1 (or is close
to it), the data is said to satisfy Zipf's Law, that is, size is
inversely proportional to rank. In other words, the largest bank would
be twice the size of the second-largest bank, three times the size of
the third-largest bank, etc. Janicki and Prescott (2006) found that
Zipf's Law did an excellent job of fitting the size distribution of
banks in 1960 and 1970, but starting in 1980 it underpredicts the size
of the largest banks.
Figure 3 shows the Zipf plot for 2013. The graph suggests that
Zipf's Law still underpredicts the size of the largest banks and,
furthermore, there are different ranges of the size distribution where
bank size is proportional to rank, but these proportions differ along
different segments of the size distribution. Furthermore, it is obvious
that the size distribution of the smallest banks is poorly described by
a power law and therefore needs to be described by some other
distribution. (6)
Interestingly, despite the severity of the financial crisis, the
Zipf plot for 2007 (not shown) looks virtually identical to Figure 3.
One reason is that changes among the distribution of smaller banks are
hard to see in the curve and, as we will see, there were significant
changes there. However, the other reason is that there were not
significant changes in concentration among the largest banks. This is
apparent in Figure 2, which shows that the market share of the 10
largest banks levels off after the crisis.
While the size distribution among the largest banks did not change
much, there were significant changes among the relative size of the
largest banks. Table 1 lists the size of the largest 10 banks in 2007
and 2013. The top three largest banks did not change, but Wachovia
ceased to exist after being acquired by Wells Fargo. Northern Trust and
HSBC exited the top 10 list, while PNC, Capital One, and Goldman Sachs
entered it.
There are two features of these numbers worth noting. First,
off-balance sheet activities have a large effect on the size of some of
these firms. For example, Wachovia is listed as having about $900
billion [right arrow]in assets in 2007. Nearly a third of that number
($269 billion) came from the off-balance sheet adjustments. (7) See
Appendix A for figures showing how big this adjustment is for the
banking sector as a whole. Second, by using Call Report data we are only
measuring assets (and off-balance sheet assets) that are held under a
bank holding company's commercial bank charters. (8) For some
financial institutions, this matters. For example, most of Goldman
Sachs' activities are done outside its bank charter. In 2013, its
balance sheet was about $912 billion (FR Y-9C), which is much larger
than the $292 billion reported in Table 2. For others it is less
important. A traditional commercial bank like Wells Fargo has most of
its assets under its commercial bank charters.
The largest changes in the bank size distribution have occurred
among smaller banks, which is something that the Zipf plot does not show
that well. Consequently, we break banks into size classes and look at
the number of banks in each class. Table 2 reports these numbers. Not
surprisingly, the biggest drop in the number of banks is in the smallest
class of banks because the majority of banks are small. More
interesting, however, is the percentage change. The biggest such change
is in banks that hold less than $100 million in assets. The drop in this
size class is about 30 percent in just five years. This is an
extraordinarily large decline. In the next three size classes, the
number of banks does not change that much, while there are increases in
the three largest categories. (9)
A closer look at banks that hold less than $1 billion further
illustrates that the smallest banks are disappearing. Table 3 breaks
down the size classes even further. There is an enormous drop of about
40 percent in the number of banks that hold less than $50 million. In
the $50-$100 million range, there is a smaller, but still large,
percentage drop of 20 percent. Above $100 million, the change is more
mixed. In some categories, the number of banks increases and in others
it decreases.
3. ENTRY AND EXIT
The recent decline in the number of banks shown in Figure 1 appears
to be a continuation of a trend that started around 1980 and, when
measured solely by the number of banks, that view would be correct.
However, there is a significant difference from any previous period.
Figure 4 reports the number of entries and exits into commercial banking
expressed as a fraction of the banking population.
[FIGURE 4 OMITTED]
The most striking observation from Figure 4 is the unprecedented
collapse of bank entry since 2009. Entry rates are on the order of 0.05
percent, which is much smaller than the long-term average of 1.5
percent. Furthermore, as we will see in the next section, entry is
actually weaker than these numbers indicate. The only period that is at
all close to this is 1993 and 1994, which followed the previous banking
crisis and the recession of the early 1990s.
The other striking observation from Figure 4 is that despite large
numbers of exits in different periods, like the mid-1980s and the
mid-1990s, entry was usually strong. For example, in 1984, when more
than 5 percent of banks exited because of failure or merger, there were
so many entrants that they equaled 3 percent of the banks that operated
at the beginning of that year. The late 1990s were similar. During the
merger wave of that period, there was a lot of entry.
It is also apparent from Figure 4 that despite the financial
crisis, exit rates during the crisis are very similar to those from the
2002-2007 pre-crisis period. The one significant difference between
these periods is the reason for exit. Table 4 lists bank exits by reason
from 2002-2013. Before the crisis, almost all exit was due to an
acquisition or merger while, during 2009-2010, failure was the most
common reason for exit. Starting in 2011, failure accounts for about
half of all exits, after which the rate of failure quickly declines.
The entry and exit rates demonstrate that the normal dynamics of
the banking industry are not such that there is a fixed stock of banks
from which banks exit over time. Instead, it is of a dynamic industry
with lots of entry and exit in both good and bad economic times. By
these perspectives, the collapse of entry is what is so striking about
the last few years.
4. A DEEPER LOOK INTO ENTRY (OR THE LACK THEREOF)
A deeper look into the source of entry implies that entry in recent
years is actually weaker than the numbers suggest. In our data, we can
identify three distinct types of entry. First, there is a charter
conversion, that is, a savings and loan, a savings bank, or a credit
union that changes its charter to a commercial banking charter. Second,
there is a spinoff, which is a bank that was formerly part of a holding
company but has become independent. Third, there is a de novo entrant,
which is a newly formed bank.
[FIGURE 5 OMITTED]
A de novo bank is a good measure of interest in entering banking
because it represents new capital, new management, and a new
organization. A charter conversion to a degree is just a relabeling of
an existing institution since there is overlap between the activities of
a commercial bank and other depository institution charters. Similarly,
a spinoff is just another way of legally organizing bank assets and
managers that are already in the banking sector.
Figure 5 lists the number of de novo entries for each year since
1960. The only two periods in which there is a sharp decline in the
number of de novo banks are the early 1990s and the last few years. The
former period coincides with the recession of the early 1990s and the
end of a commercial banking crisis, but de novo entry numbers quickly
rebound. In contrast, the de novo entry numbers in the recent period are
truly abysmal. In 2011, there were three de novo banks; (10) in 2012,
there were zero, and in 2013, there was only one. This last one was Bank
of Bird-in-Hand, which was formed in Lancaster County, Pa., to serve the
Amish community.
[FIGURE 6 OMITTED]
Spinoffs are unusual and to our knowledge have not been studied in
the banking literature. There are several reasons for why a bank holding
company might undertake one. One reason is that a bank holding company
might sell one of its healthy bank charters to outside investors because
the holding company is in financial trouble. For example, in 2012 the
bank holding company Capital Bancorp sold several of its banks to local
investors while it filed for Chapter 11 bankruptcy (Stewart 2012). A
second reason is that management thinks the bank will be better managed
separately rather than jointly. For example, in 2005 Midwest Bank
Holdings sold one of its subsidiaries, Midwest Bank of Western Illinois,
to local managers and investors because the bank's agricultural
lending focus did not fit well with the holding company's Chicago
growth strategy (Jackson 2005).
Figure 6 reports the number of spinoffs by year for our data set.
In general, spinoffs are unusual, though there was a spike in the
mid-1980s and there were 16 in 2009.
The final type of entry that we can identify is a charter
conversion. A depository institution may want to switch charters because
it wants to expand certain types of lending (e.g., savings and loans and
credit unions face limits on the type of lending that they do). Table 5
shows entry by type since 2002, and this makes clear that most entries
since 2011 came from charter conversions.
5. DECOMPOSING THE DROP IN THE NUMBER OF BANKS
The two trends we have identified--the decline in the number of
small banks and the collapse of entry--are related. As we emphasized
earlier, the dynamics of bank growth matter for the size distribution.
In particular, the pool of small banks changes over time. Some grow to a
new size class and some exit. These factors alone would reduce the
number of small banks, so the flow into this pool matters a lot. For the
smallest class of banks, de novo banks are a critical part of the flow
in. Many of these banks start small, so they replenish the stock of
small banks, even as other ones are leaving that class.
We can get a sense of just how much the recent decline in small
banks is due to the drop in bank entry by running a simple
counterfactual. We break banks into the seven size classes of Table 2,
calculate the fraction of banks in each size class that move to another
size class in each year, and then take the average over the 2008-2013
period. (11) We then use these transition probabilities along with some
counterfactual assumptions on entry to see what would have happened to
the number of banks under more typical entry conditions.
Table 6 shows the average annual transition probabilities for the
2008-2013 period. Each row takes all the banks in a given size class and
reports the fraction of them that are in each size class in the
succeeding year. For example, of banks that are less than $100 million,
3 percent exited, 91 percent stayed in the same size class, and 6
percent moved up to the next highest size category. (12)
For our counterfactual experiment, we take the number of banks in
each size category in 2007 (column 2 in Table 2) and multiply this by
the transition probabilities. For entry, we take the average entry rate
over the 2008-2013 period and--for the counterfactual part--we add
enough additional entrants so that the number of entrants equals 129,
which was the average number of new entrants over the 2002-2007 period.
We put these entrants into size categories in the same proportion as new
entrants during the 2002-2007 period. (13)
Table 7 reports the number of banks in each size category for 2013
and the number that would have existed under the counterfactual
assumption on entry. It also lists the difference, expressed in absolute
and percentage terms. With the counterfactual entry, there would have
been 567, or 10.7 percent, more banks. There would still be fewer banks
than in 2007, when there were 6,153, but a lot more than the actual
5,317 in 2013. The actual number of banks dropped in this period by 836,
while under the counterfactual the number would have only dropped by
269. This means that the weaker entry accounts for the rest of the drop,
which is about 68 percent of the total.
Among size classes, the biggest difference among banks is in the
less than $100 million size class. In the counterfactual, there are 22
percent more banks. Much of this difference is directly accounted for by
the lack of entry. Under the counterfactual entry assumptions, 129 banks
enter per year, and most of them enter the smallest size class.
Furthermore, in each year, 91 percent of those new entrants stay in this
class, so over time new entry adds a lot of banks to this size class.
6. WHAT ACCOUNTS FOR THE LACK OF ENTRY?
The literature on bank entry has identified three main factors that
are positively correlated with bank entry. The first is that entry is
more likely in fast-growing, profitable, and concentrated markets
(Dunham 1989; Moore and Skelton 1998), presumably because potential
profits are higher in this type of market. The second is that entry is
more likely after recent mergers (Dunham 1989; Keeton 2000; and Berger
et al. 2004). Starting a bank requires experienced bankers and there are
more people available after a merger since mergers often involve
layoffs. (14) The third factor is that entry is more likely when
regulatory restrictions on entry are relaxed (Ladenson and Bombara 1984;
Lindley et al. 1992), presumably because any decrease in entry cost will
make it more profitable for a potential bank to enter.
Analysis and discussion of the recent lack of entry have focused on
the poor economic conditions and the increase in regulatory compliance
costs. The recent economic recovery has been very weak, which has
certainly reduced the potential return from entering. Adams and Gramlich
(2014) examine entry at the county level with an ordered probit model
estimated on U.S. data from 1976 to 2013. Based on this model, they
conclude that 75 percent to 80 percent of the decline in bank entry over
the last few years is due to low interest rates and a lack of demand for
banking services. They point out that community bank profits are heavily
dependent on the net interest margin, that is, the spread between
deposit rates and lending rates, and with present Federal Reserve
monetary policy pushing lending rates down, this margin is relatively
small.
[FIGURE 7 OMITTED]
While these results are suggestive, they are far from definitive.
There are plenty of periods where net interest margins declined, yet
entry did not collapse. Morris and Regehr (2014) study the historical
pattern of net interest income in community banks after recessions since
the mid-1970s. They observe significant drops in this revenue source
during all recessions and argue that the recovery in net interest income
after the recent recession is not that different from the 2001-2002
recession and is actually higher than in the 1981-1982 recession.
Furthermore, as we showed in Figure 4, entry rates were much higher
after every earlier recession. Indeed, the Adams and Gramlich (2014)
model includes a dummy variable for the post-crisis period (2010 and
after) that is also important for explaining the recent lack of entry.
Their model also predicts that, even if the net interest margin and the
economy recovered to 2006 levels, there would still be almost no entry.
It seems then that while the net interest margin is important, there may
be other factors at work.
[FIGURE 8 OMITTED]
The other line of analysis is that regulatory costs are
discouraging entry. There are two distinct, but often mixed together,
arguments used here. The first argument is that the general increase in
regulations resulting from the implementation of the Dodd-Frank Act of
2010 have made banking significantly more costly by requiring more
resources to be used for complying with regulations and that,
furthermore, there are economies of scale in complying with these
regulations.
Peirce, Robinson, and Stratmann (2014) surveyed community bankers
about compliance costs. The bankers responded that their median number
of compliance staff increased from one to two. (15) Other than for the
smallest banks, this is not a big increase in number of employees, but
there are other sources of compliance costs that could be reflected in
the non-interest expense category of the Call Report income statement.
Figure 7 shows non-interest expense as a percentage of assets for
banks with less than $1 billion in assets and for those with $1 billion
to $10 billion in assets. For the smaller class, this ratio did not
change much between 2007 and 2013, and while it is higher for the larger
class, it is still lower than it was in 2000. If compliance costs are
really increasing, then they are being swamped by changes in other
expenses.
The non-interest expense number does not break out expenses between
compliance and non-compliance costs, but starting in 2008 the Call
Report added some subcategories of expenses, including costs related to
legal fees, auditing, consulting, and advisory expenses. Presumably,
some of these costs are related to the costs of complying with
regulations. Figure 8 shows these costs measured as a percentage of
assets for banks with less than $1 billion in assets.
There is an increase in these expenses from 2008 to 2011, but the
increase is relatively small and, more importantly, the size of these
expenses is just too small to have a big effect on bank profitability.
For example, entirely eliminating these expenses would only increase the
return on assets by 10 basis points.
Based on this data, if regulatory costs are significantly impacting
bank expenses and profitability, it is because other costs are declining
to offset the increase or regulatory costs are affecting the operations
of banks in such a way that less revenue is being generated. For
example, many community bankers say that their leaders spend a lot of
their time reading, interpreting, and reacting to the rules, and that
for small banks, in particular, this pulls them away from things like
making loans and managing their staff. (16) This kind of cost is not
something we can measure in the Call Report data.
The second argument related to regulatory change is that the costs
of entry have increased due to regulations. To start a bank in the
United States, organizers are required to get a banking charter from
either a state or the federal government and to obtain deposit insurance
from the FDIC. Once the organizers pass these hurdles, the de novo bank
is under heightened supervision for a period of time. One way in which
these costs have gone up is that the intensity of supervision of newly
chartered banks has increased. In 2009, the FDIC raised the period from
three to seven years under which FDIC-supervised, newly insured
depository institutions are subject to higher capital requirements and
more frequent examinations. Furthermore, FDIC approval is now required
for changes in business plans during this seven-year period (Federal
Deposit Insurance Corporation 2009).
[FIGURE 9 OMITTED]
A second way in which these entry costs may have gone up is that
the application process has lengthened, become more rigorous, and gotten
more expensive. There have been so few de novo banks the last few years
that there is not much direct data on this cost. However, organizers of
the one de novo bank in 2013 claim that the application process was
significantly longer and more intensive than in the past (Peters 2013).
7. LOOKING AHEAD
The future number of banks will depend on the conditions under
which bank entry rates recover. If the main reason for the lack of entry
is the low net interest margin, then entry numbers should recover when
the economy improves and the Federal Reserve raises interest rates. If
regulatory costs are the main reason for the lack of entry, then it will
depend on how these change over time.
Regardless of the reason for the lack of entry, until entry
recovers (and assuming that exit does not decrease) the number of banks
will continue to decline. To illustrate how this drop could be affected
by changes in entry rates, we ran two experiments similar to the
counterfactual that we ran earlier. In both, we divided the banking
industry into the same seven size categories we used earlier. Like in
the earlier counterfactual experiment, we took the annual transition
probabilities between size categories, exit rates from each category,
and the entry rate for the 2008-2013 period. We then took the size
distribution of banks in 2013 and calculated what the number of banks
would be in 10 years if these transition rates did not change. We then
took the same transition probabilities and only raised the entry rate to
match the historical average of 1.5 percent and then calculated what the
number of banks would be in 10 years under this more typical entry rate.
(17)
[FIGURE 10 OMITTED]
Figure 9 shows the number of banks through 2013 and then the two
different forecasts. While both forecasts predict a continued decline in
the number of banks, there is a substantial quantitative difference
between them. The number of banks under the existing trend drops another
1,000 banks over 10 years, while it only drops by about 500 banks under
historic entry rates.
8. CONCLUSION
Since the financial crisis began, the biggest change to the size
distribution of banks has been the decline in the number of small banks.
We document that much of this decline is due to the lack of entry. We
discussed several reasons for why there might be less entry, including
macroeconomic conditions, regulatory costs, and regulatory barriers to
entry. Regardless of the reasons for the decline, however, it is clear
that to a large degree the number of banks as well as the size
distribution of banks in the future will depend on whether entry
recovers.
APPENDIX A: OFF-BALANCE SHEET ITEMS
Banks can make commitments that are not directly measured by a
traditional balance sheet. For example, a loan commitment is a promise
to make a loan under certain conditions. Traditionally, this kind of
promise was not measured as an asset on a balance sheet. As documented
by Boyd and Gertler (1994), providing this and other off balance sheet
items has become an important service provided by banks, which means
that traditional balance sheet numbers do not accurately report some of
the implicit assets and liabilities of a bank.
We account for loan commitment and other off-balance sheet items
like derivatives by converting them into credit equivalents and then
adding them to on-balance sheet assets. We use the weights used by
regulators to determine credit equivalents for capital purposes. Some of
these adjustments are made starting in 1983, but many are added in 1990.
The weights as of 2013 are reported in Table 8. Figure 10 demonstrates
the importance of the adjustment starting in 1990 by plotting aggregate
assets and loans with and without the adjustment.
APPENDIX B: TRANSITION MATRIX
One interesting thing that can be done with the transition matrix
is to calculate the steady-state distribution of bank size. If the size
distribution at time t is vector [s.sub.t] and P is the transition
matrix (also commonly called a Markov matrix), then the size
distribution at t + n is
[s.sub.t + n] = [P.sup.n][s.sub.t].
If the transition matrix has the property that a bank starting in
any category has a positive probability of moving to any other size
category in a finite number of steps, then several theorems can be
proven. In particular, there exists a unique stationary size
distribution, that is, there exists s, such that s = [P.sub.s].
Furthermore, regardless of the initial distribution, the size
distribution will converge to this unique distribution.
For the transition matrix in Table 6, Table 9 shows the stationary
distribution. There is a large fraction of banks in the over $50 billion
size category. The reason for this concentration is that in the
transition probabilities over the 2008-2013 period, 99 percent of banks
in the largest size category stayed in it each year. Consequently, if a
bank enters this category, it is very unlikely to leave, so banks
accumulate there. In the recent period, this reflects the lack of merger
activity among the largest banks and that the largest banks were
prevented from failing by the federal government during the crisis. In
past periods, transition probabilities for the largest size class were
very different. For example, over the 2000-2005 period, only 91 percent
of banks in the largest size class stayed there.
The stationary distribution is useful for illustrating what
direction the transition probabilities are taking the size distribution.
As a long-term forecast, however, it is less valuable. It can take many
iterations for a distribution to converge to its stationary distribution
(over 200 in this case) and, as Janicki and Prescott (2006) show,
properties of transition matrices for the banking industry have changed
several times over the last 50 years.
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We would like to thank Huberto Ennis, Joe Johnson, Thomas Lubik,
and John Weinberg for helpful comments. The views expressed here are
those of the authors and not necessarily those of the Federal Reserve
Bank of Richmond or the Federal Reserve System. E-mail:
Edward.Prescott@rich.frb.org.
(1) There were even larger percentage declines in the number of
savings institutions (savings and loans and savings banks) and credit
unions. In 2007, there were 1,250 savings institutions and 8,268 credit
unions. In 2013, there were 936 savings institutions and 6,687 credit
unions, drops of 25 percent and 19 percent, respectively. (Sources:
Savings institution numbers are from the Federal Deposit Insurance
Corporation [FDIC] State Banking Performance Summaries. Credit union
numbers are from NCUA Quarterly Call Reports.)
(2) Bank size distribution should have an effect on bank
productivity as well, but it is difficult to measure bank productivity.
(3) See Jayaratne and Strahan (1997) for a history of bank
branching restrictions and Kane (1996) for a description of the
Riegle-Neal Act.
(4) An alternative way for scaling the data would be to use a price
index like the consumer price index. We do not use this measure because
that price index was designed to measure changes in the price of goods
and we are interested in changes to the size of a bank's balance
sheet, not what it charges to provide bank services. Furthermore, there
have been much larger changes in total assets in the banking industry
than in price levels.
(5) For a description of the use of power laws in economics, see
Gabaix (2009). For a discussion of their use to applications as diverse
as word frequency, population of cities, and earthquake strength, see
Newman (2005). For examples of their application to firm size, see
Axtell (2001) and Luttmer (2007).
(6) It is common in applications that the bottom part of the
distribution is not well described by a power law distribution, so
scientists typically leave this part out of their analysis. For example,
when looking at bank size distribution, Janicki and Prescott (2006) only
consider the largest 3,000 banks when they assess how Zipf's Law
fits the size distribution of banks. Recent work by Goddard et al.
(2014) develops a more general formulation by fitting a distribution in
which there is a power law for the largest banks, a lognormal
distribution for small banks, and an endogenous cutoff between the two
classes of banks. See also Goddard, Liu, and Wilson (2014) for an
analysis of bank growth rates.
(7) The four largest off-balance sheet equivalents for Wachovia
were unused loan commitments with an original maturity exceeding one
year ($74 billion), securities lent ($59 billion), derivatives ($50
billion), and financial standby letters of credit ($40 billion).
(8) For an analysis of how the activities of large bank holding
companies have changed over the crisis, see Ennis and Debbaut (2014).
(9) To check the robustness of this result we also performed this
analysis on other measures of bank size including on-balance sheet
assets, deposits, and loans, both scaled and unscaled (nominal).
Qualitatively, the results were similar for all these measures except
for scaled loans.
(10) These three banks were Alostar, Cadence, and Certusbank, which
were all formed to acquire failed banks.
(11) See Adelman (1958), Simon and Bonini (1958), and Janicki and
Prescott (2006) for more information about transition probabilities and
how they can be used to assess the dynamics of an industry.
(12) Appendix B contains some more analysis of the transition
matrix.
(13) In the 2002-2007 period, 81 percent of new entrants started in
the under $100 million size category, 15 percent started in the
$100-$500 million size category, 2 percent started in the $500-$1,000
million size category, and 2 percent started in the $1,000-$5,000
million size category.
(14) At a longer time horizon, an industry with frequent mergers
may create an incentive to start a bank with the goal of selling it in
the future.
(15) For an analysis of potential increases in costs to community
banks of hiring additional compliance staff, see Feldman, Schmidt, and
Heineche (2013).
(16) Personal conversations with bankers by the second author.
(17) There are obvious limitations to this exercise. In particular,
entry and exit decisions are determined simultaneously in a market.
Nevertheless, we think this simple exercise is useful because exit rates
did not change that much from before the crisis to after it, so this
assumption is plausible.
Table 1 Ten Largest Banks
Bank 2007 Bank 2013
(billions) (billions)
JP Morgan Chase 2,503 JP Morgan Chase 2,518
Bank of America 2,096 Bank of America 1,756
Citigroup 1,824 Citigroup 1,614
Wachovia 904 Wells Fargo 1,519
Bank of New York 823 Bank of New York 600
Mellon Mellon
State Street 708 State Street 523
Wells Fargo 580 U.S. Bancorp 386
U.S. Bancorp 290 PNC 323
HSBC Holdings 277 Capital One 298
Northern Trust 258 Goldman Sachs 292
Notes: Size of the 10 largest banks measured by assets, expressed
in 2010 dollars. The asset measure includes off-balance sheet
conversions and only includes activities under the banks'
charters.
Table 2 Drop in Number of Banks by Size Class
Size Class
(millions) 2007 2013 Change % Change
< 100 2,538 1,771 -767 -30.2
100-500 2,706 2,634 -72 -2.7
500-1,000 455 453 -2 -0.0
1,000-5,000 338 333 -5 -1.5
5,000-10,000 48 50 2 4.2
10,000-50,000 39 44 5 12.8
> 50,000 29 32 3 10.3
Total 6,153 5,317 -836 -13.6
Table 3 Drop in Number of Small Banks by Size Class
Size Class
(millions) 2007 2013 Change % Change
< 50 1,230 725 -505 -41.1
50-100 1,308 1,046 -262 -20.0
100-200 1,407 1,357 -50 -3.6
200-300 687 678 -9 -1.3
300-400 359 372 13 3.6
400-500 253 227 -26 -10.3
500-750 290 296 6 2.1
750-1,000 165 157 -8 -4.8
Table 4 Commercial Bank Exit by Reason since 2002
Year Total Failures Acquisition/
Exits Mergers
2002 169 7 162
2003 176 1 175
2004 206 3 203
2005 169 0 169
2006 240 0 240
2007 232 1 231
2008 180 17 163
2009 158 98 60
2010 195 126 69
2011 168 80 88
2012 181 37 144
2013 171 18 153
Notes: Failed banks were obtained from the FDIC's Historical
Statistics on Banking and then compared with our calculated list
of exits. Banks that did not fail were treated as an acquisition/
merger. Because we are measuring a bank at the holding company
level and multiple failed banks can be part of the same holding
company, we report fewer failures than the FDIC.
Table 5 Commercial Bank Entry by Type since 2002
Year De Novo Spinoff Conversion
2002 74 10 6
2003 90 7 10
2004 104 13 12
2005 132 8 3
2006 147 9 5
2007 140 6 8
2008 72 4 10
2009 38 0 0
2010 7 16 3
2011 3 6 12
2012 0 5 20
2013 1 3 11
Table 6 Annual Transition Probabilities Between Size Classes for
2008-2013
Size Class 100- 500-
(millions) Exit < 100 500 1,000
< 100 0.03 0.91 0.06 0.00
100-500 0.03 0.02 0.93 0.02
500-1,000 0.04 0.00 0.06 0.84
1,000-5,000 0.04 0.00 0.01 0.04
5,000-10,000 0.04 0 0 0
10,000-50,000 0.03 0 0 0
> 50,000 0.01 0 0 0
Size Class 1,000- 5,000- 10,000-
(millions) 5,000 10,000 50,000 > 50,000
< 100 0.00 0 0 0
100-500 0.00 0 0 0
500-1,000 0.05 0 0 0
1,000-5,000 0.90 0.01 0 0
5,000-10,000 0.03 0.86 0.06 0.00
10,000-50,000 0.01 0.04 0.92 0.01
> 50,000 0 0 0 0.99
Notes: Entries in bold reflect the fraction that stay in the same
size class. Rows may not add to 1 due to rounding.
Table 7 Number of Banks by Size Class with Counterfactual Entry
Size Class Data Counterfactual Difference % Difference
(millions) 2013 2013
< 100 1,771 2,276 505 28.5%
100-500 2,634 2,711 77 2.9%
500-1,000 453 448 -5 -1.1%
1,000-5,000 333 329 -4 -1.2%
5,000-10,000 50 48 -2 -4.0%
10,000-50,000 44 40 -4 -9.1%
> 50,000 32 32 0 0.0%
Total 5,317 5,884 567 10.7%
Notes: Number of banks in each size class in 2013 compared with
numbers under the counterfactual assumption that the number of
entrants in 2008-2013 is the same as in 2002-2007.
Table 8 Off-Balance Sheet Items and Credit Equivalents as of 2013
Item Conversion Factor
Financial Standby Letters of Credit 1.00
Performance and Standby Letters of Credit 1.00
Commercial Standby Letters of Credit 0.20
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 Off-Balance Sheet Liabilities 1.00
Unused Loan Commitments (maturity > 1 year) 0.50
Derivatives --
Notes: Conversion factors used by regulators for determining
credit equivalents of off-balance sheet items in 2013. The source
is FFIEC 041 Schedule RC-R www.ffiec.gov-forms041.htm. Credit
equivalents for derivatives do not have a direct conversion
factor but instead are based on the current and future possible
credit exposure.
Table 9 Stationary Distribution based on Transition Probabilities
between Size Classes for 2008-2013
Size Class Stationary Distribution in
(millions) Distribution 2013 Data
< 100 0.23 0.33
100-500 0.45 0.50
500-1,000 0.10 0.09
1,000-5,000 0.10 0.06
5,000-10,000 0.02 0.01
10,000-50,000 0.03 0.01
> 50,000 0.06 0.01
Notes: Columns do not add to 1 due to rounding.
