An examination of entry and competitive performance in rural banking markets.
Feinberg, Robert M. ; Reynolds, Kara M.
1. Introduction
The 1994 Riegle-Neal Act ushered forth a new era in banking
deregulation. As noted by former Federal Reserve Chairman Alan Greenspan
in a 2005 speech, deregulation resulted in a 50% decline in the number
of banks due to industry consolidation. However, this decline did not
necessarily indicate that the level of competition declined; Greenspan
(2005) further notes that despite the decline in the number of banks,
measures of local market banking competition remained relatively stable
between 1990 and 2005.
This article explores the nature of competition in rural banking
markets over the decade following the 1994 Riegle-Neal Act. Using a
recently developed empirical model that utilizes the number of banks as
well as the value of deposits in a cross-section of rural markets, we
decompose the impact of the entry of new banks into resulting changes in
per capita demand and the costs/profits of local banks in 1994 and 2004.
The results support Greenspan's claim that banking markets have
become more competitive in the 10 years following passage of the
Riegle-Neal Act.
2. Literature Review
There is a long empirical literature on entry--both determinants
and effects--usually based on manufacturing industry data. Early banking
entry articles include Hanweck (1971) and Rose (1977). More recently,
Amel and Liang (1997) present interesting results on bank entry fairly
closely related to this article's focus. They jointly explain bank
profits and entry over the 1977-1988 period for about 2000 rural
counties and about 300 urban markets (metropolitan statistical areas)
and find that supranormal profits promote entry, as do population and
population growth, and that entry has the anticipated procompetitive
effect of reducing profits, though only in rural markets.
Most of the previous studies look at bank entry in the
pre-Riegle-Neal Act (banking deregulation) period. However, since then
Berger et al. (2004), Seelig and Critchfield (2003), and Keeton (2000)
have all found--though with somewhat differing definitions of merger
activity and samples--that merger activity generally tends to promote de
novo entry. These findings are consistent with merger activity and/or
the presence of "big banks" in a market as signaling to
potential entrants the opportunities for supranormal profits to be
earned. (1)
Others have recently studied market dynamics in local banking
markets. Both Dick (2007) and Cohen and Mazzeo (2007b) find that the
incumbent banks in markets tend to expand via new branches to aid in
deterring new entry when demand grows. Similarly, Berger and Dick (2007)
find that early entrants in banking markets seem to be able to entrench
their positions and have persistently higher market shares.
The work by Bresnahan and Reiss (1991) stimulated a wave of
empirical research on entry. They explain entry in terms of the
cross-sectional response to market size; specifically, they hypothesize
that if the per firm market size needed to support a given number of
firms is getting higher with the number of firms in the market, then
competition must be getting stronger. In other words, the fact that
larger sales are required to offset the fixed costs of entry implies
more competitive pricing. A discrete choice model relates these
"entry thresholds" and how they change with subsequent entry
to predictions about price behavior associated with increasing numbers
of firms. (2) Bresnahan and Reiss (1991) take the view that isolated
rural markets are best suited to testing hypotheses regarding entry,
generally because of the difficulty in accurately drawing market
boundaries in metropolitan areas or even in rural counties adjacent to
metropolitan statistical areas (MSAs).
Cetorelli (2002) uses the Bresnahan and Reiss (1991) (BR)
methodology to examine local banking markets and explain (equilibrium)
market structure by population and other county economic
characteristics; the article analyzes numbers of banks in a large sample
of nonmetropolitan counties for 1999. While we would argue that
contiguous rural counties may not represent the most appropriate
geographic market definition for local banking, his estimated
ordered-probit coefficients suggest significant market power at least
until there are five banks in a county. (3)
Cohen and Mazzeo (2007a) apply a variant of the BR approach to
rural banking markets. They look at data for a large number of rural
banking markets in 2000 and 2003 to examine the nature of competition
within and across three types of institutions: multimarket banks,
singlemarket banks, and thrifts. As in this article, they choose to
define markets in terms of Bureau of Labor Statistics "labor market
areas" (LMAs), which combine contiguous counties depending on
commuting patterns to better proxy geographical markets for financial
services. Cohen and Mazzeo (2007a) find significant product
differentiation (that competition within types is more aggressive than
it is across types) and that variable profits are significantly reduced
by the second firm in a given type, this reduction becoming smaller for
subsequent entry.
We also use a variant of the BR approach to examine endogenous
market structure in local banking markets (where price and cost
information are difficult to obtain for the bundle of services
provided). However, we consider only rural LMAs at least one market
removed from an MSA and not adjacent to any other sample LMA. Although
this restriction--designed to minimize errors in market definition and
correlations across markets--makes our sample of markets somewhat
smaller than that used in other recent studies of banking entry, it does
encompass 278 rural markets (across 39 states) in the United States.
We also consider the issue of banking competition in small rural
markets in a somewhat different manner than do Cetorelli (2002) and
Cohen and Mazzeo (2007a), applying the methodology of Abraham, Gaynor,
and Vogt (2007) (AGV). (4) AGV extend the BR approach by incorporating
information on quantity to analyze the level of competition in the U.S.
hospital industry. They claim (p. 266) that using information about
quantity "allows us to separate changes in fixed cost associated
with entry from changes in the toughness of competition." In their
sample of hospital markets, they find that relatively few firms are
required to bring competitive behavior (by reducing variable profits and
increasing market quantity), with limited effects beyond three firms in
a market.
Unlike Cohen and Mazzeo (2007a) and Mazzeo (2002), the AGV model
assumes that firms produce a homogenous product. (5) But, unlike these
aforementioned articles, this model does not have to assume that fixed
costs of entry remain constant as the number of firms in the market
grows. For this reason, we believe that the AGV model is ideally suited
to study competitive conditions in the banking market. The requirement
of homogeneity in the context of local consumer banking seems less
onerous than the assumption that market crowding with increased numbers
of banks has no impact on entry costs (as might be due to the need for
greater marketing expenses). The model allows us to use observed data on
market structure and quantity (but not prices) to study the level of
competition in a market.
3. Model
As noted previously, we utilize an econometric model derived in
Abraham, Gaynor, and Vogt (2007). In the following paragraphs, we
provide a brief outline of the model. The market demand for banking
services is defined by
Q = d(P, X)S(Y), (1)
where per capita demand, d(P, X), is a function of price and
exogenous demand shifters (X), such as per capita income. The total
market size, S(Y), is an increasing function of population. Each
bank's costs are characterized by constant average variable costs,
A VC(W), and a fixed cost, F(W), both of which depend upon cost
shifters, W.
As in Bresnahan and Reiss (1991), we assume that each market
reaches a symmetric equilibrium in price. The equilibrium market price
in a market with N firms, [P.sub.N](X, W, [[theta].sub.N]), depends upon
demand and cost conditions and the degree of competition, as represented
by [[theta].sub.N]. The equilibrium market price determines the
equilibrium values of per capita quantity, fixed costs, and variable
profit margin (price minus average variable costs), or d([P.sub.N], X),
[F.sub.N](W), and [V.sub.N]([P.sub.N], W), respectively.
We observe the number of banks (N) and the quantity of deposits (Q)
for each market. A bank will enter the local market only if it will earn
non-negative profits. The Nth firm in the market earns profits equal to
[[PI].sub.N] = [V.sub.N]S/N[d.sub.N] - [F.sub.N]. (2)
The minimum market size per firm needed to support N firms,
[S.sub.N], can be found by solving Equation 2 for the zero-profit
condition. As in Bresnahan and Reiss (1991), we calculate the ratio of
the minimum per firm market size needed to support a market with N + 1
versus N firms, or the entry threshold ratio, as
[[S.sub.N+1]/[S.sub.N]] =
[[F.sub.N+1]/[F.sub.N][[[V.sub.N][d.sub.N]/[V.sub.N+1][d.sub.N+1]]. (3)
As discussed above, Bresnahan and Reiss (1991) hypothesize that if
the per firm market size needed to support a given number of firms is
getting higher with the number of firms in the market, then competition
must be getting stronger. Stronger competition reduces prices and, thus,
profit margins; as a result, a larger market size is needed to cover the
fixed costs of entry. A threshold ratio greater than one implies that
competition is getting stronger, while a threshold ratio equal to one
implies that the degree of competition remains unchanged with the entry
of an additional firm. Threshold ratios should converge to one as the
market converges to perfect competition with the number of firms.
As can be seen from Equation 3, the entry threshold ratio in this
model is the product of the change in fixed costs that occurs due to the
entrance of a new firm ([F.sub.N+1]/[F.sub.N]) and the change in
variable profits per capita. If fixed costs do not change with entry,
then convergence of the entry threshold ratio to one implies convergence
of the market to a competitive one, as in Bresnahan and Reiss (1991).
However, it is equally possible that the convergence of the entry
threshold is instead driven by the convergence of the change in fixed
costs in the industry. In other words, the decrease in the entry
threshold ratio may be due to the fact that fixed costs increase
significantly with the entry of the second firm, but less and less with
the entry of additional firms. By incorporating data on per capita
market demand ([d.sub.N]), the AGV methodology allows us to decompose
the entry threshold ratios into a quantity effect
([d.sub.N+1]/[d.sub.N]), or the competition effect, and the cost effect.
The total quantity of deposits in the market is equal to
[Q.sub.N] = [Sd.sub.N]. (4)
Following AGV, we utilize the following specifications:
S = exp(Y[lambda] + [[epsilon].sub.s]) (5)
[d.sub.N] = exp(X[[delta].sub.x] + W[[delta].sub.w] +
[[delta].sub.N] + [[epsilon].sub.d]) (6)
[V.sub.N] = exp(X[[alpha].sub.x] + W[[alpha].sub.w] +
[[alpha].sub.N] + [[epsilon].sub.v]) (7)
[F.sub.N] = exp(W[[gamma].sub.w] + [[gamma].sub.N] +
[[epsilon].sub.w]). (8)
In these equations the parameters [[delta].sub.N], [[alpha].sub.N],
and [[gamma].sub.N] are coefficients on dummy variables for the market
structure, or the number of banks in the market. They capture the
differences in per capita quantity, average variable profit margins, and
fixed costs between markets with one firm and markets with N firms.
Substituting Equations 5-8 into Equation 2 and taking logs, we find
that the Nth firm will enter when
Y[lambda] + X([[delta].sub.x] + [[alpha].sub.x]) +
W([[delta].sub.w] + [[alpha].sub.w] - [[gamma].sub.w]) + [[delta].sub.N]
+ [[alpha].sub.N] - [[gamma].sub.N] - ln N + [[epsilon].sub.s] +
[[epsilon].sub.d] + [[epsilon].sub.v] - [[epsilon].sub.F] > 0. (9)
Denote [[mu].sub.x] = [[delta].sub.x] + [[alpha].sub.x],
[[mu].sub.w] = [[delta].sub.w] + [[alpha].sub.w] - [[gamma].sub.w], and
[[mu].sub.N] = [[gamma].sub.N] - [[alpha].sub.N] + ln (N) -
[[delta].sub.N]. Furthermore, allow [[epsilon].sub.[pi]] to equal the
sum of the error terms in Equation 9. Because the number of firms will
be the max {N: [[PI].sub.n] > 0}, we can rewrite the empirical model
as (6)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (10)
If [[epsilon].sub.[pi]] is normally distributed, then Equation 10
can be estimated as a standard ordered probit.
The quantity equation is obtained by substituting Equations 5 and 6
into Equation 4 and taking logs:
ln [Q.sub.N] = Y[lambda] + X[[delta].sub.x] + W[[delta].sub.W] +
[[delta].sub.N] + [[epsilon].sub.Q], (11)
where [[epsilon].sub.Q] = [[epsilon].sub.s] + [[epsilon].sub.d] +
[epsilon], and [epsilon] captures measurement error.
Identification and Empirical Methodology
Although our primary variables of interest, the market structure
dummy variables [[delta].sub.N], could be estimated from Equation 11,
these dummies are endogenous. Markets with high unobserved components of
demand and market size ([[epsilon].sub.s] and [[epsilon].sub.d]) will
have both a higher value of market demand and a greater number of firms
in the market (via the entry equation). To account for this endogeneity,
we jointly estimate Equations 10 and 11. As explained in AGV, the
empirical model is equivalent to a selection model in which the entry
Equation l0 selects which market structure dummy we will be estimating.
The parameters of the selection model are identified by excluding the
determinants of fixed costs from the demand equation. Specifically, we
exclude the physical size of the market and a measure of the liberalness
of the state-level regulatory climate (as of 1994), both of which we
expect to affect fixed costs of entry but not variable profits or
demand. (7)
Joint estimation of the quantity and entry equation allows for
separate identification of the impact of the explanatory variables and
market structure on per capita demand ([[delta].sub.w], [[delta].sub.x],
[[delta].sub.N]) from variable profits and fixed costs ([[alpha].sub.x],
[[alpha].sub.w] - [[gamma].sub.w], [[alpha].sub.N] - [[gamma].sub.N]).
As noted above, the fact that we can identify the effect of entry on the
per capita quantity demand ([[delta].sub.N]) allows us to identify the
competitive effects of entry on the market.
The errors in the ordered probit and quantity equations are highly
correlated, as they have two terms in common, [[epsilon].sub.s] and
[[epsilon].sub.d]. Therefore, we assume a variance components model in
which
[[epsilon].sub.[pi]] = [v.sub.[pi]] + [rho][eta] (12)
[[epsilon].sub.Q] = [v.sub.Q] + [eta]. (13)
We assume that [v.sub.[pi]] and [v.sub.Q] are independently and
normally distributed with means of zero and standard deviations of
[[sigma].sub.[pi]] and [[sigma].sub.Q], respectively. Furthermore, we
assume that [eta] is independent of both [v.sub.[pi]] and [V.sub.Q] and
is normally distributed with a mean of zero and a standard deviation of
[[sigma].sub.[eta]]. (8) If the parameter [rho] is positive, then the
two errors are positively correlated. Joint estimation of Equations 10
and 11 allows us to separately identify the variance of the entry
equation error, [[sigma].sub.[pi]], which is typically normalized to one
in ordered probit regressions. (9)
The model is estimated using maximum likelihood. We choose to use
Gaussian quadrature techniques to integrate the likelihood function over
the distribution of [eta]. (10) Haan and Uhlendorff (2006) find in their
analysis that numerical integration of the likelihood function using
Gaussian quadrature results in virtually the same parameter estimates as
maximum simulated likelihood based on Halton sequences, but with more
stable results.
4. Data
The data sources used are the Federal Deposit Insurance
Corporation's Summary of Deposits Data and the Federal Reserve
System's National Information System, along with census population,
land area and retail sales estimates, and Bureau of Economic Analysis
personal income and wage estimates. Table 1 presents some descriptive
statistics on the sample of 278 nonmetropolitan Bureau of Labor
Statistics LMAs for 1994 and 2004. (11) The sample was constructed as
all LMAs (which are generally individual counties, but sometimes
combinations of counties) that were at least one market away from an MSA
and not adjacent to another in the sample. (12)
The choice of rural markets somewhat isolated from metropolitan
areas (and from each other) was designed, as discussed in Bresnahan and
Reiss (1991), to allow for more accurate measurement of market entry.
(13) The choice of the two time periods, 1994 and 2004, allows us to
examine the implications for competitive behavior in local banking
markets of the surge in bank branching activity occurring after the
passage of the Riegle-Neal Act in 1994.
Many of the markets are quite small, with an average population in
1994 of 18,208 (ranging in size from 610 to 137,710). The mean number of
banking institutions per market was 4.7 in 1994 (rising slightly to 4.9
by 2004), varying between 0 and 19; (14) while certainly distinctions
remain, as noted above we consider both banks and thrifts as
"banking institutions" and do not (as do Cohen and Mazzeo
[2007a]) address the issue of how closely competitive they are. (15) We
do, however, consider credit unions as a competitive threat to both
banks and thrifts, especially in small rural markets (and include a
credit union variable as a demand shifter).
The average population per bank/thrift is less than 4000. The data
suggest surprisingly low thresholds for multiple banks and thrifts;
seven of the eight markets with mean populations of 1500 or less over
the 1994-2004 period and 13 of the 18 markets with populations under
2300 had monopoly banks or thrifts in both years. In contrast, no
markets averaging over 7250 in population had monopoly banks. At the
other end of the spectrum are four relatively large markets which may be
outliers in the sample: two in Hawaii, one in South Carolina, and one in
California--all with at least 115,000 in population both sample years,
while the next largest is more than 20,000 smaller. However, results are
not sensitive to the inclusion of these very large rural markets.
In order to implement the AGV methodology, a measure of output is
needed; we choose bank/thrift deposits as this variable. On one hand,
this may be viewed as an input into (part of) what banks are
selling--loans--while, on the other hand, this may not seem a bad proxy,
to the extent that we view the output of banks as a bundle of services
(one of which is providing a depository role). (16)
5. Econometric Results and Interpretation
As noted earlier, we consider two time periods in our analysis: (i)
1994, when state-level regulation was still likely to be a major
determinant of entry patterns and potential competition from entry was
likely to be less significant, and (ii) 2004, when--a decade past the
Riegle-Neal Act--bank branching and entry were virtually unregulated and
one might expect to see more competition resulting in local markets.
(17)
As listed in Table 1, we include a number of potential demand
shifters in the model, including income per capita, retail activity
(retail sales per capita), and the presence of competition from local
credit unions. (18) We include the average wage in the market as a
potential cost shifter. We expect fixed costs to increase with the
physical size of the market (land area). Intuitively, the cost of
serving the market may increase with the physical size as banks are
forced to invest in more branches. As noted above, the final explanatory
variable we include is a measure of the regulatory environment of the
state, which we view as a proxy for fixed costs of entry that should not
affect quantity demanded or variable profits. Results from the maximum
likelihood estimation of the model are included in Table 2.
As expected, the parameter estimates associated with market
population are highly significant and positive. The coefficients
indicate that a 1% increase in market population increased the quantity
of deposits in the market by approximately 0.5% in 1994 and nearly 0.7%
in 2004. The remaining parameter estimates associated with Equation 11
are listed in Table 2 in the per capita quantity ([delta]) section. The
single variable cost shifter included in the model, average wage, has
the expected negative impact on per capita quantity in both years, with
a 1% increase in the average wage raising prices and, thus, decreasing
per capita quantity by 0.1% in 1994 and 0.3% in 2004. Two of the primary
demand shifters, income and retail sales per capita, have significant
positive impact on per capita demand in both years. As one might expect,
as income levels and retail activity in a market increase, so do the per
capita quantity of bank deposits. (19)
Only some of the coefficient estimates associated with variable
profits are significant, in part reflecting the positive correlation
between per capita personal income and per capita retail sales. Variable
profits increase with the income per capita of the market in both years.
The negative coefficient on retail sales per capita in 1994 (while
surprising) is far smaller than the anticipated positive coefficient on
per capita income. Estimates confirm that costs increase with the
average wage in the market. The variable measuring the state regulatory
climate is positive and significant in the 1994 subsample, suggesting
that those markets with more liberal regulatory mechanisms (as of 1994)
have higher fixed costs. (20) Parameter estimates suggest that fixed
costs increase with the physical size of the market in the 2004
subsample, perhaps reflecting the increase in branch banking in the 2004
sample.
Estimates of the standard errors of the model's errors are
fairly stable over the two subperiods. Recall that the parameter P
represents the degree of correlation between the error in the entry
equation and the error in the quantity equation. Given the error
structure of the model, one might also think of this variable as the
degree of correlation between the unobserved factors influencing demand
and those unobserved factors influencing the firm's costs. The
estimate for p is negative in the 1994 subsample but positive in the
2004 subsample. While we had no a priori belief regarding the direction
of the correlation prior to estimating, it is slightly surprising that
the direction of the correlation should change over the 10-year period.
This may reflect changes in the importance of omitted variables that we
do not observe.
Tables 3 and 4 analyze the market structure dummies by calculating
entry threshold ratios and the per firm population thresholds,
respectively. The threshold ratios from the 1994 subsample suggest that
the third firm requires about 48% more per firm population than the
second to be profitable, and the fourth firm requires a 53% increase in
per firm population when compared to the third. The 5/4 and 6/5
thresholds continue to decrease and reach closer to one, suggesting that
the market is becoming more competitive.
If one assumes that fixed costs are constant in the number of firms
in the market, the reduction in the threshold ratio suggests that
competition is pushing prices lower and lower, with the market reaching
closer to a competitive equilibrium. However, banks (in markets at mean
values of all explanatory variables) continue to have market power at
least through the entry of the seventh bank.
The threshold ratios from 2004 suggest a similar pattern. The third
bank requires 54% more per firm population when compared to the second,
and the fourth bank requires 62% more per firm population than the
third. The threshold ratios decline through entry of the sixth bank
prior to increasing slightly with entry of the seventh bank in the
market.
The benefit of the AGV method is that we do not have to assume that
fixed costs are constant in the number of firms that enter the market,
thus providing a more accurate depiction of the level of competition in
the marketplace. Note that the decreasing thresholds found in 1994 and
2004 could be occurring even if there are no changes in the competitive
conditions as firms enter the market if the fixed costs increase with
the number of banks in the market. Similarly, an increase in the ratio
with the entry of the seventh bank that we found in both years could be
due to interactions between the rate at which fixed costs increase and
the rate at which markets reach a competitive equilibrium.
Tables 5 and 6 decompose the threshold ratio into the per capita
demand effect and the variable profit/fixed cost effect for 1994 and
2004, respectively. In this decomposition, we expect the per capita
demand effect to initially be some fraction below one. Intuitively, the
entrance of new firms causes the market to become more competitive. As
prices fall, per capita demand will increase, thus the ratio
[d.sub.N]/[d.sub.N] + 1 will be less than one. This ratio should,
however, gradually increase and stabilize at one as the marginal
increase in the level of competition with each additional entrant will
fall until the market eventually becomes completely competitive. Tables
5 and 6 include p-values associated with the null hypotheses that (i)
the per capita quantity contribution to the threshold ratio remains
unchanged with entrance of a new firm and (ii) this component of the
threshold ratio is equal to one, or the per capita demand remains
unchanged with entry of the new firm, suggesting that the market has
become competitive. Note that the overall threshold effect is the
product of the per capita quantity effect and the average profit effect.
These results indicate that in 1994 the second firm requires a per
firm market size only 70% as large as the first firm. In other words,
per capita demand increases by approximately 30% with the entry of the
second firm. Per capita demand increases by an additional 21% and 24%
with the entrance of the third firm and fourth firm, respectively; as
indicated in Table 5, hypothesis tests indicate per capita demand (or
the level of competition) increases by the same amount with the entrance
of the fourth firm as it did with the entrance of the third firm
(failing to reject this equal effect with a p-value of 0.08). Entrance
of a fifth firm results in no statistically significant change in per
capita demand (with a p-value of 0.51), suggesting that the market has
become competitive by this time. This result is consistent with the
findings in Cetorelli (2002), who finds in his analysis of banking
markets in 1999 that significant market power is suggested at least
until the number of banks in a county reaches five. Strangely, the
thresholds for entrance of the sixth and seventh firms suggest that per
capita demand increases again, by 15% and 22%, respectively, as the
number of firms in the market grows, which makes a clear prediction on
competitive conditions from these results more difficult.
The threshold estimates for 2004 behave in a more predictable
manner, with one exception. For example, the estimates suggest that per
capita demand increases by 36% with the entrance of the second firm.
However, there is no statistically discernable change in per capita
demand after the entrance of the third firm, suggesting that the market
has become competitive by this point. (21) This result is consistent
with the findings in Cohen and Mazzeo (2007a), who estimate that
variable profits are significantly reduced by the second firm of a given
type and this reduction becomes smaller for subsequent entry. The
exception to this clear pattern in our estimates is the entry threshold
for the fifth firm, which indicates that per capita demand increases by
33% with the fifth firm.
It is likely that this is a statistical anomaly, but it also points
to possible weaknesses in our empirical approaches. As noted above,
deposits may not be the most appropriate measure of demand for banking
services. Ideally, one might want a quantity measure that more directly
determines usage, such as number of bank accounts held in the market or
number of withdrawals or deposits. Unfortunately, these data are not
publicly available, and the alternative measures of quantity that we
tried, such as the number of bank branches in the county, produced
results qualitatively similar to those presented here.
Nevertheless, the results are consistent with the view that local
banking markets have become more competitive in the era of bank
deregulation. While markets needed, at the very least, five firms to
reach competitive conditions in 1994, our estimates suggest that by 2004
markets with as few as three firms could be considered highly
competitive.
6. Conclusion
Other work has examined determinants of entry in local banking
markets. In this article we apply to this sector a promising new
extension to the Bresnahan and Reiss (1991) framework. Examining rural
markets in both 1994 and 2004, we find in the earlier period demand
effects of entry consistent with modest reductions in price, suggesting
increasing competition, up until the entry of the fifth firm. In
contrast, three-firm markets seem relatively competitive in 2004.
While our results are not as clear-cut as we would have liked, they
are suggestive of greater competition in banking markets
post-Riegle-Neal. Whether this increase in competition is in fact due to
the greater threat of entry associated with the Riegle-Neal Act, the
rise of Internet banking, or other changes affecting the banking sector
is a topic for another day.
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Robert M. Feinberg * and Kara M. Reynolds([dagger])
* Department of Economics, American University, Washington, DC
20016-8029, USA; E-mail
[email protected]; corresponding author.
([dagger]) Department of Economics, American University,
Washington, DC 20016-8029, USA; E-mail
[email protected].
We thank John Pepper and several anonymous referees for helpful
comments on earlier drafts of this article, though all errors and
omissions remain those of the authors. Received May 2008; accepted
January 2009. 36:680-99.
(1) A similar result is found in a nonbanking context by Toivanen
and Waterson (2005), who explain patterns of fast food entry in the
United Kingdom by market structure and find that the presence of a major
rival increases entry (this presence is viewed as a proxy for future
growth and a means of learning by the potential entrant).
(2) Strictly speaking, while Bresnahan and Reiss (1991) and the
literature following typically use the term "entry" to
describe the topic of analysis, what is really at issue is endogeneity
in market structure.
(3) Adams and Amel (2007) present further results on bank entry,
also finding past entry to induce future entry, and provide a nice
review of the previous bank entry literature.
(4) A somewhat similar approach was adopted by Asplund and Sandin
(1999) in a study of local competition among Swedish driving schools.
(5) Generally, in the presence of product differentiation, entry
threshold ratios are less informative about the degree of competition in
the market. However, for routine financial services that consumers
generally need from local banks (deposits, checking, ATM access, small
loans), the assumption of homogeneity seems plausible.
(6) As is typical in the literature following the BR approach, we
create a residual category of markets; we choose this to be markets with
seven or more banks. While the exact cutoff is arbitrary, our main
results are not very sensitive to this choice.
(7) The state regulatory measure is set equal to 1 if the state
(based on appendix table B6 in Berger, Kashyap, and Scalise [1995])
allowed all of the following: limited branching, statewide branching,
limited multibank holding companies, statewide multibank holding
companies, and interstate multibank holding companies.
(8) As discussed in Mroz (1999), imposing a normal distribution can
result in bias if [eta] is not normally distributed. To avoid this bias,
we experimented with using a nonparametric distribution, specifically a
discrete factor approximation. Most of the specifications using discrete
factor approximations failed to converge, which we believe can be
attributed to the fact that the parameters of the discrete factor
approximation are underidentified if the true distribution of the error
is normal, as also noted in Mroz (1999).
(9) The variance of the entry equation error is identified by
constraining the parameter on market population size, [lambda], to be
equal across the two equations.
(10) The parameter values presented in this article were estimated
using six points of support.
(11) The sample of LMAs is available from the authors upon request.
(12) Specifications in which we exclude the 10 Bureau of Labor
Statistics LMAs that incorporate more than one county were similar to
those presented here. Thus, our results are robust to whether we define
markets using rural labor market areas or rural counties.
(13) Due to this relative isolation from nearby markets, we ignore
market characteristics in neighboring regions. For work noting the
impact of distance on lending decisions, see Degryse and Ongena (2005)
and Agarwal and Hauswald (2007).
(14) In 1994, there is 1 market with no banks; 20 with one bank; 32
with two; 53 with three; 52 with four; 31 with five; 34 with six; 17
with seven; 11 with eight; 12 with nine; and 15 with 10 or more banks.
(15) For a nice, concise discussion of similarities (and some
differences) between banks and thrifts, see
http://www.frbsf.org/econrsrch/wklyltr/wklyltr98/el98-13.html.
(16) AGV use hospital admissions as their measure of quantity. As
with local banks, hospitals offer a bundle of services, and total
admissions was taken to be a reasonable proxy for the quantity of the
service provided. In specifications not presented here, we utilized the
number of branches in the county as an alternative definition of
quantity. Most of the parameter estimates were qualitatively the same as
those presented here, as was the analysis of market competition.
(17) We do not, however, claim that differences observed between
1994 and 2004 are due to the change in regulatory policy incorporated in
that legislation.
(18) Recent evidence on the role of credit unions in local
financial services markets is somewhat mixed. Amel and Hannan (1999)
find commercial banks alone to constitute a relevant "antitrust
market," while Feinberg (2002) supports the view of credit unions
as fringe suppliers in a broader local consumer financial services
market.
(19) The counterintuitive positive effect of credit union presence
in 1994 may reflect an endogeneity between local banking demand growth
and credit union entry.
(20) While somewhat counterintuitive, one possible explanation
could be greater costs of cross-state multibank entry versus the
within-state or new small bank entry typical in more restrictive states.
(21) The hypothesis tests fail to reject the null hypothesis that
per capita demand does not change with the entrance of the fourth firm
or that the per capita quantity ratio [d.sub.3]/[d.sub.4] is different
than one, with a p-value of 0.34. Given that the hypothesis tests also
fail to reject the hypothesis that the per capita quantity ratio changes
with the entrance of the fourth firm, in other words that
[d.sub.2]/[d.sub.3] is different than [d.sub.3]/[d.sub.4], with a
p-value of 0.07, it seems reasonable to infer that there is some
statistical evidence to suggest that the market has become competitive
by the entrance of the third firm.
Table 1. Descriptive Statistics (n = 278)
Mean Min Max
1994
Number of banks 4.719 0.000 19.000
Deposits ($millions) 189.493 0.000 1186.000
Population (thousands) 18.208 0.610 137.710
Credit union presence 0.356 0.000 1.000
Average wage (thousands) 17.907 12.279 29.256
Income per capita (thousands) 16.594 8.576 32.523
Retail sales per capita
(thousands) 4.963 1.139 11.576
2004
Number of banks 4.942 0.000 21.000
Deposits ($millions) 260.982 0.000 2468.000
Population (thousands) 19.021 0.685 162.970
Credit union presence 0.435 0.000 1.000
Average wage (thousands) 25.088 17.355 44.318
Income per capita (thousands) 24.161 12.674 51.125
Retail sales per capita
(thousands) 7.627 1.466 21.845
Land area (thousand square miles) 1.248 0.167 11.206
State regulatory measure 0.309 0.000 1.000
Table 2. Maximum Likelihood Parameter Estimates
1994
Standard
Parameter Estimate Error
Market size ([lambda])
Market population 0.5087 ** 0.0073
Per capita quantity ([delta])
Constant 2.7428 ** 0.1660
Average wage -0.1112 ** 0.0430
Income per capita 0.2754 ** 0.0256
Retail sales per capita 0.4540 ** 0.0105
Credit union presence 0.1184 ** 0.0098
[[delta].sub.2] 0.3500 ** 0.0152
[[delta].sub.3] 0.5852 ** 0.0151
[[delta].sub.4] 0.8592 ** 0.0168
[[delta].sub.5] 0.8506 ** 0.0179
[[delta].sub.6] 1.0078 ** 0.0193
[[delta].sub.7] 1.2520 ** 0.0258
Variable profits: demand shifters ([[alpha].sub.x])
Credit union presence -0.1426 ** 0.0622
Income per capita 1.3396 ** 0.2346
Retail sales per capita -0.4760 ** 0.0813
Variable profits: cost shifters ([[gamma].sub.w] -
[[alpha].sub.w])
Constant 7.6270 ** 2.9268
Average wage 1.0594 ** 0.2391
Fixed costs ([[gamma].sub.w])
State regulatory measure 0.1533 ** 0.0616
Land area -0.0026 0.036
Entry effects ([[gamma].sub.n] - [[alpha].sub.n])
[[gamma].sub.2] - [[alpha].sub.2] 1.2239 ** 0.3667
[[gamma].sub.3] - [[alpha].sub.3] 1.4632 ** 0.3797
[[gamma].sub.4] - [[alpha].sub.4] 1.8318 ** 0.3975
[[gamma].sub.5] - [[alpha].sub.5] 1.9092 ** 0.4124
[[gamma].sub.6] - [[alpha].sub.6] 2.0798 ** 0.4229
[[gamma].sub.7] - [[alpha].sub.7] 2.4291 ** 0.4404
Standard errors and correlations
[[sigma].sub.vQ] 0.0446 ** 0.0014
[[sigma].sub.v[pi]] 0.3960 ** 0.0336
[[sigma].sub.[eta]] 0.2166 ** 0.0027
[rho] -1.0712 ** 0.2591
2004
Standard
Parameter Estimate Error
Market size ([lambda])
Market population 0.6860 ** 0.0070
Per capita quantity ([delta])
Constant 3.2067 ** 0.1702
Average wage -0.2738 ** 0.0383
Income per capita 0.5166 ** 0.0299
Retail sales per capita 0.2760 ** 0.0109
Credit union presence 0.0175 0.0109
[[delta].sub.2] 0.4458 ** 0.0188
[[delta].sub.3] 0.4067 ** 0.0217
[[delta].sub.4] 0.4237 ** 0.0218
[[delta].sub.5] 0.8183 ** 0.0246
[[delta].sub.6] 0.7575 ** 0.0341
[[delta].sub.7] 0.7481 ** 0.0253
Variable profits: demand shifters ([[alpha].sub.x])
Credit union presence -0.0169 0.0686
Income per capita 0.9201 ** 0.2075
Retail sales per capita 0.0782 0.0930
Variable profits: cost shifters ([[gamma].sub.w] -
[[alpha].sub.w])
Constant 4.5247 * 2.6022
Average wage 0.7118 ** 0.2453
Fixed costs ([[gamma].sub.w])
State regulatory measure 0.1346 0.0683
Land area 0.0344 ** 0.0422
Entry effects ([[gamma].sub.n] - [[alpha].sub.n])
[[gamma].sub.2] - [[alpha].sub.2] 1.4236 ** 0.3700
[[gamma].sub.3] - [[alpha].sub.3] 1.4673 ** 0.3684
[[gamma].sub.4] - [[alpha].sub.4] 1.6661 ** 0.3706
[[gamma].sub.5] - [[alpha].sub.5] 2.2372 ** 0.3745
[[gamma].sub.6] - [[alpha].sub.6] 2.2616 ** 0.3792
[[gamma].sub.7] - [[alpha].sub.7] 2.4106 ** 0.3849
Standard errors and correlations
[[sigma].sub.vQ] 0.0528 ** 0.0017
[[sigma].sub.v[pi]] 0.4567 ** 0.0362
[[sigma].sub.[eta]] 0.2600 ** 0.0038
[rho] 0.3135 ** 0.2384
**, * indicate those parameters significant at the 5%
and 10% level, respectively.
Table 3. Threshold Ratios
1994 2004
Standard Standard
Ratio Estimate Error Estimate Error
[S.sub.2]/[S.sub.1] 7.839 ** 3.955 6.976 * 3.734
[S.sub.3]/[S.sub.2] 1.487 ** O.152 1.545 ** O.180
[S.sub.4]/[S.sub.3] 1.534 ** O.114 1.624 ** O.138
[S.sub.5]/[S.sub.4] 1.421 ** 0.087 1.533 ** 0.108
[S.sub.6]/[S.sub.5] 1.217 ** 0.063 1.302 ** 0.079
[S.sub.7]/[S.sub.6] 1.371 ** 0.089 1.415 ** 0.098
**, * indicate those parameters significant at the 5%
and 10% level, respectively.
Table 4. Per Firm Population Thresholds Threshold Ratios
Number of Banks 1994 Threshold 2004 Threshold
1 204 173
2 1243 948
3 1591 1273
4 2194 1873
5 2872 2658
6 3269 3251
7+ 4235 4363
Table 5. Threshold Ratios' Decomposition (1994)
Component 2/1 3/2 4/3
Overall ([S.sub.N + 1]/[S.sub.N]) 7.839 1.487 1.534
Fixed cost and profit effect 11.124 1.881 2.017
Per capita quantity effect
([d.sub.N]/[d.sub.N + 1]) 0.705 0.790 0.760
p-value ([H.sub.0]: [d.sub.N]/
[d.sub.N + 1] = [d.sub.N + 1]/
[d.sub.N + 2]) 0.000 0.075
p-value ([H.sub.0]:
[d.sub.N]/[d.sub.N + 1] = 1) 0.000 0.000
Component 5/4 6/5 7+/6
Overall ([S.sub.N + 1]/[S.sub.N]) 1.421 1.217 1.371
Fixed cost and profit effect 1.409 1.424 1.750
Per capita quantity effect
([d.sub.N]/[d.sub.N + 1]) 1.009 0.855 0.783
p-value ([H.sub.0]: [d.sub.N]/
[d.sub.N + 1] = [d.sub.N + 1]/
[d.sub.N + 2]) 0.000 0.000 0.002
p-value ([H.sub.0]:
[d.sub.N]/[d.sub.N + 1] = 1) 0.506 0.000 0.000
Table 6. Threshold Ratios' Decomposition (2004)
Component 2/1 3/2 4/3
Overall ([S.sub.N + 1]/[S.sub.N]) 1.424 1.467 1.666
Fixed cost and profit effect 2.223 1.411 1.695
Per capita quantity effect
([d.sub.N]/[d.sub.N + 1]) 0.640 1.040 0.983
p-value ([H.sub.0]: [d.sub.N]/
[d.sub.N + 1] = [d.sub.N + 1]/
[[d.sub.N + 2]) 0.000 0.068
p-value ([H.sub.0]: [d.sub.N]/
[d.sub.N + 1] = 1) 0.031 0.336
Component 5/4 6/5 7+/6
Overall ([S.sub.N + 1]/[S.sub.N]) 2.237 2.262 2.411
Fixed cost and profit effect 3.319 2.128 2.388
Per capita quantity effect
([d.sub.N]/[d.sub.N + 1]) 0.674 1.063 1.010
p-value ([H.sub.0]: [d.sub.N]/
[d.sub.N + 1] = [d.sub.N + 1]/
[[d.sub.N + 2]) 0.000 0.000 0.305
p-value ([H.sub.0]: [d.sub.N]/
[d.sub.N + 1] = 1) 0.000 0.036 0.701
