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Working Paper Series
Internet Banking: An Exploration in
Technology Diffusion and Impact
WP 13-10R
Richard Sullivan
Federal Reserve Bank of Kansas City
Zhu Wang
Federal Reserve Bank of Richmond
This paper can be downloaded without charge from:
http://www.richmondfed.org/publications/
Internet Banking: An Exploration in Technology
Diffusion and Impact∗
Richard Sullivan†, Zhu Wang‡
August 2014
Working Paper No. 13-10R
Abstract
Taking Internet banking as an example, we study diffusion and impact of costsaving technological innovations. Our theory characterizes the process through
which such an innovation is adopted sequentially by large and small firms, and
how the adoption affects firm size distribution. Applying the theory to an empirical
study of Internet banking diffusion among banks across 50 U.S. states, we examine
the technological, economic and institutional factors governing the process. The
empirical findings allow us to disentangle the interrelationship between Internet
banking adoption and change in average bank size, and explain the variation in
diffusion rates across geographic regions.
JEL classification: G20; L10; O30
Keywords: Technology diffusion; Firm size distribution; Internet banking
∗
We thank Dean Amel, Ernst Berndt, Sean Chu, Robert DeYoung, Mark Doms, Boyan Jovanovic and
participants at the NBER Summer Institute Productivity Potpourri Meeting, Federal Reserve System
Applied Microeconomics Conference, Federal Reserve System Financial Structure and Regulation Meeting, and various seminars for helpful comments. Nathan Halmrast, Christian Hung and Emily Cuddy
provided valuable research assistance. The views expressed herein are solely those of the authors and do
not necessarily reflect the views of the Federal Reserve Bank of Kansas City, Federal Reserve Bank of
Richmond, or the Federal Reserve System.
†
Federal Reserve Bank of Kansas City; rick.j.sullivan@kc.frb.org.
‡
Federal Reserve Bank of Richmond; zhu.wang@rich.frb.org.
1
Introduction
Technology diffusion is a complex process through which potentialities of technological
innovations are turned into productivity. The economic environment where the diffusion
takes place affects the pace of diffusion, and the diffusion itself may also have feedback
on the environment. To better understand this process, researchers are interested in a
series of important questions: For example, which types of firms tend to be early adopters
of technological innovations, what factors determine the different diffusion rates across
heterogenous adopter groups or geographic regions, and what impact the diffusion may
have on the market and firm performance.
In this paper, we address these questions using a recent innovation, Internet banking,
as a concrete example. Internet banking is defined as a bank providing a website that
allows customers to execute transactions on their accounts. In the United States, the
history of Internet banking can be traced back to 1995 when Wells Fargo first allowed
its customers to access account balances online.1 Ever since then, banks have steadily
increased their online presence. Figure 1 plots the adoption of Internet banking for instate banks between 2003-2007.2 In-state banks refer to commercial banks focusing on
operating in a single state, which accounted for more than 90 percent of the U.S. banking
population during this period.3 The figure shows that 51.8 percent of in-state banks
adopted Internet banking in 2003, and the ratio rose to 81.5 percent in 2007.4
1
Internet-only banks account for a very small fraction of the U.S. banking population (less than 0.5
percent even during the dot-com boom years). In this paper, we will focus on the Internet banking
adoption among traditional brick-and-mortar banks. See Wang (2007) and DeYoung (2005) for studies
on Internet-only banks.
2
Data Source: Call Report. Since 2003, depository institutions have been required to report whether
their websites allow customers to execute transactions on their accounts. Our sample ends in 2007 because
the adoption had become almost universal by then and we also want to avoid the disruption of the Great
Recession.
3
More specifically, a bank is classified as an in-state bank if all its deposits are in the state of the bank’
headquarter. As will become clear, focusing on in-state banks allows us to avoid the complications of
interstate banking when comparing Internet banking adoption and bank size distributions across states.
In 2003, there were 7,712 commercial banks in the United States, among which 7,183 were in-state banks
(i.e., 93 percent).
4
A similar diffusion pattern can be found if we instead consider all U.S. commercial banks. In 2003,
53 percent of all commercial banks adopted transactional websites, and the ratio rose to 82 percent in
2007. In the meantime, the number of U.S. households that were using Internet banking rose from 30
million in 2003 to 45 million in 2007 (Source: Online Banking Report #224, January 2014).
2
Adoption Rate
Deposits ($ Millions)
300
100%
250
80%
200
60%
150
40%
100
20%
50
0
0%
2003
2004
2005
Internet Banking
2006
2007
Average Bank Size
Figure 1: Internet Banking Adoption and Average Bank Size
There is also substantial heterogeneity of the adoption pattern. Looking across size
groups, large banks appear to have an advantage adopting the innovation than small
ones. As shown in Figure 2, 90.5 percent of in-state banks with deposits over $300 million
reported that they had a transactional website in 2003, compared to only 10.5 percent
of in-state banks with deposits under $25 million. The adoption of Internet banking also
varies significantly across geographic regions. Figure 3 compares Internet banking adoption by in-state banks across U.S. states in 2003. The northeast and the west regions
had the highest adoption rates, while the central regions of the country had the lowest.
These observations point to the important questions: Why do large banks tend to be
early adopters of the Internet innovation? What determines the different diffusion rates
across banking groups and geographic regions?
Meanwhile, the diffusion of Internet banking has taken place in a continuously changing environment. Since the early 1990s, the U.S. banking industry had been through
a major deregulation and consolidation (Janicki and Prescott, 2006).5 As a result, the
5
According to FDIC Quarterly Banking Profile Graph Book, there were about 100 interstate bank
mergers and 200 intrastate bank mergers per year between 2003 and 2007.
3
Adoption rate
100%
80%
60%
40%
20%
0%
2003
2004
< $25
2005
$25‐$100
2006
$100‐$300
2007
> $300
Figure 2: Internet Banking Adoption by Bank Size (Deposits: Millions)
number of commercial banks dropped substantially while the bank size distribution also
shifted (Figure 1 plots the average deposits of in-state banks between 2003-2007). This
suggests further interesting questions: Considering that bank size is an important factor for adopting Internet banking, how much has banking deregulation affected Internet
banking adoption? At the same time, how much, if any, has Internet banking adoption
influenced the bank size distribution?
Motivated by the aforementioned observations and questions, we study the endogenous
diffusion and impact of Internet banking in this paper. The benefits of Internet banking
are twofold. On the one hand, it brings convenience to bank customers, allowing them to
use services from banks in distance and avoid hassles to go to ATMs or branches. On the
other hand, it generates substantial cost savings to banks. Most banking websites provide
balance transfer and bill payments services, and some even process online applications
for deposits, loans and credit cards.6 This allows banks to conduct standardized, low6
For instance, a survey conducted by the Federal Reserve Bank of Kansas City shows that in the tenth
Federal Reserve District, more than 70 percent commercial bank websites provided balance transfer and
bill payment services, and less than 20 percent allowed for online application for deposits, loans or credit
cards in 2006.
4
Figure 3: Internet Banking Adoption by State (2003)
value-added transactions through the online channel, while focusing their resources on
more specialized, high-value-added transactions (e.g., business lending, personal trust
services, investment banking) through branches. In fact, the ratio of bank employees
(and bank tellers) to deposits have been declining since the late 1990s.7 This is consistent
with continuous progress in IT technology, including the increasing adoption of Internet
banking.
In our following analysis, we first construct a theory that models banks’ cost savings
of adopting Internet banking. We consider a competitive banking industry, where banks’
sizes are primarily determined by cost constraints (For simplicity, we abstract from consumers’ convenience benefits of using Internet banking as well as banks’ strategic motives
of adoption, which will later be incorporated in our empirical analysis).8 The theory sug7
Between 1997 and 2007, the number of bank employees per million-dollar deposits fell from 0.44 to
0.24, and the number of bank tellers per million-dollar deposits fell from 0.14 to 0.09. (Data sources:
Commercial bank employees and tellers are from the BLS, and commercial bank deposits are from the
FDIC).
8
Alternatively, we could model a differentiated banking market, where banks engage in strategic
competition on price and service levels. Such a model might be more realistic, but on the other hand
could be too complicated to explain the high-level patterns of Internet banking diffusion and impact.
5
gests that as Internet banking is initially introduced, large banks enjoy cost advantages in
becoming early adopters and gaining a further increase in size. Over time, due to environmental changes (e.g., demand shift, technological progress, and/or industry deregulation),
the innovation gradually diffuses into smaller banks. The model yields a closed-form solution and generates -shape logistic diffusion curves that are well documented in the
literature.
We then apply the theory to an empirical study of Internet banking adoption among
in-state banks across 50 U.S. states. Our theory highlights cost savings as a key determinant of Internet banking adoption, and provides a parsimonious regression framework
to evaluate the causal effects between Internet banking adoption and average bank size.
Particularly, the model implies estimating a simultaneous equation system, which jointly
determines Internet banking adoption rate and average bank size. We then augment this
equation system with empirical variables that control for technological, economic, and
institutional factors as well as consumers’ benefits of using Internet banking. Employing
instrument variables in our simultaneous-equation estimation, we are able to disentangle
the positive interactions between Internet banking adoption and change in average bank
size, and explain the variation in diffusion rates across U.S. geographic regions.
Our paper is related to a considerable literature that studies technology adoption. For
example, Karshenas and Stoneman (1993) summarize four important mechanisms affecting the adoption of new technology, namely rank, stock, order, and epidemic effects.9
Several recent studies have also looked at the Internet and related technology adoption in
the banking industry.10 However, few existing studies have explicitly considered the endogenous interactions between technology adoption and firm size distribution. This paper
is an attempt to fill the gap. Particularly, we revise the popular threshold diffusion model
9
Geroski (2000) provides a review of the theoretical models.
For example, Hernández-Murillo et al. (2010) study a panel of commercial banks for 2003-2006 and
show that banks adopt online banking earlier in markets where their competitors have already done
so. DeYoung et al. (2007) study a sample of U.S. banks in the late 1990s. They find that branching
intensity and online banking are complementary and online banking adoption positively affects the bank’s
future performance. Courchane et al. (2002) develop and estimate a model for early adoption of Internet
banking. They find that relative bank size and demographic information predictive of future demand
positively influence Internet banking adoption. Furst et al. (2001) estimate a logit model for Internet
banking adoption in a sample of national banks. They find that larger banks and banks that are younger
and better performing are more likely to adopt Internet banking.
10
6
to account for the interaction between technology adoption and firm size distribution,
and derive -shape logistic diffusion curves. The approach that we develop in this paper
goes beyond the Internet banking application and connects to broader research in industry dynamics (e.g., Jovanovic 1982, Hopenhayn 1992), firm size distribution (e.g., Lucas
1979, Sutton 1997, Cabral and Mata 2003), and technology diffusion (e.g., Griliches 1957,
David 1969, Comin and Hobijn 2004, 2010, Wang 2008, Manuelli and Seshadri 2014).
The paper is organized as follows. Section 2 presents a model of technology diffusion
in a competitive industry, which explores the interactions between technology adoption
and changing firm size distribution. Section 3 applies the theory to an empirical study on
Internet banking diffusion among in-state banks across 50 U.S. states. Section 4 concludes.
2
The model
In this section, we construct a theoretical model of technology diffusion. While the model
is in the context of Internet banking, its implication is general and applicable to costsaving innovations in other industries.
2.1
Environment
The industry is composed of a continuum of banks which produce homogenous banking
services. Banks behave competitively, taking the market price of banking services as
given. We assume banks are heterogenous in productivity, which yields size differences.
At a point in time , the market demand takes a simple inelastic form — consumers are
willing to pay for an amount of banking services. Over time, and might be
shifted by economic forces, such as changes in population, consumer income, or competing
services.11
11
Our following empirical study will focus on in-state banks, a subsample of the banking population.
Therefore, it is consistent and reasonable to assume that these (in-state) banks face exogenous and
, which are determined by the overall banking market conditions, including the competition from large
interstate banks. In fact, in the empirical study, we will include the out-of-state bank presence in the
state banking market as a regressor to control for the demand for the services of in-state banks.
7
2.2
Pre-innovation equilibrium
Before the technological innovation arrives, the industry is at a steady state. Taking
the market price as given, an individual bank maximizes its profit under the existing
technology:
= −
where is the profit, is the price, is the output, and 0 and 1 are cost
parameters.
Profit maximization yields
=(
1
−1
) .
(1)
Banks are heterogenous in the cost parameter , so there is a distribution of bank
size measured by output. Historically, bank size fits well with the log-logistic distribution
(See Figure 4 for an example)12 , which has the cdf function
Pr( ≤ ) = () = 1 −
1
1 + 1 2
(2)
with the mean () and Gini coefficient given as
−12
() = 1
Γ(1 +
1
1
)Γ(1 − )
2
2
where Γ denotes the gamma function Γ() ≡
R∞
0
=
1
2
−1 exp(−).
Rewriting the log-logistic distribution into a more intuitive form, we have
() = 1 −
1
1 + (())1
(3)
where = Γ(1 + )Γ(1 − )
12
Figure 4 uses deposits as a measure of bank size. We also used assets as an alternative measure of
bank size and the plot is very similar. The log-logistic distribution is an easily tractable representative
of the larger group of positively skewed distributions. As will become clear, it also connects our study to
the typically observed logistic diffusion curves.
8
Density
0.25
0.2
0.15
0.1
0.05
0
0
25
50
75
100
125
150
175
200
225
250
275
300
Bank Deposits ($ Millions)
Histogram
Log-logistic Distribution
Figure 4: Bank Size Distribution (In-State Banks 1990)
At equilibrium, industry demand equals supply, so that
() =
where is the number of banks.
Note that our assumption of log-logistic size distribution is robust to environmental
1
changes. For example, shocks to price , mean productivity ( 1− ), or demand may
affect the mean bank size () and/or the number of banks , but not other properties
of the distribution.13
2.3
2.3.1
Post-innovation equilibrium
Individual bank decision
The technological innovation, Internet banking, arrives at a point in time (which we
normalize as time 0). Thereafter, at each period, an individual bank decides whether to
13
1
1
Note that 1− decreases in for 1. Hence, 1− can be interpreted as a productivity measure.
9
adopt the innovation or not ( = adopt; = not adopt):
= { }
where = −
−
= −
Note that 1 is the cost saving by adopting the innovation, and 0 is the period
cost of adoption.14
Solving the maximization problems yields
1
−1
−1
)
;
, =
1
−1
−1
)
−
= (
, =
= (
An individual bank adopts Internet banking iff ≥ , and hence there is a threshold
size ∗ for adoption:
= =⇒ ∗ =
1
( −1
)( −1 − 1)
The size threshold for adoption suggests that large banks have an advantage adopting the innovation. Considering the randomness of environment in reality, this result is
expected to hold statistically in the data, as shown in Figure 2.
2.3.2
Aggregate adoption
Given the bank size distribution defined in Eq (3) and the adoption threshold ∗ , the
aggregate adoption rate of Internet banking is
= 1 − (∗ ) =
where
= (
1
1 + (∗ ( ))1
1
−1
) ,
∗ =
(4)
1
( −1
)( −1
− 1)
We then derive the following Proposition 1.
14
The period cost may include the rental cost of equipment and the cost of maintaining the website.
10
Proposition 1 The adoption rate rises with an increase in consumer willingness-to1
pay , mean bank productivity ( 1− ), and cost saving , but falls with an increase in
adoption cost .
1
Proof. Equation 4 implies that 0, ( 1− ) 0, 0 and
0.
2.3.3
Average bank size
Note that ( ) is not directly observable after Internet banking is introduced. The
observed average bank size is
() =
Z
∗
( ) +
Z
∞
( ) = ( ) + [
∗
0
1
−1
− 1]
Z
∞
( )
∗
Given that follows the log-logistic distribution , we have
Z
∞
∗
( ) = ( )[1 − (1 + 1 − ; (∗ ))]
where is the incomplete beta function defined as
Γ( + )
( ; ) ≡
Γ()Γ()
Z
0
−1 (1 − )−1 with 0 0 0
and
( ; 0) = 0
( ; 1) = 1
Therefore, the observed mean bank size () can be derived as
1
() = ( ){1 + [ −1 − 1][1 − (1 + 1 − ; 1 − )]}
(5)
Proposition 2 then follows.
Proposition 2 The mean bank size () rises with an increase in consumer willingness1
to-pay , mean bank productivity ( 1− ), and cost saving , but falls with an increase
in adoption cost .
11
Proof.
Given Proposition 1, Eq (5) implies that () 0, () 0,
1
()( 1− ) 0 and () 0.
2.4
Industry dynamics
Equations (4) and (5) describe the post-innovation industry equilibrium at a point in
time. Note that we have so far omitted time subscripts on all variables. To discuss the
industry dynamics, we now add them back and show that the diffusion path derived from
our model closely follows a logistic curve, a path well documented in the literature on
technology diffusion.
Consider a banking industry under continuous environmental changes (e.g., demand
shift, technological progress or industry deregulation). As a result, consumer willingness1
to-pay , mean bank productivity (1− ), Internet banking cost saving , and adoption
cost may change constantly. Therefore, we specify simple laws of motion as follows:
1
1
= 0
−1 − 1 = ( 0−1 − 1)
= 0
(1− ) = (01− ) ,
1
1
(6)
1
where 0 , 0 , 0 , and (01− ) are initial conditions at time 0.
The diffusion path of Internet banking can be derived from Eqs (4) and (6) as
=
1
1+
∗
(
( ))1
=
1
1
∗
1 + [0
(0 )]1 { − − − (−1) }
(7)
We may compare the formula derived in (7) with the classic logistic diffusion model
(e.g., Griliches 1957, Mansfield 1961), which assumes that the hazard rate of adoption
rises with cumulative adoption due to contagion effects
̇
1
= =⇒ =
1
1 −
1 + ( 0 − 1)−
(8)
where is the fraction of potential adopters who have adopted the innovation at time ,
and is a constant contagion parameter.
12
Comparing Eq (7) with Eq (8), we find that our formula is equivalent to the classic
logistic diffusion model under very reasonable assumptions. In particular, the diffusion
parameters traditionally treated as exogenous terms now have clear economic meanings
— The contagion parameter is determined by the growth rates of consumer willingnessto-pay, industry deregulation, and technological progress; the initial condition 0 is the
fraction of banks that find it profitable to adopt the innovation at the initial time 0:
=(
+ + − )
−1
0 =
1
1+
∗
[0
(0 )]1
Over time, as more banks adopt the innovation, the mean bank size keeps rising and
the aggregate size distribution of banks shifts towards a new steady state. In the long
run, as all banks have adopted the innovation, the cumulative distribution of bank size
converges to () which is again a log-logistic distribution but with a higher mean:
() = 1 −
1
1
1 + [ Γ(1+)Γ(1−)
]1
( )
( ) = ( ) −1
Figure 5 illustrates the industry dynamic path. Before Internet banking is introduced,
the banking industry stays at a pre-innovation size distribution, drawn with a dotted line.
After Internet banking becomes available, in the long run, the banking industry converges
to a post-innovation long-run size distribution, drawn with a solid line. In between, the
bank size distribution is at a transitional path, drawn with a dashed line. During the
∗
transition, at a point in time , there is a size threshold
, which splits the original
∗
size distribution. For banks with size ≥
, the size distribution resembles the
1
1
∗
∗
post-innovation long-run distribution in the range ∈ [ −1
∞), so −1
is the
∗
minimum size of adopters. Meanwhile, for banks with size
the size distribution
∗
resembles the pre-innovation one, so
is the maximum size of non-adoptors. There
1
1
∗
∗
∗
∗
will be no bank in the size range between (
−1
). Over time,
and −1
fall due to environmental changes (e.g., demand shift, technological progress or banking
deregulation). As a result, Internet banking diffuses into smaller banks, and the bank size
distribution gradually converges to the post-innovation long-run distribution.
13
Density G’(y)
M axim um Size
of Non-adoptor
y* n,t
Pre-Innovation
Distribution
M inim um Size
of Adopter
t1/(ß-1)y* n,t
Transitional
Distribution
B ank S ize y
Post-Innovation
Long-run D istribution
Figure 5: Illustration of the Industry Dynamics
3
Empirical study
In this section, we apply our theory to an empirical study on the diffusion and impact of
Internet banking. The sample that we consider includes all in-state banks in each of the
50 U.S. states between 2003-2007. The definitions and summary statistics of our empirical
variables are shown in Tables A1 and A2 in the Appendix.
3.1
Simultaneous equations
According to our theory, the diffusion and impact of Internet banking can be characterized
by two simultaneous equations (an adoption equation and a bank size equation) as follows.
Note that the adoption equation (4) can be rewritten into a log-linear form:
ln(
1
) = − ln − ln
− ln + ln + ln( −1 − 1) + ln ( )
1−
−1
(9)
An empirical approximation of the bank size equation (5) can be written as
ln () = ln ( ) + 1 [ ln(
14
1
)] + 2 ln( −1 − 1)
1−
(10)
Therefore, Eqs (9) and (10) imply
ln(
1
) = 0 + 1 ln () + 1 [(1 − 2 ) ln( −1 − 1) + ln − ln ]
1−
(11)
)(1 + 1 ) 1 = 1(1 + 1 ).
where 0 = −(ln + ln −1
Also, Eq (1) suggests
= (
1
1
1
−1
1
)
ln −
ln + ln ( 1− )
=⇒ ln ( ) =
−1
−1
Hence we can rewrite Eq (10) as
ln () = 0 + 1 [ ln(
where 0 =
1
1−
1
1
1
)] + 2 ln( −1 − 1) +
ln + ln ( 1− )
1−
−1
(12)
ln .
The two equations (11) and (12) are determined simultaneously. Note that the variable
1
is in Eq (11) but not in (12), and ( 1− ) is in Eq (12) but not in (11). Therefore,
they can serve as exclusion restrictions that identify structural parameters.
3.2
Empirical specifications
In the empirical study, we estimate the following simultaneous equations based on Eqs
(11) and (12) using state-level data of Internet banking adoption and average bank size,
where each state is indexed by and each year is indexed by :15
ln(
X
X
) = 0 + 1 ln(() ) +
ln( ) +
ln( ) + (Adoption)
1 −
ln(() ) = 0 + 1 [ ln(
15
X
X
)] +
ln( ) +
ln( ) +
1 −
Note that our sample includes all in-state banks between 2003-2007.
15
(Size)
• is the adoption rate of Internet banking; is the Gini coefficient of bank size
distribution,16
• () is the average bank size in terms of deposits,17
• denotes variables shared by both equations, e.g., variables affecting (price of
bank services) and/or (cost saving due to Internet banking), or variables affecting
1
both (adoption cost of Internet banking) and ( 1− ) (mean bank productivity),
• denotes variables only in the Adoption equation, e.g., variables affecting only,
1
• denotes variables only in the Size equation, e.g., variables affecting ( 1− ) only.
Below is a list of the empirical variables used in our estimation. For most of those
variables, we take the log transformation and prefix the variables with “ln” in the notation.
Tables A1 and A2 in the Appendix provide more details on each variable.
The dependent variables in the two equations are as follows.
(1) lnTRANODDS_GINI: Log odds ratio for Internet banking adoption adjusted by
the Gini coefficient, constructed using the following two variables TRANS — Adoption
rate for transactional websites and GINI — Gini coefficient for bank deposits.
(2) lnDEPOSITS: Log average bank size, constructed by the variable DEPOSITS —
Average bank deposits.
As our theory suggests, we consider three groups of explanatory variables and
, listed as follows.
: Variables in both Adoption and Size equations
METRO — Ratio of banks in metropolitan areas to all banks,
LOANSPEC — Specialization of lending to consumers,18
16
Because we do not observe the counterfactual Gini coefficient of bank size distribution in the sample
period, we use the sample Gini coefficient as a proxy. Alternatively, we could use the fixed pre-sample
Gini coefficient, but the regression results are fairly similar. As shown in Appendix Table A2, the Gini
coefficients have large cross-section variation but very small time-series variation.
17
We also used bank assets as an alternative measure of bank size and the results are very similar.
18
Defined by consumer loans plus 1-4 family mortgages divided by total loans.
16
OFF_DEP — Bank offices per value of deposits,
RMEDFAMINC — Real median family income in 1967 dollars,
POPDEN — Population density,
AGE — Average age of banks,
HHINET — Household Internet access rate,
WAGERATIO — Ratio of computer analyst wage to teller wage,
BHC — Ratio of banks in bank holding companies to total banks,
DEPINT — Ratio of deposits in out-of-state banks to total deposits,
REGION and YEAR — Dummies.
: Variables only in Adoption equation
IMITATE — Years since the first bank in the state adopted a transactional website,
COMRATE — Adoption rate of high-speed Internet among commercial firms in 2003,
calculated as an average of urban firms’ and rural firms’ internet adoption using METRO
to weight urban and rural location. Essentially, COMRATE measures in-state banks’
exposure to other commercial firms’ Internet adoption in each state.
: Variables only in Size equation
DEPOSITS90 — Average bank deposits in 1990,
INTRAREG — A dummy variable for whether the state had intrastate branching
restrictions after 1995.
Variables in affect both Internet banking adoption and average bank size. Take
HHINET for example: If more households have access to the Internet, local banks may
get more cost savings from adopting Internet banking. However, Internet access also
allows households to reach non-local banking services (e.g., interstate banks), which may
then lower demand and consumer willingness-to-pay for local banking services. AGE
1
is another example: Established banks typically achieve higher productivity ( 1− ), so
they may enjoy an advantage in adopting Internet banking. However, established banks
may also face a higher Internet banking adoption cost compared to young banks given
that they have to adapt Internet banking to their legacy computer systems.
17
The decision on exclusion restrictions and is a matter of economic judgement. We
include two variables in : the number of years since the first bank in the state adopted
a transactional website (IMITATE) and Internet adoption rate among commercial firms
of the state (COMRATE). They are expected to affect the bank size only through their
effects on Internet banking adoption. The former variable, IMITATE, is from the Online
Banking Report, a publication keeping track of the development of Internet banking. The
evidence suggests that the first wave of Internet banking was largely driven by exogenous
factors (such as entrepreneurs’ risk-taking experiments) rather than cost-benefit calculations suggested by our model. In fact, the correlation between a state’s first Internet
banking adoption (measured by IMITATE in 2003) and the average bank size in 1990
is -0.001. This justifies IMITATE being a valid instrument, and we conjecture that a
higher value of IMITATE may help Internet banking adoption by providing more local
expertise on bank-specific website design and performance. The latter variable, COMRATE, is constructed based on the information provided by Forman et al (2003). The
effect of COMRATE might be ambiguous in theory. One the one hand, a higher value
of COMRATE may help Internet banking adoption through the imitation effect. On the
other hand, it may delay Internet banking adoption by competing away local resources for
Internet installation and maintenance. Therefore, we will rely on our empirical estimation
to evaluate the overall effect of COMRATE.
We include two variables in : a dummy variable for whether the state had intrastate
branching restrictions after 1995 (INTRAREG) and average bank deposits in 1990 (DEPOSITS90). The former value is from Kroszner and Strahan (1999) and the latter is from
the Call Report. Both variables are expected to affect the adoption of Internet banking
only through their effects on average bank size: INTRAREG may negatively affect the
average bank size by imposing high regulation costs; DEPOSITS90 may be positively correlated with current average bank size through the persistence of underlying productivity
variables.
18
3.3
Estimation results
Our following discussions focus on the estimation results based on 2SLS (two-stage least
squares) models, shown in Tables 1a and 1b. Both the first-stage (reduced-form equation) and the second-stage (structural equation) results are reported. For comparison
and robustness checks, we also include in the Appendix the LIML (limited information
maximum likelihood) estimation results and the OLS results.
3.3.1
Model validation
The 2SLS results suggest that the instrument variables we use are valid and strong. In
the first-stage adoption equation, the coefficients on both lnIMITATE and lnCOMRATE
are statistically significant and have signs consistent with our identification story. In the
first-stage bank size equation, the coefficients on both INTRAREG and lnDEPOSITS90
also have the expected signs and lnDEPOSITS90 is statistically significant.
The relevance of the instruments is also confirmed by F-tests in the first-stage regressions. As a rule of thumb, the F-statistic of a joint test whether all excluded instruments
are significant should be bigger than 10 in case of a single endogenous regressor. As shown
in Table 1a, this is satisfied in both our adoption and bank size regressions.
Moreover, because we have two instruments for each endogenous variable, we can perform the overidentification test. This test checks whether both instruments are exogenous
assuming that at least one of the instruments is exogenous. As shown in Table 1a, the
2 statistics show that we cannot reject the null hypothesis that our instruments are
exogenous in either the adoption or the bank size equation.
Finally, we test whether the 2SLS estimates are statistically different from the OLS
estimates. The is done by re-running second-stage regressions where the residuals from
the first-stage regressions are included (Wooldridge 2010, Chapter 5).19 This test is robust
to heteroscedasticity given that the robust variance estimator is used. The results in Table
1a show that for both the adoption and the bank size equations, the coefficients of the
first-stage residuals are statistically significant, which confirm that instrumenting does
19
An alternative is to run the Hausman test, but the Hausman test is only valid under homoscedasticity
and involves the cumberome generalized inversion of a non-singular matrix.
19
Table 1a: Estimated 2SLS Models of
Transactional Website Adoption and Size of Bank Deposits
Reduced Forms
lnTRANODDS_GINI
Structural Equations
lnDEPOSITS
lnDEPOSITS (fitted)
lnTRANODDS_GINI
lnDEPOSITS
0.5716
(0.0848)***
lnTRANODDS_GINI (fitted)
1.3033
(0.2686)***
lnIMITATE
lnCOMRATE
INTRAREG
lnDEPOSITS90
lnMETRO
lnLOANSPEC
lnRMEDFAMINC
lnPOPDEN
lnAGE
lnHHINET
lnBHC
lnWGRATIO
lnDEPINT
lnOFF_DEP
Constant
2
0.3384
0.3933
0.1135
(0.1506)**
(0.2848)
(0.1754)
-3.7200
-4.9335
-0.9002
(0.7026)***
(1.0055)***
(0.9023)
-0.0574
-0.1001
-0.0272
(0.0493)
(0.0764)
(0.0831)
0.2613
0.4572
0.1164
(0.0463)***
(0.0694)***
(0.0973)
0.5357
0.7520
0.1060
0.0431
(0.1231)***
(0.2166)***
(0.1636)
(0.2536)
0.1319
0.3773
-0.0837
0.2191
(0.1191)
(0.2138)*
(0.1441)
(0.1918)
-0.3799
0.2582
-0.5276
0.7551
(0.3451)
(0.5425)
(0.3653)
(0.5659)
-0.0490
0.0994
-0.1059
0.1580
(0.0329)
(0.0681)
(0.0426)**
(0.0616)**
-0.2213
0.2163
-0.3449
0.4933
(0.0872)**
(0.1581)
(0.1063)***
(0.1668)***
2.3160
1.0941
1.6906
-1.9396
(0.3779)***
(0.6718)
(0.3598)***
(0.7602)**
1.2176
1.9964
0.0764
0.4143
(0.1804)***
(0.4520)***
(0.2211)
(0.4943)
-0.3093
-0.5468
0.0033
-0.1298
(0.2177)
(0.3983)
(0.2575)
(0.4067)
0.0059
-0.1557
0.0949
-0.1626
(0.0342)
(0.0477)***
(0.0327)***
(0.0460)***
0.1035
-0.3453
0.3009
-0.4823
(0.0762)
(0.1175)***
(0.0851)***
(0.1184)***
-8.9911
-1.2171
-8.2948
(1.3336)***
(2.3079)
(1.3169)***
Adjusted R
N
0.83
227
0.78
227
Weak instrument test: F(2,201)†
31.7
18.45
0.75
227
-4.52***
Exogeneity of regressors-Wald test
0.00
Overidentification test: Chi2(1)
10.5330
(2.8205)***
0.74
227
-3.24***
0.03
* p<0.1; ** p<0.05; *** p<0.01
†
Critical values: 19.93 (10%), 11.59 (15%)
Notes: Equations are estimated using two-stage least-squares for the time period 2003 to 2007. Robust standard errors are in parentheses.
Estimated coefficients for year and regional dummies are shown in Table 1b.
20
Table 1b: Estimated 2SLS Models of
Transactional Website Adoption and Size of Bank Deposits
Year and Region Dummy Variables
Reduced Forms
lnTRANODDS_GINI
d2004
d2005
d2006
d2007
Southeast
Far west
Rocky mtn
Southwest
New England
Mid-east
Great Lakes
Structural Equations
lnDEPOSITS
lnTRANODDS_GINI
lnDEPOSITS
0.1068
-0.0636
0.1431
-0.2087
(0.0477)**
(0.0975)
(0.0578)**
(0.0908)**
0.2408
-0.0383
0.2627
-0.3630
(0.0666)***
(0.1251)
(0.0779)***
(0.1297)***
0.3517
-0.1251
0.4232
-0.5983
(0.0883)***
(0.1502)
(0.0911)***
(0.1657)***
0.4693
-0.1317
0.5446
-0.7626
(0.1030)***
(0.1764)
(0.1061)***
(0.2060)***
0.0849
0.2575
-0.0623
0.1442
(0.0866)
(0.1378)*
(0.1010)
(0.1585)
0.1203
0.9697
-0.4340
0.8207
(0.0907)
(0.1666)***
(0.1534)***
(0.1825)***
-0.0450
0.3365
-0.2374
0.3965
(0.0790)
(0.1515)**
(0.0877)***
(0.1538)***
0.1561
0.3933
-0.0688
0.1862
(0.0942)*
(0.1335)***
(0.0898)
(0.1537)
-0.0632
0.3811
-0.2810
0.4719
(0.1314)
(0.2509)
(0.1406)**
(0.2074)**
-0.1308
-0.3424
0.0647
-0.1675
(0.1582)
(0.2099)
(0.1527)
(0.2712)
-0.0590
-0.3125
0.1196
-0.2372
(0.0700)
(0.1332)**
(0.0871)
(0.1476)
* p<0.1; ** p<0.05; *** p<0.01
Notes: Equations are estimated using two-stage least-squares for the time period 2003 to 2007. Robust standard errors are in
parentheses. Estimated coefficients for other variables in the model equations are in Table 1a.
21
matter for the estimation.
3.3.2
Economic findings
We now turn to the economic findings based on the second-stage estimation results shown
in Tables 1a and 1b. Both structural models fit data well, with an 2 of 0.75 for the adoption equation and 0.74 for the bank size equation. Most signs of estimated coefficients, and
all of those that are statistically significant, are consistent with our theoretical predictions.
The findings are summarized as follows.
In the adoption equation (Table 1a, column 3), the coefficient on the fitted value of
lnDEPOSITS is positive and statistically significant. In the size equation (Table 1a, column 4), the coefficient on the fitted value of lnTRANODDS_GINI is also positive and
statistically significant. The findings support our theoretical results that Internet banking
adoption has a positive causal effect on average bank size, and vice versa. Quantitatively,
considering a Gini coefficient equal to 0.57 (the average value in 2003), the results imply that holding everything else constant, a 10 percent increase in average bank size
would increase the adoption odds ratio by about 10 percent, and a 10 percent increase
of adoption odds ratio would increase the average bank size by about 7.4 percent. To
put things into perspective, we may consider a case where the Internet adoption rate
is 56.4 percent and the average bank deposits are $311 million, which are mean values
of 2003 data. Therefore, based on the 2003 data (Table A2 in the Appendix), a onestandard-deviation increase of average bank deposits from the mean would increase the
Internet banking adoption rate from 56.4 percent to 77.1 percent.20 On the other hand, a
one-standard-deviation increase of Internet banking adoption from the mean would raise
the average bank deposits from $331 million to $482 million, an increase of 55.0 percent.21
These findings are in sharp contrast with the OLS regression results (Table A4a in the
Appendix, columns 1 and 2). Without addressing the endogeneity of regressors, the OLS
results underestimate the impact of lnDEPOSITS and lnTRANODDS_GINI by more
than a half.
0564
This is calculated by solving , where 057×[ln( 1−
)−ln( 1−0564
)] = 05716×[ln(311+496)−ln(311)]
0564+0136
0564
21
This is calculated by solving , where ln() − ln(311) = 13033 × 057 × [ln 1−0564−0136
− ln 1−0564
]
20
22
We also find that Population density (lnPOPDEN) has significant effects on both
Internet banking adoption and average bank size. Its effect on Internet banking adoption
is negative, suggesting a higher demand for Internet banking in locations with higher cost
of travel to bank branches. Its effect on bank size is positive, which confirms that banks
in urban areas enjoy more business.
The average bank age in a state (lnAGE) is statistically significant in both equations.
The negative coefficient in the adoption equation implies that as the average age of a
state’s banks increases, the adoption rate falls. This results is consistent with previous
findings that de novo banks were more likely to adopt Internet banking than incumbent
banks (Furst et al. 2001). New banks may find it cheaper to install Internet banking
technology in a package with other computer facilities compared to older banks who must
add Internet banking to legacy computer systems. Meanwhile, the positive coefficient
on lnAGE in the size equation indicates that bank size increases with age, which can be
reasonably explained by the accumulation of business expertise and reputation.
Household access to the Internet (lnHHINET) is also statistically significant in both
equations. Greater household access to the Internet is associated with a higher adoption
of Internet banking, but a smaller average bank size. Both effects are consistent with our
discussion above in Section 3.2: If more households have access to the Internet, local banks
may get more cost savings from adopting Internet banking. However, Internet access also
allows households to reach non-local banking services (e.g., out-of-state banks), so it
negatively affects local bank size.
Competition from out-of-state banks (lnDEPINT) significantly affects Internet banking adoption and in-state bank size. The estimates suggest that more deposits in outof-state banks push more in-state banks to adopt Internet banking (possibly in order to
compete for business). Meanwhile, more competition from out-of-state banks leads to
smaller size of in-state banks.
Bank offices per value of deposits (lnOFF_DEP) is statistically significant in both
equations. The positive coefficient in the adoption equation implies that banks with more
offices may try to explore the synergy between branch banking and Internet banking.22
22
This finding is consistent with optimization of branch network size that compasses both branch-based
23
The negative coefficient in the size equation suggests that average bank size is smaller
where banks have a high number of branches relative to their deposits.
Finally, the year dummies are all statistically significant in both equations. After
controlling for the other explanatory variables, there is a positive year trend for Internet
banking adoption, but a negative year trend for average in-state bank size. In contrast,
most regional dummies are not significant or have a negative sign in the adoption equation,
in comparison with the excluded PLAIN states which has the lowest Internet banking
adoption. This suggests that the observed cross-region differences of Internet adoption are
mainly driven by the other explanatory variables in our model rather than the remaining
regional fixed effects. We will discuss more on this below.
For robustness checks, we ran a series of additional regressions. First, we used bank
assets instead of deposits as an alternative measure of bank size. Second, we explored
different samples by looking at state-chartered banks instead of in-state banks or excluding
states with a small number of banks (e.g. states with fewer than 10 banks). Third, we
employed Fuller’s LIML estimators as an alternative way of conducting IV regressions
(See Tables A3a and A3b in the Appendix), which have been shown more robust than
2SLS estimators with respect to weak instruments in some recent studies (Murray, 2006).
The results are all very similar.23
3.4
Regional variations
Our empirical findings above offer useful insights for understanding the diffusion and impact of Internet banking. The results show positive interactions between Internet banking
adoption and average bank size. As explained by our theory, this is because large (more
efficient) banks enjoy scale economies of adoption by spreading the fixed adoption cost.
Moreover, our findings can help explain the variation of Internet banking adoption across
geographic regions. Particularly, why do the northeast and the west regions have the
highest adoption rates, while the central regions have the lowest (See Figure 3)?
The following Table 2 presents regional averages of variables that are found signifiand non-branch based activities (Hirtle, 2007).
23
All the robustness check results are available upon request.
24
cantly affecting Internet banking adoption in the first-stage regression. Far West, Plains
and New England are used to represent the west, central and northeast regions respectively.24 As shown, the Plains region had a similar number of states and a similar Gini
coefficient of bank size in 2003 as the Far West and New England, but the Internet banking adoption rate was much lower. Compared with the other two regions, we find that the
Plains region has smaller initial bank size, lower household Internet access, fewer banks
in metro markets, and older bank vintages. Based on the coefficients (marginal effects)
that we uncovered from the first-stage regression, we conclude that these are the factors
that have contributed to slow diffusion of Internet banking in the Plains region. On the
other hand, our findings reject several alternative hypotheses that may sound appealing,
including imitation of early adopters, Internet adoption of commercial firms, and bank
holding company membership. In fact, some of those could have been the Plains region’s
advantage for adoption.
Table 2: Mean Values of Selected Variables by Region
(Far West, Plains and New England 2003)
Variables*
Effect on IB
Far West
Plains
New England
6
7
6
TRANS
0.71
0.43
0.67
GINI
0.59
0.60
0.50
OBS (States)
DEPOSITS90
+
217.9
37.5
289.9
IMITATE
+
5.80
6.71
6.40
HHINET
+
61.1
55.5
60.4
METRO
+
0.95
0.51
0.79
BHC
+
0.66
0.87
0.62
COMRATE
−
0.90
0.90
0.88
AGE
−
25.6
81.6
68.1
*See Table A1 for variable definitions and sources.
24
Similarly, we can compare variations of Internet banking adoption between any other regions. The
values of variables for all eight U.S. regions are reported in Table A5 in the Appendix.
25
We also rule out several other factors that are only found significantly affecting Internet
banking adoption in the second-stage regression, such as deposits held in out-of-state
banks, population density, and bank offices per value of deposits. Because those factors
show significantly opposite effects on the average bank size in the second-stage regression,
their overall effects on Internet banking adoption become insignificant in the first-stage
regression where the interaction effects between Internet banking adoption and average
bank size are taken into account.
For example, as our second-stage estimation results show, holding everything else constant, an increase of interstate banking competition (measured by lnDEPINT) reduces the
average size of in-state banks, but also pushes in-state banks to adopt Internet banking
more aggressively. Quantitatively, when we take into account the feedback effects between
Internet banking adoption and average bank size, the overall positive effect of lnDEPINT
on Internet banking adoption becomes negligible while the overall negative effect on average in-state bank size remains relatively large. To see this more clearly, our second
stage coefficient estimates show that a unit increase of lnDEPINT would directly increase
lnTRANODDS_GINI by 0.095 unit, but reduce lnDEPOSITS by 0.163 unit. However,
when we take into account the indirect effects through the interactions between lnTRANODDS_ GINI and lnDEPOSITS, the final effect on lnTRANODDS_GINI is reduced to
less than 0.01 unit, and the final effect on lnDEPOSITS remains more than 0.15 unit.25
This is consistent with the coefficient estimates obtained in our first-stage regressions.
The finding sheds light on variables that are important when allowed to affect adoption
of Internet banking directly but whose effects diminish after accounting for feedback
effects on the bank size. In the case of interstate banking, deregulation directly affects
in-state banks in terms of both their size and Internet banking adoption, but these effects
largely offset one another. Similarly, population density (POPDEN) and bank offices
per value of deposits (OFF_DEP) each affects in-state banks in terms of both size and
Internet banking adoption but the effects offset one another. These variables thus become
25
Using the second-stage coefficient estimates, we can solve the simultaneous equations and get the
= 00077;
overall effects of lnDEPINT: (lnTRANODDS_GINI)/(lnDEPINT)= −01626×05716+00949
1−05716×13033
while (lnDEPOSITS)/(lnDEPINT) = 13033×00949−01626
=
−01526
1−05716×13033
26
unimportant in explaining regional differences in adoption rates of Internet banking.
4
Conclusion
This paper studies the diffusion and impact of cost-saving technological innovations. Our
theory suggests that when such an innovation is initially introduced, large firms enjoy cost
advantages in becoming early adopters and gaining a further increase of size. Over time,
due to environmental changes (e.g., demand shift, technological progress, and/or industry
deregulation), the innovation gradually diffuses into smaller firms. As a result, the aggregate firm size distribution shifts towards a new steady state with a higher mean, and
the technology adoption follows an -shape logistic curve. Overall, there exists important
positive interactions between technology adoption and average firm size.
Applying the theory to an empirical study of Internet banking diffusion among banks
across 50 U.S. states, we examine the technological, economic and institutional factors
governing the process. The empirical findings allow us to disentangle the interrelationship
between Internet banking adoption and the change of average bank size, and explain the
variation of diffusion rates across geographic regions.
The theoretical and empirical approach that we develop in this paper goes beyond the
Internet banking application. It provides a framework for studying the causal effects between technology adoption and changing firm size distribution, which can also be applied
to other cases of technology diffusion. Examples may include banks’ adoption of ATMs,
farms’ adoption of tractors, or manufacturing firms’ adoption of assembly lines, just to
name a few.
References
[1] Berger, Allen and Loretta Mester (2003). “Explaining the Dramatic Changes of
Performance of U.S. Banks: Technological Change, Deregulation and Dynamic
Changes in Competition,” Journal of Financial Intermediation, 12(1), 57-95.
27
[2] Cabral, Luis, and Jose Mata (2003). “On the Evolution of the Firm Size Distribution:
Facts and Theory,” American Economic Review, 1075-1090.
[3] Comin, Diego and Bart Hobijn (2004). “Cross-Country Technological Adoption:
Making the Theories Face the Facts,” Journal of Monetary Economics, 51(1),
39-83.
[4] Comin, Diego and Bart Hobijn (2010). “An Exploration of Technology Diffusion,”
American Economic Review, 100(5): 2031—59.
[5] Comin, Diego, Mikhail Dmitriev and Esteban Rossi-Hansberg (2012). “The Spatial
Diffusion of Technology,” NBER Working Paper No. 18534.
[6] Courchane, Marsha, David Nickerson and Richard J. Sullivan (2002). “Investment in
Internet Banking as a Real Option: Theory and Tests,” The Journal of Multinational Financial Management, 12(4-5), 347-63.
[7] David, Paul A (1969). “A Contribution to the Theory of Diffusion,” Stanford University Research Center in Economic Growth Memo 71.
[8] DeYoung, R., W.W. Lang, D.L. Nolle (2007). “How the Internet Affects Output
and Performance at Community Banks,” Journal of Banking and Finance, 31,
1033-1060.
[9] DeYoung, R. (2005). “The Performance of Internet-Based Business Models: Evidence
from the Banking Industry,” Journal of Business, 78, 893-948.
[10] Forman, Chris, Avi Goldfarb and Shane Greenstein (2003). “The Geographic Dispersion of Commercial Internet Use,” Rethinking Rights and Regulations: Institutional Responses to New Communication Technologies, Cambridge: MIT Press,
113-45.
[11] Furst, Karen, William Lang and Daniel Nolle (2001). “Internet Banking in the US:
Landscape, Prospects, and Industry Implications,” Journal of Financial Transformation, 2, 45-52.
[12] Geroski, P.A. (2000). “Models of Technology Diffusion,” Research Policy, 29, 603-625.
28
[13] Griliches, Zvi (1957). “Hybrid Corn: An Exploration in the Economics of Technological Change,” Econometrica, 25, 501-522.
[14] Hernández-Murillo, Rubén, Gerard Llobet, Roberto Fuentes (2010). “Strategic Online Banking Adoption,” Journal of Banking and Finance, 34(7), 1650-1663.
[15] Hirtle, Beverly (2007). “The Impact of Network Size on Bank Branch Performance,”
Journal of Banking and Finance, 31, 3782-3805.
[16] Hopenhayn, H. A. (1992). “Entry, Exit, and Firm Dynamics in Long Run Equilibrium,” Econometrica, 60(2): 1127-1150.
[17] Janicki, H. and E. Prescott (2006). “Changes in the Size Distribution of U.S. Banks:
1960-2005,” Federal Reserve Bank of Richmond Economic Quarterly, 92, 291-316.
[18] Jovanovic, Boyan (1982). “Selection and Evolution of Industry,” Econometrica, 50(3),
649-670.
[19] Karshenas, M., P.L. Stoneman (1993). “Rank, Stock, Order and Epidemic Effects in
the Diffusion of New Process Technologies: An Empirical Model,” RAND Journal
of Economics, 24, 503—528.
[20] Kroszner, Randall and Philip Strahan (1999). “What Drives Deregulation? Economics and Politics of the Relaxation of Banking Branching Restrictions,” Quarterly Journal of Economics, 114(4), 1437-1467.
[21] Lucas, Robert (1978). “On the Size Distribution of Business Firms,” Bell Journal of
Economics, 9(2), 508-23.
[22] Manuelli, Rodolfo and Ananth Seshadri (2014). “Frictionless Technology Diffusion:
The Case of Tractors,” American Economic Review, 104(4), 1368-1391.
[23] Mansfield, Edwin (1961). “Technical Change and the Rate of Innovation,” Econometrica, 29, 741—66.
[24] Murray, Michael (2006). “Avoiding Invalid Instruments and Coping with Weak Instruments,” Journal of Economic Perspective, 20(4), 111-132.
29
[25] Stoneman, Paul (2002). The Economics of Technological Diffusion. Oxford: Blackwell.
[26] Sutton, John (1997). “Gibrat’s Legacy,” Journal of Economic Literature, 35(1), 4059.
[27] Wang, Zhu (2007). “Technological Innovation and Market Turbulence: The Dot-com
Experience,” Review of Economic Dynamics, 10(1), 78-105.
[28] Wang, Zhu (2008). “Income Distribution, Market Size and the Evolution of Industry,”
Review of Economic Dynamics, 11(3), 542-565.
[29] Wooldridge, Jeffrey M. (2010). Econometric Analysis of Cross Section and Panel
Data, MIT Press.
30
Table A1: Empirical Variable Definitions and Sources
Variable name
TRANS
TRANODDS
GINI
DEPOSITS
METRO
LOANSPEC
OFF_DEP
RMEDFAMINC
POPDEN
IMITATE
AGE
HHINET
WGRATIO
INTRAREG
BHC
DEPINT
COMRATE
DEPOSITS90
Definition
Adoption rate for transactional websites
Odds ratio for adoption of transactional websites
Gini coefficient for bank deposits
Average bank deposits
Ratio of banks in metropolitan areas to all banks
Specialization of lending to consumers (consumer loans plus 1-4
family mortgages / total loans)
Bank offices per value of deposits
Call Report; FDIC
Summary of Deposits
Median family income (in 1967 dollars)
U.S. Census Bureau
Population density
Statistical Abstract of
the United States
Years since the first bank in the state adopted a transactional website Online Banking
Report
Average age of banks
Call Report
Household access rate for Internet
Statistical Abstract of
the United States
Ratio of computer analyst wage to teller wage
Bureau of Labor
Statistics
Indicator variable for whether the state had branching restrictions
Krozner and Strahan,
after 1995
1999
Ratio of banks in bank holding companies to total banks
Call Report
Ratio of deposits in out-of-state banks to total deposits
FDIC Summary of
Deposits
Adoption rate of high-speed internet among commercial firms
Forman, et.al., 2003
Average bank deposits in 1990
Call Report
Regional dummy variables:
SE
FARWEST
ROCKYMTN
PLAINS
SW
NWENGLND
MIDEAST
GRTLAKE
Source
Call Report
Call Report
Call Report
Call Report
Call Report
Call Report
Bureau of Economic
Analysis
Southeast: AL, AR, FL, GA, KY, LA, MS, NC, SC, TN, VA, WV
Far West: AK, CA, HI, NV, OR, WA
Rocky Mountain: CO, ID, MT, UT, WY
Plains: IA, KS, MN, MO, NE ,ND, SD
Southwest: AZ, NM, OK, TX
New England: CT, MA, ME, NH, RI, VT
Middle East: DC, DE, MD, NJ, NY, PA
Great Lakes: IL, IN, MI, OH, WI
Notes: Data are for individual states.
Variables for banks are unweighted averages for those located in individual states. Selected banks are full-service, retail commercial
banks.
Data for adoption of high-speed internet among commercial firms is for 2003. COMRATE is an average of urban firms’ and rural
firms’ internet adoption, using METRO to weight urban and rural location.
BEA Regions are a set of Geographic Areas that are aggregations of the states. The regional classifications, which were developed
in the mid-1950s, are based on the homogeneity of the states in terms of economic characteristics, such as the industrial
composition of the labor force, and in terms of demographic, social, and cultural characteristics. For a brief description of the
regional classification of states used by BEA, see U.S. Department of Commerce, Census Bureau, Geographic Areas Reference
Manual, Washington, DC, U.S. Government Printing Office, November 1994, pp. 6-18;6-19.
31
Table A2: Summary Statistics
2003
2005
2007
VARIABLE
Mean
S. D.
Min
Max
Mean
S. D.
Min
Max
Mean
S. D.
Min
Max
TRANS
0.564
0.136
0.263
0.852
0.729
0.121
0.456
0.949
0.830
0.095
0.624
0.978
TRANODDS
1.588
1.063
0.357
5.750
3.880
3.474
0.837 18.501
7.888
7.930
1.659 44.004
GINI
0.574
0.122
0.338
0.847
0.568
0.119
0.325
0.862
0.583
0.117
0.305
DEPOSITS*
$311
$496
$65
$3,307
$406
$783
$67 $4,028
$486
$970
METRO
0.741
0.187
0.295
1.000
0.741
0.184
0.300
1.000
0.737
0.185
0.298
1.000
LOANSPEC
0.373
0.121
0.144
0.608
0.351
0.122
0.137
0.581
0.333
0.124
0.102
0.574
OFF_DEP
0.023
0.008
0.003
0.037
0.021
0.008
0.003
0.034
0.020
0.008
0.003
0.031
RMEDFAMINC**
$93.5
$13.9
$70.0
$126.9
$93.6
$13.9
$70.0 $129.2
$95.3
$12.6
$72.1 $131.1
POPDEN
148.0
179.6
1.1
821.4
153.4
181.5
820.6
148.9
175.8
IMITATE
6.745
1.132
4.000
9.000
8.783
1.114
6.000 11.000
10.791
1.103
AGE
58.7
23.2
6.7
111.7
59.2
23.9
7.4
112.5
60.4
25.6
5.8
121.5
HHINET
54.4
6.2
38.9
67.6
57.6
6.1
42.4
70.1
60.7
6.2
46.0
71.6
WGRATIO
3.035
0.238
2.417
3.396
3.056
0.218
2.689
3.497
3.049
0.268
2.230
3.572
INTRAREG
0.234
0.428
0.000
1.000
0.239
0.431
0.000
1.000
0.256
0.441
0.000
1.000
BHC
0.776
0.118
0.444
0.931
0.792
0.121
0.429
0.937
0.808
0.110
0.579
0.940
DEPINT
0.283
0.185
0.002
0.741
0.351
0.197
0.005
0.843
0.341
0.192
0.020
0.831
COMRATE
0.889
0.026
0.778
0.921
0.889
0.026
0.777
0.922
0.889
0.027
0.776
0.922
DEPOSITS90*
$207
$365
$26
$2.393
$207
$369
$26 $2,393
$209
$382
SE
0.255
0.441
0
1
0.261
0.444
0
1
0.279
0.454
0
1
FARWEST
0.106
0.312
0
1
0.087
0.285
0
1
0.093
0.294
0
1
ROCKYMTN
0.106
0.312
0
1
0.109
0.315
0
1
0.093
0.294
0
1
SW
0.085
0.282
0
1
0.087
0.285
0
1
0.093
0.294
0
1
NWENGLND
0.106
0.312
0
1
0.109
0.315
0
1
0.093
0.294
0
1
MIDEAST
0.085
0.282
0
1
0.087
0.285
0
1
0.070
0.258
0
1
GRTLAKE
0.106
0.312
0
1
0.109
0.315
0
1
0.116
0.324
0
1
PLAINS
0.149
0.360
0
1
0.152
0.363
0
1
0.163
0.374
0
1
5.2
0.908
$71 $5,057
5.4
822.7
8.000 13.000
$26 $2,393
Notes: Sample population includes the 50 states in the U.S. and the District of Columbia. The sample size varies from year to year
because the transactional website adoption rate reached 100% for some observations and TRANODDS cannot be calculated. The actual
sample size in 2003, 2005, and 2007 is 47, 46, and 43.
See Table A1 for variable definitions and sources.
*In millions.
**In thousands
32
Table A3a: Estimated LIML Models of
Transactional Website Adoption and Size of Bank Deposits
Structural Equations
lnTRANODDS_GINI
lnDEPOSITS (fitted)
lnDEPOSITS
0.5716
(0.0820)***
lnTRANODDS_GINI (fitted)
1.3040
(0.3192)***
lnIMITATE
0.1135
(0.1872)
lnCOMRATE
-0.9002
(0.8624)
INTRAREG
-0.0272
(0.0994)
lnDEPOSITS90
0.1162
(0.0956)
lnMETRO
lnLOANSPEC
lnRMEDFAMINC
lnPOPDEN
lnAGE
lnHHINET
lnBHC
lnWGRATIO
lnDEPINT
lnOFF_DEP
Constant
0.1060
0.0428
(0.1619)
(0.2556)
-0.0837
0.2190
(0.1313)
(0.1856)
-0.5276
0.7553
(0.2979)*
(0.4753)
-0.1059
0.1581
(0.0398)***
(0.0578)***
-0.3449
0.4935
(0.0779)***
(0.1414)***
1.6906
-1.9412
(0.3632)***
(0.8974)**
0.0033
-0.1295
(0.2708)
(0.4423)
0.0764
0.4135
(0.2032)
(0.4498)
0.0949
-0.1626
(0.0293)***
(0.0418)***
0.3009
-0.4824
(0.0743)***
(0.1017)***
-8.2948
(1.3989)***
2
10.5383
(3.1675)***
Adjusted R
N
0.75
227
0.74
227
Weak instrument test: F(2, 201) †
31.7
15.9
* p<0.1; ** p<0.05; *** p<0.01
†
Critical values: 8.68 (10%), 5.33 (15%).
Notes: Equations are estimated using limited information maximum likelihood for the time period
2003 to 2007. Estimated coefficients for year and regional dummy variables are shown in Table
A3b.
33
Table A3b: Estimated LIML Models of
Transactional Website Adoption and Size of Bank Deposits
Year and Regional Dummy Variables
Structural Equations
lnTRANODDS_GINI
d2004
d2005
d2006
d2007
Southeast
Far west
Rocky mtn
Southwest
New England
Mid-east
Great Lakes
lnDEPOSITS
0.1431
-0.2088
(0.0600)**
(0.1004)**
0.2627
-0.3633
(0.0731)***
(0.1414)**
0.4232
-0.5987
(0.0866)***
(0.1855)***
0.5446
-0.7631
(0.1032)***
(0.2333)***
-0.0623
0.1440
(0.1104)
(0.1744)
-0.4340
0.8206
(0.1444)***
(0.1724)***
-0.2374
0.3965
(0.0948)**
(0.1473)***
-0.0688
0.1861
(0.1152)
(0.1889)
-0.2810
0.4718
(0.1539)*
(0.2050)**
0.0647
-0.1677
(0.1422)
(0.2312)
0.1196
-0.2373
(0.1006)
(0.1614)
* p<0.1; ** p<0.05; *** p<0.01
Notes: Equations are estimated using limited information maximum
likelihood for the time period 2003 to 2007. Estimated coefficients for other
variables in the model equations are in Table A3a.
34
Table A4a: Estimated OLS Models of
Transactional Website Adoption and Size of Bank Deposits
Structural Equations
lnTRANODDS_GINI
lnDEPOSITS
lnDEPOSITS
0.2467
(0.0436)***
lnTRANODDS_GINI
0.5674
(0.1390)***
lnIMITATE
0.1915
(0.1530)
lnCOMRATE
-2.0247
(0.7779)***
INTRAREG
-0.0628
(0.0743)
lnDEPOSITS90
0.2873
(0.0734)***
lnMETRO
lnLOANSPEC
lnRMEDFAMINC
lnPOPDEN
lnAGE
lnHHINET
lnBHC
lnWGRATIO
lnDEPINT
lnOFF_DEP
Constant
Adjusted R2
N
0.3926
0.2939
(0.1280)***
(0.2201)
0.0511
0.3086
(0.1205)
(0.1851)*
-0.4229
0.5603
(0.3247)
(0.5378)
-0.0844
0.1115
(0.0324)***
(0.0544)**
-0.3696
0.2814
(0.0928)***
(0.1488)*
1.7774
-0.3372
(0.3507)***
(0.6960)
0.5697
1.2538
(0.1616)***
(0.4409)***
-0.1073
-0.5205
(0.2257)
(0.3756)
0.0487
-0.1614
(0.0281)*
(0.0434)***
0.1244
-0.4006
(0.0629)**
(0.1104)***
-5.8434
5.2588
(1.1062)***
(2.3939)**
0.82
227
0.79
227
* p<0.1; ** p<0.05; *** p<0.01
Notes: Equations are estimated using ordinary least squares for the time period 2003 to 2007.
Robust standard errors are in parentheses. Estimated coefficients for year and regional dummy
variables are shown in Table A4b.
35
Table A4b: Estimated OLS Models of
Transactional Website Adoption and Size of Bank Deposits
Year and Region Dummy Variables
Structural Equations
lnTRANODDS_GINI
d2004
d2005
d2006
d2007
Southeast
Far west
Rocky mtn
lnDEPOSITS
0.1362
-0.0824
(0.0482)***
(0.0866)
0.2750
-0.0949
(0.0658)***
(0.1071)
0.4246
-0.2122
(0.0820)***
(0.1273)*
0.5507
-0.2509
(0.0980)***
(0.1349)*
0.0847
0.2411
(0.0850)
(0.1412)*
-0.0500
0.8825
(0.1094)
(0.1566)***
-0.1454
0.3632
(0.0712)**
(0.1457)**
Southwest
New England
Mid-east
Great Lakes
0.0829
0.3457
(0.0796)
(0.1326)***
0.0842
0.3914
(0.1112)
(0.2245)*
0.2995
-0.2680
(0.1223)**
(0.2222)
0.1716
-0.2620
(0.0731)**
(0.1356)*
* p<0.1; ** p<0.05; *** p<0.01
Notes: Equations are estimated using ordinary least-squares for the time
period 2003 to 2007. Robust standard errors are in parentheses. Estimated
coefficients for other variables in the model equation are in Table A4a.
36
Table A5: Mean Values of Selected Variables by Region 2003
VARIABLE
TRANS
TRANODDS
GINI
DEPOSITS*
METRO
LOANSPEC
OFF_DEP
RMEDFAMINC**
POPDEN
IMITATE
AGE
HHINET
WGRATIO
INTRAREG
BHC
DEPINT
COMRATE
DEPOSITS90*
OBS (States)
New
England
0.666
2.031
0.495
429.7
0.794
0.475
0.019
109.7
358.6
6.400
68.1
60.4
2.884
0.000
0.621
0.324
0.883
289.9
6
Mideast
0.689
2.476
0.668
1152.9
0.936
0.481
0.014
107.5
416.2
7.500
64.8
56.0
3.209
0.000
0.768
0.224
0.880
985.5
Southeast
0.525
1.267
0.514
190.7
0.708
0.441
0.026
82.2
132.3
7.000
53.6
48.6
3.015
0.250
0.785
0.313
0.889
116.7
Great Lakes
0.534
1.225
0.668
257.1
0.769
0.459
0.021
97.9
191.5
7.800
78.6
52.8
3.183
0.000
0.854
0.184
0.902
118.0
Plains
0.427
0.801
0.596
101.3
0.509
0.294
0.028
93.2
39.2
6.714
81.6
55.5
3.125
0.571
0.873
0.164
0.898
37.5
Rocky
Mountain
0.561
1.382
0.485
131.6
0.681
0.279
0.025
92.4
20.1
6.000
47.9
58.0
2.905
0.600
0.822
0.305
0.866
63.7
5
12
5
7
5
Notes: See Table A1 for variable definitions and sources. See Table A2 for the national average of variables.
*In millions. **In thousands
37
Southwest
0.532
1.390
0.699
251.5
0.766
0.320
0.023
81.5
50.0
6.500
46.3
50.0
3.074
0.250
0.774
0.379
0.885
169.6
Far West
0.706
3.031
0.585
378.2
0.949
0.179
0.019
100.3
75.6
5.800
25.6
61.1
2.922
0.000
0.656
0.382
0.901
217.9
4
6
@FedFRASER