The Rank, Stock, Order and Epidemic
Effects of Technology Adoption:
An Empirical Study of Bounce Protection Programs
Marc Anthony Fusaro
East Carolina University
Department of Economics
A-427 Brewster Building
(252) 328-2872
(252) 328-6743 (fax)
FusaroM@ecu.edu
The author would like to thank Rob Porter, Shane Greenstein, Ron Braeutigam, Bill Rogerson,
and Nick Kreisle, for helpful comments and ideas.
The Rank, Stock, Order and Epidemic
Effects of Technology Adoption:
An Empirical Study of Bounce Protection Programs
January 2007
Abstract:
Karshenas and Stoneman (1993) gathered four theories of technology adoption: the
rank, stock, order and epidemic effect. Tests of these four effects reveal support for
rank and epidemic but not the stock or order effects. Since then numerous other
studies have tried to find evidence in support of the stock and order effects. But
evidence has been elusive, until now. Further, a survey by Frame and White (2004)
concludes that much more work is needed into financial innovation. In this paper
accomplishes three goals, (1) evidence is found to support certain technology
adoption theories (the order effects and possibly the stock effects). (2) Since the
technology under consideration is a financial innovation called bounce protection,
the paper answers Frame and White’s call for papers. And (3) refinements are made
to the Karshenas and Stoneman methodology and found to be superior to the original
empirical model.
Key Words: Banking, Bounce Protection, Checking Account, Diffusion, NSF fees, Overdraft
Protection, Technology Adoption
The author would like to thank Rob Porter, Shane Greenstein, Ron Braeutigam, Bill Rogerson,
and Nick Kreisle, for helpful comments and ideas.
2
Technology Adoption
1. INTRODUCTION
Students in introductory economics learn that the key to productivity growth and societal
wealth in the long run is technological advancement. On the firm level, superior technology can
drive a firm’s performance and competitiveness. Achieving these societal and firm results
necessitates not just the development of new technology but also its diffusion. For instance,
Krugman (1994) implicates delays in new technology adoption as a contributing factor to the
slowdown in productivity growth during the 1970s. Further, if early mover advantages are
persistent, then a firm’s delay in adopting is a persistent rather than a transitory disadvantage. The
literature contains several theories, but less empirical evidence, to explain how and why firms adopt
new technology. The contributions of this paper are threefold. First it provides some of the first
evidence for early mover advantages as a driver of adoption. Second, it makes methodological
contribution. Third, it answers Frame and White’s (2004) call for more research into financial
innovations.
Technology adoption models seek to explain why and when firms adopt new technology and
why some firms adopt earlier than others. Hoppe (2002) and Geroski (2000) survey the theoretical
adoption literature. The models could be divided into three types: heterogeneous firms, information
spreading, and competitive models. Deep empirical evidence supports the firm heterogeneity or
rank effects models. Indeed nearly every empirical adoption study confirms that firm size is a factor
in adoption. Less empirical work has been done on the information spreading or epidemic models
(Abdulai and Huffman, 2005, is one example). While little empirical evidence currently exists to
support the competitive models, this paper is one of the first to do so.
3
Technology Adoption
The competitive models can be further categorized but empirical evidence to distinguish or
support these is scant, until now. Karshenas and Stoneman (1993) and Abdulai and Huffman (2005)
consider four rather than three effects. They divide competitive models into two categories, the
stock and order effect. Both imply that adoption is negatively related to the share of the market
which has adopted. Stock effects can be summarized in single period models, whereas order effects
refer to persistent early mover advantages1. Karshenas and Stoneman (1993), Abdulai and Huffman
(2005) and Colombo and Mosconi (1995) fail to find any support for the stock or order effects.
Genesove (1999) and Mulligan and Llinares (2003) confirm competitive effects but do not attempt
to distinguish between the two effects or to control for other potential effects. Molyneux and
Shamroukh (1996) finds evidence that contradicts the predictions of the stock and order effects.
Specifically, they show that adoption is increased by competitor adoption. Gouray and Pentecost
(2002) find evidence to support the order effect but reject the stock effect. In the current study,
evidence is found to support the order effect and the rank effect (including a positive effect on firm
size); the epidemic effect is rejected; and the results are consistent with but not determinative of the
stock effect. This is the first study – with the possible exception of Gouray and Pentecost – to
confirm the validity of the competitive models (stock and order effects).
This paper also fills a void in studies of financial innovation, a literature which is surveyed
by Frame and White (2004). The common theme of their article is the paucity of research on the
rather broad area of financial innovation. This paper fills an area which is especially lacking,
diffusion studies. The financial innovation being considered is bounce protection, a product/process
offered to retail bank customers. It provides a good opportunity to test the adoption theories given
1
More complete descriptions of all four effects are provided in section (3).
4
Technology Adoption
above and simultaneously help fill the lack of research on financial innovation. Bounce protection
is process/product whereby a bank pays overdrawn checks rather than returning – bouncing – them2.
While it is fine to test the diffusion of bounce protection as a process, at the core of the process lies
a technology, the algorithms for determining which customers pose a risk if their checks were to be
paid. Algorithms and accompanying computer software, legal compliance, and other support are
sold by several consultants to the banking industry operating under brand names such as “NoBounce” and “Courtesy Pay”.
Bounce protection has appeared a few places in the literature. Fusaro (2006) finds that 20%
of overdraft checks are intentional, (i.e., customers are writing are themselves payday loans) with
the other 80% being checking account mistakes. Fusaro (2003) finds evidence that customers
appreciate bounce protection as they tend to migrate toward banks offering the service. Bar-Ilan
(1990) models what he called “overdrafts” and what is more precisely called an “overdraft
protection line of credit” (see section 2). He studies a situation where bounced checks do not occur.
The empirical framework used here follows the design of Karshenas and Stoneman. The
model described in section (4) is the Karshenas and Stoneman model with some modifications. A
data set of banks is used to test for the presence of four technology adoption theories and to test the
effectiveness of the model changes. The changes are found to be improvements on the original
framework. And evidence is found to support the rank, stock and order effects. But the data fail to
support the epidemic effect. These results differ from the Karshenas and Stoneman and Abdulai and
Huffman papers which supported the epidemic effect but failed to show evidence for the stock or
order effects.
2
Bounce protection is defined in more detail in section (2).
5
Technology Adoption
This paper accomplishes three goals. First, it shows evidence for the competitive models,
in particular, the stock and order effects. Second, it fills a void in financial innovation diffusion
studies. Third, it provides methodological improvements to Karshenas and Stoneman’s empirical
model. The rest of the paper proceeds as follows. Section (2) contains some background on the
industry and the definition of bounce protection. Section (3) covers the rank, stock, order and
epidemic effects and the variables used to identify each. Section (4) describes the structural model
and the estimation strategy. Section (5) describes the data. Results and analysis are in section (6).
Section (7) offers some concluding remarks.
2. INDUSTRY BACKGROUND–WHAT IS BOUNCE PROTECTION?
When a check is presented for payment in excess of the account balance, several things can
happen. The bank can transfer money from a savings account to cover the check. It can loan money
to the customer to cover the check at a predetermined interest rate. It can pay the check, allowing
a negative balance in the account (with no interest charged). Or it can return, or bounce, the check.
The first two options are called overdraft protection. Usually the customer applies for
overdraft protection. When a savings account is used for overdraft protection, the bank transfers
money from a designated savings account to the checking account and charge a small fee, usually
between $2 and $5. With a line-of-credit based overdraft protection, the bank loans enough money
to cover the shortfall, usually with an interest rate comparable to credit cards and often without a fee.
In June 2004, 90% of US banks offered one or both kinds of overdraft protection.
6
Technology Adoption
For customers not enrolled in overdraft
Figure 1: Definition of Bounce Protection
protection or for those whose savings account
An overdraft check is presented for
payment. What can happen?
or line of credit is exhausted, the check is an
overdraft. Then the bank faces a decision –
bounce the check or pay it. Historically, for
good customers – high net worth or first time
If customer has Overdraft Protection:
Î Bank transfers money from
another account at the bank
Ï Bank loans money to cover the
overdraft
overdrafters – a bank officer often decided to
If no overdraft protection, bank can:
Ð Bank pays overdraft checks
pay the check, allowing the account to have a
Ñ Bank bounces overdraft checks
* Bounce Protection *
negative balance. In recent years, several
banks started paying overdrafts for more than just their best customers. Many use systematic
methods for determining which overdrafts to pay and which to bounce. A policy of paying the
majority of overdrafts is called a bounce protection program. The definition of bounce protection
is summarized in figure (1).
Some consider the bounce protection a loan, as the money to pay the overdraft is coming
from the bank’s funds rather than from any of the customer’s deposit accounts. Other work (Fusaro,
2006) suggests that it is a closer substitute to a bounced check than to a payday loan. To the extent
that bounce protection constitutes a loan, it is rather similar to an overdraft protection line-of-credit.
With the line-of-credit the customer must apply for the overdraft protection line-of-credit in
advance; a credit check is performed; and the bank is subject to onerous lending regulations. The
bounce protect is a stopgap for people who do not have overdraft protection available. Bounce
protection targets different consumers than overdraft protection – those with less elastic demand
measured across time or individual. That said, the author has noticed – but not yet been able to
quantify – that some banks are intentionally replacing overdraft protection with bounce protection.
7
Technology Adoption
3. RANK, STOCK, ORDER AND EPIDEMIC EFFECTS
The goal of an adoption study is to explain why firms adopt with different lags from the
introduction of the technology. Several theories have been advanced to explain observed adoption
patterns. Hoppe (2002) and Geroski (2000) survey the theoretical literature on adoption. Karshenas
and Stoneman (1993) bring together four of the effects considered in the theoretical literature, the
epidemic, stock, order, and rank effects. This section contains a brief description of each with a
discussion of the variables used to measure each effect.
3.1 Epidemic Effect
The epidemic effect states that a new technology, like a disease, spreads by contact.
According to an epidemic model, each firm learns about the existence of a new technology only
from contact with a previous adopter. Firms may gain human capital relevant to operating the new
technology from contact with other adopters. An example of this literature is Mansfield (1968 and
1989). This effect is often taken to be correlated with time. Indeed, in Karshanas and Stoneman
(1993) [henceforth KS] and Hannan and McDowell (1987), the time factor in the model is taken to
represent the epidemic effect.
In the case of the banking firm and bounce protection, bank managers attend industry
association conferences at which they could learn about bounce protection. They also conduct
research on the products offered by their competitors. If the epidemic effect is present it likely
operates through one of these channels. KS find evidence for epidemic effects in their analysis; but
8
Technology Adoption
in the banking industry case considered here, there is no support for this effect. This particular
product seems to spread through consultants’ sales forces rather than company to company.
3.2 Stock Effect
Also known as game-theoretic models, the stock effect is based on the premise that the
returns to technology adoption decline with the number of firms utilizing the technology; when the
technology is rare it imparts a competitive advantage to its users, but as the technology becomes
ubiquitous no firm as an advantage. Given a cost of adoption, some number of firms adopt beyond
which adoption is unprofitable. As the cost of the technology declines, the market can support more
firms using the new technology. In stock effect models, firms are homogeneous.
Models such as that of Reinganum (1981) and Gotz (1999) specify stock effects. The former
specifies that technology reduces production costs, leading to higher output, which then leads to
lower prices, lowering the returns to adoption. The latter uses a variation of the Dixit-Stiglitz model.
In the case of bounce protection, the mechanism is different. Research shows that consumers
migrate toward banks offering bounce protection (Fusaro 2003). As more banks adopt bounce
protection, there are fewer customers to attract from the fewer banks not offering the service. KS
fails to find any evidence for the stock effect. The findings of this paper are consistent with the
stock effect, but the model is not capable of identifying stock effects in the presence of order effects.
3.3 Order Effect
Like the stock effect, the order effect depends on the number of adopters but it differs in that
the order effect depends on the number of adopters at the time of adoption. Early adopters accrue
9
Technology Adoption
benefits that are persistent even as followers adopt. For example, the first adopter establishes itself
as the market leader – the brand name; the market leader has the inside track to get limited resources
such as skilled labor or supply contracts or prime land. The later a firm adopts, the less benefit
accrues because limited resources are hard to acquire and customers view the early adopters as more
advanced. Thus, when adoption costs are sufficiently high, it is profitable to be the first adopter but
not the second or third. As costs decrease, adoption becomes profitable for a second bank, then a
third, etc.
The order effect is particularly appealing intellectually in the case of bounce protection.
Many banks do not advertise bounce protection for regulatory reasons. As a result, the only
customers who know of its existence are those who experienced it (i.e., those who have overdrafted
and had their checks paid). Thus, bounce protection helps banks retain customers rather than attract
customers.
Again, firms are ex ante homogeneous. However, the adoption decision causes a persistent
ex post heterogeneity. Theoretical models of this type can be found in Ireland and Stoneman (1985)
and Fudenberg and Tirole (1985). The only relevant variable is the market share of adopters at the
time firm i adopted. KS fail to find evidence for the order effect but this research finds such
evidence.
3.4 Rank Effect
The rank effect is based on a presence of exogenous firm heterogeneity. This heterogeneity
causes firms to have differing returns to adoption and thus differing reservation prices. As the price
declines, it falls below more firms’ reservation prices and more firms adopt. These simple models
10
Technology Adoption
assert that a firm’s adoption decision is a function of a vector of firm characteristics. Davies (1979)
and Ireland and Stoneman (1986) have rank effect models.
Typically, variables such as firm size, output growth, firm age, research and development
expenditure, corporate independence of the unit of observation, and market factors such as
concentration ratio are thought to influence the rank effect. In the case of bounce protection, some
additional variables are appropriate.
Firm Size: Most adoption studies find larger institutions adopting earlier. This is usually
thought to be due to scale factors, risk factors, and capital availability. Previous work has
recognized that smaller firms could be more flexible and able to respond faster but usually find the
scale, risk, and capital factors dominate. These results confirm a positive correlation between firm
size and adoption.
Output Growth: In the case of capital technology adoption, a growing firm is naturally
augmenting its existing stock of machines. In order to adopt, it must see a benefit of installing new
technology over old rather than the stronger condition of replacing old with new technology.
Bounce Protection is a change in policy which involves an infusion of intellectual capital, but the
issue of replacing existing capital does not exist. Since the technology here is scalable, no new
capital is required to accommodate growth. KS used market growth because they do not have data
on firm growth. This variable is included for comparison with previous studies; however, there is
no reason to expect it to be significant. The results confirm that market growth is not a factor in
adoption of bounce protection. Using firm growth rate rather than market growth does not change
the result.
Corporate Status: A unit in a larger organization could have access to investment capital or
it could suffer from a lack of flexibility. Because the typical pricing scheme for this product is a
11
Technology Adoption
share of the revenue generated by bounce protection (e.g., its cost is proportional to its size),
investment capital is unlikely to be relevant. The flexibility issue is supported by anecdotal evidence
so we would expect a unit of a larger corporate entity to be less likely to adopt bounce protection.
The results of the logit indicate that a corporate overlord slows adoption. But in the full model this
variable is statistically insignificant.
Concentration Ratio: Competitive factors could lead to slower or faster adoption rates.
Indeed, models have predicted both. This variable is included as a summary of those competitive
forces. Competitive factors in adoption have been specified in models by Hoppe (2000), Riordan
(1992), and David and Olsen (1992). The results indicate that more concentrated markets are more
likely to adopt.
Profit Pressure: One factor mentioned by industry insiders is the spread between interest
margins and non-interest expenses. This variable – profit pressure – is said to influence bounce
protection adoption thus: When interest margins decline to the point that they can not cover fixed
(non-interest) expenses, bank managers are pressured to find alternative, risky, sources of revenue.
Many have turned to bounce protection, a lucrative, but regulatorily risky, new method of increasing
fee revenue. This variable was found to be significant by Fusaro (2006). Though this variable could
easily be questioned based on economic theory, it is tested empirically and no evidence is found to
support it.
Prices: The levels of ATM and NSF fees are endogenous, but they are used as a proxy for
other underlying issues such as the presence of a business strategy to generate revenue from fees
rather than from interest margins. These prices are found to be insignificant.
Urban: Banks located in rural counties behave differently from those in metropolitan areas.
Since bounce protection is a way of augmenting customer service, it is more frequently used in rural
12
Technology Adoption
areas where customer service is more highly valued. Metropolitan areas are more likely to be
innovators. The results confirm the latter.
In section (4), a model of the rank, stock, and order effects is presented. Empirical results
are presented in section (6).
4. A MODEL OF TECHNOLOGY ADOPTION
The basic structure of a model to describe technology adoption derives from Hannan and
McDowell (1987). In this section, the KS (Karshenas and Stoneman, 1993) model is presented.
Refinements are presented and tested in section (6.2). Define gijtτ as the increment in period τ profit
for firm i, in market j if the firm adopted a bounce protection program in period t.
Define Ri to be the vector of factors, inherent to firm i, that may make it more or less likely
to benefit from adoption. This vector represents the rank effect. Let Fjt be the number of adopters
at time t in market j. The stock and order effects both depend on the number of firms to adopt (stock
depends on the number at the current period; order depends on the number at time of adoption).
Then the increment in time τ profit derived from adopting the technology at time t is a function of
Ri, Fjτ and Fjt:
(
gijtτ = g Ri , F jt , F jτ
)
which says that gijtτ is a function of firm characteristics, the number of firms in market j that had the
technology at time t (i.e., at the time of firm i’s adoption), and the number of firms that have the
technology at time τ (i.e., contemporaneous to the profit being measured). Naturally t#τ and we
13
expect
Technology Adoption
dg
dF t
and
dg
dF τ
to be negative if order and stock effects respectively are present.
Summing this profit increment over time from adoption forward, gives the total discounted
increment in profit from adopting bounce protection at time t:
∞
G =
t
ij
∫e
τ
=t
− r (τ − t )
(
)
g Ri , F jt , F jτ ∂τ
Notice that Gijt is indexed by i, j, and t but not by τ. The first two are the bank and market
respectively since profit, G, depends on bank specific factors and market specific factors. The
superscript t indicates that summed future discounted profit depends on the adoption time since
adoption price varies over time and since a bank’s position in the order of adoption will change with
adoption date (i.e. order effects are relevant). The profit, G, is not indexed by τ since we summed
(i.e., integrated) over the profit in each post-adoption period, gijtτ.
Adoption occurs in the period when discounted future profit from adopting net of price of
adoption (Pt) is greatest. See KS for more on this arbitrage condition for adoption3. This allows
for situations where a firm waits for prices to decline. The arbitrage condition can be expressed as
the maximization problem:
[
max e − rt Gijt − P t
t
]
The solution to this problem gives the following first order condition:
3
Intuition behind the arbitrage condition is that banks time their adoption for maximum
benefits. They balance a falling price of the technology against the cost of waiting to adopt. KS
also consider a profit condition where by banks adopt once the net present value of adoption is
positive. KS test these two conditions and find the arbitrage condition to be a better predictor of
adoption. Thus the arbitrage condition is used here.
14
Technology Adoption
dP
dg dF
⎧
e − rt ⎨rP t −
− g Ri , F jt , F jt +
dt
dF dt
⎩
(
)
1
r
⎫
⎬=0
⎭
See KS for details. Multiply the exponent term to the right hand side and call the resulting
expression yit:
yit = rP t −
(
)
dP
dg dF
− g Ri , F jt , F jt +
dt
dF dt
1
r
This equation is the benefit from waiting to adopt. The first term is due to interest earned on the
price of adoption, the second is due to paying more (less) when the price increases (decreases). The
third term is due to foregone current benefits of adoption. The last term is due to lost benefits from
moving down the order of adoption. Notice that the third argument of g (the stock effect) is now
evaluated at date t (adoption date). Since the second and third arguments are both evaluated at the
same time period in this equation, collapse the arguments of g [e.g., g(Ri, Fjt, Fjt) = g(Ri, Fjt)]. For
convenience of estimation, specify a linear functional form for g and g' . Then we get
yit = rP t −
dP
dF
− ρRi + ςF jt + φ0 + φρ Ri + φσ F jt
dt
dt
(
) (
)
1
(2)
r
In the presence of positive (negative) rank effects, the coefficients in the vector, ρ , will be
negative (positive). The opposite sign is because g enters the equation above with a negative sign.
In the presence of order effects, the φ coefficients will be negative and ς will be positive. If there
are stock effects, ς will be positive. The results support the rank and order effects and are consistent
with the stock effect.
The expression yt is the slope of future discounted profit to be earned from adopting bounce
protection at t net of adoption cost. Or yt is net marginal benefit of adopting at t. Figure (2) shows
future discounted profits, G , plotted against adoption date, t; y is the slope of this curve. This is the
15
Technology Adoption
path of profits from adopting bounce protection for a typical bank. Naturally a bank should adopt
at the peak of the curve (point B). A bank on the upward sloping portion of the curve (near point
A) can benefit from waiting to adopt, whereas one on the downward sloping portion of the curve
(near point C) has missed its prime opportunity to adopt and should do so immediately.
The epidemic effect is added to the empirical model in section (6), which describes the
empirical strategy and reports results. The following section describes the data.
5. THE BANK DATA
Data are combined from three sources. The primary data set is a national sample of bank
prices and fees4 (Fees Database). These data are augmented by the Consolidated Reports of
Condition and Income (Call Reports) and Summary of Deposits (SOD). The fees database is a
sample of 2487 bank-years, collected each June from 2000 to 2004. However, only the 711
observations collected in 2004 can be used for the primary estimation. The data contain an indicator
for a bounce protection program and the level of various bank fees. The Call Reports contain balance
sheet and income statement information such as deposits, assets, and fee income. They are publicly
available from the Federal Reserve and the FDIC. The SOD data are available from the FDIC and
contains deposit information at the branch level, which is used to calculate market shares.
In the 2004 data, a distinction is made between a formal and an informal bounce protection
program. A formal program is one which has well established criteria determining which overdrafts
4
These data are collected by Moebs Services, Lake Bluff, IL.
16
Technology Adoption
are paid and which are bounced. An informal program is one in which a bank official has the
discretion to bounce or pay an overdraft. The full sample can not be used for two reasons. First,
adoption dates are observed for only the banks in the 2004 sample. Second, the adoption date is not
clear for banks the offer an informal program since often this type of program is adopted graudally.
A quarter, 182, of the banks offer a formal bounce protection program at the time of data collection.
These banks were called to determine the date they adopted the program. Based on their answers,
the data was coded in six month intervals going back five years. The average adoption date was two
years before the data collection (censoring date) with a standard deviation of 17 months. Fifteen
banks adopted prior to five years pre-collection; these are considered initial adopters.
The time series of prices, Pt, shows a steady rate of decline of prices. This is estimated from
conversations with industry insiders. KS discuss a potential of bias from using a potentially
endogenous variable (prices) as an explanatory variable. However, the smooth downward trend used
for the price series suggests that endogenous prices may not be a problem here. While this smooth
downward trend does not match the ex-post market price, the crucial feature to a potential adopting
bank is that future prices to adopters are falling. It is unlikely that banks have any more insight into
future prices. Thus, we believe that our price series is an accurate representation of banks
expectations of future prices.
Table (1) shows summary statistics for the data. The average bank is in a market where 32%
of banks offer bounce protection and 68% of the market is held by the top 5 banks. Markets are
Consolidated Metropolitan Statistical Areas (CMSAs), Metropolitan Statistical Areas (MSAs) or
rural counties. Market concentration ratio is calculated using the SOD branch deposit data for each
market. All banks in the market are used in this calculation not just sample banks. Thus, for each
sample bank we have an accurate measure of market concentration rather than an estimate from the
17
Technology Adoption
Table 1: Summary Statistics of Depository Data Set
Variable
Obs
Mean
Std. Dev.
Min
Max
Units
Bounce Protect Program
Formal Program
Informally Overdraft
Market Bounce Protection
NSF Charge
Surcharge
711
711
711
711
454a
.256
.595
32.25
24.10
1.49
–
–
19.12
5.14
0.40
0
0
3.45
5.00
0.50
1
1
88.46
36.76
3.00
Indicator
Indicator
%
$
$
Adoption Date (formal prgm)
Before sample period
During sample
Never (Censored)
Interest Rateb
15
167
529
711
–
Fall 02
–
192
–
17 months
–
124
–
–
–
94
–
Fall 04
–
602
Basis Points
Deposits
Large Bank
Medium Bank
Deposit Growth
Market Concentration
Urban Bank
711
711
711
711
711
711
2954
.086
.444
12.5
68.5
.714
24300
–
–
18.1
16.0
–
0.5
0
0
–7.89
43.9
0
427000
1
1
115
100
1
$ Million
Indicator
Indicator
% rate
%
Indicator
Date
Evolution of Adoption: Percentage, hazard ratec of sample offering bounce protection:
Jun 99 Dec 99 Jun 00 Dec 00 Jun 01 Dec 01 Jun 02 Dec 02 Jun 03 Dec 03 Jun 04 Dec 04
2.1% 2.4% 2.5% 3.5%
4.6% 7.3%
8.7% 13.9% 15.9% 22.4% 25.5% 25.6%
–
0.4%
2.2%
4.3%
7.9%
11.4%
a
Some small banks have no ATMs; others offer free use of theirs; 454 banks charge a surcharge.
b
At date of adoption or date of censor for those not adopting.
c
Hazard Rate is the ratio of those adopting in period t to those who had not adopted as of period t-1.
sample data.
Obviously, market rate of adoption (Ftj) is measured not for all banks but based on a random
sample of banks. Many rural counties and some small MSAs have fewer than 10 observations. For
such markets, adoption rate would be measured too imprecisely. These observations are pooled
within a state, essentially making the assumption that rural counties and small MSAs within a state
share adoption rates.
The bottom segment of the graph shows the evolution of the program. Only 2.1% of the
18
Technology Adoption
banks in the sample adopted prior to the sample period. The pace of adoption was slow in the first
few periods but accelerated subsequently with many more banks adopting later. Abstracting from
apparent seasonality, the lower growth occurs in the earlier periods, with the exception of the final
period. This pattern seems to indicate that epidemic effects are present. The logit estimation in
section (6.1) also points to the possibility of epidemic effects but the full model results argue against
epidemic effects. The next section presents the data estimation and results.
6. ESTIMATION RESULTS
This section reports the results of a logit estimation before reporting the results of the full
model.
6.1 Cross Sectional Logit Estimation
Cross sectional estimation does not utilize the time at which a firm adopted. In the literature,
this type of adoption study is common because data on the time of adoption are rare. Rather, most
adoption studies, having only a cross section of data, see previous adopters and non adopters.
Studies using such data can evaluate the rank and sometimes epidemic effects but not the stock or
order effects.
Table (2) shows that most estimation results are as expected. The first set of estimations on
the top portion of the table contains all of the variables listed in section (3) which correspond to KS.
The lower portion of the table (Model 2) shows the results of estimation using a shorter list of
19
Technology Adoption
covariates. The shorter covariate vector is used in estimating the full model reported in section
(6.2). In column (a), the dependant variable is an indicator for whether the bank has a formal bounce
protection program. A formal program is one that has well defined terms as to whether a check with
insufficient funds will be paid or returned. The dependent variable in columns (b) and (c) is an
indicator for any type of bounce protection program, one that is formalized or one where check
return decisions depend on the judgement of a bank officer. Column (b) reports results from 2004
data only, the same sample as column (a). Column (c) uses data from 2000 to 2004. All variables
for an observation from year x, both dependent and independent, were collected in year x. Column
(c) uses the most data; column (b) is offered for comparison with column (a). Column (a) is offered
for comparison with the full model below, especially the version with restricted variables – model
(2) – as the same covariates are used in the full model.
The percent of the market offering bounce protection is highly significant and positive in all
six formulations. This variable could be interpreted as evidence for the epidemic effect as Bartoloni
and Baussola (2001) do. This interpretation is consistent with the accelerating adoption pattern
shown on the bottom portion of table (1). This result could also be interpreted as evidence against
the competitive theories, as the stock and order effects both imply that this coefficient be negative.
As mentioned earlier, other competitive models have predicted the positive relationship found here.
The model results, shown in the next section, better distinguish these effects.
The inclusion of market concentration is another attempt to capture competitive factors. This
variable is significant, for the informal bounce protection regressions [columns (b) and (c)] but not
significant for the formalized programs [column (a)]. The sign is
20
Technology Adoption
Table 2: Logit Estimates
Dependant variable:
Formal Bounce
Protection Programb
Column (a)
Model (1)
Constant
Epidemic Effect:
Pct. of Market offering BP
Competitive Factors
Market Concentration
Rank Effect:
Bank Size
Large Bank Indicator
Medium Bank Indicator
Not Part of Corp Struct.
Market Growth
Pressure
NSF Fee
ATM Surcharge
Urban
Year Indicators
Likelihood Ratio
Model (2)
Constant
Epidemic Effect:
Pct. of Market offering BP
Competitive Factors
Market Concentration
Rank Effect:
Bank Size
Medium Bank Indicator
Not Part of Corp Struct.
Urban
Year Indicators
Likelihood Ratio
Formal or Informal Bounce
Protection Programb
Column (b)
Column (c)
Coef
Std Error
Coef
Std Error
Coef
Std Error
–8.942*
1.496
–11.59*
2.52
–7.520*
1.130
6.161*
0.661
9.640*
1.301
7.522*
0.578
0.916
0.857
3.763*
1.462
1.435^
0.581
0.303*
–0.620
0.594^
0.767*
–0.711
–0.962a
0.031
–0.741a
0.355
0.101
0.534
0.246
0.228
0.890
1.380a
0.023
0.563a
0.318
0.194
0.246
0.560
0.479
2.093
0.083a
–.0013
–1.20a*
0.427
0.141
0.753
0.383
0.324
1.938
1.00a
.0320
0.448a
0.488
0.173^
–0.152
0.194
0.677^
–0.185
1.31a
–0.083
–0.272a
–0.083
Yes‡
323.9*
0.074
0.359
0.176
0.300
0.651
1.05a
0.014
0.219a
0.216
104.6*
193.6*
–8.036*
1.131
–11.98*
2.377
–7.407*
0.952
6.356*
0.653
9.501*
1.232
7.571*
0.574
0.708
0.843
3.083^
1.387
1.416†
0.573
0.276*
0.777*
0.796*
0.359
0.065
0.204
0.227
0.316
0.277^
0.571‡
0.519
0.356
0.126
0.341
0.320
0.480
0.142*
0.265‡
0.684†
–0.069
Yes‡
320.4*
0.053
0.148
0.300
0.215
186.5*
96.95*
Sample Size (Years)
711 (2004)
713 (2004)
2487 (2000–4)
‡
In Millionths
significant at: 90%, ^95%, *99%
b
A formal bounce protection program is one in which the bank has well established criteria to
determine when to pay a bad check; this data was collected in 2004 only. An informal program is any
in which bank managers sometimes pay bad checks if they feel that it is good for business. Any
bounce protection program is a formal or informal program.
a
21
Technology Adoption
positive signaling that less competitive markets are more likely to adopt the new technology. In
most theoretical and empirical adoption work the opposite is true, competition drives markets to
adopt new technology. Since this result holds only for informal programs, which are more prevalent
at small banks, most likely it indicates that smaller banks use bounce protection to compete with
larger banks in markets where large banks dominate (concentrated markets).
The other explanatory variables are intended to capture the rank effect. As most adoption
studies find, larger firms are more likely to adopt. Bank size is measured by the log of deposits and
two indicators for medium and large banks. The continuous variable is positive and significant as
is common in adoption studies. For a formal program, medium sized banks – those between 100
million and a billion in assets – are more likely to have a formal program. The results for informal
programs are surprising as common wisdom holds that community banks pioneered this practice.
22
Technology Adoption
For a formalized program, the significance of medium sized banks may indicate that large banks are
reluctant to adopt while the regulatory issues are still in question.
Banks that are not part of a greater bank holding company are more likely to adopt the formal
program. This result favors the theory that a corporate structure inhibits flexibility over the theory
that a corporate parent could provide funds for capital adoption. Urban banks are no more likely to
adopt, at least after the effects of market concentration and bank size are taken into account.
The variables dealing with market growth, the level of banks fees and pressure do not prove
to be significant and so are not retained in model (2), though in the case of NSF fees, it is hard to
draw any conclusions since it is surely endogenous to the adoption decision.
6.2 The Full Model
Two of the contributions of this research are to improve on the KS empirical methodology
and to find one of the first examples of the stock and order effects. In accordance with those two
goals this section is divided into two parts. In the first, the empirical model is presented and its
ability to fit the data is compared to the KS methodology. The second section presents empirical
results for the rank, stock, order and epidemic effects.
6.2.1 An Empirical Model
Maximum likelihood estimation is used here. In particular the survival time likelihood
function is:
L(α , ρ, φ , ς ) = ∏ h(a , ρ, φ , ς ) S (a , ρ , φ , ς )
B
Before describing the hazzard (h) and survivor (S) functions a word of intuition should be made.
23
Technology Adoption
Figure (2) shows future discounted profits, G , plotted against adoption date, t; y (marginal benefit
net of marginal cost of adopting at t) is the slope of this curve. Optimally, a bank should adopt at
the peak of the curve (point B) where adoption is highest. A bank on the upward sloping portion
of the curve (near point A) can benefit from waiting to adopt, whereas one on the downward sloping
portion of the curve (near point C) has missed its prime opportunity to adopt and should do so
immediately.
Pre-sample adopters, should adopt at point B and be observed on the downward sloping
portion of the curve (where y is negative) at the inception of data collection.5 For these banks, the
probability of adopting pre-sample (or in the period of first availability) is hi(t) = Pr{yit + g < 0} if
t=1. Here, g is an error term. Firms at point A when the technology becomes available will arrive
at the peak and adopt and thus have the hazard hi(t) = Pr{yit + g = 0}. KS combine the equality and
inequality to get one weak inequality, hi(t) = Pr{yit + g # 0}, which they estimate. However, since
the pre-sample and during-sample adopters are distinguishable to the researcher, a better estimation
procedure is to use the above strong inequality for those banks who adopted prior to the beginning
of data collection and use the equality following it for all other observations. That is, banks that
adopted before data collection should be on the declining portion of the profit curve around point
C when data collections begin; all other adopters should be observed arriving at point B at the top
5
If data collection corresponds with the initial availability of the technology then we can
think of these banks as being near point C when the technology is first available and should be
observed adopting immediately. This will not change the hazard function math which follows.
24
Technology Adoption
Figure 2 Future Discounted Profit of
Adopting Bounce Protection at time t
of the curve and adopting. Non adopters should be
near point A at the censoring date. The optimization
technique should reflect this.
In the first case (pre-sample adopters), the
equation can be estimated as KS do. The adoption
condition is yit + g # 0. Assuming g is distributed
with some distribution function V(g), the hazzard rate
(instantaneous probability of adoption) is hi(t , –yit) =
Pr{yit + g # 0} = V(–yit). In the second case, rather than choosing coefficients to minimize yit, we
choose coefficients to get yit as close to zero as possible, or to minimize (yit)2 . So in the hazzard
function the yit is replaced with (yit)2 . The exponential functional form is imposed thus eliminating
any need for parameter restrictions to guarantee a positive hazard. The parametric hazards for the
inequality and equality cases respectively are
hi (t , R, F ) = e
− yit
and
( )
hi (t , R, F ) = e
− yit
2
where the expression y accounts for the rank, stock and order effects. In order to incorporate
epidemic effects, consider the Weibull distribution of adoption time. See KS for a derivation and
explanation of the epidemic effect modeling. Consider the following intuition for the use of the
Weibull. If the explanatory variables fully explain adoption then there will be no duration
dependence and α will be unity. If, as the epidemic effect posits, adoption will accumulate
momentum over time then α will be greater than unity. In other words, α>1 implies that banks are
more likely to adopt later rather than earlier which suggests the epidemic effect. Incorporating
epidemic effects with the respective hazards above yields.
25
Technology Adoption
(
hi t , Ri , F
t
j
) = αt (e )
− yit
α −1
α
(
and
hi t , Ri , F
t
j
) = αt
α −1
⎛ − ( yit ) ⎞
⎜e
⎟
⎝
⎠
2
α
(3) and (4)
These hazard functions imply the respective survivor functions:
(
S t , Ri , F
t
j
)
( )
t
= exp ⎡− t α e − yi
⎢⎣
α
⎤
⎥⎦
(
and
S t , Ri , F
t
j
)
⎡ α ⎛ − ( yit )2 ⎞ α ⎤ (5) and (6)
= exp ⎢− t ⎜ e
⎟ ⎥
⎝
⎠ ⎥⎦
⎢⎣
Pulling together the likelihood function from above, equations (4), (6) and (2) yields the
following estimation function. In order to get the estimation function for the KS methodology we
would simply use equation (3) and (5) rather than equations (4) and (6) – the second and third lines
respectively – below.
L(α , ρ, φ , ς ) =
∏ h(α , ρ,φ ,ς ) S (α , ρ,φ ,ς )
B
(
2
− yt
h(α , ρ, φ , ς ) = αt α −1 e ( i )
(
)
α
)
⎡ α − ( yit )2 α ⎤
S (α , ρ, φ , ς ) = exp ⎢ − t e
⎥⎦
⎣
dF
dP
yit = rP t −
− ( ρRi + ςFi ) + φ0 + φρ Ri + φς Fjt
dt
dt
(
)
1
r
where Ri is the vector of variables representing the rank effect; ρ is the vector of coefficients on Ri;
Pt is the price of adoption; Fjt is the fraction of market j banks who have adopted before time t; ΔP
and ΔF are the one period (half year) changes in prices and adoption rates respectively; r is the
interest rate; φ0 is the coefficient on
vector Ri and the scalar
Δ F ; φ is the vector of coefficients on the interaction of the
r ρ
Δ F ; and φ is the coefficient on the interaction of F t and Δ F .
ς
j
r
r
In order to test the efficacy of the proposed methodology adjustment both techniques are
estimated. Results are reported in the second column of Table (4) , labeled “y”, for estimation when
26
Technology Adoption
equation (3) is used as the hazard function, as KS do. In the first column, labeled “y2”, reported is
the method that uses the equation (4) hazard for those that adopt during the sample period but retains
the equation (3) hazard for those banks that adopt prior to the sample period. They give qualitatively
similar results – signs and significance of coefficients do not differ greatly. However, the
improvement recommended here has a significantly better fit than the method used by KS; the value
of the log likelihood is higher (–649 compared to –702 for the KS method which implies a
likelihood ration test statistic of 105.05).
6.2.2 Results for Rank, Stock, Order and Epidemic Effects
The rank effect is measured by the vector of coefficients ρ, the order effect is in the
coefficients φ , the stock effect is in the coefficient ς , and the epidemic effect is in α. If the
epidemic effect is present then α>1. Thus if we find α to be statistically below one (1) then there
is negative time dependence which is at odds with the epidemic effect. A positive value for the
coefficient ς is indicative of both stock effects and order effects.
Negative values for the
coefficients φ signal the order effect. Specifically, if φ is positive then there are no order effects;
if ς is also positive then this must be due to the
presence of stock effects. If φ is positive and ς is
negative then there are neither order effects nor
Table 3: What the Results Indicate
About The Stock and Order
Effects
ς<0
ς>0
φ<0
contradiction
Order
maybe Stock
φ>0
no Order
no Stock
no Order
Stock
stock effects. If φ is negative there are order
effects; if ς is also negative then there is a
contradiction since the negative φ implies order
effects and the negative ς implies no order effects.
If φ is negative and ς is positive then order effects are present but the presence of stock effects are
27
Technology Adoption
inconclusive; this is because the order effects can cause both (i.e. there is no need for order effects
to explain this result). The rank effect is present if the coefficients in the vector ρ are non-zero.
However, a negative coefficient implies direct association with adoption; a positive coefficient
implies an inverse association with adoption. Recall, as noted in section (4), that these variables
enter equation (2) – note the “-g” – with a negative sign, and thus enter the hazzard, survivor and
likelihood functions, with a negative sign. Therefore, the coefficients here should have opposite
signs from their interpretation.
First, consider the epidemic effect. A finding of α>1 would indicate positive duration
dependence. KS found duration dependence, which they interpret as evidence for the epidemic
effect. Table (4) shows the estimated value of α for bounce protection. The result, α<1, implies
negative duration dependence, which indicates fewer adoptions as time progresses. This is in
contrast to the findings of the cross sectional logit estimation in section (6.1) where firms in high
adoption markets are more likely to adopt. This result indicates that the logit result is more likely
to result from competitive effects than from epidemic effects.
28
Technology Adoption
Consider, now, the stock and order effects. These effects are tested by the coefficient ς and
by the vector of coefficients φ. Table (4) shows that ς is positive and φ is negative which indicates
that order effects are present and stock effects are possible but not certain. The term ς is positive
and statistically significant. Since φ is a vector, consider first statistical significance then the sign.
Table (4) reports the results of a likelihood ratio test on the vector of terms φ = [φ0,φρ,φς], which
Table 4: The Stock, Order, Rank, and Epidemic Effects
Hazard Functiona
y2
Coef
Epidemic Effect (α)
r*P
dP/dt
Rank Effect (ρ)
Bank Size
Medium Sized Bank
Not Part of Corporate Structure
Market Concentration
Urban
Stock/Order Effect (ς)
F
Order Effect (φ)
(F’/r)
(F’/r) Bank Size
(F’/r) Medium Sized Bank
(F’/r) Not Part of Corp Str.
(F’/r) Market Concentration
(F’/r) Urban
(F’/r) F
Likelihood Ratio test of Order
Effects: (φ0 = φρ = φς = 0)
y
Std Error
Coef
Std Error
0.029
0.721*
0.030
–0.00128*
–0.00123^
0.00044
0.00059
–0.00264*
–0.00326^
0.00100
0.00146
–0.127*
–0.149‡
–0.147
–0.667‡
–0.172
0.037
0.087
0.098
0.378
0.134
–0.404*
–0.262
–0.384
–2.765^
–0.995^
0.114
0.266
0.316
1.158
0.454
1.989^
0.899
5.348‡
2.775
–1.816*
0.013
–0.210*
0.207*
0.657^
0.237^
2.270*
0.484
0.029
0.056
0.055
0.280
0.101
0.601
–5.145*
0.108
0.123
0.135
1.946*
0.911*
6.297*
1.861
0.077
0.137
0.154
0.758
0.282
1.663
0.710*
225.8*
158.1*
Log Likelihood
-649.67
-702.19
Wald Statistic
282.7*
180.0*
‡
^
Number of Observations: 711
Significant at: 90%, 95%, *99%
a
Hazard function 1 uses the hazard in equation (3) which is also used by K&S
Hazard function 2 uses the method recommended herein which uses the equation (3) hazard for
individuals who adopted before the sample beginning but uses the equation (4) hazard for any
observation that is observed adopting.
29
Technology Adoption
shows them to be statistically significant in both regressions. To determine the sign of φ, consider
the sum φ[1,R,F]’, which is the function dg/dF . The fitted values of this sum have mean values of
–0.19 and – 0.34 respectively in the two estimations. Further, in the first estimation, there are no
positive observations; in the second, 2 of the 711 observations are positive. Thus, with a
consistently negative estimate for dg/dF , we may conclude that collectively φ is negative. The
positive and significant result on ς indicates that stock effects and/or order effects are present. The
negative sign on φ indicates that the order effect is present. Thus, in the presence of order effects,
the model cannot confirm the existence of stock effects. The results are, however, consistent with
stock effects.
The various elements of the rank effect are consistent with expectation and the logit
estimation. As is noted in section (4) and in this section on page (27), these coefficients should have
the opposite sign from what they did in Table (2) and from their interpretation. The estimation is
comparable (i.e., has the same sample and dependent variable) to the column (a) model (2) logit
estimation.
Bank size, having no corporate structure, market concentration and urban are all negative.
Thus the results show that more concentrated markets are more likely to adopt the technology, the
same result as in the logit estimation. See section (6.1) for discussion of this result. Larger banks
are more likely to adopt the technology. Bank size could have a bit of a concave shape as being a
medium sized bank is significant at the 10% level only in one of the equations. Size being positively
correlated with adoption is the most consistent result across the literature. Units of a bank holding
company, though significant in the logit estimation are not significant here. Urban banks are not
significant in the logit regressions nor in the first regression here.
The full model shows no evidence to support the epidemic effect. It shows a rank effect of
30
Technology Adoption
bank size and market concentration. But this paper is one of the first to find evidence of the order
effect. And the results are consistent with stock effects also. This is one of the first papers to find
evidence of the persistence of early mover advantages in this literature.
7. CONCLUSION AND POLICY CONCERNS
Most of the empirical technology adoption literature is limited by having only a cross section
of adopters and non-adopters at a single point in time. This makes them unable to test certain
theories on the adoption of new technology. This is why the literature is absent, with one exception,
any evidence that stock or order effects exist. The data used here are supplemented with adoption
dates so that the stock and order effects can be estimated. Evidence is found for the order effect and
while the stock effect can not be separately confirmed the results are consistent with the stock effect.
As in most other studies rank effects are present, most notably a firm size effect. Epidemic effect
is not supported by the results.
The model used here is due to Karshenas and Stoneman (1993). A flaw in the model is
discovered and a remedy is proposed. The revised methodology is estimated along with the original
methodology. While results are qualitatively similar the revised methodology provides significantly
better fit to the data.
The results of this research have some lessons for consumers. While bounce protection was
pioneered at smaller community bank the results of this research indicate that large banks are now
more likely to adopt bounce protection. Thus bounce protection will spread to the majority of the
31
Technology Adoption
banking public quickly. Other research (Fusaro, 2003) found that, on balance, consumers prefer
banks with bounce protection, although this study did not distinguish between formal and informal
bounce protection. The stock and order effects are both based on the idea that there is a limit to
adoption. One possible explanation for this could be that a segment of customers are harmed by
bounce protection and seek out banks that do not offer it. Thus more thorough work on the welfare
effects of bounce protection could be useful.
The rank effect variables contain little cause for concern over customer abuse. High fee
banks are no more likely to offer bounce protection. Urban banks, also, are no more likely to adopt.
These results do not raise new concerns about consumer protection but they certainly are not
definitive in dispelling the possibility that segments of the consumer population are worse off with
the spread of bounce protection.
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Technology Adoption
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