=Paper=
{{Paper
|id=Vol-2280/paper-16
|storemode=property
|title=Modeling and Forecasting the Diffusion of ATM/POS Terminals and Debit/Credit Cards
in Albania
|pdfUrl=https://ceur-ws.org/Vol-2280/paper-16.pdf
|volume=Vol-2280
|authors=Alma Braimllari Spaho,Elva Mezini
|dblpUrl=https://dblp.org/rec/conf/rtacsit/SpahoM18
}}
==Modeling and Forecasting the Diffusion of ATM/POS Terminals and Debit/Credit Cards
in Albania==
https://ceur-ws.org/Vol-2280/paper-16.pdf
Modeling and forecasting the diffusion of ATM/POS terminals and
debit/credit cards in Albania
Alma Braimllari (Spaho) Elva Mezini
Statistics and Applied Informatics Dept. Data Analysis Specialist
Faculty of Economy, University of Tirana Alosys Communications
alma.spaho@unitir.edu.al elvamezini@hotmail.com
customers, to deliver a wider range of services at lower
costs, and offer 24-hour banking support to customers.
Albanian banking has come a long way in electronics
Abstract banking in the past years. At the end of 2017, out of 16
The advancement of information technology commercial banks operating in Albania, 15 are offering
has enhanced delivery of banks' services, and e-banking services (Table 1, Appendix). E-banking
has an enormous effect on development of products/services offered by banks include: ATM
more flexible payments methods and more (Automated Teller Machine), EPOS (Electronic Point
user-friendly banking services. Commercial of Sale), virtual POS, Internet Banking, Phone
banks in Albania to be competitive have Banking, Mobile/SMS banking, Electronic (debit,
started to offer electronic banking services in credit, prepaid) Cards. Actually, twelve banks offer
year 2004. This paper aims to study the Internet banking; eight of them have some form of
diffusion process of electronic payment Mobile Banking and two banks provide mobile
instruments in Albania. The main objective of payments with 3rd party platform operator. Among all
this research is to model and to forecast the e-banking services offered from banks in Albania,
diffusion of electronic payment instruments ATM was the most popular channel, followed by
such as ATMs, POS, credit cards and debit electronic credit/debit cards, internet banking and
cards, using the data from Central Bank of EPOS [SR14].
Albania. After it was confirmed that the The proliferation of bankcards and non-cash payment
diffusion of each electronic payment technologies, such as ATMs and POS terminals has
instrument follow the S-shaped curve, the been one of the most relevant innovations in payment
Logistic and Gompertz models were estimated systems over the past several decades. In 2004
using STATA software. The parameters of commercial banks in Albania offered for the first time
Logistic and Gompertz models give card based services. Debit cards are issued against a
information on the diffusion speed and the current or savings account and their usage is restricted
maximum potential number of each electronic to funds held in the particular bank account. A credit
payment instrument, terminals or cards. These card is essentially a payment instrument through which
findings are useful to regulators, commercial purchases can be made utilizing credit provided by the
banks, bank customers, other financial issuing bank. ATMs offer considerable benefits to both
institutions, and policy makers. banks and their depositors. The usage of machines
offers depositors cash withdrawal at more convenient
times and places for them, than during working hours at
1. Introduction bank branches. Banks also aimed to foster the use of
cards at the point of sale for purchase transactions,
The banking industry has undergone significant installing POS card payment devices. With the
operational changes over the last decade, thanks to adoption of POS machines by merchants, electronic
advances in information technology. The information cards can be alternatively used to make purchases.
technology advancement has produced more effective Therefore, the final usage of debit cards will depend on
and efficient channels to deliver banking services. One consumers’ attitudes as well as on the availability of
of the offspring of information technology in banking POS systems and ATMs. Debit cards are used for cash
operations is electronic banking (e-banking). This withdrawals at ATMs and for purchasing transactions
technology allows banks to get closer to their at POS terminals. Debit and credit cards have been the
2
main payment instruments that have substituted cash at Other than the diffusion of an innovation, researchers
the POS terminals. also consider technological substitution, where an
The promotion of the use of electronic payment existing technology is replaced by a newer one.
instruments for transactions among economic actors is Decrease in the price of substitute technology and/or
relatively important to the Albanian economy, when increase in the price of substituted method increase the
considering the fact that the use of cash in the economy probability of technology diffusion [KMG11]. Also,
has a cost of around 1.7 % of GDP for the Albanian the results of the study of [KMG11] provide evidence
economy [BoA17]. The use of bank cards in ATM and that degree of substitutability of teller with ATM in
POS terminals shows that cash withdrawals from ATM India is high, but ATM is not a perfect substitute.
terminals have the main share in transactions with The main objective of this research is to model and
cards, an indicator of a largely cash-based economy. In predict the electronic payment instruments diffusion in
2017, about 18.91 million cards transactions, equal to Albania, in order to help businesses and policy makers
ALL 200 billion, were processed in total. Of total to implement the most suitable strategies. Once it
transactions, about 90% were cash withdrawals from confirmed that the diffusion of each instrument follows
ATMs and only 9.17% were customer payments the S-shaped diffusion curve, it was estimated the
through cards at POS terminals. Card payments at POS logistic function and Gompertz function with three
terminals point to a predominant debit card parameters, using STATA software. The parameters of
transactions. However, in terms of value, credit card both models give information on the diffusion speed,
transactions are significantly higher than debit card and the maximum potential number of each instrument
ones. The low use of cards as a payment instrument in the study.
shows the familiarity level of the public, the low level
of financial education, and the limited infrastructure of
POS terminals offered from enterprises. 2 Material and Methods
Most of the literature approximated the S-shaped curve
for technological diffusion using either the logistic
model or Gompertz model. Both of these models 2.1 Diffusion models
generate S-shaped curves with a few early adopters, The literature on the diffusion of emerging technology
then a more rapid period of adoption, then a slower generally uses S-curves to predict the diffusion process.
conclusion. The Gompertz curve is less symmetric than Because the new technology typically at first grows
the logistic curve, where in the initial growth rate is not slowly, then exhibits a growth rate greater than 1,
as high and its decline more gradually. The Logistic followed by a period of slower growth (growth rate less
and Gompertz model each have unique characteristics, than 1) and finally stops developing. The empirical S-
making them useful models in empirical studies of curve literature, in the technology-diffusion context has
diffusion. In their study, [MI06] reviewed studies on tended to focus on just two functional forms: logistic
the modelling and forecasting of the diffusion of model and Gompertz model [Fra94, BN06].
innovations. They cover a large body of literature The logistic model is described by the differential
which looks at many different mathematical equation
formulations of an S-shaped diffusion and list fifteen S- y ay(c y) (1)
shaped growth curve equations. This study imposes two
where y(t) represent the total diffusion at time t, c the
extreme hypotheses that explain this shape, which are
saturation level (the maximum expected level) of the
those based on the dynamics of a (broadly
technology and a is the coefficient of diffusion which
homogeneous) population and those based on the
describes the diffusion speed. The saturation level of
heterogeneity of the population. In their study,
diffusion is a critical and often questionable parameter
[QCR16] analyzed the diffusion patterns of non-cash
[MVS08]. The diffusion speed is proportionate to the
payments in China and based on Logistic and Gompertz
population that has already adopted the service,
model they found that POS terminals have shown a
denoted by y and the remaining market potential
higher diffusion rate than ATMs.
represented by (c-y).
3
The solution the logistic model (1) is given by model. The out-of-sample data cover the two last year
c (2016-2017).
y(t ) a ( t t0 )
(2) The choice of functional form for a particular
1 e
where y(t) is the estimated diffusion level at time t, c is technology provides important insights. It helps to
the maximum level of diffusion such that c lim y(t ) ); characterize the dynamics of the trend. Certain
t technologies are described best by one functional form
a is the speed of convergence of y(t) to its limit and and other technologies by another. There are many
characterizes the curvature of the diffusion path or different model selection criteria. Since our models
speed of diffusion; t0 is the moment of time when have only one explanatory variable, the time, and the
technology diffusion achieved half of its maximum same number of parameters, they are all equivalent to
level. minimizing the sum of squared errors (SSE). Some
The Gompertz model is described by the differential other criteria used here are, Akaike Information Criteria
equation (AIC) and Bayesian Information Criteria (BIC). The
y a y(ln c ln y) (3) best model is the model which has the smaller value of
The solution of which is given by AIC and BIC. To evaluate the performance of the best
a ( t t0 ) fitted or forecasted model is used the Root Mean
y(t ) cee (a > 0) (4)
Square Error (RMSE) given by the following
where c is the upper limit of the solution path or n
maximum penetration level, c lim y(t ) ; a is a measure
1
t equations: RMSE ( yi yˆi )2 .
n i 1
of the speed of convergence of y(t) to its limit and
characterizes the curvature of the diffusion path or
speed of diffusion; t0 is the moment of time when
technology diffusion achieved the share 1/e ≈ 36.8% of 3 Results
its maximum level.
The important feature of the Gompertz path is that the
diffusion goes faster at the beginning but becomes 3.1 Descriptive analysis
slower over time. This leads to a relatively short period According to the Central Bank of Albania data, the
of rapid expansion and to a relatively long period of number of ATM terminals was increased from 93 in
gradual growth up to the maximal level. The logistic 2004, to 826 in 2015 and to 747 in 2017. The higher
curve is more symmetric, the growth rate (measured number of ATMs was in year 2015. The figure 1
as y / y ) is initially not as high as in the Gompertz indicates that the number of ATM is increased from
curve and it declines more gradually [JSF07]. 2004 to 2015 and then in years 2016 and 2017 the
number of ATMs is decreased. At the end of 2017, the
number of ATMs decreased by 6.63% compared with
2.2 Data 2016.
The data used for this analysis are taken from the
Central Bank of Albania database [BoA18]. The
dataset contains information about the number of
ATMs, POS terminals, debit cards and credit cards for
the period of time 2004-2017 in Albania.
To estimate the parameters of the Logistic and
Gompertz models the nonlinear least squares method
and STATA software were used.
For forecasting, a model that fits best to the in-sample
data does not necessarily provide more accurate
forecasts. Therefore, the performance of out-of-sample
forecasts is used to help for the selection of a diffusion
4
ATM terminals, the speed of diffusion was 0.522 and
.Figure 1: Development in ATM and POS terminals half of its maximum level was achieved in 2005. The
The number of POS terminals is increased from 155 in results show that logistic model has the best
2004, to 4903 in 2010, and to 7294 in 2017 (Figure 1). performance in describing the ATM technology
At the end of 2017, the number of POS terminals diffusion. The fit of each model is measured by the
increased by 2.57% compared with 2016. The number values of AIC, BIC, and RMSE. These measures
of virtual POS terminals is increased from 3 in 2013, to indicated that logistic data fits best to the actual data
20 in 2014, and 28 in years 2016 and 2017. Terminals and also is the best to predict the number of ATMs.
for the use of electronic money cards recorded very
positive developments. They showed an increase from Table 1: Estimated parameters of the diffusion models
597 in 2015, to 680 in 2016 and 1391 in 2017; the for ATM and POS terminals
increase was 104.56% compared with the end of 2016.
ATM terminals POS terminals
Parameter Logistic Gompertz Logistic Gompertz
* * *
c 828.84 848.56 6264.78 6890.75*
a 0.794* 0.522* 0.623* 0.365*
t0 2006.63* 2005.84* 2008.24* 2007.44*
R2 0.9993 0.9982 0.9953 0.9964
2
R adj 0.9990 0.9975 0.9937 0.9952
AIC 108.95 120.34 177.05 173.74
BIC 110.41 121.79 178.51 175.19
In-sample 17.65 28.37 301.37 262.67
. Out-of- 61.09 76.75 880 565.86
sample
Figure 2: Developments in debit, credit and e-money Note: Significance level: * , p < 1%.
cards
The results of Logistic model for POS terminals
The number of cards in circulation is increased, from indicated a maximum level of 6264 and the speed of
33288 debit cards in 2004 to 914119 debit cards in diffusion was 0.623. POS technology has achieved half
2017; and from 806 credit cards in 2004 to 96312 of its maximum level in year 2008. The results of
credit cards in 2017. In 2017, the number of debit and Gompertz model indicated a maximum level of 6890
credit cards increased by 4.9% and 12.1%, POS terminals, the speed of diffusion was 0.365 and
respectively, compared with 2016. The number of half of its maximum level was achieved in 2007. The
electronic money cards is increased from 32873 in results indicate that Gompertz model has the best
2015 to 42860 in 2017. performance in describing the POS technology
diffusion. The values of AIC, BIC, and RMSE reveal
that Gompertz data fits best to the actual data and also
3.2 Results of diffusion models is the best to predict the number of POS.
The results of Logistic model for the number of debit
The results of Logistic model for ATM terminals cards indicated a maximum level of 791086 cards and
number indicated a maximum level of 829 and the the speed of diffusion was 0.568 and half of its
speed of convergence to the saturation (maximum) maximum level was achieved in year 2007. The results
level was 0.794. ATM technology has achieved half of of Gompertz model indicated a maximum level of
its maximum level in year 2006. The results of 828036 debit cards, the speed of diffusion was 0.370
Gompertz model indicated a maximum level of 848 and half of its maximum level was achieved in 2006.
5
The results show that Gompertz model has the best 6890 POS terminals, generated by Gompertz model,
performance in describing the diffusion of debit cards. was achieved in 2016
The values of AIC, BIC, and RMSE indicate that
Gompertz data fits best to the actual data, and
800
Gompertz model is the best to predict the number of
debit cards.
600
Table 2: Estimated parameters of the diffusion models
for debit and credit cards
400
200
Debit cards Credit cards
Parameter Logistic Gompertz Logistic Gompertz
0
* * *
c 791086 828036.6 108504.2 206043.5* 2005 2010 2015 2020 2025
year
* * * *
a 0.568 0.370 0.429 0.150 ATM Fitted Logistic ATM
* * * Fitted Gompertz ATM
t0 2007.25 2006.29 2012.33 2014.33*
R2 0.9959 0.9971 0.9984 0.9978
2
R adj 0.9946 0.9961 0.9978 0.9970 Figure 3: Actual and predicted number of ATM using
AIC 292.68 288.60 218.96 222.67 Logistic and Gompertz functions
BIC 294.13 290.06 220.41 224.12
8000
In-sample 37282.7 31464.26 1727.34 2016.03
Out-of- 108166.5 85615.42 2841.14 9050
6000
sample
Note: Significance level: * , p < 1%.
4000
The results of Logistic model for the number of credit
cards in Albania indicated a maximum level of 108504
2000
cards and the speed of diffusion was 0.429. Half of the
maximum level of credit cards was achieved in year
2012. The results of Gompertz model indicated a
0
saturation (maximum) level of 206043 credit cards, the 2005 2010 2015 2020 2025
year
speed of diffusion was 0.150 and half of its saturation POS Fitted Logistic POS
level was achieved in 2014. The results show that Fitted Gompertz POS
Logistic model has the best performance in describing
the diffusion of credit cards. The values of AIC, BIC,
and RMSE indicate that Logistic data fits best to the Figure 4: Actual and predicted number of POS using
actual data and also the Logistic model is the best to Logistic and Gompertz functions
predict the number of credit cards in Albania.
3.4 Prediction of debit and credit cards
3.3 Prediction of ATM and POS terminals In the figure 5 are shown the actual and predicted data
In the figure 3 are shown the actual and predicted data about the number of debit cards using both models. The
for ATM terminals. The saturation level of 828 ATMs, saturation level of 791086 debit cards obtained from
generated by logistic model, was achieved in 2015. logistic model was achieved during the period 2014-
Figure 4 shows the actual and predicted data for POS 2015.
terminals using both models. The saturation level of
6
200000 400000 600000 800000 1.0e+06
4 Conclusions
Developing models that explain the growth process is
critical for policy formulation, capacity planning and
introduction of new products and technologies.
Electronic payment instruments (growth) projection
informs providers of these services/ products about the
potential consumer base.
In this paper, Logistic and Gompertz models were used
to describe and to forecast the number of ATM/POS
terminals and debit / credit cards in Albania. The
0
2005 2010 2015 2020 2025
year results indicated that:
Debit cards Fitted Logistic Debit Cards related to ATM terminals, logistic data fits best to
Fitted Gompertz Debit Cards
the actual data and logistic model is the best to
predict the number of ATMs;
about POS terminals, Gompertz data fits best to the
Figure 5: Actual and predicted number of debit cards actual data and Gompertz model is the best to
using Logistic and Gompertz functions predict the number of POS terminals;
related to debit cards, Gompertz data fits best to
150000
the actual data and Gompertz model is the best to
predict the number of debit cards; and
about credit cards, logistic data fits best to the
100000
actual data, and logistic model is the best to predict
the number of credit cards in Albania.
Also, the results indicated that the diffusion of ATMs
50000
and POS terminals, and also debit cards have achieved
their maturity level, whereas the diffusion of credit
cards is increasing and its maturity level is predicted to
0
achieve around the year 2025.
2005 2010 2015 2020 2025
year In the future research, the factors influencing the
Credit Cards Fitted Logistic Credit Cards diffusion process of electronic payment instruments can
Fitted Gompertz Crebit Cards be studied using panel data modeling. Also, the
diffusion of virtual POS terminals, e-money terminals
and e-money cards can be studied in future research.
Figure 6: Actual and predicted number of credit cards
using Logistic and Gompertz functions
Figure 6 indicate the actual and predicted data about
the number of credit cards using both models. The References
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