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 number of credit cards will continue to increase and according to the results of logistic model the saturation [SR14] A. Spaho, and T. 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