“Efficiency assessment of banking systems’ performance”

Globalization processes define the modern trends in world economic development, including both international financial markets and the banking systems of different countries. The study aims to evaluate the efficiency of the banking systems of Ukraine and 17 European countries in order to choose the appropriate measures, concerning its increasing. The Data Envelopment Analysis (DEA) was chosen as a tool for evaluating the efficiency of the banking systems; the calculations were made using the Banxia Frontier Analyst software. Also, the BBC and CCR models of linear program- ming were used to define the existing relationship between the studied indicators. As a result of the study, the groups of efficient and inefficient banking systems were identified, which allowed determining the existing reserves, possible managerial tools and decisions for improving the inefficient banking systems’ performance. Besides, graphical interpretation of the current position (rank) of certain country bank system in relation to other countries’ banking systems was presented. The developed approach is aimed at improving bank management at the macro level and enhancing the efficiency of banking systems. of activity at all or failure to observe logical interrelation between con-secutive stages of the management decision-making process – analysis, planning, control, and regulation. The tools for evaluating the current state (efficiency of the analysis unit) and the possibility of comparison of the analysis unit with similar ones are of particular importance, since the absence of full systems of information support of the management process, lack of attention to system analysis, di-agnostics and forecasting of activity on macro level can lead to making false managerial decisions.


INTRODUCTION
The financial sector of any country occupies a central place in the process of its economic development. There is a positive relationship between the development of real and financial sectors, especially in terms of financial intermediation, which makes the financial sector very important for the development of any economy. Since banks are key players in the financial market in many countries of the world, the stability and efficiency of the banking system significantly affect the financial system and the economy as a whole.
Given this, ensuring stability and efficiency at the banking system level is impossible without using modern tools and technologies of bank management. In the banking sphere, a failure to formulate a clear concept of development leads to either lack of planning of activity at all or failure to observe logical interrelation between consecutive stages of the management decision-making process -analysis, planning, control, and regulation. The tools for evaluating the current state (efficiency of the analysis unit) and the possibility of comparison of the analysis unit with similar ones are of particular importance, since the absence of full systems of information support of the management process, lack of attention to system analysis, diagnostics and forecasting of activity on macro level can lead to making false managerial decisions.
The concept of efficiency is measured and can be defined as the relation of useful products to the total cost of the object. Evaluating the efficiency of a banking system allows the top management to control whether it has achieved the planned or rejected development and take appropriate corrective measures to ensure the achievement of the set goals. Besides, the assessment of the efficiency of the banking system and its comparison with the systems of other countries helps the central bank manage and regulate banking activity more efficiently in the country.

LITERATURE REVIEW
The concept of the efficiency of any system is complex and multifaceted. The concept of efficiency as a general indicator for all kinds of business was first formulated in the early works of Edgeworth (1881) and Pareto (1927); its empirical realization was implemented in the work of Shepard (1953). Efficiency in economics is interpreted as the maximum potential ratio between input and output of the product development process, which shows the optimal distribution of available resources, which allows for reaching the maximum potential ( According to Drucker (1963), efficiency can be defined as the ability of an organization to achieve results with minimal input resources. According to Jaouadi and Zorgui (2014), efficiency summarizes the idea of production in the best way, which means that efficiency is focused on using the minimum costs to get the best result. In other words, the optimized use of resources produces the best products at lowest prices. In management, efficiency can be considered a study of the optimized use of internal factors of a firm. On the other hand, the concept of efficiency results in the efficiency of factors and achievement of the goal, not considering the way and optimized use of resources.
Determining the efficiency of banks and banking systems remains a discussion among researchers. To determine bank efficiency, first, it is necessary to decide on the nature of approaches to understanding banking activity. Two basic approaches are widely used in the literature on banking theory, namely production and intermediary (Sealey & Lindley, 1977). Berger and Humphrey (1997) argue that none of these two approaches is perfect because they cannot fully cover the dual role of financial institutions as providers of account services and financial intermediaries. They note that the production approach may be somewhat better for assessing the efficiency of banking outlets, and the intermediary approach may be more acceptable for evaluating financial institutions as a whole.
Considering the importance of financial institutions, many studies are aimed at assessing the activity of banks in different countries ( Berger and Humphrey (1997) analyzed 130 studies that examined 21 different countries to measure the efficiency of banks using parametric and non-parametric methods, which shows the importance of efficiency studies in this sector. Haralayya (2021) investigated top six implementation challenges of core banking technology. Morozova et al. (2019) assessed the banking system's efficiency under the influence of the capital concentration factor. The authors have reported the capital efficiency as the dependence of the total income of banks in Ukraine in terms of the volume of their capital and liabilities based on constructing the models of the nonlinear Kobb-Douglas regression for the data of the Ukrainian banks. Besides, bank efficiency was calculated based on actual data and standard values for each factor as a measure in the Euclidean space to the limit of efficiency groups. Kozmenko and Vasyl'yeva (2008) considered the impact of increasing the efficiency of commercial banks on the improve-ment of the financial and credit mechanism to ensure the innovative development of Ukraine. Also, Kozmenko and Belova (2015) investigated the establishment of systemically important banking institutions as a foundation of stabilization measures of the country's economy. Leonov et al. (2014) analyzed the impact of stock market development as an alternative to households' savings allocation in banks.
Some scientists, such as Kuzmenko and Koibychuk (2018), analyzed the efficiency of the Ukrainian banking system and the efficiency of the banking system in the context of gender policy. The general indicator of the banking system's efficiency was constructed using relative normalization and Harrington's desirability function. The impact of gender policy indicators on the efficiency of the banking system was determined using correlation-regression and factor analysis tools.  Charnes et al. (1978), is based on mathematical methods for measuring the efficiency of a single group of decision-making units that use the same input and output data. By transforming the programming task with endless solutions into an approach to linear programming, DEA identifies the most influential business units and indicates what the inefficient units should do to become ef-ficient. In other words, DEA allows defining the best practices from the point of view of efficiency.
The first study the DEA applied to financial institutions was Sherman and Gold's (1985) study, which assessed 14 bank branches. These authors have confirmed that traditional efficiency measurement methods, such as profitability and transaction costs, have not been so acceptable as they did not take into account the complexity of each branch's operations and did not consider the numerous results generated by multiple inputs. After this research, the banking sector became one of the main areas of interest for DEA application.
Despite the high popularity of DEA in the research aimed at measuring bank efficiency in recent years, there are no scientific works aimed at analyzing the banking system's efficiency in Ukraine by this method. Besides, there are no studies that reflect the effectiveness of the Ukrainian banking system among the bank systems of European countries, which has caused the choice of the research topic.

METHODS
To calculate the efficiency of bank systems, it is expedient to use Banxia Frontier Analyst software. This software is a tool that allows making calculations using the Data Development Analysis (DEA) technology. Throughout the world, DEA is used to assess the effectiveness of homogeneous object systems dealing with the same activity types and using the same resources. At the same time, efficiency is understood by the ratio of the value of input parameters to the sum of the values of output parameters.
DEA is based on using linear programming to construct a non-parametric linear surface (production line) based on the existing data. Performance evaluation is then conducted concerning this surface or production line. After the calculations, a comparative peer-to-peer process is undertaken, and future potential for improving the evaluation event for inefficient units is assessed. The following methodological approach is reasonable for assessing the efficiency of the banking system of Ukraine and the European countries (based on DEA analysis), which provides: • construction of BCC model of linear programming of conditional input minimization; • construction of CCR model of linear programming of conditional output maximization.
Mathematical formalization of constructing input-oriented BCC model of linear programming of conditional inputs and output-oriented CCR model of linear programming of the maximal ratio of conditional outputs with constant scale efficiency is as follows: where θ -the level of the country's banking system efficiency; u i -specification of an econometric model of dependence of the country's banking system's efficiency on the category of conditional outputs; y i -і-th specification of conditional outputs; v i -specification of an econometric model of dependence of the country's banking system's efficiency on the category of conditional inputs; x iі-th specification of conditional inputs.
Conditional inputs and outputs for DEA analysis should be determined using the main component method, which involves studying the relationships between the investigated indicators. It can reveal hidden indicators (factors) responsible for the existence of linear statistical relations (correlations) between them. Besides, the determination of more influential factors in the conditions of conducting the research of factors among the main chosen indicators, as well as the detection of statistical connection, determine the substantiation of the conclusions concerning the efficiency of certain influences on the investigated system.

RESEARCH RESULTS AND DISCUSSION
The combination of selected factors that influence the efficiency of the Ukrainian banking system is According to calculations, the scree plot was obtained (see Figure 1). Figure 1 shows that of the 13 main components offered by the program, it is advisable to select 5 or 6. To finally determine the number of principal components of final calculations, the values of factors should be analyzed (Table 1).
According to Table 1, only the factors with their own values larger than one should be chosen, i.e., in this case, it is the first five factors. These five selected factors describe the quality of the representation of received data by 88.9%. Having left only five main components in the analysis, a table of coordinates of the initial factors in the space of the new allocated elements will be obtained (Table 2).
According to Table 2, it is necessary to highlight the variables (observations) with the maximum (absolute) value of the factor coordinates for these factors. The total value of the factor load of the variable with any factor indicates that the variable is more strongly associated with this factor; that is, the larger the value of the factor coordinate of the variable, the better the variables show the structure represented by this factor. The coordinates are displayed for both main and auxiliary variables.
As can be seen from Figure 2, the first factor axis, corresponding to its own value 4.48, most closely correlates with the following major variables: Based on the selected factors, a table of source data for all countries of Europe and Ukraine was formed (Appendix C, Figure C4).      According to the data received, the banking systems of only five European countries showed their inefficiency: Finland (60.2% of efficiency from the standard banking system), France (76.1%), Portugal (68.6%), Slovakia (69%), and Spain (46.8%). Other countries that participated in the analysis showed 100% efficiency; that is, their effectiveness is either at the same level as the standard or higher than the standard. Ukraine also has an efficient banking system, according to the calculations.
The distribution graph ( Figure 5) provides a visual indication of the range of efficiency estimates and the number of countries with their points in each range. Thus, one country is in the range of 41-50, one in 51-60, two in 61-70, 1 in 71-80, and 13 countries in the efficient range, that is, they are 100% efficient.
Having defined efficiently working objects of the research in the range of 17 European countries and Ukraine, according to the input-oriented BCC model of conditional inputs minimization,      A comparison of the available reserves and the potential growth in the efficiency of banking systems in the countries whose banking systems were found to be inefficient according to the analysis results under both DEA analysis models are presented in Table  D1 of Appendix D. The table presents an in-depth interpretation of the feasibility of activating certain areas of strategic banking systems for countries with inefficient banking systems as a result of the analysis.

CONCLUSION
The aim of the study was to assess the efficiency of the banking systems of Ukraine and 17 different European countries in order to select appropriate measures and tools to improve it. The DEA was utilized as the efficiency assessment instrument of the banking systems and the computations were made using the Banxia Frontier Analyst software.
As a result of the study, an input-oriented BCC model and output-oriented CCR model were constructed. At the same time, conditional inputs and outputs were calculated based on the administrative fold of the efficiency parameters of the functioning of banking systems. During the study, the groups of efficient and inefficient bank systems were defined, existing reserves and the potential for efficiency improvement for countries with inefficient bank systems were identified. The graphic interpretation of the current position of distinct bank systems relative to similar systems of other countries was further illustrated. The results can be used to improve the bank supervision based on assessing bank systems efficiency of different countries and their comparison, as the proposed method is aimed at improving bank management at the macro level. This approach allows for a comparative analysis of efficiency; building a visualization of weights for further information activity; carrying out the more effective distribution of available resources; finding the information needed for developing a planning strategy, etc. All of the above can be used by the top management of a bank in the process of developing and implementing strategic and tactic management decisions.  n/a n/a n/a n/a n/a n/a n/a n/a  Figure C1. Analysis of the results and potential for improving the efficiency of the French banking system as of 2020 for the BCC model Figure C2. Analysis of the results and potential for improving the efficiency of the banking system of the Slovak Republic as of 2020 for the BCC model Figure C5. Analysis of the results and potential for improving the efficiency of the Spanish banking system as of 2020 for the BCC model Figure C3. Analysis of the results and potential for improving the efficiency of the Portuguese banking system as of 2020 for the BCC model Figure C4. Analysis of the results and potential for improving the efficiency of the Finnish banking system as of 2020 for the BCC model APPENDIX D Central bank assets to GDP (%) -70 -51