Assessing Bank Performance Using Malmquist Productivity Index Approach and One-Step System GMM Dynamic Panel Data Model

This article evaluated the total factor productivity of Ethiopian banks from 2011 to 2020 using the DEA-based Malmquist productivity index and one-step system GMM dynamic data approaches. The study covered the 14 banks that were operational during the study period and examined the regressive, stable, and progressive nature of their productivity taking into account both the production and intermediary role of banks. We used constant returns to scale to compare the efficiency and productivity and establish a benchmark for bank performance. Interest expense, operating non-interest expense, and deposits were used as input variables and interest income, operating non-interest income, and loan and advances as output variables to analyze the productivity change of banks in their production role while deposits and loans were used as input and output variables, respectively to study productivity change of banks in their intermediation role. The study concludes nominal efficiency change both due to improved operations and management practices as well as increased economies of scale and deterioration in technological efficiency. We also conclude nominal regress in total bank factor productivity during the study period and a regressive, and progressive impact of technology, and improved management practices on the productivity of Ethiopian banks, respectively. Consequently, we suggest a thorough feasibility study in the technology choice of banks.

The financial sector is critical to the efficient allocation of resources, economic growth, and the creation of jobs. The financial sector has grown markedly in advanced nations in the past few decades while developing economies have been reforming their financial sector during the same period to bring changes. In many emerging economies, financial development has played a key role in their economic development endeavor. Policymakers often believe that financial development boosts productivity, which in turn brings economic growth.
Given the rising problems of globalization and increasing competition, banks as one of the most important financial institutions must be capable of implementing sound financial management practices. Following the economic crisis and the subsequent decline in the demand for banking products along with the use of cutting-edge innovations in the access and production of financial services, many countries have initiated a major reorganization of their financial sectors with a focus on the banking sector (Mansour & El Moussawi, 2020). This is attributed to the dominant role of banks within the financial sector and owning of most of the sector's resources and capabilities. Wheelock and Wilson (1999), Haralayya & Aithal (2021), and Shair et al. (2021) conceptualize efficiency as the difference between observed input and output levels, as well as related ideal values. Bank efficiency is the most important issue in the financial sector as it directly impacts the stability of the banking sector and the effectiveness of the country's economic policy (Yilmaz, 2013). Bank efficiency scores are indicators of the industry's overall performance which also is used to measure the influence of government policy and regulation on economic performance (Wheelock & Wilson, 1999;Sadalia et al., 2018;Nhan et al., 2021).
The Ethiopian banking industry is home to a large regional powerhouse like the Commercial Bank of Ethiopia with a $20 billion asset base and other very smaller banks. It operates in a fairly conventional manner with paper-pushing branches though it also parallelly makes use of sparks of "digital disruption" (Ayalew, 2021).
Ethiopia now has 17 private and 1 state-owned bank which is a significant rise from 1990's sole state-owned bank and only 7 in 2000 (Aluko & Ibrahim, 2020;Dinku, 2021;Gemeda Edeti & Chand Garg, 2021). Over the last decade, an in- Domestic savings, as indicated by national accounts figures, increased to 24% of GDP in FY 2017-18, up from less than 10% a decade before. Simultaneously, cash in circulation has decreased over the last decade, from 7% to 4% of GDP and 17% to 9% of banking assets. This can be ascribed to improved absorption of cash into the banking system instead of stashing it "under mattresses" and other informal methods.
Also, as Ethiopia doesn't have a capital market, the majority of saving and investment activities are carried out through the banking system. Besides, the Ethiopian banking industry appeared to be a key employer in the formal sector, with about 90,000 employees. This is a roughly threefold growth over ten years and a double growth over five years. After the government, banks are anticipated to be among the major formal sector employers in the economy although manufacturing sector employment numbers are not yet publicly available. This made bank productivity an important field of study by financial economists, practitioners, and policymakers (Garamu, 2016).
Generally, banking in Ethiopia has played a critical role in widening financial access, increasing national savings, and supporting important public and private initiatives during the last decade. Banks have recently emerged as vital suppliers of employment, income, and taxes. Despite the several outstanding achievements listed above, Ethiopian banks' performance remains limited and trailing in some key areas. In particular, Ethiopia's banking expansion is: 1) much more modest in comparison to GDP and peer countries; 2) has done more to improve proximity to the population rather than active usage by the population; 3) has provided much stronger support for the public sector rather than the private sector; and 4) has not yet provided the specific forms and features of financing to match local private sector needs.
Few studies have been carried out to examine bank efficiency and productivity in Ethiopia (Lelissa, 2014;Garamu, 2016;Lema, 2016;Lelissa & Mohammed, 2016;Ram & Mesfin, 2019;Berhe, 2021). Garamu (2016) and Berhe (2021) (2019) that didn't explain their approach as production or intermediation, others including Lelissa & Mohammed (2016), Berhe (2021), and Garamu (2016) used the intermediation approach. However, the intermediation model is more appropriate when the conversion of deposit to loan is a challenge: a character of well-developed financial systems. As such previous studies missed the context of underdeveloped and developing financial systems in which Ethiopia is a part.
The challenge of the Ethiopian banking system is mobilizing enough deposits, but not loan conversion, though loan conversion is also important (Bayiley, 2013). Nonetheless, using the intermediation approach over and above the production approach would add value and make the analysis more complete and robust. In addition to this, extant literature studied the productivity of Ethiopian banks up to 2017 (Berhe, 2021;Garamu, 2016;Lelissa & Mohammed, 2016;Ram & Mesfin, 2019) indicating a temporal research gap in the study of the productivity of Ethiopian banks.
From the gap analysis presented above, the current research aims to fill both methodological and temporal gaps. Therefore, the current study employed the Malmquist productivity index approach and production approach along with the intermediation approach to fill a methodological gap within the existing. The study also used a one-step system GMM dynamic panel model to capture changes in productivity of Ethiopian banks over time. A one-step system GMM dynamic panel model offers a lower bias and higher efficiency than other approaches such as the standard first-difference GMM estimator (Bayiley, 2021). Finally, the study used the most available recent data from 2011 to 2020 to fill the temporal gap.
The rest of the paper has been structured as follows. Section II covers extant literature, Section III research methodology, Section IV the results and discussions, and Section V the conclusion and policy implication aspects.

Function of Banks
The roles banks play in an economy made them one of the most closely regulated and extensively studied institutions throughout the world. Banks are involved in the financial intermediation and payment of goods and services as well as provision of a wide range of financial services, ranging from checking accounts and savings plans to loans to businesses, consumers, and governments.
Investment banking, insurance protection, financial planning, guidance for merging firms, the selling of risk-management services to businesses and individuals, and a slew of other new services, including fintech (Syukriadi & Sunitiyoso, 2021;

Measuring the Output of Banks
The empirical research on productivity measurement, as well as the assessment of cost and economies of scale, and the study of bank efficiency, all begin with measuring bank production. However, there is no agreement among academics on how to define bank production (Alfredsson et al., 2018;Gonzalez-Gomez et al., 2022). This is due to the intangible, multifaceted, and interrelated character of the services banks provide. Banks, for example, offer a diverse variety of services that are frequently difficult to separate and price separately, while other services are supplied for free.
Based on classical microeconomic theory, there are three main techniques of quantifying bank output in the literature: 1) Production Approach: Benston (1965) and Bell and Murphy (1968) proposed the production method to support the idea that banks "create" various types of loans and deposits utilizing labor and capital as inputs. Output should be assessed in terms of what banks do that causes operating expenditures to be incurred (Benston et al., 1982). However, detractors argue that the cost criteria are ineffective in distinguishing financial inputs from financial outputs. Furthermore, neither volume (number of accounts or transactions) nor value words are consistently applied in this method. mediation role, i.e., how they take deposits and acquire capital, which they then transform into loans and other assets. The value of loans is used to calculate output, whereas deposits, labor, and capital are used to calculate inputs. The question of whether deposits should be regarded as output (production method) or input (intermediation approach) is very important and represents the fundamental difference between the two approaches. Deposits can be considered output if they are linked to the supply of non-directly priced services such as liquidity, safekeeping, and payment services (free checkbooks, ATM usage, and so on) that consumers get in exchange for their deposits. Deposits, on the other hand, may qualify as input because the monies collected through deposits are used to "produce" loans and other bank assets.
3) User cost Approach: The user-cost method empirically tackles the problem by determining whether a bank asset or obligation is an input or an output based on the user cost of money (Izadikhah, 2018;Isakin & Serletis, 2018;Humphrey, 2020). Hancock (1985) extended on this technique by developing a production theory for financial businesses with empirically known inputs and outputs. The difference between a benchmark rate (representing the bank's opportunity cost) and the interest rate (rate of return) associated with keeping this asset is the user cost of money for bank assets. The difference between the interest rate connected with this liability and the benchmark rate is the user cost of money for a

Productivity and Efficiency
The productivity and efficiency of banks are commonly used to determine performance (Chen et al., 2018;Djaghballou et al., 2018;Alexakis et al., 2019). The ratio of output to the elements that allow it to happen is called productivity (Raymond et al., 2015;Tsolas et al., 2020). When an index of outputs changes at a faster rate than an index of inputs, productivity changes (LEE et al., 2010;Abbott, 2018;Moutinho et al., 2018). If the unit utilizes a single input to create a single output, this ratio is simple to calculate. If the production unit, on the other hand, uses many inputs to make multiple outputs, the inputs and outputs must be aggregated such that productivity remains the ratio of two scalars. The idea of efficiency is similar, but not identical though many authors in the efficiency literature do not distinguish between productivity and efficiency. For example, both productivity and efficiency are defined as the ratio of output to input by Green & Sengupta (1996), Bouyssou (2003), Bahrini (2015), Zelenyuk (2020). Instead of being defined as the ratio of outputs to inputs, efficiency may be defined as the distance between input and output, and the amount of input and output that defines a frontier, the best feasible frontier for a business in its cluster (industry).
Finally, productivity and efficiency may be characterized in a variety of ways.
First, if the frontier is defined as the ratio of outputs to inputs, productivity and efficiency are distinct, and the latter can only be measured through the relative performance of decision-making units (DMUs) (Baqaee & Farhi, 2019;Baležentis & Sun, 2020). Second, they are linked because productivity growth may be broken down into efficiency and technological advancement. The former relates to the more efficient input utilized in production under the same technology, while the latter refers to an upward movement in the production frontier as a result of a technology change. Malmquist (1953)  With an expanded window analysis, they followed the intermediation method to DEA and found deregulation improved the overall efficiency of Tunisian commercial banks.

Methodology and Approach
The goal of this article is to assess how Ethiopian banks' production has changed over time. A Malmquist productivity index technique is used for this purpose. The data type, data sources, and analytic method utilized to achieve the goal of interest are presented in the next section.

Data Type and Source
The Ethiopian Commercial Bank is constituted of 16 private banks and one state-owned bank. The current analysis includes 14 banks (13 privately held banks and 1 state-owned bank) due to data limitations. That is, the analysis excludes Enat Bank, Debub Global Bank, and Addis International Bank. To evaluate the productivity changes of the banks under study secondary data on input variables output variables are collected from the audited balance sheets and income statements of the banks under study.

Selection and Use of Input-Output Approach
An investigation of banking efficiency can be conducted using either production or an intermediation method. In the "production approach", the bank is viewed as a business that uses fixed assets and labor inputs to offer services such as depositing cash, disbursement of loans, and remittances. The amount of bank total deposit and or total loan is frequently used to represent the output, while the Open Journal of Business and Management number of employees (labor) and capital expenditures on fixed assets is used to represent the inputs (capital). Banks act as an intermediate between lenders and depositors under the "intermediation method", accepting deposits and other money to offer finance and alternative investments. The output is measured by income or profit from financing, total deposits, and any other non-interest-bearing income while inputs are usually denoted by operating costs and costs of providing financing to customers.
Based on the analysis presented above and aiming to examine the sensibility of estimated efficiency scores to alternative methods of measuring banking activity, this study focuses on two major approaches: the intermediation approach and the production approach (Table 1, Table 2).

Malmquist Productivity Index
This approach has three key MPI favorable conditions that distinguish it from other methods (Bansal et al., 2022;Xie et al., 2021;Dar et al., 2021). To begin with, there is no premise of cost reduction or benefit amplification. Second, information and yield expenses are not anticipated. Third, assuming board information is available, the method allows for the degradation of profitability into two categories. The MPI is based on distance functions, output distance functions for an output-oriented index, and input distance functions for an input-oriented index. The index is applied to the measurement of total factor   represents production point at time t and t + 1 respectively. The subscript "I" denotes the input orientation of the MPI model.
MPI in Equation (3)  x y . This means that the efficiency change is calculated by dividing the efficiency in (t + 1) period by the efficiency in t period. The index uses period t as well as period t + 1 technology. A geometric mean of two MPIs is used to calculate productivity growth. When the MPI G I value is larger than one, which means that overall productivity increased from period t to period t + 1. A number less than one implies a decrease in total production. MPI 1 G I = indicates stagnation in productivity between the period t and t + 1.
Using the concepts of input-oriented efficiency change (EFFCH) and inputoriented technology change (TECHCH), the input-oriented geometric mean of MPI (i.e., Malmquist total productivity change index) may be deconstructed as shown in Equation (4).
The first and second terms represent the efficiency change and the technology change respectively. MPI given by Equation (3) and Equation (4) can be defined using DEA like a distance function. That is, the components of MPI can be derived from the estimation of distance functions defined on frontier technology. The formal derivation of MPI was presented by Färe et al. (1997), Oh & Lee (2009), Casu et al. (2016 and it is the most common approach among the different ways created to estimate a production technology (Howcroft & Ataullah, 2006;Dorri & Rostamy-Malkhalifeh, 2017). By utilizing both CRS and VRS DEA frontiers to estimate the distance functions in Equation (4), the efficiency change (EFFCH) can be decomposed into scale efficiency change (SECH) and pure efficiency change (PECH) components. A scale efficiency change (SECH) is given in Equation (5).
In addition, the pure efficiency change (PECH) is given in Equation (6

The Intermediate Approach
The standard deviation results presented in Table 3 indicate the performance gap analyzed using the intermediate approach. It indicates the performance gap among sample banks in terms of interest and non-interest income, total loan disbursed, interest and non-interest expense, and total deposits mobilized. Also, a bank with a maximum output variable (in the year 2020) is more than 1530 times the size of a bank with a minimum output variable (in the year 2011). Also, a bank with a maximum input variable is more than 224 times the size of a bank with a minimum input variable. Both the output and input variable comparison designate a huge performance gap among sample banks. (Table 4) Moreover, the standard deviation results presented in Table 4 indicate the performance gap measured using the production approach. The result indicates the performance gap among sample banks in terms of total deposits mobilized, total loan disbursed, employees compensation, provision for doubtful loans and other assets, general expenses, and fixed assets. Also, the result shows a bank with a maximum output variable (in the year 2020) is more than 224 times the size of a bank with a minimum output variable (in the year 2011). Likewise, a bank with a maximum input variable is more than 809 times the size of a bank with a minimum input variable. Juxtaposing both results indicate a vast performance gap among sample banks.

Malmquist Productivity Change
The Malmquist productivity index is made up of five components that are used to assess performance. Efficiency changes, pure efficiency changes, scale efficiency changes, technological changes, and total factor productivity changes are among them. The Malmquist productivity index allows you to compare productivity changes within the banking industry as well as between groupings. As a result, with the aid of this metric, low achievers may be able to catch up. Total factor productivity, as the name suggests, refers to all elements affecting commercial bank output; more particularly, changes in total factor productivity include increases in efficiency and technology. The following is how Malmquist's total factor productivity is interpreted. The mean productivity change of individual banks during nine years is shown in Table 6. Out of the 14 commercial banks, 11 have a total factor productivity score of less than one. This shows that approximately 78.6% of the banks are not able to increase their total factor productivity (regressing in total factor productivity) during the study period of nine years. The remaining 21.4 percent of the bank can increase their factor productivity. Out of the 14, only 9 (64.3%) banks Y. T. Bayiley  were able to increase their efficiency, whereas 3 (21.4%) remained constant, neither progress nor regress in achieving efficiency, and only 2 (14.3%) show regress of efficiency.

Production Approach of Malmquist Productivity Change
Pure efficiency change and scale efficiency change are two types of efficiency change. As mentioned earlier, pure efficiency improvement is attributed to improved operations and management practices, whereas scale efficiency improvement is related to returns to scale effects. Any type of efficiency change score greater than one indicates improvement, whereas less than one indicates regress.
According to Table 6 Finally, the mean value of efficiency change scores of banks was greater than one while the mean value of technology change scores was less than one. Given that total factor productivity is the product of efficiency change and technology Open Journal of Business and Management change, its score was less than one. From this, we can deduce that while banks have shown improvement in catching up to the best-practice, they were not able to increase outputs with a given level of inputs. Figure 2 demonstrates that Abay Bank recorded the highest mean positive change in TFP of 4.8%. As indicated in Table 6, the 4.8% productivity achieved for the Abay Bank contains an efficiency growth of 5.2% and technological regress of 0.4%. Commercial Bank of Ethiopia shows the lowest average TFP transform with an average deterioration of around 17.8% in the total factor productivity change.

Result Using Intermediate Approach
From the table Total factor productivity, the responsibility of commercial banks is growing constantly in Ethiopia's banking sector. The yearly average total factor productivity changes of listed commercial banks during the study period was 0.991 as shown in Table 7, implying that the sample banks could have reduced their input by about 0.9 percent to achieve the same point of output. This   It can be noted that the level of efficiency change, technical efficiency change, pure efficiency change, scale efficiency change, total factor productivity change is continuously fluctuating throughout the years 2012 to 2020.
This indicates a minor productivity change among the sample banks over the study period.
According to   of the empirical data, the total factor productivity variation is 0.991, which is less than 1, indicating a 0.9% decline throughout the research period (2012-2020).
Total factor productivity has fallen as a result of deteriorating technological efficiency in privately held commercial banks.

Determinants of Bank Efficiency
After looking at efficiency as an important determinant factor of performances, we have moved the quantitative analysis to explore which of the inputs and outputs variables are the determinant factors of efficiency. The bank efficiency score is regressed using one-step system GMM using efficiency as the dependent variable with the previous year bank efficiency, total deposit growth, total loan growth, branch expansion growth, and size as explanatory (determining variable) without separating the bank into distinct categories. From the result, we can infer that the lag of individual bank efficiency, deposit growth rate, loan growth rate, bank growth rate (natural logarithm of the total asset) has a significant and positive impact on the efficiency of the banks. On the other hand, branch expansion has a negative and insignificant impact on the efficiency of the bank (Table 9).

Conclusion
The current study used the DEA-based Malmquist Index and measures the changes in total factor productivity and efficiency of Ethiopian commercial banks during the period 2011-2020. The paper used aggregate panel data covering the 14 commercial banks that were operational in Ethiopia during the study period. The total factor productivity change, measured by the Malmquist productivity index, was decomposed into efficiency change and technology change while the efficiency change was decomposed into pure and scale efficiency changes. The technology change represented innovation in the banking system and the pure efficiency changes the core efficiency gained due to improved operations and Open Journal of Business and Management management practices. Besides, the scale efficiency change was used to measure efficiency gains due to scale effects. We found nominal efficiency change both due to improved operations and management practices as well as increased scales. However, a deterioration in efficiency was observed as a result of technological change. Moreover, total factor productivity, which entails the overall changes in efficiency and technology, showed a nominal regress during the studied period. Hence, we conclude a regressive, and progressive impact of technology, and improved management practices on the productivity of Ethiopian banks, respectively.
The paper also concludes private banks were more efficient in mobilizing resources than the state-owned bank though no notable difference was observed in converting deposits to loans. Following this, we also conclude the production approach as the preferred model in analyzing Ethiopian banks' productivity change compared to the intermediation approach. Moreover, we conclude little difference in total factor productivity change using both the production (0.964) and the intermediation (0.991) approaches.
Finally, via the one-step system GMM paned data model we conclude deposit growth rate, loan growth rate, bank size has a significant and positive impact on the efficiency of Ethiopian banks except for branch expansion.

Practical Implication
The nominal regress in productivity owing to technological change cast doubt on the appropriateness of technology choice of Ethiopian banks. Thus, banks need to make a thorough feasibility study in their choice of technology.

Policy Implication
The relatively poor performance of the state-owned bank in resource mobilization may partially be related to its monopoly in accessing the financial resources of the Federal government. Such preferred treatment might have limited the competitiveness of the bank in deposit mobilization. Thus, if the state-owned bank has to improve its efficiency in deposit mobilization, it has to recraft its deposit mobilizing strategy and align such performance with attractive incentives.

Conflicts of Interest
The author declares no conflicts of interest regarding the publication of this paper.