Technical and allocative efficiency of commercial banks in Ethiopia

Abstract

This paper investigated the technical and allocative efficiency of commercial banks in Ethiopia. The analysis was based on unbalanced panel data of 19 banks over the period of 1990-2022. The study has applied shadow pricing approach to estimate and decompose the overall cost inefficiency into technical and allocative components. Findings reveal that publicly owned commercial bank is technically more efficient than privately owned commercial banks. Evidence also found that, on average, small and recently established privately owned banks are technically more efficient than other large private owned banks in Ethiopia. All banks are found allocative inefficiency due to over-utilization of loanable funds and physical capital relative to labor input. The overall result also shows that greater cost saving in public owned commercial bank in Ethiopia could be achieved by optimizing input use, while such cost advantage in private owned banks could be attained by improving managerial efficiency.

Impact Statement

In developing countries like Ethiopia where secondary financial markets are tiny or non-existent, promoting safe and robust commercial banking system is an important prerequisite for economic growth and development. The safety and soundness of the banking system are inextricably linked to economic efficiency of individual commercial banks. This study estimate and decompose cost efficiency of Ethiopian commercial banks into technical and allocative efficiencies (inefficiencies). The results of the study provide a valuable information to the shareholders, government and regulators in designing policies that improve the profitability and competitiveness of commercial banks.

Keywords:

• Technical efficiency
• allocative efficiency
• commercial banks in Ethiopia
• shadow price
• Fourier Flexible cost function

REVIEWING EDITOR:

• Dr David McMillan University of Stirling
• United Kingdom of Great Britain and Northern Ireland

SUBJECT CODES:

• Microeconomics
• industrial economics
• financial institutions
• banking industry

1. Introduction

The overall well-being and performance of nearly all contemporary economies are closely tied to the viability of their financial system. In nations such as Ethiopia, where secondary capital markets are either non-existent or in their early stages, the extent to which the system brings the desired economic benefits relies greatly, among other factors, on the efficiency of the commercial banking sector (World Bank, 2002). An efficient commercial banking system is a critical and inextricable part of economic growth and development because it determines the speed of capital formation and technological progress. The level of efficiency is an important indicator of commercial banks’ competitive viability (Abidin et al., 2021); hence, promoting their efficiency plays a vital role in maintaining safe and sound banking system. The level of efficiency varies across banks and over time, and thus investigating the efficiency of commercial banks has important policy implications as only banks that operate efficiently remain in the business.

The microeconomic notion of efficiency, more formally, economic or overall efficiency (EE) of individual firms encompasses both technical and allocative (or price) efficiency components. Technical efficiency (TE) refers to a firm’s success in minimizing waste, either by producing the maximum possible output using a given level of inputs, or by producing the same level of output using the minimum possible inputs. On the other hand, allocative efficiency (AE) refers to a firm’s ability to combine inputs and/or outputs in optimal proportions in light of prevailing prices (Fried et al., 2008; Kumbhakar & Lovell, 2000).

The need to decompose the overall inefficiency (EI) of individual firms is often justified by the fact that the causes of technical efficiency (TI) and allocative inefficiency (AI) are different. Specifically, firms in the same industry with similar technologies could attend different level of TE due to differences in managerial ability and effort in minimizing wastage (Fried et al., 2008). Thus, knowledge of the level of TI could help banks to take corrective measures, thereby gaining competitive advantage. Conversely, AI is frequently attributed to government policies and regulations; sluggish or incomplete adjustments to price changes (Huang et al., 2011), and macroeconomic conditions (Isik & Hassan, 2002; Sanchez et al., 2013). Hence, understanding the nature of AI could help enact and enforce public policies and regulations that aim to improve the performance of commercial banks while preserving the safety and soundness of the system.

There is a large number of empirical works on the efficiency of commercial banks. Most of these studies investigated the overall or the TE of banks (for example, Abdulahi et al., 2023; Abidin et al., 2021; Agama et al., 2023; Alemu, 2016; Bayuny & Haron, 2017; Dong et al., 2014; Jiménez-Hernández et al., 2019; Lema, 2017), while some studies dealt with the technical as well as the AE (AI) of banks (for example, Auwalu, 2019; Batir et al., 2017; Huang et al., 2011; Ouertani et al., 2020; Sanchez et al., 2013). The findings of these studies show evidences that the level of TE (TI) varies across banks, while the nature of AI of commercial banks is mainly input specific (Huang et al., 2011; Ouertani et al., 2020). Empirical evidences also show that the dominant source of banks’ inefficiency could be either technical (Auwalu, 2019; Huang et al., 2011) or allocative in nature (Ouertani et al., 2020; Sanchez et al., 2013). Thus, while it is helpful to understand the nature and causes of efficiency (inefficiency) differences across individual commercial banks, it is also worth identifying the costs of inefficiency to design and implement appropriate interventions.

Although valuable as information, the conclusions drawn from these prior studies are mixed and cannot be generalized to other economies. Differences in the findings of studies from different countries could be explained primarily by the existing disparities in technological advancements, competitive landscapes, and policy and regulatory frameworks across most economies. This indicates the need for country-specific, empirically supported evidence that can aid in formulating interventions tailored to a country’s unique circumstances.

The purpose of this study is to investigate the TE and AE of commercial banks in Ethiopia. The issues are worth considering topic in Ethiopian context for a number of reasons. First, unlike most other contemporary economies, the country’s financial system is shielded from external competitions. Second, the system lacks secondary capital market, and domestic commercial banks are the sole source of funds for productive investments. Third, the banking industry of the country can be characterized as an oligopolistic market structure, wherein a single publicly owned commercial bank alone holds a market share exceeding 50%, while more than 20 domestic privately owned commercial banks account for the remaining share. Another notable feature of the country’s banking industry is that public and privately owned banks are often faced unequal treatment. Thus, the relative performance of banks according to their size and ownership forms is an important empirical question. Moreover, the nature and cost of AI of Ethiopian commercial banks is worth considering because, unlike in most contemporary economies, banks in the country are highly regulated, and also since 2009, they have been operating under unstable and unfavourable macroeconomic conditions and restrictive policy environment.

This study contributes to the existing literature on banks’ efficiency at least in two ways. First, this study, to our best knowledge, is the first to estimate and decompose the EE of Ethiopian commercial banks into TE and AE components. Although they are few, the existing studies in Ethiopia focus on TE (TI) of individual banks (for example, Abdulahi et al., 2023; Agama et al., 2023; Alemu, 2016; Lema, 2017). By placing exclusive emphasis on the technical side of efficiency, these studies have ignored the potential cost-saving benefits that could be achieved by optimizing resource allocation. In addition to producing more complete information, a joint estimation of TE and AE of commercial banks is warranted to avoid potentially misleading policy conclusions that could arise from the possible correlation between the two components (Huang et al., 2011). In spite of this, researchers in Ethiopia as well as in other countries give less serious attention to AE (AI) of individual banks. Except some early studies from different countries, such as Huang et al. (2011), Sanchez et al. (2013), Auwalu (2019), Ouertani et al. (2020), and few others, most of the existing empirical works deal with either the overall or the technical aspect of bank efficiency (inefficiency). Empirical knowledge on AE (AI) of commercial banks in developing countries is particularly crucial as the information can be a valuable aid to design policy interventions that promote safe and sound commercial banking system.

Second, the study contributes to the existing literature on the efficiency of banks by extending the limited empirical application of econometrics method. The empirical analysis of most prior studies relies on a non-parametric approach, namely Data Envelopment Analysis (DEA) (for example, Abdulahi et al., 2023; Abidin et al., 2021; Agama et al., 2023; Alemu, 2016; Auwalu, 2019; Bayuny & Haron, 2017; Jiménez-Hernández et al., 2019; Lema, 2017; Sanchez et al., 2013). As a non-parametric approach, DEA can be applied without imposing any explicit functional form and distributional assumptions. However, like any non-stochastic methods, the approach is highly sensitive to measurement errors and other data noise. Moreover, the DEA does not produce information regarding the nature of input-specific AI.

The two most widely used parametric (econometrics) methods are: Stochastic Frontier Approach (SFA) and Shadow Pricing Approach (SPA). For example, Dong et al. (2014) applied both DEA and SFA to analyse cost efficiency of Chinese commercial banks. The SPA, on the other hands, applied to estimate and decompose efficiency of commercial banks by some prior studies, such as Huang et al. (2011) and Ouertani et al. (2020). The SFA requires an arbitrary distributional assumption and restrictive functional form to estimate AE (AI) components. Moreover, the SFA rules out estimation of the nature of input-specific AI. The SPA, conversely, permits modelling and estimating the nature and cost of bank’s AI parametrically imposing neither restrictive functional form nor arbitrary distributional assumptions (Atkinson & Cornwell, 1994; Fried et al., 2008; Kumbhakar & Lovell, 2000). Thus, the empirical analysis of this study relies on the SPA.

The reminder of this paper is organized as follows. In Section 2, we discuss the related literature. In Section 3, we present the methodology used in this study. The empirical findings and discussions are presented in Section 4. Finally, the summary and conclusion of the study are presented in Section 5.

2. Related literature review

2.1. Causes and costs of technical and allocative inefficiency of banks

The notion of EE of individual banks that correspond to cost minimization framework is cost efficiency (CE). CE measures a firm’s success in producing a given level of output with the minimum possible cost in the best practice firm. A firm is said to be cost inefficient (CI) if it incurs extra or unnecessary costs to produce a given level of output. The source of a firm’s CI¹ can be either ‘technical’, arising from excessive utilization or wastage of inputs, or ‘allocative’, arising from optimization errors in input use, given prevailing prices (Fried et al., 2008; Kumbhakar & Lovell, 2000).

The source of variation in the level of TE (TI) of individual firms in the same industry with similar technologies often attributed to differences in managerial decision making ability and effort (Fried et al., 2008). The level and cost of TE (TI) of individual banks thus strongly related to their asset quality via managerial quality because banks with incompetent and less rigorous senior management expected to incur extra cost (Berger & DeYoung, 1997). At bank level analysis, the level of managerial ability and efforts may not fully observable; consequently, we infer it, and thus the level of TE (TI), among other things, from bank specific characteristics and from external production environment in which banks operate.

Banks’ characteristics, such as ages of operation, size and ownership forms could produce differential efficiency effects. Firms’ age of operation usually uses as a proxy measure of learning-by-doing (Ayalew, 2021). Early entrants are often expected to be more technically efficient than later entrants because their managers and employees can learn through experience and become more skilled at their tasks. Large firms tend to be in business longer and therefore benefit more from economies of experience and learning effects than smaller firms (Nooteboom, 1993). In the banking industry, there may also be a positive relationship between age and size because building technology, enhancing managerial expertise, and improving worker skills takes time and huge resources (Huang et al., 2011). Thus, large commercial banks could outperform smaller banks because their economies of expertise (learning) and information allow them to reduce costs of credit creations (Aduba & Izawa, 2021). Smaller commercial banks, on the other hand, could perform better than large banks by pursuing efficiency as competitive strategy (Abidin et al., 2021; Isik & Hassan, 2002). The quantity and quality of managerial effort, and thereby the level of technical efficiency also expected to be less in public owned firms than private firms since the dispersed and non-transferable nature of public ownership may reduce managerial efforts or/and may give room for opportunistic behaviour (Fried et al., 2008; Huang et al., 2011; Isik & Hassan, 2002).

In the standard theory of the firm, managers are expected to operate efficiently due to competitive pressures. In contrast, the quantity of managerial effort often expected to vary inversely with market power, protection, and subsidies (Fried et al., 2008). The effects of competition on bank efficiency in the banking sector are not agreed upon. Both market power and competition can have positive or negative effects on banks’ efficiency. Competition may cause some banks to be less strict with collateral requirements, screening and monitoring; consequently, it could lead to a greater default rate among borrowers (Borauzima & Muller, 2022; Yagli, 2020). Similarly, limited competition could reduce banks’ efficiency either by attracting riskier borrowers and/or encouraging banks to take risk (Boamah et al., 2022). Indeed, a bank that take more risk may grant loans without proper credit rating and monitoring; hence, they could enjoy cost advantage and appear more efficient, at least in the short-term (Berger & DeYoung, 1997).

The causes of AI, by contrast, is frequently attributed to government policies and regulations of the industry under consideration; sluggish or incomplete adjustments to price changes; managerial objectives other than profit or cost optimization; macroeconomic or market conditions. High competition along with restrictive regulatory framework may force banks to choose a suboptimal mix of inputs and banking services (Isik & Hassan, 2002; Sanchez et al., 2013; Yagli, 2020). Deviation from optimization behavior is often expected to be higher in public owned firms than private owned firms. Economics literature identified a number of reasons why managers of public owned firms likely to deviate from optimization behavior. One possible reason is that institutional restrictions in public firms may limit managers’ ability to adjust quantities and prices of outputs and inputs freely and instantly in response to changing market conditions (Huang et al., 2011). Similarly, managers of public owned banks may pursuit objectives other than cost minimization or profit maximization. This might be due to the fact that the scope of managers’ self-serving (or opportunistic) behavior and/or their tendency to meet the requisition of the government is likely to be higher in public owned banks than in private owned banks (Huang et al., 2011; Isik & Hassan, 2002). Unhealthy macroeconomic conditions are also another factors that trigger AI. For example, high inflation can increase the cost of borrowing and the likelihood of default; consequently, it may reduce demand for private loans and/or lead banks to make suboptimal decisions (Boamah et al., 2022; Isik & Hassan, 2002; Sanchez et al., 2013).

Firms that operate in imperfect market setting are assumed to minimize the shadow cost rather than the actual cost. Put differently, firms in distorted market settings may tend to make their optimal production and input use decisions based on the shadow rather than the actual prices (Atkinson & Cornwell, 1994; Kumbhakar & Lovell, 2000). Shadow prices are internal or firm-specific prices which combine observed market prices with all these factors that interface the efficient operation of the market. In the commercial banking industry, shadow prices of outputs (or inputs) may account for the sources of AI.

2.2. Overview of the commercial banking industry in Ethiopia

Ethiopian financial sector liberalized and deregulated in 1994. Since then important changes have been occurring in the structure of the country’s financial system. In the commercial banking industry, such changes are witnessed by the growth of the number of domestic private owned commercial banks, expansion of branch offices, computerization, and growth of other technology based banking system. Currently, the industry consist 1 public owned commercial bank, namely commercial bank of Ethiopia (CBE), and more than 24 private owned commercial banks.

Ethiopian financial system has some notable features that makes it differs from most contemporary economies. First, the system is completely closed to foreign entities (both for foreign financial institutions and foreigners) and thus all private commercial banks are domestically owned. Second, the country’s financial system lacks secondary capital market, and private banks rely largely on deposit funding. The absence of secondary capital market also makes commercial banks to be the only source of funds for private investments. Third, the banking industry of the country can be described as an oligopolistic market structure. This is because CBE alone holds a market share exceeding 50%, while more than 20 domestic privately owned commercial banks account for the remaining.

The regulatory environment is the other notable characteristic of Ethiopia’s financial system. Commercial banks in the country are highly regulated. The regulatory environment of the sector is characterized by restrictive lending policy and substantial collateral requirements for every private loans. In addition to the objective of stabilizing the banking system, the lending policies and regulations of the National Bank of Ethiopia (NBE) are influenced by macroeconomic conditions and sector-specific policies. In general, within the past two decades, commercial banks in the country have passed through different policy and regulatory constraints. In particular, since 2009, the NBE has been imposing tight monetary policies that aimed at stabilizing inflationary pressure in the country.

Another key feature of the commercial banking industry in the country is unequal treatment of banks. Though they operate side by side, the public and private banks in the nation often face unequal treatments. The government often protects CBE from domestic competitive pressures through some sort of explicit and implicit subsidies (and policies, see below); for instance, the bank mobilizes and administers almost all public sector low cost funds with a monopoly. Moreover, public and private owned commercial banks in the country frequently face different set of regulations. For example, since 2011, the NBE had imposed directive that require all privately owned commercial banks to invest 27% of their every new loan disbursements in NBE bills² for five years at a very low interest rate; below what they pay for depositors. CBE is not exceptional; aside from its profit oriented activities, the bank has been serving as a primary source of low-cost funds for almost every mega projects of Ethiopian government. Since 2011, privately owned banks have also been supporting the country’s growth and transformation plan (GTP) by offering medium-to long-term loans at low rates; for instance, almost all banks in Ethiopia have invested huge amounts of money on the 5-year bonds that issued by the government to finance the construction of Great Ethiopian Renaissance Dam (GERD).

The combination of all these above factors lead commercial banks in the country to increase their lending rates on private loans and the rate they pay for depositors over the past years (NBE, 2021; Zwedu, 2014), even though the real interest rates remain negative (NBE, 2021). Zwedu (2014) argued that the regulatory and policy constraints together with unstable macroeconomic conditions negatively affecting the allocative performance of Ethiopian commercial banks; thereby undermine their contributions to the nation’s economic growth and development efforts.

2.3. Empirical literature review

There are ample empirical works on the efficiency of commercial banks, both in developed and developing countries. These works primarily differ in terms of the concept of efficiency (inefficiency), the estimation approach they employed, and the economic and regulatory environment where they were conducted. A large number of these empirical works have focused on either the EE (EI) or TE(TI) of commercial banks (for example, Abdulahi et al., 2023; Abidin et al., 2021; Agama et al., 2023; Alemu, 2016; Bayuny & Haron, 2017; Dong et al., 2014; Jiménez-Hernández et al., 2019; Kutlar et al., 2017; Lema, 2017), while some studies have attempted to investigate TE(TI) and AE(AI) of individual banks (for example, Auwalu, 2019; Batir et al., 2017; Huang et al., 2011; Ouertani et al., 2020; Sanchez et al., 2013).

The estimates of efficiency (inefficiency) of individual banks and the underling factors explaining the source substantially vary across these studies. For example, as for bank size, a study by Sanchez et al. (2013) found a positive and statistically significant effect of size on TE, AE and CE of sample banks in Latin American countries. Somehow similar conclusion regarding the effect of bank size on TE of commercial banks reached by the study of Jiménez-Hernández et al. (2019) in Latin America and the study by Kutlar et al. (2017) in Turkey. Contrary to this, a study by Ajisafe & Akinlo (2014) and Nainggolan et al. (2022) in Nigeria and a study by Batir et al. (2017) in Turkey reported a negative and statistically significant effect of size on the level of TE of commercial banks.

Regarding the effect of banks’ ownership form, the findings of previous studies are also mixed. For example, a study by Dong et al. (2014) found that public owned banks in China perform more in cost efficiently than private owned domestic as well as foreign banks. As the authors suggested, public owned banks outperform private banks in China because they receive implicit guarantees and subsidies from the government; thereby enjoy lower cost funds than private banks. Similarly, Huang et al. (2011) showed empirical evidence that publicly owned banks outperform private owned domestic banks in East European countries. Opposed to this, uunderperformance of publicly owned banks reported in some studies from different countries (for example, Abidin et al., 2021; Batir et al., 2017). Some studie also documented insignificant effect of ownership types on the performance of commercial banks (for example, Jiménez-Hernández et al., 2019).

The findings of previous studies in Ethiopia also show somehow inconsistent results. For example, Alemu (2016) estimated the efficiency scores and found, on average, privately owned commercial banks outperform public owned banks in terms of overall as well as pure TE. Contrary to this, Agama et al. (2023) found that the public owned commercial bank is more efficient than private owner commercial banks. Further, the authors found that, among privately owned commercial banks, the smaller banks are more efficient than the larger banks in Ethiopia. However, instead of measuring bank size in terms of total assets, as in most prior empirical works on commercial banks’ efficiency, Agama et al. (2023) measured the size of private banks in Ethiopia using the volume of total loan. Lema (2017) and Abdulahi et al. (2023) examined the determinants of the TE of commercial banks in Ethiopia. Lema’s (2017) results show statistically insignificant effect of bank size and ownership form on the TE of banks. Abdulahi et al. (2023) reached somehow inconsistent findings regarding the effect of bank size on TE of Ethiopian commercial banks. Specifically, the authors found a positive and significant effect of size on banks’ TE.

In addition to this, efficiency differences between large and small banks could be explained by risk taking tendency since banks that take risk may enjoy cost advantage, at least in the short run. For example, a sudy by Saleh & Afifa (2020) found a significant negative effect of bank size on profitability of Jordanian commercial banks, and they suggest the role of banks’ risk-taking behavior on profitability. An empirical work by Borauzima & Muller (2022) show that smaller banks in Africa tend to respond competitive pressure by taking more risks than the larger counterparts.

As far as banks input optimization is concerned, the findings of a cross-country study by Huang et al. (2011) show a slight variation in input misallocation of banks across countries. More specifically the authors found, on average, banks in most transitional countries suffered from AI due to over-utilization physical capital and loanable funds relative to labor inputs. Similarly, Ouertani et al. (2020) found that banks in Islamic countries suffer from AI due to underutilization of labor input. Regarding the effect of banks ownership form on banks AE (AI), Huang et al. (2011) show empirical evidence that publicly owned banks in transitional countries perform allocatively better than private owned domestic banks. In contrast, Batir et al. (2017) reported domestic privatly owned banks allocatively outperform publicly owned banks in Turkey. Moreover, Batir et al. (2017) found a positive and statestically significant effect of size on banks’ AI.

Banks’ optimization decision can also be influenced by macroeconomic conditions. For instance, Sanchez et al. (2013) found a negative and statistically strong effect of high inflation on both cost and revenue AE of banks in Latin American countries. The authors argued that high inflation reduces banks’ AE because the increase in funds available in the banking system lacks a corresponding increase in the demand for private loans. Batir et al. (2017) documented a negative and statestically strong effects of GDP growth and high inflation rate on the level of AE of banks in Turkey. Using banking sector data from ninety (90) frontier and emerging economy (FEEs), Boamah et al. (2022) show empirical evidence that high inflation reduces banks’ risk-taking incentives and increase diversification toward non-interest income. Zwedu (2014) argued that high rate of inflation, tight monetary policies, and low return on government securities leads Ethiopian commercial banks to engage in extensive deposit mobilization and physical expansions.

Regarding the dominant source of cost of inefficiency, the findings of previous study are somehow inconclusive. Huang et al. (2011) found that the cost of banks’ inefficiency in transitional countries dominated by underutilization or wastage of inputs than wrong input combinations. Similar conclusions also reached by Auwalu (2019) in Nigeria. Contrary to this, Sanchez et al. (2013) found that AI dominate TI of banks in most Latin American countries. Similarly, Batir et al. (2017) in Turkey and Ouertani et al. (2020) in Islamic countries found AI as the dominant source of cost of inefficiency of banks.

In summary, as our discussion hereinabove shows, most prior studies have reached conflicting conclusions about the level and source of TI, and the nature and the cost of AI. In addition to this, the objective and the methodologies used in these studies substantially different. The empirical analysis of most of these previous studies estimate efficiency scores for banks relying on nonparametric approaches, namely Data Envelopment Analysis (DEA) (for example, Abidin et al., 2021; Agama et al., 2023; Alemu, 2016; Auwalu, 2019; Batir et al., 2017; Bayuny & Haron, 2017; Kutlar et al., 2017; Lema, 2017; Sanchez et al., 2013), while some other studies combine DEA with stochastic frontier approach (SFA) (Dong et al., 2014). The SFA also used to estimate CE of banks in some previous studies, such as Borauzima & Muller (2022), Nainggolan et al. (2022) and others. Some few empirical works, such as Huang & Wang (2003, 2004), Huang et al. (2011) and Ouertani et al. (2020), estimated the TI and AI of commercial banks applying Shadow Pricing Approach (SPA).

The DEA is a non-parametric mathematical programming approach. As any deterministic approaches, DEA requires no arbitrary functional form and distributional assumptions. In spite of its simplicity and frequent uses in applied works, the DEA criticized on some grounds. Primarily, the approach is sensitive to measurement error and other noise in the data. Moreover, the DEA does not produce information regarding the nature of input-specific AI. Prior empirical studies attempt to avoid the measurement error and the ‘noise’ problem of DEA applying either SFA or SPA. The main difference between SFA and SPA is in modelling and estimating AI. In SFA, a firm’s deviation from its optimization behaviour modelled in error-component structure; therefore, estimating AE (AI) the firm requires imposition of an arbitrary and restrictive functional form and distributional assumptions. In addition to this, the SFA often criticized by the fact that it rules out estimation of systematic firm responses to non-random differences between market and shadow price; hence, it provides no information regarding the nature of input-specific AI (Atkinson & Cornwell, 1994; Kumbhakar & Lovell, 2000).

Instead of modelling and estimating AI by means of error components, as in SFA, AI in SPA is modelled and estimated parametrically by scaling up market prices or as a function of other factors. Therefore, the SPA requires neither arbitrary and restrictive functional form nor distributional assumptions. Moreover, if panel data are available, the SPA also has an added advantage of permitting the estimation of firm-specific TE (TI) together with firm-and-input-specific AE (AI) (Atkinson & Cornwell, 1994; Fried et al., 2008; Kumbhakar & Lovell, 2000). Thus, the empirical analysis of this study relies on the SPA.

3. Methodology

3.1. Model specification

3.1.1. Theoretical model specification

Following Atkinson & Cornwell (1994), Huang & Wang (2003, 2004), Huang et al. (2011), and others, we assume that commercial banks in Ethiopia choose inputs to minimize shadow costs, $C_i^s\left(\mathit{\text{kw}},x\right)=\sum _{j=1}({k_{\mathit{\text{ji}}}w}_{\mathit{\text{ji}}})(x_{\mathit{\text{ji}}}{a}_i),$ to produce a given level of output (service), where ${\mathrm{C}}_{\mathrm{i}}^{\mathrm{s}}(.)$ shadow cost of the ${\mathrm{i}}^{\mathrm{\text{th}}}$ bank ($i=1,2,\dots .N$); $\mathit{\text{kw}}$ and $x$ are vector of shadow prices and input quantities, respectively; ${\mathrm{x}}_{\mathrm{\text{ji}}}$ and ${\mathrm{w}}_{\mathrm{\text{ji}}}$ are the quantity and market price of input $\prime \mathrm{j}\prime ,$ respectively; $a_i$ ($0<a_i\le 1,$) is a bank-specific input TE(TI) parameter; ${{\mathrm{k}}_{\mathrm{\text{ji}}}\mathrm{w}}_{\mathrm{\text{ji}}}$ is shadow price of input $\prime \mathrm{j}\prime ;$ and ${\mathrm{k}}_{\mathrm{\text{ji}}}$ is input-specific allocative parameters that scale observed input prices.

The ${\mathrm{i}}^{\mathrm{\text{th}}}$ bank is TE (TI) in inputs if $a_i=1$ ($a_i<1$). Similarly, input-specific AE (AI) parameters measures divergence between shadow and market prices of input. The ${\mathrm{i}}^{\mathrm{\text{th}}}$ bank is said allocatively efficient in input $\prime \mathrm{j}\prime$ when ${\mathrm{k}}_{\mathrm{\text{ji}}}=1.$ Conversely, if ${\mathrm{k}}_{\mathrm{\text{ji}}}<1({\mathrm{k}}_{\mathrm{\text{ji}}}>1),$ then the ${\mathrm{i}}^{\mathrm{\text{th}}}$ bank is said to be allocatively inefficient because it acts as if the shadow price of input $\prime \mathrm{j}\prime$ is less than (greater than) the corresponding actual price; thus, it respond systematically by over-utilizing (under-utilizing) the ${\mathrm{j}}^{\mathrm{\text{th}}}$ input$.$

The input AE (AI) of the ${\mathrm{i}}^{\mathrm{\text{th}}}$ bank established from the first-order condition of shadow cost minimization condition. Let ${\mathrm{x}}_{\mathrm{\text{ji}}}^{\mathrm{*}}\mathrm{ }(\mathrm{\text{kw}}/a_i,\mathrm{y})$ denotes the resulting optimal quantity of input $\prime \mathrm{j}\prime ,$ where $\mathrm{y}$ denotes a vector of outputs. Then, the dual form of the shadow cost function of the ${\mathrm{i}}^{\mathrm{\text{th}}}$ bank can be defined as (2.1) $$C_i^s\left(\mathit{\text{kw}}/a_i,y\right)=\sum {k_{\mathit{\text{ji}}}w}_{\mathit{\text{ji}}}{x}_{\mathit{\text{ji}}}^{\mathrm{*}}(\mathit{\text{kw}}/a_i,y)$$(2.1)

By applying Shephard’s Lemma to the dual form of the shadow cost function, we can define the observed quantity of input $\prime \mathrm{j}\prime$ used by the bank to minimize the shadow cost as (2.2) $$x_{\mathit{\text{ji}}}^{\mathrm{*}}=\frac{\partial C_i^s\left(\mathit{\text{kw}}/a_i,y\right)}{\partial {k_{\mathit{\text{ji}}}w}_{\mathit{\text{ji}}}}\mathrm{ }$$(2.2)

And the corresponding shadow cost share equations (2.3) $$S_{\mathit{\text{ji}}}^s=\frac{\partial \mathit{\text{ln}}{C}^s\left(\mathit{\text{kw}}/a_i,y\right)}{\partial \mathit{\text{ln}}{k_{\mathit{\text{ji}}}w}_{\mathit{\text{ji}}}}=\frac{{k_{\mathit{\text{ji}}}w}_{\mathit{\text{ji}}}{x}_{\mathit{\text{ji}}}^{\mathrm{*}}}{C^s\left(\mathit{\text{kw}}/a_i,y\right)}\mathrm{ }$$(2.3)

From the shadow cost-share equation, the actual expenses on input $\prime \mathrm{j}\prime$ can be expressed as ${w_{\mathit{\text{ji}}}x}_{\mathit{\text{ji}}}^{*}=C^s\left(\mathit{\text{kw}}/a_i,y\right)*S_{\mathit{\text{ji}}}^s{k}_{\mathit{\text{ji}}}^{-1}.$ The shadow cost function is homogeneous degree one in ${{\mathrm{k}}_{\mathrm{\text{ji}}}\mathrm{w}}_{\mathrm{\text{ji}}},$ and thus, the observed total expenditure of the ${\prime \mathrm{i}}^{\mathrm{\text{th}}}\prime$ bank can be defined as (2.4) $$E_i=\sum w_{\mathit{\text{ji}}}{x}_{\mathit{\text{ji}}}^{\mathrm{*}}=\frac{1}{a_i}\mathrm{ }{C}^s\left(\mathit{\text{kw}},y\right)\sum _{j=1}{S}_{\mathit{\text{ji}}}^s{k}_{\mathit{\text{ji}}}^{-1}$$(2.4)

Technically inefficient is costly to the firm because it results in the over-utilization of all inputs by the proportion equals ${1/a}_i.$ In natural logarithmic form (2.5) $$\mathit{\text{ln}}{E}_i={\mathit{\text{lnC}}}^s\left(\mathit{\text{kw}},y\right)-\mathit{\text{ln}}{a}_i+\mathit{\text{ln}}|\sum _{j=1}{S}_{\mathit{\text{ji}}}^s{k}_{\mathit{\text{ji}}}^{-1}|\mathrm{ }$$(2.5) where $-\mathit{\text{ln}}{a}_i$ is bank specific cost of input TI. Alternatively, it can be interpreted as the percentage by which a bank can lower costs by reducing the usage of all the inputs, holding the output constant. Similarly, $\mathrm{\text{ln}}|\sum _{\mathrm{j}=1}{\mathrm{S}}_{\mathrm{\text{ji}}}^{\mathrm{s}}{\mathrm{k}}_{\mathrm{\text{ji}}}^{-1}|\mathrm{ }$ captures the deviation of the actual cost from shadow cost-minimizing quantities of inputs owing to AI. The sum of all inputs cost share in a firm is one; thus, the shadow cost diverge from actual cost if ${\mathrm{k}}_{\mathrm{\text{ji}}}<1({\mathrm{k}}_{\mathrm{\text{ji}}}>1)$) in a given firm. Therefore, the term represents the cost of input AI.

Finally, the actual cost share of input $\prime \mathrm{j}\prime$ can be defined as: (2.6) $$S_{\mathit{\text{ji}}}^a=\frac{w_{\mathit{\text{ji}}}{x}_{\mathit{\text{ji}}}^{\mathrm{*}}}{E_i}=\frac{S_{\mathit{\text{ji}}}^s{k}_{\mathit{\text{ji}}}^{-1}}{\sum _{j=1}{S}_{\mathit{\text{ji}}}^s{k}_{\mathit{\text{ji}}}^{-1}}\mathrm{ }$$(2.6)

In our specification above, $a_i$ does not appear in shadow or in actual cost share equations because it results in the overutilization of all inputs equi-proportionately (Atkinson & Cornwell, 1994; Huang & Wang, 2003).

3.1.2. Empirical model specification

Following Huang & Wang (2003), Huang et al. (2011), Borauzima & Muller (2022), and others, we choose the Fourier Flexible (FF) functional form. The FF is a global approximation, and hence can well represent the true but unknown cost function (Gallant, 1981, 1982). Following this, we specified the dual shadow cost function (Equation 2.1(2.1) $$C_i^s\left(\mathit{\text{kw}}/a_i,y\right)=\sum {k_{\mathit{\text{ji}}}w}_{\mathit{\text{ji}}}{x}_{\mathit{\text{ji}}}^{\mathrm{*}}(\mathit{\text{kw}}/a_i,y)$$(2.1) ) in the FF form as follows: (3.1) $${\mathit{\text{lnC}}}_{\mathit{\text{it}}}^s\left(\mathit{\text{kw}},y\right)={\beta }_0+{\sum }_{j=1}^n{\beta }_j\mathit{\text{ln}}{k}_{\mathit{\text{jit}}}{w}_{\mathit{\text{jit}}}+{\sum }_{h=1}^m{\gamma }_h\mathit{\text{ln}}{y}_{\mathit{\text{hit}}}+0.5\left[\sum _{j=1}\sum _{g=1}{\beta }_{\mathit{\text{jg}}}\mathit{\text{ln}}{k}_{\mathit{\text{jit}}}{w}_{\mathit{\text{jit}}}\mathit{\text{ln}}{k}_{\mathit{\text{git}}}{w}_{\mathit{\text{git}}}+\sum _{j=1}\sum _{g=1}{\phi }_{\mathit{\text{jg}}}\mathit{\text{ln}}{y}_{\mathit{\text{jit}}}\mathit{\text{ln}}{y}_{\mathit{\text{git}}}\right]+\sum _{j,h=1}{\vartheta }_{\mathit{\text{jh}}}\mathit{\text{ln}}{k}_{\mathit{\text{jit}}}{w}_{\mathit{\text{jit}}}\mathit{\text{ln}}{y}_{\mathit{\text{hit}}}+{\omega }_{t}t+0.5{\omega }_{\mathit{\text{tt}}}{t}^2+\sum _n[A_n\mathrm{\text{cos}}\hspace{0.17em}\left(x_n\right)+B_n\mathrm{\text{sin}}\left(x_n\right)]+\sum _n\sum _p{[A}_{\mathit{\text{np}}}\mathrm{\text{cos}}\hspace{0.17em}\left(x_n+x_p\right)+B_{\mathit{\text{np}}}\mathrm{\text{sin}}\hspace{0.17em}\left(x_n+x_p\right)]+\sum _n[a_n\mathrm{\text{cos}}\hspace{0.17em}\left(z_n\right)+b_n\mathrm{\text{sin}}\left(z_n\right)]+\sum _n\sum _p{[a}_{\mathit{\text{np}}}\mathrm{\text{cos}}\hspace{0.17em}\left(z_n+z_p\right)+b_{\mathit{\text{np}}}\mathrm{\text{sin}}\hspace{0.17em}\left(z_n+z_p\right)]+\sum _n\sum _p\sum _q{[a}_{\mathit{\text{npq}}}\mathrm{\text{cos}}\hspace{0.17em}\left(z_n+z_p+z_q\right)+a_{\mathit{\text{npq}}}\mathrm{\text{sin}}\hspace{0.17em}\left(z_n+z_p+z_q\right)]$$(3.1) where ${\mathit{\text{lnC}}}_{\mathit{\text{it}}}^s\left(\mathit{\text{kw}},y\right)$ is the natural logarithm of the shadow cost of the ${\mathrm{i}}^{\mathrm{\text{th}}}$ bank at time $\prime \mathrm{t}\prime .$ ${\beta }_{\mathit{\text{gj}}}={\beta }_{\mathit{\text{jg}}}$ and ${\mathrm{\phi }}_{\mathit{\text{jg}}}={\mathrm{\phi }}_{\mathit{\text{gj}}}\forall g\ne \mathrm{j}.$ ${\mathrm{x}}_{\mathrm{n}}$ is the scaled log-price of the ${\mathrm{n}}^{\mathrm{\text{th}}}$ input and ${\mathrm{z}}_{\mathrm{n}}$ is the scaled log-quantity of the ${\mathrm{n}}^{\mathrm{\text{th}}}$ output.

We scaled the log-input prices and log-output quantities using the technique suggested by Gallant (1982). For example, we scaled the log-price of the ${\mathrm{n}}^{\mathrm{\text{th}}}$ input as ${\mathrm{x}}_{\mathrm{n}}=\mathrm{\lambda }(\mathrm{\text{ln}}{\mathrm{w}}_{\mathrm{n}}+\mathrm{\text{ln}}{\mathrm{\theta }}_{\mathrm{n}}):$ where $\lambda =6/\left(\mathit{\text{ln}}{w}_n^{\mathrm{\text{max}}}+\mathit{\text{ln}}{\theta }_n\right);\mathrm{\text{ln}}{\theta }_n=0.00001-\mathit{\text{ln}}{w}_n^{\mathrm{\text{min}}}$ and $\mathrm{\text{max}}$ and $\mathrm{\text{min}}$ represent the maximum and minimum, respectively. We included linear ($\mathrm{t}$) and quadratic (${\mathrm{t}}^2)$ time-trend variables to determine the effect of technical progress on bank costs. To conserve the degree of freedom, we assumed a neutral technological change.

The shadow cost share equation of the ${\mathrm{j}}^{\mathrm{\text{th}}}$ input corresponding to Equation (3.1)(3.1) $${\mathit{\text{lnC}}}_{\mathit{\text{it}}}^s\left(\mathit{\text{kw}},y\right)={\beta }_0+{\sum }_{j=1}^n{\beta }_j\mathit{\text{ln}}{k}_{\mathit{\text{jit}}}{w}_{\mathit{\text{jit}}}+{\sum }_{h=1}^m{\gamma }_h\mathit{\text{ln}}{y}_{\mathit{\text{hit}}}+0.5\left[\sum _{j=1}\sum _{g=1}{\beta }_{\mathit{\text{jg}}}\mathit{\text{ln}}{k}_{\mathit{\text{jit}}}{w}_{\mathit{\text{jit}}}\mathit{\text{ln}}{k}_{\mathit{\text{git}}}{w}_{\mathit{\text{git}}}+\sum _{j=1}\sum _{g=1}{\phi }_{\mathit{\text{jg}}}\mathit{\text{ln}}{y}_{\mathit{\text{jit}}}\mathit{\text{ln}}{y}_{\mathit{\text{git}}}\right]+\sum _{j,h=1}{\vartheta }_{\mathit{\text{jh}}}\mathit{\text{ln}}{k}_{\mathit{\text{jit}}}{w}_{\mathit{\text{jit}}}\mathit{\text{ln}}{y}_{\mathit{\text{hit}}}+{\omega }_{t}t+0.5{\omega }_{\mathit{\text{tt}}}{t}^2+\sum _n[A_n\mathrm{\text{cos}}\hspace{0.17em}\left(x_n\right)+B_n\mathrm{\text{sin}}\left(x_n\right)]+\sum _n\sum _p{[A}_{\mathit{\text{np}}}\mathrm{\text{cos}}\hspace{0.17em}\left(x_n+x_p\right)+B_{\mathit{\text{np}}}\mathrm{\text{sin}}\hspace{0.17em}\left(x_n+x_p\right)]+\sum _n[a_n\mathrm{\text{cos}}\hspace{0.17em}\left(z_n\right)+b_n\mathrm{\text{sin}}\left(z_n\right)]+\sum _n\sum _p{[a}_{\mathit{\text{np}}}\mathrm{\text{cos}}\hspace{0.17em}\left(z_n+z_p\right)+b_{\mathit{\text{np}}}\mathrm{\text{sin}}\hspace{0.17em}\left(z_n+z_p\right)]+\sum _n\sum _p\sum _q{[a}_{\mathit{\text{npq}}}\mathrm{\text{cos}}\hspace{0.17em}\left(z_n+z_p+z_q\right)+a_{\mathit{\text{npq}}}\mathrm{\text{sin}}\hspace{0.17em}\left(z_n+z_p+z_q\right)]$$(3.1) is defined as follows: (3.2) $$S_{\mathit{\text{jit}}}^s\left(\mathit{\text{kw}},y\right)={\beta }_j+{\beta }_{\mathit{\text{jg}}}\mathit{\text{ln}}{k}_{\mathit{\text{git}}}{w}_{\mathit{\text{git}}}+{\vartheta }_{\mathit{\text{jh}}}\mathit{\text{ln}}{y}_{\mathit{\text{hit}}\mathrm{ }}$$(3.2)

The homogeneity of degree one in shadow input prices, which is used in Equation (2.4)(2.4) $$E_i=\sum w_{\mathit{\text{ji}}}{x}_{\mathit{\text{ji}}}^{\mathrm{*}}=\frac{1}{a_i}\mathrm{ }{C}^s\left(\mathit{\text{kw}},y\right)\sum _{j=1}{S}_{\mathit{\text{ji}}}^s{k}_{\mathit{\text{ji}}}^{-1}$$(2.4) , implies the following: $$\sum _{j=1}{\beta }_j=1\mathrm{ }{\sum }_{h=1}^m{\gamma }_h=\sum _{j,g=1}{\beta }_{\mathit{\text{jg}}}=\sum _{j,h=1}{\vartheta }_{\mathit{\text{jh}}}=\sum _{j,g=1}{\phi }_{\mathit{\text{jg}}}=0$$

After adding the TE(TI) and AE(AI) components, the logarithm form of the observed total expenditure of the ${\mathrm{i}}^{\mathrm{\text{th}}}$ bank at time $\prime \mathrm{t}\prime$ can specified as (3.3) $$\mathrm{\text{ln}}{\mathrm{E}}_{\mathrm{\text{it}}}={\mathrm{\text{lnC}}}_{\mathrm{\text{it}}}^{\mathrm{s}}\left(\mathrm{\text{kw}},\mathrm{y}\right)‐\mathrm{\text{ln}}{a}_i+\mathrm{\text{ln}}|\sum _{\mathrm{j}=1}{\mathrm{S}}_{\mathrm{i}}^{\mathrm{s}}{\mathrm{k}}_{\mathrm{i}}^{-1}|\mathrm{ }$$(3.3)

The actual cost share of input $\prime \mathrm{j}\prime$ corresponding to Equation (3.3)(3.3) $$\mathrm{\text{ln}}{\mathrm{E}}_{\mathrm{\text{it}}}={\mathrm{\text{lnC}}}_{\mathrm{\text{it}}}^{\mathrm{s}}\left(\mathrm{\text{kw}},\mathrm{y}\right)‐\mathrm{\text{ln}}{a}_i+\mathrm{\text{ln}}|\sum _{\mathrm{j}=1}{\mathrm{S}}_{\mathrm{i}}^{\mathrm{s}}{\mathrm{k}}_{\mathrm{i}}^{-1}|\mathrm{ }$$(3.3) can be defined as: (3.4) $$S_{\mathit{\text{jit}}}^a=\frac{[{\beta }_j+{\beta }_{\mathit{\text{jg}}}\mathit{\text{ln}}{k}_{\mathit{\text{git}}}{w}_{\mathit{\text{git}}}+{\vartheta }_{\mathit{\text{jh}}}\mathit{\text{ln}}{y}_{\mathit{\text{hit}}}]k_{\mathit{\text{jt}}}^{-1}}{\sum _{j=1}({\beta }_j+{\beta }_{\mathit{\text{jg}}}\mathit{\text{ln}}{k}_{\mathit{\text{git}}}{w}_{\mathit{\text{git}}}+{\vartheta }_{\mathit{\text{jh}}}\mathit{\text{ln}}{y}_{\mathit{\text{hit}}})k_{\mathit{\text{jt}}}^{-1}}$$(3.4)

We allowed $a_i$ to vary across banks but not over time. TE of each bank measured relative to the most efficient bank in the industry. For the most technically efficient bank (e.g. bank $g$) the associated efficiency parameter is normalized to 1 ($a_g=1),$ and the relative input TE can then be defined as $a_i=a_i/a_g.$

The actual cost and cost share functions are homogeneous of degree zero in ${\mathrm{k}}_{\mathrm{\text{ji}}}\prime \mathrm{s};$ thus, we measured banks’ input AE (AI) in relative terms. We chose one input (e.g. input $\prime h\prime$) arbitrarily as a ‘numeraire’ input³ and then normalized the corresponding $\mathrm{ }{\mathrm{k}}_{\mathrm{\text{hi}}}$ to 1 for all $\prime \mathrm{i}$’. For example, the ${\mathrm{i}}^{\mathrm{\text{th}}}$ bank is labelled as allocatively inefficient in terms of the ${\mathrm{j}}^{\mathrm{\text{th}}}$ input relative to the ${\mathrm{h}}^{\mathrm{\text{th}}}$ when ${\mathrm{k}}_{\mathrm{\text{ji}}}/{\mathrm{k}}_{\mathrm{\text{hi}}}={\mathrm{k}}_{\mathrm{\text{ji}}}\ne 1.$ An estimate ${\mathrm{k}}_{\mathrm{\text{ji}}}$ < 1(${\mathrm{k}}_{\mathrm{\text{ji}}}$> 1) implies over-utilization (under-utilization) of input $\prime j\prime$ relative to input $\prime h\prime .$ In our empirical estimation, we parameterized input-specific AE (AI) allowing it to vary across banks and over time as (3.5) $$k_{\mathit{\text{jit}}}=k_{0\mathit{\text{ji}}}+k_{1j}t+k_{2j}{t}^2$$(3.5) where ${\mathrm{k}}_{0\mathrm{j}\mathrm{i}}$ is a vector of bank-specific dummy variables that capture input AI and ${\mathrm{k}}_{1\mathrm{j}}$ and ${\mathrm{k}}_{2\mathrm{j}}$ are input-specific but bank-invariant parameters that capture cost of input AI over time. As far as input TE (TI) is concerned, we choose the following parsimonious functional form for the input TE(TI) parameters: (3.6) $$a_{\mathit{\text{it}}}=a_{0i}‐\mathrm{\text{exp}}({\omega }_{t}t+0.5{\omega }_{\mathit{\text{tt}}}{t}^2)$$(3.6) where $a_{0i}$ is a vector of bank-specific dummy variables, and ${\omega }_t$ and ${\omega }_{\mathit{\text{tt}}}$ are invariant across banks but vary over time. The inclusion of time variables in (3.6) implies that, in addition to variation across banks, TE (TI) in input varies over time, but in similar way for all banks. Our specification of the TE (TI) and AE(AI) parameters above is similar to those used by Huang & Wang (2003). After appending additive multivariate error terms and dropping one of the share equations, the above equations are jointly estimated by the non-linear seemingly unrelated regression (NLSUR) method without imposing any distributional assumptions.

3.2. Data and descriptive summary

The empirical analysis of this study is based on unbalanced panel data covering 19 commercial banks in Ethiopia from 1990 to 2022, totalling 325 observations. The data comprise one state owned bank-commercial bank of Ethiopia (CBE)⁴ and 18 privately owned domestic banks (we excluded four new banks that operate only for a year). The main data used in this study comes from annual banks’ final audit reports that obtained from the National Bank of Ethiopia (NBE). However, some additional supportive information was collected from each bank’s annual reports available on their web page on the Internet as well as from the NBE annual reports.

The public owned banks (CBE) is the largest and the oldest (in our data set) commercial bank in the country. As shown in Table 1, Panels A and B, the bank alone accounts for approximately 56% of all commercial banking assets. The bank also shared 36% of loans and advances, 54% deposit mobilization, 37% capital and reserves, and 25% branch offices of the banking industry in Ethiopia.

Table 1. Summary statistics. Panel A. Distribution of commercial Banks by their relative market share in the industry.

Bank category	Number of Banks(observations)	Assets^a (%Share)	Loans & Advances^a (%Share)
CBE	1 (32)	991,319 (56)	287,008.5 (36)
Group 1	3 (80)	327,243 (18.6)	225,388.4 (28)
Group 2	4 (90)	225,346 (12.8)	149,401.8 (18.7)
Group 3	5 (70)	151,910.6 (8.6)	95,797.7 (12)
Group 4	6 (53)	65,123.7 (3.7)	41,617.4 (5)

^a Amount Measured in Millions of Ethiopian Birr.

Source: computed from 2021 annual final audit report.

Panel B. Market Share distribution of commercial banks by their deposit mobilization, capital and branch offices.

Bank category	Deposit Mobilization^a (%Share)	Capital & Reserve^a (%Share)	Number of Branches (%Share)	Operating years
CBE	735,296 (54)	53,826.5 (37)	1920 (25)	33
Group 1	265,718.6 (19.5)	34,836.2 (37)	2055 (27)	26-28
Group 2	189,974.2 (14)	25,696.1 (24)	1714 (22)	18-25
Group 3	121,500.8 (9)	21,149.5 (17.6)	1229 (16)	13-17
Group 4	50,135.5 (3.7)	10,223.4 (14.5)	682 (10)	5-12

^a Amount Measured in Millions of Ethiopian Birr.

Source: computed from 2021 annual final audit report.

To account for the effect of size and age differences on the managerial performance of privately owned commercial banks, we further subdivided private banks into four relatively homogeneous groups. The classification was based on the 2021⁵ status of the relative market share (such as assets, loans and advances, deposit mobilization, and capital and reserves) of commercial banks in the industry. The share of branch offices in the industry and number of operating years were also used as additional criteria. The first group (Group 1) consists of three relatively large private banks operating in the market for 26 to 28 years. These banks together account for about 18.6% of assets, 28% loans and advances, 19.5% deposit mobilization, 37% capital and reserves, and 27% branch offices in the banking industry. The second group (Group 2) consists of four moderately large private banks, which together account for approximately 12.8% of all commercial banking assets. Together, these banks shared 18.7% loans and advances, 14% deposit mobilization, 24% capital and reserves, and 22% branch offices of the banking industry in the country (See the market share and other criteria for the remaining group in Table 1: Panels A and B).

Our classification of commercial bank outputs and costs is based on an intermediation approach. The outputs used in this study, all measured in millions of Ethiopian birr, are loans and advances⁶ (${\mathrm{y}}_1$) (excluding provision for doubtful debts); total investments (${\mathrm{y}}_2$), which include all interest earning assets, such as treasury bills, government bonds, deposits with foreign banks, and other similar assets; and non-interest income (${\mathrm{y}}_3$), which includes service charge and commission income, net gain on foreign currency transactions, net gain on equity investment in associates, and other related income. Inputs are measured by loanable funds (deposits and other borrowed funds) (${\mathrm{X}}_1$), labor (${\mathrm{X}}_2$), and physical capital (${\mathrm{X}}_3$). The main data used in this study contain no information on the number of bank employees⁷; therefore, we approximated the number of labor inputs from total assets (net of total fixed assets)⁸. The unit price of deposits (${\mathrm{w}}_1$) is measured by taking the ratio of total interest expenses to total deposits and borrowed funds; the unit price of labor (${\mathrm{w}}_2$) is derived by taking the ratio of expenses on salary and benefits to total assets, and the ratio of general non-labor operating expenses (excluding provision for doubtful loans and other assets) to the book value of fixed assets (net depreciation) is used as a proxy for the price of physical capital (${\mathrm{w}}_3$). The total costs include operating and financial costs (interest expenses).

In addition to variables dictated by microeconomic theory, we included three extra covariates in (3.3) which have the potential to influence a bank’s cost and efficiency. The first of these is the ratio of financial (or equity) capital to total asset of the individual banks and is used to control for differences in banks’ lending capacity and heterogeneity of their managers risk preference ($\mathit{\text{fk}})$ (Berger & Mester, 1997; Dong et al., 2014). The second variable is the ratio liquid assets⁹ to total assets($\mathit{\text{lq}}).$ We included it to capture banks’ ability mitigate external shock (Saleh & Afifa, 2020; Borauzima & Muller, 2022). We also included the ratio of loan-loss provisions to total loans ($\mathit{\text{pl}})$ as a proxy for banks’ loan quality and risk-taking tendency (Jiménez-Hernández et al., 2019; Saleh & Afifa, 2020; Ayalew, 2021).

Table 2 presents the descriptive statistics of bank outputs, input prices, and cost variables used to estimate the shadow cost model. Total investments, followed by total loans constitute¹⁰ the main types of outputs and non-interest income. Regarding the cost share of inputs, on average, a large portion of bank expenses go to deposits and borrowed funds, followed by physical capital, while the share of expenses on employees from total bank expenses accounts for the least.

Table 2. Summary statistics on output quantities, input prices, and cost.

Variables	Mean	Standard deviation
Total loans and Advances (${\mathrm{y}}_1$)^a	52,467.03	400,814.7
Total investments (${\mathrm{y}}_2$)^a	59,795.47	378,393.7
Non-interest income(${\mathrm{y}}_3$)^a	4,512.05	26,790.71
Price of deposits and borrowed funds (${\mathrm{w}}_1$)	0.03	0.03
Price of labour(${\mathrm{w}}_2$)	0.02	0.01
Price of physical capital (${\mathrm{w}}_3$)	0.86	0.47
Total cost($\mathrm{E})$^a	10,257.06	57,400.54
Actual cost share of deposit	0.42	0.12
Actual cost share of labour	0.28	0.07
Actual cost share of physical capital	0.30	0.11
Total capital and reserves/total asset $(\mathit{\text{fk}})$	0.15	0.08
Liquid assets/total asset $(\mathit{\text{lq}})$	0.20	0.10
Loan-loss provisions /total loan $(\mathit{\text{pl}})$	0.12	0,16

Number of Observations 325.

^a Measured in Millions of Ethiopian Birr.

4. Empirical analysis

4.1. Model specification tests and estimation strategies

We begin our analysis by diagnosing the relevancy of the three extra variables we included in (3.3) applying the Wald test. The test result justifies the inclusion of these additional variables in level and in second order terms. But we excluded the interaction among these variables because the jointly test outcome rejected the alternative hypotheses. Further, to conserve the degree of freedom and also to avoid the problem of multicolinearity, we did not allow for further interactions of these variables with input prices and outputs.

Since the input AI component makes Equation (3.3)(3.3) $$\mathrm{\text{ln}}{\mathrm{E}}_{\mathrm{\text{it}}}={\mathrm{\text{lnC}}}_{\mathrm{\text{it}}}^{\mathrm{s}}\left(\mathrm{\text{kw}},\mathrm{y}\right)‐\mathrm{\text{ln}}{a}_i+\mathrm{\text{ln}}|\sum _{\mathrm{j}=1}{\mathrm{S}}_{\mathrm{i}}^{\mathrm{s}}{\mathrm{k}}_{\mathrm{i}}^{-1}|\mathrm{ }$$(3.3) and Equation (3.4)(3.4) $$S_{\mathit{\text{jit}}}^a=\frac{[{\beta }_j+{\beta }_{\mathit{\text{jg}}}\mathit{\text{ln}}{k}_{\mathit{\text{git}}}{w}_{\mathit{\text{git}}}+{\vartheta }_{\mathit{\text{jh}}}\mathit{\text{ln}}{y}_{\mathit{\text{hit}}}]k_{\mathit{\text{jt}}}^{-1}}{\sum _{j=1}({\beta }_j+{\beta }_{\mathit{\text{jg}}}\mathit{\text{ln}}{k}_{\mathit{\text{git}}}{w}_{\mathit{\text{git}}}+{\vartheta }_{\mathit{\text{jh}}}\mathit{\text{ln}}{y}_{\mathit{\text{hit}}})k_{\mathit{\text{jt}}}^{-1}}$$(3.4) highly nonlinear, estimating the system applying maximum likelihood method by imposing distributional assumptions on TE (TI) term is difficult. Therefore, we employed a two-step approach to obtain bank-specific TE (TI). In the first step, we assumed EE, and then estimated Equation (3.3)(3.3) $$\mathrm{\text{ln}}{\mathrm{E}}_{\mathrm{\text{it}}}={\mathrm{\text{lnC}}}_{\mathrm{\text{it}}}^{\mathrm{s}}\left(\mathrm{\text{kw}},\mathrm{y}\right)‐\mathrm{\text{ln}}{a}_i+\mathrm{\text{ln}}|\sum _{\mathrm{j}=1}{\mathrm{S}}_{\mathrm{i}}^{\mathrm{s}}{\mathrm{k}}_{\mathrm{i}}^{-1}|\mathrm{ }$$(3.3) jointly with two of the three input cost share equations by the method of NLSUR, and then we computed the input allocative parameters applying duality theory. Here and hereinafter, we dropped the cost-share equation of physical capital input and used the input’s price to imposed linear homogeneity restriction. Moreover, we choose physical capital arbitrarily as a ‘numeraire’ input¹¹.

Our specification of input TE (TI) in (3.6) in terms of bank-specific dummy variables follows from the fixed-effects (FE) nature of our treatment of it in (3.3). But we also applied the Hausman specification test on (3.3) so as to check if the bank-specific effects are adequately modelled by random-effects (RE) than the FE¹². The test rejected modelling the adequacy of random effects at 5% level of significance. Thus, in the second step, after controlling AI term explicitly, we estimated the cost model to yield bank-specific input TE (TI) parameters using FE method. Finally, after re-parameterizing the TE (TI) and AE (AI) components, we estimated Equation (3.3)(3.3) $$\mathrm{\text{ln}}{\mathrm{E}}_{\mathrm{\text{it}}}={\mathrm{\text{lnC}}}_{\mathrm{\text{it}}}^{\mathrm{s}}\left(\mathrm{\text{kw}},\mathrm{y}\right)‐\mathrm{\text{ln}}{a}_i+\mathrm{\text{ln}}|\sum _{\mathrm{j}=1}{\mathrm{S}}_{\mathrm{i}}^{\mathrm{s}}{\mathrm{k}}_{\mathrm{i}}^{-1}|\mathrm{ }$$(3.3) and two input share Equation (3.4)(3.4) $$S_{\mathit{\text{jit}}}^a=\frac{[{\beta }_j+{\beta }_{\mathit{\text{jg}}}\mathit{\text{ln}}{k}_{\mathit{\text{git}}}{w}_{\mathit{\text{git}}}+{\vartheta }_{\mathit{\text{jh}}}\mathit{\text{ln}}{y}_{\mathit{\text{hit}}}]k_{\mathit{\text{jt}}}^{-1}}{\sum _{j=1}({\beta }_j+{\beta }_{\mathit{\text{jg}}}\mathit{\text{ln}}{k}_{\mathit{\text{git}}}{w}_{\mathit{\text{git}}}+{\vartheta }_{\mathit{\text{jh}}}\mathit{\text{ln}}{y}_{\mathit{\text{hit}}})k_{\mathit{\text{jt}}}^{-1}}$$(3.4) jointly with Equations (3.5)(3.5) $$k_{\mathit{\text{jit}}}=k_{0\mathit{\text{ji}}}+k_{1j}t+k_{2j}{t}^2$$(3.5) and (3.6)(3.6) $$a_{\mathit{\text{it}}}=a_{0i}‐\mathrm{\text{exp}}({\omega }_{t}t+0.5{\omega }_{\mathit{\text{tt}}}{t}^2)$$(3.6) applying NLSUR. The NLSUR method fits a system of nonlinear equations by feasible generalized nonlinear least squares. In our initial estimation, the square time terms included in (3.5) appeared to inflate the standard errors of firm-specific parameters. This may indicate the presence of a highly linear relationship with other variables; therefore, we excluded them from our final estimated model.

4.2. Discussions

The FF cost function¹³ fitted the data well. As Table 3 shows, most of the coefficients associated with the log of input prices and log of output quantities are statistically significant. The coefficients of the linear and quadratic time trends also appeared statistically significant. The negative sign of the coefficient of time trend indicates the presence of cost-saving technological progress in the Ethiopian commercial banking industry, although the positive coefficient of the square trend term suggests that the contribution of technical advances in the industry declined over time. Regarding the coefficients associate with time-varying cost of input AI, our results show a mixed picture. Specifically, the positive but statistically insignificant sign of the coefficient of time varying loanable funds implies that the cost of misallocation of the input by Ethiopian commercial banks is neither getting worse nor better during the time under consideration. In contrast, the negative and statistically significant time varying coefficient of labor input suggests that the cost of misallocation of the input among banks in Ethiopia decrease over time.

Table 3. Parameter estimates of fourier flexible shadow cost function.

Variables	Coef	Se	Variables	Coef	Se
Constant	−70.1536***	21.9504	${\mathit{\text{lnw}}}_1{\mathit{\text{lnw}}}_2$	−0.1231***	0.001
${\mathit{\text{lnw}}}_1$	0.1646***	.0103	${\mathit{\text{lnw}}}_1{\mathit{\text{lny}}}_1$	0.0029***	0.0007
${\mathit{\text{lnw}}}_2$	0.3174***	0.0096	${\mathit{\text{lnw}}}_1{\mathit{\text{lny}}}_2$	0.0037***	0.0009
${\mathit{\text{lny}}}_1$	6.5546***	1.7039	${\mathit{\text{lnw}}}_1{\mathit{\text{lny}}}_3$	0.0090***	0.0011
${\mathit{\text{lny}}}_2$	0.3697	0.6069	${\mathit{\text{lnw}}}_2{\mathit{\text{lny}}}_1$	0.0030***	0.0007
${\mathit{\text{lny}}}_3$	18289	1.9033	${\mathit{\text{lnw}}}_2{\mathit{\text{lny}}}_2$	−0.0092***	0.0008
$\mathit{\text{lnpl}}$	0.2945***	0.0207	${\mathit{\text{lnw}}}_2{\mathit{\text{lny}}}_3$	0.0135***	0.0011
$\mathit{\text{lnfk}}$	−0.8694***	0.2069	${\mathit{\text{lny}}}_1{\mathit{\text{lny}}}_2$	−0.0415	0.0328
$\mathit{\text{lnlq}}$	0.5202***	0.1477	${\mathit{\text{lny}}}_1{\mathit{\text{lny}}}_3$	−0.0369	0.0288
${\mathit{\text{lnw}}}_1^2$	0.1598***	0.001	${\mathit{\text{lny}}}_2{\mathit{\text{lny}}}_3$	−0.0996***	0.0367
${\mathit{\text{lnw}}}_2^2$	0.1480***	0.0011	$t$	−0.1367***	0.029
${\mathit{\text{lny}}}_1^2$	−0.2124***	0.0474	${\mathrm{t}}^2\mathrm{ }$	0.0013***	0.0003
${\mathit{\text{lny}}}_2^2$	0.1333*	0.073	$\mathit{\text{Dep}}\_t$	0.0012	0.0015
${\mathit{\text{lny}}}_3^2$	0.0806	0.1183	$\mathit{\text{Lab}}\_t$	−0.0056***	0.0013
${\mathit{\text{lnpl}}}^2$	0.0234***	0.0017
${\mathit{\text{lnfk}}}^2$	−0.3677***	0.0965
${\mathit{\text{lnlq}}}^2$	0.3267***	0.0947

Notes: Notations $t$ and $t^2$ denote linear and quadratic time trends, respectively. Dep_t and Lab_t are included to capture the cost of AI of funds and labour inputs over time, respectively.

***significant at 1%, **significant at 5%, *significant at 10%.

Parameter estimates of bank-specific input TE and AE are reported in Table 4. As shown in Column 2, all coefficients associated with bank-specific TE are highly significant. As our results indicate, on average CBE outperforms all privately owned commercial banks, regardless of their size. However, across privately owned commercial banks, our estimates of bank-specific parameters indicate that, on average, the level of TE of privately owned banks decrease uniformly as their size increase. Put alternatively, on average, small privately owned commercial banks in Ethiopia are relatively good in producing the same level of output using minimum inputs than large privately owned banks.

Table 4. Estimates of efficiency parameters.

Bank category	TE	AI
		Funds $({\mathbf{X}}_1)$	Labor $({\mathbf{X}}_2)$
CBE	1.00***	0.8156***	1.6786***
	(0.0016)	(0.1632)	(0.1391)
Group 1	0.66***	0.8678***	1.6102***
	(0.0016)	(0.167)	(0.1423)
Group 2	0.70***	0.8970***	1.6192***
	(0.0016)	(0.1698)	(0.1447)
Group 3	0.81***	0.9135***	1.6539***
	(0.0017)	(0.1767)	(0.1504)
Group 4	0.91***	0.9609***	1.6815***
	(0.0018)	(0.1805)	(0.1537)

Standard errors in parentheses.

***significant at 1%, **significant at 5%, *significant at 1%.

CBE is the largest and the oldest bank in Ethiopia, and thus one possible explanation for the bank’s outperformance could be its superiority in managerial expertise and its cost advantage in economies of information. However, a more likely explanation for the relative outperformance of CBE could also be the cost advantage that the bank enjoys in mobilizing huge amounts of low cost public funds with monopoly. Our result regarding the outperformance of public owned bank is somehow comparable to the findings of some previous studies in other countries, such as Huang et al. (2011) and Dong et al. (2014), while contradict with the results of some others, such as Batir et al. (2017) and Abidin et al. (2021). Comparing with the findings some prior studies in Ethiopia, our result somehow support the efficiency score result of Agama et al. (2023) and Abdulahi et al. (2023) but inconsistent with the findings of Alemu (2016) and Lema (2017).

Our result regarding the average outperformance of small banks relative to large private owned commercial banks in Ethiopia seems somehow inconsistent with the argument for cost saving effect of economies of experience (learning) and information (Aduba & Izawa, 2021). A plausible explanation could be that small banks in Ethiopia may pursue cost efficiency as a strategy to survive the stiff competition (Abidin et al., 2021; Isik & Hassan, 2002). For instance, as later entrants, small banks could enjoy substantial cost advantage by avoiding (or learning from) the mistakes of early entrant private banks. Moreover, as later entrants, small banks may also take some cost advantage by recruiting experienced and trained employees from other early established private banks¹⁴. This may allow small banks to reduce the time and costs needed to upgrading managerial quality and the skill of workers. Another possible explanation for the outperformance of smaller banks relative to larger private banks in Ethiopia could be ‘skimping’ behaviour. Specifically, smaller private banks in Ethiopia could appear technically more efficient than the larger counterparts if they tended to grant more risky loans by spending fewer resources than usual. We derive our suspect from the recent empirical findings of Borauzima & Muller (2022), who found that smaller banks in Africa respond competitive pressure by taking more risks than the larger counterparts. Generally, our finding on the outperformance of smaller banks relatively larger privately owned banks contradict with the findings of some previous studies from other countries, such as Sanchez et al. (2013) and Jiménez-Hernández et al. (2019), but consistent with the findings of Ajisafe & Akinlo (2014). Agama et al. (2023) also found a similar effect of size, as measured by total loan, on the TE of privatly owned commercial banks in Ethiopia. However, our results should also be treated with caution because the cost function does not account for extra revenue that can be obtained by improving service quality that can be achieved by incurring extra costs (Berger & Mester, 1997).

The parameter estimates of bank and input-specific AI are also reported in Columns 3 and 4 of Table 4. Unlike input TI, input AI does not vary across different bank categories. As our results show, on average, all commercial banks in Ethiopia, regardless of their ownership types and size, are inclined to over utilize deposits and other loanable funds and underutilize labor inputs relative to physical capital input in the years under consideration. Put alternatively, the result suggests that, on average, banks in the country tend to over-utilize physical capital and loanable funds relative to labor input during these years covered by the data.

Our result is consistent with Zwedu (2014) and NBE (2021), who already documented the existent of high rate of deposit mobilization and extensive physical expansion and investments tendency among Ethiopian commercial banks. NBE’s report also indicates a growing trend in banks’ loan disbursement. However, the total amount of the loan is largely dominated by public loans as the share of private loans has been decreasing since 2010 (Zwedu, 2014). Thus, our results regarding underutilization of labor might be linked to under-provision of private loans or mis-utilization of funds by Ethiopian commercial banks¹⁵ because private loans provisions require more labor input than public loans and other non-interest income sources. While full investigation of the econometrics causation is beyond the purpose of this paper, we can offer a number of possible justifications for this. First, in Ethiopia, access to private loans is difficult due to restrictive lending policy of the NBE. Second, for the last 15 years, the country’s commercial banks have been operating under high rate of inflation and tight monetary policy, which increase the cost of borrowing, thereby the likelihood of default; consequently, reduce both the supply and demand for private loans (Boamah et al., 2022; Borauzima & Muller, 2022; Le & Ngo, 2020; Sanchez et al., 2013). The combination of these factors may give incentive for Ethiopian commercial banks to generate profits from alternative sources by investing their excess funds in physical capital. For example, commercial banks in the country generate noninterest income by renting part of their building and by sharing their ATMs to other banks’ customers. Banks also invest in ATMs because the technology allows them to reduce their operating expenses, such as labor costs (Le & Ngo, 2020).

In addition to factors explained hereinabove, we can also mention two additional possible reasons that could prompt Ethiopian banks’ over-utilization of funds and physical capital relative to labor input. First, the need to compensate for interest income losses and avoid liquidity problem associated with low return of public loans that the country’s commercial banks have been offering since 2009. For example, banks’ physical expansions in small towns and remote areas could be motivated by the need to mobilize low cost funds. Second, the number of private banks in Ethiopia grow rapidly over the last 20 years. Thus, our result regarding overutilization of physical capital by Ethiopian banks (especially smaller banks) could be the outcome of their non-price competitive strategy to survive the growing competitive pressure. For example, branch expansion and other physical capital investments, especially in urban areas, improve banks’ accessibility and service quality.

Generally, physical capital is typically more expensive than labor; therefore, our results of under-utilization of labor relative to other inputs indicate that Ethiopian commercial banks are incurring extra cost by producing their outputs (services) in an allocatively inefficient manner (i.e. using the wrong input mix). Banks also incur extra cost by investing their funds in less profitable activities. Thus, we can conclude that banks in the country could minimum cost by employing more labor input and by reducing physical expansion, holding the level of outputs (services) constant. Moreover, reduction in deposit mobilization implies reduction in public loans since banks could increase their interest margin or generate more revenue with minimum cost by reallocating the funds to private loans. As for private banks, reduction for deposit mobilization also implies increasing equity capital (Huang et al., 2011). This is because banks with lower equity ratios pay interest on higher portions of their loanable funds. Our findings consistent with Huang et al. (2011) and Ouertani et al. (2020), who found similar input AI in different countries.

The dominant source of cost inefficiency among commercial banks can be either TI, AI or both components of EI. We estimated the percentage of potential cost savings resulting from achieving TE ($a_i=1),$ AE ($k_{\mathit{\text{ji}}}=1,\forall i,j),$ or both ($a_i=1;k_{\mathit{\text{ji}}}=1)$ by comparing one minus the ratio of restricted fitted expenditure (this is with and without imposing the appropriate parameter restrictions) to unrestricted fitted costs. The technique applied here to decompose the overall cost of inefficiency is that used by Atkinson & Cornwell (1994) and also suggested by Kumbhakar & Lovell (2000).

The estimates of the cost of inefficiency are presented in Table 5. As shown in Column 2, on average, during the years under consideration, commercial banks in Ethiopia incur about 28% extra cost due to EI. Further, on average, the cost of TI (22.6%) appeared three times higher than the cost of AI (7.2%) of banks. Put differently, on average, commercial banks in Ethiopia have suffered more from TI than AI. This is in line with the findings of Huang et al. (2011) and Auwalu (2019), while it contradict with the findings of Sanchez et al. (2013), Batir et al. (2017) and Ouertani et al. (2020).

Table 5. Cost of economic, technical, and allocative inefficiency.

Bank Categories	Cost of EI (%)	Cost of TI (%)	Cost of AI (%)
CBE	13.33	0	13.11
Group 1	37.18	34.43	4.50
Group 2	34.44	30.19	5.83
Group 3	24.50	19.56	6.56
Group 4	19.32	9.23	10.76
All Private banks	30.08	25.02	6.53
All banks	28.43	22.55	7.18

As far as the cost and the dominant source of inefficiency between public and private banks are concerned, our results indicate that, on average, the cost of EI is higher in private banks than in public bank. This is somehow comparable with the findings of Huang et al. (2011), while it contradicts with Batir et al. (2017). Moreover, as reported under Column 3, the cost of TI increase as the size of privately owned commercial banks increase; this strengthen our findings in terms of the level of TE. Higher cost of TI relative to AI in privately owned banks in Ethiopia may suggest that managers of these banks are relatively good at optimizing input use in light of prevailing market prices, but not as good at producing a given level of service using the minimum possible level of inputs. However, as shown under Column 4, the cost of AI increases as the size of privately owned commercial banks decrease. This might lead us to conclude that smaller banks in Ethiopia relatively suffer more from regulatory and policy constraints, and other market related and unfavourable macroeconomic conditions than larger privately owned commercial banks in Ethiopia.

Furthermore, the cost of AI appears to be higher in publicly owned bank than privately owned commercial banks. CBE is a primary source of low cost funds for the government; this may lead us to conclude that the bank’s credit allocation may not totally driven by cost minimization or/and profit maximization motives. Our result regarding the allocative outperformance of privately owned commercial banks relative to publicly owned bank not in line with the findings of Huang et al. (2011) in transitional countries, but somehow similar to the findings of Batir et al. (2017) in Turkey.

In summary, the extra cost of EI in privately owned commercial banks in Ethiopia dominated by underutilization or wastage of inputs than wrong input combinations. The extra cost for public bank, on the other hand, is dominantly attributed to choosing an incorrect input mix rather than excessive input usage. Thus, our results suggest that greater cost savings in private banks can be achieved by improving managerial efficiency, while a greater cost reduction in public owned bank can be realized by optimizing input use. However, as we mentioned before, our results should be treated with caution, given the problem of the cost function in penalizing high-quality banks.

4.3. Robustness check

To ensure robustness of our results regarding the FE estimates of bank-specific input TE of Ethiopian commercial banks, we re-estimated (3.3) using a two-step procedure as suggested by Kumbhakar & Lovell (2000). In the first step, we ignored $\mathit{\text{ln}}{a}_i$ and estimated the model using NLSUR regression method. In the second step, the cost frontier residual ${\epsilon }_{\mathit{\text{it}}}={\beta }_0-\mathit{\text{ln}}{a}_i+v_{\mathit{\text{it}}}$ were obtained and estimated by MLE technique assuming $\mathit{\text{ln}}{a}_i$ is truncated normal $\sim (\mu ,{\delta }_a^2)$ and independent of $v_{\mathit{\text{it}}};$ where $v_{\mathit{\text{it}}}\mathrm{ }$ denotes a random error term: $v_{\mathit{\text{it}}}\sim N(0,{\delta }_v^2).$ Finally, the Jondrow et al. (1982) (cited in Kumbhakar & Lovell, 2000) technique applied to estimate $\mathrm{l}n{a}_i.$ In the stochastic frontier approach, TE of individual banks is measured relative to the estimated frontier rather than the best-practice bank, i.e. relative to a zero value for $\mathrm{l}n{a}_i.$ In practice, it is very unlikely that any firm in the sample is fully TE. Thus, for the purpose of comparison to our results using FE and RE methods, we normalized our stochastic frontier efficiency estimates to be deviations from the largest observed value of ${ a}_i,$ so that the most TE bank in the sample has efficiency of one. We also reported the RE estimates.

As shown in Table 6, the two techniques produce fairly similar results.¹⁶ However, these results are slightly different from our FE estimates in two ways. First, our FE estimates of TE rank of privately owned banks in Group 4 and Group 3 now appears different. Second, unlike the FE estimates, the RE and MLM estimates of input TE suggest some sort of homogeneity among Ethiopian commercial banks.

Table 6. RE and MLE estimates of technical efficiency of banks.

Bank Categories	RE	MLE
CBE	1.00	1.00
Group 1	0.90	0.90
Group 2	0.93	0.93
Group 3	0.95	0.94
Group 4	0.98	0.96

5. Summery and conclusions

This study has been primarily concerned with investigating the TE(TI) and AE(AI) of Ethiopian commercial banks. The study applied a FF shadow cost function to unbalanced panel data that include 19 Ethiopian commercial banks and covered the period 1990-2022. The empirical analysis of the study relied on NLSUR method.

The results indicate that public-owned commercial bank and small, newly established privately owned commercial banks in Ethiopia are technically more efficient than other relatively large, early established privately owned commercial banks. Moreover, our findings indicate that, on average, the level of TE of privately owned banks decreases as their size increase. Evidence also shows that all commercial banks in Ethiopia are inclined to over-utilize loanable funds and physical capital relative to labor input in the years under consideration. Moreover, on average, the cost of TI is found larger in privately owned banks, while AI appears to dominate the cost of EI in publicly owned bank in Ethiopia.

Several policy conclusions can be drawn from the results of this study. First, privately owned commercial banks in Ethiopia could enjoy a substantial cost advantage by improving and upgrading their managerial staff, whereas relaxing the regulatory constraints on publicly owned commercial bank could allow managers of the bank to achieve greater cost savings by optimizing input use. Second, increasing both the proportion of labor input use relative to physical capital, and decreasing public loan provisions and increasing capitalization could allow commercial banks in Ethiopia to render their services least costly. Moreover, much of the period covered by the data used in the study corresponds to the period of high inflation and negative real interest rate; therefore, our results underscore the importance of ensuring stable economic environment so as to promote the safety and soundness of the commercial banking system in Ethiopia.

Although the information obtained by this study is valuable, a lot of empirical questions remain intact. First, due to lack of outputs price data, we failed to investigate banks’ revenue or profit efficiency, which account for differences in the quality of banking service provision. Thus, future study on profit or revenue efficiency could yield more complete evidence. We also acknowledge that our interpretations regarding the causes of AI are gross that do not necessarily prove economic causation. Therefore, future research is needed to our better understanding of the impact of regulatory, policy, market and macroeconomic conditions on the AE (AI) of commercial banks in Ethiopia. Finally, the economic implication(s) of some non-traditional banking activities by Ethiopian commercial banks is (are) worth considering topic.

Authors’ contributions

Bisrat Getinet Chane: conception, writing draft, methodology, data management and analysis, interpretation and discussion. Desta Yohannes Dalalo: writing literature, discussion, revising and editing the intellectual contents. Berhanu Dereja Gebremichael: writing literature, discussion, revising and editing the intellectual contents. All authors read and approved the final manuscript and the views expressed here are the authors’ alone.

Disclosure statement

The authors declare that they have no competing interests.

Data availability statement

Data will be available upon request from the corresponding author, [Bisrat Getinet Chane].

Additional information

Funding

The authors received no direct funding for this research.

Notes on contributors

Bisrat Getinet Chane

Bisrat Getinet Chane is a lecturer in the department of economics at Wolkite University, Ethiopia. His research interests include microeconomics impact evaluation, efficiency and risk analysis.

Desta Yohannes Dalalo

Desta Yohannes Dalalo is a lecturer in the department of accounting and finance at Wolkite University, Ethiopia. His research interests include financial performance, corporate governance and risk.

Berhanu Dereja Gebremichael

Berhanu Dereja Gebremichael is a lecturer in the department of accounting and finance at Wolkite University, Ethiopia. His area of interest includes corporate governance and financial performance.

Notes

1 There is no established theory on the causes of TI and AI of commercial banks; therefore, we have developed them, in an ad hoc fashion, from the available studies.

2 This directive repealed in 2018

3 The choice of the ‘numeraire’ input has no impact on the results.

4 The government also owned two other banks in Ethiopia, namely the development bank of Ethiopia DBE) and construction and business bank (CBB). We excluded them in this study because they have different goals and objectives than other commercial banks. Moreover, the DBE obtains its funds from other commercial banks, primarily from CBE, whereas the CBB ceased to operate few years before.

5 We used 2021 data because our data contain no information on CBE’s 2022 report.

6 Our data set does not separately state the type of loans offered by all commercial banks.

7 Banks in Ethiopia started to publish their annual report on their web-page in 2009/10, and almost all banks that operate before 2009/10 did not publish their earlier reports on their page. Hence, we can’t find complete information about the number of employees from every bank’s annual report available on the internet.

8 Similar approximation also used by some other previous studies, such as Huang et al. (2011), Dong et al. (2014), Batir et al. (2017) and others.

9 Liquid assets include cash on hand, cash at bank and commercial banks’ reserves at NBE.

10 The final audit report of CBE in our data does not include the direct loans that the bank made to public sectors. What we found from the bank’s annual report on the internet is also not complete because no report published online before 2009. Therefore, so as to avoid any bias, we did not include these incomplete data.

11 AE(AI) is homogeneous degree one in input quantity (Kumbhakar & Lovell, 2000); hence, equi-proportional changes in all inputs do not affect our computation of AI parameters.

12 We reported the RE outputs under subsection 4.3.

13 The Fourier series expansion terms reported at the appendix part

14 For example, as Zwedu (2014) reported, private banks in Ethiopia recruit their high level employees from the public banks. But our analysis includes only CBE, which pays relatively higher salary and bonuses for its staffs than private owned banks in Ethiopia

15 Additionally, Ethiopia has been under civil war since 2018.

16 All these results are available on request from the authors.

Appendix

Table

Variables	Coef	Se	Variables	Coef	Se
coslnw1	0.0158	0.0574	sinlny2	0.57	1.1349
coslnw2	−0.1020*	0.0532	sinlny3	0.4249	0.6042
sinlnw1	−0.2821***	0.0606	coslny1lny2	0.2268	0.4
sinlnw2	−0.3248***	0.0586	coslny1lny3	1.3245***	0.3513
coslnw1lnw2	−0.1777***	0.0311	coslny2lny3	0.384	0.3843
sinlnw1lnw2	−0.1627***	0.0432	sinlny1lny2	1.1889***	0.3637
coslny1	3.8565***	1.0537	sinlny1lny3	0.0725	0.2586
coslny2	−1.7503	2.384	sinlny2lny3	−0.6619	0.6942
coslny3	1.3104	1.5646	coslny1lny2ln3	−0.0577	0.1356
sinlny1	−1.8386***	0.6412	sinlny1lny2ln3	0.6193***	0.1416