Operational Performance Modelling of Indian Banks: A Data Envelopment Analysis Approach

Abstract

The rising level of non-performing loans (NPLs) posits risk on the operational working of the banking sector. The study focuses on developing an operational performance model for banks by considering the NPLs. The study uses non-parametric methodology to develop a non-oriented and non-radial Data Envelopment Analysis (DEA) model with NPLs as undesirable output. The dataset of 39 Indian commercial banks for period of 5 years is selected for the study. The findings of the study prove that considering risk into performance modelling leads to an unbiased efficiency indicator. Also, the non-parametric test confirms the relationship between operational efficiency and ownership. The study uses non-orientation modelling results to reveal inefficient sources within under-performing banks. As per the findings, slack variable analysis reveals two problem areas: ‘fixed assets’ and ‘NPLs’. A higher focus on improving utilization of fixed assets as well as controlling the level of rising NPL (risk) is highly significant for benchmarking performance. Overall, the study supports the business decision to control excess inputs and outputs for banks to achieve the efficient frontier. Significant managerial implications are linked to findings of the study focusing towards performance improvement of banks.

Keywords

Banking data envelopment analysis operational performance non-performing loans performance improvement undesirable output

Introduction

A bank holds key importance in any country’s economy by flowing and managing funds. Any fluctuation in the banking sector affects the monetary growth of the country. Therefore, there is an insistent need to critically measure bank efficiency in view of the ever-intensifying competitive banking situation. One of the significant concerns in banking performance is estimating the operational efficiency (Bhattacharya et al., 1997). The timely estimation of operational efficiency is needed not only to assess the functioning of banks but also to examine the kind of operational inefficiencies to focus on improvement measures that can be taken by the management. Traditionally, the use of financial ratios to estimate operational efficiency faces certain limitations (Yeh, 1996). This led to development of two major approaches in the field of measuring banking efficiency: parametric approaches like thick frontier approach, stochastic frontier approach and distribution free approach, and non-parametric approaches such as data envelopment analysis (DEA; Berger & Humphrey, 1997).

Identifying multiple variables for banking performance measurement is complex in nature. Research shows that the non-parametric approach outperforms the parametric approach in concern to efficiency measurement (Svitalkova, 2014). Under the non-parametric analytical approach, DEA is found to be most prominently used for efficiency assessment. It develops the efficiency frontier by employing multiple input and output variables without forming any functional relationship between factors as required in statistical approaches. The basic DEA models can be classified into radial and non-radial DEA models, depending on the shape of the efficiency frontier. The proportional category of DEA model comprises of the Banker–Charnes–Cooper (BCC) model and Charnes–Cooper–Rhodes (CCR) model, whereas the non-radial DEA model includes the slack-based measure (SBM) model, additive model and Russell measure model. Färe and Lovell (1978) suggested the use of a non-radial model that overcomes the weaknesses of radial models. Research shows that the non-radial model accounts for slacks present in efficiency score, which is ignored by the radial model. The non-radial slacks are important for managerial decision-making regarding the evaluation of performance. The non-radial efficiency, thus, possesses better discriminatory power compared to radial measure to efficiency (Fukuyama & Weber, 2009). Again, Färe and Grosskopf (2010) suggested the utilization of the SBM model, which does not neglect the input and output slack in estimating the efficiency score. Research shows a diversified area of application to evaluate performance, which ranges from manufacturing to education to financial and insurance institutions (Seth et al., 2020; Sreekumar & Mahapatra, 2011).

The current study adds to the limited research on developing countries by evaluating the operational efficiency of the Indian banking system, which is considered as the main pillar of developing growth and has undergone a rigorous policy framework to sustain in the reformative markets. According to the Reserve Bank of India (2019), the sudden demonetization of 85% of the currency in 2016 led to a rise in deposits (combined with slow loan growth), resulting in a fall in the credit–deposit ratio. Since 2017, the loan growth has been on the decline. Amidst of these regulatory changes, the state-owned institutions are reeling under the pressure of declining loan growth and rising bad assets. Since 2013, the value of non-performing assets has risen by almost 25% per year. The past five-year trend shows deterioration in bank balance-sheet, no specific gains from capital expenditure and rise in stressed assets. The rising non-performing loans (NPLs; risk) leading to balance sheet deterioration is a matter of serious concern for Indian banking system. With all these issues, the Indian banking system is observed to be battling with challenges that affect its real time performance (Bhatia & Mahendru, 2018).

The overall banking efficiency is reflected from the level of NPLs a bank sustains while performing banking activities (Bawa et al., 2019). Realizing the effect of rising NPLs on the performance of banks, Färe et al. (1989) proposed the inclusion of undesirable factors in combination with desirable factors into the performance measurement model using the DEA approach. Still, several studies omitted the impact of NPLs as risk factors while estimating banking performance (Emrouznejad & Anouze, 2010; Henriques et al., 2018; Pandey & Singh 2015). The results obtained from the previous study states that banking efficiency is biased if risk factor is not taken into consideration (Berger & Humphrey, 1997). The recent literatures show that researchers started incorporating risk as either as exogenous (Fernandes et al., 2018; Gulati & Kumar, 2017) or endogenous (Jayaraman & Srinivasan, 2014; Yang, 2017).

The present study is a move towards this direction by incorporating risk as undesirable output to assess the operational performance of Indian banks. The domain for study includes commercial (public as well as private) banks of India. Data for validation is taken to be a 5-year period (2015–2019). The expected outcome of the study is to explore whether the inclusion of an undesirable output (such as NPLs) is significant or not while measuring operational performance. The non-parametric test is applied to check the sensitivity of the empirical findings across different model and ownership categories. The bootstrap efficiency scores are used instead of DEA efficiency scores to rank the banks.

Therefore, the significant contribution of the study can be summarized in two points:

Development of operational model with undesirable output: The research framework with the undesirable SBM model and the SBM model (without undesirable output) is developed to substantiate the efficacy of including undesirable output in computing the operational performance of banks.

Non-radial empirical findings: The study uniquely demonstrates ways in which efficiency results as obtained by non-radial model can be interpreted to identify areas of improvement within the banks.

Significantly, the findings of the study will help the decision-makers to explore exact shortcomings with inefficient banks. With problem identification, the rationale of the study is thus established in the first section. Following is the flow of the paper: The second section discusses extensive literature survey, supported with gaps and objectives. The third section is the model development where DEA is discussed thoroughly for this study. The fitness of two different models 1 and 2 are discussed in the fourth section. The selection of variables and data collection is discussed in the fifth. Empirical validation is explicitly analysed in section six. The seventh section discusses managerial significance and implications. The study ends with concluding remarks discussed in the eighth section highlighting significant contributions, limitations and future research directions.

Literature Review

Post the first application of DEA to study efficiency of financial institution by Sherman and Gold (1985), the extant literature has been devoted to bank efficiency studies of developed countries (See & He, 2015; Zha et al., 2016) as well as developing economies (Davidovic et al., 2019; Sufian & Kamarudin, 2016;). Pioneer work of efficiency measurement of Indian banks refers to Bhattacharya et al. (1997). For encompassing risk into bank efficiency studies, basically, there exists two streams of the literature, ‘by considering risk as control or exogenous variable’ and ‘considering risk as by-product of loan production process or endogenous variable.’ To make the literature survey more relevant, the following section focuses on empirical studies covering both streams: risk as exogenous variable and risk as endogenous variable.

Risk as Exogenous Variable

For encompassing risk into bank efficiency studies, the previous studies show significant output. Hsiao et al. (2010) probed the influence of foremost financial restructuring on the functioning of the Taiwanese banking system by applying DEA. In the next stage, efficiency scores are explained using variables such as NPL, ownership, capital adequacy, GDP and growth rate. See and He (2015) tested NPL as one of the explanatory variables of technical efficiency of the Chinese banking system along with other variables such as equity to asset ratio, public listing and ownership. Findings suggested a positive relationship between NPL and technical efficiency but did not confirm a significant relationship between them. Stewart et al. (2016) analysed the effectiveness of Vietnamese banks using two-stage methods. Second stage analysis for NPL as exogenous variable is performed using bootstrap regression. Tan and Anchor (2017) measured the influence of liquidity, credit, insolvency and capital risk on the performance of Chinese banks for the time range of 12 years. Fernandes et al. (2018) studied the relationship between various determinants of risks and performance of European domestic banks.

The DEA approach can be effectively used to study the effect of any policy changes on the performance of banks. Gulati (2013) studied the impact of deregulation programme through estimating the cost efficiency performance of Indian banks. The relationship of cost efficiency with an exogenous variable like NPA was also tested. Sathye and Sathye (2015) studied the relationship between automatic teller machine (ATM) outlay and production efficiency of banking units. Variables such as size, risk, ownership, soundness and ATM intensity are tested as exogenous variables to analyse their effect on bank efficiency. Kaur and Gupta (2015) argued that bank efficiency is independent of level of NPA, size and business per employee. Gulati and Kumar (2017) used bootstrapped truncated regression as second stage analysis to test the significant relationship between bad output and operating efficiency. The result did not confirm the ‘bad management hypothesis’ proposed by Berger and DeYoung (1997). Alhassan and Tetteh (2017) tested the hypothesis that ‘bank risk significantly impacts efficiency’. The study used loan loss provision as proxy for bank risk and confirmed a negative relationship with bank performance.

Risk as Endogenous Variable

Being an important by-product of the banking intermediation process, it is appropriate to treat NPLs as an endogenous factor to analyse bank efficiency. Matthews and Zhang (2010) constructed five different models to quantify the performance of city commercial banks of China. A combination of varied inputs and outputs is used along with NPL as bad output to arrive at a robust result. Chen et al. (2015) developed a hybrid DEA model considering NPL as an undesirable input for the Taiwanese banking system. The study proved that NPL causes large-scale inefficiency in banks. Zhu et al. (2016) evaluated banking performance by taking NPLs as risk factors. Sufian and Kamarudin (2016) studied NPL as one of the determinants of Malaysian banking efficiency. Yang (2017) addressed the problem of rising NPA by developing DEA models to suggest NPA reduction plans for Taiwanese banks. Simper et al. (2017) also treated NPLs as bad output, and equity and loan loss provisions as good inputs. Zhu et al. in 2018 combined three different models with different input-outputs to examine the impact of risk preference on the efficiency of Chinese banks. Findings suggest modest risk preference as most suitable for the progress of Chinese banking. Almanza and Rodríguez (2018) proved the importance of including undesirable output into the production model by confirming the significant difference between models when NPL is not considered. Partovi and Matousek (2019) analysed the performance of Turkish banks for the period of 2002 to 2017 by focusing on NPLs as undesirable output. Significant findings confirmed the negative impact of NPL on the banking efficiency.

Berger and DeYoung (1997) highlighted the limitation of including NPL as an undesirable output that forms the part of the production process and not assuming it as a controlled variable. In the Indian context, Fujii et al. (2014) included NPL in the performance model to measure the technical efficiency of Indian banking system and confirmed the significance of NPL towards banks inefficiency. Jayaraman and Srinivasan (2014) explored the profit efficiency by considering NPL as an undesirable output for Indian banks. The empirical result revealed that Indian banks need to work upon improving the utilization of input-output mix to increase profit efficiency. Puri and Yadav (2014) studied the efficiency of Indian public sector banks (PSB) by developing a fuzzy DEA model including NPL as an undesirable fuzzy output. Wijesiri et al. (2017) developed a multi-activity DEA model by including NPL as a bad output to measure the financial and social performance of 26 Indian PSBs. Ahmad (2017) confirmed through his empirical findings that lower share of NPLs (asset quality) leads to higher benefits from income diversification compared to the banks with higher asset quality for Indian banking system.

After referring to the extensive literatures in both global and Indian context, the significant gap area is identified as follows:

Comparing the undesirable SBM model result with SBM model is not addressed significantly in the service sector, such as banking to measure operational performance.

Using empirical insights from a non-radial DEA model to identify the areas of inefficiencies that cause lower operational performance for banks is also not much discussed in the previous literatures.

Following the highlighted gap(s), the objective(s) of the study is framed as under the following:

To develop the undesirable SBM model and SBM model to calculate the operational performance of Indian banks using multiple DEA models.

To perform slack value analysis to identify areas that require improvement within inefficient banks.

To use the bootstrapping estimate to identify benchmark and inefficient banks.

To test the robustness of the developed models across ownership category of banks.

Research Methodology

Data Envelopment Analysis

Charnes et al. (1978) augmented Farell’s (1957) efficiency measurement concept of single input-output to using linear combination of multiple input-output to construct relative efficiency frontier for decision-making units (DMUs). The relative efficiency score estimated ranges between 0 and 1, and it also determines whether DMU is operating at constant, increasing and decreasing return to scale. As the name suggests, DEA envelops all inefficient DMUs by constructing the efficient frontier. The CCR model, also referred to radial model, assumes constant return to scale by assuming that DMUs function at optimal scale and calculates the overall technical efficiency. The BCC model extended the CCR model to evaluate pure, technical and scale efficiency at variable return to scale (Banker et al., 1984). A major drawback of the radial model is the assumption of proportional changes without accounting for slacks (input surpluses and output deficits) in the efficiency score. This led to the advancement of non-radial models of DEA that is based on SBM to estimate the efficient frontier. As proposed by Tone (2001), the SBM model measures efficiency, referring to the non-proportional point on the frontier to identify the benchmark banks. The critical contribution of using non-radial model is that it can locate the source as well as explain the level of inefficiency with respect to each input and output variable selected.

Model 1: Slack-based Measure Model

For n DMUs, each having m input vector and v output vector (j = 1,2, 3, …, n). Matrices for each vector of inputs and outputs is represented as X = x_ij (i = 1,2,…, m), Y = y_uj (u = 1,2, …, v), assuming X > 0, Y > 0. The model assumes intensity vector λ equal to 1 under the assumption of variable return to scale. The production possibility set comprising the variables used in the model is defined as follows:

δ = {(x, y)}} x \geq X λ, y \leq Y λ, λ = 1

(1)

The objective equation for SBM model with non-orientation under variable return to scale is as follows:

μ = \min \frac{1 - \frac{1}{m} \sum_{i = 1}^{m} \frac{s_{i}^{-}}{x_{i 0}}}{1 - \frac{1}{t} \sum_{u = 1}^{v} \frac{s_{u}^{+}}{y_{u 0}}}

(2)

Subject to the following constraints:

\begin{matrix} x_{0} = X λ + s^{-} \\ y_{0} = Y λ - s^{+} \\ λ = 1 \end{matrix}

(3)

Where, ρ denotes non-proportional slack or optimal efficiency score (0 < ρ ≤ 1), s^– and s⁺ indicates input-output slack, respectively. A DMU with ρ score value as unity and slack values as zero, is termed efficient.

Model 2: Undesirable Slack-based Measure Model

For n DMUs, each having inputs, good (desirable) outputs and bad (undesirable) outputs, as symbolized by vectors $x \in R^{m}, y^{g 0 o d} \in R^{s_{1}} and y^{b a d} \in R^{s_{2}}$ , respectively. Matrices for each vector is represented as $X = {x_{1}, \dots, x_{n}} \in R^{m \times n}, Y^{g o o d} = {y_{1}^{^{g o o d}}, \dots, y_{n}^{^{g o o d}}} \in R^{s_{1} \times n} and Y^{b a d} = {y_{1}^{b a d}, \dots, y_{n}^{b a d}} \in R^{s_{2} \times n}$ , assuming X, Ybad, $Y^{b a d}, Y^{g o o d} > 0$ . Intensity vector is $λ \in R^{n}$ and is equal to 1 under variable return to scale assumption. Production possibility set (µ) is defined as follows:

μ = {(x, y^{b a d}, y^{g o o d}) ∣ x \geq X λ, y^{b a d} \geq Y^{b a d} λ, y^{g o o d} \leq Y^{g o o d} λ, λ = 1

(4)

Objective equation of SBM model with undesirable output adapting variable return to scale with non-orientation is as follows:

ρ = \min \frac{1 - \frac{1}{m} \sum_{i = 1}^{m} \frac{s_{i 0}^{-}}{x_{i 0}}}{1 + \frac{1}{s_{1} + s_{2} (\sum_{r = 1}^{s_{1}} \frac{s_{r}^{g o o d}}{y_{r 0}^{g o o d}} + \sum_{r = 1}^{s_{2}} \frac{s_{r}^{b a d}}{y_{r 0}^{b a d}})}}

(5)

Subject to the following constraints:

\begin{matrix} x_{0} = X λ + s^{-} \\ y_{0}^{g o o d} = Y λ - s^{g o o d} \\ y_{0}^{b a d} = Y λ + s^{b a d} \\ s^{-} \geq 0, s^{b a d} \geq 0, s^{g o o d} \geq 0, λ = 1 \end{matrix}

(6)

Where bad output excesses, input excesses and good output shortfalls vectors are represented as $s^{-} \in R^{m}, s^{b a d} \in R^{s_{2}}$ and $s^{g o o d} \in R^{s_{1}}$ . ρ denotes the optimal efficiency value, 0 <ρ ≤1. Therefore, the efficient DMU with bad output is given by ρ = 1 and all bad output excesses, input excesses and good output shortfalls values equal to 0. For inefficient DMU, SBM projection is as follows:

\begin{matrix} {\hat{x}}_{0} \leftarrow x_{0} - s^{- *} \\ {\hat{y}}_{0}^{g o o d} \leftarrow y_{0}^{g o o d} - s^{g o o d} \\ {\hat{y}}_{0}^{b a d} \leftarrow y_{0}^{b a d} - s^{b a d^{*}} \end{matrix}

(7)

A necessary optimization model under variable return to scale is developed for 39 banks to estimate the slack-based score of technical efficiency for each bank incorporating undesirable output (risk). Value for coefficient of efficiency lies between 0 and 1. Any bank with SBM score of technical efficiency equal to 1 with value of slacks as 0 is termed as SBM-efficient. Figure 1 shows the structure of undesirable SBM model developed to measure operational performance of banks.

Figure 1.

Source: The authors.

Bootstrapping

A common problem associated with non-parametric DEA is the absence of differentiation between efficient DMUs due to lack of statistical support. Since DEA is constructed on linear programming, the estimated efficiency scores often lack statistical support due to its deterministic characteristics. Plenty of DEA-related studies ignored these uncertainty-related issues of estimates. Therefore, the present article applied bootstrapping calculations based on R codes developed by authors, performing 1,000 bootstrap iterations on model equation (1.5). Although this bootstrapping procedure is not based on Simar and Wilson (2004), this performed approach derives statistical properties compared to biased computations, confidence intervals and correction trends.

Fitness of Model

The present study develops two non-oriented SBM models to evaluate the operational efficiency of Indian banks with the idea of studying the impact of undesirable output. These two models differ by choice of output variables:

Model 1 considers ‘total advances and loans’ by ignoring the significance of NPLs.

Model 2 bifurcates ‘total advances and loans’ into ‘NPLs’ as undesirable (risk) outputs and ‘performing advances and loans’ as desirable output.

There are three directions in which each inefficient bank is anticipated onto the efficient frontier.

Under input-oriented, the model keeps the present output level and purposes to lower the input amounts by as much as possible.

Under output-oriented, the model maximizes the output levels keeping the present input levels.

Under non-oriented, models deal with output surpluses and input deficits simultaneously by mutually maximizing both.

The non-radial model with non-orientation is constructed with the objective to simultaneously reduce inputs as well as bad outputs and to expand the good outputs with the view to develop the operational performance of Indian banks. The combination of non-radial model with non-oriented approach is proved to be more suitable for estimating performance of banks (Juo et al., 2012). In addition, the model chooses variable return to scale assumption by believing that all banks do not function at an ideal scale (Banker et al., 1984). Figure 2 illustrates the flow of the article highlighting the stepwise procedure for evaluation of operational performance.

Figure 2.

Source: The authors.

Selection of Variables and Data Collection

Production and intermediation are two standard approaches used for selecting variables for DEA modelling (Drake et al., 2009). Production approach, proposed by Benston (1965), considers banking unit as a provider of services to consumers exercising fixed inputs such as assets, capital and labour, which provides services such as advances and deposits. On the other hand, Sealey and Lindley (1977) proposed intermediation approach that includes fund collection and loan conversion depicting the intermediary function. Berger and Humphrey (1997) recommended that intermediation approach is well-matched for evaluating the performance of banking system, whereas production approach is more fit for studies to measure performance of bank branches. Fethi and Pasiouras (2010) also recommended intermediation approach to be more prevalent after reviewing 151 studies relating to banking system. An ever-increasing competitive environment driven by market challenges shows the importance of measuring financial intermediation efficiency. Considering the literature and current significance, the intermediation approach is chosen to select variables for developing operational performance model using non-radial DEA approach.

As NPL is an important by-product of the intermediation process of banks, it cannot be disregarded in the performance measurement model. The present research includes NPLs (risk factor) as bad output (Avkiran, 2015; Zha et al., 2016). The study incorporates performing loans and advances, investments and non-interest income as good outputs. Input variables incorporates net worth, operating expenses, fixed assets and deposits (Table I). Net worth is included as a proxy for capital adequacy, which is a significant indicator of performance as per Basel Accord. Operating expenses is a significant operational input that results in profitability and impacts efficiency (Zha et al., 2016). Fixed assets consist of building, land and equipment included as proxy for scale expansion and impacts profitability (Gulati & Kumar, 2017; Sahoo & Tone, 2009). While evaluating the intermediation role of banks, deposit is an important input factor. Following the work of Gulati and Kumar in 2016, the bank’s equity capital is considered as quasi-fixed input without specifying any association with price, linking both risk-return trade-off and risk-based capital constraints that bank owners face.

Investments comprises the sum of marketable securities and long-term investments (Gulati & Kumar, 2017; Sahoo & Tone, 2009). Modifying the loan amount by including NPLs makes a new factor stated as performing loans. It is basis of interest income that supports liquidity and security for usual operations of banking by delivering banking stability information (Gulati & Kumar, 2017; Sahoo & Tone, 2009). If a model with unadjusted amount is developed, the efficiency score might be overestimated. Non-interest income characterizes added income that helps banks in improving efficiency (Gulati & Kumar, 2017; Sahoo & Tone, 2009).

Table 1.

List of Selected Variables.

Variables	Model 1	Model 2
Inputs	Net worth Operating expenses Fixed assets Deposits	Net worth Operating expenses Fixed assets Deposits
Desirable (good) outputs Undesirable (bad) outputs	Total advances and loans Investment Non-interest income	Performing advances and loans Investment Non-interest income Non-performing loans

Source: The authors.

The data for selected variables is collected from the website of the Reserve Bank of India and Indian Banks Association, and with the study period of 5 years (2015–2019) for the total of 39 Indian banks. Therefore, the total observation is equal to 195, which covers 20 PSB and 19 private sector banks (PBs). The names of banks with codes are illustrated in Table A1. There are two reasons for selecting a 5-year study period.

First, the study period covers the most recent dataset.

Second, the study period covers major reforms such as digitization, recapitalization, demonetization and consolidation, that greatly impacts the functioning of banks.

For two apparent reasons the foreign banks are excluded from the analysis:

First, limited presence in Indian banking system.

Second, required expertise in off-balance sheet activities.

The Bharatiya Mahila Bank and associate banks of the State Bank of India (SBI) merged with the SBI in April 2017. Hence, SBI data for the study period of 2015 to 2017 is the aggregate of the Bharatiya Mahila Bank and associate banks of SBI. Bandhan Bank Limited (Ltd.) and IDFC First Bank Ltd were dropped from the sample as they started operation after 2015. IDBI bank is considered as a PB because of its ownership pattern. Correlation coefficients of selected variable is tested to check the isotonicity property of variables to be included for undesirable SBM model. Correlation matrix shows the statistically significant positive value for each variable justifying its use for measuring efficiency (Table 2). Also, the descriptive statistics of each selected factors are presented in Table 3.

Table 2.

Correlation Matrix of Selected Factors.

Variables	Net Worth	Operating Expenses	Fixed Assets	Deposits	Performing Advances and Loans	Investments	Non-interest Income	Bad Output
Net worth	1.0000
Operating expenses	0.8960	1.0000
Fixed assets	0.6523	0.9767	1.0000
Deposits	0.7457	0.9623	0.7689	1.0000
Performing advances and loans	0.8154	0.9060	0.9230	0.5976	1.0000
Investments	0.5341	0.8290	0.8990	0.8010	0.6523	1.0000
Non-interest income	0.6489	0.8890	0.9100	0.8120	0.6473	0.8792	1.0000
Bad output	0.5823	0.8124	0.5434	0.7623	0.9235	0.8254	0.6365	1.0000

Source: The authors.

Table 3.

Descriptive Statistics of Selected Inputs and Outputs.

Variables	Mean	Median	Minimum	Maximum
Net worth	5,333.83242	536.89117	4,619.32310	6,024.36838
Operating expenses	5,333.83242	536.89117	4,619.32310	6,024.36838
Fixed assets	3,055.41776	918.34618	1,880.27421	4,336.89713
Deposits	230,605.02811	30,603.16904	18,3213.68680	264,097.57531
NPL	22,405.94900	33,113.87268	4,319.73896	81,520.82753
Performing advances and loans	175,430.44632	9,260.53854	166,770.86815	190,928.55560
Investments	74,503.06443	6,814.34266	67,207.92189	83,831.35285
Non-interest income	15,711.55263	27,406.69375	2,912.99738	64,731.16005

Source: The authors.

Result and Findings

The collected dataset is analysed using the software named DEA Solver Learning Version 3.0. The results are presented in four sub-sections fulfilling the four objectives sequentially.

Descriptive Analysis of Efficiency Scores

Table 4 gives the average efficiency values from SBM model under variable return to scale with non-orientation for five years (2015–2019). As evident, the highest efficiency value is 0.9276 in 2018 whereas the lowest efficiency value is 0.8789 in 2015. The empirical findings verify growth in efficiency of banks with exception in the year 2018–2019. The findings also show an abrupt rise in efficiency score in the year 2017–2018. On comparing the efficiency values for model 1 and model 2, there is significant difference in efficiency values from 2015 to 2019, signifying the importance of including risk factor into the model without which efficiency score are underestimated (Berger & Humphrey, 1997; Table 5). The efficiency score for each year is significantly higher when NPL is taken as undesirable output. Efficient frontier is made up of benchmark or the top performing banks.

The overall efficiency score has increased in model 2 compared to model 1, with the number of benchmark banks also increasing. As per model 1, 10 out of 39 banks constitute the reference set, whereas in model 2, a total of 17 out of 39 banks is with an overall technical efficiency score of 1, indicating optimal resource allocation and performs the best.

The number of benchmark banks increase, showing the impact of including undesirable output into model 2.

Banks that constitutes the benchmark and defines operational efficiency for both model 1 and 2 is presented in Table 6. It is worthwhile to identify benchmark banks for each category of banks—public and private. Most inefficient banks are also identified for model 1 and model 2. All banks with efficiency values equal to 1 constitute the reference set for inefficient banks. A bank-wise efficiency score for Models 1 and 2 is offered in Table A2. The slack value of selected factor signifies deviation from performance, which can be worked upon by working on improvable spaces.

Table 4.

Descriptive Statistics of Efficiency Scores.

Descriptive Statistics	2015	2016	2017	2018	2019
Average	0.8789	0.8791	0.9069	0.9276	0.9142
SD	0.1816	0.1805	0.1547	0.1450	0.1832
Maximum	1	1	1	1	1
Minimum	0.4742	0.4695	0.4902	0.4479	0.3222

Source: The authors.

Table 5.

Comparison of Efficiency Scores for Model 1 and 2.

Year	Model 1	Model 2	P-value
2015	0.8961	0.8789	.0078
2016	0.8997	0.8791	.0126
2017	0.9245	0.9069	.0172
2018	0.8167	0.9276	.0176
2019	0.9064	0.9142	.0206
Average	0.8887	0.9013	.1109

Source: The authors.

Table 6.

Benchmark and Inefficient Banks for Model 1 and 2.

Category	Ownership	Model 1	Model 2
Benchmark banks	Public	AB, CB, SB, UCO, UB, SBI	BoB, SB, UCO, UB, UBI, VB, SBI
Benchmark banks	Private	TMB, ABL, ICICI, YES	CUB, TMB, DBL, RBL, ABL, DCB, HDFC, ICICI, IBL, YES
Inefficient banks	Public	DB	DB
Inefficient banks	Private	JKB	JKB

Source: The authors.

Performance Improvement Analysis

Following Li et al., (2019), this study adopts the approach of estimating mean factor efficiency to identify causes of inefficiency occurring in the inefficient banks. The improvement for individual input and output variable is estimated by exercising the relationship between actual and predicted estimates of the variables. Mean factor efficiency index for input variable is ratio of predicted estimates divided by actual estimates, whereas mean factor efficiency index for output variable is ratio of actual estimates divided by predicted estimates. Abbreviations used for banks are presented in Table A1.

Banks that require the greatest improvement in each input and output variable from 2015 to 2019 are shown in Table 7. Banks with inefficient ‘net worth’ are found to be KMB, IDBI and KVB during the study period. Looking at undesirable output variable ‘NPLs’, banks that need major improvement include JKB, IDBI and LVB. Similarly, for all the other variables, inefficient banks are identified. The mean factor efficiency for each input and output factor is displayed in Table 8. From 2015 to 2018, the ‘net worth’ efficiency is proved to be highest, followed by other inputs. In the year 2019, the ‘operating efficiency is shown to be highest compared to other inputs. On the output side, mean factor efficiency of ‘performing advances and loans’ is shown to be highest from 2015–2017. The ‘investment’ efficiency is highest for 2018–2019 compared to other outputs. This signifies that most inefficient sources that require major improvement are the ‘fixed assets’ as input variables and ‘NPLs’ as undesirable output variables.

Table 7.

Banks with Most Inefficiency in Input and Output Variables.

Variables	Inefficient Banks
Net worth	IDBI, KMB, KVB
Operating expenses	DB, IOB, KMB
Fixed assets	IOB, JKB, KMB
Deposits	CBI, IDBI, JKB
NPL	IDBI, JKB, LVB
Performing advances and loans	CBI, DB, IOB, IDBI
Investments	CSB, FB, IDBI, KMB
Non-interest income	BoM, JKB, PS

Source: The authors.

Table 8.

Mean Factor Efficiencies for Each Input and Output Variables.

	Inputs					Good Output
Year	Net Worth	Operating Expenses	Fixed Asset	Deposit	Bad Output NPL	Total Advances Less NPL	Investment	Non-interest Income
2015	0.98989	0.98273	0.89560	0.98509	0.83540	0.99731	0.98020	0.95843
2016	0.98716	0.97626	0.83365	0.97457	0.81470	1.00000	0.98610	0.94191
2017	0.98714	0.98200	0.92151	0.98640	0.87573	0.99841	0.99622	0.98224
2018	0.99141	0.97784	0.94519	0.97542	0.98067	0.99233	0.99605	0.98912
2019	0.97319	0.99104	0.93513	0.98003	0.93552	0.99351	0.99818	0.98199

Source: The authors.

Table 9 shows the mean factor efficiencies for input and output variables for PBs and PSBs. The PSBs have higher mean factor efficiency of ‘net worth’ compared to PBs for all years, except 2018. PSBs performed better than PBs in the context of operating efficiency for all years except 2017 and 2018. Results show the following inferences:

For input variable ‘fixed assets’, mean factor efficiency for PBs is considerably higher in years 2016, 2018 and 2019. However, in 2015 and 2017, the PSBs efficiency was higher in terms of ‘fixed assets.’ In case of input variable ‘deposits’, PBs scores better in the years 2015, 2016 and 2019.

For undesirable output variable ‘NPLs’, mean factor efficiency for PBs is better than PSBs for only 2 out 5 years (2015 and 2016).

The value of mean factor efficiency for ‘performing loans’ is higher for PBs compared to PSBs for all years except 2018.

Mean factor efficiency results for ‘investment’ and ‘non-interest income’ are in sharp contrast. The value of mean factor efficiency for ‘investment’ is higher for PSBs, whereas for ‘non-interest income’, the PBs perform better. Low mean factor efficiency indicates inefficiencies, highlighting improvable spaces required for inefficient bank in the context of input surpluses and output deficits.

Table 9.

Mean Factor Efficiencies for Each Input and Output Variables According to Ownership Differences.

		Inputs					Good Output
Year	Category	Net Worth	Operating Expenses	Fixed Asset	Deposit	Bad Output NPL	Total Advances Less NPL	Investment	Non-interest Income
2015	Public	0.99287	0.98895	0.89825	0.98478	0.82807	0.99638	0.99063	0.94774
2015	Private	0.98501	0.96902	0.88867	0.98611	0.89147	1.00000	0.95382	0.97562
2016	Public	0.99252	0.97855	0.79267	0.97101	0.80292	1.00000	0.98759	0.92980
2016	Private	0.97915	0.97140	0.94044	0.98537	0.90366	1.00000	0.98238	0.96063
2017	Public	0.99807	0.98117	0.95143	0.98640	0.89888	0.99775	0.99861	0.97687
2017	Private	0.97134	0.98358	0.81555	0.98640	0.76313	1.00000	0.98966	0.99130
2018	Public	0.98758	0.96603	0.89908	0.97556	1.00000	0.99377	0.99854	0.77425
2018	Private	0.99557	0.99920	0.99920	0.95918	0.97807	0.98956	0.97825	1.00000
2019	Public	0.99627	0.99288	0.93040	0.97659	0.93727	0.98995	1.00000	0.97290
2019	Private	0.96964	0.98785	0.94953	0.98804	0.92798	1.00000	0.99391	0.99423

Source: The authors.

Ranking Based on Bootstrap Efficiency Score

Bootstrap scores are different from DEA estimates, breaking the efficiency score of 1 by removing bias. Thus, we focus on bootstrap estimates to rank the banks. Bootstrap efficiency scores obtained from Frontier Efficiency Analysis with R (FEAR) package of R software is used to rank the banks as stated in Table 10. Results show the following rankings:

The top efficient bank, HDFC bank, a PB, leads amongst the group of 39 banks with the bootstrap score corresponding to 1.0235.

IBL, also a PB, acquires the subsequent position with bootstrap score equal to 1.0211.

Amongst the top 10 efficiently performing banks, five banks are PBs (HDFC, IBL, CUB, SIB and DBL) and the rest five are PSBs (CPB, PNB, BoB, UBI and UCO). However, the top three banks are all PBs (HDFC, IBL, CUB).

DB and JKB discovered to acquire the last ranking in the group of 39 banks according to the bootstrap efficiency scores.

Hypothesis testing is done that justifies the use of bootstrapping for ranking the banks. Rank correlation coefficient of Spearman’s (rho = 0.72892823) signifies positive correlation between DEA-scores-based ranking and bootstrap-based ranking, as they move in same direction with the same magnitude.

Table 10.

Ranking Based on Bootstrap Scores.

Bank Code	Bootstrap Score	Ranking	Bank Code	Bootstrap Score	Ranking	Bank Code	Bootstrap Score	Ranking
HDFC	1.023556	1	ICICI	0.999667	14	KB	0.954091	27
IBL	1.021090	2	YES	0.997871	15	CSB	0.933724	28
CUB	1.012913	3	UB	0.997741	16	BoI	0.928428	29
CPB	1.011380	4	SBI	0.996173	17	FB	0.877306	30
SIB	1.011296	5	AB	0.994878	18	KVB	0.860997	31
PNB	1.006622	6	LVB	0.991689	19	OBC	0.840939	32
DBL	1.005966	7	RBL	0.991598	20	CBI	0.838946	33
BoB	1.005366	8	ABL	0.990062	21	IB	0.829875	34
UBI	1.003584	9	CB	0.983191	22	KMB	0.759062	35
UCO	1.002606	10	ABB	0.974759	23	BoM	0.743150	36
PS	1.002467	11	VB	0.974650	24	IOB	0.722743	37
TMB	1.002253	12	IDBI	0.973977	25	DB	0.709932	38
DCB	1.001338	13	SB	0.965436	26	JKB	0.563826	39
Null Hypothesis: No correlation between ranking based on DEA efficiency scores and bootstrap efficiency scores
Spearman’s rank correlation coefficient (rho) = 0.72892823
Two-tailed p-value = .0000
Result: Reject the null hypothesis

Source: The authors.

Robustness Results

As already discussed, the average efficiency difference between two models is significant. This section discusses the significant efficiency difference between PSBs and PBs considering model 1 and model 2. The non-parametric test (Wilcoxon test) is preferred over the parametric test based on the non-functional relationship between selected factors. Table 11 gives the Wilcoxon test results for PSBs and PBs from 2015 to 2019. Results show the following results for two models:

For model 2, there exists significant difference between ownership for all the years at significance level of 10%.

For model 1, the efficiency difference between ownership is significant for 4 out of 5 years at a significance level of 10%.

This empirical finding proves that ‘impact of risk is significant across ownership differences.’

Table 11.

Wilcoxon Results Based on Ownership.

Year	Model	Bank	Average Efficiency	P-value
2015	Model 1	Public	0.90207	.0122911
		Private	0.88978
	Model 2	Public	0.85018	.0213
		Private	0.90905
2016	Model 1	Public	0.89231	.0135429
		Private	0.90740
	Model 2	Public	0.84883	.03713
		Private	0.91104
2017	Model 1	Public	0.93109	.01509
		Private	0.91754
	Model 2	Public	0.89648	.05887
		Private	0.91778
2018	Model 1	Public	0.72875	.0915337
		Private	0.90919
	Model 2	Public	0.89319	.06221
		Private	0.96376
2019	Model 1	Public	0.95096	.18045
		Private	0.85943
	Model 2	Public	0.93231	.07057
		Private	0.89518

Source: The authors.

Conclusively, the objectives defined for the study are fulfilled upon analysis. These are as follows:

On comparison of efficiency scores for model 1 and 2, signifies the importance of including risk factor into the model without which efficiency score are underestimated. This finding fulfils Objective 1.

Mean factor efficiency analysis successfully highlighted the most inefficient sources that require major improvement. Low mean factor efficiency indicates inefficiencies, highlighting improvable spaces required for inefficient bank in relation to input excesses and output shortfalls. This satisfies Objective 2.

Bootstrapping approach used for identifying benchmark banks is justified through hypothesis testing. This result satisfies Objective 3.

Also, the impact of risk is significant across ownership differences. This proves Objective 4.

Theoretical and Managerial Significance

The highly competitive environment of banking system coupled with deteriorating balance sheet is deemed to push banks towards higher risk. Risk being an important by-product of bank’s operational process, it cannot be ignored while evaluating operational performance of banks (Partovi & Matousek, 2019). The proposed approach is an effort to develop a multiple DEA model framework that is well suited to study the influence of risk as an undesirable output on the operational performance of banks. The finding of the study states the significant difference between average efficiency score due to inclusion of undesirable output. Non-oriented non-radial model permits the factor efficiency analysis that highlights the improvable spaces required for inefficient bank in terms of input surpluses and output deficits. Empirical findings of this study infer the following managerial implications:

Inclusion of NPLs into performance measurement model leads to unbiased efficiency indicator, which is significantly different when efficiency is estimated without including risk as bad output (Yang, 2017).

Implementation of non-oriented DEA modelling helps bank managers to simultaneously increase output levels and decrease input levels for inefficient banks to achieve the desired efficiency level (Juo et al., 2012).

Application of concept of mean factor efficiency, the inefficient level of individual inputs and outputs are identified to estimate improvable spaces required for inefficient banks to become efficient. As per the findings, slack variable analysis reveals two problem areas: ‘fixed assets’ and ‘NPLs’. Higher focus on improving utilization of fixed assets as well as controlling the level of rising NPL (risk) is highly significant for benchmarking performance.

For instance, the banks like DB, IOB and KMB can improve the operational efficiency score by reducing the operational expenses and by proper utilization of excess fixed assets. Also, the banks must improve the level of performing loans to have greater impact on operational efficiency level.

Nevertheless, policies targeted to improve the efficiencies of individual input and output for each inefficient bank may be framed for significant performance improvement.

Discussion and Conclusion

To summarize, this present study is an effort to develop multiple DEA and its modelling framework that fits to study the influence of risk as undesirable output on the operational performance of banks. Due to the inclusion of an undesirable output, the finding of the study states the significant difference between average efficiency scores. The significant contribution (novelty) of the study is the proposed modelling framework incorporating undesirable output for operational performance measurement of banks. The robustness of using two different models is proved significant across ownership differences for the Indian banking system. This contributes to adequate assessment of policy measures tailored to meet the operational performances differentials across PSBs and PBs. Therefore, the empirical findings confirm the relationship between operational efficiency, risk and ownership difference for the Indian banking system. An attempt has been made to highlight the inefficient factors causing operational inefficiency in banks.

The limitations of the study entail the scope of future research. The study concerns specifically to the Indian banking system; therefore, its findings cannot be generalized to compare with other countries due to different factors such as geographical proximities, nature of operations and the ownership criteria. The present developed model is a static one, ignoring the link between consecutive periods. In consideration with a greater number of operational issues considering efficiency, the future study may further be directed in line of development of dynamic models; this awaits further study.

Appendix A

Table A1.

Bank Name and Code.

No.	Bank Name	Code	No.	Bank Name	Code	No.	Bank Name	Code
1	Allahabad Bank	ABB	14	Dhanlaxmi Bank Limited	DBL	27	Oriental Bank of Commerce	OBC
2	Andhra Bank	AB	15	Federal Bank Limited	FB	28	Punjab & Sind Bank	PS
3	Axis Bank Limited	ABL	16	HDFC Bank Limited	HDFC	29	Punjab National Bank	PNB
4	Bank of Baroda	BoB	17	ICICI Bank Limited	ICICI	30	RBL Bank Limited	RBL
5	Bank of India	BoI	18	IDBI Bank Limited	IDBI	31	South Indian Bank Limited	SIB
6	Bank of Maharashtra	BoM	19	Indian Bank	IB	32	State Bank of India	SBI
7	Canara Bank	CB	20	Indian Overseas Bank	IOB	33	Syndicate Bank	SB
8	Catholic Syrian Bank Limited	CSB	21	IndusInd Bank Limited	IBL	34	Tamilnad Mercantile Bank Limited	TMB
9	Central Bank of India	CBI	22	Jammu & Kashmir Bank Limited	JKB	35	UCO Bank	UCO
10	City Union Bank Limited	CUB	23	Karnataka Bank Limited	KB	36	Union Bank of India	UB
11	Corporation Bank	CPB	24	Karur Vysya Bank Limited	KVB	37	United Bank of India	UBI
12	DCB Bank Limited	DCB	25	Kotak Mahindra Bank Limited	KMB	38	Vijaya Bank	VB
13	Dena Bank	DB	26	Lakshmi Vilas Bank Limited	LVB	39	YES Bank Limited	YES

Source: The authors.

Table A2.

Efficiency Score for Model 1 and Model 2.

Bank Code	Model 1	Model 2	Bank Code	Model 1	Model 2	Bank Code	Model 1	Model 2
ABB	0.87914	0.79381	PNB	0.97798	0.90086	KB	0.90262	0.94969
AB	1.00000	0.94568	SB	1.00000	1.00000	KVB	0.74410	0.81067
BoB	0.96128	1.00000	UCO	1.00000	1.00000	LVB	0.90078	0.88627
BoI	0.73062	0.75661	UB	1.00000	1.00000	RBL	0.88290	1.00000
BoM	0.77288	0.72302	UBI	0.85440	1.00000	SIB	0.86724	0.96533
CB	1.00000	0.95263	VB	0.96336	1.00000	ABL	1.00000	1.00000
CBI	0.69482	0.81005	SBI	1.00000	1.00000	DCB	0.87444	1.00000
CPB	0.96232	0.94315	CUB	0.99998	1.00000	HDFC	0.97808	1.00000
DB	0.55826	0.63897	TMB	1.00000	1.00000	ICICI	1.00000	1.00000
IB	0.85072	0.83936	CSB	0.94956	0.95991	IBL	0.83254	1.00000
IOB	0.75128	0.72745	DBL	0.99996	1.00000	KMB	0.68944	0.71330
OBC	0.79882	0.77418	FB	0.85268	0.81814	YES	1.00000	1.00000
PS	0.86480	0.87816	JKB	0.59304	0.55122	IDBI	0.96934	0.81334

Source: The authors.

Footnotes

Declaration of Conflicting Interests

The authors declared no potential conflicts of interest with respect to the research, authorship and/or publication of this article.

Funding

The authors received no financial support for the research, authorship and/or publication of this article.

ORCID iD

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References

Ahamed

M. M.

(2017). Asset quality, non-interest income, and bank profitability: Evidence from Indian banks. Economic Modelling , 63(4), 1–14.

Alhassan

A. L.

, & Tetteh

M. L.

(2017). Non-interest income and bank efficiency in Ghana: A two-stage DEA bootstrapping approach. Journal of African Business , 18(1), 124–142.

Almanza

, & Mora Rodríguez

J. J.

(2018). Profit efficiency of banks in Colombia with undesirable output: A directional distance function approach. Economics: The Open-Access, Open-Assessment E-Journal , 12(30), 1–18.

Avkiran

N. K.

(2015). An illustration of dynamic network DEA in commercial banking including robustness tests. Omega , 55(6), 141–150.

Banker

R. D.

, Charnes

, & Cooper

W. W.

(1984). Some models for estimating technical and scale inefficiencies in data envelopment analysis. Management Science , 30(9), 1078–1092.

Bawa

J. K.

, Goyal

, Mitra

S. K.

, & Basu

(2019). An analysis of NPAs of Indian banks: Using a comprehensive framework of 31 financial ratios. IIMB Management Review , 31(1), 51–62.

Benston

G. J.

(1965). Branch banking and economies of scale. The Journal of Finance , 20(2), 312–331.

Berger

A. N.

, & Humphrey

D. B.

(1997). Efficiency of financial institutions: International survey and directions for future research. European Journal of Operational Research , 98(2), 175–212

Berger

A. N.

, & DeYoung

(1997). Problem loans and cost efficiency in commercial banks. Journal of Banking & Finance , 21(6), 849–870.

10.

Bhatia

, & Mahendru

(2018). Measurement of revenue efficiency of scheduled commercial banks across ownership in India. IUP Journal of Bank Management , 17(2), 20–49

11.

Bhattacharyya

, Lovell

C. K.

, & Sahay

(1997). The impact of liberalization on the productive efficiency of Indian commercial banks. European Journal of Operational Research , 98(2), 332–345

12.

Charnes

, Cooper

W. W.

, & Rhodes

(1978). Measuring the efficiency of decision making units. European Journal of Operational Research , 2(6), 429–444

13.

Chen

M. J.

, Chiu

Y. H.

, Jan

, Chen

Y. C.

, & Liu

H. H.

(2015). Efficiency and risk in commercial banks—Hybrid DEA estimation. Global Economic Review , 44(3), 335–352

14.

Davidovic

, Uzelac

, & Zelenovic

(2019). Efficiency dynamics of the Croatian banking industry: DEA investigation. Economic Research-Ekonomska Istraživanja , 32(1), 33–49.

15.

Drake

, Hall

M. J.

, & Simper

(2009). Bank modelling methodologies: A comparative non-parametric analysis of efficiency in the Japanese banking sector. Journal of International Financial Markets, Institutions and Money , 19(1), 1–15.

16.

Emrouznejad

, & Anouze

A. L.

(2010). Data envelopment analysis with classification and regression tree—A case of banking efficiency. Expert Systems , 27(4), 231–246.

17.

Färe

, & Grosskopf

(2010). Directional distance functions and slacks-based measures of efficiency. European Journal of Operational Research , 200(1), 320–322.

18.

Färe

, Grosskopf

, Lovell

C. K.

, & Pasurka

(1989). Multilateral productivity comparisons when some outputs are undesirable: A nonparametric approach. The Review of Economics and Statistics , 71(1), 90–98

19.

Färe

, & Lovell

C. K.

(1978). Measuring the technical efficiency of production. Journal of Economic theory , 19(1), 150–162.

20.

Farrell

M. J.

(1957). The measurement of productive efficiency. Journal of the Royal Statistical Society: Series A (General) , 120(3), 253–281.

21.

Fernandes

F. D. S.

, Stasinakis

, & Bardarova

(2018). Two-stage DEA-truncated regression: Application in banking efficiency and financial development. Expert Systems with Applications , 96(6), 284–301

22.

Fethi

M. D.

, & Pasiouras

(2010). Assessing bank efficiency and performance with operational research and artificial intelligence techniques: A survey. European Journal of Operational Research , 204(2), 189–198.

23.

Fujii

, Managi

, & Matousek

(2014). Indian bank efficiency and productivity changes with undesirable outputs: A disaggregated approach. Journal of Banking & Finance , 38(1), 41–50.

24.

Fukuyama

, & Weber

W. L.

(2009). A directional slacks-based measure of technical inefficiency. Socio-Economic Planning Sciences , 43(4), 274–287.

25.

Gulati

(2015). Trends of cost efficiency in response to financial deregulation. Benchmarking: An International Journal , 22 (5), 808–838.

26.

Gulati

, & Kumar

(2017). Analysing banks’ intermediation and operating efficiencies using the two-stage network DEA model. International Journal of Productivity and Performance Management , 66(4), 500–516.

27.

Henriques

I. C.

, Sobreiro

V. A.

, Kimura

, & Mariano

E. B.

(2018). Efficiency in the Brazilian banking system using data envelopment analysis. Future Business Journal , 4(2), 157–178.

28.

Hsiao

H. C.

, Chang

, Cianci

A. M.

, & Huang

L. H.

(2010). First financial restructuring and operating efficiency: Evidence from Taiwanese commercial banks. Journal of Banking & Finance , 34(7), 1461–1471.

29.

Jayaraman

A. R.

, & Srinivasan

M. R.

(2014). Analyzing profit efficiency of banks in India with undesirable output—Nerlovian profit indicator approach. IIMB Management Review , 26(4), 222–233.

30.

Juo

J. C.

, Fu

T. T.

, & Yu

M. M.

(2012). Non-oriented slack-based decompositions of profit change with an application to Taiwanese banking. Omega , 40(5), 550–561.

31.

Kaur

, & Gupta

P. K.

(2015). Productive efficiency mapping of the Indian banking system using data envelopment analysis. Procedia Economics and Finance , 25(7), 227–238.

32.

, Chiu

Y. H.

, Lin

T. Y.

, & Huang

Y. Y.

(2019). Market share and performance in Taiwanese banks: Min/max SBM DEA. Top , 27(2), 233–252.

33.

Matthews

, & Zhang

N. X.

(2010). Bank productivity in China 1997–2007: Measurement and convergence. China Economic Review , 21(4), 617–628.

34.

Pandey

, & Singh

(2015). Evaluating the performance of commercial banks in India using Malmquist and DEA approach: Some evidence. IUP Journal of Bank Management , 14(2), 22

35.

Partovi

, & Matousek

(2019). Bank efficiency and non-performing loans: Evidence from Turkey. Research in International Business and Finance , 48(2), 287–309.

36.

Puri

, & Yadav

S. P.

(2014). A fuzzy DEA model with undesirable fuzzy outputs and its application to the banking sector in India. Expert Systems with Applications , 41(14), 6419–6432.

37.

Reserve Bank of India (2019). Handbook of statistics on the Indian economy . https://dbie.rbi.org.in

38.

Sahoo

B. K.

, & Tone

(2009). Decomposing capacity utilization in data envelopment analysis: An application to banks in India. European Journal of Operational Research , 195(2), 575–594.

39.

Sathye

, & Sathye

(2015). Loan quality, ownership and efficiency of Indian banks: A bootstrap truncated regression approach. Indian Journal of Economics and Business , 14(2), 289–306.

40.

Sathye

, & Sathye

(2017). Do ATMs increase technical efficiency of banks in a developing country? Evidence from Indian banks. Australian Accounting Review , 27(1), 101–111.

41.

Sealey

C. W.

Jr , & Lindley

J. T.

(1977). Inputs, outputs, and a theory of production and cost at depository financial institutions. The Journal of Finance , 32(4), 1251–1266.

42.

See

K. F.

, & He

(2015). Determinants of technical efficiency in Chinese banking: A double bootstrap data envelopment analysis approach. Global Economic Review , 44(3), 286–307.

43.

Seth

, Chadha

, & Sharma

(2020). Benchmarking the efficiency model for working capital management: Data envelopment analysis approach. International Journal of Productivity and Performance Management , 70(7). https://doi.org/10.1108/IJPPM–10–2019–0484.

44.

Sherman

H. D.

, & Gold

(1985). Bank branch operating efficiency: Evaluation with data envelopment analysis. Journal of Banking & Finance , 9(2), 297–315.

45.

Simper

, Hall

M. J.

, Liu

, Zelenyuk

, & Zhou

(2017). How relevant is the choice of risk management control variable to non-parametric bank profit efficiency analysis? The case of South Korean banks. Annals of Operations Research , 250(1), 105–127

46.

Sreekumar

, & Mahapatra

S. S.

(2011). Performance modeling of Indian business schools: A DEA-neural network approach. Benchmarking: An International Journal , 18(2), 221–239.

47.

Stewart

, Matousek

, & Nguyen

T. N.

(2016). Efficiency in the Vietnamese banking system: A DEA double bootstrap approach. Research in International Business and Finance , 36(1), 96–111.

48.

Sufian

, & Kamarudin

(2016). Determinants of efficiency in the Malaysian banking sector: Does bank origins matter? Intellectual Economics , 10(1), 38–54.

49.

Svitalkova

(2014). Comparison and evaluation of bank efficiency in selected countries in EU. Procedia Economics and Finance , 12(5), 644–653.

50.

Tan

, & Anchor

(2017). The impacts of risk-taking behaviour and competition on technical efficiency: Evidence from the Chinese banking industry. Research in International Business and Finance , 41(3), 90–104.

51.

Tone

(2001). A slacks-based measure of efficiency in data envelopment analysis. European Journal of Operational Research , 130(3), 498–509.

52.

Wijesiri

, Martínez-Campillo

, & Wanke

(2019). Is there a trade-off between social and financial performance of public commercial banks in India? A multi-activity DEA model with shared inputs and undesirable outputs. Review of Managerial Science , 13(2), 417–442

53.

Yang

C. C.

(2017). Reduction of non-performing loans in the banking industry: An application of data envelopment analysis. Journal of Business Economics and Management , 18(5), 833–851.

54.

Yeh

Q. J.

(1996). The application of data envelopment analysis in conjunction with financial ratios for bank performance evaluation. Journal of the Operational Research Society , 47(8), 980–988.

55.

Zha

, Liang

, Wu

, & Bian

(2016). Efficiency evaluation of banks in China: A dynamic two-stage slacks-based measure approach. Omega , 60(3), 60–72.

56.

Zhu

, Wang

, Yu

, & Wu

(2016). Technical efficiency measurement incorporating risk preferences: An empirical analysis of Chinese commercial banks. Emerging Markets Finance and Trade , 52(3), 610–624.