How efficient are Indian banks? An application of stochastic frontier analysis

Abstract

Purpose

This study aims to investigate the efficiency of Indian commercial banks from 2002 to 2018 using the stochastic frontier analysis.

Design/methodology/approach

This study uses the parametric approach of the stochastic frontier to examine the technical efficiency of banks acknowledging exogenous shocks, omitted variables and measurement errors, filling a gap in the existing financial literature. The scope of this study was constrained to 71 scheduled commercial banks to make it manageable and productive with 1,036 observations.

Findings

The results show that the mean technical efficiency of new private banks remained constant at 92.7% during the study period because of technology diffusion in banking systems. The technical efficiency of the nationalized, old private and foreign banks has enhanced over the period because of the efficient utilization of various innovative information technology services such as mobile banking, cheque truncation system, magnetic ink character recognition. However, the foreign banks are still laggards with a mean technical efficiency of 81.7%. The empirical findings suggest that new private sector banks depict higher efficiency than nationalized, old private and foreign banks.

Research limitations/implications

This study’s sample represents all categories of banks (public, private and foreign) including the banks that merged or consolidated during the period of study. To achieve the desired results, the authors incorporate the consolidated and merged banks in their data set. Further, the authors excluded all scheduled small finance banks and scheduled payment banks from their analysis, as these entities commenced operations post-2015. Additionally, the authors also excluded regional rural banks because of their distinct mandate aimed at servicing the rural populace and agricultural sector.

Originality/value

This study contributes to the literature on the performance of conventional banks in general and emerging markets, in particular, using the most recent data and covering a relatively long period using the stochastic frontier approach.

1. Introduction

In a fast-growing world, information technology (IT) is proven to be the cornerstone of the recent financial revolution (Bikker and Haaf, 2002; Berger, 2003; Dangolani, 2011; Khanna and Gaur, 2021; Oppong and Pattanayak, 2019; Wang et al., 2022). With the advent of IT post-liberalization in India, the banking industry operates in a highly competitive environment gradually allowing private and foreign banks to strategically exploit the untapped market (Bhattacharyya et al., 1997; Sensarma, 2006; Chen et al., 2018; Goyal et al., 2019; Akhtar et al., 2021b; Akhtar et al., 2022). The entrance of private and foreign players has paved the way for several revolutions in the Indian banking industry posing a direct threat to the domestic banks and compelling their performance appraisal. Since then, the Indian banking industry has gained tremendously and proved crucial in the development of the emerging economy with improvement in the efficiency and productivity of the financial industry (Bhattacharyya and Pal, 2013; Lenka and Sharma, 2017; Akhtar et al., 2021a; Dar et al., 2021; Pradhan et al., 2021; Shah et al., 2022).

In the past decades, the world has witnessed two major financial shocks, i.e. the Global Financial Crisis of 2007–2009 followed by the ongoing COVID-19 pandemic. In the wake of these events, the world economy is reeling and an economic recession is looming across the globe including the developed economies of the USA, members of the European Union, etc. (Ball, 2014; Boyson et al., 2014; Reinhart and Rogoff, 2014; Funke et al., 2016; Romer and Romer, 2017; Duprey et al., 2017; Berger and Demirgüç-Kunt, 2021; Chen et al., 2021). On the contrary, previous studies have reported that the Indian banking industry has emerged immune to these shocks, such as the global financial crisis (Eichengreen and Gupta, 2013; Gulati and Kumar, 2016; Kumar et al., 2016; Wanke et al., 2022) and the COVID-19 pandemic (Rakshit and Basistha, 2020; Goswami, 2022). Owing to this, examining the performance and efficiency of commercial banks has gained momentum among researchers, academicians and policymakers in India. This stems from an explosion of literature focusing on the performance of banks in India. Consequently, the investigation of the profitability and efficiency of the Indian banking industry assumes significance.

While previous studies have used a variety of tools and measures to examine the bank performance (Aigner et al., 1977; Charnes et al., 1978; Banker et al., 1984; Haslem et al., 1999; Lin and Chiu, 2013; Shaverdi et al., 2016; Akhtar et al., 2020; Azmi et al., 2020; Chaturvedi et al., 2021), a majority among them have been conducted in developed economies (Seiford and Zhu, 1999; DeYoung and Rice, 2004; Pasiouras and Kosmidou, 2007; Barros et al., 2012; Alfadli and Rjoub, 2020). Similarly, substantial financial literature advocates the examination of bank performance in developing economies alike (Mukherjee et al., 2002; Ataullah and Le, 2006; Abdul Rahman and Rosman, 2013; Goyal et al., 2019; Saeed et al., 2020; Akhtar et al., 2022; Azmi and Akhtar, 2022). A majority of these studies have used two common approaches to evaluate the performance of the banks, i.e. non-parametric data envelopment analysis or data envelopment analysis (DEA) (Charnes et al., 1978; Asmild et al., 2004; Fethi and Pasiouras, 2010; Avkiran, 2015; Shawtari et al., 2018; Henriques et al., 2020) and parametric stochastic frontier analysis (SFA) (Kraft and Tırtıroğlu, 1998; Mokhtar et al., 2006; Tsionas, 2021) including India (Bhattacharyya et al., 1997; Tandon et al., 2014; Kaur and Gupta, 2015; Akhtar et al., 2021a; Preeti and Roy, 2022). However, we find a dearth of studies using the parametric SFA approach to gauge the bank’s performance (Mohamad et al., 2008; Tran et al., 2020; Dar et al., 2021; Kutlu, 2022).

SFA was pioneered by Aigner et al. (1977), whereas DEA was coined by Charnes et al. (1978) to estimate total factor productivity. Both efficiency measurement approaches have their own advantages; however, the literature argues the superiority of the SFA measure. First, SFA assumes that observed inefficiencies in production processes are due to random factors (noise) and inefficiencies (Theodoridis and Psychoudakis, 2008). Second, DEA measures relative efficiency using multiple input/output characteristics of each decision-making unit (DMU) simultaneously and is suitable for measuring the efficiency of a particular process (Huang et al., 2017). While SFA allows for the inclusion of explanatory variables that might affect inefficiency, such as firm-specific characteristics or environmental factors. Third, DEA assumes inputs and outputs are fixed and known; and focuses solely on comparing the relative efficiency of DMUs based on their input–output relationships. Therefore, using a random variable model such as SFA is appropriate as compared with DEA.

To overcome this scenario, the present paper has used the stochastic frontier approach (SFA) over several non-parametric approaches, which acknowledges exogenous shocks such as the Great Financial Crisis of 2007, omitted variables and measurement errors. SFA differs from the non-parametric DEA primarily in the underlying assumptions they use when estimating the efficient frontiers (Silva et al., 2017). Further, unlike non-parametric techniques, SFA analysis aids in hypothesis testing for model specification. We used the parametric approach to investigate the efficiency and performance of the Indian banks.

The present empirical analysis aims to add to the financial literature in the following ways. First, our study used a data set of 71 commercial banks. In particular, our sample represents all categories of banks (public, private and foreign) based on the possession of comprehensive data sets containing all necessary information essential for the analysis. To achieve the desired results, we incorporate the consolidated and merged banks in our data set, as most of the nationalized banks were operational during the period of study and merged only in 2019. Further, State Bank of India (SBI) associate banks are not abandoned but rather merged with SBI itself. Second, our study covers the period of 2002–2018, a total of 17 years including the period of the global financial crisis of 2007. Hence, we used the SFA approach in an attempt to capture the effects of random shocks (Bhattacharyya and Pal, 2013).

The remaining of our paper is organized as follows. Section 2 describes the data set and the empirical model SFA specifications. Section 3 defines relevant input and output variables used in our empirical analysis and also exhibits their descriptive statistics. Section 4 discusses the main findings of our empirical results, while Section 5 concludes the paper.

2. Data and methodology

Data

The present study is based on secondary data. The study used unbalanced panel data consisting of selected variables for a period of 17 years (2002 to 2018). The reason behind the selection of the study period from 2002 to 2018 is manifolds and driven by several strategic considerations. For example, in 2003–2004, electronic payment systems were initiated in India, alongside The Reserve Bank of India’s (RBI) implementation of the real-time gross settlement system, and the Institute for Development and Research in Banking Technology, Hyderabad’s setting up of a national financial switch to facilitate apex-level connectivity of other switches established by banks for the better operation of ATMs nationwide (RBI, 2005). The period from 2004 to 2008 marked a notable surge in the adoption of core banking solutions, along with intensive attention to networking. During this time, most banks have worked on their corporate networks to facilitate inter-branch and branch-controlling office communication electronically, while inter-bank and inter-city communication was carried out through the Indian financial network. The banks have also incorporated various IT-enabled banking systems such as magnetic ink character recognition and cheque truncation systems (Khan and Abdulla, 2023). A total of 12 new private sector banks had been given licenses under the guidelines issued in 1993 and 2001. Moreover, some significant private banks (Kotak Mahindra, Yes Bank, IDFC First Bank, etc.) and foreign banks (Doha Bank, SBM Bank etc.) received the operational licenses during the 2002–2018 period. Finally, the sample period concluded in 2018, as many public sector banks were merged/consolidated into larger banks and also some of the significant foreign banks, such as Citibank have closed their operations in India.

We obtained our data from the electronic database ProwessIQ 2.5, a corporate database developed by the Center for Monitoring the Indian Economy. The RBI’s publications, including the RBI Bulletin (monthly), Report on Trend and Progress of Banking in India, Handbook of Statistics on Indian Economy, multiple issues of Statistical Tables Relating to Banks in India and Basic Statistical Returns of Scheduled Commercial banks, have also provided secondary data and information. In addition, we have extracted data from annual reports of sampled banks and other valuable publications of various banks in India. In addition, data published by the Indian Banking Association in monthly bulletins, special issues and annual publications on “Performance Highlights of Banks” have been used.

Pre-analysis, all the monetary values of the variables used in the present study are deflated by an implicit price deflator at 2010–2011 constant prices. Data tabulation in the appropriate manner was facilitated by first recording the raw data in the form of various variables in a master table. The present study exclusively selected commercial banks operating in India based on the criterion of data availability throughout the designated study period. This methodological approach was undertaken to ensure the integrity and reliability of the research findings. Specifically, banks were chosen only if they possessed complete data sets containing all requisite information deemed necessary for the analysis. This stringent criterion was implemented to mitigate potential sources of bias or inaccuracies arising from incomplete or deficient data. Furthermore, we excluded all scheduled small finance banks and scheduled payment banks from our analysis as these entities commenced operations post-2015. Additionally, we also excluded regional rural banks (RRBs) because of their distinct mandate aimed at servicing the rural populace and agricultural sector. The operational dynamics inherent to RRBs diverge significantly from those characterizing other commercial banks, thus warranting their exclusion from our study. Hence, the scope of this study has been constrained to 71 scheduled commercial banks to make it manageable and productive with 1,036 observations in total. The sample represents all categories of banks, which includes 20 Nationalized banks, 8 SBI and associates banks, 12 old private sector banks, 7 new private sector banks and 24 foreign banks.

Methodology

The evaluation of a firm’s performance involves assessing its efficiency by comparing its actual output or inputs to the potential or optimal ones. The concept of measuring firm efficiency was introduced by Farell in 1957, building upon the ideas of Koopmans and Debreu (1951). One aspect of efficiency is technical efficiency which measures an organization’s ability to produce maximum output from a given set of inputs. Firms located on the production frontier are considered technically efficient, but in reality, there is often a gap between assumed technical efficiency and actual performance. Technical inefficiency can negatively affect overall economic efficiency and profitability. As a result, understanding and improving technical efficiency is crucial for the better performance of economic units.

There are two main approaches for evaluating relative efficiency across firms using the best-practice frontier: the non-parametric frontier approach and the parametric frontier approach. The non-parametric frontier approach was the first approach, developed by Debreu (1951), Farrell (1957) and later elaborated by Banker et al. (1984), Färe and Grosskopf (1994) and others to measure the technical efficiency through estimating a production frontier. Later, Winsten (1957) introduced a new econometric-based approach named corrected ordinary least square. The approach is based on the econometrics-based measurement of the production frontier and uses the parametric estimation of the frontier, widely known as SFA, developed autonomously by Aigner et al.(1977) and Koop and Steel (2001). SFA uses econometrics techniques to estimate a stochastic non-deterministic production frontier. The elementary idea of this approach is that deviation from the frontier could be partly out of the control of the firm under analysis, thus, leaving room for random noise.

The present study uses the SFA because of its advantages over non-parametric methods. The superiority of SFA is manifold, such as it overcomes the assumption of non-parametric methods, which presume that all differences in a firm’s performance are due to inefficiency. This assumption is flawed because it ignores exogenous shocks, omitted variables and measurement errors. SFA uses econometrics techniques to estimate a stochastic non-deterministic production frontier. Deterministic frontier is not recommended because of the relative complexity of statistical inference in deterministic frontier models (Cornwell and Schmidt, 2008). The stochastic frontier production function proposed by Aigner et al. (1977) defined the disturbance term as the sum of symmetric normal and negative with an error term with two parts, one for random effects and another for technical inefficiency. One part represents technical inefficiency, i.e. the factors that are controlled by the firms, and the other represents those effects that cannot be controlled by the firms and left out explanatory variables (Hjalmarsson et.al., 1996).

Contrastingly, the nonparametric approach (DEA) does not rely on the definition of a functional form characterizing the underlying technology and therefore avoids misspecification problems. Nonetheless, a drawback of this technique is that it is deterministic and ignores the stochastic error term which implies that deviations from the frontier are entirely attributed to inefficiency effects (Paradi et al., 2011; Henriques et al., 2020). As a result, technical efficiency ratings obtained from the nonparametric approach are generally lower than those obtained under the parametric SFA alternative (Coelli and Fleming, 2004; Kumbhakar and Lovell, 2003; Ahmadzai, 2017).

Henceforth, the primary advantage of the parametric SFA approach is that it incorporates a composed error structure with a two-sided symmetric term and a one-sided component which permits to distinction between inefficiency and exogenous shocks. The one-sided component reflects inefficiency, while the two-sided error captures the random effects and exogenous shocks outside the control of the production unit, including measurement errors and other statistical noise typical of empirical relationships (Aigner et al., 1977; Meeusen and Van den Broeck, 1977). In addition, it allows hypothesis testing and construction of confidence intervals (Wadud and White, 2000). The disadvantages of this approach are the need to assume a functional form for the frontier technology and for the distribution of technical inefficiency term of the composite error term (Ahmadzai, 2017). It is noteworthy to mention that hypothesis testing can be done using either approach, however, hypothesis testing regarding model specification can only be done in SFA. In a nutshell, using parametric methods imposes a functional form on the data set, which is highly appreciable in the measurement of the efficiency of any firm or industry.

Battese and Coelli (1992) developed a model for dynamic panel data sets that considers the effect of stochastic technical inefficiency. The stochastic composition of the inefficiency components enables the estimation of both time-varying technical inefficiency and technological change reflected by time dummies in the stochastic frontier. Kumbhakar (1991) and Reifschneider and Stevenson (1991) proposed a single-stage maximum likelihood approach to handle this problem. Battese and Coelli (1995) extended the model to allow for panel data sets and unequal distribution of inefficiency. But later the truncated distribution function was accepted (Van den Broeck et al., 1994).

Panel data analysis provides a more efficient estimation of unknown parameters and technical efficiency prediction than that of cross-section data. It also allows for the relaxation of certain distributional assumptions and examination of how technical efficiency evolves (Durlauf and Johnson, 1995). Individual-specific effects in the inefficiency model can be incorporated to use the panel nature of the data (McDonald and Roberts, 2002). Hjalmarsson et al. (1996) and Wang (2002) suggest using individual-specific effects in the inefficiency model to better use the panel nature of the data. This would make it possible to obtain a within estimator. However, the truncated nature of the inefficiency distribution prevents removing specific effects by taking first differences or subtracting means from the data, as differenced truncated normal distributions do not result in a recognizable distribution (Wang, 2002). In this study, the Battese and Coelli (1992) model is employed for panel data analysis to evaluate firm efficiency.

Aigner et al. (1977) introduced a novel specification for the stochastic frontier production function for cross-sectional data with an error term consisting of two components: one for random effects and the other for technical inefficiency. The majority of the research in this field uses two-stage estimation methods, first estimating the frontier production function and calculating firms’ predictive efficiencies. In the second stage, the estimation of the inefficiency effect model is used to identify the factors affecting the variations in efficiencies among firms. Kumbhakar (1991) and Reifschneider and Stevenson (1991) introduced a stochastic frontier model for cross-sectional data that estimates the parameters of both the stochastic frontier and the inefficiency model simultaneously. The (Battese and Coelli, 1992) specification for panel data is used in the present study, expressed as follows: (1) $$\mathit{Y}{\mathit{ }}_{\mathit{it}}=\mathit{ exp }\left(\mathit{ }{\mathit{x}}_{\mathit{it}}\mathit{ \beta }+\mathit{ }{\mathit{V}}_{\mathit{it}}-\mathit{ }{\mathit{U}}_{\mathit{it}}\mathit{ }\right)$$where,

Y_it denotes the production for the t^th observation (t = 1,2,3…T) for the i^th firm (i = 1,2,3…N).

x_it is a vector of (1×k) input Variables of the i^th firm at time t.

β is a vector of (1×k) unknown parameters to be estimated.

V_it are assumed to be independent and identically distributed random errors with a normal distribution having a mean of 0 and an unknown variance σ_v².

U_it are non-negative random variables, linked to the technical inefficiency of production, which are independently distributed, such that U_it is obtained by truncated (at 0) normal distribution with mean µ_it and variance σ². Where µ_it is defined as: $$\mathit{\mu }{\mathit{ }}_{\mathit{it}}=\mathit{ }{\mathit{z}}_{\mathit{it}}\mathit{ \delta }+\mathit{ }{\mathit{W}}_{\mathit{it}}$$where,

Z_it is (m × 1) vector of variables linked with technical inefficiencies of production of a firm.

δ is (m × 1) vector of unknown parameters to be estimated.

W_it are unobservable random variables, which are considered to be independently distributed, attained by truncation of the normal distribution with mean 0 and unknown variance σ² such that U_it is non-negative (z_itδ ≥ − W_itδ).

U_it is defined by Battese and Tessema(1993) as: $${\mathit{U}}_{\mathit{it}}={\mathit{U}}_{\mathit{i}}\left\{\mathit{exp}\left[-\mathit{\eta }\left(\mathit{t}-\mathit{T}\right)\right]\right\}$$where,

U_i is considered to be a non-negative random variable specific to a firm and is independently distributed as non-negative truncations at 0 of the distribution N $\left(\mathit{\mu },{\mathit{\sigma }}_{\mathit{u}}^2\right)$.

η is an unknown parameter that needs to be estimated, and it determines whether inefficiencies are time-varying or time-invariant.

In this model, the technical inefficiency effect for the i^th firm in the t^th time is represented by the product of an exponential function of time U_i{exp[−η(t − T)]} which involves the unknown parameter, η, and the non-negative random variable, which is the technical inefficiency effect for the i^th firm in T time, the last year of the data set. If η is positive, then −η (t − T) ≡ η (T − t) is positive for t < T and so exp[−η (T − t)] > 1, which suggests that the technical inefficiencies of industries decline over time. However, if η is negative, then η (T − t) < 0 and therefore technical inefficiencies increase over time.

We have followed Battese and Corra’s (1977) specifications for variance parameters: $${\mathit{\sigma }}_{\mathit{s }}^2\equiv \mathit{ }{\mathit{\sigma }}_{\mathit{v}}^2+{\mathit{\sigma }}^2$$ $$\mathit{\gamma }\equiv \frac{\mathit{ }{\mathit{\sigma }}^2}{\mathit{ }{\mathit{\sigma }}_{\mathit{s}}^2}\mathit{ }$$The value of γ lies in the middle of 0 and 1. A value of 0 for γ implies that the variance of the inefficiency effects is 0 and all deviations from the frontier are solely attributed to random noise. Value γ = 1 illustrates that all deviations are because of technical inefficiency.

The technical efficiency of the i^th firm at t^th time given by: $$\mathit{T}{\mathit{E}}_{\mathit{it}}\mathit{ }=\mathit{ exp }\left(-{\mathit{U}}_{\mathit{it}}\mathit{ }\right)$$To assess the significance of the parameters by restricting the model test of the hypothesis is conducted. Generalized likelihood ratio statistics (λ) is used to conclude the significance of the restrictions imposed upon the model (Greene, 1980; Stevenson, 1980).

The log-likelihood function of equation (1) is defined as follows: $$\begin{array}{l}{\mathit{L}}^{\mathit{*}}\left(\mathit{\beta },\mathit{\delta },{\mathit{\sigma }}_{\mathit{u}}^2,{\mathit{\sigma }}_{\mathit{v}}^2;{\mathit{y}}_{\mathit{it}}\right)=-\mathit{ }\frac{1}{2}\left({\displaystyle \sum }_{\mathit{i}=1}^{\mathit{N}}{\mathit{T}}_{\mathit{i}}\right)\mathit{ ln}\left(2\mathit{\pi }{\mathit{\sigma }}^2\right)\hfill \\ -\frac{1}{2}\mathit{ }{\displaystyle \sum }_{\mathit{i}=1}^{\mathit{N}}{\displaystyle \sum }_{\mathit{t}=1}^{\mathit{T}}\frac{\left({\mathit{y}}_{\mathit{it}}-{\mathit{x}}_{\mathit{it}}\mathit{\beta }+{\mathit{z}}_{\mathit{it}}{\mathit{\delta }}^2\right)}{{\mathit{\sigma }}^2}-\frac{1}{2}\mathit{ }{\displaystyle \sum }_{\mathit{i}=1}^{\mathit{N}}{\displaystyle \sum }_{\mathit{t}=1}^{\mathit{T}}\mathit{ln}\frac{\mathit{\phi }\left({\mathit{d}}_{\mathit{it}}\right)}{\mathit{\phi }\left({\mathit{d}}^{\mathit{*}}{}_{\mathit{it}}\right)}\hfill \end{array}$$where,

L*(.) is the likelihood function $${\mathit{d}}_{\mathit{it}}=\frac{{\mathit{z}}_{\mathit{it}}\mathit{\delta }}{{\left(\mathit{\gamma }{\mathit{\sigma }}^2\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}$$ $${\mathit{d}}_{\mathit{it}}^{\mathit{*}}=\frac{{\mathit{\mu }}_{\mathit{it}}^{\mathit{*}}}{{\left(\mathit{\gamma }\right(1-\mathit{\gamma }\left){\mathit{\sigma }}^2\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}$$ $${\mathit{\mu }}_{\mathit{it}}^{\mathit{*}}=\left(1-\mathit{\gamma }\right){\mathit{z}}_{\mathit{it}}\mathit{\delta }-\mathit{\gamma }\left({\mathit{y}}_{\mathit{it}}-{\mathit{x}}_{\mathit{it}}\mathit{\beta }\right)$$The test statistics of the generalized likelihood ratio are defined by: $$\mathit{\lambda }=-\mathit{ }2\mathit{ ln }\left[\mathit{L}\left({\mathit{H}}_0\right)/\mathit{L}\left({\mathit{H}}_1\right)\right]$$where,

L(H0) and L(H1) refer to the likelihood function values under the null hypothesis, H0 and the alternative hypothesis, H1, respectively. λ has an approximate chi-square distribution with degrees of freedom equal to the number of imposed restrictions. Under the null hypothesis γ = 0, which postulates that technical inefficiency is not existent in the model and γ = δ_i = 0, which postulates that inefficiency effects are not stochastic, λ has a mixed chi-square distribution with the degree of freedom equal to the number of restrictions levied (Battese and Coelli, 1995).

Selection of inputs and outputs variables

To evaluate a bank’s efficiency and productivity, choosing the right input and output variables is of paramount importance. Any organization’s appraisal process is a complicated endeavor, including various factors. Previous researchers have suggested that a multi-factor performance model can be used to assess banks’ performance (Akhtar et al., 2021a). After a careful review of the financial literature, it is evident that the intermediation and production techniques are the two widely used methods in the selection of both the input and output constructs (Sealey and Lindley, 1977; Humphrey, 1985; Hancock, 1986; Berger and Humphrey, 1991, 1992; Fixler and Zieschang, 1992; Boďa and Piklová, 2018; Sanyal et al., 2019). Both approaches are most widely used, as they apply the conventional microeconomic theory of the firm to banking, with the only difference in the specification of banking activities (Fortin and Leclerc, 2007). As per the intermediation concept, commercial banks’ primary goal is to convert deposits (liabilities) into assets (loans). Řepková, (2014) states that the banks employ labors to convert their deposits into loans.

Furthermore, the production method assesses output in monetary terms, with the total amount of expenses equaling the sum of all interest and operational costs. The manufacturing strategy, on the other hand, prioritized the number of financial services and operating costs. The interest costs incurred on the value of deposits are not included in this approach, as deposits are seen as outputs. Both techniques, however, are questioned because deposits include both input and output constructs that are difficult to disaggregate empirically (Kumar, 2008).

In academic discourse, it is acknowledged that the intermediation technique, while valuable, may inadvertently disregard significant aspects of banking operations, such as the assessment of risks associated with individual loans and the evolving landscape of banking regulations (Boďa and Zimková, 2021). Notably, within the literature, the intermediation approach enjoys greater prominence among researchers, who converge on the perspective that banks primarily function as intermediaries for financial services. Under this paradigm, banks leverage deposits as capital for revenue-generating activities (Goddard and Wilson, 2016). Consequently, it is posited that conceptualizing deposits as inputs, rather than outputs, aligns more logically with this operational framework (Bhatia et al., 2018). The previous studies posit that the intermediation technique is good for evaluating bank efficiency, while the production technique is the most suitable technique for calculating the efficiency at the branch level, according to Berger and Humphrey (1997). Furthermore, gathering data for the production strategy is a difficult task. In light of the aforementioned limitations and to achieve our goal of analyzing the bank’s efficiency, we used the intermediation technique in this research.

Various methods for selecting factors for measuring bank performance have been established in earlier studies (Sherman and Gold, 1985; Berg et al., 1993; Saha and Ravisankar, 2000; Sathye, 2003; Sahoo et al., 2007; Kumar et al., 2016; Akhtar et al., 2022). Deposits (x1), borrowings (x2), total expenses (x3) and net fixed assets (x4) were used as inputs in this study (x4). The reality that the primary task of banks is to collect funds from those who have an excess of them and to lend those funds to the needy ones for profit supports input choice. The banks also borrow money from the reserve bank and other commercial banks, known as borrowing. Overall, the various personal costs, including wages and other associated costs, are the third input total expenses, and they account for a considerable amount of the bank’s overall cost. Furthermore, the last input net fixed asset has been taken into account: the value of net fixed assets obtained after deducting the value of depreciation from fixed assets whereas output includes loans and investments (y1) (Ray and Das, 2010).

3. Results and discussions

The study used data from 71 out of the 135 operating scheduled commercial banks in India, including 20 nationalized banks, 8 SBI and associates, 12 old private sector banks, 7 new private sector banks and 24 foreign banks, covering the period from 2002 to 2018. The total number of observations is 1,036. Table 1 summarizes the descriptive statistics of the output and input variables used in the stochastic frontier model in our study. We obtained our sampled variable data from the annual publication of RBI, namely, Report on Trend and Progress of Banking in India (RBI Report, 2018). An acceptable level of variability has been witnessed in the variables used in this study.

Table 1 illustrates the summary statistics of the variables used in the stochastic frontier model. The average output (loan and investments) is INR 808,145m, and the standard deviation is INR 1,712,960m. The minimum output of the bank is INR 82.77m, whereas the maximum output is INR 24,990,000m, which points towards the array in size of the banks operating in India. Among all the other input variables, the mean of the deposits is the largest, i.e. INR 724,474m, which indicates that the deposit is the most substantial input variable.

Table 2 illustrates the estimated coefficient value of inputs for six separate models. To estimate the technical efficiency of banks, six different models have been applied. In the first model, i.e. the ordinary least square (OLS), the coefficient values of all the inputs are found to be highly significant. In all the trans-log production models (i.e. T1, T2, and T3), which take into account the substitution effect between the variables, most of the coefficients of variables are observed to be highly significant. In the fourth model, i.e. time invariant model, which assumes that the production function does not have any impact concerning technological improvement, 13 out of 16 coefficients of variables come out to be statistically significant. As the time-variant (TV) model has been selected based on the likelihood ratio (LR) test, the result of this model is discussed in detail in Table 4.

The results of the likelihood ratio tests are presented in Table 3. To determine the best model for the analysis, five LR tests were conducted on various models. The likelihood ratio test statistic is equal to two times the difference between logarithmic values of the unrestricted and restricted maximum likelihood estimates and follows a mixed chi-square distribution with the degree of freedom equal to the number of independent restrictions under the null hypothesis. If λ exceeds the critical value, the limitations set by the null hypothesis are no longer valid and are therefore rejected. (Coelli and Battese, 1996). The results of the tests are explained as follows:

The first null hypothesis, H0: β₀ = 0, says that the production function does not have any constant term. The hypothesis is rejected with conviction as the test statistic of 718.06 surpasses the mixed chi-square statistic in Table 1 of Kodde and Palm (1986), indicating a strong rejection. Therefore, it is specified that the constant term is appropriate for the model.

The second null hypothesis, H0: β_it = 0, says that the production function does not have any impact on technological improvement. As the test statistic is 696.42, which is higher than the tabular mixed chi-square statistic, the null hypothesis is rejected. Hence, it suggests that there is an improvement in the technical change and so technical terms must be included in the model.

The third null hypothesis, H0: β_ij = 0, says that there is no substitution effect between the input variables. This hypothesis is strongly rejected, as the test statistic is 1111.98, which is greater than 11.91 at a 5% tabular mixed chi-square statistic. This further indicates that the cross-product must be included in the model.

The fourth null hypothesis, H0: γ = μ = 0, says that technical efficiency effects have a half-normal distribution, which is again rejected, as the test statistic is 15.50 which is higher than the tabular mixed chi-square statistic. Thus, it is concluded that the truncated normal distribution is a more suitable choice than the half-normal distribution. This result is further supported by Battese and Coelli (1992).

The fifth null hypothesis, H0: γ = 0, says that the model is time-invariant. This hypothesis is rejected, as again the test statistic is 15.50, which is higher than 2.71 at a 5% tabular mixed chi-square statistic. Hence, it indicates that the technical efficiency effect varies considerably over time. Therefore, a TV model must be used.

Based on the generalized log LR tests, a time-varying model recommended by Battese and Coelli in 1992 is found to be most appropriate. Table 4 displays the parameter estimates for the inefficiency model within the stochastic frontier. As the trans-log function involves multiple interdependent input variables, the coefficients must be interpreted considering both individual and interaction terms.

The coefficients for deposits and borrowings are positive and statistically significant, suggesting a direct relationship with the output. As the coefficients of variables in the production function reflect the share of inputs or elasticities to inputs. Whereas, total expenses and net fixed assets have an inverse relationship with the output. However, the coefficients of total expenses and net fixed assets are not found to be statistically significant.

The positive coefficient of the linear time trend (t) implies an upward shift of the efficiency frontier over time, indicating increased efficiency. However, the negative value of deposits when interacting with borrowings suggests that the combination of these two variables has a negative effect on the output. While when the deposits variable interacts separately with total expenses and net fixed assets, the estimate of interaction terms comes out to be positive and statistically significant, signifying a positive relationship with the output.

The estimate of an interaction term between borrowings and total expenses is 0.07, i.e. positive and statistically significant, inferring that the combination of borrowings and total expenses has a positive impact on the output. Whereas, the coefficient of the interaction term between the borrowings and net fixed assets is 0.1 and statistically insignificant. When total expenses interact with net fixed assets, the estimate of the interaction term comes out to be negative and statistically significant, implying that when the combination of total expenses and net fixed assets increases then the output will decrease. When the time variable interacts separately with deposits and borrowings, the estimate of interaction terms comes out to be positive and statistically significant, implying a positive relationship with the output. Whereas, the coefficients of interaction terms between the time variable and total expenses, and time variable and net fixed assets are negative and statistically significant, inferring an inverse relationship with the output variable. The test outcomes reveal that the input elasticities sum to less than one, suggesting that the production function displays decreasing returns to scale (Das and Kumbhakar, 2012).

Table 5 represents the yearly summary statistics of means, standard deviations and coefficient of variation of technical efficiency of Indian banks from 2002 to 2018. Overall, mean technical efficiency of the Indian banking industry is observed to be 89%. On average, a 12.35% variation is observed over time, indicating an acceptable level of dispersion. The mean technical efficiency of the Indian banks improved from 0.86 (or 86%) in 2002 to 0.89 (or 89%) in 2018, a growth of 3.5%. This increase in efficiency indicates that Indian banks are moving closer to the frontier and closing the gap to the efficient frontier. This improvement could be attributed to the effective use of IT and reforms in the Indian banking industry and increased competition through the lifting of entry and branch restrictions in Indian banking appear to have had a positive impact on the banks’ efficiency (Reddy and Nirmala, 2013).

However, the study period reveals a significant amount of inefficiency in the operations of Indian banks on average. The average technical inefficiency of Indian commercial banks is 0.11. On the basis of the selected parameters used in this study, the result indicates that on average Indian bank is missing out on 11% of its potential output compared to the best-practice bank, because of operational inefficiencies.

Figure 1 represents the temporal average efficiency scores of banks in India during the span of 17 years. Figure 1 illustrates that the Indian banks have followed an upward trend over the years from an average efficiency score of 0.86 in 2002 to 0.89 in 2018, thereby indicating a percentage increase in the average efficiency scores by approximately 3.5% over the 17 years. In the year 2002, the mean technical score for the banks was 0.86, which remained the same in the subsequent year, while it increased to 0.88 in the year 2004. One of the reasons for this improvement was the effect of the Securitization and Reconstruction of Financial Assets and Enforcement of Security Interest, which facilitated the banks to a rapid recovery of non performing assets (NPAs) (Khan and Abdulla, 2023). It may also be attributed to the fact that RBI had implemented the real time gross settlement system during the year 2003–2004.

Between 2004 and 2008, the average efficiency scores remained relatively steady. However, in 2009, there was an increase in the efficiency score from 0.88 to 0.90. From 2004 to 2008, numerous banks began implementing core banking solutions and prioritized the improvement of their networking capabilities (RBI, 2005). As a consequence of these advancements, there has been an improvement in customer service and increased output, leading to enhanced efficiency.

During the period from 2009 to 2012, the average efficiency scores of banks declined from 0.90 to 0.88 because of the global financial recession. However, from 2013 to 2018, despite challenging NPA conditions, Indian banks maintained relatively stable efficiency scores of around 0.89. This stability can be attributed to the positive impact of technology integration in banking systems such as the introduction of the unified payments interface in 2016 which counterbalanced the negative effects of NPAs (Mahesh, 2021).

Table 6 displays the mean technical efficiency and standard deviation for different bank groups. Nationalized banks have the least variability in mean technical efficiency, whereas the old private and new private sector banks show similar levels of fluctuation. On the other hand, the foreign bank group exhibits the highest variation in mean technical efficiency compared to other bank groups.

Based on the given information, the New Pvt. Sector banks are regarded as the highest-performing group, followed closely by the Nationalized banks. In contrast, the old private sector banks and foreign banks consistently demonstrated lower technical efficiency than the average for Indian banks. Notably, the foreign banks group exhibited the lowest efficiency among all the bank groups.

The Indian banking system has faced inefficiencies, evident in the average technical inefficiency across various bank categories. Nationalized banks have an average technical inefficiency of 0.076, implying a potential efficiency improvement of 7.6% by adopting the practices of the most efficient bank. The technical inefficiency scores for older private sector banks, newer private sector banks, and foreign banks are 0.129, 0.073, and 0.183, respectively. On average, nationalized banks operate at 7.6% lower efficiency than the most efficient banks. Likewise, there is room for improvement for older private sector banks (12.9%), newer private sector banks (7.3%) and foreign banks (18.3%) if they match the performance of the most efficient bank.

Figure 2 shows the mean technical efficiency of various bank groups, including nationalized banks, older private sector banks, newer private sector banks and foreign banks. During the period under examination, the new private sector banks were determined to be the most efficient group, with nationalized banks close behind. Both of these groups surpass the industry average. In contrast, older private sector banks and foreign banks perform below the industry average, with foreign banks being the least efficient of all the bank groups.

The success of new private sector banks can be attributed to a stricter regulations as compared with foreign banks, their profit-oriented approach, effective management and optimal use of technology (Djalilov and Piesse, 2019). A stricter bank regulation encourages competition leading to the deregulation of market access and the antitrust law, ultimately enhancing efficiency and contributing to overall financial stability (Yin, 2021; Baral and Patnaik, 2023). In recent years, we witnessed a surge in private sector banks, as they maintain a healthier asset quality with lower levels of non-performing assets (NPAs). As a result, their overall share of assets, including deposits and lending activity increases.

Nationalized banks have shown improved performance, rivalling other groups except for newer private sector banks. This indicates reduced inefficiency, as they compete successfully. With an extensive branch network, they offer both interest-based and non-interest-based services. Being public sector banks, they handle fee and commission transactions for various organizations, potentially boosting their income. Adopting advanced technology, new recruitment processes and introducing new services have further enhanced their operations and performance prospects (Reddy and Nirmala, 2013).

The subpar performance of older private sector banks can be attributed to their challenges in transitioning from regulated government controls to market-oriented environments. Their lower efficiency, compared to foreign banks, is influenced by factors such as inappropriate allocation size, degrading credit deposit ratio, the need to fulfil social objectives and shortcomings in management and technology implementation, which hinder their ability to adapt to economic changes (Bansal et al., 2018; Dsouza et al., 2022).

The findings of our study have a novel contribution implying an inferior performance of foreign banks, compared to other bank groups. This may be attributed to the fact that the mean technical efficiency of the foreign bank group exhibits the highest level of variability among all bank groups. Certain banks within this group have demonstrated significantly superior performance than others. Additionally, banks whose parent institutions are based in developed countries have exhibited notably better performance than those affiliated with parent banks situated in developing nations. This discrepancy in performance is likely attributable to the enhanced expertise and technological integration characteristic of banks originating from developed countries.

Despite their significant contribution to the Indian banking industry, foreign banks find it hard to gain the trust of Indian consumers. As of 2022, they account for a mere 3.8% share of total loans and approximately 5% of total deposits. One conceivable rationale may lie in the tendency for foreign banks to concentrate their operations in metropolitan areas and Tier 1 cities. Therefore, the inefficiency of foreign banks stems from a lack of established business structures, infrastructures and extensive use of expensive technology, along with significant expenses incurred in expanding their asset portfolios through retail loans (Sensarma, 2008; Reddy and Nirmala, 2013; Ali et al., 2022; Chen and Hsu, 2022).

Table 7 illustrates the ranks of individual banks from highest to lowest, based on their technical efficiency estimates. The rankings of foreign banks demonstrate a significant variation (also supported by their std. deviations, Table 6), with four of them appearing in the top ten and eight appearing in the bottom ten (Clarke et al., 2003). The first rank has been assigned to Mizhu Bank Ltd., rank 35, i.e. the middle rank is assigned to Catholic Syrian Bank Ltd. and the last rank is given to HSBC Bank Oman SAOG.

State Bank of Indore is ranked first among public sector banks (overall rank 2), followed by State Bank of India (overall rank 4). The worst-performing public sector bank is the Bank of India (overall rank 46). Among the old private sector banks, the best-performing bank is Tamilnad Mercantile Bank Ltd. (overall rank 10), followed by Jammu and Kashmir Bank Ltd. (overall rank 12), while the last rank among old private sector banks is assigned to Nainital Bank Ltd. (overall rank 61).

The best-performing bank among new private sector banks is ICICI Bank Ltd. (overall rank 6), followed by HDFC Bank Ltd. (overall rank 9), whereas the worst among them is IndusInd Bank Ltd. (overall rank 49). The highest rank among the foreign banks is given to Mizhu Bank Ltd. (overall rank 1), followed by Antwerp Diamond Bank N V (overall rank 3), and the worst-performing bank among them is HSBC Bank Oman SAOG (overall rank 69).

4. Conclusion

In this study, we estimate the efficiency of the Indian commercial banks from 2002 to 2018 using the SFA. We used the parametric SFA over several non-parametric approaches in our study because of several reasons. First, the non-parametric methods presume that any difference in a firm’s performance will be idiosyncratic to inefficiency. Owing to this assumption, the exogenous shocks, omitted variables and measurement errors are overlooked. Second, the SFA aids in hypothesis testing, which cannot be feasible using non-parametric techniques. Further, the efficiency score obtained by a non-parametric test (DEA) may lead to false conclusions if there exists inaccuracy in the sample size or variable selection process. Hence, we used the SFA approach in an attempt to capture the effects of random shocks. To our knowledge, this is the most relevant approach to address the issues.

The empirical outcomes indicate that the mean technical efficiency level of the new private banks remained constant at 92.7% during our study. It may be noteworthy to highlight that despite rising NPAs in Indian banking, the efficiency scores of the new private banks exhibit resistance and remain stagnant. This may be attributed to the gains emanated by new private banks because of technological diffusion in the banking system post-liberalization. The technical efficiency of the nationalized, old private and foreign banks has enhanced over the period because of the efficient utilization of various innovative IT services such as mobile banking, cheque truncation system, magnetic ink character recognition. However, the foreign banks are still laggards with a mean technical efficiency of 82.7%.

Our empirical findings suggest that new private banks depict higher efficiency than other sector banks. Overall, the technical efficiency of banks operating in India has significantly improved post-2015 and is consistent with the findings of Akhtar et al. (2022). Finally, the outperformance of new private banks being the most technically efficient among the three forms of banks, suggests that Indian consumers put more trust in new private banks, and they are more suitable and viable in the Indian banking scenario. Nevertheless, the Indian banking industry performance has improved in the sample period, despite the rising NPA and technological disruptions.

The findings of our study have significant implications for policymakers, regulators, and stakeholders in the Indian banking industry. It is imperative to recognize the crucial role of technology in enhancing the efficiency of commercial banks operating in India. It implies that the implementation of advanced technologies such as blockchain and artificial intelligence will bring positive synergy in the Indian banking industry. The government and central bank should encourage innovation, supervision and integration of the banking sector with Fintech companies. Further, future studies may focus on employing alternative measures, such as a parametric test to evaluate the performance of Indian banks.

The authors would like to thank Jamia Millia Islamia, Woxsen University and University of the People for facilitating the support to conduct this research.

Author Contributions: All the authors have contributed equally.

Funding: This research is not being funded.

Availability of data and material: The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.

Conflicts of Interest: The authors declare no conflict of interest.

Figure 1.

The temporal average efficiency of banks in India (2002–2018)

Figure 2.

Bank group-wise mean technical efficiency

Table 1.

Summary statistics of variables used in the stochastic frontier analysis (values expressed in C millions)

Variable	Mean	SD	Min	Max
Loans and investments	808,145	1,712,960	82.77	24,990,000
Deposits	724,474	1,399,705	40.21	18,360,004
Borrowings	74,487	201,636	0.89	2,448,001
Total expenses	74,009	143,168	82.28	1,904,000
Net fixed assets	7,536	16,396	1.4	300,649

Source: Authors’ calculation

Table 2.

The estimated parameters of the stochastic production frontier model

_frontier	OLS	T1	T2	T3	TIN	TV
Ll	0.7275*** (0.0129)	0.4228*** (0.0310)	0.5026*** (0.0544)	0.0611 (0.0830)	0.5109*** (0.0535)	0.5006*** (0.0547)
Lk	0.1007*** (0.0060)	0.0536*** (0.0092)	0.3187*** (0.0287)	0.3406*** (0.0290)	0.3462*** (0.0288)	0.3454*** (0.0290)
Lm	0.1500*** (0.0193)	0.4959*** (0.0414)	0.0090 (0.0625)	0.3801*** (0.0889)	0.0167 (0.0615)	−0.0424 (0.0615)
Ln	−0.1068*** (0.0142)	−0.0631** (0.0217)	−0.0064 (0.0487)	0.0790 (0.0577)	−0.0156 (0.0482)	−0.0227 (0.0490)
T		−0.0008 (0.0113)	0.0257* (0.0107)	0.0508*** (0.0105)	0.0312** (0.0106)	0.0377** (0.0131)
Tlm		−0.0435*** (0.0043)	−0.0275*** (0.0038)	−0.0147*** (0.0041)	−0.0266*** (0.0037)	−0.0263*** (0.0038)
Tlk		0.0045*** (0.0010)	0.0040*** (0.0009)	0.0038*** (0.0008)	0.0051*** (0.0009)	0.0053*** (0.0009)
Tll		0.0346*** (0.0033)	0.0197*** (0.0030)	0.0066 (0.0034)	0.0213*** (0.0030)	0.0203*** (0.0030)
Tln		−0.0021 (0.0018)	−0.0027 (0.0016)	−0.0005 (0.0018)	−0.0049** (0.0017)	−0.0051** (0.0017)
Lllk			−0.0836*** (0.0043)	−0.0823*** (0.0050)	−0.0863*** (0.0042)	−0.0868*** (0.0043)
Lllm			0.0286*** (0.0065)	0.0667*** (0.0139)	0.0297*** (0.0063)	0.0322*** (0.0064)
Llln			0.0541*** (0.0060)	−0.0101 (0.0104)	0.0518*** (0.0059)	0.0496*** (0.0061)
Lklm			0.0732*** (0.0065)	0.0494*** (0.0074)	0.0692*** (0.0065)	0.0702*** (0.0066)
Lkln			−0.0012 (0.0048)	−0.0032 (0.0046)	0.0031 (0.0048)	0.0035 (0.0048)
Lmln			−0.0637*** (0.0065)	−0.0090 (0.0148)	−0.0615*** (0.0065)	−0.0583*** (0.0065)
ll2				0.0301*** (0.0064)
lk2				0.0140*** (0.0013)
lm2				−0.0625*** (0.0132)
ln2				0.0101 (0.0058)
Tt				−0.0006* (0.0003)	−0.0015*** (0.0003)	−0.0014*** (0.0003)
Constant	2.3149*** (0.0974)	2.6455*** (0.1448)	2.4270*** (0.2604)	2.4709*** (0.2476)	2.2596*** (0.2553)	2.5426*** (0.2617)
usigmas
Constant	−1.1130*** (0.2237)	−0.9016*** (0.2175)	−2.3399*** (0.2327)	−2.9091*** (0.2354)	−2.3644*** (0.2351)	5.7752 (16.4135)
vsigmas
Constant	−3.0169*** (0.0462)	−3.1740*** (0.0461)	−3.5093*** (0.0461)	−3.6673*** (0.0460)	−3.5350*** (0.0462)	−3.5117*** (0.0461)
Mu
iniStat						137.6555 (2262.6676)
Constant						−1578.9741 (25923.8391)
gamma
yearT						0.0013 (0.0111)
Observations	1036	1036	1036	1036	1036	1036

Notes: OLS = ordinary least square; T1 = Translog production model one; T2 = Translog production model 2; T3 = Translog production model 3; TN = time invariant model; TV = time variant model; t statistics are in parentheses, and ***, **, *indicate significance at 10, 5 and 1%, respectively

Source: Authors’ calculation

Table 3.

Generalized log likelihood ratio tests

Null hypothesis	Degree of freedom	Test statistic value (λ)	Critical value at 5%	Decision
β0 = 0	1	718.06	2.71	Reject H0
βtl = βtk = βtm = βtn = 0	4	696.42	8.76	Reject H0
βlk = βlm = βln = βkm = βkn = βmn = 0	6	1111.98	11.91	Reject H0
γ = μ = 0	2	15.50	5.14	Reject H0
γ = 0	1	15.50	2.71	Reject H0

Notes:λ is a likelihood ratio static calculated as –2 [log (likelihood (H0) – log (likelihood (H1)]. The corresponding critical value is referred to in Table 1 by Kodde and Palm (1986, Econometrica).

Source: Authors’ calculation

Table 4.

The estimated parameters of Battese and Coelli (1992) stochastic production frontier model

Variables	Parameter	Coefficient	z values
Deposit	βL	0.50***	9.16
Borrowing	βK	0.35***	11.99
Total expenses	βM	−0.04	−0.7
Net fixed assets	βN	−0.02	−0.47
Time	βt	0.04**	2.87
Deposit × Borrowing	βLK	−0.09***	−20.09
Deposit × Total expenses	βLM	0.03***	5.03
Deposit × Net fixed assets	βLN	0.05***	8.22
Borrowing × Total expenses	βKM	0.07***	10.76
Borrowing × Net fixed assets	βKN	0.01	0.72
Total Expenses × Net fixed assets	βMN	−0.06***	−8.95
Time × Time	βtt	−0.01***	−4.83
Time × Deposit	βtL	0.02***	6.87
Time × Borrowing	βtK	0.01***	6.12
Time × Total expenses	βtM	−0.03***	−6.98
Time × Net fixed assets	βtN	−0.01**	−3.06
Constant	β0	2.54***	9.74
Mu(Inistat)	Μ	458.08	0.04
Constant		−5255.73	−0.04
Gamma (Yeart)	Γ	0.01	0.12
Usigmas	σu	6.98	0.25
Vsigmas	σv	−3.51***	−76.2

Notes:***, **, *indicate significance at 10, 5 and 1%, respectively

Source: Authors’ calculation

Table 5.

Yearly summary statistics of means, standard deviations and coefficient of variation of technical efficiency: 2002–2018

Year	Mean efficiency	SD	Coeff. of var.
2002	0.86	0.14	15.76
2003	0.86	0.14	15.64
2004	0.88	0.11	12.22
2005	0.88	0.12	13.30
2006	0.88	0.10	10.97
2007	0.89	0.11	12.88
2008	0.88	0.11	12.93
2009	0.90	0.07	8.00
2010	0.89	0.10	11.72
2011	0.88	0.12	13.58
2012	0.88	0.12	13.45
2013	0.89	0.09	10.50
2014	0.88	0.10	11.11
2015	0.89	0.10	10.85
2016	0.89	0.09	10.01
2017	0.88	0.10	11.80
2018	0.89	0.10	11.29
Average	0.89	0.11	12.35

Source: Authors’ calculation

Table 6.

Bank group-wise overall mean technical efficiency and standard deviation

Ownership	Mean technical efficiency	SD
Nationalized banks	0.924	0.022
Old Pvt. sector banks	0.871	0.052
New Pvt. sector banks	0.927	0.049
Foreign banks	0.817	0.167

Source: Authors’ calculation

Table 7.

Ranking of banks based on their performance

Bank name	Rank	Bank name	Rank	Bank name	Rank
Mizuho bank ltd.	1	Union Bank of India	24	B N P Paribas	48
State Bank of Indore	2	Indian Overseas Bank	25	IndusInd Bank Ltd.	49
Antwerp Diamond Bank NV	3	Punjab National Bank	26	RBL Bank Ltd.	50
State Bank of India	4	Allahabad Bank	27	Bank of Nova Scotia	51
MUFG Bank Ltd.	5	United Bank of India	28	Barclays Bank Plc	52
ICICI Bank Ltd.	6	State Bank of Mysore	29	Citibank N A	53
Bank of America N A	7	UCO Bank	30	Chinatrust Commercial Bank	54
Punjab and Sind Bank	8	Axis Bank Ltd.	31	ING Vysya Bank Ltd.	55
HDFC Bank Ltd.	9	Federal Bank Ltd.	32	Royal Bank of Scotland N V	56
Tamilnad Mercantile Bank Ltd.	10	State Bank of Patiala	33	Dhanlaxmi Bank Ltd.	57
Indian Bank	11	State Bank of Bikaner and Jaipur	34	DCB Bank Ltd.	58
Jammu and Kashmir Bank Ltd.	12	Catholic Syrian Bank Ltd.	35	State Bank of Mauritius Ltd.	59
Credit Agricole Corporate and Invst. Bank	13	Andhra Bank	36	Bank of Ceylon	60
Central Bank of India	14	Canara Bank	37	Krung Thai Bank Public Co. Ltd.	60
Kotak Mahindra Bank	15	Bank of Baroda	38	Nainital Bank Ltd.	61
Oriental Bank of Commerce	16	Corporation Bank	39	DBS Bank Ltd.	62
IDBI Bank	16	Syndicate Bank	40	Mashreq bank PSC	63
Bank of Maharashtra	17	Lakshmi Vilas Bank Ltd.	41	Bank of Bahrain and Kuwait BSC	64
State Bank of Travancore	18	Yes Bank Ltd.	42	Deutsche Bank AG	65
Karnataka Bank Ltd.	19	Standard Chartered Bank	43	JP Morgan Chase Bank	66
City Union Bank Ltd.	20	State Bank of Saurashtra	44	Abu Dhabi Commercial Bank Ltd.	67
Karur Vysya Bank Ltd.	21	Dena Bank	45	AB Bank Ltd.	68
State Bank of Hyderabad	22	Bank of India	46	HSBC Bank Oman SAOG	69
Vijaya Bank	23	Hongkong and Shanghai Banking Corporation Ltd.	47

Source: Authors’ calculation