We gathered data from various sources such as the Central Bank of India (RBI), Indian Banking Association (IBA), and Annual Reports of respective banks to assess the performance of small finance banks. Our study employs different variables (Table 1) for this purpose. To measure efficiency, we consider factors like loans and advances (Patra, B et al., 2022; Abdulahi, S A et al., 2023), deposits (Henriques, L C et al., 2018), total assets (Abdulahi, S A et al., 2023), interest income (Milenkovi´c, N et al., 2022), interest expenses (ALMANSOUR, A. Y, 2021), non-interest income, net profits, and operating expenses (Dar, A et al., 2021).
The study evaluates the operational performance of Small Finance Banks (SFBs) during the period 2019 to 2022, utilizing the available data. The analysis also considers the impact of the pandemic (Covid-19) on SFBs, specifically how macroeconomic variables have influenced their efficiency. During the pandemic, the central bank played a critical role in safeguarding the banks' interests. This involved strengthening balance sheets, providing essential liquidity support, and ensuring financial sector stability. Additionally, the Government of India took steps to establish the National Asset Reconstruction Company Limited (NARCL), aimed at facilitating the recovery process and improving the financial position of stressed banks (Report on Trends and Progress of Banking in India, 2020-21).
Table:1 DEA Input-Output table
Output Variables
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Input Variables
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Description
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Loans and Advances
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Total Assets
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Loans and advances extended to customers, along with total assets, collectively constitute the entirety of fixed assets
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Interest Income
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Deposits
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Interest income includes the total income received on loans and advances. Whereas deposits are the total deposits including time, demand and saving deposits.
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Non-interest Income
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Interest Expenses
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Non-interest income comprises earnings from commissions, fees, and all other revenue sources of the banks. Interest expenses infers the amount paid on all kinds of deposits.
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Net Profits
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Operating Expenses
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Net profits encompass their total earnings after subtracting all expenses, taxes, and interest payments from their overall revenue. Operating expenses of banks includes employee expenses, administrative expenses, rent and lease expenses, marketing expenses, IT expenses, Depreciation and Amortization and Professional consultancy fees.
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Source: Based on literature, 2023.
In this current analysis, we have selected ten small financial banks: ‘Capital Small Finance Bank Ltd, Equitas Small Finance Bank Ltd, ESAF Small Finance Bank Ltd, Fincare Small Finance Bank Ltd, Jana Small Finance Bank Ltd, North East Small Finance Bank Ltd, Suryoday Small Finance Bank Ltd, Ujjivan Small Finance Bank Ltd, Utkarsh Small Finance Bank Ltd and Au Small Finance Bank Ltd’. This selection is based on their establishment (Srikanth, M et. al (2021)) and operationalization phases (IBA statistics, 2023).
We aim at evaluating banks' performance concerning their efficiency in managing asset quality, generating income, handling deposits, and making investments (Amirteimoori A, et. al 2023). Data Envelopment Analysis (DEA) is considered the most suitable method for assessing bank efficiency (T, Subramanyam (2023), Henriques, C L. et. al (2018), Kumar, V., & Kar, S. (2021)). Therefore, our study employs a two-stage DEA approach to measure the performance of these Small Finance Banks during the period 2019–2021.
3.1 Methodology and research model
The application of the DEA framework to assess the effectiveness of industrial entities using input and output parameters is highly commendable. Devised by the innovative trio of Charnes, Cooper, and Rhodes (CCR) in 1978, DEA stands as a robust linear programming method. By evaluating the comparative efficiency ratings of various Decision-Making Units (DMUs) within a specific sample, DEA unveils valuable insights regarding their performance. In this analysis, the CCR paradigm proves to be a powerful tool for measuring the efficiency of individual DMUs. By calculating the maximum ratio of the total weighted outputs to the total weighted inputs, this model reveals the true level of efficiency achieved by each DMU. It offers a comprehensive measure that captures both the overall performance and the allocation of resources within the units under scrutiny.\(\)\(Efficiency=\frac{Aggregate weighted outputs}{Aggregate weighted inputs}\)
The establishment of weights within the proportion is guided by a vital constraint: the similarity ratios for every Decision-Making Unit (DMU) must remain below one. Consequently, the integration of numerous inputs and outputs condenses into a more straightforward depiction via the notion of 'virtual input' and 'virtual output,' eliminating the necessity for direct weight allocation. This strategy adeptly distinguishes the efficiency standing of each DMU within the sample, separating those identified as efficient from those that do not measure up. Operating as a technique along the efficient frontier, DEA effectively identifies inefficiencies exhibited by distinct DMUs.
Rather than attempting to correlate a DMU's performance with statistical means that may not align with its specific circumstances, DEA achieves this by comparing the DMU with analogous, established efficient counterparts. Through the utilization of this relative assessment, DEA provides valuable insights into the comparative performance of DMUs, facilitating targeted improvements and establishing a benchmark against the most proficient units in the dataset. The original CCR model can be used to methodologically explain the properties of DEA. Take into account N devices (each referred to as a DMU) that transform p inputs into q outputs, where p may be greater, equal to, or less than q. A DMU's efficiency is determined using the model below.
\(Max{e}^{0}=\frac{{\sum }_{J=1}^{q}{u}_{j}^{o}{y}_{j}^{o}}{{\sum }_{i=1}^{p}{v}_{i}^{o}{x}_{i}^{o}}\) ………………………………Equation-I
Subject to
$$\frac{{\sum }_{q=1}^{Jq}{u}_{q}^{o}{y}_{q}^{n}}{{\sum }_{i=1}^{i}{v}^{o}{x}_{q}^{n}}\le 1;n=1,.....N$$
$${v}_{i}^{o},{u}_{q}^{o}\ge 0;i=1......I:q=1.......q$$
Where \({y}_{q}^{n},{x}_{q}^{n}\) are positive known outputs and inputs of nth DMU and \({v}_{i}^{o},{u}_{q}^{o}\) are variable weights to be determined in order to be DEA efficient, Interpreting (i) of the efficiency score e0 = 1 must be satisfied; otherwise, it is DEA inefficient. The objective function of the problem is non-linear and fractional, making it challenging to solve as stated. The aforementioned non-linear programming issue, however, was converted into a linear one as follows by Charnes et al., (1978).
\(Max{h}^{0}={\sum }_{q=1}^{q}{u}_{q}^{o}{y}_{q}^{o}\) .........…………………………………. Equation-II
Subject to
$${\sum }_{i=1}^{J}{v}_{q}^{o}{x}_{i}^{o}=1,{\sum }_{j=1}^{J}{u}_{q}^{o}{x}_{q}^{n}-\sum {v}^{0}{x}_{q}^{n}\le 0;n=1........N$$
$${v}_{i}^{o}\ge \sum ,{u}_{q}^{o}\ge \sum ,i=1...I,q=1......q$$
DEA analysis enables the researcher to choose inputs and outputs based on managerial priorities. Nevertheless, DEA does possess certain constraints. The DMUs identified as efficient are merely efficient relative to the others within the dataset. It's conceivable that a unit beyond the dataset could attain higher efficiency than the most proficient DMU within the dataset. The present investigation embraced an output-oriented methodology (Patra B et. al, 2022), signifying the aim to maximize output while utilizing the provided inputs.
The notion of decision-making units is introduced in a manner akin to that of entities, where each entity is evaluated as a component of a collective that employs inputs to generate outputs. The assessment's outcome, quantified as efficiency scores, spans a range from 0 to 1, representing the level of efficiency achieved by the DMUs. In essence, a DMU is deemed efficient when it achieves the pinnacle score of 1, or conversely, and for parameter estimation within the model encompassing censored data, the Ordinary Least Squares (OLS) technique is utilized; however, due to data characteristics, estimation results might lack consistency. Given the data attributes, the study adopted the Data Envelopment Analysis -Tobit model grounded in Maximum Likelihood Estimation (MLE) to scrutinize the factors influencing the efficiency of small finance banks from 2019 to 2022.
Tobit model (Tobin, 1958) suggested the equation as follows:
$${I}_{i}=\left\{\begin{array}{c}{I}_{i}^{*}={p}_{i}\beta +\epsilon , {I}_{i}>0\\ 0, {I}_{i}^{*}\le 0\end{array}\right.$$
Where β is the regression function, \(\epsilon\) is error term, \({p}_{i}\) is the explanatory variable, and \({I}_{i}\) is the efficiency value vector calculated by the DEA- BCC model. Efficiency of banks considered the dependent variable which is defined by bank specific variables (Abdulahi S. M. et. al 2023) and Macro variables (Drake, L. et. al (2006). Therefore, in our study statistical estimation of Tobit regression is estimated as follows:
\({TE}_{i,t}= {\beta }_{0}+{\beta }_{1}{Car}_{i,t}+{\beta }_{2}{Cdr}_{i,t}+{\beta }_{3}{Lr}_{i,t}+{\beta }_{4}{Loggdp}_{i,t}+{\beta }_{5}{Loginf}_{i,t}+{Ɛ}_{it}\) ------(1)
Where \({TE}_{i,t}\) = Technical Efficiency scores, \({Car}_{i,t}\)= Capital Adequacy Ratio, \({Cdr}_{i,t}\)= Credit Deposit Ratio, \({Lr}_{i,t}\)= Liquidity ratio, \(Loggdp\)= Log of GDP at constant Price 2011-12, \({Loginf}_{i,t}\)= Log of Inflation, Inflation measured by CPI approach (Annual reports (2019–2022) Ministry of statistics and Programme implementation, GOI)
Next section exhibits the empirical results of DEA approach and Tobit regression by following the conclusion and policy implication.