An Evaluation of the Technical,Pure Technical and Scale Efficiencies in the Indian Banking Industry using Data Envelope Analysis

Abstract

A well-developed and efficient banking sector is the fundamental requirement for smooth functioning of any economy. The present study is an attempt to examine the technical, pure technical and scale efficiencies of the Indian banks across different ownership categories for the period 2009–2012. About 7 out of the 44 banks selected lie on the efficiency frontier and form the reference set for their peers. Further, it is observed that efficiency scores do not vary much across the public sector, private sector and foreign banks. Performance of the public sector and private sector banks is almost at par with respect to technical efficiency whereas in the case of foreign banks, there lays scope for improving scale efficiency. A second stage regression analysis is carried out using Tobit regression to examine the determinants of efficiency. Non-interest income emerges the most important determinant of efficiency of banks in India.

Keywords

Data envelope analysis (DEA)Overall technical efficiency (OTE)Pure technical efficiency (PTE)Scale efficiency (SE)Tobit regression (TR)

Introduction

A healthy and smooth functioning financial system is the backbone of any efficient economy. It does not only boost up the domestic demand and savings, but also is an important pull factor for attracting foreign investments contributing to the very essential capital formation and further development and deepening of financial markets. The growth spiral thus has a well-developed financial system as the driving force. The banking sector is an integral part of this financial system and plays a fundamental role in economic development. The performance of the banking sector is more closely linked to the economy than perhaps that of any other sectors. The recent global financial crisis and its ripple effects spreading across the globe have reemphasized the importance of an efficient as well as a regulated banking system.

The Indian Banking industry governed by the Banking Regulation Act of India, 1949 can be broadly classified into two major categories, non-scheduled banks and scheduled banks. Scheduled banks comprise of commercial banks and the cooperative banks. In terms of ownership, commercial banks can be further grouped into nationalized banks, the State Bank of India and its group banks, regional rural banks and the private sector banks (the old/new domestic and foreign).

Since independence, banking industry in India has undergone structural changes to cope up with the evolving social and economic context of development. It has moved gradually from a regulated environment to a deregulated market economy. The pace of transformation has been even more significant in recent times with technology acting as a catalyst. Advances in information and communication technology have enabled banks to introduce new products and delivery channels, and strengthen their internal control systems. All these changes are expected to have significantly affected the way banks combine inputs to produce and deliver their products and services having a bearing on their efficiency and productivity.

With the eruption of the global financial crisis in 2007, growth rate of the Indian economy came under arrest notwithstanding the sound banking system, negligible exposure of Indian banks to sub-prime assets and relatively well-functioning financial markets. The Indian banking sector emerged relatively unscathed from the headwinds of the west (owing to prudential investment and regulatory norms of the country’s central bank i.e., Reserve Bank of India), but high inflation and depreciating rupee at the domestic front have created a challenging operational environment for Indian banks.

Given the backdrop, the present study has been undertaken to study and analyze the comparative efficiency of nationalized, private and foreign banks for the period 2009–2012 using Data Envelopment Analysis (DEA). The study proceeds as follows. The next section presents a brief insight into the existing literature on efficiency measures of Indian banks based upon DEA. This is followed by an explanation of methodology and the precise framework of DEA used for measuring efficiency scores. The section following this presents the results of the study in three parts. The first part focuses on measuring the overall technical efficiency (OTE), pure technical efficiency (PTE) and scale efficiency (SE) of the sample 44 banks. The second part examines if there is any significant impact of ownership on the efficiency scores (as calculated in part one) of banks. Lastly, the study explains the determinants of the overall technical efficiency of different banks using Tobit regression.

Review of Literature

In the global context, there is extant literature available on measurement of the banking sector efficiency using DEA. In the Indian context, however there was hardly any attempt in this direction until the 1980s. In their extensive international literature survey, Berger and Humphrey (1997) pointed out that out of 130 efficiency analyses of financial institutions covering 21 countries; only about 5 per cent examined the banking sectors of developing countries. Keshari and Paul (1994) were perhaps the first to estimate the efficiency of banks using the frontier approach. Below mentioned is a snapshot of some of the prominent studies undertaken on efficiency of the Indian banking sector using DEA.

Table 1.

List of Studies on Indian Banks Efficiency

Sl	Year	Author/authors	Title of Study	Methodology	Selected Variables	Findings in Brief
1.	1994	P.K. Keshari and M.K. Paul	Relative efficiency of foreign and domestic banks	Stochastic frontier production function	Input Labor, capital and materials. Output Sum of amount of total deposits and advances of a bank	Foreign banks and domestic banks are not significantly different in terms of their efficiency
2.	1997	A. Bhattacharya, C.A.K Lovell and P. Sahay	The impact of liberalization on the productive efficiency of Indian commercial banks	1. DEA for calculating radial technical efficiency 2. Stochastic frontier analysis	Inputs Interest expense and operating expense Output Advances, investments and deposits	Publicly owned Indian banks were the most efficient followed by foreign owned banks and privately owned banks
3.	2003	Milind Sathye	Efficiency of banks in a developing economy: The case of India	DEA	Inputs-Model A Interest expenses, non-interest expenses Output-Model A Net interest income and non-interest income Inputs-Model B Deposits and staff numbers Output-Model B Net loans and non-interest income	Mean efficiency score of Indian banks compares well with the world mean efficiency score and the efficiency of private sector commercial banks as a group is, paradoxically lower than that of public sector banks and foreign banks in India
4.	2002	A. Mukherjee, P. Nath and M.N. Pal	Performance benchmarking and strategic homogeneity of Indian banks	1. DEA 2. Multiple correlation clustering	Inputs Net worth, borrowings, operating expenses, number of employees, number of branches Output Deposit, net Profit, advances, Non-interest income interest spread	Public sector banks are more efficient than private or foreign banks although this could be due to the fact that public sector banks have a larger number of customers and are more widespread than foreign banks, the latter generally catering for small niche markets
5.	2004	T.T. Ram Mohan and Subhash C. Ray	Productivity growth and efficiency in Indian banking: A comparison of public, private and foreign banks	DEA	Inputs Interest cost and operating cost Output Loan income, investment income and non-interest income	PSBs performed significantly better than private sector banks but not differently from foreign banks. Superior performance of PSBs is to be ascribed to higher technical efficiency
6.	2004	Abhiman Das, Ashok Nag and Subhash C. Ray	Liberalization, ownership, and efficiency in Indian banking: A nonparametric approach	DEA	Inputs Borrowed funds, number of employees, fixed assets and equity. Output Investments, performing loan assets and other non-interest fee based income	Indian banks are not much differentiated in terms of input or output oriented technical efficiency and cost efficiency. However, they differ sharply in respect of revenue and profit efficiencies
7.	2006	Sathya Swaroop Debasish	Efficiency performance in Indian banking: Use of data envelopment analysis	DEA	Inputs Total deposits received, Total liabilities, Labour related administrative costs, capital-related administrative cost, operating expenses, fixed assets, total borrowings, net worth, net NPA Output Total loans extended, Total investments, Net profits, Interest and related revenues, Non-interest income, Short-term securities issued by official sectors, Net interest margin	Foreign owned banks were on average most efficient and that new banks are more efficient that old ones, which are often burdened with old debts
8.	2000	A. Saha and T.S. Ravishankar	Rating of Indian commercial banks: A DEA approach	DEA	Inputs Branches, staff expenditure, non-staff expenditure Output Deposits, advances, investments, spread, total income, interest margin, non interest margin	Public sector banks have in general, improved their efficiency scores over the period 1991/92 to 1994/95
9.	2008	Sunil Kumar & Rachita Gulati	Technical, pure technical, and scale efficiencies in Indian public sector (1992–2005)	1. DEA 2. Logistic regression analysis 3. Slacks and targets setting 3. input-	Inputs physical capital, labour and loanable funds. Outputs net-interest income, and non-interest income, while input vector contains three	Public sector banks operate at 88.5 per cent level of overall technical efficiency. Exposure of the banks to off-balance sheet activities has a strong and positive impact on the overall technical efficiency of banks.
11.	2011	Subroto Chowdhury	Effect of financial Crisis in efficiency and strategic homogeneity of Indian commercial banks: An empirical investigation	1. DEA 2. Cluster analysis	Inputs Interest expenditure and operating expenditure Output Deposit, advances and investments	The global financial crisis failed to have any impact on the technical efficiency of the Indian banking sector.
12.	2012	Mukesh Kumar and Vincent Charles	Evaluating the performance of Indian banking sector using data envelopment analysis during post-reform and global financial crisis	1. DEA 2. Malmquist productivity index 3. Jackknifing analysis	Inputs Total cost and total deposits Output Total loan other earning assets	The performance of public sector banks is at par with private sector banks in terms of efficiency.

Source: Author’s self-compilation.

A bird’s eye view of the studies in Table 1 indicates that much of the existing literature in the Indian banking sector has focused on measurement of efficiency for the period ranging from early 1990s to mid-2000. Most of the attempts have been made (i) to gauge the impact of deregulation and liberalization measures on the efficiency and productivity of the Indian banks and (ii) to examine the impact of ownership on the efficiency of banks. The results vary depending upon the variables used and the time period of study.

The present study thus in comparison to previous studies considers more recent data for the purpose of examining the efficiency scores of nationalized, private and foreign banks. Also not much light has been shed upon on the environmental factors affecting banking efficiency and most of the existing studies are confined to countries other than India.¹ The study in its second stage, investigates into the determinants of efficiency for banks using Tobit censored regression.

Objectives of the Study

To examine the overall technical, pure technical and scale efficiency of the public sector, private sector and foreign sector banks for the period 2009–2010 to 2011–2012 as this was the period characterized by slowdown in the domestic economy exercising considerable pressure on the banking sector.

To identify the factors influencing overall technical efficiency of banks for the period of study.

Data and Methodology

The study is carried out across 19 nationalized banks, 15 private sector banks and 10 foreign banks² for the period 2009–2012. The secondary data for the same has been extracted from the publications of Reserve Bank of India and Indian Banking Association.

The study is divided into three parts as discussed. Part one deals with calculating overall technical efficiency, pure technical efficiency and managerial efficiency³ for different categories of banks. Part two further proceeds with hypothesis testing⁴ so as to find out if there is any difference in the efficiency of different banks with respect to their ownership structure. Finally in part three, the study examines the determinants of overall technical efficiency (so obtained in part one) using Tobit censored regression.⁵

DEA Framework

In the recent years, besides the conventional financial ratios, the stochastic frontier (parametric) model and DEA (non-parametric) model have emerged as the two alternative techniques for examining efficiency of banks worldwide. The choice of DEA technique for the present study is inspired by a number of reasons. Firstly, a non-parametric study in contrast to a parametric study, in case of panel data allows for substantial variations embedded in data to be revealed (Alam, 2001). Secondly, as Evanoff and Israilevich (1991) note, use of DEA allows the researcher to work with less data, fewer assumptions and a smaller sample. A rule of thumb commonly used with DEA suggests that the number of observations in the data set should be at least three times the sum of the number of input and output variables (Cooper et al., 2000).⁶ Thirdly, DEA does not require any a priori assumption of a functional form relating to inputs and outputs. Most importantly, DEA allows the analyst to select inputs and outputs in accordance with a managerial focus and hence opens the door to what-if analysis (Sathye, 2003).

Speaking broadly, DEA is a nonparametric method. It is a linear programming methodology to measure the efficiency of multiple decision-making units (DMUs)⁷ and it generalizes the Farrell’s (1957) technical efficiency measure to the multiple-inputs and multiple-outputs case. As an efficient frontier technique, DEA identifies the inefficiency in a particular DMU by comparing it to similar DMUs regarded as efficient. The efficient DMUs lie on the ‘efficiency frontier’ and the inefficient DMUs lie below this frontier. The DMUs that lie on the frontier are the best practice institutions and retain a value of one; those enveloped by the extreme surface are scaled against a convex combination of the DMUs on the frontier facet closest to it and have values somewhere between 0 and 1 (Kumar, 2008). The distance of a DMU from the ‘efficiency frontier’ denotes the inefficiency of the DMUs lying below the frontier and can be done away with by emulating the ‘best practices’ of the efficient DMUs lying on the frontier. Following Bhattacharya et al. (1997), the present study constructs a single ‘grand frontier’ which envelops the pooled input output data of all the banks for the period of study.

In addition, DEA models can be either constant or variable returns to scale. The original formulation of the DEA model introduced by Charnes et al. (1978), also denoted as CCR hereafter, assumes Constant Returns to Scale (CRS) and presents the production frontier as a piecewise linear envelopment surface. Assuming that there are n DMUs, each with m inputs and s outputs, the relative efficiency score of a test DMU p is obtained by solving the following model proposed by Charnes et al. (1978):

\begin{array}{l} \max \sum_{k =1}^{s} v_{k} y_{k p} \\ s .t \sum_{j =1}^{m} u_{j} x_{j p} =1 \\ \sum_{k =1}^{s} v_{k} y_{k i} - \sum_{j =1}^{m} u_{j} x_{j i} \leq 0 ​ \forall i \\ v_{k}, u_{j} \geq 0 ​ \forall k, j \end{array}

where, k = 1 to s; j = 1 to m; i = 1 to n

y_ki = Amount of output k produced by DMU i,

x_ji = Amount of input j utilized by DMU i,

v_k = Weight given to output k,

u_j = Weight given to input j.

The above problem can be run n times for obtaining the relative efficiency scores of all the DMUs.

The measure of efficiency so obtained from the CRS model is known as overall technical efficiency (OTE) of a firm and is a comparative measure of how well it actually processes inputs to achieve its outputs, as compared to its maximum potential for doing so, as represented by its production possibility frontier. This OTE measure is inclusive of scale efficiencies (SE) and hence provides for inefficiencies due to size of operations of a DMU. This model was further extended by Banker et al. (1984), hereafter referred to as BCC, to take into account impact of returns to scale within the group of DMUs to be analyzed. The underlying objective is dual; first, to identify the most efficient scale size for each DMU and second, to find the technical efficiency score. This is achieved by imposing convexity restriction to the envelope requirements.

The above CRS linear programming problem can be easily modified to account for VRS by adding the following constraints to above model:

_{s}_{s} 1

The model so obtained is a variable returns to scale model and provides a measure of pure technical efficiency (PTE) devoid of any scale effects. PTE purely reflects the deviations from the frontier due to managerial inefficiency and is used as a managerial performance index. A measure of scale efficiency can be obtained as a ratio of OTE to PTE

SE \frac{{OTE}_{CCR}}{{PTE}_{BCC}}

The measure of SE aids the manager in choice of the optimum size. PTE and SE are mutually exclusive and non-additive. At this point it is important to note that if a DMU is identified as efficient in the CCR model, it will also be efficient in the BCC model. However, the converse is not necessarily true.

It is possible to create and estimate either an input orientation model or an output orientation model under both CCR and BCC envelopment. An input orientation identifies the efficient consumption of resources while holding outputs constant. The output orientation provides estimates of the amount by which outputs could be proportionally expanded given existing input levels. The present study undertakes the measurement of efficiency scores of banks using the input-oriented approach⁸ under both CCR and BCC models.⁹ The model is consistent in the context of current Indian banking environment characterized by shrinking margins, pressure to minimize the cost of inputs and generate maximum revenue.

Choice of Variables

The issue of explicit definition and measurement of banks’ inputs and outputs stands long debated in DEA. There are two common approaches to the variable selection in bank performance evaluation in DEA: Intermediation approach and production approach. In the intermediation approach, the banks are considered as intermediaries using deposits as an input in the production process. The production approach, on the other hand considers banks as service providers, thus this approach considers deposits as an output involving the creation of value added for which customers bear an opportunity cost. Berger and Humphrey (1997) pointed out that, although there is no ‘perfect approach’, the intermediation approach may be more appropriate for evaluating entire financial institutions because this approach is inclusive of interest expenses, which often account for one-half to two-thirds of total costs. Moreover, the intermediation approach may be superior for evaluating the importance of frontier efficiency to the profitability of financial institutions, since firms can achieve profit maximization by minimizing total costs and not just production costs (Casu and Molyneux, 2000). Besides, interest expenses often account for one-half to two-thirds of total costs that the production approach ignores. The intermediate approach accommodates interest expenses. Besides, interest expenses often account for one-half to two-thirds of total costs that the production approach ignores. The intermediate approach accommodates interest expenses. Following the modern empirical literature (Molyneux et al. (1996); Mester, 1996), the present study uses the intermediation approach with restricted choice of variables.¹⁰ The input variables have been selected as deposits and assets whereas output variables have been restricted to interest income and non-interest income. The choice of the inputs and outputs has been guided by choices made in previous studies and data availability. The choice also stands consistent with the recent trends in the Indian banking industry. Lately, besides the traditional borrowing and lending activities, banks have been emphasizing on transactions generating more of no-fund based income¹¹ to fuel the growth in revenues.

DEA Results for Efficiency Evaluation

Tabulated below are the input-oriented efficiency scores obtained from the CCR and BCC models.

An analysis of the above efficiency scores reveal that only 7 banks out of the sample of 44 banks have been able to remain consistently efficient for the period 2010–2012. The relative inefficiency for the remaining banks can be measured as the radial distance from the efficiency frontier. Punjab & Sind Bank and Punjab National Bank are the other two public sector banks which have delivered a PTE score of 1. This can be interpreted as optimum managerial efficiency that is, the bank is using minimum inputs to deliver the given level of output. The inefficiency in OTE thus owes to scale inefficiencies. Indian bank is the only public sector bank which has maintained an overall technical efficiency of 1 for the period under study. In the private sector, consistent performance has been displayed by three banks namely Axis Bank, ICICI Bank and Kotak Mahindra Bank. City Union Bank, Lakshmi Vilas Bank and HDFC Bank have attained PTE score of 1, implying there is scope to reach the efficiency frontier by doing away with inherent scale inefficiencies. In foreign banks category, Bank of America, Barclays Bank and RBS (Royal Bank of Scotland) have maintained an OTE score of 1 whereas Standard Chartered Bank and BNP Paribas have managed PTE score of 1.

Table 2.

Break-up of Efficiency Scores

DMU No.	DMU Name	Mean OTE Under CRS	Mean PTE Under VRS	Mean STE Under VRS
Public Sector Banks
1	Allahabad Bank	0.948026	0.962209	0.985269
2	Andhra Bank	0.975663	0.985831	0.98938
3	Bank of Baroda	0.817852	0.832945	0.982017
4	Bank of India	0.880756	0.902313	0.975388
5	Bank of Maharashtra	0.907299	0.969649	0.935554
6	Canara Bank	0.916388	0.973318	0.941446
7	Central Bank of India	0.905436	0.944374	0.959447
8	Corporation Bank	0.976301	0.986753	0.989154
9	Dena Bank	0.89905	0.987293	0.910589
10	Indian Bank	1	1	1
11	Indian Overseas Bank	0.967323	0.979525	0.987405
12	Oriental Bank of Commerce	0.971678	0.985465	0.98618
13	Punjab & Sind Bank	0.931379	1	0.931379
14	Punjab National Bank	0.994084	1	0.994084
15	Syndicate Bank	0.937513	0.952273	0.984585
16	UCO Bank	0.893018	0.910611	0.980886
17	Union Bank of India	0.928947	0.948349	0.979255
18	United Bank of India	0.889709	0.937366	0.949047
19	Vijaya Bank	0.933007	0.966581	0.965697
Private sector banks
20	Axis Bank Ltd.	1	1	1
21	City Union Bank Ltd.	0.971885	1	0.971885
22	HDFC Bank Ltd.	0.922806	1	0.922806
23	ICICI Bank Ltd.	1	1	1
24	Indusind Bank Ltd.	0.963461	0.972616	0.990359
25	ING Vysya Bank Ltd.	0.916923	0.95441	0.961911
26	Kotak Mahindra Bank Ltd.	1	1	1
27	Tamilnad Mercantile Bank Ltd.	0.97715	0.989883	0.987014
28	The Federal Bank Ltd.	0.956339	0.974573	0.981282
29	The Jammu & Kashmir Bank Ltd.	0.847627	0.85657	0.989947
30	The Karnataka Bank Ltd.	0.87696	0.895258	0.979302
31	The Karur Vysya Bank Ltd.	0.922848	0.929366	0.993054
32	The Lakshmi Vilas Bank Ltd.	0.977956	1	0.977956
33	The South Indian Bank Ltd.	0.896994	0.903869	0.992338
34	YES Bank	0.8535	0.87323	0.977179
Foreign banks
35	Bank of America NA	1	1	1
36	Barclays Bank PLC	1	1	1
37	BNP Paribas	0.840556	1	0.840556
38	Citibank N.A.	0.735157	0.987732	0.744598
39	DBS Bank Ltd.	0.643577	0.750331	0.865786
40	Deutsche Bank AG	0.933891	0.964757	0.968634
41	JPMorgan Chase	0.694279	0.850087	0.815598
42	Standard Chartered	0.850631	1	0.850631
43	HSBC	0.713963	0.884393	0.808597
44	RBS	1	1	1

Source: Author’s self-compilation.

As it can be observed from Table 3, mean technical efficiency scores under CRS have slightly improved for the public sector banks over the years with the OTE averaging to 91.69 per cent for the 3 year period. In other words, this can be interpreted as inputs can be reduced by 8.31 per cent to reach the efficiency score of 1 which is the case when all the DMUs would lie on the efficiency frontier. The PTE score has again shown marginal improvement from 94.67 per cent to 95.31 per cent from 2010 to 2012. Scale efficiency which can be calculated as the ratio of overall technical efficiency to pure technical efficiency, remains more or less unchanged for 3 years averaging to 96.71 per cent.

Table 3.

Mean Efficiency Scores of Public Sector Banks for the Period 2010–2012

Period	OTE*	PTE**	SE***
2010	0.916388158	0.946755526	0.9682999
2011	0.913919529	0.945467176	0.9670688
2012	0.920549127	0.953170325	0.9660778
Mean score	0.916952271	0.946755526	0.9671488

Source: Author’s self-compilation.

Notes: (i) *OTE-Overall technical efficiency.

(ii) **PTE-Pure technical efficiency.

(iii) ***SE-Scale efficiency.

A glance at the efficiency scores above depicts that private sector banks beat their public sector counterparts by a small margin of 1.63 per cent on an average in the overall technical efficiency. Again there is a very nominal difference of 1.18 per cent in the efficiency of private sector banks and public sector banks respectively. This implies that in terms of managerial efficiency, banks under the above two categories that is, public sector and private sector are equally efficient. Scale efficiency for private sector banks stands at a robust 97.85 per cent, quiet at par with their public sector peers.

Table 4.

Mean Efficiency Scores of Private Sector Banks for the Period 2010–2012

Period	OTE	PTE	SE
2010	0.940477	0.960452	0.979142
2011	0.94048	0.96045	0.97914
2012	0.933288	0.954802	0.977477
Mean score	0.93808	0.958568	0.978587

Source: Author’s self-compilation.

Table 5.

Mean Efficiency Scores of Foreign Banks for the Period 2010–2012

Period	OTE	PTE	SE
2010	0.82363	0.94591	0.86466
2011	0.77954	0.93239	0.83082
2012	0.7809	0.92563	0.83732
Mean Score	0.79469	0.93464	0.84427

Source: Author’s self-compilation.

The OTE for foreign banks in India has deteriorated from 82.36 per cent in 2010 to 78.09 per cent in 2012. This implies that inputs can be decreased by as high as 22 per cent approximately for the foreign banks to reach the efficient frontier. Also, this figure is way behind the efficiency of the public sector and private sector banks. As regards PTE, the foreign banks are almost as efficient as their peers in the public and private sector, whereas for SE, foreign banks are again laggards having mean efficiency score of 84.42 per cent against the average score of 96.71 per cent of the public sector banks and 97.87 per cent of the private sector banks. This can be explained as follows. In terms of managerial efficiency, foreign banks are as efficient as their other two counterparts but due to their limited branch network their presence is not widespread and hence low scale efficiency. The latter in turn exercise a downward pressure on OTE.

Observing and analyzing the descriptive statistics provided in Table 6 it is apparent that mean OTE score is highest for the private banks (93.89 per cent) and they are closely followed by their the public sector counterparts with of an efficiency score of 93.01 per cent. Foreign banks are operating at a much lower OTE level of 84.12 per cent. This means inputs can be reduced by at least 15.88 per cent to produce the same level of output. The extent of managerial efficiency as depicted by PTE is marginally higher for the public sector banks (95.87 per cent) as compared to the private banks (95.65 per cent) and foreign banks (94.37 per cent). This leads us to believe that for foreign banks, the source of inefficiency can be primarily accounted for by the scale inefficiencies rather than managerial efficiency.

The statistical tests that can be relied upon for testing the above hypothesis would either be parametric or non-parametric depending upon the normality of data. Broadly speaking, parametric tests assume the data is normally distributed while non–parametric tests do not go with the underlying assumption of normality. Accordingly, ANOVA (i.e., analysis of variance) is used under parametric category and Kruskal–Wallis test is used under non-parametric category. At this stage, it becomes relevant to check the data for normality. Null hypothesis assumes that data is normally distributed and following test statistics in Table 7 rejects the null hypothesis:

Table 6.

Descriptive Statistics of Efficiency Measures for Public Sector, Private Sector and Foreign Banks

Statistics	Public Sector Banks	Private Sector Banks	Foreign Banks
Overall Technical Efficiency (OTE)
No. of banks	19	15	10
Mean	0.930180386	0.938963267	0.841205367
Median	0.931378667	0.956338667	0.845593667
Standard deviation	0.010403204	0.013522425	0.043768159
Minimum	0.817852333	0.847627	0.643576667
Maximum	1	1	1
Pure Technical Efficiency (PTE)
No. of banks	19	15	10
Mean	0.958792981	0.956651622	0.943730033
Median	0.971483167	0.974573	0.993865833
Standard deviation	0.010076285	0.013315779	0.027467707
Minimum	0.832945333	0.856570333	0.750331333
Maximum	1	1	1
Scale Efficiency (SE)
No. of banks	19	15	10
Mean	0.969829544	0.981668911	0.889439967
Median	0.980885667	0.987014333	0.8582085
Standard deviation	0.005723177	0.005077842	0.029882176
Minimum	0.910589	0.922806333	0.744598
Maximum	1	1	1

Source: Author’s self-compilation.

Table 7.

Tests of Normality

	Kolmogorov–Smirnov^a			Shapiro–Wilk
	Statistic	df	Significance	Statistic	df	Significance
Mean OTE	0.155	44	0.010	0.847	44	0.000
Mean PTE	0.212	44	0.000	0.793	44	0.000
Mean SE	0.253	44	0.000	0.712	44	0.000

Source: Author’s self compilation.

Note: ^aLilliefors significance correction.

Observing the test statistic in Table 7, it can be concluded that data is not normally distributed (95 per cent confidence level), hence, the study proceeds with application of Kruskal–Wallis test to find out if there is any significant difference between the efficiency of the public sector banks, private sector banks and foreign banks.

Table 8.

Kruskal–Wallis Test

	Banks
	Banks	N	Mean Rank
Mean OTE	Public sector banks	19	22.89
	Private sector banks	15	25.53
	Foreign sector banks	10	17.20
	Total	44
Mean PTE	Public sector banks	19	20.76
	Private sector banks	15	23.40
	Foriegn sector banks	10	24.45
	Total	44
Mean SE	Public sector banks	19	21.89
	Private sector banks	15	27.60
	Foriegn sector banks	10	16.00
	Total	44

Source: Author’s self compilation.

Table 9.

Test Statistics^a,b

	Mean OTE	Mean PTE	Mean SE
Chi-square	2.567	0.673	4.987
df	2	2	2
Asymp. significance	0.277	0.714	0.083

Source: Author’s self compilation.

Notes: (i) ^aKruskal–Wallis Test.

(ii) ^bGrouping Variable: banks.

Interpreting the test statistics in Table 9, as the p value in case of all the three efficiency score is more than 0.05, so we fail to reject the null hypothesis (95 per cent confidence level) and hence it can be conveniently inferred from the above data that there is no significant difference in the performance of the public sector banks, private banks and foreign banks.

Tobit Regression

One of the criticisms of the traditional DEA approach is the difficulty of drawing statistical inference. The same has been addressed by Grosskopf (1996), who suggested a two-stage procedure. In the first stage, DEA is used to estimate efficiency scores. In the second stage, regression analysis is used to explain the efficiency scores. One concern, however, is that efficiency scores are censored. Accordingly, Tobit regression model which accommodates both continuous and categorical variables is used as it can account for truncated data.

The empirical model designed to explain efficiency is described below: _i_{0 +}₁₂₃₄₅₆₇₈_i

where, i_i = overall technical efficiency score of the ith bank derived from CCR model in previous section;

AQ = Asset quality;

BPE = Business per employee;

CA = Capital adequacy;

NII = Net interest income;

LnS = Log of asset size;

ROA = Profitability;

PPE = Profit per employee;

O = Ownership and

β₀, β₁, β₂ … β₈ are the regression parameters to be estimated by using the Tobit model and ε_i = error term

The above selected variables are intrinsic factors capable of exercising influence on the efficiency of banks and are commonly used in literature.¹² The sign of the coefficients of these variables depicted in Table 10 below, s the direction of the influence, and standard hypothesis testing is used to assess the strength of the relationship.

Size is measured by the logarithm of total assets. Size may lead to positive effects on bank efficiency if there are significant economies of scale. However, for banks that become extremely large, the effect of size could be negative due to bureaucratic and other reasons. Hence, the precise impact is not certain and left to be decided by the regression model. Asset quality measured as a ratio of net non-performing assets to net advances may bear a negative impact on the efficiency of banks if the same is sub-standard. It is assumed that larger business per employee, profit per employee and profitability will have a positive impact on the efficiency. Non-interest income captures the effect of diversification of the bank’s activities and there is no a priori expected sign. Capital adequacy reflects the capital strength of the banks and according to Isik and Hassan (2003) well capitalized banks are more technically efficient, thus the expected sign with bank efficiency is positive. Ownership is defined as a binary variable, 0 for nationalized banks and 1 for private and foreign banks.

Table 10

Description of the Explanatory Variables

Predictor	Description	Expected Relation with Efficiency
Asset quality (AQ)	Net NPANet advances	–
Business per employee (BPE)	(Deposits + Advances)Total employees	+
Capital adequacy (CA)	Tier I capital + Tier II capitalRisk weighted assets ◊ 100	+
Exposure to off-balance sheet items (EOBI)	Non-interest incomeTotal assets ◊ 100	+
Size (LnS)	Log of total assets	+/–
Profitability (ROA)	Net profitTotal assets	+

Source: Author’s self compilation.

It becomes important to note here as observed by Gulati (2011), the above model explains ‘inefficiency’ rather than efficiency, and hence the sign of the coefficients need to be reversed for explaining efficiency—positive coefficient implies an inefficiency increase whereas a negative coefficient means an association with inefficiency decline or increased efficiency.

The regression results listed in Table 11 above indicate that most influential variable impacting efficiency is non-interest income. The coefficient is statistically significant and bears a negative sign implying a positive impact of diversification of banking business beyond brick and mortar activities of borrowing and lending. Business per employee and capital adequacy are the other two significant variables influencing efficiency of banks. The sign of the coefficients is also in agreement with a priori expectations. The profit per employee variable though significant bears almost a negligible impact on the efficiency score. Ownership, which is measured as a binary variable has a statistically insignificant coefficient. This implies banks in India are operating in a competitive environment driven by market forces and ownership as such does not rope in as a source of efficiency.

Table 11.

Tobit Regression

Variable	Coefficient	Standard Error	z-statistic	Probability
C	1.219961	0.254524	4.793100	0.0000
Asset quality	–0.002894	0.012241	–0.236419	0.8131
Business per employee	–5.88E-05	1.49E-05	–3.942338	0.0001
Capital adequacy	–0.014213	0.004981	–2.853411	0.0043
Log asset size	–0.061454	0.234766	–0.261765	0.7935
Non-interest income	1.48E-05	7.20E-06	2.047986	0.0406
Profit per employee	0.001394	0.000582	2.392582	0.0167
Ownership	–0.038478	0.024956	–1.541864	0.1231
Profitability	–0.015948	0.021315	–0.748193	0.4543

Source: Author’s self compilation.

Conclusions and Future Scope

The study examines the performance of Indian banks under different ownership structure for the period 2010–2012. DEA technique is used to evaluate the efficiency scores and it is observed that:

Only 7 out of 44 selected banks are efficient during the period of slowdown in domestic economy. These 7 banks define the efficiency frontier. Out of these efficient banks, only one bank is from the nationalized category (Indian Bank), the other three from the private sector (Axis bank, ICICI bank and Kotak Mahindra Bank) and remaining three from the foreign sector (Bank of America, Barclays and RBS).

Further, OTE score is found to be the least for foreign banks whereas the private sector banks have marginally outperformed the public sector banks. However, the difference in the efficiency scores is not found to be statistically significant.

PTE of the nationalized, private and foreign banks in the post financial crisis period is robust at more than 90 per cent for all category of banks included in the study. Thus it is believed that with respect to managerial efficiency, the banks across different ownerships are equally competitive.

SE is again the least for foreign banks and at par for nationalized and private banks.

Non-interest income is the most influential factor impacting efficiency. Hence banks need to focus on diversified product offerings such as credit cards, consumer finance and wealth management on the retail side and on fee-based income and investment banking on the wholesale banking side. These require new skills in sales & marketing, credit and operations. As business per employee has also been identified as an important factor impacting efficiency, a well-trained and competitive workforce should be an essential focal point for the managers.

Overall, the study concludes that difference in the efficiency scores of these different categories is not statistically significant and performance of the nationalized and private sector banks has been robust with average OTE score of more than 90 per cent during the post global financial crisis period. The results obtained from the study are in close conformity with the previous studies. Kumar and Charles (2012) in their article conclude that the performance of PSBs is at par with the private sector banks in terms of efficiency. Dwivedi and Charyulu (2011) in their study state that banks across different categories have performed equally well. Gulati (2011) in her study reports that ownership structure has a weak effect on the performance of banks as the efficiency differences between the public and private sector banks are not statistically significant. With liberalization of the banking sector, PSBs have witnessed gradual reduction in government control and a fresh orientation towards improved profitability thus making them more competitive. Moreover, factors such as stringent RBI norms, adoption of improved risk management practices, superior role of information technology, focus on improved customer service quality, etc. have ensured a satisfactory performance for Indian banks successfully withstanding the crisis.

The results of this study can be further investigated by expanding the magnitude of inputs and outputs. Also the study can be carried out over a longer period of time and can incorporate returns to scale and Malmquist indices of total factor productivity change (TFP).

Footnotes

Notes

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