Critical Analysis of Technical and Allocative
Efficiency in Indian Commercial Banks
Uday Kumar Jagannathan1, Nagesha Holenasipur Nanjundaiah2 and Franco Chiryath3
1Assistant
professor, 2Associate professor, 3MBA Student
Faculty of Management and Commerce, Ramaiah University of Applied Sciences, Bengaluru 560054
E-Mail: [email protected]
Abstract
The banking sector in India was liberalized in 1991. Ever since, the sector has seen entrants from private as well
as foreign banks. The public banks (nationalized as well as SBI group) continue to hold a majority share of
deposits from the sheer size and presence (number of physical branches). As more of the population seeks financial
inclusion from the system, it is obvious that while public banks will continue to grow, they will face increased
competition from private and foreign banks. The Narashimham commission (1991) laid out guidelines for superior
performance and improved productivity of the banking sector. Post implementation of this commission,
commercial banks have seen great vitality and improved investments in private and public domain. This paper
pertains to measurement of efficiency in the Indian banking sector between 2002-2010, a period of growth and
consolidation in the sector. While revenues and costs are helpful in measuring the profitability of banks, another
significant measurement is efficiency of banks. Though profit can contribute directly to the valuation of the banks,
it leaves out certain important concerns pertaining to banking efficiency. Banking efficiency helps us in
understanding how well the physical as well as human assets are being deployed in the banks’ operation. The
measured efficiencies can provide insights into the relative position of any particular bank in the competitive
space. Sub-efficient banks will possibly need to adapt their operations to match the efficient ones. There is also the
opportunity of merging the sub-efficient bank with a larger/more efficient one to exploit economies of scale or best
practices.
Key words: Data Envelopment Analysis, Decision making Unit, Technical efficiency
Salamouris [8] measured the Greek bank
performance using DEA. Isik and Kabir [9] used a
DEA-type Malmquist total factor productivity
change Index to examine productivity growth,
efficiency change, and technical progress in Turkish
commercial banks whilst the deregulation of
financial markets in Turkey, Guan and Dipinder [7]
also used DEA in calculation of bank efficiencies.
1. INTRODUCTION
The concern of whether any particular banking
operation outputs can be simulated with a
combination of inputs from other banking
operations is an important one. This forms the
basics of efficiency analysis. One of the techniques
used in the determination of efficiency is “data
envelopment analysis” or DEA. This technique was
first used by Farell (1957) [6] . Details on data
envelopment analysis may be obtained in the
seminal work of “Measuring the efficiency of
decision making units" by Charnes, Cooper &
Rhodes (1978) [3]. It has been tradition to manage
business (and banks) using ratio analysis. While
ratios offer valuable insights, they do not consider
aspects like economies of scale. Cook et al.(2000)
[5] investigated the use of quantitative variable in
bank branch evaluation using DEA.
In the Indian context, some research has been done
on the efficiency of Indian banking, notably Pardeep
Kaur and Gian Kaur [10], who studied the cost
efficiency of Indian banks between 1991-2008.
They also examined the benefits of mergers of
banks in the Indian landscape and improvements if
any of efficiency scores post-merger. Milind
Satyhye [13] examined the efficiency of Indian
banks for 1997-1998. Bhattacharya et al [1] in 1997,
as well as Chatterjee [4] in 1997 and Saha [12] have
performed research on the efficiency of Indian
banks. For the purpose of analysis and use of
software to calculate technical, cost and allocative
efficiencies, one can refer Coelli T.J [14]
DEA technique is a non-parametric method in
operations research used for the estimation of
production frontiers. It empirically measures the
productive efficiency of decision making units
(DMU), for our purposes a DMU would be a given
bank. While a variety of outputs and inputs can
possibly be selected to perform DEA analysis, for
purposes of finding inputs and outputs which are
common to a diverse set of commercial banks, it is
often helpful to use information from banks’
balance sheets and income statement to perform
analysis.
3. NOMENCLATURE
θ
λi
Yi
Xi
ci
Efficiency of DMU0
Weight of a particular DMUi
Vector of Output of DMUi
Vector of Input of DMUi
Unit Cost of Inputi
Abbreviations
2. LITERATURE REVIEW
DEA
DMU
SBI
Camanho and Dyson [2] examined the bank branch
performance under price uncertainty. Halkos and
6
Data envelopment analysis
Decision making unit
State Bank of India
RBI
Reserve Bank of India
4
MODELS
SOLUTION
BEING
USED
(deposits, advances, investments) along with two
sets of inputs (interest expended, operational
expenses) and (employees, capital and reserves)
were selected for the purpose of the analysis. For the
second set of inputs, corresponding cost information
was wage per employee, cost of funds.
FOR
The banking sector in India can be broadly
classified into public banks, foreign banks, private
banks and banks under the SBI group. Under these
different categories, a study has been initiated to
measure the banking efficiency of each bank using
data envelopment analysis. Once the efficiency is
assigned to a given bank for each of the years
between 2002 and 2010, one can observe trends in
upward/lateral or downward movement of
efficiency indices. Although the foreign, private,
public and SBI group of banks operate under
different regulatory conditions, they are analyzed
together for calculating efficiency scores.
The first model (hereafter model 1) measured the
intermediation efficiency of commercial banks in
India. The second model (model 2) measured
production efficiency and costs of the inputs were
cost of funds and wage per employee respectively.
Thus, model 1 yielded technical efficiency alone,
because it did not contain cost information. Model 2
contained physical inputs and also their costs and
therefore was possible to obtain technical efficiency
as well as cost efficiency from this model.
Allocative efficiency which is a ratio of cost
efficiency to technical efficiency was another output
of this model.
Efficiency as measured by DEA can be divided into
two aspects, viz. technical efficiency and cost
efficiency. Technical efficiency measures how best
a decision making unit (in our context, a DMU or a
bank in particular) is able to maximize its output for
a given set of inputs. It is that point where the DMU
cannot achieve more output with a given level of
input or cannot produce the same level of output by
decreasing one or more inputs, while holding the
other inputs the same. Technical efficiency can be
obtained by finding the combination of DMUs with
the least input for the output evidenced by the DMU
in question.
The analysis was run for all banks in a given year,
from 2002 to 2010 both included. Therefore the
software was run 9x 2 = 18 times (9 years, 2
models) and 9 sets of efficiency scores result from
processing each model. Each time the software was
run; all banks for a fiscal year were taken as one
batch. Model 1 output included the technical
efficiency of each bank, while model 2 outputs
included cost efficiency, technical efficiency and
allocative efficiencies.
Cost efficiency can be determined by finding the
combination of DMU which yield the lowest
possible cost for the output evidenced by the DMU
in question.
For purposes of analysis, the average efficiencies for
a year were used by bank category. By category we
mean foreign banks, public banks, private banks and
SBI group. Therefore a set of 9x4 = 36 data points
are available for each type of efficiency. Model 1
yielded 36 data points while model 2 yielded 36x3 =
108 data points for analysis (3 different types of
efficiencies in model 2)
Shown below are the definitions for the calculation
of technical efficiency and cost efficiency.
Basic model & definition: Technical
efficiency
Data used for each fiscal by bank category is given
in Table 4a-4d. These data summarize the number
of banks per period by category, the interest income
and other income, deposits and associated cost of
funds, employees and wage per employee
respectively. It may be noted that for the actual
analysis, per bank data was used for obtaining
efficiency of each DMU.
Min θ
Subject to
∑ λi Xi <= θX0 (i = 1,…., n)
∑ λi Yi >= Y0 (i = 1,…., n)
λi >= 0
Basic model & definition: Cost efficiency
Min ∑ ci0 x0 (i = 1,…., m)
s.t
xi0 >=∑xij λj (i =1,….,m, j=1….n)
yr0 <= ∑ yrj λj (r = 1,…., s, j=1…. n )
∑ λj= 1 (j = 1,…., n)
The software used for the purpose of calculating
DEA is called DEAP version 2.1 and is
downloadable for free from the centre for efficiency
and productivity at The University of Brisbane,
Queensland, Australia. All outputs are a result of the
use of this software.
λj>= 0
for s outputs, m inputs and n DMUs
5. METHODOLOGY
6. RESULTS AND ANALYSIS
Data from the RBI web site, “a profile of Indian
banks” [14] was used to obtain data for fiscal years
2002 to 2010 and the DEA analysis was run on the
dataset. Two models were used in the analysis, each
model yielding a different set of efficiency results.
The two sets of vector outputs – one for each of two
models (interest income, other income) and
The results obtained from the study were tabulated
and shown as the average technical efficiency by
fiscal year for model 1 and the average technical,
cost and allocative efficiency by fiscal year for
model 2. Graphs (Fig 1 & Fig 2a-2c) were plotted to
7
display the various efficiency outputs from the 2
models.
banks. Private banks at present measured lowest in
cost efficiency terms across all categories. Positive
correlation in cost efficiency was observed between
public, SBI group and foreign banks. The standard
deviation of cost efficiency from Table 2c was
lowest for foreign banks (0.05) and highest (0.15)
for public banks.
Referring Fig 1 (model 1 results), technical
efficiency in the years between 2002 and 2010
followed a non-linear pattern, not indicative of any
systematic increase or decrease in the time frame.
The foreign banks were ahead in terms of technical
efficiency, exceptions include year 2003 to 2005,
when SBI group and public banks’ efficiencies were
higher than the foreign banks. Then again in 2009,
the SBI group and public banks showed efficiency
levels higher than that of the foreign banks. Private
banks were clearly behind the public banks and SBI
group in technical efficiency, however not by a lot.
Efficiency measurements across bank categories
show positive correlation over the measured time
frame and more so among public, SBI group and
private banks. The correlation of efficiencies
between foreign banks and other categories was
low. The standard deviation of technical efficiencies
(Table 1) shows lowest values for foreign banks
(.06) and highest for public banks (0.09).
Allocative efficiency measures showed that the
private banks performed consistently well or better
than other bank categories. Also noteworthy is that
public banks and SBI group lagged foreign banks in
allocative efficiency until 2005 after which foreign
banks became the laggard in this measure.
Allocative efficiencies were strongly correlated
across categories especially among SBI group,
public and private banks. The standard deviation for
foreign banks’ allocative efficiency was lowest
(0.03) versus (0.15) for public banks (Table 2b).
Table 1: Technical efficiency+ by year and
category (Model 1)
Foreign
Private
SBI *
2002
0.72
0.68
0.64
2003
0.84
0.80
0.85
2004
0.74
0.74
0.78
2005
0.70
0.70
0.74
2006
0.87
0.77
0.79
2007
0.86
0.77
0.79
2008
0.79
0.62
0.64
2009
0.72
0.67
0.73
2010
0.81
0.57
0.62
Correlations between technical efficiency from
model 1, cost of funds, advance to deposit ratio and
profit per employee showed little correlation
between any two variables with the exception of
profit per employee and advance to deposit ratio
(0.53), cost of funds and efficiency (-0.42),
suggesting that decreases in cost of funds are
beneficial to improving technical efficiency scores
of the bank.
Referring Fig 2a, (model 2 results) technical
efficiency in the years between 2002 and 2010 again
followed a non-linear pattern with SBI group and
public banks ahead of others in terms of technical
efficiency, without any exception in any fiscal year.
All categories consistently showed an efficiency of
0.5 or higher, though the foreign and private banks
scored relatively lower in technical efficiency than
the SBI group and public banks. This implies that
SBI group and public banks exhibited better
production efficiency than their foreign and private
peers. However, foreign and private banks were
more effective at turning deposits into advances, as
depicted in table 4b. Also noteworthy is that private
banks’ technical efficiency was on the ebb, while all
other bank categories showed stability in levels of
technical efficiency. 2005 was a year of efficiency
declines for all categories of banks. Positive
correlation in technical efficiency was exhibited
between SBI group, public and foreign banks. The
standard deviation (Table 2 a) shows lowest values
for public banks (0.04) and highest values for
private banks (0.07)
Stdev
0.06
0.08
0.08
*
SBI indicates SBI and group banks
+ average values for year and category
Table 2a: Technical efficiency by year and
category (Model 2)
Foreign
Private
SBI *
2002
0.56
0.73
0.76
2003
0.58
0.77
0.79
2004
0.58
0.77
0.78
2005
0.44
0.71
0.77
2006
0.61
0.75
0.83
2007
0.61
0.74
0.87
2008
0.60
0.67
0.91
2009
0.63
0.67
0.88
2010
0.60
0.56
0.80
Stdev.
0.06
0.07
0.05
Table 2b: Allocative efficiency+ by year and
category (Model 2)
Foreign
Private
SBI
2002
0.71
0.81
0.67
2003
0.73
0.82
0.70
2004
0.70
0.80
0.60
2005
0.72
0.79
0.70
2006
0.80
0.90
0.91
2007
0.78
0.90
0.91
2008
0.78
0.90
0.96
2009
0.73
0.91
0.98
2010
0.75
0.89
0.90
Stdev.
0.03
0.05
0.13
In terms of cost efficiency represented in Table 2c
and depicted in fig 2c, the private banks were
leaders between 2002 and 2005 but lost this position
to the public banks and SBI group, both of which
have been at the top of the cost efficient measures
since. Foreign banks lagged in cost efficiency
showed improved performance as compared to
private banks, whose efficiency levels in 2010 were
low enough to displace the earlier lagging foreign
8
Public
0.60
0.81
0.76
0.76
0.80
0.83
0.65
0.73
0.62
0.09
Public
0.76
0.80
0.78
0.76
0.80
0.82
0.85
0.87
0.84
0.04
Public
0.63
0.63
0.60
0.69
0.85
0.88
0.95
0.97
0.93
0.15
Table 2c: Cost efficiency+ by year and category
(Model 2)
Foreign
Private
SBI
Public
2002
0.42
0.60
0.50
0.46
2003
0.45
0.64
0.55
0.49
2004
2005
2006
0.44
0.32
0.50
0.62
0.56
0.66
0.53
0.53
0.76
0.49
0.52
0.68
2007
0.48
0.66
0.79
0.72
2008
0.48
0.61
0.87
0.81
2009
2010
Stdev
0.45
0.46
0.05
0.61
0.50
0.05
0.86
0.72
0.15
0.84
0.78
0.15
Table 4a: No. of commercial banks by fiscal
& category
Table 3b: Correlation, allocative efficiency,
model 2
Foreign Private
SBI
Public
Foreign
1
0.69
0.69
0.59
Private
1
0.97
0.94
SBI
1
0.98
Public
1
Private
SBI
Public
1
0.46
0.63
0.54
1
0.17
-0.10
1
0.96
Private
SBI
Public
Private
29
SBI
8
Public
19
2003
2004
32
32
29
29
8
8
19
19
2005
2006
32
28
29
22
8
7
19
20
2007
2008
28
28
22
22
7
7
20
20
2009
2010
31
31
22
22
7
7
20
20
Year
Foreign
Private
SBI
Public
2002
2003
0.77
0.74
0.69
0.66
0.47
0.48
0.51
0.52
2004
2005
0.75
0.86
0.63
0.70
0.51
0.56
0.52
0.61
2006
2007
0.86
0.84
0.74
0.75
0.69
0.76
0.68
0.70
2008
2009
0.84
0.77
0.77
0.78
0.77
0.73
0.72
0.72
2010
0.69
0.77
0.77
0.71
Table 4c: Cost of funds by fiscal & category
Table 3c: Correlation, cost efficiency model
2
Foreign
Foreign
32
Table 4b: advance to deposit ratio by fiscal
& category
Table 3a: Correlation, cost efficiency, model 2
Foreign Private
SBI
Public
Foreign
1
0.46
0.63
0.54
Private
1
0.17
-0.10
SBI
1
0.96
Public
1
Foreign
Year
2002
1
Year
Foreign
Private
SBI
Public
2002
2003
6.44
5.46
7.15
6.34
7.49
6.70
6.69
5.96
2004
2005
3.97
3.65
5.33
4.63
5.56
4.78
4.98
4.40
2006
2007
4.49
4.21
4.78
5.30
4.71
5.09
4.36
4.87
2008
2009
4.17
4.33
6.34
6.77
6.32
6.54
5.88
6.17
2010
3.12
5.91
5.70
5.47
Table 4d: avg. profit/employee fiscal &
category
Table 3d: Correlation, allocative efficiency
model 2
Foreign
Private
SBI
Public
Foreign
Private
SBI
Public
1
0.69
0.69
0.59
1
0.97
0.94
1
0.98
1
9
Year
2002
2003
Foreign
9.16
13.91
Private
2.50
2.73
SBI
1.36
1.89
Public
0.97
1.57
2004
2005
20.42
11.06
4.35
1.18
2.96
2.43
2.31
2.31
2006
2007
27.33
26.92
3.12
3.63
2.28
2.94
2.75
3.26
2008
2009
45.18
39.61
4.74
5.24
3.56
4.39
4.19
4.79
2010
18.02
5.15
4.81
5.75
Table 5: Measurement of correlation
coefficients between technical efficiency
from model 1, cost of funds, advances to
deposits and profit per employee
Cost of
Funds
Adv.
to
Dep.
Profit
per
empl.
1.00
-0.42
-0.07
0.28
1.00
-0.35
-0.51
1.00
0.53
AE
Tech
Eff.
Cost of
funds
Adv.
to dep.
Profit
per
empl.
Tech
Eff.
Allocative efficiency Model 2
1.00
1.05
1.00
0.95
0.90
0.85
0.80
0.75
0.70
0.65
0.60
0.55
0.50
0.45
0.40
0.35
0.30
0.25
0.20
0.15
0.10
0.05
0.00
2001
Foreign
Public
Private
SBI
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
Year
Fig 2b – Allocative efficiency: model 2
Technical Efficiency Model 1
Cost efficiency Model 2
1.00
0.80
Foreign
0.40
Private
CE
Nationalized
TE
0.60
SBI
0.20
0.00
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011
Year
0.95
0.90
0.85
0.80
0.75
0.70
0.65
0.60
0.55
0.50
0.45
0.40
0.35
0.30
0.25
0.20
0.15
0.10
0.05
0.00
2001
Foreign
Public
Private
SBI
2002 2003
2004
2005
2006 2007
2008
2009 2010
2011
Year
Fig 1 Technical efficiency: model 1
Fig 2c – Cost efficiency: model 2
TE
Technical efficiency Model 2
1.00
0.95
0.90
0.85
0.80
0.75
0.70
0.65
0.60
0.55
0.50
0.45
0.40
0.35
0.30
0.25
0.20
0.15
0.10
0.05
0.00
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011
7. CONCLUSIONS AND FURTHER
RESEARCH
Banking environments around the world operate
under different macroeconomic conditions of
liquidity, inflation, interest rate, regulations on
investment and ownership to name a few. Therefore,
studies on efficiency are often conducted
constrained by macroeconomic boundaries such as
country. In India, the public banks and SBI group
are owned by the government and operate under
various regulatory constraints. In spite of these
regulations, they showed efficiency levels close to
other categories when measured for intermediation
efficiency and higher scores when measured for
production efficiency.
Foreign
Public
Private
SBI
Technical efficiency scores are highly dependent on
the types of inputs and outputs selected for analysis.
In this study, two models are used, one to study
efficiency of intermediation, and the other to study
the efficiency of production. While in the former,
the foreign banks emerged as leaders, in the latter
model, the public banks and SBI group clearly had
higher technical efficiency scores.
Year
Fig 2a - Technical efficiency: model 2
10
Public banks and SBI group scored higher on cost
efficiency and this may be due to economies of
scale enjoyed by them. Tests on capital and reserve
versus cost efficiency scores may provide evidence
on relationship between size and cost efficiency.
[6] Farrell, M.J. (1957) "The Measurement of
Productive Efficiency,"Journal of the Royal
Statistical Society vol. 120, pp. 253–281
[7] Guan, H.L. and Dipinder, S.R. (2005),
“Competition, Liberalization and Efficiency:
Evidence from a Two-Stage Banking Model on
Banks in Hong Kong and Singapore”,
Managerial Finance 31, No. 1, 52-77
Further research can be conducted on impact of
macroeconomic events like inflation and interest
rates on efficiency scores of commercial banks.
Research can also be done on measuring events like
divestment, capital structure changes, and
acquisitions on the efficiency scores of commercial
banks in India. Impact of major events like the
financial crisis of 2008 on efficiency scores can also
be examined.
[8] Halkos, G.E. and Salamouris, D.S. (2004)
“Efficiency Measurement of the Greek
Commercial Banks with the Use of Financial
Ratios: a Data Envelopment Analysis
Approach”, Management accounting Research
15, No. 2, 201-224
[9] Isik, Ihsan and Kabir Hassan, M (2003),
“Financial Deregulation and Total Factor
Productivity Change: An Empirical Study of
Turkish Commercial Banks”, Journal of
Banking and Finance 27, No. 8, 1455-1485
8. REFERENCES
[1] Bhattacharya, A., Lovell, C.A.K., and Sahay,
P. (1997) “The impact of liberalization on the
productive efficiency of Indian commercial
banks”, European Journal of Operational
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[10] Kaur, Pardeep and Kaur, Gian (2010), “Impact
of mergers on the cost efficiency of Indian
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[2] Camanho A.S., Dyson and R.G (2005) “Cost
Efficiency
Measurement
with
Price
Uncertainty: a DEA Application to Bank
Branch Assessments”, European Journal of
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http://www.rbi.org.in/scripts/AnnualPublicatio
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[3] Charnes, A., W. Cooper, & E., Rhodes (1978)
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approach”, European Journal of Operations
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[4] Chatterjee, G. (1997) “ Scale Economies in
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25-59
[13] Satyhye, Milind (2003), “Efficiency of banks
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(2000),
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Computer
Program”
11