A Study of the Efficiency of Indian Banks – A DEA analysis

A Study of the Efficiency of Indian Banks – A DEA analysis

Abstract:

Introduction:

The structure of Indian banking has evolved greatly over the recent past, and with removal of ₹500 and ₹1000 from circulation, it is hard to fully understand the change in efficiency on the banks operating in India in the future. This study aims to provide a benchmark of efficiency using the DEA approach so that that the results of the future can be compared to the results presented in this study as a method of determining whether removal of currency from circulation has resulted in an increase, decrease or no effect on the efficiency of the banks operating in India.

Literature Review:

Before diving in to the research it is important to provide some background of previous analysis conducted by other economists. There are several empirical analyses of the efficiency on Indian banks however most the literature looks in to difference of efficiency the state-owned banks and foreign banks.

Dude (0000) presents one of the earliest evaluations on Indian banks, however a lot of analysis is provided using old data with a lack of reliability. It is not until Satye (2003) used statistical software to determine efficiency values of 1990’s banks that a solid economic base for comparison was formed. His work concluded that public sector banks have a higher efficiency score than privately owned banks.

This work was further build on by Kumbhakar and Sarkar (2004), who explored the cost efficiency using a stochastic cost frontier model with specification of translog cost function. Their results incorporated over 50 banks with a clear analysis that deregulation lead to an increase in cost inefficiency of banks, which leads other economist (i.e. DUDE0000) to believe that a similar conclusion will occur this time around.

During the deregulation period, Kumbhakar and Sarkar (2004) showed that private and foreign banks (of which there were an insignificantly small quantity) had a much larger cost efficiency off around 80% compared to the 58% of public sector banks. With the lower level of efficiency, could be attributed to the lack of deposits and fixed assets, due to deregulation of some currency, which resulted in a lower level of loans and investment for the public banks.

Ranmohan and Ray (2004) looked at the analysis conducted by Kumbhakar and Sarkar (2004) and compared the revenue maximising efficiency of banks in India. Interestingly, their work showed that public sector banks were better than foreign institutions. They believe that the private banks had a greater presence around India, with around 4 times as many branches, which directly lead to an increase in output for the banks, however the data was later determined to be insignificant.

Further research conducted by Das et al (2004), showed that the deregulation could be advantageous for India as it is expected to increase efficiency and productivity however it can have different effect on different ownership structures. While Sturm and Williams (2004) found that there was a decrease in the total factor productivity in foreign and domestic banks however data from Turkish banks, collected by Isik and Hassan (2003), showed that foreign banks benefitted the most from the more competitive environment than the state-banks.

 Finally, although the changes are expected to be positive there have been concerns raised by economists previously regarding the adverse effects on the risk-taking behaviour of market participants. However, due to a lack of quality literature there is no known connection between productivity, deregulation and risk-taking (Zhao et al. 2006)

Methodology:

It is usual to measure the performance of banks using financial ratios, however Yeh (1996) presents the argument that to draw a valid analysis there would be a high reliance on benchmark ratios which could be arbitrary and may mislead analysts when drawing conclusions. Sherman and Gold (1985) build on the work of Yep to explain that financial ratios don’t fully capture the effect operations, marketing, or financing.

Originally, the approach of using a using an efficient frontier started by Farrell (1957) – as explained by DUDE(0000)– had become more popular as a more quantitative approach. This simple measure of a firm’s efficiency accounts for multiple inputs. From this, the Charnes et. al.  (1978) introduced the Data Envelopment Analysis (DEA) which is a non-parametric linear programming approach, capable of handling multiple inputs and outputs. (Asmild et. al., 2004)

DEA is a mathematical programming technique that measures the efficiency of a decision-making unit (DMU) relative to other similar DMUs with the simple restriction that all DMUs lie on or below the efficiency frontier (Seiford and Thrall, 1990). DEA also identifies, for inefficient DMUs, the sources and level of inefficiency for each of the inputs and output (Charnes et al., 1995). It provides a means of comparing the efficiency of DMUs with each other based on several inputs and / or outputs. It derives its name from a theoretical efficient frontier which envelops all empirically-observed DMUs. (Repkova, 2014)

Methodology, the characteristics of DEA can be described using the original model proposed by Charnes, Cooper and Rhodes – henceforth referred to as CCR. Considering that an analysis of “N” number of DMU’s that convert “I” inputs to “J” outputs, where the input can be greater, smaller, or equal to the outputs (Satye, 2003). The CCR model presupposes that there is no significant relationship between the scale of operations and efficiency by assuming constant returns of scale (CRS).  This is used to derive the following CCR model: CCR MODEL

In contrast to CCR model, Banker et al. (1984) present a slightly different model in which there is a variable output with respect to the scale. (DUDE 0000) Additionally, in this model, economic efficiency is decomposed to pure technical efficiency and scaled efficiency to measure the output to scale as efficiently as possible. (DUDE 0000)              BCC Model

Whereas technical efficiency measures the ability of a bank to produce a given set of output with minimal inputs under the assumption of variable returns to scale. While scale efficiency measures whether a bank produces at an optimal size of scale. (Hauner and Peiris, 2007)

The reason that DEA is used to determine the efficiency is because it allows for variables of different units (e.g. Rupees, staff, loans etc.) without the need of standardisation. Satye (2003) explains that DEA allows for benchmarking which has been investigated in banking by a variety of literature like Mester (1996); Miller and Noulas (1996) etc.  However, there are limitations of using DEA analysis such as the comparison of efficiency is relative to the most efficient DMU and its likely that there could be a more efficient DMU outside of the sampled data.

This analysis uses a variety of banks from the public sector, private sector and foreign banks operating in India. However, some of the banks had to left out of the analysis due to a serious lack of reliable data. Although, there is current dispute over the variables used for conducting DEA, this study employs the intermediation approach to define inputs and outputs. Karimzadeh (2012) explains that under this approach, banks are treated as financial intermediaries that combine deposits, labour, and capital (inputs) to produce loans and investment (outputs). When conducting DEA, it is important to associate weights with all function.

To determine the weights on each input, we start by calculating employees expense per capita which is calculated by dividing employees’ expenses by the overall number of employees. For the second input, price of fixed assets, ….

Additionally, a Malmquist index, based on the model by Fare et al. (1985) is used to separate changes in technology (shifts of the frontier), technical efficiency and scale efficiency (movements relative to the frontier). The Malmquist productivity function introduced by Caves, Christensen, and Diewert (1982) as explained by Rammohan and Ray (2004) is the ration of the levels of technical efficiency of two firms measured against a reference technology characterized by constant returns to scale.

DEA Results and Discussion:

Looking at the results of productivity efficiency using the CCR model the overall efficiency of banks has increased by 1% from the 85% to 86% (Table 1), although that number may not to a true representation of the results. Foreign banks are the most efficient at converting their inputs to outputs with an average of 93% efficiency and a small variation of only 5% around mean.

It can be seen from the data in Table 3 that majority of banks within the foreign sector are within the fourth quartile while most private sector banks are within the third quartile. Banks within this sector have a much lower average efficiency score of only 76% suggesting that ideally just more than three-quarters of the inputs could be used to produce the same amount of outputs. With one bank being so inefficient as to be only 34% efficient. Ideally, this bank would only need a third of its inputs to provide the same level of outputs. This could be because of the inefficiency in handling PART OF INTER..APPR, this is backed up by DUDE(0000) who found the same trend using similar inputs and outputs.

Between the average efficiencies of private sector banks and foreign banks, falls the productivity efficiency of public sector banks at an average of 87%, but it should also be noted that the quantity of banks explored within the sector is the lowest because a lot of these banks failed to provide reliable data.

These results from the CCR model can be explained by the evidence presented by DUDE (0000) that suggests that foreign banks have a greater knowledge because of larger scale of their operations in increasing their efficiency however an opposing view argued by DUDE (0000) suggests that an increase in scale can often lead to a decrease in efficiency, a factor not considered within the CRR model; which leads us on to the BCC analysis.

The efficiency scores were expectedly higher when using a BCC model (Table 4), with overall efficiency increasing to 90%. Over the two years there a smaller increase in each of the sector, but that could be because they are already extremely efficient. Even Private Sector banks have increased from 76% (CCR model) to 83% (BCC model). Using Table 6, most banks jumped from the third quartile up to the fourth.

There was also an increase of the number of relies on the efficiency frontier jumping from the 10 originally to 12 in the BCC model. This is most likely because BCC models allow for variable returns to scale which achieves more efficiency than the model with the constant returns to scale. The higher efficiency value is caused by the fact that the BCC model decomposes inefficiency of production units into two components: the pure technical inefficiency and the inefficiency to scale. Values of efficiency computed by VRS reach higher values than efficiency computed by CRS by eliminating the part of the inefficiency that is caused by a lack of size of production units. (CZECH 0000)

It is important for banks to deduce the factors that leads to this inefficiency, so that can deal with them. The cost efficiency is split it in to technical and allocation efficiency, using the formula CE = AE/TE. The results from Table 7 show that most of the inefficiency comes from allocative inefficiency rather than technical efficiency. This means that the inefficiency is most likely due to “wrong” inputs at the “prevailing input prices” (GERMAN 0000), rather than waste of inputs. Technical efficiency rose from 90% to 91% from 2014 to 2015 showing there is still room of improvement in producing more outputs from the same level of inputs.

Furthermore, the panel data was used to measure productivity change using the Malmquist index. However, technical efficiency, scale efficiency nor technology changed significantly over the two years for any of the banking sectors – it would be best to use data from around 10 years for more conclusive results. Satye (0000) measures changes in Indian banks and exhibit positive productivity changes over the time-period 2004-2010 which shows banks are moving towards a move efficient future and closer towards the efficient frontier.

Finally, to explain the differences in productivity efficiencies among different sectors within the banking industry. Several explanatory variables were regressed (shown in Table 9) using a Tobit model because the efficiencies have a value between 0 and 1.

QML standard errors and covariance’s are calculated as there is a chance of heteroscedasticity, and a R-squared value of 86% shows that values are close to the regression line. The first variable is GDP growth, DUDE(0000) shows that GDP growth has a clear relationship with banking efficiency as changes in macroeconomic performance can have an effect on respective cost structures. For example, if a bank has a higher ratio of interest to administrative costs than other competing banks, an economic slump could result in a loss and hence a loss of efficiency. The data from Table 9 shows a there is a negative relationship with GDP significant to the level of 1%.

Moving on to size, a measure of the total assets within the Indian banking system. Size would have a positive to market power, the larger banks would have lower for their inputs which can be seen in the results as foreign banks have the largest positive relationship. Additionally, with the larger banks the cost of increasing scales of returns will decrease because factors like fixed costs (e.g. research) will result in greater efficiency. The results show a positive relationship with foreign sector followed by private and then public sector all within a significance of 5%.

Furthermore, inspired by the work of GERMAN (0000), the component of RISK which is defined by Berger and Mester (1997) by the volatility of a bank’s return on assets. It is argued that risk creates cost as it creates administrative costs. This holds true for my data as all the sectors present a negative correlation which shows that all types of banks struggle to manage risk within a 5% significance.

Lastly, one of the main features for success of any firm or bank is its staff.  EXPEMPL is the personal expense per employee, which has a positive relationship within all sectors of the banks all within a significance of 10%. Brunner et al. (2003) showed that quality of the bank’s staff might influence the cost efficiency only if output per employees also increased proportionally to the compensation presented to the employees.

Limitations of DEA analysis

Future Research (Brazil 0000)

Asmild, M., Bogetoft, P., & Hougaard, J. (2004). Rationalising Inefficiency: A study of Canadian bank Branches. University of Copenhagen.

Banker, R., Chanes, A., & Cooper, W. (1984). Some Model for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis. Management Science 30, 1078-1092.

Bas, A., & Ghosh, S. (2006). Financial deregulation and efficiency: An empirical analysis of Indian banks during the post reform period. Review of Financial Economics, 193-211.

Charnes, A., Cooper, W., & Rhodes, E. (1978). Measuring the efficiency of decision-making units. European Journal of Operational Research, 2, 429-444.

Charnes, A., Cooper, W., Lewin, A., & Seiford, L. (1995). Data Envelopement Analysis: Theory, Methodology and Applications. New York: Springer-Verlag.

Farrell, M. (1957). The Measurement of Productive Efficiency. Journal of the Royal Statistical Society, 120(3), 253-290.

Hauner, D., & Peiris, S. (2008). Banking efficiency and competition in low income countries: the case of Uganda. Applied Economics, 40(21), 2703-2720.

Karimzadeh, M. (2012). Efficiency Analysis by using Data Envelopment Analysis: Evidence from Indian Banks. International Journal Latest Trends Financial Economics Society, 2(3), 228-237.

Mester, L. (1996). A study of bank efficiency taking into account risk preferences. Journal of Banking and Finance, 20(6), 1025-1045.

Miller, S., & Noulas, A. (1996). The technical efficiency of large bank production. Journal of Banking and Finance, 20(3), 495-509.

Repkova, I. (2014). Efficiency of the Czech banking sector employing the DEA window analysis approach. Procedia Economics and Finance 12, 587-596.

Sathye, M. (2003). Efficiency of banks in a developing economy: The case of India. European Journal of Operational Research, 148, 662-671.

Seiford, L., & Thrall, R. (1990). Recent Development in DEA: the Mathematical Programming Approach to Frontier Analysis. Journal of Econometrics, 7-38.

Sherman, H., & Gold, F. (1985). Bank Branch Operating Efficiency. Journal of Banking and Finance, 9(2), 297-315.

Yeh, Q. (1996). The application of date envelopment analysis in conjunction with financial ratios for bank performance evaluation. Journal of Operational Research Society, 47, 989-988.

Appendix:

Table 1: Bank efficiency measured using the CCR Model during 2014

Total Economic Efficiency (CCR model)
N	Mean	SD	Min	Max
Public Sector	26	0.87	0.08	0.76	1
Private Sector	32	0.76	0.13	0.34	1
Foreign Banks	35	0.93	0.05	0.68	1
Total banks	93	0.85	0.09	0.58	1

Table 2: Bank efficiency measured using the CCR Model during 2015

Total Economic Efficiency (CCR model)
N	Mean	SD	Min	Max
Public Sector	26	0.89	0.08	0.76	1
Private Sector	32	0.77	0.11	0.41	1
Foreign Banks	35	0.93	0.05	0.68	1
Total banks	93	0.86	0.08	0.61	1

Table 3: Number of Banks in four quartiles of efficiency scores using CCR Model during 2014-2015

Public Sector	Private Sector	Foreign Sector	Total
Lowest efficiency (Q1 ≤ 0.25)
Second Quartile (0.26 ≥ Q2 ≤ 0.50)		3		3
Third Quartile (0.51 ≥ Q3 ≤ 0.75)	1	21	4	36
Fourth Quartile (0.76 ≥ Q2 < 1)	25	8	31	54
Total	26	32	35	93
Frontier (efficiency = 1)	2	3	5	10

Table 4: Bank efficiency measured using the BCC Model during 2014

Total Economic Efficiency (BCC model)
N	Mean	SD	Min	Max
Public Sector	26	0.91	0.06	0.72	1
Private Sector	32	0.82	0.10	0.62	1
Foreign Banks	35	0.95	0.04	0.79	1
Total banks	93	0.89	0.07	0.71	1

Table 5: Bank efficiency measured using the BCC Model during 2015

Total Economic Efficiency (BCC model)
N	Mean	SD	Min	Max
Public Sector	26	0.91	0.08	0.76	1
Private Sector	32	0.83	0.09	0.64	1
Foreign Banks	35	0.95	0.05	0.80	1
Total banks	93	0.90	0.07	0.73	1

Table 6: Number of Banks in four quartiles of efficiency scores using BCC Model during 2014-2015

Public Sector	Private Sector	Foreign Sector	Total
Lowest efficiency (Q1 ≤ 0.25)
Second Quartile (0.26 ≥ Q2 ≤ 0.50)
Third Quartile (0.51 ≥ Q3 ≤ 0.75)	2	3	2	7
Fourth Quartile (0.76 ≥ Q2 < 1)	24	29	33	86
Total	26	32	35	93
Frontier (efficiency = 1)	3	3	6	12

Table 7: Descriptive Statistics: Efficiency scores

2014			2015
Public	Private	Foreign	Public	Private	Foreign
Technical Efficiency	0.92	0.82	0.96	0.91	0.86	0.96
Allocative Efficiency	0.78	0.66	0.81	0.79	0.71	0.84
Cost Efficiency	0.91	0.82	0.95	0.91	0.83	0.95

Table 8: Net Productivity change 2014-2015: Malmquist decomposition by market and size

Technical Change	Scale Efficiency	Technology	Total factor productivity
Private Sector	1.01	0.99	0.99	0.99
Public Sector	1.00	0.99	1.01	1.01
Foreign Sector	1.01	0.98	1.01	0.99

Table 9: Tobit Regression model – factors explaining differences in efficiency

Private Sector		Public Sector		Foreign Sector
Coefficient	P-Value	Coefficient	P-Value	Coefficient	P-Value
GDP	-0.00749	0.1012	-0.000875	0.1216	-0.00124	0.1182
SIZE	8.65×10-08	0.0000	1.73×10-06	0.0000	6.42×10-07	0.0000
RISK	-0.45321	0.0023	-0.26345	0.0028	-0.34673	0.0019
EXPEMPL	0.00207	0.0978	0.00371	0.1042	0.01032	0.0891