Research Article - (2016) Volume 3, Issue 4
Dept. of Statistics, Dr BAM University Aurangabad, Maharashtra, India
Objective: The main objective of this paper is developing new hybrid model of CCR model and BCC model of DEA as non-parametric technique with Multiple Regression Analysis as parametric technique to ranking Nationalised Banks of India. We have verified ranking results obtained through three methods with Statistical test as non-parametric test.
Research Methods: In this paper we have applied Data Envelopment techniques such as input oriented Constant Returns to Scale model and input oriented Variable Returns to Scale model. These models integrated with Multiple Regression Analysis technique for ranking Indian Banks. Also these obtained results have been verified using Spearman’s Rank Correlation test.
Results: In this study, 20 Nationalised banks are selected to identify the ranking of each banks using above mentioned three methodologies. The results indicate that the Bank of Baroda, Punjab National Bank and IDBI Bank Ltd are efficient frontier banks out of 20 banks using DEA models. As per methodology of Statistical Multivariate Regression Analysis, the Bank of Baroda, IDBI Bank Ltd and Punjab National Bank were getting first, second and third rank respectively.
Conclusion: We have concluded that the CCR model, BCC model and Multiple Regression Analysis techniques are positively correlated with each other as per Spearman’s rank correlation test result.
Linear Programming Problem, Data Envelopment Analysis, Multivariate Regression Analysis, Indian Banking.
Indian banking sector is one of the largest banking system in the world. Indian banking system is mainly divided into Public Sector Banks and Private Sector Banks. The Public Sector Banks are further divided into two categories as Nationalised Banks and SBI group banks and Private Sector Banks are divided into Foreign Banks and Domestic Private Banks. The Nationalised Banks in India play the pivotal role of Indian economy. The major market has been captured through Nationalised Banks. Our research has major focus on to improve efficiencies and effectives of Nationalised Banks of India. The purpose of this paper is to propose a hybrid methodology based on Data Envelopment Analysis (DEA) and Statistical Regression analysis that addresses to this issue of efficiency using data from Nationalised Indian banks.
Over the past two decades, data envelopment analysis (DEA) has become a popular methodology for evaluating the relative efficiencies of decision making units (DMUs), many researches has been chosenbanks are decision making units. They have proved the different DEA models are useful for efficiency measurement of banks andits target setting. Data Envelopment Analysis is an approach to estimate the production function of organizations and organizational units and enables the assessment of their efficiency. The comparison of empirical results produced by DEA and Multivariate Regression Analysis is still uncommon in bank efficiency literature. Multivariate Regression Analysis is useful tool to predict the independent value of variable from one and more than one dependent variable. Regression analysis is a statistical tool that is used to investigate the relationship between variables. It is a parametric technique that requires the specification of a production function.
DEA provides an estimation of the production function to which each individual Decision Making Unit’s (DMU’s) efficiency score can be compared. Furthermore, DEA offers a number of advantages over traditional techniques including its ability to identify reference units for each DMU. These characteristics prove to be a very useful managerial tool as it aids in establishing potential causes and methods of improvement for the identified inefficient.
Literature review
Data Envelopment Analysis (DEA) is a linear programming technique to assess the efficiencies of decision making units (DMU) when multiple variables are taken into account. Literature related to efficiency studies can be traced back to Farrell [4], who treated the production frontier as the basis for efficiency assessment. The Charnes, Cooper and Rhodes (CCR)1described a mathematical programming formulation for the empirical evaluation of relative efficiency of a Decision Making Unit (DMU) on the basis of the observed quantities of inputs and outputs for a group of similar referent DMUs. The Banker, Charnes and Cooper (BCC) [6] provideda formal link between DEA and estimation ofefficient production frontiers via constructs employedin production economics. Satye [10] used DEA to study the relative efficiency of Indian banks in the late 1990’s with that of banks operating in other countries. He found that the public sector banks have a higher mean efficiency score as compared to the private sector banks in India, but found mixed results when comparing public sector banks and foreign commercial banks in India. Kumbhakar and Sarkar [11] estimated the cost efficiency of public and private sector banks in India by using the stochastic cost frontier model with specification of translog cost function.
The Seiford and Zhu [8] examined the performance of the top 55 US banks using a two-stage DEA approach. Results indicated that relatively large banks exhibit better performance on profitability, whereas smaller banks tend to perform better with respect to marketability. Drake and Howcroft [12] assessed the relative efficiency of UK clearing bank branches using DEA method. This paper utilized the basic efficiency indices and extended the analysis by examining the relationship between size and efficiency. Many of these studies find that state-owned banks are more efficient than private and foreign banks (Bhattacharyya and Pal [19]; Sharma [20]), find that foreign banks are actually the most efficient. R. Kiani Mavi [17] estimated the ranking of banks branches using DEA and multivariate regression analysis, results indicate that the efficiency calculated from CCR model and multivariate regression model has positively correlated. Premachandra [21] examine the capability of DEA in assessing corporate bankruptcy by comparing it with logistic regression (LR).The main objective of this paper to assesses efficiency of Indian banks using DEA technique and Multivariate Regression Analysis techniques.
Data Envelopment Analysis
Data has been collected from RBI website for evaluation. Data Envelopment Analysis is a linear programming procedure for a frontier analysis of inputs and outputs. The input-oriented DEA model under the assumption of constant return to scale &variable return to scale can be used for calculation of input-oriented technical efficiency. In this study, we estimate the CCR model proposed by Charnes et al. (1978) and BCC model proposed by Banker et al. (1984), which allows for variable returns to scale. The input-oriented CRS &VRS model can be written as:
The basic input-oriented CRS model for ‘n’ DMUs with ‘m’ inputs and ‘s’ outputs proposed by CCR, the relative efficiency score of pth DMUs is given by
Where, k = 1 to s (number of outputs);
j = 1 to m (number of inputs);
i = 1 to n (number of DMUs);
Yki = amount of output k produced by DMU i;
Xji = amount of input j utilized by DMU i;
Vk = weight given to output k and Uj = weight given to input j.
The fractional programme shown in Equation (1) can be reduced to LPP as follows:
This model is called CCR inputoriented DEA model. The efficiency score of ‘n’ DMUs is obtained by running the above LPP ‘n’ times.
Multivariate Regression Analysis
The Multivariate linear regression model can be return in below form
Where Y is the dependent variable
and 
is the ith independent
variable. Therefore 
is the
coefficient of 
a is constant and
is the
estimation error term.
In this paper, we have analyzed efficiency of Indian Banks using hybrid approach of DEA and Regression analysis. In this paper, we have taken data of 20 Nationalised Indian Banks during financial year of 2012-13. We have used two input measure such as interest expended (X1), operating expenses (Y2) and one output measure as total income (Y) (total income is summation of Interest income and other income). Data has been collected from RBI website for the financial year 2012-13.
Table 1: Data table for financial year 2012-13
In this paper, we have used the inputorientation CCR model, input-orientation BCC model of DEA and Multivariate Regression analysis model to evaluate performance measurement of Nationalised Banks and also comparative study on parametric and non-parametric techniques. We have applied Spearman’s rank correlation test to testing the result obtained from CCR, BCC and Multivariate regression.
The table 2 shows efficiency and ranking of each bank using input oriented CCR model and input oriented BCC model, last column show ranking obtained through Multiple regression analysis. The both CCR and BCC result indicates that Bank of Baroda, Punjab National Bank and IDBI Bank Ltd. are efficient frontier and their ranks are one. Other than these three banks, efficient frontier banks using BCC model are Bank of Maharashtra, Canara Bank, Corporation Bank, Dena Bank, Punjab and Sind Bank, and United Bank of India. The remaining banks are inefficient and their scores are less than one. The CCR and BCC efficiency score of DMUs are calculated by using R Software and detail result has shown in CCR & BCC columns of Table 2.
Table 2: Ranking using CCR, BCC and Multivariate Regression models
We have used multivariate regression model for this data, then the linear regression equation as:
Y=-5688+1.11X1+1.964X2+ 
Error of estimation can be computed by subtracting Y from the actual amount of the output variable (income) for each DMU. DMUs are ranked based on descending error. The results are shown in last two columns of Table 2. The Multiple regression result indicates that the Bank of Baroda is topper bank out of these banks and its rank is one. The IDBI Bank Ltd and Punjab National Bank are getting second and third rank respectively.
The below descriptive Statistics summary show overall Nationalised Banks efficiency obtained through input oriented Constant Return to Scale model of DEA. Result indicates that out of 20 banks only three banks are efficient and having score one.
Descriptive Statistics Summary of Overall Banks using CCR model using R software-
>summary(e)
Summary of efficiencies
The technology is crs and input orientated efficiency
Number of firms with efficiency==1 are 3
Mean efficiency: 0.957
Eff range # %
0.8<= E <0.9 3 15
0.9<= E <1 14 70
E ==1 3 15
Min.1st Qu.Median Mean 3rd Qu. Max. 0.8865 0.9412 0.9632 0.9572 0.9785 1.0000
The below descriptive Statistics summary show overall Nationalised Banks efficiency obtained through input oriented Variable Return to Scale model of DEA. Result indicates that out of 20 banks, nine banks are efficient (i.e.45% banks distribution data covered) and having score one.
Descriptive Statistics Summary of Overall Banks using BCC model using R software
>summary(e)
Summary of efficiencies
The technology is vrs and input orientated efficiency
Number of firms with efficiency==1 are 9
Mean efficiency: 0.98
Min.1st Qu.Median Mean 3rd Qu. Max. 0.8952 0.9654 0.9917 0.9803 1.0000 1.0000
The below Spearman’s rank correlation test result show, it has applied for testing comparison between rank obtained through CCR model, BCC model and Multiple Regression model. Result indicates that CCR model and Multivariate regression model are positively correlated with each other and its correlation is 0.961.Also result indicates that Multiple regression and BCC model of DEA are positively correlated with each other but as compare to CCR model are less correlated.
See table no. 3
Table 3: Spearman’s Rank correlation test
This paper presents a unique approach of DEA &Multivariate Regression Analysis for evaluating Indian banks performance. We have considered group of Nationalised Indian Banks (i.e. 20 banks), it has been analyzed for effectiveness using DEA & Multivariate Regression Analysis. We have investigated the performance of Indian banks by using input orientated CCR, BCC based DEA model &Multivariate Regression Analysis (Result has been shown in table 2). The result shown that the Bank of Baroda, IDBI banks ltd and Punjab National Banks has most efficient. We have tested and verify the relative efficiency results of CCR model, BCC model and Multivariate regression model using nonparametric Spearman rank test. The results show that there is positively and significantly correlated between the set of rankings. This study provides scope for further research using larger input sample size to test the robustness of the results.
