Executing and interpreting cost efficiency of banks through VRS cost DEA

In the previous article, discussed and interpreted the findings of cost efficiency using constant returns to scale (CRS) Cost Data Envelopment Analysis (DEA). Here, in the current article, variable returns to scale  or VRS cost DEA to check the variation of results from CRS cost DEA and will interpret the results accordingly.

Changes in instruction file for VRS cost DEA

The following changes are must for performing VRS cost DEA;

  1. Replace the code in the second last line to “1” so that while executing VRS frontier is achieved
  2. Rename the results file according to need
Instruction file for executing VRS Cost DEA

Instruction file for executing VRS Cost DEA

However, the variables for total capitals, deposits, total loans, profits, costs to labor and fixed deposit rates are same as used in the previous article. Furthermore, input-oriented efficiency analysis is conducted in this article. Thus, increasing or decreasing returns to scale depending on the input variable (total capital and deposits). Furthermore, to check that, same price values can be used for using VRS cost DEA, as mentioned in the book by Huguenin, (2012), where the author has discussed the price variables for VRS model. DEAP.EXE file was run to execute VRS cost DEA.

Summary of efficiency measures

Efficiency Summary result

Efficiency summary result

Technical efficiency

Analysis of the VRS cost DEA indicated technical efficiency for four banks, bank 7 (ICICI), bank 8 (HDFC), bank 9 (Vijaya bank) and bank 10 (Nainital Bank). Thus, these banks have technical efficiency and need not minimize its input values. Furthermore, the inefficient bank 6 (Axis Bank), the technical efficiency is 0.079. Thus, bank 6 will have to decrease its total capitals and deposits by 92.1% to become efficient for variable change in loans and profits (the values of outputs also change in VRS technical efficiency as mentioned while performing VRS DEA). Due to variable change in both input and output for given price values, the inefficient banks will have to minimize their values for higher outputs at minimal inputs (Coelli, 2008). Similar interpretations for inefficient banks.

Graph showing technical efficiency

Graph showing technical efficiency

Allocative efficiency

Allocative efficiency shows the ability of a firm to use the inputs in optimal proportions, given their respective prices (Kocisova, 2014). Three banks; 7, 8 and 9 showed allocative efficiency. The efficient banks are using their input in proportion by minimizing its finances for given costs to labor and fixed deposit prices. In case of bank 6, which has allocative efficiency of 0.767, reflects that it will have to minimize it input finances by 23.3%. By minimizing the finances for total profits and deposits bank 6 can become allocative efficient. Similar interpretations or other inefficient banks.

Please note: Bank 10 shows technically efficient but is not allocative efficient. This is because even though technically the bank is efficient. However, for price value the total capitals and deposits must decrease by 40% to become allocative efficient. Technical efficiency does not calculate price values but allocative efficiency and cost efficiency does.

Graph showing Allocative efficient banks

Graph showing Allocative efficient banks

Cost efficiencies

Cost efficiency show poor cost management and poor cost management leads to lower bank profits (Kocisova, 2014). However, bank 7, 8 and 9 are cost efficient banks. This remains same because as mentioned in previous articles, cost efficiency is dependent on organizations that are both technically and allocative efficient. Moreover, inefficient bank is 6th bank with a value of 0.061. Cost efficiency is given by the multiplication of allocative efficiency and technical efficiency. Moreover, actual costs or finances must decrease in order to increase the returns to scale by 93.9%.

Graph showing Cost efficient banks

Graph showing Cost efficient banks

Summary of cost minimizing input quantities

The VRS cost DEA indicated bank 6 as inefficient, it can be interpreted that; in order to lower or minimize the input values by 93.9%, the total capitals should be 6190.893 and deposits should be 60195.281 against initial values of 105833.000 and 357968.000. Similarly for bank 5 (United Bank of India), according to cost efficiency, it needs to minimize its value by 96.3% for the cost efficient value of 0.037. Thus, banks 5 which initially had values of 131952.000 and 116401.000 for total capitals and deposits, will now decrease its total capitals and deposits by 4759.031 and 49002.678 to become cost efficient.

Cost minimizing summary

Cost minimizing summary

Percentage of minimizing change for Total Capitals and Deposits to become cost efficient

Percentage of minimizing change for Total Capitals and Deposits to become cost efficient

Furthermore, the graph indicates that efficient banks 7, 8 and 9 need not change its values by 0%. Thus, a 0% change in total capitals and deposits shows efficient bank or organization. However, inefficient banks like bank 3 (Central Bank of India) needs to minimize its total capitals by 70% and deposits by 84%. Thus, by minimizing the values will make the bank efficient. Similar interpretations for other inefficient banks.

Comparing the variations of findings from CRS cost DEA

Only a few minute differences from the findings fro both CRS and VRS cost DEA. They are;



Only two banks were efficient in terms of technical, allocative and cost efficiency Three banks were efficient for allocative and cost efficiency, but four banks were efficient for technical efficiency
Percentage minimization change is higher e.g. Bank 1 showed minimization by 85.9% Percentage minimization change is higher e.g. Bank 1 showed minimization by 85.1%

The table shows variation in the values of cost efficiency on performing both CRS and VRS cost DEA. In CRS frontier, the output variables remain constant, while in VRS frontier, output variable does not remain constant, but changes proportionally to scale efficiencies (Coelli, 2008).

In the next article, we will evaluate another model of DEA, i.e. Malmquist DEA using the data envelopment analysis program (DEAP). This will help to differentiate and understand its importance in performing efficiency or benchmarking tests.


  • Coelli, T. J. (2008). A Guide to DEAP Version 2.1: A Data Envelopment Analysis (Computer) Program. CEPA Working Papers, 1–50. Retrieved from https://absalon.itslearning.com/data/ku/103018/publications/coelli96.pdf.
  • Huguenin, J.-M. (2012). Data Envelopment Analysis (DEA) – A pedagogical guide for decision makers in the public sector (Vol. 41). Lausanne: idheap.
  • Kocisova, K. (2014). Application of Data Envelopment Analysis to Measure Cost, Revenue and Profit Efficiency. Statistika, 94(3), 47–94.
Avishek Majumder

Avishek Majumder

Research Analyst at Project Guru
Avishek is a Master in Biotechnology and has previously worked with Lifecell International Private Limited. Apart from data analysis and biological research, he loves photography and reading. He loves to play football and basketball in his spare time with an avid interest in adventure and nature. He was also a member of the Scouts in his school and has attended Military training.
Avishek Majumder

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