Executing and interpreting cost efficiency of banks through VRS cost DEA

By Avishek Majumder & Priya Chetty on December 24, 2017

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.

Priya is the co-founder and Managing Partner of Project Guru, a research and analytics firm based in Gurgaon. She is responsible for the human resource planning and operations functions. Her expertise in analytics has been used in a number of service-based industries like education and financial services.

Her foundational educational is from St. Xaviers High School (Mumbai). She also holds MBA degree in Marketing and Finance from the Indian Institute of Planning and Management, Delhi (2008).

Some of the notable projects she has worked on include:

  • Using systems thinking to improve sustainability in operations: A study carried out in Malaysia in partnership with Universiti Kuala Lumpur.
  • Assessing customer satisfaction with in-house doctors of Jiva Ayurveda (a project executed for the company)
  • Predicting the potential impact of green hydrogen microgirds (A project executed for the Government of South Africa)

She is a key contributor to the in-house research platform Knowledge Tank.

She currently holds over 300 citations from her contributions to the platform.

She has also been a guest speaker at various institutes such as JIMS (Delhi), BPIT (Delhi), and SVU (Tirupati).



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