In the previous article “Importing the data and defining the variable” the steps for data extraction and execution of results were discussed. Here, the findings for Multi-stage based* constant returns to scale (CRS)* are extracted and analyzed and presented. The findings and the interpretations are on the basis of input-oriented multi-staged *CRS* Data Envelopment Analysis. Input variables are Total Capital and Deposits while the output variables are Total loans and Profits.

## Comparative analysis of bank efficiency in *CRS* model

From the results of efficiency summary; banks 7 and 8. Thus, ICICI bank and HDFC bank has efficiency value of 1.000. Other banks have values less than 1.000 which indicates the need to improve their input variables. This is possible by either decreasing or increasing the input levels.

For example, in case of Allahabad bank, they need to improve its efficiency by 89.2% followed by SBI with 85.8%. In terms of other private banks, Axis banks need to improve its efficiency by 46%.

Thus, a bank is said to have efficient performance when the efficiency value is 1.

## Summary of Slacks

This is a value which shows the discrepancy in the constant or proportional change of input and output variables (Coelli, 2008). It also represents the amount of value for improvement in both input and output. The image below reflects that the 1st bank should either increase or decrease the deposits by 129597.661 to become efficient. Slacks only show the variable discrepancy between the constant output and input. It is only perceived that the value must be either increased or decreased (Cooper, Seiford, & Zhu, 2011). Similarly, the 6^{th} bank can either increase or decrease their input of Total Capitals by 2102.055 to become efficient.

## Summary of Peers

The term Peer or Reference set indicates an inefficient firm to follow or as a reference (Coelli, 2008). The inefficient firms such as bank 1 can follow the input-output trend of any of 8 or 7. But the efficient banks don’t have to follow any firm. Furthermore, peer weight is a number of variables that can be followed for the respective reference firm (Cooper et al., 2011). For the 1^{st} firm, since it has peers value for 7 and 8. Thus, it can follow 0.6% of the total capitals and deposits of bank 8. Furthermore, it can also follow 25% of deposits of the bank 7 to become efficient. Finally, peer count shows the number of times a peer firm is being used as the reference unit. The 8th bank has been used as a peer 5 times, while bank 7 is used 8 times.

## Summary of Targets

This shows the model that is to be followed for the preferred and perceived Total Capitals and Deposits that will help in making the case banks efficient (Cooper et al., 2011). However, the Total Capitals and Deposits (input targets) remain the same for efficient organizations. Thus, for Bank 1; for constant output of Total Loans and Profits, it must have an efficiently proportional Total capital of 710170.519 and Deposits of 98048.384. So Bank 1 can increase the financials of Total Capitals by 710170.519 and Deposits by 98048.384. Similar interpretations are possible for all inefficient banks.

Target value are different from slacks value. Slacks show discrepancies while Summary of targets show predicted value.

The graph below show the percentage of difference change. 0% change shows that the banks are efficient and do not need to change their values. For bank 1 it needs to change its total capital by 86% and deposits by 93% to become efficient. Similar interpretations are possible for other banks as well.

## Radial Movement, Slack Movement, and Projected Value

The Radial Movement shows the adjusted proportionality of input and output variables (Coelli, 2008). Radial Movement gives the value for input-output variables for improvement (Coelli, 2008). The radial values for the bank 1 are -193903.733 for Total capital, Deposits is -1485544.680 and -129597.661. The projected value of input for the 1^{st} bank against each output is 32002.267 (Total Capital) and 115579.658 (Deposits).

Bank 1 can adopt Total Loans of 1870260.000 and Total profit of 258214.000 output values to achieve efficiency. The values are to be decreased by -193903.733 and -1485544.680 for Total Capital and Deposits respectively. Similarly, interpretations are possible for other inefficient firms. Projected value shows the proportionality of input and output for every radial and slack movement.

Multi-stage based *CRS* analysis (Output-oriented) is represented in the next article across case firms based on output variables.

#### References

- 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. - Cooper, W. W., Seiford, L. M., & Tone, K. (2007).
*Data Envelopment Analysis*.*Data Envelopment Analysis: A Comprehensive Text with Models, Applications, References and DEA-Solver Software: Second Edition*. https://doi.org/10.1007/978-0-387-45283-8. - Cooper, W. W., Seiford, L. M., & Zhu, J. (2011). Handbook on Data Envelopment Analysis. In
*Chapter 1:Data Envelopment Analysis*(pp. 1–39). https://doi.org/10.1007/978-1-4419-6151-8_1.

Interpreting summary of peers and projected values in VRS-DEA | Output oriented DEA to determine the efficiency of private and public sector banks |

### Avishek Majumder

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can v plot time series data in DEAP. i want to find out the result of 1 dmu for 11,10 and 35 years respectively.

Hi Neha,

Good Day!

Yes, you can use time series data in DEAP, even for 1 DMU.

Dear sir

if you have the interpretation of frontier output using frontier 4.1?

Hi Thaya,

Apologies for the delayed response. I have been working on Frontier DEA. Will soon present the outcomes and interpretations.

Hi there,

How you got the % number in this “For example, in case of Allahabad bank, they need to improve its efficiency by 89.2% followed by SBI with 85.8%. In terms of other private banks, Axis banks need to improve its efficiency by 46%.”

Also, what is the right answer of why you used only CRS why not CCR, VRS or BCC? If I would like to use the DEA which one of CRS, CCR, VRS and BCC I should use.

Dear Mike,

Apologies for the delayed response.

As per your query for %, any efficiency value is shown by 1, which means 100%. If any of the DMUs show 0.87 efficiency score, it means the DMU show efficiency of 87% with lags of 13%.

First, you have to choose if you want the CCR model or BCC model. These are two basic models in DEA, then you may show if you want to show constant returns or variable returns.

can we use above 50 variables in DEAP 2.1

Hi Meena,

No in DEAP we cannot use more than 15 variables (output and input included). You may use MaxDEA basic.

Hello Mr. Majumder,

Please could you explain me how to calculate the percentage of change in each inputs of the firms or banks according to your example to become efficient.

Thanks you in advance!!