# Output oriented DEA to determine the efficiency of private and public sector banks

By Avishek Majumder & Priya Chetty on September 22, 2017

The previous article depicts the analysis and interpretation of the Input oriented multi-staged constant returns to scale (CRS). Output oriented multi-staged Constant returns to scale data envelopment analysis (CRS-DEA) is, however, based on a different principle. It says that “an inefficient unit is made efficient through the proportional increase of its outputs, while the inputs proportions remain unchanged” (Coelli, 2008).  The output variables are either increased or decreased irrespective of the input variables (Total Capital and Deposits).

## Efficiency based on Output oriented CRS-DEA

Bank 7 and 8 are efficient with values of 1.000 amongst the 10 sample banks. Bank 7 and 8 are only Banks that has an efficient or proportional Total Loans and Profit. Interpretation for the Banks indicates the need to improve Total Loans and Profits by either decreasing or increasing the Total Loans and Profits levels. 86% for Bank 1, 89% for 2, 68% for Bank 3 and so on for other Banks.

The above figure, shows the trend of case banks in the case of efficient of output oriented analysis.

## Summary of slacks

Next, in the analysis is the summary of slacks. As mentioned before, the summary of slacks represents the value which shows the discrepancy in the constant or proportional change of Output and Input variables. The analysis, indicated that all the Banks except for 7 and 8, has slacks that caused a proportional change of Output and Input variables. Interpretation indicates that Bank 1 with the proportionality of Total Loans and Profit (output variables) either decreased or increased by 914837.979 to become efficient. Similarly, Bank 6 has to improve its efficiency by increased or decreased Total Loans and Profit by 38976.844. For the rest of the inefficient Banks, similar interpretations are to be made.

## Summary of Peers

Interpretation indicates that Bank 1 must either follow the input-output variables of 7th and 8th Bank. Similarly, Banks 2 and 3 can only follow the proportional input-output variables (Total Capital: Deposits: Total Loans: Profits) of 7th Bank. So, as to become efficient given the values of the output variables. This is either because the 2nd and the 3rd Bank do not have the estimated constant Total Capitals and Deposits to follow 8th Bank’s organizational performance model. Again, peer weights of Bank show that the Bank 1 can either follow 44% of the 8th Bank’s values or follow 179% of the 7th Bank’s value. Similarly, Bank 2 can follow 53% of the output variables of Bank 7 to become efficient.

However, Bank 7 and 8 as the benchmarked Bank or reference Bank whose output-input proportionality can be followed to become efficient, has been benchmarked or referred 8 and 5 times respectively.

## Summary of Targets

In case of summary of targets, the Loans and Profit targets (output targets) remain the same for efficient organizations.

For example, Bank 7 and 8 have the same targets, while other banks have targeted total loans and profits (output variables).

Interpretations indicate that Bank 1  with a constant input of Total Capital (225906.000) and Deposits (815884.021) gives efficiently proportional Total Loans of 13202282.048 and Profit of 1822748.739.

The graph shows the percentage of difference change. In this case, between the actual loans and total profits and the projected loans and total profits for the banks to become efficient. For bank 4 it needs to change its loans and total profits by 85% to become efficient. Similarly, for other banks 0% change shows that the banks are efficient and need not change their values.

## Radial movement, slack movement and projected value

Individual bank wise efficiency results (firm by firm results) are the outcome of choosing the ‘Multi-stage’ form of analysis (Coelli, 2008).

Interpretations indicate that the adjusted proportionality of input and output are 11332022.048 and 1564534.739 for the 1st firm. However, there is slack movement in the 2nd bank along with radial movements of 1299187.687 and 478733.944 of 1157187.536. This shows that with a change or improvement of 1157187.536, Bank 2 can become efficient. This is by achieving the projected value of 2614082.223. Thus, for every radial and slack movement, the proportionality of input and output variables is represented as projected value (Gang & Zhenhua, 2014).  Thus, the projected values show the actually perceived variables for proportional input and output values. This can help make an organization efficient.