In the previous article, execution of cost efficiency using data envelopment analysis program (DEAP). Moreover, differences between Multi-stage and Cost- **data envelopment analysis (DEA)** was also discussed. However, the article will only interpret the results from cost efficiency analysis from the constant returns to scale (CRS) frontier.

## Summary of technical, allocative and cost efficiency

As mentioned in the previous article in the differences section, performing Cost-**DEA** in DEAP gives three efficiency measures, technical, allocative and cost efficiency (Beasley, 2003). However, the technical efficiency shows the same results as we had found while interpreting the input-oriented multi-stage CRS-DEA. Moreover, amongst the ten banks, bank 7 (ICICI bank) and bank 8 (HDFC bank) show technical efficiency of “1” reflecting the highest efficiency of two banks.

### Allocative efficiency

Coelli, (2008, p.4), defines Allocative efficiency as “efficiency measure that reflects the ability of a firm to use the inputs in optimal proportions, given their respective prices”. However, Coelli, (2008) also mentions that allocative efficiencies are similar to slacks. However, allocative efficiency is given by the ratio of the minimum costs required by the DMU to produce a given level of outputs (cost efficiency) and the actual costs of the decision making units (DMU) adjusted for Technical Efficiency (TE) (Brack & Jimborean, 2009).

Allocative efficiency= Cost efficiency/technical efficiency

Henceforth the graph indicates bank 7 (ICICI bank) and bank 8 (HDFC bank) with allocative efficiency value of “1”. So, bank 7 and bank 8 are using its input in proportion by minimizing its cost for costs to labor and fixed deposits prices. The inefficient bank 1 (SBI), however, can minimize its input costs of total capitals and deposits by 0.03% to become efficient for given prices of costs to labor and fixed deposits prices. Similar interpretations can be made for all allocative inefficient banks (Akeem & Moses, 2014).

### Interpretations

The results for cost efficiency where both bank 7 (ICICI bank) and bank 8 (HDFC bank) shows *cost efficiency* value of “1”. However, an organization is economically cost efficient if it is both technically and allocatively efficient. Cost efficiency is also known as economic efficiency (Watkins, Hristovska, Mazzanti, Wilson, & Watkins, 2013). Thus, to check the efficiency of banks, cost efficiency is the best model, as it uses both technical and allocative efficiency measures to evaluate cost efficiency (Mokhtar, Abdullah, & Alhabshi, 2007).

Henceforth, efficient banks 7 and 8, are technical and allocative efficient with the cost-efficient value. Furthermore, the inefficient bank 1, are inefficient technically and allocative with 0.141. Moreover, bank 1 has to minimize its total capitals and deposits by 85.9% to become *cost-efficient*.

Furthermore, the graph represents inefficient banks such as Bank 9 (Vijaya Bank) to improve its input values (total capitals and deposits) by 89.7% to become *cost-efficient*.

## Summary of cost minimizing input quantities

Summary of cost minimizing input quantities is similar to projected values of input-oriented multi-stage CRS-DEA (Watkins et al., 2013). However, the values represented on the basis of given prices of costs to labor and fixed deposits is the only difference. Furthermore, the values are not dependent on constant values of Loans and Profits (output variables). However, in the summary of efficiencies, bank 7 and 8 showed efficiency technically, allocatively and costs.

### Interpretations

Thus, in the values below, there is no change of these banks for total capitals and deposits. However, bank 1 showed inefficiency and total capitals and deposits must decrease by 32002.267 and 115579.658 to become cost-efficient. These inputs lowered by 85.9% with a cost-efficient value of 0.141. Similarly, bank 5 (United Bank of India) which showed a cost-efficient value of 0.014 needs to minimize its inputs by 98.6%. Thus, bank 5 has a minimized projected value of 1891.087 and 5735.817 for total capitals and deposits respectively. Similar interpretations for other inefficient banks.

Henceforth, the graph presents a number of input finances changed. In addition, the banks would show efficiency at given constant prices of the costs to labor and fixed deposits. However, cost **DEA** indicates that the inefficient banks must minimize their total capitals and deposits to a great extent to become cost-efficient.

Furthermore, in the next article, we will execute Cost** DEA **variable returns to scale (VRS) model to check if the findings are similar to the current findings of not.

#### References

- Akeem, U. O., & Moses, F. (2014). An empirical analysis of allocative efficiency of Nigerian commercial Banks: A DEA approach.
*International Journal of Economics and Financial Issues*,*4*(3), 465–475. Retrieved from http://www.scopus.com/inward/record.url?eid=2-s2.0-84922984119&partnerID=40&md5=084ad9548d1587a4660be16dae7c8731. - Beasley, J. E. (2003). Allocating fixed costs and resources via data envelopment analysis.
*European Journal of Operational Research*,*147*(1), 198–216. https://doi.org/10.1016/S0377-2217(02)00244-8. - Brack, E., & Jimborean, R. (2009).
*The Cost-Efficiency of French Banks*. Paris. - 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, William W.Seiford, Lawrence M. Tone, K. (2007).
*DATA ENVELOPMENT ANALYSIS A Comprehensive Text with Models , Applications , References Second Edition*(2nd ed.). New York: Springer. - Mokhtar, H. S. A., Abdullah, N., & Alhabshi, S. M. (2007). Technical and Cost Efficiency of Islamic Banking in Malaysia.
*Review of Islamic Economics*,*11*(1), 5–40. - Shahooth, K., Al-delaimi, K., & Battall, A. H. (2006). Using Data Envelopment Analysis To Measure Cost Efficiency With an Application on Islamic Banks.
*Scientific Journal of Administrative Development*,*4*, 134–156. - Watkins, K. B., Hristovska, T., Mazzanti, R., Wilson, C. E., & Watkins, B. (2013). Measuring technical, allocative, and economic efficiency of rice production in Arkansas using Data Envelopment Analysis.
*Southern Agricultural Economics Association (SAEA) Annual Meeting*, (Associate and Agricultural Economist), 1–31.

### Avishek Majumder

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