# MALMQUIST index summaries interpretations from DEA

In the previous article, we had discussed and interpreted results and terms from the results of distance summaries in Malmquist* ***data envelopment analysis (DEA)**. This article, discusses and interprets the rest of the results from Malmquist **DEA***. *Furthermore, the analysis of Malmquist index summaries for both output and input frontiers are interpreted.

Malmquist index summary indicated and introduces effch as technical efficiency change, techch as technological change, pech as pure technical efficiency change, sech as scale efficiency change and tfpch as total factor productivity change (TFP) (Coelli, 2008).

## Interpretations and definitions of Malmquist index (input-oriented)

Technical efficiency change shows the change in the amount of output produced from constant input due to changes in financial values (Kumar & Gulati, 2008). However, both hospital 1 and 3 (Apollo and Wockhartd) showed efficiency for technical change for year 2 and 3 (2014-2015 and 2015-2016). On the contrary, Fortis Hospital showed inefficiency of 0.796 for year 2 and 0.972 for year 3. Hence, Hospital 2 needs to improve its average revenues per occupied bed and revenue from operations by either increasing or decreasing its operative and salaries expenditure by 20.4% for the year 2014-2015. Similar implications with 2.8% change for the year 2015-2016 to become efficient.

### Technological change

It is however different from technical efficiency. It shows the increase of output finances over constant input finances (Gulati, 2011). All the hospitals are inefficient and thereby needs to increase its average revenues per occupied bed and revenue from operations by 71.6% (Apollo), 81.5% (Fortis) and 84.9% (Wockhartd) for the year 2014-2015. Similarly, changes required are 3.4% (Apollo), 0.7% (Fortis) and 2.3% (Wockhardt) for the year 2015-2016 over constant operative and salaries expenditure to become efficient.

### Pure technical efficiency change

It is the value provided by the overall technical efficiency from *variable return to scale (VRS)* model (Gulati, 2011; Kumar & Gulati, 2008). Thereby, inefficient utilization of input finances there indicates a change in the pure technical efficiency. However, from the analysis, the pure technical efficiency of the case hospitals is 1.000. Henceforth, the hospitals have been appropriately utilizing its operative and salary expenditure for efficient average revenues per occupied bed and revenue from operations.

Pure technical efficiency is given by PTE= OT x SE. Where; PTE is pure technical efficiency, OT is overall technical efficiency and SE is scale efficiencies.

### Scale efficiency change

It is another part of the overall technical efficiency given by *VRS* model. The efficiency change shows the increasing or decreasing returns to scale. However, the analysis indicated Fortis hospital with variable returns to scale inefficiency of 27.4% and 2.8% for the years 2014-2015 and 2015-2016 respectively. Henceforth, hospital 2 either has increasing returns or decreasing returns by 27.4% and 2.8% for the years 2014-2015 and 2015-2016 respectively.

Scale efficiency is given by the ratio of overall technical efficiency upon pure technical efficiency (Gulati, 2011; Kumar & Gulati, 2008).

### Total factor productivity change

It is a variable which indicates total output growth relative to the rise in financial inputs (Comin, 2006). Total Factor Productivity (TFP) is a part of output independent of inputs for checking production efficiency (Afonso, Ayadi, & Ramzi, 2013). Henceforth, the efficiency and intensity of the inputs utilized in producing effective results for the organization. This value is totally dependent on the pure technical, technical and technological efficiency of the organization. However, analysis indicated that in the year 2014-2015, the hospitals showed growth in output by 28.4% (Apollo), 14.7% (Fortis) and 15.1% (Wockhartd). On the contrary, for the year 2015-2016, growth in output was 96.6% (Apollo), 96.5% (Fortis) and 97.7% (Wockhartd). Henceforth for bank 1, the productivity rose by 68.2% for technological and technical change by 1.000 and 0.966 respectively.

Quick note:Values for 1^{st}year was not represented from the analysis as for the hospitals with data for 2012-2013 was not available. Henceforth, could not contrast the output and input finances and thereby could not provide results for 2013-2014 (Coelli, 2008).

## Interpretations and definitions of Malmquist index (output-oriented)

Similarly, output-oriented Malmquist **DEA** found that the technical and technological efficiency changes gave the same results as in input-oriented. Henceforth, similar interpretations made as done in the previous section. However, *VRS* model found that in the year 2014-2015 the pure technical efficiency for hospital 2 was 0.257 and scale efficiency change of 0.634, different from the input-oriented result. Henceforth, the similarity in results indicates both *CRS* and *VRS* model’s productivity index always based on the appropriate utilization of input variables.

## Malmquist index for annual means and firm means

The analysis for the annual means indicated for the year 2014-2015, the total factor productivity change with 0.185 or 18.5% from the previous year (2013-2014). However, it rose to 0.969 or 96.9% on an average for all the hospitals. Henceforth, for the year 2014-2015, a growth in the output variables by 18.5% contributed by the technical and technological change of 0.927 and 0.200 on an average. Similar interpretation possible for the year 2015-2016.

However, in case of annual means and firm means values on contrasting to input oriented Malmquist **DEA** showed similar results. Furthermore, in case of annual mean, the year 2014-2015 showed variation in pure technical efficiency and scale efficiency with 1.079 and 0.859 respectively. Moreover, the firm mean for hospital 2 for pure technical efficiency and scale efficiency are 1.121 and 0.785 respectively. Thereby, indicating that productivity index dependent on the appropriate utilization of input variables.

## Concluding the ranks of the hospitals

Lastly, after all the evaluations the technical efficiency change for hospital 1 was 1.000. Furthermore, technological efficiency of 0.524 from the *CRS* model and pure and scale efficiency change by 1.000 and 1.000 from the *VRS* model giving a productivity value of 0.524. Similar interpretations possible for hospital 2 and 3. Henceforth, no significant change or differences on evaluations of input and output oriented Malmquist** DEA** seen.

However, from the total factor productivity value, the rank of the hospital are presented. The table shows the hospitals with the best productivity whereby optimally utilizing the input variables are represented in the table below (Afonso et al., 2013).

Table for comparing the productivity index of the case hospitals;

Hospital |
TFP value |
Rank |

Apollo | 0.524 | 1 |

Fortis | 0.377 | 3 |

Wockhartd | 0.385 | 2 |

Henceforth, the best productivity index presented by Apollo Hospital. However, Malmquist **DEA** never shows benchmarking values. Multistage **DEA** is performed to benchmark the hospitals.

#### References

- Afonso, A., Ayadi, M., & Ramzi, S. (2013). Assessing productivity performance of basic and secondary education in Tunisia: a Malmquist analysis.
*Working Papers Department of Economics 19, ISEG – School of Economics and Management*,*5*(1), 104–128. - 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. - Comin, D. (2006). Total Factor Productivity.
*New York University*, (August), 1–5. http://doi.org/10.1057/9780230280823_32. - Gulati, R. (2011). Evaluation of technical , pure technical and scale efficiencies of Indian banks : An analysis from cross-sectional perspective Estimation of technical , pure technical and scale efficiencies of Indian banks : An analysis from cross-sectional perspective.
*The 13th Annual Conference on Money and Finance in the Indian Economy*, 1–30. - Kumar, S., & Gulati, R. (2008). An examination of technical, pure technical and scale efficiencies in GCC banking.
*American J. of Finance and Accounting*,*1*(2), 152. http://doi.org/10.1504/AJFA.2008.019950.

## Discuss