The Malmquist productivity index or more commonly malmquist DEA (Data Envelopment Analysis) was first incepted by the researcher Malmquist in 1953 as a quantity to be used in the analysis of consumption of inputs (Färe, Grosskopf, & Margaritis, 2011).
R. S. Fare in 1994, however, developed a DEA-based Malmquist productivity index to check the productivity change over time (Fuentes & Lillo-Bañuls, 2015). In addition, according to Färe et al., (2011); the index decomposed into two components, one measuring the change in the technology frontier and the other the change in technical efficiency. The Malmquist productivity index can measure the ratio of DEA efficiencies in two different time periods with shifting DEA efficiency frontiers (Coelli, 2008). Färe et al., (2011) mentions that Malmquist productivity index can theoretically divided into two components;“catch-up” and “frontier shift”. However, the catch-up measures how much closer to the frontier a Decision Making Unit (DMU) or organization moves, while the frontier does not move. Moreover, frontier is composed of DEA efficiency measure. However, DMUs’ among all firms in a time period; the frontier shift means change at industry level.
Key features of Malmquist DEA
Furthermore, in the following points key features of Malmquist DEA to differentiate it between Cost efficiency and Multistage DEA is discussed.
- Best for productivity index testing along with efficiency measurement.
- It only works for more than one time period for any given DMU.
- Requires input and output variables for all the years.
- Balanced data for all the years and firms.
- Can perform both CRS (constant returns to scale) and VRS (variable returns to scale)– DEA and input and output oriented DEA.
Applications of Malmquist DEA
- To check the timelines of change in efficiencies over the period which is given by the malmquist productivity index (Fuentes & Lillo-Bañuls, 2015).
- Assess the performance of the organizations of over more than one year (Färe et al., 2011).
- In addition, to contrast the performance measurement and efficiency and to check the consistency of the DMUs (Yoruk & Zaim, 2005).
- Consequently another application is that it can be used to measure the productivity growth over the time and its efficiency change and technological change (Liu & Wang, 2008).
- Finally, one major application and advantage over other models is that it can be used for regress and progress of a DMU in different periods with efficiency and technology variations without considering the present value of money (Liu & Wang, 2008).
Hospitality Industry in India; A case study
This study considered three renowned hospitals of India, namely; Apollo Hospital, Fortis Hospital and Wockhartd Hospitals. Furthermore, in this case study, the data extracted from the annual reports of the three hospitals available at their official website. However, the annual reports range is for the years 2014 to 2016 (3 years). Hence in this study three years of timeline is considered. Moreover, for relevance of the study the input and output variables from the research done by Bhat, Verma, & Reuben, (2001) on hospitality industry has been adopted. Consequently, the input variable were; Total Expenditure and Number of Doctors and Nurses, while the output variables are Average revenue per occupied bed per day and Revenue from operations. Furthermore, both the frontiers will be conducted; CRS (constant returns to scale) and VRS (variable returns to scale) for Malmquist DEA to understand the change of findings and results.
Extracting and presenting the data in Malmquist DEA
- Extract data from the annual reports and present in MS Excel
- Next, input the data in Notepad
- Finally, open the instruction file and change the codes as follows
- Change the Time Period to 3 (Since this is a dataset with three years of information)
- Next, 0 for Input oriented
- Change to 0 for CRS-DEA
- Next, 2 for both Input and output
- Change to 2 for Malmquist DEA
- Finally add no. of firms to 3
Malmquist DEA is a model that is best used when there is more than one year of data and malmquist productivity index is to be found. However here efficiency evaluation of firms whereby financial data considered to conduct Malmquist DEA. Lastly, in the next article however, we will represent the findings and interpretations from evaluating Malmquist CRS-DEA.
- Bhat, R., Verma, B. B., & Reuben, E. (2001). Hospital Efficiency: An Empirical Analysis of District Hospitals and Grant-in-aid Hospitals in Gujarat. Journal of Health Management, 3(2), 167–197. https://doi.org/10.1177/097206340100300202.
- 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.
- Färe, R., Grosskopf, S., & Margaritis, D. (2011). Malmquist productivity indexes and DEA. In International Series in Operations Research and Management Science (Vol. 164, pp. 127–149). https://doi.org/10.1007/978-1-4419-6151-8_5.
- Fuentes, R., & Lillo-Bañuls, A. (2015). Smoothed bootstrap Malmquist index based on DEA model to compute productivity of tax offices. Expert Systems with Applications, 42(5), 2442–2450. https://doi.org/10.1016/j.eswa.2014.11.002.
- Liu, F. H. F., & Wang, P. hsiang. (2008). DEA Malmquist productivity measure: Taiwanese semiconductor companies. International Journal of Production Economics, 112(1), 367–379. https://doi.org/10.1016/j.ijpe.2007.03.015.
- Yoruk, B. K., & Zaim, O. (2005). Productivity growth in OECD countries: A comparison with Malmquist indices. Journal of Comparative Economics, 33(2), 401–420. https://doi.org/10.1016/j.jce.2005.03.011.