Applied decomposition of Malmquist, cost Malmquist, and allocation Malmquist indices by considering changes in cost-efficiency and technology

Document Type : Research Paper

Authors

1 Behin KaraPajouhesh Institute of Operations Research, Tehran, Iran

2 School of Mathematics, Iran University of Science and Technology, Tehran, Iran

Abstract

So far, various decompositions of the Malmquist productivity growth index have been presented. Although factors such as efficiency, scale, and technology have already been examined, there is no factor measures productivity growth from a financial perspective by covering costs. The purpose of this article is to show the impact of cost-efficiency changes as an important component on the productivity growth indices. This article evaluates the rate of productivity growth in the cost space and decomposes the Malmquist productivity growth index into components of cost-efficiency and Allocative efficiency. Then a similar Decomposition for the cost Malmquist index and the allocation Malmquist index based on changes in cost-efficiency and price effect obtained. In the following, we get the relation between the Malmquist index, the Cost Malmquist index, and the allocation Malmquist index with changes in technology and cost-efficiency. Then we model, and calculate the parsing factors of Malmquist indices related to decision-making units using data envelopment analysis and input distance functions. Finally, the data obtained from a real case study modeled and compared the results of previous Malmquist indices with the new Malmquist indices, and the preference of new decompositions have been analyzed.

Keywords

Main Subjects

References

Banker, R.D., Charnes, A., Cooper, W.W. (1984).Some models for estimating technical and scale inefficiency in data envelopment analysis. Management Science, 30(9), 1078-1092.
Brooke, A.D., Kendrick, A., Meeraus, A., Raman, A. (1998). GAMS: A User Guide. GAMS Development Corporation, Washington, DC.
Camanho, A.S., Dyson, R.G. (1999). Efficiency, size, benchmarks, and targets for bank branches: An application of data envelopment analysis. Journal of Operational Research Society, (50), 903-915.
Camanho, A. S., Dyson, R.G. (2005). Cost efficiency measurement with price uncertainty: a DEA application to bank branch assessment. European Journal of Operational Research, 161(2), 432-460.
Camanho, A.S., Dyson, R.G. (2008).A generalization of the Farrell cost-efficiency measure applicable to non-fully competitive settings. Omega, 36(1), 147-162.
Caves, D. C., Christensen, L. R., Divert, W. E. (1982).The economic theory of index number and the measurement of input, output, and productivity. Econometric a, 50(6), 1393-1414.
Charnes, A., Cooper, W.W., Lewin, A.Y., Seiford, L.M. (1994). Data Envelopment Analysis: Theory, Methodology, and Applications. Kluwer Academic Publishers, Norwell, MA
Charnes, A., Cooper, W. W., Rhodes, E. (1978).Measuring the efficiency of decision-making units. European Journal of Operational Research, 2(6), 429-444.
Cooper, A.Y., Lewin, L.M. Seiford (Eds.), Data Envelopment Analysis: Theory, Methodologies, and Applications, Kluwer Academic Publishers, Boston, 1995.
 
Cooper, W.W., Seiford, L.M., Tone, K. (2000). Data envelopment analysis: A comprehensive text with models, applications, references, and DEA-solver software. Kluwer Academic Publisher, Dordrecht.
 
Fang, L., Li, H. (2015). Cost efficiency in data envelopment analysis under the law of one price. European Journal of Operational Research, 240(2), 488-492.
 
Fare, R., Bogetoft, P. (2006).Allocative efficiency of technically inefficient production units., European journal of operational research, (168), 450-462.
 
Fare, R., Grosskopf, S, Understanding the Malmquist productivity index, Discussion Paper no. 94-95, Southern Illinois University, Illinois, 1994.
 
Fare, R., Grosskopf, S., Lindgren, B., Roos, P. (1992), Productivity changes in Swedish analysis pharmacies (1980-1989) a non-parametric Malmquist approach. Journal of Productivity, 3, 85-102.
 
Fare, R., Grosskopf, S., Norris, M., Zhang, A. (1994), Productivity growth, technical progress, and efficiency changes in an industrial country. American Economic Review, 84(1), 66-83.
 
Fare, R., Primont, D. (1995).Multi-output production and duality: Theory and application, Springer Science.
 
Farrell, M.J., (1957).The measurement of productive efficiency, Journal of the Royal Statistical Society, (120), 253-81.
 
Malmquist, S. (1953).Index numbers and indifferent surface: Trabuco’s de Statistical, (4), 209-242.
Maniadakis, N., Thanassoulis, E., (2004).A cost Malmquist productivity index. European Journal of Operational Research, 154(2), 396-409.
 
Paradi, J.C., Zhu, H., (2013).A survey on bank branch efficiency and performance with data envelopment analysis. Omega, 41, 61-79.
Ray, S. C. (1988). Data Envelopment Analysis, nondiscretionary inputs, and efficiency: an alternative interpretation. Socio-Economic Planning Sciences, (22)4, 167–176.
Shephard, R.W., Theory of Cost and Production Functions, Princeton University Press, Princeton, New Jersey, 1970
 
Thanassoulis, E., Silva, M. C. A., (2018).Measuring Efficiency through Data Envelopment Analysis, Impact, 2018(1), 37-41.
 
Walheer, B. (2018). Cost Malmquist productivity index: an output-specific approach for group comparison. Journal of productivity analysis, 49(1), 79-94.
 
Walheer, B., (2018).Disaggregation of the cost Malmquist productivity index with joint and output specific inputs. Omega, 75(3), 1-12.
Journal of Industrial and Systems Engineering
Volume 13, Issue 3
July 2021
Pages 41-60

Files

History

  • Receive Date: 01 December 2020
  • Revise Date: 01 May 2021
  • Accept Date: 01 June 2021

Share

How to cite

Statistics