Global Malmquist and cost Malmquist indexes for group comparison

China; Circularity; Global cost Malmquist index; Global Malmquist index; Groups; Infeasibility; Business and International Management; Social Sciences (miscellaneous); Economics and Econometrics

Abstract :

[en] The Malmquist index (MI) has demonstrated its usefulness in comparing the performances of Decision Making Units (DMUs) performances. The global MI (GMI) has been suggested as a means to overcome three drawbacks of the MI: non-circularity, disparate measurements, and infeasibility. Recently, it has appeared that the MI can also be used to compare groups of DMUs. While this new function of the index has also increased its usefulness, it presents the same drawbacks as the MI. In this paper, we define the global counterpart of the MI for group contexts. We also consider the case where DMUs have an economic optimization behavior by proposing a global cost MI (GCMI). The GCMI requires the observation of the input prices. As it may represent a strong assumption, we propose solutions. These two novel indexes equip the practitioners with a new toolkit. We illustrate the usefulness of our new indexes with the Chinese energy sector.

Disciplines :

Quantitative methods in economics & management

Author, co-author :

Walheer, Barnabé ; Université de Liège - ULiège > HEC Liège : UER > UER Economie : Microéconométrie et économétrie appliquée

Language :

English

Title :

Global Malmquist and cost Malmquist indexes for group comparison

Publication date :

2022

Journal title :

Journal of Productivity Analysis

ISSN :

0895-562X

eISSN :

1573-0441

Publisher :

Springer

Peer reviewed :

Peer Reviewed verified by ORBi

Available on ORBi :

since 17 June 2022

Statistics

Number of views

72 (4 by ULiège)

Number of downloads

65 (1 by ULiège)

More statistics

Scopus citations^®

Scopus citations^®
without self-citations

OpenCitations

OpenAlex citations

Bibliography

Afsharian M, Ahn H (2015) The overall Malmquist index: a new approach for measuring productivity changes over time. Ann Oper Res 226:1–27
Althin R (2001) Measurement of productivity changes: two Malmquist index approachest. J Product Anal 16:107–128
Aparicio J, Crespo-Cebada E, Pedraja-Chaparro F, Santinc D (2017) Comparing school ownership performance using a pseudo-panel database: a Malmquist-type index approach. Eur J Oper Res 256:533–542
Asmild M, Hougaard JL, Balezentis T (2017) Multi-directional productivity change: MEA-Malmquist. J Product Anal 46:109–119
Berg SA, Førsund FR, Jansen ES (1992) Malmquist indexes of productivity growth during the deregulation of Norwegian banking 1980-1989. Scand J Econ 94:211–228
Bogetoft P (1996) DEA on relaxed convexity assumptions. Manag Sci 42:457–465
Brandt L, Van Biesebroeck J, Zhang Y (2012) Creative accounting or creative destruction? Firm-level productivity growth inChinese manufacturing J Dev Econ 97:339–351
Brandt L, Van Biesebroeck J, Zhang Y (2014) Challenges of working with the Chinese NBS firm-level data hina Econ Rev 30:339–352
Camanho AS, Dyson RG (2006) Data envelopment analysis and Malmquist indices for measuring group performance. J Product Anal 26:35–49
Caves DW, Christensen LR, Diewert WE (1982) The economic theory of index numbers and the measurement of input, output and productivity. Econometrica 50:1393–1414
Chambers RG, Färe R (1994) Hicks-neutrality and trade biased growth: a taxonomy. J Econ Theory 64:554–567
Charnes A, Cooper WW (1962) Programming with linear fractional functionals. Nav Res Logist Q 2:429–444
Charnes A, Cooper WW, Rhodes E (1978) Measuring the efficiency of decision making units. Eur J Oper Res 2:429–444
Charnes A, Cooper WW, Wei QL, Huang ZM (1989) Cone ratio data envelopment analysis and multi-objective programming. Int J Syst Sci 20:1099–1118
Chen Y (2003) A non-radial Malmquist productivity index with an illustrative application to Chinese major industries. Int J Product Econ 83:27–35
Chen Y, Ali AI (2003) DEA Malmquist productivity measure: new insights with an application to computer industry Eur J OperRes 159:239–249
Cherchye L, De Rock B, Dierynck B, Roodhooft F, Sabbe J (2013) Opening the black box of efficiency measurement: input allocation in multi-output settings. Oper Res 61:1148–1165
Cherchye L, De Rock B, Walheer B (2015) Multi-output efficiency with good and bad outputs. Eur J Oper Res 240:872–881
Cherchye L, De Rock B, Walheer B (2016) Multi-output profit efficiency and directional distance functions. Omega 61:100–109
Cherchye L, Moesen W, Rogge N, Van, Puyenbroeck T (2007) An introduction to benefit of the doubt composite indicators. Soc Indic Res 82:111–145
Cho T-Y, Wang T-Y (2017) Estimations of cost metafrontier Malmquist productivity index: using international tourism hotels in Taiwan as an example. Empir Econ 31:1–34
Cook WD, Seiford LM (2009) Data Envelopment Analysis (DEA) - thirty years on. Eur J Oper Res 192:1–17
Cooper WW, Seiford LM, Zhu J (2004) Handbook on data envelopment analysis, second edition, Springer
Cooper WW, Seiford LM, Tone K (2007) Data envelopment analysis: a comprehensive text with models, applications, references and DEA-solver software, second edition, Springer
Daraio C, Simar L (2007) Robust and nonparametric methods in efficiency analysis. methodology and applications, Springer
Debreu G (1951) The coefficient of resource utilization. Econometrica 19(3):273–292
Deprins D, Simar L, Tulkens H (1984) Measuring labor efficiency in post offices. In: Marchand M, Pestieau Tulkens H (eds) The Performance of Public Enterprises Concepts and Measurements. Elsevier, Amsterdam, p 247–263
Despotis DK, Sotiros D, Koronakos G (2016) A network DEA approach for series multi-stage processes. Omega 61:35–48
Diewert WE, Fox KJ (2017) Decomposing productivity indexes into explanatory factors. Eur J Oper Res 256(1):275–291
Emrouznejad A, Yang G-L (2016a) CO2 emissions reduction of Chinese light manufacturing industries: A novel RAM-based global Malmquist-Luenberger productivity index. Energy Policy 96:39–410
Emrouznejad A, Yang G-L (2016b) A framework for measuring global Malmquist-Luenberger productivity index with CO2 emissions on Chinese manufacturing industries. Energy 115:840–856
Fang L, Li H (2015) Cost efficiency in data envelopment analysis under the law of one price. Eur J Oper Res 240:488–492
Fang M, Shao S, Yang L (2015) Combining global Malmquist-Luenberger index and generalized method of moments to investigate industrial total factor CO2 emission performance: a case of Shanghai(China). Energy Policy 79:189–201
Färe R, Grosskopf S (1996) Intertemporal production frontiers: with dynamic DEA. Kluwer Academic Publishers, Boston
Färe R, Grosskopf S, Norris M, Zhang Z (1994) Productivity growth, technical progress, and efficiency change in industrialized countries. Am Econ Rev 84(1):66–83
Färe R, Karagiannis G (2017) The denominator rule for share-weighting aggregation. Eur J Oper Res 260:1175–1180
Färe R, Zelenyuk (2003) Aggregation of cost efficiency: indicators and indexes across firms. Eur J Oper Res 146:615–620
Färe R, Zelenyuk (2007) Extending Färe and Zelenyuk (2003). Eur J Oper Res 179:594–595
Farrell M (1957) The measurement of productive efficiency. J R Stat Soc Ser 1, General 120(Part 3):253–281
Fried H, Lovell CAK, Schmidt S (2008) The measurement of productive efficiency and productivity change. Oxford University Press
Frisch R (1936) Annual survey of general economic theory: the problem of index numbers. Econometrica 4:1–38
Fuentes R, Lillo-Banuls A (2016) Smoothed bootstrap Malmquist index based on DEA model to compute productivity of tax offices. Expert Syst Appl 42:2442–2450
Huang C-W, Ting C-T, Lin C-H, Lin C-T (2013) Measuring non-convex metafrontier efficiency in international tourist hotels. J Oper Res Soc 64:250–259
Huang M-Y, Juo J-C (2015) Metafrontier cost Malmquist productivity index: an application to Taiwanese and Chinese commercial banks. J Product Anal 44:321–335
Kao C (2010) Malmquist productivity index based on common-weights DEA: the case of Taiwan forests after reorganization. Omega 38:484–491
Kao, H. Y., & Chan, C. Y. (2013). A discriminative multi-objective programming method for solving network DEA. In Advances in Intelligent Systems and Applications-Volume 1 (pp. 327–335). Springer, Berlin, Heidelberg
Kao C (2017) Measurement and decomposition of the Malmquist productivity index for parallel production systems. Omega 64:54–59
Kao C, Hwang S-N (2014) Multi-period efficiency and Malmquist productivity index in two-stage production systems. Eur J Oper Res 232:512–521
Kao H-Y, Chan C-Y, Wu D-J (2014) A multi-objective programming method for solving network DEA. Appl Soft Comput 24:406–413
Kerstens K, Vanden, Eeckaut P (1999) “Estimating returns to scale using non-parametric deterministic technologies: a new method based on goodness-of-fit”. Eur J Oper Res 113(1):206–214
Kevork LS, Pange J, Tzeremes P, Tzeremes NG (2017) Estimating Malmquist productivity indexes using probabilistic directional distances: an application to the European banking sector. Eur J Oper Res 261:1125–1140
Kuosmanen T, Cherchye L, Sipilainen T (2006) The law of one price in data envelopment analysis: restricting weight flexibility across firms. Eur J Oper Res 170:735–757
Leleu H (2009) Mixing DEA and FDH models together. J Oper Res Soc 60(12):1730–1749.
Li SK, Ng YC (1995) Measuring the productive efficiency of a group of firms. Int Adv Econ Res 1(4):377–390
Malmquist S (1953) Index numbers and indifference surfaces. Trabajos de Estatistica 4:209–242
Maniadakis N, Thanassoulis E (2004) A cost Malmquist productivity index. Eur J Oper Res 154:396–409
Mayer A, Zelenyuk V (2014) Aggregation of Malmquist productivity indexes allowing for reallocation of resources. Eur J Oper Res 238:774–785
O’Donnell CJ (2012) An aggregate quantity framework for measuring and decomposing productivity change. J Prod Anal 38:255–272
Oh DH (2010) A global Malmquist-Luenberger productivity index. J Prod Anal 34:183–197
Oh DH, Lee J-D (2010) A metafrontier approach for measuring Malmquist productivity index. Empir Econ 38:47–64
Oh DH, Lee J-D (2017) A sequential global Malmquist productivity index: productivity growth index for unbalanced panel data considering the progressive nature of technology. Empir Econ 52:1651–1674
Pastor JT, Asmild M, Lovell CAK (2011) The biennial Malmquist productivity change index. Socio-Econ Plan Sci 45:10–15
Pastor JT, Lovell CAK (2005) A global Malmquist productivity index. Econ Lett 88:266–271
Pastor JT, Lovell CAK (2007) Circularity of the Malmquist productivity index. Econ Theory 33:591–599
Peyrache A (2014) Hicks-Moorsteen versus Malmquist: a connection by means of a radial productivity index. J Product Anal 41(3):435–442
Petersen NC (1990) Data envelopment analysis on a relaxed set of assumptions. Manag Sci 36:305–314
Podinovski VV (2004a) On the linearization of reference technologies for testing returns to scale in FDH models. Eur J Oper Res 152(3):800–802
Podinovski VV (2004b) Local and global returns to scale in performance measurement. J Oper Res Soc 55(2):170–178
Portela MCAS, Thanassoulis E (2010) Malmquist indices for measuring productivity in the presence of negative data: an application to bank branches. J Banking Finance 34:1472–1483
Ray S, Delsi E (1997) Productivity growth, technical progress and efficiency change in industrialized countries: Comment. Am Econ Rev 87:1033–1039
Shepard RW (1953) Cost and production functions. Princeton University Press
Shepard RW (1970) Theory of cost and production functions. Princeton University Press
Shestalova V (2003) Sequential Malmquist indices of productivity growth: an application to OECD industrial activities. J Product Anal 19:211–226
Sickles RC, Zelenyuk V (2019) Measurement of productivity and efficiency. Cambridge University Press
Thanassoulis E, Shiraz RK, Maniadakis N (2015) A cost Malmquist productivity index capturing group performance. Eur J Oper Res 241:796–805
Tohidi G, Razavyan S (2013) A circular global profit Malmquist productivity index in data envelopment analysis. Appl Math Model 37:216–227
Tohidi G, Razavyan S, Tohidnia S (2012) A global cost Malmquist productivity index using data envelopment analysis. J Oper Res Soc 63:72–78
Tulkens H (1993) On FDH analysis: some methodological issues and applications to retail banking, courts and urban transit. J Product Anal 4:183–210
Varian HR (1984) The non-parametric approach to production analysis. Econometrica 52:579–598
Walheer B (2016a) A multi-sector nonparametric production-frontier analysis of the economic growth and the convergence of the European countries. Pac Econ Rev 21(4):498–524
Walheer B (2016b) Growth and convergence of the OECD countries: a multi-sector production-frontier approach. Eur J Oper Res 252:665–675
Walheer B (2018a) Cost Malmquist productivity index: an output-specific approach for group comparison. J Product Anal 49:79–94
Walheer B (2018b) Disaggregation of the Cost Malmquist Productivity Index with joint and output-specific inputs. Omega 75:1–12
Walheer B (2018c) Labour productivity growth and energy in Europe: A production-frontier approach. Energy 152:129–143
Walheer B (2018d) Scale efficiency for multi-output cost minimizing producers: the case of the US electricity plants. Energy Econ 70:26–36
Wang Y-M, Lan Y-X (2011) Measuring Malmquist productivity index: a new approach based on double frontiers data envelopment analysis. Math Comput Model 54:2760–2771
Wang C, Lee J, Chang Y (2012) Measuring productivity in the biotechnology industry using the global Malmquist index. Appl Econ Lett 19:807–812
Xue M, Harker PT (2002) Note: ranking DMUs with infeasible super-efficiency DEA models. Manage Sci 48:705–710
Yang YL, Huang CJ (2009) Estimating the Malmquist productivity index in the Taiwanese banking industry: a production and cost approach. Taiwan Econ Rev 37:353–378
Ylvinger S (2000) Industry performance and structural efficiency measures: Solutions to problems in firm models. Eur J Oper Res 121:164–174
Yu MM (2007) The capacity productivity change and the variable input productivity change: a new decomposition of the Malmquist productivity index. Appl Math Comput 185:375–381
Zelenyuk V (2006) Aggregation of Malmquist productivity indexes. Eur J Oper Res 174:1076–1086
Zelenyuk V (2016) Aggregation of scale efficiency. Eur J Oper Res 240:269–277
Zhang C, Liu H, Bressers HTA, Buchanan KS (2011) Productivity growth and environmental regulations-accounting for undesirable outputs: analysis of China’s thirty provincial regions using the Malmquist-Luenberger index. Ecol Econ 70:2369–2379
Zhang N, Choi Y (2013) Total-factor carbon emission performance of fossil fuel power plants in China: a meta frontier non-radial Malmquist index analysis. Comput Econ 46(3):375–388
Zhang N, Zhou P, Kung C-C (2015) Total-factor carbon emission performance of the Chinese transportation industry: a bootstrapped non-radial Malmquist index analysis. Renew Sustain Energy Rev 41:584–593
Zhu N, Liu Y, Huang Q, Emrouznejad A (2017) An allocation Malmquist index with an application in the China securities industry. Oper Res 17:669–691
Zimmermann HJ (1978) Fuzzy programming and linear programming with several objective functions. Fuzzy Sets Syst 1:45–55