The data envelopment analysis (DEA) technique is well known for computing the Malmquist-Luenberger productivity index (MLPI) in measuring productivity change in the decision-making units (DMUs) over two consecutive periods. In this research, we detect infeasibility of the directional distance function (DDF) based DEA model of MLPI under the variable returns to scale technology when data takes on negative values. We address this problem by developing a novel DDF-based DEA model that computes an improved MLPI. We extend the DDF approach to the dynamic network structure and introduce the dynamic MLPI for analyzing the performance of DMUs over time. We also develop the dynamic sequential MLPI to detect shifts in the efficient frontiers due to random shocks or technological advancements over time. The dynamic network structure in the two indexes comprises multiple divisions in DMUs connected vertically by intermediate productivity links and horizontally over time by carryovers. The proposed models are feasible and bounded with undesirable features and negative and non-negative data values. Real data of 39 Indian commercial public and private banks from 2008 to 2019 used to illustrate the two indexes.
Keywords: Data envelopment analysis, directional distance function, dynamic network structure, productivity change, dynamic Malmquist-Luenberger productivity indexes
@article{RO_2022__56_2_649_0,
author = {Bansal, Pooja and Mehra, Aparna},
title = {Malmquist-Luenberger productivity indexes for dynamic network {DEA} with undesirable outputs and negative data},
journal = {RAIRO. Operations Research},
pages = {649--687},
year = {2022},
publisher = {EDP-Sciences},
volume = {56},
number = {2},
doi = {10.1051/ro/2022023},
mrnumber = {4407585},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ro/2022023/}
}
TY - JOUR AU - Bansal, Pooja AU - Mehra, Aparna TI - Malmquist-Luenberger productivity indexes for dynamic network DEA with undesirable outputs and negative data JO - RAIRO. Operations Research PY - 2022 SP - 649 EP - 687 VL - 56 IS - 2 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/ro/2022023/ DO - 10.1051/ro/2022023 LA - en ID - RO_2022__56_2_649_0 ER -
%0 Journal Article %A Bansal, Pooja %A Mehra, Aparna %T Malmquist-Luenberger productivity indexes for dynamic network DEA with undesirable outputs and negative data %J RAIRO. Operations Research %D 2022 %P 649-687 %V 56 %N 2 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/ro/2022023/ %R 10.1051/ro/2022023 %G en %F RO_2022__56_2_649_0
Bansal, Pooja; Mehra, Aparna. Malmquist-Luenberger productivity indexes for dynamic network DEA with undesirable outputs and negative data. RAIRO. Operations Research, Tome 56 (2022) no. 2, pp. 649-687. doi: 10.1051/ro/2022023
[1] and , Translation invariance in data envelopment analysis. Oper. Res. Lett. 9 (1990) 403–405. | Zbl | DOI
[2] , and , On the inconsistency of the Malmquist-Luenberger index. Eur. J. Oper. Res. 229 (2013) 738–742. | MR | DOI
[3] , and , The directional distance function and the translation invariance property. Omega 58 (2016) 1–3. | DOI
[4] , , , and , Testing the consistency and feasibility of the standard Malmquist-Luenberger index: environmental productivity in world air emissions. J. Environ. Manage. 196 (2017) 148–160. | DOI
[5] , and , A new slacks-based measure of Malmquist-Luenberger index in the presence of undesirable outputs. Omega 51 (2015) 29–37. | DOI
[6] , An illustration of dynamic network DEA in commercial banking including robustness tests. Omega 55 (2015) 141–150. | DOI
[7] and , Infeasibility and directional distance functions with application to the determinateness of the luenberger productivity indicator. J. Optim. Theory App. 141 (2009) 55. | MR | Zbl | DOI
[8] and , The luenberger productivity indicator: an economic specification leading to infeasibilities. Econ. Modell. 26 (2009) 597–600. | DOI
[9] , and , The economic theory of index numbers and the measurement of input, output, and productivity. Econ. J. Econ. Soc. 50 (1982) 1393–1414. | Zbl
[10] , , and , Passenger facility charge vs. airport improvement program funds: a dynamic network DEA analysis for US airport financing. Transp. Res. Part E: Logistics Transp. Rev. 88 (2016) 76–93. | DOI
[11] , , , , , and , Two phase data envelopment analysis approaches to policy evaluation and management of army recruiting activities: tradeoffs between joint services and army advertising. In: Center for Cybernetic Studies. University of Texas-Austin Austin, Texas, USA (1986).
[12] , A non-radial Malmquist productivity index with an illustrative application to Chinese major industries. Int. J. Prod. Econ. 83 (2003) 27–35. | DOI
[13] and , Scale efficiency in two-stage network DEA. J. Oper. Res. Soc. 70 (2019) 101–110. | DOI
[14] , and , Productivity and undesirable outputs: a directional distance function approach. J. Environm. Manage. 51 (1997) 229–240. | DOI
[15] , , and , An Introduction to Efficiency and Productivity Analysis. Springer Science & Business Media (2005).
[16] , and , Measuring performance of two-stage network structures by DEA: a review and future perspective. Omega 38 (2010) 423–430. | DOI
[17] , and , Financial liberalization and banking efficiency: evidence from Turkey. J. Prod. Anal. 27 (2007) 177–195. | DOI
[18] , and , A modified Malmquist-Luenberger productivity index: assessing environmental productivity performance in China. Eur. J. Oper. Res. 269 (2018) 171–187. | MR | DOI
[19] , and , The infeasible problem of Malmquist-Luenberger index and its application on China’s environmental total factor productivity. Ann. Oper. Res. 278 (2019) 235–253. | MR | DOI
[20] and , A mathematical model for dynamic efficiency using data envelopment analysis. Appl. Math. Comput. 160 (2005) 363–378. | Zbl
[21] and , Measurement of productivity index with dynamic DEA. Int. J. Oper. Res. 8 (2010) 247. | Zbl | DOI
[22] and , A framework for measuring global Malmquist-Luenberger productivity index with CO2 emissions on Chinese manufacturing industries. Energy 115 (2016) 840–856. | DOI
[23] , and , A semi-oriented radial measure for measuring the efficiency of decision making units with negative data using DEA. Eur. J. Oper. Res. 200 (2010) 297–304. | Zbl | DOI
[24] , and , DEA-based Malmquist productivity indexes for understanding courts reform. Soc.-Econ. Planning Sci. 62 (2018) 31–43. | DOI
[25] and , Intertemporal production frontiers with dynamic DEA. In: Kluwer Academic, collaboration with R. Briinnlund et al. Boston (1996). | DOI
[26] , and , Production Frontiers. Cambridge University Press (1994).
[27] , , and , Productivity growth, technical progress, and efficiency change in industrialized countries. Am. Econ. Rev. 84 (1994) 66–83.
[28] , , , and , Productivity and energy efficiency assessment of existing industrial gases facilities via data envelopment analysis and the Malmquist index. Appl. Energy 212 (2018) 1563–1577. | DOI
[29] and , Measuring Japanese bank performance: a dynamic network DEA approach. J. Prod. Anal. 44 (2015) 249–264. | DOI
[30] and , Japanese bank productivity, 2007–2012: a dynamic network approach. Pac. Econ. Rev. 22 (2017) 649–676. | DOI
[31] , and , A Nerlovian cost inefficiency two-stage DEA model for modeling banks’ production process: evidence from the Turkish banking system. Omega 95 (2020) 102198 | DOI
[32] , A generalized DEA model for inputs (outputs) estimation under inter-temporal dependence. RAIRO-Oper. Res. 53 (2019) 1791–1805. | MR | Zbl | Numdam | DOI
[33] and , A note on the Malmquist productivity index. Econ. Lett. 47 (1995) 169–175. | Zbl | DOI
[34] , , and , Two-stage DEA in banks: terminological controversies and future directions. Expert Syst. App. 161 (2020) 113–632.
[35] , , , and , A multi-perspective dynamic network performance efficiency measurement of an evacuation: a dynamic network-DEA approach. Omega 60 (2016) 45–59. | DOI
[36] and , Resolving the deposit dilemma: a new DEA bank efficiency model. J. Banking Finance 35 (2011) 2801–2810. | DOI
[37] , Ranking of countries in sporting events using two-stage data envelopment analysis models: a case of Summer Olympic Games 2016. Central Eur. J. Oper. Res. 26 (2018) 951–966. | MR | DOI
[38] and , Data Envelopment Analysis (DEA) with integer and negative inputs and outputs. J. Data Envelopment Anal. Decis. Sci. 2013 (2013) 1–15. | DOI
[39] and , Impact of NPA and loan write-offs on the profit efficiency of Indian banks. Decision 47 (2020) 35–48. | DOI
[40] , Dynamic data envelopment analysis: a relational analysis. Eur. J. Oper. Res. 227 (2013) 325–330. | MR | DOI
[41] , Network data envelopment analysis: a review. Eur. J. Oper. Res. 239 (2014) 1–16. | MR | DOI
[42] , Network Data Envelopment Analysis: Foundations and Extensions. Springer (2017). | MR | DOI
[43] , and , Modelling a multi-period production process: evidence from the Japanese regional banks. Eur. J. Oper. Res. 294 (2021) 327–339. | MR | DOI
[44] , Environmentally sensitive productivity growth: a global analysis using Malmquist-Luenberger index. Ecol. Econ. 56 (2006) 280–293. | DOI
[45] and , Super-efficiency measurement under variable return to scale: an approach based on a new directional distance function. J. Oper. Res. Soc. 66 (2015) 1506–1510. | DOI
[46] and , A directional distance based super-efficiency DEA model handling negative data. J. Oper. Res. Soc. 68 (2017) 1312–1322. | DOI
[47] and , Super-efficiency based on the directional distance function in the presence of negative data. Omega 85 (2019) 26–34. | DOI
[48] , The decomposition of malmquist productivity indexes. J. Prod. Anal. 20 (2003) 437–458. | DOI
[49] , and , Measuring macroeconomic performance in the OECD: a comparison of European and non-European countries. Eur. J. Oper. Res. 87 (1995) 507–518. | Zbl | DOI
[50] and , Efficiency assessment using a multidirectional DDF approach. Int. Trans. Oper. Res. 27 (2020) 2064–2080. | MR | Zbl | DOI
[51] , Index numbers and indifference surfaces. Trabajos de Estadistica y de Investigacion Operativa 4 (1953) 209–242. | MR | Zbl | DOI
[52] , and , A review of dynamic data envelopment analysis: state of the art and applications. Int. Trans. Oper. Res. 25 (2018) 469–505. | MR | Zbl | DOI
[53] , and , A modified semi-oriented radial measure for target setting with negative data. Measurement 54 (2014) 152–158. | DOI
[54] and , Super SBI Dynamic Network DEA approach to measuring efficiency in the provision of public services. Int. Trans. Oper. Res. 25 (2018) 715–735. | MR | DOI
[55] , and , Decomposing agricultural productivity growth using a random-parameters stochastic production frontier. Empirical Econ. 57 (2019) 839–860. | DOI
[56] and , A sequential Malmquist-Luenberger productivity index: environmentally sensitive productivity growth considering the progressive nature of technology. Energy Econ. 32 (2010) 1345–1355. | DOI
[57] and , Measurement of multiperiod aggregative efficiency. Eur. J. Oper. Res. 193 (2009) 567–580. | MR | Zbl | DOI
[58] and , Malmquist-type indices in the presence of negative data: an application to bank branches. J. Banking Finance 34 (2010) 1472–1483. | DOI
[59] , and , Negative data in DEA: a directional distance approach applied to bank branches. J. Oper. Res. Soc. 55 (2004) 1111–1121. | Zbl | DOI
[60] and , Productivity growth, technical progress, and efficiency change in industrialized countries: comment. Am. Econ. Rev. 87 (1997) 1033–1039.
[61] and , Technological inefficiency indexes: a binary taxonomy and a generic theorem. J. Prod. Anal. 49 (2018) 17–23. | DOI
[62] , Undesirable outputs in efficiency valuations. Eur. J. Oper. Res. 132 (2001) 400–410. | Zbl | DOI
[63] and , Modeling undesirable factors in efficiency evaluation. Eur. J. Oper. Res. 142 (2002) 16–20. | Zbl | DOI
[64] , and , A modified slacks-based measure model for data envelopment analysis with ‘natural’ negative outputs and inputs. J. Oper. Res. Soc. 58 (2007) 1672–1677. | DOI
[65] , Sequential Malmquist indices of productivity growth: an application to OECD industrial activities. J. Prod. Anal. 19 (2003) 211–226. | DOI
[66] , Technical change and the aggregate production function. Rev. Econ. Stat. 39 (1957) 312–320. | DOI
[67] , , and , A new dynamic range directional measure for two-stage data envelopment analysis models with negative data. Comput. Ind. Eng. 115 (2018) 427–448. | DOI
[68] and , Dynamic DEA: a slacks-based measure approach. Omega 38 (2010) 145–156. | DOI
[69] and , Dynamic DEA with network structure: a slacks-based measure approach. Omega 42 (2014) 124–131. | DOI
[70] and , Non-parametric efficiency, progress and regress measures for panel data: methodological aspects. Eur. J. Oper. Res. 80 (1995) 474–499. | Zbl | DOI
[71] , Malmquist productivity index for multi-output producers: an application to electricity generation plants. Soc.-Econ. Plan. Sci. 65 (2019) 76–88. | DOI
[72] and , Technical progress, inefficiency, and productivity change in us banking, 1984–1993. J. Money Credit Bank. 31 (1999) 212–234. | DOI
[73] , and , Undesirable outputs and weighting schemes in composite indicators based on data envelopment analysis. Eur. J. Oper. Res. 245 (2015) 517–530. | MR | Zbl | DOI
[74] , , and , Efficiency evaluation of banks in China: a dynamic two-stage slacks-based measure approach. Omega 60 (2016) 60–72. | DOI
[75] , Malmquist productivity index decompositions: a unifying framework. Appl. Econ. 39 (2007) 2371–2387. | DOI
Cité par Sources :
