doi: 10.3934/jimo.2022058
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Sequential Malmquist-Luenberger productivity index for interval data envelopment analysis

Department of Mathematics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi, 110016, India

*Corresponding author: Pooja Bansal

Received  August 2021 Revised  February 2022 Early access April 2022

Data envelopment analysis (DEA) based productivity indexes models are widely applied to evaluate the productivity of decision-making units over a period. This study proposes a productivity index for evaluating environmentally sensitive productivity growth while excluding the possibility of spurious technical regress. This innovative index has been created by combining directional distance functions, sequential DEA, undesirable data, and the concept of interval DEA. With this combination, the traditional sequential Malmquist-Luenberger productivity index (SMLPI) has been reformulated as an interval DEA problem to present a novel productivity index named interval SMLPI. We propose a decomposition of the developed index utilizing both constant returns to scale and variable returns to scale frontiers as the benchmark, which allows us to quantify scale efficiency change with interval data. To exhibit the capability of the proposed extension of SMLPI, we model a framework for Indian commercial banks and measure productivity change intervals for twenty-one banks from 2011 to 2018. The empirical findings elucidate that the scale efficiency change plays an essential role in driving productivity change. ICICI Bank had the highest average marginal productivity gain of 1.5007 between 2011 and 2018, whereas Karur Vysya bank had the highest average marginal productivity decline of 0.9411.

Citation: Pooja Bansal. Sequential Malmquist-Luenberger productivity index for interval data envelopment analysis. Journal of Industrial and Management Optimization, doi: 10.3934/jimo.2022058
References:
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show all references

References:
[1]

F. Aiello and G. Bonanno, On the sources of heterogeneity in banking efficiency literature, J. Economic Surveys, 32 (2018), 194-225.  doi: 10.1111/joes.12193.

[2]

J. AparicioJ. BarberoM. KapelkoJ. T. Pastor and J. L. Zofío, Testing the consistency and feasibility of the standard malmquist-luenberger index: Environmental productivity in world air emissions, Journal of Environmental Management, 196 (2017), 148-160.  doi: 10.1016/j.jenvman.2017.03.007.

[3]

J. AparicioJ. T. Pastor and J. L. Zofio, On the inconsistency of the malmquist–luenberger index, European J. Oper. Res., 229 (2013), 738-742.  doi: 10.1016/j.ejor.2013.03.031.

[4]

A. ArabmaldarE. K. Mensah and M. Toloo, Robust worst-practice interval dea with non-discretionary factors, Expert Systems with Applications, 182 (2021), 115256.  doi: 10.1016/j.eswa.2021.115256.

[5]

M. Arana-JimenezM. C. Sánchez-GilA. Younesi and S. Lozano, Integer interval DEA: An axiomatic derivation of the technology and an additive, slacks-based model, Fuzzy Sets and Systems, 422 (2021), 83-105.  doi: 10.1016/j.fss.2020.12.011.

[6]

A. G. AssafR. Matousek and E. G. Tsionas, Turkish bank efficiency: Bayesian estimation with undesirable outputs, J. Banking & Finance, 37 (2013), 506-517. 

[7]

N. Aydin and G. Yurdakul, Analyzing the efficiency of bank branches via novel weighted stochastic imprecise data envelopment analysis, RAIRO Oper. Res., 55 (2021), 1559-1578.  doi: 10.1051/ro/2021067.

[8]

H. AziziA. Amirteimoori and S. Kordrostami, A note on dual models of interval DEA and its extension to interval data, International J. Industrial Mathematics, 10 (2018), 111-126. 

[9]

H. Azizi and Y. Wang, Improved DEA models for measuring interval efficiencies of decision-making units, Measurement, 46 (2013), 1325-1332.  doi: 10.1016/j.measurement.2012.11.050.

[10]

R. D. BankerA. Charnes and W. W. Cooper, Some models for estimating technical and scale inefficiencies in data envelopment analysis, Management Science, 30 (1984), 1031-1142.  doi: 10.1287/mnsc.30.9.1078.

[11]

P. BansalS. KumarA. Mehra and R. Gulati, Developing two dynamic malmquist-luenberger productivity indices: An illustrated application for assessing productivity performance of indian banks, Omega, 107 (2022), 102538.  doi: 10.1016/j.omega.2021.102538.

[12]

P. Bansal and A. Mehra, Multi-period additive efficiency measurement in data envelopment analysis with non-positive and undesirable data, Opsearch, 55 (2018), 642-661.  doi: 10.1007/s12597-018-0343-z.

[13]

P. Bansal and A. Mehra, Directional distance function based super efficiency integer dynamic data envelopment analysis model, Data Envelopment Analysis Journal, 4 (2019), 149-186.  doi: 10.1561/103.00000025.

[14]

P. Bansal and A. Mehra, Integrated dynamic interval data envelopment analysis in the presence of integer and negative data, J. Ind. Manag. Optim., 18 (2022), 1339-1363.  doi: 10.3934/jimo.2021023.

[15]

R. BansalS. Kar and S. Gupta, Efficiency assessment of consumer's electronics sector: Data envelopment analysis, J. Asia-Pacific Business, 22 (2021), 279-297.  doi: 10.1080/10599231.2021.1983502.

[16]

C. P. BarrosS. Managi and R. Matousek, The technical efficiency of the Japanese banks: Non-radial directional performance measurement with undesirable output, Omega, 40 (2012), 1-8.  doi: 10.1016/j.omega.2011.02.005.

[17]

A. N. Berger, International comparisons of banking efficiency, Financial Markets, Institutions & Instruments, 16 (2007), 119-144.  doi: 10.1111/j.1468-0416.2007.00121.x.

[18]

A. N. Berger and L. J. Mester, Inside the black box: What explains differences in the efficiencies of financial institutions?, Working Papers, 21 (1997), 895-947.  doi: 10.21799/frbp.wp.1997.01.

[19]

J. BoussemartW. BriceK. Kerstens and J.-C. Poutineau, Luenberger and Malmqist productive indices: Theroretical comparisons and empirical illustration, Bull. Econ. Res., 55 (2003), 391-405.  doi: 10.1111/1467-8586.00183.

[20]

J. BoussemartH. LeleuZ. ShenM. Vardanyan and N. Zhu, Decomposing banking performance into economic and credit risk efficiencies, European J. Oper. Res., 277 (2019), 719-726.  doi: 10.1016/j.ejor.2019.03.006.

[21]

D. W. CavesL. R. Christensen and W. E. Diewert, The economic theory of index numbers and the measurement of input, output, and productivity, Econometrica: J. Econometric Society, 50 (1982), 1393-1414. 

[22]

A. CharnesW. W. CooperB. GolanyL. Seiford and J. Stutz, Foundations of data envelopment analysis for Pareto-Koopmans efficient empirical production functions, J. Econometrics, 30 (1985), 91-107.  doi: 10.1016/0304-4076(85)90133-2.

[23]

A. CharnesW. W. Cooper and E. Rhodes, Measuring the efficiency of decision making units, European J. Oper. Res., 2 (1978), 429-444.  doi: 10.1016/0377-2217(78)90138-8.

[24]

Y. Chen, A non-radial Malmquist productivity index with an illustrative application to Chinese major industries, International J. Production Economics, 83 (2003), 27-35.  doi: 10.1016/S0925-5273(02)00267-0.

[25]

Y. ChenJ. WangJ. ZhuH. D. Sherman and S. Y. Chou, How the Great Recession affects performance: A case of Pennsylvania hospitals using DEA, Ann. Oper. Res., 278 (2019), 77-99.  doi: 10.1007/s10479-017-2516-1.

[26]

G. Q. ChengL. Wang and Y. M. Wang, An extended three-stage dea model with interval inputs and outputs, International J. Comput. Intelligence Systems, 14 (2021), 43-53.  doi: 10.2991/ijcis.d.201019.001.

[27]

K. ChoiC. Kim and H. J. Kim, Multi-period efficiency and productivity changes in global automobile: A VRS–VRM and SML productivity index approach, Expert Systems with Applications, 86 (2017), 77-86.  doi: 10.1016/j.eswa.2017.05.022.

[28]

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Figure 1.  The structure of an Indian commercial bank
Figure 2.  The geometric mean of SMLPI under CRS and VRS production technology and scale efficiency change factor under pessimistic situation
Figure 3.  The index value of SMLPI under CRS and VRS production technology and scale change factor under optimistic situation
Table 1.  The inputs, desirable and undesirable outputs employed in the empirical analysis
Inputs 1. Labor
2. Equity
3. Capital
Desirable outputs 1. Deposits
2. Performing loans
3. Investments
Undesirable output 1. Non-performing loans
Inputs 1. Labor
2. Equity
3. Capital
Desirable outputs 1. Deposits
2. Performing loans
3. Investments
Undesirable output 1. Non-performing loans
Table 2.  Normalized data of 2018 for 21 Indian commercial banks; except labour, the bounds of the data values are measured in lakhs
Banks Labor Capital Equity Deposits Performing loans Investments NPAs
State bank of India 11 2.88 [73.22, 75.7] [896.82, 949.33] [561.42, 650.21] [361.34, 393.5] 357.88
Axis bank 15 9.37 [117.18, 121.77] [816.23, 1001.34] [805.26, 903.35] [282.28, 319.44] 302.91
Bank of Baroda 10 7.01 [58.37, 67.38] [768.48, 844.08] [547.82, 619.58] [230.81, 243.61] 310.34
Bank of India 9 24.75 [49.86, 65.74] [726.82, 739.2] [465.17, 483.95] [189.38, 209.53] 400.31
Canara Bank 9 8.37 [41, 41.71] [608.79, 683.86] [440.95, 488.3] [164.92, 174.65] 325.84
HDFC Bank 18 7.79 [161.51, 223.82] [1208.74, 1384.78] [1063.03, 1229.16] [413.54, 450.15] 39.02
ICICI Bank 17 19.93 [163.24, 167.93] [847.46, 1011.78] [800.05, 909.08] [288.79, 321.91] 431.16
Punjab National Bank 10 5.85 [42.6, 47.46] [667.98, 716.43] [440.16, 485.63] [205.48, 224.22] 515.93
United Bank of India 7 110.37 [27.96, 42.3] [472.99, 496.6] [177.71, 190.52] [191.22, 224.33] 379.53
City Union bank 8 7.94 [49.75, 53.43] [392.61, 412.71] [322.73, 341.41] [94.16, 95.87] 56.74
Development credit bank 16 65.00 [59.24, 61.83] [506.48, 552.09] [421.27, 456.94] [131.2, 147.74] 30.95
Indian overseas bank 8 110.46 [27.26, 29.98] [489.74, 504.06] [213, 213.01] [155.05, 168.4] 460.75
Karnataka Bank 9 24.68 [47.24, 48.75] [548.97, 557.82] [391.88, 415.61] [134.85, 140.02] 122.29
Karur Vysya Bank 10 13.13 [56.59, 57.29] [513.98, 526.37] [377.5, 386.43] [126.6, 140.37] 168.3
Lakshmi Vilas bank 8 32.77 [26.29, 29.8] [397.75, 426.41] [255.94, 295.38] [135.17, 137.84] 186.63
Oriental Bank of Commerce 8 16.98 [30.83, 31.62] [553.9, 556.33] [328.87, 329.39] [187.55, 201] 383.22
South Indian Bank 8 14.37 [41.64, 41.71] [572.06, 594.95] [417.61, 428.28] [144.3, 145.84] 112.44
Allahabad bank 7 18.89 [22.93, 26.34] [470.54, 478.16] [252.2, 280.93] [151.58, 168.68] 273.76
Andhra Bank 7 30.59 [27.6, 30.02] [527.42, 530.92] [309.87, 319.02] [165.27, 165.4] 322.45
Indian Bank 7 12.39 [47.57, 48.66] [537.12, 566.07] [403.74, 430.55] [173.24, 184.11] 153.68
UCO Bank 3 24.46 [14.13, 15.85] [192.72, 193.12] [73.38, 81.52] [75.2, 77.72] 149.24
Banks Labor Capital Equity Deposits Performing loans Investments NPAs
State bank of India 11 2.88 [73.22, 75.7] [896.82, 949.33] [561.42, 650.21] [361.34, 393.5] 357.88
Axis bank 15 9.37 [117.18, 121.77] [816.23, 1001.34] [805.26, 903.35] [282.28, 319.44] 302.91
Bank of Baroda 10 7.01 [58.37, 67.38] [768.48, 844.08] [547.82, 619.58] [230.81, 243.61] 310.34
Bank of India 9 24.75 [49.86, 65.74] [726.82, 739.2] [465.17, 483.95] [189.38, 209.53] 400.31
Canara Bank 9 8.37 [41, 41.71] [608.79, 683.86] [440.95, 488.3] [164.92, 174.65] 325.84
HDFC Bank 18 7.79 [161.51, 223.82] [1208.74, 1384.78] [1063.03, 1229.16] [413.54, 450.15] 39.02
ICICI Bank 17 19.93 [163.24, 167.93] [847.46, 1011.78] [800.05, 909.08] [288.79, 321.91] 431.16
Punjab National Bank 10 5.85 [42.6, 47.46] [667.98, 716.43] [440.16, 485.63] [205.48, 224.22] 515.93
United Bank of India 7 110.37 [27.96, 42.3] [472.99, 496.6] [177.71, 190.52] [191.22, 224.33] 379.53
City Union bank 8 7.94 [49.75, 53.43] [392.61, 412.71] [322.73, 341.41] [94.16, 95.87] 56.74
Development credit bank 16 65.00 [59.24, 61.83] [506.48, 552.09] [421.27, 456.94] [131.2, 147.74] 30.95
Indian overseas bank 8 110.46 [27.26, 29.98] [489.74, 504.06] [213, 213.01] [155.05, 168.4] 460.75
Karnataka Bank 9 24.68 [47.24, 48.75] [548.97, 557.82] [391.88, 415.61] [134.85, 140.02] 122.29
Karur Vysya Bank 10 13.13 [56.59, 57.29] [513.98, 526.37] [377.5, 386.43] [126.6, 140.37] 168.3
Lakshmi Vilas bank 8 32.77 [26.29, 29.8] [397.75, 426.41] [255.94, 295.38] [135.17, 137.84] 186.63
Oriental Bank of Commerce 8 16.98 [30.83, 31.62] [553.9, 556.33] [328.87, 329.39] [187.55, 201] 383.22
South Indian Bank 8 14.37 [41.64, 41.71] [572.06, 594.95] [417.61, 428.28] [144.3, 145.84] 112.44
Allahabad bank 7 18.89 [22.93, 26.34] [470.54, 478.16] [252.2, 280.93] [151.58, 168.68] 273.76
Andhra Bank 7 30.59 [27.6, 30.02] [527.42, 530.92] [309.87, 319.02] [165.27, 165.4] 322.45
Indian Bank 7 12.39 [47.57, 48.66] [537.12, 566.07] [403.74, 430.55] [173.24, 184.11] 153.68
UCO Bank 3 24.46 [14.13, 15.85] [192.72, 193.12] [73.38, 81.52] [75.2, 77.72] 149.24
Table 3.  Productivity change intervals applying models $ (M2) $ and $ (M3) $
Banks 2011-12 2012-13 2013-14 2014-15 2015-16 2016-17 2017-18
State bank of India [0.671, 1.142] [0.801, 1.375] [0.803, 1.238] [0.864, 1.34] [0.859, 1.545] [0.708, 1.444] [0.68, 1.305]
Axis bank [0.708, 1.345] [0.691, 1.374] [0.689, 1.162] [0.798, 1.305] [0.782, 1.13] [0.78, 1.284] [0.63, 1.291]
Bank of Baroda [0.663, 1.194] [0.705, 1.452] [0.73, 1.395] [0.731, 1.239] [0.731, 1.32] [0.568, 1.349] [0.638, 1.663]
Bank of India [0.716, 1.251] [0.806, 1.529] [0.724, 1.289] [0.764, 1.145] [0.718, 1.344] [0.478, 1.416] [0.586, 1.717]
Canara Bank [0.718, 1.336] [0.734, 1.544] [0.66, 1.384] [0.644, 1.47] [0.603, 1.664] [0.462, 1.599] [0.575, 1.905]
HDFC Bank [0.854, 1.266] [0.802, 1.166] [0.793, 1.488] [0.733, 1.503] [0.806, 1.373] [0.765, 7.03] [0.154, 1.411]
ICICI Bank [0.914, 1.294] [0.681, 0.913] [1.009, 1.484] [0.546, 0.777] [0.886, 1.169] [0.778, 9.107] [0.1, 1.352]
Punjab National Bank [0.007, 1.079] [0.654, 1.381] [0.69, 1.478] [0.692, 1.614] [0.639, 1.943] [0.512, 1.782] [0.565, 1.774]
United Bank of India [0.63, 1.22] [0.72, 2.07] [0.524, 1.643] [0.646, 1.773] [0.689, 1.775] [0.389, 1.616] [0.567, 2.285]
City Union bank [0.74, 1.3] [0.622, 1.221] [0.627, 1.216] [0.704, 1.23] [0.791, 1.257] [0.789, 1.257] [0.785, 1.257]
Development credit bank [0.777, 1.147] [0.875, 1.123] [0.798, 1.128] [0.808, 1.118] [0.928, 1.313] [0.766, 1.2] [0.841, 1.277]
Indian overseas bank [0.66, 1.242] [0.676, 1.404] [0.628, 1.268] [0.782, 1.472] [0.578, 1.259] [0.607, 1.557] [0.669, 1.751]
Karnataka Bank [0.797, 1.122] [0.711, 1.382] [0.701, 1.444] [0.652, 1.375] [0.683, 1.379] [0.662, 1.265] [0.717, 1.305]
Karur Vysya Bank [0.636, 0.957] [0.78, 1.419] [0.686, 1.23] [0.609, 1.148] [0.8, 1.351] [0.774, 1.243] [0.605, 0.938]
Lakshmi Vilas bank [0.626, 1.162] [0.601, 1.741] [0.555, 1.924] [0.54, 1.65] [0.684, 1.642] [0.692, 1.555] [0.541, 1.441]
Oriental Bank of Commerce [0.822, 1.16] [0.817, 1.232] [0.823, 1.165] [0.787, 1.327] [0.705, 1.221] [0.545, 1.694] [0.591, 2.163]
South Indian Bank [0.684, 1.14] [0.596, 1.204] [0.722, 1.362] [0.663, 1.426] [0.596, 1.435] [0.655, 1.487] [0.677, 1.478]
Allahabad bank [0.842, 1.03] [0.732, 1.25] [0.686, 1.419] [0.614, 1.374] [0.688, 1.31] [0.6, 1.408] [0.714, 2.349]
Andhra Bank [0.732, 1.016] [0.724, 1.353] [0.688, 1.44] [0.666, 1.541] [0.723, 1.401] [0.542, 1.544] [0.679, 2.011]
Indian Bank [0.731, 1.009] [0.755, 1.309] [0.769, 1.269] [0.755, 1.181] [0.841, 1.307] [0.651, 1.46] [0.687, 1.724]
UCO Bank [0.632, 1.322] [0.634, 1.557] [0.703, 1.601] [0.731, 1.318] [0.744, 1.392] [0.48, 1.375] [0.62, 1.653]
Marginal productivity progress 5 15 15 13 17 16 15
Banks 2011-12 2012-13 2013-14 2014-15 2015-16 2016-17 2017-18
State bank of India [0.671, 1.142] [0.801, 1.375] [0.803, 1.238] [0.864, 1.34] [0.859, 1.545] [0.708, 1.444] [0.68, 1.305]
Axis bank [0.708, 1.345] [0.691, 1.374] [0.689, 1.162] [0.798, 1.305] [0.782, 1.13] [0.78, 1.284] [0.63, 1.291]
Bank of Baroda [0.663, 1.194] [0.705, 1.452] [0.73, 1.395] [0.731, 1.239] [0.731, 1.32] [0.568, 1.349] [0.638, 1.663]
Bank of India [0.716, 1.251] [0.806, 1.529] [0.724, 1.289] [0.764, 1.145] [0.718, 1.344] [0.478, 1.416] [0.586, 1.717]
Canara Bank [0.718, 1.336] [0.734, 1.544] [0.66, 1.384] [0.644, 1.47] [0.603, 1.664] [0.462, 1.599] [0.575, 1.905]
HDFC Bank [0.854, 1.266] [0.802, 1.166] [0.793, 1.488] [0.733, 1.503] [0.806, 1.373] [0.765, 7.03] [0.154, 1.411]
ICICI Bank [0.914, 1.294] [0.681, 0.913] [1.009, 1.484] [0.546, 0.777] [0.886, 1.169] [0.778, 9.107] [0.1, 1.352]
Punjab National Bank [0.007, 1.079] [0.654, 1.381] [0.69, 1.478] [0.692, 1.614] [0.639, 1.943] [0.512, 1.782] [0.565, 1.774]
United Bank of India [0.63, 1.22] [0.72, 2.07] [0.524, 1.643] [0.646, 1.773] [0.689, 1.775] [0.389, 1.616] [0.567, 2.285]
City Union bank [0.74, 1.3] [0.622, 1.221] [0.627, 1.216] [0.704, 1.23] [0.791, 1.257] [0.789, 1.257] [0.785, 1.257]
Development credit bank [0.777, 1.147] [0.875, 1.123] [0.798, 1.128] [0.808, 1.118] [0.928, 1.313] [0.766, 1.2] [0.841, 1.277]
Indian overseas bank [0.66, 1.242] [0.676, 1.404] [0.628, 1.268] [0.782, 1.472] [0.578, 1.259] [0.607, 1.557] [0.669, 1.751]
Karnataka Bank [0.797, 1.122] [0.711, 1.382] [0.701, 1.444] [0.652, 1.375] [0.683, 1.379] [0.662, 1.265] [0.717, 1.305]
Karur Vysya Bank [0.636, 0.957] [0.78, 1.419] [0.686, 1.23] [0.609, 1.148] [0.8, 1.351] [0.774, 1.243] [0.605, 0.938]
Lakshmi Vilas bank [0.626, 1.162] [0.601, 1.741] [0.555, 1.924] [0.54, 1.65] [0.684, 1.642] [0.692, 1.555] [0.541, 1.441]
Oriental Bank of Commerce [0.822, 1.16] [0.817, 1.232] [0.823, 1.165] [0.787, 1.327] [0.705, 1.221] [0.545, 1.694] [0.591, 2.163]
South Indian Bank [0.684, 1.14] [0.596, 1.204] [0.722, 1.362] [0.663, 1.426] [0.596, 1.435] [0.655, 1.487] [0.677, 1.478]
Allahabad bank [0.842, 1.03] [0.732, 1.25] [0.686, 1.419] [0.614, 1.374] [0.688, 1.31] [0.6, 1.408] [0.714, 2.349]
Andhra Bank [0.732, 1.016] [0.724, 1.353] [0.688, 1.44] [0.666, 1.541] [0.723, 1.401] [0.542, 1.544] [0.679, 2.011]
Indian Bank [0.731, 1.009] [0.755, 1.309] [0.769, 1.269] [0.755, 1.181] [0.841, 1.307] [0.651, 1.46] [0.687, 1.724]
UCO Bank [0.632, 1.322] [0.634, 1.557] [0.703, 1.601] [0.731, 1.318] [0.744, 1.392] [0.48, 1.375] [0.62, 1.653]
Marginal productivity progress 5 15 15 13 17 16 15
Table 4.  Scale efficiency change intervals for Indian commercial banks from 2011 to 2018
Banks 2011-12 2012-13 2013-14 2014-15 2015-16 2016-17 2017-18
State bank of India [0.726, 1.036] [0.874, 1.271] [0.862, 1.167] [0.91, 1.238] [0.921, 1.347] [0.781, 1.307] [0.726, 1.265]
Axis bank [0.917, 1.102] [0.825, 1.22] [0.803, 1.065] [0.873, 1.112] [0.872, 1.047] [0.826, 1.171] [0.691, 1.266]
Bank of Baroda [0.749, 1.063] [0.787, 1.275] [0.818, 1.32] [0.77, 1.225] [0.74, 1.302] [0.577, 1.337] [0.644, 1.646]
Bank of India [0.757, 1.189] [0.834, 1.412] [0.768, 1.234] [0.789, 1.133] [0.734, 1.308] [0.497, 1.387] [0.604, 1.698]
Canara Bank [0.765, 1.25] [0.765, 1.457] [0.695, 1.343] [0.657, 1.436] [0.613, 1.629] [0.472, 1.58] [0.582, 1.874]
HDFC Bank [0.914, 1.187] [0.841, 1.105] [0.832, 1.413] [0.769, 1.419] [0.844, 1.291] [0.734, 5.86] [0.171, 1.21]
ICICI Bank [1.027, 1.158] [0.766, 0.881] [1.042, 1.399] [0.588, 0.806] [0.899, 1.139] [0.682, 7.857] [0.105, 1.407]
Punjab National Bank [0.008, 1.058] [0.667, 1.366] [0.695, 1.452] [0.696, 1.594] [0.646, 1.884] [0.528, 1.741] [0.578, 1.734]
United Bank of India [0.645, 1.185] [0.732, 1.933] [0.549, 1.592] [0.652, 1.725] [0.696, 1.676] [0.412, 1.571] [0.586, 2.216]
City Union bank [0.742, 1.27] [0.628, 1.209] [0.635, 1.208] [0.706, 1.22] [0.79, 1.25] [0.793, 1.251] [0.787, 1.243]
Development credit bank [0.877, 1.053] [0.929, 1.052] [0.869, 1.063] [0.877, 1.066] [0.945, 1.226] [0.793, 1.176] [0.845, 1.239]
Indian overseas bank [0.697, 1.178] [0.695, 1.355] [0.649, 1.257] [0.788, 1.438] [0.599, 1.247] [0.609, 1.529] [0.673, 1.721]
Karnataka Bank [0.833, 1.049] [0.754, 1.311] [0.738, 1.372] [0.681, 1.318] [0.701, 1.339] [0.675, 1.254] [0.723, 1.29]
Karur Vysya Bank [0.676, 0.926] [0.805, 1.359] [0.71, 1.207] [0.629, 1.148] [0.8, 1.334] [0.777, 1.239] [0.61, 0.938]
Lakshmi Vilas bank [0.647, 1.132] [0.626, 1.671] [0.566, 1.812] [0.556, 1.618] [0.683, 1.604] [0.702, 1.547] [0.551, 1.419]
Oriental Bank of Commerce [0.846, 1.12] [0.83, 1.213] [0.824, 1.157] [0.792, 1.307] [0.717, 1.217] [0.549, 1.643] [0.606, 2.112]
South Indian Bank [0.698, 1.111] [0.609, 1.195] [0.727, 1.353] [0.669, 1.409] [0.605, 1.42] [0.663, 1.477] [0.681, 1.464]
Allahabad bank [0.843, 1.024] [0.734, 1.233] [0.694, 1.402] [0.616, 1.351] [0.69, 1.305] [0.602, 1.408] [0.715, 2.282]
Andhra Bank [0.733, 1.007] [0.732, 1.34] [0.701, 1.418] [0.668, 1.493] [0.724, 1.388] [0.542, 1.53] [0.685, 1.981]
Indian Bank [0.743, 0.991] [0.754, 1.284] [0.767, 1.254] [0.756, 1.174] [0.838, 1.293] [0.653, 1.45] [0.685, 1.699]
UCO Bank [0.657, 1.266] [0.651, 1.506] [0.712, 1.553] [0.736, 1.302] [0.754, 1.364] [0.492, 1.363] [0.61, 1.59]
Marginal scale efficiency progress 5 15 15 11 17 14 15
Banks 2011-12 2012-13 2013-14 2014-15 2015-16 2016-17 2017-18
State bank of India [0.726, 1.036] [0.874, 1.271] [0.862, 1.167] [0.91, 1.238] [0.921, 1.347] [0.781, 1.307] [0.726, 1.265]
Axis bank [0.917, 1.102] [0.825, 1.22] [0.803, 1.065] [0.873, 1.112] [0.872, 1.047] [0.826, 1.171] [0.691, 1.266]
Bank of Baroda [0.749, 1.063] [0.787, 1.275] [0.818, 1.32] [0.77, 1.225] [0.74, 1.302] [0.577, 1.337] [0.644, 1.646]
Bank of India [0.757, 1.189] [0.834, 1.412] [0.768, 1.234] [0.789, 1.133] [0.734, 1.308] [0.497, 1.387] [0.604, 1.698]
Canara Bank [0.765, 1.25] [0.765, 1.457] [0.695, 1.343] [0.657, 1.436] [0.613, 1.629] [0.472, 1.58] [0.582, 1.874]
HDFC Bank [0.914, 1.187] [0.841, 1.105] [0.832, 1.413] [0.769, 1.419] [0.844, 1.291] [0.734, 5.86] [0.171, 1.21]
ICICI Bank [1.027, 1.158] [0.766, 0.881] [1.042, 1.399] [0.588, 0.806] [0.899, 1.139] [0.682, 7.857] [0.105, 1.407]
Punjab National Bank [0.008, 1.058] [0.667, 1.366] [0.695, 1.452] [0.696, 1.594] [0.646, 1.884] [0.528, 1.741] [0.578, 1.734]
United Bank of India [0.645, 1.185] [0.732, 1.933] [0.549, 1.592] [0.652, 1.725] [0.696, 1.676] [0.412, 1.571] [0.586, 2.216]
City Union bank [0.742, 1.27] [0.628, 1.209] [0.635, 1.208] [0.706, 1.22] [0.79, 1.25] [0.793, 1.251] [0.787, 1.243]
Development credit bank [0.877, 1.053] [0.929, 1.052] [0.869, 1.063] [0.877, 1.066] [0.945, 1.226] [0.793, 1.176] [0.845, 1.239]
Indian overseas bank [0.697, 1.178] [0.695, 1.355] [0.649, 1.257] [0.788, 1.438] [0.599, 1.247] [0.609, 1.529] [0.673, 1.721]
Karnataka Bank [0.833, 1.049] [0.754, 1.311] [0.738, 1.372] [0.681, 1.318] [0.701, 1.339] [0.675, 1.254] [0.723, 1.29]
Karur Vysya Bank [0.676, 0.926] [0.805, 1.359] [0.71, 1.207] [0.629, 1.148] [0.8, 1.334] [0.777, 1.239] [0.61, 0.938]
Lakshmi Vilas bank [0.647, 1.132] [0.626, 1.671] [0.566, 1.812] [0.556, 1.618] [0.683, 1.604] [0.702, 1.547] [0.551, 1.419]
Oriental Bank of Commerce [0.846, 1.12] [0.83, 1.213] [0.824, 1.157] [0.792, 1.307] [0.717, 1.217] [0.549, 1.643] [0.606, 2.112]
South Indian Bank [0.698, 1.111] [0.609, 1.195] [0.727, 1.353] [0.669, 1.409] [0.605, 1.42] [0.663, 1.477] [0.681, 1.464]
Allahabad bank [0.843, 1.024] [0.734, 1.233] [0.694, 1.402] [0.616, 1.351] [0.69, 1.305] [0.602, 1.408] [0.715, 2.282]
Andhra Bank [0.733, 1.007] [0.732, 1.34] [0.701, 1.418] [0.668, 1.493] [0.724, 1.388] [0.542, 1.53] [0.685, 1.981]
Indian Bank [0.743, 0.991] [0.754, 1.284] [0.767, 1.254] [0.756, 1.174] [0.838, 1.293] [0.653, 1.45] [0.685, 1.699]
UCO Bank [0.657, 1.266] [0.651, 1.506] [0.712, 1.553] [0.736, 1.302] [0.754, 1.364] [0.492, 1.363] [0.61, 1.59]
Marginal scale efficiency progress 5 15 15 11 17 14 15
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