A firm-specific Malmquist productivity index model for stochastic data envelopment analysis: an application to commercial banks

Financial Innovation

Table 12 Statistical description of stochastic Malmquist productivity index (SM)

Alpha	Indicators	2014–2015	2015–2016	2016–2017	2017–2018	2018–2019	2019–2020	2020–2021
0.1	Min	0.7501	0.7257	0.7782	0.7360	0.1979	0.9239	0.3967
	Median	0.9717	0.9751	1.1152	0.9259	0.9810	1.3353	1.0976
	Max	1.5087	1.1227	2.7271	1.2416	2.4239	2.0255	1.6751
	Mean	0.9588	0.9686	1.2203	0.9466	0.9789	1.3999	1.0319
	Std	0.1789	0.1060	0.4328	0.1320	0.4538	0.2539	0.2892
0.3	Min	0.7727	0.7228	0.7813	0.7172	0.2081	0.9010	0.4113
	Median	0.9742	0.9848	1.1078	0.9354	0.9788	1.3299	1.0594
	Max	1.5098	1.1427	2.7470	1.2013	2.6389	1.8013	1.5980
	Mean	0.9829	0.9686	1.2278	0.9354	1.0061	1.3374	1.0159
	Std	0.1621	0.1043	0.4385	0.1380	0.4997	0.2285	0.2714
0.5	Min	0.7536	0.6476	0.9080	0.6237	0.2240	0.7956	0.4316
	Median	1.0327	0.9981	1.1283	0.9430	0.9940	1.2176	1.0358
	Max	1.1767	1.1492	1.5909	1.1708	2.8217	1.7291	1.4149
	Mean	1.0019	0.9668	1.1542	0.9272	1.0357	1.2569	0.9801
	Std	0.1123	0.1428	0.1966	0.1560	0.5476	0.2702	0.2395