Efficiency of Indian Banks – private versus public sector banks: A two-stage analysis

Figures & data

Table 1. Description of variables in the Tobit estimation

Variable Type	Name	Description
Dependent Variable	Efficiency Scores (ES)	Estimated DEA Efficiency scores for business, profit, and Z-Score efficiencies.
Independent Variable	Government Ownership (G)	The percentage of Government shareholding of each bank for PSBs
	NPA Percentage (NPA)	The percentage of non-performing assets to total assets
	Capital Percentage (CAP)	The percentage of Capital amount (shareholders amount) to total assets
	Return on Assets (ROA)	The average net income/profit to total Assets
	Loan Loss Provisions (PROV)	Log of Total Loss Provisions kept by the banks as per regulatory guidelines for any dilution in the value of assets
	Salaries and other expenses percentage (SE)	The percentage of salaries and other expenses on Employees to the total business mix of the bank
	Market Share (MRS)	The share of the total business of the banks as compared to total business of all the banks in the group
	Head office at Mumbai is dummy (HO)	Value 1 is considered for the banks whose corporate office is at Mumbai
	Large size of the bank is dummy (SIZE)	Value 1 is considered for the banks whose average business size is more than ₹ 4 lakh crores
	New aged bank is dummy (AGE)	Value 1 is considered for the private banks that got established after the year 1991. The year is known for its major economic reform in India. AGE Dummy is not used for PSBs as all the PSBs in India were established prior to 1991.

Table 2. Average efficiency scores of PSBs and private banks 2004–2020

Public Sector Banks							Private Sector Banks
Type of Efficiency	Business Efficiency		Profit Efficiency		Z-Score Efficiency			Business Efficiency		Profit Efficiency		Z-Score Efficiency
Bank Name	Input	Output	Input	Output	Input	Output	Bank Name	Input	Output	Input	Output	Input	Output
ALB*	0.77	0.78	0.65	0.67	0.61	0.84	AXB^	0.81	0.89	0.71	0.71	0.16	0.61
AB *	0.85	0.80	0.76	0.66	0.77	0.75	CSB	0.62	0.39	0.53	0.10	0.52	0.71
BOB	0.99	0.99	0.66	0.73	0.37	0.68	CUB	0.85	0.82	0.94	0.89	0.96	0.99
BOI	0.96	0.98	0.52	0.70	0.37	0.60	DCB	0.91	0.50	0.90	0.45	0.93	0.89
BOM	0.87	0.78	0.81	0.49	0.81	0.63	DNLB	0.78	0.51	0.73	0.36	0.73	0.71
CAN	0.91	0.92	0.65	0.70	0.35	0.65	FB	0.61	0.59	0.59	0.55	0.24	0.53
CBI	0.67	0.69	0.33	0.40	0.31	0.59	HDFC^	0.79	0.86	0.86	0.87	0.40	0.94
CORP*	0.99	0.99	0.87	0.85	0.85	0.85	ICICI^	0.97	0.98	0.83	0.83	0.09	0.65
DENA *	0.95	0.77	0.93	0.53	0.93	0.77	INSB^	0.78	0.74	0.74	0.68	0.73	0.81
INB	0.81	0.80	0.89	0.86	0.85	0.93	JKB	0.60	0.57	0.55	0.52	0.33	0.55
IOB	0.76	0.74	0.60	0.73	0.54	0.78	KB	0.69	0.66	0.55	0.46	0.34	0.53
OBC*	0.99	0.98	0.81	0.63	0.72	0.76	KVB.	0.70	0.65	0.73	0.65	0.58	0.68
PSB	1.00	0.87	1.00	0.51	1.00	0.88	LVB	0.75	0.68	0.59	0.28	0.59	0.55
PNB	0.80	0.91	0.62	0.78	0.36	0.81	RBL	1.00	0.59	0.98	0.44	0.96	0.89
SBI	1.00	1.00	0.95	0.97	0.10	0.73	SIB.	0.71	0.67	0.47	0.37	0.29	0.37
SNB*	0.74	0.75	0.54	0.51	0.53	0.58	YB^	0.96	0.95	0.88	0.97	0.78	0.86
UCO	0.89	0.90	0.66	0.62	0.64	0.59
UBI	0.94	0.94	0.66	0.67	0.42	0.65
UNDB*	0.77	0.68	0.69	0.37	0.69	0.61
VB*	0.97	0.88	0.94	0.62	0.94	0.78
Mean	0.88	0.86	0.73	0.65	0.61	0.72	Mean	0.78	0.69	0.72	0.57	0.54	0.70
SD^$	0.10	0.11	0.17	0.15	0.25	0.11	SD^$	0.13	0.17	0.16	0.24	0.29	0.18
CV^$	0.12	0.12	0.24	0.24	0.41	0.15	CV^$	0.16	0.25	0.22	0.43	0.54	0.25

Source: Authors calculation; Full name of Banks in Appendix A.I * Banks got merged with other public sector banks in the list after year 2019; ^ Banks established after year 1991, known as new age banks started with better banking technologies; $—SD = Standard Deviation, CV = Coefficient of Variation

Figure 1. Business efficiency.

Figure 2. Profit efficiency.

Figure 3. Z-Score efficiency.

Table 3. Descriptive statistics of explanatory variables in the Tobit model

Variables	Mean	Max.	Min.	S.D.	Skw.	Kur.	J.B	JB.P	C.V.
	Public Sector Banks
G	76.93	93.13	58.86	9.94	−0.27	1.93	1.19	0.55	0.13
NPA	1.93	2.75	1.18	0.43	−0.13	2.36	0.40	0.82	0.22
CAP	0.77	2.50	0.05	0.64	0.97	3.52	3.34	0.19	0.84
ROA	0.16	0.78	−0.47	0.34	−0.23	2.15	0.78	0.68	2.08
PROV	10.32	11.95	9.01	0.77	0.06	2.60	0.15	0.93	0.07
SE	0.57	0.73	0.40	0.10	0.05	1.91	1.00	0.61	0.18
MRS	5.07	28.84	1.24	6.01	3.29	13.62	130.20	0.00	1.18
Private Banks*
NPA	0.96	2.19	0.19	0.47	0.95	4.25	3.43	0.18	0.48
CAP	0.79	2.80	0.10	0.79	1.38	3.76	5.42	0.07	1.00
ROA	0.68	1.60	−0.25	0.57	−0.28	2.06	0.80	0.67	0.83
PROV	9.06	11.42	6.90	1.49	0.20	1.90	0.92	0.63	0.16
SE	0.64	0.96	0.46	0.16	0.86	2.36	2.23	0.33	0.25
MRS	5.54	26.36	0.55	7.89	1.77	4.64	10.11	0.01	1.42

Sources: Authors calculation; *No Government holding for the private banks. Note: Mean- Average S.D—Standard Deviation, SKw.- Skewness, Kur.—Kurtosis, J.B.—Jarque–Bera test, JB.P- P value of Jarque–Bera test, C.V.—Coefficient of variation.

Table 4. Correlation matrix

Private Banks
	NPA	CAP	ROA	PRO	SE	MRS	HO	SIZE	AGE
NPA	1
CAP	−0.12	1.00
ROA	−0.70*	−0.25	1.00
PRO	−0.49	−0.37	0.65*	1.00
SE	0.16	0.68*	−0.61*	−0.61*	1.00
MRS	−0.32	−0.38	0.55*	0.80*	−0.37	1.00
HO	−0.48	0.11	0.44	0.62*	−0.02	0.63*	1.00
SIZE	−0.32	−0.36	0.49	0.75*	−0.33	0.75*	0.62*	1.00
AGE	−0.51*	−0.08	0.59*	0.81*	−0.29	0.74*	0.78*	0.71*	1.00

* Significant at 5% level. Simple correlation among two regressors up to 0.8 to 0.9 does not indicate severe multi-collinearity (Mayers, 1990, Midi et al., 2010, Goswami et al., 2019)

Table 5. Tobit regression results for various efficiencies

	Business Efficiency				Profit Efficiency				Z-Score Efficiency
	PSBs		Private Banks		PSBs		Private Banks		PSBs		Private Banks
	Input	Output	Input	Output	Input	Output	Input	Output	Input	Output	Input	Output
G	0.003 (0.002)	0.003*** (0.002)			−0.001 (0.004)	0.003 (0.003)			0.0004 (0.004)	−0.002 (0.004)
NPA	0.12** (0.05)	0.05 (0.05)	0.06 (0.05)	0.14** (0.06)	0.24** (0.11)	0.03 (0.09)	0.06 (0.07)	0.08 (0.10)	0.19 (0.10)	0.07 (0.10)	0.16 (0.12)	0.12 (0.06)
CAP	−0.07** (0.03)	−0.07** (0.03)	0.23* (0.04)	0.07** (0.03)	−0.03 (0.77)	−0.002 (0.05)	0.14* (0.03)	0.02 (0.05)	−0.04 (0.06)	−0.05 (0.06)	0.14** (0.06)	0.01 (0.03)
ROA	0.06 (0.07)	0.01 (0.06)	0.07 (0.05)	0.14*** (0.06)	0.30*** (0.14)	0.23*** (0.11)	0.24* (0.07)	0.37* (0.10)	0.26*** (0.13)	0.18* (0.01)	0.36** (0.13)	0.40* (0.07)
PROV	−0.17* (0.03)	−0.08* (0.02)	−0.02 (0.03)	0.04 (0.03)	−0.25* (0.06)	0.09*** (0.05)	−0.06 (0.03)	0.02 (0.05)	−0.22* (0.05)	0.01*** (0.04)	−0.10 (0.06)	−0.06*** (0.03)
SE	−0.75* (0.17)	−0.72* (0.14)	−0.37*** (0.19)	−0.32 (0.23)	−0.63*** (0.34)	−0.63** (0.27)	−0.02 (0.26)	−0.03 (0.39)	−0.48 (0.32)	0.14 (0.29)	0.32 (0.48)	0.81** (0.25)
MRS	0.02* (0.005)	0.02* (0.01)	0.01 (0.01)	−0.003 (0.01)	0.03* (0.01)	0.01** (0.01)	0.002 (0.01)	0.001 (0.01)	0.003 (0.01)	−0.001 (0.01)	−0.03 (0.02)	−0.01 (0.01)
HO	−0.04 (0.03)	−0.07** (0.03)	0.04 (0.07)	0.02 (0.06)	−0.13*** (0.06)	−0.06 (0.05)	0.10 (0.07)	0.13 (0.11)	−0.10 (0.06)	−0.05 (0.06)	0.14 (0.13)	0.06 (0.07)
SIZE	0.08*** (0.04)	0.10** (0.04)	0.09 (0.11)	0.07 (0.12)	−0.09 (0.09)	−0.06 (0.07)	0.14 (0.13)	−0.12 (0.20)	−0.20** (0.08)	−0.13 (0.08)	0.13 (0.24)	0.21 (0.13)
AGE			−0.06 (0.07)	0.10 (0.09)			−0.06 (0.10)	0.02 (0.14)			0.08 (0.18)	0.11 (0.29)
_cons	2.55* (0.33)	1.74* (0.28)	0.85** (0.36)	0.19 (0.43)	3.16* (0.68)	−0.34 (0.55)	0.89 (0.47)	0.04 (0.71)	2.87 (0.64)	0.66 (0.60)	0.74 (0.88)	0.34 (0.46)
LR ${\chi }^2$	31.77	41.06	35.63	36.17	24.11	26.21	31.52	31.32	40.58	42.15	29.97	34.79
Prob > ${\chi }^2$	0.0002	0.0000	0.0000	0.0000	0.0041	0.0019	0.0002	0.0003	0.0000	0.0004	0.0004	0.0001
Log Likelihood	27.8082	34.6713	25.6767	24.2907	16.8506	22.7335	22.674	16.045	17.9294	21.1189	12.679	22.9705

*, **, and *** denote significance from zero at 1%, 5%, and 10% level respectively. Values in the parenthesis are standard errors.

Table

PSBs		Private Banks
ALB	Allahabad Bank	AXB	Axis Bank Ltd.
AB	Andhra Bank	CSB	C S B Bank Ltd.
BOB	Bank Of Baroda	CUB	City Union Bank Ltd.
BOI	Bank Of India	DCB	D C B Bank Ltd.
BOM	Bank Of Maharashtra	DNLB	Dhanlaxmi Bank Ltd.
CAN	Canara Bank	FB	Federal Bank Ltd.
CBI	Central Bank Of India	HDFC	H D F C Bank Ltd.
CORP	Corporation Bank	ICICI	I C I C I Bank Ltd.
DENA	Dena Bank	INSB	IndusInd Bank Ltd.
INB	Indian Bank	JKB	Jammu & Kashmir Bank Ltd.
IOB	Indian Overseas Bank	KB	Karnataka Bank Ltd.
OBC	Oriental Bank Of Commerce	KVB.	Karur Vysya Bank Ltd.
PSB	Punjab & Sind Bank	LVB	Lakshmi Vilas Bank Ltd.
PNB	Punjab National Bank	RBL	R B L Bank Ltd.
SBI	State Bank Of India	SIB.	South Indian Bank Ltd.
SNB	Syndicate Bank	YB	Yes Bank Ltd.
UCO	Uco Bank
UBI	Union Bank Of India
UNDB	United Bank Of India
VB	Vijaya Bank

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