Technical efficiency and total factor productivity of rural banks in Ghana

Figures & data

Table 1. Selected interventions in the rural financial sector of Ghana

Period	Interventions	Motives
1988–2000	Rural Finance Project (RFP)—(World Bank support)	• Restructured and streamlined rural banking operations • Capacity-building in financial auditing, loan recovery, and credit administration systems
2001–2009	Rural financial services project (RFSP)—(GOG, World Bank, IFAD and AFDB)	• Strengthened capacities of RCBs individually and as a system • Created ARB Apex Bank to transform RCBs into efficient financial institutions • (2004–2007) Initiated computerization program (RCBs experienced labor-saving efficiencies)
2010–2012	Ghana rural banks computerization & interconnectivity project (GRBCIP)–MCC-Ghana Compact 1)	• Computerization and networking of RCBs with modern banking infrastructure for efficient service delivery • 52 RCBs with 333 branches had been computerized by June 2011 (ARB Apex Bank)
2008–2014	Rural and agricultural finance programme (RAFiP)—IFAD	• RAFiP supports Ghana’s rural financial system by enhancing institutional performance • Activities relate to efficiency and sustainability of the rural banking system

Table 2. Regional distribution of RCBs in Ghana

Region	Total number	No. of RCBs selected
Ashanti	25	20
Brong Ahafo	20	13
Central	21	20
Eastern	22	18
Greater Accra	7	5
Northern	7	5
Upper East	5	4
Upper West	4	3
Volta	12	8
Western	14	11
Total	137	107

Source: Bank of Ghana Bank, January 2013.

Table 3. Descriptive statistics for input and output variables

		Stats	2009	2010	2011	2012
Output variable	Netloans	Mean	2,015.02	2,431.23	3,411.65	4,618.43
		Sd	1,967.85	2,122.01	2,887.51	3,856.54
		Min	40.22	88.88	84.69	132.08
		Max	11,000.00	10,025.00	14,750.00	19,333.33
Input variables	Deposits	Mean	3,474.86	4,756.15	6,834.66	8,872.20
		Sd	3,128.62	4,233.90	5,997.91	7,765.51
		Min	136.67	164.11	236.46	277.82
		Max	20,250.00	25,500.00	33,500.00	41,000.00
	Fixed assets	Mean	727.01	894.55	1,337.21	2,016.79
		Sd	685.78	802.65	1,166.10	1,782.96
		Min	45.54	46.06	55.73	68.07
		Max	4,000.00	4,725.00	5,675.00	8,966.67

Source: Author’s calculations based on Apex Data (in million Ghana cedis).

Table 4. Parameter estimates for the stochastic frontier models

Variables	Parameter	TRE (Model 1)	TFE (Model 2)	BC95 (Model 3)	BC92 (Model 4)
		Coeffs (SE)	Coeffs (SE)	Coeffs (SE)	Coeffs (SE)
Cons	α	0.1346*** (0.0277)		0.3920*** (0.0394)	1.1155*** (0.1513)
βklnXik	βk	0.5743*** (0.0279)	0.3065*** (0.0236)	0.9434*** (0.0429)	0.3398275*** (0.0649)
lnXklnXk	γk	−0.1779*** (0.0221)	−0.2955*** (0.0143)	−0.1107** (0.0440)	−0.1926*** (0.0425)
βmlnXim	βm	0.0816*** (0.0248)	0.0997*** (0.0275)	0.0621** (0.0376)	0.1071*** (0.0298)
lnXmlnXm	γm	−0.0333 (0.0204)	−0.0125 (0.0146)	−0.1614*** (0.0361)	−0.0664*** (0.0235)
lnXik × lnXim	θkm	0.0247 (0.0197)	0.0395** (0.0120)	0.1218*** (0.0404)	0.0346 (0.02505)
T	ϑo	−0.0311*** (0.0051)	−0.0215** (0.0064)	−0.0366*** (0.0106)	−0.0237*** (0.0072)
lnXik × T	θk	0.0060** (0.0024)	0.01512*** (0.0025)	−0.0068 (0.0045)	0.0218*** (0.0042)
lnXim × T	θm	−0.0014 (0.0022)	−0.0061** (0.0021)	0.0021 (0.0040)	−0.0028 (0.0025)
T^2	ϑ01	0.0034*** (0.0003)	0.0039*** (0.0004)	0.0021*** (0.0006)	0.0014*** (0.0003)
Variance parameters
Sigma_u		0.3486*** (0.0094)	0.3585*** (0.0063)	1.9145* (1.0100)	0.2070*** (0.0427)
Sigma_v		0.0593*** (0.0074)	3.28E-10 (1.1700)	0.3071*** (0.0120)	0.0411**** (0.0015)
Lambda		5.8775*** (0.0151)	1.0900*** (0.0063)	6.2338*** (1.0087)

* Significance Level at 10%.

** Significance Level at 5%.

*** Significance Level at 1%.

Table 5. Likelihood-ratio test of models

LR χ^2(66) = 2,499.36 Prob > χ^2 = 0.0000
Assumption: Model (1, 3, 4) nested in model (2)
Model	Obs	ll(model)	df	AIC	BIC
TRE	1,605	71.57	13	−117.14	−47.18
TFE	1,605	481.50	106	−751.00	−180.63
BC95	1,605	−878.94	13	1,783.87	1,853.82
BC92	1,605	39.19	14	−50.38	24.96

Source: STATA post-estimation test.

Figure 1. Quarterly mean technical efficiency.

Figure 2. Mean technical efficiency of RCBs (2009–2012).

Table 6. Technical efficiency bounds and bank classification

Bounds^1	Mean technical efficiency ranges	Class	Number of RCBs
High/upper quartile	≥0.8721	Leaders	29
Middle quartile	0.7554–0.8721	Moderate	53
Lower quartile	≤0.7554	Laggards	25

¹ Bounds were calculated based on Quartiles.

Figure 3. Quarterly changes in TFP, EFFCH, and TECH.

Figure 4. Cumulative TFP change and component–SFA analysis.

Table

Models	Functional form
1. Greene (2005a), True fixed- effects model	$ln{y}_{it}={\mathit{\alpha }}_i+{\mathit{\beta }}^T{x}_{it}+v_{it}-u_{it}$
2. Greene (2005a), True random-effects model	$ln{y}_{it}=(\mathit{\alpha }+w_i)+{\mathit{\beta }}^T{x}_{it}+v_{it}-u_{it}$
3. ML random-effects (RE) time-varying efficiency decay model (Battese & Coelli, 1992)	$y_{it}={\mathit{\alpha }}_0+f(x_{it,}t;\mathit{\beta })+v_{it}-u_{it}$;
	$u_{it}=\left[e\left(-\mathit{\gamma }(t-T_i\right)\right]u_i$
4. ML random-effects (RE) time-varying inefficiency effects model (Battese & Coelli, 1995)	yit = xitβ + (vit − uit)
	$u_i\sim N^{+}\left({\mathit{\gamma }}^{\prime }z,{\mathit{\sigma }}_u^2\right)$
	$v_{it}\sim N\left(0,{\mathit{\sigma }}_u^2\right)$

Table

RCB	EFFCH	TECH	TFP
1	1.005	1.006	1.011
2	0.998	1.006	1.005
3	1.000	1.018	1.018
4	0.981	1.011	0.991
5	1.012	1.005	1.015
6	1.034	1.007	1.040
7	0.974	1.009	0.982
8	1.011	1.004	1.015
9	1.064	1.007	1.071
10	1.018	1.024	1.042
11	0.961	1.004	0.964
12	0.984	1.009	0.994
13	1.015	1.011	1.026
14	0.935	1.012	0.946
15	1.004	1.017	1.021
16	0.987	1.002	0.989
17	0.975	1.007	0.982
18	1.059	1.012	1.072
19	0.970	1.023	0.991
20	1.015	1.010	1.025
21	1.020	1.022	1.041
22	1.106	1.002	1.110
23	1.012	1.014	1.026
24	1.012	1.014	1.027
25	1.104	1.010	1.115
26	1.012	1.012	1.024
27	0.998	1.012	1.009
28	0.959	1.007	0.965
29	0.992	1.011	1.004
30	0.948	1.017	0.964
31	0.945	1.034	0.978
32	1.014	1.020	1.033
33	0.973	1.008	0.981
34	0.988	1.007	0.995
35	0.999	1.009	1.007
36	0.987	1.016	1.002
37	1.055	1.006	1.063
38	1.193	1.018	1.214
39	1.021	1.004	1.025
40	1.068	0.998	1.062
41	0.986	1.026	1.012
42	1.002	1.005	1.007
43	0.982	1.008	0.989
44	0.966	0.976	0.943
45	1.071	0.979	1.049
46	1.024	1.015	1.038
47	1.027	0.993	1.019
48	0.989	1.015	1.003
49	1.025	1.012	1.037
50	1.035	1.000	1.034
51	1.014	1.005	1.018
52	0.992	1.006	0.998
53	0.973	1.006	0.978
54	0.980	0.991	0.971
55	1.001	1.000	1.000
56	0.993	1.011	1.004
57	1.045	1.019	1.065
58	1.012	1.020	1.032
59	1.161	0.991	1.144
60	1.114	1.007	1.121
61	0.964	0.998	0.962
62	0.988	1.010	0.997
63	0.997	1.026	1.023
64	1.034	1.022	1.056
65	0.980	1.012	0.991
66	0.995	1.015	1.010
67	1.041	1.018	1.060
68	0.999	1.010	1.008
69	1.020	1.013	1.033
70	0.997	1.003	0.999
71	0.995	1.018	1.013
72	0.964	0.992	0.954
73	1.005	1.026	1.031
74	0.990	1.018	1.008
75	0.990	1.003	0.992
76	1.034	1.010	1.044
77	1.014	1.019	1.032
78	1.009	1.015	1.024
79	1.096	1.005	1.102
80	1.104	1.005	1.108
81	1.075	1.006	1.082
82	0.972	1.009	0.981
83	1.030	1.007	1.036
84	0.979	1.008	0.986
85	0.980	1.009	0.989
86	0.996	1.028	1.023
87	0.981	1.016	0.996
88	1.013	1.002	1.015
89	1.034	1.014	1.048
90	0.991	1.023	1.014
91	1.009	1.005	1.013
92	1.015	1.018	1.033
93	0.983	1.021	1.003
94	0.990	1.017	1.007
95	0.974	1.025	0.999
96	0.974	1.001	0.974
97	1.049	0.992	1.040
98	1.004	1.026	1.030
99	1.134	1.014	1.154
100	0.996	1.008	1.003
101	1.088	0.997	1.085
102	1.098	1.006	1.103
103	0.994	1.008	1.001
104	1.000	1.008	1.007
105	1.013	1.014	1.026
106	1.027	1.018	1.045
107	1.011	1.013	1.025
Mean	1.013	1.010	1.023

Table

RCB	Bank name	RCB	Bank name	RCB	Bank name
1	Abokobi Area	37	Bessfa	73	Lower Pra
2	Ada	38	Bia Torya Comm	74	Manya Krobo
3	Adansi	39	Bonzali	75	Mfantesman Comm
4	Adonten	40	Borimanga	76	Mponua
5	Afram	41	Bosomtwe	77	Mumuadu
6	Agave	42	Brakwa Breman	78	Naara
7	Agona	43	Builsa Comm	79	Nafana
8	Ahafo Ano	44	Butawu	80	Nandom
9	Ahafo Comm	45	Buuwuloso One-St	81	Nkoranman
10	Ahantaman	46	Capital	82	Nkoranza Kwabre
11	Akatakyiman	47	Citizens	83	North Tongu
12	Akim Bosome	48	Dangme	84	North Volta
13	Akoti	49	Derma Area	85	Nsoatreman
14	Akrofuom	50	Drobo Comm	86	Nwabiagya
15	Akuapem	51	Dumpong	87	Nyakrom
16	Akyem Mansa	52	East Mamprusi	88	Nyankumasi Ahenk
17	Akyempim	53	Eastern Gomoa As	89	Nzema Manle
18	Amanano	54	Ekumfiman	90	Odotobri
19	Amansie West	55	Enyan Denkyira	91	Odupongkpehe
20	Amantin & Kasei	56	Fiagya	92	Okomfo Anokye
21	Amenfiman	57	Fiaseman	93	Otuasekan
22	Ankobra West	58	Ga	94	Sekyedumase
23	Anum	59	Gbi	95	Sekyere
24	Asante Akyem	60	Gomoa	96	Shai
25	Asawinso	61	Gomoa Ajumako	97	Sissala
26	Asokore	62	Jomoro	98	South Akim
27	Assinman	63	Juaben	99	South Birim
28	Asubonten	64	Kaaseman	100	Suma
29	Atiwa	65	Kakum	101	Tizaa
30	Atwima	66	Kintampo	102	Toende
31	Atwima Kwanwoma	67	Kumawuman	103	Twifu
32	Atwima Mponua	68	Kwabibirem	104	Union
33	Avenor	69	Kwahu	105	Unity
34	Awutu Emasa	70	Kwahu Praso	106	Upper Amenfi
35	Baduman	71	Kwamaman	107	Upper Manya Kro
36	Bawjiase Area	72	Lawra Area

Greene, W. (2005a). Fixed and random effects in Stochastic Frontier models. Journal of Productivity Analysis, 23, 7–32. doi:10.1007/s11123-004-8545-1

 Web of Science ®Google Scholar

Battese, G. E., & Coelli, T. J. (1992). Frontier production functions, technical efficiency and panel data: With application to paddy farmers in India (pp. 149–165). Berlin: Springer.

 Google Scholar

Battese, G. E., & Coelli, T. J. (1995). A model for technical inefficiency effects a Stochastic Frontier function for panel data. Empirical Economics, 20, 325. doi:10.1007/BF01205442

 Google Scholar