Spatial competition on rural bank efficiency: Evidence from Indonesia

Figures & data

Table 1. Variables definition and summary statistics

Variable	Symbol	Definition	Obs	Mean	St. Dev	Min	Max	P25	P50	P75
Distance	DISTANCE	Distance from bank to nearest rival bank (in meters)	20,443	5,687	14,222	8.91	102,507	478.92	1,212	3,813
Log Natural Distance	LN_DISTANCE	Natural log of distance from bank to a nearest rival bank	20,443	7.131	1.807	2.187	11.538	6.172	7.100	8.246
Boundary	BOUNDARY	Area of Thiessen polygon for each bank (in km squared)	20,443	1,190	4,140	0.224	31,100	9.727	69.5	406
Log Natural Boundary	LN_BOUNDARY	Natural log of the area of Thiessen polygon for each bank	20,443	18.067	2.541	12.322	24.159	16.090	18.056	19.823
HHI	HHI	The market concentration of assets	20,443	1,197.19	1,565.70	155.32	8,405.31	541.23	715.88	1,257.20
Log Natural HHI	LN_HHI	Natural log of market concentration of assets	20,443	6.585	0.977	5.045	9.037	6.294	6.574	7.137
GDP	PROV_GDP	Growth of provincial GDP by Expenditures in Constant Prices	20,443	0.054	0.010	−0.001	0.084	0.052	0.054	0.059
Inflation	PROV_INF	Provincial Inflation	20,443	0.043	0.038	−0.041	0.179	0.023	0.040	0.056
Total Assets	Y	Total Assets (billion rupiah)	20,443	53.6	92.3	1.961	602	11.6	22.5	49
Price	P	Total revenues to total assets	20,443	0.367	0.125	0.167	0.757	0.277	0.343	0.430
Total Cost	TC	Total Interest Expenses + Total Operational Expenses (billion rupiah)	20,443	15.60	26.00	0.653	174	3.365	6.907	15.5
Outputs:
Loans	$Q_1$	Loans to other rural banks + Loans to commercial banks + Loans to non-bank-related parties + Loans to non-bank-unrelated parties (billion rupiah)	20,443	40.10	70.8	1.305	464	8.221	16.7	36.7
Other earning assets	$Q_2$	Interbank placement (billion rupiah)	20,443	11.4	21.3	0.183	138	1.928	4.367	10.1
Non-interest income	$Q_3$	Non-interest income (billion rupiah)	20,443	0.677	1.160	0.011	7.867	0.125	0.290	0.694
Inputs:
Price of labor	$P_1$	The ratio of administrative expenses to total assets	20,443	0.106	0.052	0.023	0.276	0.068	0.097	0.134
Price of physical capital	$P_2$	The ratio of depreciation expenses to fixed assets	20,443	0.606	0.186	0.135	0.924	0.481	0.619	0.754
Price of borrowed funds	$P_3$	The ratio of interest expenses to total deposits	20,443	0.095	0.044	0.034	0.292	0.069	0.086	0.106
Netput 1	$N_1$	Fixed assets (billion rupiah)	20,443	0.914	1.666	0.014	10.7	0.160	0.344	0.818
Netput 2	$N_2$	Equity (billion rupiah)	20,443	8.806	13.6	0.516	89.7	2.526	4.482	8.509

This table presents the definition of all variables and their summary statistics. The sample covers all Indonesian rural banks from 2014:Q1 to 2018:Q4. All financial ratios are winsorized at a 1 percent level on the top and bottom of the distribution. I also annualized all financial variables. All level financial variables are denominated in billions of Indonesian rupiah (IDR), deflated using the 2014 Consumer Price Index (CPI) deflator.

Table 2. Correlation matrix

	DISTANCE	BOUNDARY	W1	W2	W3	LERNER	MC	HHI	PROV_GDP	PROV_INF
DISTANCE	1
BOUNDARY	0.63^a	1
W1	0.07^a	0.14^a	1
W2	−0.05^a	0.01^a	0.27^a	1
W3	−0.06 ^a	−0.17^a	−0.09^a	−0.08^a	1
LERNER	−0.03^a	0.05^a	0.02^a	0.02^b	−0.16^a	1
MC	0.05^a	0.02^a	0.38^a	0.10^a	0.18^a	−0.84^a	1
HHI	0.20^a	0.30^a	0.08^a	0.01^a	0.03^a	−0.03^a	0.06^a	1
PROV_GDP	−0.07^a	−0.19^a	−0.04^a	0.00^a	0.13^a	−0.05^a	0.04^a	0.03^a	1
PROV_INF	0.03^a	0.01^a	0.03^a	−0.00^a	0.04^a	−0.40^a	0.39^a	0.04^a	0.05^a	1

^asignificant at 1 percent level

^bsignificant at 5 percent level

^csignificant at 10 percent level

This table presents the pairwise correlation between independent variables. The sample covers all Indonesian rural banks from 2014:Q1 to 2018:Q4. All financial ratios are winsorized at the 1 percent level on the top and bottom of the distribution. I also annualized all financial variables. All level financial variables are denominated in billions of Indonesian rupiah (IDR), deflated using the 2014 Consumer Price Index (CPI) deflator.

Table 3. Stochastic Frontier Analysis (SFA) estimation using distance as a spatial variable

$\mathit{l}n\frac{TC}{W_3}$	Coefficient		Coefficient
Frontier
$ln\left(Q_1\right)$	0.9984*** (10.60)	$ln\left(Q_1\right)ln\left(\frac{P_1}{P_3}\right)$	−0.0264* (−1.84)
$ln\left(Q_2\right)$	0.5161*** (9.08)	$ln\left(Q_1\right)ln\left(\frac{P_2}{P_3}\right)$	0.0507*** (3.13)
$ln\left(Q_3\right)$	−0.0586 (−1.42)	$ln\left(Q_2\right)ln\left(\frac{P_1}{P_3}\right)$	−0.0379*** (4.39)
$ln\left(N_1\right)$	0.1913*** (3.50)	$ln\left(Q_2\right)ln\left(\frac{P_2}{P_3}\right)$	0.0050 (0.46)
$ln\left(N_2\right)$	−0.4120*** (−5.45)	$ln\left(Q_3\right)ln\left(\frac{P_1}{P_3}\right)$	−0.0082 (−1.30)
$ln\left(\frac{P_1}{P_3}\right)$	1.096*** (9.68)	$ln\left(Q_3\right)ln\left(\frac{P_2}{P_3}\right)$	0.0124* (1.70)
$ln\left(\frac{P_2}{P_3}\right)$	0.6247*** (5.22)	$ln\left(N_1\right)ln\left(\frac{P_1}{P_3}\right)$	−0.0037 (−0.36)
$\frac{1}{2}{\left[ln\left(Q_1\right)\right]}^2$	0.0839*** (5.50)	$ln\left(N_1\right)ln\left(\frac{P_2}{P_3}\right)$	−0.1150*** (−8.59)
$ln\left(Q_1\right)ln\left(Q_2\right)$	−0.1867*** (−25.77)	$ln\left(N_2\right)ln\left(\frac{P_1}{P_3}\right)$	0.0554*** (4.81)
$ln\left(Q_1\right)ln\left(Q_3\right)$	−0.0009 (−0.18)	$ln\left(N_2\right)ln\left(\frac{P_2}{P_3}\right)$	0.018 (1.28)
$\frac{1}{2}{\left[ln\left(Q_2\right)\right]}^2$	0.1433*** (24.38)	$ln\left(N_1\right)ln\left(Q_1\right)$	−0.0214*** (−2.81)
$ln\left(Q_2\right)ln\left(Q_3\right)$	0.0037 (1.09)	$ln\left(N_1\right)ln\left(Q_2\right)$	0.0144*** (2.94)
$\frac{1}{2}{\left[ln\left(Q_3\right)\right]}^2$	0.0017 (0.50)	$ln\left(N_1\right)ln\left(Q_3\right)$	0.0003 (0.11)
$\frac{1}{2}{\left[ln\left(N_1\right)\right]}^2$	−0.0088 (−1.26)	$ln\left(N_2\right)ln\left(Q_1\right)$	0.0956*** (8.94)
$ln\left(N_1\right)ln\left(N_2\right)$	0.0227*** (3.77)
$\frac{1}{2}{\left[ln\left(N_2\right)\right]}^2$	−0.1315*** (−11.59)	$ln\left(N_2\right)ln\left(Q_2\right)$	0.0256*** (4.41)
$\frac{1}{2}{\left[ln\left(\frac{P_1}{P_3}\right)\right]}^2$	0.2370*** (10.40)	$ln\left(N_2\right)ln\left(Q_3\right)$	−0.0007 (−0.18)
$ln\left(\frac{P_1}{P_3}\right)ln\left(\frac{P_2}{P_3}\right)$	−0.1202*** (−5.31)	constant	−0.6114 (−1.30)
$\frac{1}{2}{\left[ln\left(\frac{P_2}{P_3}\right)\right]}^2$	−0.1662*** (5.49)
Mu
DISTANCE	0.0294*** (4.98)
HHI	0.12998*** (12.01)
PROV_GDP	1.2416 (1.42)
PROV_INF	11.42*** (42.07)
ZONE1	0.3069*** (7.11)
ZONE2	0.1986*** (5.84)
ZONE3	0.2044*** (5.14)
STATE	0.0956 (1.14)
PRIVATE	0.0649 (0.82)
Constant	−1.6184 (−12.01)
Cost-efficiency	Mean 0.8243	Min 0.7903	Max 0.8631

This table presents the SFA estimation of bank cost efficiency using distance as a spatial variable. ***, **, * indicate significance at the 1 percent, 5 percent, and 10 percent levels, respectively. The numbers in parentheses are t-statistics.

Table 4. Stochastic Frontier Analysis (SFA) estimation using boundary as a spatial variable

$\mathit{l}n\frac{TC}{W_3}$	Coefficient		Coefficient
Frontier
$ln\left(Q_1\right)$	1.0012*** (10.64)	$ln\left(Q_1\right)ln\left(\frac{P_1}{P_3}\right)$	−0.0246* (−1.72)
$ln\left(Q_2\right)$	0.5103*** (8.97)	$ln\left(Q_1\right)ln\left(\frac{P_2}{P_3}\right)$	0.0496*** (3.06)
$ln\left(Q_3\right)$	−0.0612 (−1.48)	$ln\left(Q_2\right)ln\left(\frac{P_1}{P_3}\right)$	−0.0371*** (−4.30)
$ln\left(N_1\right)$	0.1926*** (3.52)	$ln\left(Q_2\right)ln\left(\frac{P_2}{P_3}\right)$	0.0058 (0.53)
$ln\left(N_2\right)$	−0.4006*** (−5.30)	$ln\left(Q_3\right)ln\left(\frac{P_1}{P_3}\right)$	−0.0092 (−1.46)
$ln\left(\frac{P_1}{P_3}\right)$	1.1001*** (9.72)	$ln\left(Q_3\right)ln\left(\frac{P_2}{P_3}\right)$	0.0130* (1.77)
$ln\left(\frac{P_2}{P_3}\right)$	0.6154*** (5.14)	$ln\left(N_1\right)ln\left(\frac{P_1}{P_3}\right)$	−0.0032 (−0.31)
$\frac{1}{2}{\left[ln\left(Q_1\right)\right]}^2$	0.0852*** (5.60)	$ln\left(N_1\right)ln\left(\frac{P_2}{P_3}\right)$	−0.1167*** (−8.69)
$ln\left(Q_1\right)ln\left(Q_2\right)$	−0.1864*** (−25.74)	$ln\left(N_2\right)ln\left(\frac{P_1}{P_3}\right)$	0.0527*** (4.59)
$ln\left(Q_1\right)ln\left(Q_3\right)$	−0.0009 (−0.17)	$ln\left(N_2\right)ln\left(\frac{P_2}{P_3}\right)$	0.0203 (1.44)
$\frac{1}{2}{\left[ln\left(Q_2\right)\right]}^2$	0.1431*** (24.35)	$ln\left(N_1\right)ln\left(Q_1\right)$	−0.0210*** (−2.76)
$ln\left(Q_2\right)ln\left(Q_3\right)$	0.0036 (1.06)	$ln\left(N_1\right)ln\left(Q_2\right)$	0.0147*** (2.99)
$\frac{1}{2}{\left[ln\left(Q_3\right)\right]}^2$	0.0015 (0.47)	$ln\left(N_1\right)ln\left(Q_3\right)$	0.0003 (0.11)
$\frac{1}{2}{\left[ln\left(N_1\right)\right]}^2$	−0.0098 (−1.41)	$ln\left(N_2\right)ln\left(Q_1\right)$	0.0936*** (8.78)
$ln\left(N_1\right)ln\left(N_2\right)$	0.0231*** (3.82)	$ln\left(N_2\right)ln\left(Q_2\right)$	0.0256*** (4.41)
$\frac{1}{2}{\left[ln\left(N_2\right)\right]}^2$	−0.1308*** (−11.55)	$ln\left(N_2\right)ln\left(Q_3\right)$	−0.0005 (−0.12)
$\frac{1}{2}{\left[ln\left(\frac{P_1}{P_3}\right)\right]}^2$	0.2376*** (10.43)	constant	−0.6670 (−1.41)
$ln\left(\frac{P_1}{P_3}\right)ln\left(\frac{P_2}{P_3}\right)$	−0.1183*** (5.22)
$\frac{1}{2}{\left[ln\left(\frac{P_2}{P_3}\right)\right]}^2$	−0.1697*** (−5.60)
Mu
BOUNDARY	−0.0193*** (−4.26)
HHI	0.1376*** (12.60)
PROV_GDP	0.6310 (0.71)
PROV_INF	11.48*** (42.09)
ZONE1	0.1523*** (3.31)
ZONE2	0.0611* (1.73)
ZONE3	0.1202*** (2.98)
STATE	0.1026 (1.22)
PRIVATE	0.0362 (0.45)
Constant	−1.4143 (−10.26)
Cost-efficiency	Mean 0.8195	Min 0.7872	Max 0.8593

This table presents the SFA estimation of bank cost efficiency using boundary as a spatial variable. ***, **, * indicate significance at the 1 percent, 5 percent, and 10 percent levels, respectively. The numbers in parentheses are t-statistics.

Table 5. Endogenous Panel Stochastic Frontier Analysis (SFA) using distance as a spatial variable

Dependent Variable: $ln\frac{TC}{W_3}$	Model EX	Model EN
$ln\left(Q_1\right)$	0.395* (0.200)	0.397 (0.230)
$ln\left(Q_2\right)$	0.288* (0.119)	0.275* (0.126)
$ln\left(Q_3\right)$	0.145 (0.089)	0.145 (0.092)
$ln\left(N_1\right)$	0.160 (0.123)	0.176 (0.134)
$ln\left(N_2\right)$	−0.070 (0.174)	−0.064 (0.195)
$ln\left(\frac{P_1}{P_3}\right)$	1.003*** (0.259)	0.991*** (0.275)
$ln\left(\frac{P_2}{P_3}\right)$	0.861*** (0.254)	0.872** (0.266)
$\frac{1}{2}{\left[ln\left(Q_1\right)\right]}^2$	0.130*** (0.028)	0.133*** (0.037)
$ln\left(Q_1\right)ln\left(Q_2\right)$	−0.138*** (0.015)	−0.138*** (0.018)
$ln\left(Q_1\right)ln\left(Q_3\right)$	−0.017 (0.011)	−0.018 (0.012)
$\frac{1}{2}{\left[ln\left(Q_2\right)\right]}^2$	0.124*** (0.013)	0.124*** (0.013)
$ln\left(Q_2\right)ln\left(Q_3\right)$	0.000 (0.007)	−0.001 (0.007)
$\frac{1}{2}{\left[ln\left(Q_3\right)\right]}^2$	0.004 (0.007)	0.006 (0.007)
$\frac{1}{2}{\left[ln\left(N_1\right)\right]}^2$	0.008 (0.015)	0.007 (0.016)
$ln\left(N_1\right)ln\left(N_2\right)$	0.024 (0.013)	0.023 (0.015)
$\frac{1}{2}{\left[ln\left(N_2\right)\right]}^2$	−0.105*** (0.026)	−0.103** (0.036)
$\frac{1}{2}{\left[ln\left(\frac{P_1}{P_3}\right)\right]}^2$	0.1999*** (0.055)	0.205*** (0.057)
$ln\left(\frac{P_1}{P_3}\right)ln\left(\frac{P_2}{P_3}\right)$	−0.120* (0.052)	−0.121* (0.054)
$\frac{1}{2}{\left[ln\left(\frac{P_2}{P_3}\right)\right]}^2$	0.015 (0.060)	0.010 (0.062)
$ln\left(Q_1\right)ln\left(\frac{P_1}{P_3}\right)$	−0.009 (0.032)	−0.004 (0.037)
$ln\left(Q_1\right)ln\left(\frac{P_2}{P_3}\right)$	0.084* (0.034)	0.079* (0.040)
$ln\left(Q_2\right)ln\left(\frac{P_1}{P_3}\right)$	−0.036 (0.020)	−0.037 (0.021)
$ln\left(Q_2\right)ln\left(\frac{P_2}{P_3}\right)$	−0.060** (0.022)	−0.057* (0.023)
$ln\left(Q_3\right)ln\left(\frac{P_1}{P_3}\right)$	−0.019 (0.014)	−0.022 (0.015)
$ln\left(Q_3\right)ln\left(\frac{P_2}{P_3}\right)$	0.010 (0.016)	0.012 (0.016)
$ln\left(N_1\right)ln\left(\frac{P_1}{P_3}\right)$	−0.007 (0.024)	−0.008 (0.026)
$ln\left(N_1\right)ln\left(\frac{P_2}{P_3}\right)$	−0.060* (0.028)	−0.062* (0.029)
$ln\left(N_2\right)ln\left(\frac{P_1}{P_3}\right)$	0.048 (0.026)	0.047 (0.031)
$ln\left(N_2\right)ln\left(\frac{P_2}{P_3}\right)$	−0.036 (0.030)	−0.034 (0.034)
$ln\left(N_1\right)ln\left(Q_1\right)$	−0.026 (0.016)	−0.027 (0.019)
$ln\left(N_1\right)ln\left(Q_2\right)$	−0.007 (0.011)	−0.006 (0.011)
$ln\left(N_1\right)ln\left(Q_3\right)$	0.008 (0.007)	0.008 (0.008)
$ln\left(N_2\right)ln\left(Q_1\right)$	0.045* (0.023)	0.043 (0.035)
$ln\left(N_2\right)ln\left(Q_2\right)$	0.036** (0.012)	0.037** (0.014)
$ln\left(N_2\right)ln\left(Q_3\right)$	0.002 (0.010)	0.002 (0.010)
constant	9.918*** (1.088)
Mu
DISTANCE	0.115*** (0.035)	0.002 (0.042)
HHI	0.252*** (0.056)	0.115 (0.066)
PROV_GDP	−1.922 (3.466)	−2.530 (3.558)
PROV_INF	23.710*** (0.798)	23.756*** (0.806)
ZONE1	0.739** (0.229)	0.386 (0.234)
ZONE2	0.148 (0.180)	−0.225 (0.189)
ZONE3	−0.038 (0.227)	−0.363 (0.232)
STATE	0.436 (0.503)	0.461 (0.498)
PRIVATE	0.147 (0.479)	0.113 (0.475)
Constant	−6.655*** (0.673)
Endogenous Variables
HHI	0.026*** (0.007)	0.026*** (0.007)
DISTANCE	0.017*** (0.004)	0.017*** (0.004)
Instrumental Variables
DIST_FSA_POP
BOUNDARY_PROVINCE_POP
Mean Cost-Efficiency	0.8662	0.8649
Min Cost-Efficiency	0.7963	0.7821
Max Cost-Efficiency	0.8798	0.8755

This table presents an endogenous SFA estimation of bank cost efficiency using distance as a spatial variable. Instrumental variables are included. Panel A is Model EX, and Panel B is Model EN. ***, **, * indicate significance at the 1 percent, 5 percent, and 10 percent levels, respectively. The numbers in parentheses are standard errors.

Table 6. Endogenous panel stochastic frontier analysis (SFA) using boundary as a spatial variable

Dependent Variable: $ln\frac{TC}{W_3}$	Model EX	Model EN
$ln\left(Q_1\right)$	0.386* (0.197)	0.397 (0.209)
$ln\left(Q_2\right)$	0.279* (0.118)	0.266* (0.121)
$ln\left(Q_3\right)$	0.145 (0.088)	0.150 (0.090)
$ln\left(N_1\right)$	0.163 (0.122)	0.169 (0.128)
$ln\left(N_2\right)$	−0.059 (0.173)	−0.051 (0.181)
$ln\left(\frac{P_1}{P_3}\right)$	0.991*** (0.256)	0.998*** (0.264)
$ln\left(\frac{P_2}{P_3}\right)$	0.848*** (0.252)	0.856*** (0.259)
$\frac{1}{2}{\left[ln\left(Q_1\right)\right]}^2$	0.133*** (0.028)	0.132*** (0.033)
$ln\left(Q_1\right)ln\left(Q_2\right)$	−0.138*** (0.015)	−0.136*** (0.016)
$ln\left(Q_1\right)ln\left(Q_3\right)$	−0.018 (0.011)	−0.018 (0.012)
$\frac{1}{2}{\left[ln\left(Q_2\right)\right]}^2$	0.124*** (0.013)	0.124*** (0.013)
$ln\left(Q_2\right)ln\left(Q_3\right)$	−0.000 (0.007)	−0.001 (0.007)
$\frac{1}{2}{\left[ln\left(Q_3\right)\right]}^2$	0.005 (0.007)	0.005 (0.007)
$\frac{1}{2}{\left[ln\left(N_1\right)\right]}^2$	0.006 (0.015)	0.006 (0.015)
$ln\left(N_1\right)ln\left(N_2\right)$	0.024 (0.013)	0.025 (0.014)
$\frac{1}{2}{\left[ln\left(N_2\right)\right]}^2$	−0.105*** (0.026)	−0.105*** (0.030)
$\frac{1}{2}{\left[ln\left(\frac{P_1}{P_3}\right)\right]}^2$	0.202*** (0.054)	0.207*** (0.056)
$ln\left(\frac{P_1}{P_3}\right)ln\left(\frac{P_2}{P_3}\right)$	−0.117* (0.051)	−0.119* (0.053)
$\frac{1}{2}{\left[ln\left(\frac{P_2}{P_3}\right)\right]}^2$	0.006 (0.060)	0.006 (0.061)
$ln\left(Q_1\right)ln\left(\frac{P_1}{P_3}\right)$	−0.004 (0.032)	−0.001 (0.034)
$ln\left(Q_1\right)ln\left(\frac{P_2}{P_3}\right)$	0.082* (0.034)	0.077* (0.037)
$ln\left(Q_2\right)ln\left(\frac{P_1}{P_3}\right)$	−0.034 (0.020)	−0.035 (0.020)
$ln\left(Q_2\right)ln\left(\frac{P_2}{P_3}\right)$	−0.059** (0.022)	−0.058* (0.023)
$ln\left(Q_3\right)ln\left(\frac{P_1}{P_3}\right)$	−0.023 (0.014)	−0.024 (0.014)
$ln\left(Q_3\right)ln\left(\frac{P_2}{P_3}\right)$	0.012 (0.016)	0.013 (0.016)
$ln\left(N_1\right)ln\left(\frac{P_1}{P_3}\right)$	−0.006 (0.024)	−0.007 (0.025)
$ln\left(N_1\right)ln\left(\frac{P_2}{P_3}\right)$	−0.064* (0.028)	−0.063* (0.029)
$ln\left(N_2\right)ln\left(\frac{P_1}{P_3}\right)$	0.043 (0.026)	0.043 (0.028)
$ln\left(N_2\right)ln\left(\frac{P_2}{P_3}\right)$	−0.031 (0.030)	−0.030 (0.032)
$ln\left(N_1\right)ln\left(Q_1\right)$	−0.026 (0.016)	−0.027 (0.018)
$ln\left(N_1\right)ln\left(Q_2\right)$	−0.006 (0.010)	−0.007 (0.011)
$ln\left(N_1\right)ln\left(Q_3\right)$	0.008 (0.007)	0.008 (0.008)
$ln\left(N_2\right)ln\left(Q_1\right)$	0.043 (0.022)	0.043 (0.029)
$ln\left(N_2\right)ln\left(Q_2\right)$	0.036** (0.012)	0.036** (0.013)
$ln\left(N_2\right)ln\left(Q_3\right)$	0.003 (0.010)	0.002 (0.010)
constant	9.989*** (1.077)	9.882*** (1.110)
Mu
BOUNDARY	−0.059* (0.028)	−0.081** (0.031)
HHI	0.268*** (0.056)	0.138* (0.067)
PROV_GDP	−3.266 (3.528)	−4.297 (3.603)
PROV_INF	24.079*** (0.810)	24.091*** (0.810)
ZONE1	0.242 (0.260)	0.014 (0.270)
ZONE2	−0.272 (0.193)	−0.491* (0.203)
ZONE3	−0.278 (0.232)	−0.514* (0.238)
STATE	0.458 (0.506)	0.455 (0.499)
PRIVATE	0.063 (0.482)	0.055 (0.476)
Constant	9.989*** (1.077)
Endogenous Variables
HHI	0.023*** (0.006)	0.023*** (0.006)
BOUNDARY	0.006* (0.003)	0.006* (0.003)
Instrumental Variables
DIST_FSA_POP
BOUNDARY_PROVINCE_POP
Mean Cost-Efficiency	0.8687	0.8677
Min Cost-Efficiency	0.7932	0.7845
Max Cost-Efficiency	0.8789	0.8774

This table presents an endogenous SFA estimation of bank cost efficiency using boundary as a spatial variable. Instrumental variables are included. Panel A is Model EX, and Panel B is Model EN. ***, **, * indicate significance at the 1 percent, 5 percent, and 10 percent levels, respectively. The numbers in parentheses are standard errors.

Table 7. Additional analysis (non-rural banks presence) with Stochastic Frontier Analysis (SFA)

$ln\frac{TC}{W_3}$	Coefficient		Coefficient
Frontier
$ln\left(Q_1\right)$	0.9795*** (10.44)	$ln\left(Q_1\right)ln\left(\frac{P_1}{P_3}\right)$	−0.0249* (−1.74)
$ln\left(Q_2\right)$	0.5123*** (9.03)	$ln\left(Q_1\right)ln\left(\frac{P_2}{P_3}\right)$	0.0505*** (3.12)
$ln\left(Q_3\right)$	−0.0559 (−1.36)	$ln\left(Q_2\right)ln\left(\frac{P_1}{P_3}\right)$	−0.0378*** (−4.39)
$ln\left(N_1\right)$	0.2011*** (3.69)	$ln\left(Q_2\right)ln\left(\frac{P_2}{P_3}\right)$	0.0052 (0.47)
$ln\left(N_2\right)$	−0.4078*** (−5.40)	$ln\left(Q_3\right)ln\left(\frac{P_1}{P_3}\right)$	−0.0082 (−1.30)
$ln\left(\frac{P_1}{P_3}\right)$	1.0703*** (9.49)	$ln\left(Q_3\right)ln\left(\frac{P_2}{P_3}\right)$	0.0122* (1.67)
$ln\left(\frac{P_2}{P_3}\right)$	0.6490*** (5.43)	$ln\left(N_1\right)ln\left(\frac{P_1}{P_3}\right)$	−0.0039 (−0.38)
$\frac{1}{2}{\left[ln\left(Q_1\right)\right]}^2$	0.0853*** (5.61)	$ln\left(N_1\right)ln\left(\frac{P_2}{P_3}\right)$	−0.1158*** (−8.65)
$ln\left(Q_1\right)ln\left(Q_2\right)$	−0.1868*** (−25.82)	$ln\left(N_2\right)ln\left(\frac{P_1}{P_3}\right)$	0.0555*** (4.83)
$ln\left(Q_1\right)ln\left(Q_3\right)$	−0.0011 (−0.21)	$ln\left(N_2\right)ln\left(\frac{P_2}{P_3}\right)$	0.0176 (1.25)
$\frac{1}{2}{\left[ln\left(Q_2\right)\right]}^2$	0.1434*** (24.42)	$ln\left(N_1\right)ln\left(Q_1\right)$	−0.0215*** (−2.84)
$ln\left(Q_2\right)ln\left(Q_3\right)$	0.0037 (1.11)	$ln\left(N_1\right)ln\left(Q_2\right)$	0.0145*** (2.96)
$\frac{1}{2}{\left[ln\left(Q_3\right)\right]}^2$	0.0015 (0.46)	$ln\left(N_1\right)ln\left(Q_3\right)$	0.0003 (0.10)
$\frac{1}{2}{\left[ln\left(N_1\right)\right]}^2$ $ln\left(N_1\right)ln\left(N_2\right)$	−0.0088 (−1.27) 0.0224*** (3.72)	$ln\left(N_2\right)ln\left(Q_1\right)$	0.0958*** (8.97)
$\frac{1}{2}{\left[ln\left(N_2\right)\right]}^2$	−0.1319*** (−11.62)	$ln\left(N_2\right)ln\left(Q_2\right)$	0.0257*** (4.43)
$\frac{1}{2}{\left[ln\left(\frac{P_1}{P_3}\right)\right]}^2$	0.2389*** (10.52)	$ln\left(N_2\right)ln\left(Q_3\right)$	−0.0006 (−0.14)
$ln\left(\frac{P_1}{P_3}\right)ln\left(\frac{P_2}{P_3}\right)$	−0.1204*** (−5.33)	constant	−0.5653 (−1.20)
$\frac{1}{2}{\left[ln\left(\frac{P_2}{P_3}\right)\right]}^2$	−0.1688*** (5.57)
Mu
BIG_DUMMY	−0.0225 (−0.88)
DISTANCE	0.0329*** (4.69)
HHI	0.1329*** (11.96)
PROV_GDP	1.199 (1.36)
PROV_INF	11.50*** (41.85)
ZONE1	0.3190*** (7.14)
ZONE2	0.1993*** (5.82)
ZONE3	0.2065*** (5.16)
STATE	0.1078 (1.27)
PRIVATE	0.0802 (0.99)
Constant	−1.656 (−12.13)
Cost-efficiency	Mean 0.8144	Min 0.7870	Max 0.8437

This table presents the SFA estimation of bank cost efficiency on BIG banks’ presence using distance as a spatial variable. ***, **, * indicate significance at the 1 percent, 5 percent, and 10 percent levels, respectively. The numbers in parentheses are t-statistics.

Figure A1. Thiessen Polygons for Each Province in Indonesia.

Figure A1. (Continued).

Figure A1. (Continued).

Figure A1. (Continued).

Figure A1. (Continued).