Geographic proximity, trade and economic growth: a spatial econometrics approach

Figures & data

Table 1. Descriptive statistics of variables during 1992–2016 EU.

		N + g +$\delta$	LNC	LNGDP(t-1)	DLNGDP
25 country	Min	−9.9	19.98	9.86	−0.54
	Max	10.9	27.35	11.89	0.217
	Mean	0.36	24.45	10.98	0.017
	SD	1.69	1.60	0.41	0.04

Source: Research findings.

Table 2. Estimation of panel spatial model using bilateral trade flow matrix.

Variable	GSPRE  Random  effects	SAC Fixed effects	SEM		SAR		SDM
			Fixed effects	Random effects	Fixed effects	Random effects	Fixed effects	Random effects
Constant	0.448***		−0.226		−0.591***		−0.983***
	(3.41)		(−1.52)		(−6.03)		(−4.17)
LNGDP(t-1)	−0.119***	−0.137***	−0.133***	−0.149***	−0.118***	−0.133***	−0.136***	−0.152***
	(−6.79)	(−10.71)	(−9.08)	(−10.75)	(−10.01)	(−11.95)	(−8.77)	(−9.76)
LNcapital	0.036***	0.085***	0.070***	0.087***	0.078***	0.089***	0.062***	0.072***
	(4.30)	(13.59)	(9.00)	(13.28)	(11.67)	(15.01)	(9.26)	(10.58)
(N + 0.05)	−0.009***	−0.009***	−0.008***	−0.008***	−0.008***	−0.008***	−0.008***	−0.009***
	(−10.28)	(−9.91)	(−8.78)	(−9.26)	(−8.70)	(−9.33)	(−8.98)	(−9.62)
LNGDP(t-1) *W							0.017	0.0017
							(0.85)	(0.08)
capital *W							0.0126	0.026**
							(1.11)	(2.02)
(N + 0.05)*W							0.007***	0.005***
							(3.71)	(2.87)
ρ		0.319***			0.408***	0.408***	0.412***	0.406***
		(7.61)			(17.25)	(17.26)	(17.49)	(16.83)
λ	0.940***	0.298***	0.4195***	0.411***
	(26.85)	(6.38)	(18.19)	(17.17)
$\text{empty}$	0.186
	(0.74)
LNL	1236.77	1262.24	1166.03	1244.25	1167.31	1248.77	1187.8	1263.91

*, **, and *** denote significance at 10%, 5%, and 1% level. The numbers in the () are the t–statistic.

Table 3. Results of selection model tests … with bilateral trade flow matrix (GSPRE random).

	Hypothesis H0 (restricted model)	Hypothesis H1 (unrestricted model)	Value of the test statistic (P-value)	The test result
Hausman test (to select the random effects and the fixed effects model)	SDM random	SDM fixed	H = 15.39 (0.0015)	SDM fixed
	SAR random	SAR fixed	H = 15.98(0.0011)	SAR fixed
	SEM random	SEM fixed	H = 16.64 (0.0008)	SEM fixed
LR test (for nested models)	SAR fixed	SDM fixed	LR = −40.98 ()
	SEM fixed	SAC fixed	LR = −192.42 ()
	SAR fixed	SAC fixed	LR = −189.86()
	SEM random	GSPRE random	LR = 14.96(0.0048)	GSPRE random

Table 4. Estimation of panel spatial model using geographical distance matrix.

Variable	GSPRE Random effects	SAC Fixed  effects	SEM		SAR		SDM
			Fixed effects	Random effects	Fixed effects	Random effects	Fixed effects	Random effects
Constant	−0.2			−0.20		0.07		0.3***
	(−1.46)			(−1.47)		(0.232)		(3.58)
LNGDP(t-1)	−0.14***	−0.13***	−0.16***	−0.14***	−0.07***	−0.01	−0.16***	−0.15***
	(−9.74)	(−9.43)	(−12.04)	(−9.72)	(−6.23)	(−1.40)	(−10.54)	(−9.21)
LNcapital	0.07***	0.08***	0.09***	0.07***	0.04***	0.003	0.09***	0.06***
	(8.92)	(11.14)	(13.21)	(8.84)	(6.28)	(0.98)	(12.64)	(8.24)
(N + 0.05)	−0.008***	−0.007***	−0.008***	−0.008***	−0.007***	−0.005***	−0.009***	−0.008***
	(−7.50)	(−7.48)	(−8.09)	(−7.52)	(−7.16)	(−5.06)	(−8.03)	(−6.92)
LNGDP(t-1) *W							0.06***	0.05***
							(11.15)	(8.50)
capital *W							−0.04***	−.02***
							(−11.89)	(−8.61)
(N + 0.05)*W							0.002***	0.001***
							(4.24)	(2.46)
ρ	0.11	0.11***			0.31***	0.31***	0.31***	0.31***
	(1.17)	(5.14)			(128.66)	(121.42)	(113.15)	(117.09)
λ		−0.05	0.10***	0.11***
		(−0.91)	(8.92)	(9.57)
$\text{empty}$	0.12***
	(9.55)
LNL	1129.30	1209.75	1205.88	1128.68	884.90	838.92	954.10	878.16

*, **, and *** denote significance at 10%, 5%, and 1% level. The numbers in the () are the t–statistic.

Table 5. Results of selection model tests … with geographical distance matrix (SAC fixed).

	Hypothesis H0 (restricted model)	Hypothesis H1 (unrestricted model)	Value of the test statistic (P-value)	The test result
Hausman test (to select the random effects and the fixed effects model)	SDM random	SDM fixed	H = 17.67(0.0005)	SDM fixed
	SAR random	SAR fixed	H = 43.54(0.0000)	SAR fixed
	SEM random	SEM fixed	H = −15.75()
LR test (for nested models)	SAR fixed	SDM fixed	LR = 138.393(0.0000)	SDM fixed
	SEM fixed	SAC fixed	LR = 7.7418(0.0517)	SEM fixed
	SAR fixed	SAC fixed	LR = 649.6816(0.0000)	SAC fixed
	SEM random	GSPRE random	LR = 1.2458(0.7420)	SEM random

Table 6. Estimation of panel spatial model using geographical distance & export flow matrix.

Variable	GSPRE  Random  effects	SAC Fixed effects	SEM		SAR		SDM
			Fixed effects	Random effects	Fixed effects	Random effects	Fixed effects	Random effects
Constant	0.25***		0.373***		0.073		−0.239**
	(4.27)		(3.67)		(1.20)		(−2.15)
LNGDP(t-1)	−0.034***	−0.107***	−0.0747**	−0.134***	−0.029***	−0.121***	−0.1***	−0.166***
	(−4.00)	(−10.62)	(−2.10)	(−9.86)	(−3.73)	(−10.89)	(−7.24)	(−11.49)
LNcapital	0.0057**	0.072***	0.019	0.064***	0.012***	0.076***	0.055***	0.056***
	(2.45)	(12.87)	(1.34)	(9.36)	(4.36)	(12.65)	(7.31)	(8.93)
(N + 0.05)	−0.007***	−0.007***	−0.007***	−0.008***	−0.006***	−0.008***	−0.008***	−0.008***
	(−7.44)	(−8.88)	(−7.53)	(−9.29)	(−6.28)	(−9.16)	(−8.64)	(−9.95)
LNGDP(t-1) *W							0.032	0.119
							(0.51)	(1.60)
capital *W							−0.014	0.173***
							(−0.52)	(4.29)
(N + 0.05)*W							0.022***	0.010**
							(3.82)	(1.83)
ρ		2.57***			2.23***	1.975***	2.124***	1.906***
		(17.37)			(17.03)	(14.97)	(15.36)	(13.56)
λ	2.420***	−1.14***	2.431***	2.166***
	(19.13)	(−4.45)	(19.02)	(14.77)
$\text{empty}$	−2.857***
	(−3.30)
LNL	1190.996	1269.35	1188.93	1253.00	1174.14	1262.54	1192.82	1290.9

*, **, and *** denote significance at 10%, 5%, and 1% level. The numbers in the () are the t–statistic.

Table 7. Results of selection model tests … with geographical distance & export flow matrix (GSPRE random).

	Hypothesis H0 (restricted model)	Hypothesis H1 (unrestricted model)	Value of the test statistic (P-value)	The test result
Hausman test (to select the random effects and the fixed effects model)	SDM random	SDM fixed	H = 28.98(0.0000)	SDM fixed
	SAR random	SAR fixed	H = 143.46 (0.0000)	SAR fixed
	SEM random	SEM fixed	H = 18.66(0.0003)	SEM fixed
LR test (for nested models)	SAR fixed	SDM fixed	LR = −37.36 ()
	SEM fixed	SAC fixed	LR = −160.84()
	SAR fixed	SAC fixed	LR = −190.42()
	SEM random	GSPRE random	LR = 124.008(0.0000)	GSPRE random

Table 8. Estimation of panel spatial model using geographical distance & import flow matrix.

Variable	GSPRE Random effects	SAC Fixed effects	SEM		SAR		SDM
			Fixed effects	Random effects	Fixed effects	Random effects	Fixed effects	Random effects
Constant	0.2432***		0.257***		0.086		−0.189*
	(2.63)		(2.87)		(1.39)		(−1.68)
LNGDP(t-1)	−0.0385*	−0.090***	−0.042**	−0.125***	−0.034***	−0.119***	−0.092***	−0.142***
	(−1.80)	(−10.43)	(−2.02)	(−9.28)	(−4.23)	(−10.85)	(−6.77)	(−9.66)
LNcapital	0.008	0.059***	0.009	0.062***	0.012***	0.072***	0.0499***	0.058***
	(1.21)	(11.74)	(1.35)	(9.33)	(4.60)	(12.08)	(6.45)	(9.07)
(N + 0.05)	−0.0067***	−0.007***	−0.007***	−0.008***	−0.006***	−0.008***	−0.008***	−0.008***
	(−7.27)	(−8.95)	(−7.42)	(−9.52)	(−6.56)	(−9.14)	(−8.71)	(−9.98)
LNGDP(t-1) *W							−0.006	0.0049
							(−0.11)	(0.07)
capital *W							0.0018	0.134
							(0.07)	(3.54)
(N + 0.05)*W							0.021***	0.013**
							(4.10)	(2.66)
ρ		2.651***			2.009***	1.756***	1.87***	1.636***
		(25.97)			(18.01)	(15.69)	(15.40)	(13.18)
λ	2.139***	−1.729***	2.139***	1.92***
	(19.68)	(−9.08)	(19.69)	(15.78)
$\text{empty}$	−0.618
	(−0.37)
LNL	1199.82	1293.77	1199.75	1262.6	1187.6	1271.64	1204.69	1289.57

*, **, and *** denote significance at 10%, 5%, and 1% level. The numbers in the () are the t–statistic.

Table 9. Results of selection model tests … with geographical distance & import flow matrix (GSPRE random).

	Hypothesis H0 (restricted model)	Hypothesis H1 (unrestricted model)	Value of the test statistic (P-value)	The test result
Hausman test (to select the random effects and the fixed effects model)	SDM random	SDM fixed	H = 5.40(0.1449)	SDM random
	SAR random	SAR fixed	H = 131.20(0.0000)	SAR fixed
	SEM random	SEM fixed	H = −3.48()
LR test (for nested models)	SAR fixed	SDM fixed	LR = −34.18()
	SEM fixed	SAC fixed	LR = −188.04()
	SAR fixed	SAC fixed	LR = −212.34()
	SEM random	GSPRE random	LR = 125.56(0.0000)	GSPRE random

Table 10. Estimation of panel spatial model using geographical distance & bilateral trade flow matrix.

Variable	GSPRE Random effects	SAC Fixed effects	SEM		SAR		SDM
			Fixed effects	Random effects	Fixed effects	Random effects	Fixed effects	Random effects
Constant	0.3027***		0.295***		−0.32***		0.0936
	(3.11)		(2.65)		(−3.29)		(1.36)
LNGDP(t-1)	−0.066	−0.097***	−0.049	−0.129***	−0.099***	−0.12***	−0.043***	−0.155***
	(−1.33)	(−10.51)	(−1.59)	(−9.52)	(−8.06)	(−10.87)	(−4.68)	(−10.48)
LNcapital	0.018	0.06***	0.0109	0.063***	0.058***	0.074***	0.016***	0.057***
	(0.87)	(12.29)	(1.04)	9.33	(8.05)	(12.35)	(4.83)	(8.92)
(N + 0.05)	−0.007***	−0.007***	−0.007***	−0.008***	−0.08***	−0.008***	−0.007***	−0.008***
	(−6.71)	(−8.93)	(−7.06)	(−9.42)	(−8.42)	(−9.17)	(−7.52)	(−10.02)
LNGDP(t-1) *W							−0.006	0.0301
							(−0.34)	(0.82)
capital *W							0.002	0.079***
							(0.24)	(3.99)
(N + 0.05)*W							0.0128***	0.006**
							(4.68)	(2.26)
ρ		1.333***			0.97***	0.934***	1.073***	0.878***
		(21.96)			(15.75)	(15.39)	(17.91)	(13.30)
λ	1.137***	−0.764***	1.14***	1.020***
	(18.90)	(−6.95)	(19.42)	(15.31)
$\text{empty}$	−0.210975
LNL	1194.63	1282.09	1194.74	1258.16	1191.42	1267.72	1193.76	1290.37

*, **, and *** denote significance at 10%, 5%, and 1% level. The numbers in the () are the t–statistic.

Table 11. Results of selection model tests … with geographical distance & bilateral trade flow matrix (GSPRE random).

	Hypothesis H0 (restricted model)	Hypothesis H1 (unrestricted model)	Value of the test statistic (P-value)	The test result
Hausman test (to select the random effects and the fixed effects model)	SDM random	SDM fixed	H = 116.61 (0.0000)	SDM fixed
	SAR random	SAR fixed	H = −15.92()
	SEM random	SEM fixed	H = 18.30 (0.0004)	SEM fixed
LR test (for nested models)	SAR fixed	SDM fixed	LR = −4.68 ()
	SEM fixed	SAC fixed	LR = −174.7()
	SAR fixed	SAC fixed	LR = −181.34()
	SEM random	GSPRE random	LR = 127.06(0.0000)	GSPRE random

Table 12. Summary of model selection.

Model with different matrix	Import flow matrix	Export flow matrix	Bilateral trade flow matrix	Geographical distance matrix	Geog. & import flow	Geog. & export flow	Geog. & bilateral trade flow
Hausman test
SDM fe vs SDM re	−117.36	143.50	15.39	17.67	5.40	28.98	116.61
	()	(0.0000)	(0.0015)	(0.0005)	(0.1449)	(0.0000)	(0.0000)
SAR fe vs SAR re	16.06	209.49	15.98	43.54	131.20	143.46	−15.92
	(0.0011)	(0.0000)	(0.0011)	(0.0000)	(0.0000)	(0.0000)	()
SEM fe vs SEM re	16.50	−16.75	16.64	−15.75	−3.48	18.66	18.30
	(0.0009)	()	(0.0008)	()	()	(0.0003)	(0.0004)
LR test
SDM fe vs SAR fe	−1.894	−62.68	−40.98	138.393	−34.18	−37.36	−4.68
	()	()	()	(0.0000)	()	()	()
SAC fe vs SEM fe	−190.66	−193.04	−192.42	7.7418	−188.04	−160.84	−174.7
	()	()	()	(0.0517)	()	()	()
SAC fe vs SAR fe	−188.02	247.6	−189.86	649.6816	−212.34	−190.42	−181.34
	()	(0.0000)	()	(0.0000)	()	()	()
GSPRE re vs SEM re	24.28	44.24	14.96	1.2458	125.56	124.008	127.06
	(0.0001)	(0.0001)	(0.0048)	(0.7420)	(0.0000)	(0.0000)	(0.0000)

Table 13. Summary of results for the selected model.

Model with different matrix	Import flow matrix	Export flow matrix	Bilateral trade flow matrix	Geographical distance matrix	Geog. & import flow	Geog. & export flow	Geog. & bilateral trade flow
Constant	0.365**		0.448***		0.2432***	0.25***	0.3027***
	(2.55)		(3.41)		(2.63)	(4.27)	(3.11)
LNGDP(t-1)	−0.102***	−0.140***	−0.119***	−0.13***	−0.0385*	−0.034***	−0.066
	(−5.45)	(−10.87)	(−6.79)	(−9.43)	(−1.80)	(−4.00)	(−1.33)
LNcapital	0.033***	0.087***	0.036***	0.08***	0.008	0.0057**	0.018
	(3.56)	(13.90)	(4.30)	(11.14)	(1.21)	(2.45)	(0.87)
(N + 0.05)	−0.009***	−0.009***	−0.009***	−0.007***	−0.0067***	−0.007***	−0.007***
	(−10.36)	(−9.74)	(−10.28)	(−7.48)	(−7.27)	(−7.44)	(−6.71)
LNGDP(t-1) *W
capital *W
(N + 0.05)*W
ρ		0.646***		0.11***
		(7.65)		(5.14)
λ	1.795***	0.611***	0.940***	−0.05	2.139***	2.420***	1.137***
	(27.18)	(6.53)	(26.85)	(−0.91)	(19.68)	(19.13)	(18.90)
$\text{empty}$	0.636312		0.186		−0.618	−2.857***	−0.210975
	(1.28)		(0.74)		(−0.37)	(−3.30)
LNL	1235.36	1258.74	1236.77	1209.75	1199.82	1190.996	1194.63