Networks in Japanese regional agro-food economies: an empirical exploration of the network linkage model

Ishikawa, Kiyotaka

doi:10.1186/s40008-023-00316-9

Journal of Economic Structures

The Official Journal of the Pan-Pacific Association of Input-Output Studies (PAPAIOS)

Table 8 Estimates of elasticity of substitution

From: Networks in Japanese regional agro-food economies: an empirical exploration of the network linkage model

id		LS FE		IV FE
id		\(\theta\)	\(\theta -1\) s.e	\(\theta\)	\(\theta -1\) s.e	1st F	Overidentification	Endogeneity
hok	1	0.903	0.075	0.032	0.419	5	1.8 (0.408)	3 (0.077)
	2	1.159	0.074	1.709	0.197	200	2.8 (0.244)	15 (0.000)
	3	1.161	0.101	2.587	0.668	2	5.4 (0.069)	13 (0.000)
	4	0.908	0.021	0.878	0.025	589	38.1 (0.000)	4 (0.037)
	5	1.044	0.036	0.495	0.214	18	7.2 (0.007)	10 (0.001)
	6	1.039	0.024	1.110	0.067	142	2.4 (0.305)	2 (0.205)
	7	0.990	0.016	1.132	0.054	325	3.6 (0.060)	8 (0.004)
	8	0.996	0.038	1.398	0.190	35	1.7 (0.187)	8 (0.005)
	9	1.030	0.023	1.256	0.092	29	6.2 (0.044)	8 (0.006)
	10	1.015	0.021	1.057	0.032	179	0.9 (0.646)	3 (0.076)
	11	1.119	0.058	1.578	0.203	90	8.8 (0.012)	6 (0.013)
	12	1.102	0.033	1.118	0.045	1176	0.8 (0.678)	0 (0.550)
	13	0.909	0.026	1.122	0.075	21	1.0 (0.593)	8 (0.006)
	14	0.954	0.019	0.919	0.018	229	3.7 (0.157)	4 (0.047)
	15	1.373	0.028	3.339	0.111	185	42.9 (0.000)	1514 (0.000)
	16	0.943	0.026	1.543	0.484	1	18.3 (0.000)	3 (0.074)
	17	1.058	0.060	0.779	0.309	4	2.8 (0.245)	0 (0.546)
	18	1.055	0.034	0.842	0.165	3	2.9 (0.089)	1 (0.227)
	19	0.945	0.052	0.215	0.203	21	32.1 (0.000)	9 (0.003)
	20	1.025	0.034	1.311	0.258	9	2.3 (0.322)	2 (0.185)
	21	1.031	0.037	1.573	0.471	3	0.1 (0.741)	2 (0.144)
toh	1	0.907	0.134	3.160	3.559	1	0.2 (0.672)	3 (0.070)
	2	1.078	0.076	1.455	0.154	214	19.4 (0.000)	10 (0.002)
	3	1.312	0.135	0.961	0.176	14	17.2 (0.000)	2 (0.170)
	4	0.867	0.016	0.699	0.018	1204	31.8 (0.000)	169 (0.000)
	5	1.041	0.042	0.155	0.232	19	15.4 (0.000)	17 (0.000)
	6	0.919	0.026	0.541	0.055	114	55.0 (0.000)	74 (0.000)
	7	1.078	0.018	1.226	0.051	127	48.5 (0.000)	9 (0.003)
	8	1.154	0.027	1.503	0.064	66	88.1 (0.000)	58 (0.000)
	9	1.097	0.039	2.872	0.709	3	16.1 (0.000)	62 (0.000)
	10	1.196	0.022	1.514	0.040	74	65.7 (0.000)	136 (0.000)
	11	1.207	0.046	3.638	0.494	39	7.3 (0.026)	460 (0.000)
	12	0.831	0.037	0.584	0.052	674	6.0 (0.050)	54 (0.000)
	13	1.103	0.115	0.571	0.223	12	0.5 (0.764)	2 (0.122)
	14	0.972	0.031	0.863	0.033	222	8.7 (0.013)	20 (0.000)
	15	1.392	0.032	3.328	0.102	182	73.1 (0.000)	818 (0.000)
	16	0.958	0.042	1.618	0.314	2	43.5 (0.000)	7 (0.011)
	17	0.992	0.067	−1.857	0.994	5	3.9 (0.145)	23 (0.000)
	18	1.091	0.038	3.674	0.739	7	7.7 (0.021)	207 (0.000)
	19	0.992	0.064	5.825	2.089	4	0.3 (0.597)	94 (0.000)
	20	1.042	0.033	3.638	3.172	0	18.3 (0.000)	10 (0.002)
	21	1.023	0.046	4.198	1.314	4	0.0 (0.905)	67 (0.000)
kan	1	1.070	0.108	0.426	0.194	13	14.8 (0.001)	12 (0.001)
	2	1.253	0.063	1.583	0.110	336	2.6 (0.269)	31 (0.000)
	3	1.233	0.071	0.475	0.313	4	11.9 (0.003)	8 (0.005)
	4	0.783	0.019	0.705	0.016	1338	53.1 (0.000)	68 (0.000)
	5	0.965	0.025	0.748	0.085	11	41.0 (0.000)	5 (0.033)
	6	0.990	0.027	0.359	0.118	33	72.2 (0.000)	78 (0.000)
	7	0.946	0.019	1.364	0.076	58	32.2 (0.000)	29 (0.000)
	8	1.031	0.019	1.152	0.084	30	1.1 (0.302)	3 (0.069)
	9	1.024	0.021	0.637	0.091	14	134.0 (0.000)	18 (0.000)
	10	1.009	0.024	1.068	0.029	56	3.7 (0.053)	4 (0.055)
	11	1.128	0.026	1.325	0.153	10	5.8 (0.056)	2 (0.193)
	12	0.982	0.031	0.551	0.077	205	3.3 (0.191)	78 (0.000)
	13	0.985	0.051	0.845	0.061	86	1.7 (0.431)	9 (0.003)
	14	1.004	0.010	1.390	0.073	158	3.9 (0.048)	43 (0.000)
	15	1.396	0.025	3.294	0.086	249	63.5 (0.000)	1500 (0.000)
	16	1.015	0.039	1.527	0.198	5	44.6 (0.000)	14 (0.000)
	17	1.005	0.053	0.135	0.456	4	33.8 (0.000)	11 (0.001)
	18	1.065	0.036	2.247	0.430	5	25.0 (0.000)	53 (0.000)
	19	0.990	0.045	−0.697	0.599	5	57.3 (0.000)	45 (0.000)
	20	1.046	0.038	2.027	0.464	4	12.5 (0.002)	16 (0.000)
	21	1.024	0.032	1.302	0.178	14	15.7 (0.000)	6 (0.018)
chb	1	1.386	0.112	4.568	1.638	2	1.3 (0.533)	21 (0.000)
	2	1.202	0.049	1.552	0.088	292	2.4 (0.308)	46 (0.000)
	3	1.346	0.129	0.286	0.511	3	11.0 (0.004)	2 (0.157)
	4	0.750	0.024	0.630	0.019	728	19.3 (0.000)	76 (0.000)
	5	1.019	0.024	1.314	0.077	13	10.2 (0.006)	15 (0.000)
	6	1.001	0.018	0.788	0.052	65	18.5 (0.000)	20 (0.000)
	7	1.120	0.027	1.202	0.026	116	69.9 (0.000)	13 (0.000)
	8	1.063	0.022	1.361	0.071	17	10.0 (0.007)	32 (0.000)
	9	1.194	0.040	2.307	0.241	15	2.0 (0.374)	181 (0.000)
	10	1.049	0.022	1.269	0.042	30	5.6 (0.060)	32 (0.000)
	11	1.091	0.028	1.155	0.297	2	39.4 (0.000)	0 (0.809)
	12	0.986	0.025	0.836	0.052	652	29.8 (0.000)	23 (0.000)
	13	0.992	0.034	1.484	0.280	19	6.8 (0.009)	4 (0.058)
	14	0.953	0.009	0.980	0.026	411	8.5 (0.014)	3 (0.076)
	15	1.352	0.029	3.120	0.079	297	19.0 (0.000)	3465 (0.000)
	16	1.062	0.036	2.187	0.451	3	32.6 (0.000)	35 (0.000)
	17	1.105	0.069	2.667	0.494	7	6.4 (0.042)	18 (0.000)
	18	1.039	0.039	0.687	0.142	5	26.3 (0.000)	5 (0.032)
	19	0.998	0.040	0.345	0.237	9	21.8 (0.000)	11 (0.001)
	20	0.963	0.046	−2.265	1.089	5	0.8 (0.373)	115 (0.000)
	21	1.032	0.042	2.291	0.384	10	18.2 (0.000)	30 (0.000)
kin	1	1.271	0.085	2.345	0.432	3	9.2 (0.010)	8 (0.006)
	2	1.269	0.054	1.455	0.092	348	5.4 (0.068)	11 (0.001)
	3	1.375	0.133	0.127	0.573	4	3.6 (0.059)	3 (0.066)
	4	0.831	0.033	0.747	0.029	642	35.3 (0.000)	16 (0.000)
	5	1.052	0.021	1.186	0.054	21	22.1 (0.000)	5 (0.021)
	6	1.008	0.022	0.619	0.079	31	13.0 (0.002)	51 (0.000)
	7	1.055	0.023	1.131	0.018	208	73.0 (0.000)	22 (0.000)
	8	0.978	0.026	0.928	0.127	8	0.9 (0.641)	0 (0.690)
	9	0.795	0.027	0.234	0.112	28	74.1 (0.000)	61 (0.000)
	10	0.945	0.022	0.788	0.040	43	23.1 (0.000)	23 (0.000)
	11	1.071	0.021	1.101	0.110	42	0.6 (0.732)	0 (0.818)
	12	1.027	0.028	0.736	0.069	266	8.0 (0.019)	33 (0.000)
	13	0.970	0.068	0.814	0.054	64	4.0 (0.139)	12 (0.001)
	14	1.015	0.011	0.964	0.024	201	9.9 (0.007)	12 (0.001)
	15	1.379	0.023	3.000	0.081	211	173.8 (0.000)	1174 (0.000)
	16	1.003	0.021	1.611	0.382	2	5.8 (0.016)	12 (0.001)
	17	1.056	0.060	2.344	0.373	8	15.9 (0.000)	15 (0.000)
	18	1.054	0.038	1.334	0.265	5	19.0 (0.000)	1 (0.277)
	19	0.983	0.045	0.701	1.488	1	19.3 (0.000)	0 (0.796)
	20	1.034	0.040	−0.460	0.481	6	16.1 (0.000)	59 (0.000)
	21	1.004	0.048	1.546	0.277	8	52.8 (0.000)	5 (0.027)
chg	1	1.296	0.137	6.802	2.161	5	2.5 (0.284)	94 (0.000)
	2	1.116	0.047	1.426	0.079	279	3.5 (0.174)	17 (0.000)
	3	1.466	0.145	3.577	1.236	2	0.1 (0.808)	5 (0.024)
	4	0.878	0.019	0.712	0.019	867	39.9 (0.000)	167 (0.000)
	5	0.913	0.020	0.811	0.030	111	21.2 (0.000)	30 (0.000)
	6	0.942	0.030	0.583	0.128	19	58.8 (0.000)	14 (0.000)
	7	1.064	0.018	1.099	0.026	210	12.3 (0.002)	4 (0.050)
	8	1.050	0.031	0.890	0.120	61	26.1 (0.000)	2 (0.145)
	9	0.991	0.021	0.745	0.047	41	114.9 (0.000)	20 (0.000)
	10	0.959	0.027	0.873	0.039	58	6.9 (0.009)	4 (0.036)
	11	0.973	0.028	0.612	0.151	30	32.9 (0.000)	5 (0.022)
	12	1.044	0.028	0.946	0.046	730	42.4 (0.000)	10 (0.002)
	13	1.017	0.045	0.932	0.071	188	23.2 (0.000)	3 (0.084)
	14	1.033	0.012	1.081	0.030	292	4.1 (0.126)	6 (0.019)
	15	1.411	0.033	1.741	0.046	176	182.8 (0.000)	63 (0.000)
	16	0.980	0.031	−0.048	0.552	2	11.3 (0.001)	19 (0.000)
	17	1.046	0.087	−0.121	0.459	8	1.9 (0.396)	9 (0.003)
	18	1.020	0.049	−0.349	1.086	1	0.1 (0.754)	6 (0.017)
	19	0.934	0.047	0.197	0.363	9	0.3 (0.616)	10 (0.002)
	20	0.989	0.037	−0.058	0.428	6	0.1 (0.814)	18 (0.000)
	21	1.002	0.034	2.756	1.317	1	4.4 (0.037)	9 (0.003)
sik	1	1.175	0.106	2.866	0.636	15	4.3 (0.115)	21 (0.000)
	2	1.010	0.058	2.295	0.593	6	3.7 (0.054)	11 (0.001)
	3	1.428	0.167	2.138	0.460	6	1.2 (0.272)	2 (0.128)
	4	0.784	0.022	0.588	0.020	642	54.7 (0.000)	332 (0.000)
	5	1.010	0.038	0.518	0.179	10	24.6 (0.000)	8 (0.006)
	6	0.852	0.032	0.584	0.046	155	5.8 (0.056)	47 (0.000)
	7	0.974	0.015	1.639	0.208	51	1.2 (0.271)	14 (0.000)
	8	1.064	0.016	1.232	0.059	148	2.3 (0.320)	14 (0.000)
	9	0.789	0.042	0.543	0.052	504	58.0 (0.000)	38 (0.000)
	10	0.664	0.050	0.256	0.100	85	6.0 (0.049)	28 (0.000)
	11	0.987	0.025	1.136	0.123	86	37.0 (0.000)	1 (0.338)
	12	0.546	0.053	0.224	0.053	1197	101.0 (0.000)	48 (0.000)
	13	0.823	0.036	0.377	0.312	7	9.5 (0.002)	2 (0.181)
	14	0.912	0.020	1.242	0.042	229	19.2 (0.000)	121 (0.000)
	15	1.333	0.022	3.255	0.104	186	84.1 (0.000)	1649 (0.000)
	16	0.975	0.047	3.425	2.155	1	2.9 (0.234)	24 (0.000)
	17	1.290	0.109	2.422	0.696	8	1.5 (0.218)	2 (0.131)
	18	1.035	0.047	−0.873	0.380	13	2.5 (0.288)	61 (0.000)
	19	0.946	0.046	−2.403	0.867	15	0.6 (0.725)	144 (0.000)
	20	1.014	0.037	0.033	0.267	8	98.5 (0.000)	16 (0.000)
	21	1.049	0.048	2.434	0.670	4	0.0 (0.954)	10 (0.001)
kyu	1	1.160	0.120	1.799	0.374	4	31.1 (0.000)	3 (0.080)
	2	0.891	0.057	0.563	0.140	137	6.6 (0.037)	11 (0.001)
	3	1.232	0.138	0.604	0.291	3	6.4 (0.042)	2 (0.166)
	4	0.877	0.014	0.841	0.014	1883	69.0 (0.000)	26 (0.000)
	5	0.967	0.019	1.196	0.084	35	16.9 (0.000)	6 (0.019)
	6	1.007	0.021	0.008	0.209	15	2.4 (0.125)	49 (0.000)
	7	0.954	0.025	1.491	0.082	51	37.7 (0.000)	46 (0.000)
	8	1.162	0.031	1.814	0.132	21	103.4 (0.000)	59 (0.000)
	9	1.363	0.030	2.054	0.090	59	42.5 (0.000)	268 (0.000)
	10	1.215	0.033	1.890	0.078	49	62.1 (0.000)	321 (0.000)
	11	1.067	0.021	1.842	0.174	43	9.5 (0.009)	124 (0.000)
	12	0.647	0.045	−0.088	0.082	290	7.3 (0.026)	233 (0.000)
	13	1.069	0.042	0.009	0.378	27	5.1 (0.024)	17 (0.000)
	14	0.947	0.016	0.898	0.036	152	2.5 (0.285)	3 (0.072)
	15	1.306	0.025	2.812	0.075	223	131.8 (0.000)	493 (0.000)
	16	0.995	0.024	2.047	0.653	2	0.7 (0.401)	23 (0.000)
	17	1.015	0.103	−3.975	1.446	5	0.9 (0.646)	52 (0.000)
	18	1.031	0.039	0.403	0.269	3	1.1 (0.285)	12 (0.001)
	19	0.974	0.043	−2.389	1.184	4	0.0 (0.994)	76 (0.000)
	20	1.020	0.033	−0.206	0.443	4	0.1 (0.775)	22 (0.000)
	21	1.033	0.053	2.043	0.391	19	4.3 (0.038)	17 (0.000)
oki	1	1.124	0.109	1.822	0.471	7	8.8 (0.003)	2 (0.169)
	2	1.474	0.149	3.898	0.807	19	0.2 (0.926)	36 (0.000)
	3	0.447	0.167	0.512	1.399	11	1.4 (0.494)	0 (0.955)
	4	0.617	0.025	0.566	0.019	878	3.9 (0.141)	35 (0.000)
	5	0.855	0.135	0.008	0.456	17	6.7 (0.034)	8 (0.005)
	6	0.859	0.020	0.908	0.037	183	6.8 (0.033)	4 (0.056)
	7	1.087	0.012	1.034	0.015	1339	0.1 (0.943)	37 (0.000)
	8	1.192	0.042	1.063	0.070	54	3.9 (0.139)	7 (0.008)
	9	1.087	0.075	0.141	0.346	6	5.6 (0.062)	21 (0.000)
	10	1.154	0.020	1.331	0.046	60	1.7 (0.190)	11 (0.001)
	11	0.897	0.063	0.619	0.081	295	24.6 (0.000)	24 (0.000)
	12	1.182	0.076	1.356	0.068	159	14.3 (0.001)	11 (0.001)
	13	0.923	0.104	0.642	0.137	81	1.7 (0.191)	3 (0.096)
	14	1.085	0.086	1.089	0.085	3874	2.5 (0.111)	0 (0.503)
	15	1.388	0.030	1.826	0.064	109	49.6 (0.000)	50 (0.000)
	16	1.029	0.048	5.028	3.527	1	2.3 (0.318)	38 (0.000)
	17	1.088	0.166	0.925	0.666	3	39.0 (0.000)	0 (0.808)
	18	1.135	0.051	3.574	0.854	9	46.6 (0.000)	58 (0.000)
	19	1.031	0.110	−0.949	0.891	6	50.6 (0.000)	7 (0.009)
	20	1.022	0.038	0.005	0.311	9	104.3 (0.000)	27 (0.000)
	21	1.195	0.069	2.591	0.368	10	45.1 (0.000)	20 (0.000)

(1) For sector classification (id), see Tables 2 and 3. Final demand sector (id = 0) is omitted
(2) All variables are taken first difference of log-transformed values in the period 1970–2015 (9 observations every 5 years after 1975 for Okinawa, 10 observations every 5 years after 1970 for the rest)
(2) LS FE is a least square fixed effect estimator with panels of input sectors. Standard error is cluster-robust assuming heteroskedasticity over input sectors
(3) FE IV is a fixed effect estimator with the instrumental variables: macro-TFP in output region, CGPI of output sector and input sectors. Standard error is cluster-robust assuming heteroskedasticity over input sectors. 1st F is the result of F test under null hypothesis that explanatory variables are weakly correlated with instruments. Overidentification is the result of Sargan–Hansen test under null hypothesis that all instruments are correlated with residuals. Endogeneity is the result of Davidson–MacKinnon’s J test under null hypothesis that an ordinary least squares estimator of the same equation (i.e., LS FE) yields consistent estimates

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