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A Bayesian Spatial Approach – Online Appendix – Agglomeration and Firm-level Productivity: A Bayesian Spatial Approach – Online Appendix – Yoshihiro HASHIGUCHI∗ Kiyoyasu TANAKA Institute of Developing Economies Institute of Developing Economies September 2014 Contents • Appendix A: k-nearest neighbors spatial weighting matrix (Tables 1 and 2) • Appendix B: Spatial Durbin model (Table 3) • Appendix C: List of county names (Tables 4–6) ∗Corresponding author. Address: 3-2-2 Wakaba, Mihama-ku, Chiba-shi, Chiba 261-8545, Japan. Fax: +81-43-299-9763 E-mail: Yoshihiro [email protected] 1 Appendix A: k-nearest neighbors spatial weighting matrix We provide the estimation results of the model in Hashiguchi and Tanaka (2014) using several knn (k-nearest neighbors) spatial weightingP matrices. The elements = = Nc = of knn weight matrix is specified as wc j dc j j dc j, and dc j 1 if county j is county c’s k-nearest neighbors. k is the number of nearest neighbors for county c, given by econometrician. In this appendix, we use k = 3; 4; 5; 6; 7; 8; 9; 10 for robustness check. Tables 1 and 2 show the estimation results. These estimates are basically unchanged from the original results based on the queen-type contiguity weight matrix. [Tables 1 and 2] Appendix B: Spatial Durbin model Hashiguchi and Tanaka (2014)’s model can be extended to the spatial Durbin model by adding W log Uc into Equation (5) of the original paper. In this appendix, to check the robustness of the paper’s results, we show the estimation results of the extended model. As Table 3 reports, coefficient estimates of both log Uc and W log Uc have large variance and are insignificant. These results may be caused by the collinearity among log Uc and W log Uc. However, the other estimates are basically unchanged from the original results in Hashiguchi and Tanaka (2014). [Table 3] Appendix C: List of county names [Tables 4, 5 and 6] 2 Table 1: Estimation results based on a knn weighting matrix (Bayesian IV model, log A f = log FD f ) k = 3 Mean Stdev 95%L Median 95%U βA 0.0228 0.0052 0.0126 0.0228 0.0330 βh 0.1490 0.0032 0.1427 0.1490 0.1553 βEX 0.0258 0.0064 0.0132 0.0258 0.0384 βK 0.2101 0.0021 0.2060 0.2101 0.2143 βL 0.5944 0.0037 0.5871 0.5944 0.6015 µ0 1.5679 0.2411 1.1035 1.5654 2.0526 µU 0.0048 0.0171 -0.0289 0.0047 0.0384 ρ 0.4075 0.0825 0.2394 0.4079 0.5665 k = 4 Mean Stdev 95%L Median 95%U βA 0.0225 0.0052 0.0122 0.0225 0.0327 βh 0.1488 0.0032 0.1424 0.1488 0.1552 βEX 0.0259 0.0064 0.0134 0.0259 0.0386 βK 0.2102 0.0021 0.2060 0.2102 0.2143 βL 0.5942 0.0037 0.5870 0.5943 0.6014 µ0 1.5097 0.2568 1.0192 1.5057 2.0328 µU 0.0044 0.0173 -0.0295 0.0044 0.0383 ρ 0.4289 0.0888 0.2463 0.4302 0.5976 k = 5 Mean Stdev 95%L Median 95%U βA 0.0220 0.0052 0.0118 0.0220 0.0323 βh 0.1487 0.0032 0.1423 0.1487 0.1550 βEX 0.0261 0.0064 0.0135 0.0260 0.0387 βK 0.2102 0.0021 0.2060 0.2102 0.2143 βL 0.5941 0.0037 0.5869 0.5941 0.6013 µ0 1.3415 0.2574 0.8528 1.3360 1.8693 µU 0.0037 0.0170 -0.0296 0.0037 0.0371 ρ 0.4930 0.0898 0.3069 0.4949 0.6622 k = 6 Mean Stdev 95%L Median 95%U βA 0.0220 0.0052 0.0117 0.0220 0.0323 βh 0.1487 0.0032 0.1424 0.1487 0.1551 βEX 0.0260 0.0064 0.0134 0.0260 0.0386 βK 0.2102 0.0021 0.2060 0.2102 0.2143 βL 0.5942 0.0037 0.5870 0.5942 0.6013 µ0 1.3146 0.2676 0.8099 1.3076 1.8668 µU 0.0021 0.0171 -0.0315 0.0020 0.0357 ρ 0.5061 0.0944 0.3092 0.5084 0.6828 3 Table 2: Estimation results based on a knn weighting matrix (continued) k = 7 Mean Stdev 95%L Median 95%U βA 0.0220 0.0052 0.0117 0.0220 0.0323 βh 0.1487 0.0032 0.1424 0.1487 0.1551 βEX 0.0260 0.0064 0.0134 0.0260 0.0386 βK 0.2102 0.0021 0.2060 0.2102 0.2143 βL 0.5942 0.0037 0.5870 0.5942 0.6013 µ0 1.2962 0.2763 0.7750 1.2887 1.8661 µU 0.0012 0.0172 -0.0325 0.0012 0.0350 ρ 0.5149 0.0981 0.3100 0.5172 0.6987 k = 8 Mean Stdev 95%L Median 95%U βA 0.0221 0.0052 0.0119 0.0221 0.0324 βh 0.1487 0.0032 0.1424 0.1487 0.1551 βEX 0.0260 0.0064 0.0134 0.0260 0.0387 βK 0.2102 0.0021 0.2060 0.2102 0.2143 βL 0.5942 0.0037 0.5870 0.5942 0.6013 µ0 1.2811 0.2841 0.7448 1.2741 1.8650 µU 0.0001 0.0172 -0.0337 0.0001 0.0340 ρ 0.5229 0.1016 0.3113 0.5250 0.7129 k = 9 Mean Stdev 95%L Median 95%U βA 0.0224 0.0052 0.0122 0.0224 0.0326 βh 0.1489 0.0032 0.1425 0.1489 0.1552 βEX 0.0259 0.0064 0.0134 0.0259 0.0386 βK 0.2102 0.0021 0.2060 0.2102 0.2143 βL 0.5943 0.0037 0.5870 0.5943 0.6014 µ0 1.2662 0.2953 0.7125 1.2570 1.8768 µU 0.0010 0.0173 -0.0329 0.0009 0.0350 ρ 0.5265 0.1058 0.3049 0.5296 0.7233 k = 10 Mean Stdev 95%L Median 95%U βA 0.0224 0.0052 0.0121 0.0224 0.0326 βh 0.1489 0.0032 0.1425 0.1489 0.1552 βEX 0.0259 0.0064 0.0134 0.0259 0.0386 βK 0.2101 0.0021 0.2060 0.2102 0.2143 βL 0.5943 0.0037 0.5871 0.5943 0.6014 µ0 1.2846 0.3060 0.7153 1.2729 1.9186 µU 0.0005 0.0174 -0.0337 0.0005 0.0348 ρ 0.5209 0.1105 0.2889 0.5256 0.7244 4 Table 3: Model with W log Uc Mean Stdev 95%CI log A f = log FD f βA 0.0223 (0.0052) [0.012, 0.033] βh 0.1486 (0.0032) [0.142, 0.155] βEX 0.0260 (0.0064) [0.013, 0.039] βK 0.2102 (0.0021) [0.206, 0.214] βL 0.5941 (0.0037) [0.587, 0.601] µ0 1.2468 (0.2386) [0.802, 1.746] µU -0.0239 (0.0290) [-0.081, 0.033] µ˜ U 0.0353 (0.0362) [-0.036, 0.106] ρ 0.5121 (0.0819) [0.335, 0.665] log A f = log LD f βA 0.0105 (0.0066) [-0.002, 0.023] βh 0.1527 (0.0028) [0.147, 0.158] βEX 0.0258 (0.0065) [0.013, 0.039] βK 0.2103 (0.0021) [0.206, 0.215] βL 0.5953 (0.0035) [0.588, 0.602] µ0 0.9824 (0.2204) [0.574, 1.448] µU 0.0155 (0.0326) [-0.048, 0.080] µ˜ U 0.0179 (0.0378) [-0.056, 0.092] ρ 0.5415 (0.0815) [0.365, 0.692] log A f = log FN f βA 0.0332 (0.0058) [0.022, 0.044] βh 0.1555 (0.0027) [0.150, 0.161] βEX 0.0229 (0.0064) [0.010, 0.036] βK 0.2099 (0.0021) [0.206, 0.214] βL 0.5976 (0.0035) [0.591, 0.604] µ0 1.0348 (0.2205) [0.621, 1.494] µU -0.0002 (0.0309) [-0.061, 0.061] µ˜ U 0.0243 (0.0363) [-0.047, 0.096] ρ 0.5186 (0.0834) [0.340, 0.675] Sample size: 97947 Note:µ ˜ U is the coefficient of W log Uc. 5 Table 4: List of county names id Prefecture-level County-level id Prefecture-level County-level 1 Shanghai Huangpu∗ 41 Lianyungang Lianyungang Dist. 2 Shanghai Minxing 42 Lianyungang Ganyu 3 Shanghai Baoshan 43 Lianyungang Donghai 4 Shanghai Jiading 44 Lianyungang Guanyun 5 Shanghai Pudongxin 45 Lianyungang Guannan 6 Shanghai Jinshan 46 Huaiyin Huaiyin Dist. 7 Shanghai Songjiang 47 Huaiyin Lianshui 8 Shanghai Qingpu 48 Huaiyin Hongze 9 Shanghai Nanhui 49 Huaiyin Xuyi 10 Shanghai Fengxian 50 Huaiyin Jinhu 11 Shanghai Chongming 51 Yancheng Yancheng Dist. 12 Nanjing Nanjing Dist. 52 Yancheng Xiangshui 13 Nanjing Lishui 53 Yancheng Binhai 14 Nanjing Gaochun 54 Yancheng Funing 15 Wuxi Wuxi Dist. 55 Yancheng Sheyang 16 Wuxi Jiangyin 56 Yancheng Jianhu 17 Wuxi Yixing 57 Yancheng Dongtai 18 Xuzhou Xuzhou Dist. 58 Yancheng Dafeng 19 Xuzhou Fengxian 59 Yangzhou Yangzhou Dist. 20 Xuzhou Peixian 60 Yangzhou Baoying 21 Xuzhou Tongshan 61 Yangzhou Yizheng 22 Xuzhou Suining 62 Yangzhou Gaoyou 23 Xuzhou Xinyi 63 Yangzhou Jiangdu 24 Xuzhou Pizhou 64 Zhenjiang Zhenjiang Dist. 25 Changzhou Changzhou Dist. 65 Zhenjiang Danyang 26 Changzhou Liyang 66 Zhenjiang Yangzhong 27 Changzhou Jintan 67 Zhenjiang Jurong 28 Suzhou Suzhou Dist.
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