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

Table 1 Assessment of IO table projections via LQs for EA-19 countries (2010 and 2015)

From: Performance of bidimensional location quotients for constructing input–output tables

Countries 2010 2015
CILQ FLQ \(\left( \delta \right)\) AFLQ \(\left( \delta \right)\) 2D-LQ \(\left( {\alpha ;~\beta } \right)\) CILQ FLQ \(\left( \delta \right)\) AFLQ \(\left( \delta \right)\) 2D-LQ \(\left( {\alpha ;~\beta } \right)\)
STPE
Austria 73.4995 69.6879 (0.18) 68.2299 (0.20) 66.6016 (0.50; 0.12) 75.4435 70.9785 (0.19) 69.0646 (0.21) 67.0937 (0.68; 0.13)
Belgium 75.4562 68.6528 (0.21) 68.3947 (0.24) 66.7671 (0.80; 0.14) 77.0734 69.3534 (0.25) 68.7097 (0.26) 67.5910 (0.92; 0.15)
Estonia 92.2069 81.6705 (0.13) 81.1942 (0.17) 77.5070 (1.10; 0.12) 94.3536 82.6840 (0.12) 82.7006 (0.18) 77.1978 (1.04; 0.12)
France 51.6088 50.1284 (0.17) 49.3062 (0.20) 48.0252 (0.86; 0.09) 55.0476 53.1773 (0.19) 52.2111 (0.20) 49.9730 (1.10; 0.10)
Germany 56.5391 55.4739 (0.18) 54.9237 (0.31) 53.3835 (0.26; 0.21) 58.0644 56.8606 (0.20) 55.7934 (0.32) 54.2872 (0.44; 0.21)
Italy 55.5537 52.0088 (0.08) 50.9841 (0.13) 49.0212 (1.10; 0.07) 55.2133 54.2537 (0.12) 53.0440 (0.15) 51.0279 (1.04; 0.09)
Latvia 91.0184 83.7678 (0.15) 81.7131 (0.17) 75.9635 (1.52; 0.07) 90.7480 82.8537 (0.17) 79.7378 (0.18) 74.7490 (1.28; 0.08)
Slovakia 80.1889 75.2500 (0.15) 73.3860 (0.18) 72.3167 (0.86; 0.08) 83.9898 77.8713 (0.19) 76.0804 (0.20) 75.5784 (0.98; 0.10)
Slovenia 82.1660 78.6179 (0.09) 79.4358 (0.14) 75.1431 (0.26; 0.10) 84.6056 78.7981 (0.12) 78.8749 (0.14) 76.5708 (0.32; 0.11)
Spain 56.6842 56.3444 (0.06) 54.8686 (0.09) 53.7071 (1.04; 0.02) 61.0079 60.1019 (0.10) 58.8638 (0.13) 58.4667 (0.92; 0.08)
MAD
Austria 0.0044 0.0041 (0.18) 0.0040 (0.20) 0.0040 (0.50; 0.12) 0.0043 0.0040 (0.19) 0.0039 (0.21) 0.0038 (0.68; 0.13)
Belgium 0.0046 0.0042 (0.21) 0.0041 (0.24) 0.0041 (0.80; 0.14) 0.0045 0.0041 (0.25) 0.0040 (0.26) 0.0040 (0.92; 0.15)
Estonia 0.0048 0.0042 (0.13) 0.0042 (0.17) 0.0040 (1.10; 0.12) 0.0048 0.0042 (0.12) 0.0042 (0.18) 0.0039 (1.04; 0.12)
France 0.0033 0.0033 (0.17) 0.0032 (0.20) 0.0031 (0.86; 0.09) 0.0034 0.0033 (0.19) 0.0032 (0.20) 0.0031 (1.10; 0.10)
Germany 0.0036 0.0036 (0.18) 0.0035 (0.31) 0.0034 (0.26; 0.21) 0.0036 0.0035 (0.20) 0.0035 (0.32) 0.0034 (0.44; 0.21)
Italy 0.0038 0.0037 (0.08) 0.0037 (0.13) 0.0035 (1.10; 0.07) 0.0040 0.0039 (0.12) 0.0038 (0.15) 0.0037 (1.04; 0.09)
Latvia 0.0058 0.0053 (0.15) 0.0052 (0.17) 0.0048 (1.52; 0.07) 0.0050 0.0046 (0.17) 0.0044 (0.18) 0.0041 (1.28; 0.08)
Slovakia 0.0047 0.0045 (0.15) 0.0043 (0.18) 0.0043 (0.86; 0.08) 0.0050 0.0046 (0.19) 0.0045 (0.20) 0.0045 (0.98; 0.10)
Slovenia 0.0047 0.0045 (0.09) 0.0045 (0.14) 0.0043 (0.26; 0.10) 0.0047 0.0044 (0.12) 0.0044 (0.14) 0.0043 (0.32; 0.11)
Spain 0.0039 0.0039 (0.06) 0.0038 (0.09) 0.0037 (1.04; 0.02) 0.0040 0.0040 (0.10) 0.0039 (0.13) 0.0039 (0.92; 0.08)
MAPE
Austria 0.0191 0.0181 (0.18) 0.0177 (0.20) 0.0173 (0.50; 0.12) 0.0196 0.0185 (0.19) 0.0180 (0.21) 0.0175 (0.68; 0.13)
Belgium 0.0196 0.0179 (0.21) 0.0178 (0.24) 0.0174 (0.80; 0.14) 0.0201 0.0180 (0.25) 0.0179 (0.26) 0.0176 (0.92; 0.15)
Estonia 0.0240 0.0212 (0.13) 0.0211 (0.17) 0.0202 (1.10; 0.12) 0.0245 0.0215 (0.12) 0.0215 (0.18) 0.0201 (1.04; 0.12)
France 0.0134 0.0130 (0.17) 0.0128 (0.20) 0.0125 (0.86; 0.09) 0.0143 0.0138 (0.19) 0.0136 (0.20) 0.0130 (1.10; 0.10)
Germany 0.0147 0.0144 (0.18) 0.0143 (0.31) 0.0139 (0.26; 0.21) 0.0151 0.0148 (0.20) 0.0145 (0.32) 0.0141 (0.44; 0.21)
Italy 0.0137 0.0135 (0.08) 0.0133 (0.13) 0.0128 (1.10; 0.07) 0.0144 0.0141 (0.12) 0.0138 (0.15) 0.0133 (1.04; 0.09)
Latvia 0.0237 0.0218 (0.15) 0.0213 (0.17) 0.0198 (1.52; 0.07) 0.0236 0.0216 (0.17) 0.0207 (0.18) 0.0194 (1.28; 0.08)
Slovakia 0.0209 0.0196 (0.15) 0.0191 (0.18) 0.0188 (0.86; 0.08) 0.0218 0.0203 (0.19) 0.0198 (0.20) 0.0197 (0.98; 0.10)
Slovenia 0.0214 0.0205 (0.09) 0.0207 (0.14) 0.0195 (0.26; 0.10) 0.0220 0.0205 (0.12) 0.0205 (0.14) 0.0199 (0.32; 0.11)
Spain 0.0147 0.0147 (0.06) 0.0143 (0.09) 0.0140 (1.04; 0.02) 0.0159 0.0156 (0.10) 0.0153 (0.13) 0.0152 (0.92; 0.08)
SD-MAD
Austria 0.0137 0.0137 (0.00) 0.0134 (0.05) 0.0135 (0.56; 0.01) 0.0135 0.0135 (0.01) 0.0130 (0.06) 0.0130 (0.74; 0.01)
Belgium 0.0151 0.0144 (0.12) 0.0144 (0.15) 0.0143 (0.56; 0.06) 0.0153 0.0141 (0.15) 0.0140 (0.18) 0.0141 (0.80; 0.07)
Estonia 0.0150 0.0132 (0.09) 0.0134 (0.15) 0.0129 (0.80; 0.05) 0.0151 0.0129 (0.10) 0.0132 (0.16) 0.0126 (0.62; 0.07)
France 0.0086 0.0084 (0.09) 0.0081 (0.13) 0.0075 (0.92; 0.03) 0.0092 0.0087 (0.15) 0.0082 (0.19) 0.0074 (0.92; 0.05)
Germany 0.0102 0.0102 (0.00) 0.0101 (0.09) 0.0097 (0.62; 0.00) 0.0101 0.0101 (0.00) 0.097 (0.11) 0.0092 (0.80; 0.01)
Italy 0.0108 0.0100 (0.19) 0.0097 (0.24) 0.0094 (0.98; 0.09) 0.0112 0.0102 (0.19) 0.0100 (0.23) 0.0093 (1.16; 0.11)
Latvia 0.0168 0.0161 (0.06) 0.0156 (0.13) 0.0145 (1.10; 0.03) 0.0167 0.0166 (0.02) 0.0159 (0.10) 0.0148 (0.92; 0.01)
Slovakia 0.0140 0.0139 (0.02) 0.0137 (0.10) 0.0136 (0.44; 0.02) 0.0155 0.0154 (0.03) 0.0150 (0.10) 0.0151 (0.50; 0.02)
Slovenia 0.0145 0.0140 (0.05) 0.0145 (0.10) 0.0141 (0.08; 0.06) 0.0162 0.0156 (0.06) 0.0157 (0.11) 0.0154 (0.14; 0.06)
Spain 0.0110 0.0109 (0.06) 0.0105 (0.11) 0.0104 (0.92; 0.00) 0.0125 0.0123 (0.08) 0.0120 (0.13) 0.0122 (0.56; 0.03)
Theils
Austria 61.1455 61.1455 (0.00) 59.6314 (0.06) 60.4973 (0.56; 0.02) 61.4834 61.4269 (0.01) 59.0615 (0.07) 59.3308 (0.80; 0.02)
Belgium 72.3667 68.5536 (0.13) 68.6360 (0.15) 68.2197 (0.62; 0.07) 74.7101 68.7492 (0.16) 68.4625 (0.19) 68.5660 (0.80; 0.07)
Estonia 82.3278 72.5117 (0.09) 73.7562 (0.15) 70.8120 (0.86; 0.06) 87.1358 74.7504 (0.10) 76.3152 (0.16) 73.0488 (0.62; 0.07)
France 47.0037 45.8011 (0.09) 44.0643 (0.13) 41.0625 (0.92; 0.03) 51.6500 48.7922 (0.16) 46.6069 (0.19) 42.2002 (0.98; 0.05)
Germany 49.6259 49.6259 (0.00) 49.3755 (0.10) 47.5895 (0.62; 0.01) 50.3366 50.3366 (0.00) 48.8274 (0.12) 46.5817 (0.80; 0.02)
Italy 58.2963 54.3184 (0.18) 53.0215 (0.23) 50.9990 (0.98; 0.09) 61.7249 57.1349 (0.18) 55.6855 (0.23) 52.1613 (1.16; 0.11)
Latvia 78.4507 74.9980 (0.07) 72.7200 (0.13) 67.3222 (1.10; 0.03) 72.9161 72.2389 (0.03) 69.0737 (0.10) 64.4627 (0.92; 0.01)
Slovakia 65.9687 65.4229 (0.03) 64.3763 (0.10) 64.2581 (0.44; 0.03) 69.3574 68.5305 (0.04) 66.8900 (0.11) 67.3646 (0.56; 0.02)
Slovenia 74.6075 71.8624 (0.05) 74.3736 (0.10) 72.1310 (0.14; 0.06) 79.5425 76.4087 (0.07) 77.0159 (0.12) 75.8484 (0.20; 0.06)
Spain 52.9878 52.2704 (0.06) 50.4862 (0.11) 49.8286 (0.92; 0.00) 58.4636 57.3348 (0.08) 55.9103 (0.13) 56.9373 (0.62; 0.03)
  1. The optimal parameter values for each LQs are indicated in parentheses. The global minimum for the statistic is shown in italic