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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