Table 1 The estimated results of standard GSFM and the copulas-based GSFM

Rubber

Constant

− 0.694

0.096

0.173

1.246

0.458

0.851

0.619

0.520

lnGDP_i

0.107^***

0.027

1.122^***

0.017

1.039^***

0.003

0.806^***

0.099

lnGDP_j

1.829^***

0.071

0.870^***

0.045

1.898^***

0.015

0.654^***

0.042

lnPOP_i

− 1.802

0.050

− 0.438

0.034

− 2.075

0.035

− 3.265

0.135

lnPOP_j

0.674^**

0.063

1.667^**

0.045

0.817^*

0.081

9.953^*

0.246

lnDist_ij

− 8.220

0.215

− 3.029

0.129

− 9.654

0.168

− 13.639

0.164

lnEX_i

0.381^**

0.015

0.153^**

0.008

0.464^**

0.036

0.620

0.058

lnEX_j

− 2.555

0.011

− 1.330

0.034

− 3.637

0.058

− 2.897

0.440

\({\sigma }_{\mu }\)

0.471^***

0.336

0.056^***

0.013

0.878^*

0.223

0.371^**

0.234

\({\sigma }_{\nu }\)

0.299^*

0.065

0.836^**

0.011

0.199^**

0.046

0.169^*

0.294

\({\rho }_{1}\)

− 0.319

0.098

0.934^***

0.053

− 0.990

0.177

\({\rho }_{2}\)

0.252^**

0.051

0.990^***

0.001

− 0.053

0.268

\({\rho }_{3}\)

–

–

0.720^**

0.029

–

–

\({\rho }_{4}\)

–

–

0.410^*

0.064

–

–

AIC

1526.374

1466.382

796.600

1386.497

BIC

1627.396

1514.035

852.198

1434.152

Cassava

Constant

0.59

0.192

0.101^***

0.651

0.615^**

0.139

0.627

2.886

lnGDP_i

1.23^***

0.063

1.752^***

0.001

1.188^***

0.051

1.232

0.054

lnGDP_j

0.03

1.882

0.483^***

0.054

0.062^**

0.029

− 0.459

1.953

lnPOP_i

− 3.32^***

0.155

0.415^*

0.010

3.172^**

0.006

− 3.069

0.141

lnPOP_j

8.73

0.184

0.404^***

0.022

0.244

0.072

9.137

0.055

lnDist_ij

− 12.92^***

0.627

− 0.945^*

0.024

− 12.477

0.030

− 12.117

0.553

lnEX_i

0.02

0.043

− 0.784^***

0.007

0.023^**

0.027

0.031^***

0.036

lnEX_j

− 2.36^***

0.845

− 0.109^***

0.112

− 1.782

0.041

− 2.367

0.655

\({\sigma }_{\mu }\)

0.456^**

0.195

0.035^***

0.005

0.647^**

0.033

0.489

0.041

\({\sigma }_{\nu }\)

0.691^***

0.013

0.324^***

0.016

0.541^*

0.077

0.324

0.163

\({\rho }_{1}\)

0.568^***

0.084

0.653^***

0.049

0.990

0.492

\({\rho }_{2}\)

− 0.104^***

0.068

0.790^***

0.001

− 0.084

0.268

\({\rho }_{3}\)

–

–

0.471^*

0.015

–

–

\({\rho }_{4}\)

–

–

0.054^*

0.043

–

–

AIC

1425.386

1392.558

633.073

1247.293

BIC

1528.394

1440.216

688.671

1294.948

Fruits

Constant

0.971

0.099

0.161^***

0.791

0.106^*

0.171

0.130

0.687

lnGDP_i

1.371

0.088

1.493^***

0.074

1.325^***

0.064

0.730

0.100

lnGDP_j

− 6.968

0.042

1.191^***

0.141

0.920^**

0.026

− 0.649

3.605

lnPOP_i

− 1.129

0.017

− 1.127

0.204

− 0.579

0.150

− 0.245

0.262

lnPOP_j

5.837

0.062

1.737^**

0.200

0.5412^*

0.091

0.449

0.120

lnDist_ij

− 3.631

0.074

− 3.032

0.818

− 1.120^*

0.074

− 0.458

1.020

lnEX_i

− 2.611

0.053

− 0.249^**

0.052

− 0.218^***

0.030

− 0.042

0.068

lnEX_j

1.207

0.071

0.010^***

0.095

− 0.413

0.035

0.292

1.206

\({\sigma }_{\mu }\)

0.598

0.018

0.472^***

0.070

0.627^**

0.056

0.896

0.077

\({\sigma }_{\nu }\)

0.364

0.845

0.147^*

0.104

0.644^*

0.011

0.572

0.259

\({\rho }_{1}\)

0.833^**

0.154

0.790^***

0.048

0.990

0.596

\({\rho }_{2}\)

− 0.096^*

0.268

0.490^***

0.001

− 0.089

0.268

\({\rho }_{3}\)

–

–

0.500^***

0.020

–

–

\({\rho }_{4}\)

–

–

0.620

0.043

–

–

AIC

1437.306

1338.892

677.982

1380.869

BIC

1527.359

1386.557

733.580

1428.524

Vegetables

Constant

− 3.940

1.156

0.206^***

1.285

0.210

1.055

0.313^**

0.2987

lnGDP_i

2.288^***

0.083

2.295^***

0.084

2.332^**

0.073

0.414^***

0.092

lnGDP_j

− 0.719

0.158

− 0.786^**

0.213

− 0.785

0.024

− 0.213

0.682

lnPOP_i

− 1.352

0.212

− 1.386

0.211

− 1.416

0.096

− 1.754

0.573

lnPOP_j

4.502^***

0.711

2.176^*

0.646

2.2198^***

0.022

3.701^*

0.173

lnDist_ij

− 1.966

0.831

− 2.099

0.824

− 2.146^***

0.063

− 4.929

0.929

lnEX_i

0.270^**

0.056

0.268^**

0.054

0.264^***

0.047

0.751^**

0.626

lnEX_j

− 2.439

1.002

− 2.105

0.983

− 2.016

0.090

1.629^***

0.110

\({\sigma }_{\mu }\)

0.611^***

0.216

0.656^***

0.111

0.815^*

0.078

0.768

0.522

\({\sigma }_{\nu }\)

0.343^**

0.399

0.648^***

0.246

0.404^**

0.033

0.008^***

0.524

\({\rho }_{1}\)

0.732^**

0.307

0.677^***

0.068

0.594

0.280

\({\rho }_{2}\)

− 0.080^*

0.268

0.990^*

0.001

− 0.046

0.380

\({\rho }_{3}\)

–

–

0.063^***

0.017

–

–

\({\rho }_{4}\)

–

–

0.137^**

0.035

–

–

AIC

1426.396

1335.973

676.152

1358.847

BIC

1493.472

1383.636

749.725

1406.502

Herbs

Constant

− 5.853

0.091

0.2483^***

5.468

0.197^**

4.568

0.323

0.743

lnGDP_i

4.532^***

0.053

0.389^***

0.056

0.375^**

0.047

0.101^**

0.096

lnGDP_j

− 3.046

0.415

0.867^***

0.231

1.222^***

0.163

− 1.085

0.348

lnPOP_i

− 1.008

0.191

− 1.399

0.142

− 1.169

0.114

− 1.251

0.244

lnPOP_j

3.584

0.582

3.633

0.384

2.705^**

0.629

3.632^*

0.243

lnDist_ij

− 3.167^***

0.764

− 4.943^*

0.564

− 4.206^***

0.456

− 4.281

0.958

lnEX_i

5.823^*

0.053

0.559^**

0.037

0.544^**

0.032

0.544^***

0.063

lnEX_j

− 3.184

0.081

− 1.112

0.611

− 0.148

0.499

− 0.062

0.144

\({\sigma }_{\mu }\)

0.295^***

0.193

1.175^**

0.235

0.505^**

0.259

0.841^**

0.139

\({\sigma }_{\nu }\)

0.475^*

0.222

3.182^*

0.338

1.927^**

0.386

0.500

0.456

\({\rho }_{1}\)

0.369^***

0.012

0.087^***

0.116

0.990

0.352

\({\rho }_{2}\)

− 0.523

0.089

0.190^*

0.001

− 0.092

0.268

\({\rho }_{3}\)

–

–

0.320^**

4.199

–

–

\({\rho }_{4}\)

–

–

0.020^***

0.643

–

–

AIC

1472.386

1367.127

648.123

1339.762

BIC

1496.364

1414.773

760.190

1387.417