# Construction of the Belt and Road Trade Cooperation Network from the Multi-Distances Perspective
## Variables and Model Expansion
### Expansion of Gravity Model Based on Multiple Distances
#### 2.2.1 Modeling  
To determine the impact of geographic distance, factor endowment distance, cultural distance, and institutional distance on international trade flows, this study used the extended gravity model to complete positive research. The gravity model was first proposed by [PERSON] and [PERSON] [16; 17], and then successfully applied to the positive research of international trade flows. Based on the assumptions of Constant Elasticity of Substitution (CES) and monopolistic competition in the single-sector economy, [PERSON] [40] theoretically introduced the multilateral trade resistance model, laying a theoretical foundation for the gravity model. On this basis, we expanded the gravity model as follows:  
\[X_{ij}=(\frac{Y_{i}Y_{j}}{Y_{w}})(\frac{\tau_{ij}}{P_{i}P_{j}})^{1-\sigma} \tag{4}\]The above formula shows that country \(i\)'s exports to country \(j\) are dependent on the economic scale of the two countries (\(Y_{i}\) and \(Y_{j}\)), the composite price indices of the two countries (\(P_{i}\) and \(P_{j}\)), the bilateral trade resistance (\(\tau_{ij}\)), and the world nominal income (\(Y_{w}\)). The bilateral trade resistance \(\tau_{ij}\) can be further explained as:  
\[\tau_{ij}=\prod_{i=1}^{m}D_{i}^{\gamma m}\times\exp{(\sum_{k=1}^{n}\gamma_{k}V _{ij})} \tag{5}\]  
where \(D_{i}\) is the \(m\) quantitative factors hindering the trade between the countries and \(V_{ij}\) is the \(n\) qualitative factors hindering the trade between the countries. These factors include natural and human barriers. Based on this, these natural and human barriers were further divided into geographic distance (_DIS_), factor endowment distance (DKL), cultural distance (CD), and institutional distance (ID) in Equation (5). After substituting Equation (5) into Equation (4) and performing logarithmical linearization, the formula could be changed into the following:  
\[\begin{split} lnX_{ij}=&-lnY_{w}+[lnY_{i}+(\sigma- 1)lnP_{i}]+\left[lnY_{j}+(\sigma-1)lnP_{j}\right]+\gamma m(1-\sigma)lnDIS_{ij} \\ &+\gamma m(1-\sigma)lnDKL_{ij}+\gamma m(1-\sigma)lnCD_{ij}+ \gamma m(1-\sigma)lnID_{ij}\end{split} \tag{6}\]  
Since the composite price index is usually not available, the above formula cannot be directly computed. Therefore, using the viewpoints expressed by [PERSON] [36], we substituted it with the relative geographic distance between the two countries. The country with the farther geographic distance had a lower output and generally a higher composite price index. After the above treatment, we obtained the following equation:  
\[\begin{split} lnX_{ijt}=\beta_{0}+\beta_{1}lnY_{it}+\beta_{2}lnY _{jt}+\beta_{3}lnDIS_{ijt}+\beta_{4}lnDKL_{ijt}+\beta_{5}lnCD_{ijt}+\beta_{6} lnD_{ijt}+\mu_{ijt}\end{split} \tag{7}\]  
China is the only exporting country in the regressions, so China only varied in the time dimension and not across trading partners and could be identified by a time trend. Therefore, we eliminated China's GDP in the final regression equation as:  
\[\begin{split} lnX_{ijt}=\beta_{0}+\beta_{2}lnY_{jt}+\beta_{3} lnDIS_{ijt}+\beta_{4}lnDKL_{ijt}+\beta_{5}lnCD_{ijt}+\beta_{6}lnD_{ijt}+\mu_{ijt}\end{split} \tag{8}\]  
where \(i,j,\) and \(t\) denote China, the Belt and Road country, and the year, respectively, and \(X_{ijt}\) is China's the export flows to country \(j\) in year \(t\). Due to the serious lack of service trade data for the countries, the export data in this study only included the trade in goods. The data were obtained from the uncomtrade database. \(Y_{jit}\) denotes the economic scale of the Belt and Road country in year \(t\). GDP was used to represent the economic scale of a country. The data were obtained from the World Bank. _DISjt_, _DKLijt_, _CDijt_, and _IDjt_ represent the geographic distance, factor endowment distance, cultural distance, and institutional distance between China and the Belt and Road country in year \(t\), respectively.