**2. Methodology**

#### *2.1. Spatial Weight Matrix*

The spatial weight matrix is an indispensable element in the spatial econometric model. The spatial weight matrix can incorporate the unique spatial relationships of variables into the econometric model. Common spatial weight matrices are first-order contiguity matrix, geographical distance matrix and economic distance matrix.

2.1.1. First-Order Contiguity Matrix

First order adjacency matrix is a type of adjacency matrix, which mainly reflects the relationship between the local area and surrounding areas, that is, there is a common vertex or boundary between the two regions (Figure 2). The matrix limits the effective range of spillover effect and emphasizes that only the queen contiguity regions have obvious spillover effect. For example, the effective range of knowledge spillover effect is within 300 km (generally beyond the scope of a province in China) [39]. The expression of the first-order adjacency matrix is as follows:

$$\mathcal{W}\_{\vec{\mathbb{ij}}}^{\mathbb{C}} = \begin{cases} 1, & \text{i and j are queen containing relations} \\ & 0, & \text{others} \end{cases} \tag{1}$$

**Figure 2.** Queen contiguity.

#### 2.1.2. Geographical Distance Matrix

Tobler's First Law of Geography pointed out "Everything is related to everything else, but near things are more related to each other" [40]. The geographic distance matrix best reflects this idea. Although this matrix does not limit the scope of spillover effects, it is believed that spillover effects weakens with increasing geographic distance. The expression of geographical distance matrix is as follows:

$$\mathcal{W}\_{\mathbf{i}\mathbf{j}}^{\rm D} = \begin{cases} \ 1/\mathbf{d}^2 \ \text{i} \neq \mathbf{j} \\\ 0, \ \mathbf{i} = \mathbf{j} \end{cases} \tag{2}$$
