4.3.1. Replacing the Spatial Weight Matrix

This paper adopts the spatial weight matrix of queen contiguity to verify the robustness of the estimation results. If there is a common boundary or a common contact point between two places, these two places are considered adjacent. Then we set the weight 1, otherwise 0 [57]. When performing the spatial measurement, this paper performs row normalization on the adjacent spatial weight matrix, that is, divides each element in the matrix (denoted as *<sup>w</sup>ij*) by the sum of the elements in its row to ensure the sum of the elements in each row is 1, that is, *wij* <sup>=</sup> *<sup>w</sup>ij*/ <sup>∑</sup> *j <sup>w</sup>ij*. Row normalization yields the average of each region's neighbors. In order to verify the true spatial autocorrelation relationship, the GDP per capita of the explained variable is selected to calculate Moran's index. The significance is

tested by the Monte Carlo simulation method. Moran's index is greater than 0, and the Z value is greater than 1.96. After performing up to 99,999 permutations, the *p* value is always close to 0, indicating the existence of spatial autocorrelation.

After the spatial autocorrelation relationship is verified, the adjacent spatial weight matrix is used to construct a spatial econometric model. In this paper, SDM, SAR, and POLS models are set as follows:

$$\text{GDPPC}\_{\text{it}} = \rho \sum\_{j=1}^{n} W\_{\bar{\eta}}^{\prime} \text{GDPPC}\_{\bar{\eta}\text{it}} + \beta^{\prime\prime} \text{CORE}\_{\bar{\eta}\text{t}} + \theta \sum\_{j=1}^{n} W\_{\bar{\eta}}^{\prime} \text{CORE}\_{\bar{\eta}\text{it}} + \beta^{\prime\prime} \text{CONT}\_{\bar{\eta}\text{t}} + \theta \sum\_{j=1}^{n} W\_{\bar{\eta}}^{\prime} \text{CONT}\_{\bar{\eta}\text{it}} + \mu\_{i} + \tilde{\xi}\_{i} + \varepsilon\_{i\text{t}} \tag{12}$$

$$GDPPC\_{it} = \rho \sum\_{j=1}^{n} \mathcal{W}\_{ij}^{\prime} GDPPC\_{jt} + \beta^{\prime\prime} CORE\_{it} + \beta^{\prime\prime} CONT\_{it} + \mu\_i + \boldsymbol{\xi}\_t + \boldsymbol{\varepsilon}\_{it} \tag{13}$$

$$\text{GDPPC}\_{it} = \beta^{\prime\prime} \text{CORE}\_{it} + \beta^{\prime\prime} \text{CONT}\_{it} + \mu\_i + \tilde{\xi}\_t + \varepsilon\_{it} \tag{14}$$

where Equations (12)–(14) are the SDM, SAR, and POLS models, respectively. The explained variable GDP per capita, core explanatory variables, control variables, and other variables are consistent with the base model, but *W*- *ij* is replaced by the queen contiguity weighting matrix and normalized. The model results are shown in Table 7.


**Table 7.** Results of robustness check.

Note: \*\*\* significant at the 1% level; \*\* significant at the 5% level; \* significant at the 10% level; T statistics in parentheses.

### 4.3.2. Adjusted Sample Period

In 2018, President Xi Jinping announced the integrated development of the YRD region and raised it as a national strategy. From a regional perspective, the integrated development of the YRD solves the problem of unbalanced regional development, and the integration of the YRD can play a guiding and exemplary role. Shanghai, Jiangsu, and Zhejiang are all developed regions, while Anhui is underdeveloped. The integration of the YRD needs to drive the neighboring regions with poor conditions through the regions with good conditions so that the elements flow and gather in Anhui. The YRD region should strengthen cooperation in infrastructure construction, technological innovation, industrial development, and ecological environment construction to achieve collaborative innovation and development. Therefore, the article adopts the method of reducing the sample period to avoid the impact of the policy, that is, to exclude data from 2018 and 2019. The model sample period focuses on 2007–2017, and other explained variables, explanatory variables, and control variables remain unchanged. The article also reports the results of the SAR and SDM models to reduce the bias of the model results. The results are shown in Table 8.


**Table 8.** Results of robustness checks from 2007–2017.

Note: \*\*\* significant at the 1% level; \*\* significant at the 5% level; \* significant at the 10% level; T statistics in parentheses.
