4.3.5. Variance Decomposition

Variance decomposition can explain the contribution of each variable shock in the system. It can be seen from Figure 8 that the change of the atmospheric environment system mainly came from its own change impact, which is consistent with the practice in China. The governance and improvement of the atmospheric environment system are mainly regulated by administrative means. In the short term, the change of the industrial system is attributed to itself, but in the long term, it is jointly affected by its own change and the impact of the change of the atmospheric environment system. In phases 1–4, the contribution rate of the impact of the industrial system itself to its variance was close to 1, but it dropped to 37% in the subsequent phases. In comparison, the explanation degree of the change of the atmospheric environment system U1 to the industrial system U2 reached 63%.

**Figure 8.** Variance decomposition.

#### **5. Conclusions**

The quality of the atmospheric environment affects the high-quality and sustainable development of the economy, and the optimisation and upgrading of the industrial system is an important way to improve the efficiency of economic and social operations. Analysing the relationship and interaction between the two systems is significant in promoting the coordinated development of the environment and economy. By constructing the theoretical analysis framework of coupling and coordination between the atmospheric environment system and the industrial system, this paper clarified the two systems' internal mechanisms of the interaction and coordinated development. Then, it put forward the combination of the coupling coordination model and the VAR model and provided the analysis and evaluation method of the relationship between them from the two perspectives of "static" and "dynamic".

The atmospheric environmental quality is an important factor affecting the development of Taiyuan. For many years, Taiyuan has also been committed to adjusting the industrial structure to make the industrial development adapt to the local environmental carrying capacity. Therefore, based on the theoretical analysis framework and the proposed evaluation method, this paper empirically analysed the data of the typical resource-based city Taiyuan from 2003 to 2017. The results show that: (1) Based on the results of the coupling coordination model, the interaction between the two systems in Taiyuan was obvious and developed towards benign coupling. However, there were still fluctuations in some years, reflecting that the two systems are still in the transition stage of "mutual running in and tend to coordination—high-level coupling coordination". (2) According to the results of the VAR model, the impact of the two systems on each other was mainly in the medium and long term and dominated by the effect of the atmospheric environment system on the industrial system.

Based on the above analysis results, the following policy implications can be obtained. Firstly, Taiyuan should continue to maintain the coordination and sustainability of atmospheric environmental governance and industrial structure adjustment. It should promote and maintain the synchronous and orderly development between the two systems. Secondly, it should be optimised from within the industrial system to improve the scientificity and effectiveness of industrial policies, so as to enhance its internal and external benefits, and then promote the sustainable development of the two systems in Taiyuan and make the two systems enter a high-level coupling and coordinated development stage. Thirdly, when formulating and evaluating urban environmental and industrial policies, central government departments should fully consider the particularity of different urban development stages and the long-term effect of policies so as to avoid "one size fits all" and short-sighted behaviour.

This paper presented an analysis framework and long-term evaluation method of the relationship between the urban atmospheric environment system and the industrial system, which provides theoretical and methodological guidance for policymakers to evaluate relevant policies. However, because some data cannot be obtained through public channels, only the evaluation results of Taiyuan from 2003 to 2017 were presented. Relevant policy departments can conduct the internal evaluation with reference to the methods proposed in this paper and take measures according to the latest situation of the two systems. On the other hand, this paper's evaluation and analysis methods were mainly studied from the macrosystem level. In the future, we can further analyse the response of micro-subjects (such as enterprises) to different types of environmental regulation and industrial structure adjustment policies in different stages, find the action mechanism at the micro-level, and then provide more targeted policy suggestions. In addition, in recent years, the COVID-19 pandemic has had a significant impact on all economies in the world, and the global health crisis has become an external factor that cannot be ignored. The impact of this factor on the atmospheric environment industry coupling system proposed in this paper will be worthy of more extensive and in-depth research in the future.

**Author Contributions:** Conceptualisation, X.Z. and L.W.; methodology, J.Z.; software, J.Z.; validation, X.Z., J.Z. and L.W.; formal analysis, X.Z., J.Z. and L.W.; investigation, J.Z.; resources, J.Z. and L.W.; data curation, J.Z. and L.W.; writing—original draft preparation, J.Z. and L.W.; writing—review and editing, X.Z., J.Z. and L.W.; visualisation, J.Z.; supervision, X.Z.; project administration, X.Z.; funding acquisition, X.Z. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Natural Science Foundation of China, grant number 72003009.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The sources of relevant data acquisition have been described in the text.

**Acknowledgments:** The authors dedicate their earnest gratitude to the editor and the anonymous reviewers for their active comments, which improved the quality of the manuscript.

**Conflicts of Interest:** The authors declare no conflict of interest.
