# The Impact of Polycentric Structure on CO\({}_{2}\) Emissions: Evidence from China
## 1 Introduction  
The 2030 Agenda for Sustainable Development offers a visionary roadmap for a sustainable future. There is global consensus on coordinating spatial expansion, economic growth, and the environment to achieve sustainable development [1; 2]. Sustainable Development Goal 11 (SDG 11) aim to create inclusive, safe, resilient, and sustainable cities and communities for all. However, the increasing threat of climate change looms over our living environments. The most recent progress report on SDG 13, which focuses on climate action, highlights the urgent need to reduce CO\({}_{2}\) emissions, as they reached a historic high in 2021 [3]. In countries like China, rapid urbanization and the concentration of resources in major cities exacerbate CO\({}_{2}\) emissions. Consequently, finding a balance between resource integration and sustainable development has become a critical challenge in urban planning. Research has shown that adopting a polycentric structure can be beneficial in terms of resource integration and optimizing efficiency [4]. Thus, clarifying the impact of polycentric structure on CO\({}_{2}\) emissions can help direct the practice of sustainable development. However, the relationship between polycentric structure and CO\({}_{2}\) emissions has not reached consensus. Some studies prove that the polycentric structure takes advantage of the integration of resources and optimizes the efficiency of factors [5]. Thus, it can alleviate CO\({}_{2}\) emissions [4; 6]. It's important to note that some studies have raised concerns about polycentricity, suggesting that it may lead to higher household emissions, increased industrial manufacturing [7], and greater household heating demands [8], all of which couldcontribute to higher CO\({}_{2}\) emissions. While the other studies demonstrate a non-linear relationship between polycentric structure and CO\({}_{2}\) emissions [9; 10]. This highlights the need for further exploration and discussion to better understand the intricacies of this relationship. The inconsistencies in the relationship between polycentricity and CO\({}_{2}\) emissions can be explained by four reasons: First, this relationship stems from a balance among diverse influence pathways. Previous studies have examined pathways such as reduced commuting duration, traffic congestion, household carbon emissions, and industrial emissions [7; 11]. Focusing on different pathways could lead to inconsistent findings regarding the connection between polycentric structures and CO\({}_{2}\) emissions. Second, the sample areas vary from study to study. For example, [PERSON] and [PERSON] [7] found that polycentric structure aggravates CO\({}_{2}\) emissions in Italy, while [PERSON] et al. [6] and [PERSON] et al. [11] discovered a positive association between polycentricity and CO\({}_{2}\) mitigation in China. One plausible reason is that the impact of polycentric structures on CO\({}_{2}\) emissions may be influenced by factors such as regional resource dependence and the level of market integration. Third, even within the same country, diverse scales of study regions may lead to a different association between polycentric structures and CO\({}_{2}\) emissions. The evidence from Chinese cities showed a negative association between polycentric structure and CO\({}_{2}\)[11], while the evidence from Chinese provinces demonstrated a U-shaped relationship [9]. Fourth, the measurement of core variables and the robustness of methods can also influence the results. The influence of the morphological polycentric index differs from that of the functional dimensions of polycentric structures. Additionally, conducting multiple robust tests is recommended to mitigate endogeneity and determine more accurate associations between spatial structures and CO\({}_{2}\) emissions [6]. This study evaluates the impact of morphological polycentricity on CO\({}_{2}\) emissions in China using a panel dataset from 279 cities spanning from 1999 to 2017.