Much research has been conducted to find evidence of the environmental Kuznets curve (EKC) in the relationship between air-pollutant concentration and economic development. A major focus of EKC-related research has so far been to identify the turning point illustrated by EKC theory or to predict the moment when the turning point will occur. In our research, via analyzing the relationship between an aggregate social-development-representative variable (the Socio-demographic Index or SDI) and the population-weighted concentration of PM 2.5 , we propose that the overall relationship takes the form of a tilted-S shape with two types of turning points rather than one. Additionally, our research shows that the EKC is highly country-specific, making it extremely difficult to predict the positions of both turning points based on the historical development or trajectories of other countries. Therefore, we conclude that EKC theory is not a useful tool to predict the location of the turning points. However, for short-term prediction of the relationship, we advocate the use of support vector regression, which can forecast the evolution, unless rapid changes are occurring. We suggest that policy makers should not anchor their hopes on predicting turning points from previous studies, but should put more effort into dealing with present particulate matter pollution.

中文翻译：

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社会发展与环境颗粒物污染的关系：我们能否预测转折点？

已经进行了大量研究，以寻找空气污染物浓度与经济发展之间关系中环境库兹涅茨曲线 (EKC) 的证据。迄今为止，EKC 相关研究的一个主要焦点是确定 EKC 理论所说明的转折点或预测转折点发生的时刻。在我们的研究中，通过分析总体社会发展代表变量（社会人口指数或 SDI）与 PM 2.5 人口加权浓度之间的关系，我们建议整体关系采用倾斜 S 的形式具有两种类型的转折点而不是一种的形状。此外，我们的研究表明 EKC 具有高度的国家特定性，这使得根据其他国家的历史发展或轨迹来预测这两个转折点的位置变得极其困难。因此，我们得出结论，EKC 理论不是预测转折点位置的有用工具。然而，对于关系的短期预测，我们提倡使用支持向量回归，它可以预测演变，除非正在发生快速变化。我们建议政策制定者不应将希望寄托在预测以往研究的转折点上，而应更加努力应对当前的颗粒物污染。我们提倡使用支持向量回归，它可以预测演变，除非正在发生快速变化。我们建议政策制定者不应将希望寄托在预测以往研究的转折点上，而应更加努力应对当前的颗粒物污染。我们提倡使用支持向量回归，它可以预测演变，除非正在发生快速变化。我们建议政策制定者不应将希望寄托在预测以往研究的转折点上，而应更加努力应对当前的颗粒物污染。