China's rapid economic growth (15% annually from 1979-2016) fueled by industrialization and urbanization has resulted in significant carbon dioxide emissions, making it the world's largest emitter. This necessitates clean energy development (CED) to mitigate CDE, enhance energy security, and achieve sustainable economic growth. The research question focuses on the role of CED in reducing CDE and promoting economic growth. Given significant regional disparities in China's industrial structure, resource endowment, and development levels, this study aims to explore the linear and nonlinear impacts of CED on CDE and economic growth across the eastern, central, and western regions. The study's importance lies in providing region-specific insights for policy formulation to optimize CED's contribution to both environmental sustainability and economic advancement.

Existing literature explores the relationship between CED, CDE, and economic growth, with some studies highlighting the potential of CED to reduce CDE and promote sustainable growth through industrial structure upgrades and technological advancements. However, other studies find no significant impact of CED on CDE reduction. Many studies assume linear relationships between these variables, which may not accurately capture the complexity of economic interactions. Furthermore, the majority of previous studies focus on macro-level analyses, neglecting important regional differences. This research aims to address these limitations by employing a non-parametric additive regression model to capture both linear and nonlinear relationships at the provincial level, thus offering a more nuanced understanding of the effects of CED.

The study employs a non-parametric additive regression model to analyze panel data from 30 Chinese provinces covering 1979-2016 (actual data) and 2017-2030 (predicted data). This model is chosen to address the limitations of linear models in capturing the complex nonlinear relationships between variables. The model for economic growth is based on the Solow model, incorporating clean energy (CE) and urbanization as additional factors. The model for CDE is based on the STIRPAT model, expanding it to include factors like energy intensity, energy structure, and environmental regulation. The dependent variable for the economic growth model is per capita GDP, while for the CDE model it is total CDE calculated from fossil fuel consumption and a carbon emission factor. Independent variables include clean energy production (calculated as the proportion of clean energy in total energy production), urbanization rate, labor input, capital investment, technological progress (measured using the Malmquist productivity index), energy intensity, energy consumption structure, environmental regulation index, and population size. Data forecasting for 2017-2030 utilizes ARIMA models for stable variables and a double exponential model for others. Before the regression analysis, the endogeneity of clean energy in both models was tested using Durbin-Wu-Hausman and Engle-Granger tests to ensure the reliability of the results. The non-parametric additive regression model was then used to estimate the linear and nonlinear effects of CED on economic growth and CDE. The model's performance is compared against a linear regression model using the residual sum of squares, confirming the superior fit of the non-parametric model. A robustness test is conducted using GDP instead of per capita GDP as the dependent variable in the economic growth model.

Linear analysis shows that CED does not significantly contribute to CDE reduction or economic growth across the three regions. However, nonlinear analysis reveals substantial regional variations: **Economic Growth:** * **Eastern Region:** A W-shaped relationship—initial hindrance due to high initial investment costs, followed by slight fluctuations, and finally, a positive contribution in the later stages. * **Central Region:** A gentle W-shaped relationship—initial minimal effect, followed by a gradual positive contribution. * **Western Region:** An inverted U-shaped relationship—initial positive contribution from abundant hydropower resources gradually decreasing over time due to the diminishing role of energy costs in production. **CDE:** * **Eastern Region:** An M-shaped relationship—initial lack of significant impact, followed by fluctuations, and finally a positive contribution to CDE reduction in the later phase. * **Central Region:** A gentle W-shaped relationship—initial positive impact from hydropower, followed by diminishing returns as energy consumption growth outpaces CED. * **Western Region:** A U-shaped relationship—initial positive impact from hydropower, followed by a decrease as economic growth increases fossil fuel consumption. The non-parametric additive regression model provided a significantly better fit than the linear regression model, as indicated by substantially lower residual sums of squares.

The findings highlight the limitations of a linear perspective in understanding the complex relationship between CED, economic growth, and CDE. The regional disparities underscore the need for tailored policies to effectively utilize CED. The initial negative impacts on economic growth in several regions are primarily attributable to the high investment costs in the initial phases of CED. However, as the scale of clean energy production expands, its contribution to economic growth becomes more pronounced. Similarly, while CED does not initially reduce CDE significantly, its contribution becomes more substantial in the later stages. This suggests that initial investments and supportive policies are crucial for stimulating the growth of the clean energy sector and subsequently maximizing its positive impacts on both economic growth and CDE reduction.

The study demonstrates the importance of considering nonlinear relationships and regional contexts when analyzing the effects of CED. Policy recommendations include regionally-tailored support to encourage clean energy development, particularly in the early stages of development. This could include financial incentives, tax breaks, and other forms of government support. Future research should focus on more detailed regional analyses, exploring the specific factors contributing to regional variations and further refining the predictive models used. In addition, investigating the influence of technological progress and innovation on the long-term relationship between CED and economic growth could offer valuable insights for policy formulation.

The study relies on predicted data for the period 2017-2030, which introduces uncertainty into the results. The accuracy of the predictions depends on the validity of the forecasting methods used, which may limit the generalizability of some findings to other regions or countries. Furthermore, the study does not delve into the specific policies and technological advancements that contribute to the regional differences observed. A more in-depth investigation of these factors would be beneficial for creating more targeted and effective policies.