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This study aims to investigate the impact of renewable energy consumption on the economic growth of G7 countries and explore the potential nonlinear relationship between the two variables. Initially, the NARDL model is employed to analyze the G7 countries, allowing for the control of nonlinear relationships and considering asymmetric effects. The findings of the NARDL model reveal an asymmetric long run cointegration relationship between renewable energy consumption and economic growth in Canada and the US, while other countries show different dynamics. Subsequently, a causal dynamic impact analysis is conducted to gain further insights into the relationship between renewable energy consumption and economic growth. In the next step, the advantage of panel data analysis is utilized to investigate the overall impact across all G7 countries. For this purpose, the study extends the NARDL model to the PNARDL (Panel Nonlinear Autoregressive Distributed Lag) model, which facilitates the control of asymmetric effects and nonlinearity in the panel data model. In this context, this study is one of the first studies to control the nonlinearity in panel data analysis. The results from the PNARDL model demonstrate that renewable energy has a positive long-term relationship with economic growth in G7 countries; however, this relationship is statistically insignificant. [ABSTRACT FROM AUTHOR]

A comprehensive understanding of the impact of renewable/non-renewable energy consumption on ecological quality and economic growth can serve to the sustainability of energy, ecology, and economy. This paper provides a new perspective of the comprehensive system of the 3E model, and introduces indicator of social factor to examine the non-linear effects of urbanization on energy, economy, and the environment. A threshold panel regression model is developed using the data of 120 countries in the last 20 years. In the proposed model, renewable energy and non-renewable energy are explanatory variables, economic growth and ecological footprint are explained variables, and urbanization are threshold variable. Non-linear relationships are concretized and quantified in the research of global and different income groups. The results show that global renewable energy can promote economic growth while improving the environment. As the urbanization rate increases, the negative effect of renewable energy on the ecological footprint first weakens and then increases, and the positive coefficient on the economy maintains a growth trend. Non-renewable energy has a more obvious positive effect on economic growth, but it increases the ecological footprint. The development of urbanization strengthens its promotion of the economy and reduces its pressure on the environment. From the perspective of different income groups, renewable energy does not always suppress the ecological footprint. The energy transition reduces economic growth in the initial stages of urbanization in certain regions. After crossing the threshold, the coefficient changes of different income groups have similarities and differences. Based on the conclusions, some recommendations are put forward, including promoting the transformation of energy consumption structure, improving energy efficiency and accelerating the process of urbanization. The model in this paper is suitable for investigating the nonlinear impact of urbanization on the 3E system through panel data, and can provide theoretical support for studying the threshold effect of a country or economy. This study also shows the importance of renewable energy and the indirect effects of urbanization, which is helpful for formulating global sustainable and coordinated development policies. [Display omitted] • A new perspective of the energy-economy-environment (3E) model is proposed. • Threshold models enable the non-linear relationships to be concretized and quantified. • Global renewable energy improves the environment while promoting economic growth. • Urbanization reduces the pressure on the environment from energy consumption. • Urbanization strengthens the positive effect of energy on economic growth. [ABSTRACT FROM AUTHOR]