Modeling the environmental Kuznets Curve: A stochastic approach using economic and climate data.

This research chooses Pakistan as an ideal case to explore the connection between economic expansion and carbon emissions, by incorporating a novel approach of using coupled stochastic equations to estimate this dynamic interaction.The GDP (Gross domestic product) in Pakistan has been ascending over the time of 1960-2023, with short episodes of stagnation (mid 80s) and decline (1973, 2009). Since 2010, the growth rate has been rising annually, reaching 4.71% in 2016. At the beginning of economic development, countries like Pakistan focus on building industries and infrastructure, heavily relying on fossil fuels, resulting in increased carbon emissions. Initially, economic growth leads to more pollution due to a lack of strict environmental regulations and advanced technology. However, after reaching a certain level of development, countries can invest in cleaner technologies and enforce environmental regulations, leading to reduced emissions. This relationship is visualized as an inverted U-shaped curve, known as Environmental Kuznets Curve. This study analyzes the Environmental Kuznets Curve (EKC) by offering stochastic differential equations to explore the dynamic relationship between economic expansion and carbon emissions in Pakistan. The results show that Pakistan follows the EKC hypothesis, with a turning point, beyond which emissions begin to decline. Our model of stochastic differential equations, when optimized with Differential Evolution Algorithm, proved to be in agreement with the research hypothesis. This research focuses on the significance of aligning national policies with sustainable development goals (SDG), particularly in attaining sustainable economic development with minimum environmental hazards. This research yields valuable insights to government and policy makers to balance economic development with environmental sustainability, achieving sustainable future for Pakistan.