An improved gray Bernoulli model for estimating the relationship between economic growth and pollution emissions

The environmental Kuznets curve (EKC) hypothesis is used to describe the relationship between economic development and environmental pollution. In this paper, an EKC-estimating method based on an improved nonlinear gray Bernoulli model (NGBM) is proposed from the perspective of gray system modeling. First, a non-equigap NGBM is established taking the GDP per capita and pollutant emission as the input and output of the gray system, respectively. Then, a particle swarm optimization algorithm is used to find the parameters in the nonlinear model. Finally, the EKC is validated by applying it to the per capita emission of wastewater, SO₂, CO₂, and soot in China. The results show that the new method proposed in this paper optimizes the exponent of the NGBM which allows it to describe the trends in the different morphological data very well, resulting in a higher fitting accuracy. China's per capita emission of wastewater, SO₂, CO₂, and soot show trends corresponding to monotonically increasing, inverted U-shaped, S-shaped, and N-shaped changes, respectively.