In terms of the shape of the EKC, debates and further studies have shown other variations from the inverted-U shape originally proposed: cubic function and L-shaped curves. Torras and Boyce (1998) suggested that instead of a quadratic function, the EKC actually follows a cubic one. This allows for the possibility that a downturn in pollution (at the peak of the inverted U) can be followed by a later upturn, that is, a reversal of the tendency for pollution levels to decline with further increases in per capita income. These findings imply that beyond some point, high-income levels, rather than.
