The underlying idea behind the environmental Kuznets curve is that GDP per capita initially increases environmental degradation but later reduces the environmental degradation as the result of the development brought about by the increase in per capita GDP leading to the adoption of environmental friendly technology. Thus the specification is that environmental degradation is a function of GDP per capita and GDP per capita square.. Co2=f(GDPPC, GDPPC^2)

This is tantamount to saying, it increases co2 emission in the short run and reduces it in the long run giving an inverted U shape. I believe this model can be correctly modeled using the OLS regression method. However, recent findings has shown that most papers use this same specification with ARDL which have both short and long estimates. That is, both GDP per capita and ita square appears in both the long and short run estimate. Then, if the result appears that both GDP per capita and its square have positive and negative significant effect respectively in both short run and long run. Does it mean EKC holds in both short and long run.