The formula of the "turning point" in a Kuznets curve (where the dependent variable reaches its maximum value) is exp(-ß1/2*ß2). ß1 is the coefficient of the linear GDP and ß2 is the coefficient of the squared GDP.
For a single country, this turning point is of course suitable. But does it still apply to a cross-country panel regression where different countries have very different GDP levels (but we only have one turning point)?
Many thanks!
My personal feeling is that you don't have to. But it is more grounded on personal work that scientific evidence. Even with comparable countries, the Kuznetz curve exhibits large differences due to history, sociology, and economic insertion in the globalisation process.
As higlighted in the question, most international empirical studies exploring the income-emissions nexus employ a panel dataset of countries and rely almost exclusively on the use of conventional longitudinal econometric techniques such as fixed and random effects methods. These methods produce constant slope coefficients across heterogeneous countries and as such fail to capture country level heterogeneity in Kuznets Curve explorations. This implies that the use of standard panel methods, especially for a group of largely heterogeneous countries, may not provide useful information on country specific turning point incomes where the Kuznets Curve exists.
Yaduma et al (2015) argue that investigating the income-emissions relationship at different percentiles of the conditional emissions distribution may be more informative about turning point incomes relative to estimations focused on the conditional mean alone. This paper applies the quantile fixed effects technique for the CO2 EKC and two groups of economic development (OECD and Non-OECD countries) and six geographical regions - West, East Europe, Latin America, East Asia, West Asia and Africa. The results from the use of this technique with those of conventional fixed effects method reveals that the latter may indeed give flawed results depending on the conditional quantile examined
Natina Yaduma, Mika Kortelainen & Ada Wossink (2015) The environmental
Kuznets curve at different levels of economic development: a counterfactual quantile regression analysis for CO2 emissions, Journal of Environmental Economics and Policy, 4(3): 278-303, DOI: 10.1080/21606544.2015.1004118
Well, once again, I am a little bit out of my expertise here. But, with fixed effects you can capture a lot of things, including what is intereting you. So, given the econometric limitations of fixed effects in panel data (see Greene and Hensher) I would recommend to limit your analysis to what is culturally homogeneous. You can't fix for the errors in the errors terms. The choice is yours and you can argue.
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