"High levels of carbon emissions and rising income inequality are interconnected challenges for the global society. Commonly-applied linear regression models fail to unravel the complexity of potential bi-directional transmission channels. Specifically, consumption, energy sources and the political system are potential determinants of the strength and direction of the dependence between emissions and inequality. To capture their impact, this study investigates the conditional dependence between income inequality and emissions by applying distributional copula models on an unbalanced panel data set of 154 countries from 1960 to 2019. A comparison of high-, middle-, and low-income countries contradicts a linear relationship and sheds light on heterogeneous dependence structures implying synergies, trade-offs and decoupling between income inequality and carbon emissions. Based on the conditional distribution, we can identify determinants associated with higher/lower probabilities of a country falling in an area of potential social and environmental sustainability."

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