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In order to identify the impact mechanism between income inequality and carbon emissions and clarify the nonlinear relationship between income inequality and carbon emissions in different degrees, so as to provide theoretical support for government departments to formulate policies of reducing carbon emission and optimizing resource allocation efficiency, we investigated the relationship between carbon emissions and domestic income inequality in the United States and France from 1915 to 2019 using wavelet decomposition and Quantile-on-Quantile regression. The results imply that 1) For France, the impact of income inequality on carbon emissions is negative when the income inequality is low. With the increase of income inequality, the impact of income inequality on carbon emission changes from negative to positive, and the increase of carbon emissions will amplify the effect. For United States, with the deepening of income inequality, its emission enhancing effect has been gradually reversed. In addition, the impacts of carbon emissions on income inequality in the two countries are quite similar. 2) In the short term, the relationship between income inequality and carbon emissions in the two countries has obvious random volatility characteristics. 3) In the medium term, there is a three-dimensional inverted “V” shaped relationship between income inequality and carbon emissions across quantiles in the United States. As mentioned for France, on the contrary, a three-dimensional “V” shaped relationship across quantiles exists. 4) In the long run, the relationship between income inequality and carbon emissions in the United States is “V” shaped across quantiles. Carbon emissions in France are mainly inhibited by domestic income inequality. According to the empirical results, we recommend that the governments should make greater efforts to ensure the synergy between income distribution and environmental governance to ensure a sustainable and prudent development of economy.

The Emission-Inequality Nexus: Empirical Evidence From a Wavelet-Based Quantile-on-Quantile Regression Approach