This paper intends to test the non-linear relationship between $CO_2$ emissions and income by employing cointegration model of the time-varying income elasticity. We select France, UK, Italy, Japan, US, China, India, Mexico and Korea and use non-parametric time series analysis on each country in order to estimate its own effect of income on $CO_2$ emission. The main results indicate that the $CO_2$ emission-income elasticities vary over time and the income elasticities of the Annex I countries tend to be higher in absolute terms than those of developing countries. In addition, we find that emission-income elasticities decrease for Annex I countries over time, whereas those for developing countries increase.