Research on three-stage dynamic relationship between carbon emission and urbanization rate in different city groups

China is in a stage of rapid new urbanization, carbon emissions in regions the urbanization stages of which are different exhibit different characteristics. Based on the environmental Kuznets Curve, this paper calculates the carbon emissions of 32 provinces in China over 1978-2014 by IPCC. Using the Auto-regression Distributed Lag Model, we analyze the three-stage dynamic relationship between carbon emissions and urbanization rate in different city groups. And the influence of energy intensity and energy structure on this relationship is analyzed. Our finding shows that: The relationship between urbanization rate and carbon emissions is a three-stage dynamic relationship. In the provinces of Cluster 1 where the proportion of the service industry is the most and the urbanization rate is high, the shape of the three-stage curve is positive increase, positive decrease and negative increase; In the provinces of Cluster 2 which mainly depend on the manufacturing industry and have medium urbanization rate, the shape of the three-stage curve is positive decrease, positive increase and negative increase; In the provinces of Cluster 3 which mainly rely on the tourism industry and the husbandry industry and have lower urbanization rate, the shape of the three-stage curve is positive increase, positive increase and negative decrease. The decreasing effect of energy intensity on the carbon emissions is different significantly under different urbanization stages, and the decreasing effect is significant in the provinces of Cluster 1. The decreasing effect that energy structure has on carbon emissions is not significant, because the fossil fuels-dominated energy structure remains unchanged in China. Above all, this study can provide theoretical guidance for local governments to formulate carbon emission reduction plan in future.