Abstract: In this paper, an endogenous growth model with dual constraints of energy consumption and carbon emission is developed by introducing both, a non-renewable energy and a renewable energy, which can both serve for intermediates. And the global vector auto regression(GVAR)model is established with spatial correlation to analyze the dynamic impact on economic growth and carbon emissions by controlling energy consumption of every province of China.The results show that by using renewable energy, improving cleaner technologies and the marginal output of non-renewable energy, the goal of energy consumption assessment can be achieved, under the constraints of reducing carbon emissions and promoting economic growth.The goal of energy consumption has a strong constraint to provinces consuming more energy but a weak constraint to others, which have greater potential to energy conservation.Because the structure of the energy consumption adjusts against the tide, the carbon emission is not decreasing in some provinces. Furthermore, the problems in the process of reducing energy consumption are tried to be found. The results show that technology research has little effect on adjusting the structure ofenergy consumption and finding renewable energy. And technology research also has little effect on reducing carbon emission.Although relying on the adjustment of traditional energy price can reduce the carbon emission but this would limit economic growth.

Key words: controlling energy consumption, GVAR model, carbon emission