The aim of this paper is to investigate bi-directional spillovers into residential and industrial sectors induced by energy efficiency improvement (EEI) in both the short- and long-term, and the impact of nesting structure as well as the size of elasticities of substitution of production and utility functions on the magnitude and the transitional dynamic of rebound effect. Developing a dynamic general equilibrium model, we demonstrate that residential EEIs spillovers into the industrial sector through the labor supply channel and industrial EEIs spill-overs into the residential sector through the conventional income channel. Numerical simulations calibrated on the U.S. suggest that not taking into account these spillover effects could lead to mis-estimate the rebound effect especially of residential sector EEIs. We also demonstrate how the size and the duration of the rebound effect depend on the value of elasticities of substitution. Especially, the elasticity of substitution between energy and non-energy consumption in household utility and the elasticity of substitution between physical capital and labor in production play a major role. Numerical simulations suggest that alternative sets of value for the elasticities of substitution may give sizable different patterns of rebound effects in both the short- and long-term. In policy terms, our results suggest that energy effciency policies should be implemented simultaneously with rebound effect offsetting policies by considering short- and long-term wide-economy feedbacks. As a consequence, they recall for considering debates about what type of policy pathways is more effective in mitigating the rebound effect.