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This study extends a neoclassical growth model to include the accumulation of physical capital and energy consumption within a panel of fifty states (plus the District of Columbia) in the U.S. The theoretical model allows us to examine the implications for convergence in economic growth and energy intensity. From the theoretical model, we formulate an empirical approach using a dynamic panel model that is estimated using a general method of moments framework to test the conditional rates of convergence. The empirical results indicate convergence in energy intensity, and our estimates accurately predict both the growth in and convergence of energy intensity across our entire sample. Consistent with other findings in the literature, our results imply that energy use, over the past four decades, plays a small and positive role in state-level, per capita economic growth and convergence. Based on these results, we discuss policy implications for state-level income growth and energy consumption.