In this paper we employ a dataset of three dimensions - state, sector, and year - to estimate the short- and long-run price elasticities of state-level electricity demand in the United States. Our sample covers the period 2003-2015. We contribute to the literature by employing instrumental variable estimation approaches, using the between estimator, and pursuing panel specifications that enable us to control for multiple dimensions of fixed effects. We conclude that state-level electricity demand is very price inelastic in the short run, with a same-year elasticity of -0.1. The long-run elasticity is near -1, larger than often believed. Among the sectors, it is industry that has the largest long-run price elasticity of demand. This appears to in part be due to electricity-intensive industrial activities clustering in low-price states.