This paper presents empirical evidence on the relationship between energy consumption and GDP in Colombia during the period 1970 to 2009. The results show that the series are not stationary, i.e. are individually I (1); in addition we find a long term relationship between both variables. Through a VECM we estimate short and long term elasticities to analyze the dynamics of adjustment. The results show that in the short-term the conservation hypothesis holds (i.e. no evidence of a short-term relationship of energy consumption to GDP). In the long-term, however, we find evidence of a feedback mechanism between both variables. Yet, this paper provides evidence that policymakers can implement policies aimed at energy conservation without hurting economic growth.