This paper extends the author's previous analysis of the causal relationship between GDP and energy use in the U.S. post-war period to a cointegration analysis. The study uses a vector autoregression (VAR) model to examine the relationship between GDP, energy input, capital, and labor inputs. The results show that cointegration does occur, and energy input cannot be excluded from the cointegration space. The findings are consistent with macroeconomic dynamics and contradict claims in the literature that there is no cointegration between energy and output based on bivariate models. The analysis also supports the idea that energy is a limiting factor in economic growth, with shocks to energy supply tending to reduce output. The study uses various unit root tests to determine the integration properties of the variables and employs the Johansen procedure for cointegration analysis. The results are presented in three models, each with different specifications, and show that energy Granger-causes GDP, either unidirectionally or through a mutually causative relationship. The findings strengthen the conclusion that energy is a significant factor in economic growth and provide support for basic macroeconomic "stylized facts" concerning business cycle propagation and increasing returns.This paper extends the author's previous analysis of the causal relationship between GDP and energy use in the U.S. post-war period to a cointegration analysis. The study uses a vector autoregression (VAR) model to examine the relationship between GDP, energy input, capital, and labor inputs. The results show that cointegration does occur, and energy input cannot be excluded from the cointegration space. The findings are consistent with macroeconomic dynamics and contradict claims in the literature that there is no cointegration between energy and output based on bivariate models. The analysis also supports the idea that energy is a limiting factor in economic growth, with shocks to energy supply tending to reduce output. The study uses various unit root tests to determine the integration properties of the variables and employs the Johansen procedure for cointegration analysis. The results are presented in three models, each with different specifications, and show that energy Granger-causes GDP, either unidirectionally or through a mutually causative relationship. The findings strengthen the conclusion that energy is a significant factor in economic growth and provide support for basic macroeconomic "stylized facts" concerning business cycle propagation and increasing returns.