In the industrial sector, improvement in energy efficiency is indicated via a reduction in energy intensity. Accordingly, improvements in energy efficiency implies production of more goods and services using the same amount of energy inputs or production of the same amounts of goods and services using lower quantity of energy inputs, which does not necessarily imply an actual reduction of energy consumption. Since a reduction in energy intensity produces a reduction in GHG emissions only if it results in a reduction of actual energy consumption, the extent of its contribution to a reduction in GHG emissions is not certain. This study investigates the empirical relationship between GHG emissions and energy intensity in Canadian industries. Using fixed effect, random effect, and panel stochastic frontier methods I find the elasticity of GHG-output ratio with respect to energy intensity is about 0.4. The policy implication is that a policy measure that reduces energy intensity by 1% reduces GHG intensity by 0.4 percent, all else remaining the same. This elasticity is linked to the emission-tax-induced rise in energy price through the energy-price elasticity of energy intensity to offer policy implications.