This paper attempts to estimate a panel "frontier" whole economy aggregate energy demand function for 29 countries over the period 1978 to 2006 using parametric stochastic frontier analysis (SPA). Consequently, unlike standard energy demand econometric estimation, the energy efficiency of each country is also modeled and it is argued that this represents a measure of the underlying efficiency for each country over time, as well as the relative efficiency across the 29 OECD countries. This shows that energy intensity is not necessarily a good indicator of energy efficiency, whereas by controlling for a range of economic and other factors, the measure of energy efficiency obtained via this approach is. This is, as far as is known, the first attempt to econometrically model OECD energy demand and efficiency in this way and it is arguably particularly relevant in a world dominated by environmental concerns with the subsequent need to conserve energy and/or use it as efficiently as possible. Moreover, the results show that although for a number of countries the change in energy intensity over time might give a reasonable indication of efficiency improvements; this is not always the case. Therefore, unless this analysis is undertaken, it is not possible to know whether the energy intensity of a country is a good proxy for energy efficiency or not. Hence, it is argued that this analysis should be undertaken to avoid potentially misleading advice to policy makers.