Lucas Bretschger has an interesting new paper in Resource and Energy Economics titled: "Energy prices, growth, and the channels in between: Theory and evidence". The paper argues that countries with higher energy use per capita grow slower in the long-run though reductions in energy use lower output in the short-run. The long-run effect is due to an induced increase in capital accumulation and because the model is similar to AK endogenous growth models, innovation. The paper is motivated by the stylized fact that in a sample of 37 countries, countries with higher per capita energy use grow slower. The sample includes mostly developed countries but also China and India.
This negative correlation is, however, easy to explain in terms of catch-up growth dynamics. As we show in our stylized facts paper, there is a strong positive correlation between the level of GDP per capita and the level of energy use per capita. Per capita income in countries such as China and India has risen faster than in the developed countries due to the fact that they are poorer and undergoing catch-up growth. This results in a spurious negative relationship between energy use per capita and the rate of economic growth.
This is not to say at all that Bretschger's theoretical model is wrong, but the motivation can easily be explained in another way. In fact, I'm very sympathetic to the idea that plentiful energy resources could slow the rate of economic growth as I discussed in my presentation at the AARES conference in Rotorua and my upcoming Arndt-Corden seminar on 17th March.
Bretschger also estimates an econometric model that is loosely related to his theoretical model (for example, using energy quantity rather than price due to a lack of internationally comparable data - a big problem for energy economics) that regresses the investment/output ratio on energy intensity and GDP (there are additional equations). It is not surprising that reduced energy intensity could encourage increased investment if it represents increased energy efficiency - this is one of the factors in macro-level rebound as in Harry Saunders (1992) model.
The bottom line is that the energy-output relationship is quite complicated and is probably not at all well captured by reduced form time series models. Bretschger is also making this point with his paper.