# Can technical change have a negative growth rate?

Using the following nested CES function

I have backed out augmentation indices $$A_L$$ and $$A_E$$. Where $$A_L$$ is a labour-augmenting technical change index and $$A_E$$ is an energy-augmenting technical change index. $$Y$$ is GDP, $$K$$, $$L$$ and $$E$$ are factors of production.

Implied technical change indices are shown below:

What puzzles me is that the energy-augmenting technical change index $$A_E$$ is downward sloping (or has a negative growth rate). Usually, one would expect technical change to have a positive trend or at least no trend (no growth). I am now trying to make sense of this result.

One possible explanation I can think of is the presence of energy efficiency rebound effect. As energy-specific technologies are introduced, greater quantities of energy is consumed since the technical progress reduces the price of effective energy. Cheap energy induces greater consumption offsetting the efficiency gains.