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Using the following nested CES function

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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:

enter image description here

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.

I would appreciate your comments and suggestions.

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