One of the little known facts of energy economics is that in the long-run data that we have available the value of energy relative to the value of output has fallen over time. The chart shows the data for Sweden. Output here is gross output. Relative to GDP the ratio was 1:1 or above in the early 19th century. That fact seems to rule out structural change as an explanation of the trend. Agriculture today doesn't have such a high energy cost share. If the elasticity of substitution between energy and other inputs is one, then the cost share of energy in each industry should stay the same no matter how much technological change takes place. So the data suggest that the elasticity of substitution between energy and capital is less than one (if technological change has improved energy efficiency). That implies that there are limits to substitution between energy and capital as is believed by most ecological economists if not all economists.
So I've been trying to get an estimate of the elasticity of substitution from this data supplied by my co-author, Astrid Kander. That's not so easy, because we need to take into account the rate of technological change and estimating the rate of technological change is always hard. That's because technological change is just everything that we can't explain in a model and when you throw a time trend or similar variable into a regression model the computer doesn't know that that is supposed to be technological change, gets confused and comes up with nonsense :)
You have to give the model more information and so that is what we are going to have to do.
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