I wrote this paper with Astrid Kander a few months ago following my visit to Lund, but it has only just been added to RePEc.
In the paper, we develop a simple model of economic growth that allows for a significant role for energy and we apply the model to the Swedish data for the 19th and 20th centuries. To keep things as simple as possible the model is an extension of the famous Solow growth model. Output is measured in terms of gross output without netting out intermediate inputs which allows us to include energy as a regular production input alongside capital and labor. Both technological change and the supply of energy are treated as exogenous in this model but the capital stock evolves endogenously.
We find that the expansion in the supply of energy services over the last couple of centuries has reduced the apparent importance of energy in economic growth despite energy being an essential production input. We find that the elasticity of substitution between a capital-labor aggregate and energy is less than unity, which implies that when energy services are scarce they strongly constrain output growth resulting in a low output steady-state. When energy services are abundant the economy exhibits the behavior of the “modern growth regime” with the Solow model as a limiting case.
This figure, from the paper, attempts to illustrate this point:
It shows the effect of labor-augmenting technological change (the only type in most aggregate growth models) of the size of the optimal capital stock as a function of the amount of effective energy per effective worker. The larger the amount of energy services available per worker the greater the effect of technological change on the capital stock and hence on the output of the economy. Sigma refers to the elasticity of substitution between energy and capital. The smaller it is the sharper the transition from a state where the response of the capital stock is very small to one where it is large. The bottom line is that when energy supply is limited innovation has little impact on growth unless it is innovation directed at increasing the productivity of energy. This is the situation that we argued applied before the industrial revolution.
The expansion of energy services is found to be a major factor in explaining the industrial revolution and economic growth in Sweden, especially before the second half of the 20th century. In the latter period, labor-augmenting technological change becomes the dominant factor driving growth. We can sum this up with a "growth accounting" exercise (not included in the paper):
Capital, labor, and energy are simply the quantities of these inputs. Labor Aug. refers to labor augmenting technological change and energy aug. to energy augmenting technical change. Total factor productivity is a weighted mean of these two components. Energy quality refers to the effects of the shift from lower quality to higher quality fuels over time. Over time capital accumulation and labor augmenting technological change have been more and more important. Increase in energy supply and energy augmenting technological change were most important in the late 19th century, energy quality in the early 20th century. Hence, the claim that energy's importance in growth has declined over time. But it still makes a significant contribution and if energy supply was curtailed in the future could again become more important.
This paper, which we currently are working on a revise and resubmit, is just the first part of what we hope will be an ongoing collaboration on these issues.