• Falling cost share is not consistent with normal growth models, with Constant Elasticity of Substitution (CES=1)• If the price of one factor goes up there will be a movement along the isoquant so that less of that factor is used and the cost share will stay constant.
Cobb –Douglas original production function• Y=AL α K1- α• Y is GDP, L is labor hours, K is physical capital (machinery and buildings) and A is the total factor productivity (TFP).• Alfa (α) is the wage share of GDP. This rests on the assumption that the salary corresponds to the marginal contribution of labor.
Cobb-Douglas cont.• The factor income shares for labor (α) respectively capitalists ((1- α) are used as weights to model the contribution of labor and capital to GDP under the assumption of constant returns to scale.• In growth accounting is what grows fast and gets paid much that gets the largest explanatory power.• If capital grows at the same pace as GDP (which is normal for developed countries) it will only explain roughly a third of GDP growth in the growth accounting framework, because the weight of capital, judged by its cost share, is often only about as much (0.3- 0.4).• As a consequence all conventional growth accounting ends up with a large role for total factor productivity (TFP); what is not explained by more capital per worker (capital deepening) is explained by higher efficiency in the combined use of capital and labor.
If energy is included• Normally energy has no importance, since its cost share is so low in modern economies (10%)
How to make energy matter• For energy to play a more fundamental role in a growth accounting framework it is necessary to modify the basic model assumptions.• One possibility is to edge away completely from the neoclassical idea of compensation to the factors of production according to their marginal productivity, and allow any kind of weights as long as the sum of weights are 1 (constant returns to scale), but this can lead to severe theoretical difficulties. (Ayres, R., and B. Warr (2009), p190- 195. Some results of their modeling seem counterintuitive and unrealistic: the marginal productivity of labor approaches zero when workers are equipped with more capital.)• Another possible adjustment, which we follow here, is to allow restrictions for the degree of substitution between energy, labor and capital.
Why is energy less important after 1950?• Because it is abundant and cheap (low cost share, just an illusion?)• Or because the economy basically grows on basis of something else? Information Technology (IT)?
Support for the IT idea useful work / GDP [GJ/1000$] 3,5 3,0 2,5 2,0 1,5 1,0 0,5 USA Japan UK Austria 0,0 1900 1915 1930 1945 1960 1975 1990 2005
Global Challenge• Most of the world is not just growing on basis of IT, the developing world take the second and third industrial revolution simultaneously• Demand pull – rising prices of energy• Climate change: What will a brake on coal use imply for economic growth and welfare?