Energy Demand, Inter-Fuel Substitution and Decarbonisation in a Technology-Consistent Model

The standard specification of energy demand and inter-fuel substitution in E3 models, mostly CGE models, is a nested production structure of CES functions. The standard treatment of energy in these models is a nesting structure of two or three levels, where in the first nest energy is substituted against other production factors and is in the second nest split up into the single energy types. The separability assumption on which this nested treatment of energy is based contradicts the empirical facts of thermodynamics and energy technology characteristics. The objective of this paper is the foundation of a different treatment of energy demand, which still fits into the general framework of factor substitution, but deals with energy in a way that is consistent with thermodynamic empirical facts. The basic idea is that the inputs of capital and energy in an industry are neither fully substitutive or complementary, but linked by underlying production processes with different energy efficiencies, where energy specific capital (gas turbines, coal furnaces, etc.) is combined with the specific energy input (gas, coal, etc.) for producing output. The input of each energy type per unit of output is given by a Kaya-identity of, firstly, a technology component (measuring the efficiency of each process) and, secondly, a capital structure-component (measuring the mix of processes for producing total output). The latter drives long-run changes in the energy mix and therefore in CO2 emissions. The differential equation of motion for the capital structure-component basically depends on the share of new investment across processes and the depreciation rate. A shift in investment towards 100 percent non-fossil technologies is a prerequisite for decarbonisation and can lead to steep decreases in CO2 emissions after the peak. The other sensitive variable is the depreciation rate that determines the time span within which the capital structure-component reacts to 100 percent non-fossil investment. A numerical example as well as historical empirical data of countries beyond the carbon peak show the interplay of investment shares and depreciation rates and their importance for steep decarbonisation.