Industry-mix effects at different levels of sectoral disaggregation: a decomposition of inter-country differences in energy costs

Abstract

This article develops a decomposition of inter-country differences of unit energy costs (UEC) of the manufacturing sector. UEC are decomposed into a structural (industry-mix) component and an autonomous component that captures all other effects like, e.g., differences in energy efficiency and energy prices. Based on NACE 3-digit level data from Eurostat’s Structural Business Statistics the industry-mix component can be quantified on different levels of sectoral disaggregation. The results show that not only industry-mix effects on the conventional (typically NACE 2-digit) but also those measurable at higher levels of disaggregation are relevant for comparison of energy costs across countries.

Appendix 1: Methodology: decomposition of industry-mix and autonomous effects on 2nd- and 3rd-level

Both industry-mix effects, ${\Delta }_{{{\bar{\mathbf{B}}}}} e$ and ${\Delta }_{{{\mathbf{\bar{\bar{B}}}}}} e$, can be further decomposed in the following manner. Introducing the matrices ${\bar{\mathbf{B}}}^{j}$ and ${{\bar{\bar{\mathbf{B}}}}}^{m}$, where $m=1,\dots K$, for which the $j$-th respectively the $m$-th column corresponds to the respective column in ${\bar{\mathbf{B}}}$ as well as ${{\bar{\bar{\mathbf{B}}}}}$ and all other columns include exclusively zero-values, allows to extend the decomposition model:

$$e = {\mathbf{\bar{e}^{\prime}}} \cdot \left( {{\bar{\mathbf{B}}}^{1} + {\bar{\mathbf{B}}}^{2} } \right) \cdot {\mathbf{b}} = {\mathbf{\bar{\bar{e}}^{\prime}}} \cdot \left( {{\mathbf{\bar{\bar{B}}}}^{1} + \cdots + {\mathbf{\bar{\bar{B}}}}^{K} } \right) \cdot \left( {{\bar{\mathbf{B}}}^{1} + {\bar{\mathbf{B}}}^{2} } \right) \cdot {\mathbf{b}}.$$

(8)

and

$${\Delta }_{{{\bar{\mathbf{B}}}}} e = {\Delta }_{{{\bar{\mathbf{B}}}^{1} }} e + {\Delta }_{{{\bar{\mathbf{B}}}^{2} }} e,\quad {\Delta }_{{{\bar{\bar{\mathbf{B}}}}}} e = {\Delta }_{{{\bar{\bar{\mathbf{B}}}}^{1} }} e + \cdots + {\Delta }_{{{\mathbf{\bar{\bar{B}}}}^{K} }} e.$$

(9)

These decompositions allow distributing industry-mix effects between the energy-intensive and non-energy-intensive industry or attributing it to specific sectors at the NACE 2-digit level. A further modification of the decomposition model allowing to calculate the decomposition given in Eq. (9) as well as a decomposition of the autonomous effect, ${\Delta }_{{{\mathbf{\bar{\bar{e}}}}}} e$, is based on the diagonalisation of ${\mathbf{\bar{\bar{e}}}}$. Let $\varvec{\bar{\bar{E}}}$ be a matrix with the main diagonal $\varvec{\bar{\bar{e}}}$ and all other elements being zero. This allows rearranging the decomposition model in Eq. (6) as follows:

$${\tilde{\mathbf{e}}} = {{\bar{\bar{\mathbf{E}}}}} \cdot {{\bar{\bar{\mathbf{B}}}}} \cdot {\bar{\mathbf{B}}} \cdot {\mathbf{b}},$$

(10)

where $\widetilde{\mathbf{e}}$ is a vector of length $L$ and sum $e$ whose m-th element gives the additive contribution of the m-th 3-digit level sector to the overall UEC. Equation (10) would also allow decomposing the industry-mix effects according to the contribution of industries and subindustries. Nevertheless, a more disaggregated decomposition of industry-mix effects than the one available by Eqs. (8–9) is not possible because the vectors $\mathbf{b}$, ${\bar{\mathbf{b}}}_{j}$ und ${{\bar{\bar{\mathbf{b}}}}}_{jk}$ are vectors with shares as elements, which must sum up to 1, such that the elements are not independent of each other. Dependent components in decomposition analysis must be treated with caution (cf. Dietzenbacher and Los 2000). This is why Eqs. (8–9) are used for decomposing the industry-mix effects and only the autonomous effect is decomposed according to the diagonalisation approach given in Eq. (10).