Sectoral Energy Demand Analysis

Abstract

The purpose of this chapter is to consider energy demand at the sector level. Major energy using sectors such as industry, transport, and households have their specific features that an aggregated analysis cannot capture. A sector level analysis provides a better understanding of the demand by identifying relevant drivers. This chapter first presents the disaggregation of energy demand, discusses the information issues and introduces frameworks/tools for a disaggregated analysis.

Appendices

Annex 4.1: Hierarchical Decomposition

The level of disaggregation affects the results of decomposition. The more disaggregated the group, the more relevant and reliable is the measurement. But the limit for disaggregation is given by data availability. In such a case, a hierarchical measurement of the effects is done.

The structural effect identified with aggregated analysis can be further split into sub-structural effect and sub-intensity effect. The total structural effect is obtained by the multiplication of macro structural effect and sub-structural effect. The real intensity effect is obtained by the multiplication of macro sectoral intensity effect (for sectors without sub-sectors) and sub-sectoral intensity effect (for sectors with sub-sectors).

In such a case, the extension of the basic energy intensity equation takes the following form:

$$ EI = \sum\limits_{i} {\sum\limits_{j} {\frac{{e_{ij} }}{{Q_{ij} }}\frac{{Q_{ij} }}{{Q_{i} }}} } \frac{{Q_{i} }}{Q} = \sum\limits_{i} {S_{i} } \sum\limits_{{}} {(SEI_{ij} SS_{ij} )} $$

(4.32)

where

e_ij =:

energy consumption in subsector j of sector i;

Q_ij =:

activity of subsector j in sector i;

SEI_ij =:

subsectoral energy intensity in subsector j of sector i;

SS_ij =:

subsectoral share of subsector j in sector i.

Other variables have same meaning as before.

Differentiating equation 4.32 yields

$$ \frac{1}{EI}\frac{dEI}{dt} = \sum\limits_{i} {\frac{{W_{i} }}{{S_{i} }}} \frac{{dS_{i} }}{dt} + \sum\limits_{i} {W_{i} } \left[ {\sum\limits_{j} {\frac{{w_{ij} }}{{s_{ij} }}} \frac{{ds_{ij} }}{dt} + \sum\limits_{j} {\frac{{w_{ij} }}{{e_{ij} }}} \frac{{dEI_{ij} }}{dt}} \right] $$

(4.33)

where

S_i =:

sectoral share at the overall level;

s_ij =:

subsectoral share of sub-sector j in sector I;

W_i =:

weight at the sectoral level;

w_ij =:

weight at the subsectoral level;

EI_ij =:

energy intensity of sub-sector j in sector i

Equation 4.33 can be rewritten as

$$ \frac{dEI}{EI} = \sum\limits_{i} {\frac{{W_{i} }}{{S_{i} }}} dS_{i} + \sum\limits_{i} {} \sum\limits_{j} {W_{i} \frac{{w_{ij} }}{{s_{ij} }}} ds_{ij} + \sum\limits_{i} {} \sum\limits_{j} {W_{i} \frac{{w_{ij} }}{{e_{ij} }}} de_{ij} ] $$

(4.34)

Integration of Eq. 4.34 between two years in discrete form results in the following equation:

$$ \ln \left( {\frac{{EI^{T} }}{{EI^{0} }}} \right) = \sum\limits_{i} {W_{i} } \ln \left( {\frac{{S_{i}^{T} }}{{S_{i}^{0} }}} \right) + \sum\limits_{i} {} \sum\limits_{j} {W_{i} w_{ij} \ln \left( {\frac{{s_{{_{ij} }}^{T} }}{{s_{{_{ij} }}^{0} }}} \right)} + \sum\limits_{i} {} \sum\limits_{j} {W_{i} w_{ij} \ln \left( {\frac{{e_{{_{ij} }}^{T} }}{{e_{{_{ij} }}^{0} }}} \right)} $$

(4.35)

The first term measures the structural effect at the upper level (i.e. sectoral level), the second term measures the intra-sectoral structural effect and the third term measures the intensity effect (which is also called the real intensity effect).

Example: Table 4.13 presents value added (million dollars) and energy consumption (Mtoe) for various sectors for three years (T0, T1 and T2). Table 4.14 provides the break-up of industrial energy consumption and value additions. Required is decomposition of energy intensity between T0 and T2.

Table 4.13 Energy and activity details at sectoral level

Table 4.14 Sub-sectoral details for industry

Value addition is in million dollars in 1990 prices and energy consumption in Mtoe.

Answer: For the decomposition, first sectoral shares and energy intensities have to be calculated. Using the information in Table 4.15, the necessary calculations are performed for decomposition. Results are given in Table 4.16.

Table 4.15 Shares, intensities and weights for decomposition calculations

Table 4.16 Results of energy intensity decomposition

Annex 4.2: Translog Cost Function

The translog cost function is considered to be the second order approximation of an arbitrary cost function. It is written in general form as follows:

$$ \begin{aligned} \ln C & = \alpha_{0} + \sum {\alpha_{i} } \ln P_{i} + 0.5\sum\limits_{i} {\sum\limits_{j} {\gamma_{ij} \ln P_{i} \ln P_{j} } } \\ & \quad + \alpha_{Q} \ln Q + 0.5\gamma_{QQ} (\ln Q)^{2} + \sum\limits_{i} {\gamma_{Qi} } \ln Q\ln P_{i} \\ \end{aligned} $$

(4.36)

where C = Total cost, Q is output, Pi are factor prices, i and j = factor inputs.

This cost function must satisfy certain properties:

• homogeneous of degree 1 in prices;

• satisfy conditions corresponding to a well-behaved production function;

• Cost function is homothetic (separable function of output and factor prices) and homogeneous.

Accordingly, the following parameter restrictions have to be imposed:

$$ \begin{aligned} &\sum {\alpha _{{\text{i}}} } = 1 \\ &\gamma _{{{\text{ij}}}} = \gamma _{{{\text{ij}}}} ,{\text{i}} \ne {\text{j}} \\ &\sum\limits_{{\text{i}}} {\gamma _{{{\text{ij}}}} } = \sum\limits_{{\text{j}}} {\gamma _{{{\text{ij}}}} } = 0 \\ \sum\limits_{{\text{i}}} {\gamma _{{{\text{Qi}}}} } = 0 \\ \gamma _{{{\text{Qi}}}} = 0\,\,{\text{and}} \\ &\gamma _{{\text{QQ}}} = 0 \\ \end{aligned} $$

(4.37)

The derived demand functions can be obtained from Shepherd’s lemma

$$ X_{i} = \delta C/\delta P_{i} $$

(4.38)

Although these functions are non-linear in the unknown parameters, the factor cost shares

(M_i = P_iX_i/C) are linear in parameters.

$$ M_{i} = \alpha_{i} + \sum\limits_{j} {\gamma_{ij} (\ln P_{j} )} \,{\text{for}}\,{\text{i}} = {\text{factor}}\,{\text{inputs}},{\text{ j}} = {\text{factor}}\,{\text{inputs}},{\text{i}}\# {\text{j}} $$

(4.39)

These share equations are estimated to obtain the parameters. Only n–1 such equations need to be estimated as the shares must add to 1.

The own price elasticity of factor demand is obtained as follows:

$$ E_{ii} = \partial \ln X_{i} /\partial \ln P_{i} $$

(4.40)

$$ X_{i} = \frac{C}{{P_{i} }}\left( {\alpha_{i} + \sum\limits_{j} {\gamma_{ij} (\ln P_{j} } } \right) $$

(4.41)

$$ \begin{aligned} \ln X_{i} & = \ln C - \ln P_{i} + \ln (\alpha_{i} + \sum\limits_{{}} {\gamma_{ij} (\ln P_{j} } ) \\ & = \ln C - \ln P_{i} + \ln M_{i} \\ \end{aligned} $$

(4.42)

$$ \begin{aligned} & \partial \ln X_{i} /\partial \ln P_{i} = \frac{\partial \ln C}{{\partial \ln P_{i} }} - 1 + \frac{{\gamma_{ii} }}{{M_{i} }} \\ & E_{ii} = M_{i} + \frac{{\gamma_{ii} }}{{M_{i} }} - 1 \\ \end{aligned} $$

(4.43)

$$ E_{ii} \, = \,(M_{i}^{2} \, - M_{i} \, + \gamma_{ii} )/M_{i} $$

(4.44)

The cross-price elasticity can be derived similarly as

$$ E_{ij} = (\gamma_{ij} + M_{i} M_{j} )/M_{i} $$

(4.45)

Allen partial elasticity of substitution is given by:

$$ \sigma_{ij} = (\gamma_{ij} + M_{i} M_{j} )/M_{i} M_{j} $$

(4.46)

Source: Pindyck (1979)