Energy Demand Forecasting

Abstract

This chapter presents alternative approaches used in forecasting energy demand and discusses their pros and cons. It covers both simple approaches based on indicators and more sophisticated approaches using econometric methods, end-use method and other techniques. The chapter builds on the materials presented in Chaps. 3 and 4 and explains how demand analysis tools are extended to make forecasts for the future.

Annex 5.1: Mathematical Representation of Demand Forecasting Using the Input–Output Model

The value of output relations in a set of inter-industry accounts can be defined as:

$$ X_{i} = \sum\limits_{j = 1}^{n} {X_{ij} + \sum\limits_{k = 1}^{r} {F_{ik} } } ;i = 1,2, \ldots n $$

(5.12)

where X_i is the value of total output of industry i, X_ij is the value of intermediate goods’ output of industry i sold to industry j, and F_ik is the value of final goods’ output of industry i sold to final demand category k (net of competitive import sales).

The final demand arises from a number of sources, which is shown in Eq. (5.13):

$$ \sum\limits_{k = 1}^{r} {F_{ik} } = C_{i} + \Delta V_{i} + I_{i} + G_{i} + E_{i} - M_{Fi} $$

(5.13)

where C_i is the value of private consumer demand for industry i final output, V_i is the value of inventory investment demand for industry i final output, I_i is the value of private fixed investment demand for industry i final output, G_i is the value of government demand for industry i final output, E_i is the value of export demand for industry i final output and M_Fi is the value of imports of industry i final output (and often referred to as competitive imports).

It is assumed that intermediate input requirements are a constant proportion of total output, which is expressed as:

$$ a_{ij} = \frac{{x_{ij} }}{{X_{j} }} $$

(5.14)

where a_ij is the fixed input–output coefficient or technical coefficient of production.

Equations (5.12), (5.13) and (5.14) can be written more concisely in matrix form as

$$ {\text{X}} = {\text{AX}} + {\text{F}} $$

(5.15)

F:

vector of final demand

A:

matrix of inter-industry coefficients

X:

vector of gross outputs

The well-known solution for gross output of each sector is given by

$$ {\text{X}} = \left( {{\text{I}} - {\text{A}}} \right)^{ - 1} {\text{F}} $$

(5.16)

where I is the identity matrix, and (I−A)⁻¹ is the Leontief inverse matrix.

Thus, given the input–output coefficient matrix A, and given various final demand scenarios for F, it is straightforward to calculate from Eq. (5.15), the corresponding new values required for total output X, and intermediate outputs x_ij of each industry.

For energy analysis, the basic input output model is extended to include energy services. It is considered that the input–output coefficient matrix can be decomposed and expanded to account for energy supply industries (e.g. crude oil, traditional fuels, etc.), energy services or product equations (e.g. agriculture, iron and steel, water transportation).

Equation (5.16) is modified to a more general system as shown in Eq. (5.17)

$$ \begin{aligned} & {\text{A}}_{\text{ss}} {\text{X}}_{\text{s}} + {\text{A}}_{\text{sp}} {\text{X}}_{\text{p}} + {\text{F}}_{\text{s}} = {\text{X}}_{\text{s}} \\ & {\text{A}}_{\text{ps}} {\text{X}}_{\text{s}} + {\text{A}}_{\text{pi}} {\text{Xi}} + {\text{F}}_{\text{p}} = {\text{X}}_{\text{p}} \\ & {\text{A}}_{\text{is}} {\text{X}}_{\text{s}} + {\text{A}}_{\text{ii}} {\text{X}}_{\text{i}} + {\text{F}}_{\text{i}} = {\text{X}}_{\text{i}} \\ \end{aligned} $$

(5.17)

where

X_s:

output vector for energy supply,

X_p:

output vector for energy products,

X_i:

output vector for non-energy sectors,

F_s:

final demand for energy supply,

F_p:

final demand for energy products,

F_i:

final demand for non-energy sectors,

A_ss:

I/O coefficients describing sales of the output of one energy/ supply conversion sector to another energy conversion sector.

A_sp:

I/O coefficients describing how distributed energy products are converted to end-use forms.

A_si:

0 implying that energy supplies are not used by non-energy producing sectors. Energy is distributed to the non-energy producing sectors via energy product sectors.

A_ps:

I/O coefficients describing how energy products—final energy forms—are used by the energy supplying industries.

A_pp:

0 implying that energy products are not used to produce energy products

A_pi:

I/O coefficients describing how energy products—final energy forms are used by non-energy producing sectors.

A_is:

I/O coefficients describing the uses of non-energy materials and services by the energy industry.

A_ip:

0 implying that energy product sectors equipment require no material or service inputs. This is because they are pseudo sectors and not real producing sectors.

A_ii:

I/O coefficients describing how non-energy products are used in the non-energy producing sectors.

If we rewrite Eq. (5.6) in the summary form,

X^E = A^E X^E + F^E, where the superscript E indicates energy input–output matrices, the equivalent equation of Eq. (5.16) is

$$ {\text{X}}^{\text{E}} = \left( {{\text{I}} - {\text{A}}^{\text{E}} } \right)^{ - 1} {\text{F}}^{\text{E}} $$

(5.18)

We could then calculate the various alternative final energy demand scenarios, the corresponding new total output requirements for non-energy industry and energy supply industry and energy services output and their respective intermediate outputs. Some perspective on inter-fuel substitution could also be gained, if one were satisfied that prices would not significantly influence the substitution process and if one were satisfied that the assumption of constant input output relationships would be true in practice.

Source Based on Chap. 7, Macro-Demand Analysis, of Codoni et al. (1985). See also Miller and Blair (1985).