Modelling UK energy demand

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Derek Hodgson and Keith Miller

ABSTRACT

This chapter describes recent energy demand modelling by the Economics and Statistics Division of the Department of Trade and Industry (DTI) (formerly the Department of Energy), focusing on some of the ongoing research into the domestic sector's energy demand. Various sectoral long-term own-price energy and output elasticities are reported with particular emphasis on the domestic sector, reflecting the most recent research efforts. These are compared with previous estimates of elasticities and reasons for the differences are suggested. (Long-term cross-price elasticities are not reported here as the fuel splitting tool, the Science and Policy Research Unit's boiler model, is currently being updated.) The results show that the DTI long-term elasticities are broadly similar to those obtained by other researchers. Some differences in the elasticity estimates are inevitable, however, as econometricians have access to different information sources. This is reflected in the different levels of disaggregation used in their final models. In this respect the DTI has good access to disaggregated data sources and consequently its models tend to be more disaggregated than those used by other researchers. Thus the DTI energy model is less likely to suffer from aggregation bias than most other UK energy models.

INTRODUCTION

This chapter begins by describing the recent history of the DTI energy model and then proceeds to discuss the current version of the model in terms of the estimation techniques used, the data and the results. The estimated output and price elasticities and their properties are discussed in Sections 7.4 and 7.5. Finally, in Section 7.6, our recent research efforts into domestic sector energy demand are described, with the demand being divided into energy demand for heating, cooking and appliances. The energy demand model structure is presented in diagrammatic form in Appendix 7A and an overview of the model is given in Appendix 7B.

7.1 HISTORY

Econometric models of energy demand and supply were originally introduced by the Department of Energy (now part of the DTI) for energy planning reasons. The Sizewell B Inquiry in 1983 was the last occasion on which the model was explicitly used to provide published energy projections for this purpose. Following the Sizewell B Inquiry the role of long-term energy modelling diminished, in line with the market-based approach adopted by the government (see Price (1991) for the background to official energy modelling).

However, by the late 1980s a need to produce estimates of future levels of pollutants led to a resurgence of interest in energy modelling and to substantial redevelopment of the Department's model. The results from this model were subsequently published in October 1989 as Energy Paper 58. During 1991 further revisions to the model used in Energy Paper 58 were made and the results from this revised model were published as Energy Paper 59. Based on the 1991 version of the model the then Secretary of State for Energy, in a Parliamentary Question of 6 December 1991, gave the following range of CO2 emissions (in million tonnes of carbon):

1990 2000 2005 2020

160 156-178 166-200 188-284

It should be noted, however, that the model described below (1992 version) includes a new set of domestic sector equations which were estimated during 1992. This did not alter significantly the CO2 ranges reported above.

The last paper describing the government's energy model was published in Helm et al. (1989). That paper essentially described the energy model used for the Sizewell B Inquiry. The equations used in the model were simple partial adjustment equations. Since those equations were estimated econometrics has improved significantly in terms of both modelling techniques and the software available to researchers. The latest version of the energy model takes advantage of these improvements and is based on a set of econometric equations that have been estimated in unrestricted error correction form, e.g.

Y is energy demand, X is a vector of exogenous variables such as prices, income and output, a is a coefficient and bt, c and d, are vectors of coefficients. The use of the unrestricted error correction model is preferred to the partial adjustment model since it has three advantages over the latter.

1 It allows for greater flexibility between short- and long-term price and output effects.

2 Energy demand can adjust at different speeds to changes in prices and output.

3 The historic data play a larger role in estimating the equation.

ESTIMATION TECHNIQUE

The unrestricted error correction functional form was applied to annual data derived from the Digest of United Kingdom Energy Statistics (DUKES). Since energy demand data are only available on a reliable basis from the early 1950s onwards it was decided not to use cointegration techniques (see Engle and Granger (1991) for a discussion of this technique) to estimate the equations as unit root tests typically require around a hundred observations. The above functional form encompasses the previous partial adjustment functional form and allows the data to play a larger role in the estimation process.

The energy demand data taken from DUKES were collected on the basis of the 1968 Standard Industrial Classification (SIC) until 1984 when it was transferred onto the 1980 SIC. Although the Department of Energy did its utmost to put these data on a consistent 1980 SIC basis, a dummy taking the value of 1 from 1984 onwards was inserted into each equation to allow for any inconsistencies in the SICs. A dummy was also used in the equations to allow for the miners' strike in the mid-1980s. Each equation was estimated by ordinary least squares using the econometric software package Microfit (Pesaran and Pesaran 1991). The diagnostics given in this package were used to derive the final equation for each sub-sector. Most of the equations were estimated over the period 1954-88.

ENERGY DEMAND DATA

Energy demand is divided into five sectors:

1 Transport

2 Other industry

3 Service

4 Domestic

5 Iron and steel

These sectors are further subdivided into more appropriate sub-sectors for estimation purposes. Thus the transport sector's energy demand is subdivided into gasoline, Derv and aviation fuel etc. The non-transport sectors are initially subdivided by type of final consumer. Having split the sectoral energy demands into the main categories of final consumers these demands are in turn divided between the principal fuel types. One obvious problem with this approach is that information at this level of disaggregation is often poor. In order to deal with this problem specific sectoral information has been taken from various Energy Efficiency Office (EEO) publications. In the domestic sector end use demands have been derived on the basis of data provided by the Building Research Establishment. Appendix A shows the current level of disaggregation used in the model.

Energy demand within the model is measured and estimated in terms of 'useful therms' rather than delivered therms. There are two reasons for using this numeraire of energy demand. First the switch away from coal to oil and more recently to gas exaggerates, when measured in delivered therms, the reduction in energy intensity since the war. This suggests that what we should be interested in estimating is the effective demand for energy or useful energy demand. Useful energy demand can be thought of as what the energy consumer actually requires once all the losses and inefficiencies have been deducted from the delivered amount of energy (usually measured in therms). Thus useful energy demand relates to the demand for energy services rather than energy demand itself. In order to compute useful energy demands each fuel was converted into therms, and then factors defined between 0 and 1 were applied to these data to produce useful therm data. Note that the factors used to convert from therms to useful therms vary both by fuel and sector.

The second reason for using useful therms rather than delivered therms as the energy numeraire is that when prices of fuels are being compared, for fuel substitution purposes, it is important that their prices are compared on the same basis as the energy consumer would compare them. In other words they must be compared on a useful therm basis. To a certain extent the differing efficiencies of fuels will be reflected in their thermal prices, which is why electricity and gas usually command a premium over coal and oil.

The long-term elasticities resulting from this estimation process are shown below in Section 7.2.1 It should be noted that industrial and service sector fossil fuel switching is largely determined by the Science Policy Research Unit's (SPRU) model. Using the SPRU model to determine the demand for fossil fuels in the industrial and service sectors is preferred to econometric cross-price elasticities for several reasons.

1 The SPRU model contains specific information about energy contracts such as the minimum quantities of energy that must be purchased, e.g. interruptible gas, information which econometric cross-price elasticity estimates ignore.

2 Over a range of prices one fuel is likely to dominate energy demand and so econometrically based cross-price elasticities are likely to be misleading.

3 The SPRU model incorporates information on when it is economic to replace fuel-specific capital equipment with capital equipment that uses a different fuel.

The above suggests that fuel switching models based on econometric cross-price elasticities could be misleading as the cross-price elasticities themselves may be unstable over time.

LONG-TERM ELASTICITIES 7.4.1

Long-term price elasticities

For a discussion of the elasticities given in Table 7.1 with respect to energy taxation and CO2 emissions see Hodgson (1992).

The own long-term price elasticities of the DTI's energy model can be compared with those produced by the Operational Research Executive of British Coal (BC) (see Gregory et al. 1991); these are shown in Table 7.2. A comparison of the industrial own-price elasticities shows the average to be identical for both models. The higher DTI oil and gas elasticities are offset by the somewhat higher BC coal and electricity elasticities.

The iron and steel electricity price elasticities differ considerably between the energy models. Whereas the DTI was unable to find any significant price effects, BC found a relatively large elasticity of -0.7. Two reasons are suggested for this difference. First, the BC work appears to use more aggregated data than that used for the DTI model, which specifically relates electricity consumption to arc steel production. Since electricity in this sector is almost wholly used for arc steel production it is possible that the BC work may not capture this relationship adequately. Second, the BC paper suggests that they have used levels type equations rather than the unrestricted error correction equations used by the DTI. It is possible that this difference in modelling technique may explain the rather high electricity elasticity obtained by BC. Interestingly both models estimate the coal elasticity to be -0.2. Since coal, in the form of coke, is the major fuel consumed in this sector this is an important result. Overall the DTI model has a larger average price elasticity than the BC model, -0.35 compared with -0.2.

When comparing elasticities between studies it is important to note that the industrial structure changes over time and so the inclusion or exclusion of a

Table 7.1 DTI energy model own long-term price elasticities

Sector Average Electricity Coal Oil Gas

Iron and steel -0.35 Negligible -0.2 -0.8

Sector

Average

Electricity

Coal

Oil

Gas

Heating

N/A

-0.54

-0.49

-0.45

-0.20

Cooking

N/A

-0.1

N/A

N/A

-0.1

Appliance

N/A

N/A

N/A

N/A

N/A

Average

Gasoline

Derv

Aviation fuel

Transport

-0.2

-0.3

-0.2

-0.1

Table 7.2 British Coal's own long-term price elasticities

Sector

Average

Electricity

Coal

Oil

Gas

Industry

0.6

-0.5

-1.0

-0.6

-1.3

Iron and steel

-0.2

-0.7

-0.2

-0.3

-0.3

Servicea

-0.35

-0.1

-0.3 and -1.1

-0.2

-1.5 and -0.4

Domestic

-0.1

-0.8

-0.3

-0.5

-0.6

Average

Gasoline

Derv

Aviation fuel

Transport

-0.1

N/A

N/A

N/A

Source: Gregory et al. 1991

Notes: aThe British Coal elasticity estimates divide the service sector into public administration and miscellaneous. The former is shown first in these tables. N/A, not available.

Source: Gregory et al. 1991

Notes: aThe British Coal elasticity estimates divide the service sector into public administration and miscellaneous. The former is shown first in these tables. N/A, not available.

time trend in the energy demand equation can have a crucial impact on the final estimated elasticities/ coefficients. In the service sector individual elasticities differ somewhat in both models, although the average price elasticities are virtually identical.

The DTI average transport sector long-term energy price elasticity is twice as large as that found in the BC study. Again this difference may be the result of different levels of aggregation and functional form. Dargay (see Hawdon 1992) using an irreversible model for road transport demand found a long-term price elasticity of -0.1 (although her 'maximum previous price' variable had a long-term elasticity of -1.5) and -0.4 using a reversible model. Since the DTI average elasticity falls between the two Dargay estimates there is some support for it; however, it should be remembered that Dargay's work excludes non-road transport demand.

Long-term output elasticities

Hawdon (1992), referring to work done by Beenstock and Dalziel, shows their industrial long-term output elasticity to be 1.1 and their energy price elasticity to be -0.29. Assuming industry refers to both the other industry and the iron and steel sectors, it can be seen from Table 7.3 that the DTI industrial long-term output elasticities are both less than 1.1. The average DTI industrial long-run price elasticity is somewhat higher than -0.29. Beenstock and Dalziel appear to have used log-linear equations and so the comments given for BC's use of this functional form also apply to this work. Since their equations are only estimated between 1953 and 1982 they do not capture the shake-out of manufacturing industry in the 1980s and the long-term impact of the 1979 hike in oil price. Thus the energy price elasticity of -0.29 given by Hawdon may be too low in absolute terms and the output elasticity too high. Lynk (again shown in Hawdon) for the period 1944-81 estimates the

Table 7.3 DTI energy model own long-term income-output elasticities

Sector

All fuels

Electricity

Coal

Oil

Gas

Industry

0.82

1.73

N/A

N/A

N/A

Iron and steel

1.0

1.0

1.0

1.0

1.0

Service3

0.6

2.7

N/A

N/A

N/A

Domesticb

0.2

0.3

-2.4

-0.2

0.3

Average

Gasoline

Derv

Aviation fuel

Transport

N/A

0.81

1.25

OECD GDP=

2.07

UK RPDY =i

0.31

Notes: aThis value is for space and water heating demand only. bSpace and water heating only.

RPDY, real personal disposable. income; N/A, not available.

Notes: aThis value is for space and water heating demand only. bSpace and water heating only.

RPDY, real personal disposable. income; N/A, not available.

long-term industrial output and price elasticities to be 0.44 and -0.69 respectively. The DTIs industrial price elasticities are broadly similar to Lynk's -0.69, although his output elasticity is around half of that found by the DTI.

Dargay, in her work referred to above, found the long-term road transport output elasticity to be either 0.7 or 1.49 depending on whether a reversible or irreversible model was used. Since the DTI's gasoline and Derv long-term output elasticities fall within these two estimates her work again tends to support the DTI elasticities. Dargay also uses unrestricted error correction mechanisms in her work so comparisons with the DTI's model are somewhat easier to make, as one does not need to make an allowance for different functional forms.

PROPERTIES OF ELASTICITIES

Since energy elasticities are often used to evaluate environmental policy measures such as carbon taxes it is important that policy-makers realize that elasticities are not constant over time. Recall the own-price elasticity formula:

dEPg

Consider the first ratio in this formula. It can be thought of as representing the possibilities for energy conservation. At low price levels the first ratio will be relatively large, suggesting that the possibilities for energy conservation are plentiful. However, as PE increases, due say to a carbon tax, the possibilities for energy conservation will decline as they are gradually taken up and so the first ratio will fall. Note, however, that the second ratio will be increasing and so the value of the elasticity is indeterminate.

Own energy price elasticities will also vary considerably depending on the market penetration of the particular fuel being considered. Suppose for instance that a fuel has a low level of market penetration so that the value E in the elasticity formula is relatively small. If the price of fuel E (i.e. PE) now falls, then assuming that the first ratio in the elasticity formula remains constant the elasticity will fall over time as E increases. In the context of UK energy demand an obvious example of this process at work is the introduction of natural gas to the industrial market in the late 1960s.

Essentially similar arguments to those made above for own energy price elasticities can also be made for energy cross-price elasticities. The point to come out of these examples is clear: estimates of elasticities are only valid for a short period of time as changes in market shares etc. will lead to variations in the value of the elasticities. This has obvious implications for those using elasticities in policy-related work.

One important factor which must be remembered when examining individual long-term output-income energy elasticities is that as the energy saturation level is approached this elasticity tends to zero. This is particularly important in the case of modelling work associated with projecting long-term CO2 emissions, as a log log functional form will result in energy demand being greatly overestimated. This overestimation of energy demand/CO2 will increase with time. In order to avoid putting explicit ceilings into the DTI energy model several of the equations have been estimated in linear log form, i.e.

which has the elasticity b/Y. Thus the income-output elasticity declines as income rises over time. This functional form has the desirable property that successive equal increments in income-output have less and less impact on the growth in energy demand. Once a saturation level has been reached the impact of energy efficiency measures becomes somewhat clearer to perceive as energy consumption can only decline as the result of energy efficiency measures being introduced. Much of the non-econometric modelling of CO2 emissions is based around saturation levels being reached in the near future, e.g. see the Building Research Establishment's work.

Saturation levels are particularly important for bottom-up models. Bottom-up models are essentially databases of the existing stock of capital equipment. They also usually take account of economic investment in new equipment and the scrapping of existing capital equipment. These databases can be used to determine the level of projected energy consumption by assuming that energy consumers use the most cost-efficient technology to meet their useful energy demand requirements. Although an important approach, the bottom-up approach does suffer from the drawback that it can only capture relative price effects, i.e. switching between fuels, and not absolute price effects. Furthermore at levels of energy consumption below the saturation level bottom- up models have difficulty in capturing the impact of increases in income-output on energy demand. In recognition of the importance of bottom up effects on energy consumption the DTI energy model incorporates a number of capital stock features which help to limit the future growth in energy consumption. Probably the most important of these is the SPRU model. As Appendix 7A shows, the SPRU model is used to determine the boiler fuel shares in the industrial and service sectors.

DOMESTIC SECTOR MODELLING 7.6.1

Domestic sector energy demand for heating purposes

Another sector where stock effects and saturation levels are important is in the domestic sector. In order to capture the impact of saturation effects logit models are used to project the proportion of households owning central heating (CH). Initially a logit model is used to project the percentage of households owning central heating, with a saturation level of 100 per cent. This percentage is then divided amongst households with different types of CH; gas, electricity, oil and solid fuel. Once again this is achieved by using logit models. Relative price effects play an important part in determining which fuels are used for CH purposes in the logit equations. Since a large portion of households will never have access to gas, because of the high connection charges in remote areas, the percentage of households who can have access to gas is limited to 90 per cent of all households.

Having estimated the percentage of households owning each type of CH the next step is to use this information to estimate energy consumption. This is done by estimating space and water heating equations for each fuel type, with the above CH stock variables included in these equations as regressors. It should be noted that CH energy demand is only one part (admittedly the major part) of total domestic sector space and water heating demand. Thus additional regressors are also added to the space and water heating energy demand equations in order to capture the impact of non-CH stock factors such as portable gas heaters. Some of the space and water heating equations have been estimated in linear log form. Thus any remaining saturation effects not captured by the CH stock logit equations are dealt with in the demand equations.

Recent DTI research suggests the domestic sector space and water heating elasticities given in Table 7.4. Currently we are evaluating SURE and multinomial estimation techniques to see if they can significantly improve upon these preliminary results.

The domestic sector also uses energy for two other reasons:

Table 7.4 Domestic sector heating price elasticities

Energy demands Gas

Oil

Coal

Electricity

P

Gas

-0.2

+0.55

+0.30

+0.54

r i

Oil

+0.1

-0.45

Negligible

Negligible

c e

Coal

Negligible

Negligible

-0.49

Negligible

s

Electricity

Negligible

+1.36

+0.52

2 Appliances_

1 Cooking

2 Appliances_

Domestic energy demand for cooking purposes

Energy consumption for cooking purposes is dominated by gas and electricity. Some oil and solid fuel is also used for cooking purposes but the amounts involved are so small that it makes more sense to enter them as exogenous assumptions rather than as separate equations. The split between gas and electricity is approximately 55:45. Although a small number of cookers are dual fired most are not and so it is important to model the stock of cookers prior to estimating individual fuel demands. In order to do this we begin by modelling the percentage of households with gas cookers, again applying the above 90 per cent ceiling. Using the assumption that each household owns one cooker it is then possible to derive the total fuel demands by multiplying the number of households using a given fuel for cooking purposes by the average annual fuel consumption per cooker for that fuel.

Total gas cooker fuel demand is obtained by assuming that a typical gas cooker consumes some 50 therms a year. This estimate of average per annum gas cooker consumption can be adjusted during the projection period in line with likely improvements in gas cooker efficiency.

Average electric cooker consumption per annum is estimated via an equation that has a lower limit of 370 kW h. Thus average annual electric cooker consumption cannot fall below this limit during the projection period. This lower limit was obtained from Energy Efficiency Series 13 (DEN 1990b).

Using the above domestic cooker equations the long-term price elasticities given in Table 7.5 were obtained. Note that we were unable to find a significant real personal disposable income term in any of the equations. This lack of significance can be attributed to the fact that total cooker energy demand long ago saturated and so the only remaining item of interest is which fuels meet this saturated level of energy demand. Saturation effects aside, one would expect that increasing real incomes would tend to reduce cooker

Table 7.5 Domestic sector cooking price elasticities

Gas Electric

demand since households will increasingly eat out rather than eat at home. Thus domestic sector cooker consumption will to a certain extent be substituted by additional service sector cooker consumption, e.g. restaurants and cafeterias.

Domestic appliances energy demand

The amount of energy consumption attributable to appliances is a particularly difficult area to model as the econometrician is trying to model the energy consumption of appliances that may not even exist yet. An example will perhaps illustrate the problems involved in estimating this type of energy consumption. Suppose in 1950 we were trying to prepare forecasts of appliance energy consumption. We would have found it difficult (if not impossible) to forecast the energy consumption of appliances not yet invented, such as video recorders and personal computers. Furthermore, although many new domestic appliances would appear to have great energy-saving potential, this is not always the case. A case in point is microwaves which are thought to be energy efficient. What is often missed, however, is the additional uses to which microwaves can be put, as they can be used to defrost food as well as cook it. When this type of additional energy consumption is taken into account the savings obtainable from new appliances is often very much smaller than originally thought. Thus the sudden introduction of a new appliance does not always invalidate projections of energy demand made prior to that new appliance being introduced.

It is precisely these considerations that today' s energy econometricians are required to incorporate into their models if CO2 emissions are to be meaningfully projected beyond the year 2000. In fact, both econometric and bottom-up models are deficient in this area. The approach adopted up to now by the DTI is similar to that adopted for space and water heating demand. Initially the stock of appliances is modelled by relating it to income etc. This stock estimate is then entered into an appliance energy demand equation, along with other variables, and the estimate of future appliance energy demand is arrived at by projecting this equation into the future. Because of the problems outlined above domestic appliance energy consumption is the most difficult part of total domestic energy consumption to model. Fortunately, however, appliance energy consumption is only some 14 per cent of total domestic energy consumption and so relatively

Energy demands

Figure 7.1 Total domestic sector appliance energy demand Source: Building Research Establishment large errors in this component of domestic energy consumption do not alter the total greatly. Appliance energy consumption has traditionally been the fastest growing component of domestic energy consumption; since 1986, however, it has shown some signs of saturating (Figure 7.1). We are currently investigating the data shown in the above chart to discover if appliance energy demand has indeed saturated or if there has been some misallocation of total domestic energy demand, resulting in too little demand in this subsector. Once this analysis has been completed it is likely that at least some of the estimated elasticities will alter.

Certainly the energy appliance demand data post-1986 sits uneasily with the growth in real personal incomes over this period, which suggests that appliance demand has not saturated. The latter is also supported by the relatively high electricity-income elasticity shown in Table 7.3 for domestic space and water heating energy demand. Since electricity demand for cooking purposes is relatively well defined, any missing appliance demand must appear in space and water heating electricity demand.

CONCLUSIONS

This chapter has discussed some of the improvements in econometric techniques that have recently been incorporated into the DTI energy model. Several of the equations used in the model are of the error correction model type and the problems encountered in estimating these equations have been described. Future developments to the model will include the introduction of a new model of industrial and service sector boiler heat, incorporating combined heat and power technologies.

NOTE

The work described in this chapter is based on work in progress and is not therefore a definitive guide to the DTI energy model; interested researchers should contact Keith Miller directly for details of more recent modelling work.

1 Cross-price elasticities have been omitted because the DTI energy model is currently being updated by the inclusion of a revised SPUR boiler model. The boiler model's function is to split the overall demand for heat in

APPENDIX 7A ENERGY DEMAND MODEL STRUCTURE

the industrial sector into demands for individual fossil fuels. It is therefore a major determinant of cross-price elasticities. It is hoped to report the results of this work in 1994.

APPENDIX 7B

DEPARTMENT OF TRADE AND INDUSTRY ENERGY MODEL OVERVIEW

Precipitation Soil Microb Feedback

Part II

Energy, the economy and greenhouse gas abatement

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