Ln a a2[ln Y a6In Vl

where ln denotes natural logarithm, (-1) denotes a lag of one year, a1, a2, a3, a4, a5, a6 are parameters, E is total delivered energy in million therms, Y is a measure of economic activity, T is the deviation from trend temperature, RPE is the price of energy relative to that of all goods and services, time is a time trend and e is an error term.

Equations of this form were estimated as non-linear equations (note that parameter a6 appears three times) with the parameter a4 representing the price elasticity and a6 the lag on the price effect, both being imposed at 'consensus' values using the estimation packages MREG (Peterson 1992) and Microfit (Pesaran and Pesaran 1991). A full discussion of the logic behind the equations and their properties is given by the UK DEn (1989a:77-91); the specification allows for lagged effects of relative prices but not of any other variable. The reasoning behind this lagged response is that the history of energy prices up to the previous year is embodied in the stock of energy-using equipment used in the current year; it is this stock, combined with the economic activity and the average temperature in the current year which determines energy demand.

Table 9.1 shows the estimated or imposed long-term activity and price elasticities for each sector. The low price elasticities agree with those from other studies adopting a single-equation, partial framework (Vernon and Wigley 1982; Westoby and Pearce 1984; Beenstock and Dalziel 1986; Hunt and Manning 1989; Lynk 1989) including the estimates of the DEn. Table 9.2 gives some conventional test statistics, although it is recognized that some of these may not be valid owing to the presence of the lagged dependent variable in the regressions.

These equations have been introduced into MDM to provide a starting point for further analysis, but it should be recognized that there are problems with the specification, some of which are covered in the literature. Indeed the DEn model has been developed in recent years to address one of these, namely the crudeness of estimating a constant lagged response together with time trends to represent improvements in energy efficiency. This has been accomplished by including the influence of the capital stock of fuel-burning appliances (Hodgson 1992) in energy demand. This is certainly an important

Table 9.1 Parameters for the aggregate energy equations—base specification 1970-90

Intercept Economic activity Short-term price effect Air temperature Time trend (%p.a.) Lag

Table 9.1 Parameters for the aggregate energy equations—base specification 1970-90

Intercept Economic activity Short-term price effect Air temperature Time trend (%p.a.) Lag

Iron and steel

0.015

1.006

-0.07

0.0

-0.8

0.8

Mineral products

0.900

0.629

-0.12

-0.06

-0.3

0.7

Chemicals

0.399

0.617

-0.065

0.0

-0.5

0.9

Other industry

0.362

0.638

-0.065

-0.05

-0.2

0.9

Rail transport

0.725

0.423

-0.040

0.0

0.0

0.8

Road transport

3.169

0.323

-0.120

0.0

0.8

0.6

Water transport

1.249

0.034

-0.020

0.0

0.0

0.8

Air transport

1.770

-0.02

-0.040

0.0

0.7

0.8

Domestic final use

2.438

0.390

-0.120

-0.07

0.0

0.6

Other final use

1.042

0.396

-0.060

-0.04

0.0

0.8

Table 9.2 Test statistics for the aggregate energy equations—base specification 1970-90 t ratio

Intercept

Economic activity

Air temperature

Time trend

DW

SE(%)

Iron and steel

0.08

10.04

3.85

0.974

1.99

5.2

Mineral products

2.42

4.65

3.33

2.09

0.966

2.56

3.4

Chemicals

2.55

4.05

3.68

0.874

2.55

3.6

Other industry

1.95

4.19

3.32

1.58

0.975

1.87

2.5

Rail transport

2.00

1.79

0.848

1.78

4.6

Road transport

8.71

3.27

5.83

0.990

2.44

1.6

Water transport

2.66

0.13

0.096

1.39

8.6

Air transport

4.72

0.09

4.01

0.941

1.69

4.2

Domestic final use

7.49

5.89

6.67

0.891

2.25

2.0

Other final use

2.88

2.73

2.96

0.603

1.85

2.7

Table 9.3 Price elasticities for various lags in aggregate energy equations—base specifications 1970-90

Column

1

2

3

4

5

6

7

8

9

Lag

Unrestricted

Imposed

0

0.2

0.4

0.6

0.8

0.9

0.95

Iron and steel

0.108

-0.350

0.110

0.125

0.142

0.155

0.170

0.195

0.248

Mineral products

0.035

-0.400

-0.035

-0.012

0.009

0.000

-0.028

-0.033

-0.021

Chemicals

0.087

-0.650

0.316

0.266

0.191

0.065

-0.268

-0.919

-2.220

Other industry

0.021

-0.650

0.169

0.147

0.097

-0.027

-0.369

-0.955

-2.078

Rail transport

0.092

-0.200

-0.270

-0.275

-0.279

-0.275

-0.249

-0.198

-0.099

Road transport

-0.134

-0.300

-0.119

-0.163

-0.237

-0.384

-0.747

-1.366

-2.577

Water transport

0.096

-0.100

0.083

0.093

0.112

0.158

0.310

0.580

1.045

Air transport

-0.169

-0.200

-0.167

-0.184

-0.219

-0.307

-0.573

-1.066

-2.022

Domestic final use

-0.334

-0.300

-0.071

-0.091

-0.124

-0.186

-0.339

-0.589

-1.071

Other final use

-0.300

-0.300

-0.047

-0.051

-0.057

-0.071

-0.099

-0.109

-0.052

Table 9.4R2 for various lags in aggregate energy equations—base specifications 1970-90

Column

1

2

3

4

5

6

7

8

9

Lag

Unrestricted

Imposed

0

0.2

0.4

0.6

0.8

0.9

0.95

Iron and steel

0.99

0.98

0.987

0.987

0.987

0.985

0.982

0.979

0.978

Mineral products

0.98

0.97

0.982

0.983

0.982

0.979

0.974

0.970

0.969

Chemicals

0.87

0.89

0.704

0.785

0.846

0.884

0.895

0.890

0.885

Other industry

0.97

0.98

0.941

0.954

0.964

0.972

0.977

0.979

0.980

Rail transport

0.90

0.86

0.659

0.741

0.806

0.852

0.856

0.832

0.813

Road transport

0.99

0.99

0.993

0.994

0.993

0.991

0.988

0.985

0.984

Water transport

0.65

0.14

0.323

0.423

0.455

0.417

0.301

0.208

0.155

Air transport

0.99

0.95

0.982

0.983

0.980

0.975

0.963

0.953

0.946

Domestic final use

0.96

0.90

0.924

0.925

0.919

0.906

0.883

0.867

0.858

Other final use

0.81

0.64

0.718

0.742

0.741

0.714

0.664

0.632

0.613

development for long-term analysis, but it is much more complex and demanding of data than the original DEn specification.

Another improvement would be the use of the cointegration procedure in estimating responses. There is a problem in the estimation of the DEn equations of identifying the price elasticity when the lagged dependent variable is introduced. This is illustrated by Table 9.3 which shows the unrestricted estimates of the maximum long-term price elasticities when different lags (a6 in (9.1)) are imposed. The first column gives the elasticities calculated from the unrestricted equations; the second column shows the elasticities imposed to obtain the results reported in Table 9.1; column 3 shows the elasticities with zero lag; and columns 4-9 show the elasticities for lags imposed at 0.2, 0.4, 0.6, 0.8, 0.9 and 0.95 respectively. Clearly, for most users, the longer the lag, the more negative the price elasticity. Table 9.4 shows that goodness of fit as measured by £2 is not much help and that a range of long-term price elasticities is consistent with high values of R2 in most sectors. The imposed elasticities were found by inspecting the properties of the equations to ensure a reasonable goodness of fit, estimated effects of activity variables and consistency with earlier estimates.

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