Endogenous technological progress in fossil fuel demand

Laurence Boone, Stephen Hall, David Kemball-Cook and Clare Smith

ABSTRACT

This chapter reports on work to develop energy demand sectors for the Global Econometric Model (GEM), maintained jointly by the London Business School and the National Institute for Economic and Social Research. We have derived data for the total fossil fuel energy consumption, energy prices, GDP and general prices for the main OECD countries (Belgium, Canada, France, Germany, the Netherlands, Italy, Japan, the UK and the United States). We then apply multivariate cointegration tests to test for the presence of cointegration between this set of variables. We find remarkably similar relationships in terms of price elasticities and in terms of trend increases in energy efficiency across all the countries. We then go on to estimate full dynamic models for all the countries. Finally in this chapter we consider the relationship between long-term growth, increasing energy efficiency and energy prices and calculate some illustrative trade-offs which leave CO2 emissions unchanged.

INTRODUCTION

In recent years concern has increased about the build-up of greenhouse gases in the atmosphere, and in particular emissions of CO2 arising from the burning of fossil fuels. Much analysis has been devoted to assessing the economic cost of stabilizing or reducing CO2 emissions by means of economic instruments such as a special tax on fossil fuels weighted according to carbon content. In this chapter an econometric analysis of the determinants of fossil fuel demand in nine OECD countries is conducted. The chapter poses three questions.

1 What is the historical relationship between fossil fuel consumption, fossil fuel prices and GDP in each country?

2 What is the historical trend in this relationship?

3 If the historical patterns were maintained what would be the economic cost of limiting energy consumption assuming various scenarios for GDP growth?

This is the first part of work which will incorporate the resulting energy demand equations into the Global Econometric Model (GEM) maintained jointly by the National Institute and the London Business School. The focus of the study is on the G7 countries, as well as Belgium and the Netherlands. The overall objectives of the research are to model the international macroeconomic consequences of measures to reduce emissions of CO2, hence shedding light on the benefits and costs of an abatement strategy and the impact of such a policy, not only within a particular country but also throughout the world, while taking into account the effect on trade and competitiveness.

This chapter attempts to build fossil fuel demand equations for nine OECD countries (Belgium, Canada, France, Germany, Italy, Japan, the Netherlands, the United Kingdom and the United States) as a function of gross domestic product (GDP), energy prices relative to the GDP deflator, and time, used as a proxy for technological innovation. First, the time-series properties of the variables, namely fossil fuel consumption, fossil fuel prices relative to the GDP deflator and GDP, are studied under the Johansen procedure. This leads to the construction of a cointegrating relationship which is close to the Cobb-Douglas representation that most previous studies have used. Several possible forms of the potentially cointegrating equation (vector autoregression (VAR) with or without a restricted or an unrestricted constant) are tested with the Johansen procedure in order to get the most accurate long-run relationship. This also allows us to estimate all the different possible relationships between fossil fuel consumption and relative prices, with a negative sign expected. The impact of technology is taken into account via a time trend, whose sign is also expected to be negative.

Recognizing that this treatment of the impact of technology is unsatisfactory, this set of estimates is regarded as only the first step towards a model which fully endogenizes the technological innovation factor so that ultimately it will be possible to assess the effects of policy on the rate of innovation. The following general model is proposed as a means of approaching the problem. First, begin by specifying a standard error correction model for energy demand:

where A is first difference, E is the log of fossil fuel energy demand, X is the log of price relative to the GDP deflator, T is time, a, fi, y are coefficients, p, q are maximum number of lags and u is an error term. If Tt was simply a deterministic trend this would be a conventional model. But if the trend is generated as follows the model is much richer.

where g is the rate of increase of the trend (possibly stochastic) and Z represents a vector of other explanatory variables. A restricted form of this model (when both the error terms are set to zero and the coefficients on Z are zero) gives the special case of a standard deterministic time trend. More generally, when this restriction is relaxed the time trend becomes stochastic and its determination can be modelled through the set of extra explanatory variables Z (e.g. structural changes, investment, expansion in non-fossil fuel consumption). This model, when it is fully implemented, will allow for the endogenous treatment of technological progress within an empirical econometric model.

Most of this chapter will be concerned with a preliminary analysis of the model with deterministic progress. The intention is to build a set of error correction models for each country. This leads to a reduced dynamic representation of fossil fuel consumption whose congruence is tested through a set of diagnostic tests. From the error correction models the long-run equilibrium equations can be investigated. A simulation of the movement in the relative price of fossil fuel required to maintain constant fuel consumption in the nine countries is then considered under different assumptions about GDP growth. This highlights differences across countries and the various costs that such a goal implies. There are two main conclusions. First, it is possible to derive broadly similar cointegrating relationships between fossil fuel consumption and prices for the nine countries studied. Second, according to these estimates, and assuming that there is no

policy intervention, the annual increases in fossil fuel prices necessary to stabilize consumption would vary considerably between countries. For instance, assuming growth in real GDP of 3 per cent per annum across the G9, required annual price rises would need to be as high as 17.8 per cent in the Netherlands but zero in France, Belgium and Japan. The chapter concludes with a brief initial exploration of the full stochastic technological progress model.

ENERGY DEMAND AND GROSS DOMESTIC PRODUCT IN GLOBAL

MODELS1

In energy economy models the link between energy use and macroeconomic variables is typically represented by the energy intensity coefficient, defined as energy consumption per unit of GDP In industrialized countries energy intensity has been in steady decline since the early 1970s or before, and the rate at which it is expected to continue to decline is critical to the predictions of models concerning greenhouse gas emissions. All models simulate the effect of policies to control greenhouse gas emissions by constructing a 'business-as usual' base-case scenario and then making departures from it by means of policy changes such as the introduction of carbon taxation. The main global models concerned with greenhouse gas emissions, reviewed by Boero et al. (1991), are summarized in Table 8.1.

The general equilibrium models and the optimal growth models make use of a constant elasticity of substitution (CES) aggregate production function of the form

where Y is final output, E is energy input and F represents other factor inputs. H, a and b are parameters. The elasticity of substitution a between energy and other factors is then given by a=1/(1-p), where 0<a<<,

In parameterizing the models to yield paths for energy intensity in the base-case scenario, Whalley and Wigle (1990), Nordhaus and Yohe (1983) and Nordhaus (1990a) assume neutrality in technological change (i.e. it affects all factors of production equally, with only the H parameter being affected). The other studies allow for energy-saving technological progress, as modelled by parameters a and b.

In almost all studies, GDP growth is treated exogenously in the base case. Various assumptions are then made about the base trend of energy intensity (i.e. the trend it would follow in the absence of policy changes). The standard assumption of declining energy intensity is attributed to a number of factors, and here it is important to separate the factors that are not connected with movements in energy prices from those which are. The non-price factors which affect energy use are summarized by Boero et al. (1991) as follows:

1 'exogenous' energy-saving technological progress (i.e. that which would happen anyway, regardless of price changes);

2 policy-induced technological change;

3 elimination of inefficient technologies or 'no regrets' changes (i.e. measures which are already cost effective in their own right, such as certain energy conservation measures);

4 changes in the composition of GDP

Boero et al. point out that almost all studies amalgamate the non-price factors into a single 'exogenous energy-efficiency' parameter, which applies equally in the base case and in the simulations. For instance, Manne and Richels (1990) use the term 'autonomous energy-efficiency improvements' (AEEI), modelled by a decline in the coefficient b. The problem with this approach, which Boero et al. point out, is that non-price factors do not apply equally in the base and the constrained cases because policies to constrain emissions will affect non-price factors 2 and 3 above. It would therefore be unwise to assume that policy-induced changes were equivalent in the base case and the simulations. Indeed, a strong case has been made for the merits

Table 8.1 Summary of features of global models

Study model

Period Type of model

Particular features

Regions

Edmonds and Reilly 1975-2050 Partial equilibrium

Nordhaus and Yohe (1983) 1973-2100 General equilibrium

1973-2025 Partial equilibrium

Edmonds and Barnes (1990a, b) revised IEA-ORAUa

Manne and Richels (1990) 1990-2100 Partial equilibrium energy ETA-MACRO model Optimal growth macro model

Nordhaus (1990a)

1990-2100 Optimal growth

Whalley and Wigle (1990) 1990-2030 Static computable general equilibrium

Burniaux et al. (1991 a, b) 1990-2025 Dynamic computable GREEN general equilibrium

Detailed energy sectors

Nested CES for energy inputs

Two strategies: global agreements and OECD unilateral

Solves sectoral and macro models interactively. CES production function with nested Cobb-Douglas Cobb-Douglas function. Interaction between emissions and growth

Simple energy sector with two types of energy. CES production functions Fully clearing markets. Mix of CES and Leontief production functions_

Nine regions Global Nine regions

Five regions

Six regions Six regions Seven regions

Note: aThe IEA-ORAU model has also been used by Reilly et al. (1987), (1988) and Waide (1992).

Mintzer (1987), Darmstadter and Edmonds

Table 8.2 Assumptions made by studies about energy elasticity and energy intensity

Study

Energy demand own-price elasticity

Energy intensity 'autonomous' rate of decline (% p. a.)

Edmonds and

OECD

1975

2050

Reilly (1983a, b)

Residential

-0.9

0.0

0.0

Commercial

-0.9

1.0

1.75

Industrial

-0.8

0.0

0.0

Transport

-0.7

Non-OECD

-0.8

1.0

1.3

Nordhaus and

Residential

-0.9

(Neutral technological progress)

Yohe (1983)

Productivity growth

Yohe (1983)

Productivity growth

Study Energy demand own-price Energy intensity 'autonomous' rate of decline (% p. a.)

elasticity

Study Energy demand own-price Energy intensity 'autonomous' rate of decline (% p. a.)

elasticity

Transport

-0.8

Industrial

-0.7

1975-2000

2000-25 2025 on

High

3.4

0.9 0.1

Middle

2.3

1.6 1.0

Low

1.2

2.3 1.9

Edmonds and

-0.7

1.0

Barnes (1990a)

Edmonds and

Low

-0.2

Low

0.0

Barnes (1990b)

Reference

-0.7

Reference

1.0

High

-1.2

High

2.0

Reilly et al.

-0.65 (mean)

1.0

(1987)

-0.70 (median)

Mintzer(1987)

High emissions

-1.1

High emissions

0.2

Base

-0.8

Base

0.8

Modest policy

-0.7

Modest policy

1.0

Slow build-up

-0.7

Slow build-up

1.5

Marine and Richels (1990)

1990-2050

Whalley and Wigle (1990)

inputs) Oil exporters

Bumiaux et al. (1990a, b) GREEN

Between -0.3 and -0.6 (substitution elasticities with capital, labour respectively)_

OECD

Rest of world 1.0

2050-2100

1990-2050

Whalley and Wigle (1990)

USA -0.4

USA

0.5

0.5

Other OECD -0.3

Other OECD

0.5

0.5

Rest of world -0.3

CIS/EE

0.25

0.5

China

1.0

0.5

Rest of world

0.0

0.5

Approximately -0.7 (substitution elasticity between energy and other

(Neutral technological progress) Productivity growth

inputs) Oil exporters of supply-side measures such as tightened energy standards and government spending on energy conservation to complement demand-side measures, such as a carbon tax to stabilize greenhouse gas emissions (Lazarus et al., 1992). In particular, the issue of revenue recycling or the use of carbon tax revenue to fund supply-side measures is not adequately addressed in this approach.

If 'exogenous' changes in energy intensity are assumed to apply equally in base cases and simulations, this may understate the potential for energy saving and overstate the costs of abatement. For example, Williams (1990) argues that the annual autonomous decline in energy intensity of 0.5 per cent to 1.0 per cent postulated by Manne and Richels (1989) is too low because it underestimates the potential for policy-induced conservation measures. A single parameter which has the same value in base and constrained cases is likely either to underestimate energy efficiency on one side or overestimate energy efficiency on the other. Table 8.2 (taken from Tables 4.3 and 4.4 of Boero et al.) lists the assumptions made by various studies about the 'autonomous' or 'base-case' path of energy intensity.

Hogan and Jorgenson (1990) criticize what they call the 'conventional wisdom' behind the assumption that, in the absence of relative price changes, energy intensity should decline. This is reflected in Table 8.2 by the various assumptions for autonomous decline in energy intensity. Hogan and Jorgenson report estimates of sectoral productivity trends for the United States and find that, contrary to conventional wisdom, most sectors are becoming more energy intensive rather than less so, i.e. there is an autonomous tendency for the share of energy relative to output to rise rather than decline. Such a trend, they say, has been swamped in the last twenty years by the effects of large changes in the relative price of energy, but in the long term it could prove to be significant. The implication of their findings, if true for countries like the United States, is that the studies are substantially underestimating the costs of greenhouse gas abatement. Indeed, they suggest that the studies may underestimate the cost of abatement by as much as half the total cost. This illustrates the importance of isolating the relative price effects on energy demand from those of autonomous technological change.

Table 8.2 also summarizes the assumptions made about the long-run own-price elasticity of demand for energy, or the elasticity of substitution between energy and other inputs as an approximation to the former when the energy share of GDP is small. Most studies make assumptions that the elasticity is less than unity but quite high nevertheless, with most assuming that it is greater than 0.5.

CONSTRUCTION OF CONSUMPTION AND PRICE VARIABLES

Consumption data

Since the present study is concerned with emissions of CO2, and the carbon content of different fuels varies, consumption of different fossil fuels is the focus rather than aggregate energy. The UN Energy Database (United Nations 1992) for the period 1950-89 (annual data) was used to define the consumption of coal, gas and oil2 for each of the nine main countries of the GEM, namely the G9.3

Consumption of coal has decreased over the past forty years, but much more slowly since the first oil crisis. While consumption in the United Kingdom, Germany and France is still steadily diminishing, consumption in Japan and the United States has risen slightly over the period 1950-90. The United States is the biggest consumer of the G9, consuming around three times the level in the United Kingdom, which has been the second highest consumer since 1976. Since 1983, Japan seems to have reached British levels of coal consumption. Consumption in Belgium, Italy, the Netherlands and Canada is far below France, which is itself a relatively small consumer with about a third of British levels over the past fifteen years.

Consumption of petroleum products increased dramatically until the first oil price shock in 1973, and remained remarkably stable at very high levels over the following six years. However, the second oil crisis in 1979 led to a fall in consumption in all G9 countries. Thus, in 1982 the aggregate level of consumption was

Figure 8.1 Consumption of petroleum products (log of t.o.e.) for the United States, United Kingdom and Germany nearly half the 1979 level. And finally, since 1987 an increasing trend in consumption for the G9 as a whole can be discerned. Japan is the greatest consumer of petroleum after the United States, consuming more than twice the level of Germany, the United Kingdom or France (all which are roughly the same). In all nine countries except the United States, the path followed by consumption is almost the same, characterized by two dips corresponding to the two oil shocks, followed by a slight upward trend in the late 1980s. It is only in the United States that consumption of petroleum products had recovered to pre-1973 levels by 1990. This is illustrated in Figures 8.1 and 8.2 for the United States, Japan, Germany, the United Kingdom and France.

Natural gas consumption in all countries shows the same features—a constant path until 1968, then a dramatic increase to 1979. Since the second oil price shock, consumption of natural gas has tended to stay at 1979 levels. The United States consumes much more natural gas than the rest of the G9. The United Kingdom is the second largest consumer, considerably above the rest of the G9, and exhibits the most dramatic rising trend. However, it is still significantly behind the United States. Germany is the smallest consumer, with the path of consumption remaining unchanged between 1950 and 1990.

Figure 8.1 Consumption of petroleum products (log of t.o.e.) for the United States, United Kingdom and Germany nearly half the 1979 level. And finally, since 1987 an increasing trend in consumption for the G9 as a whole can be discerned. Japan is the greatest consumer of petroleum after the United States, consuming more than twice the level of Germany, the United Kingdom or France (all which are roughly the same). In all nine countries except the United States, the path followed by consumption is almost the same, characterized by two dips corresponding to the two oil shocks, followed by a slight upward trend in the late 1980s. It is only in the United States that consumption of petroleum products had recovered to pre-1973 levels by 1990. This is illustrated in Figures 8.1 and 8.2 for the United States, Japan, Germany, the United Kingdom and France.

Natural gas consumption in all countries shows the same features—a constant path until 1968, then a dramatic increase to 1979. Since the second oil price shock, consumption of natural gas has tended to stay at 1979 levels. The United States consumes much more natural gas than the rest of the G9. The United Kingdom is the second largest consumer, considerably above the rest of the G9, and exhibits the most dramatic rising trend. However, it is still significantly behind the United States. Germany is the smallest consumer, with the path of consumption remaining unchanged between 1950 and 1990.

8.2.2 Price data

Data on both prices and taxes were obtained from the International Energy Agency (IEA 1991a) for the period 1978-90 (annual data). Oil and natural gas prices followed the same path over the whole period. Roughly speaking, they rose dramatically after the second oil price shock in 1979 until the mid to early 1980s, after which they decreased for about five years before a new increasing trend can be discerned. Coal prices remained constant between 1978 and 1991 and were generally lower than petroleum prices over the whole period. However, in France coal becomes the most expensive energy commodity after the two oil price shocks.

Figure 8.2 Consumption of petroleum products (log of t.o.e.) for France, Japan and the United Kingdom

Oil had the highest tax, while taxes on coal and gas were at roughly the same lower level. In nearly all the countries, oil taxes rose steadily between 1978 and 1991. In Belgium, there was a short break in this increasing path between 1987 and 1989. In the United States, the rising trend started only in 1983. Prices before and after tax of oil for the United States and France are illustrated in Figures 8.3 and 8.4.

Data for the average (after-tax) price of fossil fuel were obtained by weighting by consumption the prices of oil, coal and gas.4 This average price of fossil fuels relative to the price deflator of GDP exhibits the same features for the whole G9—a dramatic increase from 1979 to the beginning of 1982, then the relative price stays at this very high level until the end of 1985 when the relative price decreases steadily.

Figure 8.2 Consumption of petroleum products (log of t.o.e.) for France, Japan and the United Kingdom

Oil had the highest tax, while taxes on coal and gas were at roughly the same lower level. In nearly all the countries, oil taxes rose steadily between 1978 and 1991. In Belgium, there was a short break in this increasing path between 1987 and 1989. In the United States, the rising trend started only in 1983. Prices before and after tax of oil for the United States and France are illustrated in Figures 8.3 and 8.4.

Data for the average (after-tax) price of fossil fuel were obtained by weighting by consumption the prices of oil, coal and gas.4 This average price of fossil fuels relative to the price deflator of GDP exhibits the same features for the whole G9—a dramatic increase from 1979 to the beginning of 1982, then the relative price stays at this very high level until the end of 1985 when the relative price decreases steadily.

COINTEGRATION ANALYSIS

The seminal paper in the development of cointegration analysis was that of Engle and Granger (1987), who developed the concept of cointegration under the assumption that the cointegrating vector was unique and who proposed a range of tests for assessing whether a set of variables cointegrate, as well as discussing the estimation of a cointegrating vector of parameters. An early example of this methodology may be found in Hall (1986). Johansen (1988) proposed a more general framework for considering the possibility of multiple cointegrating vectors and this framework also allows questions of causality and general hypothesis tests to be carried out in a more satisfactory way. This is described in Hall (1989) and a more detailed textbook account may be found in Cuthbertson et al. (1992).

Johansen (1988) sets his analysis within the following very general framework. First, define a vector autoregressive (VAR) model of a set of variables A'as where Xt is a vector of N variables of interest, ni are N*N coefficient matrices, k is the maximum lag length and et is a vector of error terms. This is simply an unrestricted dynamic system for the set of variables X.

Figure 8.3 Price and tax of petroleum products in the United States

Much of the power of this approach can be attributed to the fact that a complete system wherein all the variables have equal status is being considered. There are no exogenous and endogenous variables and so assumptions about the exogeneity of some of the variables do not need to be incorporated into the model right from the beginning, as often happens with more traditional modelling methods. This system may be expressed in vector error correction form (VECM) as

where r= [(/ +jr,), (/ + JT, + JI2) f/-H JTt + ... +

and I is the identity matrix. Non-stationarity of X implies that n will have deficient rank. If there is no cointegration within the system n will be a matrix with rank zero. In general the rank of this matrix will be equal to the number r of distinct cointegrating vectors in the system. The heart of the Johansen procedure is to decompose 77 into two matrices a and ft, both of which are X'r, such that n = afl (8.5)

The rows of ft may be defined as the r distinct cointegrating vectors and the rows of a show how these cointegrating vectors are incorporated into each equation in the system. Johansen then gives a maximum likelihood estimation technique for both a and ft, based upon canonical correlation, and he outlines a set of suitable tests which allow examination of hypotheses about the matrices and the number of cointegrating vectors which exist. The estimation is based on the solution to a generalized eigenvalue problem where the eigenvectors are shown to be the parameters of the cointegrating vector and the eigenvalues are the basis for the testing procedure. By testing ft, restrictions such as parameter constraints on the long-run properties of

Price before tax Tax

Figure 8.4 Price and tax of petroleum products in France

Price before tax Tax

Figure 8.4 Price and tax of petroleum products in France the data or price homogeneity may be tested. By testing a, the manner in which these long-run relationships affect the variables in the system may be tested.

In the empirical work presented below, the dependent variable is the relative share of fossil fuel consumption to GDP for each country, where fossil fuel consumption is the total of oil, natural gas and coal consumption for that country. The explanatory variables are the average price of fossil fuels relative to GNP (or GDP), where the former is the average of prices after tax of oil, gas and coal weighted by consumption. It is to be expected that total fossil fuel consumption is negatively associated with relative average price. A time trend is included as a proxy for technological progress, leading to a simple equation of proportional fossil fuel demand as a function of price and technological innovation.

Time-series properties of the data

For the nine countries, the analysis of the univariate time-series properties of GDP, fossil fuel consumption and relative price is the first step to a cointegrating regression. If successful this should lead to an error correction representation. Each variable was subjected to tests for the presence of a unit root, with the tests being applied to the variables in levels as well as in first and second differences. The augmented Dickey-Fuller (ADF) and the Phillips tests appeared to give results most consistent with each other and with intuition, and so results from these tests are reported.

At each stage the null hypothesis is the presence of a unit root in the variable (as differenced). A sequential testing procedure is undertaken until the null hypothesis is rejected. Thus, failure to reject the null hypothesis on the level of the variable means that the variable is at least integrated of order 1; failure at the next stage implies integration of at least order 2, and so on. A summary of the results is shown in Table 8.3.

For the nine countries results generally indicate fossil fuel consumption to be integrated of order 2 (I(2)), i.e. the second difference is stationary but the first difference is non-stationary. The log of GDP/GNP is generally either I(2) or on the border between I(1) and I(2). One apparent exception is the case of Belgian GDP, where the results indicate I(0) but a glance at the data shows the data to be clearly non-stationary. The relative price of fossil fuels is either I(2) or close to the frontier between I(1) and I(2). Hereafter, the simplifying assumption that these data series are I(2) is made. First and second differences of relative price for Germany and Italy are shown in Figures 8.5 and 8.6.

Cointegrating properties of the data

If in the long run two (or more) macroeconomic time series move together, even though they are trended, the difference between them will remain constant. This relationship may characterize a long-run equilibrium. The Johansen procedure, outlined above, provides a maximum likelihood way of estimating these relationships. A number of options are available within the Johansen procedure; in particular the length of the VAR must be chosen and the treatment of the constant within the model will affect the distribution of the test statistics. In the first instance a very general VAR specification was tested. Since the data are quarterly this involved four lags. Differences in the treatment of the constant may be summarized as follows:

1 without a constant;

Table 8.3 Summary of stationarity properties for each variable by country

Level First difference Second difference

Level First difference Second difference

Table 8.3 Summary of stationarity properties for each variable by country

ADF

Phillips

ADF

Phillips

ADF

Phillips

Belgium (bg)

bgcl

-2.87

-1.44

-0.96

-1.92

-4.09

-6.84

I(2)

bgrpl

-4.01

-3.60

-1.93

-2.66

-4.55

-6.72

I(2)

bgyl

-1.21

-0.54

-1.67

-2.26

-3.69

-8.60

I(2)

Canada (cn)

cncl

-3.03

-1.03

-2.56

-1.99

-1.73

-6.82

I(2/3)

cnyl

-0.14

-0.04

-2.18

-5.70

-3.92

-16.2

I(1/2)

cnrpl

-2.32

-1.67

-1.91

-3.51

-3.56

-9.90

I(1/2)

France (fr)

frcl

-3.35

-1.25

1.44

-1.93

-2.93

-6.80

I(2)

fryl

1.41

1.27

-2.63

-7.80

-3.77

-20.2

I(1/2)

frrpl

-0.48

-0.12

-1.68

-6.44

-4.12

-22.3

I(2)

Germany (ge)

gecl

-2.80

-0.98

-2.19

-2.36

-2.16

-6.80

I(2/3)

geyl

-2.13

-0.66

-2.38

-8.86

-3.79

-22.3

I(1/2)

gerpl

-0.30

0.41

-1.73

-5.11

-3.08

-16.0

I(1/2)

Italy (it)

itcl

-0.96

-0.94

-1.78

-2.70

-4.02

-6.84

I(2)

Level

First difference

Second difference

ADF

Phillips

ADF

Phillips

ADF

Phillips

ityl

-0.09

-0.42

-2.80

-5.72

-4.48

-15.1

I(1/2)

itrpl

0.40

-0.43

-2.19

-6.22

-5.42

-11.9

I(1/2)

Japan (jp)

jpcl

-0.21

-0.18

-1.94

-2.58

-3.68

-6.87

I(2)

jpy!

2.23

1.17

-2.52

-7.87

-4.34

-21.2

I(1/2)

jprpl

-0.62

-0.47

-2.50

-6.03

-4.67

-17.6

I(1/2)

Netherlands

(nl)

nlcl

-1.60

-1.38

-1.53

-2.61

-4.33

-6.89

I(2)

nlyl

1.38

1.65

-1.82

-1.48

-1.99

-6.44

I(2/3)

nlrpl

-0.67

-1.15

-0.85

-0.96

-2.30

-3.54

I(2/3)

United Kingdom (uk)

ukcl

-4.72

-1.67

-2.19

-2.89

-4.77

-6.80

I(2)

ukyl

2.16

1.74

1.29

-8.73

-3.14

-23.4

I(1/2)

ukrpl

-1.77

-1.22

-1.59

-2.14

-3.00

-7.65

I(2/3)

United States (us)

uscl

-2.13

-0.99

-2.21

-2.15

-2.67

-6.80

I(2/3)

usyl

0.13

0.44

-2.69

-5.13

-4.00

-12.9

I(1/2)

usrpl

-0.53

-0.38

-2.20

-4.69

-3.80

-15.5

I(1/2)

Notes: cl, log of consumption of fossil fuels; yl, log of GDP; rpl, log of price of fossil fuels relative to price deflator of GDP.

The critical values at the 5 per cent and 1 per cent levels are -2.8 and -3.4 respectively. Statistics in italics exceed the 1 per cent levels.

The final column indicates the conclusion, e.g. 'I(1/2)' indicates that the statistics are not unanimous, with one indicating I(1) and the other I(2).

Notes: cl, log of consumption of fossil fuels; yl, log of GDP; rpl, log of price of fossil fuels relative to price deflator of GDP.

The critical values at the 5 per cent and 1 per cent levels are -2.8 and -3.4 respectively. Statistics in italics exceed the 1 per cent levels.

The final column indicates the conclusion, e.g. 'I(1/2)' indicates that the statistics are not unanimous, with one indicating I(1) and the other I(2).

2 with a restricted constant—in that case, the ECM (8.4) contains a constant within the term in the longrun matrix only; in other words, constants are associating with the cointegrating vector;

3 with an unrestricted constant—if the ECM has some equations without cointegrating vector (simple difference equation), these equations will still contain constants.

The two last cases characterize, respectively, the presence of a random walk without drift and the presence of a deterministic trend in the variables.

For each country, the dependent variable is the ratio of fossil fuel consumption to GDP (in logs), where fossil fuel consumption is the total of oil, natural gas and coal consumption for that country. The principal explanatory variable in the cointegrating regressions is the average price of fossil fuels relative to the price deflator of GNP or GDP (again in logs), where the average (after-tax) price is that of oil, gas and coal weighted by consumption. A time trend was included in the VAR as a proxy for technological innovation. It was not possible to estimate its impact during the estimation process since the time trend is within the VAR. This was carried out separately from the procedure by regressing the eigenvector of interest on a time variable and estimating it by ordinary least squares. In all cases, the time trend presented the expected

1st difference —2nd difference

Figure 8.5 First and second differences for relative price of fossil fuel for Germany

0.08

1st difference —2nd difference

Figure 8.5 First and second differences for relative price of fossil fuel for Germany

0.08

0.06

0.04

0.02

0.06

0.04

0.02

T

I

i ?

i 1 *

f V

i , A * +

i -7W/ \jf \

* T^"

hr j +

/ *

i \

t

]

7804 8001 8101 8201 8301 8401 8501 8601 8701 8801 8901 9001

—1st difference 2nd difference

7804 8001 8101 8201 8301 8401 8501 8601 8701 8801 8901 9001

—1st difference 2nd difference

Figure 8.6 First and second differences for relative price of fossil fuel for Italy

(negative) sign, representing the impact of technological innovation on energy consumption. In addition, it is to be expected that the fossil fuel ratio is negatively associated with relative price. The data are graphed for each G9 country in Figures 8.7-8.15.5 It can be seen from Figures 8.7-8.15 that all countries tend to exhibit the same characteristic shape. The ratio of fossil fuel to GDP declined since 1978, but with a

Figure 8.7 Belgium fossil fuel consumption/GDP and relative price of fossil fuel
Figure 8.8 Canada fossil fuel consumption/GDP and relative price of fossil fuel

slowing of the decline, or even an increase, in the late 1980s. The relative price of fossil fuel shows a 'hump', rising sharply after 1979 and then falling back during the mid-1980s.

The results from the Johansen procedure are shown in Table 8.4. In the case of Germany (illustrated in Figure 8.10) there was only a very weak negative cointegrating relationship between the energy consumption ratio to GDP and relative prices. This near-absence of cointegration is due to the almost-linear decline in the consumption ratio throughout the period. The inclusion of more factors is necessary in order to derive long-term relationships which explain consumption, such as the use of non-fossil fuel sources for electricity generation in France. (Indeed, this is being investigated in ongoing research.)

For all G9 countries more than one specification gave rise to significant sets of cointegrating vectors. The vectors from the two best6 specifications are shown in the table, and the two most significant vectors from

13.1

Q CD

i—V. *****

*

■^U.Wfc

r

________

Nu

7901 B001 8101 8201 8301 8401 8501 8601 8701 8801 8901 9001

7901 B001 8101 8201 8301 8401 8501 8601 8701 8801 8901 9001

* Fossil fuel/GDP —Relative price

Figure 8.9 France fossil fuel consumption/GDP and relative price of fossil fuel

* Fossil fuel/GDP —Relative price

Figure 8.9 France fossil fuel consumption/GDP and relative price of fossil fuel

Relative price

Figure 8.10 Germany fossil fuel consumption/GDP and relative price of fossil fuel

Relative price

Figure 8.10 Germany fossil fuel consumption/GDP and relative price of fossil fuel each specification are shown, with the most significant presented first. The vector finally selected for use in the dynamic model (see below) is italicized. When both vectors from the same specification exhibited the same (desired) property of having the consumption ratio and the relative price negatively associated, the most significant vector was preferred. When the cointegrating vectors offered two contradictory relationships, i.e. negative and positive relationships between the consumption ratio and the relative price, both representations were retained and their significance was tested in the dynamic model.

The coefficients for relative prices and time trends from the cointegration analysis are shown in Table 8.5. The 'best' cointegrating relationships used to derive these involve lag lengths between four and eight and either restricted or unrestricted constants as described above. The United Kingdom, the Netherlands and Germany show the smallest elasticities of demand with respect to price, all under 10 per

Figure 8.11 Italy fossil fuel consumption/GDP and relative price of fossil fuel
Figure 8.12 Japan fossil fuel consumption/GDP and relative price of fossil fuel

cent. Belgium, France and the United States are highest at around 15 per cent with the remainder falling in between. The time trend, or technological innovation factor, varies greatly between countries. France, Belgium and Japan show the highest effect with a time trend of -4 to -5.7 per cent per annum, which is in part due to large nuclear expansion in these three countries during the estimation period. In most other countries it is around -2 per cent per annum. It should be noted that, as this trend represents change in energy intensity, a value of -2 per cent implies that with GDP growth of 2 per cent or less, consumption would be stable or decreasing.

For Italy and Japan, the two significant cointegrating vectors presented two different possible relationships between consumption and relative price, either negative (as price rises, consumption decreases)

12.7

I 126 8

-

*

\

4

V

f

. fL^

4 \

TiS

7901 8001 8101 8201 8301 8401 8501 8601 8701 8801 8901

7901 8001 8101 8201 8301 8401 8501 8601 8701 8801 8901

Figure 8.13 Netherlands fossil fuel consumption/GDP and relative price of fossil fuel

Figure 8.13 Netherlands fossil fuel consumption/GDP and relative price of fossil fuel

Fossil Iuel/GDP Relative price

Figure 8.14 United Kingdom fossil fuel consumption/GDP and relative price of fossil fuel or positive. The latter would mean that if demand is increasing then prices are rising. The impact of these two possible effects was then tested within the dynamic modelling (see below).

Table 8.4 Cointegrating regressions for each country

Specification First vector Second vector Specification First vector Second vector

Belgium Lags Constant bgrpl

Restricted

Unrestricted

18.15

18.73

15.5

15.5

14 9 ^lT-IITIIllMIIIMII-l-T-IT II

7901 8001 8101 8201 8301 8401 8501 8601 8701 8801 8901 9001

14 9 ^lT-IITIIllMIIIMII-l-T-IT II

7901 8001 8101 8201 8301 8401 8501 8601 8701 8801 8901 9001

* Fossil fuel/GDP Relative price

Figure 8.15 United States fossil fuel consumption/GDP and relative price of fossil fuel

Specification

First vector

Second vector

Specification

First vector

Second vector

bgc-y

17.27

-37.38

56.54

32.43

Canada

Lags

7

8

Constant

Restricted

726.2

52.41

Restricted

-0.51

883.0

cnrpl

-5.21

-0.310

-6.21

-7.15

cnc-y

-51.61

-4.86

4.71

-62.32

France

Lags

5

6

Constant

Unrestricted

Unrestricted

frrpl

8.49

7.59

8.11

-9.92

frc-y

57.84

-37.87

-50.14

-63.61

Germany

Lags

4

8

Constant

Unrestricted

Unrestricted

1.77

14.48

gerpl

3.97

8.33

132.8

-59.88

gec-y

62.66

-55.88

Italy

Lags

4

4

Constant

Unrestricted

Restricted

-1089

1157

itrpl

16.30

5.19

8.53

-14.73

itc-y

125.80

-9.81

85.01

Japan

Lags Constant jpc-y

Netherlands

Lags

Constant nlrpl nlc-y

United Kingdom Lags Constant ukrpl ukc-y

United States Lags Constant usrpl usc-y_

Unrestricted

Restricted

Restricted

Restricted

9.00 67.63

5.14

60.48

4189

7.95

50.04

Restricted

Restricted

Restricted

Unrestricted

6.24

47.15

3343

46.83 12.08

8.23

25.83

Notes: c-y, log of fossil fuel consumption relative to GDP; rpl, log of price of fossil fuel relative to price deflator of GDP.

Only the most significant vectors for a given specification are presented. The vector in italics is the one which was selected.

A dummy variable is used in the VAR for France, taking the value 1 from 8903 to 9002, and zero otherwise.

Table 8.5 Own-price elasticities of demand for fossil fuel share of GDP and time trends

Country

Relative price coefficient

Belgium

Canada

France

Germany

Italy

Japan

Netherlands United Kingdom United States

-0.155 -0.101 -0.147 -0.063 -0.130 -0.133 -0.085 -0.045 -0.159

-4.80 -2.17 -5.67 -3.12 -2.19 -4.06 -1.61 -2.58 -3.09

DYNAMIC MODELLING

The error correction mechanism (ECM hereafter) captures the idea that agents alter their behaviour according to 'signals' that they are out of equilibrium. Expressed more formally, an ECM representation allows the long-run components of the variables to obey equilibrium constraints, while short-run components have a flexible dynamic specification. Therefore, a typical ECM relates the change in the dependent variable to past equilibrium errors as well as to past changes in both the dependent and explanatory variables. Hence, the change in energy demand would be related to the change in relative prices and to GDP, as well as to their past changes. It would also take account of the past deviations from the equilibrium.

The relationship between error correction models and cointegrating variables is embodied in the Granger representation theorem. Amongst other things, this states that if an N*1 vector xt is cointegrated of order (1, 1) with cointegrating rank r, then the following hold.

1 There exists a vector autoregressive moving average (ARMA) representation:

where A(1) has rank r and A(0)=In, In In being the N*N identity matrix. d(L) is a scalar lag polynomial with d(1) finite, and when d(L)=1 this is a VAR.

2 There exists an error correction representation with zt=a'xt, an r*1 vector of stationary random variables:

3 The vector z, is given by where K(L) is an N*r matrix of lagged polynomials given by yIC*(L),1 with all elements of K(1). zt is interpreted as the disequilibrium or error correction term. It represents short-run deviations from the long-run equilibrium.

4 If a finite VAR representation is possible, it will have the form given by (8.3) and (8.4) above, with d(L) = 1 and bothA(L) andA*(L) being matrices of finite polynomials. This implies that the error correction model (8.4) will have only stationary variables on both sides of the equation, and so the usual stationary regression theory applies. This renders the model immune from the spurious regression problem, i.e. it provides consistent estimation and testing of the dynamic model, including the cointegrated variables.

In this case, the cointegrating vectors are the estimate of the innovation process s, as defined by where c, y and rp are the logs of, respectively, fossil fuel consumption, GDP and the price of energy relative to the price deflator of GDP and T is the time trend, while a and b are the coefficients of the Johansen cointegrating vector. Hence the ECM can be written as8

where k is a constant and the (;'=1, 2) are the lagged estimate of the innovation process et.9 Past forecasting errors are thereby taken into account in forecasting the next change in fossil fuel consumption. This general unrestricted model was estimated for the G9. It was simplified to eliminate the irrelevant parameters and redundant explanatory variables and transformed so that the disturbance term is an innovation process.

Estimates of the ECM for each country are reported in the Appendix together with a set of diagnostic statistics for each equation. The simplified and parsimonious representations of GDP for the G9 present many common features. The first is that they explain about 70-80 per cent of the quarter-by-quarter variance changes in fossil fuel demand. The standard errors of the regression cluster around 0.5 per cent, with the United States the lowest at 0.36 per cent and the Netherlands the highest at 0.68 per cent, indicating confidence ranges of about 1 per cent about the regression line.

Table 8.6 Significance of the residuals on two competing cointegrating vectors

t ratio for residual with negative relationship

t ratio for residual with positive relationship

Germany

-2.72

-3.91

Italy

-4.13

1.65

Japan

-3.52

0.76

Previous changes in fossil fuel consumption have a major impact on the change in current consumption. The coefficient on the previous quarter's change ranges from 0.57 for the Netherlands to 0.88 for Italy, and is always highly significant. In all cases the coefficient on the error correction term is significant. However, for Belgium, Canada and the United Kingdom it is only marginally so. Price movements and recent evolution of GDP seem to play an important role in the evolution of demand for fossil fuels in European countries of the G9, but apparently not so much in the case of Canada, Japan and the United States. The dynamics of the models do not generally go much beyond one lag, except in the case of the Netherlands.

In the cases of Canada, Germany, Italy and Japan, the best specifications gave rise to two possible cointegrating vectors. The more significant vector according to the maximum likelihood criterion of the two was selected, and this exhibited the expected negative relationship between the consumption ratio and relative prices. For the last three countries, the second vector exhibited a positive relationship between relative price and the consumption ratio, which would sustain the hypothesis that, as demand

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