Endogenous technical progress in fossil fuel demand: The case of France

NORTH- HOLLAND

Endogenous Technical Progress in Fossil Fuel Demand: The Case of France Laurence Boone, Stephen Hall, and David Kemball-Cook, Centre for Economic Forecasting, London Business School Economic studies aiming at assessing the impact on the economy of the various policies that could be implemented to reduce carbon emissions have a common feature. The base-case scenario, or "business as usual" scenario, assumes a technical progress represented as a time trend. This implicitly implies that non-price factors (exogenous energy-saving technical progress, policy-induced technical change, elimination of inefficient technologies, or change in the composition of GDP) will help reduce energy intensity in the future, in the same magnitudes as it has done so far, without taking account of how a given policy could affect those factors. This paper explains how an advanced econometric tool, the Kalman filter, allows the researcher to estimate technical progress in a dynamic fashion, and so that those factors are endogenous to the model. Hence, the routes for further improvement in diminishing energy intensity will be realistically assessed, and any modifications on non-price factors will be instantly taken into account as part of the stimulation procedure. We apply this methodology to France and show how it significantly alters previous conclusions on the impact of economic policies aiming at reducing carbon emissions in France.

1. INTRODUCTION In recent years, concern has increased about the build-up of greenhouse gases in the atmosphere and, in particular, emissions of carbon dioxide (CO2). The Toronto agreement (1991 ), in particular, implies a stabilization objective for CO2 emissions around the world. Most studies devoted to this subject attempt to establish a link between fossil-fuel consumption, the economic activity, and the price of fossil fuel. Furthermore, they generally involve a proxy for all the non-price factors that is called by Boreo et al. "exogenous Address correspondence to Laurence Boone, London Business School, Sussex Place, Reagent's Park, London N W I 4SA, United Kingdom. The research was carried out with the aid of a grant from the Economic and Social Research Council (No. Y320 25 3010). Received December 1994, final draft accepted May 1995. Journal o f Policy Modeling 18(2):141-155 ( 1 9 9 6 ) © Society for Policy Modeling, 1996

0161-8938/96/$15.00 SSDI 0161-8938(95)00062-X

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energy-efficiency" and that applies equally in the base and simulantion case. This is supposed to represent the declining trend in fossil-fuel consumption observed in the G-7 (see Boone, KemballCook, and Hall, 1992). However, energy policies affect non-price factors, and in this sense they are far from exogenous. Hence, to be able to implement sensible policies of CO2 emissions control, one should be able to distinguish the impact of autonomous from policy-induced technical progress on energy demand, that is, to explain with observed variables the unobservable technical progress. Estimating the impact of endogenous technical progress within a time-series framework has rarely been done, partly because of the lack of good data, but mainly because a practical framework has not been widely ~ivailable. The Kalman filter offers a methodology to estimate unobserved components such as technological change, and this paper proposes to use this technique as a way of addressing this problem. The methodology proposed here is applied to energy demand in France. This contains a trend component that cannot be entirely explained by energy prices, taxes, and so forth, which is usually explained as technological innovation leading to a more efficient use of different energy sources. The proposal here is to set up a state space representation of energy demand where the measurement equation is a standard ECM involving energy demand, real energy prices, and a declining trend in fossil-fuel consumption. This trend, representing technological innovation, is the unobservable component that is explained in a transition equation by various factors, including an autonomous stochastic growth rate. We are thus able to distinguish the parts of the total innovation trend that are endogenous and to separate out the remaining autonomous trend. This model is then estimated and optimized by maximum likelihood procedure. We argue that this decomposition of the trend may have enormous practical importance. If we find that the trend is influenced by factors under the government's control, this will give a powerful tool for controlling future energy use. On the other hand, if we find that the trend in the recent past is mainly due to factors that cannot continue, we know that future changes in energy efficiency will be very different to recent ones. In the case of France, the trend increase in fossil-fuel efficiency has been very high in recent years, but we will argue that this is explained by the growth in nuclear and hydro electricity production. Given that the scope for increases in the efficiency of these factors is now very limited in France, our conclusion is that future trend developments are likely to be very different to those of the last two decades.

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This paper is organized as follows: Section 2 presents the standard methodology of most of the previous literature, that is, a time-series study of the variables, the estimation of a cointegrating relationship leading to an error-correction model so as to get a long-run equilibrium representation. Section 3 shows how the model can be considerably improved by endogenizing the technical progress term using a state-space representation. It will be shown that we can distinguish between the impact of price and non-price factors and among these latters quantify the importance of the autonomous part of technological innovation from the policy-induced part. Section 4 discusses the results and the subsequent policy implications. 2. M E T H O D O L O G Y In this section, we develop a standard error-correction model for energy demand.

2A. Time-Series Analysis The variables of interest are fossil-fuel consumption, fossil-fuel price after tax, as well as GDP, and the deflator of GDP. We define energy intensity as the ratio of fossil-fuel consumption to GDP, and the relative price of fossil fuel as the price after tax of fossil fuel divided by the G D P deflator. An analysis of the univariate time-series properties of these variables is the first step towards establishing the existence of a cointegration relationship. The Johansen (1988) procedure applied as an integration test consists in testing for the presence of a dynamic cointegrating relationship in the variable, in level and differentiated, and a constant. If there exists one, then the level or the difference of the variable is stationary. The estimation of the cointegrating vectors is carried out as usual with the Johansen procedure. As there are three variables (energy, prices, and output), two possible relationships may be estimated. A time trend is included in the VAR so as to capture the decreasing trend in consumption. Different forms of the VAR were studied, including the possibility of a stochastic or deterministic trend.

2B. Stationarity Tests We begin by testing the variables for stationarity. Results from the Johansen analysis of the univariate time-series properties are given in Table 1.

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Table 1: Stationary Properties o f D e m a n d , Aggregate Price, and G D P Variable name FRCL FRRPL FRYL

Ha

H.

Ha

I(0)

I(1)

I(2)

2.16 3.28 0.049

2.96 2.34 7.96

9.82 13.60

Notes: The critical value at a 5 % level is 3.672. C L = log of consumption of fossil fuels. R P L = log of price of fossil fuels relative to price deflator of G D P . Y L = log of GDP.

Both demand and deflated price are second-difference stationary. GDP is first-difference stationary. Hence, energy intensity and relative price are integrated o f the same order, so that their cointegration properties can now be studied. 2C. Cointegration Properties of the Data For the cointegration analysis, a time trend was included in the VAR as a proxy for technological innovation. The expected sign o f the coefficient on the time trend is negative so that as it increases, consumption relative to GDP diminishes. As a structural break clearly occurs from the end of 1988 onwards, probably due to a change in climatic conditions, a dummy variable was introduced, taking the value zero from 7801 to 8802 and one thereafter. A search procedure allowed us to select the best model, whose particular features are presented in Table 2. It is a random walk without drift representation with 5 lags. According to the tables in Johansen and Juselius (1990), the two eigenvalues are significant at a 5-percent level in a VAR with a restricted constant. As can be seen from Table 2, there are two Table 2: T w o Cointegrating Vectors

Lag length

RPL coef

CY coef

Johansen trace test

OLS constant

OLS time coef

5 5

7.595 8.486

- 37.87 57.84

14.81 4.719

- 470.14 780.08

0.443 - 0.854

Notes: Coef = coefficients of the variable in the eigenvector. OLS constant and time coefficient are the results of the regression of the Johansen residuals on the variable time so as to quantify its impact on the evolution of energy demand.

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possible cointegrating relationships between demand and prices: One exhibits a negative relationship between prices and consumption, while the other exhibits a positive one. We would hope that the positive one may be given a demand interpretation-higher prices lead to lower d e m a n d - w h i l e the negative one would be interpreted as higher demand leading to higher prices. We test this formally below by introducing residuals from both cointegrating relationships in the following ECM. Hence, the significance of each causal relationship will be determined by rigorous estimation. However, note that if our intuition is correct, then the price elasticity of energy consumption would be about - 0 . 1 5 , which is relatively high compared to other countries in the OECD (see Boone et al., 1992). The effect of the innovation trend is also relatively high at - 1.5 percent per quarter (again this is true whatever the chosen lag length specification is chosen).

2D. Error-Correction Representation Residuals from the cointegrating vectors were included into the error-correction representation, lagged once, so that the ECM is of the form: 4

ACt = ~ A P i i=1

4

+ ~ A Y ~ + Z]_, + Z~-1 i=1

where Z i represents the residuals from the cointegrating vectors where the relationship between the two variables exhibit a positive sign for i = 1 (demand interpretation) and negative for i = 2. Estimate of the ECM is given below with a set of diagnostic statistics, standard errors in parentheses: Ac, = - 0 . 0 0 2 2 (0.00077) - O.O186Arpt

(0.0147) R 2 = 0.872 Reset(4,33) = 0.81

0.00082Z~_m + 0.0234ADum, + 0.80Act-i (0.00051) (0.0041) (0.0651) - 0.0212Arpt-4 (0.0157)

S E R = 0.0038 SK = - 1 . 4 0

DW=

1.59

E K = 7.63

LM4(4,29) = 1.44

B J(2) = 52.6

The lagged residuals from the cointegrating vector represent a causal relationship from the price towards the demand, that is, Z t was retained, confirming the intuition. Further, Z 2 (standing for how demand affects prices) was found insignificant. This explains around 87 percent of the quarter-by-quarter changes in fossil-fuel demand. Previous changes in energy consumption have

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a great impact on the change in current consumption (about 90°70 of it). The residual or error-correction term is, however, not significant at a 5-percent level and hardly at a 10-percent level. Current and previous year changes in prices explain about 5 percent of the change in consumption. This is not surprising as energy prices are controlled by the state in France as energy companies are stateowned and heavily subsidized, particularly with respect to the nuclear and hydroelectric programs.

2E. Long-Run Analysis From the error-correction representation we can derive the longrun equilibrium relationship by assuming that, in the steady state, variables in level are constant. This equilibrium relationship has a Cobb-Douglas form presenting elasticities with respect to price and time. The latter captures the trend in fossil-fuel Consumption that is not associated with non-price movements. Formally, the Cobb-Douglas representation is written as: C = A TaRP bY

where A = 0.988 is a constant, a = - 0 . 0 1 4 8 is a parameter standing for the elasticity of demand with respect to non-price factors, b = - 0 . 1 4 7 is a parameter representing the elasticity of demand with respect to price.

The elasticities with respect to price and non-price factors are negative. The latest suggests that this "time variable" might well include factors such as technical progress, energy saving measures, increase in efficiency of use, and so forth. 3. ENDOGENOUS T E C H N I C A L C H A N G E 3A. Particular Features of French Energy Policy To improve this "standard" procedure of estimation, we propose to specify the trend more fully. This latter is a proxy for technical progress, which is a rather vague term to explain a more efficient use of energy resources, a switch towards more modern, energy-saving technologies, both favored by actual energy policy, and compositional changes in the supply of energy. French energy policy is marked by a determination to promote the use of nuclear energy to generate electricity and to reduce dependence upon imported oil and gas. Production of nuclear energy has risen from 6.4 million tonnes of oil equivalent in 1978 to 65.0

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mtoe in 1991. The rise has been steady, apart from a plateau in 1981-82. This policy has contributed to a steady decline in total consumption of fossil fuel during the 1980s until 1988. However, the years following 1988 have shown continuing increases in fossil-fuel consumption, probably due to a decline in the production of hydroelectricity (from 5.2 mtoe in 1988 to an average of 3.8 mtoe in the three years following), caused by drought. Hence, France seems a perfect illustration of how the Kalman filter will allow us to endogenously explain the intrinsic change in the shape of fossil-fuel demand, quantifying the impact of the unobservable technical progress and explaining it by the particular features of the French energy market. 3B. Application of the Kalman Filter

Assuming that these variables (hydro and nuclear electricity) can be at the origin of the decreasing trend in consumption, that is, increasing technological innovation, the Kalman filter then offers a way of estimating the time trend as a function of these two factors, simultaneously with the estimation of the fossil-fuel demand equation. More formally, we set up the following state-space representation: 1. The measurement equation, which is directly inspired from the error-correction model: p

A E , = ~ o,iAXi, t_j + ~ ( E t - i - "~Xt-i + 6T,) + vt j=l

2. The transition equations explaining Tt endogenously by the subquoted factors such that: Tt = Tt-i + gt-I + rhA(n/jOt + " f l 2 A ( h / f ) t + etl gt = g t - I + e a

where (n/f) stands for the ratio of change in nuclear electricity relative to fossil-fuel consumption and (h/f) for the ratio of growth of hydroelectricity relative to fossil-fuel consumption. Thus, an increase in nuclear or hydroelectricity consumption is expected to raise technological innovation, thus producing a decrease in fossil-fuel consumption. The gt represents the autonomous technical progress and is merely a stochastic process. The estimation of the state-space representation is carried out using maximum likelihood on a function of the one-step-ahead prediction errors, suitably weighted (see Appendix).

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Table 3: A u t o c o r r e l a t i o n Function, Box Pierce, a n d Ljung Box Statistic Lag

1

Coeff -0.0912 Box Pierce 0.33 Ljung Box 0.36

2

3

4

-0.0696 0.53 0.57

-0.0040 0.53 0.57

5

6

7

-0.3264 0.0667 0.0709 0.0784 4.79 4.97 5.17 5.41 5.54 5.76 6.01 6.32

8

-0.1685 6.38 7.66

The Kalman filter estimation procedure was carried out including the same differenced dummy variable as the one that was in the ECM so as to avoid any misspecification or misinterpretation due to the structural break. The lags in the change in the dummy was as long as for the other variables so as to avoid any autocorrelation. The level of the dummy was also included in this representation. The results 1 are presented below:

Measurement equation: ACL

= -Tt

+ 0.5007 - O . O 0 5 6 ( C / Y ) t - I

- O.03762(RP)t_ ~ + O.O082(ACL)t_ ~ - O.O027(ARP)t_ 1 + O.OII7(ARP)t_4

+ 0.4365DUMt

+ 0.0121ADUMt

Transition equation: Tt = T , _ j + g t - i + O , 0 3 3 2 ( N / F ) t

+ O.I123(H/F)t

gt = g t - l

where N / F is the change in nuclear electricity consumption, and H / F is the change in hydroelectricity consumption, both relative to fossil-fuel consumption. Statistical diagnosis : M e a n o f residuals : 0.0003571 Standard deviation : 0.0030759 Coefficient o f skewness : 0.3481444 Coefficient o f kurtosis : 2.404919 B.J. Normality test : 10.4474220

The measurement equation does not differ very much from the

ECM. The trend in fossil-fuel consumption is mainly explained by the change in nuclear and hydroelectricity consumption relative to fossil-fuel consumption. Coefficients on both variables exhibit a ~The data for nuclear and hydroelectricity consumption come from the BP statistical review of energy, both in log of mtoe. As they were annual, they have been transformed in quarterly data following the same procedure as for the various fossil fuels.

PROGRESS IN FOSSIL FUEL DEMAND IN FRANCE 0.0001

149

I I,luelmr ekc.trkity ]

-5E--05 '-0.0001

-0.00015

-0.0002

Figure 1.

8201

B301

8401

8501

8601

8701

8801

8901

9001

Ratio of hydro and nuclear electricity to GDP.

positive sign so that as technical progress increases, that is, as nuclear and hydro shares of energy demand increase, the trend in fossil-fuel consumption decreases. The model satisfies a broad range of statistical diagnostics, although the BJ statistic remains too high (the interpolation process might, to a certain extent, account for this). The structural break can be explained by looking at the plot of the share o f nuclear and hydroelectricity relative to G D P presented in Figure 1. The nuclear consumption evolves steadily around the same trend over the whole time period, whereas the hydroelectricity consumption falls dramatically in 1989. Climatic changes are the cause of this fall: 1988 was a very generous year in terms of rainfall, but was immediately followed by the drought of 1989-90, which caused a fall in hydroelectricity production by as much as 40 percent compared to 1988, thereby shifting consumption from hydroelectricity towards fossil fuel. As an illustration, note that if normal consumption is around 300 kw/h, climatic fluctuations might account for variations of + / - 7 k w / h . The lack of rain lasted for more than two years, and water reserves decreased dramatically. Hence, taking into account the necessary time to reconstitute the "normal" reserves, the j u m p in fossil fuel consumption, followed by a plateau, is to be expected.

3C. Analysis of the Endogenous Technical Progress Consider the transition equation explaining the declining trend: Tt = a T t - i + bgt-t + b l A ( n / y ) t + b2 A ( h / y ) t gt = algt-i

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L. Boone, S. Hall, and D. Kemball-Cook 0.056" 0.054 0.052 0.05 0.048 0.046 0.044 0.042

8101 8201 8501 8401 8501 8601 8701 8801 8901 9001

Figure 2. Endogenous Technical Progress 1980-1990.

If the extra explanatory variables were set equal to zero, then the change in the trend would merely be a linear function of the stochastic trend gt. The inclusion of the change in the shares of growth of nuclear and hydroelectricity consumption relative to fossil-fuel consumption allows us to further explain the declining trend as technological change, and the fluctuations around this trend. One interesting feature of the state-space representation is that it allows us to consider this stochastic trend separately from other influences. Hence, we can plot the cumulative sum of the stochastic variable g and compare its evolution with the path o f endogenous technical progress (see Figures 2 and 3). The trend rises fairly steadily, implying a fairly constant rate of technical progress once the more erratic factors from hydro and nuclear are allowed for. Note that between 1982 and 1990 the total trend rises by 0.014, the autonomous part of this (gt) accounts for only 0.005. So autonomous technical progress is only a small part of the trend developments in France. Major policy implications can be derived from this. If we are right in the explanation of technological change, that is, if nuclear and hydroelectricity consumption really explain much of the declining trend in fossil-fuel demand in the past, then this has important implications for the future. Further development of both nuclear and hydroelectricity facilities is now very limited. No major hydro-related work is being done in France any more as all major rivers are already in use.

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151

-r

0.014. 0.013 0.012 0.011 0.01 0.009 0.008

0.007 0.006

0.005 0.004

8101

8201

8,501

8401

8,501

8601

8701

8801

8901

9001

Figure 3. Cumulative Sum of the Stochastic Trend.

(And this is one of the reasons why whenever a drought occurs, major switches from hydroelectricity to other energy sources can be observed as happened in 89.) At the same time, nuclear programs have dramatically slowed down, not only for political reasons (caused by ecological movements as well as safety questions arising from nuclear problems in Eastern Europe or Russia), but also because of the increasing investment costs required by more efficient nuclear plants. Thus, France has probably reached a ceiling in terms of development of nuclear and hydroelectricity facilities, which poses questions for the shape of the trend of fossil-fuel intensity in the future. A standard econometric analysis of French energy demand would therefore provide an unrealistically high estimate of technical progress. If this estimate was used as the basis of future environmental policy for example, then serious errors would occur. The methodology proposed here provides a much more flexible model of technical progress which gives a more realistic estimate of future developments. 4. CONCLUSIONS This paper has attempted to quantify the long-run relationship between economic activity, the price of fossil fuel, and fossil-fuel consumption for France. It has highlighted some specific features of France that do have a strong influence on the fossil-fuel consumption pattern.

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Price elasticity is in the higher range of price elasticities within the G-7, and the "time elasticity," that is, non-price factors elasticity of fossil-fuel demand was very high. Although the error-correction representation exhibits a number of nice econometric features, results have been greatly improved by the use of the Kalman filter. The endogeneization of technological change allows us to estimate the impact of hidden variables on fossil-fuel consumption, as well as simultaneously to estimate endogenous technical change. Furthermore, the intuition behind this is relatively straightforward. This method of estimation allows us to distinguish between autonomous and policy-induced technical progress, which is of maj or importance from a policy perspective. Hence, in the case of France, this suggests a very different pattern for the trend in the future from the one that was observed over the past 15 years. To continue the historical trend in consumption would certainly require a major change in energy policy. APPENDIX: The Kalman Filter Estimation Method

Following Harvey (1987) for the univariate case let Y, = 6'zt + ~,

(13)

be the measurement equation, where Yt is a measured variable, zt is the state vector of unobserved variables, 5t is a vector of parameters and et_NID(O,Ft). The state equation is then given as: Zt = tPZt-l + ~ W t + W

(14)

where qJ are parameters, W is extra observed variables (NF and HFhere) and ¥_NID(0,Q3, Qt being referred to as the hyperparameters. The corresponding Kalman filter prediction equations are then given by defining z* as the best estimate of zt conditional on information up to t, and Pt as the covariance matrix of the estimate z* and stating z;i,-~ = ~ z ; - j + ~W,

(15)

Ptlt- 1 = u"~Pt 1 trli" Ot

(16)

and

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Once the current observation on Yt becomes available, we can update these estimates using the following equations: Z~ = Z~/t I + Ptlt-J 8 ( Y t - ~)'Ztlt-l)/(~'Pt/t-l¢5 + Ft)

(17)

and Pt = Pitt-1 - Ptlt-1 8 8 t p t / t - l / ( 8 ' P t [ t - I

8 dr

rt)

(18)

Equations 15-18 then represent jointly the Kalman filter equations. The prediction errors, Y, - 5't/t-1, contains all the new information in Yt, and is used to update P,/t-i via the Kaiman gain. The Kalman gain is the m x l vector, Pt/t-I zt/ft : o['Pt/t-lQ -b Ft. Like P, and P,_ l, the Kalman gain is independent of the Yt's and so may be computed 'in advance. Now define the one-step-ahead prediction errors as: (19)

vt = Yt - ~)'Ztlt-t

then the concentrated log-likelihood function can be shown to be proportional to log(l) = ~,, log Oct) + Nlog t=k

v2/Nft

(20)

t

where N = T - k, and k is the number of periods needed to derive estimates of the state vector. Hence, the likelihood function can be expressed as a function of the one-step-ahead predicton errors, suitably weighted.

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