Energy demand elasticities: a reassessment Dr Tunji Abodunde, Dr Franz Wirl and Franz Koestl THE LITERATURE on the measurement of the elasticity of energy demand is extensive, and offers a wide range of models and assessments of the price sensitivity of energy demand within industrialised countries; e.g. see the survey of L. Taylor (19771, Pindyck (1979) and Energy Modelling Forum, Report 4, (1980). For a critical view of energy demand elasticities,see Kouris (1981). Although most studies employ a flexible quadratic translog specification, the discussions and recommendations focus on the implicit elasticity estimates. Now, after two major price adjustments in the energy price evolution, one might be interested to know whether these elasticities have shifted in recent years and, if so, in what direction. This question was similarly asked by Bopp (19841, in respect of a national case study on the con- sumption of liquid fuels within the United States. This paper tests the hypothesis of constant energy demand elasticities at the sectorial (industry, transport, other) and international (Belgium, France, West Germany, Italy, the Netherlands, the United Kingdom and the United States) levels v i s - h i s more general assumptions. The application of analysis of variance tests suggests that this simple relationship of constant energy demand elasticities is more robust than is often coqjectured. Based on this result, energy demand elasticities were estimated, and tests for structural breaks in sectoral energy demand were carried out. The es- timated elasticities were found to be within the range obtained in other studies, e.g. EMF, op.cit. (19811, but remained substantially below the find- ings of Pindyck (1979). Since Pindyck estimated long-run elasticities from data pooled across countries at the end of a fairly long period of stable energy prices, i.e. 1973, the difference between estimates derived from time-series data and Pindyck’s findings needs to be corrected. An explanation is attemp- ted by considering, in a dynamic and intertemporal framework, expectations rather than current price quotations as the signal for long-run adjustments. Within such a set-up, Pindyck’s original estimates may be compatible with elasticitiesderived from time-series data, if interpreted correctly. Dr Abodunde is from the Energv Studies Department, and Mr Koestl from the Statistics Section, Data Services Department, at the OPEC Secretariat irt Vienna.Dr Wirl is an Assis- tant Professor at the Technical University in Vienna. The authors wish to thank the Organi- zation of the Petroleum Exporting Countries for the use of its facilities in preparing this paper and ME M. Mimouni, Head, Energy Studies Department, and Dr A. Iwayemi,Petroleum In- dustry Financial Analyst, Economics and Finance Department,for their helpful comments. Any views espressed in it are, however, the authors’. Summer 1985 163
Transcript
Energy demand elasticities: a reassessment
Dr Tunji Abodunde, Dr Franz Wirl and Franz Koestl THE LITERATURE on the measurement of the elasticity of energy demand is extensive, and offers a wide range of models and assessments of the price sensitivity of energy demand within industrialised countries; e.g. see the survey of L. Taylor (19771, Pindyck (1979) and Energy Modelling Forum, Report 4, (1980). For a critical view of energy demand elasticities, see Kouris (1981).
Although most studies employ a flexible quadratic translog specification, the discussions and recommendations focus on the implicit elasticity estimates. Now, after two major price adjustments in the energy price evolution, one might be interested to know whether these elasticities have shifted in recent years and, if so, in what direction. This question was similarly asked by Bopp (19841, in respect of a national case study on the con- sumption of liquid fuels within the United States.
This paper tests the hypothesis of constant energy demand elasticities at the sectorial (industry, transport, other) and international (Belgium, France, West Germany, Italy, the Netherlands, the United Kingdom and the United States) levels vis-his more general assumptions. The application of analysis of variance tests suggests that this simple relationship of constant energy demand elasticities is more robust than is often coqjectured.
Based on this result, energy demand elasticities were estimated, and tests for structural breaks in sectoral energy demand were carried out. The es- timated elasticities were found to be within the range obtained in other studies, e.g. EMF, op.cit. (19811, but remained substantially below the find- ings of Pindyck (1979). Since Pindyck estimated long-run elasticities from data pooled across countries at the end of a fairly long period of stable energy prices, i.e. 1973, the difference between estimates derived from time-series data and Pindyck’s findings needs to be corrected. An explanation is attemp- ted by considering, in a dynamic and intertemporal framework, expectations rather than current price quotations as the signal for long-run adjustments. Within such a set-up, Pindyck’s original estimates may be compatible with elasticities derived from time-series data, if interpreted correctly.
Dr Abodunde is from the Energv Studies Department, and Mr Koestl from the Statistics Section, Data Services Department, at the OPEC Secretariat irt Vienna. Dr Wirl is an Assis- tant Professor at the Technical University in Vienna. The authors wish to thank the Organi- zation of the Petroleum Exporting Countries for the use of its facilities in preparing this paper and ME M. Mimouni, Head, Energy Studies Department, and Dr A. Iwayemi, Petroleum In- dustry Financial Analyst, Economics and Finance Department, for their helpful comments. Any views espressed in it are, however, the authors’.
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The following sections will investigate the hypothesis of constant elas- ticities vis-A-vis structural change in energy demand elasticities, and will try to interpret these elasticities in an intertemporal framework. The results are then presented and discussed.
The calculations within this paper are based on time-series compiled from OECD Energy Balances 1970-1982 (1984a1, OECD National Ac- counts (1984b) for energy demand and economic indicators other than energy prices. The consumer prices for different types of fuels however, are based on a laborious compilation from different sources, e.g. OPEC Secretariat, US Department of Energy, OECD and Eurostat. The data is available from the authors on request.
1 . Constant energy demand elasticities and structural breaks The question of whether income and price elasticities based on histori-
cally observed data are applicable to future developments is of vital impor- tance to long-term energy planning. Most analysts conjecture that the hy- pothesis of constant demand elasticities is too restrictive and therefore apply the more general quadratic translog relations. This specification implies that the elasticities themselves are shifting with variations in price and income. All these studies, however, end up discussing (local) elasticity estimates without revealing the likely future shifts of these important parameters. Bopp (1984) raised the question of whether the historical pattern of energy demand, in particular of liquid fuel demand within the US, was stable over the energy price adjustments. In a similar manner to Bopp’s investigation, a dynamic constant elasticity relation is employed, however, on a sectorial basis, i.e. industry, transport and other sectors. Let:
InE, = a,, + a,lnp, + azlny, + a,lnE,-, (1)
El = sectorial energy demand
p, = real price (1975) per unit aggregate energy (price of gasoline for transport)
y, = ‘income’: index of industrial production for industry; disposable income for transportation and other sectors; GDP for transportation.
The aggregation of El and p t is based on the calorific content (in calories) of the various forms of final energy products. As shown below, dif- ferent forms of aggregation have also been used. In the following, equation
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(1) describes the initial hypothesis which is called H, and which is compared with alternative and more general specifications. Most investigations on structural breaks employ the so-called Chow test,' e.g. Bopp (19841, which however, is slightly modified in this paper to retain some degrees of freedom. In particular, it is supposed that the eventual structural breaks involved only the elasticity parameters a, and a2.
The year 1974 is chosen, for obvious reasons, as the first date of a switch in consumption behaviour. Suppose that a; and a: denote the dif- ferent price elasticities applicable in the interval [61, 731 and [74, 821 respectively, and a;, a: the corresponding income elasticities. Then put:
and define differential elasticities for the second period (1974-82) of the sample:
and introduce a dummy variable E , which is zero in the years up to 1973 and one for the remainder, to obtain:
lnE, = b, + b, lnp, + b,lny, + b,lnE,-,
+ b,Elnp, + b,elny, (3)
Equation (3) represents the alternative hypothesis (called H1) that the elas- ticities differ significantly between the two different energy price regimes.
The results of the tests between these hypotheses are given in tables 2 and 3, which indicate that, except for industry, there is little evidence and need to reject the original hypothesis. But, in the case of industrial energy demand, the hypothesis of constant demand elasticities does not perform satisfactorily. Further investigations for the industry and testing structural breaks either within the income or within the price elasticity tend to support
Summer 1985 165
the conjecture in case of a break, then it is related to the output. Hence, a sub- stantial shift (i.e. the often referred structural change of the industry) is not only due to higher energy prices, but also is carried by forces outside the energy system.
The aforementioned conclusions hold against other specifications, like utilising real GDP as an explanatory income variable or different energy price aggregates. Actually, the use of efficiency units [such as those given in Nordhaus (1975) (table 111 to arrive at useful energy reduced substantially the F-statistics for the critical industrial energy demand - an indication that the magnitude of the elasticities and, in particular, of the income elasticity, is a major point in the discussion.
The above test (H1 against HO) includes an ad hoc element in separat- ing the sample rather arbitrarily into two different regimes. While in his investigation, Bopp (op.cit.) allows for dates other than 1973/1974 as possible breaks in the evolution of the energy demand pattern, a general and econo- mic dependence of the elasticities is stipulated in the following hypothesis H2. Suppose that income and price elasticities themselves depend on price and income, e.g. consider the following quadratic translog relation:
In E, = c,, + c,ln p, + c21ng, + c,ln El-l + c,(ln p J 2
as the alternative hypothesis H2. Again, analysis of variance tests allow a comparison between the different hypothesis HO and the generalisation H2. This hypothesis, however, does not explain anything significantly different from the simple hypothesis HO, except for the Italian industrial sector, des- pite its popularity in applications.
Table 1 Efficiencies of final energy uses according to Nordhaus (1 976)
Note: HO, HI, H2 represent the dflerent hypotheses about energv demand (equations (I), (3) and (4)), SSQ denotes the sum of squared residuals and F stands for the test statistic, which folio ws an F distribution. 'SigniJicant at the five per cent level. The critical values are: Fz,16 = 3.6 for HI against HO and F,,, = 3.3 for the test H2 over NO.
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Table 3
Others
Useful energy
Transport
Final energy
SSQ
Belgium H1 .064 H2 .051 HO .068
W.Germany H1 .045 H2 .044 HO ,050
France H1 .041 H2 .033 HO .048
UK H1 .015 H2 ,015 HO .020
Italy H1 .027 H2 .027 HO .037
Netherlands H1 .085 H2 .068 HO .090
us H1 .009 H2 .011 HO .012
F
0.5 1.6 -
0.9 0.7 - 1.5 2.4 -
2.8 1.7 -
3.0 1.9 -
0.5 1.6 - 2.8 0.6 -
SSQ
.05 1
.056
.057
.043
.038
.044
.018
.020
.034
.014 ,014 .018
.02 1
.022 ,028
.065
.056
.066
.007
.009
.010
F
0.9 0.2 - 0.3 0.9 - 7.3' 3.2 - 2.4 1.5 -
2.9 1.4 -
0.1 0.9 - 2.9 0.4 -
Disposable income
SSQ
.021
.025
.030
.009
.009
.009
.004
.004
.004
.004
.004
.005
.017
.015 ,020
.016
.017
.017
.005
.006
.006
F
3.7' 1.1 - 0.5 0.0 - 0.8 0.0 - 2.6 1.6 -
1.7 2.0 -
0.2 0.0 - 1.5 0.0 -
GDP
SSQ
,018 .025 .028
.007
.007
.007
.003 ,003 .003
.002
.004
.004
,015 .013 .017
.014 ,015 .016
.005
.005 ,006
F
4.6' 0.7 - 0.6 0.0 -
0.1 0.6 -
13.5' 0.0 -
0.9 1.4 - 1.2 0.3 - 1.2 1 .o -
*Significant at thefive per cent level. The critical F values are as in Table 2.
The above investigations show that the simple hypothesis HO of con- stant demand elasticities seems a sufficient proxy for analysing energy demand in the private and transport sectors, while the industrial sector should be handled more carefully.
2. A reassessment of long-run energy demand elasticities Since the aforementioned )results tend to support the hypothesis of constant demand elasticities, equation (1) was also estimated for final and aggregate
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useful energy (based on table 1). But equation (1) includes a lagged endoge- nous variable, and hence ordinary least square estimates will provide incon- sistent estimates if the errors are stochastically correlated. Therefore, it has been modified to include a first order autocorrelation among the residuals:
lnE, = a, + a,lnp, + a21ny, + a,lnE,-, + u, ( 5 )
u, is residual in equation ( 5 ) in period t
p is autocorrelation coefficient
e, is uncorrelated error process
Multiply equation ( 5 ) by the unknown autocorrelation coefficient p and sub- tract the obtained result from ( 5 ) to derive:
The disturbances of equation (6) are uncorrelated and hence, a least squares estimation is applicable, which, however, requires non-linear routines. The results obtained from relation (6) are summarised in different forms as shown in tables 4 - 6 as well as in Figures 1 - 3, and the statistical properties of relation (6) for the long-run elasticities are given in the Appendix.
The regression for final energy, except for Belgium and The Netherlands, leads to income elasticities below 1. This is an often quoted result, but counter intuitive because, for given energy prices and technology, a proportional change in output should require a similar proportional adjust- ment in energy input. There are two possible explanations for this.
First, the actual utilised shifts in the mix of secondary fuels imply a change in energy as well. For example, final energy underestimates the in- crease in effective energy input during the 1960s because of the substitution of liquids for solid fuels due to the higher conversion efficiencies of liquids in end-use. This conjecture is supported in the estimation of useful energy, which increases income elasticities in all cases, while energy price elasticities are only slightly affected (figure 1).
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Belgium France W. Germany Italy Netherlands UK us
Table 4 Long-run energy demand elasticities: industry
The second explanation attributes the observation of ‘low’ income elas- ticities to the shifts in the relative contribution of different sectors to aggre- gate industrial output. In the case where these structural changes are not themselves energy price dependent, but basically exogenously determined by technological patterns and innovation, the aggregate industry’s elasticity could be below one, although each sector’s income elasticity equals one. In such a case, the income elasticity of total industry would be an indicator of the trend of the sectorial shares rather than a proper income elasticity. Actually, the investigation of these aspects was one of the objectives of this paper, but the data available at a sectorially disaggregated level was incon- sistent and of poor quality. But, since the introduction of useful energy resulted in satisfactory results, the need for a further disaggregation seems, at least to us, not of the priority anticipated at the beginning of this research.
The differences between final and useful energy are less important for the estimations of domestic and commercial energy uses. While energy price elasticities are similar to those of industry, income elasticities tend to exceed one slightly. These properties also hold roughly for the energy demand for transport purposes, where aggregate real GDP provides a better explanation than disposable income. These results, due to little dispersion among the various countries, can be summarised into a rule of thumb; income elasticity around one, or slightly higher, and a price elasticity of around -0.5. This finding is similar to that in the EMF studies of 1980.
3. Comparison with Pindyck’s findings In an inter-temporal and dynamic framework, the concept of long-run
energy demand price elasticities seems vague or at least not free from ambiguity. Within such a theoretical ambiguity, the estimates of highly price- sensitive demand responses obtained from static investigations, such as those of Pindyck, op.cit., can be synthesised and connected to smaller price elasticities derived from time-series data. Pindyck (19791, for example, claims that only data pooled across countries can retrieve the information about long-run energy demand behaviour. But the actual and dynamic deci- sions of consumers do not fit into a static concept, since expectations about the uncertain future play an essential role. Actually, Pindyck correctly esti- mates the long-run price elasticities, i.e. the change in ultimate demand due to a permanent change in prices. Yet, actual demand behaviour will be nei- ther in this steady state nor even along a trajectory, which moves in the direc- tion of this point.
The reason for this is that consumers employ expectations rather than current price quotations to justify eventual energy conservation programmes. Now, if the consumers have rational expectations or at least
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some basic understanding of the laws of demand and supply, then current energy conservation will be based on properly expected prices. The difference between the adjustment for the current price level and the rationally expec- ted equilibrium is given in figure 4. Let (po, qo) denote price and quantities of an initial demandhpply equilibrium. The declining curves represent the short-run demand behaviour of the consumers and the upward sloping curves show the supply relation. The unbroken lines stand for the initial situ- ation before any adjustment in the market.
Now consider a shift in the supply curve from the unbroken curve to the broken line (e.g. due to increasing scarcity or cartelisation), which induces a rise from po to p,. The short-run demand curve for a long duration of price p1 is moved to the dotted line through expenditures on energy con- servation measures, which are profitable for price p1 and is given by the dotted line. The ideal steady state of the long-run optimally adjusted demand for price p, is denoted by q I.
Figure 4 tities
,' at price p, A'
I , I - Po P' P, Price
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Now, Pindyck attempts to measure the relative difference between (4, - qo) over (po - pl). It is immediately obvious from figure 4, however, that (p,, 41) is not an equilibrium point, since it is not located on the supply curve. Hence, a rational consumer will not shift his short-run demand curve towards the dotted line, but rather will limit his expenses to adjusting investments economically justifiable for a lower and properly expected price. The rational adjustment leads to the broken short-run demand curve and to the equilibrium point (p*, q*).
In short, a small consumer recognises that, if individual energy conser- vation efforts pay off at current prices, then other consumers will most likely react in a similar manner. But, if all consumers are engaged in conservation programmes, then demand will fall. Then, however, the price must also decline.
Hence, adjustment investments must be justified by a move to this new equilibrium price and not by the current quotation. Therefore, actual time- series observations cannot estimate elasticities of the Pindyck type, because observations from a trajectory to this long-run adjustment simply do not exist; instead, there are only adjustments to a state which is economically jus- tifiable for expected prices. On the other hand, Pindyck’s elasticities cannot be used for stand alone predictions of demand, because they lead to a sub- stantial underestimation of the long-run evolution of energy demand.
While Wirl (1984) also sketches the transient motions to the new equi- librium point, let us limit the following discussion to the comparative static. Suppose that short-run demand (Ed) is isoelastic in price (p) and abstract from changes in income:
InEd = 1nA - b l n p
where A is fixed in the short-run, but shiftable in the long-run:
A = Aop-A
where0 < h < 1
so that long-run demand, E: , is given by:
(7)
1nE: = lnA,-(b + h ) l n p
176
(9)
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The requirement 0 < A < 1 describes the law of diminishing re- turns from energy conservation investments. This reflects physical con- straints for conservation investments, as well as an optimal economic ranking of the feasible measures.
Similarly, assume that the new supply curve, E’, which is responsible for the price increase from p, to pi, is isoelastic:
E ’ = a p B (10)
Since the relation (10) is responsible for a price increase from p, to pl, Pindyck computes for the long-run adjustment in demand for the price p I:
and this long-run price elasticity is the sum of the short-run flexibility and the long-run adjustment (b + A). As already indicated, the consumer will not choose an adjustment path to the level of demand specified in equation (1 l), but will rather incorporate information about the supply curve into his decision. More precisely, he will choose a programme based on, and justifia- ble by, a long-run equilibrium situation. Hence, compute the intersection be- tween long-run demand and supply to obtain from:
the equilibrium point between demand and supply, the market clearing prices:
and also the quantity traded:
- (b+A) q* = A, [+] b+A+P
- (14)
Now, suppose that E i = a o p B represents the initial equilibrium point (po, q,), together with Ei = Aop-(b+A), compute p,, q, in model parameters and take the relative difference between q* and the initial demand to derive:
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+ P (lnp, - In Po) b + A + P lnq* - lnq, = -(b + A)
Hence, a percentage change in prices will induce a
(15)
reduction in long-run energy demand. A comparison of (16) with Pindyck's elasticity shows:
Hence, if actual demand adjustments move in the direction of q*, for example proportionally to the deviation from equilibrium.
I is time constant
then observations along this path do not allow inference on the demand ad- justment under myopic conditions. If, however, myopia is dominant among consumers rather than ratiorial expectation, then the actual realisation will allow the computation of the long-run elasticity in the Pindyck sense.
4. Conclusion This paper has studied recent tendencies of energy demand in industria-
lised countries at a sectorial level. The investigation indicated that the hy- pothesis of constant energy demand elasticities is to a large extent a statisti- cally justifiable hypothesis. The estimation for individual countries, using some recent data, yielded satisfactory results with comparatively minor dis- persion over the countries and these results are compatible with other findings. The consumer price sensitivity suggested by Pindyck, however, ex- ceeds our findings. Yet, the difference may stem from the difference in esti- mation and will require a different interpretation.
178 OPEC Review
Footnote
1. The Chow-test is an ana!ysis of variance test, which checks the equaliv of the variance of the residuals over dfferent sets of observations, i.e. any parameter is allowed to change. However, our approach focuses on changes of the elastic@ parameter alone. which saves two degrees of freedom.
References
Bopp, A.E. (I 984), Tests for Structural Change in US Oil Consumption, 1967- 1982,
Energy Modelling Forum (1 980), Aggregate Elasticiv of Energy Demand, Yol. 1, EMF-
Energy Economics, Octobez
Report 4.
Eurostat, Energy Price Indices 1960 - 1980, Energy Statistics Yearbook, 1981.
Kouris, G. (1 981), Elasticities - Science or Fiction? Energy Economics, April.
Nordhaus, W.D. (1977). The Demand for Energy: An International Perspective in: W.D. Nordhaus (ed): International Studies of The Demand for Energy. North Holland.
OECD, Energy Balances 1960- 1982
OECD, Energy Statistics I9 75 - 1 9 78. OPEC, Outlook for Energy & Oil Demand I982 - 1983; Internal Report.
Pindyck, R.S. (1979), The Structure of World Energy Demand, MIT Press, Cambridge, Mass.
Toylor, L.D. (1977), The Demand for Energy: A Survey of Price and Income Elasticities, in W.D. Northaus (ed): International Studies of the Demand for Energv, North Holland.
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Wid, F. (1984), Energy Conservation under Rational Expectations of the Energy Price Evolution, Working Paper, University of Technology, Vienna.
Summer 1985 179
Appendix
Table 1 Statistics of the estimated equations’ Estimated demand equations: industry
Final energy
a1
Belgium -0.42 (7.901
France -0.29 (3.90)
W. Germany -0.28 (6.20)
Italy -0.26 (7.20)
Netherlands -0.23 (3.90)
UK -0.43 (4.40)
us -0.28 (9.30)
a2
1.13 (7.40)
0.53 (2.60)
0.44 (4.1 0)
0.76 (20.30)
0.84 (2.50)
0.55 (2.70)
0.69 (1 5.00)
8 3
0.1 9 (1.80)
0.4 1 (1 .go1
0.43 (3.30)
0.26 (1 .OO)
0.38 (2.20)
P
0.33 (1.30)
-0.03 (0.10)
0.1 1 (0.30)
0.33 (1.40)
-0.1 3 (0.40)
0.42 (1.60)
0.09 (0.40)
- PIDW
0.96 1.96
0.9 1 1.93
0.94 1.94
0.98 2.00
0.97 2.00
0.88 2.22
0.93 1.98
*Figures in brackets denote absolute t-statistics, R2 denotes R’ aq‘justed for degree of freedom, D W stands for Durban Watson statistics. This description holds also for the subse- quent tables.
