interfuel substitution and energy consumption in the industrial sector

Applied Energy 6 (1980) 275 288

INTERFUEL SUBSTITUTION A N D ENERGY CONSUMPTION IN THE INDUSTRIAL SECTORt

JoHr~ KRAFT

National Science Foundation, 1800 G Street, Washington DC 20550 (USA)

and

ARTHUR KRAFT

College o] Business Administration, University o/ Nebraska-Lincoln, Lincoln, Nebraska 685881 ( usa )

SUMMARY

This paper examines the possibilities jor fuel substitution in the industrial sector. First, we determine the total demandJbrjuel and powerJor the industrial sectorJ~'om 1955 to i 972. We then examine fi~el substitution possibilitiesJor electricity and eight major Jossil Juels consumed by the industrial sector. These are coal, natural gas, residual oil, distillate oil, kerosene, liquefied petroleum gas, still gas and petroleum coke. The anaO'sis includes an estimation of the Juel split equations, the dynamic simulation o/the industrial sector demandsJor fuel and the computation of short- and long-run demand elasticities/or each Juel.

INTRODUCTION

The purpose of this paper is to present the results of an energy demand simulation model for the United States' industrial sector. We use an econometric model to determine the historical demands for fuel and power in the industrial sector. The paper should aid in the analysis of the effects of higher fuel prices on the consumption of energy in the industrial sector as well as in determining the efficiency of fuel choice decisions among electricity and fossil fuels.

Unlike many other studies which consider the demand for a single fuel, we consider total energy consumption and competition among all fuels consumed in the industrial sector. (In particular, many researchers have considered the demand for a single fuel without considering the fuel substitution possibilities with respect to other

"l'This paper does not reflect the views of the National Science Foundation. The authors retain responsibility for any errors.

275 Applied Energy 0306-2619/80/0006-0275/$02-25 ~) Applied Science Publishers Ltd, England, 1980 Printed in Great Britain

276 JOHN KRAFT, ARTHUR KRAFT

fields. For example, see Griffin,'~ MacAvoy and Noll 9 and Kennedyfl These are only a few of the many studies that treat separately the demand for a single fuel--coal, natural gas or petroleum. Two studies which consider all fuels are the Hudson and Jorgenson 6 study of inter-industry fuel substitution and the Baughman and Joskow I cross-section analysis of energy consumption in the household-commercial sector.) The model allows for substitution among all fuels consumed in the industrial sector and computes the total demand for fuel by the industrial sector. The model examines the demand for electricity and fossil fuels: coal, natural gas, kerosene, distillate fuel, residual fuel, liquefied petroleum gas, still gas and petroleum coke.

We propose to analyse the patterns of fuel choice within the industrial sector by estimating a multiple logit model of fuel choice, using prices and fuel choice experience as explanatory variables. (For a discussion of the theory of the multiple logit model see Theil 13 and McFadden. 10 For empirical applications of this model see Kraft and Kraft, a Federal Energy Administration 3 and Schmidt and Strauss.l 2) The advantage of this approach is that it allows us to consider a range of fuel choice experiences which satisfy total energy consumption within the industrial sector. By constructing a model of choice experience one can analyse energy policy decisions based on higher fuel costs.

The plan of the paper is as follows: the first section describes the data base; the second section presents the model and simulation results whilst our conclusions are given in the third section.

]'HE DATA BASE

The data collected are annual time series of fuel consumption in the industrial sector of the United States from 1950 to 1972. The price and quantity data are recorded in common physical units: natural gas in cents per 1000 ft 3, petroleum in dollars per barrel, coal in dollars per short ton and electricity in cents per kilowatt hour. In order to allow relative comparisons between fuels, all quantities and prices are converted to BTU's (i.e. the heating equivalents).

All fuel quantities are now stated in BTU's and all prices are stated in dollars per BTU. By using this approach we can compare prices and quantities in terms of equivalent heating units. (The concept of ~BTU equilibrium' is elaborated in Hausman. 5) This approach is realistic because, in the long run, large price differentials will disappear for fuels with equivalent heating potential. Comparing prices and quantities on the basis of dollars per BTU is particularly relevant when one considers energy used for fuel and power purposes. However, heat content of the fuels may be irrelevant in energy consumption as a raw material. Therefore, all products used as raw materials are excluded from the consumption totals. All quantities are recorded in thousand trillion BTU's.

INTERFUEL SUBSTITUTION AND ENEPGY CONSUMPTION IN INDUSTRY 277

Before being converted to BTU prices, the face value prices were defined as follows: (1) electricity price is the industrial marginal cost of electricity in cents per kilowatt hour (computed from Federal Power Commission (FPC) typical electricity bills catalogued by customer classes); (2) natural gas price is the average price in cents per 1000ft 3 (computed as a weighted average of inter- and intra-state contracts); (3) petroleum products used are average prices in dollars per barrel; (4) coal is bituminous coal expressed in dollars per short ton for coal purchased on contract (spot market prices are excluded). (Consistent prices were available for all fuels except kerosene, still gas, liquefied petroleum gas and petroleum coke. Since the definition for the quantity series for these fuels has changed several times between 1955 and 1972 and since they are all light fuels, it was decided to use a single price for each of these lighter fuels. For an explanation of this approach see reference 3.)

THE MODEL AND SIMULATION

The model developed consists of three basic sets of equations. The first set determines the total demand for fuel and power by the industrial sector wherein total demand is defined as the sum of all fuels consumed. The second set of equations computes the potential demand for electricity and fossil fuels used in the industrial sector. Potential demand represents the upper limit of energy consumption based on energy output rates and production. The last set of equations determines the share of each fuel in the industrial sector.

Total demand The total demand for fuel in the industrial sector is estimated in double logarithmic

form as a function of price, a proxy for industrial activity and a lagged value of total demand. The total demand for fuel (TOTFL) is defined as the sum of electricity, natural gas, petroleum fuels and coal consumed in the industrial sector for fuel and power purposes. Since the specific fuels have been converted from physical units to heating equivalents (BTU's), it is possible to sum the quantities of each fuel consumed in the industrial sector and arrive at the total demand (TOTFL) for all fuels in the industrial sector. Thus, the dependent variable, TOTFL, is the total energy consumed in the industrial sector and is the sum of electricity and the individual fossil fuels. The aggregate price variable is TO TPR. TO TPR is a weighted average of the prices for electricity and the individual fossil fuels (coal, natural gas and petroleum fuels). Each individual price is weighted by the share of each fuel lagged one year. A fuel share is defined as the quantity of each specific fuel consumed in a time period divided by total fuel consumed in the same time period. In any time period the shares sum to unity. The remaining explanatory variables used in the estimating equation are the dependent variable lagged one year (TO TFL( - 1)) and a


proxy for total demand based on industrial activity, TOTPD. The lagged dependent variable provides a dynamic adjustment mechanism. It is reasonable to believe that in any time period total demand (TOTFL) should have some relationship to demand in the previous year. This allows the demand equation to have a dynamic property. The remaining explanatory variable is TOTPD, which reflects the potential fuel demand by the industrial sector. The potential demand for each fuel is a function of the historical ratio of energy to gross product originating in the industrial sector times the level of economic activity in the industrial sector. Thus, changes in production in the industrial sector would produce changes in the potential demand for each fuel. The energy-output ratios by fuel for each industry are based on 1971 data published in the Census of Manufacturers. The levels of industrial activity are the Federal Reserve Board Industrial Production Indexes.

Thus, the total demand for energy (TOTFL) in the industrial sector is defined as a stock adjustment model wherein demand is a function of that in the previous year ( T O T F L ( - 1 ) ) and the potential demand for energy (TOTPD) as a function of increased production in the industrial sector. A final determinant of demand is the aggregate price of energy (TOTPR). The specification of the total demand equation in double-log form is:

I n ( T O T F L ) = ~l + ot21n(TOTPR) + ~31n(TOTFL( - 1)) + ot41n(TOTPD ) (1)

~1 represents the short-run price elasticity and should be negative whereas c£, ~t 3 and ~4 are expected to be positive. The estimated values for eqn (1) appear in Table 1.

TABLE 1 SUMMARY OF TOTAL ENERGY DEMAND ESTIMATES

(1955-1972)

Dependent variable ~1 (t2 ~3 (t4

In (TOTFL) 9.523 -0.097 0.184 0-517 (7.60) ( - 1.26) (1-61) (8.70)

R 2 0.983 DW 1.419 SEE 0.01662

Note: Numbers in parentheses are t-statistics.

The coefficient of determination indicates that the explanatory variables account for ninety-eight per cent of the variation in the dependent variable. The Durbin Watson statistics are inconclusive but irrelevant in the presence of a lagged dependent variable. The coefficient of the potential demand for fuel is significant at the 0.005 % level and the coefficient of the lagged dependent variable (TOTFL( - 1)) is significant at the 0.10 % level. The estimated price coefficient is insignificant. This is not surprising, however, because energy consumption is expected to be more sensitive to consumption in the previous year and energy demand derived from increased production (TOTPD), rather than price. While manufacturers could

1NTERFUEL SUBSTITUTION AND ENERGY CONSUMPTION IN INDUSTRY 279

substitute capital and labour for energy, one would not expect this to occur on a large scale. Thus, a negative but insignificant coefficient of the aggregate price variable is possible. Based on these results, the price elasticity of demand in the industrial sector is -0 .097 in the short-run and -0 .326 in the long-run.

Potential demands Potential demands are computed for electricity (ELCPD) and fossil fuels

(FOSPD). The sum of ELCPD and FOSPD is TO TPD, which is used in eqn (1) to reflect the total potential demand for energy based on increased production in the industrial sector. The potential demand for fuel, i, is defined as:

P D i = ~/i (FRB) (2)

where PD i is potential demand for fuel i; ~,~ is the ratio of the quantity of fuel i consumed to the output originating in the manufacturing sector (based on 1971 data published in the Census of Manufacturers) and FRB is the Federal Reserve Board Index of Industrial Production. The energy-output ratio (~/i) times the index of manufacturing output provides an approximation for potential demand. We assume that as output increases the demand for energy would increase based on increased activity in manufacturing and historical energy-output ratios. The converse would occur for a decrease in production. The potential demands are computed for electricity and each of the fossil fuels and then summed to produce the total potential demands for all fuels.

Fuel shares Once total demand in the industrial sector has been calculated using eqn (1), it

must be divided into demands for individual fuels. This will be done by taking the share of each fuel (S~) and multiplying it by the total demand to determine the demands for each product.

The fuel shares satisfied by the different energy products are calculated in a two- stage process. First, total demand is partitioned into the demand for electricity and the demand for other fuels (fossil fuels). Next, fossil fuels are partitioned into various products (see Fig. 1).

I Electricity

Total fuel and power demand | ["Natural gas l | Bituminous coal 1 / Residual / . / Distillate ~.Fossd fuels ,~ Liquefied gases

| Still gas ] Kerosene k. Petroleum coke

Fig. I. Fuel and power demands in the industrial sector


We now focus on a procedure for determining the market share for each energy source. The procedure is based on a probability model of fuel choice in terms of past fuel share and fuel price. We are attempting to determine the share of fuel i.

Let Si belthejshare of any fuel consumed and (1 - Si) be the share of an alternative fuel in a two-fuel world, such that S t = (1 - Si). A linear specification of the share equation is:

8 p, S~ = ct + p~ + TQi (3)

Where P~ and P~ are the relative prices of the two competing fuels and Q~ is an alternative characteristic of the two fuels. The above specification says the share (S~) of fuel i is a function of the relative prices of fuels i andj . The coefficient (B) of the relative price ratio is expected to be negative. As the price of i rises relative t o j the share of i should decrease. This linear approach is deficient for two reasons. First, the expected value of the right-hand explanatory variables may be greater than unity or less than zero. A share greater than one or less than zero has no meaning. Secondly, the disturbance term of this equation could suffer from heteroskedasticity if the relationship were cross-sectional in nature. (See Kraft and Kraft, 8 Nerlov and Press 11 and Schmidt and Strauss ~ z for further discussion of this point.)

Theft has corrected this problem by developing the multinomial logit model which allows for the estimation of continuous dependent variables confined in the zero to one range. (For an evaluation of alternative techniques see Baughman and Joskow, 1 Kraft and Kraft 8 and Theil.13) In logarithmic form the ratio becomes:

= e + B l n + ?lnQ~ (4)

The left-hand variable o feqn (4) is known as the logit and corresponds to the share for fuel i. The logit is a monotonically increasing function varying from - Go to + oo. The logit transform is not confined to the finite interval (0, 1), as is S~. The right-hand side of eqn (4) can assume any value from - oe to + oe and be consistent with the left-hand side ofeqn (4). In eqn (4), B is expected to be negative and thus as the price of fuel i increases relative to the price of j , the share (Si) of i would decrease relative to S t. Because we are attempting to estimate a relationship between fuel shares and relative prices, we choose the logit form over the linear specification for the estimation of fuel shares. Fuel choices are based on relative fuel prices, other choice characteristics and lagged values of fuel shares. Each market share is computed as the total available BTU's of fuel i relative to the total BTU's consumed. The fuel prices are measured in terms of dollars per BTU. The fuel characteristics are the potential demands for electricity (ELCPD) and the potential demands for fossil fuels (FOSPD). First, we estimate the fuel share splits between electricity and fossil fuels. Then the shares within fossil fuels are estimated (see Fig. 1). In the industrial sector there is some doubt as to whether there is any substitution between electricity

INTERFUEL SUBSTITUTION AND ENERGY CONSUMPTION IN INDUSTRY 281

and fossil fuels: fossil fuels are used basically for process heating while electricity is used for special processes. Our model, however, does allow for substitution between electricity and fossil fuels in that our first choice mechanism allows a choice between electricity and fossil fuels based on their relative prices, other characteristics and lagged fuel shares (see Table 2). Also, if there were no substitution between electricity and the fossil fuels, the first row and columns of Tables 5 and 6 would have zero elasticities. In our model the choice decision is treated as a separable hierarchy: in the first stage the split is determined between electricity and fossil fuels and subsequent splits are determined within fossil fuels.

TABLE 2 SUMMARY OF ELECTRICITY/FOSSIL FUEL SHARE ESTIMATES

(1955 1972)

Dependent variable

In (SELC/SFOS) ~1 /12 ~3

1.224 - 1.755 1-914 (2-58) ( - 4.16) (6.86)

R 2 0.842 DW 1"845 SEE 0-5556

Note: Numbers in parentheses are t-statistics.

The logit regression for the electricity fossil fuel decision is expressed as:

In (SELC/SFOS) =/31 +/32 In (PELC/PFOS) +/33 In (ELCPD/FOSPD) (5)

where/32 is expected to be negative and/31 and [33 are expected to be positive. The shares of electricity and fossil fuels are SELC and SFOS, respectively: PELC is the price of electricity and PFOS is the weighted average price of fossil fuel prices. The share ratios are determined by the relative prices and the potential demands for these fuels. The summary statistics for eqn (3) appear in Table 2. (For estimation of the logit regression a maximum likelihood or a weighted least-squares approach may be used. For a discussion of these approaches see McFadden, ~ 0 Schmidt and Strauss 12 and Theil. 1 a However, in our instances the data represented variations of national totals over time rather than cross-sectional observations in time and thus no adjustment for heteroskedasticity was made. See Hausman 5 and Kraft and Kraft. 8)

The results for the choice between electricity and fossil fuels are quite good. The coefficient of determination is significant and the individual coefficients are significant at the 0.01 level with the correct signs.

Within fossil fuels a series of multiple logit models are estimated to determine their fuel shares. Over the time interval 1955 to 1972 we estimated functions of the form:

In (SNG/SBIT)t = fl~ + fla 2 In (PNG/PB1T), +/313 In (SNG/SB1T),_

282 JOHN KRAFT, A R T H U R KRAFT

In (SBF/SBIT), =/32~ + [322 In

In (SDF/SBIT), = f131 + [332 In

In (SSG/SBIT), = [34~ + [341 In

In (SK/SBIT), = fl51 +/352 in

In (SLG/SB1T), =/36t + [362 In

In (SPC/SBIT), =/37, +/37z In

(PRF/PBIT), + fl23 In (SBF/SBIT),_ t

(PDF/PB1T), + fl33 in (SDF/SBIT),_ 1

(PSG/PBIT)~ + [343 In (SSG/SBIT),_ t

(PK/PBIT), + [353 In (SK/SBIT)t_ 1

(PLG/PBIT), + [363 in (SLG/SBIT),_,

(PPC/PBIT), + [373 In (SPG/SBIT),_ i

(6)

where S N G , SB1T, SRF, SDF, SSG, SK, S L G and S P C are shares of natural gas, bituminous coal, residual fuel, distillate fuel, still gas, kerosene, liquefied gas and petroleum coke, respectively. The first explanatory variable is the relative price ratio. From these equations we can derive other comparisons. For example, we know:

In (SNG/SDF), = In (SNG/SBIT), - In (SDF/SBIT), (7)

which yields:

In (SNG/SDF), = (/311 - [331) -t- ([312 - [332) In (PNG/PDF) , (8) + (/313 - [33.0 In (SNG/SDF),_ i

The summary statistics for the interval from 1955 to 1972 are presented in Table 3. A brief check of the results indicates that the logit regressions have the expected

signs. The relative prices have negative coefficients, which implies, for example, that as the price of natural gas increases relative to the price of bituminous coal the share of natural gas would decrease relative to the share of bituminous coal. The coefficients of the lagged share ratios are positive and less than unity.

T A B L E 3 ESTIMATES OF FOSSIL FUEL SHARES

Fuel shares /~il /~i2 /~i3 R 2 D W SEE

In (SNG/SBIT), O. 125 ( 1.80)*

In (SRF/SBIT), O. 103 (0-31)

In (SDF/SBIT), - O. 123 ( - 0 - 2 9 )

In (SSG/SBIT), - 0.032 ( - 0 . 1 9 )

In (SK/SBIT), - 1.232 ( - 2 . 1 2 ) *

In (SLG/SBIT), - 2.03 ( - 2 . 5 1 ) *

In (SPC/SBIT), - 0-232 ( - 0 . 8 2 )

- 0 . 1 1 7 0.978 0.949 1.45 0.0751 - 1.13) (15.72)* - 0 . 2 4 0 0.978 0.635 1-64 0.0770 - 1.72)* (4.83)* - 0 . 5 2 0 0~713 0.749 2-04 0-1085 - 1.03) (2.33)* - 0.224 0.828 0.907 1-63 0-0577 - 2 . 1 5 ) * (6.17)* - 0 . 0 5 5 0.650 0.545 1.62 0.1376 - 0 . 3 4 ) (4.20)* - 1.005 0.229 0.569 1.90 0.2378 - 2 . 7 9 ) * (0-95) - 0 . 1 4 9 0.843 0.912 1.82 0.1931 - 0 - 5 9 ) (11.01)*

" Note: N u m b e r s in parentheses are t-statistics. * Signif icant at the 5 9o level.


Simulations In order to test the performance of the energy demand model for the industrial

sector, the total demand equation (eqn (1)), the potential demand equation (eqn (2)), the electricity-fossil fuel share equation (eqn (5)), and the fossil fuel share equations (eqns (6)) are combined into a model and solved over the historical period. The quantity levels for each fuel are then determined by multiplying the share of electricity and fossil fuels by total demand (TOTFL). A similar procedure is used to calculate the quantity levels for fossil fuels using their shares multiplied by the level of fossil fuels. The estimated values for eqns (1), (2), (5) and (6) form a complete model which can be solved dynamically over the period from 1955 to 1972. These simulations were deterministic because the estimated equations were assumed to be without errors. In performing the simulations the actual values for all variables were entered for 1955 and earlier periods. After 1955 all variables except prices and industrial production were endogenously determined within the model. The model produces simulated values of the demand for each of the fossil fuels and electricity consumed in the industrial sector. These simulated values are compared with the actual values for fossil fuels and electricity. The relevant error measures from this simulation are shown in Table 4. The means of the actual series (M), the mean absolute error (MAE) and the mean absolute error as a percentage of the actual mean (MAE ~/oM) are reported. (For a further interpretation of MAE and MAE ~o M see Fair. z)

TABLE 4 ERROR MEASURES FOR 1955 To 1972 FOR FUELS

(in thousand trillion BTU's)

M MAE MAE % M

Bituminous coal 4791.06 189.28 3-95 Natural gas 7123.02 262-81 3-69 Residual fuel 1215.03 120.82 9.94 Distillate fuel 403-41 36-41 9.03 Kerosene 126.91 18.38 14.48 Still gas 815-26 31-26 3.83 Petroleum coke 223.95 24.73 11.04 Liquefied petroleum gas 84.34 12.37 14.67 Electricity 1868.25 11.02 5.94

Note: The error measures are calculated according to the following formulae, where A, denotes actual value. P, the value predicted by the simulation and T the number of observations contained in the simulation interval:

-/

F = I

1 MAE =

t = l

M % MAE = M/MAE

Other statistics such as root mean square error and the Theil U-statistics are avai}able from the authors.

284 J O H N K R A F T , A R T H U R K R A F T

Elastici t ies

F r o m the e s t i m a t e d logi t r egress ions we a re ab le to c o m p u t e shor t - and l o n g - r u n

d e m a n d e las t ic i t ies w i th respec t to c h a n g e s in the pr ice o f each fuel. W h i l e the own-

pr ice e las t ic i t ies for each fuel a re d i f ferent , the c ross -p r i ce e las t ic i t ies a re i n v a r i a n t

wi th respect to the d e n o m i n a t o r o f the e s t i m a t e d logi t regress ion . T h e p r o o f for this

p r o p e r t y a p p e a r s in the a p p e n d i x . T h e s h o r t - r u n o w n and c ross e las t ic i t ies for each

fuel a re p r e sen t ed in T a b l e 5 and the l o n g - r u n o w n and c ross e las t ic i t ies a re p r e sen t ed in T a b l e 6.

TABLE 5 SHORT-RUN OWN- AND CROSS-PRICE ELASTICITIES

Quantities Price elasticities PELC PBIT PRF PDF PNG PK PSG PLG

Electricity - 1-662 0.305 0 - 1 0 3 0.083 0 - 6 5 9 0.250 0-250 0-250 Bituminous coal 0.058 -0.421 0.056 0.256 0.114 0.022 0.022 0-022 Residual fuel 0.058 0.509 -0.087 0.256 0.114 0.022 0.022 0.022 Distillate fuel 0.058 0.923 0.056 - 1.318 0.114 0.022 0.022 0.022 Natural gas 0.058 0.325 0.056 0.256 -0.339 0-022 0.022 0.022 Kerosene 0.058 0-154 0.056 0.256 0.114 -0.108 0.022 0.022 Still gas 0-058 0.268 0.056 0.256 0.114 0.022 -0.667 0.022 Liquefied petroleum

gas 0-058 0 - 1 6 8 0 - 0 5 6 0.256 0 - 1 1 4 0.022 0.022 - 1.238 Petroleum coke 0.058 0.018 0.056 0.256 0.114 0.022 0.022 0.022

TABLE 6 LONG-RUN OWN- AND CROSS-PRICE ELASTICITIES

Quantities Price elasticities PELC PBIT PRF PDF PNG PK PSG PLC

Electricity - 1.635 0.395 0.115 0 . 1 0 1 0.852 0.208 0.208 0.208 Bituminous coal 0-118 - 1.486 0 - 2 1 9 0.462 0 - 8 3 5 0.067 0.067 0.067 Residual fuel 0.118 2.126 - 3.389 0.462 0.835 0 - 0 6 7 0.067 0.067 Distillate fuel 0.118 0.323 0.219 - 1.763 0.835 0.067 0.067 0.067 Natural gas 0.118 0.272 0.219 0.462 -0.924 0.067 0.067 0.067 Kerosene 0.118 0.172 0.219 0 - 4 6 2 0-835 -0.111 0.067 0.067 Still gas 0.118 0.279 0.219 0.462 0.835 0.067 - 1-189 0-067 Liquefied petroleum

gas 0-118 0 . 9 4 1 0.219 0.462 0.835 0.067 0.067 - 1.237 Petroleum coke 0.118 0.049 0.219 0.462 0.835 0.067 0.067 0.067

W h i l e all o f the own and c ross e las t ic i t ies a re o f the co r r ec t s ign, th ree th ings

shou ld be p o i n t e d out . F i r s t , for any given pr ice the c ross e las t ic i t ies a re iden t ica l excep t in the case o f the pr ice o f coal . Th i s is a p r o p e r t y o f the logi t f o r m u l a t i o n (see

the append ix ) . C o a l has d i f fe ren t c ross e las t ic i t ies because coa l is the n u m e r a i r e o f

the logi t r egress ion . S e c o n d l y , the c ross e las t ic i t ies for ke rosene , still gas, l iquef ied p e t r o l e u m gas and p e t r o l e u m c o k e are iden t ica l because the same pr ice was used for the f o u r fuels (see above) . Th i rd ly , n o r m a l l y we w o u l d bel ieve apr ior i t ha t the pr ice

e las t ic i ty o f d e m a n d s h o u l d b e c o m e la rger as one m o v e s f r o m the shor t run to the

long run. Th i s is n o t t rue in all i ns t ances if one c o m p a r e s the e las t ic i t ies r e p o r t e d in


Tables 5 and 6. Some own elasticities declined in the long-run--namely electricity and liquefied petroleum gas. The distillate fuel elasticity was the only cross elasticity for a major fuel which experienced a decline in the long run. The explanation for some of the decline could be attributed to the model formulation which is a hierarchical computation. An increase in the price of any fuel not only influences the price of that fuel but influences the split between electricity and fossil fuels through its weighted average price and the total demand for fuel for industry via its weighted average in TOTPR.

There is one final test to determine the price elasticities of demand. The price elasticities of demand for any given model should conform to the following conditions. First, all own-price elasticities of demand should be negative. Our model satisfied this condition. Secondly, the cross elasticities of demand should be positive. They are positive in all classes. Thirdly, any set of price increases of N fuels should not lead to higher demand for all N fuels, in any hierarchy. This condition holds only if the matrix of own- and cross-demand elasticities is negatively invertible. Note that the first and second conditions are not sufficient to ensure the third condition. Within the fossil fuel hierarchy the major fuels component of the industrial energy demand model conforms to our three conditions. (Electricity is not in the fossil fuel hierarchy and is thus excluded. Also, distillate is chosen over still gas because still gas is a gas produced and consumed internal to the refining process.) For example, a matrix (X) of elasticities for natural gas, bituminous coal, residual fuel and distillate fuel is defined as follows:

- 0 . 9 2 4 0.835 0-835 0-835q

0-272 - 1.486 2.126 0.323 /

X = 0.219 0-219 -3 .389 0.219 /

0-462 0.462 0.462 - 1.763~

In matrix X the own elasticities are read across the diagonal. The own elasticities are all negative and the cross elasticities are positive. The third condition mentioned above holds as the inverse of X contains no positive elements:

l -9.011 -8 .447 -8 .457 -6 .876-]

-4 .001 -4-573 -4 .300 - 3 . 2 7 2 1 X inverse /

- 1.079 - 1.080 - i.359 -0.879[ /

-3"692 -3 .695 -3"699 - 3 " 4 5 7 /

Thus, the major fuel elasticities for our model satisfy the three properties for demand elasticities.

CONCLUSIONS

In summary, we can say that fuel substitution possibilities do exist in the industrial


sector. A price increase of any one fuel should induce a decline in demand for that fuel whilst stimulating the demand for its substitute. The elasticity of demand for total energy in the industrial sector is -0-0973 in the short run and -0 .3258 in the long run. Because the cross-elasticities are non-zero, fuel substitution possibilities exist between electricity and the fossil fuels. Finally, according to the theorem of the dominant diagonal, if the prices of all N fuels increase, the total demand for energy will not increase.

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APPENDIX

Assume the dependent variable of the logit regression is a share ratio (SJS~) where the shares are constrained such that

~--~S i = 1"0

i=1 i=j

and 0 < Si < 1

The independent variables are the price ration (PJP~) and the lagged share ratio. If Q,ot is equal to the sum of the quantities Q~,j = 1 . . . . . n, associated with the shares S t, then the relative share ratios are functions of relative prices and


Qtot = ) , Q~ j = l

S L : f ( e l ' ~ s. \ P.:/

: f ? ' 2 ) Sz \PzJ

The absolute quantities Qj, having already solved for S., are

Q.(P1 . . . . . P.) = Q,,(P) = s . * Q,o,

Q,(?, ..... ?.)=Q.(?) \ s . j Q.(e) \ ? . :

02(P, . . . . . P . )=Q. (P)* ~ . =Q.(P)* \ p . j

Q.- I(P, . . . . . P . ) : Q . ( P ) * = Q " ( P ) f i T )

i

Then f o r j = 1 . . . . . n - 1, the new quantity, Qj, due to a change in price, P~, i C j. yields

- \?.,: \?n,/ I' [Q. ,gl;)j) ~Pj)]

Q~ -~(QJ + Oi) ½ .(?) "2?,,] + Q.(P)* ~.

and by rearranging AQj _ Q.(P) - Q.(P)

Qj ½ (Q.(P) * + Q.(P))

which is independent of]'. Thus the cross elasticity ofa Qj with respect to price Pi, i j is independent o f j and invariant with i. For the own elasticity the quantity change, Qi, due to a change in price, P~, gives

Q, ~(Q~ + Q~) ½(Q.(p)* ft. + Q.(P) \ p j


with i = 1, n, and is not independent of i. Thus the own elasticity is different from the cross elasticity.

In computing our elasticities it should be noted that three levels of elasticities may be computed. Let

S i = share of the ith energy input in a given sector Di = total demand for the ith energy input in a given sector T = total energy in that sector

The system elasticity reflects a change in demand for input i in response to a change in the price ofj . However, the change in pricej induces two responses in the system: a change in the total demand for energy in the sector and a change in the share of i within the sector. Thus the system elasticity is

s y s t e m ' S = ( share "~ (total "~ elasticity/ \ e l a s t i c i ty /+ \elasticity )

which can be proved readily since

Oi S i - or Qi=Si*Q,o , alot

and

aQi P j ( s s i , 8Qtot • "x P.i

OS_ i , P~ c~Q~o~ , Pj

= ?'P.i s i + OPj Q,o,

interfuel substitution and energy consumption in the industrial sector

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