DWC-8102GA-

Energy Demand Elasticities:Concept Evidence and Implications

Boum Jong Choe

Division Working Paper No. 1981-2

April 1981

Commodities and Export Projections DivisionEconomic Analysis and Projections DepartmentDevelopment Policy StaffThe World Bank

Division Working Papers report on work in progress and arecirculated for Bank staff use to stimulate discussion andcomment. The views and interpretations in a Working Paper arethose of the author(s) and may not be attributed to the WorldBank or its affiliated organizations.

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ENERGY DEMAND ELASTICITIES: CONCEPT

EVIDENCE AND IMPLICATIONS

April 2981

Prepared by: Bown Jong ChoeCommodities and Export Projections DivisionEconomic Analysis and Projections DepartmentDevelopment Policy Staff

Table of Contents

Page No.

INTRODUCTION .......... ............................ 1

CONCEPT . .......................................... 1

EVIDENCE . .......................................... 3Demand for Gasoline ....... ...................... 4Industrial Energy Demand ..... ................... 5Residential Energy Demand ..... .................. 6Total Energy Demand ....... ...................... 6

IMLICATIONS .......... ............................ 7

References ........... ............................ 8 - 9

ENERGY DEMAND ELASTICITIES: CONCEPT,

EVIDENCE AND IMPLICATIONS

INTRODUCTION

1. Likely response of energy demand to drastically higher energy pricesand increasing income is a major source of uncertainty clouding global energyprospects. Economists terms for the response are price and incomeelasticities of energy demand. Price elasticity of energy demand simply isthe percentage change in energy demand due to one percent change in energyprice when income is held constant. Income elasticity can be definedsimilarly, by interchanging income and energy price in the above definition.

2. This note is an attempt to highlight the major developments of thesubject in the recent literature. It ends with a brief discussion of theirimplications for global energy futures.

CONCEPT

3. The demand for energy of an economy consists of the demands forvarious end-use fuels such as gasoline, fuel oils, natural gas, coal andelectricity. These fuels are used either directly for transportation and fora variety of residential/commercial needs, or indirectly as a factor input forthe productive sectors and the energy transformation sector (e.g., electricitygeneration from coal). The different types of fuels compete with each otherand, jointly or individually, with other goods and services (directconsumption) or factors of production (indirect consumption). Under giventastes and production technology, the economy-wide demand for energy would bedetermined by the Level of output/income, the prices of various fuels, otherfactors of production and goods and services. This usually leads to a complexsystem.

4. To simplify the matter, most analysts make the assumption that thevarious fuels can be aggregated into "energy" and think that the users firstmake the choice between energy and other goods or factors of production andthen secondly make the choice of fuels within the energy aggregate. This ispossible only if the first choice does not affect the second choice, and viceversa. This assumption enables us to define the demand for energy and theprice of energy, and hence the elasticities of energy demand. Despite theusual index number problem associated with such aggregation, the aggregateelasticities -- for example, the price elasticity of total energy demand of aneconomy -- have the advantage of summarizing the demand characteristics interms of a few parameters.

5. If the price of one fuel goes up, the demand for that fuel decreasesbecause the users substitute non-energy goods and factors of production(output/factor substitution) and other fuels (interfuel substitution) in itsplace. The own-price elasticity of demand of a single fuel measures thepercentage change in the demand for that fuel as a result of one percentchange in its price, holding other prices constant. The percentage change inthe demand for one fuel as a result of one percent change in the price ofanother fuel is defined as cross-price elasticity of demand. The aggregate

price elasticity of energy demand is defined as the percentage change inaggregate demand due to one percent change in aggregate energy price. Becauseof interfuel substitution, one percent increase in the price of one fuel leadsto a greater percentage reduction in the demand for that fuel than thepercentage reduction in the demand for aggregate energy.

6. Factors other than income and energy price may also affect the demandfor energy. Since energy is rarely used without utilization of capitalequipment, technological progress which improves energy efficiency of capitalstock would be an important determinant of energy demand. Other relevantfactors would be tastes and life-style, geographic size of a country, socio-economic structure and weather. Some of these factors, however, areinterrelated. An increase in energy prices could induce energy-savingtechnical progress, taste changes toward more "energy diet," and changes inoutput structure toward less energy-intensive products. It is a stylized factthat income growth within a certain range has been associated with increasingshare of industrial output which is generally more energy-intensive thanagriculture and services. Income and price elasticities should, in principle,account for all changes in energy demand resulting either directly orindirectly from income and price changes respectively.

7. However, it is in fact problematical whether we can attribute pastand future structural changes--technological progress, changes in tastes andoutput structure, etc. - to either income or price changes, or both. In thelong run the structural changes become firmly imbedded in the system and itbecomes difficult to attribute the changes to any of the external factors.

8. The price variable- in any demand analysis should be the priceactually paid by the consumer. Thus the retail prices of fuels would form therelevant price variable for most of direct energy consumption; for industrialusers, it would most often be the wholesale prices. Because of the lack ofretail price information, price elasticity of energy demand has sometimes beendefined with regard to prices at various stages of transaction before finalconsumption. This has been a source of confusion. Primary price elasticityis defined with respect to the international export prices such as the OPECcrude oil price. Secondary price elasticity is defined with respect to theprice at the wholesale level, before putting on any taxes. Retail priceelasticity is defined in terms of the price actually paid by the consumer.

9. Usually, the retail price elasticity is larger than the secondaryprice elasticity, which in turn is larger than the primary price elasticity.This is a direct result of the relationship between the retail, secondary andprimary prices: retail prices are usually a certain markup over secondaryprices, and secondary prices over primary prices. The markups are eitheradditive, proportional or both. Generally, because of the additive component,a percentage price increase at the primary level will lead to less than apercentage price increase at the retail level. As the price at the primarylevel increases, the percentage price increase at the retail level wouldgradually approach that at the primary level. Therefore, one percent crudeoil price increase from 30 dollars per barrel, for example, would have greaterimpact on demand than the same percentage increase from 10 dollars per barrel,when the price elasticity of demand is the same at both points.

10. An important aspect of energy demand adjustments is that it usuallytakes a long time. Since energy is consumed through utilization of capitalstock, energy demand can be changed by: (1) adjustment of the utilizationrate of the capital stock, (2) adaptation and modification of the energyefficiency of existing capital stock, and (3) replacement of the capitalstock. The short-run elasticity refers to what can be achieved in one to twoyears, while the long-run elasticity means the totality of adjustments overtime. Long-run could be anywhere from about 10 years to 30 years. Dynamicadjustments to income changes would be fundamentally different from those toprice. The literature, however, often treats the short-run and the long-runprice and income elasticities in a parallel manner.

11. The dynamic path from the short-run to the long-run depends on therelative magnitude of the three types of adjustments at each point in time. Apriori, one would expect that the adjustment of capacity utilization ratewould occur mostly in the short-run and then quickly taper off as timepasses. On the other hand, replacement of capital stock can be achieved onlygradually over a long period. Retrofitting the existing capital stock willfall somewhere between the two extremes. The combined effect of the threetypes of adjustments defies an easy description. The dynamic path would bedifferent depending on the end-use sectors. Researchers often usedgeometrically distributed lags which assume that the initial impact of a priceincrease is the greatest and the impact diminshes geometrically over time.This formulation would be too restrictive in view of the foregoingdiscussion. An alternative is the polynomial distributed lags which canaccommodate any shape of dynamic path as far as it can be expressed as apolynomial function.

EVIDENCE

12. Studies of energy demand elasticities consist mostly of econometricestimation on the basis of historical data. The issue of relevance ofhistorical elasticities for projection takes on particular importance in thecase of energy demand because of the drastic increases in energy prices in therecent years. Experience since 1973 is too short to enlighten on the fullscope of adjustments. Recent studies can be thought of as efforts to overcomethis difficulty. Methodologically, the efforts were made in two differentdirections. One was to use cross-country data which contain greater variancein energy prices than intracountry data and the other was to use engineeringinformation to find the scope for saving energy.

13. Table 1 provides a summary of the range of the elasticity estimatesfor the three major sectors of final consumption and the economy-wide totaldemand. Some of the obviously extreme estimates were not incorporated in therange. Only the long-run elasticities are presented; the corresponding short-run elasticities will be dealt with in the discussion. Sectoral details areavailable only for the industrialized countries. Not enough developingcountries have the required data to permit an estimation of sectoral demandelasticities. Interfuel substitution elasticities are not presented herebecause the available evidence is weak and because they are not of primaryconcern in this note.

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Table 1: ENERGY DEMAND ELASTICITIES*

Income Elasticity Price Elasticity

Sectoral Demands /a

Gasoline Demand 0.7 . 1.2 -0.2 r(\., -1.5Industrial Energy Demand 0.6 -.a 1.0 -0.3 , -0.8Residential Energy Demand 0.4 -.s 1.4 -0.3 - -1.0

Total Energy Demand

Industrialized Countries 0.8 -. 1.1 -0.1 , -0.7/b

Developing Countries 1.2 r 1.9 -0.2 r-v -0.6

* Long-run and retail price elasticities unless otherwise noted./a For industrialized countries.7b Secondary price elasticities.

Source: Compiled from the references, Economic Analysis and ProjectionsDepartment.

Demand for Gasoline

14. Demand for motor gasoline received much attention in the literaturebecause of its importance in most of the industrialized countries. Gasolinedemand is unique in the sense that it does not have a serious competing fueland that its use is closely tied with automobile stock. Gasoline demandmodels usually consist of equations explaining the stock of automobiles, itsutilization rate and the average fuel efficiency of automobile stock.

15. Earlier studies of the demand for gasoline were based on time-seriesdata or intracountry cross-sectional time-series data. From annual time-series data of US or cross-sectional time-series of US states, Houthakker andVerleger [101, Chamberlain (2], Ramsey, Rasche and Allen (21] and McGillivray[17] obtained long-run income elasticities between 0.7 and 1.2 and long-runprice elasticities between -0.07 and -0.75. The corresponding short-runelasticities were 0.4 to 0.6 for income elasticity and -0.06 to -0.23 forprice elasticity. Quarterly data of US states estimated by Houthakker,Verleger and Sheehan [11] showed a low long-run price elasticity of -0.24. Itappears that the inclusion of the cross-section of states does notsignificantly alter the results. Also the geometric structure of demandadjustments used by these authors resulted in relatively large short-runelasticities, more than half of total adjustments occurring in the first year,which would contradict the automobile stock adjustment pattern.

16. Pindyck [20] and Griffin (8] employ time-series of internationalcross-section data pertaining to OECD countries. Their purpose is to make use

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of the wide variation of gasoline prices among the industrialized countries.Pindyck assumes geometric lags throughout, while Griffin uses polynomial lagsfor average fuel efficiency equation to account for the stock adjustmenteffect. As expected, the important difference from the earlier studies wasthe significantly larger estimate of long-run price elasticity of gasolinedemand, ranging from -1.3 to -1.5. Short-run price elasticities wererelatively small, only -0.05 to -0.1. Income elasticities were comparable tothose of earlier studies.

17. An attempt to explicitly incorporate the fuel efficiency standardsfor the US cars was made by Sweeny [231. He assumes that the fuel efficiencymandates by the US Government will be followed, while behavioral equations onautomobile purchases and travel are esimated from historical data. Sweeny'sincome elasticity of gasoline demand is similar to others; his short-run andlong-run price elasticities are -0.2 and -0.8 respectively, thus being onlyslightly higher than US time-series results. His model implies a dynamic pathof gasoline demand adjustments which strongly reflects the stock adjustmentaspect. Average fuel efficiency of automobile stock responds only slowly;efficiency improvement peaks in about 4 to 5 years and gradually tapers off.The impact of a gasoline price rise on mileage driven is the largest in thefirst year and then tapers off geometrically. The combined effect looks moreor less like a flat line.

Industrial Energy Demand

18. The demand for energy by the industrial sector is a derived demandfrom an aggregate production function relationship. Recent studies invariablyassume the existence of an energy aggregate as a factor of production alongwith capital and labor. Under this assumption and using the US manufacturingtime-series data, Berndt and Wood (1] and Hudson and Jorgenson [12] found thatenergy is a substitute for labor but a complement to capital. Berndt andWood found a long-term price elasticity of industrial energy demand of -0.4.The finding of capital-energy complementarity is a surprising one in view ofvarious engineering evidence that substantial energy saving can be achieved byusing more capital. Fuss [5] and Magnus [16], working with time-series dataof Canada and Netherlands respectively, also found capital-energycomplementarity and the same order of magnitude for long-run price elasticityof industrial energy demand.

19. International cross-section data, presumably more closelyrepresenting the long-run cost function, strongly repudiate the capital-energycomplementarity. Studies by Griffin [7, 8] and Pindyck (20] on the basis ofOECD time-series of cross-sections found strong capital-energysubstitutability as well as fairly large price elasticity of industrial energydemand of about -0.8. Griffin obtained a long-run income elasticity of aboutone for the OECD as a whole, while Pindyck's was a range from 0.6 to 0.9depending on countries. Nordhaus (18], using time-series of cross-sections ofsix developed countries, found a similar range for the long-run incomeelasticity. However, Nordhaus obtained long-run price elasticities of -0.48to -0.52 which are substantially lower than those of Griffin and Pindyck.

20. Evidence on the dynamics of industrial energy demand adjustments isextremely weak. Most analysts simply failed to attempt an estimation ofdynamic path. Griffin's estimation of a polynomial lag distribution yields a

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geometric type of adjustment which would be inconsistent with the capitalstock adjustment aspect.

21. Engineering studies of industrial sector energy conservationpotentials are numerous. These studies are usually highly specific to aproduction process. Engineers view of technological possibilities are oftenlimited to currently available technologies. This type of evidence couldproduce an underestimate of the true price elasticity. The engineeringevidence has yet to be integrated with the behavioral aspects of theindustrial sector demand

Residential Energy Demand

22. Studies of the residential/commercial sector energy demand present apicture similar to that of the industrial sector. Time-series estimates for acountry generally produced long-run price elasticities in the -0.3 to -0.5range. Joskow and Baughman [15] and Jorgenson [14] used the US time-seriesdata to obtain long-run price elasticity of -0.5 and -0.4 respectively, andlong-run income elasticity of 0.6 and 0.4 respectively. Time-series resultsobtained by Rodseth and Strom (22] for Norway and Fuss, Hyndman and Waverman[6] for Canada show long-run price elasticities in the -0.3 to -0.6 range, butlong-run income elasticities close to one.

23. International time-series of cross-sections results by Nordhaus [18],Griffin [8] and Pindyck [19, 20] show long-run price elasticities in the -0.7to -1.0 range, which are about twice the time-series results. The long-runincome elasticities are found to range between one to 1.4. Griffin also foundthat the dynamics of adjustments of this sector to higher prices can probablybe represented by a geometric lag structure. This is not surprising in viewof the fact that a large part of residential/commercial energy consumption isfor space heating and air conditioning, which involves relatively simpletechnology amenable to a quick fix (additional insulation, storm windows,installation of heat pumps, etc.). Adjustment of its utilization rate alsocould produce significant energy savings in a short run.

Total Energy Demand

24. The elasticities of total energy demand of the industrializedcountries are implied by the system of sectoral demand equations. The EnergyModeling Forum [4] conducted an experiment to compare aggregate demandelasticities implied by several representative energy demand models for theindustrialized countries. It showed that the long-run price elasticity at thesecondary level ranges from as low as -0.1 to a high of -0.7. Models based onstatistical parameter estimates tended to have higher long-run priceelasticity than those based on judgemental parameter estimates. If thejudgemental estimates are excluded, the range would be between -0.3 to -0.7.The aggregate income elasticity implied by the majority of the models rangesbetween 0.8 to 1.1.

25. For the developing countries, the aggregate elasticities shown inTable 1 were obtained from total energy demand relationship without anysectoral details. Studies by Choe (3] and Hoffmann and Mors (9] show that thelong-run income elasticity is significantly larger than one, with an averageof 1.3. The long-run price elasticity was estimated to be about -0.3 on the

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average. The low price elasticity estimate reflects the fact that it wasobtained from time-series variations, and thus should be interpreted as-amedium-term elasticity rather than a long-term elasticity. Hoffmann and Morsalso found that structural changes in developing countries -- increasing shareof industrial output -- are responsible for the greater-than-unitary incomeelasticity.

IMPLICATIONS

26. It is uncomforting to find out that the statistical and otherestimates of energy demand elasticities are widely divergent. To get an ideaabout what that means for the future energy demand, let us consider thefollowing numerical example.

27. Suppose that GDP of the industrialized countries will grow at 3percent per annum for the next 20 years. Then the industrialized countries'GDP in the year 2000 will be 81 percent higher than its 1980 level. Supposealso that the real price of energy at the secondary level increased 100percent as of January 1981. 1/ If the long-run income and price elasticitiesof aggregate energy demand are one and -0.1 respectively, then the aggregateenergy demand in the year 2000 will be 71 percent higher than its 1980 level(percentage change in energy demand - income elasticity x percentage change inGDP + price elasticity x percentage change in energy price). Tere weimplicitly assume that the 20 year period is the long-run. Let us now supposethat the true long-run price elasticity is -0.7 instead of -0.1. Then theaggregate energy demand in the year 2000 will be only 11 percent higher thanits 1980 level.

28. The above example merely illustrates the importance of priceelasticity when the price changes drastically. The statistical evidencesummarized above produced more stable estimates for income elasticity than forprice elasticity. From these studies it seems to be safe to conclude that theincome elasticity of total energy demand is not significantly different fromunity for the industrialized countries as a whole. For the developingcountries, the average long-run income elasticity of 1.3 appears to bereasonable in view of the structural changes these countries are likely toexperience.

29. The problem is the magnitude of the price elasticity. It seems to beinappropriate to use the low judgemental estimates because they are lower thanthe time-series estimates which probably reflect only short- to medium-termadjustments. The upper range of the price elasticity estimates revealed bysome of the recent international cross-sectional time-series studies are notwithout problems because cross-country variations include many structuraldifferences which cannot be explained by income, price and temperaturedifferences. The weight of evidence, however, appears to lean towards thecross-sectional time-series evidence on the ground that it reflects more ofthe long-term adjustments than time-series evidence.

1/ Preliminary energy price statistics of seven major industrializedcountries show that the average real price of energy to final usersincreased 95 percent between 1973 and 1980.

References

1. Berndt, E.R. and W. Wood,"Technology, Prices, and the Derived Demand forEnergy," Review of Economics and Statistics, 57 (August 1975), pp. 259-268.

2. Chamberlain, Charlotte,"Models of Gasoline Demand", unpublished workingpaper, U.S. Department of Transportation, Transportation System Center/SP-21, Cambridge, Mass., October 1973.

3. Choe, B.J.,"Energy Demand Prospects in Non-OPEC Developing Countries," inWorkshops on Energy Supply and Demand, International Energy Agency, Paris,1978, pp. 422-440.

4- Energy Modeling Forum, "Aggregate Elasticity of Energy Demand", Volume 1,Stanford University, Stanford, California, August 1980.

5- Fuss, M.A., "The Demand for Energy in Canadian Manufacturing," Journal ofEconometrics, 5 (1977) pp. 89-116.

6- Fuss, M.A., R. Hyndman, and L. Waverman, "Residential, Commercial and In-dustrial Demand for Energy in Canada: Projections to 1985 with Three Al-ternative Models," in Proceedings of the Workshop on Energy Demand, W.D.Nordhaus, ed., IIASA, Laxenburg, Austria, 1975.

7. Griffin, J.M., and P.R. Gregory, "An Intercountry Translog Model of EnergySubstitution Responses," American Economic Review, 66 (December 1976),pp. 845-857.

8. Griffin, James "Energy Conservation in the OECD: 1980 to 2000," BallingerPublishing Company, Cambridge, Mass.,1979.

9. Hoffmann, Lutz and M. Mors, "Energy Demand in the Developing World: Estima-tion and Projection up to 1990 by Region and Country," Regensburg University,Mimeographed, October 1979.

10. Houthakker, H.S, and P. Verleger, "The Demand for Gasoline: A Mixed Cross-Sectional and Time Series Analysis," unpublished paper, Data Resources Inc.,Lexington, Mass., May 1973.

11. Houthakker, H.S., P.K. Verleger, and D.P. Sheehan, "Dynamic Demand Analysesfor Gasoline and Residential Electricity," American Journal of AgriculturalEconomics, May 1974.

12. Hudson, E.A., and D.W. Jorgenson, "U.S. Energy Policy and Economic Growth,1975-2000," The Bell Journal of Economics and Management Science, 5, (Autumn1974), pp. 461-514.

13. Humphrey, D.B., and J.R. Moroney, "Substitution Among Capital, Labor, andNatural Resource Products in American Manufacturing." Journal of PoliticalEconomy, 83 (February 1975), pp. 57-82.

14. Jorgenson, D.W., "Consumer Demand for Energy," in International Studies ofthe Demand for Energy, W.D. Nordhaus, ed., North-Holland Publishing Co.,Amsterdam, 1977.

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15. Joskow, P.L., and M.L. Baughman, "The Future of the U.S. Nuclear Energy In-dustry", Bell Journal of Economics, 7 (Spring 1976), pp. 3-32.

16. Magnus, J.R., "Substitution Between Energy and Non-Energy Inputs in theNetherlands: 1950-1974," International Economic Review (forthcoming).

17. McGillivray, Robert G., "Gasoline Use by Automobiles," Working Paper 1216-2,The Urban Institute, Washington, D.C. December 1974.

18. Nordhaus, W.D., "The Demand for Energy: An International Perspective," inInternational Studies of the Demand for Energy, W.D. Nordhaus ed. North-HollandPublishing Co., Amsterdam, 1977.

19. Pindyck, R.S., "International Comparisons of the Residential Demand forEnergy," MIT Energy Laboratory Working Paper No.77-0230WP, Cambridge, Mass.,August 1977.

20. Pindyck, R.S., "The Structure of World Energy Demand". MIT Press, Cambridge,Mass., 1979.

21. Ramsey, J., A. Rasche, and B. Allen, "An Analysis of the Private and Commer-cial Demand for Gasoline," unpublished paper, Department of Economics,Michigan State University, February 1974.

22. Rodseth, A., and S. StrOm, "The Demand for Energy in Norwegian Householdswith Special Emphasis on the Demand for Electricity," research memorandum,Institute of Economics, University of Oslo, April 1976.

23. Sweeny, J., "The Demand for Gasoline in the United States: A Vintage CapitalModel," in Workshops on Energy Supply and Demand, International EnergyAgency, Paris, 1978, pp. 240-277.