A view from the macro side rebound, backfire, and Khazzoom–Brookes

Energy Policy 28 (2000) 439449A view from the macro side: rebound, back“re, andKhazzoomBrookesHarry D. Saunders*Managing Director, Decision Processes Incorporated 2308 Saddleback Drive, Danville, CA 94506-3118, USAAbstractThis paper attempts to delineate a few key insights extracted from theoretical macroeconomic considerations of the rebound issue.The goal has been to reduce these thoughts to a clear set of assertions that, if true, would be useful points of reference in the ongoingdiscussion despite their non-empirical nature. 2000 Elsevier Science Ltd. All rights reserved.Keywords: Rebound; Conservation; Growth theory1. Introduction sumptions so readily yield predictions of large reboundand even back“re.Macroeconomic theory has its perils as well as itspower. It happens to be relatively easy to “nd a theoret-ical basis for rebound and even back“re; as in theRather than dismissing neoclassical growth theory, thebetter solution is to understand what it is telling us, howit can go wrong and why, where it is useful and where not,sciences, however, economic theory must ultimately bow and how it can be adapted to generate reliable insightsto the exacting master of real-world evidence. A number consistent with empirical evidence. As a beginning, weof recent empirical studies have begun to establish a verystrong body of evidence that point to rebound e!ectsbeing relatively small * on the order of 510% (see fordemonstrate in this paper that powerful insights are to befound by careful application of top-down theoreticalmacroeconomic models of the neoclassical growth var-example Schipper and Grubb, 1998; Greening and iety.Greene, 1998). These are high-quality, compelling studies The pro!ered insights are these:that cannot be dismissed.This creates a di$culty for both theoreticians and 1. Rebound has a sound theoretical basis; however, itsempiricists. Many of the most important rebound-related magnitude and importance are an empirical ques-policy questions, such as global warming, require high- tion.level, theory-based macroeconomic tools. Such tools are 2. Back“re is not disallowed by theoretical consider-needed to examine policy remedies spanning multiple ations, and may occur in the real world in selectedeconomies and many decades. Microeconomic ap- aches and bottom-up empirical studies are not ideally 3. Back“re in theoretical models is not caused by a fail-suited to the task. Neoclassical growth theory is the ure to distinguish between fuel and energy services.obvious tool, but this is precisely where standard as- 4. Evidence of rebound or lack of it is obscured in* Corresponding author.E-mail address: (H.D. Saun-energy/GDP ratios.5. It is theoretically possible for energy/GDP ratios todecline even in the face of outright back“re.6. It is misleading to treat fuel conservation as a fuelsupply source.ders)As de“ned more formally in a later section, rebounda refers toa less than one-for-one correspondence between fuel e$ciency gainsand reduced fuel use. Back“rea is an extreme version of reboundwherein fuel e$ciency gains actually increase fuel use.7. The degree of rebound strongly depends on the fuelelasticity of substitution.8. The increase in GDP due to fuel conservation isprobably small.0301-4215/00/$ - see front matter 2000 Elsevier Science Ltd. All rights reserved.PII: S 0 3 0 1 - 4 2 1 5 ( 0 0 ) 0 0 0 2 4 - 0440 H.D. Saunders / Energy Policy 28 (2000) 4394499. Fuel e$ciency technologies that a!ect other non-fuelfactors generate substantial rebound and even back-“re.about the function f, is the basis for the neoclassicalgrowth model, due primarily to Solow (1956).In neoclassical growth terms, this fuel e$ciency gain10. The choice of production function in theoretical andempirical studies of rebound matters to the con-parameter is fuel-augmenting technical progressa. Itis the increase in the e$ciency with which fuel enters theclusions. production function (or the decrease in cost of fuel in the11. The Quebec City Hypothesis: because of rebound, cost function).the proper choice of global warming policy toolsrequires a deep understanding of the fuel elasticity ofsubstitution.Fuel conservation is the e!ect of this parameter on fueluse. Speci“cally, fuel conservation can be de“ned as theelasticity of fuel use with respect to changes in :(An historical note: the term KhazzoomBrookesaPostulate was “rst coined with the intent of creditingDaniel Khazzoom and Leonard Brookes with being the“rst in the profession to discuss the concept of rebounddln F“ . (3)dlnNote that fuel conservation so de“ned represents a de-(see Saunders, 1992). It could just as easily, and arguably cline in fuel use that is not costly to the economy (i.e., itmore accurately, be called the BrookesKhazzoom Pos- does not require a decrease in economic output totulatea. Both these researchers generously credit Jevons(1865) with being the “rst.)achieve a reduction in fuel input ). This is consistent withwhat most energy conservation advocates mean whenthey talk about conservation.Rebound is then de“ned as the quantity R:2. Some de5nitions and theoretical preliminaries R“ 1# . (4)In this paper we adopt the term fuel where others This quantity measures the percentage rebound: if theremight use energya, to distinguish physical fuel fromenergy services, a distinction that will be exploited later.Next, we de“ne fuel e$ciency gaina, fuel conserva-tiona, rebounda, and back“rea.At the macroeconomic level, the theory of energy de-is a one-for-one reduction in F due to , “! 1, andso R“ 0 (no rebound); if fuel is reduced only half as muchas the fuel e$ciency gain, R“ 0.5 (50% rebound); iffuel use is unchanged with a fuel e$ciency gain, R“ 1(100% rebound).mand almost always relies on economy-wide production Backxre occurs when fuel use actually increases asfunctions or their dual equivalent cost functions. Because a result of a fuel e$ciency gain. This corresponds tomany of the policy issues surrounding rebound contem-plate periods encompassing several decades, the long-R1 (greater than 100% rebound).term economic growth aspect of macroeconomic theoryis important. Neoclassical growth theory provides thelogical framework, and is used here. 3. The insightsSpeci“cally, we de“ne fuel ez ciency gain as the para-meter in the following formulation: The following items are put forth as insights into theissue of rebound. They derive largely from theoretical“ f (K, , F), (1)where K is capital, is labour, and F is fuel, is realeconomic output (roughly, GDP), and f is the economy- Note that this is a very general de“nition of fuel conservation thatwide production function.Note: because of duality, could also be de“nedexactly equivalently asinherently contemplates notions of behavioural response and general-equilibrium e!ects * i.e., whatever might cause F to change in responseto a change in . It also contemplates time dynamics, re#ecting thelong-run change in the rate of fuel use F (say, annual consumption ofC“ g(p , p , 1 p ), (2) fuel) spurred by a one-time change in fuel e$ciency. In this paper,a neoclassical growth framework is used. Neoclassical growth theorydeals well with time dynamics but, owing to its assumption of a singlewhere p is the price of capital, p is the price of labour,and p is the price of fuel, C is the price of economicoutput (roughly, the GDP de#ator), and g is the econ-aggregatea output, does not speak to general equilibrium issues in thesense of completely describing market clearing prices and volumes formultiple output products and multiple consumers. (It is in a sensecomplete in dealing with the supply, demand, price and utility foromy-wide cost function. capital and labour factor inputs, however.) The purpose of these de“ni-Obviously, other factor inputs besides capital, labour,and fuel can be considered in either formulation.This formulation, when combined with a dynamic in-tions is to provide precision in later discussion. No claim is intendedthat the neoclassical framework can fully capture the evolution of theparameters here de“ned, even in a theoretical sense.Such as might be accomplished by consumers forgoing automobilevestment equation and a standard set of assumptions use to reduce gasoline consumption, for example.H.D. Saunders / Energy Policy 28 (2000) 439449 441considerations, but do take account of some empirical tains more energy per C than the direct energy pur-evidence. chase that was saved in the “rst place.While they are all presented as statements of fact, inreality some of them are closer to hypotheses thanproven fact. A good hypothesis is one that generatesclarity and learning whether proved true or false. Thegoal has been to reduce these thoughts to a clear set ofassertions that, if either proved or disproved, would beuseful points of reference in the ongoing discussion.Nonetheless, I believe the odds strongly favour theirbeing true.This is a theoretical argument, not an empirical one. Itis also incorrect. Aside from the fact that we have showncases where R1 (see Saunders, 1992, 2000a) that con-tradict this conclusion, the #aws in the argument can beunderstood more directly. The argument implicitly as-sumes that a fuel e$ciency gain directly a!ects only fueluse, not the use of other factors. This may be reasonable ifone has in mind retro“ts (e.g., replacing a light bulb witha more e$cient one), but is not valid if one considers the1. Rebound has a sound theoretical basis; however, itsmagnitude and importance are an empirical question.growth and evolution of the economys capital stock overtime (where new capital vintages are being created andare entering the economy). The ceteris paribus hidden inThe straightforward application of neoclassical growththeory reveals rebound (i.e., R0 in the de“nitionsabove). This phenomenon appears across a wide varietyof assumptions about production function speci“cation( f, above) and parameter values (see Saunders, 1992,2000a).From these analyses, the source of rebound is twofold:First, a fuel e$ciency gain increases the attractivenessof fuel relative to other factors needed for production. Inproduction function terms, it increases the marginal pro-ductivity of fuel and so stimulates counterforces favour-ing its use. In cost function terms, it does this by reducingthe cost of fuel.Second, a fuel e$ciency gain increases overall eco-nomic output, . Increased economic activity then dragsup fuel use. Equivalently, a reduction in fuel cost reducesthe overall price of output, increasing output for a “xedeconomy-wide expenditure level and thereby draggingup fuel use.There is no theoretical reason to suspect that theseLovinss argument does not apply then, and fuel use canreplace other factors (in new vintages), reducing expendi-tures on more than just fuel. The money saved can bemore than the direct energy purchase that was saved inthe “rst place.A speci“c example may be helpful. Picture a break-through space heating technology that is a device able toextract signi“cantly more heat per unit of fuel input thanthe technology currently available. Someone deciding toconstruct a new building with a “xed heat comfortabudget may then “nd it more economic to scrimp oninsulation expenditures and boost the size of the heatingunit. Such a boost could more than compensate for theunits fuel e$ciency gain. Theoretically, there is nothingpreventing the energy saving technology from increasingfuel use above where it would have been for a given levelof money spent. Back“re is not ruled out by argumentslike Lovinss.Furthermore, some researchers have reported empiricalevidence of back“re in selected instances (see Roy, 2000).e!ects are not real. Empirically, the size of R will bedetermined by the actual way the economy performs. 3. Back,re in theoretical models is not caused by afailure to distinguish between fuel and energy services.2. Back,re is not disallowed by theoretical consider-ations, and may occur in the real world in selected instances. Some have argued that back“re is seen in theoreticalmodels owing to a failure to distinguish between physicalStandard and innocuous-looking production functionspeci“cations readily generate back“re, where R1 (seeSaunders, 1992, 2000a). Again, there is no theoreticalreason, given the e!ects described above are real, thatthey could not in principle be large enough to produceR greater than unity.This is in contrast to arguments that have been ad-vanced claiming back“re is impossible. For example,Lovins (1998) states:fuel and energy services (see Howarth, 1997). The argu-ment is that it is energy services that are really input tothe production of output, not raw fuel.However, as shown in Saunders (2000a), Howarthsresult depends on his choice of production function forthe energy services sector (a Leontief function). A di!er-ent choice (CobbDouglas) leads to the re-emergence ofback“re. Therefore, it is not the distinction between fueland energy services that is the source of back“re intheoretical models.Though with “ 2, F increases 20% and increases4%; “ 10, F increases 520% and increases 47%. This is a short-term e!ect that ignores the long-term investment e!ect described inIn this case, reboundR is de“ned for each factor i as 1# , where“ (dln F)/(dln ), with i“ K or (or any other factor, such asmaterials, for which there might be factor-augmenting e$ciency gains).This represents the change in fuel use due to e$ciency gains in other,Appendix B. non-fuel, factors.H.D. Saunders / Energy Policy 28 (2000) 439449 445also true for neutrala e$ciency gains that apply to the other new output-producing activities that themselvesentire production function. This appears to hold across consume fuel.a wide variety of production function speci“cations (see Therefore, the increased capital e$ciency in the steelSaunders, 1992, 2000a). industry might be expected to increase fuel use econ-The consequence of this could be signi“cant. Any fuel omy-wide, partially or perhaps even fully o!setting thee$ciency technology that is not purely fuel-augmenting fuel e$ciency gains in the steel industry itself. Moreover,will have a strong rebound-inducing component. And it it is not only capital that has been made more e!ective inis likely that many fuel e$ciency technologies are simple the steel industry. Labour has experienced large gains inways of doing things smarter that use less of not only fuel, productivity, too. In the past 15 years, productivity hasbut also less of everything. In fact, fuel conservation tripled in the past 15 years, dropping from 10.1 man-advocates are commonly heard to claim that many con- hours per ton to 3.2 man-hours per ton in 1998. Theservation technologies not only reduce fuel use, but are combination of both labour and capital e$ciency gainsless costly to install than the technologies they replace. may well have had a substantial economy-wide fuel in-Unfortunately, such technologies could be strongly re- creasing impact, invisible when looking within the sectorbound prone. itself.Two real-world examples will illustrate the distinctions A second example is the information industry. Theinvolved here. One of the clearest is found in the evolu- technology gain in computation power is of course le-tion of the US steel industry in the last 25 years. The gendary. But consider it from the perspective of howenergy price rises of the 1970s created substantial prob- individual factors have been augmented. First, let uslems for this highly energy-intensive industry. For its de“ne for our purposes the outputs of this industry to bevery survival, the industry sought new energy-saving information storage (kilobytes of permanent storage) andtechnologies. It succeeded illustriously, with energy con- speed of processing (kilo#ops) . Now think of the com-sumption per ton of steel shipped reduced by about 45% puters of, say, the late 1950s and the factors needed tosince 1975. produce these outputs. These early computers typicallyA number of process improvements contributed to required several banks of vacuum tube-“lled cabinets inthis success, but a key component of the fuel producti- large, climate-controlled rooms. They might have storagevity gains was the aggressive introduction of modern capability in the order of a few kilobytes and speeds ofelectric arc furnaces (EAFs). EAFs are the corner- a few kilo#ops. The capital per unit output was thereforestone of the mini-millsa, small e$cient plants that to- very large. A person using such a computer would rely onday produce about 40% of US raw steel production. one or more operators (not to mention maintenanceAmong their advantages, EAFs allowed scrap steel technicians), so the labour per unit output was also veryto be recycled, bypassing the most energy intens- large. Similarly, the electricity consumption per unit out-ive step of the traditional process, the blast furnace. put was very large.However, the blast furnace is one of the most Consider now the laptop computer you may have incapital intensive steps as well. Therefore, this techno- your briefcase. It may have an output capability of sev-logy has increased the e$ciency of capital as well as eral gigabytes of storage and may contain chips capableenergy. of giga#ops of processing speed. The labour required toIn neoclassical growth models, when the e$ciency of generate this enormous output is one person * you.non-fuel factors is increased, fuel use will generally in- The capital cost may be a few thousand pounds sterl-crease, ceteris paribus. The intuition here is that aug- ing or less. And the energy use per kilo#op is tinymenting a scarce factor such as capital allows its use in compared to the early days, both because chips arephysically so much more energy e$cient than vacuumtubes (not to mention climate-controlled rooms), andA neutral gain is represented by a factor that multiplies thefunction f in Eq. (1). The de“nition of rebound i