A Study to Evaluate the Effect of Reduced Greenhouse Gas Emissions on Vehicle Miles Traveled. Final Report ARB Contract Number

Transcription

1 A Sudy o Evaluae he Effec of Reduced Greenhouse Gas Emissions on Vehicle Miles Traveled Final Repor ARB Conrac Number Principal Invesigaors: Kenneh A. Small, Ph.D. Deparmen of Economics Universiy of California, Irvine Kur Van Dender, Ph.D. Deparmen of Economics Universiy of California, Irvine Prepared for he Sae of California Air Resources Board, he California Environmen Proecion Agency, and he California Energy Commission March 2005

2 DISCLAIMER The saemens and conclusions in his repor are hose of he researchers and no necessarily hose of he California Air Resources Board, he California Energy Commission, or he Universiy of California. The menion of commercial producs, heir source, or heir use in connecion wih maerial repored herein is no o be consrued as acual or implied endorsemen of such producs. i

3 ACKNOWLEDGMENTS We are graeful o Chun Kon Kim and Sunyoung Jun for research assisance, and o David Bunch, David Brownsone, Tom Golob, Charles Lave, and he saff of he Air Resources Board and he Energy Commission for many helpful conribuions and suggesions. All responsibiliy for he conclusions and views expressed lies wih he auhors. This Repor was submied in fulfillmen of Conrac Number , A Sudy o Evaluae he Effec of Reduced Greenhouse Gas Emissions on Vehicle Miles Traveled, by Universiy of California a Irvine under he sponsorship of he California Air Resource Board and he California Energy Commission. Work was compleed as of March 31, ii

4 TABLE OF CONTENTS ABSTRACT... vii EXECUTIVE SUMMARY...viii 1. Inroducion Lieraure Defining he rebound effec Sandard definiion Exensions of he Sandard Definiion Measuring he rebound effec Aggregae Time Series Sudies Aggregae Cross-secional ime series Sudies Disaggregae Sudies Assessing he effeciveness of he CAFE regulaion Conclusions from he Lieraure Survey Theoreical Refinemens Srucural-Form and Reduced-Form Models The rebound effec Rebound Effec from Regulaory Change Rebound Effec from Change in Fuel Price Rebound Effec from Change in Vehicle Prices Daa Ses Aggregae Time Series Daa Aggregae Cross-Secional Time Series Daa Disaggregae Daa Naional Disaggregae Daa Ses California Disaggregae Daa Ses Daa Se Consruced for This Sudy Empirical Models on California-Relevan Daa Sysem of Simulaneous Equaions Specificaion of he Equaions iii

5 5.2.1 Dependen Variables Independen Variables oher han R E Variable o Measure CAFE Regulaion Error Srucure Auoregression and Auocorrelaion Esimaion of he Simulaneous Equaions Resuls Srucural Equaions Rebound Effecs and Oher Elasiciies Caveas Applicaion of Models: The Rebound Effec in California Saic Rebound Effecs Over Time Dynamic Rebound Effecs Facors Offseing he Rebound Effec: Congesion and New Car Prices Conclusions References APPENDIX A: Daa Sources and Descripive Saisics APPENDIX B: Variable Measuring Srengh of CAFE Regulaion iv

6 Lis of Figures Figure 1. The rebound effec for an exogenous change in fuel efficiency... 4 Figure 2. Effec of Income on Demand Curves for Vehicle-Miles Figure 3. Procedure o Projec Rebound Effec Figure B1. Desired and Mandaed Fuel Efficiencies 59 v

7 LIST OF TABLES Table 1. Usage Equaion Table 2. Vehicle Sock Equaion Table 3. Fuel Inensiy Equaion Table 4. Rebound Effec and Oher Price Elasiciies Table 5. Comparison of Usage Equaion Table 6. Rebound Effec wih Alernaive Specificaion of Income Table 7. Projeced Rebound Effec, California Table A1. Summary Saisics for Seleced Variables Table B1. Fuel Inensiy Equaion: Reduced Form Esimaed on Daa vi

8 ABSTRACT This repor presens measures of he size of he rebound effec, by which improvemens in fuel efficiency of vehicles may cause vehicle ravel o increase. We use aggregae cross-secional ime series daa for 1966 o 2001 on all 50 U.S. saes and he Disric of Columbia. Our model conains a measure of he hisorical effecs of he federal Corporae Average Fuel Economy (CAFE) sandards, which helps sabilize resuls compared o previous lieraure. Also, our ime series is longer han previous sudies, enabling us o beer discern he difference beween shorand long-run effecs. Our bes esimae of he rebound effec for he US as a whole, over he period , is 5.3% for he shor run and 26% for he long run. We also find ha he rebound effec declines wih income. Using he average value of income for California, he shor- and long-run rebound effecs are esimaed a 2.2% and 11.3%, respecively. Our mehodology permis projecions o fuure years, including dynamic projecions accouning for changes in income occurring a he same ime as owners are adjusing from he shor o he long run. These resuls enable researchers o predic how proposed sandards for greenhouse gas emissions in California may affec he amoun of vehicle ownership and ravel. vii

9 EXECUTIVE SUMMARY Background Under A.B. 1493, he California Air Resources Board is required o regulae greenhouse gas emissions from moor vehicles. Because such emissions regulaions resul in greaer fuel efficiency, he per-mile cos of operaing a moor vehicle is reduced. One of he echnical issues he Board faces is how much his reduced cos migh increase he amoun of driving underaken by California vehicle owners. Alhough here is pas research on his, i is no specific o California and has an uncerain validiy when applied o he fuure ime period in which regulaions would ake effec. Mehods This repor aemps o answer he quesion of how big he rebound effec is likely o be in California in he near fuure. I does so by esimaing an economeric model, based on 36 years of daa in 51 saes plus he Disric of Columbia, explaining he amoun of ravel by passenger vehicles as a funcion of cos and oher facors. I specifically considers facors ha differ beween California and oher saes, such as income and degree of urbanizaion. The sandard definiion of he rebound effec relaes ravel, usually measured as vehicle miles raveled (VMT), o fuel price and fuel efficiency. Our analysis akes ino accoun ha fuel efficiency is chosen by drivers, by posulaing a hree-equaion srucural model describing how consumers choose he number of vehicles o own, he amoun of driving, and average fuel efficiency. In our heoreical secion, we use he srucural model o disinguish hree channels hrough which fuel-efficiency choices may be affeced: regulaory changes, fuel price changes, and vehicle price changes. A lieraure review produces a number of guidelines for he empirical work. Firs, a reliable esimae of he rebound effec from hisorical daa requires careful accouning for he federal Corporae Average Fuel Economy (CAFE) sandards, because hey affec fuel-efficiency choices. Second, ime-series esimaes of he long-run rebound effec are very sensiive o he economeric specificaion. The mos compelling evidence from he lieraure we reviewed is from combined ime-series and cross-secional sudies, which sugges ha he long run rebound effec in he US is around 23%. In combinaion wih he lieraure review, our review of available daa leads us o op for an economeric esimaion of he rebound effec using aggregae cross-secional ime series daa. We are able o compile such a daa se for 1966 o 2001 on a cross-secion of U.S. saes and he Disric of Columbia. Such daa provide direc evidence of he aggregae effecs ha are of policy ineres, hey enable us o idenify California-specific effecs, and hey allow us o beer disinguish among various dynamic posulaes in order o esimae more precisely he difference beween long run and shor run rebound effecs. We formulae a measure of he effecs of he CAFE sandards as he naion-wide difference beween he sandards and desired fuel efficiency. Desired fuel efficiency is prediced using an viii

10 esimaed funcion based on pre-cafe daa. This CAFE variable seems o help sabilize resuls, which have shown considerable variaion in he lieraure. Our specificaion allows for ime-varying elasiciies and rebound effecs, o reflec he possibiliy ha he rebound effec declines over ime. Such a decline has been hypohesized because he share of fuel coss in oal per mile coss declines as vehicles become more fuelefficien and as he opporuniy cos of ime spen raveling increases, due o rising incomes and more congesion. We capure hese effecs by allowing he rebound effec o vary wih income and degree of urbanizaion. One disadvanage of our daa se is ha fuel efficiency does no vary much over ime and space, making i impossible o deermine is effec separaely from ha of fuel prices, which vary a grea deal. Therefore our sudy, like mos previous ones, relies on he heoreical assumpion ha people reac he same way o a change in fuel cos wheher i arises from a change in price or a change in efficiency. This is a reasonable assumpion because fuel coss, unlike coss of operaing various elecrical appliances, are highly visible as he mooris mus refuel regularly and he expense of doing so is clearly displayed. However i is an assumpion we are unable o es saisfacorily using hese daa. Resuls Our bes esimae of he rebound effec for he US as a whole, over he period , is 5.3% for he shor run and 26% for he long run he laer value being remarkably close o he consensus from he lieraure noed above. Furhermore, he rebound effec depends on income in he expeced manner, a resul no previously measured in he lieraure. A he value of income equal o he average in California, he rebound effec is considerably smaller: 2.2% in he shor run 11.3% in he long run. Addiional esimaion resuls, like he long-run overall priceelasiciy of fuel demand (-0.46) and he proporion of i ha is caused by mileage changes (55 percen) are very much in line wih he lieraure. Projecions o fuure years are inherenly uncerain because California per capia income is expeced o rise o values no seen in our sample. Neverheless our bes effor a making such a projecion yields a long-run rebound effec ha declines o abou 7.8% in 2009 and 4.4% in We also projec a dynamic rebound effec, showing as an example ha a permanen change saring in 2009 produces an effec on VMT ha sars small, grows gradually as behavior adjuss oward a long-run response, bu hen declines as rising incomes reduce he long-run rebound effec; he maximum rebound effec in his calculaion is 5.9%. Conclusion Our resuls show a long-run rebound effec ha is quie similar o ha of oher sudies when aken as an average over he US for Is dependence on income, however, implies ha i is considerably smaller for California when projeced o he years in which greenhouse gas regulaions will ake effec. Furhermore, our empirical specificaion permis ARB saff o make year by year projecions for any regulaory scenario hey migh wish o consider, a process ha has already been uilized in formulaing background maerial for he Board s consideraion of regulaions implemening A.B ix

11 1. Inroducion Our research objecive is o produce esimaes of he rebound effec ha are useful for analyzing he impac of policies relaed o reducions of greenhouse gas emissions from privae vehicle ranspor in California. The rebound effec (or ake back effec ) is usually defined wih respec o some form of energy consumpion, such as use of fuel or elecriciy. I refers o a siuaion where a regulaory or echnological change causes an improvemen in he energy efficiency of some equipmen (e.g. an air condiioner) ha is an inpu o he producion of a desired service (air cooling). This improvemen has he side effec of making he service iself cheaper. Assuming a downwardsloping demand curve for he service, he quaniy of service demanded hen increases (people keep heir houses cooler). This in urn causes a rise in he derived demand for he energy inpu (elecriciy), hereby offseing some of he direc effec on energy consumpion of he original change. The rebound effec can be defined as he difference beween he acual quaniy of energy demanded afer he change and he hypoheical quaniy ha would be demanded if he usage of he relaed service were consan. For moor vehicles, he energy inpu is fuel and he associaed service is ravel, ypically measured as vehicle-miles raveled (VMT). In his case he rebound effec arises because when vehicles are made more fuel-efficien, i coss less o drive a given amoun so VMT goes up. Tha in urn causes more fuel o be used han would be he case if VMT were consan; he difference is he rebound effec. Obaining reliable measures of he rebound effec is poenially imporan for choosing policy insrumens o reduce emissions of greenhouse gases from moor vehicles. This is because carbon dioxide (CO 2 ) accouns for a large fracion of he oal greenhouse gas emissions from moor vehicles, and here is a close link beween CO 2 emissions and fuel consumpion. Thus, California regulaions o reduce greenhouse gas emissions will likely, as a side effec, resul in increases in vehicular fuel efficiency, making i imporan o beer undersand possible rebound effecs. Mos of he lieraure on he rebound effec is saed in erms of fuel efficiency. Proposed California regulaions will address greenhouse gas emissions raher han fuel efficiency. We have formulaed our heory o address any regulaory acion ha includes a raher direc effec on fuel efficiency, wheher or no ha is is main inen. Since his is very likely o be a primary aspec of he final regulaions, our heory and empirical findings are appropriae o analyze hose effecs of greenhouse gas regulaions ha direcly affec manufacurers and consumers choice of fuel efficiency. For hese reasons, we refer o fuel efficiency in mos of our discussion, bearing in mind ha i is one componen of he full analysis of greenhouse gas regulaions. If he rebound effec is large, he effeciveness of regulaory acions ha improve fuel efficiency is diminished unless hey are accompanied by oher measures o increase he price of VMT, such as an increased fuel ax. By conras, if he rebound effec is small, fuel efficiency 1

12 sandards are relaively effecive while he ax increase required o achieve a given objecive may be so high as o be poliically infeasible (Greening and Greene, 1997). 1 In addiion, fuel efficiency sandards or oher greenhouse gas regulaions are likely o affec he price of new vehicles. This in urn ses up a number of marke reacions, including a endency o reduce he size of he vehicle sock and an increased average age of he sock. We accoun for he firs of hese effecs hrough an equaion predicing vehicle sock. We do no accoun for he average age of he flee or he effecs ha may have on driving and on emissions; we believe ha analysis requires a more micro-based model ha explains individual household vehicle purchase decisions. 2. Lieraure In his secion, we consider in some deph a represenaive sampling of lieraure analyzing he rebound effec for fuel use in moor vehicles. Each sudy is chosen o represen a paricular empirical approach. For oher lieraure surveys on he rebound effec and relaed issues, see Greening e al (2000) and Graham and Glaiser (2002). 2.1 Defining he rebound effec Sandard definiion The rebound effec for moor vehicles is ypically analyzed in erms of an exogenous change in fuel efficiency, E, measured for example in miles per gallon (e.g. USDOE, 1996). Fuel consumpion F (in gallons per year) and ravel M (vehicle-miles raveled per year) are relaed hrough he ideniy F=M/E. The demand for fuel consumpion is herefore naurally viewed as a derived demand, arising from he demand for vehicle-miles raveled (VMT). The laer depends (among oher hings) on he variable cos per mile of driving, which includes he per-mile fuel cos, P M P F /E, where P F is he price of fuel. Therefore he demand for fuel can be wrien as: (, ) F P E F ( ) ( ) = Mˆ P ˆ M M PF / E E = E. (1) We use he noaion M ˆ () for his funcion as a reminder ha i is a very paricular form of a demand funcion: namely, one ha depends on fuel price and fuel efficiency only hrough heir raio, and ha does no depend on oher hings ha migh be influenced by fuel price and fuel efficiency. This funcion is derived more precisely in Secion Moreover, he exbook case for defending axes over sandards is less srong when accoun is aken of some realworld deviaions from exbook assumpions such as imperfec compeiion in he passenger car marke and decision-making coss for consumers. See CBO (2002) for a comparaive analysis of policy insrumens o reduce gasoline consumpion. 2

13 The simples version of he rebound effec follows immediaely from (1). The elasiciy of fuel demand wih respec o fuel efficiency, εf, E, is equal o he elasiciy of he numeraor of (1) minus ha of he denominaor (boh wih respec o E). The laer is one. The former, if fuel price is consan, is equal o he elasiciy of VMT wih respec o PM, which we denoe as εm,pm, imes he elasiciy of PM wih respec o E, which is 1. To summarize: ε = 1 ε. (2) FE, MPM, Since boh εf, E and εm,pm are negaive, he magniude (i.e. absolue value) of εf, E is smaller han one due o he effec of per-mile fuel cos on ravel (εm,pm). Equaion (2) ells us how o decompose a change in fuel consumpion ino a direc effec and a rebound effec. Muliplying boh sides by a fracional hypoheical change E/E in fuel efficiency, (2) implies ha fuel use declines as follows: F ε E E E FE, = + ε MPM,. (3) F E E E The firs erm on he far righ-hand side of (3), E/E, is he proporion ha fuel consumpion would be reduced in he absence of any changes in VMT. Le us call his he direc impac of he efficiency change on fuel consumpion. The second erm, which is negaive, is he ake-back effec from increased VMT: he reducion is less han he direc impac by his amoun. We may define he rebound effec, a posiive amoun, as he negaive of his ake-back effec: or, as a fracion of he direc effec, E B = εmpm, (4) E b = ε M, PM. (5) The siuaion is depiced graphically in Figure 1. In he upper porion, curve DM represens he demand for VMT as a funcion of per-mile fuel cos, PM. The lower porion shows fuel consumpion as a funcion of VMT a wo differen values for fuel efficiency: E 0 and E 1. Le efficiency increase from E 0 o E 1. If VMT remained consan a is iniial value, M 0, fuel consumpion would decline by amoun F 0 (he direc effec). Bu in fac VMT increases from M 0 o M 1, raising fuel consumpion by amoun R. The oal reducion in fuel consumpion is hen no F 0 bu only F= F 0 R. (In fac, here is no guaranee ha F is even posiive; heoreically, i could represen a rise in consumpion, in which case he rebound effec would be bigger han he direc effec.) The rebound effec is R in absolue erms, or R/ F 0 in relaive erms. 3

14 Figure 1. The rebound effec for an exogenous change in fuel efficiency P M P F /E 0 D M P F /E 1 F M 0 M 1 M M/E 0 F 0 F R M 0 M 1 M M/E 1 A problem wih he heory in equaions (1) (3) is ha fuel efficiency E is acually chosen by users, along wih M, raher han being se by purely echnological or regulaory consideraions. This fac has been considered by US Deparmen of Energy (1996, p. 5-11) in inerpreing he empirical measuremens of he rebound effec. Mos of hese measuremens have aken advanage of changes in fuel price PF more han changes in efficiency E. Therefore, an obvious quesion is: wha connecion is here beween he fuel-cos-per-mile elasiciy of ravel, εm, PM, and he price elasiciy of demand for fuel, εf, PF? The answer can be deermined from equaion (1) by wriing E as a funcion E(PF) of fuel price, wih elasiciy εe, PF: (, ) F P E F ˆ P F M E P =. (1 ) E P ( F ) ( ) Equaion (1 ) shows ha εf, PF can be decomposed ino wo pars: he elasiciy of ˆM wih respec o PF minus he elasiciy of E wih respec o PF. The second par is εe, PF by definiion. The firs par is found using he chain rule for differeniaion on he numeraor of (1 ): i is jus εm, PM imes he elasiciy of (PF/E) wih respec o PF, which is one minus εe, PF. Collecing hese resuls: F ( 1 ) ε = ε ε ε. (6) F, PF M, PM E, PF E, PF 4

15 This equaion also appears in USDOE (1996, p. 5-11). I provides an alernae way o measure he rebound effec, wihou ever measuring VMT elasiciies direcly. Raher, one measures he elasiciies of fuel consumpion and fuel efficiency, boh wih respec o fuel price; one hen solves equaion (6) for εm, PM, which as already explained is he proporional rebound effec: ε MPM, ε = FPF, EPF, 1 ε + ε EPF,. (7) To he bes of our knowledge no one has acually esimaed he rebound effec his way, bu USDOE (1996, Table 5-2) uses (6) o relae a se of preferred elasiciy esimaes o each oher. 2 Also, equaion (6) makes i very clear ha since empirical esimaes of εf, PF and εm, PM differ grealy, 3 i mus be ha εe, PF is considerably differen from zero; his means we should no ignore he dependence of E on PF in using (1 ) o guide empirical esimaes. Once we recognize ha E depends on PF, we mus consider more closely he deerminans of ha relaionship. When we do so, we realize ha E is chosen by consumers and/or producers. This has deeper implicaions, which make he very meanings of he elasiciies in (2) ambiguous. This is because any reasonable heory of how E responds o fuel price would recognize ha he answer depends on how much people ravel. Consumers are unlikely o spend exra money on ligh-weigh maerials and special drive rains, or o give up desired feaures such as engine power and luggage space, in order o improve fuel efficiency for a lile-used vehicle; bu hey may well do so for a vehicle hey expec o drive a lo. Thus E depends on M. Bu he logic behind he elasiciy εm, PM in equaion (2) is hen circular: M depends on PM, which depends on E, which in urn depends on M. More generally, policies such as hose aimed a carbon dioxide emissions, affec a complex se of decisions by manufacurers, such as model design and pricing, and by consumers, such as which models o purchase and how much o drive each one. Togeher hese decisions influence all he quaniies involved in (2). I is hese kinds of complexiies ha we aemp o resolve in he Secion 3. Meanwhile, we can see righ away ha ignoring he dependence of E on PF causes he rebound effec o be overesimaed. According o he argumen jus made, any unobserved facors ha cause M o be large (perhaps an unusually long commue) also cause E o be large (as he commuer chooses vehicles o reduce he fuel cos of ha long commue). This creaes a negaive correlaion beween M and PM PF/E, in addiion o ha which is in he demand funcion for vehicle-miles, M(PM). Thus he exen of he negaive effec of PM on M will be overesimaed. Equivalenly, he magniude of εm, PM, he rebound effec, is overesimaed. 2 There is a ypographical error in he las line of USDOE (1996, Table 5-2): recen esimaes of he fuel price elasiciy of fuel economy should read raher han , as is clear from he ex a he op of page 5-14 and also is necessary for consisency wih USDOE s equaion (2) on p. 5-11, which is he same as our equaion (6). 3 See USDOE (1996, pp and 5-83 o 5-87); Graham and Glaiser (2002, p. 17); and he review in Parry and Small (2002, pp ). 5

16 2.1.2 Exensions of he Sandard Definiion Besides he difficulies creaed by he endogeneiy of E, here are several oher simplificaions in he sandard definiion jus given ha need o be relaxed in a more general reamen. Firs, fuel cos is jus one of several componens of he cos of using moor vehicles. One of he mos imporan is ime coss, i.e. he opporuniy cos of he ime spen by he occupans making heir rips. Since ha cos probably grows wih rising incomes, i is quie likely ha i becomes a larger porion of he cos of using vehicles over ime in a growing economy. This would make he elasiciy of VMT-demand wih respec o fuel cos diminish over ime, as fuel coss become relaively less imporan (Greene, 1992). For example, he cos of operaing rucks is dominaed by driver wages, making fuel relaively unimporan in decisions by firms abou how o use heir vehicles and in decisions by shippers abou quaniy and mode of shipmens. More broadly, he robus growh in VMT over he las half cenury is presumably due in par o he dominance of ime and convenience in people s ravel decisions, suggesing ha changes in fuel coss are likely o play only a minor role. Alhough for simpliciy our heoreical secion does no incorporae ime rends or rising incomes, i is easy o do so in he empirical work we propose by specifying he empirical equaion so as o allow he relevan elasiciy o change wih income or over ime. A second exension, also relaed o ime coss, is o recognize ha raffic congesion may be affeced by he VMT changes ha creae he rebound effec. This effec may or may no be included in empirical measuremens of M(PM), depending on he specificaion used. In any case, one may wan o esimae explicily wheher and how much congesion is increased as a resul of rebound effecs. If congesion is subsanially increased, he rebound effec would be diminished (because he endency o increase VMT will be dampened by any increase in congesion), ye even a smaller rebound may be of greaer concern due o he cosly naure of congesion. Of course, any congesion increase ends o be somewha self-limiing because congesion iself is a deerren o more ravel. A hird exension would be o consider ha he price of fuel migh be affeced by policies affecing fuel demand, especially in a sae as large and geographically isolaed as California. Suppliers of California specific fuel mixes appear o be operaing a or near capaciy (USDOE, 2003). Furhermore, capaciy may o some exen be sraegically deermined by producers who have some influence over price. Thus a reducion in fuel demand following an improvemen in he fuel efficiency of cars may reduce he price of fuel. This endency would make he rebound effec sronger: no only does a vehicle use less fuel per mile, bu fuel iself also becomes cheaper. 2.2 Measuring he rebound effec This subsecion considers sudies ha esimae he funcion M(PM) in he numeraor of equaion (1) or (1 ). Such sudies aemp o explain vehicle-miles raveled on he basis of a number of variables, including he fuel cos per mile, PM or some proxy for i. As described in he previous subsecion, he rebound effec can be defined in fracional erms as he negaive of he elasiciy of his funcion. 6

17 I is convenien o divide sudies ino hose using aggregae daa and hose using micro (individual) daa. The former includes boh pure ime-series sudies (one observaion per year) and aggregae cross-secional ime series sudies which combine cross-secional and ime series variaion (e.g. one observaion per sae per year) Aggregae Time Series Sudies One group of sudies akes advanage of changes in fuel prices and fuel efficiency over ime o measure he effec of PM on vehicle-miles raveled. One of he mos carefully done is ha by Greene (1992), using US ime series daa for Greene considers wo complicaing facors. Firs, some or all of he variables may affec VMT slowly, hrough lagged effecs, if individuals respond only slowly o changed circumsances. Second, he unobserved influences on VMT ha are capured by he error erms may be auocorrelaed, i.e. errors for observaions close ogeher in ime may end o move ogeher; his could be caused by unobserved facors ha persis over ime, such as lifesyle facors, or by errors in daa measuremen ha are similar from one year o he nex. Greene finds he rebound effec over he enire ime period o be beween 5 and 15 percen boh in he shor and long run, wih a bes esimae of 12.7 percen. Lagged effecs are found no o be imporan, which is why he long-run effec is he same as he shor-run. 4 He also finds i is imporan o accoun for auocorrelaion, which is quie srong, he correlaion beween errors in adjacen years being esimaed a Failing o accoun for auocorrelaion resuls in spurious measuremens of lagged values; Greene believes his has misled oher researchers o find long-run effecs o be spuriously greaer han shor-run effecs. 5 Finally, Greene finds some evidence ha he fuel-cos-per-mile elasiciy declines over ime, hus enaively confirming he firs possibiliy menioned in Secion There are wo lines of evidence. Firs, Greene noes ha in a linear model he elasiciy necessarily declines over ime because P M has decreased and VMT increased over mos of he period; and he finds lile difference in qualiy of resuls beween a linear and a non-linear specificaion. Second, in he double-log model ha Greene presens for mos of his resuls, in which he elasiciy iself is an esimaed parameer, he ries specificaions in which his elasiciy (and hence he rebound effec) is allowed o differ across ime periods; hese resuls show subsanial declines in he rebound effec, from 27.4 percen in o 5.9 percen in These declines are saisically significan a he 10 percen bu no a he more rigorous 5 percen significance level. Given he sample of only 24 years forming he basis for his es, i is no surprising ha i is only 4 However, Greene s explanaion demonsraes he difficuly of inerpreing equaions in which fuel cos per mile (P F /E) is a variable, when in fac E is exogenous. Greene noes ha in he long run consumers reac o an increase in fuel price in par by increasing fuel efficiency. Bu raher han reducing he long-run effecs, as he argues, his ideally would call for a specificaion ha permis fuel efficiency o reac wih a lag o changes in fuel price. 5 Anoher sudy ha found auocorrelaion is ha by Blair, Kaserman, and Tepel (1984). They obain a rebound effec of 30 percen, based on monhly daa from Florida from 1967 hrough They did no esimae models wih lagged variables. 7

18 of marginal saisical significance, and we regard he very large decline in magniude as moderaely srong evidence for a shif over ime. Jones (1993) re-examines Greene s daa, afer including observaions for 1990, focusing on model selecion issues in ime series analysis. Jones confirms ha he auoregressive model seleced by Greene is saisically valid. However, alernaive specificaions, noably hose ha include lagged dependen variables, are accepable as well. Such models do produce long-run esimaes of he rebound effec of abou 31%, exceeding he shor-run esimaes of ca. 11%. 6 In Jones own inerpreaion, he resuls confirm Greene s esimaes of he shor-run rebound effec bu weaken Greene s conclusion regarding he absence of a larger long run effec. Schimek (1996) uses daa from a longer ime period han Greene (1992) and finds a similarly small or even smaller shor-run rebound effec. Bu he obains a larger long-run rebound effec, abou 30 percen, similar o Jones (1993). In Schimek s preferred resuls, he shor-run and long-run rebound esimaes are 7 and 29 percen. 7 He accouns for federal Corporae Average Fuel Economy (CAFE) regulaions by including a ime rend for years since 1978, and he also includes dummy variables for he years 1974 and 1979 when gasoline raioning was in effec. Schimek finds ha hese conrols improve he esimaes by reducing signs of auocorrelaion (Durbin s h-saisic falls from 2.60 o 0.93). 8 Schimek (1996, Table 2) also esimaes hree equaions which decompose fuel consumpion ino vehicle sock, flee-average fuel efficiency, and driving per vehicle. All are in double-log form. The hird of hese equaions permis fuel price and fuel efficiency o have disinc effecs; and he esimaed coefficiens are opposie in sign and nearly idenical in magniude, as would be expeced if hey ener as a raio as assumed in he specificaion used by mos auhors. This equaion also suggess a raher small shor-run rebound effec (5 6 percen) and a much larger long-run effec (21 26 percen). The hree-equaion framework offers an ideal opporuniy o explore he empirical consequences of simulaneiy beween he deerminans of VMT and fuel efficiency, bu Schimek does no explore his aspec. The possible significance of lagged dependen variables is very imporan for soring ou shor-run and long-run effecs. However i is unseled in he pure ime-series sudies, because i is difficul o disenangle he presence of a lagged dependen variable from he presence of auocorrelaion. Greene finds ha when auocorrelaion is accouned for, lagged dependen variables are no longer saisically significan. Schimek finds ha when lagged dependen variables are included, evidence for auocorrelaion becomes weak. Neiher of hese resuls demonsraes definiively which is he righ specificaion, and he answer appears sensiive o he ime period considered and he way in which CAFE sandards are conrolled for. Forunaely, cross-secional ime series sudies offer an opporuniy o obain a larger daa se wih he hope of disenangling hese wo saisical properies. 6 Esimae from he linear lagged dependen variable model (model III in Table 1). Esimaes for he loglinear model are nearly idenical. 7 Schimek (1996), p. 87, Table 3, model (3). 8 The CAFE variable makes even more difference in anoher equaion, explaining fuel consumpion, where wihou he CAFE variable income has he wrong sign and he lagged dependen variable akes an unreasonably large coefficien. See his Table 1, models (1) and (4). 8

19 2.2.2 Aggregae Cross-secional ime series Sudies Haughon and Sarkar (1996) consruc a much larger daa se which allows hem o ake advanage of differences no only across ime bu across saes. Because fuel prices vary by sae, primarily due o differen raes of fuel ax, his provides addiional opporuniy o observe is effecs on amoun of moor-vehicle ravel. This cross-secional ime series daa se for he US covers years and all of he 50 saes plus he Disric of Columbia. Furhermore, he auhors esimae boh VMT per driver and, in a separae equaion, fuel inensiy (he inverse of fuel efficiency). Unforunaely, however, he simulaneiy of hese wo equaions is no accouned for. Haughon and Sarkar s esimae of he rebound effec is abou 16 percen in he shor run, similar o Greene (1992), and 22 o 23 percen in he long run. 9 In obaining long-run esimaes, hey are able o measure boh auocorrelaion and he effecs of a lagged dependen variable wih sufficien precision o resolve some of he difficulies wih pure ime series. For auocorrelaion, hey measure he correlaion beween adjacen years o be Like Greene, hey find ha when auocorrelaion is accouned for, he effec of lagged dependen variable is much diminished; bu unlike Greene hey sill obain a saisically significan effec, one ha implies a long-run effec 32 o 45 percen larger han he shor-run effec. As for fuel inensiy, Haughon and Sarkar find i is unaffeced by he curren price of gasoline unless ha price exceeds is hisorical peak. This phenomenon is known as hyseresis, and is raionalized on he grounds ha consumers and manufacurers reac o increases in fuel price by invesing in new echnologies which, once adoped, are coninued even if price declines hereafer. CAFE effecs are aken ino accoun hrough a variable measuring he difference beween he legal minimum and acual fuel efficiency in 1975; however, ha variable is so srongly correlaed wih he hisorical maximum real price of gasoline ha hey omi i in mos specificaions, casing doub on wheher he resuling esimaes really conrol adequaely for he CAFE regulaion. I appears ha he confounding of he rebound effec wih effecs of CAFE regulaion is one of he mos limiing facors in sudies reviewed so far. Differen auhors have defined and included a variey of variables o accoun for his, and resuls seem sensiive o jus how i is done (Schimek 1996). Probably his is because he sandards were imposed abou he same ime as a major increase in fuel prices occurred, and hey became more sringen as incomes rose during he 1980s; herefore he effecs of CAFE sandards are hard o separae from hose of fuel prices and incomes. However, he problem is compounded by he fac ha here has been lile agreemen or heoreical jusificaion for he paricular forms used. Wih resuls so sensiive o inclusion of one of hese variables, we give a high prioriy o developing a heory o provide beer guidance for specifying he demand equaion so as o accoun for such regulaions. In conjuncion wih accouning for simulaneiy of fuel efficiency and ravel, i should be possible o obain more reliable resuls. 9 This paragraph is based on models E, and F in heir Table 1, p Their variable, real price of gasoline per mile, is evidenly he same as fuel cos per mile. 9

20 2.2.3 Disaggregae Sudies Recenly some sudies have used daa on individuals, eiher a cross secion in a single year or from a panel covering several years observaions on he same people. In reviewing such sudies, Greene, Kahn, and Gibson (1999) noe ha he dispariy of resuls for he rebound effec is wider han for aggregae sudies, covering a range from zero o abou 50 percen. Goldberg (1998) uses a variey of sources, including he Consumer Expendiure Survey, o esimae a suie of models explaining manufacurers design and pricing decisions as well as consumers vehicle purchase and usage decisions. One imporan innovaion is he use of insrumenal variables o accoun for simulaneiy beween he vehicle purchase and vehicle usage decision. This innovaion makes a big difference o he esimaed rebound effec, reducing i from abou 20 percen o essenially zero. However, in he usage equaion wih insrumenal variables, he variables represening vehicle ype aain asronomical ye saisically insignifican coefficiens (Goldberg s Table I), casing some doub on he abiliy of he daa se o measure his simulaneiy and hence on he reliabiliy of he zero-rebound resul. Furhermore, he uilizaion equaion is esimaed using daa only on households who purchased a new car he previous year, so is no necessarily represenaive of all vehicle users. Pickrell and Schimek (1999) esimae a vehicle-use model wih 1995 cross-secional daa from he Naional Personal Transporaion Survey (NPTS). The elasiciy of VMT wih respec o gasoline price, conrolling for ownership levels, 10 is 0.04 (model 3 wih odomeer readings as dependen variable). This low figure emerges when residenial densiy is included as explanaory variable; residenial densiy is collinear wih he fuel price, so ha i is hard o separae heir effecs. More generally, he value of a cross-secional micro daa se for a single year is diminished by he fac ha fuel prices vary only across saes, and hose variaions may be correlaed wih unobserved facors ha also influence VMT. Greene, Kahn, and Gibson (1999) use a series of large micro daa ses covering six differen years beween 1979 and The daa are drawn from he Residenial Energy Consumpion Survey in 1979 and 1981, and from Residenial Transporaion Energy Consumpion Surveys (RTECS) performed approximaely every hree years from 1985 o The auhors derive demand funcions for VMT and for fuel wihin a household producion model. This leads o separae equaions explaining VMT, fuel price, 11 and fuel efficiency, for each owned vehicle and for households wih each of four differen ownership levels of passenger vehicles (one, wo, hree, and four or more vehicles). Vehicle ownership is assumed exogenous. In order o accoun for CAFE regulaions, he usage equaions include as an explanaory variable he average fuel efficiency of all cars produced in he same model year as he vehicle whose use is being explained. 10 Hence for fuel efficiency, a leas o a large exen. 11 The fuel price is endogenous because as drivers can reac o higher fuel prices by searching harder for cheaper fuel. Also, people who drive longer disances are likely o incur lower search coss for cheap fuel, as hey simply pass more gas saions. 10

21 The raionale for leing households choose fuel efficiency, even for a fixed vehicle flee, is ha changes in fuel prices may lead households o adap he way hey use heir vehicle porfolio in a way ha affecs average fuel efficiency. A paricularly ineresing example is ha households migh respond o lower fuel cos per mile by aking longer rips (e.g. he occasional holiday rip); his would end o increase gasoline consumpion (a ype of rebound effec) ye could acually increase average fuel efficiency since long rips are more fuel-efficien han shor ones. Two resuls in Greene e al. are noeworhy. Firs, he auhors es wheher consumers care separaely abou fuel price PF and fuel efficiency E, as opposed o heir raio PM, in heir usage decision. This is a formal es of he equal and opposie signed coefficiens already noed from Schimek s sudy, and i confirms ha enering PF and E as a raio is valid. Second, he long-run rebound effec is esimaed a 23 percen overall, wih a range from 17 percen for hree-vehicle households o 28 percen for one-vehicle households. 2.3 Assessing he effeciveness of he CAFE regulaion This secion discusses some sudies ha do no focus on esimaing he rebound effec, bu which are of ineres because hey presen frameworks for analyzing CAFE ype of regulaions and produce some provocaive resuls. Klei (1990) builds an aggregae simulaion model, using daa and elasiciies from secondary sources, o analyze he effecs of sricer CAFE sandards. He shows ha he CAFE sandard may increase he sales of new cars, because he sandard acs like an implici ax on large cars and an implici subsidy on small cars. Consequenly, when supply and/or demand elasiciies in he small car markes are relaively large, oal new car sales increase afer inroducion of he sandard. Klei hen assumes ha he reducion in average driving coss afer he change in he car mix (owards small cars) leads o increased driving because of he rebound effec. 12 Consequenly, gasoline consumpion may increase wih sricer CAFE sandards. However, he acual direcion he effecs ake depends on he sringency of he sandard and on he parameers of he demand sysem. Klei (2000) updaes and exends Klei (1990). The newer sudy allows for echnologyforcing sandards as well as induced shifs in he mix of vehicles. I is found ha making CAFE sricer will increase VMT, and herefore will increase he emissions of radiional polluans (bu no of C02). 13 This of course is an inheren problem wih any VMT increase when polluans are regulaed using per-mile emissions sandards; bu acually mos of he increased emissions 12 This is a fairly loose inerpreaion of he rebound effec, as in Klei s analysis vehicle characerisics apar from fuel efficiency are no consan. Bu when consumers are forced o buy smaller cars, hey buy a less preferred car. Driving ha car generaes less uiliy han he more preferred car, and his reduces car use. Tha reducion a leas parially compensaes he effecs of he lower per mile cos, so ha Klei s esimaes of VMT impacs should be considered o be upper bounds. 13 Klei also quesions if furher reducing gasoline consumpion is beneficial, as i is already highly axed. Parry and Small (2003) argue ha he presen US gasoline axes are oo low, however. 11

22 prediced by Klei s model are due no o VMT bu raher o he shif o ligh rucks caused by heir lower energy efficiency requiremen under federal CAFE regulaions. In a similar vein, Thorpe (1997) uses a general equilibrium model of he new car marke o assess he exen o which a shif in vehicle mix dilues CAFE's abiliy o improve average fuel efficiency. Using his cenral scenario parameer and elasiciy values, 14 he finds ha average fuel efficiency acually decreased because of CAFE. The reason is ha in his model, Asian and European producers reduce heir sales of small fuel-efficien cars, increasing heir sales of midsize cars (aracing former buyers of US-buil midsize cars). Furhermore, all producers increase heir ruck sales. The overall mix shif hence is oward relaively less efficien cars. The insigh is ha he average efficiency of new sales is araced o he average fuel efficiency sandard for all sellers, boh hose ha did and did no exceed he sandard before is implemenaion. Goldberg (1996) performs a comprehensive srucural analysis of fuel-economy regulaions. She consrucs a disaggregae discree/coninuous choice model, esimaes i, and applies i o analyze policies o reduce fuel consumpion. The main finding is ha CAFE has worked well, and ha fuel axes would need o be very high o produce similar resuls. This insigh depends crucially on her economeric resuls, already discussed, which include many crucial coefficiens ha are saisically insignifican. Finally, one could ake a broader perspecive and analyze he effec of CAFE regulaions on he ranspor secor or he economy as a whole, raher han jus fuel consumpion. In doing his, he ineracion beween differen ranspor exernaliies should be aken ino accoun in assessing policies addressing one paricular exernaliy, like global warming (Harringon and McConnell, 2003). This leads o a number of observaions. For example, since congesion is believed by mos researchers o be he mos imporan exernaliy quaniaively, an increase in VMT (possibly due o he rebound effec) may be very cosly o sociey. Similarly, he combinaion of increased VMT and fixed per-mile emission sandards for many polluans will lead o increased emissions of hese polluans, wih poenially serious damage coss. There has been widespread concern ha sringen fuel efficiency sandards could lead o less safe vehicles, alhough he evidence is mixed and he effecs apparenly complex (NRC, 2002). Finally, i can be argued ha polluion-abaemen policies ha raise revenues (like axes) are o be preferred over hose ha do no (like sandards) due o heir effecs on he efficiency of he overall ax sysem (Parry and Oaes, 2000). 2.4 Conclusions from he Lieraure Survey In summary, his secion shows ha aggregae esimaes of he shor-run rebound effec are fairly robus. Esimaes of he long-run rebound effec, by conras, are sensiive o he paricular specificaion, especially he reamen of ime paerns and CAFE sandards. 14 The cenral scenario produces he sronges decrease in average fuel efficiency among all alernaive scenarios presened in Table 5. I is no he scenario wih he average parameer values, and alernaive scenarios increase average fuel efficiency. 12

23 Disaggregae cross-secional analyses end o produce a greaer range of esimaes. One disaggregae sudy ha explois boh cross-secional and emporal variaion (Greene e al., 1999) finds a long-run rebound effec of 23 percen, similar o several oher sudies. Finally, some analyses of he CAFE regulaion show ha his ype of fuel efficiency regulaion can have and indeed has had unexpeced consequences. In he following secions we ake accoun of hese lessons from he lieraure review: The sandard definiion of he rebound effec refers o exogenous changes in fuel efficiency, bu i is measured mosly by exploiing variaions in fuel price. In realiy fuel efficiency is an endogenous variable, even in he presence of fuel-efficiency regulaion. A reliable esimae of he rebound effec from US daa requires accouning for he effecs of federal CAFE regulaions. Empirical esimaes of he rebound effec show considerable sensiiviy o he specificaion, especially of he ime-series properies of he daa (auocorrelaion and lagged variables). I appears ha combined cross-secional and ime-series observaions offer he bes way o observe sufficien numbers of observaions o conrol for hese aspecs of he daa. The heoreical model in he nex secion provides a precise way o incorporae he firs wo refinemens. The hird poin is addressed in our empirical approach. 3. Theoreical Refinemens In his secion we formulae a heoreical model o provide a guideline for he economeric esimaion of he rebound effec using aggregae daa, aking accoun of some concerns raised in he previous secion. An imporan difference wih he sandard approach is ha we inroduce an explici relaion beween a regulaory variable and fuel efficiency, allowing us o rea fuel efficiency as an endogenous variable. This also permis a flexible bu well-defined descripion of how he model sysem is influenced by regulaions whose direc or indirec effecs are o increase fuel efficiency. 3.1 Srucural-Form and Reduced-Form Models We assume ha consumers choose how much o ravel (M) on he basis of heir vehicle ownership, he per-mile cos of driving and exogenous characerisics. They choose how many vehicles o own (V) on he basis of he price of new vehicles, how much hey inend o drive, he cos of driving, and oher characerisics. The fuel efficiency choice (E) is deermined joinly by consumers and manufacurers aking ino accoun he price of fuel, how much hey inend o drive, he regulaory environmen, and oher characerisics. 13

24 These assumpions consiue a srucural model, in he sense ha hey lay ou he decision-making srucure explicily. Mahemaically, hese assumpions are characerized in he following se of equaions: M = M V = V E = E ( PM, V, X M ) ( PV, M, PM, X V ) ( P, M, R, X ) F where M is aggregae VMT; V is he size of he vehicle sock (no is composiion); P V is a price index for he ownership cos of new vehicles; P F is a price index for fuel; P M P F /E is he fuel cos per mile; X M, X V and X E are exogenous variables affecing M, V and E, respecively; and R E represens one or more regulaory variables. Vehicle price P V represens he user cos of capial for a vehicle purchase, which incorporaes no only he price iself bu financing or leasing coss. The regulaory variables could represen any of a wide variey of measures ha direcly or indirecly influence flee-average fuel efficiency. The endogenous variables in sysem (8) are hose on he lef-hand side. All hree also appear on he righ-hand side (since E is par of he definiion of P M ). We make his explici as follows, wriing he endogenous variables in bold ype for clariy: E E (8) PF M = M, V, X M E PF V = V PV, M,, X V E E = E ( P, M, R, X ) F E E (9) Equaion se (9) consiues hree equaions in hree unknowns (M, V, and E). If we solve i for hose unknowns, we can wrie each of hem in erms of all he oher variables, i.e. he exogenous variables. This way of wriing he equaions makes clear how each variable depends on hings ha can be independenly varied, and so is useful for empirical work. I is known as he reduced form of he equaions, denoed here by he symbol ~: % ( V, F, E, M, E, V) ( V, F, E, M, E, V ) (,,,,, ) M M P P R X X X V V% P P R X X X E E% P P R X X X V F E M E V (10) The firs of hese equaions shows explicily, for example, ha vehicle prices (and oher deerminans of he ownership cos of capial invesed in new vehicles) do affec VMT, even hough hey do no affec operaing cos as depiced in he firs of equaions (9). Their effec is indirec, via he second of equaions (9). Presumably a higher vehicle price causes vehicle purchases o decline (lower V), which hen calls for VMT o decline (lower M). There could also be an income effec, no accouned for in he model as wrien, resuling from changes in expendiures on purchasing vehicles; bu his is likely o be smaller han he effec porrayed here and in fac is no predicable in sign because raising he price of vehicles could cause 14