Do long-haul truckers undervalue future fuel savings?

Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C. Do long-haul truckers undervalue future fuel savings? Jacob Adenbaum, Adam Copeland, and John J. Stevens 2015-118 Please cite this paper as: Adenbaum, Jacob, Adam Copeland, and John J. Stevens (2015). “Do long-haul truckers undervalue future fuel savings?,” Finance and Economics Discussion Series 2015-118. Washington: Board of Governors of the Federal Reserve System, http://dx.doi.org/10.17016/FEDS.2015.118. NOTE: Staff working papers in the Finance and Economics Discussion Series (FEDS) are preliminary materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors. References in publications to the Finance and Economics Discussion Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers.

Do long-haul truckers undervalue future fuel savings?∗ Jacob Adenbaum†, Adam Copeland‡, and John Stevens§ December 28, 2015 Abstract TheU.S.federalgovernmentenactedfuelefficiencystandardsformediumandheavytrucks forthefirsttimeinSeptember2011. Rationalesforusingthispolicytooltypicallydependupon frictions existing in the marketplace or consumers being myopic, such that vehicle purchasers undervalue the future fuel savings from increased fuel efficiency. We measure by how much long-haul truck owners undervalue future fuel savings by employing recent advances to the classic hedonic approach to estimate the distribution of willingness-to-pay for fuel efficiency. Wefindsignificantheterogeneityintruckowners’willingnesstopayforfuelefficiency,withthe elasticity of fuel efficiency to price ranging from 0.51 at the10th percentile to 1.33at the 90th percentile,andanaverageof0.91. Combiningtheseresultswithestimatesoffuturefuelsavings from increases in fuel efficiency, we find that long-haul truck owners’ willingness-to-pay for a 1percentincreaseinfuelefficiencyis,onaverage,just29.5percentoftheexpectedfuturefuel savings. Theseresultssuggestthatintroducingfuelefficiencystandardsforheavytrucksmight beaneffectivepolicytooltoraisemediumandheavytrucks’fueleconomy. Keywords: fuelefficiencystandards,durablegoods,discrete-choicedemandestimation JELclassification: D22,L51,L92 ∗WethankEdMcCartyandJohnMillerforassistancewiththedata,EugeneChungandSaritWeisburdforresearch assistance,andKennethGillinghamandJasonSavingforcomments. Theviewsexpressedherearethoseoftheauthors anddonotnecessarilyreflectthepositionoftheFederalReserveBankofNewYork,theFederalReserveBoard,orthe FederalReserveSystem. †FederalReserveBankofNewYork;e-mail: jacob.adenbaum@ny.frb.org ‡FederalReserveBankofNewYork;e-mail: adam.copeland@ny.frb.org(correspondingauthor) §FederalReserveBoard;e-mail: john.j.stevens@frb.gov

1 Introduction InSeptember2011,theU.S.federalgovernmentsetfuelefficiencystandardsformediumandheavy trucks for the first time, and in June 2015, the National Highway Transportation and Safety Administration (NHTSA) and the Environmental Protection Agency (EPA) proposed a second round of standards.1 The motivation for these policy interventions is to reduce air pollution and other negativeexternalitiesassociatedwiththeuseofmediumandheavytrucks,similartothearguments madetosetfuelefficiencystandardsforpassengercars. The effectiveness of using fuel efficiency standards to reduce negative externalities is an open question(Parryetal.,2007). Inparticular,someeconomistsarguethatfueltaxesaremoreeffective atreducingairpollution(e.g.,seeWestandWilliamsIII(2005)andreferencestherein). Asaresult, themotivationformandatingfuelefficiencystandardsoftenreliesupontheexistenceofmarketplace frictionsorconsumermyopia,bothofwhichcanleadtovehiclepurchasersundervaluingfuturefuel savings and vehicle producers under-investing in technologies that improve fuel efficiency. Indeed, the NHTSA and the EPA motivate fuel efficiency standards (NHTSA-EPA (2015), section 8.2) by listinganumberofpotentialreasonswhymediumandheavytruckownersmightundervaluefuture fuel savings. For example, imperfect information among truck owners about the effectiveness of potential fuel efficiency technologies could make owners unwilling to purchase these technologies. Alternatively,truckownersmaybemyopicwithrespecttofuturefuelcostsandthereforeunwilling to pay upfront for a technology that delivers fuel savings in the future. Finally, agency problems may exist whereby the firms that purchase the trucks do not always pay the fuel costs, and drivers arenotrewardedforoperatinginafuel-efficientmanner(e.g.,seeVernonandMeier(2012)). The NHTSA and the EPA have argued that the adoption of fuel savings technologies in the mediumandheavytruckmarketplaceisinefficientlylow,asthecostofadoptingthesetechnologies is, by their calculations, less than the expected discounted value of future fuel savings (NHTSA- EPA, 2015). Indeed, for the 2011 rulemaking, the agencies argued that engine and truck manufacturers could meet the new fuel efficiency standards using already-available technologies (NHTSA- EPA, 2011). Further, for both the 2011 standards and the proposed 2015 standards, the agencies emphasized that the anticipated fuel savings from meeting these standards is (much) greater than theexpectedcosts.2 1Fordetailsontheproposed2015rulemaking,seehttp://www.epa.gov/oms/climate/regs-heavy-duty.htm. 2For example, the NHTSA and the EPA argue that the typical buyer of a new long-haul truck in 2027 (when the 1

As a first step toward understanding whether the new fuel efficiency standards for medium and heavy trucks might be an effective policy instrument, we look for evidence that truck owners undervalue increased fuel efficiency. Rather than consider all medium and heavy trucks, we focus on class 8 long-haul trucks, which are the large truck-tractors used on highways that specialize in hauling cargo long distances. We do so because fuel efficiency is a main cost for owners of these vehicles and so should be a characteristic to which they are attuned.3 Consequently, a long-haul truck’s fuel efficiency should be reflected in its price. Although these trucks are not representative of medium and heavy trucks, long-haul trucks, which are a major part of the national transportation system for freight, disproportionately account for fuel consumption in the medium and heavy truck segment because of their high annual miles traveled and heavy payloads.4 Thus, the overall effectiveness of fuel economy standards depends, in large part, on the long-haul truck market. In addition, long-haul trucks are clearly defined in the data and contain a relatively small number of producers and products, which facilitates our market analysis. Lastly, there exist detailed data on thestockandvalueofusedlong-haultrucksthatenablesustoperformourempiricalanalysis. Weusedatafromtwosources. TheCensusBureau’sVehicleInventoryandUseSurvey(VIUS) provides information on the stock and characteristics of all medium and heavy trucks registered in the United States.5 These data provide an extraordinary amount of information on trucks, with survey respondents, i.e. truck owners, answering questions on the physical and operational characteristics of their truck.6 We use the reported truck characteristics both to identify class 8 long-haul trucks in the VIUS and to merge information on used truck prices from the Truck Blue Book. The endresultofthismergerisadatasetontheequilibriumpriceandquantityforarepresentativesample of long-haul trucks registered in the United States. We have merged the VIUS and Truck Blue Book prices for 1992 and 1997. Our results focus on 1992, although we show the results are robust secondsetofproposedstandardsarefullyphasedin)willrecouptheextracostsofthefuelefficiencytechnologiesin under 2 years (see the NHTSA-EPA June 2015 press release at http://www.epa.gov/otaq/climate/documents/ 420f15900.pdf). 3Forexample,TorreyIVandMurray(2014)(page6)reportthatfuelcostsare“oneofthetoptwocostcentersfor motorcarriers.” 4TheNHTSAandtheEPAreportthatclass7andclass8trucksaccountfor65percentoffuelconsumptioninthe heavy-dutysector(NHTSA-EPA(2011),page11). 5Priorto1997, thissurveywasknownastheTruckInventoryandUseSurvey. Thesurveywasdiscontinuedafter 2002. Seehttps://www.census.gov/svsd/www/vius/products.htmlformoreinformation. 6Thesedatahavebeenusedtostudyavarietyofempiricalquestions,e.g.,productivity(Hubbard,2003),technology adoptionandgovernance(BakerandHubbard,2004),andmergeranalysiswhichtakesintoaccounttheentryandexit ofproducts(Wollmann,2014). 2

tousingthe1997data. We use these data to estimate truck owners’ willingness-to-pay for truck characteristics, employing recent advances to the hedonic approach laid out in Bajari and Benkard (2005). Their approach allows the econometrician to recover willingness-to-pay in an environment with imperfect competition and a product characteristic that is unobserved (by the econometrician); both of these features are present in the heavy truck market. We employ a local quadratic method to infer truck owners’ willingness-to-pay for four continuous characteristics—miles-per-gallon (MPG), lifetime miles, engine size, and the truck’s weight when empty—while controlling for a number of fixed effects. This method allows us to recover nonparametrically the distribution of willingness-to-pay foreachcontinuouscharacteristic. Ourestimatesofthesedistributionshavetheexpectedsignsinthatalmostalltruckownersnegativelyvaluelifetimemilesandpositivelyvalueenginesize,emptyweight,andMPG.Inparticular, we find that the mean elasticity of MPG to price is 0.91, or that on average a truck owner is willing to pay 0.91 percent of his truck’s price for a 1 percent increase in MPG, holding all else equal. The 10th and 90th percentiles of this distribution are 0.51 and 1.33, demonstrating that there is a wide rangeoftastesforfuelefficiencyamongtruckowners. Todeterminewhetherlong-haultruckownersundervalueexpectedsavingsfromfuelefficiency, weneedtocomputethediscountedfuturesavingsfroma1percentincreaseinMPG.Thesesavings varyacrosstrucks,dependingupontheircharacteristics(suchascurrentageandfuelefficiency). We then compare these estimated savings with owners’ willingness-to-pay and find that truck owners’ undervaluediscountedfuturesavingsfromincreasedfuelefficiency. Onaverage,ownersarewilling topayforonly29.5percentofexpectedfuelsavings. Thedistributionoftheratioofthewillingnessto-pay over future fuel savings ranges from 8.8 percent at the 10th percentile to 54.5 percent at the 90th percentile. The main result of this paper, then, is that almost all long-haul truck owners undervalue expected lifetime fuel savings, which in turn suggests that imposing fuel efficiency standardscouldbeaneffectivepolicytooltoraisethefueleconomyoflong-haultrucks. A second set of results evaluates the willingness of new truck owners to adopt a suite of technologies that would dramatically improve fuel efficiency. The NHTSA and the EPA argue that technologies exist today that make it feasible for heavy duty engine and truck manufacturers to meet the fuel efficiency targets mandated in the 2011 final ruling. A concrete example is provided bytheSuperTruckprogram,agovernment-sponsoredresearchprojectwhosegoalistodemonstrate 3

that a 50 percent improvement in fuel efficiency for class 8 long-haul trucks is feasible. The final report of the SuperTruck program provides tables on both the expected fuel efficiency gains from introducing two different sets of innovations as well as the incremental costs of both packages of innovations.7 The first set of innovations is predicted to increase MPG of a current truck-tractor model by 65.3 percent, at the cost of raising the price of the truck by 26.6 percent. The second set ofinnovationsprovidesbetterfuelefficiency,increasingMPGby69.8percent,butatamuchhigher cost of a 51.0 percent increase over the current truck price. Using this information and our estimatesofwillingnesstopay,wecancalculatethefractionoflong-haultruckerspurchasing(almost) newtrucksforwhichthewillingness-to-payforfuelefficiencyishigherthantheincrementalcosts. We find that 93.6 percent of these long-haul truck owners would be willing to adopt the first set of innovations,and80.9percentofownerswouldbewillingtoadoptthesecondset. Theseresultsare encouraging then, in that the model predicts that a strong majority of new long haul truck owners, despite their undervaluation of future fuel savings, would be willing to bear the costs of adopting theSuperTrucksetoffuelefficiencyinnovations. From a policy perspective, a caveat of our results is that our analysis is based on prices and quantities in 1992 whereas the new fuel efficiency standards are being introduced in 2015, more than twenty years later. Our results, however, are based on the structural parameters of the truck owners’ problem, and it is not unusual to assume that deep parameters do not change over periods of this length. Furthermore, in the robustness section we demonstrate that our results also hold using 1997 data.8 Nevertheless, if it were the case that there have been substantial changes in the long-haultruckingindustry,ourresultsshouldbeviewedwiththeappropriateamountofskepticism. Our contribution to the literature on evaluating the effectiveness of fuel efficiency standards is twofold. First, we focus on class 8 long-haul trucks whereas previous work analyzed automobiles and light trucks, as U.S. fuel efficiency standards applied to only this subset of vehicles prior to 2011.9 However, the recent expansion of fuel efficiency standards to medium and heavy trucks raisessimilarquestionsabouttheeffectivenessofthispolicy. Tothebestofourknowledge,thispa- 7The SuperTruck final report can be found on the Department of Transportation’s website, at http://www. transportation.anl.gov/pdfs/TA/903.PDF. 8The VIUS was last conducted in 2002. However, as explained in section 3.1, we merge the VIUS data with the TruckBlueBookpricesusinga2-digitVIN.AlthoughtheCensusBureauprovideduswithaspecialtabulationofthe 2-digit VIN for each truck in the 1992 and 1997 VIUS, but declined our follow-up request for the same information fromthe2002VIUS. 9Parryetal.(2007)andHelfandandWolverton(2011)providerecentreviewsofthisliterature. 4

peristhefirsttoformallytestwhetherlong-haultruckersundervaluetheexpectedfuturediscounted gains from increased fuel efficiency. Our main result—that these truckers considerably undervalue futurefuelsavings—suggeststhatfuelefficiencystandardscouldbeeffectivetoolswhenappliedto long-haultrucks. Thesecondcontributionofourpaperisoureconometricapproach,whichhasnotyetbeenused inthisliterature.10 Weuseatechniquethathastheadvantageofallowingustononparametricallyrecoverthedistributionofwillingness-to-payinthepopulation. Specifically,weusealocalquadratic method to estimate long-haul truck owners’ willingness to pay for fuel efficiency (and other characteristics). We then aggregate these estimates across truck owners to arrive at an estimate of the distribution in the population. Allowing for heterogeniety is recognized as an important feature when estimating demand for products generally (e.g., see the beginning of section 1 in Ackerberg et al. (2007)). Further, for the specific case of estimating willingness to pay for fuel efficiency, Bento et al. (2012) and Grigolon et al. (2014) argue that it is crucial to account for heterogeneity amongconsumers. Intheliteraturefocusedonfuelefficiency,thereareempiricalpapersthatallowforheterogeneity in consumer tastes; for example, Goldberg (1998) and Grigolon et al. (2014) estimate discretechoice models with random coefficients. These approaches, however, require both an assumption about the distribution of willingness-to-pay and a panel data set.11 With our approach, we can recoverthewillingness-to-paydistributionnonparametrically,andwecandosousingonlyacrosssectionofdata. As discussed in more detail in section 2, a main identifying assumption we make is that a truck’sunobservedcharacteristicisindependentofthetruck’sother(observed)characteristics. This assumption is slightly stronger than the mean independence assumption that is commonly used in the empirical industrial organization literature.12 Nevertheless, we argue later in the paper that this assumption is reasonable when considering the market for long-haul trucks. Further, we note here that one of many differences between our approach and some of the reduced form papers in this 10Inasearchoftheempiricalliterature,wehavefoundonlytwoinstancesofpublishedarticlesthatimplementthis technique: BajariandKahn(2005)andKosteretal.(2014). 11Researcherstypicallyassumethatwillingness-to-pay,ortastesforcharacteristics,aredrawnfromaGaussiandistribution. Thesemodelscanalsobeestimatedwithdataonseveralmarkets(e.g. cities)atonepointintime. 12For example, Berry et al. (1995) and most models utilizing their estimation method assume that the unobserved characteristicismeanindependentoftheobservedcharacteristics. SeeBajariandBenkard(2005)foradetailedcomparisonofthesetwoeconometricapproaches. 5

literature, is that the latter have been able to estimate consumers’ willingness to pay under weaker identificationassumptions,albeitwithgreaterdatademands. (See,inparticular,AllcottandWozny (2014)andBusseetal.(2013).) In the next section, we introduce our model, and in section 3 we describe the data. Section 4 presents our empirical approach and the results on truckers’ willingness-to-pay for fuel efficiency and other characteristics. In section 5, we compare the willingness-to-pay estimates for fuel efficiency against our measures of the expected discounted lifetime savings from increased fuel efficiency. This comparison reveals by how much truckers’ undervalue expected discounted fuel savings. Section6concludes. 2 Model Inthissection,wepresentourmodelofdemandforpurchasinglong-haultrucks. Along-haultruck is described by two types of attributes: physical attributes observed by both truck owners and the econometricianandascalarcharacteristicwhichisobservedonlybytruckpurchasers. Thephysical characteristics used in our analysis include four continuous characteristics and a set of dummy variables that account for the truck manufacturer as well as the truck cab design. The continuous characteristics are MPG, lifetime miles, engine size (measured by cubic inch displacement), and empty weight (measured in pounds). By its nature, the unobserved characteristic is difficult to describe,butlikelyreflectsahardtomeasureattributesuchasquality. Following the notation of Bajari and Benkard (2005), let j ∈J index the trucks and i∈I index truck owners. Suppose x denotes a 1×K vector of physical characteristics, p is the price of the j j truck, and ξ is the unobserved characteristic. A truck owner i maximizes utility by selecting a j product j aswellasacompositegoodc∈R . Truckownershaveincomey. Normalizingtheprice + i ofcto1,thetruckowner’smaximizationproblemis maxu(x ,ξ ,c) i j j (j,c) subjectto p +c≤y. j i Under fairly general conditions on u, Bajari and Benkard (2005) prove there is an equilibi rium price function p˜(x,ξ ) which maps the set of product characteristics to prices and satisfies j 6

p = p˜(x ,ξ ) for all j = 1,...,J for a specific market and point in time.13 They also show that j j j the unobserved characteristics can be be identified using a single cross-section: If (p,x,ξ) are distributedjointlywithcumulativedistributionfunctionF(p,x,ξ),thentheunobservedcharacteristics ξ areequaltotheconditionalcumulativedistributionfunctionoftheprices, j ξ =F (p ). (1) j p|x=x j j Toidentifythepricefunctionandtheunobservedcharacteristics,weassumeξisindependentof x. An interpretation of this assumption is that the location of trucks in the observed characteristic space is exogenous to ξ, or at least determined prior to the revelation of consumers’ willingnessto-pay for ξ. This assumption is reasonable, because truck and engine re-designs, which involve substantialR&D,areoftendoneeveryseveralyearswhereasξcanvaryonamorefrequentbasis.14 Because we observe a single cross-section of truck owners, identification requires us to specify u;wemakethefairlystandardassumptionthat i u =β x +β ξ +c, (2) ij ij j i,ξ j whereweusethelogofthecontinuouscharacteristics: MPG,lifetimemiles,enginesize,andempty weight. Afinalassumptionisthatthechoicesetiscontinuous. Then,givenaninteriorsolution,thefirst orderconditionsimply dp˜ β =x , (3) ik jk dx jk where k indexes the four continuous characteristics. As detailed in section 4, the empirical challenge is to obtain estimates of β , the random coefficients, by estimating the derivative of the price ik function. According to our model, β represent truck owners’ willingness-to-pay for a MPG, lifeik time miles, engine size, and empty weight. The estimates of willingness-to-pay for MPG is a key component of our answer to whether truck owners undervalue the expected discounted gains from 13Theconditionsarethat(a)u iscontinuouslydifferentiableincandstrictlyincreasingincwith du >εforsome i dc ε>0andallc∈(0,y);(b)u isLipschitzcontinuousin(x ,ξ );(c)u isstrictlyincreasinginξ . i i j j i j 14Theunobservedcharacteristicmaybeinfluencedbymarketingcampaigns,forexample. 7

fuelefficiency. 3 Data With the model and its assumptions in mind, in this section we describe the data. We first explain howweconstructthedataandthenpresentsummarystatistics. 3.1 Origin of the data The data we use is a compilation of two datasets, the Census Bureau’s VIUS and the Truck Blue Book.15 The VIUS was a survey conducted every five years in order to track the stock of trucks operating in the United States. (The survey was discontinued after 2002.) The Census Bureau surveyed the owners of a random sample of trucks registered or licensed in the United States as of July 1st of the survey year and recorded both physical and operational characteristics of the sampled truck. A few of the many characteristics in the VIUS are make and model-year of the truck, the vehicle identification number (VIN), fuel mileage, and lifetime miles. This survey, then, providesadetailedlookatthestockoftruckseveryfiveyears. From the VIUS data on the stock of all trucks in 1992, we extracted a subset that fit our definition of long-haul trucks, or trucks designed for long-distance hauling. Based on conversations with industry analysts and a review of the trade press, we developed a list of criteria that trucks would need to satisfy in order to be classified as a long-haul truck. First, we eliminated any truck that is not a truck-tractor. Truck-tractors are trucks designed to pull trailers, a necessary requirement for long-distance hauling. This restriction reduced the size of the sample from 123,641 observations to 42,108, as observations on pickup trucks and other medium trucks (e.g., straight trucks or ‘box’ trucks) were eliminated. This subset, however, still contained trucks that clearly were not used to haul goods over highways. For example, trucks that were extensively used off-road or had a body type incompatible with long-distance hauling (e.g., utility truck) remained in the sample. Consequently, we further refined the set of truck-tractors by only including those that satisfied the followingcriteria: 15Before1997,theVIUSwasknownastheTruckInventoryandUseSurvey(TIUS).TheTruckBlueBookiscurrently publishedbyPrimedia. 8

1. Havethreeaxles 2. Haveeitheraconventionalorcabin-over-enginedesign 3. Haveadieselengineandairbrakes 4. Donotspendmostoftheirtimeoff-road 5. Fitalistofbodytypes16 The first restriction mainly eliminated truck-tractors with two axles; these trucks are limited by how much cargo they can pull, and they serve a niche market by hauling light loads. Similarly, this restriction ruled out trucks with four or more axles, which are a subset of trucks catering to a extremely small niche of firms typically engaged in ‘severe service’ activities. After conditioning on three axled truck-tractors, almost all trucks fulfilled criteria two and three. These constraints eliminated a few unusual trucks that are built to serve very particular demands. The fourth requirement was a check to make sure that the truck was operated in a manner consistent with long-haul trucks, whereas the last constraint ensured that the truck in question had a body type consistent withlong-distancehauling. Theserestrictionsslimmeddownthedataset,decreasingthenumberof observations from 42,108 to 26,668.17 We believe the resulting sample of observations is representativeofthestockofclass8long-haultrucksintheUnitedStatesforthe1992censusyear. Although the VIUS provides a detailed accounting of the stock of long-haul trucks in the U.S., it does not provide the prices of these trucks. For this missing information, we turned to the Truck Blue Book, a comprehensive listing of used truck prices based on their characteristics. From the publisher,weobtainedtheOctoberissuesoftheTruckBlueBookfor1992. Wethenassignedprices totrucksintheVIUSbasedontheirrecordedcharacteristics. A difficulty in merging these two datasets is that the Truck Blue Book uses a different set of characteristicstodescribeatruckcomparedtotheVIUS.Beyondmoregeneralcharacteristicssuch as make and model-year, it becomes difficult to distinguish trucks with different trim lines (e.g., differing engines or gross vehicle weight ratings). A solution to this problem is to use sections of 16Thelistofbodytypesthatwereexcludedfromourrefinedsamplewere:pickup,panelorvan,multistoporstepvan, garbagehauler,concretemixer,yardtractor,sportutility,stationwagon,minivan,andbeverage,publicutility,winchor crane,wrecker,service,oilfieldanddumptrucks. 17AsummaryofhowwefilteredthedataisprovidedintableA1intheappendix. 9

the truck’s vehicle identification number (VIN) as a link between the two data sources. The Truck Blue Book provides a portion of each truck’s VIN. The VIUS collects, but does not publish the VIN. However, we were able to obtain a portion of the VINs for 1992 from the Census Bureau that revealednoconfidentialinformation. The1992pricedatacoversusedtrucksupto8yearsofage,whichleftuswithoutpricesforthe oldest long-haul trucks. Using the sample weights, these older trucks accounted for 29 percent of thestockoflong-haultrucks. Duetothelackofpricedata,wedroppedtheseoldertrucksfromour analysis. To merge the newer trucks with prices, we first aggregated the VIUS data to the make, modelyear,cabintype,and2-digitVINlevel. Wethenmergedthesedatawiththepricedataatthis level of detail, resulting in a 75 percent match rate. For the trucks for which we could not find a match,wefurtheraggregateduptheseobservationstothemake,modelyear,cabintype,and1-digit VINlevel,andmatchedthemagainstourpricedata. Thisresultedinanadditional16percenttrucks being matched. The remainder of trucks were aggregated up to the make, model year, and cabin typelevelandmatchedtoprices. Intheend,thefinaldatasetusedforanalysishas629observations. Although we focus on 1992, we also merged the 1997 VIUS with the Truck Blue Book for October 1997 and used these data to check the robustness of our results. We merged these datasets using the method described above, in particular relying upon a 2-digit VIN acquired as a special tabulation from the Census Bureau.18 The percent of observations matched using 2, 1 or no VIN digits for the 1997 data closely mimics what we observed for the 1992 data. The final 1997 dataset usedforourrobustnesscheckhas510observations. 3.2 Data description This work focuses on seven truck characteristics: make, model-year, cabin type (i.e., conventional or cab-over-engine), engine size, weight when empty (a.k.a. empty weight), lifetime miles, and MPG. Using the VIUS, we identified the major brands that produce trucks-tractors in the United States, and we used industry information to consolidate brands that belonged to the same firm. In the end, we used six brands in our analysis: International, Kenworth, Mack, Peterbilt, Freightliner, and Ford. Freightliner is an agglomeration of brands including Freightliner, GMC/Chevy, White, and White GMC. Ford is also an agglomeration, including Ford, Autocar, Marmon, Scania, Volvo, 18Details of the how the various filters reduced the size of the 1997 VIUS data are provided in table A1 in the Appendix. 10

Table1: Long-haultruckcharacteristics Percentiles Mean SD 10th 25th 50th 75th 90th MPG 5.69 4.46 5.00 5.30 5.63 5.97 6.32 Lifetimemiles 393,332 174,846 120,000 223,931 366,873 507,375 609,519 Enginesize 18.0 1.3 13.4 16.6 18.1 18.9 19 Emptyweight 29,417 2,713 24,063 27,161 29,320 31,269 34,000 Note:MPGismilespergallonandSDisstandarddeviation.Themeanandstandarddeviationstatisticswerecomputed usingtheVIUSsampleweights.Enginesizeisadisplacementoftheengineincubicinchesandisacategoricalvariable. A rating of 18 corresponds to a displacement of 700 to 800 cubic inches, and the top range is 1001 cubic inches and above. Emptyweightismeasuredinpounds,andlifetimemilesisinmiles. andWesternStar. In the United States, conventional cabins are the dominant design, making up 74 percent of our sample. Thecab-over-enginedesignwasmorepopularinthepast,andinoursamplethefractionof cab-over-enginetrucksincreaseswithvintage;e.g.,conventionaltrucksmakeuponly52percentof vintage8trucks.19 Statistics describing the distribution of the 4 continuous characteristics are reported in table 1. Engine size is measured by the displacement of the engine in cubic inches, and survey respondents pick a rating bin which covers a range of 100 cubic inches. A rating of 18 corresponds to a displacement of 700 to 800 cubic inches, and the top range is 1001 cubic inches and above. (For comparison, the 2004 Honda Odyssey EX minivan had a displacement of just under 212 cubic inches.) Theemptyweightofatruckismeasuredinpounds,lifetimemileageisinmiles,andMPG is the miles per gallon that the truck averaged in the survey year. As table 1 demonstrates, there is substantialvariationacrosstrucksinthesefourcharacteristics. A central assumption of our model is that the product space is approximately continuous in the variables of interest, which are the four continuous characteristics. To provide a measure of how close trucks are in terms of their characteristics, we compute a nearest neighbor statistic. We then plot this statistic in figures 1 through 3 for each of the continuous characteristics. For MPG, the 19Cabin-over-engine designs were popular in the past because there existed regulations that restricted the length of the truck, where length was measured from the front bumper of the truck-tractor to back bumper of the trailer. By construction, the cabin-over-engine truck-tractors are shorter than the conventional cabins. In 1982, the federal government changed the regulation, and the length measurement focused on the trailer (and so excluded the trucktractor). 11

nearest neighbor is, on average, 0.0008 miles-per-gallon away. There are, of course, trucks on the edge of the product space that do not have close neighbors. For example, there were three trucks withlessthan4MPG,andahandfulabove8MPG.Buttheseproductsareatinypartofthesample anddonotmeaningfullyaffectourempiricalresults. Figure1: Milespergallon 100 10−1 10−2 10−3 10−4 10−5 10−6 2 4 6 8 10 12 citsitatS robhgieN tseraeN Figure2: Lifetimemiles 106 105 104 103 102 101 100 0 200 400 600 800 1000 1200 Miles per Gallon citsitatS robhgieN tseraeN Miles (thousands) Figure3: Enginesize 100 10−1 10−2 10−3 10−4 10−5 13 14 15 16 17 18 19 citsitatS robhgieN tseraeN Figure4: Emptyweight 104 103 102 101 100 10−1 10−2 10 15 20 25 30 35 40 45 50 55 Engine Size citsitatS robhgieN tseraeN Lbs (thousands) Note: Foreachtruck,thedistancetothenearestneighboriscomputedforthefourcontinuouscharacteristics. Foreach ofthesecharacteristics,thisnearest-neighborstatisticisthenplottedforeachtruckonalog-scale. For lifetime miles, the median distance of the nearest-neighbor is 337 miles and for empty weightthisstatisticis5pounds. Bothoftheseresultssuggestthattheproductspaceisapproximately continuous in these characteristics. Of the four characteristics, engine size is potentially the most problematic because it is a categorical variable. The discrete nature of this variable is smoothed out, however, when aggregating trucks in the VIUS in order to be able to merge the price data (as described in section 3.1). Although there are bunching of trucks in the highest engine size, 12

Figure5: Pricedistributionbyvintage 55 50 45 40 35 30 25 20 15 10 5 0 1 2 3 4 5 6 7 8 Vintage )sdnasuohT( sralloD Note: Abox-and-whiskerschartisdisplayedforeachvintage. Theupper,middle,andlowerhorizontallinesofthebox portioncorrespondtothe75th,50th,and25thpercentiles,respectively,ofthepricedistributionofagivenvintage. Let q and q denote the 25th and 75th quartile values, respectively. Then the upper most horizontal line, or whisker, is 1 3 equal to q +1.5(q −q ) and the lower most horizontal line is equal to q −1.5(q −q ). Finally, the plus symbols 3 3 1 1 3 1 denoteoutliers,orareallpointswhichlieabovetheupperwhiskerorbelowthelowerwhisker. figure3displayswhatlookstobesufficientcontinuityalongthischaracteristic. Indeed,themedian nearest-neighborstatisticforenginesizeis0.0008. Turning to prices, we find substantial variation in prices across trucks. Indeed, there is a large decline in prices across vintages; vintage 0 long-haul trucks (i.e., trucks less than 1 year old) have a median price of $48,875 and vintage 8 trucks (i.e., trucks that are 8 years old) have a price of $8,412 (see figure 5). Further, within each vintage there is a wide range of prices, as illustrated by the large inter-quartile ranges displayed in figure 5. For example, the inter-quartile range is greater than$5,000forvintage0trucks,whichisgreaterthan10percentofthemedianprice. Finally, to provide an overview of how these characteristics and price are related, we compute the correlations in the data among our continuous truck characteristics and price (see table 2). We find the correlations between price and each continuous variable are statistically significant. The lifetime miles and MPG are negatively correlated most likely because of technological progress; in our sample, average MPG increases as vintage decreases (i.e. as trucks get newer). The negative 13

Table2: Correlationsbetweenvariables Price MPG Lifetimemiles EngineSize Emptyweight Price 1.00 MPG 0.17∗∗∗ 1.00 Lifetimemiles −0.70∗∗∗ −0.16∗∗∗ 1.00 Enginesize −0.08∗ 0.038 0.07 1.00 Emptyweight 0.11∗∗ −0.13∗∗∗ −0.005 0.003 1.00 Note: MPG is miles per gallon. Reported are Pearson correlation coefficients. The superscripts ***, **, * denote statisticalsignificanceatthe99,95,and90percentconfidencelevels. correlation between empty weight and MPG is likely driven by the fact making a truck lighter will increaseitsMPG,allelseequal. 4 Empirics 4.1 Estimation In order to recover truck owners’ willingness to pay, we need to estimate the price hedonic and, more importantly, its derivatives (see equation 3). We accomplish this by using the data on truck pricesandcharacteristicstoestimatetheconditionaldensityofthepricefunction,denotedg(p|x ), j and its derivatives for every truck j in our sample. (Recall that p is price and x is a K×1 vector j of characteristics.) To see the connection between the derivatives of the price hedonic and of the conditionaldensity,notethat (cid:90) p(x ,ξ )= pg(p|x )dp. j j j Thentakingadvantageoflinearity,wehave ∂p (x ,ξ ) ∂ (cid:90) (cid:90) ∂g(p|x ) j j j j = p·g(p|x )dp,= p· dp, (4) j ∂x ∂x ∂x j,k j,k j,k wherek denotesanelement(aspecificcharacteristic)inx . j To impose as little parametric structure as possible, we estimate the conditional density of the price function and its derivatives using the local quadratic methods detailed in Fan and Gijbels (1996)andFanetal.(1996). Wecanestimateg(p|x )usinganonparametericregressiontechnique, j 14

becauseash→0, (cid:20) (cid:21) E K (p −p)|x ≈g(p|x ), (5) h j j j where K is a kernel density function, h is the bandwidth, and we define the scaled kernel K (x)≡ h 1K(x/h).UsingTaylor’sexpansion,weknowthatforanx intheneighborhoodofx h 0 j (cid:20) (cid:21) T dg(p|x ) 1 E K (p −p)|x ≈g(p|x )+ j (x −x )+ (x −x )TH(x −x ), (6) h j j j 0 j 0 j 0 j dx 2 j where H is the Hessian matrix of g(p|x ) with respect to x , and the superscript T denotes the j j transpose. Fanetal.(1996)redefinetherighthandsideas α +λT(x −x )+γTvech (cid:0) (x −x )(x −x )T(cid:1) , (7) j j 0 j j 0 j 0 j where vech(X) is the vectorization of the lower triangular portion of X and α ∈R,λ ∈RK,γ ∈ j j j RK(K+1)/2. They then show that (α ,λ ,γ ) can be estimated for every truck j by solving the j j j weightedleastsquaresproblem J min ∑ (cid:8) K (p −p)−α −λT(x −x )−γTvech (cid:0) (x −x )(x −x )T(cid:1)(cid:9)2 K (x −x ), (8) h n j j n j j 0 j 0 j B n j αj,λj,γjn=1 where K is a multivariate kernel weighting function with bandwidth matrix B such that K (u)= B B (1/|B|)K(||B−1u||).20 Our focus is on the price derivatives and so on the estimate of λ . Neverj theless, we include the higher-order terms in the minimization problem to reduce the bias of the estimator.21 Further, if we wanted to recover estimates of the unobservable characteristics ξ for j eachtruck,wecoulddosobycomputingthesampleanalogtoequation(1),or (cid:90) (cid:90) ˆ ξ = g(p|x )dp= α (p)dp. (9) j j j p<pj p<pj In our application, we use the univariate Gaussian kernel K(x) = √1 e−x2/2 to construct K h 2π 20Notethatifu∈R1,thenthisreducestothescaledkernelK sinceBhasonlyoneentry. h 21See Racine (2008) for a primer on nonparametric estimation, including a discussion of bias and nonparametric estimators. SeeFanandGijbels(1996)foradetaileddiscussionofbiasandlocalpolynominalestimators. 15

and K , and take the bandwidth matrix to be of the form B = hI. Since it is a scalar multiple of B the identity matrix, this means that the smoothing is done along the coordinate axes, and that our estimator smooths by the same amount in every dimension. For this reason, we normalize each of our observed variables by its standard deviation for the purposes of computing the kernel weights (sothattheyareallonthesamescale). The selection of the bandwidth parameter is a critical input of our chosen approach. We use least-squares cross-validation, a data-driven method where we choose a bandwidth that minimizes the out of sample prediction error over the sample space by estimating the model over sub-samples that leave out a single observation. Under this approach, the optimal bandwidth parameter is 2.48. Moredetailsonleast-squarescross-validationcanbefoundintheappendixE. Because the asymptotic properties of this price estimator do not depend on observing the individualfirmsinanythingotherthanthecrosssection,weareabletorecoverestimatesoftherandom coefficients from a single cross-sectional data set. Moreover, this estimator allows us to flexibly estimatethepricehedonicanditsderivativeswithoutspecifyingaparticularfunctionalform. Given our focus on estimating the derivatives of the price hedonic at the observed prices, our method of estimating the conditional densities and integrating to recover the price hedonic is computationally equivalent to estimating the price hedonic directly. In appendix D, we provide more details on this point. Inthisapplication,weusealogtransformationofthepriceinordertoestimatethepricehedonic, andreportwillingness-to-payaselasticities. 4.2 Results We are able to recover the estimates of the willingness-to-pay for each truck owner in our sample for each of the continuous characteristics: MPG, lifetime miles, engine size, and empty weight. To generate an estimate of the distribution of willingness-to-pay in the population, we aggregate across truck owners using the sample weights in the VIUS. The kernel-smoothed distribution of willingness-to-pay for fuel efficiency, our main object of interest, is plotted in figure 6.22 Our willingness-to-pay estimates are in terms of elasticities, so a coefficient of 0.6 for MPG means that 22For each graph involving a kernel-smoothed distribution, we computed the optimal bandwidth for the kernelsmoothingprocedureusingleave-one-outcross-validationtominimizethemeansquaredintegratederrorofthedistribution(seeappendixEfordetails). 16

Figure6: Distributionofwillingness-to-payformilespergallon 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 −4 −3 −2 −1 0 1 2 3 Elasticity ycneuqerF a truck owner is willing to pay 0.6 percent of his truck’s price for a 1 percent increase in MPG. Our estimates have the correct sign in that all, or almost all, truck owners value increases in MPG, engine size, and weight. Increasing MPG, or fuel efficiency, helps decrease the cost of operating a truck, and larger engine sizes make it easier to pull heavy loads. All else equal, heavier trucks are preferred because they are more comfortable to operate as, for example they typically vibrate and shake less. Further, almost all owners dislike lifetime miles, which provides us with the expected resultthatoldertrucksfetchlowerprices.23 The distribution of tastes for fuel efficiency is quite wide, with the 10th and 90th percentiles of the distribution equal to 0.51 and 1.33 respectively (see table 3 and note that standard errors are bootstrapped, see appendix E for details). There is also substantial variety in tastes for lifetime mileage, as the 10th and 90th percentiles are -1.17 and -0.37, respectively. Turning to engine size, we find that owners are quite sensitive to this measure, as they are willing to pay, on average, 1.39 23InappendixBarethefiguresillustratingthedistributionofwillingness-to-payforlifetimemiles,enginesize,and emptyweight. 17

Table3: Willingness-to-payfortruckcharacteristics(elasticities) truck mean standard Percentiles characteristic deviation 10th 25th 50th 75th 90th MilesperGallon 0.91 0.39 0.51 0.71 0.95 1.12 1.33 (0.22) (0.10) (0.30) (0.26) (0.23) (0.22) (0.23) LifetimeMiles -0.85 0.30 -1.17 -1.06 -0.93 -0.68 -0.37 (0.06) (0.06) (0.15) (0.10) (0.06) (0.06) (0.04) EngineSize 1.39 1.05 0.14 0.82 1.45 2.04 2.72 (0.45) (0.26) (0.26) (0.36) (0.53) (0.65) (0.72) EmptyWeight 0.45 0.25 0.24 0.34 0.49 0.60 0.69 (0.15) (0.06) (0.18) (0.16) (0.15) (0.15) (0.17) Note: Standarderrorsareinparenthesisandarecomputedbybootstrapping. percent of their truck’s price for a 1 percent increase in engine size (i.e. cubic inch displacement). Further,thereiswidedispersionintastesamongowners,withthoseinthelefttailofthedistribution hardlywillingtopayforincreasedenginesize(atthe10thpercentile,ourelasticityestimateis0.14) whereas those in the right tail have elasticities greater than 2 (at the 90th percentile, our elasticity estimate is 2.72). In contrast, truck owners tastes for empty weight are more narrowly distributed, withanaverageelasticityof0.45. Returning to the fuel-efficiency estimates, we find that owners of newer vintage trucks have higher levels of willingness-to-pay for MPG. We illustrate thisin figure 7, where we plot thecdf of willingnesstopayforMPGconditionalonownershavingpurchasedavintage0truckandavintage 8 truck. From vintage 0 to vintage 8, there is a leftward shift in truckers’ willingness to pay for MPG,evidencedbythemedianshiftingfrombeinggreaterthan1forvintage0truckownerstoless than1forvintage8truckowners. 5 Analysis In this section, we compare our estimates of willingness to pay for MPG to the expected lifetime savings of an increase in fuel efficiency. For each truck j in our sample, we compute the expected discounted fuel savings associated with a 1 percent increase in MPG. These savings vary across 18

Figure7: Distributionofwillingness-to-payformilespergallonconditionalonvintagepurchased 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 −1 −0.5 0 0.5 1 1.5 2 2.5 3 Elasticity ycneuqerF Vintage 0 Vintage 8 19

trucks, because they are function of the truck’s characteristics. Formally, we first define expected futurefuelcostsforatruckwithmpg as j (cid:32) (cid:33) L m(v,x ) FC(mpg )= ∑ δ(v−νj)h(ν ,v) j d(v−ν ) j j j mpg v=νj j whereListhemaximumpossiblelifetimeofatruckandδisthediscountrate. Thefunctionh(ν ,v) j istheprobabilitythatatruckofvintageν survivestoagev,m(v,x )istheexpectedannualmileage j j of a truck of vintage v with characteristics x , and d(x) is the expected price of diesel x years in the j futurefrom1992. Expectedfuelsavingsfroma1percentincreaseinMPGisthenjust FS(mpg )=FC(1.01·mpg )−FC(mpg ) (10) j j j TocomputeFS(mpg )foreverytruck j,weneedtodetermine(i)trucks’survivalrates,(ii)expected j annualmileage,(iii)thediscountrate,and(iv)expecteddieselprices. 5.1 Survival rates We use the Transportation Energy Data Book (Davis et al., 2014) for the survival rates of heavy trucks and, based on this schedule, set the maximum age of a truck, L, to 30 years.24 These survival rates are estimated using registration data on heavy trucks following the method outlined in GreenspanandCohen(1996). 5.2 Expected annual mileage To forecast trucks’ expected mileage, we use the detailed VIUS data on class 8 long-haul trucks, whichincludesavariablerecordingannualmileage. ThissubsetoftheVIUScontains26,668observationsandallowsforadetailedanalysisofhowannualmileagevarieswithatruck’scharacteristics. In these data, truck age is recorded up to vintage 9; all trucks of vintage 10 and older are recorded with the same catch-all vintage 10. Further, we find that the annual mileage of the newest trucks, vintage 0, is unreliable. Annual mileage decreases with vintage except when comparing vintage 0 24ThesurvivalratesweusearereportedintheAppendix,intableC2. 20

to vintage 1 trucks.25 This unusual feature probably reflects the fact that vintage 0 truck owners are more likely to own (and so drive) their trucks for less than a year, which makes them more likelytounderstatetheirannualmileage. Assuch,inouranalysiswedropvintage0andvintage10 observations. We use a regression to estimate how annual mileage varies with truck characteristics. In addition to fitting the data well, a goal of this approach is to forecast annual mileage out of sample, because our expected fuel savings measure takes into account the potential for a truck to be operated for 30 years. We found that a log-log specification performed best. In contrast, the linear and quadraticspecificationswetried,whileprovidingbetterin-samplefits,consistentlypredictednegative annual mileage out-of-sample. Formally, we estimate the following regression using weighted least-squares: log(miles )=θ +θ ν +θ log(mpg ) j 0 1 j 2 j 5 +θ log(engsize )+θ log(empwt )+θ cabtype + ∑κ 1 +ε , (11) 3 j 4 j 5 j k makej=k j k=1 wheremiles isannualmiles,engsize isenginesize,empwt isemptyweight,cabtype isadummy j j j j variable equal to 1 for trucks with a conventional cabin type, make is the brand of truck j, and ε j j is an error term. The variable 1 is an indicator function equal to 1 when x=y, and so controls x=y for brand differences in the above regression. The weights used when estimating the regression are theVIUSsampleweights. We find the expected result that vintage has a negative impact on annual mileage (see table 4). Further,therearelargedifferencesacrossbrandsintermsofmileage. Moresurprisingly,wefindthat theeffectofMPGonmilesdriven,althoughestimatedtobeasmallpositivenumber,isstatistically insignificant. The log-log specification provides a reasonable forecast of annual mileage out-of-sample, for vintages 10 through 30. As a rough check on these predictions, we compare them against the annual mileage reported by the old trucks in the our data (those trucks for which we only know that the vintage is greater than 9). Specifically, for these trucks we compute the 10th, 25th, 50th, 75th, and 90th percentiles of the distribution of annual miles. We then predict annual miles out- 25Vintage0are1993and1992modelyeartrucks. Vintage1are1991modelyeartrucks. Thissameoddincreasein annualmileagefromvintage0tovintage1isobservedinthe1997VIUS. 21

Table4: Predictingannualmileage,estimatedcoefficients IndependentVariable Coefficient Estimate SE Intercept 10.56 (0.17) vintage -0.10 0.00 log(mpg) 0.04 0.03 log(engsize) 0.23 0.05 log(empwt) 0.07 0.02 cabtype -0.11 0.01 Internationalbrand 0.23 0.02 Kenworthbrand 0.37 0.02 Mackbrand 0.02 0.03 Peterbuiltbrand 0.39 0.03 Freightlinerbrand 0.26 0.02 Note: Reportedaretheestimatedcoefficientsofaregressionwherethedependentvariableisthelogofannualmileage. SEisstandarderrorandFordisthereferencebrand. Thereare16,864observationsandtheR-squaredis0.13. of-sample for all (the young) trucks in the data used to estimate the regression, supposing these trucks’ vintage is equal to 10, 11, ... , and 30. We then compute the percentiles of the resulting distribution of predicted annual miles.26 We emphasize this is a rough check of our out-of-sample predictions, because truck characteristics are likely to be different across the sets of young and old trucks. Reassuringly, the distribution of predicted miles is somewhat close to the distribution of actual miles, at least for the 25th, 50th and 75th percentiles (see table 5). We have confidence then, thatourpredictionofannualmileageout-of-samplearereasonable. 5.3 Discount rate We assume that truck owners’ discount rate is 6 percent. We arrive at this rate by first taking Moody’s BAA rate as indicative of the rates that owner’s receive when seeking to finance the purchaseatruck.27 In1992,theaveragenominalrateforaBAAcorporatebondwas8.98percent. This 26Toaccountforthefactthattrucksmightbescrappedbeforereachingvintage30weusethesurvivalratesdescribed earlierinthissectionasweights. 27BAAindicatesthereismoderatecreditrisk. 22

Table5: Out-of-samplecheckonpredictedannualmileage(vintages10+) Percentiles 10th 25th 50th 75th 90th Data 3,000 8,000 27,417 52,503 80,000 Predicted 9,755 15,150 24,506 34,832 43,375 Note: Dataaretruckswithavintagegreaterthan9inthedetailedVIUSdatasetoflong-haultrucks. Thepercentiles forthesetrucks’annualmileagearecomputedusingVIUSsampleweights. Predictedareanout-of-sampleforecastof annualmiles,givenvintagesequalto10,11,... ,30. Thepercentilesofthepredictedannualmilesarecomputedusing weightsequaltotheproductoftheVIUSsampleweightsandsurvivalrates. rateseems reasonablegiven theaverage ratein1992 on48 monthnew carloansto householdswas 9.3 percent.28 Rounding to 9 percent and accounting for the 3 percent rate of inflation in 1992, we endupwithdiscountrateof6percent.29 5.4 Expected diesel prices Finally, we assume that truck owners view diesel prices as a random walk, and therefore expect future prices to be equal to the current price. Based on a combination of World Bank and Energy Information Administration (EIA) data on prices, we compute that the average price of diesel per gallonintheU.S.in1992is$1.084.30 Intherobustnesssection,were-doouranalysisassumingthat truckownershaveperfectforesightoverdieselpricesandfindthatourmainresultsdonotchange. 5.5 Expected fuel savings Fromthesedata,wecomputetheexpectedfuelsavingscorrespondingtoa1percentincreaseinfuel efficiency. In our sample, the expected fuel savings vary considerably, from a minimum of $225 to amaximumof$1,522. However,80percentoftruckownersfallbetween$489and$1,121,the10th 28ThisrateispublishedbytheBoardofGovernorsintheirG.19ConsumerCreditreport. 29We use the Bureau of Labor Statistics consumer price index for all urban wage earners to calculate the rate of inflationin1992. 30The World Bank publishes U.S.diesel prices per liter, which we converted to gallons. The (converted) prices are $1.060and$1.022for1992and1998respectively. TheEIA’spublishedpricein1998is$1.044. Applyingthepercent changeinWorldBankpricestotheEIAprice,wearriveatadieselpriceof$1.084in1992. 23

Table6: ExpectedfuturefuelsavingsbyvintageandMPG(dollars) Vintage 5MPG 6MPG 7MPG 8MPG 0 1,341 1,125 970 853 1 1,193 1,001 863 759 2 1,058 888 766 673 3 934 784 676 594 4 820 688 593 522 5 728 611 526 463 6 646 542 467 411 7 574 481 415 365 8 510 428 369 324 Note: MPGismilespergallon. Thistablereportstheexpectedfuturefuelsavingsofa1percentincreaseinMPGfora givenpairofvintageandMPG,holdingallothertruckcharacteristicsfixedattheirmeanvalues. and 90th percentiles respectively. To provide a sense of how these savings depend on the mileage and age of each truck, in table 6 we report our calculations of the expected lifetime savings for specificvintageandmileagepairs,holdingfixedallothertruckcharacteristicsattheirmeanvalues. Owners of lower MPG trucks gain the most from an increase in fuel efficiency, because their total fuelcostsareappreciablyhigher. Similarly,ownersofyoungertruckscanexpecthigherfuelsavings becausetheycanexpectmoreyearsofusageoverwhichtoaccumulatethesavings.31 Using our estimates of the price elasticities with respect to fuel efficiency, we calculate each truck owner’s willingness to pay for such an increase. We then take the ratio of a truck owner’s willingness to pay over the expected lifetime fuel savings, to measure by how much truck owners undervalue expected fuel savings. We convert this measure into a percent, aggregate across truck ownersusingtheVIUSsampleweights,andgraphits(kernel-smoothed)distributioninfigure8. Asillustratedinfigure8,truckownersconsiderablyundervaluelifetimefuelefficiencysavings. On average, owners are willing to pay for only 29.5 percent of the lifetime fuel cost savings that accruefroma1percentincreaseinMPG.Atthe90thpercentile,ownersarewillingtopayfor54.5 percent of the lifetime fuel savings and those at the 10th percentile are willing to pay for only 8.8 31In our analysis, we abstract away from tax considerations. This is because trucking corporations can treat both fuel costs and fuel-efficiency investments as expenses when calculating their net income for tax purposes. Similarly owner-operatorscandeductbothfuelcostsandfuel-efficiencyinvestmentsfromtheirtaxes. 24

Figure8: Distributionoftruckowners’valuationoflifetimefuelsavings 0.025 0.02 0.015 0.01 0.005 0 −20 0 20 40 60 80 100 Percent ycneuqerF 25

Table7: Summarystatisticsonthefuelsavingsvaluationdistribution(percent) mean standard Percentiles deviation 10th 25th 50th 75th 90th 29.5 19.3 8.8 15.8 27.1 41.9 54.5 (0.1) (0.1) (0.2) (0.2) (0.1) (0.1) (0.2) Note: Standarderrorsareinparenthesisandarecomputedusingbootstrapping. percentthesavings(seetable7). Another way to view these results is to compute the discount rate at which a truck owner’s willingnesstopayfora1percentincreaseinMPGisequaltotheassociatedlifetimefuelefficiency savings. We calculate these discount rates across all long-haul truck owners and find that it ranges from0.31to0.82(the10thand90thpercentile,respectively)withamedianvalueof0.64,whichis markedlyhigherthanthe0.06thatweassumedinsection5.3. Theheterogeneityamongtruckownerswithregardtotheirwillingnesstopayforfuelefficiency is related to their truck’s vintage. In particular, owners of newer trucks have a higher valuation of future fuel savings than owners of older trucks. We illustrate this point by plotting the cdf of the distribution of owner’s valuation of future fuel savings conditional on the owners truck being of vintage 0 and vintage 8 (figure 9). In comparing these two cdfs, we see that the median vintage 0 truck owner is willing to pay for about 53 percent of future fuel savings, whereas the median vintage 8 owners is willing to pay about 9.7 percent. This pattern is reported in Allcott and Wozny (2014) for light vehicles, and likely reflects usage, in that the average annual mileage of long-haul trucks steadily decreases by vintage. Whereas vintage 0 trucks are driven more than 100,000 miles in a year, vintage 8 trucks are driven about 63,000 miles. Because of the difference in willingnessto-pay, the model predicts that technologies that improve fuel efficiency will be disproportionately incorporatedonthenewesttrucks. Anotherdifferenceacrosstruckownersisthatthosewhichownmorefuel-efficienttruckshavea higher valuation of future fuel savings. To demonstrate this feature of our results, we divide the set oftruckownersintoquartiles,basedontheMPGoftheirtruck-tractor. Wethenplotthedistribution oftruckers’fuelsavingsvaluationforeachquartileinfigure10.32 Asillustratedinthefigure,long- 32 Ratherthanshowingastrictdecompositionoftheprobabilitydistributionofthevaluationratio,weexplicitlyreestimatethedistributionofthevaluationratioforeachquartile. Asaresult,theoptimalbandwidthsmaydifferfromthe 26

Figure9: Cdfofvintage0andvintage8truckowners’valuationoffuturefuelsavings 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 −20 0 20 40 60 80 100 Percent ycneuqerF Vintage 0 Vintage 8 27

Figure10: Truckowners’valuationoffuturefuelsavingsbyMPGquartile 0.03 0.025 0.02 0.015 0.01 0.005 0 −60 −40 −20 0 20 40 60 80 100 120 Percent ycneuqerF 1st Quartile 2nd Quartile 3rd Quartile 4th Quartile haul truckers who purchased high MPG trucks have fuel savings valuation closer to 100 percent relativetothosewhichpurchasedlowMPGtrucks. 5.6 Robustness Inthissection,weconsidertherobustnessofourmainresultalongtwodimensions. Wefirstrepeat our analysis using the 1997 VIUS and October 1997 Truck Blue Book price data. As described at theendofsection3,weareabletomergethesetwodatasetsusingthesameapproachtakenforthe 1992data. Inrepeatingourworkonthe1997datasets,wefindthatlong-haultruckerssubstantially undervalue future fuel savings, confirming the benchmark 1992 results. In fact, the undervaluation is larger in 1997, with the average long-haul trucker willing to pay for only 11.8 percent of the expected future fuel savings associated with a 1 percent increase in MPG (see the second row of table8). bandwidthchosenforthewholepopulation. Thisexplainswhyweobservenonzeromassabove80%inthedistribution ofsomeofthequartiles,butnotinthedistributionforthewholepopulation. 28

Table8: Distributionofundervaluationusingdifferentassumptions Percentiles Mean SD 10th 25th 50th 75th 90th 1992VIUS 8.8 15.8 27.1 41.9 54.5 29.5 19.3 Benchmark (0.2) (0.2) (0.1) (0.1) (0.2) (0.1) (0.1) 1997VIUS 2.4 7.5 10.8 15.8 22.9 11.8 8.5 (0.2) (0.1) (0.1) (0.1) (0.1) (0.1) (0.1) Perfectforesight 8.4 15.0 25.6 39.2 51.1 27.7 18.0 (0.2) (0.2) (0.1) (0.1) (0.2) (0.1) (0.1) Note: Benchmark results are the same as those reported in table 7. 1997 VIUS are the results when using the 1997 VIUSandOctober1997TruckBlueBookprices. Perfectforesightaretheresultswhenusingrealizedrealdieselprices from1992onward. SDisstandarddeviation. Standarderrorsareinparenthesisandarecomputedusingbootstrapping. We then checked the robustness of the assumption that truckers’ view diesel prices as a random walk by recomputing the expected future fuel savings using actual diesel prices. Annual onhighway diesel prices are published by the Energy Information Administration from 1995 onward (see table C3 in the appendix). We linearly interpolate prices for 1993 and 1994 and assume a random walk for diesel prices after 2014.33 Under this assumption, our main undervalution result still holds,withtheaveragelong-haultruckerwilling-to-payforonly27.7percentoftheexpectedfuture fuelsavingsfroma1percentincreaseinMPG. 5.7 SuperTruck analysis Inthe2011finalrulingannouncingthefuelefficiencyregulations,theNHTSAandtheEPAemphasized that heavy truck manufacturers should be able to meet the new fuel efficiency requirements using already existing technologies. Innovations such as low-resistence tires, better aerodynamics, and incremental improvements in heavy duty engines can all be used, these agencies argue, to dramaticallyimprovefuelefficiency.34 The SuperTruck program aptly makes this argument. This research program was funded by the Argonne National Laboratory and the Department of Energy with the goal of demonstrating the 33Becauseofdiscounting,howdieselpricesareextrapolatedbeyond2014haslittleeffectonourresults. 34Fordetailedarguments,seetheRegulatoryImpactAnalysisreportontheseregulationsjointlypublishedbytheEPA andtheNHTSAathttp://www.nhtsa.gov/staticfiles/rulemaking/pdf/cafe/Truck_CAFE-GHG_RIA.pdf. 29

feasibiltyofa50percentimprovementinfuelefficiencyforclass8long-haultruckscomparedwith current models.35 As part of this research program, four teams headed by different truck manufacturers modified a long-haul truck with the goal of dramatically increasing its fuel efficiency. The result from this work are summarized with the presentation of two different technology platforms. Thefirstincreasesthetruck’sMPGby65.3percentforacostequalto26.6percentofthepriceofa new truck. The second modification increases MPG by 69.8 percent for a cost equal to 51 percent of a new truck. The report than makes predictions about truck owners’ willingness to adopt these newtechnologiesovertime. GiventhefuelefficiencybenefitsandcostsofthetwoSuperTrucktechnologyplatforms,ourestimatesofwillingness-to-payprovideinsightonwhethertruckownerswouldadopteitherplatform. Inparticular,usingourestimatedelasticities,wecancomputethefractionofvintage0truckowners that would be willing to pay these costs in order to benefit from the higher fuel efficiency. For the first SuperTruck platform, a truck owner with an elasticity of 0.407=26.6/65.3 would be indifferent betweenadoptingornotadoptingthetechnologicalimprovements. Forthesecondmodification,the indifferent truck owner has an elasticity of 0.731. Based on our estimated distribution of willingnesstopayforfuelefficiencyforvintage0truckowners(seefigure7),wefindthat93.6percentof new heavy truck owners would be willing to pay the costs of the first modification for the increase fuel efficiency. The second modification would be slightly less popular, with 80.9 percent of new heavy truck owners willing to pay for the costs associated with the increase in fuel efficiency. Further, using a compensating variation approach, we find that all truck owners strictly prefer the first modificationoverthesecond. Ourresultsareencouraginginthatthemodelpredictsthatastrongmajorityofnewtruckowners are willing to bear the costs of adopting the fuel-saving innovations proposed by the SuperTruck program. A caveat with our analysis is our estimates are based on observations recorded in 1992, morethantwentyyearsago. Althoughwedonotexpectthesedeepparametersofthetruckowner’s problem to vary much with time, it is not unreasonable to worry that these elasticities may have changedovertwentyyears. 35Thefinalreportofthisprogramcanbefoundathttp://www.transportation.anl.gov/pdfs/TA/903.PDF. 30

6 Conclusion Inthispaper,weestimatethattruckownersoflong-haultruckswillingness-to-payforMPG.Wefind thereisawiderangeinwillingness-to-payacrosstruckowners,withtheelasticityoffuelefficiency topricerangingfrom0.51(10thpercentile)to1.33(90thpercentile). Onaverage,trucksownersare willingtopay0.91percentoftheirtruckpriceforaonepercentincreaseinMPG.Wethencompute the expected lifetime savings from a 1 percent increase in MPG and compare this measure against truck owners’ willingness-to-pay. Overall, we find that truck owners undervalue future gains from increased fuel efficiency. On average, we find that owners are willing to pay for only 29.5 percent oftheexpectedlifetimesavingsassociatedwitha1percentincreaseinMPG.Thislowvaluationof fuel efficiency suggests that the federal government’s policy of setting fuel efficiency standards for mediumandheavytruckscouldbeaneffectivepolicytooltoraisefueleconomy. Looking ahead, a substantial amount of research still needs to be done analyzing the effectiveness of fuel standards on medium and heavy trucks. We are interested to see whether subsequent studies on long-haul truck-tractors, which presumably will find and use different datasets and techniques, will support our main results. Furthermore, more work needs to be done determining why truckowners’undervaluefuturefuelsavings(e.g.,VernonandMeier(2012)explorehowprincipalagent problems can lead to under-investment in fuel efficiency technologies). Finally, the overall effectiveness of fuel efficiency standards depends upon their effects on more than the subset of mediumandheavytrucksthatweconsideredinouranalysis. 31

References Ackerberg, Daniel, Lanier Benkard, Steven Berry, and Ariel Pakes (2007) “Econometric Tools for AnalyzingMarketOutcomes,”inJamesHeckmanandEdwardLeamereds.HandbookofEconometrics: North-Holland. Allcott,HuntandNathanWozny(2014)“GasolinePrices,FuelEconomy,andtheEnergyParadox,” ReviewofEconomicsandStatistics,Vol.96(5),pp.779–796. Bajari, Patrick and Lanier Benkard (2005) “Demand Estimation with Heterogeneous Consumers and Unobserved Product Characteristics: A Hedonic Approach,” Journal of Political Economy, Vol.113(6),pp.1239–1276. Bajari, Patrick and Matthew Kahn (2005) “Estimating Housing Demand with an Application to ExplainingRacialSegregationinCities,”JournalofBusinessandEconomicStatistics,Vol.23(1), pp.20–33. Baker,GeorgeandThomasHubbard(2004)“ContractibilityandAssetOwnership: On-BoardComputers and Governance in U.S. Trucking,” Quarterly Journal of Economics, Vol. 119(4), pp. 1443–1479. Bento, Antonio, Shanjun Li, and Kevin Roth (2012) “Is there an energy paradox in fuel economy? A note on the role of consumer heterogeneity and sorting bias,” Economic Letters, Vol. 155(1), pp.44–48. Berry,Steve,JamesLevinsohn,andArielPakes(1995)“AutomobilePricesinMarketEquilibrium,” Econometrica,Vol.63(4),pp.841–890. Busse, Meghan, Christopher Knittel, and Florian Zettelmeyer (2013) “Are Consumers Myopic? Evidence from New and Used Car Purchases,” American Economic Review, Vol. 103(1), pp. 220–256. Davis, Stacy, Susan Diegel, and Robert Boundy (2014) “Transportation Energy Data Book,” PreparedfortheU.S.DepartmentofEnergy. 32

Fan, J. and I. Gijbels (1996) Local Polynomial Modelling and Its Applications: Monographs on StatisticsandAppliedProbability66. Fan, Jianqing, Qiwei Yao, and Howell Tong (1996) “Estimation of conditional densities and sensitivitymeasuresinnonlineardynamicalsystems,”Biometrika,Vol.83,pp.189–206. Goldberg, Pinelopi (1998) “The Effects on the Corporate Average Fuel Economy Standards in the US,”JournalofIndustrialEconomics,Vol.46,pp.1–33. Greenspan, A. and D. Cohen (1996) “Motor Vehicle Stocks, Scrappage, and Sales,” Finance and economicsdiscussionseries,v96(40). Grigolon,Laura,MathiasReynaert,andFrankVerboven(2014)“ConsumerValuationofFuelCosts and the Effectiveness of Tax Policy: Evidence from the European Car Market,” University of Leuvenworkingpaper. Helfand,GloriaandAnnWolverton(2011)“Evaluatingtheconsumerresponsetofueleconomy: a review of the literature,” International review of environmental and resource economics, Vol. 5, pp.103–146. Hubbard, Thomas (2003) “Information, Decisions, and Productivity: On Board Computers and CapacityUtilizationinTrucking,”AmericanEconomicReview,Vol.93(4),pp.1328–1353. Koster,Hans,JosvanOmmeren,andPietRietveld(2014)“AgglomerationEconomiesandProductivity: A Structural Estimation Approach Using Commercial Rents,” Economica, Vol. 81, pp. 63–85. Maclean Hunter Market Reports, Inc. (1992a) 1992 Truck Identification Book: Official Vehicle Identification,Vol.18,No.1,Chicago,IL. (1992b)TheTruckBlueBook,Vol.82,No.4,Chicago,IL. National Market Reports, Inc. (1997a) 1997 Truck Identification Book: Official Vehicle Identification,Vol.23,No.1,Chicago,IL. (1997b)TheTruckBlueBook,Vol.87,No.4,Chicago,IL. 33

NHTSA-EPA (2011) “Greenhouse Gas Emissions Standards and Fuel Efficiency Standards for Medium-andHeavy-DutyEnginesandVehicles,”PublishedintheFederalRegister[vol76(179)] onSeptember15,2011. (2015) “Proposed Rulemaking for Greenhouse Gas Emissions and Fuel Efficiency Standards for Medium- and Heavy-Duty Engines and Vehicles – Phase 2,” Draft Regulatory Impact Analysis. Parry,Ian,MargaretWalls,andWinstonHarrington(2007)“AutomobileExternalitiesandPolicies,” JournalofEconomicLiterature,Vol.45,pp.373–399. Racine,Jeffrey(2008)“Nonparametriceconometrics: aprimer,”FoundationsandTrendsinEconometrics,Vol.3(1),pp.1–88. Torrey IV, W. Ford and Dan Murray (2014) “An Analysis of the Operational Costs of Trucking: 2014Update.” Vernon,DavidandAlanMeier(2012)“Identificationandquantificationofprincipalagentproblems affectingenergyefficiencyinvestmentsandusedecisionsinthetruckingindustry,”EnergyPolicy, Vol.49,pp.266–273. West, Sarah and Robert Williams III (2005) “The cost of reducing gasoline consumptions,” AmericanEconomicReviewPapersandProceedings,Vol.95(2),pp.294–99. Wollmann, Thomas (2014) “Trucks without bailouts: Equilibrium product characteristics for commercialvehicles,”11,HarvardUniversitymanuscript. 34

TableA1: Filteringofthe1992and1997VIUSdata Observations Sampleweights number percent sum percent 1992 VIUSdataset 123,641 100.0 5,920,075,519 100.00 Onlytruck-tractors 42,108 34.1 116,817,124 1.97 Havethreeaxles 32,240 26.1 83,909,899 1.42 Haveaconventionalorcabin-over-enginedesign 31,335 25.3 81,696,386 1.38 Havedieselengineandairbrakes 30,591 24.7 79,208,583 1.34 Donotspendmostoftheirtimeoff-road 29,588 23.9 77,244,933 1.30 Hasthecorrectbodytype 26,668 21.6 70,086,661 1.18 1997 VIUSdataset 104,545 100.0 72,800,251,891 100.00 Onlytruck-tractors 27,956 26.7 1,543,752,184 2.12 Havethreeaxles 21,749 20.8 1,140,559,205 1.57 Haveaconventionalorcabin-over-enginedesign 20,611 19.7 1,074,940,667 1.48 Havedieselengineandairbrakes 19,867 19.0 1,030,056,985 1.41 Donotspendmostoftheirtimeoff-road 19,292 18.5 1,005,571,131 1.38 Hasthecorrectbodytype 17,385 16.6 919,831,799 1.26 A Filtering of the VIUS data In table A1 we report how the different filters we used to identify class 8 long-haul trucks in the VIUS reduced the size of the sample, both in terms of the number of actual observations and the impliedaggregatenumberoftrucksbaseduponthesurvey’ssampleweights. 35

FigureB1: Distributionofwillingness-to-payforlifetimemiles 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 2.5 Elasticity ycneuqerF B Willingness-to-pay figures Figures B1 to B3 illustrate the kernel-smoothed distribution of long-haul truckers willingness-topay for lifetime miles, engine size, and empty weight, respectively. As noted in the paper, for each graph,wecomputedtheoptimalbandwidthforthekernel-smoothingprocedureusingleave-one-out cross-validation to minimize the mean squared integrated error of the distribution (see appendix E fordetails). 36

FigureB2: Distributionofwillingness-to-payforenginesize 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 −10 −8 −6 −4 −2 0 2 4 6 Elasticity ycneuqerF FigureB3: Distributionofwillingness-to-payforemptyweight 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 −1 −0.5 0 0.5 1 1.5 Elasticity ycneuqerF 37

TableC2: Survivalratesbyvintage Vintage 1 2 3 4 5 6 7 8 9 10 SurvivalRate 100 100 100 98.5 96.7 94.5 92.0 89.1 86.0 82.7 Vintage 11 12 13 14 15 16 17 18 19 20 SurvivalRate 79.1 75.4 71.6 67.7 63.7 59.7 55.7 51.8 47.9 44.2 Vintage 21 22 23 24 25 26 27 28 29 30 SurvivalRate 40.6 37.1 33.7 30.6 27.6 24.8 22.2 19.8 17.6 15.5 Thescrappageratesaretakenfromtable3.14oftheTransportationEnergyDataBook (Davisetal.,2014)published bytheDepartmentofEnergy. Vintage0trucks(notshown)survivewith100percentprobability. C Details on the expected fuel savings calculations In table C2 we report the survival rates used to compute lifetime fuel savings for trucks. The scrappageratesareestimatedusingregistrationdataonheavytrucks(i.e.,truckswithagrossvehicle weight over 26,000 pounds), following the method described in Greenspan and Cohen (1996). We usethescrappageratesestimatedfora1980model-yearheavytruck.36 IntableC3wereportnominalandrealdieselprices. Nominalpricesweredownloadedfromthe Energy Information Administration and deflated using the personal consumption expenditure price indexpublishedbyBureauofEconomicAnalysis. 36In the same table are the estimated scrappage rates for a 1990 model year heavytruck. But the estimates for the 1980 model year seem more reasonable to us. This is because the median life of a 1990 model year heavy truck is estimatedtobe28.0years,adramaticincreaseovertheestimatedlifeof1970and1980modelyeartrucks,whichare 20 and 18.5 years, respectively. Using the 1990 model year scrappage estimates would increase our estimated fuel savingsfromanincreaseinMPG,reinforcingourmainresultthattrucksundervalueexpecteddiscountedsavingsfrom increasedfuelefficiency. 38

TableC3: On-highwaydieselfuelprices Year Nominalprice Realprice 1992 1.084 1.084 1993 1.092 1.066 1994 1.101 1.052 1995 1.109 1.038 1996 1.235 1.132 1997 1.198 1.080 1998 1.044 0.934 1999 1.121 0.988 2000 1.491 1.282 2001 1.401 1.182 2002 1.319 1.098 2003 1.509 1.232 2004 1.810 1.443 2005 2.402 1.861 2006 2.705 2.042 2007 2.885 2.124 2008 3.803 2.717 2009 2.467 1.764 2010 2.992 2.104 2011 3.840 2.636 2012 3.968 2.675 2013 3.922 2.612 2014 3.825 2.514 Note: 1995to2015nominalpricesarepublishedbytheEnergyInformationAdministration(EIA).The1992nominal priceisderivedfromWorldBankandEIAdataondieselprices.Specifically,theWorldBankpublishesU.S.dieselprices perliter,whichweconvertedtogallons. The(converted)pricesare$1.060and$1.022for1992and1998respectively. TheEIA’spublishedpricein1998is$1.044. ApplyingthepercentchangeinWorldBankpricestotheEIAprice,we arriveatadieselpriceof$1.084in1992. Toarriveat1993and1994prices,weusealinearinterpolationbetween1992 and 1995. To arrive at real prices, nominal prices are deflated by the personal consumption expenditure price index, publishedbytheBureauofEconomicAnalysis. 39

D Estimation details Thesolutiontotheweightedleastsquaresproblem(seeequation8)isgivenby (cid:34) (cid:35) J ωˆ (p)=(XTWX )−1XTW ∑e K (p −p) , (D1) j D D D k h k k=1 (cid:0) (cid:1) whereω (p)isthevector α (p),λ (p),γ (p) ,W =diag{K (x −x)},e isthekth unitvector,and j j j j B j k X isthedesignmatrixofequation(8)givenby D   1 (x −x)T vech((x −x)(x −x)T)T 1 1 1  1 (x −x)T vech((x −x)(x −x)T)T  2 2 2  X D =  . . . . . . . . .   (D2)   1 (x −x)T vech((x −x)(x −x)T)T J J J In particular, the notation vech(A) denotes the half-vectorization of the symmetric matrix A. I.e., if A is an l×l matrix, then vech(A) is the vector in Rl(l+1)/2 whose first l entries are the first column of A, whose subsequent l−1 entries are the second column of A below the diagonal, etc... From this solution, our estimate of the conditional density function follows immediately. It is just (cid:91) gˆ (p|x )=α (p),anditsderivativesare ∂ g (p|x )=λ ˆ (p). j j j ∂x k j j j,k We can also note the expected value of the bracketed sum in equation (D1) is mechanically just thevectorofobservedprices. Toseethis,observethattheprojectionmatrix(XTWX )−1XTW does D D D not depend on the price. Moreover, since K (p −p) is just a symmetric pdf centered at p , it must h k k bethecasethatforanyvaluesofhand p ,wehaveE(K (p −p))= p . So,takingexpectedvalue k h k k 40

ofequation(D1), (cid:34) (cid:35) J E(ωˆ (p))=(XTWX )−1XTW E ∑e K (p −p) j D D D k h k k=1 (cid:34) (cid:35) J =(XTWX )−1XTW ∑e E{K (p −p)} D D D k h k k=1 (cid:34) (cid:35) J =(XTWX )−1XTW ∑e p D D D k k k=1 =(XTWX )−1XTWp D D D In other words, this conditional density estimator agrees with the more simple local quadratic estimatorontheexpectedvalueofthepricehedonicanditsderivatives. However,theadvantageofthis more general framework is that it allows us to actually recover estimates of the unobserved characteristic. Obtaining estimates of the unobserved characteristic has proven essential when recovering thefullutilityfunctionofeachfirm,includingtheirwillingnesstopayforthediscretecharacteristics (BajariandBenkard,2005). E Bandwidth selection and standard errors InordertocomputetheoptimalbandwidthhforthebandwidthmatrixB=hI,weuseleastsquares cross-validationtechnique,asdescribedinFanandGijbels(1996). Let pˆ (x)denotetheconditional h estimate of the price hedonic at a point x, using the bandwidth h. For each truck j, construct the leave-one-out estimate pˆ (x) by estimating the model on the subsample {p,x} . We then h,−j i i i(cid:54)=j examine and attempt to minimize the prediction error p −pˆ (x ). So we choose the bandwidth j h,−j j thatminimizesthecross-validationfunction CV = 1 ∑ n (cid:2) p −pˆ (x ) (cid:3)2 w(x), (E3) i h,−j j i n j=1 wherethefunctionw(·)isaweightingfunctionthatcorrespondstothe(scaled)inverseofthesample weights. 41

In our application, we select the optimal value of h numerically, by computing the crossvalidation score for every bandwidth value between 0 and 10, at intervals of 0.01, and selecting thevalueofhwhichproducestheminimumvalue. Foroursamplein1992,thisvalueis2.48. In order to compute the standard errors for the estimates of the distribution of taste parameters, we constructed bootstrap estimates by re-estimating the model on 10,000 random re-samplings of thedata(sampledwithreplacement). Tocomputethekernelsmootheddistributions,weuseN-fold(leaveoneout)cross-validationto selectthebandwidththatminimizesthemeansquaredintegratederrorofourestimateddistribution function. Formally,if fˆ istheestimateddistributionforagivenbandwidthh,anddata{X}n ,we h i i=1 partitionthedataintoNequallysizedsub-samples(consistingofasingleobservation)byassigning toeachobservationasamples(i). Wethenminimizethecross-validationfunction (cid:90) 2 n CV(h)= fˆ2(x)dx− ∑ fˆ (X), (E4) h n h,−s(i) i i=1 where fˆ isthedensityfunctionestimatedusingallofthedataexceptthesub-sampletowhich h,−s(i) observationibelongs. 42