Roads to Prosperity? Assessing the Link between Public Capital and Productivity

BoardofGovernorsoftheFederalReserveSystem InternationalFinanceDiscussionPapers Number592 October1997 ROADSTOPROSPERITY? ASSESSINGTHELINKBETWEENPUBLICCAPITALANDPRODUCTIVITY JohnFernald NOTE: InternationalFinanceDiscussionPapersarepreliminarymaterialscirculatedtostimulate discussionandcriticalcomment. ReferencesinpublicationstoInternationalFinanceDiscussionPapers (otherthananacknowledgmentthatthewriterhashadaccesstounpublishedmaterial)shouldbecleared withtheauthor orauthors. RecentIFDPsareavailableontheWebat www.bog.frb.fed.us.

ROADSTOPROSPERITY? ASSESSINGTHELINKBETWEENPUBLICCAPITALANDPRODUCTIVITY JohnFernald* Abstract:Atamacroeconomiclevel,infrastructureandproductivityarepositivelycorrelatedintheUnited Statesandothercountries. However,itremainsunclearwhetherthiscorrelationreflectscausation,andif so,whethercausationrunsfrominfrastructuretoproductivity,orthereverse. Thispaperfocusesonroads, andfindsthatvehicle-intensiveindustriesbenefitdisproportionatelyfromroad-building:whenroadgrowth changes,productivitygrowthchangesmorein industriesthatare morevehicleintensive. Theseresults suggestthatcausationrunsfrominfrastructuretoproductivity.However,thereisnoevidencethatatthe margin,roadsofferanabove-averagereturn;road-buildinginessenceofferedaone-timeboosttothelevel ofproductivityinthe1950sand1960s.Finally,itappearsthatcongestionsignificantlyaffectsroad-services atthemargin,althoughcongestiondoesnotappearimportantbefore1973. *FernaldisaneconomistintheInternationalFinanceDivisionoftheFederalReserveBoard,andcanbe contacted at fernaldj@frb.gov. An earlier version of this paper, entitled “How Productive is Infrastructure?”,wasChapter2 ofmy 1993HarvardPh.D. thesis. I thankRobertBarre, SusantoBasu, DavidCutler,BradDeLong,AndyLevin,BenPolak,and,especially,CharlesHulten,DaleJorgenson,and GregMankiwforhelpfuldiscussionsandcomments.Ialsothankseveralanonymousrefereesandseminar participantsatanumberofuniversitiesandinstitutionswhoprovidedfeedback.Theviewsinthispaperare solelytheresponsibilityoftheauthorandshouldnotbe interpretedasreflectingtheviewsoftheBoardof Governorsof the FederalReserveSystemor of any otherpersonassociatedwiththe FederalReserve System.

Recent macroeconomicliterature documentsa strong correlationbetween infrastructureand productivityintheUnitedStatesandotherwesterneconomies.However,itremainsunclearhowtointerpret thiscorrelation. Someauthorsarguethatinfrastructureprovideshighlyvaluableservicesto theprivate sector,andthattheslowdowninpublicinvestmentaftertheearly1970sexplainsasubstantialportionofthe widelynotedproductivityslowdown,whichoccurredaroundthe sametime. Bycontrast,otherauthors arguethatpubliccapitalisendogenous,sothatcausationrunsfromproductivitytopublicinvestment,orthat thecorrelationiscompletelyspurious,reflectingamisspecificationoftrend.1 Thispaperexplorestheinterpretationofthiscorrelationbyfocusingonroads,thelargestcomponent ofpubliccapital. In 1994,thevalueoftheroadstockwas$1.2trillion,worthnearlyaquarterofprivate businessGDP. Indeed,inthe1950sand1960s,road-buildingaccountedforasubstantialfractionofcapital formationintheUnitedStates,withnetinvestmentexceedingaquarterofthevalueofnetnon-residential privateinvestment.AsshowninFigure1,roadgrowthslowedsubstantiallyaftertheearly 1970s,andin percapitatermsthestockhaschangedlittlesincethen. IaskhowchangesinroadsaffecttherelativeproductivityperformanceofU.S. industriesfrom1953 to 1989. Ifroadsareproductive,thenindustriesthatuseroadsintensivelyshouldbenefitmore. Thereare no direct measuresof industryroad-use. Butgiventhe complementarilybetweenroads and vehicles, vehicle-useprovidesanindirectmeasureofroad-intensity. Thebasicstylizedfactofthispaperisthatchangesinroadgrowthareassociatedwithlargerchanges inproductivitygrowthinindustriesthataremorevehicleintensive.First,theslowdowninproductivityafter 1973appearslargerinindustrieswithhighervehicleshares. Second,whenroadgrowthrises,productivity growthtendstoriserelativetotheaverageinvehicle-intensiveindustriesandfallinnon-vehicle-intensive industries. Thus, the data stronglysupportthe notionthat industrieswith alot of vehiclesbenefited disproportionatelyfromroad-building. Thisfindingsuggeststhattheaggregatecorrelationbetweenproductivityandinfrastructurereflects 1 Aschauer(1989,1990)documentsthecorrelationforaggregateU.S. data. Otherstudiesusing aggregate,regional,orindustrydatafortheUnitedStatesandreportinga largeproductiveroleforpublic capitalincludeMorrisonandSchwartz(1996),KocherlakotaandYi(1995),NadiriandMamuneas(1994), andMunnell(1990). Studiesusingcross-countrydataincludeBerndtandHansson(1992)andFordand Poret (1991). ScepticsincludeHoltz-Eakin(1994a),Hultenand Schwab(1991),and Aaron (1991). Gramlich(1994)surveystheinfrastructureliterature,withadditionalreferences.

causationfromchangesintheroadstockto changesinproductivity. For example,supposeroadsdonot contributetoproductivityatthemargin,butareendogenous:asaggregateproductivity(andhenceincome) rises,thegovernmentchoosestobuildmoreroads. Onewouldnotthenexpectanyparticularrelationship betweenanindustry’svehicle-intensityanditsrelativeproductivityperformancewhenroadgrowthchanges. Alternatively,supposethecorrelationisspurious,reflectingacommontrendslowdownintheearly 1970s. Thereisnoreasontoexpectalargerchangeintrendforindustriesthatusea lotofvehicles. Constructionoftheinterstatehighwaysystempeakedinthelate 1950sandearly 1960s,andwas largely completedby 1973. The results suggestthat this constructionboom substantiallyboosted productivity.In particular,thepointestimatesimplythatpublicinvestmentshadabove-averageratesof return,andcontributedabout1percentagepointmoretoproductivitygrowthbefore1973thanafter. Hence, publicinvestmentcan explaina substantialshareof the 1.3 percentage-pointslowdownin productivity growth. Theseresultsraisean importantpolicyquestion: Doespublicinvestmentoffera continuing,but neglected,route to prosperity? That is, by buildingroads, can we return to a path of renewedhigh productivitygrowth?Theindustrydatadonotsupportthisconclusion:atthemargin,wecannotrejectthat roadsnowofferanormal(orevenzero)rateofreturn. Thus,thedataseemmostconsistentwithastoryin whichthemassiveroad-buildingofthe1950sand1960sofferedaone-timeboosttothelevelofproductivity, ratherthanapathtocontinuingrapidgrowthinproductivity. Thisconclusion–thatroadswereexceptionallyproductivebefore 1973butare notexceptionally productiveatthemargin—isconsistentwithsimplenetworkarguments.2Inparticular,buildinganinterstate networkmightbeveryproductive;buildinga secondnetworkmaynot. Theconclusionisalsoconsistent withcost-benefitstudies. TheCongressionalBudgetOffice(1991),forexample,surveysthesestudiesand reportsanestimatedaveragerealreturntonewurbanhighwayconstructionof 10to20percent. Finally,Iexploretheempiricalimportanceofcongestion.TheempiricalliteraturecitedinFootnote 1generallyignorescongestion,andassumesthatpubliccapitalisapurenon-rivalpublicgood. Asaproxy for congestion,I useameasureofaggregateroaduse: totalmilesdrivenbytrucksandautos. Figure1 2 Hulten(1994)discussesthenetworknatureofinfrastructureatlength. 2

showsthatmiles-drivencontinuedtogrowsteadilyafter1973(thoughataslower,andmorevariable,rate thanbefore1973),sothattheaverageutilizationofroads(e.g., milesdrivenperunitoftheroadstock)also rosesteadily. Atanaggregatelevel,miles-drivenperhapsbettermeasurestotalroadservicesratherthan congestion,whichreducesroadservices. For anindividualproducer,however,totalmiles-drivenlargely reflectsroadusebyotherproducers,andhenceshouldreduceroadservices. Congestiondoesnotappearempiricallyimportantbefore1973,butbecomesempiricallyimportant thereafter.Theseresultsmakeintuitivesense. Whentheinterstatehighwaysystemwasfirstbuilt,adding an additionalcar to the systemmay notaffectthe servicesavailableto any otheruser. As the system becomesmorecongested,addingmorecars(andhenceincreasingtotalmilesdriven)reducestheservices availableto anyoneelse. Hence,congestionis inherentlylikelytobe a non-linearprocess. Theresults suggestthatcongestiononlybecameimportantaftertheinterstatesystemwascompleted. SectionI developsformallythegrowth-accountingimplicationsoftheideathatvehicle-intensive industriesuseroadsintensively. SectionII describesthedata,anddiscussesseveraleconometricissues. SectionIIIpresentsresults. SectionIVconcludes. I. Method The first subsectionconsiderstheproductiondecisionsof firms, and formalizesthe notionthat industriesthathavea lotof vehiclesuse roadsrelativelyintensively. Theresultingestimatingequation impliesthatwhenroadserviceschange,productivityshouldchangeby morein industriesthatare more vehicleintensive. Thesecondsubsectiondiscusseshowtomodeltheservicesofroads,takingaccountof thenetworknatureoftheroadstockandthepotentialimportanceofcongestion. i. Growthaccountingwithpubliccapital Foreachindustry,supposetheproductionofvalue-addedoutput~ dependsoninputsofnon-vehicle capitalKi,laborLi, andtransportservicesthatareproducedwithinthesectorTi. output alsodependson theHicks-NeutralstateoftechnologyUi. Transportservicesdependupontheflowofservicesprovidedby theaggregatestockofgovernmentroadsGas wellasthestockofvehiclesinthesector~.. Hence,omitting 3

timesubscriptsforsimplicity,eachsectoralproductionfunctiontakestheform3 Y, = UiF ‘(Ki,Li,T(Vi,G)). (1) Notethattheproductionfunction(1)treatspurchasedandproducedtransportdifferently. Value addednetsoutthecontributionofintermediategoodstoproduction.Soif, forexample,asectorpurchases truckingservices,thisrepresentsvalueaddedinthetruckingsector,notinthepurchasingsector. Supposeeachfirmisperfectlycompetitiveandhasconstantreturnstoscaletoprivatefactors,which itcanadjustinstantaneously.LetF~representsthederivativeoftheproductionfunctionFwithrespectto inputJ. Cost-minimizationthenimpliesthattheelasticityof outputwithrespectto J, F~/F, equalsthat input’ssharein revenue,s~i.Thesharestoprivateinputssumto one, sothereare no economicprofits. Althoughwecannotdirectlyobservetheelasticityofoutputwithrespecttoroadservices,wecanexpresse itrelativetotheelasticitywithrespecttovehicles,givenbythesharesVi: F~G F~G FVV —= —*— (2) = $j”s~j. F [ FVV)( F ) Theparameter@eiqualstherelativeoutputelasticitiesofroadsandvehicles,andisthekeyparameterlinking observedvehicle-intensitietsounobservedroaduse. Weexpectthat@iispositive,whichcapturesthenotion thatvehicle-intensivseectorsarealsorelativelyroad-intensive.Aslongas@iispositive(evenifnotconstant overtimeandindustries),theestimatingequationbelowholdsatleastapproximately. However, furtherassumptionson technologygreatlysimpli~ the formalderivation,and aid in interpretingtheresults. Bytheseparabilityassumptionin (l), @iequalstheratiooftheelasticitieswith respectto GandVinproducingtransport: Y . (#)i I (3) TVV NowsupposeallsectorshavethesameCobb-DouglastransportaggregateT,so @i=@.Therestof theproductionfimctionremainscompletelygeneral,sotheroadelasticitycanchangeovertimeaslongas it remainsproportionalto thevehicle-share. ThisCobb-Douglasassumptionon Tprovidesa first-order 3 Theappendixconsidersthecaseinwhichindustry-specificroadstocksdifferfromtheaggregate roadstock,arisingfromdifferencesinthe regionaldistributionofproductionacrossindustries. Footnote 7brieflydiscussestheappropriatenessoftheassumptionthatavalue-addedproductionfunctionexists. 4

approximationto the true productionfunction,and greatlysimplifiesthe problem. It is worth noting, however,thatformakinginferencesaboutthemarginalproductivityofroads,thesecond-ordereffectsmay be crucial. Wecan approximateamoregeneralfunctionalformbyallowingthecoefficient@tochange overtime.4 Solow’sproductivityresidual,dpi,measuresthe growthin theproductivityof privateinputsin production.Letdjrepresentthegrowthrateofinput~,dY/~.Takingthetotal(logarithmic)differentialof theproductionfunction(l), substitutinginputsharesforoutputelasticities,andrearranging,wefind: dpi dyi- sKi”dki- sLi*dli- svi”dvi q (4) = $“(sviodg) + dul. Observedproductivitygrowthdependson technologyshocksduiplusthe contributionof governmentprovidedroads. Theservicesofthese roadsenterasanexternaleffectrelatedtovehicleuse. Aggregateproductivityshocks,d~equal aweightedaverageofsectoral shocks: & = ~ widpi, (5) i wherethesectoralweightswiarethesharesofnominalvalueaddedinaggregatevalueadded.5Hence, @ = @#g + d;. (6) Publicinvestment,andhencethegrowthintheservicesoftheroadstockdg,may dependonthe growthinoutput,whichinturndependsonthegrowthinproductivityd~ In thiscase,ordinary-leastsquaresestimationofthegrowth-accountingequation(6)suffersfromsimultaneitybias. Ifpublicinvestmentdependsonaggregateincomeandhenceproductivity,bthensectoralproductivity shocksaffectroadgrowthby affectingtheaggregateshock. Giventhatcovarianceisa linearoperator, 4 UsingaCES productionfunction,for example,considerablycomplicatesthetheoreticaland econometricproblem. First, aggregationis difficultunlessallproducersare identical. Second,road growthvariesrelativelylittleafter1973(themeanis lpercen~the standarddeviation0.3percent),sothe U.S.dataprovidelittlevariationtopindown complicatedparameterizations.Allowingthecoefficientto changeapproximatesthiscomplicatedeffectina simpleway. 5 See,forexample,Jorgenson,Gollop,andFraumeni(1987,p66). b Asarefereepointedouq thismaynotbetherightmodelifindustriesarenotdistributedevenly acrossregions. Theappendixconsidersthisissueindetail. 5

equation(5)thenimpliesthatthecovariancebetweend~and dgjust equalstheweighted-averageofthe covariancebetweensectoralshocksduiandgovernmentcapitaldg. Thus,iftheaggregateregressionsuffers fromendogeneitybias,sodothesectoralregressions(4). Nowconsiderthefollowingregressiondecomposition: dui = ~i”d; + &i (7) Theresiduals&ifromequation(7)are,byconstruction,orthogonaltotheaggregateproductivityshocks,and hencetothegrowthrateofgovernmentcapital. Thefittedvalues~i-d; measuretheconditionalexpectation of the technologyshockin sectori, giventhe aggregateproductivityshock. The average “cyclicality parameter”fl.equalsone:ifthereisanaggregateproductivityshockof,say, 1percent,thenatypicalsector hasaproductivityshockof 1percent. Substitutingequations(6)and(7)intoequation(4)givesthefollowingestimatingequation: (8) Thisnon-linearregressionequation,whichI estimateinSectionIII, hasthekeyattributethatthe disturbanceterm is orthogonalto dg. Intuitively,the problemof endogeneityarises from an omitted variable,dti;bycombiningaggregateanddisaggregatedata,wecancontrolforthisomittedvariable. Sofar,Ihavesuppressedconstanttermsforsimplicity.Supposedui=Ci+dzi, withA definedby dzi=~jd; +&i.Defining~astheaverageconstant,and ~i=Ci- ~i~,theestimatingequation(8)becomes: d“i =&i+ () ”(Syi - ~i;v)dg + ~id~ + &i (9) Foranintuitiveinterpretation,supposeallindustriesareequallycyclical,sothefl.allequalone,and thatanytrendsarecommon.Thenrearrangingequation(9),wefind: dpi-d; = @-[Svi - $/] dg + Ci, (lo) Ifroadsareproductive,thenpositiveroadgrowthdgtendstomakestheidiosyncraticcomponentofsectoral productivitygrowth(dpi-d;) positiveinindustrieswithabove-averagevehicleintensities,andbelow-average in industrieswithbelow-averagevehicleintensities. In otherwords, changesin roadgrowthshouldbe 6

associatedwithlargerchangesinproductivitygrowthinvehicle-intensiveindustries. Ifroadsarenotproductive,thenchangesinroadgrowthshouldnotimplyanyparticularrelationship betweenvehicle-intensityand relativeproductivityperformance.Similarly,if the aggregatecorrelation betweenproductivityandpubliccapitalreflectscommontrends(e.g., shiftsinthe constantterms), it is unlikelythatchangesintrendaresystematicallylargerforindustriesthathavea lotofvehicles. Clearly, the formalderivationabovemakesseveralsimplifyingassumptionsthatmay nothold. Nevertheless,aslongasroadshavealargerproductiveeffectinsectorsthatarevehicleintensive,thebasic methodshouldbe fairlyrobustto misspecification.Misspecifications—arisinfgrom increasingreturns, aggregationeffects,factor-biasedtechnologicaclhange,orothersources—onlymattertotheextenttheyare systematicallycorrelatedwith vehicle-intensities. There is little reason to expectsuch a correlation. Moreover,anyresultingbias(whichcouldbeeitherpositiveornegative)islikelytobesmallrelativetothe directproductiveeffectofroadsinsectorsthatarevehicle-intensive.Misspecificationdoesaddanadditional sourceofidiosyncraticvariancetorelativeproductivityperformance,raisingstandarderrors.7 ii. Modelingroadservicesandcongestion Empirically,howshouldonemodeltheservicesofroads? TheempiricalliteraturecitedinFootnote 1generallyassumesthatthe servicesof publiccapitalare a pure, non-rivalpublicgood,withservices proportionalto the stockof capital. Two considerations—thenetworknatureof the road system,and 7Increasingreturns,for example,isprobablynota majorconcern,sincethetypicalsectorhas approximatelyconstantreturns,andthecorrelationbetweenthegrowthinroadsandaggregateinputsis -0.04. However,BasuandFernald(1997)findthatbecauseofindustryheterogeneity,aggregationaffects thecyclicalpropertiesofaggregateproductivity,andhasalargereffectonestimateswithvalueaddedthan grossoutput.TheBasu-Fernaldaggregationeffectsarevirtuallyuncorrelatedwithroadgrowth,and using gross outputgive resultsthatare virtuallyidenticalto thevalue-addedresultsreportedin SectionIII. Hence, abstractingfrom aggregationand the non-existenceof a value-addedproductionfimctionis probablyunimportanthere. As an additionalcheckfor misspecification,intheempiricalworkI addedproxiesfor energybiasedtechnicalchangeandvariablecapacityutilization.Inparticular,I addedanoil-pricedummytothe regressions(witha differenteffectby industry),whichmightmatterif technicalprogresswere more energy-biasedinvehicle-intensivesectors. Resultschangedlittle. I alsoaddedthechangeinhoursper workerasaproxyforunobservedchangesinlaborandcapitalutilization(seeBasuandKimball(1997)). Again,resultschangedlittle. 7

congestion—haveimplicationsformodelingroadservices,andinterpretingtheresults.8 First,theroadsystemformsaspatiallyinterconnectednetwork. Foranetwork,theconventional perpetualinventorymethodof measuringcapitalstocksis generallynotappropriate. In particular,the internalcompositionofthestockmatters,sincethemarginalproductivityofanyonelinkdependsonthe capacityandconfigurationofallthelinksinthe network. Usingmeasuresofthe totalstockthusmayallow ustoestimatetheaveragemarginalproductofroads inthepast, buttheseestimatesmaynotbeappropriate forconsideringthemarginalproductofadditionalroadstoday. Moreover, as Hulten (1994)notes: “Once the basic links of a network are established,the opportunitiesforcomplementaryinvestmentsdiminishandtheconstructionofnewcapacitygraduallycomes to substitutefor existingcapacity.” In otherwords,buildingtheinterstatenetworkmayhavebeenvery productive,butbuildingasecondinterstatesystemmaynotbe. Allowingthecoefficientonroadstochange overtimeprovidesonesimplewaytocapturethisidea. Second,roadsaresubjecttocongestion.Congestionmaynotbeimportantwhenanetworkisfirst built,butitbecomesimportantasmorepeopleusethesystem. For example,addinga secondcarto an interstatehighwaydoesnot reducethe servicesreceivedby the first car. At rush hour in mostcities, however,additionalcarsslowtraffic,andreducetheservicesreceivedbyexistingdrivers. Asimplewaytomodelaveragecongestionistoexpressroadservicesas -&, G . (11) Ck whereRistheroadstockandCissomemeasureofroaduseandhencecongestion.BarroandSala-i-Martin (1995)suggestthatinmodelinglong-runeconomicgrowth,aggregateoutputorprivatecapitalmightproxy for congestionC. Mankiw(1992)modelsCastheaggregatevehiclestock. In theshortrun, however, capitalandvehicle-stockproxiesdonotaccountforvariationsintheutilizationofthesestocks,whilethe output-proxyhasthedisadvantagethattheregressionalreadyincludesaggregateproductivity(closelyrelated toaggregateoutput).Inmyempiricalresults,I insteadmodelcongestionCasafunctionofthetotalmiles drivenbytrucks,automobiles,andothermotorvehicles. 8 MuchofthediscussionbelowfollowsHulten(1994),whodiscussestheimplicationsofnetworksand congestionintermsofsimplemodelsofoptimalgrowth,anddiscussestheimplicationsoftheseissuesfor econometricmodeling. 8

Theparameterk measureshowquicklytheroadservicesreceivedbyanyindividualproducerfall asaggregatemiles-drivenrise. Ifroadsareapurepublicgood,k equalsO. BarroandSala-i-Martinand Mankiwsuggestthata particularlyattractivespecificationis ifk equals1, sothat G = R/C. Withthis specification,any individualproducerappearsto have increasingreturnsto privateand publicinputs, becauseheorshetakesroad-usebyothersasgiven. Ataneconomy-wideleve~however,thereareconstant returnstoscaleifmiles drivenincreaseproportionallywithotherinputs. Withcongestion,theestimatingequationbecomes: dpi=Fi+@{SU-~iFY)d~-K{~n-~i~v)dc + ~id~ + &i (12) where~equalsk~, anddr anddcarethegrowthratesofroadsandcongestion.Inotherwords,anincrease in roads disproportionatelyhelps vehicle-intensiveindustries, while an increase in congestion disproportionatelyharmstheseindustries. A convenientinterpretationof ~ isintermsoftheimpliedannualrateofreturn: thevalueofthe increasedannualflowofgoodsandservicescomingfromanextradollarofroads. Therateofreturnequals thesumoftherealvalueofthemarginalproductsacrosssectors. LetYbeaggregatevalueadded,andP betheaggregatepricedeflator. Itcanbeshownthat:9 3““4$) (13) The intuitionis straightforward. In a Cobb-Douglasproductionfunction,the rate of return equalsthe factor’soutputelasticity(i.e., itsshare)multipliedbytheratioofoutputtotheinput. Here,theproduct@“sV istheaggregateelasticityofroads. In 1989,theaveragevehicle-sharewas1.5percent(closetotheaverage of 1.6percentfortheentireperiodfrom 1953to 1989,showninTable1). Theratioofaggregatevalue- -addedintheprivatebusinesseconomytothevalueoftheroadstockwasabout4 in1989,soforanyestimate of @,weobtainanimpliedrateofreturnbymultiplyingby(0.01504),or about6percent. 9Thiscalculationassumesthatmilesdrivenandthevehiclesharearenotaffectedbythepolicychange in the stockof roads. Empirically,in annualdatathe elasticityof milesdrivenwithrespectto roads appearssmall. RegressingthelogofmilesdrivenonlogGDP, logfuelprices,andthelogoftheroad stockgivesaroadelasticityof0.04. Estimatedindifferences,thiselasticityis0.15. 9

II. Data and Econometric Issues IuseunpublisheddataprovidedbyDaleJorgensonandBarbaraFraumenioninputsandoutputsfor 29sectorsoftheU.S. economy,fortheyears1953-1989.Thesesectorsspantheprivatebusinesseconomy, excludingagricultureandmining.Thesedataseektoprovidemeasuresofoutputandinputsthatare, tothe extentpossible,consistentwiththeeconomictheoryofproduction,andallowJorgensonto allocateU.S. productivitygrowthto itssourcesatthelevelofindividualindustries.l” The data includegross output,and inputsof capital,labor, energy, and materials. Inputsare adjustedforchangesinthecompositionofthelabor forceandthecapitalstock. Forexample,laborinput weightshours-workedbydifferenttypesofworkersbyestimatesofrelativewages,andcapitalinputweights capital-stockbydifferenttypesofcapitalbyestimatesofrelativerentalrates. Iestimatesectoralproductivitygrowthfromequation(4)asaTornquistortranslogindex,replacing differentialswithlog-differences. LetIiequalatranslog indexofvehicles andothercapital. Thenthe Tornquistindexofvalue-addedproductivitygrowthZIpii,s . Api,= 1 Aql- siiAkit–sLiA[it–sMiAmit. (14) [ ][ 1 1-sMi All quantityvariablesare logsof their uppercasecounterparts,andq, is thelogof gross output. The weights—forexample,s~i—aretheaverageinputsharesinperiodstandt-1. Dividingbytheshareofvalue addedingrossoutput(l-s~i)convertsthisfromproductivitygrowthintermsofgrossoutputtoproductivity growthintermsofaDivisiaindexofvalueadded.11 Icalculatethevehicle-sharefollowingHallandJorgenson(1967)andHall(1990),multiplyingthe currentvalueofthestockofvehiclesbyanestimateoftheusercostofcapital. Iestimate theusercostas: 10I excludedataonthegovernmentsectorbecausecompleteinputdataarenotavailable;I exclude agricultureandminingbecausemanyof theirvehiclesarenot usedon publicroads. Thesedataare availablefrom1947onwards;alongersampleperiodispreferableeconometrically,butthequalityofthe earlydataisalsolowerthanthatofthelaterdata. Inanycase,themainconclusionsappeartoberelatively robustto usingan earlieror laterstartingdate. For a completedescriptionofthedata, seeJorgenson, Gollop,andFraumeni(1987). 11SeeJorgenson,Gollop,andFraumeni(1987),p52,orBasuandFernald(1995,1997). . 10

(1 - ITC~- ~d~) r~ = (P + ~s) s = trucks,autos. (15) (1 - T) ‘ pistherequiredrateofreturnoncapital,and6,isthedepreciationrateforthisasset. ITCistheinvestment taxcredit,~isthecorporatetaxrate,andd isthepresentvalueofdepreciationallowances. FollowingHall (1990),IassumethattherequiredreturnpequalsthedividendyieldontheS&P500. FollowingJorgenson andYun(1990),I takethedepreciationratetobe25.37percentfortrucksand33.33 percentfor autos. DaleJorgensonprovidedunpublisheddataon~,ITC,,andd,. Jorgensonalsoprovidedperpetualinventory estimatesofthecurrentvalueofthestockoftrucksandautosbyindustry. Usingdata ongrosspublicinvestmentin roads(fromtheU.S. CommerceDepartment1995), I followBoskin,Robinson,andHuber(1989)andassumethatroadsdepreciategeometricallyatarateof 1.98 percentper year. Usingtheperpetual-inventorymethod,I thenestimatetheconstant-dollarvalueofthe stockofroadsforeachyear. I assumethatroadinputinagivenyeardependsonthestockofroadsatthe beginningoftheyear. TheresultingstockestimatesgenerallyexceedtheBureauof EconomicAnalysis estimatesofthenetroadstockbyasmallamount,thoughthedifferentestimateshaveanegligibleeffecton theestimatesreportedinSectionIII. To measurecongestion,I useameasureofoverallroaduse:thetotalmilesdrivenbytrucksand autosineachyear. ThesedataarefromtheFederalHighwayAdministration(variousyears). Notethatitwillgenerallybethecasethattheconstructedregressiondisturbancesare correlated acrossequations. Itiseasytoshowthat Cov( 81,,Ejj = Cov(duit,duj~ - ~i~jVar(d;). (16) Thisisingeneralnon-zero.Hence,ifweestimatetheregressionsinequations(9)or(10)asasystem,there areefficiencygainstotakingaccountofthecross-equationcorrelationsamongthedisturbances. Onbotheconomicandeconometricgrounds,Iaggregatethe29industriesinvariouswaystoreduce thenumberofequationsIestimate.Econometricallye,quation(16)impliesthattheregressiondisturbances are generallycorrelatedacross equations. Estimatingthe model as a systemof seeminglyunrelated regressionsallowsforthesecontemporaneoucsorrelations.AnecessaryconditionforSURestimationisthat 11

thenumberof observationsexceedthe numberof equations,or elsethe estimatedcovariancematrixis alwayssingular. With37years ofdata, thisnecessaryconditionfor non-singularityissatisfied,butthe resultingestimatespotentiallysufferfrom smallsampleproblems. In essence,the covariancematrixis poorlyestimated,butfeasibleGLSneverthelessinvertsitinestimatingcoefficientsandstandarderrors. The resultingestimatesarenotreliable. In addition,thereisaneconomicrationaleforcombiningindustries. Investmentsinroadshavea clear regionalor geographicalcomponent. Thelessaggregatedare the industrieswe choose,themore regionaleachindustryislikelytobe. Asdiscussedintheappendix,thecorrectmeasureofanindustry’s roadstockshouldthenbesomeappropriately-weightedmeasureofregionalstocks. Thismisspecification potentiallyleadstobiasifindustriesarenotdistributedequallyacrossregions,andiftherearesystematic differencesin growthratesof roadsacrossregions. Thisbiasalsodependsheavilyon thedeviationof vehicle-intensitiesfromtheaverage. Theappendixalsopresentssomesimplesimulations,usingregional dataonpubliccapitalgrowthfrom1971through1987,suggestingthatthebiascanbesizeable. Mymainindustrygroupingseekstominimizethebiasbygroupingindustriestoensurethatvehicleintensitiesare sufficientlydifferentfromtheaverage,andthatproductionisrelativelyevenlydistributed acrossregions. Theappendix describesthenineindustryaggregatesthatresult. Notealsothathaving vehicle-intensitiesthatdiffersubstantiallyfromtheaverageincreasesthevariationoftheright-hand-side regressorinequations(9)and(10),andhenceimprovestheprecisionofestimatesof~. Forcomparability,andtoensurethattheresultsarenotdrivenbymychoiceofaggregates,I also presentresultsforthreefictional groupings. First,Iuse(approximate)one-digitSICcodes,comprising non-durablesmanufacturing,durablesmanufacturing,construction,transportation,communications,public utilities,trade,finance-insurance-reaelstate,andservices. Second,Iusethe21 manufacturingindustries. Third,Iusetheeightnon-manufacturing,non-farming,andnon-miningindustries. III. Results Table 1liststhe29industriesthatconstitutetheprivatebusinesseconomy(excludingminingand agriculture)inthe Jorgenson-Fraumenidata. Column(1)showsaverageannualvalue-addedproductivity 12

growth from 1953to 1989;column(4)showsthechangeafter 1973.12Theindustriesare listedby the averageshareofvalueaddedgoingtovehicles,showninColumn(5). Fortheprivateeconomyasawhole, thenext-to-lastlineshowsthatproductivitygrowthwas 1.6percentperyearfrom 1953to 1989,thenfell to0.3 percentfrom 1973to 1989. Theaggregatevehicleshareaveraged1.6percent. Thegrowthinroadsaveraged4percentperyearbefore1973,butonly1percentafterthat. Suppose roadsareproductive,andthatthisslowdowninroadgrowthexplainsasubstantialportionoftheslowdown inproductivitygrowth. Sinceslowerroadgrowthshouldprimarilyaffectsectorsthatusea lotofroads, thesesectorsshouldhavehadagreaterslowdowninproductivitygrowth. Figure 2 graphsthe changein sectoralproductivitygrowthafter 1973versus averagesectoral vehicle-intensityu,singthedataincolumns(3)and(5)ofTable1,excludingtheobviousproductivityoutlier ofpetroleumproducts.13Theestimatedslope(showninthefigure)is-0.63,withat-statisticof2.30. Thus, thesimplecross-sectionaelvidenceinthefigureisconsistentwiththenotionthatsectorswithgreatervehicleintensitiestendedtoexperiencelargerproductivityslowdownsafter1973. The negativecorrelation(thoughnotalwaysitsstatisticalsignificance)isrelativelyrobustto the presenceofoutliers. For example,inFigure2, whichexcludespetroleumproducts,thecorrelationwas -0.41; includingpetroleumproductsreducesthecorrelationto -0,29 (significantataboutthe 85percent level).Excludingthetwo vehicle-shareoutliers(transportationandgasutilities)reducesthecorrelation further,to-0.24(significantataboutthe80percentlevel). However,excludingallindustrieswithaboveaveragevehicleintensitiesrestoresthecorrelationto-0.43,significantatthe95percentlevel. Althoughthecorrelationisalwaysnegative,theinfluenceofoutlierssuggeststhatchangesinroad 121973isthetraditionaldatingoftheproductivityslowdown,thoughsomedateitearlierandsome later. Later,forconvenienceIallowcoefficientstochangein 1973,aswell;itdoesnotappearthatusing otherproposedbreakdatessubstantivelychangesthepictureorthecoefficientestimates. 13Theextraordinaryproductivityperformanceofpetroleumandcoalproductsreflectsenormous annualvariabilityofannualvalue-addedproductivitygrowth,whichhasastandarddeviationof36percent peryear. Severalyearsofabnormalpositiveproductivityperformanceinthe 1980ssubstantiallyincrease thepost-1973mean. Theenormousstandarddeviation,inturn, largelyreflectstheveryhighmaterials share,whichaverages90percentofgrossoutput;value-addedisonlyIOpercentofgrossoutput. Hence, smallproductivitychangesingrossoutputtranslateintoenormousproductivitychangesinvalueadded. Fortunately,noneofthesubstantiveresultsbelowaresensitiveto including,ornotincluding,petroleum products—ortodoingtheestimationwithvalue-addedratherthangrossoutput. 13

stocksare nottheonlyimportantfeatureofthepost-1973environment. In fact,thedominantfeatureof Figure2 isthewidedispersionofproductivityperformanceafter 1973. Asdocumentedinthefinallineof Table1,thestandarddeviationofproductivitygrowthacrossindustriesincreasedfrom1.3percentbefore 1973(column2)tonearly3percentafter1973(column3).14(Evenexcludingpetroleumandcoalproducts, the standarddeviationnearlydoubles)Somesectorshavedoneextraordinarilywell, suchas petroleum products, industrialmachinery,and textiles. Other sectorshave doneextraordinarilypoorly, such as utilities,chemicals,andprinting. Hence,thoughslowerpublicinvestmentmayexplainsomeoftheslowdowninproductivitygrowth intheeconomy,itdoesnotexplainwhythevarianceofproductivitygrowthacrosssectorsincreasedafter 1973. Aschauer(1989)andothershavesuggestedthatthedeclineinpublicinvestmentisthemaincause ofthechangeinproductivityperformanceafter1973;bycontrast,thecross-industryvarianceofpost-1973 performanceevidentin Figure2 indicatesthatwhilepublicinvestmentmay explainsomeof the mean slowdown,itcannotexplainallofthechangesinproductivitymoments. Thisconclusionmatchesintuition that a wide range of influences-such as environmental regulation, oil price shocks, and microcomputers—affectetdheeconomyafter1973,withdifferenteffectsondifferentindustries. The rest of thissectionexploresthe productivityof roadsmore formally,usingthe estimating equationfromSectionI. Thisequationuseswithin-industryvariationto explorehowvariationsinroad growthisassociatedwithvariationsintherelativeproductivityperformanceofdifferentindustries.Table 2presentsthebasicresultsforfoursetsofindustries. Thefirstset,discussedintheAppendix,comprises nine“aggregate”industries,wheretheaggregatesarechosentominimizeanybiascomingfromdifferences inthe relevantmeasureofroadsacrossindustries. Thesecondsetare one-digitSICindustries. Thethird setarethe21manufacturingindustries,andthefourthsetarethe7non-manufacturingindustries. Theodd columnscontainthebasicregressions,whichassumethattheparameter@isconstantovertime. Theeven columnsallowthecoefficientonroadsto changeafter1973;thechangeinthecoefficientisshowninthe secondrowofthetable. 14Thisincreasedvariabilityshowsup intheunderlyingannualdata,aswell. Theannualstandard deviationinproductivitygrowthratesacrosssectorswas4to6percentbefore1973,and8to 15percent from 1973to 1985. 14

Consideringthe odd columnsfirst, the parameter @is alwayslarge and significant. That is, variationsinroadgrowthareassociatedwithvariationsintherelativeproductivityperformanceofdifferent industries. Forexample,inbothcolumns(1)and(3), @isabout22,withat-statisticofaround6.5. Thisfindingthat@islargeandsignificantisrobusttoindustrygroupings.Theestimatedcoefficient islargestinmanufacturing(column5), andsmallestinnon-manufacturing.Notethatthisdoesnotimply thatroadscontributedmoretoproductivityperformanceinmanufacturingthannon-manufacturingindustries. Rather,itimpliestheopposite,sincemanufacturingindustriesgenerallyhavealowvehicleintensity.Hence, whenroadgrowthincreasedinthe1950sand1960s,productivitygrowthinmanufacturingdeclinedrelative totheaverage. Oneconcern,raisedwhilediscussingFigure2,isthatresultsmaybe sensitivetooutliers.Therefore, therobustnessofresultstousingfourdifferentindustrygroupingsisreassuring. Notethattheestimating equationexplicitlyattemptstoaccountforreversecausationfromaggregateproductivityshockstoroads; the robustnessto different groupingssuggeststhat results are probably not driven by some other, unaccounted-for“endogeneity”concern. Forexample,governmentroadbuildingmightrespondprimarily toshockstohigh-vehicleindustries;thelargeestimateformanufacturingindustries(whichtendtohavefew vehicles)suggestthatthisisnota problem. Alternatively,perhapsroadbuildingrespondsespeciallyto manufacturingshocks,sincemanufacturinghasahighprofile;however,thecoefficientremainsstatistically significantin non-manufacturing.(Moreover,sincemanufacturinghas few vehicles,endogeneityfrom manufacturingproductivityshocksto roadswouldbiasedthe coefficientdown, whereasin the datathe coefficientisverylargeandpositive. Anadditionalconcernisthatresultsmightbedrivenbyoneortwoindustries. Notethatthefirst twogroupings(especiallytheaggregatedgrouping)tendtominimizetheseindividualoutliersbycombining industries. Nevertheless,Iexplored the sensitivityofresults to including,or not including,various industries.Forthebaselineaggregatedgrouping,Idroppedeach oftheninegroupsinturn,toensurethat no individualgroupingwasdrivingtheresults. Theestimateof @alwaysremainslargeandstatistically significant. For example,addingor excludingpetroleumproductsand tobacco—twoindustriesoften consideredsuspect—haslittle effect on the estimateof @in the aggregatedindustrygrouping, or in 15

manufacturing.Droppinggasutilitiesandtransportation(twooutliersfromFigure2)haslittleeffectonthe aggregated,one-digit,ornon-manufacturingresults. Thecoefficient@hasseveraleconomicinterpretations.First,wecanconvert@toanimpliedCobb- Douglascoefficientbymultiplyingbytheaveragevehicle-share,whichis 1.6percent. Hence, @equalto 22correspondstoaCobb-Douglascoefficientonroadsofabout0.35. Thisislarge,butintheballparkof other estimatesin this literature,obtainedwith very differentidentifyingassumptions. (For example, Aschauer1989,uses totalaggregatepubliccapitaland reportsa coefficientof 0.3; redoinghis simple aggregateCobb-Douglasregressionusingroadsalonegivesanalmostidenticalcoefficient). Second,we canaskhowmuchof a productivityslowdownthisestimateimplies. Averageroad growthwas4 percentperyearbefore 1973,butonly1percentafter. Thegrowth-accountingequation5 l impliesthatroadscontribute~ FVdgtogrowth;anestimateof @of22 impliesthatroadscontributeabout 1.4percentperyearbefore1973,andabout0.4percentafter. This1percentreductioninthecontribution ofroadstogrowthcompareswithatotalslowdowninproductivityof 1.3percent,showninthenext-to-last row of Table 1, column(4). Hence, the estimateimpliesthatwhileroadscannotexplainthe sizeable dispersionin industryperformanceafter 1973,theymaybe ableto explaina substantialfractionof the slowdowninmeanproductivitygrowth.15 Third,wecanaskhowtheestimaterelatestotheslopeofFigure2, whichrelatestheproductivity slowdowntovehicleintensity. Sincethegrowthin roadsfellby3 percentagepointsafter 1973,theslope shouldbe-@(O.03). @equalto22implies a slopeof-O.66, closetothe actualslopeof-O.63. Thus,the estimatesinTable1areconsistentwiththevisualdatainFigure2. Fourth,wecanconverttheestimateintoa rateofreturn. AsdiscussedinSectionIii, supposethe estimatesreflectthecurrentmarginalrelationships.Thentherateofreturnis @“~v(Y/R),or @l6percent. The estimate in column (l), for example, implies a rate of return of more than 130 percent per year—buildinganextradollar’sworthofroadsaddsmorethanadollartoGDPeveryyear. Toreducethe 15Inprinciple,roadscould“accountfor”morethan100percentoftheslowdown,ifotherfactors, suchascomputers,raisedproductivityafter 1973. 16

rateofreturntoamorereasonablelevelofperhapsone-tenthaslargelGrequiresaten-foldreductioninthe output-roadratioY/R. Hence,atthecurrentlevelofoutput,wewouldrequire10timesasmanyroads,or nearly$12trillion. Suchhighratesofreturnseemimplausibleatthemargin;equivalently,itseemsimplausiblethatthe optimalroadstockistentimesitscurrentlevel. Amuchmoreplausibleinterpretation,consistentwiththe suggestionsofHulten(1994),isthatbuildingonenetworkmayhaveaveryhighrateofreturn;butbuilding asecondnetworkmayhaveaverylowmarginalreturn. Forexample,theinterstatehighwaysystemmay havebeenextraordinarilyproductive.Butbuildingasecondinterstatehighwaysystem(letaloneninemore highwaysystems!)maynothavealargeeffectatthemargin. Toexplorethispossibility,theevencolumnsofTable2allowthecoefficienttochangeafter 1973, roughlywhentheinterstatehighwaysystemwascompleted. g5Trjepresentsthechangeinthecoefficient, sothemarginalcoefficientequalsthesumofthetwoparameters.Inallcases,thepointestimateisnegative, suggestingthatthemarginalcontributionofbuildingroadsislowerthantheaveragecontribution.Forthe aggregatedindustriesand for non-manufacturing,the pointestimatesimplythat the marginaleffectof buildingadditionalroads is negative. More accurately,for all groups, we can reject that roads are unproductiveinthepre-1973period(inthefirstrow);forallgroupsotherthanmanufacturing,wecannot rejectthatthemarginalproductivityofroadstoGDPiszero. Since the standarderrors on the post-73changein coefficientare very large, the resultsare suggestiveratherthandefinitive.Forexample,thepointestimateonthemarginaleffectofroads—thesum of@and@Tj—haasnenormousstandarderror,generallyontheorderof 15. Evenwhere~zjissignificant, asincolumn(2),theresultsarenotnecessarilyrobusttochangesinspecification(seeTable3below,for example).Econometricallyt,heproblemresultsfromthelackofvariabilityinroadgrowthinthepost-1973 period;thestandarddeviationofroadgrowthis0.9 percentbefore1973,and0.3 percentafter. Thislack of variationinthe right-hand-sideregressorreducestheinformationin thedata, and increasesstandard 16Forexample,supposetherealinterestrateisabout4percent,andthedepreciationrateofroads about2percent. Alsosupposethatthemarginalexcessburdenoftaxationis2 (atthehighendofcurrent estimates,discussed,forexample,byJorgensonandYun1990andMorrisonandSchwartz1996). Then anoptimizinggovernmentwouldsetthemarginalreturnonroadsequaltotwicetheHall-Jorgensoncost-ofcapitalof6percent. 17

errors. Thus,whilethedatastronglyrejectthepropositionthatroadsofferedanormalreturninthepre- 1973period,thedatadonotspeakstronglytothemarginaleffectofroads. However,asdiscussedinSectionIii, therearestrongapriorireasonstoexpectthatanetworkmay offerlargeone-timebenefits,butaddingasecondidenticalnetworkwillnot. Also,therearestronggrounds to be skepticalof enormous,unexploitedmarginalratesofreturnin excessof 100percent. Thus, an appropriateinterpretationofthepost-1973resultsisthatthedataareconsistentwiththesepriors—thereis noevidencethatroadsofferanabnormalreturnatthemargin. Giventhattheaggregatedindustrygroupingsareleastlikelytobesubjecttobias,Ihenceforthfocus onthatsetofindustries. Table3 addstotalmilesdrivenasa proxyforcongestion,andalsoexploresthe possibilitythatthecongestioncoefficientmaychangeovertime. Forexample,theinterstatehighwaysystem by itsverynatureisa lumpyinvestment,andwhenfirstbuilt,addinganadditionalcartothesystemmay havehadlittleeffectontheservicesavailabletoanyotheruser. Asthesystembecomesmorecongested, addingmorecars (andhencemoremilesdriven)reducestheservicesavailableto anyoneelse. Hence, congestionisinherentlylikelytobeanon-linearprocess;thechangeincoefficientprovidesaverycrude approximationtothisnonlinearity. Thefirsttwocolumnsassumethatcongestionisastablelinearfunctionofthetotalmilesdrivenby allusers. Thecoefficient capturingtheeffectofcongestion,isinsignificant.Addingcongestionhasa K, relativelysmalleffectontheroad-coefficient@,althoughitdoesreducethesizeandsignificanceof @T3. Therestofthecolumnsallowthecongestioncoefficienttochangeafter1973;~r3showsthechange inthecoefficient.Inallcases,thepre-1973coefficientisinsignificant,andoftenthewrongsigntoproxy forcongestion;butthecoefficientgenerallyrisesbyastatisticallysignificant(exceptinColumn4)amount after1973. Theestimatesimplythatafter 1973,anincreaseintotalmiles-drivensignificantlyreducesthe servicesofroadsto anyindividualproducer. Columns(4)and(5)allowthecoefficientonbothroadsandmilesdriventochangeafter1973. The pointestimatesuggeststhatroadsare lessproductiveatthemargin;butthestandarderror remainsvery large, sotheestimateisextremelyimprecise. Thecoefficientoncongestionagainrises1973,thoughthe t-statisticfallsfrom2.2 inColumn(3)to 1.2inColumn(4);multicollinearityappearstobeaproblemwith 18

disentanglingthepost-1973effects. Finally,thefifthcolumndropsthetwoleastsignificantcoefficients fromthefourthcolumn,keepingthetwo “robust”coefficients:@and~,q. Theestimateagainimplietshat roadsarehighlyproductive,andthatcongestionisimportantafter 1973. TosummarizetheresultsofTables2 and3, thedatastronglyrejectthenullhypothesisthatroads didnot,onaverage,affectrelativeindustryproductivityperformance;before1973,inparticular,thedata indicatethat roadscontributedsubstantiallytoproductivitygrowth. However,thedatadonotrejectthenull hypothesisthatroadsoffera “normal”(orevenzero)returnatthemargin. Finally,usingtotalmilesdriven asameasureofcongestion,theresultssuggestthatcongestionbecameimportantonlyafter 1973,afterthe interstatesystemwascompleted.Theseresultsareconsistentwithsimplestoriesofnetworks,suchasthose discussedbyHulten(1994). Giventheseresults,itseemsreasonabletoconsideraspecificationinwhichthehighwaysystemwas notsubjecttocongestionbefore1973;after1973,whencongestionbecameimportant,theservicesofroads taketheformofequation(11),inwhichroadsandmiles-drivenhavecoefficientsthatareequalinmagnitude. The regressionsinTable3, for example,do notrejectthisspecification(largely,ofcourse,becausethe estimatesofthemarginalcoefficientonroadsaresoimprecise). Econometrically,makingthisidenti~ing assumptionofcoefficient-equalityhastheadvantagethatmiles-drivenvarymuchmorethanroad-growth does. Hence,wecanusethevariationinmiles-driventohelppindown themarginaleffect. Notethatthis specificationimpliesthatifroadsandroad-useincreaseproportionatelyt,hereisnoincreaseinthe“services” ofroads. Table4showstheseresults. Asbefore,roadsappearstronglyproductivebefore1973. After1973, theproductivityofroadsisstatistically-significantslymaller,andwecannotrejectthatroadshaveanormal (orevenzero)return. Asa finalspecificationtest,thesecondcolumnaddsapost-1973dummyforeach industry,allowingan industry-specificchangein trend growth. Thistrend-breakshouldcaptureother influencesinthepost-1973periodthatmayaffectproductivity.Itwillonlymatteriftheindustry-specific changeintrendiscorrelatedwithvehicle-intensitiesi;fthechangeintrendiscommontoallindustries,for example,resultswillbeunaffected.Thereisnoreasontoexpectacorrelationbetweenthetrend-shiftand vehicle-intensitys,onotsurprisingly,theresultsarequalitativelyunaffected. Thestandarderror on @p,~.73 19

risessubstantially,butthecoefficientremainsstatisticallysignificant.(InotherspecificationsinTables2 and 3, addingindustry-specificpost-73dummiesmakesit more difficultto identifypost-73coefficient changes,givenmulticollinearity-thecorrelationbetweenroadgrowthandthepost-73dummyis0.85, for example. However,noneofthequalitativeconclusionsareaffected.) ThespecificationinTable4hassomeaprioriplausibility.Hence,thoughthedatadonotpindown the marginalparameterwithprecision,theseresultsagainprovidefurthersupportfor the interpretation above:roadshadanabove-normalreturnbefore1973,butprobablydonothaveanabove-normalreturn today;moreover,congestionnowreducestheproductiveservicesofroads. IV. Conclusion Industrydatafrom1953to 1989stronglysupporttheviewthatvehicle-intensiveindustriesbenefited disproportionatelyfromroad-building. First, theslowdowninproductivityafter 1973appearslargerin industrieswithhighervehicleshares. Second,whenroadgrowthrises,productivitygrowthtendstorise relativeto theaverageinvehicle-intensiveindustriesand fallinnon-vehicle-intensiveindustries. These resultssuggestthatthe aggregatecorrelationbetweenproductivityandpubliccapitalprimarilyreflects causationfrompubliccapitaltoproductivity,andthatpublicinvestmentmayaccountforasubstantialshare oftheslowdowninproductivitygrowthafter 1973. However, the industrydatado not supporttheviewthatroadsoffer an abnormalreturn at the margin,orthatreturningroadgrowthtopre-1973levelswouldraiseproductivitygrowthtopre-1973levels. In essence,theevidencesuggeststhatthemassiveroad-buildingof the 1950sand 1960s–whichlargely reflected constructionof the interstatehighwaynetwork—offereda one-timeincreasein the level of productivity,ratherthanacontinuingpathtoprosperity. Thesefindingsshedlightonotherresultsintherecentempiricalliteratureoninfrastructure.Results varywidely,dependingondataset,sampleperiodandspecification,Aschauer(1989)estimatesanaggregate Cobb-Douglasproductionfunctioninlevels,andfindsthatpubliccapitalappearsabnormallyproductive. Aaron(1991)pointsoutthatAschauer’sresultsarenotrobusttoestimatinginfirstdifferences,suggesting that perhaps Aschauer’sresults reflect a misspecificationof trend. However, the sensitivityto first- 20

differencinglargelyreflectsadramaticincreaseinstandarderrors—theaggregatedatadonothavesufficient informationtodifferentiatethetwointerpretations.TheindustryresultsinthispapersuggestthatAschauer’s simpleaggregateregressionappropriatelycapturesthehighproductivityofpubliccapitalinthepre-1973 period. Usingregionaldataonpubliccapitalalsoincreasesdatavariation(therebyimprovingprecision). Studiesusingthesedata,whichareonlyavailableafter1970,tendtofindlittleevidencethatpubliccapital hasan importantproductiveeffect. Munnell(1990)usesstatedata,andfindsthatpubliccapitalappears highlyproductive.However,Holtz-Eakin(1994)overturnsherresultswhenheincludesstate-specificfixed effects:thepoint estimatesarenegative,thoughnotsignificantlyso. Sincefixedeffectsseempreferable, he concludesthatthesedataoffer no evidencethatpubliccapitalhas a non-normal(or evennon-zero) productiveeffect. Similarly,HultenandSchwab(1991)usemanufacturinggross-outputdataon census regions,andfindnoevidencethatproductivitygrewfasterinregionswithrapidgrowthinpubliccapital. Theresultsinthispapersuggestthattheregionalfindingsmayreflectthesampleperiod:regionaldataare onlyavailablefortheperiodwhenI findnoevidencethatroadshaveanabove-normalreturn. Morerecently,MorrisonandSchwartz(1996)usestatemanufacturingdatafrom1970to 1987,and suggestthatpubliccapitalmayhavearateofreturnof20to 30percentinthemanufacturingsectoralone. Sincenon-manufacturing(roughly80percentoftheeconomy)benefitsfrompubliccapitalaswell,these resultssuggestthatpubliccapitalisfarunderprovided. Thereareseveralinterpretationsofthedifferencesbetweentheirresultsandmine. First,Morrison andSchwartzplacefewrestrictionsonhowgovernmentcapitalenterstheproductionfunction;government capitalmayprovideindirect“externalities”thatImiss,orperhapsmakepossibleotherCaballero-Lyonsstyle externalities(thoughthereisnotmuchevidencefortheseexternalitiesingross-outputdata;seeBasuand Femald1995). SinceIexplicitlyfocusonthedirecteffects,myresultsarelikelytounderstatethereturns topubliccapitalifexternalitiesareimportant.Second,however, MorrisonandSchwartzdonotcontrolfor endogeneityofpubliccapital,otherinputs,or evenoutput(allofwhichareexplanatoryvariablesintheir 21

flexiblecostfunction).17Sincestateswithhighproductivityshocksmaytendtoinvestmoreinpubliccapital, theMorrisonandSchwartzresultscouldreflecttheendogeneityofpubliccapital,andhencebe(presumably) biasedupwards. I explicitlyaccountfor theendogeneityofpubliccapital,andhencemay obtainmore reliableresults. Inanycase,itremainsunclearwhyMorrisonandSchwartzgetdifferentresultsfromotherregional studies,whoalsohavenocontrolsforendogeneity.MorrisonandSchwartzattributethedifferencestousing a flexiblefictional form, which allowsa second-orderapproximationto the cost function;but the differencesinresultsappealtobedrivenbythefirst-ordereffects,notthesecond-ordereffects. Finally, my resultshave implicationsfor interpretingthe productivityslowdown. A common presumptionisthatpre-1970slevelsofgrowthwerenormal. An alternativeinterpretationsuggeststhat perhapsitwastheimmediatepost-wardecadesthatwereunusual,witha “returntonormal”aftertheearly 1970s(e.g., Wolff1996) Myresultssupportthisinterpretation:road-buildingaccountsforasubstantial share of theproductivityslowdownby raisingpre-1973productivitygrowth,butcannotofferthe same benefitsatthemargin. Yetanotherinterpretationoftheproductivityslowdownsuggeststhatperhapstheslowdownreflects mismeasurement;Griliches(1994),for example,arguesthat an increasingproportionof the economy consistsofsectorswhereoutputispoorlymeasured. Computersmayalsomakequality-improvementasnd product-differentiatioenasier,andconventionasltatisticsmaymissthesebenefits. Theresultsinthispaper suggestthat roads contributedmuch less to productivityafter 1973than before, and from a growthaccountingperspective,canexplain a significantshareoftheproductivityslowdown. Theseresultsthus pointinthedirectionofarealslowdown. However,itmaybe that“true”productivitygrowth(afteraccountingformismeasurement)didnot slow,sincecomputer-driventechnologicalimovationsincreased.Thecomputerparadox(Solow: “Wesee computers everywhere except in the productivity statistics”) may reflect the coincidenceof the 17Theysuggestthatusinglaggedvaluesasinstruments,orusingtheHall-Rameyinstruments,has littleeffectonresultsotherthanraisingstandarderrors. Giventhatpublicandprivatecapitalarehighly autocorrelated,andgiventhattheHall-Rameyinstrumentshavenoexplanatorypowerforcapital,these attemptsmaynotresolvetheissueofendogeneity. 22

microcomputerrevolutionwiththereducedcontributionofroads. Inotherwords,evenifwefullymeasured thesubstantiatlechnologicablenefitsofcomputers,productivitystatisticsmightshownoimprovement.More generally, history may often displayunusualinfluences-road networks, computers,mass-production techniques,steamengines—thaatffectproductivityfordecades. Underthisinterpretation,roadsmayhave raisedproductivitybefore1973,justascomputersraise“true”(thoughperhapsunobserved)productivity today. 23

Appendix: The Bias from an Uneven Distribution of Industries Ifindustriesarenotdistributedevenlyacrossspace,thentheaggregateroadstockdoesnotcorrectly measureindustry-specificroad input. Instead,the appropriatemeasureshouldprobablybe aweighted average of regionalroad growth rates, weightedby the importanceof each region in the industry’s production.Thisappendixconsidersthepotentialbiasthatresultsfromincorrectlyusingtheaggregateroad stock. FollowingthederivationinSectionI, supposethatineachlocation,anindustrycanproducewith theproductiontechnologyfromequation(l), andthattheindustryhasthesamevehicleshare,su, inall regions. Aggregatingindustryproductivityoverregions,wefind: dpi=@”SVidg+i dui, (17) where~giisthegrowth inthe industry-specific inputofgovernmentroads. dgfiinturn, isdefinedby: dgi= ~j wU*dgJ, (18) whered~”isthegrowthinroadsinregionj, andWtiistheshareofindustryi’sproductioninregionj. Wecanrewriteequation(17)as dpi=@*svi*dg+ @*svi*(dg-i dg) + dti, (19) wheredgisthegrowthinthenational,oraggregate,roadstock. Assumingthatpubliccapitalisdistributed inproportiontoproduction,18thenationalroadstockdgequals: dg = ~j wJdgJ, (20) whereti’istheshareofnationalproductioninregionj. Comparing(18)and(20),(dgi-dg)iszeroifroads growatthesamerateinallregions,or ifindustriesproduceequallyacrossregions,sothatWteiqualsW“. Aggregatingoverindustries,aggregateproductivityd~is: d; = @F;~g + @[~iwlsvi(dgi - dg)] + d;. (21) Suppose,for simplicity,thattheindustrycyclicalityparameters,~.,equalunityforalli. Wecan thenwritethedifferencebetweenindustryandaggregateproductivityas: 18Thisassumptionsimplifiesnotationand interpretation. In practice,of course,government capitalisaggregated usingthe distributionof thatcapital,notthedistribution of production. If these distributionsdiffer,thenallstudiesusingtheaggregatestockofgovernmentcapitalaremisspecified.This misspecificationmattersonlyifthedifferencebetweenthetwomeasuresarecorrelatedwiththeaggregate stockofgovernmentcapital. 24

dpi - d; = (#)”(Svi - Fv)odg+ @[svi(dgi-dg) -xi wisvi(dgi- dg)] + &i, (22) where q is the idiosyncraticcomponentof industryproductivitygrowth. q maybe correlatedwiththe industry-specificdgi>butaslongastheindustryisrelativelysmall,Cishouldbe nearlyuncorrelatedwith aggregateroadgrowth. Supposeweattempttoestimatethelinearregressioninequation(22),butomittheterminbrackets. If thevehiclesharesareconstantovertime,thentheplimoftheratiooftheestimatedtotrueregression coefficientis: )[ Cov(dg,dgi-dg) eov(dg, ~~ ‘~s~k~dgk-dg~~ 1 — ‘Vi” Var(dg) - Var(dg) 1 (23) ‘Vi –‘V 1 Supposeindustryweightsare(relatively)constantovertime. Thenthisplimratioequals: )[( 4 ( 1 Cov(dg,dgi) CoV(dgd,g~) )1 plimL @ .1 + – ‘Vi “ Var(dg) – svi – x kw~svk Var(dg) - x kwksvk ‘Vi –‘V ) Withsomealgebraicmanipulation,andnotingthat~k ~ksvkequa9lsSV,wefind: 1 6 ‘V~~i‘~kwksk~k plim 1 = — (25) @ i ‘Vi –‘V (asymptotic)coefficient froma regressionofdgiondg:Cov(dg,dgi)lvar(dg). where ~ is the Byassumingthataggregatedgisappropriatewhenitisnot,regression(22)inessencesuffersfrom omittedvariablebias,withthebiasgivenbyequation(25). Equivalently,theregressiondisturbanceterm maybe correlatedwithgovernmentcapital. Thebiasdependsonboththe misspecificationof industry productivity,andthemisspecificationofaggregateproductivity. Thesemisspecificationsdependonhow wells#g proxiesfors~gi, whichinturndependsonthe K. Thereisnobiasiftheindustry-specificroad stocksarenotsystematicallydifferentfromtheaggregateroadstocks,sincethe ~ thenequal1. In otherwords, industryroad growthmatchesaggregateroad growthif there are no systematic differencesin regionalgrowthrates of roads, or if industriesare distributedevenlyacrossregions.Of course,anunequalregionaldistributionof industriescancontributeto unequalregionalroadgrowth,if regionalroadgrowthrespondsmorestronglytoproductivitygrowthofindustriesinthatregion. 25

To get a sensefor the potentialmagnitudeof thisbias, I performedsomesimplesimulations. MorrisonandSchwartz(1996,Table2)providegrowthinpubliccapitalforfourregionsofthecountryfrom 1971to 1987.19Inallregions,thegrowthratefell,butitfellmuchfasterthanaverageintheeast,andmuch slowerthanaverageinthesouth;regionalu’s, estimatedfrom 1971through1987,are0.77inthesouth, 0.84inthenorth,1.06inthewest,and1.71intheeast.Supposetherearefourindustries,eachproducing inaseparateregion,andeachofwhichisthesamesize(usingtheactualregionaldistributionofproduction for 1977,fromBEAdata,givesvirtuallyidenticalresults),andthattheaveragevehicleshareis 1.5percent. Thetableshowstheindustrybiases,forseveralcombinationsofindustryvehicleintensities. Vehicleshares(South,North,East,andWest) plim(@/@) (Dercent) (South,North,East,andWest) I (1.4, 1.4, 1.8 1.4) I (5.5, 4.6,4.4, 3.0) I I (1.6, 1.6, 1.2, 1.6) I (-2.8, -1.9,-1.6, 0.0) I I (1.0, 1.0,3,0, 1.0) I (2.1, 2,0,2.0, 1.8) I I (1.9, 1.9,0.3, 1.9) I (0.3, 0.6,0.7, 1.1) I Thebiascanbeverylarge,eventhoughthecorrelationsbetweentheregionalgrowthratesandthe aggregategrowthrateisgenerallyabove0.9. Inseveralcases,notonlyisthebiasnegative(aratiolessthan one),buttheactualsignoftheestimatedcoefficientisreversed.Thesignisambiguous,sinceitdependson thesignof(SW-SVT).hemagnitudeofthebiasalsodependsheavilyon (SW-SVT).hebiastendstobepositive ifindustrieswithabove-average~ alsohaveabove-averagevehicleshares;also,thebiasislargerinthefirst tworows,wherethedeviationsofvehicleintensitiesfromtheaveragearerelativelysmall,thaninthesecond tworows,wherethedeviationsofvehicleintensitiesarelarger. 19Thesedata, originallyfromMunnell(1990),are for allgovernmentcapital,notjust roads. Holtz-Eakin(1994a)describesestimatesofregionalroadstocks,butprovidesinsufficientdetailforthese simulations.However,regionalroadgrowthwasprobablysimilartothegrowthinallgovernmentcapital. In anycase,thesimulationsreportedhereare meantonlyto be suggestive,sinceestimatesof regional publiccapitalarenotavailableforthefill sampleperiod,andprobablysuffersubstantialmeasurement error. Theestimatesinvolveallocatingnationalcapitalstocksto regions,basedonvariousproxiesfor regionalexpenditure. For example,Holtz-Eakinestimatesbenchmarkstatecapitalstocksfor 1960by allocatingthenationalcapitalstockbasedonthestates’sharesoftotalcurrentgovernmentexpenditures in 1960. Errors inthisbenchmarkwouldsignificantlyaffectestimatesof industry-specificgovernment capitalstocks. 26

Inpractice,ofcourse,industryroadstocks varylessthaninthisexample,sinceindustriesarenot completelysegmentedbyregion. Therefore,Iestimatedindustry-specificgovernmentcapitalstocks,using BEA data on the regionaldistributionof productionin 1977,for the four regionsfor whichI have governmentcapitaldata. Ithenassessthemagnitudeofthebiasfromequation(25). AlthoughIdonothave thedatatoestimateindustry-specificgovernmentcapitalfortheentiresampleperiod,thisexercisegivesme ametrictoassesswhetherIcansafelyignoretheregionaldistributionofindustries. From1971to 1987,thecorrelationofgrowthratesforindustryandaggregategovernmentcapital isalwaysaboveO.99. Insertingthesamplevariancesandcovariancesintothebiasequation(25)foreach of the27privateindustries(allprivateindustries,excludingagriculture,mining,tobacco,andpetroleum refining),themedianbiasratiois0.88;theinterquartilerangeis0.82to 1.01. Forthenineone-digitSIC industries,themedianbiaswas1.04. Forbothgroupings,thereweretwoparticularoutliers:Trade(8.2), andServices(-0.95). Thecauseofthesubstantialbiasratioisthatthesetwoindustrieshavevehicle-shares thatareparticularlyclosetc~theaggregatevehicleshare,andhence,asequation(25)shows,thebiasratio caneasilybeverylarge. Wecannotestimatethebiasratiofortheentiresample,sinceregionalpubliccapitalisnotavailable earlier. Assumingthatintheearlierperiod,theregionalvariationinpubliccapitalgrowthrateswassimilar tothevariationinthelaterperiod,theappropriateinterpretationoftheseresultswouldseemtobethatat theone-andtwo-digitdata,thereissufficientregionalvariationintheindustriestoallowforabias(positive ornegative)ontheorderof 10percent,thoughforsomeindividualindustriesitmaybemuchlarger. Nevertheless,theresultssuggestthatbyjudiciousaggregation,wecanreducebothbias(byensuring anadequatedistributionofregionalproduction)andstandarderrors(byincreasingthedeviationofvehicle sharesfromtheaverage,henceincreasingthevariationintheright-hand-sideregressor). Iaggregatedindustriesinordertoensureanappropriatedistributionfor(SW-SV2)0. Inandofitself, thisaggregationoverheterogeneousindustriestendstosmoothregionaldifferencesinindustrylocation,and 20Notethatchoosingthe“optimal”industryaggregatesforthisproblemwouldbeverydifficult. Forexample,wecouldnotsimplyseektominimizetheregionaldifferencesinindustrydistribution,since thatwouldnotensurethatthevehiclesharesdifferby enoughfromtheaggregateto allowpreciseand unbiasedestimates.Moreimportantly,thebiasratioforanindustrydependsonthecovarianceofindustry andaggregategovernmentcapitalgrowthforeveryotherindustry. 27

hencereducethepotentialbias. I followedaninformallexicographicordering,seekingfirsttomaximize the minimumabsolutevalueof the deviationfromtheaverageshare;andthenseekingto minimizethe variationinthedeviation. Theninegroupings,aggregatedusingTornquistindices,areasfollows:21 Grouping Industries 1 ElectricandGasUtilities,Services 2 Construction,Stone-Clay-Glass,Communications 3 Transport,Trade,Lumber 4 Autos,IndustrialMachinery,FIRE 5 Furniture,Leather,PrimaryMetals 6 Paper,Food,ElectronicEquipment 7 Apparel,Printing,Misc.Manufacturing 8 Textiles,Rubber,FabricatedMetals 9 Chemicals,OtherTransportEquipment,Instruments Toassesstheequalityofthespatialdistribution,Iperformthesamesimulationasabove,calculating industrygovernmentcapitalgrowth from 1971to 1987,and then insertingthe samplevariancesand covariancesintothebiasratioformula(25). For myfinalgroupingintonineaggregates,themedianbias ratiowas0.97, andnone ofthegroupswasfarfromunity. Theindustryaggregatesdonot,ofcourse,haveanynaturaleconomicinterpretationinthewaythat, say, one-digitSIC groupingswould. With perfect competitionand constantreturns, however, this aggregationdoesnotleadto anybiasesinmyestimatingequation,sinceproductivityresidualsaggregate cleanlyundertheseconditions.AsdiscussedinSectionI, deviationsfromperfectcompetitionandconstant returnsareunlikelytohaveamajoreffectontheestimates. 21IalsoexperimentedwithincludingatenthgroupingofPetroleumProductsandTobacco. The argumentforincludingthemistohaveasmuchdataaspossible;theargumentforexcludingthemisthat theyareunusuallyvolatile,andareoftenconsideredsuspect. Iexcludedthemtoensurethatthesesuspect industriesdodriveresults. However,resultsarenotmuchaffectedinanycase. 28

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Table1 Value-AddedProductivityGrowthandVehicleSharesbyIndustry,1953-1989 Average TFP TFP Change Average Industry TFP Growth Growth Vehicle Growth 1953-73 1973-89 Share (1) (2) (3) (4) (5) Transportation 1.8 2.5 1.0 -1.4 5.5 GasUtilities -0.7 1.7 -4.2 -5.9 4.8 Stone,clay,glass 0.9 1.1 0.9 -0.2 2.8 Communications 2.8 2.7 3.0 0.3 2.6 Construction 0.6 1.3 -0.7 -2.0 2.2 ElectricUtil 2.2 3.7 0.0 -3.7 2.2 Lumber&wood 1.5 1.0 1.5 0.6 1.7 Trade 1.3 1.9 0.3 -1.5 1.7 Services 0.2 0.7 -0.5 -1.2 1.5 Food&kindredproducts 2.5 3.1 1.3 -1.8 1.3 F.I.R.E. 0.4 0.6 0.0 -0.7 1.1 Petroleumproducts 5.6 -1.2 11.6 12.8 1.0 Paperproducts 1.0 1.8 0.4 -1.4 0.9 Chemicals 3.0 4.9 0.7 -4.2 0.7 Primarymetals -0.8 -0.1 -1.5 -1.4 0.6 Furnitureandfixtures 1.6 1.4 1.8 0.5 0.6 Printing&publishing -0.1 1.0 -1.6 -2.6 0.6 Tobaccoproducts -0.2 1.5 -1.3 -2.8 0.5 Fabricatedmetals 1.1 1.3 1.2 -0.1 0.5 Electronicequipment 3.3 3.1 3.7 0.6 0.5 Motorvehicles 1.7 2.8 0.5 -2.4 0.4 Misc.manufacturing 3.0 3.1 2.6 -0.6 0.4 Instrumentsandrelated 2.2 2.4 1.9 -0.4 0.4 Apparel&textile 3.8 3.3 4.8 1.5 0.3 Industrialmachinery 2.3 1.0 4.7 3.7 0.3 Othertransport.equip. 1.3 1.1 1.5 0.4 0.3 Textilemillproducts 3.7 2.7 4.1 1.4 0.3 Rubber&plastics 1.7 2.6 0.6 -2.1 0.2 Leatherproducts 1.0 0.0 2.8 2.8 0.2 EconomyAverage 1.0 1.6 0.3 -1.3 1.6 Std.Deviation 1.4 1.3 2.8 3.2 1.3 31

Table2 BasicResults Aggregated One-Digit Manufacturing Non- Industries Industries Industries Manufacturing Industries (1) (2) (3) (4) (5) (6) (7) (8) 4 22.1 17.4 22.9 19.3 36.0 35.1 15.8 11.7 (3.3) (4.0) (3.6) (4.3) (2.7 (4.0) (4.1) (4.6) -25.3 -14.7 -11,5 -19.3 473 (11.2) (10.0) (9.5) (10.4) Note: Estimatesof equation(9) from 1953-1989 (with standarddeviationsin parentheses). @is the coefficientonroads,and@Tijsthechange coefficientafter 1973. Thefourindustry describedinthetext. 32

Table3 IncludingCongestionVariables (1) (2) (3) (4) (5) (6) 4 23.5 14.6 14.1 17.4 13.7 18.1 (4.0) (4,6) (5.5) (4.2) (5.5) (4.0) -12.7 -9,3 -6.9 @73 (11.4) (14.4) (14.5) K 2.7 -3.8 -5,2 -5.0 (4.3) (4.1) (5.1) (5.2) 10.1 5.7 8.5 7.6 K73 (4.5) (4.6) (5.6) (3.8) Note:Standarddeviationsinparentheses.@isthecoefficientonroads,and@Tijsthechangeinthecoeffient after1973. Kisthecoefficientoncongestion,and~qisthechangeinthecongestioncoefficientafter 1973 (apositivenumbersignifiesanincreaseincongestion).

Table4 UsingRoadsbefore1973,Roads/Milesafter1973 (1) (2) o 17.1 18.7 Post73 (3.1) (7.4) 5.3 6.0 oPost73 (4.5) (5.0) IncludesPost-73Industry No Yes Dummies? Note:Standarddeviationsinparentheses. 34

Figure1 RoadsandMiles-Driven(PerCapita) 4000 10000 Miles 9000 3500 ---/ 8000 7000 3000 6000 2500 5000 4000 2000 3000 1500 2000 +-Roads P.C.+ MilesP.C. 35

Figure2 ChangeinTotalFactorProductivityafter1973v.VehicleShare 0.0400 l 0.0300 . 0.0200 0.0100 l lm l l l l -0.0300 l -0.0400 l -0.0500 -0.0600 0.0000 0.0100 0.0200 0.0300 0.0400 0.0500 0.0600 VehicleShare paneltable his