The PLANET model Methodological Report: The Car Stock Module docx

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purposes.
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Responsiblepublisher‐HenriBogaert
Federal Planning Bureau
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WORKING PAPER 2-10

The PLANET model
Methodological Report:
The Car Stock Module


February2010
IngeMayeres,MaudNautet,AlexVanSteenbergen,



Abstract‐The vehicle stock module calculates the size and composition of the car stock. Its
outputisafulldescriptionofthecarstockineveryyear,by vehicle type,ageand(emission)
technology of the vehicle. The vehicle stock is
represented in the detail needed to compute
transportemissions.Theintegrationofthecarstockmodulein
PLANETwillallowtobettercap‐
turetheimpactofchangesinfixedandvariabletaxesleviedoncars.Amongtheseimpacts,the
effectontheenvironmentisofparticularinterest.
JelClassification‐R41,R48
Keywords‐Passengerroadtransport,vehiclestockmodelling
Lestravauxprésentésdanscedocumentontétéréalisés
danslecadred’unecollaborationavecleSPFMo‐

bilitéetTransports.
Hetwerkinditrapportmaaktdeeluitvaneensamenwerkingmetde
FODMobiliteitenVervoer.





WORKING PAPER 2-10


Contents
Introduction 1
1. Modelling approach 2
2. The total desired stock 3
3. Vehicle scrappage 4
3.1. Methodology 4
3.2. Observed scrappage rates 4
3.3. Estimation results 6
4. The composition of car sales 8
4.1. The nested logit model for car sales 8
4.1.1. Level 3 9
4.1.2. Level 2 10
4.1.3. Level 1 11
4.1.4. Scale parameters 11
4.2. The calibration of the nested logit model for car sales 12
4.2.1. Data 12
4.2.2. Methodology 13
4.2.3. Calibrated elasticities 14
5. Output of the car stock module 16

6. Links of the car stock module with the other modules 17
7. References 18

WORKING PAPER 2-10

List of tables
Table 1:  Estimated parameters of the loglogistic hazard function (t-statistic between brackets) 6
Table 2:  The reference equilibrium 12
Table 3:  Target elasticity values of conditional annual mileage with respect to monetary income
and variable costs 13

Table 4:  Calibrated elasticity values for average annual mileage of newly purchased cars 15
Table 5:  Calibrated elasticity values for car sale probabilities 15
Table 6:  The impacts of doubling the fixed or variable costs of different car sizes 15
Table 7:  The impacts of doubling the fixed or variable costs of gasoline and diesel cars 15
Table 8:  Input in the car stock module of year t from the other PLANET modules 17
Table 9:  Output of the car stock module of year t to the other PLANET modules 17

List of figures
Figure 1: Average scrappage rates at age 0 to 30 during the period 2000 to 2005 for diesel
and gasoline cars 5
Figure 2: Observed and estimated scrappage rates for diesel cars between 0 and 20 years old 6
Figure 3: Observed and estimated scrappage rates for gasoline cars between 0 and 20 years old 7
Figure 4: Decision structure for car purchases 9

WORKING PAPER 2-10

1
Introduction
Thecarstock module calculatesthe sizeandcomposition of thecarstock.Itsoutputisafullde‐

scriptionofthecarstockineveryyear,byvehicletype(fuel),ageand(emission)technologyof
the vehicle. The vehicle stock is represented in the detail needed to compute the
transport
emissions.
Forbuses, coaches, roadfreightvehicles, inlandnavigation and railthe carstock is not mod‐
elledindetail.Inthesecasesthemodelusesinformationaboutthevkmandtkmratherthanthe
vehiclestocktodetermineresourcecosts,environmentalcosts,etc.
Thepastversionofthe
PLANETmodelusedanexogenousevolutionofthecarstocktakenfrom
otherresearchprojects.Fromnowonthevehiclestockmoduleisintegratedintherestofthe
PLANETmodel.
Theassumptionsthataremadearedescribedinadetailedwayinthereportonthebusiness‐as‐
usualscenario
1
.Inthispaperwedescribetheworkthathasbeendonetoendogenisetheevolu‐
tionofthevehiclestock.
Thisdocumentdescribesthefirstversionofthecarstockmodule.Themethodologypresented
heremightundergosomechangesinthefuture
2
.


1
 Desmet,R.,B.Hertveldt,I.Mayeres,P.MistiaenandS.Sissoko(2008),ThePLANETModel:MethodologicalReport,
PLANET1.0,Studyfinancedbythefr ameworkconvention “Activitiestosupportthefederalpolicyonmobilityand
transport,2004‐2007”betweenthe
FPSMobilityandTransportandtheFederalPlanningBureau,WorkingPaper10‐
08,FederalPlanningBureau,Brussels.
2
 Forexample,intheactualversionofthemodel,thedefinitionofcarsiz eislinkedtocylindersize.Inthefuture,we

willlookatthepossibilitytodefinecarsizelinkedtopower.
WORKING PAPER 2-10

2
1. Modelling approach
Severalapproachesexisttomodelthemagnitudeandcompositionofthecarstock.DeJonget
al.(2002)giveareviewoftherecent(since1995)internationalliteratureoncarownershipmod‐
elling.In
PLANETwewilluseanaggregateapproach.Otherexamplesofthisapproach canbe
foundin
TREMOVE(DeCeusteretal.,2007)andASTRA(Rothengatteretal.,2000).
Wefirstdescribethegeneralprinciples,andthendiscussthedifferentstepsinmoredetail.The
generalapproachissimilarasin
ASTRAandTREMOVE.Foreachcartypethevehiclestockisde‐
scribedby vintage and vehicletype. IfStock
i(t,T)represents the vehicle stock oftype i (diesel
andgasolinecar)inyeartandofageT,thetwobasicequationsare:
Stock
i(t,0)=Salesi(t)
Stock
i(t,T)=Stocki(t‐1,T‐1)–Scrapi(t,T)forT>0
Sales
i(t)standsforthesalesofnewcarsoftypeiinyeartandScrapi(t,T)isthescrappageof
vehiclesoftypeiandageTinyeart.
Ineachyeartthestockofvehiclessurvivingfromyeart‐1iscomparedwiththedesiredstockof
vehiclesneededby the transport users.Ifthedesiredstockis largerthan
thesurvivingstock,
newvehiclesarebought.Thisapproachrequiresthedeterminationineachyearofthetotalde‐
siredvehiclestock(Section2),thenumberofvehiclesofeachtypethatisscrapped(Section3)
andthecompositionofthevehiclesales(Section4).

Themodel includesvehicles from age
0 until theagetheyare scrappedor leavethe country.
Anychangesinownershipinbetweenarenotmodelled.Noseparatecategoriesareconsidered
fornewandsecondhandvehicles.
Inafirststagenodistinctionismadebetweencarsownedbyprivatebusiness,governmentand
utilitiesonthe
onehandandpersonalcarsontheotherhand.Thisdistinctioncouldbeuseful
becausethepolicyinstrumentscanbedifferentinbothcasesandbecausechangesinthecom‐
positionofthefleetstockeventuallyfilterdowntothepersonalcarstock.Includingaseparate
categoryof fleetcars would
 require modellingthe transitionof thesecars tothe personalcar
stock. Account shouldalso be taken of exports and imports.The National Energy Modelling
System(
NEMS)ofthe US DepartmentofEnergy (US DoE,  2001)isan example ofa model that
incorporatesthedistinctionbetweenfleetandpersonalcars.
WORKING PAPER 2-10

3
2. The total desired stock
Inordertoderivethetotaldesiredstockwecanconsiderthefollowingtwoapproaches:
– toderivethedesiredstockfromthevkm,ascalculatedinthe
MODALandTIMECHOICEmod‐
ule,andtheevolutionoftheannualmileagepervehicle.Thisistheapproachthatistakenin
the
TREMOVEmodel.
– torelatethedesiredcarstocktoeconomicdevelopment,transportcostsandpopulation.The
functionrelatingthedesiredstocktoitsexplanatoryvariablesmayeitherbecalibrated(cf.
the
ASTRA model; Rothengatter et al., 2000) or estimated (cf. for example, Medlock and
Soligo,2002).Fortheothervehiclesthesameapproachasin

TREMOVEcontinuestobeused.
Thefirstapproachhasthedrawbackthatassumptionsneedtobemadeabouttheaveragean ‐
nualvehiclemileage.Thesecondapproachallowstoderiveforcarsanaverageannualmileage
byconfrontingthecarstockwiththe cartransportdemand thatisderivedinthe
MODALand
TIMECHOICEmodule.
In the firstversionof
PLANET thefirstapproach wasused.In thenewversion ofPLANET, the
secondapproachisused.Withthefirstapproachwestartfromthetotalvkmpercarthatisde‐
rivedinthe
MODALandTIMECHOICEmodule.Thenumberofvkmisthendividedbytheaver‐
ageannualmileagetogetthedesirednumberofcarsforagivenyear.Thedeterminationofthe
averageannualmileageforcarswillbediscussedinSection5.
WORKING PAPER 2-10

4
3. Vehicle scrappage
Inordertoknowthesurvivingcarstockinyeartascrappagefunctionneedstobedetermined.
Inthisversionofthemodelscrappageisassumedtobeexogenous.Inalaterstageanendoge‐
nousscrappagefunctionwillbeconsidered
3
.
3.1. Methodology
Thescrappagefunctionisestimatedforthefollowingcartypes:dieselcarsandgasolinecars.
Thescrappagerateofthesevehiclesisestimatedaccordingtotheageofthevehicle(T),witha
scrappagefunctiondeterminedby a loglogisticdistribution.Thefollowingequationgivesthe
hazard function of the loglogistic
 distribution which describes the rate at which cars are
scrappedatageTgiventhattheystayinthevehiclestockuntilthisage.
()

ρ
λ
ρ
λλρ
)(1
1
)(
T
T
consTh
+
−
+=

whereλandρareshapeandscaleparametersandconsisaconstantterm.Ifthevalueofthe
shapeparameters(λ)liesbetween0and1,theshapeofthehazardfunctionfirstincreasesand
thendecreases withage.Theloglogistic hazardfunctionis alsoconcave at first,
andthenbe‐
comesconvex.Theshapeofthishazardfunctionisclosetotheshapeofthescrappageratesfor
allvehicletypesobservedduringtheyears2000to2005
4
.Theparametersλandρandthecon‐
stanttermareestimatedonthebasisofdataobtainedfromthe
DIV.Thesearedescribedinthe
followingparagraph.
3.2. Observed scrappage rates
The DIV hasprovided uswith timeseries ofthe age distribution ofthe carfleetaccording to
fuel.Thetimeseriesrefertotheyears1997to2005(except1999).Thesedataareusedtocalcu‐
latescrappageratesaccordingtofuelandageforallreportedyears.Theobservednumber
of

scrappedvehiclesofageTisdefinedasthedifferencebetweenthenumberofvehiclesofageT
inyeartandthenumberofvehiclesofageT+1inyeart+1.Thescrappagerateisthenobtained
bydividingthenumberofscrappedvehiclesperageinyear
tbythetotalnumberofvehicleof
thisageinthefleetduringthesameyear.


3
 Ingeneral,scrappingdependsonthetechnicallifetimeofavehicle,theprobabilityofbreakdownbeforetheendof
the planned technical life and policies that directly or indirectly affect vehicle costs such as purchase taxes and 
scrapping incentives. The following studies could prove to be useful for modelling endogenous
scrappage rates:
HamiltonandMacauley(1998),DeJongetal.(2001),Loggheetal.(2006).
4
 AWeibulldistributionisoftenusedtomodeldurationdata,buttheshapeofitshazardfunction‐“s‐shape”‐does
notcorrespondwelltotheshapeoftheobservedscrappagerates.
WORKING PAPER 2-10

5
Thenextfigurepresents the average scrappageratesderivedfromthedataofthe DIV for the 
differenttypesofcarsfrom1to30yearsold.Theaveragesarecalculatedovertheperiod2000‐
2005.
Figure 1: Average scrappage rates at age 0 to 30 during the period 2000 to 2005 for diesel and
gasoline cars
-5%
0%
5%
10%
15%
20%

25%
30%
0 5 10 15 20 25 30
Diesel cars Gasoline cars

Source:
FPB based on DIV.
Thedataforgasolineanddieselcarsreferto“ordinarypassengercars”and“mixedcars”.Based
onthedataofthe
DIV,wenotesomefindings:
– Thecardatapresentsomeirregularitiesduringthefirstyearofregistration
5
.
– Thedatashowthatthescrappageratesarerelativelyhighduringthe4firstyearsofregistra‐
tion,inparticularfordieselcars.Thiscanbeexplainedbyleasedandcompanycarsleaving
thestockbeforebeing4yearsold.
– Weobservethatthescrappageratesarehigher
fordieselthanforgasolinecarsas,atagiven
age,themileageofdieselcarsishigher.
– Carsof25yearsandolderhavenegativescrappageratesbecause“old‐timers”arereentering
thestock(astaxesandinsurancecostsbecomecheaper).Manyofthosearegasolinecars.
–
Duringtheperiod1997‐2005,themarketshareofgasolinecarshas fallenfrom60%to50%.
Furthermore,thedieselstockisyoungerthanthegasolinestock.So,thereisaphenomenon
of“dieselisation”ofthecarstock.
– For the period 1997‐2005, 97% of the car stock was between
 0 and 30years old, 96% was
youngerthan20years.



5
 Somecardealers realize“fictive registrations” inordertoincreasetheir salesfigures. Vehiclesareregistered and
retiredofthestockafterlessthanamonth.So,registrationsfornewcarsareoverestimated.
WORKING PAPER 2-10

6
3.3. Estimation results
Basedontheobservedscrappageratespresentedabove,theconstantandtheparametersλand
ρoftheloglogistichazardfunctionwereestimatedbymeansofanonlinearleastsquaresesti‐
matorin
TSP.Theestimationonlytakesintoaccountvehiclesof20yearsandyounger.Thisis
donebecausethestockafterthisagebecomeslessrepresentativeasthenumberofoldvehicles
becomessmallerandsmaller
6
.Table1presentstheestimatedvaluesoftheparametersλ,ρand
consandthecorrespondingt‐statistic.ItalsogivestheR‐squaredoftheestimatedmodels.
Table 1: Estimated parameters of the loglogistic hazard function (t-statistic between brackets)
Diesel cars Gasoline cars
λ 0,075 0,076
(68,28) (53,58)
ρ 4,816 4,734
(56,23) (44,97)
Cons 0,051 0,020

(14,48) (4,63)
R
2
0,990 0,983
Figure2and3presenttheobservedandestimatedscrappageratesforthe2vehicletypes.
Figure 2: Observed and estimated scrappage rates for diesel cars between 0 and 20 years old

0%
5%
10%
15%
20%
25%
30%
0 5 10 15 20
Diesel cars : observed rates Diesel cars : estimated rates

Source:
FPB.

6
Intheperiod2000to2005,96%ofthecarstockwasbetween0to20yearsold.
WORKING PAPER 2-10

7
Figure 3: Observed and estimated scrappage rates for gasoline cars between 0 and 20 years old
0%
5%
10%
15%
20%
25%
30%
0 5 10 15 20
Gasoline cars : observed rates Gasoline cars : estimated rates
age of vehicle

Source:
FPB.
Thecomparisonoftheobservedandestimatedscrappageratesshowsthattheestimatedscrap‐
pageratesareabletoreflectratherwellthespecificitiesofthecarfleetevolution.Nevertheless,
forthe4firstyearsofregistration,theestimatedscrappageratecannotreproducethefluctua‐
tionsoftheobservedscrappagerate.

WORKING PAPER 2-10

8
4. The composition of car sales
Inthissectionwedescribethewayinwhichthetechnologychoicefornewvehiclesismodelled.
Wemodelthechoicebetweenthreecarsizes(small,mediumandbig)
7
andbetweendifferent
technologies(diesel,gasoline, hybrid diesel, hybrid gasoline,
LPGandCNG). TheEUROtypeof
thecarsisassumedtobedeterminedbytheyearinwhichitisbought.Thecarchoiceismod‐
elledbymeansofanestedlogitmodel
8
.
4.1. The nested logit model for car sales
The decision structure for determiningthe share of thedifferent car typesincar salesis pre‐
sentedinFigure4.Simultaneouslywiththechoiceofthecartype, the model alsodetermines
theannualmileageofthenewcars.InFigure4Level1describesthechoicebetweensmalland

mediumcarsontheonehandandbigcarsontheotherhand.Conditionalonthischoice,the
categoryofsmallandmediumcarsissplitintosmallcarsandmediumcars(Level2).Finally,
giventhedecisiononthecarsize,thechoicebetweendieselandgasolinecarsis
determinedat

Level3.Finally,thenumberofhybridandconventionaldieselcarsisdeterminedbyapplying
exogenous shares of these two subtypes in total diesel car sales. Similarly, total gasoline car
salesare split intoconventionalandhybridgasoline cars,
CNG cars andLPGcarsby applying
exogenoussharesforthesefoursubtypes.
Inmoreformaltermswearedealingwithamultidimensionalchoiceset:
C
1 size(small,medium,big) indexedbys
C
2 fueltype(gasoline,diesel) indexedbyf
andwetakeintoaccountthatelementsofthechoicesetC
1shareunobservedattributes.There‐
fore,wemodelanadditionallevel,wherethechoiceismadeamongdifferentcompositesizes
(small+medium,big),indexedbycs.



7
 Thecarsizesaredefinedasfollows:0‐1400cc=small,1401‐2000cc=medium,>2000ccbig.
8
 Formoreinformationaboutnestedlogitmodelsseee.g.,KoppelmanandWen(1998),Heiss(2002)andHensherand
Greene(2002).
WORKING PAPER 2-10

9
Figure 4: Decision structure for car purchases
New cars
Small
Small + Medium
Medium

DieselGasoline
Big
Big
DieselGasoline DieselGasoline
Level 1
Level 2
Level 3
Hybrid
Conventional
CNG LPG
Hybrid
Conventional


Exogenous
shares


4.1.1. Level 3
Level3describes,conditionalonthepurchaseofacarofagivensizesandcompositesizecs,
thechoiceofthefueltype.Consistentwiththediscretechoiceliterature,indirectutilityv(f|cs,s)
ofselectingalternativefgivensizesandcompositesizecsiswritten
as
()()()
scsfscsfVscsfv ,,,
η
+=

whereV(f|cs,s)isthedeterministic‘universal’indirectutilityfunction,assumedtobethesame
for everyone, and η(f|cs,s) is an individual‐specific component that reflects idiosyncratic taste

differences.BasedondeJong(1990),thefollowingfunctionalformisusedforthedeterministic
componentofindirect
utility,conditionalonthepurchaseofacaroftypef(givensandcs):
()
()
()()()()
()
()()()
()
()
scsf
ref
scsf
scsfFscsfKY
scsf
scsfMVCscsfscsf
scsf
scsfV ,
,1
,,
,1
1
,,,exp
,
1
,
ξ
α
α
βδ

β
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎣
⎡
−
−−
−
+
−
=

where MVC(f|cs,s) is themonetary variable costof travel forhouseholds buying a car of fuel
typef(givensandcs)andYrepresentsmonetaryincome.K(f|cs,s)andF(f|cs,s)aretheannual
fixedresourcecostandtheannualfixedtaxfor
acaroftypef(givensandcs).Finally,
α
(f|cs,s),
β
(f|cs,s)and
δ
(f|cs,s)


areparameters.Notethatweexpressindirectutilityinmonetarytermsby
dividingbyξ
ref(f|cs,s),themarginalutilityofincomeinthereferenceequilibrium.
WORKING PAPER 2-10

10
Theconditionalannualmileagetravelledbyanewlyboughtcarcanbeobtainedbyapplying
Roy’sidentitytotheconditionalindirectutilities:
() ()()()
[]
()()()
(
)
scsf
scsfFscsfKYscsfMVCscsfscsfscsfX
,
,,,,,exp,
α
βδ
−−−= 
Themodelthereforeallowsnotonlytodeterminethetypeofvehiclethatisbought,butalsothe
annualmileagedrivenbynewlypurchasedvehicles.Fromthepreviousequationitcaneasily
bederivedthattheelasticityoftheconditionalannualmileagew.r.t.themonetaryvariablecost
equals‐β(f|
cs,s)GVC(f|cs,s).Inaddition,α(f|cs,s)equalstheelasticityofconditionalannualmile‐
agew.r.t.monetarydisposableincome.
Assuming thatpeople selectthe fuel type that yieldshighest utility, and that the individual‐
specificcomponentsη(f|cs,s) aredistributed Gumbel i.i.d., theprobabilityofchoosing
acar of

typef(conditionalonsizesandcompositesizecs)isthengivenbythelogitexpression:
()
(
)
(
)
[
]
()()
[]
(
)
(
)
[
]
()
[]
cssIV
scsfVcss
cssf
scsfVcss
scsfVcss
scsfP
exp
,exp
,'
,'exp
,exp
,

μ
μ
μ
==
∑

μ(s|cs)isascaleparameterandisinverselyrelatedtothestandarddeviation.Ahigherμindi‐
cateslessindependenceamongtheunobservedportionsofutilityforalternativesinthesubnest
(s|cs).IV(s|cs)istheinclusivevalue:
() ()()
[]
⎟
⎟
⎟
⎠
⎞
⎜
⎜
⎜
⎝
⎛
=
∑
f
scsfVcsscssIV ,expln
μ

Itlinksthelowerandmiddlelevelofthemodelbybringinginformationfromthelowermodel
tothemiddlemodel.Itismoreorlesstheexpectedextrautilityfromsbybeingabletochoose
thebestalternativeins|cs.

4.1.2. Level 2
Level2describesthechoicebetweensmallandmediumcars,conditionaluponthechoiceofa
carbelongingtothecompositesize“small+medium”.Theconditionalprobabilityofchoosings,
givencs,isgivenby:
()
(
)
()
()
()
()
()
(
)
()
()
()
[]
csIV
cssIV
cssµ
cs
css
cssIV
cssµ
cs
cssIV
cssµ
cs
cssP

exp
exp
'
'
exp
exp
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
=
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
⎥
⎥
⎦
⎤
⎢
⎢
⎣

⎡
=
∑
λ
λ
λ

WORKING PAPER 2-10

11
λ
(cs)isascaleparameter.IV(cs)istheinclusivevalueofthesubsetofalternativesincs:
()
()
()
()
⎟
⎟
⎟
⎠
⎞
⎜
⎜
⎜
⎝
⎛
⎥
⎥
⎦
⎤

⎢
⎢
⎣
⎡
=
∑
css
cssIV
cssµ
cs
csIV
λ
expln 
For big cars, this decisionlevel is irrelevant, since the composite size ‘big’is associated with
onlyonesize(big).ThereforeP(s=big|cs=big)=1.
4.1.3. Level 1
Finally,atlevel1,themarginalprobabilityofchoosingcompositesizecsisgivenby:
()
()
()
()
()
IV
csIV
cs
cs
csIV
cs
csIV
cs

csP
exp
)(
exp
'
'
)'(
exp
)(
exp
⎥
⎦
⎤
⎢
⎣
⎡
=
⎥
⎦
⎤
⎢
⎣
⎡
⎥
⎦
⎤
⎢
⎣
⎡
=

∑
λ
ρ
λ
ρ
λ
ρ

Theoverallinclusivevalue(IV)canbewrittenas:
()
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
⎥
⎦
⎤
⎢
⎣
⎡
=
∑
cs
csIV
cs
IV

)(
expln
λ
ρ

Veryoftenρisnormalisedtoequalunity.
Theprobabilitythatonebuysacarofcompositesizecs,sizesandfueltypefisgivenby:
()
()()
()
csPcssPscsfPfscsP ,,, =

4.1.4. Scale parameters
Forthemodeltobeconsistentwithutilitymaximisationthefollowingconditionsmustbesatis‐
fiedforthescaleparameters:
()
()
()
(
)
csscscsscscsscs ,0,,and ∀>≤≤
μλρμλρ

Thismeansthatthevarianceoftherandomutilitiesatthelowestlevelsho uldnotexceedthe
varianceatthemiddlelevel,whichshouldnotexceedthevarianceatthetoplevel.Thecondi‐
tionsimplythat:
()
()
()
cs

cs
andcsscs
css
cs
∀≤<∀≤< 10,10
λ
ρ
μ
λ

With
ρ
=
λ
(cs)=
μ
(s|cs)thenestedlogitmodelreducestoajointlogitmodel( MNLmodelforthe
jointchoiceofvehiclesizeandfueltype).
WORKING PAPER 2-10

12
4.2. The calibration of the nested logit model for car sales
4.2.1. Data
Inordertoconstructareferenceequilibriumonwhichtocalibratethemodel,wecollecteddata
oncarsales,annualmileageofnewcars,variableandfixedcostsandmonetaryincomeforthe
year 2005. Table 2 gives an overview of the different cost components, monetary income
(
GDP/capita),annualmileageandsharesofthedifferentvehicletypesintotalcarsales.
Table 2: The reference equilibrium
Reference equilibrium

Small Medium Big
Fixed taxes (€/car/year)
(1)
Gasoline 448 645 1364
Diesel 447 769 1381
Variable taxes (€/100vkm)
(2)
Gasoline 6.5 8.4 10.7
Diesel 3.4 4.0 5.2
Fixed monetary costs excl. taxes Gasoline 1163 1924 4109
(€/car/year)
(3)
Diesel 1323 1955 3476
Variable monetary costs excl. taxes
(€/100vkm)
(4)

Gasoline 8.3 11.7 17.7
Diesel 6.9 7.4 9.7
GDP/capita (€/person/year) 26085 26085 26085
A
nnual mileage (km/year) Gasoline 12393 13747 17432
Diesel 14808 22731 30588
Sale probabilities
(5)
Gasoline 19.97% 8.51% 0.78%
Diesel 27.33% 39.85% 3.56%
(1)
Includes registration tax, traffic tax, radio tax and indirect taxation on purchase, insurance and control.
(2)

Includes indirect taxation on maintenance and fuel (plus the fuel excise).
(3)
Includes purchase, control and insurance costs net of taxes.
(4)
Includes fuel and maintenance costs net of taxes.
(5)
Observed shares of the different vehicle types in total car sales in base year.
Sources:
BFP, CBFA, DIV, IEA, INS, FPS Economics, SPF Mobility and Transport, VITO.
Thedataforthereferenceequilibriumshowmonetarycostsrisingwithsize. Thevariablecosts
ofdieselcarsarelowerthanthoseofgasolinecars.Thefixedcostsofdieselcarsarehigherthan
forgasolinecars,exceptforthebiggestcars.Inthecaseofbigcarsthisisbecause
theaverage
sizeofbiggasolinecarsislargerthanthatofbigdieselcars.Monetarycostscannotfullyexplain
theobservedbehaviour.Aswewillsee,somecharacteristicsorhiddentastedifferencescannot
beaccountedforbyusingcostdataalone.Aconstanttermisthereforeintroducedinthe
calibra‐
tiontotheequationforindirectutility(moredetailinthenextsection).
WORKING PAPER 2-10

13
4.2.2. Methodology
Calibrationofthemodelrequiresfurtherinformationonthevalueoftheincomeelasticityand
theelasticityw.r.t.variablecostsofannualmileage.Ourincomeandcostelasticitiesarebased
onDeJong(1990).TheincomeandcostelasticitiesofDeJong(1990)areadjustedtoaccountfor
differentiationby car
 size. This permits toobtainreasonableelasticitiesand greatlyimproves
theresults.
Table 3: Target elasticity values of conditional annual mileage with respect to monetary income
and variable costs

Elasticity w.r.t. monetary income
Small car 0.22
Medium car 0.23
Big car 0.39
Elasticity w.r.t. monetary variable costs
Small car -0.14
Medium car -0.22
Big car -0.45
Given these target elasticities and information for the base year, the parameters α(f|cs,s),
β(f|cs,s)andδ(f|cs,s)canbeeasilyobtained:
α(f|cs,s)=Targetmonetaryincomeelasticityofannualmileage
β(f|cs,s)=Targetelasticity
ofannualmileagew.r.t.monetarycost/MVCref(f|cs,s)
δ(f|cs,s)=ln[X
ref(f|cs,s)]+β(f|cs,s)*MVCref(f|cs,s)‐α(f|cs,s)*ln[Yref–Kref(f|cs,s)–Fref(f|cs,s)]
ξ(f|cs,s)=α(f|cs,s)*[Y
ref–Kref(f|cs,s)–Fref(f|cs,s)]
Giventhesevalues,indirectutilitiesV(f|cs,s)canbecalculated.Wenotethatinthefinalcalibra‐
tion,weaddedaconstant(chosentoobtainreasonableelasticityvalues)totheequationforin‐
directutility.Thisstepwasnecessary,sincewefoundthatsome
featuresofthedatainthebase
yearcouldnotbeproperlyexplainedwithinthediscretechoiceframeworkbythecostandin‐
comedataalone.Tocapturetheexistenceofunobservablecharacteristics,weaddedaconstant
totheindirectutilityfunction.Thevaluesoftheseconstantshavebeentakenas
smallaspossi‐
ble.
Giventheseparameters,thescalingparameterscanbedetermined.Forexample,givenindirect
utilities,thelowernestscalingparametersμ(s|cs)canbecalculatedasfollows:
1/μ(s|cs)=[V(“dies”|cs,s)–V(“gas”|cs,s)]/ln[P(“dies”|cs,s
)/P(“gas”|cs,s)]

Thescalingparametersfortheotherlevelscanbeobtainedinasimilarway.
WORKING PAPER 2-10

14
4.2.3. Calibrated elasticities
Table4andTable5givethecalibratedelasticitiesofconditionalannualmileageofnewlypur‐
chasedcarsandoftheprobabilitiesofbuyingthedifferentcartypes,inbothcasesw.r.t.mone‐
taryvariablecosts,fixedcostsandmoneyincome.
Theelasticityvaluesofannualmileagew.r.t.tomonetarycosts
andincomeinTable4largely
reflect the elasticities chosen in the calibration procedure. Elasticities of mileage w.r.t. fixed
costs aresignificantly smaller, ascan be expected sincethese changes onlyinfluence mileage
indirectlythroughchangesinmoneyincome.
TheelasticityvaluesinTable5reflecttoalargeextent
thestructureofthenestedutilityfunc‐
tion.Bychoosingthisfunctionalform,oneimposescertainrestrictionsonthebehaviouralreac‐
tions thatare allowed bythe model.Forexample, theclose–to–zero incomeelasticities ofex‐
penditure shares are a direct result of the homogeneity of the utility function. Similarly, the

nestingstructurewillensurethatreactionsofdifferentcategoriesinonenestoftheutilityfunc‐
tiontochangesinanothernestwillbeequal.Forexample,thecross‐priceelasticitiesofmedium
gasolineanddieselcarsw.r.t.tochangesinthepriceofsmallcarsareequal.Reactionsof
me‐
diumandsmallcarsalestochangesinthepriceofbigcarsareequal,owingtotheseparationof
bigcarsontheonehandandsmallandmediumcarsontheotherhandintheuppernestofthe
utilityfunction.
Theownpriceelasticityislesspronounced
fordieselcarsthanforgasolinecars,whilecross–
priceelasticitiesaremarkedlylarger.Smallcarsareingenerallesssensitivetochangesinthe
ownpricethanbigcars.

Togetabetterfeelforthebehaviouralimpactofachangeincarcosts,wehaveperformedsome
additionalsimulations
withthe model. Table 6summarisesthe impactsofdoublingthefixed
andgeneralisedvariablecostsofcarsofdifferentsizes.For example,doublingthefixedcostsof
smallcarswouldreducetheirsharefrom47%to36%ofcarsales.Ascanbeexpected,sucha
pricechangewould
primarilybenefitthesaleofmediumcars.
Table 7 presents the impacts of doubling the fixed andgeneralised variablecosts of gasoline
and diesel cars. Doubling the generalised variable costs of gasoline cars would decrease the
shareofgasolinecarsinsalesfrom29%toabout0%.For dieselcarsthe
doublingofthesecosts
wouldbringtheirsharefrom70%to1%.Thedoublingofthefixedcostsofdieselwouldresult
inadieselshareof0%ratherthan70%.Thismeansthatinsidethesamesizecategorydieseland
gasolinecarsarenearperfectsubstitutes.
WORKING PAPER 2-10

15
Table 4: Calibrated elasticity values for average annual mileage of newly purchased cars
Monetary variable costs Fixed costs Mone-
tary
income
Small Medium Big Small Medium Big
Gaso-
line
Diesel Gaso-
line
Diesel Gaso-
line
Diesel Gaso-
line

Diesel Gaso-
line
Diesel Gaso-
line
Diesel
Small cars
Gasoline
Diesel
-0.14
-
-
-0.14
-
-
-
-
-
-
-
-
-0.01
-
-
-0.02
-
-
-
-
-
-

-
-
0.23
0.24
Medium cars
Gasoline
Diesel
-
-
-
-
-0.22
-
-
-0.22
-
-
-
-
-
-
-
-
-0.03
-
-
-0.03
-
-

0.25
0.26
Big cars
Gasoline
Diesel
-
-
-
-
-
-
-
-
-0.45
-
-
-0.45
-
-
-
-
-
-
-
-
-0.10
-
-
-0.09

0.49
0.48
Table 5: Calibrated elasticity values for car sale probabilities

Monetary variable costs Fixed costs Mone-
tary
income
Small Medium Big Small Medium Big
Gaso-
line
Diesel Gaso-
line
Diesel Gaso-
line
Diesel Gaso-
line
Diesel Gaso-
line
Diesel Gaso-
line
Diesel

Small cars
Gasoline -3.00 2.28 0.06 0.28 0.01 0.03 -2.63 2.66 0.06 0.30 0.01 0.03 0.00
Diesel 2.00 -1.88 0.06 0.28 0.01 0.03 1.76 -2.19 0.06 0.30 0.01 0.03 0.00
Medium cars
Gasoline 0.10 0.11 -17.58 18.59 0.01 0.03 0.09 0.13 -16.37 19.55 0.01 0.03 0.00
Diesel 0.10 0.11 3.68 -4.33 0.01 0.03 0.09 0.13 3.43 -4.55 0.01 0.03 0.00
Big cars
Gasoline 0.07 0.08 0.04 0.20 -16.52 16.38 0.06 0.09 0.04 0.21 -18.18 17.55 -0.01

Diesel 0.07 0.08 0.04 0.20 3.44 -4.44 0.06 0.09 0.04 0.21 3.79 -4.75 0.00
Table 6: The impacts of doubling the fixed or variable costs of different car sizes

Share in
reference
equilibrium
Generalised variable costs x 2 Fixed costs x 2
Small Medium Big Small Medium Big
Small cars 47.29% 37.27% 61.72% 48.38% 36.04% 63.76% 48.64%
Medium cars 48.37% 57.81% 33.05% 49.48% 58.97% 30.89% 49.74%
Big cars 4.34% 4.92% 5.24% 2.14% 4.99% 5.36% 1.62%
Table 7: The impacts of doubling the fixed or variable costs of gasoline and diesel cars

Share in
reference
equilibrium
Generalised variable cost x 2 Fixed cost x 2
Gasoline Diesel Gasoline Diesel
Gasoline cars
29.26% 0.30% 98.70% 0.39% 99.52%
Diesel cars
70.74% 99.70% 1.30% 99.61% 0.48%
WORKING PAPER 2-10

16
5. Output of the car stock module
Foreachyearofthesimulation,thevehiclestockmoduleprovidesthecompositionofnewve‐
hiclesalesandcalculatesaveragecostdata.
Asdescribedabove,newvehiclesalesarecalculatedeachyearbycomparingthetotaldesired
vehiclestock (defined astotalvehicle km dividedbyaverageannualmileageof

the previous
year)totheremainingvehiclestockofthepreviousyearafterscrappage.
Salesofnewcarsarethendividedamonggasolineanddieselcarsofdifferentsizesaccordingto
theabovedemandsystem.Afinalstepcalculatestheshareof
LPG,CNGandhybridgasolineand
dieselcarsusingexogenouslydefinedshares.
Forallroadvehicletypesthevehiclestockmoduleprovidesoutputsonthreeclassesofmone‐
tarycosts whichserveasaninputof theModal andTime Choice module ofthenextyear. It
concernsweightedaverages,wherethe 
weightsarethesharesofeachfuel,sizeandEurocate‐
goryintotalmileagedriven.
Thecostcategoriesare:
– Taxespaidpervkm(includingalltaxes:indirecttaxes,excisesandfixedtaxes)
– Fuelcostspervkm(Fuelexpenditureincludingexcisesandtaxes)
– Totalmonetarycostspervkm
(Allmonetarycosts–fixedandvariable–includingtaxes)
Inaddition,thevehiclestockmoduledeterminestheannualmileageofthenewlyboughtcars.
Thisiscombinedwiththeannualmileageoftheoldercars,todeterminetheaverageannualcar
mileage.Thisisusedinthenextperiod
todeterminethetotaldesiredcarstock(bydividingthe
numberofcarvkmbytheaverageannualcarmileage).
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17
6. Links of the car stock module with the other modules
Table8andTable9summarisethelinksbetweenthecarstockmoduleandtheotherPLANET
modules.
Table 8: Input in the car stock module of year t from the other PLANET modules
Input from Yea
r

Total vehicle km of cars, LDV and HDV Modal and time choice
t
Generalised income per capita Macro
t
Taxes on the various car types Policy
t
A
verage annual mileage of cars Vehicle stock
t-1
Table 9: Output of the car stock module of year t to the other PLANET modules
Output to Yea
r
A
verage emission factors per road transport mode Welfare
t+1
A
verage monetary costs, fuel costs and taxes per road mode Modal and time choice
t+1

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18
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