Accident Cost, Speed and Vehicle Mass Externalities, and Insurance

Transcription

1 Accdent Cost, Speed and Vehcle Mass Externaltes, and Insurance 26 Dscusson Paper Lars HULTKRANTZ Orebro Unversty, Sweden Gunnar LINDBERG VTI and Centre for Transport Studes, Sweden

2 Accdent cost, speed and vehcle mass externaltes, and nsurance Dscusson Paper No Prepared for the Roundtable on Insurance Costs and Accdent Rsks (22-23 September 2011, Pars) Lars HULTKRANTZ Orebro Unversty Gunnar LINDBERG VTI and Centre for Transport Studes (CTS) Sweden September 2011

3 INTERNATIONAL TRANSPORT FORUM The Internatonal Transport Forum at the OECD s an ntergovernmental organsaton wth 52 member countres. It acts as a strategc thnk-tank, wth the obectve of helpng shape the transport polcy agenda on a global level and ensurng that t contrbutes to economc growth, envronmental protecton, socal ncluson and the preservaton of human lfe and well-beng. The Internatonal Transport Forum organses an annual summt of Mnsters along wth leadng representatves from ndustry, cvl socety and academa. The Internatonal Transport Forum was created under a Declaraton ssued by the Councl of Mnsters of the ECMT (European Conference of Mnsters of Transport) at ts Mnsteral Sesson n May 2006 under the legal authorty of the Protocol of the ECMT, sgned n Brussels on 17 October 1953, and legal nstruments of the OECD. The Members of the Forum are: Albana, Armena, Australa, Austra, Aerbaan, Belarus, Belgum, Bosna-Heregovna, Bulgara, Canada, Croata, the Cech Republc, Denmark, Estona, Fnland, France, FYROM, Georga, Germany, Greece, Hungary, Iceland, Inda, Ireland, Italy, Japan, Korea, Latva, Lechtensten, Lthuana, Luxembourg, Malta, Mexco, Moldova, Montenegro, the Netherlands, New Zealand, Norway, Poland, Portugal, Romana, Russa, Serba, Slovaka, Slovena, Span, Sweden, Swterland, Turkey, Ukrane, the Unted Kngdom and the Unted States. The Internatonal Transport Forum s Research Centre gathers statstcs and conducts co-operatve research programmes addressng all modes of transport. Its fndngs are wdely dssemnated and support polcymakng n Member countres as well as contrbutng to the annual summt. Dscusson Papers The Internatonal Transport Forum s Dscusson Paper Seres makes economc research, commssoned or carred out at ts Research Centre, avalable to researchers and practtoners. The am s to contrbute to the understandng of the transport sector and to provde nputs to transport polcy desgn. The Dscusson Papers are not edted by the Internatonal Transport Forum and they reflect the author's opnons alone. The Dscusson Papers can be downloaded from: The Internatonal Transport Forum s webste s at: For further nformaton on the Dscusson Papers and other JTRC actvtes, please emal: [email protected] 2 L. Hultkrant and G. Lndberg Dscusson Paper OECD/ITF 2011

4 Accdent cost, speed and vehcle mass externaltes, and nsurance Dscusson Paper, September 2011 Lars Hultkrant*, Gunnar Lndberg** 1 * Örebro Unversty, **VTI and Centre for Transport Studes (CTS) 1 Introducton Traffc accdents are a human tragedy that klls 1.2 mllon people worldwde annually (World Health Organaton, 2004). The cost of traffc accdents are huge and recent estmates for US alone suggest the cost to be USD 433 bllon n year 2000 or 4.3 percentage of GDP (Parry et al, 2007). A reducton of ths cost can be done n two ways, ether by reducng the number of accdents or by mtgatng the consequences of the exstng accdents. Insurance systems can contrbute to both. Vckrey (1968) suggested a partal soluton to problems of unaffordable nsurance, unnsured drvng, premum unfarness and neffcences by proposng usage-based car nsurance. In fact, several nsurance companes have now adopted Vckrey s dea n the form of Pay-As-You-Drve (PAYD) automoble nsurance (Bordoff and Noel 2008). Ths polcy enables nsurers to charge the vehcle owner per mle nstead of a pre-set number of mles per year. PAYD s offered to motorsts on an optonal bass,.e., they can also choose a conventonal scheme. 2 PAYD nsurance bulds on the mproved possbltes brought by new n-vehcle technologes for measurng dstance drven. However, there s a range of other rsk factors that could be supervsed, some of whch are already used by the nsurance ndustry. For nstance, one Swedsh nsurance provder charges a lower premum to vehcles that have an alco-lock nstalled to make t mpossble to use the vehcle for an ntoxcated drver. In ths report, we summare some work we have done on how to ncorporate two of the most mportant rsk factors; vehcle mass and speed. The possblty to dfferentate nsurance premums accordng to varous rsk factors rases questons on the nteracton between vehcle nsurance schemes and taxes. Dstance drven, 1 We are grateful to our colleagues and co-authors Sara Arvdsson, Lna Jonsson, and Jan-Erc Nlsson who partcpated n the studes summared here. 2 Another possblty s annual odometer audts. However that would probably be much more costly than electronc measurement of dstance (Bordoff and Noel, 2008). L. Hultkrant and G. Lndberg Dscusson Paper OECD/ITF

5 speedng and vehcle mass are n many countres subect to taxaton (for nstance gasolne tax for dstance, speedng tckets for speed and vehcle tax for vehcle mass). These knd of taxes can be thought of as (often mperfectly mplemented) Pgou taxes leved by a prncpal (a state regulator) that wants to control agents (motorsts) that cause varous externaltes. Insurance companes are then another prncpal nfluencng these agents. As the state and the nsurance companes have dfferent obectve functons and are subect to dfferent legal, nformatonal and technologcal constrants, taxes and nsurance programs are mperfect substtutes as nstruments for nfluencng road traffc safety. In secton 2 we wll brefly dscuss how a PAYD scheme wth a speedng penalty (ths wll here be called Pay As You Speed, PAYS) can be combned wth taxes to mplement a Pgou taxaton of road accdent externaltes. PAYS vehcle nsurance s desgned to affect speed, whch s a man rsk factor that affects the number of accdents as well as the severty of accdents. In secton 3 we summare results from a vehcle-fleet experment wth a PAYS nsurance ncentve for keepng wthn speed lmts usng a speed-alert devce. The PAYS scheme was smulated wth a monthly bonus to partcpants durng two months reduced by a non-lnear speedng penalty. Partcpants were randomly assgned nto four treatment and two control groups. A thrd control group conssted of drvers who had the devce and were montored, but dd not partcpate. We found that partcpatng drvers reduced severe speedng durng the frst month, but n the second, after havng receved feedback reports wth an account of earned payments, only those that were gven a penalty changed behavour. In sectons 4 and 5 we turn to another maor rsk factor; vehcle mass. Vehcle mass s a crucal factor for the dstrbuton of nures between occupants n nvolved vehcles n a twovehcle crash. A larger vehcle mass protects the occupants n the vehcle whle on the same tme t nflcts a hgher nury rsk on the occupants n the collson partner vehcle. In secton 4 we analyse ths mass externalty usng a database ncludng collson accdents n Sweden nvolvng two passenger cars durng fve years. In each accdent the two nvolved vehcles are dvded nto the lghter vehcle and the heaver vehcle and the effect of weght s examned separately for the two groups. We fnd that the accdent costs that fall on the lghter vehcle ncreases wth the mass of the heaver vehcle and decreases wth ts own mass. Gven that a vehcle s the heaver one n the crash, nether the own mass nor the mass of the lghter vehcle sgnfcantly affect the accdent cost. The expected external accdent cost s calculated and t s shown to ncrease rapdly wth vehcle mass. Secton 5, fnally, uses the results from the prevous secton to dscuss dfferent solutons to nternalaton of ths external accdent cost. We calculate a mass dependent multplcatve tax on the nsurance premum n a no-fault nsurance system. Sectons 2 and 3 on PAYS nsurance are bref summares of studes that wll soon be publshed, and therefore can be read n full length elsewhere, whle sectons 4 and 5 on dfferentaton wth respect to vehcle mass present more novel results and wll therefore be presented more extensvely. 4 L. Hultkrant and G. Lndberg Dscusson Paper OECD/ITF 2011

6 2 Taxes on accdent externaltes and PAYS nsurance In Hultkrant et al. (2011) we suggest a desgn of Pgou taxaton n combnaton wth PAYS nsurance n order to nternale road accdent externaltes. We descrbe a settng nvolves two prncpals (the state and an nsurance company) that affect the economc ncentves of motorsts for drvng and for drvng carefully. Whle the state regulator s assumed to am for overall socal effcency by mplementng full margnal cost prcng, the nsurance company make use of actuaral prcng to cover ther costs,.e. average cost prcng wthn rsk classes that they estmate to be homogenous. Snce nsurance companes have means for dfferentaton across rsk classes that are not avalable to the government, the nsurer can be an agent for the regulator s traffc safety polcy. Another specfc feature of ths settng, n contrast to conventonal Pgovan taxaton, s that dfferentaton can be accomplshed by self selecton. Therefore, compulsory regulaton s not necessary. For ths am, we use a modal-mx model to analye the accdent externaltes from car drvng and from speedng. The rsk of collsons s the source of a recprocal externalty wthn the group of motorsts, as every drver s ncreasng the accdent rsk of all drvers by ust beng on the road, and even more so f he or she s speedng. However, the dstrbuton of these external effects s also affected by cross-subsdaton by fscal means, snce some accdent costs such as medcal care are pad for through taxes, and through vehcle nsurance (as dfferent categores of drvers wth dfferent accdent rsk cannot, n the absence of PAYS nsurance, be separated). The model we use comprses commuters who have a choce between a car mode and a reference travel mode. Motorsts may also choose to comply or not to comply wth speed lmts; hence the model has three modes dstngushed by speed (and therefore also tme to get to destnaton) as well as accdent rsk. Wth ths model we show how the cost burden of automoble accdents s spread between non-motorsts and motorsts wth dfferent rsk profles. Further, we use the model to show how the modal mx,.e., the drvng and speedng decsons, are affected by a change from conventonal to PAYS nsurance, and, wth conventonal nsurance, by a tax on vehcle nsurance premums. We derve Pgovan prce equatons for a complete nternalaton of car accdent externaltes wth two sets of nstruments; frst a conventonal soluton that combnes two taxes, a tax on drvng (vehcle usag and a tax on speedng (speedng tckets), and second a soluton wth PAYS nsurance and a tax on vehcle nsurance. It s thus necessary to use two separate polcy nstrument snce t s mportant not only to nduce roads users to drve at legal speeds but also to strke an optmal balance between whether to use the car mode or not. Usng these prce equatons a numercal example, calbrated on Swedsh data, ndcates that the standard Pgovan tax soluton would requre very hgh speedng charges, whle the PAYS nsurance could come close to a full nternalaton wthout any substantal change of the level of vehcle taxaton n comparson to the current stuaton. In Sweden, there already exsts a 32 percent tax on the compulsory part of the vehcle nsurance. Whle the external costof drvng cars n non-congested areas n Sweden seems to be already nternaled by the current fuel tax, the external cost of speedng s only to a very small extent nternaled by the expected cost of speedng tckets. In fact, wth PAYS nsurance taxes can be L. Hultkrant and G. Lndberg Dscusson Paper OECD/ITF

7 desgned so as to reduce the role of speedng tckets. 3 Hence, the system would mean that speeders who by assumpton are not nclned to nstall the equpment could contnue ther behavor and get away wth t by payng a hgher nsurance premum. Whle ths could be nterpreted as a mechansm for payng for the rght to speed, the man dfference compared wth today would be that people currently speed wthout havng to pay (fully) for t. A caveat s, however, that vehcle nsurance s assumed to be compulsory and that all drvers actually pay. However, even when vehcle nsurance only has to cover materal vehcle damages, and even n a country wth such law-obeyng motorsts as n Sweden, a fracton of the cars are drven wthout any nsurance (and/or wthout payng vehcle taxes). That proporton would lkely ncrease f nsurance fees were rased. The use of vehcle nsurance to nternale the full socal cost of accdents would thus n a way transform the traffc survellance problem from detecton of speedng to detecton of non-nsurance. However, as montorng of non-nsured vehcles s as a rule consderably more easy than montorng of speedng we regard ths as a mnor obecton. 3 Moral haard reducton wth PAYS nsurance the Swedsh vehcle fleet economc experment In 2002, we conducted an economc experment of a PAYS nsurance scheme usng 114 motorsts n the cty of Borlänge, Sweden, that had partcpated n a technologcal tral of a speed alert ( Intellgent Speed Adaptaton, ISA) system based on n-vehcle GPS recordng of vehcle speed and poston. The study s reported n Hultkrant and Lndberg (2012). Later smlar studes have been made n Denmark (Agerholm et al. 2008) and the Netherlands (Bolderdk et al. 2011). Here we brefly summare our own study. The focus of our study s on moral haard effects among users, not on selecton effects. We study how some features of a PAYS scheme, the magntude of a partcpaton bonus and a penalty fee, affect drvng behavour of those drvers that have accepted to partcpate. Our feld experment was desgned for the purpose of evaluaton of a PAYS nsurance based on ISA equpment. A vehcle-fleet tral s very costly but we were gven an opportunty to use an already exstng fleet tral. Vehcles for ths tral had been recruted through an offer to a random sample of 1000 prvate car owners n a Swedsh cty (Borlänge, pop ) to get ISA equpment nstalled free of charge. No other economc ncentves were used n ths tral. 250 prvate car owners accepted to have ther vehcles provded wth on-board computers wth dgtal maps, GPS postonng and moble communcaton facltes. The techncal system nformed the drver about the speed lmt on a dsplay n the vehcle whle an acoustc sgnal and a flashng lght alerted hm or her f the vehcle was drven faster than the speed lmt (Bergeå and Åberg 2002). The orgnal tral was completed n December Early next year, the car owners were nformed that they could keep the equpment for some tme f they wanted. Durng the late 3 As long as the PAYS nsurance s voluntary some need for external speed montorng remans because otherwse those who stck wth conventonal nsurance wll speed even more than presently. 6 L. Hultkrant and G. Lndberg Dscusson Paper OECD/ITF 2011

8 sprng, we nvted 114 prvate car owners that stll had these devces nstalled to partcpate n an economc experment for two months (September and October 2002).These months were chosen for the man experment, because they are free from the two maor seasonal dstortons n ths part of Sweden:, that s, summer vacatons (from md June to md August) and wnter road condtons (November March), both havng maor effects on aggregate travel and speedng patterns. After the second experment month was completed, however, we had not exhausted the proect budget so we offered the partcpants to contnue for a thrd month. As wll be shown later, that turned out to be of no use snce wnter came durng that month. Car owners were nformed that they would receve a monthly bonus of 250 SEK or 500 SEK to be pad mmedately at the end of the month and that ths bonus would be reduced by a penalty each mnute they drove faster than the speed lmt 4. The se of the penalty vared n four steps, dependng on the magntude of speed volatons, between 0 and 1 SEK per mnute, or between 0 and 2 SEK per mnute 5. All partcpatng drvers, also those that would get the lump-sum bonus wthout penalty reductons, got ndvdual feedback reports on ther total tme of drvng and speedng, together wth the monthly bonus payment. Those owners that accepted to partcpate were randomly assgned to a hgh or low ntal bonus (250 SEK/month or 500 SEK/month), and to the three penalty categores (ero penalty; 0 1 SEK/mnute; and 0 2 SEK/mnute; respectvely). To always make partcpaton benefcal n monetary terms, a cap was ntroduced to the total penalty charges so that even hgh offenders would get a net payment of at least 75 SEK each month. As t later turned out, no one was even near of httng ths celng. A maorty of the car owners (95 persons out of 114) accepted to partcpate n the experment, whle nne drvers reected, and ten dd not respond. Drvers that accepted were hence randomly dvded nto sx groups as shown n Table 1. There were 16 drvers n each of the groups A-E and 15 drvers n group F. A remanng group (G) conssted of the 19 drvers that reected or dd not respond to the offer to take part n the economc experment. These non-partcpators were stll usng the equpment and had been nformed that ther drvng would be contnued to be montored for research purposes. Ths gve us opportunty both to cast some lght on self-selecton effects and to have a control group, although not randomly selected, wth ero bonus, ero penalty, and no ndvdual feedback reports. 4 Speedng s recorded and summed over month n seconds. For penalty ths s rounded downwards to whole mnutes. 5 At ths tme 1 USD 1 EURO 9 SEK, so the hghest charge corresponded to roughly 20 cents per mnute. L. Hultkrant and G. Lndberg Dscusson Paper OECD/ITF

9 Table 1. Treatment groups (partcpants) Zero penalty Low penalty level (0-1 SEK/mn) Hgh penalty level (0-2 SEK/mn) Hgh bonus (500 SEK) A C E Low bonus (250 SEK) B D F The four-step penalty scheme was progressve to reflect that accdent rsk ncreases progressvely wth the speed of the car (Nlsson 2000). The levels of the low penalty charge were set so as to correspond to the estmated external cost of speed choce, accordng to a cost-beneft model used by the Swedsh Natonal Road Admnstraton. Hence, snce the techncal speedng detecton probablty s one (or close to on, ths penalty scheme approxmates a pure Pgou fee on speedng. Those gven the low penalty scheme were charged 0.10 SEK per mnute when the actual speed exceeded the speed lmt by 0-10 percent, 0.25 SEK per mnute when speed was percents above lmt and 1.00 SEK per mnute for speed offences above 20 percent. Those car owners that were gven the hgh penalty scheme were charged twce as much. The expermental desgn makes t possble to control for a varety of effects. Frst, the nonpartcpatng group G offers control over effects on speedng evoked by external factors, such as change of weather condtons. Second, the ero-penalty groups A and B control for Hawthorn effects from beng partcpator n an experment, n whch every partcpant s gven feedback nformaton on hs/her own drvng behavour. Thrd, the two bonus levels control for ncome effects, or other possble effects from the se of the partcpaton bonus. 6 Fnally, the two penalty levels make t possble to evaluate both the effect of penaltes vs. no penaltes (comparng C and E to A, and D and F to B) and to effect of the se of penaltes (comparng C to E and D to F). However, t must be borne n mnd that the experment groups are small. Also, unfortunately, due to techncal falures of some equpment we lack some reference drvng data, n partcular for October Data records were automatcally collected once a month through moble communcaton. The data contans nformaton on geographcal X- and Y-coordnates, tme and date. Ths nformaton was recorded frequently (every tenth second) as long as the car engne was runnng. The data s summared as ndvdual speed profles for each road type (defned as roads wth dfferent speed lmts). As the technology was known from the techncal tral to have some flaws, data was fltered from outlers to protect drvers from erroneous chargng. At the end of each perod, the partcpants receved nformaton about ther speedng behavour, the sum of penalty charges and the remanng net bonus. 6 In behavoural economcs, a general observaton s that many people behave n a recprocal manner (Rabn 1993) ncludng the phenomenon of condtonal cooperaton (Fehr and Fshbacher 2002), that s, that people contrbute (to a common good) contngent upon others contrbuton. Ths could mply that drvers that were gven the hgh partcpaton reward would contrbute more (hgh complance to speed rules). Another possble effect of bonus se comes from corner effects, that s, that a drver wth low bonus s more close to the penalty cap (SEK 75) where the margnal cost of further speedng s ero. 8 L. Hultkrant and G. Lndberg Dscusson Paper OECD/ITF 2011

10 In the ndvdual feedback reports to the partcpants, speed volatons were dvded nto three severty classes; Mnor (0-10%), Medum (11-20%) and Maor ( 21%). The reports stated the total tme (mnutes) durng one month (t) that the car () had been drven faster than the speed lmt, n total, and wthn each severty class, By dvdng these varables wth the total travel tme of the car durng the same month, we computed speedng frequences; measurng the proporton of total travel tme that the car s used for drvng faster than the speed lmt, n total and wthn each severty class. In evaluatng the results, we dd pared-dfference tests, comparng across groups the dfference of the outcome varable durng one of the experment months wth the level of the same varable durng a reference month, whch here wll be the same month one year before. Thus, for drvers for whch we have all observatons, we compared the levels of the outcome varables n September and October 2002, respectvely, to these levels n September and October 2001, respectvely. However, snce our sample s small, and s further reduced by lack of observatons for some drvers n 2001, especally n October, the evaluaton of results was based on regressons, usng observatons of all ndvduals, and controllng for ndvdual covarates, that s, not on comparson of group by group averages. 3.1 Results The average partcpatng car owner (Group A-F) was 57 years old and had an annual ncome of SEK The partcpants were therefore on average older and had hgher ncome than the car owners n general percent were female (natonal average s 31 percent). Nonpartcpants (Group G) were on average 5 year younger and had an even hgher ncome than partcpants, but only the age dfference to partcpants s statstcally sgnfcant. Partcpants on average drove faster than the speed lmt around 14 percent of the drvng tme, whle non-partcpants were on average speedng 17 percent of the drvng tme. Ths dfference s, however, not sgnfcant. For Severe speedng, the proporton of drvng tme was 4 percent for partcpants and 6 percent for non-partcpants. Ths dfference s sgnfcant at the fve percent level. However, the sgnfcance dsappears n a regresson controllng for the ndvdual covarates (Sex, Age, Age squared, and Incom. Table 2 shows the fnal estmated models (after subsequent reductons followng a general-tospecfc procedur estmated for one-year dfferences of Severe speedng n the two monthly samples for September and October, respectvely. The sample ses are manly restrcted by lmted number of observatons of drvng (speedng) behavour n 2001, whch leaves 81 and 48 observatons n the two samples, respectvely. There also are a few observatons of the ncome varable mssng. As shown, for the September dfference, two varables, Age and Partcpaton, reman n the reduced model; together explanng 12 percent of the total varaton. In the reduced October dfference model, the three remanng varables are Penalty, Sex and Income*Sex; explanng 47 percent of the total varaton. 7 The average age of a car owner n Sweden s approxmately 46 years (SIKA 2006). The average annual ncome of full tme employees n 2001 was SEK L. Hultkrant and G. Lndberg Dscusson Paper OECD/ITF

11 The regresson results show that subects of all treatment groups reduced Severe speedng durng the frst experment month, whle only subects n groups that were gven speedng penaltes reduced Severe speedng durng the second month. No other treatment varables (or nteractons, not shown) were sgnfcant. Durng the economc experment partcpants sgnfcantly reduced ther speed volatons compared to non-partcpants. The tme proporton of speed volatons was reduced from around 15 percent of total drvng tme pror to the experment to between 8 percent and 5 percent durng the experment wth the lower nterval at the end of the experment perod. Non-partcpants had almost constant proporton volatons durng the experment. Durng the frst experment month the prced partcpants reduced the speed volatons more than the ero-penalty partcpants but the dfference was not sgnfcant. However, durng the second month prced partcpants reduced severe volatons sgnfcantly more than the eropenalty group; the former had a reducton of 64 percent whle the latter only had a reducton of 15 percent. As mentoned, the regresson analyss gves statstcal evdence of a partcpant effect n September and a penalty effect n October. Ths mples that a penalty charge s essental for havng a lastng effect on severe speedng, that s, the placebo or Hawthorn effects of partcpaton that seem to be present n the September sample s not statstcally sgnfcant n October. The results do not ndcate any dfference between the two penalty charge levels. Ths suggests that drvers have had a bnary decson, ether to change or not to change ther regular behavour, and that, at least for the duraton of our experment, the low level was hgh enough to exhaust the potental for that. Ths further suggests that a smpler scheme than the four-ter penalty rate we used would suffce, for nstance a flat charge per mnute for speed volatons exceedng the speed lmt by a certan margn. Fnally, there was no sgnfcant behavoural dfference between groups wth dfferent bonus levels. In concluson, our study thus suggests that economc ncentve schemes, n the form of nsurance programmes or otherwse, coupled to the use of speed montorng devces may be an effectve way of reducng severe speedng, and thereby to ncrease overall road-traffc safety. The results mply that even drvers that voluntarly have nstalled such devces n ther cars may be hghly senstve to economc ncentves. Table 2. OLS estmaton results for one-year dfferences of Severe speedng n the September and October samples, respectvely. Base (general) and reduced (specfc) models. Standard errors wthn parentheses. 10 L. Hultkrant and G. Lndberg Dscusson Paper OECD/ITF 2011

12 Varable September October Base Reduced Base Reduced Constant (0.045) (0.014) (0.070) (0.006) Partcpaton 0.025** (0.011) 0.026*** (0.009) (0.018) Penalty (0.008) (0.012) 0.021** (0.008) Hgh penalty (0.008) (0.013) Hgh Bonus (0.007) Sex (0.0075) 0.032*** (0.011) 0.062*** (0.013) Age (0.002) (0.003) Age-squared ( ) ( ) Income ( ) ** ( ) Income*Sex *** ( ) R-squared Numb. Obs Vehcle mass and accdent cost Elvk (1994) classfed the external cost n three components; the externalty generated by changed accdent rsk due to hgher traffc volume (traffc volume externalty); the cost for the rest of the socety n form of general health care etc (system externalty) and thrdly, the ncreased rsk a car drver mposes on other drvers and road user categores, such as pedestrans and cyclsts (traffc category externalty). The last component s n ths secton further refned and analysed as an externalty between dfferent car ses. In the next secton we dscuss how a Pgou scheme could be desgned to correct for ths externalty, usng a combnaton of taxes and vehcle nsurance. The change n velocty that a vehcle experences n a collson s a good measure of the severty of the crash and works as a predctor of the fatalty and nury rsk (Toy and Hammt, 2003). In a two vehcle collson where the vehcles move n the same or opposte drectons, the change n velocty s a functon of the masses of the nvolved vehcles and ther ntal L. Hultkrant and G. Lndberg Dscusson Paper OECD/ITF

13 veloctes accordng to equaton 1 where m are the masses of the vehcles and v are ther ntal veloctes 8. m v v v (1) m m The velocty change wll be greatest for the lghter vehcle whch thereby also has hgher fatalty and nury rsk. As the equaton above shows, an ncrease n own mass wll both lead to a lower velocty change for the own vehcle and a greater velocty change for the collson partner. Increased mass wll thereby mprove the vehcle s crashworthness whle n the same tme ncrease the aggressvty. Besdes change of velocty also mean and peak acceleraton works as crash severty parameters (Stgson, 2009). Whle velocty change s a functon of the masses of the nvolved vehcles the acceleraton s also nfluenced by the vehcle structure, e.g. stffness. The lterature on vehcle crashworthness versus aggressvty has to a large extent been focused on the dfference between passenger cars and lght trucks (Andersson, 2008). Apart from the larger mass of Sport Utlty Vehcles, Vans and Pckups, ther stffness and dfferent geometry compared to passenger cars contrbute to more severe nures and fataltes to the occupants n the collson partner (Gayer, 2004; Joksch, 1998; Toy and Hammtt, 2003; Whte, 2004). Our study focuses on the mass dmenson and wll thereby gnore the related nfluence of stffness and geometry when analyng the dvson of the accdent cost between the nvolved vehcles. The fact that the mass of a vehcle affects the nures and fataltes n the collson partner mples that there s an external effect of vehcle mass that could be nternaled to reach economc effcency. Wthout nternalsaton, the drver wll choose vehcle mass based only on the own benefcal effect of mass and gnore the dsadvantageous effect on the nury rsk n the collson partner. 4.1 Model and data Accdents are assumed to be blateral,.e. they nvolve two vehcles. The accdent probablty (A) depends on the level of actve care each drver takes and the annual drven dstances. The severty of the accdent n vehcle s represented by λ where λ s a functon of the traffc envronment, occupant characterstcs and vehcle characterstcs ncludng the masses of both nvolved vehcles, (, ). It s assumed that δλ /δ <0, δ 2 λ /δ 2 >0 whle δλ /δ > 0 and δ 2 λ /δ 2 >0. A larger vehcle mass decreases the nures n the own car but at the same tme ncreases the nures and thereby the accdent cost that falls on the occupants n the collson partner. Ths s n concordance wth the nfluence mass has on the velocty change n the nvolved vehcles (eq. 1). The accdent cost conssts of economc losses l n form of medcal cost and lost ncome and gref and sufferng g. The total accdent cost that falls on vehcle s expressed as λ (g+l). All 8 The formula orgnates from Joksch et al (1998), p L. Hultkrant and G. Lndberg Dscusson Paper OECD/ITF 2011

14 medcal cost s assumed to be covered by the drver through full regress ncludng regress from the socal securty system. Economc losses (l) are assumed to be fully nsured. In a strong no-fault system no potental lablty to cover the other drver s loss occurs. The nsurance premum for drver wll be: A l 1 e (2) where e s the admnstratve cost of the nsurer as a proporton of the expected loss. Drvers are expected to be rsk averse and maxme ther expected utlty wth the utlty functon U(W,,π) where U/ W>0 and 2 U/ 2 W<0. Insurance s assumed to be avalable at actuarally far rates. Two possble states are assumed, state of accdent wth a probablty of A and a state where no accdent occurs wth a probablty of 1-A. In case of an accdent the wealth (W) wll be reduced by the accdent cost due to gref and sufferng whle the economc loss s covered be the nsurance. The expected utlty of drver can be expressed as: EU 1 A W A W g P (3) where P s the prce of mass, for example through hgher fuel consumpton. The frst order condton for the choce of optmal level of vehcle mass for drver gves: EU A g l 1 e P 0 (4) and t can easly be verfed that the second order condton holds. A larger vehcle mass wll beneft the drver and passengers through a lower nury rsk that s reflected both n a lower expected cost due to gref and sufferng (g) and a lower nsurance premum as the expected economc loss (l) wll decrease. These benefts wll be weghed aganst the cost of mass n the prvate choce of vehcle. It s well known that a no-fault system wll generate a lower level of care than a tort system (Cummns et al, 2001). The level of care wth a no-fault system wll be lower than the optmal level. Besdes ths, a no-fault system wll also lead to a choce of vehcle mass that s hgher than the socal optmum f vehcle mass decreases the nury rsk n the own vehcle and ncreases the nury rsk n the collson partner. Assumng a socety of two drvers the followng frst order condton for the frst drver s socal optmal choce of vehcle mass can be derved: EU EU A g l 1 e Internal_ Beneft P A g l(1 Negatve_ Externalt y 0 (5) L. Hultkrant and G. Lndberg Dscusson Paper OECD/ITF

15 In a no-fault system the choce of vehcle mass wll be made consderng only the nternal beneft of a large mass whle the ncreased nury rsk to other road-users wll be gnored. The dataset ncludes all polce reported personal nury accdents nvolvng exactly two passenger cars n Sweden durng 1999 to sprng The dataset conssts of nformaton on the condtons at the occason of the accdent ncludng speed lmt, weather condton and nformaton on nvolved vehcles ncludng ther mass (both total weght and kerb weght), model and exstence of arbag 9. The dataset also ncludes nformaton on the drver and passengers of the vehcles, ther sex, age and ther nures f any. The nures are categorsed n three categores; slght nury, severe nury and fatalty. Table II presents descrptve statstcs. To construct a common unt for the accdent cost the offcal Swedsh valuaton for fataltes, severe and slght nures (SIKA, 2008a) n Table I s used. The valuaton s splt nto materal cost ncludng manly medcal cost and lost producton (l) and the rsk valuaton whch we take equal to the pan and sufferng loss (g). For each accdent the total accdent cost s calculated and attrbuted to the vehcle n whch the vctms where travellng. Snce all nures are categorsed n only three levels, the accdent cost attrbuted to the vehcles wll n our dataset not be fully contnuous but takes only a few values dependng on the number of nured occupants and the category of ther nures. Table I Valuaton of accdents (SEK)) Materal cost (l) Rsk Valuaton (g) Total (l+g) Fatalty Severe Inury Slght Inury SEK 10 Euro cent. Note: Materal cost ncludes only net lost producton For each accdent the lghter of the two vehcles s labelled vehcle 0 and the heaver labelled vehcle 1. Table II shows that the average total cost due to nures and fataltes s hgher n the lghter vehcle n spte of the hgher average number of passengers (ncludng the drver) n the heaver vehcle. Ths s a result of the more than twce as many fataltes n the lghter vehcles. 9 The orgnal dataset ncluded a few vehcles wth a mass above what s normally recogned as passenger cars. Accdents ncludng vehcles wth a total weght exceedng 3000 kg have therefore been excluded from the dataset, thereby reducng the number of accdents wth L. Hultkrant and G. Lndberg Dscusson Paper OECD/ITF 2011

16 Table II Descrptve statstcs Lghter vehcle Heaver vehcle Mean N Mean N Age of drver Male drver (yes=1) Number of passenger Young male drver <25 (yes=1) Number of elder passengers (>60) Speed lmt (km/h) Age of car Kerb weght (kg) Total weght (kg) Arbag (yes=1) Fataltes Severe nures Slght nures Total materal cost (SEK) Total accdent cost (SEK) Internal beneft and external cost of ncreased mass Gven that an accdent occurs we are nterested n how the characterstcs of the dfferent vehcles affect the nures and thereby the accdent cost and how ths cost s splt between the nvolved vehcles. Separate models are beng estmated for the total cost of fataltes and nures n the lghter vehcle and the cost n the heaver vehcle as a functon of the kerb weghts of the nvolved vehcles 10. The measure of cost n one vehcle s thus nfluenced by the other vehcle. Earler studes (Whte, 2004; Evans, 2001; Fredette et al, 2008) have examned how vehcle characterstcs nfluence the probablty for fataltes or severe nures gven an accdent. We, nstead, estmate the mpact of vehcle characterstcs on accdent costs, so obtanng a more drect measure of the external costs assocated wth vehcle mass. For the accdent costs of the lghter vehcle, we estmate the followng lnear model: TC 0 0Mass0 1Mass1 Arbag 0 No. ofpassengers0 SpeedRestrcton (6) The dependent varable s the total cost of fataltes and nures λ 0 (l+g) n the lghter vehcle gven a collson wth a heaver vehcle. We model the accdent cost n the lghter vehcle as a functon of the lghter vehcle s own kerb weght, the kerb weght of the heaver vehcle, the numbers of passengers n the lghter vehcle, the speed restrcton at the place of the accdent and a dummy for f the lghter car was equpped wth an arbag. In an extended model 10 It s not self-evdent whether the kerb weght (vehcle weght ncludng fuel and a drver at 70 kg) or the total weght (kerb weght and maxmum allowed load) best reflects the actual mass of the vehcle at the accdent. Both mass varables have been tested and the effect on the premum tax s not affected by the choce. L. Hultkrant and G. Lndberg Dscusson Paper OECD/ITF

17 dummes for f the drver s a male between 18 and 25 n the lghter car and the heaver car respectvely s added together wth varables measurng the sex and age of all the passengers n the lghter car. Vehcle age does not explan the accdent outcome and s therefore excluded from the models. Results for both models are presented n Table III. As expected, the cost wll be reduced wth vehcle mass for the lghter vehcle and ncreased wth the mass of the heaver vehcle. The number of passengers n the car as well as the speed lmt ncreases the cost. Exstence of an arbag decreases the cost. The own mass wll reduce the cost for the lghter vehcle wth around 1209 SEK per klogram whle every extra klogram of kerb weght of the heaver vehcle wll ncrease the cost mposed on the lghter vehcle by around 1130 SEK, a cost that s external to the heaver vehcle. We nclude dummes for male drvers between 18 and 25 for each of the vehcle types, as a proxy for the actual speed at the tme of the accdent. We also nclude separate varables for dfferent age groups and for gender so that accdent costs can dffer among the groups, e.g. because the elderly are more fragle. These dummy varables do not change the conclusons. 11 Estmatng the correspondng models for the cost of the heaver vehcle gves a qute dfferent result. For the heaver vehcle the cost due to nures and fataltes s not sgnfcantly affected by ether the own mass or the mass of the lghter vehcle. TC1 0Mass0 1Mass1 Arbag 1 No. ofpassengers1 SpeedRestrcton (7) 11 The logc behnd the drver dummy s the lack of nformaton n our dataset on actual speed of the vehcles at the tme of the accdent. Includng a dummy for f the drver s a man aged 18 to 25 s an attempt to capture the suspcon that young men drve faster than other groups and correct for ths under the assumpton that young men are overrepresented n certan vehcle and accdent types. Nether the drver dummy for the drver of the lghter nor the heaver car s sgnfcant. 16 L. Hultkrant and G. Lndberg Dscusson Paper OECD/ITF 2011

18 Table III Results weght of both vehcles Total Cost n Lghter Vehcle Total Cost n Heaver Vehcle Constant ( ) ( ) Kerb Weght lghter (426) (277) Kerb Weght heaver (498) (306) No. of Passengers ( ) ( ) Arbag ( ) (94 886) Speed Restrcton (5 563) (3 567) Male drver 18- Total Cost n Lghter Vehcle ( ) (447) (505) Total Cost n Heaver Vehcle ( ) -20 (266) 161 (305) ( ) (95 596) (5 761) (3 316) lghter ( ) ( ) Male drver heaver ( ) ( ) Sex and Age var. NO NO YES YES R Number of obs Robust standard errors n parentheses; Results non-sgnfcant at the 5 % -level n talcs Models where the costs n the nvolved vehcles are estmated as functons of the mass dfference nstead of the kerb weghts themselves are presented below (Table IV). The kerb weght dfference s both expressed as the actual dfference n kg between the heaver and the lghter vehcle and as the rato between the heaver and the lghter vehcle. L. Hultkrant and G. Lndberg Dscusson Paper OECD/ITF

19 Table IV Results weght dfference Total Cost n Lghter Vehcle Total Cost n Heaver Vehcle ( ) -63 (256) Total Cost n Lghter Vehcle ( ) Total Cost n Heaver Vehcle ( ) Constant ( ) Mass 1 -Mass (418) Mass 1 /Mass ( ) ( ) No. of Passengers ( ) ( ) ( ) ( ) Arbag ( ) (94 129) ( ) (71 108) Speed Restrcton (5 556) (3 568) (4 334) (2 763) R Number of obs Robust standard errors n parentheses, Results non-sgnfcant at the 5 % -level n talcs The model where the mass dfference s expressed as a rato nstead of an absolute dfference s harder to gve an ntutve nterpretaton to, but s a common measure n the lterature (Evans 2001, Toy and Hammt 2003, Joksch et al 1998). The estmates of the number of passengers, the speed restrcton and the arbag are almost constant across specfcatons. The mass dfference expressed as a dfference n kg or a rato s hghly sgnfcant for the cost of the lghter vehcle but not for the cost of the heaver vehcle. Models have been estmated ncludng also the absolute mass of one of the vehcles resultng n nsgnfcant estmates for the vehcle mass varable gven the mass dfference;.e. gven the mass dfference the vehcle mass per see wll not nfluence the consequences of an accdent. Our model thus suggests that mnmng the mass dfference n the fleet would be benefcary whle our result supports nether downsng nor upsng. Ths s n contrast to the results n Bueman et al (1998) that concluded that a unform mass ncrease would lower the number of fataltes and Evans (2001) that concluded that n any two-car crash a replacement of both cars wth other heaver cars by ether a fxed percentage or a fxed amount wll reduce the total fatalty rsk. 4.3 The expected external accdent cost Increasng the mass of a vehcle both ncreases the probablty to be the heaver vehcle n a collson and the expected mass dfference gven a collson wth a lghter vehcle. Both these effects affect the expected accdent cost n the collson partner. An ncreased mass also affects the expected nternal accdent cost. Snce the effect of vehcle mass dffers dependng 18 L. Hultkrant and G. Lndberg Dscusson Paper OECD/ITF 2011

20 CDF on f the vehcle colldes wth a heaver or a lghter vehcle the expected costs s the sum of the expected cost gven a collson wth a heaver vehcle and the expected cost gven a collson wth a lghter vehcle weghted wth respectvely probabltes (eq. 8 and 9). Expected External Accdent Cost E P g l(1 TC 1 P P TC 0 g l(1 P g l(1 (8) Expected Internal Accdent Cost E P g l(1 TC 0 P P TC 1 g l(1 P g l(1 (9) We use the estmated models excludng drver dummy for the total accdent cost from Table III (column 2 and 3) usng mean values for speed restrcton, arbag and number of passengers for the lghter and heaver vehcles respectvely. For each vehcle the mean mass of all vehcles wth a mass exceedng or below the mass of the vehcle n queston s used as the mass of the collson partner. The probablty to collde wth a heaver/lghter vehcle s calculated as the proporton of vehcles n our dataset that s heaver/lghter than the vehcle n queston (Fgure 1). Fgure 1 Dstrbuton of kerb weght for passenger cars nvolved n collson accdents, Sweden Kerb weght (kg) L. Hultkrant and G. Lndberg Dscusson Paper OECD/ITF

21 The probablty to be the heaver party n an accdent ncreases of course strongly wth vehcle mass. Table V shows that the expected external accdent cost doubles from around 1 mllon SEK for the lghtest vehcles up to over 2 mllon SEK for the heavest vehcles. At the same tme wll the expected nternal accdent cost declne from 1.8 mllon SEK for lghtest vehcles to only 1.1 mllon SEK for the heavest vehcles n the sample. The proporton external cost ncrease from about 36% for the lghtest vehcle to 66% for the heaver vehcle types. Table V External and nternal expected accdent cost Kerb Weght Vehcle Kerb weght f > Kerb weght f < CDF P( < ) TC_external MSEK TC_nternal MSEK TC MSEK External/TC Summary The lterature shows that vehcle mass s a crucal factor behnd how the nures are dstrbuted among the nvolved vehcles n a two-vehcle crash. A larger vehcle mass wll protect the occupants n the vehcle whle on the same tme nflct a hgher nury rsk on the occupants n the collson partner. We have here shown on Swedsh data that a kg of kerb weght of a vehcle wll ncrease the accdent cost n the collson partner by 1130 SEK gven that the collson partner s lghter than the vehcle n queston. At the same tme, a kg of kerb weght wll decrease own-vehcle accdent cost by 1209 SEK gven a collson wth a heaver vehcle. For the heaver vehcle n a collson nether own weght nor the weght of the other vehcle have any sgnfcant nfluence on accdent costs. Many of the heavest vehcles n the study are Sport Utlty Vehcles or mnbuses wth a geometry and stffness that dffers from ordnary passenger cars. Snce the dataset lacks a sutable measure for stffness the effect of stffness cannot be separated from the effect of mass. A part of the effect of mass estmated n ths study mght therefore be due to stffness. As long as the relatonshp between stffness and mass s constant between dfferent car models ths s a mnor problem n settng a correct premum tax. Ths ssue needs to be further nvestgated f a weght dependent premum tax should be ntroduced. There s an ongong debate on whether downsng the vehcle fleet would be benefcal to or undermne overall traffc safety. Crandall and Grahams study from 1989 usng aggregate data 20 L. Hultkrant and G. Lndberg Dscusson Paper OECD/ITF 2011

22 clam that the Corporate Average Fuel Economy (CAFE) program that requres a mnmum fuel effcency standard has led to lghter vehcles and thereby addtonal fataltes. Several studes have questoned Crandall and Grahams result (Ahmad and Greene, 2005) and especally emphased that a replacement of cars by lght trucks lke SUVs has lead to more fatal accdents (Whte, 2004). Our model gves no support ether to downsng the vehcle fleet or upsng t but suggests that t s the mass dfference that should be reduced. 5 Taxaton of the mass dependent externalty n a no-fault nsurance system Sweden and numerous states n the US have a no-fault nsurance system. No-fault nsurance s often used loosely to mean any nsurance whch allows the polcyholder to recover fnancal losses from ther own nsurer regardless of fault. Sweden has a more strct no-fault system wth very lmted rght to sue. In a strct system the premum wll be based solely on the nternal accdent cost. Premum tax s common n many countres (Swss Re, 2007) and Sweden recently ntroduced a tax of 32% on the premum (SFS 2007:460) whch could be seen as one way to nternalse the system externalty. However, f the external cost dffers dependng on vehcle characterstcs the government could do better wth a dfferentated premum tax that could also nternale the traffc category externalty. The prevous secton showed that n a no-fault nsurance system the drvers wll choose vehcle mass n a way that gnores the effect on the nury rsk on the collson partner. One way of nternalng the mass externalty s to let the drver pay also for nures n the other nvolved vehcle, as n eq. 10. EU 1 A W A W g P A g l(1 (10) Exp. Accdent_ cost _ n the_ collson_ partner The ncluson of the mass dependent externalty can ether be done ex post as a lablty or ex ante as an addtonal nsurance premum. The nsurance premum n the no-fault system should n the latter case be supplemented by the expected total accdent cost n the other vehcle; the new nsurance premum π equals: ' A g l(1 (11) Usng eq. 11 a multplcatve premum tax (t) on the nsurance premum (π) can be ntroduced to nternale the external accdent cost 13 : 13 Usng: ' A l(1 A g l(1 L. Hultkrant and G. Lndberg Dscusson Paper OECD/ITF

23 l(1 g l(1 ' t (12) l(1 Where l( 1 s the expected economc loss that s compensated by the nsurance company and g l( 1 s the expected total accdent cost n the collson partner. The accdent probablty A for a two-vehcle collson accdent, whch vares between drvers dependng on drven dstance, behavour and personal characterstcs, wll be calculated by the nsurance company. The expected economc loss l( 1 s estmated n the same way as the total cost (eq. 6 and 7) but usng only the materal cost component n Table I based on net lost producton. Usng the expected nternal materal cost the premum tax for dfferent vehcle masses can be calculated (Table VI). 14 Table VI Example of premum tax and bonus/malus on an average tax Kerb E(External total E(Internal materal Premum Tax Bonus/Malus on Weght cost) cost) l(1 g l(1 the average g l( 1 l( 1 l(1 premum tax MSEK MSEK The prncple to add a multplcatve tax on the thrd party nsurance premum yelds a substantal ncrease n the premum: the tax for the average vehcle s 700%. Gven that average tax, our estmatons suggest consderable dfferentaton accordng to weght: the heavest vehcles should be taxed 75% more than the average, the lghtest ones 38% less. The expected margnal external cost ncreases when the mass ncreases both because the aggressvty s hgher and the probablty of beng the heaver vehcle ncreases wth mass. At the same tme the expected nternal cost decreases. Consequently, a bonus/malus on the average tax wll not be constant and ncreases strongly wth mass (Fgure 2). Fgure 2 Bonus/Malus on the average theoretcal nsurance premum 14 In the calculatons of the expected external and nternal cost both n Table V and Table VI the small and nsgnfcant mass coeffcents from the models on the cost n the heaver vehcle are used. Calculatons have also been made where the effect on the accdent cost n the heaver vehcle of the mass s set to ero and ths only margnally changes the premum tax and bonus/malus. 22 L. Hultkrant and G. Lndberg Dscusson Paper OECD/ITF 2011

24 Bonus/Malus Kerb weght (kg) In a no-fault system, lke Sweden s, the nsurance premum s set accordng to the expected accdent cost n the nsured vehcle.a larger vehcle mass, that decreases the expected accdent cost for that vehcle wll thereby result n a lower nsurance premum. Snce the vehcle mass nfluences the nures that occur n the collson partner, one way to nternale the effect of mass s to let each vehcle pay also for the nures n the collson partner. In ths study a multplcatve premum tax that depends on vehcle mass s calculated. The ntroducton of ths premum tax wll result n an nsurance premum that ncludes both the expected materal accdent cost for the nsured vehcle and the total accdent cost n the collson partner. Such a premum tax wll rase substantal revenue for the government that wll equal the total accdent costs due to two-vehcle accdents. Whle most studes analyng the effect of vehcle mass use the fatalty or nury rsk of the drver as the measure of crashworthness or aggressvty ths study nstead looks drectly at the accdent cost due to nures and fataltes of all occupants n the nvolved vehcles. The calculated premum tax and expected costs therefore cover the nures and fataltes also for the passengers n the vehcles. Snce the premum tax s multplcatve no assumptons are made on accdent probablty, whch wll be calculated by the nsurance company n settng ther premum. In real lfe, two-car collsons are not the only type of accdents and the nsurance premum s set also n relaton to the expected loss due to sngle-vehcle accdents. Ths paper provdes a frst example, calculated from real accdent data, as to how the mass externalty can be nternaled by a tax on nsurance premums. For a premum tax that also takes nto account other types of accdents the model must be extended. For a comparson, of the 276 ndvduals that were klled n traffc accdents sttng n passenger cars n Sweden n 2007, only 72 were klled n accdents nvolvng two passenger cars whle 116 were klled n sngle vehcle accdents (SIKA, 2008b). Collson accdents between two passenger cars are therefore only a mnor part of the total expected accdent cost that the nsurance companes base ther premums on. L. Hultkrant and G. Lndberg Dscusson Paper OECD/ITF

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