NOTA DI LAVORO Paying for Safety: Preferences for Mortality Risk Reductions on Alpine Roads

Transcription

1 NOTA DI LAVOO Payng for Safety: Preferences for Mortalty s eductons on Alpne oads By hrstoph M. henberger WSL Insttute for Snow and Avalanche esearch and IED Insttute for Envronmental Decsons Swtzerland

2 SUSTAINABLE DEVELOPMENT Seres Edtor: arlo arraro Payng for Safety: Preferences for Mortalty s eductons on Alpne oads By hrstoph M. henberger WSL Insttute for Snow and Avalanche esearch and IED Insttute for Envronmental Decsons Swtzerland Summary Ths paper presents a choce experment whch values reductons n mortalty rs on Alpne roads. These roads are on one hand threatened by common road hazards on the other hand they are also endangered by natural hazards such as avalanches and rocfalls. Drawng on choce data from frequently exposed and barely exposed respondents we are not only able to estmate the VSL but to explore how the respondents dffer n ther ndvdual wllngness-to-pay dependng on personal characterstcs. To address heterogenety n preferences for rs reducton we use a non-lnear condtonal logt model wth nteracton effects. The best estmate of the VSL n the context of fatal accdents on Alpne roads s n the range of mllon wth dstnct dfferences between the urban and the mountan sample groups. We fnd the VSL to be sgnfcantly altered by socoeconomc factors but only margnally altered by the type of hazard. Keywords: Value of Statstcal Lfe hoce Experment Natural Hazard Mtgaton Traffc Safety JEL lassfcaton: D8 J7 4 Address for correspondence: hrstoph M. henberger WSL Insttute for Snow and Avalanche esearch Flüelastrasse 760 Davos Swtzerland Phone: Fax: E-mal: rhenberger@slf.ch The opnons expressed n ths paper do not necessarly reflect the poston of Fondazone En Enrco Matte orso Magenta 6 0 Mlano I web ste: e-mal: worng.papers@feem.t

3 Payng for Safety: Preferences for Mortalty s eductons on Alpne oads hrstoph M. henberger Abstract: Ths paper presents a choce experment whch values reductons n mortalty rs on Alpne roads. These roads are on one hand threatened by common road hazards on the other hand they are also endangered by natural hazards such as avalanches and rocfalls. Drawng on choce data from frequently exposed and barely exposed respondents we are not only able to estmate the VSL but to explore how the respondents dffer n ther ndvdual wllngness-to-pay dependng on personal characterstcs. To address heterogenety n preferences for rs reducton we use a non-lnear condtonal logt model wth nteracton effects. The best estmate of the VSL n the context of fatal accdents on Alpne roads s n the range of mllon wth dstnct dfferences between the urban and the mountan sample groups. We fnd the VSL to be sgnfcantly altered by soco-economc factors but only margnally altered by the type of hazard. Keywords: Value of Statstcal Lfe; hoce experment; Natural hazard mtgaton; Traffc safety JEL lassfcaton: D8; J7; 4 WSL Insttute for Snow and Avalanche esearch Flüelastrasse 760 Davos Swtzerland IED Insttute for Envronmental Decsons ETH Zürch 809 Zürch Swtzerland Tel.: ; Fax: E-mal address: rhenberger@slf.ch

4 Introducton Alpne countres nvest large amounts of money to mtgate natural hazards such as avalanches floods and rocfalls. Swtzerland for example spends approxmately 0.6% of ts annual GDP on the mtgaton of and the recovery from natural hazards PLANAT 005. Whle a part of these efforts s fnanced through prvate sources publc expendtures cover the lon s share. Publcly funded mtgaton programs have so far been focused on the costeffcent supply of mtgaton. An optmal resource allocaton would however not only consder the supply sde but also the socetal demand for safety mprovements. Stated preferences provde an operatonal bass to deduce the socetal demand for safety mprovements. Surprsngly few emprcal studes have addressed these preferences n the context of natural hazards. Brouwer and Bateman 005 studed socety s valuaton of flood control measures n the Netherlands Zha and Ieda 006 analyzed the economc value of evacuatons durng flood events n Japan and Leter and Prucner 009 estmated the socetal wllngness-to-pay WTP for reductons n avalanche rs n Austra. All of these studes used the contngent valuaton approach to elct WTP measures. Ths paper contrbutes to the scarce lterature by presentng a choce experment to value mprovements n traffc safety on Alpne roads. It has been shown that ths stated-preference approach s well-suted to the study of socetal preferences for mortalty rs reductons and even allows ndvduatng these preferences see Albern et al. 007; Bosworth et al. 008; Tsuge et al Three research obectves gude our expermental nvestgaton. Frst we want to fnd out how much socety s wllng to pay for reductons n mortalty rs on publc roads n the Swss Alps. Users of these roads are on one hand threatened by natural hazards such as snow avalanches and rocfalls. On the other hand road users face the common rs of car accdents whether t be through poor road condtons or through the dangerous behavor of other drvers. Our experment confronted survey respondents wth dscrete choces from among hypothetcal traffc safety programs to protect aganst these hazards and to reduce mortalty rss on Alpne roads. Based on ther choces we estmate the value of statstcal lfe VSL whch has become the common metrc to value lfesavng programs and envronmental regulatons nvolvng rss to human lfe Hammtt 000. Second psychometrc research on rs suggests that characterstcs such as voluntarness controllablty and orgn of a hazard affect people s rs percepton Slovc 987; Slovc et al Presumably these factors affect the economc valuaton of mortalty rs reductons McDanels et al. 99; Subramanan and ropper 000 but emprcal evdence for these effects s relatvely small hlton et al. 00; Leter and Prucner 009. To broaden ths evdence we analyze how specfc characterstcs of the hypothetcal traffc safety programs and ther perceved benefts affect the sze of the VSL estmates.

5 Thrd there s an ongong dscusson as to whether the VSL should be ndvduated accordng to age wealth health and baselne rs see Albern et al. 004; Baer et al. 008; Eechoudt and Hammtt 00; Pratt and Zechauser 996; Sunsten 004. We study how people dffer n the WTP for rs reductons based on ther soco-economc characterstcs and ther exposure to natural hazards. In other words we analyze preference heterogenety n the context of mortalty rs usng a non-lnear condtonal logt model as ntroduced by Albern et al To address these research obectves the paper s organzed as follows. Secton. begns wth a bref overvew of mortalty rss on Alpne roads and compares these rss to other causes of death. We then descrbe the desgn of our survey ncludng the attrbutes and levels selected to characterze the choce tass and summarze the characterstcs of the survey respondents. In Secton. we theoretcally deduce the VSL wthn the random utlty framewor of dscrete choce analyss and explan our modelng approach to analyze preferences for mortalty rs reductons. Selected results of the model estmatons are presented n Secton.4. We frst report the results for dfferent specfcatons of the nonlnear condtonal logt model. We then test the scope and senstvty of these results. In Secton.5 we summarze our results and ther mplcatons for valung mortalty rs reductons n the context of natural hazards. Survey development choce tas and sample characterstcs. Overvew of mortalty rss on Alpne roads Alpne roads are frequently exposed to natural hazards such as snow avalanches and rocfalls. Wthn the last 5 years three ndvduals per year have been lled on average n accdents caused by rocfall or avalanche events on Swss roads whle approxmately 500 ndvduals per year have ded n car accdents BFS 007a. Although the populaton at rs s larger n the case of car accdents only about one quarter of the Swss resdents frequently drve on Alpne roads the probablty of dyng n a rocfall or avalanche accdent on a road s statstcally small compared to other causes of death Fg.. Yet many people experence feelngs of dread when consderng the rss from natural hazards snce they are nvoluntarly borne and are out of self-control. Dread has been found to be a perceptonal factor that tends to ncrease the WTP for mtgaton hlton et al. 00; hlton et al. 006; Subramanan and ropper 000. In comparson car accdents are a well-nown rs and frequently analyzed n VSL studes de Blae et al. 00. In our survey we used car accdents as a reference rs to see whether perceptonal factors of natural hazards decrease or ncrease the socetal WTP for traffc safety on Alpne roads.

6 Fg. League table of statstcal causes of death n Swtzerland compled from BFS 007a. Snce the ndvdual rs of dyng n rocfall or avalanche accdents s small and the occurrence of such accdents s hardly predctable t s a pror unnown whose lfe wll be saved by the mplementaton of a traffc safety program. Anybody travelng on Alpne roads may potentally beneft from the rs reducton and as far as publc roads are concerned no one can be excluded from ths beneft. Thus traffc safety on Alpne roads s a publc good. The valuaton of mortalty rs reductons n the publc goods context mples three maor challenges. Frst the respondent s WTP for rs reducton depends on the sze of the affected populaton or on the sze that the respondent thns of when evaluatng the choce tass Green et al. 994; Kahneman et al. 99. Second the magntude of the cost fgures s used as a mental anchor. Green et al. 998 showed that the anchorng of prompted costs systematcally nfluences the responses n stated-preference studes. Ths can cause large bases n the valuaton of publc goods partcularly f respondents have strategc ncentves to over- or understate ther true WTP. Thrd respondents may have preferences for reductons n ther own rs n the rs to others or n expressng mercy and soldarty wth those people exposed to a rs Jones-Lee 99; Vscus et al We addressed the former two challenges by mang the survey nstrument as realstc as possble. We presented the rs reducton as a hypothetcal referendum for fnancng the future mantenance of hazard mtgatng nfrastructure and clearly stated how many fataltes each traffc safety program could avert at whch cost. To reduce strategc answerng we used a relatve bd vehcle that personalzed the cost of each of the alternatve programs relatve to 4

7 a percentage of the respondent s last tax payment. The advantage of ths relatve bd vehcle s that when converted to absolute values t corresponds to the cost ncurred to the respondent f the program were to be eventually mplemented Schläpfer 008. The thrd challenge can hardly be resolved because the respondents preferences may be smultaneously composed of egostc altrustc and warm glow motves Jones-Lee 99; Kahneman and Knetsch 99; Kahneman et al In our study context the ndvdual rs s small and the benefts of the proposed traffc safety programs are concentrated on the most exposed people. We therefore conducted the choce experment wth respondents from two dfferent regons of Swtzerland. One sample conssted of people from the mountanous regon around Davos who are frequently exposed to natural hazards on Alpne roads. The other sample conssted respondents from the cty of Zurch who are unlely to be frequently exposed. Ths splt-samplng allows testng whether less exposed respondents may have altrustc values resultng n concerns about the safety of others odrguez and Leon hoce attrbutes and levels In the desgn phase of the study four focus groups wth partcpants from both sample regons were held to explore the relevant attrbutes of traffc safety on Alpne roads the understandng of the relatve bd vehcle and the use of varous rs communcaton ads see orso et al. 00. The exploratory research also asssted n specfyng the levels of each of the relevant attrbutes so that respondents could understand mprovements n traffc safety as a result of changng attrbute levels. For ths purpose we dscussed the current level of mtgaton measures to protect Alpne roads aganst natural hazards wth a number of natural hazard experts consstng of representatves of the responsble authortes cvl engneers and scentsts. These expert ntervews provded a sem-quanttatve assessment of the current level of traffc safety on Alpne roads upon whch we developed what-f scenaros for the case that mtgaton measures would no longer be mantaned. The exploratory research resulted n the selecton of four attrbutes to descrbe traffc safety programs for Alpne roads: the number of fataltes per year that are averted by a specfc traffc safety program; the number of years over whch the program would reduce the rs; the type of road hazard aganst whch ths program s effectve; and 4 the cost of ths program to the taxpayer. Table summarzes the selected attrbutes and levels used n the choce experment. 5

8 Table Attrbutes and attrbute levels n the dscrete choce tass. Attrbute Levels of the attrbute Number of avoded fataltes per year Duraton of protecton n years Type of road hazard snow avalanches rocfalls car accdents 4 elatve costs of the program as percentage of the last tax payment % % % Attrbute descrbes the beneft of the traffc safety programs n terms of averted fataltes. Based on the expert ntervews we assumed that the number of fataltes caused by natural hazards on Alpne roads would ncrease to 0 fataltes per year f current mtgaton measures were no longer mantaned but could be ept at the current level f these measures were mantaned nto the future. Levels of the rs reducton were thus selected at 0 4 and 6 averted fataltes per year. Attrbute captures the permanence of the rs reducton. We attempted to suggest realstc perods of mtgaton benefts based upon the lfe expectancy of dfferent mtgaton measures to protect roads. In the focus groups we observed that partcpants had dffcultes n calculatng the total number of averted fataltes over the proposed perod of mtgaton benefts. We therefore decded aganst presentng dfferent mtgaton perods between choce alternatves but changed the perod of mtgaton between choce sets. Attrbute apponts the type of road hazard aganst whch protecton s provded. Avalanches and rocfalls were selected as natural hazards endangerng traffc on Alpne roads whle car accdents were chosen as a reference rs to test for perceptonal factors assocated wth these natural hazards. We explaned that car accdents can be caused by blnd curves wea crash barrers or speedng of other drvers to avod emphaszng the selfcontrolled factors of drvng. Attrbute 4 names the cost of each traffc safety program by descrbng t as a onetme payment proportonal to the respondents last annual tax payment. We provded respondents wth a converson table through whch they could easly derve ther personalzed cost-sharng for each of the programs Fg.. Marred respondents who have a ont tax nvoce were ased to dvde ther last tax payment by two n order to derve ther personalzed cost for each program. 6

9 Fg. onverson tool to calculate absolute bd amounts from percentages of taxes. Two premses determned the sze of the relatve bds. Frst the aggregated bds should cover future expendtures for mantanng the protecton of cantonal and communal roads aganst avalanches and rocfalls over the next 0 years. Second the prompted bd amounts should allow for a large range of possble VSL values Albern et al To comply wth these valdty requrements we estmated the publc mtgaton expendtures for Alpne roads based on statstcal data BFS 006; PLANAT 005. Assumng that the annual mtgaton expendtures wll reman at ther current level the present value of mtgaton expendtures over the next 0 years amounts to HF mllon whch s equal to..4% of the annual tax payments n Swtzerland BFS 007b. onsequently the relatve bd szes were selected as % % and % of the last tax payment. Tang the average annual per capta tax payment of HF 5400 BFS 007b the relatve bds would mean a onetme payment of HF 54 5 HF and HF Usng the basc VSL model outlned n Secton and assumng dscount rates for mortalty rss between 0 5% Vscus and Aldy 00 the absolute bds for the average taxpayer mply VSL values n the range of HF mllon mllon; the absolute bds for the hghest tax class mply VSL values n the range of HF mllon mllon; and the absolute bds for the lowest tax class mply VSL values n the range of HF 0.. mllon 0..7 mllon. Ths range s n-lne wth values found n two meta-analyses of VSL estmates Mroze and Taylor 00; Vscus and Aldy 00. For dervng these present values we used a dscount rate of.5% based on the nflaton-adusted ten-year spot nterest rate on Swss onfederaton bonds. 4 At the tme of the data collecton one Swss franc corresponded to 0.65 Euro. 7

10 . Survey structure To collect the data we developed a mal survey consstng of fve parts. The frst part opened wth some atttudnal questons about the percepton of natural hazards n general and ther perceved threat to roads n partcular. In the second part respondents had to balance nfrequent and severe avalanche accdents aganst frequent but less severe avalanche accdents. The thrd part contaned the actual choce tas whch prompted respondents to consder the hypothetcal prvatzaton of mantanng current mtgaton measures aganst rocfall snow avalanche and car accdents on cantonal and communal roads n the Swss Alps. We ntroduced the choce tas by statng that today only three ndvduals de each year n rocfall and avalanche accdents on roads but that ths number would qucly rse to 0 fataltes per year f mtgaton measures would no longer be mantaned. espondents were presented wth the league table of annual mortalty causes depcted n Fg. to understand the mortalty rss nvolved wth avalanche rocfall and ordnary car accdents and to algn these rss wth other causes of death. 5 espondents were then ased to magne a natonal referendum for fnancng a traffc safety program. They were told that every household would have to mae such a onetme payment on condton that the referendum was passed. The alternatve traffc safety programs were presented wthn sx choce sets. For each choce set respondents had to ndcate whch of three optons they prefer: program A program B or nether program. The last opton was a condtonal status quo whose choce mpled the wllngness to accept a rse n fataltes from currently three to 0 per year. Snce we selected three attrbutes wth three levels and one attrbute wth four levels for descrbng the programs 08 = 4 dfferent traffc safety programs were possble. onsequently a full factoral desgn would have resulted n 944 dfferent choce sets. emember that we dd not vary the tme attrbute across alternatves n a specfc choce set. We used a shfted orthogonal expermental desgn bult from conventonal fractonal factorals for lnear models Louvere et al. 000 to reduce the number of choce sets. Based on ths expermental desgn we generated 54 pars of alternatve programs segmented nto nne orthogonal blocs of sx choce sets. Accordng to Ferrn and Scarpa 007 ths expermental desgn s partcularly approprate when there s a hgh degree of uncertanty about the condtons that fnally generate the choce-based dataset. The outlned procedure resulted n nne survey versons each of whch contaned sx dfferent choce sets. To test whether dfferent framngs of the rs reducton attrbute had an 5 Ths was the rs communcaton ad most preferred by the partcpants of the focus group research. 8

11 mpact on the valuaton of the traffc safety programs we sent out two survey formats wth dfferent but logcally equvalent framngs. In ths paper we draw on the standard assumpton that choce experments are context-ndependent arlsson and Martnsson 008. We therefore neglect the hypotheszed framng effect n the dscusson below but wll dscuss t n a separate paper. 6 Subsequent to the choce tas the fourth part of the survey posed some debrefng questons asng respondents to ndcate how sure they were n ther choces and whether they had appled specfc decson heurstcs. The survey closed wth questons about the socoeconomc characterstcs of the respondents..4 espondents The survey was maled to 900 ndvduals who had prevously agreed n a phone recrutment to partcpate n the study. The sample was stratfed by age and gender wth the number of respondents roughly reflectng the age dstrbuton of the Swss resdental populaton. Half of the respondents were recruted n the mountanous regon around Davos the mountan sample and the other half n the cty of Zurch the urban sample. We requred respondents to be at least 8 years old whch s the mnmum age for votng and for obtanng a drver s lcense n Swtzerland. Table compares the soco-economc characterstcs of our respondents to those of the Swss resdental populaton confrmng that our study sample s representatve. There s a good representaton of all age groups even though respondents older than 69 years are slghtly underrepresented. Wth regard to the last tax bll there s a under samplng of the lowest ncome group. Ths correlates wth the observaton that sample has somewhat fewer respondents who have had only prmary educaton. Overall there s a far match-up of the survey partcpants wth the census data. In the choce analyss we dscarded respondents who had answered less than three of the sx choce sets assumng that they were ether not wllng or unable to respond. Three respondents chose only program A and one respondent chose only program B even when ths choce behavor was nconsstent wth ther earler choces. These respondents were also excluded from the choce analyss. The data cleanng left us wth 57 vald choces from 4 respondents correspondng to a response rate of 48%. 6 Prelmnary results suggest that the framng effect s small and does not affect the VSL estmates. 9

12 Table omparson of the sample characterstcs to the Swss resdental populaton. Varable Study sample N =4 Swss Populaton espondents Mountan Sample Urban Sample Gender a Women Men Age a or older Annual tax payments b HF 000 or less HF HF HF HF More than HF 8000 Educatonal attanment a Prmary educaton Secondary educaton Unversty educaton Apprentceshp raftsman s dploma a Based on BFS 007b. 49.0% 5.0% 49.% 50.9% 4.6% 7.9% 7.% 4.6% 5.4% 0.% 5.0% 6.% 7.% 8.9% 4.% 8.6%.8%.% 5.% 4.8% 5.9% 5.0% 48.0% 7.0% 5.5% 9.4% 6.9% 4.% 6.9% 7% 6% 6% % % 7%.% 8.%.% 45.0% 0.% b Approxmaton of the annual tax payments of the Swss populaton based on the dstrbuton of the drect federal tax payments BFS 009. Snce there are no offcal statstcs of the number of people drvng on Alpne roads we ased respondents how often they travel on these roads. Based on ths self-declared rs exposure and offcal census data for the mountanous and urban regons of Swtzerland Hornung and öthlsberger 005 we defned the baselne populaton at rs as those mllon ndvduals who drve more than once a wee on Alpne roads. As descrbed below we used ths fgure to quantfy the annual statstcal mortalty rs reducton provded by each of the traffc safety programs. 0

13 Dscrete choce model. andom utlty framewor for condtonal logt models Dscrete choce models are founded n random utlty theory McFadden 00. Appled to mortalty rss on Alpne roads random utlty theory assumes that the unobserved utlty of a specfc traffc safety program can be splt nto a determnstc component expressed by the ndrect utlty functon V and a random component ε that captures moods affects and other emotonally drven decson shortcuts used by ndvdual to evaluate the program. learly the ndrect utlty V from choosng program s determned by the program s attrbutes and the personal characterstcs of ndvdual. Formally let X denote a vector of explanatory varables descrbng program and ndvdual and denote the correspondng vector of coeffcents to be estmated. Then the random utlty perceved by ndvdual from choosng program can be wrtten as: U = V X ; ε = V ε where ε s the random component of an unnown dstrbuton ε ~ Dθ ε wth θ ε denotng the parameters of ths dstrbuton. The dchotomy of ths random utlty model UM allows a decson framewor to be constructed by assumng that ndvdual prefers mtgaton program over the alternatve mtgaton program f the utlty entaled by ths program s larger than that of any other program n the choce set J. Formally the probablty of choosng mtgaton program over any other program n the choce set s gven by: Pr X ; = Pr[ V ε > V ε ]. θ ε Based on dstrbutonal assumptons on the random component several specfcatons of the UM model have been proposed Waler and Ben-Ava 00. The wdely used condtonal logt specfcaton assumes that the random component s ndependently and dentcally IID drawn from a Type-I extreme value dstrbuton.e. ε ~ EVθ ε. The probablty that ndvdual chooses the specfc program s: Pr X ; µ = µ V X ; ] µ V X ; ] J

14 where µ s a scale parameter usually normalzed to one mplyng constant error varance Louvere et al The estmaton of the coeffcent vector nvolves maxmzng the lelhood of the stated choces. When N respondents are ased to engage n a seres of Q choce tass wth J choce alternatves the maxmzaton requres defnng a bnary choce ndcator λ q. Ths bnary ndcator taes the value λ q = f ndvdual chooses the program n choce tas q and otherwse taes the value λ q = 0. Accordngly the log-lelhood functon LL to be maxmzed over all stated choces becomes: LL N J Q λ ; θε = λq ln[pr X; θε = = q= X ]. 4. Estmatng the VSL from dscrete choce data Estmatng the VSL from dscrete choces on alternatve traffc safety programs requres specfyng the ndrect utlty functon gven n Eq.. In our study the ndrect utlty of any traffc safety program depends on ts rs reducton and on ts cost whch vares for each ndvdual due to the use of the relatve bd vehcle. haracterstcs of the traffc safety program denoted by the vector W and of the respondent denoted by the vector Z may also go nto the ndrect utlty functon. Snce these covarates do not vary over the repeated choces of an ndvdual ther vectors have to be nteracted wth ether the rs or the cost parameter. A generc form of the ndrect utlty functon V ; s then obtaned as: X V = Z W Z W 5 where and are the coeffcents of the rs and cost parameter and and are coeffcent vectors of the nteracton effects between these parameters and selected covarates. The partcular desgn of our choce tas requres some addtonal specfcatons. Whle the cost of each program was mplemented as a onetme payment to respondent the rs reducton was mplemented as a stream of annual rs reductons provded by program over the perod of mtgaton T. We used a constant exponental dscountng model to dscount the stream of rs reducton defnng the dscounted rs reducton as: T exp δ T = π exp δ t d t = π 0 δ 6

15 where δ s the mplct dscount rate and π denotes the annual rs reducton by program whch s assumed to be constant over the perod of mtgaton. 7 By nsertng Eq. 6 nto the ndrect utlty functon of Eq. 5 we may estmate the dscount rate δ drectly from the choce data. Techncally ths maes our model a non-lnear condtonal logt model. In lne wth Albern et al. 007 we then post that the margnal utlty of rs reducton for respondent s gven by the compound coeffcent vector = Z W and the margnal utlty of wealth s gven by the compound coeffcent vector = Z W. Snce the VSL s defned as the WTP for a margnal decrease n rs t results from the rato of the estmated coeffcent vectors: ˆ / ˆ = V/ / V/. 4 esults 4. Qualtatve results The respondents had relatvely homogenous atttudes toward natural hazards n general and to ther perceved threat to Alpne roads n partcular. When ased about how they assess ther own rs of beng lled through a snow avalanche or a rocfall 69% of the respondents felt barely endangered 7% felt somewhat endangered and only % felt strongly endangered; another % found t hard to tell. When comparng the rs of snow avalanches or rocfalls to roads wth common road hazards 84% of the respondents stated that they found the latter rs more threatenng % found both rss equally threatenng and only % found the rs of natural hazards more threatenng; agan % found t hard to tell. Wth regard to the current level of protecton aganst snow avalanches and rocfalls 67% of the respondents stated that roads are suffcently protected whle % would le to see better protecton. Aganst our expectatons answers to these perceptonal questons by the mountan and the urban samples were not statstcally dfferent. In Table we examne the choce frequences for traffc safety programs aganst the dfferent hazard types. Nether program was chosen n about 0% of the choce sets suggestng that respondents were not reectng the programs wthout due consderaton. The choce frequency of programs aganst rocfall accdents was slghtly hgher than for programs that protect aganst car accdents or avalanche accdents. 7 Snce the number of people at rs on Alpne roads was determned at mllon people the annual rs reducton π provded by a traffc safety program les between and avoded fataltes.

16 Table Pattern of preferences for traffc safety programs aganst dfferent road hazards. Preferred traffc safety program Percentage of choces aganst snow avalanches 4.8% aganst rocfalls 8.0% aganst car accdents 6.% nether 0.9% 4. The basc VSL model In the next sectons we report on selected results of the non-lnear condtonal logt model as outlned n Secton.. We begn by presentng two estmates of the basc VSL model Model I whose ndrect utlty functon ncludes only the personalzed cost and the dscounted rs reducton as explanatory varables see Table 4. The two estmates of Model I dffer only n the number of choce observatons. Whle the frst estmate ncludes the full sample of observatons the second s restrcted to the observatons of those respondents who also answered the atttudnal questons necessary to estmate the nteracton models presented below see Models III IV. The dfferences between the estmated coeffcents are relatvely small ndcatng that our basc model s relatvely robust aganst restrctons n the sample sze. All coeffcents are sgnfcant and have the expected sgns. The coeffcent of the rs parameter s postve ndcatng that the respondents valued rs reductons as benefts whle the coeffcent of the cost parameter s negatve showng that spendng prvate money on traffc safety programs entals a dsutlty. The dscount rate δ was estmated at.8% and.% respectvely whch s at the upper range of dscount rates reported n maret-based VSL studes Vscus and Aldy 00. The coeffcent estmates n Table 4 mply a VSL of HF 8.6 mllon 5.5 mllon for the full sample and of HF 7.64 mllon 4.95 mllon for the restrcted sample. 8 The correspondng WTP for the average traffc safety program s between HF Standard errors around the VSL estmates were calculated at HF.4 mllon 0.9 mllon for the full sample and at HF. mllon 0.85 mllon for the restrcted sample usng the Delta method see Greene 008: Techncally the VSL s estmated as ˆ / ˆ ] mllon. The multplcaton by one mllon s necessary [ snce we coded the rs reducton as and 8 nstead of and The ndvdual mean WTP for the average traffc safety program s calculated by multplyng the VSL value by the mean rs reducton provded by the programs whch s equal to

17 Table 4 Model I: Basc condtonal logt model full and the restrcted sample. Parameters Full Sample estrcted Sample oeffcent a t-stat oeffcent a t-stat Margnal utlty of rs reducton Margnal utlty of cost Dscount rate δ Number of observatons Q Number of respondents N 4 40 Log-lelhood functon LL Lelhood rato ndex b a Standard errors n parentheses; b alculated as LL /LL 0 where LL 0 denotes the log-lelhood functon of the constant-only model. 4. The effect of wealth on the VSL The use of the relatve bd vehcle allows exploraton of how the VSL vares wth wealth. Economc theory suggests that the VSL margnally ncreases wth ncreasng wealth. 0 Hammtt and Trech 007 provde two reasons for ths wealth effect. Frst wealther people lose more n absolute terms when they de. Second ther utlty cost of spendng s smaller due to the standard assumpton of decreasng margnal utlty wth respect to wealth. To test for ths wealth effect Model II ncludes an nteracton between the personalzed cost of the program and the logarthm of the last tax bll τ.e. V = τ lnτ 0 To prove ths asserton we draw on the defnton of the VSL as the margnal rate of substtuton between wealth and mortalty rs. The standard model of WTP for changes n mortalty rs defnes the VSL as u w v w p u w pv w Hammtt 000: VSL dw = where p s the ndvdual s probablty of dyng durng a defned ' ' dp perod and uw and vw denote the utltes derved from wealth condtonal on survvng or dyng n that perod. The prmes ndcate frst dervatves wth respect to wealth. Some assumptons are commonly made on the form of the utlty functons: survval s preferred to death: uw > vw; the margnal utlty of wealth s non-negatve and greater n lfe than n death: u'w > v'w 0; and ndvduals are rs averse wth respect to wealth: u"w 0 v"w 0. Under these assumptons the frst dervatve of the VSL wth respect to wealth s always postve VSL/ w > 0 and the second dervatve s always non-negatve VSL/ w 0. 5

18 whereby lnτ serves as a measure of the utlty of wealth. The nteracton term captures the dfference between how much wealther people and poorer people are wllng to pay relatve to ther wealth status. Table 5 presents the estmatons of ths model usng both the full and the restrcted sample of observatons. Table 5 Model II: ondtonal logt model wth tax nteracton full and restrcted sample. Parameters Full Sample estrcted Sample oeffcent a t-stat oeffcent a t-stat Margnal utlty of rs reducton Margnal utlty of cost Interacton wth the cost parameter: log of last tax payment τ Dscount rate δ Number of observatons Q Number of respondents N 4 40 Log-lelhood functon LL Lelhood rato ndex b a Standard errors n parentheses; b alculated as LL /LL 0 where LL 0 denotes the log-lelhood functon of the constant-only model. In lne wth theoretcal expectatons we fnd that the VSL margnally ncreases wth wealth.e. VSL/ τ > 0. In other words wealther respondents are wllng to pay proportonally more on the traffc safety programs than poorer respondents. Fg. depcts the effect of the last tax bll on the sze of the VSL estmates ndcatng that at low wealth levels the VSL s relatvely nelastc toward changes n wealth the elastcty of the VSL toward changes from HF 000 to HF 4000 n tax payments s 0.5 but becomes ncreasngly elastc at hgher wealth levels the elastcty of the VSL toward changes from HF 6000 beyond HF 8000 n tax payments s.87. The arc elastcty of the VSL over the range of tax amounts s determned at.0 but shrns to 0.84 when weghted by the class-frequency We tested other functonal forms of the utlty of wealth but these functons dd ether provde much lower log-lelhood functons or dd not converge. onsequently we used the log form and estmated the tax-specfc VSLτ V / / V / = [ / τ lnτ ]. For computatonal ease we coded the tax payment τ as and 8. 6

19 of the taxpayers n the sample. It should however be warned that the estmaton of VSL values of the second hghest tax class was based on a lmted number of respondents N = 8. Fg. Tax class-specfc VSL values estmated based on Model II. The above reported elastcty cannot be drectly converted to ncome elastctes because the Swss tax law permts tax deductons whch depend on the home canton and ndvdual characterstcs that are not necessarly related to ncome and wealth. However snce Swtzerland has a progressve tax regme the correspondng ncome elastctes of the maorty of respondents are larger than unty. Ths s nlne wth assertons by McFadden and Leonard 99 and Schläpfer 008 that ncome elastctes of WTP less than unty consttute grounds for doubtng the valdty of stated-preference studes. 4.4 The effect of personal characterstcs on the VSL Personal characterstcs other than wealth also affect the WTP for traffc safety on Alpne roads. Table 6 presents two nteracton models estmated wth the restrcted sample whch ndvduate the margnal utltes of rs reducton and wealth as urged by Sunsten 004. In ths way t becomes possble to dentfy sources of heterogenety n preferences for mortalty rs reductons. Model III nteracts the rs parameter wth the personal soco-economc characterstcs and the cost parameter wth the last tax payment of the respondent so that the VSL becomes condtonal on the respondent s bacground. 7

20 Table 6 Models III IV: ondtonal logt model wth personalzed margnal utlty of rs reducton and cost. Parameters Model III Model IV oeffcent a t-stat oeffcent a t-stat Margnal utlty of rs reducton Interactons wth the rs parameter: Age Gender female = Unversty degree yes = Sample afflaton urban sample = Sample afflaton unversty degree urban academcs = Experence wth natural hazards prevous experence = Avalanche accdent yes = ocfall accdent yes = Margnal utlty of cost Interactons wth the cost parameter: Log of last tax payment Perceved safety on roads current protecton s nsuffcent = Dscount rate δ Number of observatons Q Number of respondents N Log-lelhood functon LL Lelhood rato ndex b a Standard errors n parentheses; b alculated as LL /LL 0 where LL 0 denotes the log-lelhood functon of the constant-only model. 8

21 The sgnfcant coeffcent of the nteracton term between a sample ndcator dummy mountan sample = 0; urban sample = and the rs parameter ndcates that ceters parbus respondents from the urban sample had a 0% hgher margnal utlty of rs reducton see Table 6. Whle surprsng at frst glance we offer two possble explanatons for ths result. Frst people who are more famlar wth natural hazards mght have a hgher rs acceptance as they see these rss as part of lvng n the mountans. orrespondng statements made by focus group partcpants from the mountanous regon support ths explanaton. Second respondents from the urban sample have altrustc motves that ncrease ther margnal utlty of rs reducton odrguez and Leon 004 although ther personal beneft from traffc safety on Alpne roads s smaller than that of respondents from the mountan sample. Ths explanaton s supported by answers made by respondents from the urban sample to the debrefng questons at the end of the survey. To further explore the frst explanaton we ncluded two nteracton terms: a two-way nteracton between the rs parameter and a dummy ndcatng whether the respondent holds a unversty degree and a three-way nteracton between ths unversty dummy the rs parameter and the sample ndcator dummy. Ths revealed that respondents wth an academc bacground generally had a hgher margnal utlty of rs reducton and that ths preference was partcularly strong for academcs from the mountan sample. Accordngly non-academcs from the mountan sample placed a much lower value on rs reducton than the rest of the respondents. The debrefng questons revealed that non-academcs from the mountan sample feel enttled to the benefts of mtgaton and are not wllng to prvately contrbute to ts fnancng. The nteracton term between the age of the respondent and the rs parameter ndcates a decrease n the margnal utlty of rs reductons by approxmately 0.9% per lfe year. Ths s n lne wth emprcal observatons that the VSL decreases wth age Vscus and Aldy 00. Albern et al. 004 propose two explanatons for ths age effect that could affect the valuaton of reduced mortalty rs the ndvdual rs exposure and the utlty of wealth. As rs exposure on Alpne roads presumably declnes wth ncreasng age older people tend to travel less we tested a three-way nteracton between rs self-reported exposure and age. Ths nteracton term had a neglgbly small effect on the age coeffcent suggestng that the age effect s not caused by correlatons between exposure and age but by decreasng utlty of wealth. The nteracton term between the gender of the respondent and the rs parameter was barely sgnfcant at the 5% level and further testng by means of a bootstrap re-estmaton wth 00 random resamplngs resulted n a non-sgnfcant coeffcent. Ths corresponds wth observatons by Davdson and Freudenburg 996 who found that women and men have 9

22 smlar perceptons of most envronmental rss. Snce n both samples men were more lely to hold a unversty degree than women we tested for a three-way nteracton effect between the gender the rs parameter and the unversty dummy whch also turned out to be nsgnfcant. Thus gender had no sgnfcant mpact on the valuaton tass n ths study. The nteracton term between the tax payment and the cost parameter resulted n qualtatvely smlar results to those n Model II. We addtonally tested a three-way nteracton between the cost parameter the last tax payment and the sample ndcator dummy whch reected the hypothess that the two samples dffered wth regard to wealth n a manner that nfluenced the valuaton of the costs. 4.5 The effects of perceptonal factors on the VSL Model IV extends Model III by ncludng further nteracton terms between the rs parameter and the road hazard type between the rs parameter and perceptonal factors of rs and between the cost parameter and the respondent s apprasal of the current level of safety on Alpne roads. To ths end car accdents were coded as the reference rs.e. negatve postve coeffcents of the avalanche and rocfall dummes n 6 mply a decrease ncrease n the perceved rs compared to car accdents. The coeffcent of the nteracton term between the rs parameter and the rocfall dummy was not sgnfcant ndcatng that the perceved rs from car accdents and rocfall accdents does not dffer n a way that affects the demand for rs reducton. In comparson the nteracton term between the rs parameter and the avalanche dummy was sgnfcant and had a negatve sgn suggestng that avalanche accdents were perceved as less worthy to be mtgated. One possble explanaton for ths dfferent percepton of the three road hazard types s that avalanche accdents are relatvely rare whereas car accdents and rocfall accdents frequently occur although they do not always cause fataltes. We tested an addtonal nteracton effect between the rs parameter the hazard type and the sample ndcator dummy. Ths three-way nteracton was not sgnfcant ndcatng that the percepton of the road hazard type was not systematcally dfferent between the sample groups. The nteracton term between self-reported experence and the rs parameter showed that respondents who stated that they or ther relatves had pror experences wth natural hazards valued the margnal utlty of rs reductons less than respondents who had no pror experences. The same effect was found for the self-declared exposure but we omtted ths varable n the presented models due to ts strong correlaton wth the sample afflaton of the respondent whch would have nduced problems of heteroscedastcty Greene 008. In lne wth observatons from psychometrc rs research see Slovc et al. 000 we conclude that 0

23 respondents who had more nowledge about natural hazards perceved the rss on Alpne roads as less threatenng than those who had no pror experences. As expected the nteracton term between the cost parameter and the atttude toward the current protecton on Alpne roads was sgnfcant. espondents who stated that the current level of safety aganst natural hazards on Alpne roads was nsuffcent were wllng to spend 4% more on the traffc safety programs than those who felt that current safety was suffcent. The coeffcents of the other nteracton effects n Model IV were of comparable sze to those estmated n Model III see 6. A lelhood rato test LT showed that the ncluson of the addtonal nteracton terms between the rs parameter and the hazard type and between the cost parameter and the atttude toward current safety dd sgnfcantly mprove the model LT: χ 9 = 6.50; P < By applyng the estmated coeffcents to the actual choce observatons of the respondents one can generate dstrbutons of the VSL values mpled wth these choces Fg. 4. These dstrbutons llustrate that dependng on the ndvdual characterstcs the margnal rate of substtuton between rs reducton and money vares wthn a broad range. The 95% percentle was HF 6.4 mllon 0.7 mllon for the dstrbuton based on Model III and HF 9. mllon.5 mllon for the dstrbuton based on Model IV. The mean values of these VSL dstrbutons Model III: HF 5.7 mllon; Model IV: HF 8. mllon were substantally above the medan values Model III: HF 4. mllon; Model IV: HF 4. mllon suggestng that wealthy taxpayers contrbute overproportonally to the VSL pont estmate of Model I. Fg. 4 Dstrbutons of the personalzed VSL estmated based on Model III Panel A and Model IV Panel B. The dstrbuton mean VSL values are HF 5.74 mllon Model III and HF 8.4 mllon Model IV the 95% percentles are HF 6.7 mllon Model III and HF 9. Model IV.

24 4.6 Scope and senstvty tests The valdty of stated-preference studes s often challenged by opponents who argue that beng of hypothetcal nature the stated choces fal to be related to real transactons as observed n marets. It has therefore become standard to test the scope and senstvty of the results obtaned from stated-preference studes Heberlen et al. 005; Leter and Prucner 009. The basc requrement n every scope test of VSL estmates s that respondents receve a postve margnal utlty from rs reductons and a negatve margnal utlty of costs.e. they are wllng to pay for rs reductons but not at any prce. The results of Models I IV conform to these requrements. To control for the relablty of our orgnal estmates we cross-valdated these results usng re-estmatons wth the bootstrap method Efron and Tbshran 99. These reestmatons reled on 00 replcatons of random resamplngs wth replacement from the sample of observatons where each of these replcatons conssted of Q = 88 draws. The bootstrap estmatons yelded robust standard errors around the bootstrap coeffcents whch allowed computng 95% confdence ntervals by multplyng the bootstrap standard errors of the coeffcent estmates by.96. We then re-estmated the models by droppng all observatons from those respondents who stated n the debrefng questons that they felt partcularly uncertan about ther choces and from the frst and last choce set of every respondent. Nether of these reestmatons altered the broad pcture of the model results. The coeffcent estmates of these restrcted models were all wthn ther correspondng 95% confdence ntervals though some of the nteracton effects devated substantally from the orgnal model estmates. Table 7 exemplfes ths valdty chec for the re-estmatons of Model IV ndcatng that our orgnal coeffcent estmates are robust aganst confoundng nfluences of hdden varables. The valdty of stated-preference studes s not only determned by scope senstvty but also by the robustness of the valuaton measures toward changes n specfc attrbute levels. We therefore analyzed the effects of margnal changes n the rs and cost parameters of the traffc safety programs. Frst consder a margnal ncrease n the cost of the traffc safety program. We were nterested n how much ths ncrease would decrease the probablty Pr that ndvdual had chosen ths program.

25 Table 7 omparson of the coeffcent estmates of the re-estmated Model IV wth the 95% confdence ntervals obtaned from bootstrap standard errors. Parameters 95% confdence nterval estrcted model coeffcents lower lmt upper lmt oeffcent a oeffcent b Margnal utlty of rs reducton Interactons wth the rs parameter: age gender female = unversty degree yes = sample afflaton urban sample = sample afflaton unversty degree urban academcs = experence wth natural hazards prevous experence = avalanche accdent yes = rocfall accdent yes = Margnal utlty of cost Interactons wth the cost parameter: log of last tax payment perceved safety on roads current protecton s nsuffcent = Dscount rate δ a Sample restrcton by droppng observatons of uncertan respondents. b Sample restrcton by droppng observatons of the frst and of the last choce set for each respondent. By tang the partal dervatve of the choce probablty as defned n Eq. wth respect to the cost parameter the margnal effect becomes the detaled dervaton s gven n the Appendx: Pr M = = W Z Pr Pr = Pr Pr 7 where = Z W denotes the compound coeffcent vector of the cost nteractons. Smlarly the margnal effect of a change n the dscounted rs reducton on the choce probablty of program s gven by the detaled dervaton s gven n the Appendx:

26 Pr M = = W Z Pr Pr = Pr Pr 8 where = Z W denotes the compound coeffcent vector of the rs reducton nteractons. Snce the margnal effects dffer across ndvduals and choce sets we calculated the weghted margnal mean effects over all choce observatons Q usng the weghtng procedure outlned by Louvere et al. 000 to adust for outlyng estmates of choce probabltes that could otherwse lead to overestmatons of margnal effects. Table 8 gves the weghted mean margnal effects of changes n the rs and cost parameter for Models III IV. These mean margnal effects show that a unt change ether n the dscounted rs reducton or n the cost of a program has an nsgnfcantly small mpact on the choce probablty of a traffc safety program. Table 8 Margnal effects and pont elastctes of changes on the choce probablty of traffc safety programs. Varable Model III Model IV Margnal mean effect of change n cost Pont elastcty of cost Margnal mean effect of change n rs reducton Pont elastcty of rs reducton Based on the margnal effects t s straghtforward to derve the weghted pont elastctes of changes n rs reducton and n costs as E = M Pr and E = M Pr respectvely Greene 008. These pont elastctes measure the percentage change n the choce probablty of a partcular program wth respect to a % change n ether the rs reducton or the cost parameter of ths partcular program. For the most extensve Models III IV the choce probablty was found to be relatvely nelastc < E < 0 0 < E < ; see Table 8 suggestng that the VSL estmatons based on our non-lnear condtonal choce model are robust aganst small changes n the ey attrbutes of the traffc safety programs. Louvere et al. 000 defne the weghted margnal effect of changes n the attrbute X for all observatons Q Q Q q q ] as: M X = [M = q X Pr q = Pr q where q denotes one choce observaton M q X s the margnal effect of a change n X n ths partcular observaton and Prq denotes the choce probablty of every sngle choce observaton q. 4