Modelling the Choice and Timing of Acquiring a Driver s License: Revelations from a Hazard Model Applied to Post-secondary Students in Toronto

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1 Modellng the Choce and Tmng of Acqurng a Drver s Lcense: Revelatons from a Hazard Model Appled to Post-secondary Students n Toronto Khandker Nurul Habb, Ph.D., Peng Assocate Professor, Cvl Engneerng Unversty of Toronto khandker.nurulhabb@utoronto.ca Ctaton Habb, K.M.N Modellng the Choce and Tmng of Acqurng a Drver s Lcense: Revelatons from a Hazard Model Appled to Post-secondary Students n Toronto. Workng Paper, 43 Department of Cvl Engneerng, Unversty of Toronto 1

2 Abstract The declnng rate of acqurng drvers lcenses by young adults n developed countres has elcted concern among transportaton researchers because of the potental consequences for future urban transportaton systems. Usng a dataset collected through a large-scale survey of the students of four major unverstes n Toronto the paper employs the econometrc technque to quantfy the effects of personal/household attrbutes, land use characterstcs and publc transt accessblty ndcators on the choce and tmng of acqurng drvers lcenses by post-secondary students n Toronto. Lvng condtons of post-secondary students n the form of lvng wth parents/famly show the hghest nfluence n dscouragng and even delayng n acqurng drvers lcenses. However, the emprcal model also dentfes that better transt accessblty plays the second most crtcal role n delayng or even dscouragng the choce of acqurng a drver s lcense. Publc transt pass ownershp s proven to be an mportant moblty tool that dscourages as well as delays the acqurng of drvers lcenses by young adults. Post-secondary students lvng n densely populated neghborhoods are more lkely to delay or to not acqure a drver s lcense. Young adults who delay acqurng ther drver s lcense may reman transtusers durng ther tme as students and may also contnue to have smlar publc transt use n future. The results of ths nvestgaton suggest that ncreasng nvestment n publc transt wll have an mmedate effect n managng traffc congeston, but wll also help reduce prvate car dependency n future. Keywords: drver s lcense use, young adults, transt accessblty, hazard model, land use, transportaton

3 1. Introducton and Background The enthusasm for and the urgency felt for acqurng a drver s lcense by young adults started to decrease n developed countres n the early 1990s (Noble 005; Svak and Schoettle 01a, 01b). Canada, lke other developed countres, s also experencng a gradual and consstent declne n the rate of drver s lcense acquston by young adults between the ages of 15 to 35 (Svak and Schoettle 011). Varous stakeholders are concerned about the prospect of the next generaton of workers becomng actve n economc and socal sectors wth a smaller percentage holdng drver s lcenses compared to current or prevous generatons. Ths s also a concern to automoble manufacturers as t sgnals possble mpendng negatve economc consequences or at least a shft n the economc landscape n developng natons. However, for transportaton planners and publc health offcals, there s optmsm that a declne n the relance on prvate automoble means an ncrease n publc transt rdershp as well as an ncrease n walkng and bcyclng for transportaton (Kenworthy and Newman 011; Metz 013). Varous factors have been posted as beng responsble for the declne n acqurng a drver s lcenses by young adults n developed countres. Among the most dscussed factors are the ncreasng: the cost of car ownershp; traffc congeston that makes prvate car ownershp a less attractve opton than prevously; nvestment n publc transport and actve transportaton nfrastructures; and technologcal nnovatons that elmnate the need for physcal travel for many actvtes, etc. It s also wdely speculated that wth the contnuous creaton of new electronc gadgets and the multtude of onlne actvtes, car ownershp may no longer be perceved as an ndcator of freedom, wealth or success by the current generaton of young people compared to that of prevous generatons (Maynard 014). In addton, changng patterns of lvng arrangements of young people n many developed countres, especally n terms of delayng leavng home and/or lvng wth parents durng student lfe may be a factor (Cobb-Clark 008). Emprcal nvestgatons regardng factors nfluencng young adults decreasng nterest n acqurng a drver s lcense are needed. Vne et al. (014), for example, conducted an emprcal nvestgaton of the relatonshp between onlne actvtes and the probablty of acqurng drvers lcenses by young adults. Ther study showed that onlne actvtes ncrease the rate of acqurng drvers lcenses. Addtonal study on ths ssue wll enrch our understandngs further. From the perspectve of transportaton plannng the decrease n the declnng rate of lcense acquston by young adults s mportant as they are the next generaton of workers and wll, therefore, have a long-term nfluence on the needs and performance of future urban transportaton systems. Among young adults, post-secondary students requre partcular attenton for two reasons. Frst, ths group wll lkely become leaders n the fnancal and technologcal sectors and wll have a strong nfluence on many aspects of socety (Zhou 01). Second, postsecondary students are a sub-group of the general populaton that are often under-represented n household travel surveys used n regonal transportaton plannng and polcy nvestgatons (Lavery et al. 013). For example, post-secondary students represent more than 5 percent of the total populaton of the Greater Toronto Area (GTA) and the Hamlton area. A large-scale (5 percent sample) household travel survey of ths regon, conducted by the Transportaton Tomorrow Survey (011), captured percent of the sample share that belongs to post-secondary students. 3

4 Ths paper contrbutes to the growng lterature of emprcal nvestgatons on factors affectng the choce and tmng of acqurng a drver s lcense by young adults. It uses a dataset collected jontly by the four unverstes n Toronto n 015. The Ontaro College of Art and Desgn (OCAD) Unversty, Ryerson Unversty, the Unversty of Toronto and York Unversty formed a team n 015 to conduct a travel behavour survey of 184,000 students. Its purpose was to obtan a better understandng of ther travel behavour by presentng a more accurate representaton of ther n regonal travel n the GTA. In addton to presentng an emprcal nvestgaton, the paper also employs an advanced econometrc model to nvestgate the factors that have a sgnfcant effect on the choce and tmng of acqurng a drver s lcense by postsecondary students. Results of the study provde a clear understandng of ths group s travelrelated behavour and thus have robust polcy relevance. The remander of the paper s organzed as follows. The second secton offers a bref revew of the lterature on emprcal nvestgatons of drver s lcense acquston by young adults. The thrd secton presents an overvew of the dataset avalable for the current nvestgaton. The fourth secton contans the econometrc formulaton of the model used for emprcal nvestgaton. The ffth secton dscusses the emprcal nvestgaton. The paper concludes wth key fndngs and recommendatons for further research.. Lterature Revew The body of lterature nvestgatng the reasons for the declnng rate of drver s lcense acquston by young adults and factors that nfluence the choce and/or tmng of that acquston s lmted, but growng. In one of the earlest nvestgatons of ths ssue, Ruud and Nordbakke (005) consdered the delay n acqurng lcenses by young people as an opportunty for publc transportaton to play the role of a moblty tool and to nfluence ther future travel behavour. They dentfed that lvng wth parents and nnovatons n telecommuncaton technologes could deter young peoples nterest n drvng a car as somethng beyond just a means of travel or a moblty tool. Noble (005) nvestgated varous factor for the low acquston rates among young people n the Unted Kngdom (UK) and found that a lack of affordablty of both ownng and mantanng cars was the man reason. The study also found that the ncreasng cost of tranng for acqurng a lcense mght affect the choce of not acqurng a drver s lcense. As well, they found that there was no evdence of envronmental concern that mght nfluence the choces of not acqurng a lcense. McDonald and Trowbrdge (009) nvestgated the effects of land use characterstcs of home locatons on the choce of acqurng a drver s lcense by youth aged 16 to 19. They used a 001 Amercan Natonal Household Travel survey data to evaluate the mpacts of populaton densty on the probablty of acqurng lcenses by youth. They found that youths from densely populated neghborhoods are more lkely to delay ther acqurng of drver s lcenses n the Unted States (US). Wllams (011) nvestgated the reasons for delayng acqurng drver s lcenses n the US wth the objectve of suggestng better-lcensng polces for young people. Ths study used a sample 4

5 survey of young people between 15 to 18 years of age. It dentfed several reasons for delayng or not obtanng a lcense. These reasons ncluded: the lack of a car n the household; the cost of ownng/mantan cars; lvng wth famly/parents and thereby havng support for transportaton; avalablty of other modes of transportaton as an alternatve to drvng; and tme constrants n learnng to get a drver s lcense. Delbosc and Curre (013a; 013b; 013s), n a seres of studes, nvestgated the trends, reasons and nfluental factors for delays n acqurng lcenses by young people n developed countres. Based on a survey of 00 young adults aged 17 to 5 n Melbourne (Australa) they found the percepton of a car as an ndcator of ndependence and prosperty had been declnng. Young people were found to be more dverse n ther travel mode choces than focussng solely on a prvate car as the only desrable transportaton opton. All of these factors suggest that provdng better alternatves to drvng for transportaton would further encourage a declne n obtanng a drver s lcense by young people (Delbosc and Curre 013a). Through a synthess of relevant studes and exploratory data analyss, Delbosc and Curre (013b) dentfed several factors that nfluence the decrease n acqurng a drver s lcense by young people. These factors nclude: lvng stuaton (lvng wth parents); delay n formng famly; ncreasng costs of mantanng a prvate car along wth a decrease n ncome; economc recesson; ncreased range of publc transportaton servces; envronmental conscousness thereby percevng a prvate car as not beng envronmentally frendly; not consderng a prvate car as a status symbol; better electronc communcaton, etc. Addtonally, they presented a synthess of varous studes that hghlghted these reasons. Delbosc and Curre (013c) further examned the trend toward a declne n acqurng drvng lcenses by young people n developed countres and noted prevous studes may have establshed only a prelmnary understandng of these reasons and causes despte havng dentfed a seres of factors/varables dentfed. Ther research acknowledged that t would be dffcult to ascertan quanttatve effects of those factors/varables wthout further comprehensve nvestgaton. Recently, Delbosc and Curre (014) presented an emprcal nvestgaton on the relatonshp between young adults acqurng of drvng lcense and demographcs/lvng arrangement related varables n Melbourne. They used four repeated cross-sectonal household travel survey datasets to nvestgate the choce of acqurng drvng lcenses by the young adults (aged 18 to 30 years who may or may not be a post-secondary student) n Melbourne. The four datasets were pooled to develop one bnary logt model wth a year-specfc dummy varable. The model does not seem to have alternatve year-specfc constants and scale parameters to separate any effects of unobserved year-specfc factors. The emprcal model only ncluded personal and household related varables and found that the opportunty for hgher educaton lowered the probablty of acqurng a drver s lcense by young adults. They also found that lvng wth parents postvely nfluenced the probablty of acqurng a lcense. However, they concluded that ths fndng was not nconclusve and would requre further emprcal nvestgaton. Teff et al. (014) nvestgated the prevalence and tmng of acqurng lcenses by youth aged 18 to 0 years n the US through an onlne survey. They used a logstc regresson model for nvestgatng the factors nfluencng the choce and tmng of acqurng a lcense of the surveyed ndvduals. They found that economc reasons (low ncome and not havng access to a car) were 5

6 the most domnant factors n nfluencng the choce and tmng of acqurng a lcense. However, the avalablty of alternatve modal optons for transportaton was also found to be a hghly nfluental factor. Vne et al. (014) used multvarate logstc regresson to nvestgate the assocaton between young adults onlne actvtes and the declnng rate of acqurng a drver s lcense. The study s result was nconclusve. It used two robust datasets and wde varetes of soco-economc and land use varables to hghlght the relatonshp between onlne actvty and the choce of havng a drver s lcense. Contrary to populaton speculaton, they found that the relatonshp between the ntensty of onlne actvtes and havng a drver s lcense may not have a lnear and straghtforward relatonshp. They found that when young adults were actve n pursung onlne actvtes they were more lkely to acqure a lcense. They recommended further emprcal nvestgatons on soco-economc and other factors that mght nfluence young adults acquston of a lcense. The revew of the lterature ndcates that there s a need for a better understandng of the reasons and factors nfluencng the choce and tmng of acqurng drver s lcenses by young people. The ssue of the declnng rate of the acquston of lcenses by young adults has been dentfed as an emergng trend that has been emprcally nvestgated n the lterature only n last 5 years. Vne et al. (014) dentfed that only fve studes, ncludng ther own, avalable n transportaton lterature that study ths ssue through emprcal nvestgaton. Ths paper contrbutes to the lterature by presentng a comprehensve econometrc nvestgaton to jontly nvestgate the choce and tmng of acqurng drver s lcenses by post-secondary students. 3. Data for Emprcal Investgaton The emprcal model uses data from a student travel survey organzed jontly by four unverstes located n the GTA representng over 184,000 post-secondary students n the regon. The unverstes nvolved are OCAD Unversty, Ryerson Unversty, the Unversty of Toronto and York Unversty, the frst of these three unverstes are located n downtown Toronto. Three campuses of the Unversty of Toronto located n downtown Toronto, Mssssauga (n the Regon of Peel) and n Scarborough (an eastern outer suburb of the Cty of Toronto). The man campus of York Unversty s located n the Regon of York, and s known as the Keele campus and ts second campus s Glendon campus. Students of all of these seven campuses lve across the GTA and represent the majorty post-secondary students n the GTA 1. The survey was named as StudentMoveTo, whch was a Web-based travel dary survey that ncluded a seres of retrospectve questons regardng the acquston of a drver s lcense; home locaton; travel modes n dfferent seasons; and questons related to an opnon on or atttude towards dfferent transportaton ssues. The survey was conducted n the autumn of 015 smultaneously n all four unverstes (seven campuses) encompassng undergraduate and graduate students. It was admnstered by representatves from all four unverstes. The survey was a completely voluntary survey, whch was very well accepted by the students nvolved. Overall completon 1 The survey dd not nclude colleges and post-secondary techncal educaton centres. See 6

7 rate of the survey was around 8.5 percent and that resulted n a total of 15,6 completed responses. In ths nvestgaton, data related to personal attrbutes (ncludng drver s lcense status and age of acqurng lcense); household attrbutes (ncludng home locaton); and regular travel behavour (regular travel modes, changes n travel modes n a dfferent season) related nformaton collected n the survey are used. Home locaton of all ndvduals s matched wth relevant land use and transportaton accessblty-related attrbutes to accommodate the effects of land use and transportaton accessblty effects n the emprcal nvestgatons. However, after cleanng for mssng varable values and/or unanswered questons a total of 13,585 records were retaned for emprcal nvestgaton n the fnal dataset. In the fnal dataset, around 40 percent students do not have drver s lcenses. Fgure 1 presents (at the top) the age dstrbuton of students who have and have not acqured drver s lcenses along wth (at the bottom) the dstrbuton of age of acqurng drver s lcense. It shows a clear dstncton n the dstrbutons of the two groups. Table 1 presents the summary of varables that are avalable n the fnal dataset. Fgure 1: Dfferences n the age dstrbuton of students wth and wthout drver s lcenses and dstrbuton of age n acqurng a drver s lcense. 7

8 Table 1: Summary statstcs Contnuous Attrbute/Varable Mean Standard devaton Age (years) of acqurng drver s lcense Number of years lvng n current home Home to campus dstance n km Household sze Number of dependent chldren n home Number of cars owned by the household Dstance (km) between home and nearest bus stop Dstance (km) between home and nearest ral staton Dstance (km) between home and nearest streetcar stop Dstance (km) between home and nearest subway staton Average dstance (km) between ntersectons wthn a 1 km walkng buffer n home locaton The area (n sq. km) of the 1 km walkng buffer n home locaton Populaton densty (thousand people per sq. km) n Employment densty (thousand jobs per sq, km) n Categorcal attrbute/varable Sample proporton (%) Female 66 Undergraduate student status 74 Full-tme student status 90 Havng drver s lcense 60 Ownng a car by the student 18 Havng a carsharng membershp 6 Ownng a bcycle 49 Ownng a transt pass 40 Regular travel model for home to campus trps: Drve alone or rdeshare Transt Bcycle Walk Other Use of same travel mode n all seasons 91 Home type: Lvng arrangement: Lvng on campus Lvng n apartments/condomnums House (detached, sem-detached, row house) Others Lvng wth famly/parents Lvng wth partner Lvng alone Lvng wth roommate(s)

9 Household category: Sngle person household 11 Two people of the same generaton 19 Sngle-parent famly 10 Two parent famly 41 Others 19 Ownng resdental land phone lne 46 Locaton of home: Downtown Toronto Outsde downtown Toronto, but wthn the Cty of Toronto Outsde of the Cty of Toronto The sample average age of the post-secondary students s below 19 years and the females represent 66 percent of the sample share. The majorty of the respondents belong to undergraduate student groups and have full-tme student status. As well, the largest proporton of the surveyed ndvduals lves wth famly/parents wth the majorty of these belongng to a twoparent famly structure. Overall, t seems that the surveyed students have good transt accessblty wth less than half km of average dstance between home and the nearest bus stop. As opposed to more than one average household car ownershp, ndvdual students car ownershp s less than 0 percent. Transt seems to be the man mode for a home to school trp and more than 90 percent students n the sample do not change ther regular mode n wnter. However, transt pass ownershp level, despte dscounted transt pass optons n the regon, s lower than that of bcycle ownershp level among the surveyed post-secondary students. 4. Econometrc Models The paper ntends to nvestgate the choce and tmng of acqurng drver s lcenses by postsecondary students n Toronto. Modellng the duraton of the event (ndcated as the lcense acqurng event) startng from the age of 15 years (qualfyng age) and termnatng at the tme/age when the lcense was acqured s ths study s means to model the tmng of acqurng drvers lcenses. In ths dataset, 60 percent of respondents were dentfed as drver s lcense holders, and ther recorded age of acqurng the lcenses s noted by year of age. Addtonally, data on the tmng of drver s lcense acquston s tme-dscretzed and 40 percent rghtcensored. Rght-censored data ndcates that 40 percent of respondents were not observed to termnate ther lcense acqurng event durng the survey. The hazard-based duraton model was chosen for the study as t a robust modellng approach. However, as the tmng of acqurng a drvng lcense s reported n a rounded year format, a dscrete-tme hazard approach s necessary. As shown n Fgure 1 and Table 1, the coeffcent of varaton (rato of standard devaton to mean) of the lcense acqurng event s over 16 percent. It s clear, therefore, that consderable heterogenety exsts across the post-secondary student populaton n Toronto n the tmng of acqurng a drver s lcense. Consderng all of these a hazard model wth nonparametrc baselne and random heterogenety s the most approprate econometrc approach. Han and Hausman (1990) and Bhat (1996) dscuss the strengths of a dscrete-tme hazard model, but manly for data wthout rght-censorng. Chang and Yeh (007) developed a hazard model for rght-censored data but consdered a contnuous parametrc hazard model formulaton nstead

10 of a dscrete-tme approach. In ths paper, the dscrete-tme hazard modellng approach s extended to accommodate rght-censored data. Consder k ntervals of dscrete tmes varyng from 1,, 3,..to K for correspondng contnuous duraton varable, D, and grouped as [0, dur1], [dur1, dur], [dur3, dur4].[durk-1, ] Hazard rate of any nterval dur of any ndvdual : Pr[( dur ) D dur D dur] ( dur) lm 0 (1) here, λ ndcates the hazard rate δ s the tme step Consderng the wdely accepted proportonal hazard rate assumpton we can explan ths hazard rate through a multplcatve functon of baselne hazard rate and a covarate functon (Kefer 1988): ( dur) 0 ( dur) exp x () here, λ0(dur) s the baselne hazard rate at the nterval dur. As per proportonal hazard assumpton, f the event termnates at duraton D, the ntegrated hazard rate up to D can be expressed as a functon of a random varable ε: D 0 D 0 ( dur) d dur exp( ) ( dur) d dur exp 0 D 0 0 ) 0 D 0 x ( dur)exp 0 x d ( dur) ln ( D ) ln ( dur d dur x (3) here, Λ0(D) s the baselne ntegrated hazard rate. Consderng that the log of the baselne ntegrated hazard rate of any ndvdual,, s a constant (µ): ln ( D ) ln ( D ) exp( ) 0 0 D 0 ( dur) d dur 0 Wth the assumpton of an extreme value dstrbuton for the random term ε (whch s the logarthm of ntegrated hazard rate) the event of not havng a drver s lcense for an ndvdual wll termnate at the duraton of D and can be wrtten as: (4) 10

11 Pr( t k) Pr ln0 ( durk 1) ln0( T ) ln0( durk ) G k x G k1 x where, k ln0( durk ) G(.) 1 exp( exp(.)) (5) In the case of a homogenous hazard rate (across the populaton under nvestgaton) assumpton, the probablty that the duraton of not havng a drver s lcense termnates at an nterval k becomes: k x e e k1 x 1e 1e Pr( t k) (6) However, to accommodate a systematc heterogenety across the populaton under nvestgaton, we can consder the mxng of a postve dstrbuton. Consderng the Gamma dstrbuton of unt mean and σ varance as a postve dstrbuton for mxng, the resultng probablty equatons for event termnaton duraton at an nterval k becomes (Han and Hausman 1990; Bhat 1996): Pr( t Pr( t 1 k) 1 1 k) 1 k e k1 x 1 x e Pr( t x 1 x k) 1 1 ke 1 ke (7) Now, n case of uncensored observatons, the lkelhood, L(Uncensored), of an ndvdual who acqured the drver s lcense at the age of t: L Uncensored 1 x 1 1 1e 1 x 1 k1e 1 1 ke 1 x 1 e K x f t f k, any ntermedate nterval f t 1, the 1st nterval t K, the last nterval (9) However, for the ndvduals who were surveyed and dd not have a drver s lcense untl the tme of the survey, the correspondng data pont becomes rght-censored. Rght-censorng refers to the case that the observaton tme s not suffcently long enough to observe the termnaton of 11

12 the event of acqurng a drver s lcense. In case of such rght-censored data, we can speculate two possble cases: 1. The event wll not termnate at all, whch means the correspondng ndvdual wll never get a drver s lcense.. The event would have termnated f we could have extended the observaton tme perod long enough. Consderng a bnary logt probablty of the case that the ndvdual wll lkely to acqure a drver s lcense, the lkelhood of any observed duraton (t) needs to consder that (Chang and Yeh 007): C x L F z Luncensored 1 F z Ke 1 1 (10) here, C s an ndcator that takes the value of 1 f the observaton s uncensored and 0 f rght-censored F( γz) s the logt probablty of acqurng a lcense at all, where γz s a lnear-n-parameter functon of covarate set z and correspondng coeffcents γ for the ndvdual. These lkelhood functons are of closed form and can be estmated by the classcal maxmum lkelhood estmaton technque. In ths nvestgaton, the models are estmated by usng a program wrtten n GAUSS and usng ts MAXLIK routne (Aptech 016). Ths formulaton of the hazard model can be referred to as a splt populaton non-parametrc baselne hazard rate wth Gamma heterogenety. The splt populaton accommodates the ssue of rght-censorng through the assumpton that a porton of subjects n the populaton under nvestgaton may not have a drver s lcense durng the nvestgaton, but wll acqure t n the future. Non-parameter baselne hazard assumpton allows better for capturng of the actual process under nvestgaton rather than forcng the baselne tendency nto any parametrc dstrbuton processes. Accommodaton of Gamma heterogenety ensures an over-dsperson of duraton n terms of a dstrbuton of such systematc dsperson across the populaton. Once estmated, a careful assessment of the estmated parameters s needed to evaluate the correspondng mpacts on the choce of not havng drver s lcense or the age (tme) of acqurng a drver s lcense. The fnal model has three components to evaluate. These are: 1. Baselne hazard rate of age when post-secondary students tend to acqure ther drver s lcense;. Covarate effects on the probablty of acqurng or not acqurng drver s lcenses. 3. Covarate effects on the age (tme n years) of acqurng a drver s lcense. The baselne hazard rate at any age (duraton) nterval k can be estmated by usng the nonparametrc baselne hazard rate as: D [ d, d ] D d / 0 ( k) Pr k1 k k1 k k1 (11) 1C 1

13 Estmated parameters of the covarates do not necessarly gve a drect nterpretaton of ther effects (magntude as well as drecton) on the probablty of acqurng/not acqurng a drver s lcense as well as age (duraton) of acqurng a lcense because of non-lnear formulatons of logt probablty and proportonal hazard formulatons. However, an estmated margnal effect can reveal the relatve magntude and the drecton of such nfluences. The margnal effect of any varable on the probablty of not acqurng a drver s lcense (rght censorng) can be estmated as: 1 x ME z F z 1 F z 1 Ke (1) As the hazard functon s a functon of age K, such margnal effect should be calculated separately for each age nterval. Smlarly, for the non-parametrc baselne hazard model of the age (tme/duraton) of acqurng a drver s lcense, the margnal effects of covarates have agecategory (nterval) specfc values. The general equaton of margnal effect of any varable on age (tme/duraton) of acqurng a drver s lcense s: ME x 1 F( z) 1 1e 1 F( z) 1 k1e 1 F( z) 1 ke 1 F( z) 1 e K 1 x x 1 x x 1 x x 1e k1 1 x x ke K e e K f t f t 1, the 1st nterval k, any ntermedate nterval f t K, the last nterval As per the formulatons of the proportonal hazard model, the sgns of the estmated margnal effects have a drect relatonshp to age (tme/duraton) of acqurng a drver s lcense and an opposte relatonshp wth the correspondng hazard rates. 5. Emprcal Models and Fndngs Table presents a summary of the estmated model parameters. The presented fnal specfcaton s a splt populaton hazard model for the age of acqurng drver s lcense wth a non-parametrc baselne and Gamma heterogenety. The fnal model has a total of 59 estmated model parameters almost all of whch have over 95 percent confdence on parameter estmates. There (13) 13

14 are a few parameters wth lower than 95 percent confdence, but those are retaned as the correspondng varables have polcy sgnfcance. As per the Ch-square test aganst the constant only model (a model wthout covarates), the fnal specfcaton of a jont model wth covarate functon and rght-censor (splt populaton) probablty s statstcally justfed. In terms of goodness-of-ft, the Rho-squared value s 0.35, whch s reasonably hgh for a complcated model. The model estmated baselne and total hazard rates are presented n Fgure. The baselne hazard rate ndcates the baselne trends of acqurng drver s lcenses by post-secondary students n Toronto wthout consderng any effects of covarates. Margnal effects of covarates on total hazard rates (correspondng tme/duraton of acqurng a drver s lcense), as well as margnal effects of covarates on probablty of acqurng (aganst not acqurng) a drver's lcense are estmated by usng the model presented n Table, are presented n Fgure 3. Fgure : Estmated baselne and total hazard rates of age of acqurng drvers lcenses by postsecondary students n Toronto. Hazard rates (baselne as well as total) show zg-zag patterns. The man reason for ths pattern s the roundng of age n years whle also reportng the age at whch the drver s lcense was acqured. Overall, the baselne hazard rate ncreases wth age. Ths s due to the fact that the baselne tendency of post-secondary students n Toronto s to acqure drver s lcenses as early as possble. In fact, the baselne hazard rate ncreases tenfold from the age of 17 to the age of 30. Addtonally, the baselne trend s to acqure a drver s lcense soon as the ndvdual can legally 14

15 obtan t (age of 15). However, the nfluence of varous contexts (as depcted through covarates n the model) lowers down the hazard rate drastcally. Although the total hazard rate ncreases slghtly from the age of 15 to the ages of 17 to 18, t starts droppng gradually afterward. It s also nterestng to note that the dsperson of sample hazard rates gradually drops to almost zero beyond the age of 30. The emprcal model clearly hghlghts the very strong nfluences of dfferent factors that defne the choce and tmng of acqurng a drver s lcense. Such nfluences are dscussed n the followng. Fgure 3: Margnal effects of covarates on rght censorng and hazard rates. Comparng the baselne and total hazard rate dstrbuton, t s clear that there s a strong trend for post-secondary students to acqure ther drver s lcenses n Toronto by the age of 0. However, there s a porton of students who would obtan ther lcense by the age of 30 and perhaps would not obtan t even later n ther lves. Whle there s hgh varablty n the exact age of obtanng a drver s lcense f the lcense s acqured before the age of 0, ths varablty drops drastcally for those who acqure a lcense after the age of 0. Based on ths nvestgaton t s not possble to predct whether ths populaton (who delay n gettng a lcense of or don t get one at all) s changng over tme or not as the dataset s a cross-sectonal dataset wth retrospectve nformaton regardng the age of acqurng a drver s lcense. However, the econometrc model developed n ths study can offer observatons on the factors that nfluence the delay or haste n gettng a lcense as well as the probablty of gettng (or not gettng at all) drvng lcense n the future. Two types of margnal effects are estmated: the margnal effects of the covarates on the probablty of gettng a lcense and the margnal effects of the covarates on the age (opposte to correspondng hazard rates) at whch someone may get a lcense. It s clear that covarate effects decrease wth ncreasng age, whch means covarate effects on hazard rates ncrease wth 15

16 ncreasng age and ths s consstent wth the fact that total hazard rate drops wth ncreasng age even though the baselne hazard rate follows the opposte pattern. 5.1 Factors Influencng the Age of Acqurng Drver s Lcenses by Post-secondary Students Two of the most nfluental varables (.e., havng hghest margnal effects) that defne the age at whch a post-secondary student would acqure a drver s lcense are lvng wth famly (as opposed to lvng alone or wth partner or roommates) and the dstance between home and the nearest bus stop and these varables also have opposte effects. An ndvdual s lvng arrangement has the hghest mpact on the tmng of acqurng a drver s lcense by postsecondary students n Toronto. Lvng wth famly/parents reduces the need or urgency (lowerng the hazard rate) of gettng a lcense. However, the relatve accessblty to a transt network, n terms of the dstance between home and the nearest bus stop, counter-balances (.e., ncreases the hazard rate) the delay n gettng a lcense. The dstance between home and the nearest ral staton also has a postve effect on delayng the acquston of a drver s lcense, but ths factor s smaller than lvng close to the nearest bus stop. Thus the effect of the dstance between an ndvdual s home and the nearest subway staton to where she/he lves was not found have any statstcally sgnfcant effects. Toronto has a comprehensve bus network; a relatvely small and smple subway network wthn the man core of the cty and ral network (GO ral) desgned to serve people travellng from outsde the cty nto the cty s downtown. Ths nvestgaton mples that accessblty to transt servces s more mportant than accessblty to any partcular mode of transt (e.g., subway or ral). It s clear that students lvng n places wth lmted publc transt servce accessblty would be nfluenced to acqure ther drvng lcenses at a young age. However, havng transt passes further reduces the urgency (reducng hazard rate) of acqurng a drver s lcense. Toronto has a dscounted transt pass system for post-secondary students. Ths polcy not only allows unrestrcted use of transt servce but also has a long-term mpact on delayng the tme of obtanng a drver s lcense and thus reduces potental dependency on a prvate automoble. Next to these two varables; household car ownershp, bcycle ownershp and walkablty of the home neghbourhood (depcted as the sq km areas n home zone of a 1 km walkng buffer) have a strong mpact on the age of acqurng a drver s lcense. The car ownershp level of a household has a very strong nfluence on the tmng of post-secondary students acqurng a drver s lcense. Intutvely, a hgher number of cars would nfluence the students to obtan ther lcenses earler. However, t s found that the effect of the number of cars follows a logarthmc pattern; a decreasng rate of effect wth ncreasng number of cars. Interestngly, ownng bcycles and havng lower walkablty (depcted through a wder area for 1 km walkng buffer) around the home locaton nfluenced ndvduals to acqure a drver s lcense early. Populaton densty has a postve nfluence on delayng the acqurng of a drver s lcense. It s understandable that more densely populated neghbourhoods are more walkable neghbourhoods. The emprcal model reveals that students lvng n apartments/condomnums are more lkely to delay n acqurng ther drver s lcense. Apartments/condomnums n Toronto are mostly located n the core of the cty where the populaton densty s hgh and transt servce accessblty s also hgh. Smlarly, t s also clear that students lvng outsde downtown Toronto 16

17 are more lkely to acqure ther drver s lcense earler than those lvng n downtown Toronto. Populaton densty drops beyond the mmedate area of downtown Toronto. When comparng all of these effects of transt servce accessblty, walkablty, bcycle ownershp and populaton densty, t s clear that smlarly to transt nvestment, nvestng n pedestran nfrastructure wll have a postve nfluence on delayng (lowerng hazard rate) the acquston of a drver s lcense by post-secondary students n Toronto. The effect of home type (apartment/condomnum as opposed to houses) may also reflect the nfluence of stablty or permanency of resdences of post-secondary students. To further nvestgate ths effect of stablty/permanence of homes, the ownershp of resdental land telephone lnes was used as a dummy varable n the model. Ths varable had an opposte effect of the effect of the home type n terms of lvng n an apartment or condomnum. Wth ncreasng relance of post-secondary students on cell phones, ths dummy varable may capture the surrogate effect of a tradtonal stable home type as opposed to a temporary home. The emprcal model reveals that post-secondary students lvng n homes wth resdental home telephone lnes are more lkely to acqure ther drver s lcenses earler than others. Ths effect s also complemented by the effect of nteracton between home to campus dstances and the number of years lvng n a current home locaton. It s observed that lvng n places that are farther from the unversty campuses and for a long tme along wth havng a resdental land telephone lne, are the factors that nfluence post-secondary students n acqurng ther drver s lcenses earler than others. Complementary to these factors, f the locaton of the home s outsde of downtown Toronto ths wll further nfluence the urgency (hgher hazard rate) of acqurng a drver s lcense. In terms of personal attrbutes, t seems that female post-secondary students n Toronto are more lkely to acqure ther drvng lcenses later than ther male counterparts. Post-secondary students who have been n unversty normally delay ther acquston of a drver s lcense than students who have not been n the unversty for a long tme. Interestngly, graduate students tend to delay acqurng ther drvng lcense longer than the undergraduate students. 5. Factors Influencng the Choce of not Acqurng a Drver s Lcense by Post-secondary Students n Toronto The presence of rght censorng s accommodated through a jont estmaton of the choce of not acqurng drvng lcense along wth hazard rate of gettng a drver s lcense by post-secondary students n Toronto. The dataset used n ths study used retrospectve nformaton about the age at whch a drver s lcense was acqured as well as the current age of those who do not have a drver s lcense yet. There s no way to know whether the students who do not have drver s lcense would not get a lcense n future, but the rght censorng probablty provdes nsght regardng the factors that can ncrease or decrease the probablty of not acqurng a drver s lcense n the future. The bnary logt model of rght censorng has an nsgnfcant and very low constant ndcatng that the varables/factors used n the nvestgaton explan most of the probablty of not acqurng drvng lcenses. Smlar to the hazard model, the effects of all varables decrease wth ncreasng age. Ths refers to the fact that the choces of acqurng or not acqurng drver s lcenses by the post-secondary students are more nfluenced by varous factors 17

18 when they are younger. Smlar to the hazard model, effects of all the varables decrease when the ndvdual ages. Effects of all varables n the bnary choce of gettng/not gettng a drvng lcense are consstent wth those n the hazard model of age for acqurng a drver s lcense except for the factor of ownng a resdental land telephone lne. Ths model component bolsters the effects of same varables n terms of the fact that f a varable nfluences the choce of not acqurng the drvng lcense, t also nfluences the ncrease the age of acqurng the lcense and vce versa. Lvng wth famly and ownng transt passes postvely nfluences the choce of not gettng a drver s lcense and these also decrease the hazard rate (thereby ncreasng the age) of acqurng a drver s lcense by post-secondary students. The accessblty of publc transt servces (dstances between home and nearest bus and ral statons); bcycle ownershp; number of cars owned by the household; dstance between home and campus nteracted wth years of lvng n same home locaton and lvng outsde Downtown Toronto postvely nfluence the choce of acqurng a drver s lcense and these factors also ncrease the hazard rate (thereby decreasng the age) of acqurng a drver s lcense by post-secondary students. One addtonal varable seems to not only to nfluence the choce of gettng a drver s lcense, but not the tmng (age) of acqurng t. Lvng wth a partner (as opposed to lvng alone or wth famly or roommates) seems to nfluence acqurng a drver s lcense, but t does not have a sgnfcant effect on the tmng of the acquston of one. However, t seems that students wth land telephone lnes tend to have a hgher probablty of acqurng a drver s lcense, but they tend to acqure t later than ther younger counterparts. 6. Concluson The paper nvestgated the factors affectng the choce and tmng of acqurng drver s lcenses by post-secondary students n Toronto. The study used the dataset collected through a travel survey of post-secondary students n Toronto jontly organzed by four unversty campuses located n Toronto: OCAD Unversty, Ryerson Unversty, York Unversty and the Unversty of Toronto. The dataset represents the majorty of post-secondary students n the GTA regon. They represent the man workforces of the regon n near future and are under-represented n regonal household travel surveys. The paper employed the econometrc modellng technque for a clear understandng of factors that nfluence the choce of acqurng or not acqurng drver s lcenses along wth the hazard rate defnng the tmng (age) of acqurng lcenses. The econometrc model clearly revealed that lvng arrangements n terms of lvng wth famly/parents have the strongest nfluence on the choce of not acqurng and/or delayng the tme of acqurng a drver s lcense by the post-secondary students n Toronto. Transt network coverage and accessblty to transt servces also proved to have strong nfluences on the choce of not acqurng and delayng the tme of acqurng a drver s lcenses by post-secondary students. Ths fndng complements our understandng that transt nvestment s not only benefcal to provde compettve servce to prvate automobles n reducng traffc congeston, emsson/polluton and health mpacts of transportaton, but also transt nvestment can drectly nfluence the next generaton n reducng ther relance on the prvate automoble. Better transt servce and transt accessblty can delay or even deter the need of for acqurng a dver s lcense by the post-secondary students. The emprcal model also revealed that a transt pass can play the 18

19 role of a deterrent n regard to the effects of household car ownershp n dscouragng postsecondary students n acqurng ther drver s lcense early. Transt passes seemed to play the role of a compettve (to the prvate car) moblty tool for post-secondary students and had a strong nfluence n not acqurng or delayng the acquston of a drver s lcense. Contrary to the role of a transt pass, bcycle ownershp had a complementary effect on acqurng a drver s lcense soon after the age of 15. Spatal context, n terms of home locaton outsde of downtown Toronto also contrbutes to early acqurng of drvng lcense by post-secondary students. Populaton and employment densty n the home zone showed opposte effects n nfluencng the choce and tmng of acqurng a drver s lcense by post-secondary students n Toronto. It seems that a hgher populaton densty nfluences the choce of not acqurng or delayng the acquston of a drver s lcense, but the opposte s true for hgher employment densty. Comparng both, t seems that a balanced land use mx (rght proportons of populaton and employment densty) may perhaps nullfy land-use effects on drver s lcense acquston rates by young adults. The paper presented nsghts nto factors causng a declne n obtanng a drver s lcense by young adults wth a case study on post-secondary students n Toronto. The paper used a closed form econometrc technque and so only systematc covarate effects are captured. The effects of atttudes towards the envronment, urban form, and the current transportaton system n the form of a latent varable would be very nterestng to decouple the actual systematc effects of covarates and apparently compounded effects of atttudes of young adults. However, ths poses a consderable methodologcal challenge and so s recommended for future research. Smlarly, even though the paper employed a dynamc econometrc technque the nvestgaton s stll crosssectonal n nature as t uses a dataset collected n one partcular survey. In order to better understand the nature and trend of declnng rate of obtanng a drver s lcense by young adults and the assocated factors ether panel data or repeated cross-sectonal data would be necessary. Perhaps repeatng the same survey n future would provde that opportunty and so s recommended as the concluson of ths paper. Acknowledgements The study was funded by an NSERC Dscovery Grant. The author wshes to thank Chrstopher Hardng for managng the StudentMoveTO survey and Sam Hasnne for helpng n processng the raw dataset. The author also wshes to thank Dr. Steven Farber for kndly sharng the land use and transt accessblty related varables that are used n the emprcal nvestgaton. The author has the sole responsblty for all comments and conclusons made n ths paper. References Aptech Inc GAUSS. Bhat, C.R A hazard-based duraton model of shoppng actvty wth nonparametrc baselne specfcaton wth nonparametrc control for unobserved heterogenety. Transportaton Research-B 30(3): Chang, H.-L., Yeh, T.-H Exploratory analyss of motorcycle holdng tme heterogenety usng a splt-populaton duraton model. Transportaton Research Part A 41:

20 Cobb-Clark, D.A Leavng home: What economcs has to say about the lvng arrangements of young Australans. The Australan Economc Revew 41(): Delbosc, A., Curre, G. 013a. Explorng the atttude of young adults towards cars and drvng lcense. Paper presented at the Australan Transport Research Forum, October 4 013, Brsbane, Australa. Delbosc, A., Curre, G. 013b. Why are young people less lkely to get a drvng lcense. Paper presented at the WCTR, July , Ro de Janero, Brazl. Delbosc, A., Curre, G. 013c. Causes of young lcensng delay: A synthess of evdence. Transport Revews 33(3): Delbosc, A., Curre, G Changng demographcs and young adult drver lcense declne n Melbourne, Australa ( ). Transportaton 41: Han, A., Hausman, J.A Flexble parametrc estmaton of duraton and competng rsk models. Journal of Appled Econometrcs 5(1): 1 8. Kefer, N.M., Economc duraton data and hazard functon. Journal of Economc Lterature. 6: Lavery, T.A., Paez, A., Kanaroglou, P.S Drvng out of choces: An nvestgaton on transport modalty n a unversty sample. Transportaton Research Part A 57: Maynard, M Curbng Cars: Amerca s Independence from the Auto Industry. Forbes Meda E-book. McDonald, N., Trowbrdge, M Does the buld envronment affect when Amercan teens become drvers? Evdence from 001 Natonal Household Travel Survey. Journal of Safety Research 40: Metz, D Peak car and beyond: The fourth era of travel. Transport Revews 33(3): Newman, P., Kenworthy, J Peak car use: Understandng the demse of automoble dependence. World Transport Polcy & Practce. 17(): Noble, B Why some young people choose not to drve. Paper presented at Assocaton for European Transport Conference. Strasbourg, France, March 005. Ruud, A., Nordbakke, S Decreasng drvng lcense rates among young people consequences for local publc transport. Paper presented at Assocaton for European Transport Conference. Strasbourg, France, March 005. Svak M., Schoettle B Recent changes n the age composton of US drvers: Implcatons for the extent, safety, and envronmental consequences of personal transportaton. Traffc Injury Preventon 1: Svak, M., Schoettle, B. 01b. Recent changes n the age composton of drvers n 15 countres. Traffc Injury Preventon 13: Svak, M., Schottle, B. 01b. Update: Percentage of young persons wth a drver s lcense contnues to drop. Traffc Injury Preventon 13: Tefft, B.C., Wllams, A.F., Grabowsk, J.G Drver lcensng and reasons for delayng lcensure among young adults ages 18 0, Unted States 01. Injury Epdemology 1:4 Transportaton Tomorrow Survey (TTS) Data Management Group, Unversty of Toronto. Vne, S.L., Latnopopous, C., Polak, J What s the relatonshp between onlne actvtes and drvng-lcense-holdng amongst young adults? Transportaton 41: Wllams, A.F Teenagers lcensng decsons and ther vews of lcensng polces: A natonal survey. Traffc Injury Preventon 1:

21 Zhou, J. 01. Sustanable commute n car-domnant cty: Factors affectng alternatve mode choces among unversty students. Transportaton Research Part A 46:

22 Table : Emprcal Model Loglkelhood of Full Model Loglkelhood of Constant-Only Model Loglkelhood of Equ-probable Model Ch-Squared aganst Constant-Only Model 76 Rho-Squared aganst Equ-probable Model 0.35 Splt Populaton Logt: Acqurng a Lcense n Future Varable Parameters t-stat Constant Log (dstance: home to nearest bus stop) Log (dstance: home to nearest ral staton) Ownng a transt pass Ownng a bcycle Log of (dstance: home to campus) x Log (years lvng n current locaton) Home outsde of downtown Toronto Log (number of cars at household) Lvng on-campus Lvng wth famly Lvng wth partner Ownng a resdental phone lne Covarate Functon of Hazard Model Parameters t-stat Area (sq km) of 1 km walk buffer Log (dstance: home to nearest bus stop) Log (dstance: home to nearest ral staton) Female Graduate student Years n the unversty

23 Ownng a transt pass Ownng a bcycle Log of (dstance: home to campus) x Log (years lvng n current locaton) Home outsde of downtown Toronto Log (populaton densty n home traffc zone) Log (employment densty n home traffc zone) Log of number of cars owned by the household Lvng n apartment/condomnum Lvng wth famly Ownng a resdental phone lne Varance of Gamma Heterogenety Non-parametrc Baselne Hazard Rates Years Parameter t-stat Years Parameter t-stat Years Parameter t-stat

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