WELFARE ANALYSIS USING LOGSUM DIFFERENCES VS. RULE OF

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1 WELFARE ANALYSIS USING LOGSUM DIFFERENCES VS. RULE OF HALF: A SERIES OF CASE STUDIES Shuhong Ma Assocate Professor School of Hghways, Chang an Unversty X an, Chna, 0 msh@chd.edu.cn Kara M. Kockelman Professor and Wllam J. Murray Jr. Fellow 1 Department of Cvl, Archtectural and Envronmental Engneerng 1 The Unversty of Texas at Austn 1 kkockelm@mal.utexas.edu 1 Phone: Danel J. Fagnant Assstant Professor Department of Cvl and Envronmental Engneerng 0 Unversty of Utah 1 dan.fagnant@utah.edu The followng s a pre-prnt, the fnal publcaton can be found n the Transportaton Research Record, No. 0: -, 01. ABSTRACT Logsum dfferences and rule-of-half (RoH) calculatons are two dfferent methods to estmate consumer surplus n transport economcs. As a tradtonal and relatvely straghtforward (and potentally more robust) procedure, RoH has been wdely used n project nvestment and polcy analyss, and much of the lterature seems to agree that logsums are somewhat superor to the RoH when valung user benefts- at least when the true travel behavors stem from random-utlty maxmzaton wth Gumbel error terms. Ths paper explores the dfferences n both methods, through a careful revew of lterature and many case study results. The comparson of RoH and logsum methods reles on three specfcatons, n order of ncreasng complexty: bnary logt, multnomal logt, and nested logt models, under a varety of settngs/scenaros. Ths work offers a closer look at three numercal examples, and concludes that the dfference between RoH and logsum solutons rses wth ncreases n travel tmes or costs, and changes n parameters. The monetzed dfferences n logsums s usually smaller than RoH soluton for welfare changes under most stuatons, and gves a more exact result for consumer surplus than RoH (whch assumes a lnear demand relatonshp wth respect to cost); Larger coeffcents on affected varables (lke travel tme and cost) n the random-utlty expressons tend to ncrease dfferences between logsum- and RoHbased estmates. Such fndngs should be of nterest to polcy-makers and planners when developng transportaton plannng and land use models and nterpretng ther results, for more accurate and rgorous and behavorally defensble project evaluatons. 1

2 Key Words: logsum dfferences, rule-of-half, consumer surplus, travel demand modelng, user benefts analyss INTRODUCTION As a tradtonal procedure for calculatng changes n user benefts (CS, consumer surplus), the Rule of Half (RoH) has been wdely used n transportaton project nvestment, polcy analyss, and operatons (e.g., tollng decsons) (see, e.g., De Raad 00, Geurs et al. 0, Brunton 01). Ths method assumes a lnear demand functon, to create a trapezod (ncludng a rectangle and a trangle) for generalzed cost savngs or losses for consumers of a good (lke transport) followng changes n costs (wth travel tme effects monetzed), as shown n Fgure 1. The area of the trapezod s the ncrement of consumer benefts and sutable for the RoH method (De Jong et al. 00, Brunton 01). In fact, CS s based on an uncompensated or Marshallan demand curve, whle compensatng varaton (CV) and equvalent varaton (EV) represent areas under compensated (Hcksan) demand curves (see, e.g., Varan []). McFadden s (, 1) logsum dfferences are based on random utlty maxmzaton (RUM) assumptons (wth Gumbel-type error terms), and used to estmate user benefts and losses, when ther travel (or other) context changes. In ths method, travel demand s estmated as a result of each ndvdual s choce context (e.g., travel tme and cost) changes, and the monetzed dfferences n all ndvduals logsum values characterze the change n consumer surplus. Bnary logt (BL), multnomal logt (MNL), and nested logt (NL) models are generally used to determne the shares of modes, and/or other choce alternatves. Ths paper nvestgates the dfferences n estmatng user benefts based on RoH versus logsum measures, va a revew of the lterature and an examnaton of three progressvely more complex applcatons, usng BL, MNL and NL specfcatons (under a seres of settngs or scenaros). Exstng lterature helps llustrate how user benefts under both methods vary by crcumstance, but does not explan when and why these dfferences occur, what parameters or varables mpact these dfferences most, and whether the three specfcaton contexts (usng BL, MNL and NL models) exhbt smlar dfferences n outcomes. Ths paper addresses each of these questons through examples and related dscussons. The work begns wth lterature revew, followed by a descrpton of methods and model specfcatons, case studes, and key fndngs. LITERATURE SYNTHESIS Several studes have nvestgated the theoretcal ssues nvolved n logsum formulatons. McFadden () outlned the mathematcal formulatons of the RUM choce model and welfare functons. Ben-Akva and Lerman () noted that the value of maxmum utlty ncreases wth choce set sze and average utlty of each alternatve. McFadden () found that the expected utlty change s bounded by the averages of these utlty changes per alternatve, weghted by the orgnal (lower) and fnal choce probabltes (upper bound), whle Herrges and Klng () used real data and three methods (a smulaton procedure, an approxmaton based on a representatve consumer approach, and some bounds on the true value of the surplus), to assess consumer surplus n preference settngs that are nonlnear n ncome. Karlstrom (000) and Daly

3 (00) dentfed condtons for when logsums are approprate, the foremost of whch requres the constant margnal utlty of money n the generalzed extreme value (GEV) model 1. Applcatons usng logsum dfferences as an evaluaton measure have been conducted n Europe, the U.S., and many other countres, for polcy and nvestment decsons n the areas of land use, congeston prcng of roadways, housng locaton and traffc analyss. For example, the EXPEDITE Consortum (00) studed the combned effects of an ncrease n car operatng costs and reductons n tran and bus/tram/metro costs to llustrate the effects of polcy measures. Odeck et al. (00) used logsums to estmate the relatve magntude of mpacts across socoeconomc groups under Oslo s cordon toll, based on changes n generalzed costs. Castglone et al. (00) used San Francsco s actvty-based model and logsum dfferences to estmate user benefts based on changes n travel costs and nduced travel. Gullpal and Kockelman (00), Gupta et al. (00), and Kalmanje and Kockelman (00) used logsum dfferences to evaluate the mpact of credt-based congeston prcng n Texas. The US DOT (00) compared results of ntegrated travel demand-land use models to those usng demand models only, and used Small and Rosen approach (1) to measure consumer beneft (also known as compensatng varaton, CV). The authors wondered whether consumer surplus measures for travel demand shfts are stll vald when land use demands shft. Essentally, travelers can offset some negatve system effects or explot transport system mprovements by movng ther home orgns, resultng n dfferent (hopefully less negatve) welfare mplcatons, but land prces also can change to offset travel benefts, resultng n hgher rents. Ma and Kockelman (01) have a new nvestgaton on such mpacts. Fnally, Geurs et al. s (0) evaluatons of Netherland s data (to antcpate clmate change mpacts and evaluate potental land-use strateges) suggest that logsum dfferences help value benefts from changes n trp producton and destnaton utlty, whch may be qute large and are not measured usng the RoH (snce RoH assumes that all accessblty benefts accrung to economc agents are attrbutable to generalzed cost changes wthn the transport system). In ths case, logsum and RoH accessblty benefts from the addtonal road-nvestment package are qute dfferent (e.g., $ versus $ mllon per year, across 1,000 persons), but on the same order-of-magntude. In contrast, ther dfferences across the dfferent land-use scenaros were very far apart ($M versus $M per year), suggestng that more welfare-characterzaton research recognzng land use s welfare mpacts may be needed. Most recently, Delle Ste and Salucc (01) proposed welfare calculaton methods n the presence of before-after correlatons (of the error terms n choce-related utltes), and ther example delvered a close correspondence n logsum dfferences versus RoH values (.e., 1.1 vs. 1. euros per month). Logsum dfferences come from RUM behavors, and BL, MNL and NL behavoral specfcatons are used to antcpate demand changes n most of the lterature surveyed here. However, other choce behavors may domnate. To nvestgate ths dea, Chorus (0) evaluated route choces under varable travel tme, congeston levels, crash exposure, and travel costs, usng both RRM (Random Regret Mnmzaton) and RUM (Random Utlty Maxmzaton) bases for the MNL specfcaton. He reled on stated preference survey data to compute the logsums whch were 1 McFadden () noted that, A random-utlty model n whch the utltes of the alternatves have ndependent extreme value dstrbutons yelds the Luce (MNL) model. Consderng non-ndependent extreme value dstrbutons leads to the generalzed extreme value (GEV) models.

4 then compared to survey responses (regardng wllngness to pay), wth only weak correlatons found. Kockelman and Lemp (0) llustrated four-level NL logsum methods (two destnatons, three modes, three tmes of day, and two routes) to equlbrate a toy network s travel tmes and choces, and then estmate class-specfc user benefts across eght scenaros. They found that road prcng can reduce congeston levels whle producng sgnfcant and largely postve consumer surplus benefts, though no drect comparsons wth RoH valuatons were conducted. Brunton (01) proposed a BL-based example to estmate user benefts n a logsum settng by mprovng bus transt through decreased travel tmes, comparng outcomes wth RoH estmates, whle notng that logsum gve a more exact result for consumer surplus than the RoH (whch assumes a lnear demand relatonshp). Koopmans and Kroes (00) and De Raad (00) compared logsum-based estmates of CS wth tradtonal vehcle-hours-lost (VHL) values, and found logsum method gve a hgher benefts and ncrease less rapdly wth ncreasng congeston level than the tradtonal VHL method. De Jong et al. s (00) comprehensve survey of logsum and RoH comparson results concluded that tradtonal RoH evaluatons should be replaced by logsum dfferences, to account for non-lnear demand assumptons. Brunton s (01) example drew a smlar concluson. However, each of these conclusons were based on sngular specfc scenaro examples (e.g., combned project mpacts from bus mprovements, enhanced capacty, and road toll polcy were not evaluated smultaneously n combnaton n any of the scenaros). Although several works suggest that logsum dfferences are better than the RoH when valung user benefts (De Jong et al. 00; Kockelman and Lemp 0; Brunton 01), they also recommend further testng, for more confdence n the detals of such results. The lterature appears somewhat mxed regardng when the RoH method should closely track logsum dfferences, and when t should gve substantally dfferent results. The followng sectons descrbe such comparsons. METHODOLOGY: Usng Rule of Half to Estmate User Benefts RoH s one tradtonal measurement for calculatng consumer surplus n transport economcs. Ths method assumes that the consumer demand (n ths case, transport demand) curve s lnear wth respect to generalzed costs, at least wthn the changng context between orgnal and new scenaros. As shown n Fgure 1, when generalzed cost changes from GC 0 to GC 1, travel demand n the form of person-trps s assumed to respond accordngly by changng from T 0 to T 1. Therefore, the change n consumer surplus ( CS) s denoted by the shaded area of the trapezod. In accordance wth Fgure 1 s llustraton, CS can be computed as follows: (1) where CS denotes consumer surplus, T 0 andt 1 are, respectvely, the transportaton demand before and after a change n scenaro context (e.g., tollng changes and/or capacty addtons), and GC 0 and GC 1 are the generalzed costs before and after the change, respectvely. Ths s a survey artcle, descrbng much of the research and many applcatons usng logsum methods before the year 00.

5 Usng logsum to estmate user benefts (consumer surplus) The purpose of measurng consumer surplus change s usually to evaluate the socal welfare mplcatons resultng from a partcular polcy or project (De Jong et al. 00). Snce consumer surplus s usually assocated wth a set of alternatves, when usng a logt model wth RUM assumpton, the change n consumer surplus s calculated as the dfference between the expected consumer surplus E(CS n ) before and after the change n context (or across scenaros). Ths procedure reles on the ndrect utlty of choce alternatves, and s formulated as follows: E( CS n ) (1/ )[ln( n e V 1 n ) ln( e V 0 n )], n, () where superscrpt 0 and 1 refer to before and after the change, α n represents the margnal utlty of ncome for person n, and can also be expressed du n /dy n (assumed to be constant n subsequent case studes nvestgated here), where Y n s the ncome of person n, U n s the overall utlty for person n, V n s the ndrect utlty for person n, and denotes the choce alternatves avalable to person n. Therefore, U n s the overall utlty for person n choosng alternatve, and V n denotes the systematc or representatve utlty for person n choosng alternatve. Ths procedure also determnes the probabltes that a gven person wll choose each of the alternatves by usng a logt model. These probabltes are estmated by evaluatng alternatve characterstcs n order to assess an ndrect utlty assocated wth that alternatve. In a MNL model, t s expressed usng the followng formula: V P e / K 1 e V where P s the probablty of a traveler choosng alternatve from alternatve choce set K; and V s the ndrect utlty of alternatve, whch s usually a lnear functon of the attrbutons of mode that descrbe ts attractveness. When usng a BL model, the only dfference s that the choce set contans just two alternatves. NL models are more complcated than BL and MNL model specfcatons due to the nested structure and typcally greater number of alternatves. However, Equaton s the bass of NL wthn-nest choce decsons, and therefore ths equaton stll governs much of the NL s behavor. CASE STUDIES In order to fully apprecate the dfferences between consumer surplus mpacts when usng logsum and RoH methodologes to estmate user benefts, three broad model categores (BL, MNL and NL models) were nvestgated here, wth several settngs or scenaros explored for each model. RoH and Logsum Valuaton Comparsons usng a Bnary Logt Model Brunton (01) developed a case study assumng 1,000 people travelng from pont A to pont B. The journey was assumed to take mnutes by bus and mnutes by car, wth assumed VOTTs at $1/hour. Under ths scenaro, user benefts were calculated from potental decreases n bus travel tme usng both RoH and logsum methodologes, assumng a BL model. In order to comprehensvely assess the dfference when usng logsum and RoH methodologes, ()

6 mprovements n bus travel tmes (from 1 to mnutes) were nvestgated here, wth outcomes shown n Table 1. The BL model s basc specfcaton and user benefts changes (usng logsum methodologes) are expressed as follows: V GC exp( V ) exp( ) exp( GC ) exp( ) () E( CS n ) (1/ )[ln( e 1 GC ) ln( e 0 GC )] () where P, V,ΔE(CS n ) are the same meanngs as above, superscrpt 0 and 1 refer to before and after the bus travel tme mprovements, GC s generalzed cost (n cents), and λ s scaled parameter (assumed here to be -0.0, as n Brunton s example). Fgure (-a1, -b1, and c1) llustrates the dfferences between RoH and logsum calculatons, along wth estmated bus travel shares as bus travel tmes fall (-a, -b, and c), all else equal. 1 Fgure -a, shows how the share of bus users ncreases non-lnearly as bus travel tmes fall, 1 wth ts graph effectvely representng a demand curve (and rotated 0 degrees). The pont at 1 whch logsum and RoH valuatons become equal as bus travel tmes fall s hghlghted by the 1 green dotted lne that crosses the curve. Ths pont s crtcal when comparng RoH- or logsum- 1 based benefts (Fgure -a1). Before ths pont, the dfferences between RoH and logsum methodologes present a trend of small-large-small (wth a maxmum dfference of $.0 per day, or.% n the two valuatons [for the 1,000 travelers]) - when bus and car travel tmes are equal), untl reachng Fgure -a s green dotted lne (the pont at whch bus travel tme s 0 mnutes less than car travel tme, the reverse of the ntal scenaro). In addton, the logsum 1 benefts curve s lower than the RoH benefts curve, meanng the benefts calculated usng logsum dfferences are lower than those calculated usng the RoH. After the nflecton pont the opposte s true, and dfferences between the two methodologes become larger agan, wth the logsum benefts curve hgher than the RoH benefts curve. Readers should note that under these crcumstances bus travel tme s less than 0% of car travel tme, an unlkely scenaro. However, the bnary logt model s structured such that the same results would be obtaned for dentcal bus travel tme reductons explored here, even f the ntal travel tmes were and 0 mnutes, respectvely, for bus and car travel, gven that the scale parameter was unchanged. Varous λ are nvestgated here, to determne parameters effects on the RoH and logsum values, 0 and ther dfferences (Fgure ). When λ = (Fgure b), the share of bus users almost lnear 1 wth respect to change n the travel tme, and user benefts calculated by RoH and logsum dfferences are almost dentcal (wth maxmum varatons between the two of just.% or $ per day, total across 00 travelers). When λ = -0.0 (Fgure c), the stuaton s smlar to λ=- 0.0, except that the dfferences between RoH and logsum valuatons s even larger (wth maxmum varatons growng to.% or $1, over the 00 affected travelers). Scale parameters (λs) wth values of , -0.00, -0.1 are also nvestgated here, as shown n Table 1. From these results, we can draw the followng conclusons: 1. If bus percentage grows approxmately lnearly wth decreasng travel tmes, the benefts 0 calculated by RoH and logsum dfferences wll be very close.

7 Under most crcumstances, RoH-calculated benefts are larger than those calculated usng logsums, though n extreme cases (lke n the very low bus travel tmes BL scenaro), RoH methods may result n smaller user benefts than logsum dfferences. Ths should generally hold true when persons shft from one hgh-use alternatve to a lower-use alternatve, as the costs of the second alternatve fall.. Fgures a, b, and c show the same trend of the dfferences between RoH and logsum valuatons, and the dfferences grow as λ ncreases n magntude. When λ les near zero (e.g., λ = to -0.00), the ratos of logsum/roh approach 1.0, meanng that the benefts calculated by RoH and logsums are almost the same. When λ grows n magntude (e.g., λ = - 0.1), the dfferences between RoH and logsums become much more substantal. RoH and Logsum Valuaton Comparsons usng a Multnomal Logt Model Equaton noted prevously shows the formula used to estmate the probablty that a traveler would select a gven mode when applyng a MNL model. Among ths equaton, ndrect utlty, V, s generally estmated as a lnear functon. Here, Equaton shows one common expresson for ndrect utlty (from NCHRP Report [Martn and McGuckn, ]):. V a b IVVT c OVVT d COST where IVTT represents the n-vehcle travel tme of mode (n mnutes), OVTT represents the out-of-vehcle travel tme of mode (nclude walk, wat and transfer tmes, n mnutes), COST denotes the out-of-pocket cost of mode (n dollars), a, b, c, and d are all constant coeffcents. Assume that there are modes (Car, Bus, Metro) travelers can choose when they travel from orgn O to destnaton D, where the dstance between O and D s 1 mles. Bus and Metro speeds are assumed to be the same as the Car speed (0 mph), however, flat 0 mnute and 1 mnute penaltes are added to Bus and Metro tmes respectvely, to represent ther added wat, access, and egress tmes. Further, bus fare s set at $0.0 per trp, metro fare s set at $ per trp, and a fxed $0.0/mle Car operatng cost s assumed, wth a $1.0 parkng fee per trp. Therefore, the total Bus travel tme s mnutes (IVTT mn and OVTT 0 mn), wth $0.0 out of pocket costs; the total Metro travel tme s mnutes (IVTT mn and OVTT 1 mn), wth $.00 out of pocket costs; and total Car travel tme s mnutes (only the IVTT), wth $.00 out of pocket costs. Alternatve specfc constants (a ) are assumed to be 0.0 for Car, -1. for Bus, and -.0 for Metro, wth b = -0.0, c = -0.00, and d = (Martn and McGuckn, ). An average ncome of $,000/year, 00 workng-hours/year, and a value of tme equal to % of ncome were also assumed, resultng n a VOTT = $1.0/hour.,000 travelers are assumed here, wth no apprecable congeston or bus capacty lmtatons. That s, the avalable roadway capacty s large enough such that travel speeds are not mpacted, and travelers who shft to the Bus or Metro modes can always fnd a space. In ths scenaro, the probabltes of a traveler selectng each mode are calculated, wth the Car mode share (0.) beng the largest, due to ts relatvely hgh utlty. Addtonally, four other scenaros are nvestgated to llustrate the dfferences n estmated user benefts compared to the base case scenaro: Scenaro 1 decreases Bus wat tmes, from the current mnutes to just -mnute wats; Scenaro smultaneously decreases Bus and Metro wat tmes, by mnutes each across () Kockelman and Lemp (0, p. ) assumed $0.0/mle operatng costs, notng that t s less than the Amercan Automoble Assocaton (AAA 00) recognzes for full-cost accountng of vehcle ownershp and use but about % more than current gas costs, assumng a 0 m/gallon vehcle.

8 progressve reductons; Scenaro ncreases Car operatng costs from $1 to $, and Scenaro smultaneously decreases Bus and Metro out-of-pocket costs from the present fares to free rdes. As prevously noted, logsum-estmated user benefts are calculated usng Equaton.Table shows how decreasng Bus OVTTs reduce overall travel tmes and ncrease bus shares. There are slght dfferences between the benefts evaluated usng logsum and RoH methodologes, and the RoH s a lttle larger than the Logsums (Scenaro 1). The other three scenaros present smlar stuatons, wth just slght dfferences between logsum and RoH methodology outcomes. Ths beng noted, the magntude of these dfferences grows larger wth greater changes from the basecase scenaro. b, c and d parameter values were also changed from -0.0, and -0.00, to -0.0, -0.1 and -0.00, respectvely. The results show smlar trends (larger parameter values result n greater dfferences between logsum and RoH valuatons), whch s largely due the mpacts of travel cost growng. RoH and Logsum Valuaton Comparsons Usng a Nested Logt Model To llumnate the user beneft dfferences estmated by RoH and logsum methodologes usng a NL model, an example of multple alternatves for travel between a sngle orgn and two destnatons s proposed here. The alternatves nclude the choce of destnaton (A versus B), mode (Auto, Bus, or Walk), and route(1, ). Fgure shows the overall nestng structure of mode-choce NL model. Ths scenaro reflects a confguraton smlar to that used n Kockelman and Lemp (0), wth two destnaton optons (A and B) avalable to each user. Destnaton A s a locaton close to the orgn (1 mle) whle destnaton B s much farther away ( mles), though the attractveness (e.g., the natural log of jobs) of Destnaton B s much more than that of Destnaton A (.e., 00 versus ). Also, Destnaton A may be reached usng motorzed modes at just mph n contrast to average speeds of 0 mph to reach Destnaton B. In the base-case scenaro, both routes to Destnaton B are dentcal, non-tolled, and free of congeston. Bus and Auto speeds are assumed to be the same; however, a flat 1-mnute penalty s added to the Bus tme to represent added wat, access, and egress tmes. Walk s only avalable to Destnaton A, wth an assumed speed of. mph. Furthermore, a fxed $0.0 per-trp Bus fare s assumed, along wth a $0.0/mle Auto operatng cost. Alternatve specfc constants (ASC m ) are assumed to be 0.0 for Auto, -1.1 for Bus, and -1. for Walk (as dscussed n Kockelman and Lemp [0]).,000 trp-makers wth $1/hour VOTTs were assumed to be travelng, and able to choose ether destnaton, any of the modes, and ether of the two routes (when travelng to the further destnaton). It s mportant to dscuss the scale parameters (whch are the nverse of the nclusve value coeffcents, and reflect the degree of substtuton that occurs between nested alternatves versus alternatves outsde the nest) n each level of the nested model. As shown n Fgure, scale parameters of 1. n the lowest nest (µ 1 for drvng to Destnaton B va Route 1 or Route ), 1. n the next lowest nest (µ for Walk versus Bus versus Auto mode), and 1. n the upper level nest (µ for Destnaton A versus Destnaton B) were assumed. The greater the scale parameter, Kockelman and Lemp (0,p. 0) developed a -layer (destnaton-mode-tod-route) NL model, scale parameters (μ 1, μ, μ, μ ) from the lowest level nest to the hghest level nest were assumed as 1., 1., 1. and 1., wth ther order consstent wth random utlty maxmzaton (Ben-Akva and Lerman ).

9 the greater the substtutablty among nested alternatves, versus other alternatves. Then, the assocated equatons, for generalzed trp costs, systematc utltes, nclusve values of the nested choces and choce probabltes are as follows: GC V dmr dmr VOTT OVTT dmr VOTT IVTT dmr ln( attrd ) - ln( attrb ) ASCm - GCdmr 1 ln[exp( 1 V, route1) exp( 1 V COST dm dm dm, route 1 d Pr d 1 ln[exp( V exp( d ) exp( ) jd j d,auto ) exp( V d,bus )] dmr ) exp( V d,walk )] () () () () () Pr dm Pr d exp( dm ) exp( ) j M dj (1) Pr dmr Pr dm exp( 1 V exp( V j R 1 dmr ) ) dmj (1) Here, GC s the generalzed cost, V stands for systematc utlty of the alternatve (as measured n dollars), denotes the nclusve value or expected maxmum utlty for an upper level alternatve, Pr( ) represents the probablty of a partcular choce, d, m and r denote Destnaton (A, B), Mode (Auto, Bus, Walk) and Route (Route1, Route). VOTT denotes the value of travel tme, μ 1, μ, and μ are scale parameters for the Route, Mode, and Destnaton, respectvely, COST represents the out-of-pocket travel costs (nclude fare, toll and operatng cost) and has no coeffcent (so that utltes are n dollars), IVTT and OVTT denote the travel tme spent n and out of the vehcle, attr characterzes the attractveness of each destnatons (and attr B s the attractveness of destnaton B), and ASC m represents the mode-specfc (alternatve-specfc) constants. Consumer surplus change estmates (ΔCS) for each scenaro were also computed. The ΔCS computaton usng normalzed logsums of systematc utltes are estmated as follows: 1 CS {ln[ dd exp( 1 d ) - ln[ exp( Whle ΔCS can be measured between any two scenaros, ths nvestgaton examnes changes n consumer surplus relatve to the base-case scenaro. The base-case scenaro assumes two dentcal, congeston-free, non-tolled routes to Destnaton B, wth scenaro summary results (ncludng destnaton, mode and route choce probabltes) shown n Table. Then, In order to compare the dfferences between user benefts usng RoH and logsum methodologes when relyng on a NL model, sx dstnctve alternatve scenaros are nvestgated. Scenaro 1 assesses flat tolls on one of the routes to Destnaton B at rates varyng dd 0 d )]} (1)

10 between $0. and $0.0 per mle. Scenaro explores the mpacts of VOTT based on a fx tollrate ($0.0 per mle). Scenaro evaluates the mpacts of varyng operatng speeds (from 0 mph to 0 mph, Route to Destnaton B), reflectng potental roadway faclty upgrades wth hgher speeds or worsenng overall congeston wth lower speeds. Scenaro changes bus wat tmes reflectng polces that ncrease or decrease the level-of-servce for publc transt, whle Scenaro alters bus fares. Scenaro vares auto operatng costs, reflectng changng gasolne prces and parkng fees. Each scenaro assumes,000 persons who want to travel (to Destnaton A or B), and wth user benefts compared across scenaros (relatve to base-case scenaro), usng RoH and logsum methodologes, wth results shown n Table. Results show that the benefts calculated when usng logsum versus RoH methodologes dffer more substantally wth travel tme changes, and the dfferences become more sgnfcant n Scenaro 1 when a route s tolled. When Autos are tolled on Route to Destnaton B n Scenaro 1, the dfference between the two become larger wth ncreased toll-rates, wth logsums valuatons typcally smaller than RoH valuatons. In Scenaro, when changng the VOTT from $1/hr to $1/hr, the logsum/roh rato rses from 0.1 to 0., suggestng that hgher values of tme may lead to more consstent results n logsum and RoH valuatons. In Scenaro,when alterng the speed from 0 mph to 0 mph on Route to Destnaton B, the logsum/ RoH ratos rse, and they are greater than/less than 1.0 when the base-case speed s greater than/less than 0 mph. The user benefts evaluated usng logsum and RoH methodologes are closer when travel speeds change modestly, from 0 mph and 0 mph, rather than more dramatcally. In Scenaro, the logsum/roh ratos fall as the Bus OVTT change ncreases. In Scenaros and (whch vary Bus fares and Auto operatng costs), there are only slght dfferences between the two methods for calculatng user benefts. Analyss of the Cases In analyzng the results of these cases and ther assocated scenaros, the followng conclusons can be drawn: 1. As the magntude of parameters and varables n utlty expresson grow, the percentle and absolute dfferences between logsum and RoH valuatons become larger.. Wth slght changes n travel tme, travel cost and other varables, the percentle and absolute dfferences between logsum and RoH valuatons are very small; but these dfferences grow as the alternatve scenaro ncreasngly dverges from the base-case scenaro. Also, when travel demand s a near-lnear functon of travel tme and other varables, the user benefts calculated usng RoH and logsum methodologes are close.. Under most crcumstances, the magntude of the mpacts (ncludng negatve user beneft valuatons) calculated usng RoH are larger than usng logsum dfferences. However, n some nstances RoH may be smaller than Logsum dfferences (e.g., when the changes n travel cost are very large, compared to base scenaros). These dfferences between estmated logsum and RoH valuatons may be further llustrated by smultaneously comparng all scenaros and modelng results, provdng a useful and quckreference framework for transport planners, managers and decson-makers. Table shows how travel tme, travel cost, tolls and other parameters nfluence the dfferences between RoH and logsum valuatons, as nput varables change n sgn and magntude. These nput changes reflect

11 potental transport polces, projects, and/or management decsons, and may serve as a reference for future plannng and decson-makng efforts. CONCLUSIONS Much work currently exsts on examnng logsum dfferences to estmate potental user benefts from varous polces or projects, but exstng comparsons between RoH and logsum benefts s largely lackng, partcularly n the context of a comprehensve comparson evaluatng the mpacts of changng travel tmes, travel costs, added tolls and other mportant parameters aspects. Ths paper uses case studes to analyze and summarze the dfferences between RoH and logsum valuatons as a measure of user benefts. As shown usng model types, the rato between logsum and RoH valuatons vares on scenaro context and the degree to whch nput parameters change. The tollway scenaro llustrates ths phenomenon, as the dfference n estmated benefts when usng these two methodologes becomes larger as toll rates grow. Ths mples the RoH method may sometmes over-estmate the effects of a gven polcy, especally when the change s sgnfcant compared to the base-case scenaro. In these three cases, the dfferences between RoH and logsum valuatons when usng the MNL model appear to be smaller than when usng ether BL or NL models. Ths s manly due to the changes n probabltes of each alternatve are almost lnear or near-lnear n MNL model compared n BL and NL models. Whle ths last concluson s ndcated by assessng results from these three specfc cases, t s possble that t may not hold under all crcumstances, so further research may be needed. Results also ndcate that when the transport demand s a lnear functon, the rato between logsum and RoH valuatons s close to 1, though transport demand usually exhbts nonlnear trends. As such, t s recommended that polcy-makers estmate user benefts usng logsum valuatons when travel tme or travel cost mpacts are antcpated to be large, snce logsums are more accurate than traveler welfare valuatons estmated usng the RoH methodology. Of course, the analyss provded here llustrates only a lmted number of dealzed scenaros under three governng model formulatons. Many other potental exploratons and scenaro extensons exst, whch could further hghlght key ssues nvolved n these dfferences. For example, other evaluatons could examne f multple nputs smultaneously change (for example, travel tmes under varyng congeston levels and toll prces). In addton, when a gven route s tolled, the entre transportaton network may be mpacted, potentally further nfluencng dfferences n logsum and RoH valuatons. One could also explore other underlyng model structures to generate the demand functons, and nvestgate whch method s more robust to other behavoral assumptons. Lnear demand functons are lkely to favor the RoH, whch was at a dsadvantage here (thanks to startng off wth a random-utlty logt-based model for all choce behavors). In summary, the comparson evaluatng the dfferences between logsum and RoH valuatons should help transportaton planners and polcy-makers understand how the choce of evaluaton methodology wll nfluence and potentally bas the expected benefts from a gven project or polcy. When relatvely mnmal mpacts are expected to the overall underlyng generalzed cost of a gven choce alternatve, the two methods are roughly equvalent. However, when changes n such costs are expected to be substantal, there s a strong chance that usng the RoH methodology may produce a substantally ms-estmated result, potentally overestmatng or underestmatng benefts by up to half. ACKNOWLEDGEMENTS

12 Dr. Jason Lemp constructed the orgnal the NL mode-choce model structure, whch was modfed by the authors for specfc scenaros, and he provded some of the reference data at the start of ths research. We also apprecate the admnstratve contrbutons of Ms. Annette Perrone, the comments of several anonymous revewers, and the fnancal support of the Chna Scholarshp Councl, whch funded the lead author s one-year stay n the U.S. REFERENCES Ben-Akva, M. and Lerman, S. R.,. Dsaggregate travel and moblty choce models and measures of accessblty, n Hensher, D. A. and Stopher, P. R. (eds.) Behavoural Travel Modellng, Croom Helm. Ben-Akva, M., Lerman, S.. Dscrete Choce Analyss: Theory and Applcaton to Travel Demand. MIT Press. Brunton P., 01. Transport User Benefts: An Alternatve to the Rule of Half. Avalable at Castglone, J., Freedman, J. and Davdson W., 00. Applcaton of a tour-based mcrosmulaton model to a major transt nvestment, San Francsco County Transportaton Authorty and PBConsult, San Francsco. Delle Ste, P., Salucc, M., 01. Transton Choce Probabltes and Welfare Analyss n Random Utlty Models wth Imperfect Before-After Correlaton. Transportaton Research Part B : 1-. Daly, A., 00. Propertes of random utlty models of consumer choce, presented to TraLog Conference, Molde. De Jong, G., Peters, M., Daly, A., Graafland, I., Kroes, E., Koopmans, C., 00. Usng the Logsum as an Evaluaton Measure. Report WR--AVV, prepared for AVV Transport Research Centre, RAND Europe. Avalable at EXPEDITE Consortum, 00. EXPEDITE Fnal Publshable Report, Report for European Commsson, DGTREN, RAND Europe, Leden. Geurs, K., Zondag, B., de Jong, G., de Bok, M., 0. Accessblty Apprasal of Land-Use / Transport Polcy Strateges: More than just Addng up Travel-Tme Savngs. Transportaton Research Part D: -. Gulpall P. and Kockelman K.M., 00. Credt-Based Congeston Prcng: A Dallas-Fort Worth Applcaton. Transport Polcy 1 (1): -. Gupta, S., Kalmanje S., and Kockelman, K., 00. Road Prcng Smulatons:Traffc, Land Use and Welfare Impacts for Austn, Texas. Transportaton Plannng and Technology, (1): 1-. Harrs, A. J. and Tanner, J. C.,. Transport demand models based on personal characterstcs, TRRL Supplementary Report UC. Herrges, J. A. and Klng, C. L.,. Non-lnear ncome effects n random utlty models, Revew of Economcs and Statstcs 1 (1): -. 1

13 Karlstrom, A., 000. Non-lnear value functons n random utlty econometrcs. Presented to the IATBR Conference, Gold Coast, Australa. ocid=hkpu_millennium&fromstemap=1&afterpds=true Koopmans, C.C. and Kroes, E.P., 00. Werkeljke kosten van fles tweemaal zo hoog (The real cost of queues twce as hgh), Economsch Statstsche Berchten :1-1. Kalmanje S., Sukumar, and Kockelman K.M., 00. Credt-based congeston prcng travel, land value, and welfare mpacts. Transportaton Research Record No. : -. Kockelman K.M., and Kalmanje S., 00. Credt-based congeston prcng: a polcy proposal and the publc s response. Transportaton Research Part A: (-): 1-0 Kockelman K.M., Lemp J.D., 0.Antcpatng new-hghway mpacts: opportuntes for welfare analyss and credt-based congeston prcng. Transportaton Research Part A, (): -. Ma, S., Kockelman, K. 01. Welfare Measures to Reflect Home Locaton Optons When Transportaton Systems are Modfed. Paper under revew for presentaton at the th Annual Meetng of the TRB, and for publcaton n Transportaton Research Record. Martn, W., McGuckn, N.. Travel Estmaton Technques for Urban Plannng. Natonal Cooperatve Hghway Research Program (NCHRP) Report. Natonal Academy of Scence, Washngton, D.C. McFadden, D.,. Modellng the choce of resdental locaton. In Karlqvst, A., Lundqvst, L., Snckars, F. and Webull, J. (eds) Spatal Interacton Theory and Resdental Locaton. North- Holland, Amsterdam. McFadden, D.,. On computaton of wllngness-to-pay n travel demand models, Dept. of Economcs, Unversty of Calforna, Berkeley. McFadden, D., 1. Econometrc models of probablstc choce. In Mansk, C. and McFadden, D. (eds) Structural Analyss of Dscrete Data: Wth Econometrc Applcatons. The MIT Press, Cambrdge, Massachusetts. Nellthorp J. and Hyman G., Alternatves to the Rule of a Half n Matrx-Based Apprasal, Odeck, J., Rekdal, J. and Hamre, T.N., 00. The Soco-economc benefts of movng from cordon toll to congeston prcng: The case of Oslo. Paper presented at TRB Annual Meetng, Washngton D.C. Raad, P.M. de, 00. Congeston costs closer examned, Monetarsng adaptve behavour usng the Logsum-method. MSc Thess, TU Delft, The Netherlands. Small, K. A. and Rosen, H. S., 1. Appled welfare economcs wth dscrete choce models, Econometrca :-. US Department of Transportaton, Federal Hghway Admnstraton (00) Case Study: Sacramento, Calforna Methodology Calculaton of User Benefts, USDoT, Varan, H.. Mcroeconomc Analyss, rd Edton. W.W. Norton & Co. 1

14 Generalzed cost GC Supply 0 Supply 1 GC 0 GC 1 Demand D(GC) T 0 T 1 Fgure1. Usng rule-of-half (RoH) to estmate user benefts Trps T 1

15 Modes Travel tme (mn) Table 1 User benefts calculated usng RoH and logsum methods, wth bus travel tme fallng (BL model specfcaton) Base scenaro λ = -0.0 Bus travel tme decreases (mn) car bus Cost (cents) Probablty Benefts ($) logsum/roh rato RoH Logsum Logsum/RoH rato λ = RoH Logsum Logsum/RoH rato λ = -0.0 RoH Logsum Logsum/RoH rato λ = , -0.00, -0.00, -0.1 λ = λ = λ = λ = Note: These benefts are calculated for 1,000 people travelng from pont A to pont B for one trp. Benefts n Fgures a, b, and c share ths same bass. 1

16 a1 (a) λ = -0.0 a b1 (b) λ = b c1 (c) λ = -0.0 Fgure. Total user benefts (per day, across 00 travelers) calculated usng RoH and logsum methods and bus share changes followng reductons n bus travel tmes c 1

17 Table. User benefts calculated usng RoH and logsum methods, assumng MNL model behavor Scenaro 1: OVTT of Bus decreases OVTT (mnutes) Car Probablty Bus Metro Logsum ($) RoH ($) Logsum/RoH rato Scenaro : OVTTs of Bus and Metro both fall Bus OVTT (mn) Metro OVTT (mn) 1 1 Car Probablty Bus Metro Logsum ($) RoH ($) Logsum/RoH rato Scenaro : Auto cost ncreases Dollar ncrease +$1 +$ +$ +$ +$ +$ +$ +$ Car Probablty Bus Metro logsum RoH Logsum/RoH rato Scenaro : Bus and Metro fares both fall Fare Reducton (%) 0% 0% 0% 0% 0% Car Probablty Bus Metro RoH Logsum Logsum/RoH rato

18 Trp µ =1. Destnaton A Destnaton B µ =1. µ =1. Auto Bus Walk Auto Bus µ 1 =1. Route 1 Route Route 1 Route Fgure. Mode-choce NL model structure

19 Table. Orgnal settngs and calculated probabltes for the base-case scenaro (NL model) Travel tme Travel cost Destnaton Mode Route (mnutes) ($) Choce probablty IVTT OVTT Fare Toll Prd Prdm Prdmr cost Opera. Bus A Auto Walk B Route Bus 0.0 Route Route Auto 0.0 Route

20 Table. User benefts calculated usng RoH and logsum methodologes usng an NL model ($) Route to Destnaton B, where Auto s tolled Toll (cent/mle) ct/m Scenaro 1 VOTT $1/hour $/hour Logsum RoH Logsum/RoH rato Route to Destnaton B, where Auto s tolled at a fxed rate (0 /mle ) whle consderng varous VOTTs Scenaro VOTT($/hr) 1 Logsum RoH Logsum/RoH rato Route to Destnaton B, wth speed varatons (Base scenaro s 0 mph) Scenaro Scenaro Route Speed Logsum RoH Logsum/RoH rato Changed Bus OVTT tmes (on wat, access, and egress tmes) Added tme -0% ( mn) -0% ( mn) -0% (1 mn) 0 +0% ( mn) +0% (1 mn) s not realstc +0% ( mn) Logsum RoH Logsum/RoH rato Changed Bus fare (decrease and ncrease) Scenaro Decrease/Increase -0% -0% -0% -0% -0% +0% +0% +0% +0% +0% Logsum RoH Logsum/ RoH rato Change Auto (car) operatng costs (decrease and ncrease) Scenaro Decrease/Increase -0% -0% -0% -0% +0% +0% +0% +0% +0% Logsum RoH Logsum/RoH rato

21 Table. Summary of the comparaton of RoH and logsum methodologes Logsum/RoH Parameter Travel Tme Travel Cost Toll BL model = = = = = b = -0.0, c = -0.01, d = Curve of Logsum/RoH wth Change Increase Relevant Polcy publc transport prorty speed control MNL model NL model b = -0.0, c = -0.0, d = b = -0.01, c =-0.0, d = toll or road prcng travel mode cost change 1