TRANSPORTATION DEMANDS IN THE COLUMBIA-SNAKE RIVER BASIN

Transcription

1 The Navgaton Economc Technologes Program March 1, 2006 navgaton economcs technologes TRANSPORTATION DEMANDS IN THE COLUMBIA-SNAKE RIVER BASIN US Army Corps of Engneers IWR Report 06-NETS-R-03

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3 March 1, 2006 navgaton economcs technologes TRANSPORTATION DEMANDS IN THE COLUMBIA-SNAKE RIVER BASIN Prepared by: Kenneth Tran Unversty of Calforna Wesley W. Wlson Unversty of Oregon For the: Insttute for Water Resources U.S. Army Corps of Engneers Alexandra, Vrgna IWR Report 06-NETS-R-03

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5 1. Executve Summary and Introducton Transportaton demands are central to Army Corps of Engneer plannng models. ACE plannng models requre demand structures over a wde range of rates. Over the last three years, the Insttute for Water Resources (IWR) and others have used a varety of approaches to estmate the demand for transportaton by waterways. These studes nclude a revealed- and stated-preference choce model of agrcultural shppers n the Upper Msssspp Rver Valley (Tran and Wlson (2004)), a stated-preference model of annual volumes shpped by Oho Rver Valley shppers of a wde range of commodtes (Stchnava, Wlson, and Burton (2005)), a panel data model of southbound monthly Upper Msssspp corn movements (Boyer and Wlson (2004), and a varety of tme seres models by Dager et al (2005) and Fuller et al. (2005). Whle panel data and tme seres approaches can provde meanngful estmates of revealed demand elastctes, they are lmted n the sense that the estmates are lkely only relevant for the observed range n rates, transt tmes and relablty levels. Ths lmted range of key varables hnders estmaton of demand parameters and forecastng under new crcumstances. The studes that use stated-preference data provde estmates over a wde range of rates, transt tmes, and relablty, whch has the potental to mprove the estmaton of demand parameters and to allow forecastng for polces and waterway mprovements under whch rates and travel tmes may change consderably. However, ths advantage of stated-preference data s mtgated by the possblty that responses by shppers to stated-preference questons may not represent the way that shppers would respond n real-world settngs. Ths trade-off presented by statedpreference data of greater varablty n relevant varables, but the possblty of less

6 realsm n shppers stated response provdes the backdrop and motvaton for the current study. The current study contnues ths stream of research dedcated towards the estmaton of transportaton demands. Ths study addresses drectly the trade-off descrbed above, namely, that stated-preference data provde greater varance n rates and tmes, whch s useful for estmaton and forecastng, and yet shppers responses to stated-preference questons mght not represent ther responses n real world settngs. The current study makes several methodologcal mprovements n the elctaton and analyss of stated-preferences. In partcular, stated-preference questons are utlzed that can be expected to be more realstc for shppers, and hence, more lkely to provde relable nformaton, relatve to standard stated-preference methods. Ths new type of stated-preference queston necesstates the use of a new econometrc method, whch s developed and appled n ths study. The econometrc method combnes each shppers choces n real-world settngs wth ther responses to the new stated-preference questons. Dfferences n shppers responses to stated-preference questons from ther responses n real world stuatons are explctly represented. The data for the study were collected through a survey of shppers n the Columba-Snake Rver Valley, mplemented by the Socal and Economc Scences Research Center at Washngton State Unversty. Eastern Washngton s one of the prmary wheat producng regons n the country and produces prmary soft whte wnter wheat. Over 90 percent of ths wheat travels to ocean termnals located n (Jessup and Casavant). The sample covers shpments from 181 of 391 elgble warehouses, whch represents a 50 percent samplng rate.

7 Shppers were asked to dentfy the optons that were avalable to them for shppng ther gran to, wth the possble optons beng, e.g., truck to Pasco and barge to, truck to a ral termnal and ral to, and so on. The shppers were asked whch of the avalable optons they chose for a recent shpment, whch consttuted the revealed-preference choces of the shppers. Stated-preference questons were asked to determne whether the shpper would choose the same or a dfferent opton under specfed changes n rates, transt tmes, or relablty. The shppers choce model were estmated on the revealed-preference data alone and on the combned revealed- and stated-preference data, utlzng the new method, dscussed above, that approprately accounts for the stated-preference questons. Explanatory varables ncluded the rates, transt tmes, and relablty of the avalable optons, as well as alternatve-specfc constants that capture the average mpact of other factors. Models wth fxed coeffcents were estmated, as well as more general models that allow the coeffcents to vary over shppers, reflectng the fact that dfferent shppers place dfferent values on transt tme and relablty. The prmary fndngs of the analyss are that: 1. Rates, transt tmes and relablty each have statstcally mportant effects on transportaton demands; 2. Elastcty estmates are provded for each opton for a wde of rate, tme and relablty changes. The arc elastctes for rate ncreases range from 1.82 to 0.38, dependng on the alternatve (e.g., barge to versus truck to Pasco and then barge to ) and on the amount of the rate

8 ncrease. Arc elastctes are smaller for transt tme ncreases, rangng from 0.89 to 0.19 dependng on the alternatve and amount of ncrease. Arc elastctes for decreases n relablty are smaller n magntude than those for rate ncreases but larger than those for transt tme ncrease, rangng from 1.51 to 0.51 dependng on the alternatve and the amount by whch relablty decreases. 3. The analyss ndcates that some shppers seem to be captve to ther current mode. About 25 percent of the shppers stated that they had no optons other than the one they currently used. Of those wth optons, our analyss ndcates that about one-thrd of them would not change alternatves f the rates for ther current alternatve were doubled. 4. The estmated models allow the value of tme and relablty to be calculated. We fnd that, on average, shppers value an extra day of transt tme about the same as an extra $1.34 per ton n hgher rates, and ths value vares consderably over shppers. The value of a one percent ncrease n relablty (.e., the chance of the shpment arrvng on tme) s estmated to be $0.16 per ton, on average, wth consderable varance over shppers. 5. The estmated models also allow calculaton of the own-prce elastcty for barge shpments as well as the cross-prce elastcty wth respect to ral rates. Our analyss mples that an own-prce arc elastcty of and a cross-prce arc elastcty wth respect to ral rates of 0.52 (wth both calculated for a ten percent change n rates.)

9 The report s organzed as follows: Secton 2 descrbes the sample of shppers Secton 3 descrbes the estmaton procedure Secton 4 gves the estmaton results Secton 5 provdes elastctes from the estmated models. 2. Sample and Data Descrpton The study examnes agrcultural shpments n the Pacfc Northwest. As dscussed by Jessup and Casavant (2004), Eastern Washngton s one of the prmary wheat producng regons n the U.S. and has the largest wheat-producng county (Whtman Country) n the Unted States. Wthn Eastern Washngton, there are17 gran producng countes of whch fve account for over 75 percent of the state s producton (Jessup and Casavant (2004)). The regon has an nterconnected transportaton system that conssts of a seres of ral lnes and the Columba-Snake rver basn. Most of the wheat (over 90 percent) produced travels to ocean termnals located n or near by ral or barge (Jessup and Casavant (2004)). Whle wheat can flow to other locatons, ths s not a promnent tendency. Ths makes the statstcal methods employed much smpler n that t allows a focus on mode choce rather than both modes and locaton choces. The data employed n the analyss were collected through a survey conducted by the Socal and Economc Scences Research Center at Washngton State Unversty. The survey nstrument and methodology along wth detaled sample summary statstcs are

10 provded and fully descrbed by Jessup and Casavant (2005). The survey was pre-tested and revewed both by academcs and target survey recpents. It was conducted n October of There was a frst malng, a follow-up postcard, and a second malng. Non-responders were also contacted after the second malng. The survey was sent to both gran and non-gran shppers. Gran shppers represent the bulk of the populaton (over 80 percent) and the bulk of the respondents (over 85 percent). There were only two refusals of the 78 frms contacted, and a total of 29 frms that completed the questonnares, representng a total of 181 of an approxmate 391 elgble warehouses. Ths gves nearly a 50 percent response rate. Shppers were asked a set of questons that relate to revealed and stated preference demand modelng. In addton, a set of questons provded characterstcs of the shpper. There are sx generc optons for shppng gran to : 1. Truck to Pasco and Barge to ; 2. Truck to another barge port and barge to ; 3. Ral to ; 4. Truck to a ral termnal and ral to ; 5. Barge to ; and 6. Other. Shppers were asked to consder ther last shpment. Frst, shppers were asked whch of these sx optons were avalable to them for ths shpment and whch opton dd they choose. For each avalable opton, they were asked to provde rates, transt tmes and relablty measures. Transt tmes were to nclude the schedulng, watng tme for

11 equpment, and travel tme. Relablty was measured by askng the shppers to estmate the percentage of tme that shpments lke ths arrve on-tme at the fnal destnaton. Table 1 provdes summary statstcs for shppers responses by opton. As expected, the rate per ton-mle by barge (opton 5, wthout truck access to barge) s the lowest of all optons. It s somewhat unexpected that the transt-tmes are also lowest for ths opton also. However, transt tmes nclude schedulng and watng for equpment, and mult-modal shpments requre added schedulng, watng for equpment, etc. Fnally, movements that nvolve barge-only or a truck-barge combnaton yeld the most relable servce, whle ralroad-alone and truck-ral nvolve the lowest relablty measures. Each shpper was asked what they would have done f the opton they choose were unavalable for sx months. Table 2 provdes a summary of these data. Whle there are some seemng analomes among the responses, e.g., swtchng to the same alternatve chosen, most of these are explaned by dfferent truck optons, dfferent ports to the rver, etc. Note that 51 of 200 respondents (over 25%) report they have no alternatves. A smlarly large share of supposedly captve shppers (.e., wth no alternatves fromn ther chosen mode) was obtaned n a survey of Upper Msssspp rver shppers (Tran and Wlson, 2004). Of those shppers who report no alternatves, most nvolve some form of barge shpments (34 of 51) or shpments to other locatons (17 of 51).

12 Table 1. Revealed Choce Data Summary Avalable Choce Rate Tme Relablty Opton N (% yes) (%) (per tonmle) (days) (%) 1. Truck to Pasco-Barge to Truck to Port-Barge to Ral to Truck to Ral-Ral to Portand Barge to Other Table 2. Revealed Choces and Next Best Alternatve Alternatve Orgnal Choce Total Total Opton Descrpton 1 Truck to Pasco-Barge to 2 Truck to Port-Barge to 3 Ral to 4 Truck to Ral-Ral to 5 Barge to 6 Other 7 No Alternatves avalable As descrbed n secton 1, the standard form of stated-preference questons were not used and an alternatve, more realstc form was used nstead. The usual procedure for stated-preference queston s to present each shpper wth a set of hypothetcal optons from whch they choose one. The rate, transt tme, and relablty of each hypothetcal

13 opton s descrbed, and the respondent s choce among the hypothetcal optons s used to nfer the relatve value placed on rates, tme and relablty. In the current study, we mplemented a procedure that we call sp-off-rp, because the stated-preference (sp) questons are based on the revealed-preference settng and choce of the shpper. Recall that each shpper was asked whch of the sx optons was avalable and whch one they chose for ther last shpment. For the sp-off-rp questons, the shpper was asked whether they would have chosen that opton f ts rate were x% hgher. For example, f the shpper had used barge (opton 4) for ther last shpment, then the shpper was asked Suppose that the rates for barge were 10% hgher than currently. Would you stll choose barge, or would you choose a dfferent opton? If the shpper sad they would choose a dfferent opton, they were asked whch opton they would choose nstead. The percent ncrease n rates was vared over shppers, chosen randomly from 10, 20, 30, 40, 50 and 60 percent changes. Smlar questons were also asked for an ncrease n transt tme and decrease n relablty. Note that these sp-off-rp questons relate to the shppers real-world choce stuaton, unlke standard sp questons that present the shpper wth a set of hypothetcal optons. In answerng the sp-off-rp queston, the shpper s facng the same optons, wth all the same factors affectng ther decson, as they actually faced when makng ther last shpment. The only change from the actual stuaton s n one of the attrbutes of ther chosen opton (rate, tme or relablty); all other factors reman the same. Ths smlarty to the real-world settng that the shpper faces gves them a greater realsm, relatve to standard sp choces, whch can be expected to translate nto more accurate and

14 generalzable estmates of shpper response to changes n rates, transt tmes, and relablty. Table 3 summarzes shppers responses to the sp-off-rp questons. A consderable degree of swtchng s evdenced overall, and the rate changes tend to accrue slghtly more swtchng than the tme and relablty changes. Specfcally, 107 of 140 would swtch n response to a rate ncrease, 98 of 146 would swtch n response to a transt tme ncrease, and 93 of 146 would change n response to a relablty decrease. Fnally, as s standard, the rates of swtchng ncrease wth the level of the change. For example, for those that have rate ncreases of 50 or 60 percent, 68 percent would swtch, whle those wth rate ncreases of 10 or 20 percent, 51 percent would swtch. Table 3. Swtchng Behavor % Change N Rate Tme Relablty Total Swtches/ Total Responses /140 98/146 93/146 In addton to the revealed and stated preference nformaton, the survey also asked the shppers to provde nformaton about ther busness. Ths nformaton ncluded: the length of tme n busness, whether they had access to ral and barge loadng facltes along wth dstances to each f they dd not have access, number of ral cars that can be

15 loaded, etc. Generally, these organzatons have been n busness a long tme. The average number of years n busness was 46 years wth about 90 percent n busness 10 years or more. In terms of loadng facltes, 205 of 206 reported they could load trucks, 91 had drect access to ral, and 25 had drect to barge. It s notable that 11 of 211 had access to all modes, and 106 of 211 had access only to truck. Access to modes s, of course, necessary for some optons, and ths causes the choce set to vary across the shppers. For example, a shpper wth access only to truckng must truck to a rver termnal, to ral, or, n one case, to the area termnals. Of the 91 carrers wth drect access to ral, the average number of ral cars that can be loaded at a gven tme s slghtly more than eght. More mportantly, about 40 percent had ral car capactes of 25 cars or more. Ths s mportant n that there are serous decreases n ral rates wth ncreases n shpment szes e.g., unt car rates are substantally lower than sngle car rates. 3. Choce Model and Estmaton In ths secton, we descrbe the econometrc method that s used to estmate choce models on the revealed-preference (rp) data and the shppers responses to the sp-off-rp questons. The presentaton s largely descrptve. For nterested readers, we provde a techncal report wth complete detals (Tran and Wlson (2005)). As stated above, the sp-off-rp questons provde greater realsm than standard sp questons, snce the sp-off-rp questons relate specfcally to the stuaton that the shpper faced for ther last shpment. However, ths realsm has mplcatons for the econometrc technques that are used to analyze the data. The sp-off-rp questons ask the shpper whch opton they would choose n the rp settng f the rate, tme, or relablty of the opton they actually chose

16 were changed. These questons have two features that need to be addressed n the estmaton. Frst, when answerng the sp-off-rp questons, the shpper s choosng among optons n the rp settng. Ths mples that the attrbutes of the optons n the rp settng, ncludng, mportantly, the attrbutes that are not observed by the researcher, affect the shpper s answer to the sp-off-rp questons. Stated n econometrc terms: The unobserved factors assocated wth each opton n the rp settng can be expected to enter the shpper s evaluaton of these optons when answerng the sp-off-rp questons. Second, the sp-off-rp questons ask the respondent about a change n the rate, tme or relablty of the opton that was chosen n the rp settng. In econometrc terms: The sp-off-rp questons are condtonal on the outcome of the rp choce. Ths condtonalty mples that the dstrbuton of unobserved attrbutes that enter the shpper s responses to the spoff-rp responses s not the uncondtonal dstrbuton, as n standard choce models, but rather the dstrbuton condtonal on the shppers rp choce. The econometrc method that we develop and apply ncorporates both of these mplcatons (Tran and Wlson (2005)). In partcular, the unobserved factors n the rp settng enters the model of the shpper s response to the sp-off-rp questons, and the probablty of each possble response s derved based on the condtonal dstrbuton of these unobserved factors, condtonal on the shpper s choce n the rp settng. We provde below the specfcaton of the model. We frst descrbe a verson wth fxed coeffcents for rate, tme and relablty. We then generalze the model to allow for random coeffcents, reflectng the fact that the relatve value of rates, tme, and relablty dffers over shppers. The next subsectons present the alternatve estmaton strateges n more detal and outlnes the choce framework. Essentally, shppers choose from the

17 array of optons n a manner that maxmzes ther payoffs whch are taken as a functon of rates, tmes of transt and relablty. The specfc form of the payoffs vares accordng to the treatment of the unknown parameters that are estmated. For readers nterested prmarly n the results may choose to skp to secton Fxed coeffcents Wth fxed coeffcents, the shpper s choce n the rp settng s a standard logt model. The shpper faces J alternatves for ts last shpment. The utlty of each alternatve depends on observed varables, namely, rate, transt tme, and relablty, as well as unobserved factors. 1 The observed varables are denoted x for alternatve (wth the subscrpt for the shpper omtted for smplcty), and the unobserved random factors are denoted collectvely ε as for alternatve. Utlty of alternatve s denoted U =x +ε. Under the assumpton that each ε s dstrbuted d extreme value, the probablty that the shpper chooses alternatve s the logt formula: P = e x e x The researcher presents the shpper wth a seres of sp-off-rp questons that are constructed on the bass of the shpper's rp choce. We provde more general notaton than s necessary for our partcular sp-off-rp questons, to facltate the use of the method n other settngs that mght use dfferent types of sp-off-rp questons. (For example, our questons ask the shpper about a change that makes the opton they chose worse; an 1 The model s framed n a utlty context although the term proft maxmzaton can be employed so long as there are no agency ssues.e., the shpper makes decsons consstent wth the frm s obectve of maxmzng proft.

18 alternatve would be to ask the shpper about a change that mproves an opton that they dd not choose.) The researcher asks T sp-off-rp questons, wth attrbutes alternatve n queston t based on alternatve havng been chosen n the rp settng. For x~ t for our questons, ~ x x for the alternatve that was chosen n the rp settng, whle t ~ x t = x for the non-chosen alternatve; however, more general specfcatons of x~ t possble. The shpper s asked to choose among the alternatves n response to each sp-off-rp queston. The shpper's choce can be affected by unobserved factors that dd not arse n the rp settng, reflectng, e.g., nattenton by the agent to the task, pure randomness n the agent's responses, or other quxotc aspects of the sp choces. These factors are labeled as η for alternatve. The relatve mportance of these factors wll be estmated, as descrbed below. The shpper obtans utlty W = ~ + ε + η t x t t from alternatve n sp-off-rp queston t. That s, the shpper evaluates each alternatve usng the same utlty coeffcents and wth the the same unobserved attrbutes as n the rp settng, wth the addton of new errors that reflect quxotc aspects of the shppers responses to the sp-off-rp questons. In response to each sp-off-rp queston, the shpper chooses the alternatve wth the greatest utlty. To complete the model, we assume that each η t s d extreme value wth scale 1/α, whch s proportonal to the standard devaton of these errors. A large value of parameter α ndcates that there are few quxotc aspects to the sp-off-rp responses and that the shppers choose essentally the same as they would n a rp stuaton under the new attrbutes. Utlty can be equvalently expressed as W = α ~ + αε + η t where now η t s d extreme value wth unt scale. t x t The sp-off-rp responses are, therefore, standard logts wth ε as an extra explanatory

19 varable. Snce the ε 's are not observed, these logts must be ntegrated over ther condtonal dstrbuton, as follows. The chosen alternatve n response to queston t s denoted k t and vector k = k,, k collects the sequence of responses to the sp-off-rp 1 T questons. The probablty of alternatve k t n response to sp-off-rp queston t, condtonal on beng chosen n the rp choce s: P k t = Pr ob = [ ~ ~ αx + αε + η > αx + αε + η k x + ε > x + ε ] α~ xk αε e t t + k t α~ x + αε e k t t t k k f ( ε x k t k + ε > x t + ε ) dε. Ths probablty s a mxed logt (Tran, 2003), mxed over the condtonal dstrbuton of t t ε = ε,. It can be smulated by takng draws from the dstrbuton of ε, 1, ε J calculatng the logt formula for each draw, and averagng the results. Draws of ε from ts condtonal densty are easy to obtan, gven the convenent form of the condtonal densty of extreme value devates (Tran and Wlson, 2005.) In partcular, the densty of ε condtonal on alternatve beng chosen n the rp settng s extreme value wth mean shfted up by -ln(p ). A draw s obtaned as -ln(p )-ln(-ln(µ)) where µ s a draw from a unform between zero and one. Condtonal on ε and on beng chosen, the densty of each ε, s extreme value truncated above at x x + ε. A draw s obtaned as -ln(-ln(m(ε )µ)), where µ s a draw from a unform between zero and one, and m ε ) = exp( exp( ( x x + ε )). Snce draws of ε are constructed ( analytcally from draws from a unform (as opposed to by accept-reect methods), varance reducton procedures can readly be appled, such as Halton draws (Bhat, 2001,

20 Tran, 2003), (t,m,s)-nets (Sandor and Tran, 2003), and modfed Latn hypercube samplng (Hess et al, 2004.) Combnng these results, and usng the ndependence of η t over t, the probablty of the agent's rp choce and the sequence of responses to the sp-off-rp questons s: P k = e ε f ( ε x + ε > x + ε ) dε e [ L1 ( ) L ( ε )] T x x where L t ~ αx t + αε kt kt e ( ε ) = α~ x e + t αε. Ths probablty s smulated by takng draws of ε from ts condtonal dstrbuton as descrbed above, calculatng the product of logts wthn brackets for each draw, averagng the results, and then multplyng by the logt probablty of the rp choce. Note that as α the smulator for the responses to the sp-off-rp questons approaches an accept-reect smulator based on the shpper s utlty functon n the rp settng wth no addtonal errors (Mcfadden, 1989; Tran, 2003, sectons and 6.5). Seen n ths lght, for large α, the logt formula for the responses to the sp-off-rp questons can be seen as a smoothed accept-reect smulator based on the true utlty ~ x + ε, whose purpose s to mprove numercal optmzaton rather than havng a t behavoral nterpretaton. 3.2 Random coeffcents Utlty s as above except that s now random wth densty h() that depends on parameters (not gven n the notaton) that represent, e.g., the mean and varance of

21 over shppers. The probablty for the rp choce s the logt formula ntegrated over the densty of : = d h L P ) ( ) ( where = x x e e L ) ( Ths s a standard mxed logt. By Bayes rule, the densty of condtonal on beng chosen s. ) / ( ) ( P h L For the responses to the sp-off-rp questons, let ), ( ε t L be the same as ) ( ε t L defned above but wth treated as an argument. The probablty of the sequence of responses to the sp-off-rp questons s ε ε ε ε ε ε ε ε d d x x h x x f L L P T k ) ( ), ( ), ( ), ( 1 + > + + > + = T P d d h L x x f L L / ) ( ) ( ), ( ), ( ), ( 1 ε ε ε ε ε ε + > + =. The probablty of the rp choce and the sequence of responses to the sp-off-rp questons s P tmes the above formula, whch s: ε ε ε ε ε ε d d h L x x f L L P T k ) ( ) ( ), ( ), ( ), ( 1 + > + =. Ths probablty s smulated by: 1. Draw a value of from ts uncondtonal densty. 2. Calculate the logt probabluty for the rp choce usng ths. 3. Draw numerous values of ε from ts condtonal densty gven usng the method descrbed above. Caluclate the product of logt formulas for the responses to the sp-off-rp questons for each draw of and average the results.

22 4. Multply the result from step 3 by the result from step Repeat steps 1-4 numerous tmes and average the results. In theo ry, only one draw n step 3 s requred for each draw n step 1; however, takng mo re than one draw n step 3 mproves accuracy for each draw of and s relatvely nexpensve from a computatonal perspectve. 4. Estmaton Results Table 4 gves the estmated parameters of a standard logt model that was estmated on the rp data alone. The estmated coeffcents of rate, tme, and relablty all take the expected sgns, and the rate and relablty coeffcents are sgnfcant at the 95 percent confdence level. The ratos of coeffcents mply that a day of extra transt tme s consdered equvalent to about 27 cents per ton n hgher rates and that decreasng relablty by 1 percentage pont s consdered equvalent to 26 cents per ton n hgher rates. These two estmated values beng nearly the same seems unreasonable. Frst, note that, absent rsk averson, the expected value of a one percent ncrease n the chance of a one-day delay s 1/100 the expected value of one day of extra transt tme. Whle unexpected delays can be more burdensome than an antcpated ncrease n transt tme, and the delay may be for more than a day, t seems doubtful that these factors are suffcent to counteract the 100-fold dfference n these expected values. Second, prevous studes on shppers' values (Shnghal and Fowkes, 2002, and Bergantno and Bols, 2005) have found that that a day of tme savngs s worth more than a one percent reducton n the chance of delay.

23 Table 4: Fxed Coeffcents Model on Revealed-Preference Data Explanatory Varable Estmated parameter Standard error T-statstc Rate, n dollars per ton Tme, n days Relablty Constant for alt Constant for alt Constant for alt Constant for alt Constant for alt 6 Mean log-lkelhood Table 5 gves the estmated parameters of a fxed-coeffcents logt estmated on the rp data along wth the responses to the sp-off-rp questons. Smulaton was performed wth 1000 pseudo-random draws of the condtonal extreme value terms, wth dfferent draws for each observaton. As expected, the level of sgnfcance for the coeffcents of rate, tme, and relablty rse consderably. The scale parameter α s estmated to be about 5.6, whch mples that the standard devaton of the addtonal unobserved porton of utlty that affects the responses to the sp-off-rp questons s less than a ffth as large as the standard devaton of unobserved utlty n the rp choces. As dscussed above, f there were no quxotc aspects to the responses to the sp-off-rp questons, such that shppers answered the same as n the rp settng wth the changed attrbutes, then the standard devaton would be zero (α unbounded hgh.) The relatvely small estmated standard devaton mples that respondents were apparently payng careful attenton to the sp-off- rp questons and answerng smlarly to how they would behave n the rp settng.

24 Table 5: Fxed Coeffcents Model on RP and SP-off-RP Data Explanatory Varable Estmated parameter Standard error T-statstc Rate, n dollars per ton Tme, n days Relablty Constant for alt Constant for alt Constant for alt Constant for alt Constant for alt 6 Scale of sp error (α) Mean log-lkelhood The relatv e values of tme and relablty seem more reasonable when the responses to the sp-off-rp questons are utlzed. In partcular, the value of tme rses from 27 to 71 cents per ton, and the value of relablty drops from 26 to 14 cents per ton. The magntudes of these changes, though large from a polcy perspectve, are not unreasonable gven the standard errors n Table 4. In fact, the changes confrm the purpose of utlzng the sp-off-rp questons, whch s to augment rp data when the rp data contan nsuffcent varaton to estmate parameters precsely. We next examne a random coeffcents specfcaton. The tme and relablty coeffcents are specfed to be dstrbuted normally wth censorng at zero. 2 That s, the coeffcent of tme s specfed as the mnmum of 0 and 2, where 2 s normally dstrbuted wth mean and standard devaton that are estmated; and the coeffcent of relablty s the maxmum of 0 and 3 wth normal 3. Ths specfcaton assures that the tme and relablty coeffcents have the expected sgn throughout ther support. Also, by havng a mass at zero, the specfcaton allows for the possblty that some shppers do 2 See Tran and Sonner (2005) for a dscusson and applcaton of censored normals and other dstrbutons wth bounded support wthn mxed logt models.

25 not care about tme or relablty (at least wthn the ranges that are relevant.) The rate coeffcent s held fxed, followng Goett et al. (2000) and Hensher et al., (2005a,b), whch mples that the dstrbuton of the value of tme and relablty s smply the dstrbuton of these varables' coeffcents scaled by the fxed prce coeffcent. 3 When we attempted to estmate the random coeffcents model wth all parameters free, the value of α rose wthout bound n the teratve maxmzaton process. Ths result, taken at face value, mples that no addtonal errors enter the sp choces, beyond the unobserved porton of utlty n the rp choces. Snce a bounded $\alpha$ was obtaned wth the fxed coeffcents model, the unbounded value n the random coeffcents model mples that dfferences n coeffcents account for the sp responses that seem quxotc n a fxed coeffcents model. That s, sp responses that appear quxotc when all shppers are assumed to have the same coeffcents for rate, tme and relablty are found not actually to be quxotc when shppers are allowed to have dfferent coeffcents. Table 6 gves the estmated parameters for a random coeffcents model wth α set at 10. Smulaton was performed wth 1000 draws of the random coeffcents and 10 draws of the extreme value terms for each draw of the random coeffcents (for 10,000 draws of the extreme value terms n total for each observaton.) As descrbed above, the large value of α can be nterpreted as provdng a logt-smoothed accept-reect smulator of the probablty of the responses to the sp-off-rp questons, whch ads numercal maxmzaton wthout reflectng the exstence of any addtonal errors. The estmated 3 Ruud (1996) ponts out that a random coeffcents model wth all random coeffcents s nearly undentfed emprcally, especally wth only one or a few observed choces per agent, snce only ratos of coeffcents are behavorally meanngful. Holdng the prce coeffcent fxed asssts wth emprcal dentfcaton. Tran and Weeks (2005) dscuss reasons for and aganst holdng the prce coeffcent fxed and compare estmaton methods when the prce coeffcent s random.

26 mean value of tme s $1.34 per ton wth a standard devaton of 0.89, and the estmated mean value of relablty s 16 cents wth a standard devaton of 7.2 cents. The mean value of tme s hgher than that obtaned wth fxed coeffcents ($1.34 versus $0.71), whle the mean value of relablty s about the same (16 cents versus 14 cents.) Fewer than 9 percent of shppers are estmated not to care about transt tme (.e., the mass at zero s less than 0.09), and fewer than 2 percent are estmated not to care about relablty. Table 6: Random Coeffcents Model on RP and SP-off-RP Data Explanatory Varable Estmated parameter Standard error T-statstc Rate, n dollars per ton Tme: mean Tme: standard devaton Relablty: mean Relablty: standard devaton Constant for alt Constant for alt Constant for alt Constant for alt Constant for alt Mean log-lkelhood Swtchng Rates and Elastctes for Each Altern atve The estmated model n Table 6 s used to forecast the mpact of changes n rates, tmes, and relablty for each of the sx alternatves. We consder frst the forecasted mpact of rate ncreases. To forecast ths mpact, the rate for each of the sx alternatves was ncreased by a gven percentage, and the estmated model was used to calculate the change n the share of shppers choosng that alternatve. Table 7 gves the percent of shppers that are predcted to change alternatves when the rate for ther chosen

27 alternatve s rased. Consder, for example, the value of 18.2 that s gven for a 10 percent rate ncrease for truck to Pasco, barge to. Ths number s nterpreted as follows: f the rate for shpments by truck to Pasco and then barge to rose by 10 percent, and the rates for other alternatves remaned the same, then the model predcts that 18.2 percent of the shppers who currently use truck to Pasco and barge to would swtch to another alternatve. Table 7: Percent of shppers who are predcted to swtch n response to Rate ncreases Percent Truck to Truck to ncrease Pasco, Port, barge barge to to Ral to Truck to ral, Ral to Barge to Other As expected, larger ncreases n rates nduces greater swtchng. For truck to Pasc o and barge to, a 10 percent ncrease n rates nd uces 18.2 percent of shppers to swtch to another alternatve, whle a 50 percent ncrease n rates nduces 65.8 percent of the shppers to swtch. Note, however, that some shppers do not swtch even when rates are rased qute consderably. For example, 13.2 percent of shppers who truck to Pasco and barge to would contnue to do so even f the rates for that alternatve were doubled.

28 The smallest swtch rates are obtaned for shppers who barge to wthout usng truck access (.e., shppers who are at a rver port.) For these shppers, a 10 percent ncrease n rates nduces only 4 percent to swtch to another alternatve. When rates are doubled, nearly two-thrds of these shppers are predcted to contnue usng barge to. As ust stated, the swtch rates for barge to are lower than for the other optons. However, comparsons of swtch rates across optons need to be consdered careful ly. The swtch rate for any alternatve represents the share of shppers who would swtch from that alternatve n response to a change n the rate for that alternatve, ncludng the truck access to barge or ral f the alternatve ncludes such access. For example, the swtch rate nduced by a 10 percent rate ncrease s lower for barge to than for truck to Pasco/barge to. However, the rate for truck to Pasco/barge to ncludes the rates for both the truck and barge portons of the shpment. If the barge rate rose by 10 percent and the truck rate remaned the same, then the total rate for truck to Pasco/barge to would rse by less than 10 percent. Suppose that truck access accounts for half of the total rate of the truck to Pasco/barge to. Then a 10 percent ncrease n barge rates would represent n a 5 percent ncrease n the total rate for truck to Pasco/barge to. The swtch rate for a 10% ncrease n barge rates, holdng truck rates constant, would therefore be about half that gven n the table: 9.1 nstead of Ths swtch rate wth respect to only barge rates s closer to that for barge to, whch does not have truck access. Table 8 gves the arc elastctes that are mpled by the swtchng rates gven n Table 7. For example, consder the elastcty of 1.82 for a 10 percent ncrease n the rate

29 for Truck to port, barge to. As shown n Table 7, the model predcts that 18.2 precent of the shppers who currently truck to Pasco and barge to wll swtch to a dfferent alternatve f the rates for that opton rose by 10 percent. Snce there s a percent reducton n response to a 10 percent ncrease n rates, the arc elastcty s 1.82 (18.2/10). The elastces decrease somewhat as rates ncrease. For example, the arc elastcty for a 20 percent ncrease n rates s lower than that for a 10 percent ncrease n rates. T hs relaton does not mply, of course, that larger rate ncreases nduce less swtchng than smaller rate ncreases. Rather, t mples that the number of shppers who swtch n response to the rate ncreases rses less than proportonally wth the sze of the rate ncrease. For example, consder a 20 percent rate ncrease for the opton of Truck to Pasco, barge to. The arc elastcty s 1.69, whch s smaller than the elastcty of 1.82 from a 10 percent rate ncrease. The elastcty of 1.69 means that, as gven n Table 7, that 33.8 percent of the shppers who chose ths opton would swtch f the rate for ths opton rose by 20 percent (snce 33.8/20=1.69.) A 10 percent rate ncrease nduces 18.2 percent to swtch and a 20 percent rate ncrease nduces 33.8 percent to swtch: the share who swtch s hgher wth a 20 percent rate ncrease than a 10 percent rate ncrease, but s not twce as hgh. As a result, the arc elastcty s lower wth a 20 percent rate ncrease than a 10 percent rate ncrease.

30 Table 8: Arc Elastctes wth respect to Rates Percent ncrease Truck to Pasco, barge to Truck to Port, barge to Ral to Truck to ral, Ral to Barge to Other Tables 9 and 10 gve swtch rates and arc elastctes for ncreases n transt tmes. These swtch rates and elasttces are lower than those for comparable ncreases n rates. Ths fndng suggests, as expected, that shppers are more responsve to changes n rates than changes n transt tme, though they are response to both.

31 Table 9: Percent of shppers who are predcted to swtch n response to Transt Tme ncreases Percent ncrease Truck to Pasco, barge to Truck to Port, barge to Ral to Truck to ral, Ral to Barge to Other Table 10: Arc Elastctes wth respect to Transt Tmes Percent ncrease Truck to Pasco, barge to Truck to Port, barge to Ral to Truck to ral, Ral to Barge to Other Tables 11 and 12 gve swtchng rates and arc elastctes for decreases n the relablty of shpments, where relablty s represented as the chance that the shppment wll arrve on tme. The swtch rates and elastctes are lower than those for rates but hgher than those for transt tme. Ths fndng that relablty elastctes are larger than

32 transt tme elastctes suggests that shppers are more concerned that the shpment arrves when scheduled than n the amount of scheduled shpment tme. Note that for some alternatves the arc elastctes are nearly the same for all levels of changes n relablty. For example, the arc elastcty for truck to port, barge to s 0.52 or 0.51 for all percent changes n relablty. Ths relaton mples that the percent of shppers who swtch n response to a reducton n relablty s essentally proportonal to the percent by whch relablty s reduced. For truck to port\barge to, 5.2 percent of shppers are predcted to swtch n response to a 10 percent reducton n relablty, and 10.4 percent twce as many are predcted to swtch n response to a 20 percent reducton n relablty. Snce the percent swtchng doubles when the percent change n relablty doubles, the arc elastcty s the same. Table 11: Percent of shppers who are predcted to swtch n response to Relablty decreases Percent ncrease Truck to Pasco, barge to Truck to Port, barge to Ral to Truck to ral, Ral to Barge to Other

33 Table 12: Arc Elastctes wth respect to Relablty Percent ncrease Truck to Pasco, barge to Truck to Port, barge to Ral to Truck to ral, Ral to Barge to Other Barge and Ral Elastctes The elastctes presented n the prevous secton pertan to the sx alternatves for shppng n the Columba/Snake rver basn. However, many of the plannng models rest on barge elaststctes and ral elasttces. There are three dfferent optons that nvolve usng barge to, namely: Truck to Pasco-Barge to, Truck to port-barge to, and Barge to. The elastcty for barge to s calculated by ncreasng the barge rate component of the total rate for these three optons and usng the model to predct the change n shares for these three optons combned. Smlarly, two optons nvolve ral to, namely: Ral to, and Truck to ral-ral to. The elastcty for ral to s calculated by ncreasng the ral rate component of the total rate for these two optons and usng the model to predct the change n shares for the two optons combned. In the data, we observe the truck and the barge porton of the total rate for each opton. For the Truck to Pasco-Barge to, the average proporton of barge costs to total costs s.45, whle for the Truck to port-barge to Portand, the average proporton

34 of barge costs to total costs s.62. Of course, the proporton of rate that s barge for the Barge to opton s 1.00 (.e., the entre rate s for barge.) Smlarly, for ral, the average proporton of ral costs to total costs s.73 for Truck to ral-ral to and 1.0 for Ral to. Table 13 presents the forecasted mpact of a 10 percent ncrease n barge rates (that s, for the porton of total costs that are for barge) and, n the lower part of the table, the mpact of a 10 percent ncrease n ral rates (that s, for the porton of total costs that are for ral.) If rates for barge to rose by 10 percent, the share of shppers usng barge would fall from to 0.555, for a declne of Ths mples that only 3.45 percent (=(0.02/0.575)*100) of the shppers who currently use barge to would swtch away from barge. Most of the shppers who swtch are forecasted to swtch to an opton that uses ral to. The share of shppers who use ral to s forecast to ncrease from to 0.429, for a rse of 0.019, whch consttutes nearly all of the barge declne of Only a very small share of shppers are forecasted to swtch to an alternatve other than barge or ral to : the share for the other opton rses by only The arc elastctes are calculated as the percent change n shares dvded by 10 snce the forecasts are for a 10 percent rse n barge rates. The own-rate elastcty for barge s very low: only The cross-rate elastcty of ral wth respect to barge rates s also low: (Note that the sgns of the elastctes are retaned n the current secton, snce own- and cross-elastctes are beng reported, whle n the prevous secton whch reports only own-elastctes, the sgns are not retaned for convenence.)

35 Table 13: Forecasted Impacts of a 10 Percent Increase n Barge or Ral Rates Barge Ral Other Change n barge rates: Shares before change Forecasted shares after change Percent change n shares Arc elastctes Change n ral rates: Shares before change Forecasted shares after change Percent change n shares Arc elastctes If rates for ral to rose by 10 percent, the share of shppers usng ral would fall from to 0.378, for a declne of Ths mples that 7.67 percent (=(0.032/0.410)*100) of the shppers who currently use ral to would swtch away from ral. Most of the shppers who swtch are forecast to swtch to an opton that uses barge to. The share of shppers who use barge to s forecast to ncrease from to 0.605, for a rse of 0.030, whch consttutes nearly all of the ral declne of The remanng share represents shppers who swtch from ral to an opton other than barge or ral to. The own-rate elastcty s hgher for ral than barge, but s stll low: the elastcty of ral share wth respect to the ral rate s -0.77, whch s about twce as large n magntude as the own-rate elastcty for barge. 6. Summary and Conclusons The demand for transportaton by mode s an essental part of plannng nfrastructure. For plannng nfrastructure, there s a need not only for demand functons by mode, but also for a wde varety dfferent shpment attrbutes such as rates and transt tmes. Often, revealed data do not provde sgnfcant varaton n the attrbutes. Ths means that the

36 demand functons are more dffcult to estmate precsely and the range of attrbutes (rates) over whch the estmaton occurs does not concde wth the rate of attrbutes (rates) needed for plannng. Whle stated preference methods overcome both dffcultes, they are often crtczed for presentng the decson-maker wth hypothetcal, and perhaps, rrelevant alternatves. In ths paper, we use a methodology that employs both types of data. Specfcally, we ground the stated preference nformaton n the revealed choce made by the shpper. The stated preference nformaton s drectly ted to the revealed choces made by the shpper, crcumventng the rrelevance ssue and, yet, provdng suffcent varaton n the attrbutes whch allow for precse estmaton of demand parameters and provdes estmates over a wde range of attrbute values necessary for plannng. In ths report, the methods are appled to the shpment of agrcultural commodtes from eastern Washngton. Almost all of the shpments travel to, makng the choce of locaton largely rrelevant. On dscusson wth ndustry analysts, sx dfferent optons account for the shpments. These optons nclude both barge and ral only alternatves as well as optons that nvolve truck to access ether barge or ral modes. We framed the choce of whch alternatve to use n terms of rates, transt tmes and relablty of each opton and calculated elastctes wth respect to each attrbute. We found that elastctes vary wth the attrbute and the level of the rate change. For rates, elastctes range from.38 to 1.82; for transt tmes, elasttces range from.18 to.89; and for relablty, elastctes range from.51 to The elastcty estmates provded are defned for each opton. In the fnal secton, we derve estmates for the elastcty of barge and ral transportaton. In partcular, there

37 were three optons that nvolved barge and two nvolvng ral. Barge rates were rased for each of these optons, and elastctes calculated; and smlarly for ral rates. The results mply that both barge and ral are nelastc, wth barge beng more nelastc than ral. In partcular, the arc elastcty of the number of shppers usng barge to wth respect to a ten percent rse n the rate for barge to s 0.34 (n magntude). The comparable elastcty for ral use wth respect to ral rate s Fnally, the quantty shpped by barge depends on the rates of alternatve modes e.g., ral. Our analyss estmates that a ten percent ncrease n ral rates wll ncrease barge demand by about 5 percent, for an arc cross-elastcty of 0.5. These fndngs are of drect relevance to the Army Plannng Models. Frst, t provdes a drect connecton between choce modelng and the elastcty of barge transportaton. The results mply low elasttctes wth respect to barge rate. The elastctes are nevertheless hgher than those used n the Army Corps Modelng, whch assume a perfectly nelastc demand up to a threshold. Second, we provde drect nformaton on the cross-prce elastcty of demand between ral and barge. Generally, n the Army Corps plannng models, barge demands are constant to a threshold, above whch all shfts to ral. The results suggest that barge and ral are substtutes, wth changes n ral rates affectng barge demand and vce versa.