ESTIMATION OF THE DEMAND FOR GRAIN TRANSPORTATION IN NORTH DAKOTA

Transcription

1 ESTIMATION OF THE DEMAND FOR GRAIN TRANSPORTATION IN NORTH DAKOTA A Thess Submtted to the Graduate Faculty of the North Dakota State Unversty of Agrculture and Appled Scence By Alan Gabrel Dybng In Partal Fulfllment of the Requrements for the Degree of MASTER OF SCIENCE Major Department: Agrbusness and Appled Economcs November 2002 Fargo, North Dakota

2 ABSTRACT Dybng, Alan Gabrel; M.S.; Department of Agrbusness and Appled Economcs, College of Agrculture, Food Systems, and Natural Resources; North Dakota State Unversty; November Estmaton of the Demand for Gran Transportaton n North Dakota. Major Professor: Dr. John Btzan. The prmary study objectve was to estmate the demand elastctes for ral and truck transportaton for gran from North Dakota to Mnneapols and Duluth. Gran movement data, as well as modal rate and characterstc data, were used to estmate the demand for gran transportaton. Demand for transportaton s treated as a derved demand and s estmated from a cost approach. Ths study utlzed the translog cost model for estmaton. From ths model, the elastctes were estmated. The elastcty estmates ndcate that ral s the domnant mode for gran shpments from North Dakota to Mnneapols and Duluth. The elastctes for ral and truck show that the demand for ral transportaton s nelastc whle the demand for truck transportaton s elastc. These results ndcate that truckng frms could ncrease revenue by decreasng prces. However, they do not, whch ndcates that the truckng ndustry s prcng near margnal cost. The ral ndustry s facng an nelastc demand, and by ncreasng rates, revenue could be ncreased. As wth the truckng example, ral frms do not. Ths practce ndcates that ndrect regulaton and other factors may be mantanng current ral rates.

3 v ACKNOWLEDGMENTS I wsh to express my sncere apprecaton to North Dakota State Unversty and especally to my advser, Dr. John Btzan, and the staff of the Department of Agrbusness and Appled Economcs along wth the Upper Great Plans Transportaton Insttute. It was through ther professonal gudance and assstance that I was able to complete my graduate studes. Specal recognton s gven to Dr. Denver Tollver, Dr. Wllam Wlson, Dr. Jm Norrs, and Dr. Won Koo for ther constructve crtcsm n revewng ths thess. Fnally, I wsh to express my apprecaton to my frends and famly for ther assstance and support through my undergraduate and graduate studes. Alf and Agnes Dybng, Wejun Huang, Heather Gbb, Sang Moon, Napoleon Tapo, Robert Madsen, and Tamara VanWechel are a great asset to have for famly and frends.

4 v TABLE OF CONTENTS ABSTRACT... ACKNOWLEDGMENTS...v LIST OF TABLES...v LIST OF FIGURES...v CHAPTER I. INTRODUCTION...1 Need for Study...1 Problem and Objectve of Study...4 Hypothess...5 Thess Organzaton...6 CHAPTER II. LITERATURE REVIEW...7 Mathematcal Programmng Models...9 Ad Hoc Models...10 Models of Modal Choce...13 Derved Demand Models...19 CHAPTER III. METHODOLOGY AND DATA...23 Background Informaton...23 Derved Demand Theory...25 Examned Factors Affectng Demand...25 Theoretcal Background...26 Model Specfcaton...31

5 v TABLE OF CONTENTS (Contnued) Estmaton Procedures...32 Data Sources...33 CHAPTER IV. RESULTS...35 Descrptve Results...35 Results of Regresson Analyss...39 Elastcty Estmates...48 CHAPTER V. SUMMARY AND CONCLUSIONS...55 Reasons for Study...55 Objectves...56 Data Sources...56 Methodology...57 Conclusons and Implcatons...57 Servce Characterstc Elastctes...60 Lmtatons and Suggestons for Further Study...62 BIBLIOGRAPHY...63

6 v LIST OF TABLES Table Page 2.1 Comparson of Elastcty Estmates by Study Share of Specfc Commodtes from North Dakota to Mnneapols and Duluth, Modal Shares from North Dakota by Commodty and Destnaton, Shares of Transportaton Costs from North Dakota by Commodty and Destnaton, Parameter Estmates for Wheat to Mnneapols Model Usng 3SLS Estmaton Parameter Estmates for Wheat to Duluth Model Usng 3SLS Estmaton Parameter Estmates for Durum to Mnneapols Model Usng 3SLS Estmaton Parameter Estmates for Durum to Duluth Model Usng 3SLS Estmaton Parameter Estmates for Barley to Mnneapols Model Usng 3SLS Estmaton Parameter Estmates for Barley to Duluth Model Usng SUR Estmaton Elastcty Estmates by Commodty and Destnaton Estmates of Modal Elastctes for Gran Shpments by CRD (at Mean Levels)...54

7 v LIST OF FIGURES Fgure Page 3.1 Map of North Dakota Crop Reportng Dstrcts Average Elevator Classfcaton by CRD Shpments to Mnneapols and Duluth by CRD and Commodty Demonstraton of the Effects of Increased Fuel Prces Demonstraton of the Impact of Lnehaul vs. Termnal Costs...61

8 1 CHAPTER I INTRODUCTION North Dakota s the leadng state n the Unted States n producton of sprng wheat, durum wheat, and barley. Accordng to the North Dakota Agrcultural Statstcs Servce, North Dakota s producton of sprng wheat, durum wheat, and barley n 2000 accounts for 42%, 71%, and 31% of the Unted States total producton for these commodtes respectvely. Of the total producton for these commodtes n , 84-95% s shpped outsde the state of North Dakota to processors or termnal markets (Vachal 2001). Ths volume of gran shpments demonstrates the mportance of gran transportaton to the marketng of North Dakota s commodtes. Most elevators face two optons for gran transportaton: truck and ral servce. The decson on whch mode to choose s dependent on many factors, most mportantly of whch s the rate assocated wth each mode. Cost mnmzaton s key when makng mode choce decsons for shppng gran. Shpment and elevator characterstcs play a role n the selecton of modal choce as well. They determne whether an elevator can take advantage of dscounted rates, whether addtonal shpments are needed, geographc locaton of termnals, and the nature of servces avalable. Need for Study The study of the demand for gran transportaton n North Dakota s not a new subject. However, the most recent study dates back to It s lkely that the compettve envronment for modal shares has changed n 20 years, whch ths study ntends to ascertan.

9 2 Estmaton of the elastcty of demand for each shpment mode wll be a useful tool for understandng the nature of ral-truck competton. As mentoned prevously, most North Dakota elevators face two transportaton choces: truck and ral. If one mode domnates the other, such as truck domnatng ral servce, t s lkely to be ndcated n the elastcty of demand for that mode. If the mode s domnated by ts compettor, t wll have a hgh elastcty. A hgh elastcty shows that a small ncrease n prce causes a shft to the competng mode. Moreover, demand elastctes at dfferent shpment dstances wll provde nsght nto the dstances where ral and truck compete. A current and accurate estmaton of the elastcty of demand for transportaton servces s also useful for regulatory purposes. When decdng approprate prces for transportaton servces for regulaton, the elastcty of demand s useful for determnng the amount of dead weght loss (DWL) to socety from varous prcng alternatves and the effect of any proposed regulated prces on socal welfare. In cases where the frm experences ncreasng returns to scale, the regulator cannot force margnal cost prcng snce t would result n losses to the frm. However, a second best soluton s possble by settng prce nversely to the elastcty of demand. Ths practce s referred to as Ramsey Prcng, and when frms have ncreasng returns to scale (MC<AC), Ramsey Prcng can be used to mnmze DWL wthout excessve njury to provder frms. The market structure due to recent ralroad mergers s another ssue whch regulators are studyng. Frms n the ralroad ndustry are characterzed as havng ncreasng returns to scale. If a frm does have ncreasng returns to scale, t means that

10 3 the frm may be able to provde servce at a lower cost than other frms. Increasng returns to scale mples that there are excess resource costs used to produce a gven quantty of servce. If further mergers are allowed to take place, the excess resource costs can be mnmzed, provdng further economc effcency to the ndustry. The mnmzaton of these costs can mprove socal welfare, whch may offset large prce effects from ncreases n market power. The degree to whch these effects may happen s dependent on the demand for transportaton. Knowledge of the elastcty of demand s needed for a transportaton frm to maxmze profts. The elastcty of demand for transportaton would ndcate what the effects of prcng changes would have on the frm s revenues. For example, f demand for transportaton s nelastc, an ncrease n prce would ncrease total revenue. Conversely, f demand s elastc, an ncrease n prce would brng about a decrease n revenue. A transportaton frm can take advantage of margnal prce ncreases or decreases to add to ts revenue by knowng the current elastcty of demand for ts partcular mode. Recently, the transportaton envronment was confronted wth fluctuatons n the prce for fuel nputs. In the summer and fall of 2001, fuel prces were at exceptonally hgh levels wth a consequent mpact on the prces for transportaton servces. Several observers commented on the lkely effect of such fuel prce ncreases on freght transport costs. However, knowng the effects depends heavly on knowledge of supply and demand condtons. The effect of ncreased fuel prces depends on the shape of demand. The relatve elastctes of supply and demand wll determne the prce effect. The ncrease n fuel prces causes a decrease n supply. If the elastcty of demand s low

11 4 relatve to the supply, the effect on prce would be hgh. On the other hand, a relatvely hgh elastcty of demand would result n a smaller effect on prce change as a result of ncrease n fuel prces. Dependng on the relatve elastctes of supply and demand, the truckng frm would have to, on one hand, ncrease rates to offset ts ncreased fuel prces. On the other hand, the ralroad servce provder would also need to ncrease rates to accommodate the rsng varable costs. It can be argued that the degree to whch the change n fuel prces would affect each mode should be dfferent, however. The truck shpper s faced wth a lmted quantty of capacty per load and, therefore, has fewer bushels over whch to spread the ncreased varable cost across. The ral provder, however, has the opportunty to ncrease tran capacty to lmt the ncreased cost compared to the truckng frm. Problem and Objectve of Study It s not known how the effect of rate changes and transportaton characterstcs wll affect modal choces among North Dakota s elevators. As mentoned prevously, the last study on ths subject was done n 1982, and the envronment may have changed over 20 years due to regulatory ssues; ncreased fuel prces, elevator sze and concentraton; changes n transportaton servces, such as shuttle trans; and countless other ssues. The objectve of ths study s to estmate the demand for transportaton servces for gran n North Dakota. Also, ths study wll estmate the prce and cross-prce elastctes for each transportaton mode n the state. The elastctes wll provde an estmaton of the shft n modal shares based on changes n rates. The demand for gran transportaton s studed as an nput or derved demand.

12 5 Treatng transportaton demand n ths manner means that transportaton servces are used as an nput to the producton process of gran marketng. Essentally, the fnshed product for gran elevators n North Dakota s gran delvered at the destnaton. Transportaton s an nput used to produce the fnshed product. Therefore, the demand for transportaton s derved from ts use as an nput to the producton process. Through dualty theory, the demand can be estmated from a cost functon approach. A translog transportaton cost functon wll be used to estmate total transportaton costs. From ths cost functon, the modal shares can be derved through Shephard s lemma. The prce and cross-prce elastctes are derved from these nput shares. The data for ths study are obtaned from the Gran Movement Database from the Upper Great Plans Transportaton Insttute, whch provdes the shpment data for specfc commodtes from North Dakota elevators to multple destnatons. Ral and truck rates are obtaned from BNSF rate books and an estmaton of truck rates across the state of North Dakota. Hypothess The hypothess of ths study s that the prce and cross-prce elastctes of modal demand n gran transportaton have changed snce 1982, when the prevous study was performed. The dfferences may be due to the changng transportaton envronment as a result of deregulaton, changes n transportaton optons, mergers, sze of elevators, shuttle programs n the state of North Dakota, and the nature of the geographc dstrbuton of elevators across the state.

13 6 Thess Organzaton Ths thess s organzed n fve chapters. Chapter I s the Introducton, Need for Study, problem statement and objectve, and Hypothess. Chapter II s a revew of past studes whch have addressed the ssue of transportaton demand from dfferent approaches. The models n the past studes examned nclude ad hoc, mathematcal programmng studes, Models of Modal Choce, and derved demand approaches. Chapter III provdes a descrpton of the theory and methodology behnd ths study as well as Estmaton Procedures. Chapter IV reports the Results of the estmaton procedures. Chapter V provdes a summary, conclusons and mplcatons of the results, lmtatons of the study, and suggestons for future studes.

14 7 CHAPTER II LITERATURE REVIEW The lterature revewed n ths chapter contans models that endeavor to develop a demand functon for transportaton modes. The demand model allows researchers to quantfy attrbutes that a shpper wll consder when makng modal choces for freght shpments. In general, there are four ways n whch transportaton demand models have been estmated. They are mathematcal programmng models, models of modal choce, ad hoc demand functons, and derved demand models (Wlson 1982). Ths study wll utlze a derved demand functon. Ths chapter serves to revew lterature pertanng to estmatng transportaton demand. Because of the large amount of studes that have estmated transportaton demand, ths revew does not cover all transportaton demand studes. In ths secton, a number of studes that are representatve of ths broad array of lterature are revewed. The revew s separated nto four sectons, one for each common type of model. Each secton ncludes an explanaton of the type of demand model gven, followed by explanatons of specfc studes usng the model. The general fndngs of the studes are also dscussed shortly followng the descrpton of the studes, and summarzed n Table 2.1 at the concluson of the revew. Before dscussng each type of model, t s useful to keep n mnd several cautons n estmatng demand models. Oum (1979a and b) voces cauton regardng several factors when constructng transportaton demand models. Oum (1979a) lsts four weaknesses that

15 8 transportaton demand models may suffer from 1. "The functonal form of the model mposes a pror restrctons on the parameters of prce responsveness of demand and ntermodal substtuton." Accordng to Oum, the Cobb-Douglas and Logt demand models mpose "unacceptable" restrctons on elastctes of substtuton (pg. 374) 2. "Snce most models are crudely specfed n ad hoc fashon wthout reference to the underlyng technology, the propertes of shppers' preference structures cannot be dentfed from the estmated demand model." (pg. 374) 3. Qualty-of-servce attrbutes are often not ncluded n demand models due to lack of data sources. 4. "Many demand models are estmated from data whch are too hghly aggregated over heterogeneous commodtes and regons to acheve reasonable accuracy." (pg. 374) It s also useful to examne the dfferent types of elastctes that are calculated n the studes. The tme frame of the elastcty calculated may have a large effect on the results obtaned. In the short run, many agrcultural frms are not able to make use of a substtute mode, or the use of a substtute s cost prohbtve. Examples of these barrers are geographc locaton, technology constrants, or mechancal constrants. In the long run, much of the frm s shpment optons are open. The frm can be more responsve to changes n prce and or servce characterstcs when the ablty to change ts nfrastructure s an opton. Therefore, the long-run elastcty estmates are lkely to be more elastc than the short-run estmates (Oum 1992).

16 9 Mathematcal Programmng Models Mathematcal programmng models are based on the concept of mnmzng or maxmzng an objectve functon subject to constrants. For transportaton demand, ths procedure nvolves mnmzng transportaton cost for a frm based on commodty supply, demand, and transportaton mode characterstc constrants. By optmzng a frm's transportaton cost subject to these constrants, a researcher can see the effects of a change n rates or characterstcs on a frm's modal choce as well as producton choces. Koo and Thompson (1982) offer a mathematcal programmng model for studyng the transportaton demand n the Unted States. A lnear programmng model was calculated usng truck, ral, and barge modes of transportaton to transport from geographc regons of producton to geographc regons of consumpton and export. The goal was to mnmze transport costs, subject to constrants on producton, storage, consumpton, and transportaton capacty. When the transportaton objectve functon s mnmzed, t represents the mnmzed transportaton and dstrbuton cost for gran transportaton n the Unted States. One aspect of Koo and Thompson's (1982) study that may be partcularly valuable s ther estmaton of transportaton costs. Truckng costs were estmated for both tandem and sem tractor-tralers. The average cost per hundred-weght (cwt.) for a sem tractor-traler was based on 260 workng days per year, 10 workng hours n a workday, average truck speed of 50 mph, on the assumpton that percent of return trp movements were drven empty. From ths, Koo and Thompson estmated the average cost per cwt. for sem tractor-tralers based upon costs n 1979 wth d representng dstance as

17 10 AC = d A smlar method was used to estmate tandem truckng costs. Whle these costs are based upon 1979 cost data, t provdes a framework for estmaton of truck costs n 2001 terms. Due to the nature of competton n the transportaton ndustry, the truck cost could be used to approxmate truck rates. It can be argued that due to the degree of competton n the truck ndustry, rates are near to margnal cost; therefore, the approxmaton s vald. Ral and barge costs are also estmated but, for the purposes of ths study, are not necessary to examne. Koo and Thompson (1982) estmated elastctes by varaton of the ral and barge rates n the mathematcal programmng problem. Exact elastcty estmates for ral and barge wth respect to own prce and cross prce, ncludng truck rates, are shown n Table 2.1. It should be noted that, wth respect to barge traffc, the own-prce elastcty s negatve, as should be expected, but the cross elastcty wth respect to truck rates s also negatve. Ths suggests that, n the case of ths study, truck transportaton s a complement to barge transportaton. Ad Hoc Models Ad hoc models are essentally statstcal models that are estmated from a statstcal perspectve wthout formal economc theory underlyng the model formulaton. Ftzsmmons (1981) uses an ad hoc model to calculate elastcty estmates for ral and barge transportaton of gran. Tme-seres data for ral volumes, ral and barge rates, and domestc gran usage are used to estmate the model. The model s a log-lnear functon that places ral volume as a functon of quantty of gran used for domestc consumpton,

18 11 Table 2.1. Comparson of Elastcty Estmates by Study Author Model Commodty Varable Truck Ral Koo & Mathematcal Gran Ral Rate Thompson Programmng Barge Rate (1982) Truck Rate Ftzsmmons ad hoc Gran & Income (1981) Soybeans Ral Rate Truck Rate Mklus et al. Logt Cherres Ral Rate (1976) Truck Rate Apples Ral Rate Truck Rate Fredlaender Derved Food Ral Rate & Spady Demand Products Truck Rate (1980) Wlson Derved Wheat Ral Rate (1982) Demand Truck Rate Oum Derved Edble Foods Ral Rate (1979b) Demand Truck Rate ral rates, and barge rates. Due to possble collnearty problems, the model s transformed to nclude a rato of barge rates to ral rates n place of barge rates. The model s estmated usng the ordnary least-squares method. The elastcty estmates are represented by the parameter estmates from Ftzsmmon's (1981) model. The results are shown n Table 2.1 where the parameter

19 12 estmates for domestc consumpton represents elastcty of ral demand wth respect to output. The remanng parameters represent the own prce and cross prce elastctes for ral transportaton. Ral transportaton demand s nelastc wth respect to output, and the cross-prce elastcty wth respect to barge rate s elastc. The own-prce elastcty for ral gran volume s Although ad hoc models have been used to forecast transportaton demand and have been ndcated to perform reasonably well (Oum 1979b), models have two major shortcomngs for nvestgatng prce responsveness and possbltes of cross modal competton. Frst, the set of varables to nclude and the functonal form to use for the estmaton of demand model are arbtrary, yet the parameter estmates are lkely to be senstve to them, and second, n general, nether the structures of shppers' preferences that the ad hoc demand models assume to be approxmate nor the propertes of approxmaton are known. Shppers' choces n modal usage depend on shpment and modal characterstcs as well as prces. These characterstcs are reflected n the shppers' preferences for modal choce. A smple example of ths comes from Mklus et al. (1976). The study quantfed the dfferences n elastctes on the modal preference for the transportaton of cherres and apples, two commodtes that are very dfferent n ther shpment characterstcs. A longer-term shppng mode may work wth apples that have a longer useful lfe but would not work wth cherres, whch are hghly pershable. These preferences, as Oum (1979a) states, are not adequately accounted for n the ad hoc models.

20 13 Models of Modal Choce Models of modal choce are dvded nto two man types: aggregate mode-choce studes and dsaggregate mode-mode choce studes. Aggregate mode-choce studes are studes whch examne shares of a fxed (constant) volume of traffc among modes. These studes focus on the mode choce behavor of a partcular geographc regon or group of shppers wth the same shpment and destnaton. The aggregate group makes modal share decsons based on transportaton and shpment characterstcs. Dsaggregate dscrete choce models concentrate on the probablty that a shpper wll make a partcular mode choce. These models nvestgate users travel-choce behavor based on attrbutes of varous modes of transport and ndvduals socoeconomc characterstcs. (Oum 1992, pg. 152) These models assume that transportaton usage s an all or nothng decson. In the case of ths study, a dsaggregate dscrete choce model would lmt the shpper to ether a ral shpment or a truck shpment. The decson n ths model s an ether/or decson for the ndvdual shpper. A mode-choce model s a model n whch the dependent varable nvolves one or more qualtatve choces. Quanttatve varables measure how much or how many whle qualtatve varables represent types or categores. For nstance, suppose t s of nterest to predct votng behavor durng an electon. Whether the person votes or not s a qualtatve varable, however, and must be assgned numercal values f t s to be used n a regresson study. Other examples nclude beng a part of the labor force or not or, for the purposes of ths paper, a shpper s preference to use ral or truck transportaton. Pndyck and Rubenfeld (1991) states that qualtatve models provde a valuable tool to analyze survey

21 14 data that nvolves qualtatve responses from the survey partcpants. In the past, for both aggregate and dsaggregate mode choce studes, logt and probt models have been used to estmate demand for transportaton servces. These two types of models are qualtatve models, and some background on these choce models s gven below. Qualtatve models have been used for estmaton of demand for transportaton servces. The two most common types are the probt and logt models. Both of these models are based upon a qualtatve choce model that provdes the probabltes that an ndvdual wll take a certan acton. The logt and probt are two examples of generalzed lnear models. The logt and probt regresson models regress a functon of the probablty that a case falls n a certan category of Y on a lnear combnaton of X varables. Y represents a partcular acton, such as votng yes or no n an electon. For example, f the voter casts hs or her ballot for yes, Y=1; f the vote s cast for no, Y=0. The ndependent varables perform the same use as n the classcal normal lnear regresson model. The slope coeffcents tell us the effect of a unt change n X on a functon of the probablty of Y. The probablty of Y s the dependent varable, not Y tself whch s an ndependent varable. The dfference between the logt and probt models s on the left-hand sde of the equaton. The logt model s the logt of Y, or the log of the odds that a case falls n one category of Y versus another. The logt model has been used extensvely for estmaton of transportaton demand. It s based on the cumulatve logstc probablty functon and s specfed as the followng for estmaton:

22 P = F( Z) = F( α + βx) = + Z = e + ( α+ βx 1 ) 1 e As mentoned above, "the dependent varable n ths regresson equaton s the logarthm of the odds that a partcular choce wll be made" (Pndyck & Rubenfeld 1991, pg. 251). Mklus et al. (1976) used a logt model to estmate demand for transportaton servces. The logt model was also appled to estmate the elastctes and cross elastctes of demand. Two data sets were used: apples and cherres. Cherres were selected because of ther hgh pershablty that brngs about the necessty for fast, relable transportaton. Apples are storable, so other modal characterstcs affect the usage of each mode. The two commodtes are expected to brng dfferent elastctes due to the nature of ther shpment characterstcs. In addton to two commodtes, geographc characterstcs are used to determne elastctes across dfferent regons. Due to the pershablty of cherres, ths factor has some mportance. The decson process of a purchaser would be broken down nto dscrete segments as follows: 1) whether or not to purchase the commodty, 2) what quantty to purchase, 3) from what producton area, and 4) what transportaton mode to employ. If the decson process of the purchaser s assumed to follow these gudelnes, t can also be assumed that the transportaton mode decson s separable and can be estmated separately. The results for Mklus et al. (1976) were elastctes for cherres and apples and are shown n Table 2.1. It should be noted that, for cherres and apples, demand for transportaton s very elastc wth respect to own-prce and cross-prces. Moreover,

23 16 elastctes are much hgher for apples than for cherres. Ths large dfference s apparently due to a pershablty consderaton. It s mentoned n the artcle that, for apples, whch are less pershable than cherres, the transport prce becomes a more mportant varable, and ral seems to be the domnant mode of shpment. The logt model s employed as follows. "For each shpment, the buyer s assumed to be faced wth a set of mutually exclusve choces, whch may nclude truck, ral, pggyback, and ar. Examnaton of varables nfluencng these choces allows an estmaton of probablty that for a gven shpment the buyer wll make a partcular choce" (Mklus et al. 1976, pg. 218) The elastctes are lmted to truck and ral due to geographc and cost consderatons. The functon tself conssts of freght charges, transt tmes, and varance n transt tmes for each mode. Snce ar and pggyback shpments are a very small proporton of shpments, agan the functon s reduced to truck and ral only. Some nterestng nferences were made from the commodty characterstcs n the expected results. Frst, "for a hghly pershable commodty, the probablty that a partcular mode s chosen s expected to be negatvely correlated wth ts own transt tme and postvely correlated wth the transt tme of competng modes (Mklus et al. 1976, pg. 218) Ths nference suggests that model choce depends on servce characterstcs as well as rates. Second, the value of the product s expected to be correlated wth the wllngness of a shpper to pay hgher freght rates. If the commodty has a hgh value, there are nterest costs assocated wth the delay n shpment. Oum (1979a) argues that aggregate logt models are not approprate to use for studyng freght demand functons, especally calculatng the prce responsveness of

24 17 shppers for three reasons. The frst argument s that aggregate logt models mpose many a pror restrctons on the parameters of prce responsveness of demand. Second, some aggregate logt models nclude a rato of prces as a dependent varable. Thrd, the structure of preference underlyng the aggregate logt model s "severely rregular and nconsstent (Oum 1979a, pg. 375). In the estmaton of the logt model, the purpose s to estmate the parameters that correspond to the probablty of a partcular modal choce. Oum (1979a) states that the logarthm of the market share rato should not be treated as a dependent varable n order to estmate the shppers' responsveness to prce changes n those two modes. Ths mples that the rato of market shares should be one of the objectves n estmaton of a model, rather than the probablty of utlzaton of a mode. Oum (1992, pg. 154) states that "mode choce studes are studes whch examne shares of a fxed volume of traffc among modes." By applyng a logt or smlar model to aggregated transportaton markets, valuable nformaton may be lost. When aggregated demand s consdered, the objectve of the study s to fnd the shfts n modal shares of a fxed quantty of freght transportaton. The decson that the frms wll make s whch mode to use rather than to use a mode at all. Oum states that an aggregate model does not take nto account "the effect of a prce change on the aggregate volume of traffc (pg. 154). Theoretcally, f the prce of transportaton ncreased, frms may choose not to shp at all versus payng hgher rates. Dsaggregate dscrete choce models assume that "consumpton s an all or nothng decson (Oum 1992, pg. 153). Ths means that a frm wll ether shp or not. If the frm

25 18 shps freght, t wll ether choose ral or truck. In dsaggregate dscrete choce models, the frm s gven the opportunty (n the framework of the model) to choose to not shp based on prce and servce characterstcs. In order to estmate consumers' transportaton choces for a populaton or a regon, a certan degree of aggregaton s requred, however. As the degree of aggregaton ncreases, the results become more applcable to a regon or populaton, but the ncluson of non-travelng (or shppng) consumers decreases from the models. Wald Abdelwahab and Mchel Sargous (1992) proposed a system of smultaneous equatons to develop a demand model for analyzng transportaton demand. The model s based on the three followng equatons: I * = Xγ + Yη + Y η ε Y = X β + ε I * > 0 Truck: ff (2) Y = X β + ε I * 0 Ral: ff (3) Equaton (1) s specfed as a bnary probt model and represents an unobserved ndex whch determnes the modal choce where Y 1 and Y 2 represent endogenous varables that represent the shpment sze by mode. X represents exogenous varables that represent market and modal attrbutes that total 18 separate varables n all. "The resduals... are assumed to be serally ndependent and have a trvarate normal dstrbuton." (Abdelwahab and Sargous 1992, pg. 54) Due to ths covarance structure, the three equatons must be estmated as a system of smultaneous equatons and estmated by the maxmum lkelhood method. From the estmaton of the probt model, the elastctes can be calculated. (1)

26 19 Abdelwahab and Sargous (1992) make the dstncton between dsaggregate and aggregate elastctes. Dsaggregate elastcty represents "the responsveness of a shpper's probablty of choosng mode." (Abdelwahab and Sargous 1992, pg. 51) Aggregate elastcty refers to the "responsveness of shppers' actons for choosng mode." Snce the aggregate elastcty s derved n ths case from dsaggregate elastctes, the elastctes tend to be more accurate. Aggregate studes make use of average values, a procedure that generally leads to underestmatng the populaton response to the proposed changes. (Oum 1979, Abdelwahab and Sargous 1992) Also, due to the fact that smultaneous equatons are used, the total market sze does not need to be fxed n order to be estmated. The unque nterrelatonshp between the smultaneous equatons demonstrates the effects of prces on the elastcty estmates. Derved Demand Models Derved demand models make use of the theory of the frm to obtan transportaton demand functons that are consstent wth economc theory. Freght transportaton has no real value to a frm f the frm has no need for transportaton. Therefore, the demand for freght transportaton s derved from the demand for a certan good or commodty. When transportaton s treated as an nput to producton, the demand for transportaton can be gleaned from a frm's cost functon when the functon s mnmzed. Derved demand models begn wth the frm s cost functon. "Dualty theory mples that f producers mnmze nput costs of producng gven outputs, and f factor prces are exogenous, then the cost functon satsfyng the usual regularty condtons contans suffcent nformaton to descrbe completely the correspondng producton

27 technology, and vce versa (Oum 1979b, pg. 151)." The cost functon s often expressed n the translog functonal form. The followng s a representatve functon: 20 lncs = α + α ln P + Bh ln Xh + 1 Aj ln P ln Xh Chsln Xh ln X h j h s s, where P = Prces of Inputs X = Characterstcs of Inputs From ths optmzed cost functon, the nput demand functons are obtaned through the Shephard's Lemma. Dfferentaton wth respect to the prce of transportaton nputs yelds the nput share equatons for transportaton servces. F C s lncs = = α + Ajln Pj + Bhln X ln P h h = T, R (Truck and Ral), where F = Frm expendtures on each mode Restrctons to ensure homogenety are mposed. Fredlaender and Spady (1980, pg. 435) state that "snce the nput share equatons are not drect demand equatons, we cannot obtan estmates of the elastcty of demand for ral and truck," so the followng equatons from Berndt and Wood (1975) are used to derve the elastctes. E = A / S + S 1 E = A / S + S j j j = L, T, R (Labor, Truck, Ral) In many cases, t s assumed that the frm s transportaton costs are separable from ts other producton costs. Ths assumpton allows the researcher to estmate a

28 21 transportaton cost functon rather than a total cost functon. Often, ths assumpton s necessary due to a lack of nformaton regardng frm producton costs and nput prces. Fredlaender and Spady (1980) attempt to provde a model for dervng an explct freght demand equaton from a general cost functon. Shephard's Lemma allows the researchers to derve a transportaton share equaton from the frm's total cost functon. Snce frms are typcally not n long-run equlbrum, the share equaton s derved from the frm's short-run cost functon. Fredlaender and Spady constructed a short-run cost functon, whch consdered labor, captal, materals and energy, ral transportaton, and truck transportaton to produce an aggregate output. The frm's cost s a functon of output; captal; materals and energy; and prce of labor, truck transportaton, and ral transportaton. The authors treat the prce of ral and truck transportaton as more than smply the transportaton rate for the servces. They develop a composte prce that consders the effects of modal characterstcs on nventory costs. Wlson (1982) uses a method smlar to Fredlaender and Spady. The translog cost functon s agan used. The cost functon n ths study s not the total cost functon, but rather the total transportaton cost functon that s called the cost of dstrbuton actvtes. Wlson assumes that transportaton nputs are separable from other nputs; therefore, transportaton cost can be examned separately from total cost. Wlson adds a trend varable to the translog functon to account for technologcal changes n transportaton and nsttutonal change. Agan, symmetry and homogenety condtons are mposed on the translog cost functon. Through the Shephard s Lemma, the modal shares are calculated. The shares represent the proporton of total transportaton cost spent on each mode. From

29 22 these transportaton share equatons, elastctes were calculated usng the same formulas from Berndt and Wood (1975). Wlson (1982) studed the demand for gran transportaton from North Dakota to selected destnatons n Mnnesota. Ths study endeavors to estmate the same demand. The elastcty estmates for the state as a whole are shown n Table 2.1. As mentoned n the Introducton, the hypothess of ths study s to see whether the nature of the gran transportaton ndustry n North Dakota has changed snce the last study was performed. Oum (1979b) assumes that the transportaton cost functon s separable from the total cost functon. In ths case, demands for hghway, ral, and water transportaton are obtaned. The prce elastctes are calculated by takng the partal dervatve of the nput demand wth respect to prce multpled by the prce dvded by the nput demand. Oum (1979b) notes that there are "errors n the adjustment to the cost mnmzng modal shares." (pg. 154) To hs share model, Oum adds a dsturbance term to the orgnal transportaton share functon and mposes lnear homogenety condtons to obtan a new modal share model. The ssues of seral correlaton and a potental lag n shpper's response to prce changes are addressed. There s a possblty of seral correlaton n the tme seres data because of potental cyclcal varatons n modal shares. The ssue of lags n shpper's response to prce changes could arse due to contractual oblgatons of the shppers, mperfect nformaton, captal nvestment, and nature of shpments. To avod these potental problems, Oum (1979b) desgned three share models: autoregressve, partal adjustment, and a combnaton of the two.

30 23 CHAPTER III METHODOLOGY AND DATA Ths chapter descrbes the Methodology and Data used to estmate gran transportaton modal demand n North Dakota. In summary, pooled cross-sectonal and tme seres gran transportaton data from were gathered, estmated, and organzed. Regresson analyss was used to analyze these data to obtan modal demand. The followng sectons descrbe the background, analyss, and data sources and modfcatons employed. Background Informaton Ths study attempts to quantfy responsveness n gran transportaton modal choce based on several characterstcs usng an econometrc model. The representatve frm n ths case s a typcal gran elevator wthn the state of North Dakota. The commodtes shpped from these elevators to be examned are hard red sprng wheat (HRS), durum wheat, and barley. It s assumed that these elevators have acted ratonally and mnmzed ther producton costs by usng optmal nputs to produce a gven value of output. Two mportant nputs n producng the fnal product of gran elevators whch s gran at termnal markets are ral and truck transportaton. Snce ralroad servce may vary based on the number of cars shpped, a track capacty varable wll be ncluded to obtan the effect of ral shpment szes on demand. The large number of elevators, and the lack of unformty n sze or capacty n North Dakota present a problem n the area of data collecton. Ths study aggregates the transportaton volumes by mode by the nne crop reportng dstrcts (CRDs) n the state.

31 24 North Dakota s dvded for statstcal and research purposes nto nne CRDs. Each dstrct s beleved to have smlar crop and producer characterstcs as well as smlar geographc locatons. A map outlnng the dfferent crop reportng dstrcts s shown n Fgure 3.1. DIVIDE BURKE RENVILLE BOTTINEAU ROLETTE TOWNER CAVALIER PEMBINA WILLIAMS MOUNTRAIL PIERCE MCHENRY RAMSEY WARD BENSON NELSON WALSH GRAND FORKS GOLDEN VALLEY MCKENZIE BILLINGS SLOPE BOWMAN 7 DUNN 4 STARK HETTINGER ADAMS MERCER GRANT MCLEAN OLIVER MORTON EDDY WELLS GRIGGS STEELE TRAILL SHERIDAN FOSTER 5 BURLEIGH KIDDER STUTSMAN 6 BARNES CASS 8 EMMONS LA LOGAN MOURE MCINTOSH DICKEY9 SIOUX RANSOM SARGENT RICHLAND Fgure 3.1. Map of North Dakota Crop Reportng Dstrcts. It s assumed that the elevators n each CRD make decsons n a smlar manner as the others n ther dstrct. Because ral rates dffer by geographc locaton and elevator sze, ths study calculated a weghted average ral rate for each CRD, weghted by elevator storage capacty. In calculatng ths average, each elevator s assumed to use the largest ral shpment sze possble. (.e., use the 52-car rate for 52-car elevators) Thus, ral rates by CRD represent the weghted average avalable to the elevators. For truck rates, a

32 25 representatve elevator whch s located near the center of the CRD s chosen from each dstrct. The ratonale for ths approach s that not all modes are avalable to each elevator n the CRD. By usng a representatve elevator whch represents the combnaton of the characterstcs of all the elevators n the CRD, a cross-secton of the elevators behavor can be obtaned. Derved Demand Theory Based on the Lterature Revew, the demand for gran transportaton s treated as an nput demand or derved demand. The fnshed product for North Dakota elevators s gran at the destnaton. Transportaton s an nput used to acheve the producton process. By treatng transportaton n such a manner, the demand for the servces can be obtaned through the frm's cost functon usng Shephard s Lemma. Snce the cost functon shows the mnmum cost of producng a gven amount of output, t can be used to descrbe the frm's producton technology (Btzan 2000). Ths allows the researcher to estmate nput demand through the frm's cost functon. Examned Factors Affectng Demand When estmatng demand for transportaton servces, t s necessary to establsh factors that affect the demand for transportaton. The obvous frst choce s the rates of the respectve modes because rates affect the quantty of transportaton servce demanded. For gran transportaton n North Dakota, these modes are ral and truck transportaton. The underlyng factor n modal choce s whether t s cost effectve. Other characterstcs that may affect elevator modal choce selecton also play a part. Average elevator track capacty s ncluded as representatve of ralroad servce.

33 26 Ths varable s ncluded to proxy the qualty of servce. If an elevator has better servce due to an ablty to shp n larger volumes, t may be more lkely to use ral. Conversely, f an elevator does not have the track capacty to take advantage of unt-tran servce, for example, the elevator may be less lkely to use ral. Dstance to the destnaton s another factor that affects modal demand. As dstance to destnaton ncreases, so does the cost of transportaton, both for the shpper and the shppng provder. It s assumed that the degree to whch each mode wll be affected s dfferent. Theoretcal Background Each elevator s assumed to have a lnk-specfc mnmzed cost functon. Ths functon descrbes the mnmum cost of transportng a gven quantty of output to a gven destnaton usng optmal combnatons of ralroad and truck servces. Past studes have assumed that gran transport servces are separable from other nputs n the producton functon. "In other words, modal decsons are assumed to be ndependent from other factor decsons such as the optmal combnatons of labor and captal (Wlson 1982, pg. 6). Some studes have gone a step further to assume that transport costs to each destnaton are separable from total transportaton costs. Ths mples that each lnk-specfc transportaton technology s unaffected by the transportaton actvty levels of all other lnks (destnatons) and the amounts of nontransport nputs used n the producton (Oum 1979b, pg. 464). The same assumpton s made n ths study. Therefore, the frms' lnk-specfc transportaton cost s estmated separately usng a transportaton cost functon.

34 27 Another ratonale for the separablty of transportaton servces s the nature of the commodty beng shpped. Gran s a low value commodty, and the costs assocated wth tme and storage are low. For hgher value commodtes, servce characterstcs and shpment tmes may attrbute more to the total logstcs cost for the frm. For ths study, however, t s assumed that gran shppers gnore the total logstcs cost of shppng gran and mnmze the gran shpment costs themselves. Another restrcton on the cost functon also apples. Homogenety of degree one s mposed, suggestng that a one-percent ncrease n the prce of nputs results n a onepercent ncrease n total cost. The frm's lnk-specfc transportaton cost functon can be specfed as follows: C = C( w, q, t ) j "whch [represents] the mnmum cost of producng output q, gven prces of w (factor prces), and technologcal characterstcs of nputs (e.g. length of haul)" (Btzan 2000, pg. 40). The gven output, n ths case, s the total amount of a commodty shpped from an elevator to Duluth or Mnneapols. Factor prces nclude ral and truck rates. Technologcal characterstcs nclude elevator track capacty, length of haul, and a tme varable to measure changes over tme. In ths study, the factors that affect elevator transportaton cost have been establshed. If the elevator's transportaton cost functon, or even the functonal form was known, estmaton would be a smple process. However, nether s known. It s necessary to choose a functonal form that does not mpose many restrctons on what the functon

35 28 should look lke. Accordng to Btzan (2000, pg. 43), "One way to approxmate an unknown functon,..., s to perform a Taylor seres expanson wth a remander. Fredlander and Spady (1980) show that the translog cost functon can be thought of as a second order Taylor seres expanson of an arbtrary functon." Followng the dervaton n Btzan (1999), an applcaton of the functon to ths study s below: 1 2 ln Cw (, qt, ) = αo + αln w + β lnq+ γ jln tj + φ(ln w) + θln wq j ωj ln wt + ρ(ln q) + ζjln tjq+ ϕ j(ln t j ) + ε 2 2 j j j By applyng Shephard's Lemma to ths transportaton cost functon, the factor share equatons for each transportaton nput are obtaned. Ths s the condtonal nput factor demand. From ths, the nput prce and cross-prce elastctes can be estmated. S lnc lnc C 1 w C w ww C xw xw = = = = ln ln C The elastctes are obtaned from ths factor share equaton n the followng manner: The general form for own-prce elastcty s ε = x w w x From Shephard s Lemma, we know that C w = x Ths dervaton mples that

36 29 ε = 2 C 2 w w x It s also known that lnc ln w = C w w C By takng the second dervatve wth respect to w, 2 lnc 2 = ln w lnc ln w w C w w ln w 2 C 2 + w wc C w C C C w w w 2 C w 2 C w2 lnc lnc lnc = 2 + w C ln w ln w ln w 2 2 C C lnc lnc lnc 2 = w w ln w ln w ln w lnc ln w 2 2 C w 1 lnc lnc lnc lnc 2 = 2 + = ε w x S ln w ln w ln w ln w From the translog ε φ α αα φ = + = 1+ S S S S S

37 30 Usng a smlar procedure, the cross-prce elastctes can be determned. ε j φj = + S S j Ths equaton provdes the Hcksan or compensated demand for transportaton, whch descrbes prce responsveness assumng constant output. It s also of nterest to calculate the Marshallan or ordnary demand for gran transportaton. Oum (1979b) and Wlson (1982) estmate the Marshallan elastctes usng a smlar formula: F = ( σ + λη) S j j j, where σ = ( α / SS ) + 1 whch s the elastcty of modal substtuton j j h = Own-prce elastcty of consumer demand for the commodty beng transported assumed by Oum to equal -1 or untary elastcty of commodty l = Proportonate change n prce of the commodty wth respect to a change n the prce of the j th mode, whch s assumed by Oum to equal 0.1 The Marshallan elastcty of demand allows for the effect of changes n modal rates on commodty prces. For example f [w ] decreased, prces to gran producers would ncrease, and/or prces to buyers would decrease. In ether case, the total quantty transported would ncrease (Wlson 1982, pg. 9). The elastcty of the Marshallan demand reflects ths effect. By varyng the level of the own-prce elastcty for consumer demand for the commodty beng transported, the effect on the Marshallan elastcty may be useful n determnng the mpact of modal rate changes.

38 31 These procedures wll provde the short-run elastcty of demand for transportaton modal demand. Snce the amount shpped by mode s only dependent on the current rate, the rate effect on the current month s shpments s examned. It s possble to get a longrun elastcty of demand for transportaton by addng tme-lagged rate varables to explan shpments. To account for changes n demand due to dfferent commodtes and destnatons, sx lnk-specfc models are estmated. One model s estmated for each commodty to each destnaton. As mentoned prevously, ths provdes a lnk-specfc cost and share functon model for each commodty and destnaton. Below s the model specfcaton, whch s dentcal for each of the sx models estmated. Model Specfcaton The model whch ths study utlzes for each commodty and destnaton s ln C(w,q,t ) = ln a 0 + a 1 lnw 1 + a 2 lnw 2 + b Q lnq + g 1 lnt 1 + g 2 lnt 2 + g 3 lnt 3 + ½ f 11 (lnw 1 ) 2 + 1/2f 22 (lnw 2 ) 2 + f 12 (lnw 1 lnw 2 ) + q 1Q (lnw 1 lnq) + q 2Q (lnw 2 lnq) + w 11 (lnw 1 lnt 1 ) + w 12 (lnw 1 lnt 2 ) + w 13 (lnw 1 lnt 3 ) + w 21 (lnw 2 lnt 1 ) + w 22 (lnw 2 lnt 2 ) + w 23 (lnw 2 lnt 3 ) + ½ r 11 (lnt 1 ) 2 + ½ r 22 (lnt 2 ) 2 + j 12 (lnt 1 lnt 2 ) + j 13 (lnt 1 lnt 3 ) + j 23 (lnt 2 lnt 3 )+ z 1Q (lnt 1 lnq) + z 2Q (lnt 2 lnq) + z 3Q (lnt 3 lnq), where w = Rate for mode ( = ral, truck) t = Servce characterstc ( = capacty, tme, dstance to destnaton)

39 32 The nput share equatons obtaned through Shephard s Lemma are as follows: S 1 = a 1 + f 11 lnw 1 + f 12 lnw 2 + q 1 lnq + w 11 lnt 1 + w 12 lnt 2 +w 13 lnt 3 S 2 = a 1 + f 22 lnw 2 + f 21 lnw 1 + q 2 lnq + w 21 lnt 1 + w 22 lnt 2 +w 23 lnt 3, where w = Rate for mode ( = ral, truck) t = Servce characterstc ( = capacty, tme, dstance to destnaton) Estmaton Procedures The translog transportaton cost functon and the nput share functon form a group of three equatons wth common parameters. Several procedures for estmatng these parameters exst. Pndyck and Rubenfeld (1981) ndcates, "Each equaton could be estmated ndependently usng ordnary least-squares, and consstent and unbased parameter estmates could be obtaned" (Pndyck and Rubenfeld 1981, pg. 308). However, ths estmaton procedure may result n lost nformaton. Sngle equaton estmaton of any of the share equatons may overlook nformaton n the cost equaton, and sngle equaton of the cost equaton may result n lost nformaton from the share equatons. By smultaneously estmatng the cost and share equatons, the possblty of lost nformaton from sngle equaton estmaton can be avoded. It may be realstc to expect that the equaton errors wll be correlated. A set of equatons that has contemporaneous cross-equaton error correlaton s called a seemngly unrelated regresson (SUR) system. At frst look, the equatons seem unrelated. However, the model conssts of a set of equatons that are lnked because the error terms across equatons are correlated. SAS s