COAL DEMAND AND TRANSPORTATION IN THE OHIO RIVER BASIN: ESTIMATION OF A CONTINUOUS/DISCRETE DEMAND SYSTEM WITH NUMEROUS ALTERNATIVES * by Kenneth Tran and Wesley W. Wlson December 2011 Abstract Coal-fred electrcty plants account for over 50 percent of the naton s electrcty. These plants can purchase coal from a large number of dfferent locatons and, often, can have a number of dfferent transportaton optons. Normally, however, from the array of dfferent optons, they use only a handful. We frame the model as that of a costmnmzaton wth a large number of nput choces, characterzed by standard Kuhn- Tucker condtons. Emprcally, we estmate a system of nput decsons that contan both zero and non-zero levels, usng a Multple Dscrete/Contnuous Extreme Value model. The payoffs from each choce are a functon of costs, coal attrbutes, and unobserved modal attrbutes, as well as the ncreased regulaton under the Clean Ar Amendment Act of 1990. * Ths research was conducted under research fundng from the Navgaton and Economc Technologes Program (NETS) of the Insttute for Water Resources of the Army Corps of Engneers. We gratefully acknowledge the research support and comments from Keth Hofseth, Wesley Walker and a host of others. Department of Economcs, Unversty of Calforna, Berkeley, CA 94720-3880. Department of Economcs, Unversty of Oregon, Eugene, OR 97403-1285.
1. INTRODUCTION Electrcty-generaton facltes around the Oho Rver are prmarly coal-fred, and coal movements account for about half of the traffc on the rver. Major nfrastructure mprovements, such as lock upgrades, have been proposed that could reduce the cost of movng coal along the rver. The U.S. Army Corps of Engneers has been mandated to assess the benefts and costs of such mprovements as a crtcal nput to Congress decson of whether to approve these publc nvestments. The benefts of mprovements and the cost/beneft comparson depends crtcally on the responsveness of demand to changes n waterway rates. Ths report analyzes coal movements n the Oho Rver regon. We assembled data on the coal purchases of electrcty-generaton plants n the area for the seventeen year perod, 1991-2007. For each plant, we obtaned data on the sources, mostly mnes, from whch the plant purchased coal and the mode of transportaton for movng the coal from the source to the plant. There are numerous coal sources avalable to these plants, and each plant chooses to buy from only a few of them. There are also often a multplcty of transportaton modes and/or modal combnatons avalable, ncludng barge, ral, truck, or a combnaton, and one of these optons s chosen for each coal purchase. We have measures of the cost of coal for the sources and modes that the plant utlzes n each year, as well as the cost for sources and modes that the plant dd not choose to use. We also have nformaton about the sulfur and ash content of coal purchased from each source, whch s an mportant aspect of clean ar regulaton as well as the confguraton of the plants makng decsons on coal. Usng these data, we estmated a model of plants choce of source and mode. Ths model descrbes the proporton of a plant s total coal purchases that t obtaned from each source
and transports by each mode. Each plant s choces are related to the cost of coal by each avalable source and mode, the attrbutes of the coal at each source, modal dummes that capture non-cost attrbutes of the modes, and varables that reflect the ncreasng strngency over tme of clean ar regulaton. The model s specfed as a multple dscrete-contnuous choce model, whch has been proposed and mplemented n smlar econometrc settngs by, e.g., Phaneuf et al. (2000), Bhat (2005), von Haefen and Phaneuf (2005), Bhat and Sen (2006), and Km et al. (2007). It s a generalzaton of a standard dscrete choce model n that t allows for multple alternatves to be chosen (as opposed to only one chosen alternatve n a standard choce model) and allows the quantty purchased through each chosen alternatve to vary (as opposed to the fxed quantty n a standard choce model.) The estmated model can be used to forecast changes n plants choce of coal sources and modes n response to changes n costs, such as those nduced by waterway mprovements. In the next secton, we descrbe the sources and characterstcs of the data, whle n Secton 3 we present the emprcal model and results. Secton 4 adds a summary of the analyss and conclusons. 2. DATA Our data were obtaned from the Platts COALdat database. 1 Ths database contans 30,253 records that represent 159,467 transactons between electrcty companes and mnes. 2 For each transacton, the followng nformaton s ncluded: the dentty and locaton of the plant recevng 1 Ths was produced by RDI, whch was a subsdary of Platts, a wholely owned subsdary of McGraw-Hll, Inc. Ths database has a number of dfferent data felds. Our data are from the Coal & Transportaton fles. 2 A record mght represent a multple of transactons n the data fle. 3
the coal, the dentty and locaton of the source of the coal movement to the plant, the tonnage, the prce pad for the coal (.e., the mne mouth prce), attrbutes of the coal, the transport mode, the transport costs, and characterstcs of the plant that can affect t choces, such as whether t has ral and/or barge access. The data span the years 1991-2007 and cover coal movements to 151 electrcty plants located n the Oho Rver Basn (ORB). The number of plants n each state are: Oho (30), Illnos (24), Indana (24), Pennsylvana (22), Kentucky (21), West Vrgna (14), Alabama (9), and Tennessee (7). 3 (herenafter sources). These plants receved coal from a total of 3550 mne coal sources Each plant reported the source of ts coal for ths database, and some plants gave transfer ponts or blendng facltes as ther sources. However, most of the recorded sources are producng mnes. The sources are prmarly located n the Oho Rver Valley, but there are sources from a total of 17 dfferent states and 5 foregn countres. In organzng the data, we frst dentfed each plant n the ORB that receved coal and the zp codes n whch t s located. 4 Mssng zp codes were added by nternet searches on cty and state nformaton (n some cases on plant name) wth assgnment statements. The zp codes were then merged nto a Census dataset that contans longtudes and lattudes. We followed the same procedure wth coal sources usng FIPS codes (zp codes were not avalable), 5 such that each source was dentfed by name, state, county and FIPS code. These data were merged by county FIPS codes nto a census dataset that contans county longtudes and lattudes. There were 57 sources for whch the COALdat lsted the FIPS as NA and others whose lsted FIPS dd not 3 The number n () represents the frequency of observatons n each state. There were 151 total plants n the data. Two were excluded n that they used solely one mode that was not consdered n the analyss (belt). 4 Mssng zp codes were added by nternet searches on cty and state nformaton (n some cases on plant name) wth assgnment statements. 4
match wth the census data. These were assgned longtudes and lattudes based on nspecton of the data about the source coupled wth nternet searches. When completed, there were 3550 sources, and 3449 lattudes and longtudes. The one wthout locaton nformaton was n the data for only one year and shpped to only one plant. In the demand model, descrbed below, each plant chooses coal sources and transport modes from all the avalable sources and modes. The set of sources and modes that were avalable to a gven plant n a gven year (called the choce set) was specfed as follows. Frst, each source that appeared n the dataset n a gven year was consdered to be avalable to all plants n that year. The cost and non-cost attrbutes of coal at each source were calculated as the tonnage-weghted average over all transactons from that source n that year. Ths averagng gves the mne mouth prce per ton, BTU per pound, percent sulfur, and percent ash for coal at each source n a gven year. The mne mouth prces n each year were converted to real terms by dvdng by the GDP prce deflator. Second, fve modes were dfferentated: 6 1. Barge alone 2. Truck alone 3. Ral alone or wth truck 4. Truck-barge combnaton 5. Ral-barge combnaton The dataset provdes nformaton on the avalablty of modes whch we used to determne whch modes to nclude n the choce set for each plant. Dstance between each source and plant was used n conjuncton wth observed modal costs to construct a measure of 6 There were a few belt movements n conjuncton wth barge, truck, and ral. These were few n number and tended to be domnated by the prmary mode. As such, they were ntegrated nto the other modal defntons. The sngle belt movements were omtted. 5
transport costs for all optons avalable to the plant. Transport costs along wth mne mouth prces form the bass for the cost of coal from alternatve sources and modes n the emprcal model. 2.1 Descrpton Fgure 2.1 shows the locaton of the plants n our analyss. Each dot represents a plant, and the deepness of the color represents the average annual tons of coal purchased by that plant. The plants are concentrated near the Oho Rver of course, but locatons range from the Msssspp Rver east to Pennsylvana and from the Great Lakes down to Alabama. Most plants use comparatvely small quanttes of coal, wth only a few n the largest tonnage category. Fgure 2.1: Utlty Plant and Sze (Average Annual Tonnages) 8,000 to 10,000 6,000 to 7,999 4,000 to 5,999 2,000 to 3,999 6
Fgure 2.2 shows the locaton of the coal sources n the dataset, wth the deepness of the color denotng the average annual tonnage from that source. Most of the sources are n the Appalachan Mountans and the Illnos Basn. However, mportant sources wth large output are also located n the Rockes, and especally Wyomng. Fgure 2.2: Average Annual Tons by Mne 1991-2007 5,000 to 13,000 1,000 to 4,999 100 to 999 0 to 99 Fgures 2.3 and 2.4 show the locaton of sources wth the color denotng the average sulfur and ash content, respectvely, of the coal from the source. Coal from the Rockes s 7
comparatvely low n both sulfur and ash. The hghest sulfur content s from sources n southern Illnos and Kentucky, whle the hghest ash content s from sources n Pennsylvana. Fgure 2.3: Average Sulfur Content Percentages 1991-2007 by Mne 7 4 0 8
Fgure 2.4: Average Ash 50 25 0 As stated above, there are numerous sources of coal avalable to the plants, and each plant chooses to buy from one or more of these sources. We dentfed, for each plant n each year, the number of sources from whch t bought coal. Fgure 2.5 shows the fracton of plants that purchased from a gven number of sources. The fracton choosng each number decreases rapdly wth number of sources. The most frequent outcome was for a plant to use only 1 source n a year. However, the number vares greatly, and the maxmum number of sources used by a plant n any one year was 74. The average sources used by a plant n a year was around 10, and, as shown n Fgure 2.6, ths average remaned about the same from 1991 to 2007. 9
Fgure 2.5 Number of Mnes Used by Plants Annually Fracton 0.02.04.06.08.1 0 20 40 60 80 Number of Mnes Used Average 0 5 10 15 20 Fgure 2.6 Average Number of Mnes Used per Plant by Year 1990 1995 2000 2005 Year 10
Fgure 2.7 gves the share of tonnage shpped by each mode, aggregated over plants, sources, and years. Ral, whch ncludes ral alone and ral-truck combnaton, obtaned the largest share, wth over 40% of the tonnage. The three barge modes combned (alone and n combnaton wth truck and barge) also captured a bt over 40%, wth 19% carred by truck alone. Fgure 2.7 Modal Shares 19.0 11.1 15.0 40.7 14.2 Barge Barge-Truck Truck Barge-Ral Ral The perod of our data, 1991-2007, represented an mportant tme for ar qualty regulaton, wth ncreasngly strct restrctons on emssons by coal-fred plants. Fgures 2.8-2.12 provde some nterestng statstcs n relaton to ths regulaton. The average sulfur and ash content of coal purchased by plants n our dataset dropped consderably durng the perod, wth sulfur content droppng by more than 30 percent and ash, whch s less heavly regulated, droppng by over 12 percent. Ths movement was accompaned by a slght reducton (about 5 percent) n the energy content of coal, measured n Btu s per pound n Fgure 2.10. Fnally, as 11
shown n Fgures 2.11-2.12, the average mne mouth cost of coal purchased, whether measured per ton or per Btu, dropped from 1991 to 2000 but then rose from 2000 to 2007, endng about 10 percent hgher than t started. Snce many factors affect average prces, ths eventual rse need not be a result of the envronmental regulaton; however, t s consstent wth the expectaton of hgher costs for cleaner coal. Percent Sulfur 1.4 1.6 1.8 2 2.2 Fgure 2.8 Average Percent Sulfur 1991-2007 1990 1995 2000 2005 year 12
Percent Ash 9 9.5 10 10.5 Fgure 2.9 Average Percent Ash 1991-2007 1990 1995 2000 2005 year BTU per Pound of Coal 11000 11200 11400 11600 11800 Fgure 2.10 Average BTU per Pound 1991-2007 1990 1995 2000 2005 year 13
FOB Prce Per Ton 20 25 30 Fgure 2.11 FOB Prce Per Ton 1990 1995 2000 2005 year costbtu.8 1 1.2 1.4 Fgure 2.12 Cost per Mllon BTU 1990 1995 2000 2005 year 14
3. DEMAND MODEL As dscussed above, numerous sources of coal are avalable to each plant, and each plant can choose to buy coal from more than one of these sources. For transportng the coal from the source to the plant, several modes are usually avalable, ncludng barge, ral, truck, or a combnaton. Our demand model descrbes the plants choce of where to buy coal and the mode by whch the coal s transported to the plant. The model s estmated on the data, descrbed above, for plants actual purchases of coal for the years 1991-2007. The estmated model relates the choces of the plant to the cost of coal by each source and mode, the sulfur and ash content of coal at each source, modal dummes, and varables that represent ncreasngly strngent emssons regulaton over tme. The model can be used to forecast the mpact of changes n costs on the modal shares and locaton of coal movements. 3.1 Specfcaton Consder a plant n a gven year. To facltate exposton, we suppress the subscrpts for plant and year, usng them only n the culmnatng expresson of the log-lkelhood functon. The plant has numerous optons avalable to t for obtanng coal. Each opton conssts of a source, such as a mne, and a mode of transportaton from the source to the plant. Let S denote the set of source-mode optons that are avalable to the plant n the year (.e., the choce set), wth the optons ndexed by. In our applcaton, the number of optons avalable to a plant n a gven year s as large as 5425, representng 1085 sources of coal and fve modes: (1) barge only, (2) truck only, (3) ral, ether only or wth truck, (4) barge-truck, and (5) barge-ral. As dscussed above, some plants do not have all modes avalable to them; for example, a plant that does not have barge access can receve coal from mnes by barge-truck or barge-ral, but not by barge 15
only. Smlarly, mnes open and close over tme, such that the number of sources avalable s dfferent n dfferent years. Each opton has attrbutes assocated wth t. Some of these attrbutes are observed by the researcher, such as the cost of coal through that opton (the mne mouth prce plus the cost of transportaton) and the sulfur content of the source s coal. These observed attrbutes are denoted by vector z. There are also attrbutes that affect the plant s choces but are not observed by the researcher; these are denoted by. The plant chooses how much coal to buy through each opton. Let x denote the quantty of coal purchased through opton, where x 0. Denote these quanttes collectvely by X x, S. The utlty, or generalzed proft, that the plant obtans from any partcular X s specfed as: z ( ) ( ) U X U x e [( x 1) 1] S S where s a vector of coeffcents of the observed attrbutes and s a scalar n the range 0 1. Ths utlty functon has the followng characterstcs: The utlty from opton s zero when no coal s purchased through that opton: z U ( x 0) e [(0 1) 1] 0 The margnal utlty of addtonal coal purchased from opton s MU ( x ) e ( x 1) z 1 16
The margnal utlty s exp( z ) at x 0, and, for <1, decreases as the quantty purchased through the opton ncreases. The rate of decrease s determned by, wth margnal utlty decreasng faster for lower values of. Wth =1, margnal utlty s constant. We refer to exp( z ) as the base margnal utlty of opton. The plant s assumed to have a requrement of buyng T unts of coal n total for the year, to meet ts producton requrements. The plant chooses the quantty to buy through each opton, subject to the constrant that the quanttes sum to T. In our applcaton, we consder coal denoted alternatvely n tons and btu's (.e., the btu output of the coal), wth estmaton performed under each defnton. Under the frst defnton, the plant s assumed to requre a certan number of tons of coal n total, whle n the second, the plant s assumed to face a btu requrement to meet the electrcty producton that t has been assgned. In ether case, the decson of the plant of where to buy the coal can be vewed as an element of an overall optmzaton procedure, n whch the allocaton of purchases among optons s optmal for whatever total s utlzed. The plant chooses X so as to maxmze generalzed profts subject to the constrant that ts purchases must meet ts total requrements. The optmzaton problem s the followng: z Max e [( x 1) 1] x S S st.. x T S x 0 S Assumng that quanttes are contnuous, the Kuhn-Tucker condton for constraned maxmzaton are the followng, where * x denote the optmzng value of x : 17
MU x e x f x * z * 1 * ( ) ( 1) 0 MU x e x e f x * * 1 * ( ) z z ( 1) 0 where s the Lagrangan multpler assocated wth the requrement for total coal purchases T. Stated n words, at the optmzng quanttes from each opton, the margnal utlty s the same for each opton from whch the plant buys, and the base margnal utlty s lower than ths amount for each opton from whch the plant does not buy. The frst condton apples because, otherwse, the plant could beneft from shftng some purchases from the opton wth lower margnal utlty to the opton wth hgher margnal utlty. The second condton apples because, otherwse, the plant would beneft from shftng some purchases from the optons from whch t s buyng to an opton from whch t s not buyng. Solvng ths constraned maxmzaton problem wth as many as 5425 optons s dffcult computatonally f the standard maxmzaton algorthms are used. However, the optmzaton can be vewed n a form that s easy to mplement and s perhaps smlar to the process that plants actually utlze. We use ths alternatve procedure for our forecastng n the sectons below. The decson process s treated as a seres of choces of where to purchase each unt of coal, startng wth the frst unt up to the T-th unt. The frst unt s purchased from the opton that has the hghest base margnal utlty. If were exactly 1, then the plant would buy all T unts from ths opton, snce the margnal utltes are constant. However, under the more expected condton that 1, purchasng one unt from an opton reduces the margnal utlty from a second unt. For the second unt of coal, the frm compares the margnal utlty of each opton, whch s the base margnal utlty for all optons except the one wth the hghest base margnal utlty, and, for that opton, s lower than ts base margnal utlty by the factor 18
(1 1) 2 1 1 1. The plant chooses to buy the second unt from the opton that has the hghest margnal utlty. If the hghest base margnal utlty s suffcently larger than the nexthghest, then the plant buys the second unt from the same opton as the frst; otherwse, the plant buys the second unt from the opton wth the second-hghest base margnal utlty. The process contnues untl the plant obtans all T unts. Note that the process can be mplemented for whatever sze of unt ncrement s deemed approprate from a pragmatc as well as realstc perspectve. Closer approxmaton to the mathematcal concept of contnuous varables s obtaned wth small ncrements, but plants are more lkely to make the decsons n larger ncrements. 7 From the plant s perspectve, s observed for each opton, whle these terms are unobserved from the researcher s perspectve. For estmaton and forecastng, we assume that each s ndependently random wth an extreme value dstrbuton. For any observed values of the x s, there s a probablty that the random s are such as to nduce the plant to choose those quanttes. Phaneuf et al. (2000) and Bhat (2005) show that the probablty of observng a gven X x, S takes the followng form. Let B( X ) S be the subset of optons from whch the plant buys strctly postve quantty, such that x 0 for each B( X ). The optons from whch the plant chooses not to buy any coal are n S but not B(X). The probablty of observng X s: 7 Note that ths process takes the s as gven, and yet the researcher does not observe these terms and treats them as random. In forecastng, we smulated the decson process by a takng a draw of S, determnng the plants coal purchases condtonal on the draw, repeatng wth a dfferent draw, and averagng the results. We used 1000 repettons (draws) for the forecasts, though we found that results were qualtatvely smlar wth only 100. 19
V (1 ) ( x 1) e PX ( ) ( BX ( ) 1)! V j B( X) ( x 1) B( X) (1 ) B( X) e j S where B (X ) s the number of optons n B(X) and V z ( 1)ln( x 1). It s nterestng to note that ths probablty s a generalzaton of a standard logt, n the followng sense. If 1, then (as dscussed above) the plant wll buy all of ts coal from one plant and P(X) reduces to the logt formula. Wth 1, dmnshng margnal utlty for purchases for any gven opton mples that n general the plant wll buy from more than one opton. 8 For estmaton, we observed a sample of 149 plants for the years 1991-2007. Let X nt denote the observed quanttes for plant n n year t. (Note that the number of elements n X nt s the number of optons avalable to plant n n year t, such that X nt has dfferent sze for dfferent plants and years.) The log-lkelhood functon for the observed choces s LL ln P( X ). To assure that the estmated value of s between zero and one, we parameterze t as 1/(1 exp( )). We maxmze the LL wth respect to the parameters and and then derve the estmate of from that of. Estmaton s facltated by the fact that the gradents of LL wth respect to and are smooth and easy to compute. nt 3.2 Estmaton Results Table 3.1 gves the estmated parameters for a model n whch the quantty of coal purchased at each opton s measured n tons. The explanatory varables are attrbutes of the optons (.e, 8 Note that even though ( 1 ) enters the denomnator of the second term, whch would seem to mply that the probablty s undefned when 1, the frst and second terms cancel to 1 when B ( X ) 1 probablty s stll defned., such that the 20
source/mode combnatons) that are avalable to the plant for buyng coal. The followng attrbutes are ncluded n the model: The total cost per ton of buyng coal through the opton, whch s the sum of the mne mouth prce and the transportaton cost by the opton s mode. Cost enters wth a negatve coeffcent, whch ndcates that, as expected, plants are less lkely to buy coal through a more expensve opton, all else held constant (ncludng, mportantly, the sulfur and ash content of the coal.) The sulfur content of the coal from the opton (whch vares over sources and years, but s constant for all modes for a gven source and year). Ths varable enters wth a dfferent coeffcent n each of three perods: pre-1995, 1995-1999, and post-1999. These three perods represent perods of ncreasngly strct regulaton under the clean ar acts. The estmated coeffcents are negatve, whch ndcates, as expected, that plants prefer coal wth lower sulfur content, all else (ncludng cost) held constant. Also, the coeffcents rse n magntude as the regulaton becomes more strct. The changes over tme are sgnfcant and farly large. For example, the dsutlty to plants of the sulfur content n coal more than doubles from pre-1995 to post-1999 (from a coeffcent of -0.0945 to - 0.2534). The ash content of coal from the opton, wth coeffcents for the three perods. The estmated coeffcents are negatve, ndcatng that plants prefer lower ash content, holdng all else, ncludng cost, constant. The coeffcents become larger n magntude over the three perods, whch s qualtatvely the same as for sulfur content. However, the dfferences over tme are consderably smaller for ash than for sulfur. The post-1999 coeffcent for ash s only twenty percent larger (n magntude) than ts pre-1995 value, 21
compared to a more than doublng for the sulfur coeffcent. Also, the change n the ash coeffcents from pre-1995 to 1995-1999 s small and not statstcally sgnfcant. These dfferences between sulfur and ash reflect the fact that the clean ar regulaton was amed toward sulfur more drectly than ash. Dummy varables for each mode, where the modes are (1) Barge alone, (2) Truck alone, (3) Ral alone or wth truck, (4) Barge-truck, and (5) Barge-ral. The coeffcents of these varables capture the net mpact of the non-cost factors assocated wth each mode. The dummy for mode 5 s omtted for dentfcaton, such that the coeffcents of the other mode dummes capture the mpact of non-cost factors relatve to the barge-ral mode. Barge-truck s sgnfcantly preferred to barge-ral, holdng cost constant; stated alternatvely: f the cost of barge-truck were the same as barge-ral, plants would tend to prefer barge-truck. Smlarly, on the bass of non-cost factors, barge alone and truck alone are estmated to be sgnfcantly less desrable than barge-ral. The parameter s estmated to be -1.1853, whch mples that s 0.7659. Recall that represents the degree of dmnshng margnal utlty assocated wth obtanng coal through a gven opton. A value of 1 represents constant margnal utlty, such that the plant buys all of ts coal from one opton. The estmate of 0. 7659 ndcates a moderate rate of dmnshng margnal utlty, consstent wth the observaton that plants generally buy from more than one opton but from far fewer optons than are avalable to them. The Btu content of coal s an mportant attrbute that vares over sources and yet s not ncluded n the model of Table 3.1. It can be entered nto the model n two ways: as an extra explanatory varable or n the defnton of the coal requrements of the plant. 22
In Table 3.2, Btu content s entered as an addtonal explanatory varable. It obtans a postve estmated coeffcent, whch ndcates that, all else held constant, plants prefer coal wth a hgh Btu content. Table 3.2: Model wth coal n tons, and Btu s per ton added as explanatory varable Explanatory varable/parameter Estmate Standard error Btu content (10,000 Btu s per lb) 0.5080 0.0802 Total cost per ton -0.0865 0.0011 Sulfur content per ton, pre-1995-0.0959 0.0126 Sulfur content per ton, 1995-99 -0.1249 0.0117 Sulfur content per ton, post-1999-0.2554 0.0114 Ash content per ton, pre-1995-0.0840 0.0033 Ash content per ton, 1995-99 -0.0899 0.0031 Ash content per ton, post-1999-0.1049 0.0035 Mode 1: Barge only -0.6957 0.0287 Mode 2: Truck only -0.0514 0.0288 Mode 3: Ral only and ral-truck -0.0088 0.0306 Mode 4: Barge-truck 0.5824 0.0231 Lambda -1.1853 0.0092 For Table 3.3, the Btu content of coal enters the plants requrement for coal. Recall n the specfcaton of the model that the plant s consdered to have a requrement for coal and to choose how much coal to buy from each opton n order to meet ths requrement. For the models of Tables 3.1 and 3.2, coal s measured n tons, such that the plant s consdered to face a requrement for a certan number of tons of coal. It mght be closer to realty to consder plants to face a Btu requrement, based on the amount of electrcty the plant s assgned to produce n the year. Table 3.3 gves a model n whch coal s measured n Btu s rather than tons (or, more precsely, n 20-mllon Btu s). That s, the tons of coal purchased through each opton s multpled by the Btu s per pound for coal from that opton (and then dvded by 10,000 for 23
scalng.) 9 Smlarly, total cost s expressed as cost per Btu, by dvdng the cost per ton by the Btu s per pound (and scalng.) To facltate comparson wth the prevous tables, sulfur and ash reman on a per-ton bass n Table 3.3. Interestngly, the dfference between the pre-1995 and post-1999 coeffcents for sulfur content s greater, ndcatng a larger mpact of regulaton, when the plants requrements are expressed n Btu s rather than tons. Table 3.3: Model wth coal n Btu s Explanatory varable/parameter Estmate Standard error Total cost of coal: $ per 20-mllon Btu s -0.1031 0.0013 Sulfur content per ton, pre-1995-0.0752 0.0128 Sulfur content per ton, 1995-99 -0.1156 0.0119 Sulfur content per ton, post-1999-0.2637 0.0115 Ash content per ton, pre-1995-0.0671 0.0033 Ash content per ton, 1995-99 -0.0766 0.0032 Ash content per ton, post-1999-0.1058 0.0038 Mode 1: Barge only -0.7207 0.0287 Mode 2: Truck only -0.0836 0.0288 Mode 3: Ral only and ral-truck 0.0129 0.0305 Mode 4: Barge-truck 0.5501 0.0231 Lambda -1.2335 0.0091 A model wth sulfur and ash expressed n per Btu s was also estmated, and the results were smlar n relatve coeffcent to those n Table 3. Also, a model was estmated n whch total cost was decomposed nto mne mouth prce and transportaton costs, wth separate coeffcents for each component. The coeffcent for transportaton cost was estmated to be consderably larger (n magntude) than that of mne mouth prce, and the dfference was statstcally sgnfcant. It s not clear what mght be causng ths dfference. However, snce dfferent coeffcents for cost components are nconsstent wth ratonal decson-makng by plants, we use the model wth one cost coeffcent for our forecastng n the next secton. 9 That s, coal s measured n unts of 20-mllon Btus: (Tons x Btu s per lb)/10,000 =(lbs/2000)* (Btu s per lb)/10,000=btu s/(2000 x10,000)=btu s/20 mllon. 24
3.3 Forecasts We use Model 3 to quantfy the mpact of regulaton and mode-specfc costs n a partal adjustment (or partal equlbrum) scenaro. We examne the mpact of regulaton by forecastng the coal purchases of plants twce: frst wth the coeffcents n Table 3.3 whch has coeffcents for sulfur and ash that rse n magntude over tme, and second wth the sulfur and cost coeffcents mantaned at ther pre-1995 estmates. Under the assumpton that the change n coeffcents was due to the enhanced regulaton, the dfferences n coal purchases between these two forecasts represents the predcted mpact of the regulaton, holdng all else, ncludng coal costs, constant. Ths analyss represents a partal adjustment, snce the change n demand that s nduced by regulaton can be expected to nduce a change n mne mouth prces for coal, wth prce rsng for cleaner-burnng coal and droppng for less clean-burnng coal, as well as perhaps a change n transportaton costs by mode. Table 3.4 gves the percent change n varous summary measures of demand that result from changng the 1995-99 and post-1999 coeffcents for coal and ash to the pre-1995 coeffcents, respectvely. Interestngly, by 2007, total sulfur content of the coal that s purchased s estmated to rse by 13.3 percent. Stated more drectly, n the absence of the strcter regulaton that started n 1995, the sulfur content of coal burned by plants would have been 13.3 percent hgher than actually occurred n 2007. 25
Table 3.4: Forecast n the absence of the strcter regulaton that started n 1995: Percent change n coal purchase characterstcs usng pre-1995 coeffcents n all years Sulfur Ash Total cost Mode 1: Barge only Mode 2: Truck only Mode 3: Ral only and wth truck Mode 4: Bargetruck Mode 5: Bargeral 1995 2.67 1.38-0.32 0.20 0.18-0.22 0.07-0.05 1996 2.68 1.23-0.38 0.19 0.18-0.20 0.11-0.16 1997 2.68 1.51-0.34 0.22 0.23-0.27 0.11-0.09 1998 2.55 1.28-0.29 0.16 0.22-0.21 0.05-0.09 1999 2.74 1.07-0.25 0.13 0.15-0.18 0.08-0.02 2000 12.61 4.09-1.08 0.63 1.23-1.11 0.45-0.48 2001 14.34 3.84-1.34 0.52 1.68-1.49 0.61-0.41 2002 15.30 3.77-1.60 1.69 2.38-2.23 0.77-0.95 2003 13.14 3.23-1.54 1.51 1.45-1.72 0.60-0.52 2004 14.02 3.92-1.75 1.22 1.45-1.69 0.69-0.72 2005 14.50 4.57-2.09 1.23 2.78-2.72 1.55-1.22 2006 15.00 3.84-2.12 0.86 1.70-1.88 0.97-0.60 2007 13.23 3.55-2.45 1.45 2.24-2.16 1.03-1.27 Ths estmate does not take two mportant consderatons nto account. Frst, plants often responded to the strcter regulaton by nstallng technologes that reduce sulfur emssons for any gven level of sulfur content n the coal. To the extent that ths technology-based response occurred, the mpact of strcter regulaton on sulfur emssons was larger than the 13.3% change n sulfur content that we estmate. Second, as dscussed above, the cost of coal can be expected to have changed as a result of regulaton, wth prces rsng for coal wth lower sulfur content and fallng for coal wth hgher sulfur content. To the extent that prce changed n ths way, our analyss, by usng the observed costs n all years for both the actual stuaton and the but-for, overestmates the mpact of strcter regulaton on sulfur content. 10 10 Wthout regulaton, the prce of cleaner coal would have been lower relatve to less-clean coal, causng a rse n the quantty of cleaner coal purchased relatve to less clean coal, such that total sulfur content, from ths prce effect alone, drops. Of course, ths prce effect occurs because of the regulaton-nduced shft n demand for clean coal relatve to less clean coal and s therefore smaller than the orgnal shft n demand. 26
The other changes n Table 3.4 are also nterestng. Ash content decreases, though consderably less than sulfur content. Ths result s consstent wth the form of regulaton, n whch controls on ash were less drect than those on sulfur. The total cost of coal purchases would have been 2.45 percent lower n 2007 n the absence of the strcter regulaton; stated conversely, the strcter regulaton ncreased plants cost of buyng coal by 2.45 percent, after they re-optmzed where they bought ther coal. (Note that the total coal purchases by each plant are fxed, such that only the composton of the total s affected by the scenaro.) In terms of mode choce, barge and truck usage would have been slghtly hgher n the absence of the strcter regulaton. Stated conversely, the strcter regulaton rased demand for ral and lowered demand for barge and truck. Consder now the mpact of a change n transportaton costs for barge movements. As an llustraton, we consder a scenaro n whch transportaton costs drop ffty percent for mode 1 (barge only) and twenty-fve percent for modes 4 and 5 (barge-truck, and barge-ral). Table 3.5 gves the percent change n varous summary measures of demand that are forecast under ths change n barge costs. By 2007, he amount of coal shpped by barge rses by only 5.15%. Ths farly small response s partly due to the fact that transportaton costs consttute a small share (about ten percent) of the total cost of buyng coal. E.g., a ffty percent reducton n transportaton costs consttutes only about fve percent reducton n total costs, such that a 5.15% response represents nelastc demand (elastcty of about 0.103) for barge shpments wth respect to transportaton cost of barge but an approxmately untary elastcty for barge shpments wth respect to total cost of coal through the barge optons. Interestngly, the reducton n barge costs decreases the total sulfur and coal content of the coal that plants purchase. Ths result suggests 27
that waterway mprovements provde an envronmental beneft that needs to be taken nto consderaton when conductng cost-beneft analyss for these mprovements. Table 3.5: Forecast under lower transportaton costs for barge: Percent change n coal purchase characterstcs from transportaton costs droppng 50% for mode 1 and 25% for modes 4 and 5. Sulfur Ash Total cost Mode 1: Barge only Mode 2: Truck only Mode 3: Ral only and wth truck Mode 4: Bargetruck Mode 5: Bargeral 1991-0.14 0.18-2.92 1.67-3.95-2.09 3.79 3.93 1992-0.11 0.17-2.96 1.74-3.85-2.04 3.79 3.79 1993-0.21 0.09-2.94 2.38-3.83-2.15 3.71 3.70 1994-0.21 0.03-3.03 2.51-4.13-2.33 3.65 4.17 1995-0.33 0.00-3.20 3.24-4.23-2.37 3.34 4.08 1996-0.31-0.01-3.17 2.73-4.13-2.32 3.53 4.32 1997-0.33-0.01-3.12 3.12-3.94-2.12 3.23 4.48 1998-0.30-0.02-3.09 2.89-3.72-2.14 3.41 4.23 1999-0.22-0.02-3.15 2.71-3.79-2.22 3.66 4.30 2000-0.41-0.21-3.31 3.39-4.00-2.11 3.13 4.61 2001-0.53-0.27-2.97 4.09-3.96-2.18 2.86 4.98 2002-0.80-0.47-3.30 5.10-5.27-3.00 2.33 6.05 2003-0.65-0.35-3.25 4.88-4.86-2.96 2.39 5.24 2004-0.62-0.35-3.30 4.26-4.95-3.10 2.65 5.67 2005-1.33-0.68-3.18 6.67-5.27-3.44 1.82 6.39 2006-0.91-0.47-2.99 4.96-5.28-3.19 2.36 6.03 2007-0.85-0.41-3.08 5.15-4.98-3.12 2.29 5.81 4. SUMMARY/CONCLUSIONS Ths paper develops and estmates a model of the demand for coal shpments n the Oho Rver Basn (ORB). Coal s by far the domnant commodty that travels by the waterway n the ORB. There are over 250 mllon tons that travel by the waterway, and about one-half of that s of coal to electrcty plants. These electrcty plants can purchase coal from a number of dfferent locatons and can usually shp by a number of dfferent modes and/or modal combnatons. We examne observed data on 151 electrcty plants from 1991-2007, and a total of 159,467 transactons over that tme perod. 28
We develop a demand model that s based on plants decsons for coal movements to the 151 plants. The plants can choose from the entrety of the mne-coal-sources and modal optons avalable to them, and can and do typcally choose from more than one of these optons. Our model represents the decson of where to obtan coal and by what modes to receve t. We frame these decsons n terms of the cost and attrbutes (sulfur and ash) of coal along wth dfferent phases of the Clean Ar Amendments of 1990. The general fndngs are that the model s statstcally sgnfcant wth expected sgns for the the estmated parameters. Total costs, attrbutes and dfferent regulatory regmes have strong statstcal effects on the demand for coal. In our forecasts, we found mportant effects from the Clean Ar Act Amendments of 1990, and, n partcular from ncreased regulaton on sulfur and, to a lesser extent, ash. In contrast, changes n transportaton rates was estmated to have a relatvely small effect on demands, whch may be attrbuted to a number of factors, ncludng the fact that transport costs are only a small porton of the costs of buyng coal and producng electrcty. 29
REFERENCES Bhat, Chandra, 2005, A multple dscrete-contnuous extreme value model: formulaton and applcaton to dscretonary tme-use decson, Transportaton Research, Part B, Vol. 39, pp. 679-707. Bhat, Chandra, and Sudeshna Sen, 2006, Household vehcle type holdngs and usage: an applcaton of the multple dscrete-contnuous extreme value (MDCEV) model, Transportaton Research, Part B, Vol. 40, pp. 35-53. Km, Jaehwan, Greg Allenby, and Peter Ross, 2007, Product attrbutes and model of multple dscreteness, Journal of Econometrcs, Vol. 138, pp. 208-230. Phaneuf, Danel, Catherne Klng, and Joseph Herrges, 2000, Estmaton and welfare calculatons n a generalzed corner soluton model wth an applcaton to recreaton demand, Revew of Economcs and Statstcs, Vol. 82, pp. 83-92. Von Haefen, Roger, and Danel Phaneuf, 2005, Kuhn-Tucker demand system approaches to non-market valuaton, n R. Scarpa and A. Albern, eds., Applcatons of Smulaton Methods n Envronmental and Resource Economcs, Ch 8., pp. 135-157, Dordrecht: Sprnger. 30