DUOPOLY IN THE RAILROAD INDUSTRY: BERTRAND, COURNOT, OR COLLUSIVE?

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1 Please do not quote. DUOPOLY IN THE RAILROAD INDUSTRY: BERTRAND, COURNOT, OR COLLUSIVE? Clfford Wnston Brookngs Insttuton Scott M. Denns U.S. Department of Transportaton Vkram Maheshr Brookngs Insttuton Abstract: We develop an equlbrum model of entry n ral transportaton markets for coal to test emprcally one of the oldest controverses n economc theory: How are prces determned n duopoly markets? We fnd that competton between Unon Pacfc and Burlngton Northern n the Powder Rver Basn of Wyomng and Montana s most accurately characterzed by Bertrand s theory that prce-settng duopolsts wll sell ther dentcal product at the compettve prce. We dentfy the features of coal transportaton markets that facltate such behavor and brefly dscuss the polcy mplcatons of our fndngs. August 2004 We are grateful to Davd Brownstone, Jay Ezrelev, Theodore Keeler, Roger Noll, Sam Peltzman, and Peter Ress for helpful comments.

2 Introducton What wll happen to prces when two producers of an dentcal good compete? Economsts have debated ths queston for nearly 200 years, narrowng the outcomes to margnal cost prcng (Bertrand behavor), monopoly prcng (collusve proftmaxmzng behavor), or somethng between these extremes based on the market demand for the output that s smultaneously offered by the two compettors (Cournot behavor). It s standard practce n economcs for theory to dentfy a wde range of possble behavoral outcomes n a market and for emprcal work to ndcate the most lkely outcome. In the case of duopoly competton, however, relatvely lttle emprcal research exsts. Ths paucty of evdence s partcularly surprsng because many anttrust and regulatory polcy ssues turn on whether consumer welfare wll be sgnfcantly enhanced f an ncumbent monopolst must face a compettor. Competton n ralroad markets offers a classc example of ths stuaton. Lke many ndustres deregulated n the past 25 or so years, ralroads responded to ther economc freedom n 1980 by consoldatng through mergers. The most recent merger wave, whch began n the md-1990s, left two major ralroads n the western Unted States, Burlngton-Northern Santa Fe and Unon Pacfc, and two n the east, Norfolk Southern and CSX. As a result, most U.S. shppers have only two ral carrers competng for ther busness, and some have only one. Of course, even monopolst ralroads wll often face ntense competton from motor or water carrers, so most shppers have ganed substantally from deregulaton of the surface freght transportaton system (Wnston (1998), Denns (2001)). Nonetheless, so-called captve shppers and the varous organzatons that represent them complan that ral rates are not always reasonable and

3 2 that the Surface Transportaton Board the successor to the Interstate Commerce Commsson wth the authorty to determne the legalty of rates n accordance wth maxmum rate regulatons does lttle to protect them. 1 Grmm and Wnston (2000) pont out that the Board s rate complant process s tme-consumng, costly, and complex and that few rates are successfully challenged. In response to such charges, Congress has been consderng legslaton to ncrease ral competton. The legslaton s not yet fnal, and one vtal ssue stll pendng s whether ral competton s suffcent f a captve shpper has access to an addtonal ralroad. Recent developments n ral transportaton markets for coal shpped from the western Unted States provde a natural experment for analyzng how ral prces are affected when a monopoly carrer s subject to competton from another ralroad. In ths settng, a ral transportaton market s a route wth a coal mne at the orgn and an electrc utlty plant at the destnaton. Begnnng n the late 1970s, Burlngton Northern was the only ral carrer that shpped coal from the Powder Rver Basn n Wyomng and Montana to electrc utltes natonwde. In 1985, the Interstate Commerce Commsson authorzed the Chcago & North Western ralroad to buld track nto the southern end of the Powder Rver Basn thus enablng ts subsequent merger partner, Unon Pacfc, to compete n a growng number of markets wth Burlngton Northern n transportng Powder Rver Basn coal to the naton s power plants. In ths paper, we develop a structural econometrc model of Powder Rver Basn markets for coal transportaton by ral treatng Unon Pacfc s entry as endogenous. Parameter estmates of the model enable us to smulate the behavor of market rates over tme, solatng the effect of Unon Pacfc s entry that creates duopolstc competton n 1 Under maxmum rate gudelnes, shppers can challenge a rate f t exceeds 180 percent of varable costs and f the ralroad n queston has no effectve competton.

4 3 these markets. We fnd that the path of coal transport rates approaches the long-run margnal cost of ral servce n markets that UP has entered, suggestng that duopoly ralroad prcng n Powder Rver Basn markets s consstent wth Bertrand competton. We dentfy the features of coal transportaton markets that facltate such behavor and brefly dscuss the polcy mplcatons of our fndngs. A Bref Overvew of Powder Rver Basn Coal Transportaton Markets Coal from the Powder Rver Basn (PRB) n Wyomng and southern Montana burns cleaner than most coal mned n the Unted States because of ts lower sulfur and ash composton. Demand for PRB coal ncreased substantally between 1988 and 1997 (fgure 1) because the 1990 amendments to the Clean Ar Act requred electrcty generatng plants to reduce ther emssons. By swtchng to PRB coal, a plant can remove sulfur doxde for $113 per ton, whereas a plant burnng eastern coal must spend $322 per ton to remove the pollutant by nstallng scrubbers. 2 Because vrtually all PRB coal shpped to electrc utlty plants moves by ral for most or all of the journey, ralroads do not compete drectly wth trucks or barge transportaton n these markets. Burlngton-Northern Santa Fe (BN) began transportng substantal amounts of coal from the Powder Rver Basn n the late 1970s and enjoyed a monopoly. But n 1985, authorzed by the ICC, Unon Pacfc (UP) began to buld nto the regon. Competton between the carrers ntensfed as UP gave a growng number of plants alternatve access to PRB coal. As power plants contracts wth BN expred, they were able to renegotate ther contracts n a duopoly market. Gven that mnng and ral servce n the Powder Rver Basn are relatvely new, UP and BN have been able to 2 These fgures are from Coal Age, volume 104, August 1999.

5 4 employ the most effcent operatons possble, unencumbered by the older ral nfrastructure and outdated technology that ralroads have been sheddng snce deregulaton. In 1999, a thrd ralroad, the Dakota, Mnnesota & Eastern Ralroad Corporaton, ndcated an nterest n connectng ts network to the Powder Rver Basn. Local landowners, however, have opposed the proposed ral lne, and t has yet to be bult. In sum, Powder Rver Basn coal transportaton markets provde a natural settng for an emprcal test of duopoly behavor because the characterstcs of PRB coal dstngush ts supply and demand from other domestc coal markets and because utltes that receve PRB coal by ral transportaton face ether a monopoly suppler or a duopoly n whch both carrers, BN and UP, offer nearly dentcal servces. A Structural Econometrc Model of Ral Transportaton Markets for Coal Emprcal ndustral organzaton research has addressed the two key aspects of our problem, competton wthn a market and the mpact of new entry, separately. Authors such as Porter (1983) and Parker and Roller (1997) have characterzed the compettveness of a duopolstc market, focusng on dfferent sources of collusve behavor, whle authors such as Bresnahan and Ress (1990, 1991) and Berry (1992) have explored the determnants of entry, focusng on the number of compettors n a market and the mpact of entry on costs. A few authors have estmated compensatng varatons to test explctly for alternatve compettve outcomes n duopoly markets (e.g., Brander and Zhang (1990), Fscher and Kamerschen (2003)). Compensatng varatons, however, are based on statc

6 5 compettve condtons, whch make them unrelable n markets such as ral, where dynamc changes n competton occur as contracts expre and a new entrant s able to compete for a shpper s busness. 3 Our approach characterzes the duopoly behavor of Unon Pacfc and Burlngton Northern by analyzng the effect of UP s entry whch creates duopolstc competton on coal transportaton prces over tme. We develop a model of demand and supply for coal transportaton by ral, where entry affects supply. We then specfy a model of carrer entry and derve the lkelhood functon to jontly estmate the central nfluences on market prces, tons of coal shpped, and the decson to enter a market. Fnally, we solate the effect of entry on equlbrum ral transportaton prces and compare the estmated prce path wth an ndependent estmate of the long-run margnal costs of transportng coal by ral. Demand. Our emprcal analyss wll be conducted on a panel of electrc utlty plants. We specfy power plant s demand for ral transportaton, D t Q t D, at tme t as: D D Q t = D( pt, X t ; ut ), (1) where p s the prce of ral transportaton (n dollars per ton-mle), X contans t exogenous nfluences on demand, and u t s an error term that s assumed to be 2 σ Q dstrbuted normally wth mean zero and varance. The exogenous nfluences on coal shppers demand for ral transportaton that we nclude are the length of haul from the mne mouth to the plant, whch controls for 3 Brander and Zhang (1993) estmate conjectural varatons over tme for arlne routes nvolvng competton between Amercan Arlnes and Unted Arlnes but stll nvoke assumptons that may prevent them from capturng the dynamc aspects of duopoly competton.

7 6 servce qualty, and dummy varables to ndcate whether the plant can receve non-prb coal by ral or water transportaton, whch controls for alternatve coal sources. Greater lengths of haul or an alternatve source of coal should reduce the demand for ral shpments of PRB coal. Because ral transportaton s derved demand (n ths case, t s an nput nto the fnal producton of electrcty), we specfy the maxmum theoretcal output that s, nameplate capacty, of a gven plant and the average natonal prce of natural gas (to capture substtuton wth an alternatve source of energy). We use nameplate capacty nstead of electrcty actually generated because capacty s not affected by the type of coal that a plant chooses to burn. We also nclude an ndex to capture the sulfur doxde emsson caps mposed n 1995 on some but not all plants to mplement the standards set by the 1990 amendments to the Clean Ar Act. The ndex takes on values between zero and one, wth hgher values ndcatng that specfc plants are allowed to emt greater amounts of SO 2. Because the caps are based on a plant s emssons and fuel use fve years before passage of the 1990 amendments, t s reasonable to treat the caps as exogenous. 4 Nameplate capacty and natural gas prces should have a postve effect on the demand for PRB coal, thereby ncreasng the demand for ral transport. The sgn of the emssons caps s ndetermnate because n response to the caps, plants mght reduce ther demand for all sources of coal and produce less or substtute cleaner PRB coal for other coal sources and mantan output. The frst adjustment would cause ther demand for ral transportaton to fall whle the second would cause ther demand to rse. As noted, the passage of the 1990 amendments to the Clean Ar Act ncreased demand for PRB coal by encouragng all electrc utltes to seek low-cost ways to reduce 4 Schmalensee et al. (1998) provde a dscusson of emssons caps.

8 7 polluton. Our demand specfcaton captures ths effect wth a dummy varable ndcatng the years snce the act s passage. Ths dummy should have a postve sgn. Fnally, we specfy a tme trend, as well as fxed effects at the regonal, utlty (some utltes own multple plants), and plant level to capture any unmeasured nfluences on ral demand n these dmensons. Supply. In a market of homogeneous frms facng a demand elastctyη, proft maxmzaton mples that frm k s prcng behavor can be characterzed as: θ k p 1 + = MC( qk η whereθ k s frm k s conduct parameter, MC s ts margnal cost functon, and q k s ts output. Followng Porter (1983), we aggregate ths condton across frms such that the relatonshp between market supply prce, output, and entry effectvely characterzes an ndustry supply curve. Thus, we specfy the supply prce of ral transportaton to power plant at tme t as: ), S pt S = S( Qt, Et, Zt ; εt ), (2) where the prce s a functon of the quantty of coal transported, S Q t carrer, E, and exogenous supply characterstcs, Z. The error term, t t, entry of the second ε t, s assumed to be dstrbuted normally wth mean zero and varance σ 2 p. We measure entry wth a dummy varable that ndcates whether a plant can receve PRB coal from two ral carrers at tme t. As noted, t may take tme for a new entrant to nfluence ral prces because a shpper may be locked nto a contract rate wth the ncumbent ralroad for several years. Thus, we also nclude the number of years after entry that a second ral compettor offers a plant servce from the Powder Rver Basn.

9 Both varables should have a negatve effect on ral prces unless carrers engage n some 8 form of collusve behavor. 5 In contrast to some markets (e.g., arlnes), potental ral competton s not lkely to be a relevant factor n PRB markets because negotatons over contract rates occur only when actual entry s assured that s, UP s commtted to ncurrng the sunk costs of layng new track that connects a utlty wth the UP network. Exogenous nfluences on ral prces consst of other sources of competton and varables capturng ral costs. We nclude two dummy varables to ndcate whether plants can receve coal from outsde the Powder Rver Basn by an alternatve ralroad or by water transportaton. Both measures of source competton should have a negatve effect on ral prces. We capture the nfluence of ral costs on prces by specfyng ral ndustry operatng expenses (whch effectvely amounts to a ral cost ndex) and the length of haul from the mne mouth to the plant. 6 We expect hgher operatng costs to ncrease prces, whle greater lengths of haul should reduce prces per ton-mle because of economes of dstance n ral transportaton. Fnally, we nclude a tme trend to account for techncal change n ral transport, as well as fxed effects at the regonal, utlty, and plant level to capture unmeasured nfluences on prces n these dmensons. Entry. Unon Pacfc dd not elect to serve all routes where a utlty receved PRB coal; thus, t s approprate to treat ts entry decsons as endogenous n our framework because they are undoubtedly based on specfc market condtons for coal transportaton. Generally, entry represents a strategc decson consstent wth proft maxmzng 5 Schmdt (2001) and Grmm, Wnston, and Evans (1992) have found that an ncrease n the number of ral carrers n a market lowers ral rates. 6 Gven that route specfc operatng costs were not avalable, we ntally specfed the cost ndex usng ndustry operatng costs per ton-mle. But we found that ths measure performed poorly n the model, possbly because t was spurously correlated wth the dependent varable whch s also denomnated n dollars per ton-mle. Thus, we constructed the cost ndex usng operatng costs.

10 9 behavor. Berry (1992), for example, specfed proft avalable to frm k by enterng market as: f ( X, Z, N), k = where X contans characterstcs affectng demand, Z k contans characterstcs affectng costs, and N s equal to the number of frms n the market. Entry s assumed to occur k when k > 0, hence the probablty of entry can be wrtten n terms of the varables that comprse X, Z, and N. Ths specfcaton of entry s a useful startng pont, but t needs to be modfed for our stuaton. Frst, Unon Pacfc s entry decsons are confned to markets served by a sngle carrer of PRB coal. Whle ths means that the number of ral carrers of PRB coal s equal to one and does not vary by route, t would be expected that UP s entry s nfluenced by the presence of source competton from alternatve ral carrers and water transportaton that could supply a plant wth non-prb coal. We therefore use the ral and water source competton dummes to capture the presence of addtonal compettors n the market. Berry does not specfy prce n hs model, mplctly allowng ts nfluence to be captured by the number of frms n the market and assumptons about compettve behavor. In our case, Unon Pacfc can expect that devatons from monopoly ral prces set by Burlngton Northern reflect the presence of water or source competton, thus we too do not specfy entry as an explct functon of prce. Furthermore, n our model the equlbrum quantty of coal that s transported mplctly determnes the

11 market prce. We therefore post that the revenue-related nfluences on entry smplfy to the tons of coal that s shpped and the length of haul. 7 Fnally, UP s entry decsons are also nfluenced by the costs of enterng and competng n a market. To enter a route, UP must ncur the sunk costs of layng down new track that connects a utlty wth the UP network. We capture ths cost by specfyng the buld-out dstance from the plant to the closest non-ncumbent ral lne. We expect that as the requred buld-out ncreases, UP s lkelhood of entry decreases. Even f UP can enter a market, t must consder ts operatng costs. We control for ths effect usng a 10 cost ndex based on ndustry operatng expenses per ton-mle. 8 In addton, UP wll clearly be at a compettve dsadvantage aganst BN n a gven market f t has to haul ts freght a greater dstance than BN has to haul ts and vce-versa. To account for ths, we specfy the dfference between UP s length of haul and BN s length of haul. Hgher operatng costs and relatvely greater lengths of haul wll lower UP s probablty of entry. Fnally, we also nclude a tme trend, as well as fxed effects at the regonal, utlty, and plant level to capture unmeasured nfluences on entry n these dmensons. Gven these consderatons, we can specfy UP s entry decson n market at tme t as: E t = E( L Qt, Yt ; ν t ), (3) 7 The quantty of coal that was shpped n a gven market tended to be statonary throughout the perod covered by our sample unless a second ralroad entered the market. Thus, we dd not specfy lagged values of tons shpped n the entry equaton. 8 Industry operatng costs denomnated n dollars per ton-mle produced a more satsfactory statstcal ft n terms of log lkelhood than operatng costs denomnated n dollars. Note that n contrast to the supply equaton, the dependent varable n ths case s not expressed n dollars per ton-mle.

12 11 where L, the length of haul, and Qt, the quantty of coal demanded, yeld ton-mles of coal transported, Y t captures exogenous cost and competton consderatons, and the error term ν s assumed to be dstrbuted normally wth mean zero and varance. t (Wthout loss of generalty, we can set equal to 1.) In ths formulaton, we smply observe the number of ralroads n a market, whle proft s a latent varable. Thus, takes on a value of one or zero dependng on whether UP has entered the market (ndcatng whether > 0 ). t 2 σ E 2 σ E Lkelhood functon. The system of equatons ((1), (2), and (3)) can be jontly estmated by full nformaton maxmum lkelhood, accountng for both endogenous and exogenous nfluences and the correlaton of the errors across the equatons. The approprate lkelhood functon s obtaned from the jont probablty densty functon of each decson varable n our system. The dependent varables n the demand and nverse supply equatons are contnuous; because we observe entry nstead of proft, the dependent varable for the entry equaton s dscrete. Accordngly, we take the followng steps to jon the three random varables. The jont dstrbuton of the demand and nverse supply equatons can be expressed as bvarate normal, condtonal on entry. Gven that entry s nfluenced by utltes demand for coal, we calculate the dstrbuton of entry condtonal on demand. We then construct the lkelhood functon by dervng the jont uncondtonal densty for prce, quantty, and entry. Suppressng the tme subscrpts for smplcty, the dstrbutons of the demand and nverse supply equatons are gven by: E t

13 12 Q D 2 ~ N( µ ( p, X ), σ ) and (4) Q Q p S ~ S 2 p N( µ ( Q, E, Z ), σ ), (5) p where µ Q and µ p are the means of quantty and prce, respectvely. Because prce and quantty are dstrbuted normally, we can express ther jont dstrbuton as a bvarate normal random varable condtonal on entry as: f p, Q E ~ exp(.5( Q + ~ p 2ρ ~~ p, QQp ) /(1 ρ p, Q )) =, 2πσ σ 1 ρ p Q 2 p, Q (6) where the tlde desgnates that the normal random varable has been standardzed (mean zero, varance one), and ρ ndcates the correlaton between the errors of p and Q. 9 p, Q We assume UP enters a route only when profts are postve; that s, = f ( L Q, Y ; ν ) > 0. But proft s a latent varable; thus, we focus on the entry behavor that s observed and postulate: Pr( E = 1) = Pr( > 0) = Pr( ν > ( δ 0 + δ1q L + Y δ 2 )), where the δs are estmable parameters. Gven that the error termν s dstrbuted as a normal random varable wth mean zero and varance σ E 2 = 1, t follows that Pr( E = 1) = Φ( δ 0 + δ1q L + Yδ 2 ), (7) where Φ s the cumulatve densty functon for a standard normal random varable. However, because the error tem ν s undoubtedly correlated wth quantty Q, the entry probablty equaton (7) would yeld based parameter estmates n ts current form. We address ths problem by estmatng these parameters as part of a system of 9 See, for example, Greene (2003), Appendx B, pp

14 equatons where we treat entry, prce, and quantty as endogenous and obtan consstent estmates of ther parameters n the approprate equatons usng exogenous varables n the entre system as nstruments. Gven that we can obtan a consstent estmate for δ 1 accountng for the correlaton between the errors of the entry and demand equaton ρ E,Q, we can wrte the condtonal probablty densty functon for entry as a bnomal random varable: 13 f E ( E Q ) = E Φ ( δ 0 + δ 1 ( ρ E, Q ) Q L + Yδ 2 ) + (1 E )[ 1 Φ ( δ + δ ( ρ ) Q L + Y δ )] E, Q 2 (8) If E = 1, only the frst term n the equaton s swtched on, and f = 0, only the second term s. We can now derve the jont densty of entry, prce, and quantty as the product of the condtonal densty gven n equaton (8) and the margnal densty of prce and quantty, namely: f E, p, Q = f E p, Q f p, Q. (9) The margnal densty can be wrtten as a weghted sum of bvarate normal random varables. In equaton (6), supply prce s condtonal on entry. To obtan the uncondtonal dstrbuton, we evaluate the prce gven n equaton (5) for entry values of E=1 and E=0, whch yelds: E f. 10 (10) p, Q = Pr( E = 1) f p, Q E= 1 + Pr( E = 0) f p, Q E = 0 10 When we substtute entry nto the stochastc formula for prce gven n equaton (5), we account for ρ p,e, the correlaton of error terms n the nverse supply equaton and n the entry equaton.

15 14 Usng equaton (9), our jont probablty dstrbuton s then equal to the product of equatons (8) and (10), whch we denote as f E, p, Q. As noted, we are smultaneously computng the entry probabltes as stochastc functons of nstrumented quantty. Gven the jont probablty densty functon, the lkelhood functon we wsh to maxmze wth respect to the parameters of the demand (1), supply (2), and entry (3) models, Θ (ncludng the ρs), s the product taken over all N observatons N L( Θ) = Θ. = 1 f E, p, Q; In our estmatons, the demand and supply equatons take a logarthmc functonal form, whch s plausble (see, for example, Porter (1983)) and fts the data better than a lnear functonal form. Sample and Estmaton Results Our emprcal analyss s based on the shppng actvty of the 48 electrc utlty plants n operaton from 1984 to 1998 that burned at least one mllon tons of Powder Rver Basn coal n a representatve year, The sample ends at 1998 because by 1999 electrc utltes began to wn a handful of maxmum rate cases before the Surface Transportaton Board, so recent reductons n coal rates could potentally be attrbutable to resdual regulaton. 11 The plants n our sample account for nearly 75 percent of all Powder Rver Basn coal shpped by ral. Of the 48 plants, 31 were served by a sngle ralroad throughout the sample perod and 17 experenced entry sometme between 1985 and Of the No utltes n our sample receved a lower ral rate durng by wnnng a maxmum rate proceedng.

16 plants, 10 used only PRB coal. A few of the sngle-served plants came on lne after 1984, thus our fnal sample conssts of 696 observatons. The data sources for the varables used n our analyss and ther sample means are presented n table 1. It s mportant to pont out that vrtually all ralroad coal traffc s transported under prvate contracts that do not reveal the shpper s rate. Thus, we collected publcly avalable data from the U.S. Department of Energy, Energy Informaton Admnstraton, and estmated ral rates for electrc utltes as the dfference between the delvered prce per ton of coal that s consumed at the plant and the prce per ton of coal at the mne mouth. The delvered prce of coal reported by the utlty ncludes all the costs ncurred by the utlty n the purchase and delvery of the fuel to the plant (FERC (1995)). The mne mouth prce reported by the mne s the total revenue receved usng the actual F.O.B. ral sales prce (EIA (1995)). Dvdng the dfference by the length of haul yelds prce per ton-mle. Subsequent dscussons that we had wth ralroad personnel confrmed that our estmates of ral rates n PRB markets were qute close to actual ral rates. Based on these data, a smple comparson of freght rates n monopoly and duopoly markets from 1995 to 1998 suggests that a second entrant has reduced rates and that rates n duopoly markets have fallen over tme as contracts between the ncumbent carrer and shppers have expred (table 2). Of course, ths comparson does not hold other nfluences on rates constant; we do so by estmatng our model of ral transportaton supply, demand, and entry n Powder Rver Basn markets. Full nformaton maxmum lkelhood (FIML) estmates of the model are presented n table 3. As noted, we specfed a tme trend to control for unobserved temporal effects and fxed utlty and plant effects, but they were statstcally 15

17 16 nsgnfcant n the supply, demand, and entry equatons and ther excluson had lttle effect on the other parameter estmates so they are not ncluded n the specfcaton presented here. 12 Generally, the coeffcents have ther expected sgns and are statstcally sgnfcant. The demand for ral transportaton of coal s nelastc, whch s plausble. The demand elastcty of 0.38 s algned wth prevous research and reflects the small share of transport costs n the prce of electrcty and consumers nelastc demand for electrcty. 13 Another factor that may lmt plants response to coal rates s that utltes tend to run ther larger coal-fred plants at close to operatonal capacty whch n most cases s fxed for the perod covered by our sample. Gven that the margnal revenue assocated wth an nelastc ndustry demand curve s negatve, t appears that ralroads are not engagng n sngle-perod collusve proft maxmzaton or Cournot behavor. However, ths concluson may be premature to the extent that the carrers conduct s consstent wth ether form of behavor subject to constrants mposed by competton n wholesale electrcty markets or the threat of maxmum rate regulaton. 14 The elastcty of ral prces wth respect to tons shpped n the nverse supply equaton, 0.02, s not statstcally sgnfcantly dfferent from zero, ndcatng that ral s operatng at constant returns to scale. Although ralroads generally exhbt economes of traffc densty (Braeutgam (1999)), our fndng ndcates that they are able to exhaust 12 We also nteracted the fxed effects wth operatng costs to allow ths varable to vary across plants, but the fxed effects were statstcally nsgnfcant. 13 Wnston, Grmm, Cors, and Evans (1990) estmate of the prce elastcty of demand for ral transportaton of coal was It should also be noted that we have estmated the market, as opposed to ndvdual frms, demand curve. Gven the zero-sum nature of competton n the transportaton market, UP gans traffc at the expense of BN, a frm may enter a market only f t can operate on the elastc part of ts demand curve.

18 17 these economes n PRB markets by movng large shpments n unt coal trans. Btzan and Keeler (2003) also fnd that ralroads exhaust economes of densty at some pont. The parameter estmates for the ral competton varables n the (nverse) supply equaton are of central mportance for our purposes. We fnd that the ntal entry of a second carrer nto a Powder Rver Basn market reduces ral rates 15 percent and that ths effect becomes stronger over tme, albet at a dmnshng rate. 15 For example, after four years of entry, durng whch tme some contracts are lkely to have expred, a second entrant wll have reduced ral rates by a thrd. 16 As stressed throughout the paper, coal shppers negotate contract rates wth ralroads that generally last for several years. Accordng to our fndngs, contract rates dampen the ntal mpact that a new ral entrant has on observed prces. But as shppers contacts expre they are able to play one ralroad off aganst another and obtan lower rates when they negotate new contracts. Apparently, carrers have not been successful n reachng a tact understandng to prevent such competton from developng. 17 As noted, we dd not expect potental competton to have an nfluence on rate rates. If t dd, ts effect would be partly captured n the tme 15 We also estmated a model that lagged the ntal entry varable, but ths dd not lead to a better statstcal ft. 16 Based on our coeffcents, ths estmate s obtaned by calculatng: (1-exp(-0.161))+ln(1+ 4 years)*0.117=33.7 percent. We expressed the persstent effect of ral entry as ln(1 + years of entry) because ln(1) =0 and ln (0) s undefned. Ths specfcaton captures dmnshng margnal reductons n ral prces caused by the entry of a second carrer. We explored other functonal forms for ths varable ncludng a Box-Cox transformaton and also specfed tme dummes to ndcate specfc years snce the entry of the second carrer, but ths functonal specfcaton produced the best statstcal ft. 17 Scherer (1990) provdes examples n other ndustres where large buyers play one seller off aganst another to elct prce concessons.

19 trend or year dummes as UP entered more markets, but these varables were statstcally nsgnfcant. The remanng parameter estmates reflect the workngs of standard economc forces. Ral prces respond to operatng costs, economes of dstance, and other sources of competton. 18 A 1 percent rse n ral operatng costs ncreases ral rates roughly 2 percent. Ths fndng s consstent wth the ralroad ndustry s resdual regulatory envronment that allows carrers to set rates that are 180 percent above varable costs (Denns (2001)). In addton, many markets n our sample are served by only one carrer. A 1 percent ncrease n the length of haul decreases rates 0.17 percent. Smlar economes of dstance have been found n other studes (Braeutgam (1999)). Ral source competton lowers ral rates almost 20 percent, whle water source competton lowers ral rates 14 percent. However, each of these forms of competton has less mpact on 18 prces than a second entrant n the Powder Rver Basn has after just one year. 19 Ths fndng s consstent wth Grmm and Wnston s (2000) estmate of the relatve mpact of drect and source competton on ral rates. Utltes demand more coal shpped by ral from the Powder Rver Basn as ther nameplate capacty ncreases, as natural gas prces rse, and after the passage of the Clean Ar Act of We also fnd that electrc utltes located n the South have a greater demand than other utltes n the country for coal shpped by ral from the Powder Rver 18 It has been argued that shppers who provde ther own ral cars reduce ral costs and thus receve a lower rate. We specfed the percentage of a utlty s coal traffc that s shpped n ts prvate cars n the nverse supply equaton, but t had a statstcally nsgnfcant effect on ral prces and s not ncluded here. We suspect that ths fndng s due to the fact that most of the plants n our sample shp large shares of ther coal n prvate cars. 19 After one year, a second entrant n the PRB reduces ral prces by (1-exp(-0.161)) + ln(1+1 year)*0.117=23 percent.

20 19 Basn. Southern power plants tend to be larger than others and face more rapdly growng demand, so they may have a preference for large shpments of coal that can be sent by unt coal trans. The Powder Rver Basn s able to accommodate ths preference more easly than other coal-producng regons n the country because ts mnes generate more coal than other sngle mne mouths. Utltes demand less coal as ther dstance from a coal mne n the Powder Rver Basn ncreases, f they can receve coal from another source by water transportaton, and as ther sulfur doxde emsson caps become tghter (.e., the ndex becomes smaller), leavng them to choose between reducng output or purchasng emssons permts. 20 Apparently, mantanng output and emssons by substtutng PRB coal for non-prb coal s a less effcent opton than reducng output. Fnally, Unon Pacfc s entry nto markets n the Powder Rver Basn balances potental revenues and costs n a manner consstent wth proft-maxmzng behavor. 21 UP s attracted to markets wth greater traffc, as measured by ton-mles, and dscouraged from enterng markets wth hgher operatng costs and where t faces a cost dsadvantage because t has to haul ts traffc further than BN has to haul ts. 22 UP s also dscouraged from enterng markets that requre hgher captal requrements because of a longer buld 20 Holdng ral prces constant, we dd not fnd that the presence of ral source competton had a statstcally sgnfcant effect on ral demand. The presence of water source competton affects demand because t s less expensve to shp coal by water than by ral. 21 We could not obtan estmates for the water and ral source competton dummes n the entry equaton because UP dd not enter any markets that had these forms of competton; thus, the dummes were hghly collnear determnants of UP s entry decsons. As expected, there were no mprovements from ncludng prce along wth the quantty of coal shpped n the entry equaton. In fact, the prce coeffcent had the ncorrect sgn. 22 By denomnatng ndustry operatng costs n ths equaton by dollars per ton-mle, we capture the noton that UP would tend to be dscouraged less from enterng a gven route as operatng costs ncreased f t could acheve economes of dstance.

21 20 out. As ndcated by the estmated error correlaton coeffcents, the unobserved components of the entry and demand equatons are most strongly related whle the unobserved components of the entry and prce equatons are least strongly related. FIML estmaton produces the most effcent estmates of our parameters but all of the estmates could be contamnated f any of our equatons are msspecfed or f the errors are not normally dstrbuted. Because we were partcularly concerned that the coeffcents for the entry varables could be affected by msspecfcaton of the equatons or the error dstrbuton, we specfed a smpler model by assumng entry s exogenous and estmated the supply and demand model by two-stage least squares (2SLS). These estmates, also shown n table 2, are generally smlar to the FIML estmates. Compared wth FIML, the 2SLS estmate of the mpact of UP s ntal entry on prces s somewhat greater, and the estmate of UP s persstent effect s less, but the FIML and 2SLS estmates of the combned effects are vrtually the same. Ths s consstent wth the small magntude of the error correlaton coeffcent ρ E, p. The smlarty of the parameter estmates should mtgate potental concerns wth specfcaton errors that may arse from usng FIML.

22 21 Characterzng Duopoly Behavor We have argued that ral competton n the Powder Rver Basn provdes a natural settng for testng theores of duopoly behavor because a monopolst ralroad n the regon, Burlngton Northern, has gradually begun competng wth a new entrant, Unon Pacfc, to supply a homogeneous servce. We use the FIML parameter estmates to smulate the effect of UP s entry on ral prces for coal transportaton. Ths exercse s complcated by the fact that several other varables besdes UP s entry could affect ral rates. Thus, we hold all varables except UP s entry varable and ts persstent effect on prces at ther 1984 levels that s, before UP began enterng PRB markets. We then use the nverse supply and demand equatons to predct market equlbrum prces n response to the changes n UP s entry behavor over tme. We can assess whch theory of duopoly behavor s consstent wth the evdence by comparng the smulated prce path wth an estmate of the long-run margnal cost of transportng coal by ral. It s reasonable to make ths comparson because n PRB markets ral s characterzed by constant returns to scale whch allows margnal cost prcng to be fnancally vable. In addton, shppers and carrers enter nto rate negotatons wth a vew toward the long run because contracts typcally last for several years. If UP and BN engage n collusve proft-maxmzng behavor, smulated prces should reman at ther monopoly (pre-up entry) level. If the carrers engage n Bertrand competton, smulated prces should approach margnal cost. And f they engage n Cournot competton, smulated prces should stablze between these extremes. To mantan consstency wth the predcted prce path, we obtan an ndependent estmate of the long-run margnal cost of transportng coal by ral that does not reflect changes n ral markets after 1984 that may have affected costs. The estmated equaton

23 for margnal cost s from Wnston, Grmm, Cors, and Evans (1990) and s based on data 22 generated n the early 1980s. 23 We assume that margnal costs are not affected by UP s entry, whch s reasonable because PRB coal transportaton markets are relatvely new, and both carrers have been able to employ the latest technology and most effcent operatons. Thus, margnal costs are held constant n our smulaton. The prce path and long-run margnal cost were converted to 1998 dollars usng approprate ndces; the estmate for the margnal cost of transportng coal n 1984 (n 1998 dollars) s roughly 1.9 cents per ton-mle. Usng Btzan and Keeler s (2003) ralroad cost functon yelds a margnal cost estmate for unt tran output of 1.8 cents per ton-mle (n 1998 dollars). Our estmate s also consstent wth those obtaned by Bereskn (2001) and Ivald and McCullough (2001) that are based on unt tran operatons. To repeat, the prce path and margnal costs do not represent predctons of actual ral prces and costs followng UP s entry because other nfluences on rates and costs are held constant at ther 1984 values. Fgure 2 shows that n the markets that UP has entered at some pont between 1984 and 1998, duopoly ralroad prcng behavor has evolved slowly, but t can be reasonably characterzed by Bertrand competton because ral prces approach margnal cost. From 1985 to 1994, ral prces dd not change much from ther monopoly level. But snce 1994, they have fallen sharply as UP has expanded servce to a suffcently 23 The actual equaton for margnal cost s: MC = -$19.06*Route Densty + $8.338*Tons + $0.0164*Ton-mles, where route densty s ton-mles/route mles; based on the sze of the carrers networks, we assumed route mles were equal to 20,000. We use ths equaton to predct the margnal cost of shppng the amount of coal actually transported n each market where UP competes wth BN. Because the parameter estmates were obtaned usng a sample of all commodtes shpped by ral and gven that we are nterested n the margnal cost of transportng coal, the resultng estmate was adjusted by the rato of the relatvely lower cost of shppng bulk versus manufactured commodtes usng cost estmates n Fredlaender and Spady (1981) and by the relatve ncrease n bulk traffc snce deregulaton n 1980.

24 large cohort of plants and as BN has been forced to compete wth UP for shppers traffc because ts contracts have expred. Although our estmate of long-run margnal cost s consstent wth other estmates n the lterature, one could argue that f we (and others) have overestmated margnal costs by a modest amount, then ral competton would be better characterzed by Cournot than by Bertrand. Recall, however, that Cournot behavor s nconsstent wth our nelastc demand estmate unless ralroads are constraned by the threat of maxmum rate regulaton a vew that s strongly dsputed by captve shppers. Moreover, we estmate that roughly half of the 54 percent declne n actual ral prces from 1984 to1998 could be attrbuted to the addtonal competton suppled by UP and, as shown n table 2, prces were stll declnng n duopoly markets n the fnal years of our sample. As tme contnues to pass followng the entry of a second carrer and as contracts contnue to expre after 1998, the prce path would undoubtedly draw closer to margnal cost even f the latter were somewhat lower than we estmated. Indeed, the pervasve use of contract rates n ral freght transportaton s probably the most mportant reason why Bertrand s predcton s realzed. Each carrer faces the prospect of gettng none of a utlty s busness for several years unless t lowers ts rate n response to a compettor s bd. Gven that a typcal contract mght call for fve mllon tons of coal to be shpped annually for at least fve years, a ralroad has a lot to lose f t does not compete fercely for a utlty s busness and allows the utlty to take ts traffc elsewhere. Another factor that facltates Bertrand competton s that coal transportaton s a homogeneous commodty. Both BN and UP use the same technology to transport coal 23

25 24 from the same source over smlar routes, often usng cars that are suppled by the shppers themselves. The average of and varablty n ther transt tmes are smlar, and the low value of coal ensures that shppers place lttle weght on non-transport logstcs costs. All these factors make t extremely dffcult for ether ralroad to convnce shppers that they are provdng a dfferent, let alone superor, servce. Product dfferentaton, prmarly through advertsng, can explan why some olgopolsts have been able to mantan hgh prce-cost margns (e.g., Baker and Bresnahan (1985)). Ths strategy, however, s not effectve n ral freght transportaton. Fnally, gven that BN ntally provded ral servce for all the utltes that demanded PRB coal, UP dd not have any profts to lose by supplyng addtonal capacty n ths market. Moreover, UP could gan revenue from addtonal traffc only by cuttng nto BN s traffc. Thus, the two were lkely to end up as Bertrand compettors because t s more dffcult to behave as Cournot compettors n zero-sum stuatons. Conclusons We have developed a model of ralroad transportaton markets for coal to test one of the oldest controverses n economc theory: How are prces determned n duopoly markets? Of the avalable theores, we have found that ral competton n the Powder Rver Basn s most accurately characterzed by Bertrand s theory that prce-settng duopolsts wll sell ther dentcal product at the compettve prce. Ths fndng s of broad nterest because recent theoretcal work related to duopoly behavor has ncluded game theoretc models that focus on outcomes between the polar cases of proft-maxmzng colluson and margnal cost prcng. Perfectly

26 compettve outcomes are generally thought to be a rarty. Our results suggest that more theoretcal attenton should be gven to the factors that generate Bertrand competton. Emprcal evdence of Bertrand competton s also of nterest to polcymakers as they ponder whether there s suffcent competton n the ralroad ndustry. Grmm and Wnston (2000) addressed shppers and carrers dssatsfacton wth the Surface Transportaton Board by recommendng that polcymakers encourage these partes to negotate an end to the Board, whch would allow full deregulaton to go forward. As part of the negotatons, shppers and carrers would agree on condtons that would enable captve shppers to have access to another ral carrer. The evdence obtaned here ndcates that that the drect competton resultng between two ral carrers s suffcent to generate low rates for shppers. 24 In addton to ralroads, polcy ssues surroundng duopoly competton have arsen n ndustres such as telecommuncatons and electrcty as they slowly undergo the transton to partal deregulaton. Ths paper has dentfed some of the compettve condtons that are conducve to Bertrand competton. Future work may be able to buld on ths evdence to dentfy other duopoly markets that are lkely to be characterzed by ths type of behavor Negotatons would also recognze that although ralroads proftablty has mproved snce deregulaton, the ndustry s not yet earnng a normal rate of return.

27 References 26 Baker, Jonathan B. and Tmothy F. Bresnahan, The Gans from Merger or Colluson n Product-Dfferentated Industres, Journal of Industral Economcs, 33, June 1985, pp Bereskn, C. Gregory, Sequental Estmaton of Ralroad Costs for Specfc Traffc, Transportaton Journal, 40, Sprng 2001, pp Btzan, John D. and Theodore E. Keeler, Productvty Growth and Some of Its Determnants n the Deregulated U.S. Ralroad Industry, Southern Economc Journal, 70, October 2003, pp Braeutgam, Ronald R., Learnng About Transport Costs, n Jose Gomez-Ibanez, Wllam B. Tye, and Clfford Wnston, edtors, Essays n Transportaton Economcs and Polcy: A Handbook n Honor of John R. Meyer, Brookngs Insttuton, Washngton DC, Brander, James A. and Anmng Zhang, Market Conduct n the Arlne Industry: An Emprcal Investgaton, RAND Journal of Economcs, 21, Wnter 1990, pp Brander, James A. and Anmng Zhang, Dynamc Olgopoly Behavor n the Arlne Industry, Internatonal Journal of Industral Organzaton, 11, September 1993, pp Berry, Steven T., Estmaton of a Model of Entry n the Arlne Industry, Econometrca, 60, July 1992, pp Bresnahan, Tmothy F. and Peter C. Ress, Entry n Monopoly Markets, Revew of Economc Studes, 57, October 1990, pp Bresnahan, Tmothy F. and Peter C. Ress, Entry and Competton n Concentrated Markets, Journal of Poltcal Economy, 99, October 1991, pp Denns, Scott M., Changes n Ralroad Rates Snce the Staggers Act, Transportaton Research Part E: Logstcs and Transportaton Revew, 37, March 2001, pp Federal Energy Regulatory Commsson (FERC), Form 423, Monthly Report of Cost and Qualty of Fuels for Electrc Plants, Fscher, Thorsten and Davd R. Kamerschen, Prce-Cost Margns n the U.S. Arlne Industry Usng a Conjectural Varaton Approach, Journal of Transport Economcs and Polcy, 37, May 2003, pp

28 27 Fredlaender, Ann and Rchard Spady, Freght Transport Regulaton, MIT Press, Cambrdge, Massachusetts, Greene, Wllam, H., Econometrc Analyss 5 th edton, Prentce Hall, New Jersey, Grmm, Curts and Clfford Wnston, Competton n the Deregulated Ralroad Industry: Sources, Effects, and Polcy Issues, n Sam Peltzman and Clfford Wnston, edtors, Deregulaton of Network Industres: What s Next?, Brookngs Insttuton, Washngton, DC, Grmm, Curts, Clfford Wnston, and Carol Evans, Foreclosure of Ralroad Markets: A Test of Chcago Leverage Theory, Journal of Law and Economcs, 35, October 1992, pp Ivald, Marc and Gerard McCullough, Densty and Integraton Effects on Class I U.S. Freght Ralroads, Journal of Regulatory Economcs, 19, March 2001, pp Parker, Phlp M. and Lars-Hendrk Roller, Collusve Conduct n Duopoles: Multmarket Contact and Cross-Ownershp n the Moble Telephone Industry, RAND Journal of Economcs, 28, Summer 1997, pp Porter, Robert H., A Study of Cartel Stablty: The Jont Executve Commttee, , Bell Journal of Economcs, 14, Autumn 1983, pp Scherer, F.M., Industral Market Structure and Economc Performance, 2 nd edton, Rand McNally, Chcago, Schmalensee, Rchard, Paul L. Joskow, A. Denny Ellerman, Juan Pablo Montero, and Elzabeth M. Baley, An Interm Evaluaton of Sulfur Doxde Emssons Tradng, Journal of Economc Perspectves, 12, Summer 1998, pp Schmdt, Stephen, Market Structure and Market Outcomes n Deregulated Ral Freght Markets, Internatonal Journal of Industral Organzaton, 19, January 2001, pp Unted States, Department of Energy, Energy Informaton Admnstraton (EIA), Form EIA-7A, Coal Producton Report. Wnston, Clfford, U.S. Industry Adjustment to Economc Deregulaton, Journal of Economc Perspectves, 12, Summer 1998, pp Wnston, Clfford, Thomas Cors, Curts Grmm, and Carol Evans, The Economc Effects of Surface Freght Deregulaton, Brookngs Insttuton, Washngton DC, 1990.

29 Table 1. Sample Means and Data Sources of the Varables* Varable Unts Mean Data Source Freght charge $/ton-mle Energy Informaton Admnstraton, Cost and Qualty of Fuels and Coal Industry, Annual Tons of coal shpped 1000 tons 2757 EIA, Cost and Qualty of Fuels, Annual Presence of second ral compettor Dummy Feldston, Coal Transportaton Manual, Annual Ral source competton Dummy Feldston, Coal Transportaton Manual, Annual Water source competton Dummy Feldston, Coal Transportaton Manual, Annual Nameplate Capacty Mllon KWH EIA, Annual Electrc Generator Report, form EIA-860, Annual SO 2 emssons caps 1000 tons EPA, Clean Ar Act, Ttle IV Natural gas prce $/1000ft EIA, Hstorcal Gas Annual, 2000 Ral ndustry operatng expenses Length of haul from mne to plant Length of Buld- Out for entrant n 1984 Incumbent length of haul mnus new entrant length of haul *All values are n 1998 dollars where approprate. $ Bllons Amercan Assocaton of Ralroads, Ralroad Facts, Annual Mles 1024 RDI, Coal Rate Database, 1997 Mles Rand McNally, Ralroad Atlas (1982) and Commercal Atlas and Marketng Gude (1991) Mles Rand McNally, Ralroad Atlas (1982) and Commercal Atlas and Marketng Gude (1991)

30 Table 2. Comparson of Ral Rates n Monopoly and Duopoly Markets* Year Average Freght Charge: Monopoly Markets Average Freght Charge: Duopoly Markets *All freght charges are n 1998 cents per ton-mle

31 Table 3. Structural Supply, Demand, and Entry Parameter Estmates (Standard Errors are n parentheses) * denotes that the varable has been transformed by natural logarthm. FIML Coeffcents 2SLS Coeffcents Varable Supply Demand Entry Supply Demand Freght charge ($/ton mle)* Dependent Varable (0.150) -- Dependent Varable (0.237) Tons of coal shpped to plant (thousands)* (0.023) Dependent Varable c (0.056) (0.023) Dependent Varable Supply Characterstcs Drect ral competton dummy (1 f a plant can receve Powder Rver Basn coal from two competng ralroads; 0 otherwse) (0.051) -- Dependent Varable (0.076) -- Number of years after the onset of competton that a second ral compettor offers a plant servce from the Powder Rver Basn; (1 + years of entry)* (0.030) Ral ndustry operatng expenses a * (0.105) Demand Characterstcs Plant Nameplate Capacty (mllons of KWH) (0.049) Average natonal prce of natural gas ($/1000ft 3 ) (0.085) Clean Ar Act (1990) dummy (1 f the Clean Ar Act has been passed; 0 otherwse) (0.142) South regonal dummy (1 f plant s located n the South; 0 otherwse) b (0.098) Plant SO 2 emssons cap ndex (defned as (emssons cap) -1 for plants subject to emssons (0.149) caps; 1 for plants not subject to caps) Shpment Characterstcs Length of haul from mne mouth to plant (mles)* (0.028) (0.040) (0.408) (0.097) c (0.056) Dfference n potental entrant s and ncumbent s length of haul (mles) (0.001) Buld-out dstance crca 1984 (mles)* (0.062) Source Competton Ral source competton dummy (1 f a plant can receve coal from a non Powder Rver Basn (0.055) source by a competng ralroad; 0 otherwse) Water source competton dummy (1 f a plant can receve coal from a non Powder Rver Basn source by water transportaton; 0 otherwse) (0.054) Constant (0.467) Other Parameters ρ p,q = ; ρ E,p = ; ρe,q = (0.020) (0.027) (0.123) 2 σ p = ; (0.006) 2 σ Q = (0.156) (0.114) (0.054) (0.108) (0.164) (0.127) (0.143) (0.110) (0.306) (0.775) (0.062) (1.501) (0.034) (0.129) (0.541) (0.292) (1.009) Summary Statstcs Number of Observatons Log lkelhood at convergence R