serialusairways

SimulatingtheDynamicEffectsofHorizontalMergers:U.
S.
AirlinesC.
LanierBenkardStanfordUniversityandNBERAaronBodoh-CreedU.
C.
BerkeleyJohnLazarevNewYorkUniversityThisversion:April2019AbstractWeproposeasimplemethodforstudyingthemedium-andlong-rundynamiceffectsofhorizontalmergersthatbuildsonthetwo-stepestimatorofBajari,Benkard,andLevin(2007).
Policyfunctionsareestimatedonhistoricalpre-mergerdata,andthenfutureindustryoutcomesaresimulatedbothwithandwithouttheproposedmerger.
Weapplyourmethodtotworecentairlinemergersaswellasonethatwasproposedbutblocked.
Wendthatlow-costcarriersplayacrucialroleincreatingoffsettingentry.
Insomecases(United-USAirways),themodelpredictssubstantialscopeforoffsettingentry,whileinothers(Delta-Northwest)itdoesnot.
Thus,thedynamicanalysisiscomplementarytoandyieldsdifferentconclusionsthanthestaticanalyses.
TherstdraftofthispaperwasMarch2009.
WethankSteveBerry,SeverinBorenstein,PhilHaile,DarinLee,andJonLevinfortheirusefulinput.
Correspondence:lanierb@stanford.
edu;acreed@haas.
berkeley.
edu;jlazarev@nyu.
edu1IntroductionAntitrustenforcementistaskedtoprotectandpromotecompetition.
Despitebeingavitalpartofindustrydynamics,mergers—especiallythosebetweendirectcompetitors—maypresentaconsequentialthreattocompetitionwithintheindustry.
Thecentralquestionofmergerreviewiswhethertheeffectofamerger"maybesubstantiallytolessencompetition.
"1Thestaticeffectsofahorizontalmergerareunambiguous.
Bydenition,horizontalmergersbetweenrmsleavetheindustrywithfewercompetitorsand,therefore,lesscompetition.
Whethercompetitionislessenedsubstantiallydependsontherolethatthemergingrmsplayinthecompetitiveprocess.
Amergerbetweenlargermsproducingclosesubstitutesinaconcentratedindustryismorelikelytolessencompetitionthatamergerbetweensmallerrmsthatproduceindirectsubstitutesinanindustrywithmanyactivecompetitors.
Thesimplestmethodtoevaluatethestaticeffectsofamergeroncompetitionistocomputepre-andpost-mergerconcentrationmeasuresassumingnopost-mergerchangesinmarketshares.
Largeincreasesinconcentrationarepresumedtolessencompetitionsubstantially(Shapiro(1996),USDepartmentofJustice(2010)).
Moresophisticatedmethods(BerryandPakes(1993),Berry,Levinsohn,andPakes(1995),Nevo(2000))areavailableforanalyzingmergersinmarketswithdifferentiatedproducts,wherecompetitionbe-tweenrmsdependscriticallyontheprecisecharacteristicsofeachrm'sarrayofproducts.
Thesemethodsproviderichermodelsofchangesinpost-mergerpricesandmarketshares,butstillrelyonastaticmodelthatholdsthesetofincumbentrmsandproductsxed.
Antitrustenforcement,however,recognizesthefactthatcompetitionisinherentlyadynamicprocess.
Forthatreason,astaticanalysismaynotbeabletocapturethefulleffectofamergeronthecompeti-tivenessoftheindustry.
Ingeneral,thestaticmodelsdonotaccountforpost-mergerchangesinrms'behavior.
Bychangingrms'incentives,amergermightleadtodifferentlevelsofentry,exit,investment,andpricingthanoccurredpre-mergerinbothmergingandnon-mergingrms(BerryandPakes(1993),Gowrisankaran(1999)).
Lastly,severalpapershaveshownthatdynamicscanweakenthelinkbetweenmarketstructureandperformance(BerryandPakes(1993),PakesandMcGuire(1994),EricsonandPakes(1995),Gowrisankaran(1999),FershtmanandPakes(2000),Benkard(2004)),makingthepre-/post-mergersnapshotofmarketconcentrationandmarkupslessrelevantforunderstandingthemedium-andlong-runeffectsofamergeroncompetition.
Amergerthatlooks"bad"intheshortrunmay,nevertheless,fallshortofhavingasubstantialnegativeimpactoncompetitioninthelongrunifitcreatesaprotableopportunity1Section7oftheClaytonActof1914.
1fornewrmstoenterthemarketandreducemarketconcentration.
Whentwoairlinesmerge,theindustrylosestwosmallerairlinesandgainsanew,biggerone.
Intheshortrun,marketsservedbybothofthemergingairlinesaredirectlyaffectedbythemergerasthesemar-ketsimmediatelyloseadirectcompetitor.
Whetherornotthislossattractsanewentrantisultimatelyanempiricalquestion.
Additionally,sincetheincentivesofthemergedairlineschange,inthemediumrunthemergermayaffectcompetitioninmarketswithoutpre-mergeroverlap.
Forexample,sincethemergedairlinesservealargernetworkofmarkets,previouslyunprotableroutesmaybecomemoreattractiveforentry.
Oncepassengersareownintoahub,theycannowreachmoredestinationswithouthavingtochangetheircarrier.
Atthesametime,thecombinednetworkofthemergedairlinesislikelytocontainredundantroutes.
Thatcouldincentivizethemergedairlinestodecreaseoreveneliminatesomeduplicativeroutesinthemediumorlongrun.
Again,whetherornotthesedynamiceffectslessencompetitionsubstantially,requiresanempiricalanalysis.
Thecontributionofthispaperistodevelopasimplesetoftechniquesforanalyzingthepotentialdy-namiceffectsofamergerandtoapplythesetechniquestothreerecentlyproposedmergersintheU.
S.
airlineindustry.
Importantly,sinceourmethoddoesnotrequireestimatingthefundamentalparametersofanun-derlyingstructuralmodel,orsolvingforacounterfactualequilibrium,itisapracticalmethodforregulatorstousegiventhetighttime-frameunderwhichmergersareevaluated.
Westartwiththestandardframeworkthatmostexistingworkonempiricaldynamicoligopolyhasreliedupon–thatofEricsonandPakes(1995)(hereafterEP).
2ThisframeworkmodelsadynamicindustryinMarkovperfectequilibrium(MPE).
Equilibriaofthismodelcannotbefoundanalytically,sotheymustinsteadbecomputednumerically.
Ingeneral,insertingmergersintothisframeworkrequiresadetailedmodelofhowmergersoccur(asinGowrisankaran(1999)),resultinginacomplexmodelthatisdifculttocomputeorapplytodata.
Toovercomethischallenge,weextendtheinsightofBajari,Benkard,andLevin(2007)(hereafterBBL).
Putinthebroadestterms,themaininsightofBBListhefollowing:theequilibriumtoacomplicateddynamicgamecan,undercertainassumptions,bedirectlyobservedinthedata.
Insteadofrepeatedlysolvingthemodelfordifferentvaluesofunknownparameterstryingtondanequilibriumthatcloselymatchestheobserveddata,onecanproceedittwosteps.
Therststepistoestimatetheequilibriumofthemodel,i.
e.
therms'strategyfunctions,directlyfromthedata.
Thesecondstepistoplugtheseestimatedstrategiesintotheequationsdenedbytheequilibriumconditionsofthemodel,whichcantypicallyallowonetosolvefortheunknownparametersmuchfaster.
2Foranoverview,seeAckerberg,Benkard,Berry,andPakes(2007).
2BuildingonBBL,thispapershowsthatitispossibletoquantifythedynamiceffectsofahorizontalmergerintheEP/BBLframeworkbyaddingjustonesimplifyingassumption:weassumethattheequilib-riumbeingplayeddoesnotchangeafterthemerger,inthesensethatrms'strategyfunctionsremainthesame.
Underthisassumption,wecanuseBBL'sforward-simulationproceduretosimulatethedistributionoffutureindustryoutcomesbothwithandwithoutthemerger.
Wecanthencomputemedium-andlong-runconcentrationmeasurestoevaluatethedifferentialimpactofthemergeroncompetition.
Thisallowsustoincorporatetheeffectsofoffsettingentryintothe(static)analysisofconcentrationcommonlyusedaspartofantitrustevaluations.
Theproposedassumptionisbothrestrictiveandtestable.
Forexample,thisassumptionwouldholdifmergersareastandardoccurrenceinequilibrium.
Alternatively,itmighthappenifmergersareveryrare,sothatequilibriumplayisnotstronglyaffectedbythelikelihoodoffuturemergers,whetherornotthemergerinquestionhappens.
Ontheotherhand,theassumptionwouldnotholdintheeventthatallowingtheproposedmergerwouldrepresentasubstantivechangeinantitrustpolicy.
Inthatcase,thefactthatthemergerisallowedtogothroughmightchangerms'unobservedbeliefsaboutfutureplay,changingtheirstrategyfunctions.
Thislimitssomewhattheapplicabilityofourmethods,butthebenetisthatourmethodsarevastlysimplerthanthealternativeofcomputinganewpost-mergerequilibriumtothegame,anoptionthat,whileattractive,wouldbecomputationallyinfeasibleinmostcases.
Notethatourmethodsarenotintendedtoreplacestaticantitrustanalyses,describedinShapiro(1996)andNevo(2000),whichseektomeasuretheshort-runeffectsofaproposedmergeronprices,marketshares,etc.
Whenusedinisolation,ourmethodsgeneratepredictionsaboutthemediumandlongtermeffectsofamergeronindustrystructure,whichcanoftenbehighlyinformativeabouttheanti-competitiveeffectsofamerger.
Forexample,ourdynamicanalysiscanrevealwhetherornotoff-settingentryislikelytoreduceshort-runmarketcompetitioninparticularmarkets,whichmightdeterminewhetheramergerispresumedtobeanti-competitiveinthelongrun.
However,industrystructuremayonlybeapartofthestory.
Occasionally,ahorizontalmergermaygeneratebothpro-andanti-competitiveeffects.
Tobalancethem,itmaybenecessarytoquantifythewelfareeffectsofthesepredictions,whichwouldrequireanexplicit,short-runmodelofconsumerdemandandmarketsupply.
Thus,inouropinion,mergeranalysesshouldincludebothofthesetools.
WeapplytheproposedmethodtotheU.
S.
airlineindustry,whichhasrecentlygonethroughanumberoflargeandsomewhatcontroversialmergers.
Ourfocusisnarrow.
Wedonotattempttoperformafull-scaleprospectivemergeranalysisoftheproposedmergers.
Instead,wewanttoevaluatethedifferentialimpactofeachoftheproposedmergersontheyearlyentry/exitdecisionsofeachairlineatthelevelofindividual3non-stoproutesbetweenpairsofmetropolitanareas.
Ourestimatesarebasedondatafrom2003to2008.
Wechose2003asthestartingperiodoftheanalysistoavoidtheimmediateaftermathoftheterroristattacksonSeptember11,2001.
Wechose2008astheendperiodbothbecauseitwasthelastperiodpriortotherecentwaveofmergers,andbecauseitavoidsthesevereeconomicdownturnexperiencedduringthe2008nancialcrisis.
Weusethisdatatoestimatetheairlines'strategyfunctions,whicharemapsfromthecurrentstateofthemarketcompetitiongameintoadecisionaboutwhichnetworkofnonstoproutestoserveinthefollowingyear.
Theestimatedstrategyfunctionsexhibittwoimportantfeatures.
First,weestimatecompetitioneffectsthatarequitelarge.
Forexample,wendthat,inamarketwithtwoincumbentcarriers,forapotentialentrantindifferentbetweenenteringandnot,theexitofoneincumbentincreasestheprobabilityofentryby34%(from50%to84%).
Asacomparativebenchmark,theexitofoneincumbentcompetitorisestimatedtoberoughlyhalfaslargeastheincumbencyeffectofairlinepresenceonagivenroute,aneffecttypicallythoughttobelarge.
Estimatedcompetitioneffectsarelargerinmarketswithfewerincumbents,andsmallerinmarketswithmoreincumbents.
Theselargecompetitioneffectsgivethemodelthepotentialtogenerateoffsettingentryafteramerger.
However,whetherornotthereisoffsettingentryonagivencitypairalsodependscriticallyontheavailabil-ityofpotentialentrantswhosenonstoproutenetworkrationalizesentryforthatcitypair.
SimilarlytoBerry(1992),wendthatthesizeofanairline'snetworkateachendoftheroute(asmeasuredbyhowmanycitiesitservesfromeachend)isanimportantdeterminantofentry.
Forapotentialentrantindifferentbetweenenteringagivenrouteandnot,wendthatoneadditionalcityservedfromanendpointcityincreasestheprobabilityofentryontheroutebyabout10%.
Inaddition,competitionattheendpointcitiesmatters.
Airlineswithhighermarketsharesatendpointcitiesaremorelikelytoenteragivencitypair.
Ourmodeldoesnotallowustodeterminewhethertheseeffectsaredrivenbydemandorcostfactors.
Airlinesarealsomorelikelytoenteracitypairifanendpointisanownhub,andlesslikelytoenterifanendpointisacompetitorhub.
Airlinesarealsomorelikelytoenternonstoprouteswhenthereisnoconvenientalternativeone-stopitineraryintheircurrentnetwork.
Tosummarize,duetothelargecompetitioneffects,theempiricalmodelislikelytopredictoffsettingentryafteramergeronrouteswherethereisatleastonerealisticpotentialentrantwitharichroutenetworkinthevicinityoftherouteinquestion.
However,theexistenceofrealisticpotentialentrantsisfarfromguaranteedandvarieswidelyintheU.
S.
airlinenetwork.
Weconsiderthreedifferentrecentlyproposedmergers:United-USAirways(UA-US),Delta-Northwest(DL-NW),andUnited-Continental(UA-CO).
TheUA-USmergerwasproposedin2000andrejectedby4antitrustauthorities.
TheDL-NWmergerwasapprovedinlate2008.
TheUA-COmergerwasapprovedinlate2010.
Accordingtostaticmeasuresofconcentration,allthreeoftheseproposedmergershadgreatpotentialtoharmconsumers.
Forexample,DL-NWandUA-UScreatedsevenandsixnewmonopolynon-stoproutesrespectively.
Allthreemergersalsocreatedlargeincreasesinconcentrationforatleastafewcitieswhenviewedasawhole,oftenatexistinghubswhereconcentrationwasalreadyhigh.
Absentoffsettingentryorlargecostsynergies,theseeffectspointtoahighlikelihoodofpriceincreasesandconsumerharm.
Weuseourestimatedstrategyfunctionstosimulatethe10-yeareffectsofthethreemergers.
WendthattheUA-USmergerwouldhavehadsubstantialpotentialforoffsettingentry.
Fromastaticperspective,UnitedandUSAirwayshadsignicantnetworkoverlap,particularlyintheDCandPhiladelphiaareas,soshort-runreductionsincompetitionwouldhavebeensignicant.
However,becausetheairlines'networksoverlappedinareaswithheavylowcostcarrierpresence,ourmodelsuggeststhattheanticompetitiveeffectslikelywouldhavebeeneliminatedwithinafewyearsbylowcostcarrierentry,particularlybySouthwestandJetBlue.
Thismergerwasblockedbasedonastaticanalysis,butourresultsindicatethatadynamicanalysiswouldhaveledtoadifferentconclusion.
LikeUA-US,theDL-NWmergerwaspredictedtohaveastrongshort-runanticompetitiveeffect.
UnlikeUA-US,oursimulationsshowverylittlescopeforoffsettingentryinthiscase.
Ourmodelsuggeststhatthemarketswherethemergerleadstoreductionsincompetitionarewellinsulatedfromentry.
TheUA-COmergerappearssomewhatmorebenignthantheothertwomergersintheshortrun,butoursimulationsagainsuggesttherewasverylittlescopeforoffsettingentry.
Ironically,itistheselasttwomergersthatwereapprovedandexecuted.
Therestofthepaperisorganizedasfollows.
Section2discussestherelatedliteratureandalternativesithasproposed.
WegiveadetaileddescriptionofourmethodinSection3.
Section4showshowtoapplyourmethodtotheU.
S.
airlineindustry.
Section5describesourdataandprovidestheconclusionsofasimplestaticmergeranalysis.
Insection6,weshowhowtouseeconometricandmachine-learningtechniquestoestimatetheairlines'strategyfunctions.
Welookforbutndnoempiricalevidencethatwouldinvalidatethemainsimplifyingassumptionthatthispaperreliesupon.
Insection7,weevaluatethedynamiceffectsoftheproposedairlinemergers.
Section8concludes.
52AlternativeApproachesandRelatedLiteratureAcademicliteratureandpolicymakersalikerecognizethefactthatahorizontalmergermaynotalwayssubstantiallylessencompetitionandthatsometimesastaticanalysismayoverestimateitsnegativeeffects.
Tworecentpapers–Li,Mazur,Park,Roberts,Sweeting,andJun(2018)andCiliberto,Murry,andTamer(2018)–seektoaddresseconomicquestionsthataresimilartoours.
They,however,buildonadifferentsetoftoolstoperformtheiranalysis.
Specically,theyuseacross-sectionofairlinemarketstoestimateacompleteinformationtwo-periodentry/exitmodel.
Theyusethismodeltoevaluatethelikelihoodofpost-mergerentry.
Aspecialemphasisisplacedontheimportanceoftheunobservablemarketcharacteristicsthatmayintroduceselectionintheairlines'entryandexitdecisions.
Boththeirandourapproachesrecognizethesamechallenge:airlines'decisionstoenterorexitmaybedrivenbymultiplecomplicatedfactors.
Thesolutions,however,aresomewhatdifferent.
Thetwo-periodentry/exitpaperscompressthesecomplicatedfactorsintoasingleunobservablevariable.
Thedistributionofthisunobservablethenbecomestheobjectofinterest.
Oncethisdistributionisrecovered,themodelissolvedforacounterfactualindustrystructureinwhichthemergerisexogenouslyexecuted.
Incontrast,ourapproachrecognizesthefactthatpaneldatamayprovidesuperiorinformationonwhattheseunderlyingunobservablefactorsmaybe.
Specically,weemploymachine-learningtechniquesthatallowustomaketheunobservedpartoftheentry/exitdecisionsasmuchobservableaspossible.
Across-sectionanalysis,duetodatalimitations,wouldnothaveallowedustoachievethisgoal.
Second,thetwo-periodentry/exitpapershavetoassumethattheunobservedpartwouldstaythesamewhetherornotthemergergoesthrough.
Dependingonwhichfactorscontributetothisunobservable,thisassumptionmaybeproblematic.
Forexample,ifthemainforcebehindtheunobservablepartistheoverallsizeoftheairline'snetwork,thenthemergerwillnecessarilyaffectit.
Ourapproachcontrolsforthesefactorsexplicitly.
Third,unlikethetwo-periodpapers,ourapproachrecognizesthefactthatmergersmaybeendogenous(NockeandWhinston(2010)),i.
e.
apartoftheequilibriumindustrydynamics.
Finally,despitebeingbuiltonamorecomplicateddynamicoligopolymodel,ouranalysisiscomputationallysimplerandfaster.
Itisespeciallysuitedtodata-richindustriesthatexhibitrichvariationinmarketstructuressuchastheU.
S.
airlineindustry.
Thereareseveralotherrelatedpapersintheliteraturethatwehavenotmentionedyet.
ProbablytheclosestpapertooursisCollard-Wexler(2014),whichusesaBresnahanandReiss-styleempiricaldynamicmodeltoevaluatethehysteresiseffectsofamergerfromduopolytomonopolyintheready-mixconcretein-dustry.
Thepaperndsthatmergertomonopolywouldgenerateabout15yearsofmonopoly.
Theapproachinthepaperissimilartoours,butisevensimplerthanoursasitassumeshomogeneousrms.
6Threeotherrecentpapers(Jeziorski(2014a),Jeziorski(2014b),andStahl(2009))usedynamicmodelssimilarinspirittoourstoconsiderrecentmergerwavesinradioandbroadcasttelevisionrespectively.
However,thegoalsofthesepapersarequitedifferentfromours.
Theyusedataonpastmergersprimarilytoevaluatetheforcesthatdrovethemergerwaves,butalsotoevaluate(expost)thewelfareeffectsofthemergerwaves.
Ourpaperinsteadfocusesonthepotentialfuturedynamiceffectsofproposedmergers.
Therearealsoseveralpaperslookingatpastairlinemergers.
Mostnotably,Borenstein(1990)evaluates(expost)theanticompetitiveeffectsoftwoairlinemergersthatoccurredinthemid-1980s,eachofwhichledtosubstantiallyincreasedconcentrationatamajorhub.
Hendsthatthereisevidenceofbothpriceincreasesandcapacityreductionsatthesehubsafterthemergers.
KimandSingal(1993)doesabroaderexpostevaluationoffourteenairlinemergersinthe1980s.
Overalltheyndthatafteramergerboththemergedandunmergedrmssubstantiallyincreasedfares.
Peters(2006)alsodoesanex-postevaluationofstaticmergersimulations(asinNevo(2000))usingveairlinemergersfromthemid-1980s.
Hendsthatthestandardmodeldoesnotdoverywellatpredictingthepriceeffectsofthesemergers,andappearstoomitsomeimportantsupply-sidefactors(e.
g.
,costorconduct).
Therearealsosomeimportantresultsintheliteratureregardingairlinenetworkstructureandairlinecompetitionthatarerelevanttoourwork.
Borenstein(1991)ndsevidencethatacarrierthathasadominantmarketshareofightsoutofagivencityhasincreasedmarketpoweronroutesoutofthatcity,evenonindividualrouteswheretheremaybesubstantialcompetition.
Borenstein(1989)similarlyshowsthatbothanairline'smarketshareonanindividualrouteanditsshareattheendpointcitiesinuenceitsabilitytomarkuppriceabovecost.
Ourresultsechothesendings.
Berry(1992)estimatesastaticmodelofairlineentrywithheterogeneousrmsandnds,similarlytoBorenstein(1989),thatanairline'smarketshareofroutesoutofagivencityisanimportantdeterminantofentryintootherroutesfromthatcity.
CilibertoandTamer(2009)estimatesastaticentrymodelthatallowsformultipleequilibriaandforasymmetricstrategies.
Boguslaski,Ito,andLee(2004)estimatesastaticentrymodelforSouthwestthattsthedataextremelywellandhelpedinspiresomefeaturesofourmodel,suchasthewaywedeneentryandexit.
UsingtherapidexpansionofSouthwesttogeneratevariationinthelevelofthreatofroute-levelentry,GoolsbeeandSyverson(2008)showsthateventhethreatofentrycausesincumbentairlinestodroptheirfaressignicantly.
OtherrelevantstaticairlineentrypapersincludeSinclair(1995)andReissandSpiller(1989).
Anotherrecentpaper(AguirregabiriaandHo(2012))estimatesastructuraldynamicoligopolymodelofairlineentrythatissimilartoourmodel,andcomputesequilibriumentrystrategiesforairlines.
Ourapproachissimplerandlessambitious.
However,anadvantageoftakingasimpleapproachisthatwecan7includearichersetofairlinenetworkstatevariablesinourmodel,potentiallyallowingformorerobustnetwork-widerouteoptimizationonthepartofrms,ratherthanfocusingononerouteatatimeinisolationfromthebroadernetwork.
Inaddition,wecanavoidsomeofthesimplications(e.
g.
,theuseofinclusivevalues,theassumptionthatrouteentryisdeterminedbyroute-specicprots)thatisrequiredtomaketheestimationthemodelofAguirregabiriaandHo(2012)tractable.
3NotationandMethodologyWestartwithabriefcharacterizationofourgeneralapproach.
Ourhopeisthattheapproachissimpleenoughtobeusedinawidevarietyofsettingsbypractitionersandacademics.
Weapplytheapproachtoairlinesinthesectionsthatfollow.
3.
1TheGeneralModelThegeneralmodelcloselyfollowsBBLandisageneralizationoftheEPmodel.
Thedeningfeatureofthemodelisthatactionstakeninagivenperiodmayaffectbothcurrentprotsand,byinuencingasetofcommonlyobservedstatevariables,futurestrategicinteraction.
Inthisway,themodelcanpermitmanyaspectsofdynamiccompetition,suchasentryandexitdecisions,mergers,learning,productentryandexit,investment,dynamicpricing,bidding,etc.
ThereareNrms,denotedi=1,.
.
.
,N,thatmakedecisionsattimest=1,2,Conditionsattimetaresummarizedbyacommonlyobservedvectorofstatevariablesst∈SRL.
Dependingontheapplication,relevantstatevariablesmightincludetherms'productioncapacities,theirtechnologicalprogressuptotimet,thecurrentmarketshares,stocksofconsumerloyalty,orsimplythesetofincumbentrms.
Giventhestatest,rmschooseactionssimultaneously.
Theseactionsmightincludedecisionsaboutwhethertoenterorexitthemarket,investmentoradvertisinglevels,orchoicesaboutpricesandquantities.
Letait∈Aidenotermi'sactionattimet,andat=(a1t,aNt)∈Athevectoroftimetactions.
Fornotationalsimplicity,wedenoteaitasascalar.
However,thereisnoreasonthatitcannotbevectorvalued.
Wewillassumethatbothactionsatandstatesstareobservedbytheresearcher.
Weassumethatbeforechoosingitsaction,eachrmireceivesaprivateshockνit,drawnindependentlyacrossagentsandovertimefromadistributionGi(·|st)withsupportViRM.
Theprivateshockmightderivefromvariabilityinmarginalcostsofproduction,prots,orsunkcostsofentryorexit.
Wedenotethevectorofprivateshocksacrossrmsasνt=(ν1t,.
.
.
,νNt).
Again,wehavedenotedνitasascalar,butthere8isnoreasonthatitcannotbevectorvalued.
Weassumethatνitisnotknowntotheresearcher.
Theassumptionofiidprivateshocksisextremelytroublesomeinthiscontext.
Inmanyempiricalapplicationstherewouldbeserialcorrelationintheseshocks.
Anexamplewouldbeaseriallycorrelatedunobserveddemandshifter.
Intheempiricalworkwewilladdressthisissuebybothtestingforserialcorrelationandalsousingsomesimpleapproachestoaccountforit.
Thereisalsoongoingresearchinthisareaaimedatgeneralizingtheseapproaches.
3Tocompletethemodel,BBLandEPoutlineprimitivesofthedynamicoligopolymodelthatdetermineperiodprotsandtheevolutionofstates.
Weassumethatthestateatdatet+1,denotedst+1,isdrawnfromaprobabilitydistributionQ(st+1|at,st).
ThedependenceofQ(·|at,st)ontherms'actionsatmeansthattimetbehaviormayaffectthefuturestrategicenvironment.
Thiswouldbethecase,forexample,forentry/exitdecisionsorlong-terminvestments.
Insomeapplications,somedetailsofthestatetransitionfunction,suchastheinvestmenttechnology,mightalsobeassumedtohaveaspecicstructure.
Otheraspectsoftransitions,suchastheMarkovprocessdeterminingaggregatedemand,mightbeexogenousandspeciedquitefreely.
Othersmayevenbedeterministic,asinthecaseofrmage.
BBLandEPalsospecifyindetailaperiodprotfunction,investmentprocess,andentryandexitpro-cesses.
Whiletheseareimportantfundamentalsofthemodel,wewillomitthemhereforbrevityandbe-cause,aswewillsee,inourapproachitispossibletoproceedwithoutassuminganyparticularspecication.
Thisaspectalsomakestheapproachmoregeneral.
Toanalyzeequilibriumbehavior,wefocusonpurestrategyMarkovperfectequilibria(MPE).
InanMPE,eachrm'sbehaviordependsonlyonthecurrentstateanditscurrentprivateshock.
Formally,aMarkovstrategyforrmiisafunctionσi:S*Vi→Ai.
AproleofMarkovstrategiesisavector,σ=(σ1,.
.
.
,σn),whereσ:S*V1*.
.
.
*VN→A.
Here,wesimplyassumethatanMPEexists,notingthattherecouldbemanysuchequilibria.
4Foreachagentitheequilibriumgeneratesadistributionoveractionsaitconditionalonstatesgivenbythemeasureofthesetofνitsuchthatactionaitischosenunderequilibriumstrategyσi(3.
1)Pi(a|st)={νit|σi(st,νit)=a}dGi(νit|st)BBLshowsthatthefullmodelabovecanbeestimatedintwosteps.
Intherststep,agents'strategyfunctions,σ,andthestatetransitionprobabilitydistribution,Q(st+1|at,st),areestimatedfromobservations3SeeforexampleArcidiaconoandMiller(2011),KasaharaandShimotsu(2009),Lazarev(2019).
4DoraszelskiandSatterthwaite(2010)DoraszelskiandSatterthwaite(2010)provideconditionsforequilibriumexistenceinacloselyrelatedmodel.
9onactionsandstates.
Inasecondstep,remainingprotfunctionparametersareestimated.
3.
2TheGeneralMethodOurapproachismuchsimplerthanBBLinseveralrespects.
Primarily,wewillnotattempttoestimatetheprotfunctionparametersoranyoftheotherdynamicparametersofthemodelsuchasentrycosts,exitvalues,oranyotherinvestmentcostsparameters.
Releasingourselvesfromthisburdenhasthebenetofallowingustoestimateasimplerandmoregeneralrststage.
Considerthe"reducedform"equilibriumdistributionofactionsgivenstates,Pi(ait|st),givenby(3.
1).
Sinceactionsandstatesareobserved,itisstraightforwardtorecoverthesedistributionsfromthedataforeveryagenti.
Similarly,wecanalsorecoverthetransitionprobabilitydistributionsQ(st+1|at,st).
Undertheassumptionsofthemodel,thesetwosetsofdistributionscompletelydeterminethejointdistributionofallfutureactionsandstatesconditionalonanystartingstateoftheworlds0.
(3.
2)Pr(a0,(a1,s1)at,st)|s0)=P(at|st)Q(st|at1,st1).
.
.
P(a1|s1)Q(s1|a0,s0)P(a0|s0)Howcanweusethesedistributionstoevaluatethelong-runeffectsofamergerAssumingthattheequilibriumstrategyproleisthesamebothbeforeandafterthemerger,anassumptionwediscussindetailbelow,amergerissimplyachangeintheinitialstateoftheindustry,s0.
Forexample,inanindustrywiththreesymmetricrmswithequalcapacities,afteramergertheindustryhastworms,onewithtwicethecapacityastheother.
Afteramergerbetweentwoairlines,wereplacethetwomergingairlineswithasinglelargerairlinewhosenetworkistheunionofthenetworksofthetwomergingcarriers.
Usingequation(3.
2),itisstraightforwardtodeterminethefuturedistributionofindustryoutcomesbothwithandwithoutthemerger.
Inpractice,oncetherststepestimateshavebeenobtained,weusetheBBLforwardsimulationproceduretosimulatethedistributionoffuturemarketoutcomesbothwithandwithoutthemerger.
Thesetwodistributionscanthenbedirectlycompared.
Wecanevencompareindustrystructuresatdifferenttimesinthefuture:5years,10years,orwhateveristheperiodofinterest.
3.
3RelationtoBBLThebiggestadvantageoftheapproachofthispaperisthatitmakesmuchweakerassumptionsontheunderlyingeconomicmodelthantheBBLestimatordoes.
Toestimatethesecondstageparameters,intherststageBBL(andsimilarlyalltwostepapproachesinthespiritofHotzandMiller(1993))mustrecovertheactualequilibriumstrategyfunctions,σi,fromthedynamicgame.
Inordertoestimatethem,thestrategy10functionsmustbeidentied,whichplacessubstantialrestrictionsontheunderlyingmodel.
Forexample,identicationwouldtypicallyrequiretheprivateshockνibesingledimensional.
Thiswouldrestricttheresearchertomodelingeitherasingledimensionalcostshockorasingledimensionaldemandshock,butnotboth.
Incontrast,inourmodeltheprivateshockscanbemultidimensional,allowingtheunderlyingmodeltocontainmanydimensionsofbothcostanddemandshocks(suchascostanddemandshocksforeachcity,city-pair,airline,etc).
Identicationofthestrategyfunctionswouldalsotypicallyrequirestrongfunctionalformassumptions,includingthattheprivateshocksentertheprotfunctionadditively.
Incontrast,ourapproachplacesnorestrictionsonthefunctionalformofthestructuralmodel.
Theprivateshockscanalsoentertheunderlyingmodelinanyway.
Thereasonourapproachissogeneralisthatthedistributionofactionsconditionalonstatesisalwaysidentied.
Itissimplyobserveddirectly.
Ofcourse,therearealsocoststhatcomewithgeneralizingthemodelinthisfashion.
Oneisthat,underourassumptions,wecannotcomputecounterfactualsthatwouldoccuriftheequilibriumregimechanges.
Computingsuchcounterfactualswouldbedesirable,butinthecontextofindustrydynamicsittypicallycomesatgreatcost,bothinmodelingassumptionsandcomputationalburden.
Forairlinemergers,webelievetheserequirementswouldbeparticularlyonerous.
Instead,weimposethepolicyinvarianceassumption,whichisnotrequiredinmorestructuralanalysessuchasBBL.
Wenowdiscussthisassumptioninmoredetail.
3.
4ThePolicyInvarianceAssumptionOurapproachmakestheimportantassumptionthattheequilibriumstrategyprolesremainthesamebothbeforeandafterthepotentialmerger.
Inanymodelwherethemergerispartofequilibriumplaythisas-sumptionwouldhold.
Wearethereforeimplicitlymaintaininganassumptionthatthepolicyenvironmentisconstantinthepastdataandinthefutureperiodofinterest,whetherornotthemergertakesplace.
Ifsomethingaboutthepolicyenvironmentweretochange,eitheratthepointofthemergeroranyothertime,thenequilibriumbehaviormightchange,andthepastestimatesorthefuturesimulationsmaybeinvalid.
Inthecontextofmergers,wemightparticularlyworryaboutevaluatinga"game-changing"merger,i.
e.
,onethatwouldneverhavebeenapprovedunderthepastpolicyregime.
Ifsuchamergerweretogothrough,wemightexpectthatrmswouldupdatetheirbeliefsaboutthefuturepolicyregime,andnewequilibriumstrategieswouldresult.
Ourmethodwillinsteadevaluatewhatwouldhavehappenedintheindustryhadthemergertakenplacewiththeoriginalequilibriumstrategiesremaininginplace.
TheonlywaythatweknowoftofullyevaluateagamechangingpolicychangewouldbetocomputeanewMPEstrategyproleunderthenewpolicy,amuchmoredifcultundertakingthantheonewepropose.
Certainlysuchanapproach11wouldbeintractableintheairlinemodelweoutlinebelow.
3.
5EstimatingWelfareEffectsTheproceduredescribedabovegeneratesthejointprobabilitydistributionofactionsandstates(3.
2)ateverypointintimeforboththemergerandnomergercases.
Inmanycases,knowingthesedistributionsmayalreadybeenoughtoshedlightonthemediumandlong-runcompetitiveeffectsofamerger.
Forexample,intheapplicationtoairlinemergers,weusetheestimatesofthesedistributionstocomputemeasuresofmarketconcentrationovertimeanddeterminewhen/ifoff-settingentryislikelytoeliminatetheshort-runincreaseinmarketconcentrationcausedbyamerger.
Amorepreciseestimateofthewelfareimplicationsofamergerwouldrequire,inaddition,astaticmodelofdemandandsupplythatmapsthedistributionofobservedstatessttoequilibriumprices,quantities,andconsumerwelfare.
Forexample,inmanymarketsthemodelofBerry,Levinsohn,andPakes(1995)(BLP)wouldbeappropriateforthispurpose(thoughlikelynotforairlines–seebelow),anditisstraightforwardtojoinaBLPmodelwiththedynamicmodelabove,provingthatsuchanapproachwouldbebroadlyapplicable.
Thisadditionallyshowsthatthedynamicandstaticapproachesarecomplementary.
Thedynamicap-proachaloneprovidesonlythefuturedistributionofstatesst(anddynamicactions).
Thisdistributioncanbeusedtocomputerudimentarymeasuresofconcentration,suchasHHIs,butdoesnotyieldprecisemeasureofwelfare.
Thestaticapproachaloneprovidesonlyamappingfromstatestowelfare.
Thestaticapproachprovidesprecisemeasuresofwelfare,butrequiresanassumptionaboutwhathappenstothedistributionofstates(andtypicallyresearchersandpolicymakersjustassumethatnothinghappensbesidesthemerger).
Webelievethat,puttogether,thetwomethodscanbemademorepowerful.
Theairlineindustryhasrichdataonairlinepresenceandarelativelysimpleproductspace,soiswellsuitedtothedynamicanalysis.
Ontheotherhand,duetodynamicpricingandpricediscriminationanddatalimitations(itisnotpossibletoobserveconsumers'choicesetsatthetimeofpurchase),webelievethatprovidingacrediblestaticwelfareanalysisforairlineswouldbeahighlycomplexandambitiousundertakingthatdeservesaseparatepaper.
3.
6IdenticationUndertheiidassumptionandgiventhatactionsandstatesareobserved,theoreticalidenticationisstraightforward.
However,inpracticetherecouldbeanissueintheempiricalimplementationoftheapproachiftherewerenotenoughpastdatatoidentifyalloftheareasofthechoicedistributionsP(at|st)ofinterest.
12Forexample,itwouldbedifculttoestimatethedynamiceffectsofamergertomonopolyforanindustrythathadalwayshadatleasttwormsinthepastdata.
Theresimplywouldbenodatathatwouldtellusthelikelihoodofentrywhenthereisamonopolist.
Wewillseebelowthatinourairlinesexamplethedataaresufcientlyrichthatthisissuewillnotarise.
Nevertheless,itissomethingtowatchoutforinotherapplications.
Aseparateidenticationissue,thatwediscussfurtherbelow,isthefailureoftheiidassumption.
4Application:AModeloftheU.
S.
AirlineIndustryWenowoutlineamodeloftheUSairlineindustry.
Intheinterestofkeepingthemodelassimpleaspossible,wewillmodelonlyairlineroutepresence.
Itwouldbepossible,computationallytractableeven,toalsomodeltheextentofentry(e.
g.
,numberofseatsorightsperday)oneachroute,butwebelievethatthemarginalbenetofdoingsomaynotbeworththeadditionalcomplexity.
Ourhopeisthatthecurrentapproachisbotheasytounderstandandalsoprovidesthemaininsightstobegleanedfromthedynamicanalysis.
Consideranairtransportationnetworkconnectinganitenumber,K,ofcities.
Anonstopightbetweenanypairofcitiesiscalledasegment.
Weindexsegmentsbyj∈{1,.
.
.
,J}andnotethatJ=K(K1)/2,thoughofcoursenotallpossiblesegmentsmaybeservicedatanygiventime.
Thereareaxednumber,A,ofairlines.
Asentryofnewairlinecarriersisveryrare,itwouldnotbepossibletoestimatethelikelihoodofnewentryoccurringusingpastdata,sowewillruleitoutintheanalysis.
EachairlineihasanetworkofsegmentsdenedbyaJdimensionalvector,ni.
Thejthelementofniequalsoneifairlineicurrentlyiessegmentjandiszerootherwise.
LettheJ*AmatrixNbethematrixobtainedbysettingthenetworkvariablesforeachairlinenexttoeachother.
WecallNtheroutenetwork.
Inordertotravelbetweentwocities,consumersarenotrequiredtotakeanonstopight,butmightinsteadtravelviaoneormoreothercitiesalongtheway.
Thus,wedenethemarketfortravelbetweentwocitiesbroadlytoincludeanyitineraryconnectingthetwocities.
Belowwewillarguethatitinerariesinvolvingmorethanonestoparerarelyowninpractice,andwillrestricttherelevantmarkettoincludeonlynonstopandone-stopights.
Marketsareindexedbym∈{1,.
.
.
,J}.
Airlinejmaximizesthetotalprotfromallmarketsitserves.
Protsdependoncitypaircharacteristics,zm,aswellasthestrengthofcompetitioninthemarketasdescribedbytheairlineroutenetwork,Nt.
Wewillnotmodeldemandindetail,butweimaginethattherearelikelytobeunobservedprotshiftersatthe13citypairandperhapsairlinelevels.
Wewillassumethatdecisionsaremadeindiscretetimeatyearlyintervals.
Eachyear,t,anairlinecanmakeentryandexitdecisionsattheroutesegmentlevelthatwillbereectedinthenetworkthenextyear,Nt+1.
Changingtherm'snetworkmayalsoinvolvecosts.
Thoughwewillnotmodelthemexplicitly,weimaginetherearethreepotentialsourcesofcosts,inorderfromlargesttosmallest:(a)costsofopeningorclosinganewairline,(b)costsofopeningorclosingoperationsatagivenairport,(c)costsofopeningorclosingoperationsonagivenroutesegment(inwhichbothendpointsalreadyhaveservice).
Belowwewillndthat(a)and(b)arelargeenoughtomaketheseeventsrareinpractice.
Eachperiod,eachairlinechoosesitsnextperiod'snetworksoastomaximizetheexpecteddiscountedvalueofprots.
LetZtbeavectorconsistingoftheprotshifterszmforallmarketsminperiodt,andassumethatZtisMarkov.
NotethatthenotationallowsZttocontainaggregatevariablesthatarerelevanttoallmarkets.
AMarkovperfectequilibriuminthismodelischaracterizedbyasetofstrategyfunctionsoftheform:nt+1i(Nt,Zt,νit),whereνitrepresentsthevectorofalloftheunobservedprotandcostshiftersforairlineiinallmarkets.
Assumingsymmetry,thesefunctionswouldhavethepropertythatpermutingtheorderofairlinesinNt(andcorrectlyupdatingtheindexi)wouldnotchangethevalueofthefunction.
However,whilesymmetryiscommonlyassumedinmanyapplicationsofdynamicgames,herecompletesymmetrymaynotbeagoodassumptionasthereareatleasttwokindsofairlines:hub-and-spokeandpoint-to-point(or"lowcost")carriers.
Thisissomethingthatwewillexploreempirically.
Themodelaboveresultsinasetofbehavioralprobabilitydistributionsforeachairline:(4.
1)Pr(nt+1i|Nt,Zt)thatcorrespondtotheequilibriumdistributionofactionsconditionalonstatesinthegeneralmodelabove.
Ifweknewtheunderlyingprimitivesofthemodel,theseprobabilitiescouldbeobtainedbycomputinganequilibrium.
However,inourcontextcomputinganequilibriumisoutofthequestion,andfurthermoretherearealmostsurelygoingtobemanyequilbria(withassociatedstrategyfunctionsandbehavioralprobabilitydistributions).
Alternatively,wewillfollowthegeneralmethoddescribedaboveandbeginbyattemptingtorecoverthesedistributionsempirically.
144.
1AbstractionsIntryingtokeepthemodelsimple,wehavenecessarilyomittedsomeimportantfeaturesoftheairlineindustry.
Mostnotably,inmodelingtheairlinenetworkandentryandexit,wehavemodeledpresenceonlyandhavenotaccountedfortheextentofentry(e.
g.
,thenumberandsizeofights).
Asmentionedabove,thereisplentyofavailabledatasoitwouldbepossibletomodeltheextentofentry.
However,itwouldmakethemodelandestimationmorecomplex,surelybeyondwhatwouldbedesirableinatypicalmergeranalysisbyantitrustauthorities.
Additionally,itisnotobvioustousthatthebenetjustiesthecostofsuchananalysis,whichwouldprimarilybeaslightlymoreprecisemeasureofpost-mergerconcentration.
Finally,wewillnotexplicitlyallowforhubformationanddestruction.
Oursetofcitycharacteristicsvariables,Zt,willincludewhetherornotacityisahubforagivenairline,butthiswillbetreatedasexogenousandxed.
Airlinescangrowandshrinktheirnetworksineachcity(hubsandnon-hubs),buttheycannotformnewhubsordissolveoldones.
Whileitwouldberelativelystraightforwardtorelaxthisassumptionintheory,formingnewhubsordissolvingoldhubsisalsoquiterareinthedata,makingitdifculttomodelempirically.
54.
2PolicyInvarianceWenowdiscusssomepotentialscenariosforwhichthepolicyinvarianceassumption(Section3.
4)mightfail.
First,onemightworrythatthescaleofthenewlymergedairlinesare"outofsample.
"However,entrydecisionsaremadeattheroutelevelinourempiricalmodel,andtheincentivesdrivingdecisionsarenetworkandcompetitionfeaturesthatarelocaltotherouteandthecity-pair.
Therefore,whilethepost-mergerairlinemaybelargerthananyexistingairlines,theincentivesfacedoneachrouteareofasimilarscaletothosefacedbytheairlinesinoursample.
Second,perhapscostefcienciesuniquetothemergedairlinemightmakeanewentrystrategyoptimal.
Thecoststypicallycitedbymergingairlinesareeitherxedcosts(e.
g.
,integratinginformationsystems)ormoreefcientusageofcity-speciccapital(e.
g.
,hangarspace).
Theformerareirrelevantforentrydecisions,andthelatterarecapturedbyourcityserviceandconcentrationmeasures.
Finally,de-hubbingandslotconstraintsmightaltertheincentivesofthepost-mergerairline.
Asdis-cussedinSection7,wedoseesomemildde-hubbingofthepost-mergerairline,buttheeffectsarenotstrong.
Alleviatingslotconstraintsisoftencitedasapro-competitive,merger-specicefciency,andmanyrecentmergerhavebeenapprovedonlyafterthemergingairlinesagreedtotransfersomeoftheirslotsto5TheonlyhubbingordehubbingeventintheperiodcoveredbyourdataisDeltadissolvingtheirDallas-FortWorthhubin2005.
15theircompetitors.
Itisoutsidethescopeofthispapertodeterminetowhatextentthesedivestitureshelped.
However,thefactthatonly3outof60citiesinourdatahadaslotconstrainedairportmakesusbelievethattheimpactofslotconstraintsisunlikelytobearst-orderissueinouranalysis.
5DataTheprincipledatasourceistheBureauofTransportationStatistics(BTS)T-100DomesticSegmentDatasetfortheyears2003-2008.
Morehistoricaldataisreadilyavailable.
However,duetothelargeimpactoftheeventsof9/11ontheairlineindustry,weview2001and2002asnotrepresentativeofthecurrentindustry,sowedroppedthosefromoursample.
Wedidnotusedatafromyearsprioreitherbecauseourmodelrequiresustouseaperiodwhereairlines'entry/exitstrategyfunctionsarerelativelystationary,andwefeltthatthiswasnotlikelytobetrueoverlongertimehorizonsduetochangesinpolicy,technology,etc.
However,wenotethatwehavetriedextendingallofourestimationsbackallthewayto1993andachievedverysimilarresults.
TheT-100segmentdatasetpresentsquarterlydataonenplanedpassengersforeachsegmentownbyeachairlineintheU.
S.
Thedatadenesasegmenttobeanairporttoairportightbyanairline.
Aone-stoppassengerticketwouldthereforeinvolvetwoightsegments.
Weusedataforthesegmentsconnectingthe75largestairports,wheresizeisdenedbyenplanedpassengertrafc.
ThedatawasthenaggregatedtotheCompositeStatisticalArea(CSA)wherepossibleandtothemetropolitanstatisticalareawhenthiswasnotpossible.
Theendresultwassegmentdataconnecting60demographicareas(CSAs).
Notethatthismeanswearetreatingmultipleairportsatthesamecityasone.
Wefeelthatthisismoreappropriateforourpurposesthantreatingthemasseparatedestinations.
AppendixAcontainsthelistofairportsincludedineachdemographicarea.
Althoughtheairlinestrategyfunctionisdenedovertheroutesegmententrydecisions,wealsoallowairlinestocarrypassengersbetweenapairofCSAsusingone-stopitineraries.
Thecombinationofnon-stopandone-stopservicebetweentwoCSAsisdenotedthe"market"betweentheCSAs.
Usingthedataonitinerariesactuallytravelledasaguide(DB1B),wedeneanairlineaspresentinamarketifeither(1)theairlineprovidesserviceontheroutesegmentconnectingthetwoCSAsOR(2)theairlineprovidesserviceontworoutesegmentsthatconnecttheCSAsandtheightdistanceofthetwosegmentsislessthanorequalto1.
6timesthegeodesicdistancebetweentheCSAs.
Itinerariesthatusetwoormorestopsareextremelyrareintheairlineticketdatabasesoweexcludethispossibilityentirely.
NotethatincertainplaceswesupplementtheT100SdatawithdatafromtheT100M"market"database,theDB1Bticketdatabase,and16theHouseholdTransportationSurvey(tourismdata).
Therearemanyightsthatshowupinourdataasownbyregionalcarriers(e.
g.
,MesaAir)thatareinfactownundercontractwithamajorcarrier.
Ontheseights,themajorcarriersellstheticketsand,typically,theplanewouldhavethemajorcarrier'snameontheoutsideandwouldgenerallyappeartopassengerstobeownedbythemajorcarrier(thoughinmanycasesitisnot).
Majorcarrierscancontractwithdifferentregionalairlinesindifferentpartsofthecountryandcontractschangeovertimeintermsofwhatroutesarecovered.
Regionalcarriersmayalsoysomeroutesundertheirownname,sellingticketsthemselves.
Flightsownbyregionalcarriersrepresentabout25-30%oftheightsinthemajorcarrier'snetworksinourdata(seeAppendixA.
3),soignoringthemcouldpotentiallybeveryproblematic.
Inouranalysis,weattributeightsownbyregionalcarrierstothemajorcarrierthattheyarecontractedto.
Thatis,ifMesaiesaplaneundercontractforDelta,wewillcallthataDeltaightforthepurposesoftheanalysisandtreatitidenticallytoaightthatDeltaiesitself.
TheT100datasetweusetodescribetheroutenetworksoftheairlinescontainsnumerousightsthatarenotregularlyscheduled,suchascharterights,andevenightsdivertedduetoweatherorequipmentproblems.
Asaresult,ifweweretodeneairlinemarketpresencebytheexistenceofasmallnumberofightsonagivenmarket,wewouldpickupaverylargenumberofphantomentriesthatdidnotrepresentregularlyscheduledservice.
Ourgoalistodescribestablefeaturesoftheairlinenetworksratherthanidiosyncraticightsown.
Wethereforedeneanairlineashaving"entered"asegmentifatleast9000passengersarecarriedonasegment,roughlycoincidingwithasingledailynonstopight,ineachoffourconsecutivequarters.
Symmetrically,anairlinehas"exited"asegmentifithasnotcarried9000passengersonasegmentineachoffourconsecutivequarters.
OurentrydenitionisexplainedmorethoroughlyinAppendixA.
5.
1DataSummaryTable1listssummarystatisticsforsegmentandmarketpresencebyairline.
Southwesthasthemostnonstoproutes,followedbythethreemajorcarriers:American,United,andDelta.
Becausethemajorshavehub-and-spokenetworks,ascomparedwithSouthwest'spoint-to-pointnetwork,theyarepresentinasmanyormoreone-stopmarketsasSouthwestdespiteyingfewernonstoproutes.
AstrikingfeatureofthedataistherapidexpansionofSouthwestandJetBlue.
Theothermajorairlinesaregrowingmuchmoreslowly.
6Onaverageairlinesenterandexitbetweenveandtenpercentoftheirroutesperyear.
Table2listssummarystatisticsfortheairline'snetworks,concentratingonthevariablesthatwewilluse6GrowthinUSAirways'networkislargelyduetothemergerwithAmericaWest.
17intheestimations.
Anobservationinthedataisanairline-year-citypair;therearetenairlines(notcountingAmericaWestbeforeitwasmergedintoUSAirways)and1770citypairs.
5.
1.
1CityPairCharacteristicsInthepastliterature,themostcommonlyusedmeasureoftheunderlyingdemandforairtravelbetweentwocitiesistheinteractionofthepopulationsofthecities.
Thispopulationvariableisintendedtomeasurethetotalpossiblenumberofvisitsbetweenresidentsofthetwocities,butitalsohasthedisadvantagethatitignoresmanyotherimportantfeaturesofdemandsuchascityproximity,availabilityofalternativemethodsoftransport,industrialactivity,etc.
Weinsteadusethevariable"Log(2002PassengerDensity),"whichmeasuresthelogactualpassengerdensity(enplanements)foreachmarketintheyear2002.
Thedensityvariablehelpscapturemanyoftheunobservableaspectsofmarketdemandthatarepeculiartoagivencitypair.
Boguslaski,Ito,andLee(2004)haveshownthatpassengerdensitydoesaverygoodjobinpredictingSouthwest'sentrybehavior.
Notethatincasessuchasunservedmarkets,wherethedensityvariableequalszero(over25%ofcases–seeTable2),wesetLog(Density)equaltozero.
Apotentialproblemwithusingthedensityvariableisthat,becausedensitydependssomewhatontheairlinenetworks,itwouldbeendogenous.
Tomitigatethisissue,ratherthanmeasuringdensitylaggedoneperiod,whichwouldbevalidundertheiidassumptionbutinvalidotherwise,wemeasuredensityintheperiodjustpriortoourestimationsample.
Asarobustnesscheckwehavealsotriedusingdensitylaggedoneperiod,withsimilarresults.
Tocaptureunderlyingdemandinunservedmarkets,wherepassengerdensityiszero,wealsoincludetheproductofthepopulationattheroute'sendpointcities,interactedwithadummyforwhethertherouteisunserved.
Wealsoconstructaseconddensitymeasurethatwecall"Log(PassengerDensityinNewMarkets)"thatreectsaparticularroutesegment'simportanceineachairline'soverallnetworkofmarkets(nonstopandone-stopights).
Specically,thisvariableequalsthelogdifferenceintotalpassengerdensityonthenetwork(in2002)onthenonstopandone-stopmarketsservedwithandwithouttheroutesegmentun-derconsideration.
Itismeanttocapturetotalpotentialrevenuegain/lossacrosstheentirenetworkfromadding/subtractingeachroutesegmentindividually.
Thisvariablewasinspiredbyanecdotalevidencesug-gestingthatAmericanAirlinesusesasimilarmeasureinmakingitsentrydecisions.
7Notethatthisvariableiszeromorethan50%ofthetime,reectingboththepresenceofunservedmarketsasabove,andalsothefactthatsomeroutesinanairline'snetworkareextraneous,inthesensethattheydonotaddanynewmarketstothenetworkbutmerelyduplicateexistingserviceinamoreconvenientway.
7ThisanecdotehasbeenrelayedbySteveBerryinseveraltalksbutnot,toourknowledge,inprint.
18Afourthdemandvariable,"percenttourist,"measuresthepercentageofpassengerstravellingineachmarketwhoreportedthattheirtravelwasforthepurposeoftourismintheHouseholdTransportationSurvey.
Wefoundthatothercitycharacteristicssuchashouseholdincomehadnoexplanatorypowerinourdatasoweexcludedthemfromtheanalysis.
5.
1.
2CompetitionVariablesInourestimationsweusealargenumberofvariablesthatattempttocharacterizecompetitiononeachroutesegment.
Firstwedividecompetitorsintonon-stopandone-stoptohelppickupconsumers'preferencefornon-stoptravel,aswellasanycostconsiderations.
Theaveragecity-pairhasslightlylessthanonenon-stopcompetitorand3.
5one-stopcompetitors.
Ofcoursebothofthesevariableshaveveryskeweddistributionswithmanyzerosandafewcity-pairsthathavemanycarriers.
Wealsomeasurethenumberofcode-shareagreementsthateachairlinehasoneachroutesegment.
8Codesharesarefairlyrare.
Wehavealsocomputedalargenumberofconcentrationmeasuresforeachmarket.
Thevariable"HHIAmongOthers(Market)"directlymeasurestheconcentrationamongrivalcarriersonthecitypairinques-tion,includingbothnon-stopandone-stopcompetitors.
TheHHIamongcompetitorsaveragesabout5000inoursample(whereHHIrangesfrom0to10,000).
Thereisalsosubstantialevidence(Borenstein(1989),Borenstein(1990),Borenstein(1991),Berry(1992))thatthesizeofacarrier'soperationsattheendpointcitiesinuencesacarrier'smarketpowerontravelbetweenthosecitiesindependentlyofconcentrationonthemarketitself.
Thus,wealsoincludevariablesmeasuringacarrier'smarketshareateachendpointcity("OwnShare(City)Large/Small").
Theuseof"Large"and"Small"refertothelargestandsmallestvalueoutofthecity-pairconnectedbytheroutesegment.
Forsimilarreasonswealsoincludemeasuresofconcentrationateachendpointcity("HHIAmongOthers(City)Large/Small").
Notethatthesevariablesmightalsoinuenceentryforcostreasons.
IfwemeasuredthemarketshareandHHIvariablesinthenaturalway,usingthenumberofenplanedpassengers,thenitwouldnotbepossibletosimulatefuturevaluesofthecompetitionvariablesunderamergerwithoutalsoestimatingademandsystemthatpredictedenplanedpassengersatfuturedates.
Thus,weinsteadmeasurealloftheHHIvariablesusingthenumberofroutesservedoutofeachcity.
Itturnsoutthatthisyieldsessentiallyidenticalestimatesempirically.
Ournalmeasureofcompetitioniswhetherornotacompetitorhasahubontheroute.
Ownhubsaretreatedseparatelybelow.
8Thisvariableiscompiledfromdatathatisseparatelymeasuredforeachairlinepair-routesegmentusingtheticketdata.
195.
1.
3NetworkCharacteristicsForeachcity-pairroutesegmentwealsohavealargenumberofmeasuresoflocalnetworkcharacteristics.
Wemeasuresegment(non-stop)presenceandmarket(feasibleone-stop)presenceseparately,aswellasendpointpresence("PresentatBothAirports(notMarket)").
Thesevariablesarenon-nestedinthesensethatanairlinecaneitherservearoutesegmentorbe"PresentatBothAirports(notMarket)",butnotboth.
Alloftheseshouldhavelargeeffectsonmarketpresencethroughthecostside.
Wemeasurehowmanyendpointcitiesareahubforeachairline.
Wealsomeasurehowconvenientthemostconvenienthubistotheroutesegmentbytakingthenon-stopdistanceanddividingbytheone-stopdistancefortheclosesthub.
Ifahubisveryconvenient,nearlyonastraightlinebetweenthetwocities,onemightexpectthattheairlinecouldveryeasilyservetherouteviaone-stoptravel.
Wealsomeasurethedistancetothenearesthubforeachend,ranked(Large/Small),whichismeanttobeameasureofhowcentraltothenetworkthetwoendpointsare.
Finally,wemeasurethesizeofeachairlines'networkattheendpointcitiesusingthenumberofnon-stopdestinationsservedateachendpointcity,ranked(Large/Small).
Thisvariablecouldinuencemarketpresencethroughboththedemandandthesupplysides.
Notethatitisdifferentthanthesharevariablesabovebecauseitmeasuresnetworksizeratherthannetworkshare.
5.
2ASimpleStaticMergerAnalysisWiththenotableexceptionofSouthwest,U.
S.
airlineshavehub-and-spokenetworks.
Asaconsequence,outof1770possiblecitypairsinourdata,thetypicalmajorairlineiesonly150-220nonstoproutes(in2008),whilestillcovering1100-1500citypairswithreasonableone-stopconnections.
Forcomparison,Southwesties323nonstoproutesandcoversonly1042markets.
(SeetherstcolumnofbothpanelsofTable3.
)Inthissection,weperformananalysisoftheimmediateeffectsofmergersonmarketconcentration,whichwecontrastwiththemedium-andlong-runeffectsinlatersections.
Table3summarizesthelevelofcompetitionfacedbyeachairlineacrossitsnonstoproutes(panelA)andfeasibleone-stopmarkets(panelB).
Southwest,DeltaandNorthwestaretheairlinesmostisolatedfromcompetitioninthesensethattheyhavethemostmonopolyandduopolynonstoproutes.
Asaresult,theovernighteffectofaDL-NWmergeristocreateanairlinewith108monopolynonstops,farandawaythemostofanyairline.
Thestoryisslightlylessstarkwhenweincludefeasibleone-stops.
However,eventhen,DL-NWhas31monopolyone-stopmarketsandanadditional97duopolyone-stopmarkets.
Theothertwopotentialmergersweconsider,UA-US,andUA-CO,createairlineswithonlyabout35monopolynonstops,20andonly13monopolyone-stopmarkets.
Table3alsoshowstheextenttowhichthedatacovermanydifferentmarketstructures.
Almosteveryairlineiesmultiplerouteswithallcombinationsof0to6nonstopcompetitorsand0to10onestopcom-petitors.
Wealsoobservemanydifferentpairsandtripletsofairlinesacrossmarkets.
Thisrichvariationincompetitioniswhatallowsustoempiricallyidentifytherelationshipbetweencompetitionandrouteentry.
Tomeasuretheshort-runanticompetitiveeffectsofeachmerger,wecomputeHHIsbeforeandafterthemerger,intermsof2008passengersenplaned.
Table4showsthetenworstaffectednonstoproutes(city-pairs)forthethreemergersintermsofincreaseintheHHI.
ForDL-NW,therearesevennonstoproutes–outofCincinnati,Minneapolis,SaltLakeCity,andMemphis,allhubs–wherethemergeressentiallycreatesamonopolycarrier.
ThreeotherroutesbetweenAtlanta(alsoahub)andthesecitiesmoveessentiallytoduopoly.
TheHHIchangesrangefrom1500-5000points.
Allofthesemarketsviolatethemergerguidelinesbyaverylargemargin.
Absentoffsettingentry,priceswouldbeexpectedtorisesubstantiallyontheseroutesafterthemerger.
ForUA-US,weseealmostthesamepattern,withsixmonopolyroutescreated,mostlyoutofDC,Philadelphia,andCharlotte.
ForUA-CO,thestoryisnotquiteasbad–thereisonlyonemonopolyroutecreated–butthepatternsstillwouldviolatethemergerguidelinesbyalargemargin.
Thereisalsosubstantialevidence(Borenstein(1989),Berry(1992))that,duetofrequentyerprograms,marketconcentrationoutofacityasawholeisalsoanimportantdeterminantofmarketpower.
Table5showstheveworstaffectedcitiesintermsofHHIincreaseacrossallightsfromthecity.
Again,weseelargeHHIincreasesinmarketsthatwerealreadyveryconcentrated,clearlyinviolationofthemergerguidelines.
ThemergerthatlooksworstbythismeasureisagainDL-NW,whileUA-COappearstheleastbad.
ForUA-US,theworstcasecitiesareCharlotte,Philadelphia,andDC.
Concentrationatthesecitieswascitedasthemainreasonthatthemergerwasblocked.
TheHHIresultsprovideashort-runsnapshotoftheincreaseinconcentrationthatwouldresultfromthethreeproposedmergers.
Bytheseshort-runmeasures,allthemergerslookprettybad,inthesenseofincreasingconcentrationandleadingtoupwardpricepressure.
Ofcourse,argumentscanstillbemadeinfavorofthemergers.
Largecostsavingscouldoffsettheharmfromdecreasedcompetition.
However,costsavingswouldhavetobelargeandsystemwidetojustifytheincreasesinconcentrationseeninmanymarkets.
Wewillnotexplorethisavenueinthispaper.
Alternatively,itmaybethatentrycostsarelowandthatthecitiesdiscussedabovearelikelytoexperienceoffsettingentryinashortperiodoftime.
Below,weuseourdynamicmodeltoexplorethispossibilitybysimulatingmediumandlongertermmarketoutcomes.
216EmpiricalImplementation6.
1OverviewTheprimarydifcultywithestimatingtheairlinemodelisthat,intheirgeneralform,thechoiceprobabilitiesin(4.
1)arehighdimensionalandwouldbeidentiedonlybyvariationinthedataovertime.
Variationacrossairlinescouldalsobeusedifweweretoassumesomesymmetryacrosscarriers.
However,giventhatthereareatleast,inprinciple,twotypesofcarriers,hub-and-spokecarriersandlowcostcarriers,wedonotnecessarilywanttoimposesymmetryacrossallcarriers.
Attheveryleastweshouldexplorethisempirically.
Furthermore,giventhatwehaveonlytencarriersandsixyearsofdata,thatstillonlyleaves60observationstodetermineaveryhighdimensionalsetofprobabilities.
Therefore,toestimatetheseprobabilitieswewillrequiresomesimplications.
Mostnotably,wewillneedtouseatleastsomeofthevariationinthedatawithinanairline'snetwork(acrosscitypairs)toidentifythestrategyfunctions.
Inprinciple,allsegmentsinthewholesystemarechosenjointly,andwewouldlikethemodeltoreectthat.
However,italsoseemsunlikelythattheentrydecisionsareverycloselyrelatedforsegmentsthataregeographicallydistantandnotconnectedinthenetwork.
Thus,ourempiricalapproachwillbetostartwithafairlysimplemodel,andthenaddcomplexityuntilweexhausttheinformationinthedata.
Asarobustnesscheck,wewilltestforanyremainingcomplementarityofentrydecisions.
Thesimplestmodelwecanthinkofwouldallowtheentrydecisionsacrosssegmentstobecorrelatedonlythroughobservablefeaturesofthemarket,sothiswillbeourbasemodel.
Inthebasemodel,weassumethatthereareonlynonstopsegmentlevelshocksandthattheseshocksareindependentacrossnonstopsegments.
Wemodelsegmentpresence(entry/stayin=1,exit/stayout=0)usingaprobitmodel.
Tables6and7showthebaselineprobitestimatesforroutepresenceusingdatapooledforallairlines.
Table6includesyeardummies,citydummies,andalloftheroutedemandvariables,whileTable7addsroutexedeffectsanddropsallvariablesthathavenovariationattheroutelevel.
Tohelpinterpretthecoef-cientmagnitudes,thethirdcolumnofeachtablereportsthemarginaleffectsoftheestimatedcoefcientsforanairlinethatisindifferent(inexpectation)betweenentering/stayinginandexiting/stayingout,whilethefourthcolumnreportsthemarginaleffectsofaoneSDchangeineachvariable.
6.
2SeriallyCorrelatedUnobservedShocksBeforediscussingtheestimates,werstconsidertheimportantissueofseriallycorrelatedunobservedshocks.
Recallthattheprimaryeffectofseriallycorrelatedmarketleveldemandorcostshockswouldbetobiasthecompetitioncoefcientsupward(morepositive/lessnegative).
Thisisbecauseahighervalueofthe22shockwouldalsoleadtopersistentlymoreentryandlessexit,andmakeitappearasifcompetitionwaslessunfavorablethanitreallywas.
Therstspecication(Table6)controlsforunobservedshocksusingcityxedeffectsanddetaileddemandvariables.
Theideaistomakedemandshocksasobservableaspossible,leavinglittleunexplained.
Thesecondspecicationusesmoredetailedroutexedeffects(Table7).
Whilewefoundthatthedemandvariablesdidhelpremovesomeofthebiasinthecompetitioncoef-cients,itisclearfromtheestimatesinTable6thatthisstrategyhasnotentirelyworked.
Thecoefcientonnonstopcompetitorsisverysmall(-0.
14).
Mostimportantly,itis23timessmallerthanthecoefcientonroutepresence(3.
25),suggestingthatitwouldtake23additionalnonstopcompetitorstooffsettheeffectofbeingpresentonaroute.
Toaddanotherpointofcomparison,theestimatedcoefcientonnonstopcompeti-torsisofsimilarmagnitudetothecoefcientforaddingasingleconnectingightoutofthelargestendpointcityontheroute.
Theestimatedcompetitioneffectsinthismodelseemimplausiblysmall.
MovingtotheestimatesfromthemodelwithroutexedeffectsinTable7,wecanseethattheestimatedcompetitioncoefcientsarenowanorderofmagnitudelarger.
Accordingtotheseestimates,ittakesonlytwocompetitors(-2.
93)tofullyoffsettheeffectofroutepresence(2.
48).
Thismagnitudeseemsmuchmoreplausible.
Tofurtherinvestigatethisissue,wealsoimplementastatisticaltest.
Lazarev(2019)suggeststestingtheMarkovpropertyoftheobserveddistributionofactionsgivenstatesagainstageneralalternative.
Inoursettingtheenormoussizeofthestatespacewouldmakesuchatestimpractical.
Furthermore,withsuchalargestatespace,thattestislikelytohaveverylowpower,andthusfailuretorejectitwouldnotbeveryconvincing.
Instead,toachieveabalancebetweenpowerandgeneralityofthealternative,totestforaviolationoftheMarkovpropertywere-estimatedthesamemodelsincludingthevariable"presencetwoperiodsago.
"UnderthenullhypothesisthattheobserveddistributionofactionsgivenstatesisMarkov,thecoefcientonthisvariableshouldbezero,i.
e.
,presencetwoperiodsagoshouldnothaveanyremainingexplanatorypowerintheprobitmodel.
Ontheotherhand,ifthereisaseriallycorrelateddemandorcostshock,thenpresencetwoperiodsagowouldbeafunctionofthisshockanditscoefcientshouldbenonzero.
Forthemodelwiththedemandvariablesandcityxedeffectsonly,westronglyrejectthenullhypothesis(p=0.
004).
Thisndingsupportsourconclusionthatthemagnitudeofthecompetitioneffectsinthemodelwithcityxedeffectsisimplausiblylow.
Forthemodelwithroutexedeffects,wefailtorejectthenull(p=0.
883).
Moreover,thecoefcienton"presencetwoperiodsago"isestimatedtobeveryclosetozero(0.
015),suggestingthattheimpactofanyremainingunobservedheterogeneityonthecoefcientestimatesislikelytobeminimal.
WethereforeproceedbyusingthespecicationinTable7asourbasemodel.
236.
3BaseModelEstimatesWenowdiscussthebasemodelestimatesinTable7.
First,considerthecompetitionvariables.
Theeffectofnonstopcompetitorsisestimatedtobestrongandnonlinear.
Themarginaleffectofgoingfromzerotoonenonstopcompetitor(-1.
93)isstronglynegative,almostaslargeinmagnitudeastheeffectofmarketpresence(2.
48).
Thesearethetwolargestcoefcients.
Addingasecond,third,orfourthcompetitoralsohasstrongnegativeeffects,startingabouthalfthesizeoftherstcompetitorandtrendingsmaller.
Addingcompetitorsabovefourwasnotestimatedtohaveafurthereffect,perhapsinpartbecausetherearealimitednumberofrouteswithmorethanfournonstopcompetitorssotheseeffectsareestimatedwithlessprecision.
Theeffectofone-stopcompetitionwasconsistentlyfoundtobesmallandinsignicantsothatvariableisomittedfromourbasemodel.
Wealsofoundthatthemarketstructureatthetwoendpointcitiesplaysasignicantrole,particularlythelargerendpointcity.
Foranairlineindifferenttomarketpresence,atenpercentincreaseinmarketshareatthelargerendpointcityleadstoa11.
7%increaseintheprobabilityofentry/presence.
Forthesmallerendpointcitythiseffectis7.
2%.
Similarly,themoreconcentratedcompetitionisatthelargerendpointcity,themorelikelythatanairlineenterstheroute.
Finally,ifacompetitorhashubatoneendpoint,entry/presenceissignicantlylesslikely—themarginaleffectforanindifferentairlineis-23%.
Thesendingsareconsistentwithpriorliteraturethatndsthatmarketpowerattheendpointcitiesincreasesmarketpoweronalltheroutesoutofthosecities.
Notethatconcentrationatthesmallerendpointisestimatedtohaveanegativeeffect,thoughthatcoefcientisinsignicant.
Theotherimportantfactordeterminingentry/presenceisthethicknessoftheairline'sroutenetworkinthevicinityoftheendpointcities.
Asmentionedabove,priorroutepresenceisthesinglemostimportantvariable.
Thisrepresentsthe"stickiness"inairlineentrydecisionsandislikelyinducedbytheeffectofanysunkcostsofentrysuchasthecostsofsettingupoperationsatanairportandofadvertisingthenewroute.
Otherthanpriorroutepresence,themostimportantnetworkvariablesarethenumberofnonstopcitiesservedateachendpoint.
Addingasinglenonstoprouteoutofthelargerendpointcityincreasestheprobabilityofentry/presenceby11%,whileaddingasinglenonstoprouteoutofthesmallerendpointincreasestheprobabilityofentry/presenceby9%.
Notethatthesevariablesvarywidelyinthedata,sothismeansthattheyhavealargeamountofexplanatorypowerinthemodel.
Theyarethereforeamongthemostimportantvariablesinthemodel(alongwiththecompetitionvariables)becausetheyplayalargeroleindeterminingwhatairlinesarepotentialentrantsforaparticularroute.
Wealsofoundthatendpointhubshavealargesignicantpositiveeffectonentry/presence,andhub24conveniencehasanegativeeffect,presumablybecausetherouteiseasilyservedbystoppingatthehubinstead.
Distancetonearesthubdoesnotaddmuchoncetheunitsareaccountedfor.
6.
4ModelFitToevaluateinsamplet,Table8computespsuedoR-squaredstatisticsfordifferentsubsetsofthedata.
ThersttwocolumnsofthetablecomputeapsuedoR-squaredbyairline,forrouteswheretheairlinesstaysin,androuteswhereitstaysout.
Theseare,ofcourse,theeasiestroutestopredict,asairlineroutepresenceisstaticformostroutesfromoneyeartothenext.
Lookingrstatthestayers,wecanseethatrouteswhereanairlinestaysouthavepsuedoR-squaredsthataretypicallygreaterthan0.
99,sothemodelismatchingtheseroutesalmostperfectly.
Routeswhereairlinesstayinarealsomatchedveryclosely,withthepossibleexceptionofJetBlue,whichisayoung,rapidlyexpandingairlineinourdataperiod.
ColumnsthreeandfourcomputepsuedoR-squaredsonlyforrouteswithnewentryandexit.
ThesepsuedoR-squaredsaremuchlower,averagingaround0.
2,withexitpredictedslightlybetterthanentry.
Thisisaverystricttestofthemodelasitaskswhetherthemodeliscapableofpredictingexactlywhichnewrouteseachairlineenters/exitseachyear.
WethereforeviewthesepsuedoR-squaredsasactuallyquitehigh.
Inordertoseemoreclearlywhichaspectsofthedatathemodelisttingwell,thenaltwocolumnsofthetableshowthetofthemodelin2008,whenitissimulatedfortheentiredataperiod2003-2008using2002asastartingpoint(andneverupdatedusingtheactualoutcomes).
Againweconsideronlyrouteswithnewentryandexitoverthatperiod.
ThesepsuedoR-squaredsareextremelyhigh,averagingaround0.
65,withexitttingbetterthanentry.
Overall,weconcludethatthemodeltsnewentryandnewexitverywellbyairline-route,butislessgoodatpredictingtheexactyearofnewentry/exit.
Inotherwords,themodelpredictsthemarginalroutesverywellbutisnotasgoodatpredictingthetimingofnewentry/exitontheseroutes.
Thefactthatthemodeldoesnotcapturetimingwellisperhapsnotsurprisingasourdatadonothavegoodmeasuresofyeartoyeardemandorcostvariationattheroutelevel.
(Themainsourceofyearlydemand/costvariationistheyeardummies.
)6.
5Robustness/ModelSelectionInthissectionwedescribeseveralattemptsatgeneralizingthebasemodelthatallfailed.
Arecurringthemeisthatthegeneralizationsimprovethein-sampletofthemodel,butfailtestsofoverttingusingcrossvalidation.
256.
5.
1NonparametricEstimationSincetheprimaryuseforthebasemodelistopredictairlineentrybehaviorwithandwithoutmergers,itseemspotentiallyfruitfultoconsidermachinelearningapproachesdevelopedforpredictionmodels.
More-over,inourcontext,sincethefunctionalformofthestrategyfunctionsisunknown,BBLsuggestsestimatingthemnonparametrically.
Inthissectionweexplorethesepossibilitiesbyreestimatingthebasemodelusinganarticialneuralnetwork(ANN)ofvaryingdimensions.
TheANNhastheabilitytomatcharbitrarynonlinearities,includinginteractionsbetweenvariables.
TheimplementationoftheANNusedherehadalinearinputlayerandlogitmiddlelayers,andwasestimatedusingmaximumlikelihoodwithanormalerror.
Thismakesitanonlinearprobitandadirectgeneralizationofthelinearprobitmodelabove.
TheANNiscomputationallyintensivetoestimate,soitwasestimatedontheversionofthebasemodelabovewithoutxedeffects.
TheANNwasestimatedwith10-foldcrossvalidation.
Table9liststhevalueofthecross-validationlikelihoodforthelinearprobit,aswellastheANNwithsuccessivelyhigherdimension.
AswemaketheANNricher,thein-sampletimprovessubstantially(notreported),butthecross-validationresultsshowthatthisimprovementisduetoovertting.
Crossvalidationpicksthelinearprobitasthepreferredmodel,rejectingallofthenonparametricmodels.
Webelievethisresultisprimarilycausedbythefactthatthelinearprobitmodelisalreadyexplainingmuchofthevariationinthedata(seediscussionoftable8above),leavinglittleroomfornonlinearitiestoimprovethetofthemodel.
Additionally,manyoftheexplanatoryvariablesinthemodeltakeononlyasmallnumberofvalues,sononlinearitiesarenotimportantforthesevariables.
6.
5.
2LASSOandFixedEffectSelectionAnimportantissuewithpredictionmodelsisoverttingfromincludingtoomanyvariablesinthemodel,whichproducesunbiasedbutnoisypredictions.
Wefoundabovethattheroutexedeffectswereeffectiveatcontrollingforunobservedseriallycorrelatedshocks,butthedrawbackofhavingsomany(1770)ofthemisthatthereisthepotentialformanyofthemtobepoorlyestimated,resultinginovertting.
Toaddressthisissue,weattemptedtouseLASSOtoreducethesetofxedeffectsandreduceoutofsamplepredictionerror,asmeasuredbycrossvalidationlikelihood.
Unfortunatelywewereunsuccessfulinthisendeavor.
WhenLASSOwasappliedtothefullbasemodel,itdidsignicantlyimprovethecrossvalidationlikelihood.
However,theresultingmodelestimatesweresimilartothoseaboveforthebasemodelwithoutxedeffects:thecompetitioncoefcientswereunrealisticallysmallandtheestimatedmodelfailed26thetestforseriallycorrelatedunobservederrors.
WealsomadeasecondattemptatusingLASSO,whereweonlyappliedLASSOtothexedeffectscoefcients,holdingtherestofthecoefcientsxedattheirvaluesestimatedinthebasemodelwithallthexedeffectsincluded.
Perhapsnotsurprisingly,thisprocessyieldedbestestimatesthatincludedalmostallofthexedeffects.
Itdidslightlyreducethecrossvalidationlikelihood,butthisimprovementwasachievednotbyreducingthenumberofxedeffects,butbyshrinkingallofthexedeffectestimatestowardzero.
Wethereforeproceedbelowwiththebasemodelincludingallthexedeffects.
6.
5.
3AsymmetricStrategyFunctionsAnothergeneralizationweexploredwastoallowtheprobitentryfunctionstodifferacrossairlines.
Themostobviousapproachhereistogroupcarriersintotwogroups:traditional"hub-based"carriersandpoint-to-point"lowcost"carriers.
Wealsoexploredestimatingdifferentstrategyfunctionsforeachairline.
Notethatsuchanapproachissomewhatcomplicatedbythefactthattheairlines'networksarenotentirelyover-lapping.
Ineachcase,wefoundsimilarresultstothoseabove:allowingforseparateprobitentryfunctionsincreasedthein-samplet.
However,thecoefcientestimateswereingenerallessprecise,andmorefre-quentlyshowedunrealisticsignsormagnitudesthanthebasemodelestimatesabove,givinguslesscon-denceinthem.
Moreover,crossvalidationagainrejectedtheasymmetricstrategyfunctionsinfavorofthesymmetricbasemodelabove.
Inaddition,weexploredaddingairlinedummiestothebasemodel.
Forthemodelwithoutroutexedeffects,theonlyairlinedummythatshowedupasmatteringatallintermsofmagnitudeandstatisticalsignicancewasJetBlue,whichisincludedinthemodelintable6.
Forthemodelwithroutexedeffects,alloftheairlinedummieswereinsignicantandclosetozero,sotheywereomitted.
6.
5.
4CitySpecicShocksThenalgeneralizationweexploredwastogeneralizethevariancestructureoftheprobitmodel.
Theideahereistotrytocapturethefactthattheremightbecityspeciccostanddemandshocksthataffectentrydecisionsforallroutesoutofagivencity.
Anecdotally,itoftenseemsthatairlinesexpandandcontracttheirnetworksonacitywidebasisratherthanroutebyroute,andcity-specicshocksmayhelpexplainthisbehavior.
Thebasemodelassumesthatshocksareindependentacrossroutes.
Letnt+1ijindicatepresenceforairlineionroutejinperiodt+1,andletxij,trepresentalloftheexplanatoryvariablesinthebasemodelabove.
Theninthisnewversionofthemodel,airlineiispresenton27routej,(nt+1ij=1),if(6.
1)xij,tβ+γntij+ξj1,t+1+ξj2,t+1+ij,t+1>0whereξj1,t+1andξj2,t+1aredrawnfromaN(0,τ2)andarecityspecicshocksforcitiesj1andj2,theendpointcitiesforroutej;ij,t+1arei.
i.
d.
marketshocksdrawnfromaN(0,σ2);andγisanentrythreshold.
Notethatthisformulationsimplyaddsξj1,t+1andξj2,t+1tothebaseprobitmodelabove.
ThecityspecicshocksgenerateacorrelationstructureintheroutepresencevariablessuchthattheshocksfortheroutebetweenCSAkandlandtheroutebetweenCSAmandnhaveanormaldistributionwithmeansgivenbythelefthandsideof(6.
1)andvariancematrixΣwhereΣkl,mn=2τ2+σ2,ifk=mandl=n,τ2,ifk=morl=nbutnotboth,0,otherwise.
.
Estimatingthismodelissimilartoestimatinga1770-dimensionalprobitmodel.
Itisquitecomputationallyintensive,andwasonlymadefeasibleusingaGibbssamplingroutinethattakesfulladvantageofthespecialstructureofthecovariancematrix.
9Toreducecomputationalburden,itwasagainnecessarytousethebasemodelwithoutxedeffectsforthisexercise.
Wefoundnosupportforthismodelinthedata.
IntheGibbssampler,theestimateofτ,thevarianceofthecityshocks,collapsestozero.
TheGibbssamplingdistributionsbecomedegeneratewhenthishappens,whichinvalidatestheapproach,sowedonotreporttheestimateshere.
7Results:SimulatingtheLong-RunEffectsofAirlineMergersTables10-14showsimulationresultsforthehub/lowcostpooledmodelaboveoverthe10yearsfollowingourdataset(i.
e.
,2009–2018).
Werunfoursimulations:nomergers,DL-NWonly,UA-USonly,andUA-COonly.
Theestimationsincludeyeardummiesthatabsorbaggregateshockstotheindustry.
Forthesimulations,wehavetochooseforecastvaluesfortheseshocks.
Sincewearenotsomuchinterestedinforecastingaggregatedemand,andareinsteadmainlyinterestedinthedifferencesbetweenthenomergerandmergercases,howwesetthemdoesnotseemtooimportanttotheresultsaslongastheyaresettobereasonably9Detailsoftheprocedureareavailablefromtheauthorsuponrequest.
28stable.
Inordertomimicwhatapre-mergerantitrustanalysismightentail,inthesimulationsbelowwechosetosetthemsuchthatthetotalnumberofroutesservedbyallairlineswasroughlyconstantoverthesimulationperiodforthebase(nomerger)case.
7.
1EffectsonOverallAirlineNetworksWerstassesstheeffectofthemergersonthetotal(national)sizeoftheairlines'networksofroutesandmarkets.
LookingatTables10and11,weseethatthemodelpredictsthattheDL-NWandUA-COmergersreducethetotalnumberofroutesservedbycompetitorairlines(relativetonomerger),whilethedeniedUA-USmergermodestlyincreasesthenumberofroutesservedbycompetitors.
Thatis,atthenationallevelthereismoreoffsettingentryinthelattermerger.
Theeffectoncompetitorlowcostairlinesisgenerallylargerthantheeffectoncompetitorhub-and-spokecarriers.
Lookingmoreclosely,theDL-NWmergercausesamodestdecreaseinthenumberofroutesservedbyAmerican,United,Continental,andJetBluetenyearsafterthemerger.
ThelargestnegativeeffectofthemergerisimposedonSouthwest,whosenetworkis10%smallertenyearsafterthemergerthanitwouldhavebeenwithoutthemerger.
Thiseffectisreectedinslowernetworkgrowthratherthannetworkshrinkage.
Surprisingly,USAirways'snetworkis10%largertenyearsafterthemerger,althoughthisistheresultofaslowerrateofshrinkage.
Theneteffectisthatcompetingairlinesserve33fewerroutesintotalifthemergeroccurs.
Bythisaggregatemeasure,thedynamiceffectofthemergerisactuallyworsethanthestaticone.
TheUA-COmergerhassimilareffectstotheDL-NWmerger.
Americanservesmodestlyfewerroutesunderthemerger,butSouthwestisgreatlyaffectedwitha10%smallernetworkasaresultofthemerger.
USAirways,whichwaspredictedtoshrinkbyalmost10%intheabsenceofamerger,insteadretainsthesameroutenetworksize.
Delta,Northwest,JetBlue,andAlaskaarealmostcompletelyunaffectedatthisaggregatelevel.
Theneteffectisthatcompetitorsserve4fewerroutesifthemergeroccurs.
TheUA-USmergerhasalmostnoeffectonthetotalnumberofroutesservedbythehub-and-spokecarriers.
TheprimaryeffectsarethatSouthwestserves18fewerroutesthanwouldbethecasewithoutthemerger,butthisisoffsetbya21routeincreaseinthesizeofJetBlue'snetwork.
Theneteffectisthatcompetitorairlinesserve7moreroutesifthemergeroccurs.
Formostoftheairlines,qualitativelysimilareffectsareseenintheone-stopmarketsservedbytheairlines(righthandpanelofTable11).
But,therearesomeexceptions.
Forexample,AmericanandUnitedseetheirnetworkofmarketsgrowslightlydespiteservingfewernonstoproutes.
IncontrastthenetworkofUSAirwaysmarketsgrowsbylessthan2%despiteexperiencinga10%growthinitsnonstoproutenetwork.
Themergersimulationsalsomakepredictionsaboutthetimerequiredforthesenetworkchangesto29occur(Table11).
Themergedairlineaggressivelyentersroutesintheyearfollowingthemergerbecausetheradicallychangednetworkofthemergedairlineprovidesstrongincentivesforexpansionincertainmarkets.
Meanwhile,fortheairlinesthatarenotpartofthemerger,thechangesinthenetworkoccurmoregraduallyovertime.
7.
2EffectsonCompetitionwithincities(CSAs)Nextweassesstheeffectsofthethreemergersontheworstaffectedcities(Table12).
Themainquestionweareinterestedinistowhatextentthelargestaticanti-competitiveeffectsshownearlier(Table5)arerelievedbyentryoverthetenyearsimulationhorizon.
10Wendthatthedynamiceffectsonairlinecompetitionatthecitylevelaredifferentforeachofthethreemergers.
Accordingtothesimulations,inthecaseofDL-NW,thereisessentiallynooffsettingentryintheworstaffectedcities.
Infact,therearesomemarkets(MEM,BDL)whereweseetheopposite.
Inthesecitiesthemergerstiesentry,typicallybySouthwest,andalsoleadstoincreasedentrybythemergedcarrier,increasingitsoverallmarketshare.
Theseeffectsstronglysuggestthatpriceswouldriseinthesemarkets,atleastintheabsenceofverylargecostsynergies.
However,wealsonotethatthereisasmallpotentialoffsettingeffectthatconsumersmayalsobenetfromtheconveniencefrombeingabletoyonecarriertomoredestinations.
Intheothertwomergers,thesimulationsdogenerateoffsettingentryintheworseaffectedcities.
Asaresult,inbothcasestheconcentratingeffectsofthemergerarereducedovertime.
ForUA-US,mostofthisoffsettingentrytypicallycomesfromJetBlue.
ForUA-CO,thereisalsooffsettingentrybySouthwest.
ForUA-CO,after10yearsnewentryhasoffsetalargefractionoftheinitialriseinconcentration.
7.
3EffectsonCompetitiononRoutesWenowlookatthesimulatedeffectsofthethreemergersonindividualroutes(Tables13and14).
StartingagainwithDL-NW,weseethattheimmediateeffectofthemergeristomovesixroutesandthreemarketsfromduopolytomonopoly.
Aftertenyears,thesimulationssuggestthatthisnumberwillincreasesuchthattherewillbe14moremonopolyroutesthaniftherewerenomerger.
Thenumberofmonopolyroutesincreasesovertimefortworeasons.
First,thereislittlescopeforoffsettingentryonthemonopolizedroutes.
Ontheseexistingroutes,themergerseemslikelytocausepermanentpriceincreases.
However,inaddition,themergedcarrierentersnewroutesthatwerepreviouslyunserved,andtheseroutesbecomemonopolies.
10HerewecomputeHHIsby#ofroutesservedratherthanpassengersenplaned,sincethatiswhatwemodel.
ComputingpredictedHHIbypassengersenplanedwouldrequireamodelofpassengerdemand.
30ThereasonDL-NWentersthesemarketsisthatithasincreasedlevelsofserviceattheendpoints,whichcausesthesemarketstobecomeeconomicallyviable.
(Ourmodelcannotdistinguishwhetherthisisfordemandorcostreasons.
)Thisnewentryeffectseemsverylikelytobewelfareenhancing,potentiallyoffsettingsomeoftheharmcausedbythemergerfromhigherprices.
TheUA-USmergerhasthegreatestimmediateeffectonindividualroutes,withnineroutesandthreemarketsmovingfromduopolytomonopoly.
However,inthismergerthereissubstantialoffsettingentry.
Thismergeralsoleadstosubstantialnewentryonpreviouslyunservedroutes.
Thus,attheendofthetenyearsimulationperiod,therearetwelverouteswithnewservice,andyetanetofonlythreeadditionalmonopolyroutes.
Infact,inthesimulations,aftertenyears,competitionattherouteleveldoesnotseemtobesubstantiallyreducedfromwhatitwouldhavebeenwithoutthemerger,whilethereismoreservice.
Itseemsplausiblethatthismergerincreasedwelfareaftertenyears.
Ironically,itwastheonlymergerofthethreetobeblocked.
Ofthethreemergers,theUA-COmergerhasthesmallestimmediateimpactoncompetitionattheroutelevel,withonlyoneadditionalmonopolyrouteandactuallytwofewermonopolymarkets(becausethemergerimmediatelycreatesviableone-stopservicewhereitdidnotpreviouslyexist).
Aftertenyearsthereisaneteffectofveadditionalmonopolyroutes,butthereisnewserviceonnineroutes.
Thus,aftertenyearsthismergeralsoseemstohavefairlybenignoveralleffectsattheroutelevel.
8ConclusionsWedrawtwosetsofconclusionsfromthisresearch.
Therstisthatourmethodprovidesasimpleyeteffectivewaytoprovidesomeempiricalinsightandrigortoquestionsofhowaparticularmergerwillaffecttheevolutionofanindustryovertime.
Whilewehaveappliedthemethodtoairlines,itcouldequallywellbeappliedtomanyindustries,solongasthereisrichenoughpastdataavailable.
Agreatadvantageofthemethodisthatitrequiresminimaleconometrictoolsandcomputationalpower.
Aprimaryweaknessintheapproachisthatitassumesthatmergerpolicyisheldconstant.
Anidealmethodofevaluatingmergerpolicymightinvolvecomputingnewequilibriatothemodelunderalternativepolicies.
However,suchanapproachwouldbetheoreticallycomplexand,inmanycases,computationallyinfeasible.
ClearlycomputinganequilibriumforthecomplexU.
S.
airlinenetworkentrygamewouldbefarbeyondwhatiscurrentlypossible.
Ouranalysisofthetwocompleted(DL-NWandUA-CO)mergersandonecontested(UA-US)mergersuggestthatthecontestedmergerwouldhavehadlessofananticompetitiveeffectthanthetwoapproved31ones.
Whilethisissomewhatironic,itisrathereasytoexplain.
Fromastaticperspective,thehighdegreeofoverlapintheUA-USmergermakesitappearthatonmanyroutestwodirectcompetitorswillbemerged.
However,fromadynamicperspective,thenetworkoverlapforUnitedandUSAirwayswasprimarilyinareaswhereJetBlueandSouthwestwereexpanding,andthedecreaseincompetitionwouldincreasetheincentivesfortheselow-costcarrierstoenterthelesscompetitiveroutesdominatedbythemergedrm.
Ontheotherhand,thetwoapprovedmergersreducedtheincentivesforthelow-costcarrierstoexpand,whichhelpedperpetuatetheanticompetitiveeffectsofthemergers.
Thelargerhub-and-spokeairlinesappeartohaveanatbestweakincentivetoenterroutesevenafteramergerreducescompetition,andpartoftheblameforthislackofpotentialentrantsisthestronginuenceofhubsonthenetworkexpansionstrategiesoftheseairlines.
Finally,aninterestingandunforeseenndinginouranalysisisthescopefornewserviceonmarginalroutes.
Theeffectofhavingarichernetworkinthemergedcarrierbothincreasesthepotentialdemandforeachadditionalnonstoproute,andalsopotentiallydecreasesthecostofservingsuchroutes.
Accordingtoourmodel,somecombinationoftheseeffectscanleadtonontrivialnewserviceasadirectresultofthemerger,potentiallyoffsettingsomeoftheharmfromhigherpricesonrouteswithreducedcompetition.
Ourmethodologyismeanttoassesswhetherornotthemedium-andlong-runevolutionoftheindustrywillbesubstantiallysimilarwithandwithouttheproposedmerger,notmakeprecisepredictionsaboutfutureoutcomes.
Importantly,theantitrustcaselawhasrecognizedthisnuanceexplicitly.
InBrownShoe,theSupremeCourtnoted:"Congressusedthewords'maybesubstantiallytolessencompetition'toindicatethatitsconcernwaswithprobabilities,notcertainties.
"11Comparingoursimulationswiththerealizedoutcomeiscomplicatedbyarangeoffactorsincludingtheimpactofthegreatrecession,thethreeairlinemergersthatoccurredinthe2008-2014time-frame,andthechoicebysomeairlinestoeffectivelyde-hubfromsomecitiesfollowingtherespectivemergers.
Wecanuseourmodeltosimulatetheoutcomeofthesuccessivemergers,andwedonotndgeneraltrendsinthedifferencesbetweenoursimulationsandreality.
12Fortheveworstaffectedcitiesofthe2008DL-NWand2010UA-COmergers(seeTable11),wendthatourpredictionsofwhetheroff-settingentryamelioratedthestaticincreaseinmarketconcentrationby2013arecorrectin7ofthe10casesdespitetherelativelyshortsimulationhorizon.
1311BrownShoev.
UnitedStates,370U.
S.
294,321-22(1962).
Seealso,USDepartmentofJustice(2010):"Mostmergeranalysisisnecessarilypredictive,requiringanassessmentofwhatwilllikelyhappenifamergerproceedsascomparedtowhatwilllikelyhappenifitdoesnot.
"12Inordertohelpmakethesimulationsmatchthelargeeconomicshocksfromthenancialcrisis,wesetaggregateyeardummiessothattheygivethebestmatchbetweenthesimulationsandtheactualdata,butthesedummiesdonothelpinmatchingcity-orairline-specicshocksduetothenancialcrisis.
13Recallthatouranalysissuggeststhemodeliseffectiveatidentifyingmarginalroutesthataretargetsforentry,butthemodelislessaccurateatpredictingpreciseyearsofentrythanlonger-termentrypatterns.
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35ADataAppendixAsanexampleoftheCSAaggregation,theCSAcontainingSanFranciscocontainstheOaklandInterna-tionalAirport(OAK),theSanFranciscoInternationalAirport(SFO),andtheMinetaSanJoseInternationalAirport(SJC).
Oncethedatawasaggregated,passengersfromallthreeairportsintheSanFranciscoBayAreaCSAweretreatedasoriginatingfromtheCSAasopposedtotheindividualairportswithintheCSA.
Thisaggregationcapturesthefactthattheseairportsaresubstitutesbothforpassengertrafcandforairlineentrydecisions.
TheportionoftheT100datasetthatweusecontainsquarterlydataonpassengerenplanementsforeachairlineonsegmentsconnectingbetweenthe60demographicareasofinterestforourstudy.
ThesegmentdataisinprinciplesoaccuratethatifaNY-LAightisdivertedtoSanDiegoduetoweather,thenitshowsupinthedataashavingowntoSanDiego.
Thisleadstotherebeingafairamountof"phantom"entryoccurrencesintherawdata.
Toweedouttheseone-offights,anairlineisdenedtohaveenteredasegmentthatithadnotpreviouslyservedifitsends9000ormoreenplanedpassengersonthesegmentperquarterforfoursuccessivequarters.
Thelevelchosenisroughlyequivalenttorunningonedailynonstopightonthesegment,averylowlevelofserviceforaregularlyscheduledight.
Forexample,ifairlineXsendsatleast9000passengersperquarteralongsegmentYfromthethirdquarterof2005throughthesecondquarterof2006(inclusively),thenitisdenedtohaveenteredsegmentYinthethirdquarterof2005.
Ifanairlineenteredasegmentinanyquarterofagivenyear,thenitissaidtohaveenteredduringthatyear.
Onceanairlinehasenteredasegment,itisconsideredpresentonthatsegmentuntilanexitevenhasoccurred.
Wedeneexiteventsymmetricallywithourentrydenition.
Ifanairlineisdenedtobe"In"onasegment,foursuccessivequarterswithfewerthan9000passengersenplanedonthesegmentdenesanexitevent.
Therefore,ifairlineXhadbeeninonsegmentYinquarter2of2005,butfromquarter3of2005throughquarter2of2006theairlinehadfewerthan9000enplannedpassengers,theairlineisnotedashavingexitedsegmentYinquarter3of2005.
Onceanairlinehasenteredasegment,itisdenedaspresentonthatsegmentuntilanexitevenoccursforthatairlineonthatsegment.
Similarly,onceanairlinehasexitedasegment,itisdenedasnotpresentonthesegmentuntilanentryeventoccurs.
Thedataonsegmentpresenceisinitializedbydeninganairlineaspresentifithad9000ormoreenplanedpassengersonasegmentinquarter1of2003andnotpresentotherwise.
36A.
1HubDenitionsbyCSAAmerican:LosAngeles,CA;Ft.
Lauderdale,FL;Chicago,IL;St.
Louis,MS;NewYork,NY;Dallas,TXUnited:LosAngeles,CA;SanFrancisco,CA;Denver,CO;Washington,D.
C.
;Chicago,ILSouthwest:Phoenix,AZ;LosAngeles,CA;Oakland,CA;Denver,CO;Chicago,IL;Baltimore,MD;LasVegas,NVDelta:Atlanta,GA;NewYork,NY;Cincinnati,OH;SaltLakeCity,UTContinental:NewYork,NY;Cleveland,OH;Houston,TXNorthwest:Detroit,MI;Minneapolis/St.
Paul,MN;Memphis,TNUSAirways:Washington,D.
C.
;Charlotte,NC;Philadelphia,PAJetBlue:LongBeach,CA;FortLauderdale,FL;NewYork,NYAmericanWest:Phoenix,AZ;LasVegas,NVAlaska:Anchorage,AK;LosAngeles,CA;Portland,OR;Seattle,WA37A.
2CSAAirportCorrespondencesCSAcodeCSAAirportsPop2000MedianInc.
#pass(mark,2000)#deps200012BUR,LAX,ONT,SNA16373645520696336629165197432MDW,ORD9312255544216234320069921222EWR,JFK,LGA2136179756978588820136895294ATL4548344529575533740649997637OAK,SFO,SJC7092596666575113113150384418DAL,DFW5346119491464977083658046313BWI,DCA,IAD7538385677524231168651479945PHX3251876481243310281336751026HOU,IAH4815122464803154755938808019DEN2449054551493131130930026429LAS1408250491713108130729996810BOS,MHT,PVD1582997513102934906636098223FLL,MIA5007564430912930914627586857STL2698687483612567494030388031MCO1697906439522545914023647820DTW5357538504712539681628011035MSP3271888584592512472426779753SEA3604165539002249734223832044PHL5833585532661881245824177855SLC1454259503571620536914817315CLT1897034444021605231719854217CVG2050175480221528348619771850SAN2813833563351511856516392158TPA2395997418521437320714422146PIT2525730416481397982318279143PDX1927881492271213452715031930MCI1901070501791132085715156814CLE2945831440491084204719268125HNL87615660485103208787117936MSY136043639479949769110813847RDU131458949449922125313788833MEM12052044106586517731181318BNA138128745194855202712025856SMF19301495407177289528086754SJU2509007194037067099512416BDL1257709599126963738849865AUS12497635048469500398286427IND18435884839968856669313451SAT17117034326366240187763216CMH1835189470756163317897011ABQ7296494307058716867111634MKE16895724779954458519063042PBI50075644309153763855145248RNO3428854897452942116147528JAX11227504732349553616086038OGG1280945757348405094951949RSW23959974185246292974288311BUF11701114194737709705420752SDF12924824294337028215711940OMA8032014882635858274992060TUS8437464152135003233944039OKC11609423974333675555326059TUL9085284051232536875358221ELP6796223096831421434703224GEG417939416672933340429477BHM1129721432902884829438399BOI4648404696026672424153741ORF234403318152577507393262ALB825875508282438339371083ANC31960560180229326321837A.
3RegionalCarriersToaccountforightsoperatedbyregionalcarriers,weperformedthefollowingsteps.
First,usingapubliclyavailablerepresentativesampleofallairlineticketssoldintheUnitedStates("DB1B"),weidentiedroutesoperatedbyregionalcarriers.
Foreachrouteandregionalcarrier,weidentiedhowmanyticketseach38mainlinecarriersoldoneachregionalpartnerwithinagivenquarterandthecorrespondingshares.
Wethentooktheseshares,multipliedbythetotaltrafcoftheregionalcarrierandaddeditdirectlytototaltrafcofthecorrespondingmainlandcarrier.
Weusedthiscombinedtrafctodeterminewhetherornotagivenmainlineairlineiscurrentlyoperatinginagivenroute.
Thetablebelowillustrateswhyaccountingforregionalcarriersmaymakeasignicantdifferenceinournetworkanalysis.
Inparticular,itshowsthatfailingtoaccountforregionalcarrierswillsystematicallydistortthefullscopeofallmainlinecarriers'networks.
Anymodelthattriestorationalizesuchdistorteddatawillinevitablystruggle,especiallygiventhefactthatmainlinecarriersregularlychangethesetofregionalcarrierstheycontractwithanddosometimesalternatebetweenregionalservicewithmainlineservicebasedonbothdemandandcostfactors.
TableA.
1:FractionofRoutesServedWithoutRegionalAfliatesFractionofRoutesServedWithoutRegionalAfliatesYear200220032004200520062007American0.
8320.
8160.
7670.
7420.
6980.
700United0.
7830.
6810.
6420.
6620.
6700.
660Southwest1.
0000.
9930.
9420.
9480.
9660.
991Delta0.
7950.
7140.
6850.
630.
6200.
596Continental0.
9230.
8770.
8920.
8880.
6400.
630Northwest0.
8930.
8790.
8040.
7930.
8140.
796USAirways0.
8490.
7580.
8850.
8890.
8590.
873JetBlue1.
0000.
9410.
6540.
8130.
6080.
880AmericaWest0.
9700.
9100.
880N/AN/AN/AAlaska0.
5950.
6920.
7750.
7560.
7670.
72139BTablesandFiguresTable1:AirlineRouteandMarketStatistics,2003-2008NonstopRoutesMarketsCarrierAvgMinMaxEntry/yrExit/yrAvgMinMaxAmerican22421923278126012371296United18216619362133112371372Delta2302202411414145314001504Continental1211031471029207721126Northwest15513616962117311451215USAirways158146190146730665982Southwest2982693231549378241042JetBlue3216518112861226Alaska4137432111594123DL+NW3733493861814156615501579UA+US309292341167145513791494UA+CO28625432115314851396152340Table2:AirlineRouteandMarketStatistics,2003-2008RegressorAvgSDMin25%50%75%MaxCityPairCharacteristics:Log(2002PassDens)7.
65.
600111316Pop1*Pop2(*1e-12)*Dens=00.
823.
20000.
3482Log(Pass.
Den.
NewMarkets)2.
74.
60005.
516%Tourist0.
370.
35000.
330.
671CompetitionVariables:NumberNon-StopComps.
0.
760.
9900016NumberOne-StopComps.
3.
5202459NumberCSAgreements0.
0510.
2300003HHIAmongOthers(Market)0.
490.
44000.
5111HHIAmongOthersLarge(City)0.
320.
150.
0120.
20.
280.
420.
72HHIAmongOthersSmall(City)0.
170.
0790.
00540.
130.
160.
20.
68OwnShareLarge(City)0.
160.
1600.
0510.
110.
210.
85OwnShareSmall(City)0.
0560.
068000.
0420.
0740.
77CompetitorHubonRoute0.
680.
4700111NetworkCharacteristics:PresentinSegment0.
090.
2900001PresentinMarket(notSeg)0.
410.
4900011PresentBothApts(notMarket)0.
180.
3800001NumberofHubs0.
150.
3700002HubConv(NSdist/OSdist)0.
760.
280.
0110.
570.
890.
991DistNearestHubLarge(100s)129.
3058.
61848DistNearestHubSmall(100s)4.
44.
901.
22.
95.
547#NonstopsLarge(City)8.
412024856#NonstopsSmall(City)2.
33.
1002353DistanceVariables:Distance>2500.
950.
2101111Distance>5000.
840.
3701111Distance>10000.
580.
4900111Distance>15000.
370.
4800011Distance>20000.
220.
4200001Distance>25000.
110.
3200001Distance>30000.
0750.
260000141Table3:U.
S.
AirlineRouteNetworkCompetitionThistableliststhetotalnumberofsegments/marketsownbyeachairline,followedbythenumberofsegments/marketswheretheyaretheonlycarrier,wherethereisoneadditionalcarrier,etc.
withnumberofcompetitorsequalto2008:segmentsTotal012345678910AvgAmerican(AA)223214966413111400002.
27United(UA)1904317149229400002.
51Southwest(WN)32351949264147100001.
76Delta(DL)220646635172113400001.
64Continental(CO)14630452813189300001.
88Northwest(NW)1574260331551100001.
29USAirways(US)19030465438138100001.
93JetBlue(B6)50048101411300003.
58Alaska(AS)4361711333000001.
74DL+NW36610812563332113300001.
41UA+US341358512161288300001.
99UA+CO320347899573813100002.
09withnumberofcompetitorsequalto2008:marketsTotal012345678910AvgAmerican(AA)127213295810517423726121912043135.
44United(UA)13666218711320927126521812043135.
36Southwest(WN)10421149648313616919716811438135.
33Delta(DL)148913509914323827427622012043135.
15Continental(CO)1125714336715221724221712043135.
71Northwest(NW)11451519598015320423420512043135.
52USAirways(US)982521425510715222120312043135.
79JetBlue(B6)226001372129505943137.
33Alaska(AS)123211121217141411314135.
37DL+NW15803197150249303312247135431304.
31UA+US14831357121204286342265139431304.
58UA+CO15261338144250329311260125431304.
48Note:the13marketsthatareservedbyALL11carriersareasfollows:Boston-LosAngeles,Boston-LasVegas,Boston-SanFrancisco,Boston-Phoenix,Boston-SanDiego,LosAngeles-Washington,LosAngeles-Miami,LosAngeles-Orlando,Washington-LasVegas,Wash-ington-SanFrancisco,Washington-SanDiego,Miami-SanFrancisco,Orlando-SanFrancisco42Table4:Top10NonstopRoutesbyHHIIncrease,PassengersEnplaned,2008DL-NWHHIPassengersCSA1CSA2PrePostChngCVGMSP505699824926CVGDTW495498754921BHMMSP5156100004844MSPSLC523799024665DTWSLC526398854622ATLDTW360666223016ATLMSP349458122318MEMSAN767894681790BDLMEM763292551623ATLMEM401655121496UA-USHHIPassengersCSA1CSA2PrePostChngOAK,SFO,SJCPHL546799814514CLTDEN5931100004069CLTMDW,ORD434280643722BUR,LAX,ONT,SNAPHL644299783536OAK,SFO,SJCPIT684599753130BWI,DCA,IADMSY362267203098BWI,DCA,IADPHL661694872871CLTOAK,SFO,SJC7235100002765DENPHL278548942109BWI,DCA,IADPIT333752551918UA-COHHIPassengersCSA1CSA2PrePostChngCLEDEN527698044528DENHOU,IAH322754512224DENEWR,JFK,LGA338551741789BWI,DCA,IADCLE380851851377HOU,IAHMDW,ORD303143051274CLEMDW,ORD289239011009BWI,DCA,IADHOU,IAH58966847951HOU,IAHOAK,SFO,SJC69637906943EWR,JFK,LGAOAK,SFO,SJC17832629846EWR,JFK,LGAMDW,ORD2989379080143Table5:Top5CitiesbyHHIIncrease,PassengersEnplaned,2008DL-NWHHIPassengersCSAPrePostChngMEM528465911307MSP53726013641CVG75588131573DTW49125458546BDL16792106427UA-USHHIPassengersCSAPrePostChngCLT65337477944PHL33574104747BWI,DCA,IAD15592288729PIT17722442670ALB21542712558UA-COHHIPassengersCSAPrePostChngCLE41084778670EWR,JFK,LGA16311943312OMA15011787286HOU,IAH47384988250MSY1626186924344Table6:ProbitforEntry/Exit/Stay,AllCarriersUnits/1SDVariableRangeBetaSEMargEffMargEffDemandVars:Log(2002PassDens)[0,16]0.
0430.
0120.
020.
10Pop1*Pop2(*1e-12)*Dens=0[0,82]0.
0140.
0100.
010.
02LogPass.
Den.
NewMarkets[0,0.
02]11.
84.
44.
70.
02%Tourist[0,1]0.
140.
070.
060.
02CompetitionVars:NumberNonStopComps.
{0,.
.
.
,6}-0.
140.
03-0.
06-0.
06NumberOne-StopComps.
{0,.
.
.
,9}-0.
010.
02-0.
00-0.
01NumberCSAgreements{0,.
.
.
,3}0.
220.
060.
090.
02CompetitorHubonRoute{0,1}-0.
170.
07-0.
07-0.
03HHIAmongOthers(Market)[0,1]-0.
370.
06-0.
15-0.
06HHIAmongOthersLarge(City)[0,1]2.
080.
410.
830.
12HHIAmongOthersSmall(City)[0,1]1.
190.
740.
480.
04OwnShareLarge(City)[0,1]3.
810.
461.
520.
25OwnShareSmall(City)[0,1]2.
530.
551.
010.
07NetworkVars:PresentinRoute{0,1}3.
250.
091.
300.
38PresentinMarket(notRoute){0,1}0.
340.
080.
130.
07PresentBothApts(notMarket){0,1}0.
260.
080.
100.
04NumberofHubs{0,1,2}0.
580.
070.
230.
09HubConv(NSdist/OSdist)[0,1]-0.
360.
15-0.
15-0.
04DistNearestHubLarge(100s)1000mi0.
060.
060.
030.
02DistNearestHubSmall(100s)1000mi-0.
200.
11-0.
08-0.
04#NonstopsLarge(City){0,.
.
.
,57}0.
110.
030.
040.
05#NonstopsSmall(City){0,.
.
.
,54}-0.
070.
10-0.
03-0.
01Distance>250{0,1}0.
240.
090.
100.
02Distance>500{0,1}-0.
190.
07-0.
08-0.
03Distance>1000{0,1}-0.
240.
07-0.
10-0.
05Distance>1500{0,1}-0.
180.
08-0.
07-0.
03Distance>2000{0,1}-0.
030.
09-0.
01-0.
01Distance>2500{0,1}-0.
140.
13-0.
06-0.
02Distance>3000{0,1}-0.
800.
27-0.
32-0.
08JetBluedummy{0,1}0.
580.
090.
230.
07N79650Likelihood-2639FixedEffectsYear,CityTestforMarkovunobservables:CoeffSEp-value0.
2390.
0830.
00445Table7:ProbitforEntry/Exit/Stay,AllCarriers,RouteFixedEffectsUnits/1SDVariableRangeBetaSEMargEffMargEffDemandVars:LogPassDensNewMkts[0,0.
02]10.
125.
734.
040.
02DirectCompetitors:1NonstopComp{0,1}-1.
930.
13-0.
77-0.
352NonstopComps{0,1}-2.
930.
17-1.
17-0.
393NonstopComps{0,1}-3.
790.
20-1.
51-0.
324NonstopComps{0,1}-4.
790.
27-1.
91-0.
24>4NonstopComps{0,1}-5.
270.
32-2.
10-0.
15OtherCompVars:NumberCSAgreements{0,.
.
.
,3}0.
210.
080.
080.
02CompetitorHubonRoute{0,1}-0.
570.
16-0.
23-0.
11HHIAmongOthersLarge(City)[0,1]1.
980.
580.
790.
12HHIAmongOthersSmall(City)[0,1]-1.
181.
13-0.
47-0.
04OwnShareLarge(City)[0,1]2.
930.
621.
170.
19OwnShareSmall(City)[0,1]1.
790.
770.
720.
05NetworkVars:PresentinRoute{0,1}2.
480.
080.
990.
29PresentinMkt(notRoute){0,1}0.
180.
080.
070.
04NumberofHubs{0,.
.
.
,2}0.
510.
090.
210.
08HubConv(NSdist/OSdist)[0,1]-0.
420.
21-0.
17-0.
05DistNearestHubLarge(100s)1000mi0.
120.
080.
050.
04DistNearestHubSmall(100s)1000mi-0.
270.
15-0.
11-0.
05#NonstopsLarge(City){0,.
.
.
,57}0.
270.
050.
110.
13#NonstopsSmall(City){0,.
.
.
,54}0.
240.
140.
090.
03N79650Likelihood-2114FixedEffectsYear,RouteTestforMarkovunobservables:CoeffSEp-value0.
0150.
0990.
88346Table8:MeasuresofFitbyAirline:AllAirlinesPooled,RouteFE'sActualLastPeriodStatusFullSampleSimulatedStayStayNewNewNewNewAirlineInOutEntryExitEntryExitAmerican(25,27)0.
9790.
9950.
1770.
1740.
5230.
578United(24,17)0.
9780.
9960.
2110.
2630.
6530.
748Southwest(66,12)0.
9730.
9890.
2340.
1730.
6580.
604Delta(31,52)0.
9720.
9950.
1910.
2370.
5690.
845Continental(39,7)0.
9780.
9960.
2480.
1690.
7030.
791Northwest(19,11)0.
9850.
9980.
0850.
2150.
5230.
784USAirways(86,29)0.
9730.
9960.
6710.
2310.
7570.
687JetBlue(33,0)0.
9260.
9960.
1250.
3960.
446NaNAlaska(5,1)0.
9710.
9990.
1380.
4170.
4901.
00047Table9:ModelSelection:ProbitandANNdimensionModelCVLikelihoodProbit-618ANN(dim=0)-630ANN(dim=1)-641ANN(dim=2)-686ANN(dim=3)-697ANN(dim=4)-730ANN(dim=5)-75748Table10:10yearsimulations,MedianNonstopRoutesServedMediannumberofroutesserved,byyearYear012345678910NomergerAmerican227225224223223222221221220218217United198199199199198198197196196195194Southwest325332337343349354360365370375379Delta220215211207203199196193190187184Continental146145145145144144143143142142141Northwest157157156155154153151150149148147USAirways227224220217214211209206203201198JetBlue5053576165697479838893Alaska4342424242424242424141DL-NWmergerAmerican227225223222220219217216214213211United198199198198197196195194193192191Southwest325330333336338340342344345346348DL+NW366371373375376377378379380381381Continental146146145144143141140139138137136-merged-00000000000USAirways227227226225224223222221221220219JetBlue5054586164677174788185Alaska4343434342424242424242UA-USmergerAmerican227229228227226225223222220219217UA+US358366370374378381384387389391393Southwest325337343347351354356358359361361Delta220219216212207203199195192189186Continental146147147146145144143142141141140Northwest157160159158157156154153151150149-merged-00000000000JetBlue5059657177838995101108114Alaska4344444444444444444444UA-COmergerAmerican227226224223221220219217216215213UA+CO326331335337340342343345346347348Southwest325331334338341343346348349351352Delta220216211207202198194191188185183-merged-00000000000Northwest157158157155154152151150148147146USAirways227228228228228228228228228228228JetBlue5054586266717580848993Alaska434343434343434343434349Table11:NonstopRoutesServed:SimulatedDistributioninYear10NumberofNonstopRoutesServedNumberofMarketsServedCarrierbasemeanstdminmaxq0.
25medq0.
75basemeanstdminmaxq0.
25medq0.
75NomergerAmerican2272178189254212217223128412903011951421126812861312United1981938165221188194199137013643412091459134313671388Southwest32537912336420372379387107414594812541611142814621493Delta2201858158221179184190148914142813001498139614171435Continental1461414121158138141144112511332610311201111211341155Northwest1571474132165144147150114511361110591195113111351141USAirways227198916523519219820412351116509131252108411201153JetBlue50931057134879310022643055195625393430468Alaska4341424573841441231672382246152168183DL-NWmergerAmerican2272117186242206211216128412923111811424126812901314United1981907166218185191195137013773112441452135713791399Southwest32534812299389339348356107413585511401517132113601397DL+NW36638111345426374381389158015851015211619157915861591Continental1461365116149133136139112511232610281189110211241145-merged-0000000000000000USAirways227219818725121421922512351136479201287110711411170JetBlue5085104812178859122642755220645388426464Alaska4342427583942451231612574240144162180UA-USmergerAmerican2272178193249212217222128412972911731415127512921316UA+US3583939358428387393399151215401314661580153215411550Southwest32536112320405354361369107414174612221555138614191450Delta2201868160214181186191148914601713711512145014611472Continental1461405120159137140143112511302610301195111011331151Northwest1571495133170145149152114511461510891222113611441154-merged-0000000000000000JetBlue50114117717410611412222650356297721466503540Alaska4344429614144471231692375253154170185UA-COmergerAmerican2272137188244208213218128412892911681421126712851311UA+CO3263489316385342348354153015651314971602155715661574Southwest32535212309399344352360107413625411401539132613631400Delta2201836158207179183187148914571713781504144714581469-merged-0000000000000000Northwest1571464132165143146149114511441510731220113411411151USAirways227228819625822222823312351142479251277111211461176JetBlue50941062131879310022644454266666406443480Alaska434342859414346123169237923915417018650Table12:Top5Cities,StaticvsSimulatedDynamicEffectDL-NWStaticDynamicCSA#Carriers(Pre)PrePost(Yr0)NoMerger(Yr10)Merger(Yr10)MEM65904645156796571MSP65861637956766215CVG65977635861306332DTW74374491844604898BDL71787220215592272UA-USStaticDynamicCSA#Carriers(Pre)PrePost(Yr0)NoMerger(Yr10)Merger(Yr10)CLT74452559244824512PHL73363395429663146BWI,DCA,IAD92098272623132542PIT82580299618983272ALB71882218816551882UA-COStaticDynamicCSA#Carriers(Pre)PrePost(Yr0)NoMerger(Yr10)Merger(Yr10)CLE74271468342064355EWR,JFK,LGA91946211919612078OMA71524174515241745HOU,IAH83921426138664160MSY81678188617061853Note:HHIsinthistableareby#routesservedandthereforedifferfromthoseinTable5.
51Table13:SimulatedNonstopRoute-LevelMarketStructuresinYear10Year0Year10Numberof.
.
.
meanstdminmaxq0.
25medq0.
75Nomergermarketswith0carriers8468464832869843846849marketswith1carrier5115127488538507512517marketswith2carriers2502437214271238243248marketswith3carriers9810268012598102106marketswith>=4carriers656645182646669DL-NWmergermarketswith0carriers8468344820848831833836marketswith1carrier5175267501552522526531marketswith2carriers2442408210265235240245marketswith3carriers10010167712797101105marketswith>=4carriers636945586676972UA-USmergermarketswith0carriers8468344820852831834836marketswith1carrier5205157487540511515520marketswith2carriers2652568227285250256261marketswith3carriers98106684130102106110marketswith>=4carriers415944477575962UA-COmergermarketswith0carriers8468374822852834837839marketswith1carrier5125177491543512517521marketswith2carriers2542478220276242247252marketswith3carriers95104681129100104108marketswith>=4carriers63664508163666852Table14:SimulatedMarket-LevelMarketStructuresinYear10Year0Year10Numberof.
.
.
meanstdminmaxq0.
25medq0.
75Nomergermarketswith0carriers251921228171920marketswith1carrier776755293646770marketswith2carriers113115891153109115120marketswith3carriers17916112121227152160169marketswith>=4carriers137614081613311453139814091419DL-NWmergermarketswith0carriers251721126161719marketswith1carrier806955590666972marketswith2carriers1401358103187129134139marketswith3carriers20718718136263173185198marketswith>=4carriers131813622212621426134813641378UA-USmergermarketswith0carriers251721127161719marketswith1carrier806745485646770marketswith2carriers149119990161113119125marketswith3carriers24820713163257197206215marketswith>=4carriers126813601812891412134813611373UA-COmergermarketswith0carriers251721027161719marketswith1carrier756745386646669marketswith2carriers118113790148108112117marketswith3carriers20317912139231171178186marketswith>=4carriers13491395141317143513861396140553