Ackerberg and Rysman2005

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Unobserved Product Differentiation in Discrete-Choice Models: Estimating Price Elasticitiesand Welfare EffectsAuthor(s): Daniel A. Ackerberg and Marc RysmanSource: The RAND Journal of Economics, Vol. 36, No. 4 (Winter, 2005), pp. 771-788Published by: Wileyon behalf of RAND Corporation

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RANDJournal f EconomicsVol.36,No.4, Winter005pp.771-788

Unobserved p r o d u c t differentiation indiscrete choicem o d e l s estim ting p r i eel sticities n d w e l f a r e e f f e t sDanielA. Ackerberg*andMarc Rysman**

Commonly seddiscrete-choicemodelssuch as logit,nested ogit,andrandom-coefficientsmodelsplace verystrongrestrictionson howunobservable haracteristic pacechangeswith the numberof products.Weargue(andshow with Monte Carloexperiments) hatthese restrictionscan leadto biased estimatesof price elasticities and the welfareconsequences rom additionalproducts.In addition,these restrictionscan identifyparameters hat are not intuitively dentifiedgiven thedata at hand. Wesuggestan alternativemodel that does not have thesepropertiesandpresentastructural nterpretation f themodel.MonteCarloexperiments nd an empiricalexampleshowthat this issue can be importantnpractice.

1. Introductionm Therecent literaturen appliedeconomics,andempiricalIndustrialOrganizationn partic-ular,hasoftenturned o discrete-choicemodels to estimatedemand or differentiated roductsordifferentalternatives. n thesemodels,consumerutilityfunctions,market hares,and substitutionpatternsdependon productcharacteristicshat are observedby the econometrician. n addition,these modelstypicallyallow for unobservedproductcharacteristicshrough he inclusionof someformof symmetricunobservedproductdifferentiation SUPD).1The most commonexamplesof SUPD arelogit errors n consumers'utilityfunctions(seeMcFadden,1974).Theeconomicjustification or includingunobservableproductdifferentiationis thataneconometricianypicallydoes notobserveallof theproductcharacteristics hatarerele-vantto consumers'choices. Froman econometricstandpoint,allowingfor unobservableproduct

*Universityof Californiaat Los Angeles; [email protected].**BostonUniversity;[email protected].

Theauthorswish to thankseminaraudiencesatthe FederalReserveBank,Boardof Governors,StanfordGraduateSchool of Business, UCLA,CarnegieMellon, UBC, JohnsHopkins,Georgetown,SITE,the Department f Justice,andthe EconometricSociety meetings.We also wish to thankAviv Nevo, Ariel Pakes,two referees,and the Editor or theircomments.Particular hanks are due to Anne Hall for her important omments on a later draft of the article. Rysmanreceived financialsupport rom NSF grantno. SES-0112527.SNotableexceptionsareBresnahan 1987), Feenstraand Levinsohn(1995), and Leslie (2004).

Copyright? 2005, RAND. 771

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772 / THERANDJOURNAL FECONOMICSdifferentiation ftenprevents hese models frompredictingzero market hares.Its inclusion canalso ease estimation.Weargue hatwhileSUPDinitselfmaybehelpful,commonlyusedmodels(e.g., logitmodels,probitmodels,nestedlogit models, and therandom-coefficientmodelsof Berry,Levinsohn,andPakes (1995; henceforthBLP)) implement t in an undesirableway.These models assume thateach productaddedto the marketaddsone additionaldimension to SUPD space. This featureresults in very little congestion n unobservedcharacteristic pace and can be problematicin situationswheredifferentconsumersface differentnumbersof products,becauseconsumersare drawn eitherfrom differentgeographiesor from different time periods.2Researchersmayintuitivelythinkthat in marketswith moreproducts,unobservablecharacteristic pace shouldfillup in some sense. These standardmodelsplace strongrestrictionson how this occurs.We show that these restrictionsplay a majorrole in econometric identificationof two ofthe majorquantitiesof interest n differentiated-product arkets.Firstare the welfareeffects ofnew products.This problem s one that has been recognized, e.g., in Trajtenberg1990), Petrin(2002), BerryandPakes(1999), andBajariand Benkard 2001). Because of thelack of crowdingin the standardreatmentof SUPD, welfarecalculations n standardmodels tend to overpredictgains from the introductionof new products.This problemhas potentiallyseriousimplicationsforpolicy issues such as the constructionof priceindices.3Second and less recognizedare the implicationsof SUPD on estimatedsubstitutionpat-terns. We arguethatusing the standardversions of SUPD can lead to misleadingeconometricconclusionsregardingpriceelasticities,in terms of bothmagnitudesand statisticalsignificance.Restrictionsof standardSUPD force variation n the numberof products n the choice set toidentify (or help identify)price elasticities.Interestingly,we show that with these restrictions,one can often identify priceelasticitieswithoutobservingmeaningfulvariationn prices.Thissource of identificationrelies entirelyon assumptionsabout unobservablecharacteristic pace.These assumptionsare even moreunreliable f, as is oftenthecase, defining differentproductshas some arbitrarinesso it.4There are two previousapproaches n the literature hat address these issues. The firstsetof work(e.g., BLP (1995) and Petrin(2002)) tries to reducethe importanceof SUPD by linkingsubstitutionpatterns o observablecontinuouscharacteristicse.g., BLP) or observedgroupings(e.g., the nestedlogit). ThisapproachkeepsSUPD(e.g., logiterrors) n themodelbutattempts oreduce its importance.These methodologieswork to the extent thatthe econometricianobservesthe relevantproductcharacteristics.However,as inflexible SUPD still exists in these models, itseffects can still exist.5A second andmorerecentapproach,advocatedby BerryandPakes(1999) andBajariandBenkard(2002), eliminates SUPD altogether rom the model.6In their purehedonic models,productsare unobservablydifferentiatedonly with respectto a single dimensionalunobservedcharacteristic.As newproducts nter, hisunobserved haracteristicpacebecomes morecrowded.While these approachesareintuitivelyvery attractiven the sense thatthere areno ad hoc logit

2There are many examples. Berryand Waldfogel(1999), Crawford 2000), Arcidiacono(2005), and Rysman(2004) face cross-sectionalvariationn the numberof availableproducts.Berry,Levinsohn,andPakes(1995), Bresnahan,Stern,andTrajtenberg1997), Petrin 2002), andCrawford ndShum(2005) facetemporalvariation.Nevo (2001), TownandLiu (2003), and Shum(1994) face both.This list is farfromexhaustive.3While we believe thatour methodologieswill provide better stimates of these welfareeffects, the welfaregains of anynew productwill dependon theshapeof thedemandcurveat very high prices.Thus,unlessone observesawide rangeof prices,any calculationof welfaregains is going to relyon fairly structural ssumptionsaboutthe upperportionof the demandcurve.4 Forexample,with carsandcomputers, he empiricaldefinitionof whatconstitutesa choice clearlyhas somearbitrarinesso it (e.g., BMW 3 Seriesversus(BMW 330, BMW 325) versus(BMW 330i, BMW 330Ci, BMW 330 Ciconvertible)).5 In addition to logit errors,these approaches ypically allow for a scalar unobservedproductcharacteristiccorresponding o each product.However,as these scalarunobservedproductcharacteristics re equally valued by allconsumers, heydo not play a majorrole in determining heextentof productdifferentiation.6Feenstraand Levinsohn(1995) also estimatea multidimensionalpurehedonic model, albeit withoutany un-observedcharacteristics.

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ACKERBERGND RYSMAN / 773errors,heyarealsoeithermorecomputationallyntensive BerryandPakes)or moredata ntensive(BajariandBenkard) han standardmodels includinga logit error.7This articlesuggests a thirdapproach,which we interpretas somewhatof a compromisebetween the above two. We arguethat it is the unnecessary nflexibilityof standardogit errorsthat can adverselyaffect estimates of parametersof interest such as substitutionpatternsandwelfare effects. As such, we keep logit errors n our model but allow themto be considerablymore flexible than s currentlydone.Thisflexibilityallowsaneconometrician o estimatehow fastunobserved haracteristicpace expandswiththe additionof newproducts,not assume t as priorwork does. Inpractice,ourapproach imply putsfunctionsof thenumberof products n amarket(and/or he numberof productsn agroupornest)into the discrete-choiceestimatingequation.Weshowthatthismodel has a structuralinterpretation--onewhere new productscrowdoutexistingproducts n retailstoreor shelf space.Althoughthis model of crowdingout is very stylized,itis intuitiveandcapturesphenomena hatwe believeactuallyoccurin markets.8Ourflexiblelogiterror mposesno additional omputational urden,andthus ourapproachs considerably implerto implement hanBerryand Pakes(1999) as well as less data ntensivethanBajariandBenkard(2002). On theotherhand,thosewith a more structuraleaning might prefer heirmethods n thattheycompletelyeliminate adhoc logit errors,while we only makethemmore flexible.9We proceedas follows. In Section 2 we argue(1) that traditionaldiscrete-choicemodelsplace unnecessaryrestrictionson SUPD, (2) thattheserestrictions an identify parametershatintuitivelyshouldnotbe identified,and(3) that hese restrictions anbiasestimatesof parametersof interest.Section 3 introducesour model of productcongestion and discusses estimation.InSection 4 we presentMonte Carloresults showingthat in the presence of productcongestion,standard stimationprocedures angivebiasedresults sometimesverylarge)andthat hesebiasestendto be in particular irections.Section5 appliestheestimator o dataon YellowPagesdemandfrom Rysman (2004). We find that the adjustments ignificantlyaffect predictions.Section 6discusses a multiplicativeadjustment,which provides manyof the same benefitsfor estimationwith a slightlydifferent heoreticalmotivation.Lastly,notethatmuchof ourapplications re focused on thecontextof estimatingaggregateddiscrete-choicemodels. These models aretypicallyestimated on dataacross markets in spaceor time) where one often observeschangesin the size of the choice set andwhereourconcernsare relevant.However,our commentsandtechniquesareequally applicablefor discrete-choicemodels estimatedon individual-leveldata(e.g., product,employment,or transportationhoice)whenthere arechangesin the choice set over individualsortime.

2. Unobserved differentiationn common discrete-choice models0 This sectionargues hatassumptionsboutunobservableharacteristicpaceused n tra-ditionaldiscrete-choicemodelsarerestrictive,nd that hisleads to undesirabledentificationresults.Webriefly uggest ursolution o theproblem,which s formalizednd urthermotivatedin Section3. We use thenestedlogit model to formally llustrateour identificationpoints,butwediscuss the extension of ourargumentso a full random-coefficientsmodel.o Identification. We startby usingderivative-baseddentificationargumentso show how thenestedlogit model handleseconomically nterestingvariationn a restrictiveway.Forexposition,

7 Anotherpossible critiqueof these hedonicmodelsis thatwhileunobserved haracteristicpacemayexpand oomuch with logit errors, t may expandtoo little with the purehedonic models, at least when unobservedcharacteristicspaceis modelledas one-dimensional.8Forexample,retailstores often sell only a small subset of the availablewholesaleproducts.Computer etailers,e.g., typically displaybetween 10 and 30 computers,while the totalnumberof wholesalecomputersavailable n a givenyearis between 150 and250 (Pakes,2003). Presumably,his is due to the costs of retailspace.9 An interesting ssue is to what extent these variousmodels are observationallyequivalent n terms of marketshares,marketsharederivatives,or marketsharechangeswith new products see, e.g., Anderson,DePalma,and Thisse(1992) andMcFaddenandTrain 2000)). Regardlessof observational quivalence, he fact that heliterature asgravitatedtowardusing models including ogit errorsmakes ourresultsrelevant.

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774 / THERANDJOURNAL FECONOMICSassumethereare J productsand an outsideoption,labelledproduct0. The J productsarein onegroup(nest)g and theoutsideoptionis in a groupby itself. In the nestedlogit model,the utilityobtainedby consumer fromproduct (j > 0) is

uij = o + XjIf + ?ig(0) + Sij,whereEij s distributedype-Iextremevalue,and 'ig(a) is constant oreachindividualwithin theproductnestand distributed uchthatTiga) + ,ij s distributedtype-Iextremevalue(see Cardell,1997). Note thateij representsconsumeri's idiosyncratictaste for good j and jigrepresentsi's idiosyncratictaste for products n groupg. As is standard,we assume uio = Wio(a) 8io,normalizing he mean utilityof the outsideoptionto zero.The parameter E [0, 1] measurescorrelation n unobservedutilityamong products n the nest. Lowervalues of a imply strongerwithin-groupsubstitutionrelative to across-groupsubstitution in this case, substitution o theoutsidealternative). nwhatfollows, we interpretXj as thepriceof product , butourargumentstrivially applyto elasticities withrespectto generalproductcharacteristics.10Denote the marketsharefor firmj as sj, the marketsharefor the entiregroupof insideproductsassg,and themarket hare orj withingroupg assjil. We thenhave(Cardell,1997)11,12

exp (fo + Xjip) DJl =, sg = s+ j=sjl s,, whereD= exp(o+Xk 1).Jlg 1exp (,o + Xkfll) e1+ Dr1) (1)Thereare threeforms of variationn datathat dentifytheparametersl anda in thenestedlogitmodel.13Thefirst ypeis variationnwithin-groupmarket haresdue tochanges nobservableproductcharacteristics.Lookingat the derivativecorrespondingo this type of variation ells uswhatparameters reidentifiedby the variation.14 he derivatives

=Sjlg= fliSjlg(l - Sjlg), (2)ax1suggestingthat this typeof variationdentifies01.The second and thirdtypes of variationarechangesin groupmarketshares(sg) due to (1)changesin observableproduct haracteristics nd(2) changes n the numberof products.To focuson group-levelchanges,assume Xj = X Vj. In thatcase, the derivativesof groupshares, withrespectto X and J are

ag ggg((- sg) - Sg) (3)aX iJ JThissuggeststhat hereare wosourcesof identification ora: cross-group witching romchangesin the numberof productsandcross-groupswitchingfromchangesin observedcharacteristics.Note thattherearealsotwo sourcesof identification orfll: within-group witchingfromchanges

10We ignore endogeneityissues regardingprice,which has been a focus of theprior iterature.The pointsin ourarticlearevalidwhetherpricemovementsarepurelyexogenousor whether heyareendogenousandone must findsomeexogenous source of pricevariation.I1Note that the normalization andnotation)usedaboveandin the following identificationargumentss differentfrom the normalizationused by Berry(1994). To convertourparameterso Berry's(denotethese as flBerry nd(Berry),one can use the transformations = 1 - aBerryandP = f(Berry/la= [fBerry/(l - 'Berry).12While the descriptionof ouridentificationargumentswould be slightlydifferentwith the Berrynormalization,themodelsare dentical.Oneneeds to be morecarefulwiththesealternative ormalizationswhentherearemultiplenests(see, e.g., Hensherand Greene(2002).).13Note that the constant erm o is identifiedby the level of the insideproductmarket hares.14Note that these comparative taticscorrespond o hypothetical experiments we wouldlike to do in the data toidentify parameters.C RAND 2005.



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ACKERBERGND RYSMAN / 775in observedcharacteristics ndcross-groupswitchingfromchangesin observedcharacteristics.Given that these threecomparative tatics (asglaX, asg/aJ, and asj/aXj) map into only twostructural arameters01 andor), he modelimpliesa restrictive elationshipbetween the effects.This restrictive elationship asinteresting mplications or dentification.Observingmarketswhereproductcharacteristicsor price) differ across marketsbut the numberof products s thesame in all marketscan identifyboth o and 61.Therefore,a researcher an identifythe effectsof addinga product o the choice set (e.g., the additionalwelfaregeneratedby the new product)withouteverobservingvariationn the numberof products.Perhapsevenmoreunintuitively, necanidentifycross-priceelasticities betweenproductsn thegroupwithouteverobservingchangesinrelativepricesof theproducts forasimple exampleof this,see the firstpartof Section3). Moregenerally,notonlydopricechangesplaya rolein identifyingpriceelasticities,but ess intuitively,changesin thenumberof productsplaya role in identifyingpriceelasticities.Similarly,notonlydo observedchangesin the numberof productsplaya role in identifyingthe effects of changingthe numberof products, ess intuitively,changesin prices or characteristicswill play a role inidentifyingthese effects.15Arethese unintuitive ourcesof identification elievable?Clearly his identifications comingfrom something n the structure f the demand model.Thus,the answer to this questionshoulddependon whether his structures believable. Wearguethrough he rest of the articlethatwhatis generating hisidentifications avery peculiarand unintuitivepropertyof standardogit errors.As such,our answerto the abovequestionwouldbe no.o Properties of logit errors. Any model includinglogit errors mplicitlymakesrestrictiveassumptionsabouttherelationshipbetween unobservable haracteristicpaceand thenumberofproducts.Specifically, ogit errors mplythatthe dimensionof unobservable haracteristicpaceexpands proportionallyo the numberof products.To see this, note thatwe can write consumeri's set of logit errors orthe J productsas

Eil = dlleil + + dlJ ei

eiJ = dJl1il + + dJJEiJ,where djk are dummyvariableswith djk = 1 if andonly if j = k, djk = 0 otherwise. Writtenin this way, we can interpret ogit errorsas representinga J-dimensionalcharacteristic pace:(Eil, ?..., iJ) areconsumer 's preferencesoverthe J dimensions,and the vector(djl,..., djj)representsproduct 's location n the J-dimensionalspace.Withthisinterpretation,otethat f we addanotherproduct J + 1)to themodel,thisproductdifferentiates n anentirelynewdimension(thatof dj+l,j+1),which is associatedwith a newlogiterrorEij+I.Thus, the dimensionalityof unobservedcharacteristic pace expands by 1 with theadditionof the new product.Another mplicationof logit errors s that all productsare equidistant rom each otherinunobserved haracteristicpaceandthisdistanceremainsconstantasthe numberof productsn themarket hanges.In asense,there s no crowding ut or congestion nunobserved haracteristicspace.This is counterintuitiven thefollowing way.Withclassicalproduct-differentiation odelssuch as the Hotelling model or the Salop circularmodel in mind, one would naturallyexpectproducts n more dense markets o be closer n characteristicpace.16

15One's choice of instruments an affect how thesecomparative taticsplay a role in identifyingparameters.Forexample,supposeone has the choice of using (1/J) E xj and/orJ as an instrument forwithin-group hare n theBerry(1994) inversion) n the nestedlogit model. Using only (1/J) xj (J) as aninstrumentwouldcorrespond o fitting hesecond (third)comparative tatic moreclosely and wouldprobably ead to better(worse) estimates of priceelasticitiesand worse (better)estimatesof welfare effects. If one uses both instruments or a combinationof the two, e.g., E xjas suggested in BLP), which comparativestatic is fitted better will dependon the relative amountsof variation n(1/J) 1 xj and J in the data.16 In logit characteristic pace, if one randomlychooses two productsfrom a market,the expected differencebetween Eil andEi2is the same regardlessof the numberof products n the markets.In contrast,consider a Hotelling? RAND 2005.



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776 / THERANDJOURNAL FECONOMICSAs will become clear later,it is these strongassumptionsabout the relationshipbetweenunobservable haracteristicpaceand the numberof products hatgenerate he unintuitive den-tificationresults above. Therefore,unless one completely believes in this no crowdingoutpropertyof logiterrors,one shouldprobablynotbelievethese sourcesof identification ndworry

aboutobtainingbiased estimatesof parameters e.g., a and t), price elasticities, and welfarecalculations.17o More-general models. Thearguments f the firstpartof thissection were basedon a fairlysimplenested ogitmodel. Do random-coefficientsmodels withlogiterrors e.g., BLP,McFaddenand Train 2000), andNevo (2001)) ornestedlogit models withmore-complicated estingstruc-tures have similaridentificationproperties?We believe so. Comparative tatics in these modelsaretoo complicated o formulateargumentsike the above.However,we can appealto a numberof informalarguments.First,note thatthe nested logit model is in fact a random-coefficientsmodel--one wherethe randomcoefficient s on a groupdummyvariableandhas aparticular is-tributionparameterized ya). Theintuitionbehind heseidentification esultsshouldnotchangeif random oefficientsare nsteadoncontinuous haracteristics nd/orareassumed o havenormaldistributions.18econd,as with thenestedlogit model,all of the parameterswould be identifiedif one estimated a random-coefficientsmodel on a set of marketsall with the same numberofproducts.Therefore,anyvariationdueto the fact thatmarketshavedifferentnumbersof productsis necessarilyhandled n a restrictiveway.Third,ourMonte Carloresults on random-coefficientmodels suggestthattheyhave similarproblems.Generally,we believethatanymodelincludingstandardogit errorswill havesimilarprop-erties, and thatidentification n these models is suspectunless one believes the unintuitiveandrestrictiveassumptions nherent n standardogit errors.o Proposed solution. Wenowbrieflypreviewourproposedsolution o theproblem,showingthat it eliminates theperverse dentification esultsdiscussedabove.Later, n Section3, we givea structuralnterpretation f oursolution. This structuralnterpretationorresponds o relaxingthe nocrowdingout assumptionof standardogit errors.Wepropose addinga functionf(J; y) withparameter to the termfi + Xj431n the nestedlogit model (1), i.e.,

exp (fo + Xjpli+ f(J; y)) DaSj=g , 1+D Sj = SjgSg,S kjlg=1exp(B0+ Xk l + f(J; Y))1 + D SJwhere D = exp(fo +Xk4l + f(J; y)). (4)k=l

With this model,the threecomparative tatics discussed above areaSjlg = plSjlg(l )Sg) = g( - Sg) = sg(1 - sg) + f(J; y)Xj aX g -ag(l Sg) y+f(J;y)}. (5)

model whereproductsspacethemselvesout as muchas possible.Withtwo products n themarket, he expecteddistancebetween two randomly hosenproducts withoutreplacement)s trivially1,with threeproductsn themarket heexpecteddifference s 1/3*1 + 2/3*1/2 = 2/3, withfourproducts t is 3/6*1/3 + 2/6*2/3 + 1/6*1 = 5/9, and withfive products t is4/10*1/4 + 3/10*2/4 + 2/10*3/4 + 1/10*1 = 1/2.17The CESdemandsystemalso does not displaycrowding,andis in fact subjectto manyof the criticismsaboutelasticities andwelfareeffects thatwe make of logit-basedmodels. Extensions of ouradjustment o the CES model areavailable rom the authors.18In otherwords, we expect that in these models, comparative tatics in entry andexit will also play a role inidentifying price elasticities, and comparative tatics in prices will play a role in identifyingthe effects of additionalproducts.Again, this identifications likely to be highlyrelianton the exact structure f errors.

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ACKERBERGND RYSMAN / 777Thefirst wocomparativetaticsarethe same asbefore,butthethirdnowdependsonanadditionalparameter, , in the new function.19Note that hisadjustment ives thenestedlogit modeltheabilityto matchallof the observedvariationn the data.In thismodel, 1lwill be identifiedby variation nwithin-groupmarket haresdue to changesin observableproductcharacteristics.Conditionalon 6, o is identifiedby changesingroupmarket hare nresponse ochanges nobservableproduct haracteristics, ndconditionalon a, y is identifiedby changesin groupmarketshare n responseto changesin the numberofproducts. n this adjustedmodel,one cannotidentifythe effect of addinga product o the choiceset withoutobservingvariation n the numberof products,nor identify cross-priceelasticitiesbetweenproducts n thegroupwithoutobservingchanges n relativepricesof theproducts.Moregenerally,in this model we expect price elasticities to be identifiedby price variation,not bychangesin thenumberof products.Similarly,effects of changingthenumberof productsshouldbe identifiedby actualchangesin the numberof products,not by changesin prices.In essence,this adjustedmodel eliminates theunintuitive ourcesof identificationdescribedearlier.3. A structural nterpretationm In this section we exhibita structuralmodel thatgenerates he adjustment uggested n theprevioussection. Thisprovidesa structuralnterpretationf the newparameters,which can aid inunderstandingndadding urther othe model(forinstance,writinga first-orderondition ortheproducers). t also shows how theadjustmentdetailedabovecorresponds o a more flexiblelogiterror hat eliminates the nocrowdingout assumptionof standardogit errors.We also discussestimation ssues.o Intuition behind the model. Webeginwith a story.Supposeone is interestedn estimatinga nestedlogit model of competitionbetween fast food firms(one nest is the fastfood restaurantsand one nest is a composite outside good). Data is obtained on prices andmarketshares fortwo time periodsof data. In the firsttime periodthere is only one firm, MD, and in the secondperiodthereis entryand thustwo firms,MD and BK. Supposethatprices areidenticalfor allfirmsin all periods,thatin the firstperiodMD has a 50%marketshare,and that in the secondperiodbothMD and BK have 25% market hares.Since theentryof BK steals market hareonlyfrom MD (andnot theoutsidealternative),a nestedlogit model will necessarilyestimateo = 0, i.e., that the within-groupvariance s zero.Thisa = 0 implies (1) thatMD and BK are identical n all respectsto all consumers,and(2) thatthe cross-priceelasticitybetweenMD andBK is infinite.Note thatidentificationhere has comesolely fromchangesin the numberof products,as there s no variation n prices.Now consideran alternativetoryof what s goingoninthisdata.Suppose hesefirmsoperatethroughoutlets(franchises)andthere s important eographicaldifferentiationi.e., all else equal,consumers end togo to thenearestoutlet ocation).Other hangeographicdifferentiationhroughtheir outlet locations, the food servedby BK and MD is identical. In the firstperiodtherearetwo outlets,both franchised o MD. In the secondperiodthere are also two outlets,butone ofthe MD outlets has been taken over by BK. Since prices remainconstant and MD and BKserve identicalfood, this story is perfectlyconsistentwith the marketshare data above. But isthe nestedlogit predictionof infinitepriceelasticitiescorrect n this example?We wouldexpectnot. Due to the geographicdifferentiation,we wouldexpect a pricecut by BK to only partiallycut into MD's marketshare.Thenestedlogit modelestimateof a = 0 is highly misleadinghere:unintuitive estrictionsof themodel (rather hanvalidpricevariation)areincorrectly dentifyingpriceelasticities to be infinite.Theintuitionbehind hisstorycanmotivatea structuralmodel in which J enters hediscrete-choice estimatingequation.In the example,unobservedcharacteristic pace (in this case, outlet

19Notethatouradjustedmodel s somewhatn thespirit f McFadden's1975) universalogit model,whichsomewhatrbitrarilyncludes haracteristicsf allproductsn theutilityunctionoraparticularroduct.ncontrast, efocuson a specific djustmentndprovide structural odelgeneratinghisadjustment.? RAND 2005.



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778 / THERANDJOURNAL FECONOMICSlocations)is subject o congestion: heentryby BK reducesthenumberof outletsMD has. Thiscrowding tthe outlet evel confounds heobservation hata newproducthasentered.Standardlogit-basedmodelssimplydo notdeal well withsuchcongestion,hence theincorrectlypredictedpriceelasticities.We now presenta formalmodel of such retailcrowdingor productcongestionthat deals with this issue. If we were to take this model to the fast food datadescribedabove,priceelasticities would not be identified--anintuitiveoutcomegiventhe lack of anyvariation nprices.o A model of product congestion. Supposethat the productsof interestare sold througharetail marketconsistingof R retail outlets. As in the aboveexample,we considerthe standardcase wheremarketsharesareobservedat the product evel: data at the retailoutletlevel are notobserved.Modellingunobservedretail outlets is simply a way of motivatingourmore generallogit errors. Assume that each retail outlet sells only one of the wholesale products,and thatproduct is sold in Rj retailoutletswhere>j Rj = R. The twist of ourcongestionmodel is thatlogit errorsrepresent diosyncratic,unobservedconsumerpreferencesover retail outlets ratherthan overproducts.(In the next section we expandthe model to one in which consumers havelogit errorsbased aroundboth retail outlets andproducts.)Precisely,the logit utilityfunction forconsumer purchasing rom retail outletr takes the form

Uijr = uj + ir,where uj measuresmeanproductquality.A typicalspecification oruj is uj = XjS - apj + j,where (Xi, 4j) areproduct 's characteristicsobservedand unobservedrespectively)and pj isits price.The importantdistinctionbetween this and a standardogitmodel is that t containsEir,not Eij. Intuitively,Eir might capture he fact thatconsumers ive differentdistancesfromthe Rretail outlets.Note how this modelcapturescongestionas new productsenter the market. n the standardlogit model,whennew productsenterthemarket,new Eijare drawn or the new products. n theextreme versionof ourcongestionmodel, wherethe numberof retailstores R does not changeas new productsenter,there are no new unobservable erms drawn.The dimensionalityof theunobservedcharacteristic paceremainsthe same as the new productssimplycrowd out the oldproducts rom retail stores.Toaggregate he model to the level of observation theproduct evel), we need to aggregateoverretail outlets.The shareof product is thesum of the sharesof all the retailoutletsthatcarryproduct . As theprobabilityhat buysfromr is the sameacrossoutlets thatcarryj, the marketsharefor product is

R e is (6)1 + 'k Rkeukeuj+ln(Rj)

1 + kek+ln(Rk) (7)Note that thedifferencebetween ourcongestionlogitmodel and a standardogit model is simplythe additional ermln(Rj) in the market harefunction.o Estimating the model. With individual-leveldata,(6) could be estimatedby maximumlikelihood. Withaggregatedata,this model can be estimatedusingthe Berry(1994) inversion:

In( s) = u +ln(Rj).s o ) /Inpractice,one needsto parametricallypecify Rj. In thesimplestcase, whereeachproductis sold in anequalnumberof retailstores,we have Rj = R/J and we need only specify R. One

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ACKERBERGNDRYSMAN / 779exampleis

R = yo+ 1J,where J is the numberof products.As scalingup R is unidentifiableromthe constantterminthe utilityfunction,a normalizations necessary,anobvious one being

R = y +(1 - y)J.Thisresults in theestimatingequation

In S)= u + In(y/J + - y). (8)S O ) /This specification s attractive n that it nests the pure logit model (y = 0) as well as the purecongestionmodel (y = 1). With y = 0, the numberof retailoutlets (andcorrespondingly hedimensionof SUPD) increasesproportionallyo the numberof products,whereaswith y = 1 itdoes notchangein the numberof products. ntermediate ases arecapturedby 0 < y < 1.Anothersuggestionfor parameterizinghe additiveterm is to let ln(Rj) = y In(J). In thiscase, y = 0 is still the standardogit model and y = -1 is still a full crowdingmodel (in thesense thatexpectedwelfaredependson observableproductcharacteristics utnotthe numberofproducts).A nice attribute f this specification s that n contrast o (8), this specificationcanbeestimatedwithOLS orIV techniques.A drawback s that hisspecificationacksaclear structuralinterpretationf theparameter.Last,notethatone mightestimateR(J) nonparametrically. iventhat J is discrete, this is extremely simple: one just includes indicator functionsfor differentmarket ize (witha normalization orone J).o Extensions of the model. The assumption hatall productsare soldby anequalnumberofretailstoresmightnot seemreasonable.However,givenno dataonretailers, t is hard o imaginehow one could intuitively separateout effects of productcharacteristicsand price on utilitiesversustheireffects on thenumberof retailstorescarrying heproduct.To formalizethis, supposethat

Rj = f(J)exjT',so thatproductcharacteristicsdo affect Rj. In this case, rl is not separately dentified fromfl, the parametersn the utility function.With other specificationsof R , the different effectsmight be identifiedcomputationally,but this identificationwould be completely dependentonnonlinearities.As such, we suggest the specificationwhere all productsare sold by an equalnumberof stores.The assumption hat ogiterrorsare notcorrelated orthesameproduct old across differentoutletsmay also seem unreasonable.However,we can obtain a verysimilarestimatingequationin a model thatrelaxes this assumption.Supposeconsumers have unobserved astes over bothproductsandretailstores,i.e.,Uijr = Uj + elj + P2,r -Uj+Ci+Pijr

Ej is consumer 's product-specificaste,e2r is consumer 's productretailoutlet-specifictaste,andp is a weightingparameterhat measures he relative mportanceof the two unobservables.This formulation s very similar to the standardnested logit model. With the standardnestedlogit distributionalassumptions(Ei3rdistributed ype-I extremevalue, Ei. distributed uch thatElj + pe2r distributedype-Iextremevalue),we get the followingproduct-levelmarket hares:ij ijr

[R exp )]p exp(uj + p ln(Rj))J1 +k k[exp ( 1)] + Ek exp(uk+ p ln(Rk))'l : 10 RAND 2005.



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780 / THERANDJOURNAL FECONOMICSwhere Rj is the numberof retail storesin whichproduct is sold. Then we have the estimatingequation,

In sj = uj + p ln(Rj).(So)Consider the specification n(Rj) = y In(J). In this case, y andp are not separately dentified,only theirproductpy is. While a differentspecificationfor Rj mightlead to separate dentifi-cation of p and y, it would againbe based on a nonlinearity.This lack of identification s nota drawback,because separating he parameters e.g., p versus y) is irrelevant or empiricalorwelfareimplications.It meansthatouroriginalmodel is robust o unobserved astesatboththeproductand retail store level.

io Application to more-general discrete-choice models. The above subsectionsadded con-gestion to a simple logit model.We can similarlyaddcongestionto more-realisticmodels suchas nested logit and random-coefficientsmodels. For example, considerthe nested logit utilityfunction:Uijr = Uj + ?ig + Sir,

where jig is consumer 's idiosyncratic astes forproducts n groupg. Note that this nested errortermis defined overproductgroupingsand not retailstoregroupings since retailstoresare notobservable,one cannotgroupthem).The variable8ir is still a retailstore-specificunobservable.With this utilityfunction,productsharesaregiven by

s Rkea

k+

g-Rke

)S1 = Sj gSg= [ 2e U (EkEgkLkEgj ke 1. L + g ( kEgRkeaand estimationcanproceedusingtheBerry(1994) inversion:20

In ) = uj + aIln(Rj) + (1 - a)nsjlg.s o ) /Again, we need to parameterizen(Rj) to estimate this model. The simplest approachwouldbeto do exactlywhatwe did in thelogit model,specifyingln(Rj) as equalto either n(y/J + 1 - y)or y ln(J). As a more ambitiousandflexiblealternative,one mightwantto allow congestiontovaryacrossproducts. notherwords,one might expectgoodsin one nestto crowdout(intermsofretailspace) goods in the same nest more thangoods in differentnests. One could accommodatethispossibility by, e.g., allowingRj to dependonthenumberof products n thenestas well asthetotal numberof products.Withmultiple-levelnestedlogit models or otherGEVmodels (e.g., themodel of Bresnahan,Stem,andTrajtenberg1997)), one couldallow morecomplexRj functions.In random-coefficientsmodels like BLP,one could againsimply addln(y/J + 1 - y) ory ln(J) to the conditional(on randomcoefficients)marketshareequations.Again, while thisallowscongestion,it assumesthatthecongestionoccursequallyacrossproducts.A more flexibleapproachmightlet Rj be a weightedcountof the numberof products n the market,wheretheweights dependon how close otherproductsareto j in characteristic pace.Forinstance,onecould specify Rj as

JRj = 1 :((Xj - Xk)*(cov(X))-'(Xi - Xk)),k=l

20Note thatwe now(and n the restof thearticle) seBerry's1994)normalization,lthoughwe still use ourredefined . Formally,o transformheseparametersand heparametersn equation9)) to Berry's arameters,se0 = 1 - rUBerrynd0 = fBerry.G RAND 2005.



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ACKERBERGNDRYSMAN / 781where0 is the normalprobabilitydensity unction.Thisspecifications similar nspirit ocountingproducts n the same nest differentlythanproducts n differentnests in the nested logit model.Intuitively, esearchersmightexpectthatproducts hatareclose together n observedspacecrowdeach other out more thanmoredistantproducts; his specificationallows for thispossibility.4. MonteCarloresults0 In this section we use Monte Carlosimulations o studyhow standardogit-basedmodelsperformwhendata aregeneratedaccording o ourcongestionmodels.Inparticular,we examinehow well the standardmodels estimateprice elasticities andthe welfareeffects of new productintroductions.Wefindpotentially argebiases in bothquantitiesacross avarietyof specifications,suggestingthat gnoringcongestioncanbe problematicn practice.o Nested logit model. The rows of Table1 containvariousspecificationsof ourcongestionmodelin anested ogitframework.nall specifications,we simulatedata rom averylargenumberof markets N = 5,000). Because of thislargeamountof data,there s verylittle estimationerrorin our estimates(andresultingelasticities), so these estimates can essentiallybe interpretedasasymptoticresults.In each market, hereare between 1 and 10 products,distributeduniformlyacross this range.Therearetwo nests in each market; he first contains all the inside products,the second containsonly the outside alternative. n the base specification,price is drawnfroma normaldistributionwith mean 2 and variance.2.21The constantterm in utility is 1 and thecoefficient on price is -1. The nestedlogit parameter is initiallyset at .8. As is standard,heutilityfrom the outsidealternative s normalized o zero.The variousspecifications n the rows of thetablechangevariousparameters f the model.The nested ogit subrowscontain heresultsof naivenestedlogitestimationon thesedata,usingthe standardBerry(1994) inversionwiththe numberof products n themarket J) and themeancharacteristicn the market((1/J) Xj) as instruments or the endogenoussj g.22 Because ofthelargeamountof data,the truth ubrows n the tables arenotonly theestimationresultsfromourcongestionmodels,butalso the truevaluesof these quantities since we use a largeamountof data andthetruth s ourcongestionmodel).Thecolumnsof thetablecontainvariouselasticityand welfare calculations at the estimates.Elasticities are computedfor the mean marketwithJ = 5 andXj = 2 Vj. Cross-priceelasticityis (ask/aXj)(Xj/sk), outside-goodpriceelasticityis(aso/aXj)(Xj/so). Welfare ncrease refersto the percentage ncreasein welfaremovingfrom amarketwith 1product o a marketwith 10products.The firstrow of Table1 contains resultsfor the full congestionmodel. In this model y = 1,i.e., thenumberof retailoutlets does notchangeas thenumberof productsncreases.Naivenestedlogitestimationof thismodelgives extremelypoorresults.The nestedlogitestimatestheaverageown-price elasticityto be -11.07, while the actualown-priceelasticity is -2.29. Within-groupcross-priceelasticities are off by an orderof magnitude,and estimatesof across-group to theoutsidealternative)priceelasticities areabout70% of theirtrue value.While in actuality here sno welfaregain movingfrom 1 product o 10 products since in the full-congestionmodel newproducts completely rowdout the old ones), the nestedlogit estimatessuggesta gainof 20%.Interestingly,n this case the nestedlogit modeldoes a reasonable ob atmatchingwelfaregains(at least in an absolutesense), buta terrible ob atpriceelasticities.23There is a clear intuitionas to why, in the presence of congestion, standardestimationmethodsareproneto overestimatewithin-group ross-priceelasticitiesandunderestimate cross-group cross-priceelasticities. The standardnestedlogit specificationunderestimates he nesting

21Note that the McFaddenand Train(2000) resultregarding he generalityof the mixed multinomial ogit (orrandom-coefficients)modeldoes not applyto datagenerated rom ourmodel. The reason s that n ourcongestionmodel,thedistribution f theunobservable erm for eachwholesaleproductdependson the numberof otherwholesaleproducts.22Half of this variation n priceis within-market, alf is across-market.23In generatingourdata,we also allowed a scalarunobservedcharacteristic aluedequallyby consumers,$j, togenerateaneconometricerrorat the aggregate evel (see Berry,1994). The varianceof (j acrossproductswas set at .5.

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782 / THE RAND JOURNALOFECONOMICSTABLE1 MonteCarlo Resultsfor NestedLogitModel

Outside- WelfareOwn-Price Cross-Price GoodPrice Increase

Parameters Estimator Elasticity Elasticity Elasticity (%)r = 1 Truth -2.29 .21 .11 0(Fullcongestion) NestedLogit -11.07 254 .07 20.00' = .95 Truth -2.28 .22 .12 28.40

NestedLogit -4.85 .97 .09 60.60r = .80 Truth -2.25 .25 .15 94.30

NestedLogit -2.98 .49 .13 146.40r= .5 Truth -2.21 .29 .19 184.50NestedLogit -2.42 .36 .18 233.20

r = .95 Truth -8.28 1.71 .11 6.50a = .2 NestedLogit -1.39 2.29 .10 30.90r =.95 Truth -2.18 .31 .21 23.00fo = 2 Nested Logit -4.95 1.04 .16 48.20r = .95 Truth -4.75 .24 .04 33.50fi = -2 NestedLogit -7.87 1.26 .03 110.10r =.95 Truth -1.09 .16 .11 23.00Mean(X) = 1 NestedLogit -2.39 .52 .08 48.20r = .95 Truth -2.28 .22 .12 28.40

Var(X)= .95 NestedLogit -3.51 .61 .10 110.50

parametera (e.g., in row 1 the standardnested logit model estimatesa = .093 while in truth,a = .8). Consideragainthe estimatingequationunderouradjustment:ln s) = - apj + (1 - a)ln(sjg) + a ln(Rj(J)) + 4j. (9)

The standard pproachgnoresthe terma ln(Rj(J)). Recall thatRj(J) will decline in J if thereis any congestion,i.e., if the numberof retail stores in which product j is sold declines in J.Typicallythe within-group hare, n(sjlg),will also decline in J, so the omitted variablewill bepositivelycorrelatedwithln(sjlg)(andoneof the instruments orIn(sjig),J). This will tend tobiasthe estimateof a downwardn the standard estedlogit model.Theunderestimate f a suggeststoo much insulationbetween groups.As such, across-group ubstitutions estimated to be tooweak, andwithin-group ubstitution oo strong.Rows 2 through9 perturbhe parameters f the model. In rows2 through4, the congestionparametery is varied.As would be expected, the nested logit estimatesare closer to the truthas y decreases(recallthaty = 0 implies no congestion,i.e., the standardnestedlogit model isthe truth).However,even at y = .5, thereare still significantbiases in the nested logit results.Row 5 changes the nesting parametera from .8 to .2. While the nestedlogit does a bit betteron price elasticities (proportionally),t does worse with welfarepredictions.Rows 6 through8respectivelychangethe constant erm n theutilityfunction, he slopeterm n theutilityfunction,andthe mean of price.The largebiases in priceelasticities and welfare calculationscontinue topersist. In the last row of the table, the varianceof price is increased n the simulated dataset.Interestingly,estimatesof price elasticities get considerablybetter,while estimates of welfarechangesworsen.We believetheintuitionbehindthis result s that ncreasing he variance n priceincreases the data'sinformationon the second comparative tatic (in Section 2) relativeto thethirdcomparativestatic. This will tend to move parameters uch thatthe second comparative0 RAND 2005.



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ACKERBERGAND RYSMAN / 783TABLE2 MonteCarlo Resultsfor Random-Coefficients odel(RCM)

Outside- WelfareOwn-Price Cross-Price GoodPrice Increase

Parameters Estimator Elasticity Elasticity Elasticity (%)r = .95 Truth -4.31 .09 .08 5.1

RCM -9.69 1.7 .07 29.20r = .80 Truth -4.28 .12 .11 19.40RCM -5.66 .62 .11 41.90r = .5 Truth -4.23 .19 .17 44.10

RCM -4.6 .35 .17 58.40r = .95 Truth -4.55 .08 .06 3.80o1 = .4 RCM -1.14 1.76 .05 22.60r = .95 Truth -4.06 .38 .35 14.50#o = 4 RCM -9.34 1.89 .28 62.30r = .95 Truth -6.38 .02 .02 .80fl = -3 RCM -14.21 2.69 .01 6.10r = .95 Truth -2.05 .21 .21 15.40Mean(X) = 1 RCM -3.65 .69 .17 66.20r = .95 Truth -4.31 .09 .08 5.10Var(X)= .95 RCM -6.13 .76 .07 30.80

static is moreclosely satisfied,but the thirdcomparative taticis less closely satisfied.Since thesecondcomparative taticis directlyrelatedto elasticities,while the thirdcomparative taticismore related to welfarechangesdue to changesin the numberof products, his improves priceelasticityestimates,but worsens estimates of welfare effects.o Random-coefficients (BLP) model. We also simulate a random-coefficientsogit model.This is the typeof modelused in BLP.We againuse 5,000 marketswith the numberof productsdistributeduniformly rom 1 to 10. Price is againdrawn roma normaldistributionwith mean2and variance 2. The constant erm in the utilityfunction is initiallyset at 2. We allow a randomcoefficienton price, equalto 01 = exp(op,z), wherez is a standard ormal,andinitially,f1l= -2and or, = .2. We impose thatthe data is drawn from a crowdingmodel with crowdingtermIn(y/J + 1 - y). In Table2, rows marked RCM orrespond o estimates of a naiveBLP-stylerandom-coefficientsmodel with aregular ogiterror usinga constant,Xj, J, and(1/J) E Xj asinstruments).Rows marked truth orrespond o estimatesof a random-coefficientsmodelwithour more flexiblelogit error again,this corresponds o thetrue elasticities and welfareeffects).Examining hetable, hefirstrow considers he case wherey = .95.As inthe nested ogitcase,both elasticities and welfare calculationsareconsiderablybiased with the naive RCM.Again,aswe lowerthe level of crowding, he standardRCM does better,buttherearestill significantbiaseswheny = .5.Theremaining owsin thetableagainperturbheparameters f themodel,andagainnot muchchanges:biasesinbothprice elasticityandwelfarecalculationspersist.As in the nestedlogit results,increasing he varianceof theobservedcharacteristicn the lastrow improvespriceelasticitiesbutworsenswelfarecalculations.The worseningof welfare calculations s marginal,though.Thismaybe dueto the factthatas the varianceof theobservablecharacteristicncreases,therelative mportance f logit errors n the modeldecreases.One wouldexpectthiseffectto tendto improvebothpriceelasticities andwelfarecalculations,perhapscounteractinghe worseningof welfarecalculationsdue to thecomparative taticeffect.24 nsummary, urMonte Carloresults

24This does match the fast food franchisestoryin Section 3, where the nested logit model predictsa = 0, thuscorrectlymeasuring he welfaregains due to the entryof BK to be zero.0 RAND 2005.



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784 / THERANDJOURNAL FECONOMICSsuggest thatignoring possible congestionandusing standardogit errorscan significantlybiasestimates of priceelasticities and welfareeffects, even in random-coefficient,BLP-stylemodels.5. Empirical xamplem We end with an empiricalexample. Rysman(2004) studiesa dataseton the Yellow Pagesindustry,measuring hepositivefeedback oopbetween consumers'choice of directory whichisdrivenby the amountof advertisingn thedirectory)andretailers'placementof advertisementsndirectories whichis drivenbyconsumerusage patterns).Rysmanmodelsthe consumer'sdecisionas a discretechoice between availabledirectoriesand anunspecifiedoutsideoption.He observesacross-sectionof directoriesandusagebehaviorwhere consumers n differentgeographicmarketshave access to differentnumbers f directories.Figure1shows thepercentageof consumers ervedby differentnumbersof directories.The variance n this numberof directoriesmakes this is anaturalplaceto applythetechniquespresented n thisarticle.25Correctly stimating heelasticityof usageto thequantityof advertisingn a directory s importantormeasuring heimportanceofthe feedback oop. In addition,correctlymeasuring he welfare benefitsof competingdirectoriesis importantor thepolicy questionstudied n the article.26Thedatasetconsistsof observationson thenumberof uses, perhousehold,permonth, n thedistributionareas of 428 directories n 1996.27We assume that a representative onsumerneedsinformationof the kind she could find in the Yellow Pages M times per month.The exogenousparameterM is constantacrossmarkets.Each time a consumerneeds information, he can useone of the YellowPages in the area or turnto the outsideoption.The utilityto consumer fromusing directory is

Uij = j1 ln(Aj) + Xj2 +j + ij.The variableAj is the quantityof advertisingat directoryj, andthe matrixXj representsde-mographicvariables hatmayaffectusage.28The variable4jrepresentsdirectory-specificactorsthatare unobservable o the econometrician, uch as the qualityof the book or regional usagehabits.We estimate this model and a model with our adjustment.A complicatingfactor is thatYellowPagesdistribution reasoverlapwith each other.A directorymayface no competitors orsome of its consumersand one or morecompetitors or anothergroupof consumers.Althoughwe observethese distribution reas,we cannotdistinguishhow muchusagecomes fromdifferentportionsof a directory'sdistribution rea.Evenso, implementing he simplelogit model is straightforward.Weobservesj (themarketshare ordirectory ) andso(themarket hare ortheoutsideoption)29ndirectory 's totalmarket,and submarketsareasof a directory'smarket hat are servedby a uniformset of directories)aredistinguishedonly by thepresenceof an irrelevant lternative. nderthelogit model,theratiosj /so is independentof thepresenceof thesealternatives, o sj /so is the same in each submarket.

25 Thatis, the effect thatincreasingthe varianceof X will tend to make the estimatedmodel matchthe secondcomparative tatic betterand the thirdcomparative tatic worse.26 Since YellowPagesarenot soldthrough etailstores, here s no literalretailcongestion n thismarket.However,one can thinkof ourcongestionmodel as capturing hepossibilitythathouseholdshave a limited amountof bookshelfordrawer pace, and throwout books that don't fit.27The policy questionis whether or not welfareimprovesas competition ncreases.Multipledirectoriesreducemarketpower but dissipatenetworkeffects. Rysman also estimates retailer demand for advertisingand a publisher'sfirst-order ondition for settingthe quantityof advertising.Here,we focus only on theconsumer'sdecision.28The datawere collectedby NationalYellowPagesMonitor.NYPMsurveyrespondentsmaintaindiariesof theirYellowPages usage forone week. NYPMnormallysurveysbetween 1,000 and3,000 people perMSA, although t used11,200respondentsn the Los Angeles area.Thisusuallyresults n at leasta few hundred espondents ven forverysmalldirectories.29As a measure of advertising,Rysmanuses the numberof pages in a book times the numberof columns in adirectory.The number s multipliedby .8 for directories hat areobservablysmaller than a standarddirectory.For Xj,each directory s associatedwith a centralcounty,andXj comes fromcounty-levelcensus data.

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ACKERBERGNDRYSMAN / 785FIGURE1NUMBEROF DIRECTORIESER PERSON

50

40 39.1 38.1030

E 20 16.10)aL

15.1 1.2 0.2 0.1 0.11 2 3 4 5 6 7 8Number

Therefore,we canuse the standardogit equation.For the simple logit model,we estimateln(sj) - In(so)= a ln(Aj) + Xj[p+ j.

To implementthe crowdingmodel, we take the crowdingterm to be the population weightedaverageof Rj across submarkets. n thatcase, we estimateIn(sj) - In(so)= a ln(Aj) + Xjf + ln(Rj) +j,

whereRj= Y *jkR(k).EK(j)

Here, K(j) is the set of submarketsn j's marketarea, /jk is the percentageof j's populationthatlives in submarket , andJ(k) is the numberof products n submarket .We use twospecificationsof thecrowding ermRj. The first s theparameterizationuggestedinSection3: Rj = -(y +(1 - y)J)/J. The secondspecifications nonparametric; e allow theRjto takeon differentvaluesfor each J. Weobserveveryfew marketswithmorethen 5 directories,so we restrictmarketswith 6, 7, or 8 directories o have the sameadjustmentparametern thenonparametric ase. We estimate both specifications by the generalizedmethod of moments(Hansen, 1982)using the same set of instruments s in Rysman(2004).Resultsappear n Table3. Parameter stimatessuggestthatcongestionis important. n theparametric ase, y = .62 andis preciselymeasured.Recall thaty = 0 implies no crowdingandy = 1 is full crowding.In thenonparametricase, theparametersor thecrowding erm arecloseto being monotonicin J and decrease at a decreasingrate. Wald tests rejectthe joint equalityof the estimates for different J. Regardingestimates of the otherparameters,he two crowdingmodels findcoefficientscloserto zerothanthesimple logitmodel,presumablyo compensate orthe effect of the crowdingterms on elasticities.Table4 presentselasticityand welfare estimates.The columns on the left presentelasticitiesof usage with respectto advertising.While differences across are nottremendously arge,thereare some differences between the models. First, it appears hat the standard ogit specificationoverestimates lasticitiesby 10% o 20%.Second,the standardogitmodelunderpredicts hangesin elasticitiesas the numberof products ncreases. When the numberof productsgoes from 1 to8, the standardogit model shows thatelasticityincreasesby 14%,whereasthecrowdingmodelsboth find thatelasticityincreasesby 23%. This coincides with our intuitionabout how standardlogit-basedmodels restrictthe extent to which crowdingcan occur as the numberof productsincreases.? RAND 2005.



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786 / THERANDJOURNAL FECONOMICSTABLE3 EstimationResultsfor YellowPagesData

Parametric NonparametricStandard CrowdingTerm CrowdingTerm

Variable Coefficient StandardError Coefficient StandardError Coefficient StandardErrorAdvertising .705 (.069) .631 (.070) .632 (.073)Constant -6.08 (1.07) -4.92 (1.01) -4.94 (1.17)% urbanpopulation -.023 (.006) -.016 (.005) -.013 (.005)% ived in differentcounty .078 (.015) .058 (.013) .061 (.016)% ived indifferentstate .047 (.020) .031 (.017) .027 (.023)% own house -.019 (.012) -.020 (.011) -.021 (.012)%graduatedhighschool -.042 (.014) -.032 (.012) -.040 (.013)%graduated ollege -.015 (.016) -.023 (.014) -.007 (.016)Per-capitancome .029 (.021) .032 (.018) .022 (.022)Telcobook 1.156 (.103) 1.050 (.100) 1.018 (.103)County populationgrowth .003 (.016) .012 (.014) .016 (.015)% takepublictransporation -.035 (.030) - .023 (.027) - .041 (.034)% have not moved .072 (.016) .047 (.015) .054 (.019)Populationdensity -1.11E-0 (3.88E-05) -8.39E-05 (3.43E-05) -7.20E-0 (3.50E-05)Gamma .616 (.120)Adjustment

J=1 0 FixedJ = 2 -.350 (.142)J = 3 -.343 (.177)J = 4 -.743 (.217)J = 5 -.865 (.308)J = 6, 7, 8 -.967 (.364)

More strikingare the welfare calculations.The logit model predictsthat even the 7th and 8thYellow Pages directories mplynontrivialwelfareincreases,overa thirdof what the firstdirec-tory generates.On the otherhand,the crowdingmodel implies much lower benefits from newdirectories.Whengoing from 1 to 8 directories, he standardmodel finds thatwelfare increasesby over400%.Underthe crowdingmodels, welfareincreasesby 180% and 146% forthe para-metricandnonparametricases. Theserates of increasearepreciselymeasuredandsignificantlydifferentacrossmodels.Note that thenonparametricmodelactuallyfinds thatwelfare decreasesfor when going from 3 to 4 directories.The possibility that welfare actuallyincreases is wellwithinconfidenceintervals orthese estimates,and thisresultdisappearswhen we parameterizeTABLE4 SummaryVariables or YellowPagesData

Elasticity Firms' WelfareFirms Standard Parametric Nonparametric Standard Parametric Nonparametric

1 .55 (.052) .45 (.053) .45 (.054) .20 (.007) .28 (.025) .27 (.026)2 .58 (.056) .52 (.057) .52 (.060) .36 (.012) .37 (.012) .36 (.026)3 .60 (.058) .55 (.059) .54 (.060) .51 (.015) .45 (.019) .50 (.044)4 .61 (.059) .56 (.060) .57 (.064) .63 (.018) .52 (.032) .46 (.061)5 .62 (.060) .57 (.061) .58 (.066) .74 (.020) .59 (.044) .50 (.108)6 .63 (.061) .57 (.062) .58 (.066) .84 (.022) .66 (.055) .53 (.136)7 .64 (.062) .58 (.063) .59 (.066) .93 (.023) .72 (.064) .60 (.149)8 .64 (.062) .58 (.063) .59 (.067) 1.02 (.024) .78 (.073) .66 (.159)

Increase %) 410.5 (5.4) 180.5 (49.4) 146.1 (67.3)

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ACKERBERGND RYSMAN / 787the crowdingfunction. For assessing welfare gains to new products,and to a lesser extent inestimatingadvertisingelasticities, standardogit-basedmodels appear o give biased results inthis data

6. An alternativeapproachm In this sectionwe brieflyproposeanalternative pproach o allowing crowding n standarddiscrete-choicemodels. Intuitively,this approachtries to model a situation where additionalfirmsenteringthe marketdifferentiate nto dimensions of unobservedcharacteristic pace thatconsumerscare less about.Thisseemsto make ntuitivesense;forexample, n a marketwithonlya few breakfastcereals,cerealsmay be primarilydifferentiatedby how healthy they are or howcrunchy heyare.In amarketwithmanycereals,cerealsmaybeprimarily ifferentiated nly bythecharacters ntheirboxes,likelyaless importantharacteristic.Ackerberg ndRysman 2003) (seewww.rje.org/main/sup-mat.html),onstructa structuralmodel exhibitingthis property.Appliedto a basic logit model, this model generatesmarket haresof the form

=exp (gJ,r)1 + Ek Jr)xpwhere g(J; r) is a function of the numberof products n the marketand a parameterr. Notethe similaritybetween this model and the model of Section 3. Both allow J to enter the marketshareequation: he formeradjuststhe equation multiplicatively, he latteradjustsit additively.Thismultiplicativeadjustment ssentiallyallows the varianceof the logit errors o dependon J.AckerbergandRysman(2003) show thatthe implicationsof this multiplicative pproachareverysimilar o what we derivedabove for the additive pproach.A gt(J, r) thatdecreases n Jimpliesthat welfarebenefitsof new products n crowdedmarketsareattenuated,hatelasticitiesincrease n more crowdedmarkets relative o a case withouta crowding erm),andthatthethreecomparative tatics from Section 2 can be matched with the additionalparameter . They alsodiscuss estimationandstudythe impactof the adjustmentn MonteCarlo studies similar o thosehere.7. Conclusion? This articlehighlightsproblems hatarise as aresultof thewaythatstandard iscrete-choicemodels handlesymmetricunobservedproductdifferentiation.We show thatrestrictiveassump-tions about therelationshipbetween the numberof products n a marketand the dimensionalityof unobservedcharacteristic pace can lead to significantlybiased estimatesof elasticities andwelfarechanges.Wesuggesta straightforwarddjustmenthat ntroduces he numberof productsin a market nto the estimatingequation.We presenta structuralnterpretationf our solutions,showinghow it could arisefrom anagentmaximizationproblem.We end with MonteCarloandempiricalevidence showingthatthis issue canbe importantn practice.ReferencesANDERSON, S., DE PALMA, A., ANDTHISSE,.-F.Discrete Choice Theoryof ProductDifferentiation.Cambridge,Mass.:MITPress, 1992.ARCIDIACONO,. AffirmativeAction in HigherEducation:How Do Admissionand FinancialAid Rules Affect FutureEarnings? Econometrica,Vol. 73 (2005), pp. 1477-1524.BAJARI,.ANDBENKARD,.L. DiscreteChoice Modelsas StructuralModelsof Demand:Some EconomicImplicationsof CommonApproaches. WorkingPaper,StanfordUniversity,2001.- AND . DemandEstimationwith HeterogeneousConsumersandUnobservedProductCharacteristics:AHedonicApproach. NBER WorkingPaperno. 272, 2003.BERRY,.T. EstimatingDiscreteChoice Models of ProductDifferentiation. ANDJournalofEconomics,Vol.25 (1994),pp. 242-262.C RAND 2005.



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