1TherstbestsellerlistofbookswaspublishedintheUSbyTheBookmanin1895seeBassettandWalter2001PublishersWeeklycompileditsrstbestsellerlistin1913TheinuentialNewYorkTimesbestsellerlistwasrstpublish ID: 469042
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Whenmenarebroughttogethertheynolongerdecideatrandomandindependentlyofoneanother;theyinuenceoneanother.Multiplexcausescomeintoaction.Theyworrymen,draggingthemtorightorleft,butonethingthereistheycannotdestroy,thisistheirPanurgeock-of-sheephabits.Andthisisaninvariant.HenriPoincaré,TheFoundationsofScience,19131IntroductionConsideraconsumerwhohasdecidedtopurchaseanentertainmentgoodlikeamusicalbum,acomputergame,orabook.Whichsuchgoodwouldonechooseamongthemyriadofpossiblechoices?Sincethesegoodsareoftenexperiencegoods,thequalitiesofthesegoodsare,tovaryingextents,uncertaintotheconsumerpriortoconsumption.Consumersofexperiencegoodsmaybasequalitypredictionsontheirownex-perience.Forexample,manyconsumerspurchasecreativeworksofauthorsthattheylikedinthepast.Someconsumersmaybasetheirqualityinferencesonrec-ommendationsreceivedfromfriendsandrelatives.Otherconsumershavegreatcondenceintherecommendationsofprofessionalreviewers.Morerecently,ithasbecomecommonplaceforconsumerstolearnaboutnewproductsbyevaluatinginformationconcerningthepastpurchasesofconsumerstheydonotknowpersonally.Intoday'smarketplace,informationconcerningpastpurchasesisincreasinglyoftensummarizedandreadilyavailableintheformofbestsellerlists.Bestsellerlistsarecompiledforgoodsasdiverseasbooks,music,DVDs,movies,computergames,electronicgadgetsandhouseholdappliances.1Thispaperaimstomeasuretheeffectontheconsumers'willingnesstopayofchangesinthepublicinformationconcerningthebestsellerrankofproducts.Theprimarycontributionofthepaperistoprovideempiricalevidencethatthepast 1TherstbestsellerlistofbookswaspublishedintheU.S.byTheBookmanin1895(seeBassettandWalter2001).Publishers'Weeklycompileditsrstbestsellerlistin1913.TheinuentialNewYorkTimesbestsellerlistwasrstpublishedin1942.Therstmusicbestsellerlist(thencalledahitparade)wasrstpublishedbyBillboardMagazinein1940.Currently,manyretailerspublishbestsellerlistsforseveralcategoriesofgoods.Amazon.com,forinstance,displaysonitswebsitehourly-updatedbestsellerlistsforabout30productcategoriesincludingbooks,electronics,automotive,homeimprovement,andgroceryandgourmetfood.2 expectedvalueofthesedifferencesisinvariant,estimatescanbecomputedusingsimulationmethods.Priortopurchasinganapp,consumersmaybecomeawareofthedownloadranksofthetopappsduringthepreviousday.Sincedownloadrankschangesig-nicantlyovertime,priorrankingscanbeusedasaregressortomeasuretheeffectofthepublicrankinformationontheconsumers'willingnesstopayinthepresentperiod.Animportantconcernintheevaluationofestimationresultsisthepossibleendogeneityofprevioussalesranks.Whileyesterday'srankscannotbeaffectedbytheunobservablesthataffectappdemandstoday,itispossiblethattheshocksthataffectthedemandforaproductarecorrelatedovertime.Ifso,yesterday'srankswouldbecorrelatedwithtoday'sdemandshocksandtheleast-squaresestimatesoftheranks'effectondemandneednotreectacausalrelationshipbetweenrankinformationandwillingnesstopay.Theinstitutionaldetailsoftheappmarketsuggestgoodproxiesforthepastrankinformationthatareuncorrelatedwiththedemandshocks.Thelistoftop100appsisdisplayedonseveralscreens.Thenumberofappsperscreenvariesfromdevicetodevice,buttheranks25and50providenaturalbreakpointsforthevisibilityofapps.Forinstance,onboththeiphoneandtheipodtouchdevicesthetopvedownloadedappsappearontherstscreen,thentheappswithranks6to25canbebrowsedbyscrollingdowncontinuously.Theranks26-50arethenavailablebyfollowingalinkthatappearsontherstscreenjustbelowtheappwithrank25.AsinstrumentsforthelaggedranksIusethemovementsofpastsalesranksfromaparticularrankofranks,asdeterminedbythesebreakpoints.Thesemovementsarecorrelatedwiththepastranks,butuncorrelatedwiththecurrentdemandshocks.Theestimationresultsindicatethatthepositionofanapponthelistofprevious-periodbestsellersisanimportantdeterminantofpresent-perioddemands.There-sultsshowthat,allelseequal,thewillingnesstopayofconsumersisdecreasingsteeplywiththesalesrankofanapp.Forinstance,thevalueattributabletotheprevious-periodrankof1isroughlytwiceaslargeasthecorrespondingvalueforrank2.2Inturn,thevalueattributabletorank2isabout30%largerthanthecorre-spondingvalueforanappwithrank3.Onlineretailerscommonlycompileandprominentlydisplaybestsellerlists.Giventhecostofdoingso,theseretailersmustgainsomeeconomicadvantage.Re- 2Asformostbestsellerlists,increasingrankscorrespondtolesspopularproducts.4 therstconsumerpreferstoactliketheothers.Theformeriscalledexpectationin-teractionandthelatteriscalledpreferenceinteraction.Manski(2000)emphasizedthatitisimportantforanalysisandforpolicytodistinguishbetweenexpectationinteractionsandpreferenceinteractions.Inourmarket,whenchoosingaproduct,aconsumermayfollowotherconsumersbecauseshebelievesthattheothercon-sumershavebetterinformation,orbecauseshehasapreferenceforimitation.Consumersendowedwithbestsellerinformationmayalsofollowothercon-sumersbecausetheybelievethatanyidiosyncraticnoisethataffectstheirproductqualityexpectationsdoesnotaffecttheaggregateconsumptiondecisions.Inreality,weknowverylittleaboutthereasonswhyconsumersfollowotherconsumers.Itislikelythatintheappmarketexpectationinteractionsareatworkinshapingthepur-chasedecisionsoftheconsumers.Theanonimityofbestsellerlistsmaydampentheroleofpreferenceinteractionsinmarkets.Inanycase,thepresentanalysismain-tainsanagnosticviewabouttheparticularmechanismthroughwhichtheaggregateconsumptiondecisionsofthecrowdaffectconsumers'preferences.Thispaperiscloselyrelatedtotwopapersthatinvestigatetheimpactoncon-sumersoflearningaboutthepastconsumptionchoicesofotherconsumers.TherstpaperbyCai,ChenandFang(2009)reportsresultsofarandomizedeldexperi-mentconductedinarestaurantsetting.Theirexperimentisdesignedtodistinguishbetweentheinformationaleffectofexpandingtheconsumers'knowledgeofthechoiceset(calledthesaliencyeffect)andtheinformationaleffectofobservationallearning.Theauthorsprovideevidencethatthedemandsforthemostpopularvedishesincreasesignicantlyasaresultofrevealinginformationabouttherankingofthetopvedishes.Theyndlittlesupportforthehypothesisthatsalesaredrivenbyasaliencyeffect.Theresultsoftheircontrolledeldexperimentsindicatethatmostoftheincreaseinthesalesofthetopdishesoccurasaresultofobservationallearning.Theauthorssuggestthatapartialexplanationforthecommonpracticeofdisplayingpopularityinformationonretailers'websitesisobservationallearning.Thepresentpaperbringsanewcontributiontothisvaluableinsightbyprovidingdirectmarketevidencethatpopularityinformationaffectsdemands.Cai,ChenandFang(2009)consider“lumpy”informationaleffectsinthesensethattheeffectofrevealinginformationaboutthemostpopulardishisnotdistinguishedfromtheeffectofrevealinginformationaboutthesubsequentfourpopulardishes.Icomple-menttheirndingsbyprovidingestimatesofhowdemandsareaffectedbyeachof6 retaintheassumptionthatsalesfollowapowerlaw,myestimationprocedureisdif-ferentfromtheproceduresdevelopedbyChevalierandGoolsbeeandBrynjolfsson,HuandSmith,andpermitsestimationofthedemandparametersofinterestwithoutknowledgeoftheparametersofthepowerlaw.Peoplehaveaperhapsinnatetendencytojointhecrowd.AstheexperimentsofMigram,BickmanandBerkowitz(1969)suggest,thismayhappenevenwhenthepeopleinthecrowddolittleelsethanstareattheemptysky.Thetendencytojointhecrowdcouldimplythatindividualsperceiveadistincteconomicadvantagefromfollowingtheactionsofothers.Ifso,onemayexpecttoseethatpopularitybegetspopularityinmarketswherepopularityispublic.Theexperimentalnd-ingsofCai,ChenandFang(2009)andSalganik,DoddandWatts(2006)showthatpopularitybegetspopularityintwoimportantmarkets.Popularityalsobegetspopularityinthenewsmedia,asshownbyThorson(2008).Heranalysisindicatesthatmost-emailedlistsdisplayedintheon-lineeditionsofnewspapersliketheNewYorkTimesandLosAngelesTimes,aswellasthelargerfamilyofnewsrecommen-dationengines,affectconsumersbehaviorbyprovidingconsumerswithnewwaystonavigateinformation.Citationsofacademicresearchseemtofollowasimilarpopularitypattern.7Thereisverylittlewrittenintheeconomicsliteratureonthesubjectofbest-sellerlists.Sorensen(2007)analyzestheimpactoftheNewYorkTimesbestsellerlistonsalesandonproductvariety.Hendsthatthelistingofabookonthebest-sellerlistcausesamodestincreaseinsales.Theobjectiveofthisresearch,likeoneofSorensen's(2007)researchobjectives,istomeasuretheeffectofbestsellerinformationondemand.Theavailabilityofpricesisthemosttangibleadvantageofthedataavailableforthisstudy.Becauseoflimitedinformationonsalesprices,Sorensenwasabletoonlyfocusonhowbestsellerstatusaffectstheautocorrelationofsales.Sincetheappmarketdatacontaindetailedpriceinformation,thisstudyinvestigateshowbothpricesandbestsellerstatusaffectproductdemands.Iturnnexttoashortpresentationoftheinstitutionaldetailsofthesoftwaremarketandofthedata. 7SeeMerton's(1968)discussionofthe“Mattheweffect”inscience.Foranopposingview,seeSimkinandRoychowdhury(2005),whoarguethatcitationsgeneratedaccordingtoaprocessbywhichascientistpicksthreepapersatrandom,citesthem,andalsorandomlycopiesaquarterofthesepapers'referenceststheempiricalcitationdistributionquitewell.8 throughamobileappstoreinterface,orthroughawiredconnectiontoapersonalcomputer.Theinterfaceforthewireddownloadisamulti-platformprogramcalleditunesthatisdevelopedandofferedasafreedownloadbyApple.Downloadsre-quireauserIDandapassword.ConsumersareuniquelyidentiedbytheiruserID.InordertoregisterwithApple,aconsumermustprovideavalidcreditcardnumberandthecard'sbillingaddress.Theverylargenumberofappsinthestoremakesitimpracticalforconsumerstosampleoftheentiresetofapps.Appleiswellawareofthisfactandfacilitatestheprocessofproductdiscoverybyconsumers.Itprovidesprominentlydisplayedlinkstothemostdownloadedappsbothonthemobileappinterfaceandontheitunesprogram.Importantly,themobileappstoreinterfacedisplaysonitsmainpagelinkstothetop25mostdownloadedfreeandpaidproducts,andranks26-50areavailablebyfollowingasubsequentlink.SeeFigure3intheAppendix.Thewireditunesinterfacealsoprominentlydisplaysthetop10freeandpaidappsonitsrstpage.Listsofthetop100mostdownloadedfreeandpaidappsareavailableintheitunesinterfaceoneclickawayfromthemainstorepage.Inadditiontotheselists,Applefacilitatesproductdiscoverybyconsumersthroughlistsoffeaturedproductsand,ontheitunesinterface,stafffavoriteproducts.Also,Appleprovideslistsofmostdownloadedappsbycategoryandallowsconsumerstosearchproductsbyname.12Developersandindustryexpertsperceivethetop100freeandpaidlistsasthemostimportantwaysforconsumerstolearnaboutapps.Importantly,sinceappsaresoldinmanycountries,therankingsarecomputedseparatelyforeachofthemorethan60countrystores.ThedataemployedinthepresentpaperconcernthedownloadranksofappssoldintheUnitedStatesstore,whichisthelargeststoreintermsofnumberofappssold.Asidefromreleasingquarterlyaggregatedownloadgures,Appledoesnotre-leaseinformationaboutthenumberofappsappdownloadedfromitsstore.Impor-tantly,Applehasnotreleasedanyinformationaboutthedetailsofcomputingthetop100mostdownloadedapps.Theinformationavailableconcerningthecomputationofdownloadranksis 12InSeptember2009,withthereleaseofitunes9.0,Applehasaddedalistofthetop100grossingappstothepreviouslypublishedlistsoftop100freeandtop100paidappsbythenumberofdownloads.10 paidapps.Sincetheempiricalpartofthispaperusesonlydataonpaidapps,Inowdiscusssomeofthecharacteristicsofthepaidappdata.Theaveragepriceofapaidappduringtheobservationperiodwas$2.72,withastandarddeviationof$2.25.Theminimumpriceofanappwas$0.99,andthemaximumpricewasasizable$29.99.Themedianpriceofanappduringtheobservationperiodwas$1.99.Onaverage,apaidappappearsinthetop100mostdownloadedliston31days.However,theappsthathaveatleastoncereachedthetop50appearonthetop100listforanaverageof45days,andtheappsthathavereachedthetop10appearonthetop100listforanaverageof63days.Thedistributionofthenumberofdaysonthe100mostdownloadedlistishighlyskewed,asindicatedbythemediannumberofdaysonthelistequalto18.Thisskewnessindicatesthatafewappssurviveonthelistforalongtime.Some15appsremainedonthetop100listfortheentireobservationperiod.However,mostappsremainonthetop100listforthreeweeksorless.Someappsappearonthetop100list,thenleavethelistandreturntothelistaftersometime.Thisprocessmayrepeatafewtimesforafewappsinthedata.Figure1displaysahistogramofthenumberofdaysonthetop100mostdownloadedlistapp.14 14Clearly,thenumberofdaysonthelistforappsthatenteredthelistatthebeginningandtowardtheendoftheobservationperiodisnotaccurate.However,thesamehighlyskeweddistributionofnumberofdaysonthelistobtainswhenIdroptheappsthatenteredthelistduringtherstandlast20daysoftheobservationperiod.Notableisthat15appshavesurvivedonthelistduringtheentireobservationperiod.12 r(j;t�1)ofproductjattimet�1,themeanutilityprovidedtoconsumersisgivenbydjt=Xjb�a�Pjt�Mr(j;t�1);(1)whereXjarecharacteristicsofproductj,Pjtisthepriceofproductjattimet,andMi(i=1;:::;100)aretherank-dependentparametersofprincipalinterestinestimation.Consumeriderivesrandomutilityuijtfromchoosingproductjattimet,givenby:uijt=djt+ej+ejt+xijt;(2)whereejtisani.i.d.,acrossproductsandacrosstime,disturbancerepresentingj'sunobservedcomponentofutilityattimet,ejrepresentsaproductxedeffect,andtheshocksxijtaredistributedindependentlyacrossconsumers,productsandtimeaccordingtotheType-Iextremevaluedistribution.16Assumption1isconsistentwithevidencefromappdevelopersandindustryanalyststhatproductsalesintheuppertailofthesalesdistributionaregovernedbyapowerlaw.Forthedevelopersthatmadepublictheirappranksandsales,apowerlawappearstottheirdataquitewell.17Importantly,Iassumeapowerlawdistributionofunitsalesonlyintheuppertailofthedistributionofsales,notfortheentiredistribution.Assumption2ismostlikelyinnocuousinlargemarkets.Itmakespossiblethecalculationoflogmarketsharesandensuresthatthesupportofsalesintheuppertailisboundedawayfromzero.Assumption3isstandardintheempiricalliteratureondiscreteconsumerchoice(seeBerry1994).Thedifferencebetweenthemean-utilityspecicationin(1)andtheutilityspecicationinthestandarddiscretechoicemodelisthepresenceoftheparametersM.Theseparametersrepresentchangesinwillingnesstopaythatareduetorankinginformation.PositivevaluesoftheparametersMrepresentincreasesinthewillingnesstopayofconsumers,whilenegativevaluesrepresentdecreasesinthewillingnesstopay.ThefollowinglemmaprovidesarelationshipbetweenthethesalesrankingsofproductsanddifferencesinmarketsharesundertheassumptionthatsalesarePareto 16Whilethetheoreticalmodelassumesthatthedisturbanceejtisi.i.d.,inSection5Idiscussthepossibleimplicationsofautocorrelationandprovidesomerobustnesschecks.17Onesuchaccountisatwww.joelcomm.com/app_store_ranktosales_revealed.html.15 parametersexpressthedifferencesinconsumerutilitythatresultfromthepublicinformationconcerningthemarketshareranksofaproductattimet�1.Totheextentthattheutilityofconsumerswhochooseaproducttodayisaffectedbythepublicinformationconcerningthemarketshareranksofproductsyesterday,oneexpectstheestimatesofrank-dependentparametersMtobesignicantlydifferentfromzero.Estimatingequation(4)iscomplicatedbythepossibleendogeneityofpriceandlaggedranks.Thispossibleendogeneityisdiscussedinthenextsection.Thexedproducteffectshelptocaptureanyunobservablecomponentsofproductqualitythataretime-invariantandmaybecorrelatedwithpriceorwithpreviousranks.Theavailabledatadonotallowthedirectestimationof(4).Note,however,thatthemarketshareoftheproductwithdownloadrankk+1attimetcanbeexpressedaslnsk+1;t�lns0t=Xk+1b�a�Pk+1t�Mr(k+1;t�1)+ek+1+ek+1t:(5)Subtracting(5)from(4),wehavelnskt�lnsk+1;t=ˆXktb�a�ˆPkt�Mr(k;t�1)+Mr(k+1;t�1)+ˆek+(ekt�ek+1t);(6)whereˆXkt=Xkt�Xk+1;t,ˆPkt=Pkt�Pk+1;tandˆekisthedifferencebetweenthexedeffectsthatcorrespondtotheproductswithdownloadrankskandk+1.Noticethat(6)doesnotcontaintheshareoftheoutsidegood.However,thedifferencesinmarketsharesonthelefthandsidearenotobserved.Lemma1showsthatwhensalesareParetodistributed,thelefthandsideof(6)isexponentiallydistributed.Ifrescaledappropriately,theparameterofthedistributionthatgovernsthelefthandsidedifferencesisnotdependentontheparameterstobeestimated.Accordingly,theseunobservedmarketsharescanbesimulatedandtheequationofinterestcanbeestimatedasifmarketshareswereknown.ReplicatingtheprocessmanytimeswithdifferentdrawsofthelefthandsidevariablepermitsestimationofthecoefcientsM.Arelationshipbetweentherank-specicvaluesMandthesalesranksofthetopproductscanbeformulatedbasedonthefollowingtheorem.Theorem1Givenassumptions1-3,fork21;:::;99andfort1;thefollowinghold:i.ykt=kq(lnskt�lnsk+1t)arei.i.d.exponentiallydistributedwithmean17 ofsalesneednotbethesame.ThereasonisthatthelocationparameterSmtofthepowerlawisallowedtovaryovertime.Thevariationofthisparameterdoesnotaffecttheresultsbecauseintheestimationprocedurethisparameterisdifferencedaway.Iturnnexttoadiscussionoftheestimationprocedureandoftheresults.5EstimationandResults5.1EstimationProcedureThissectionprovidesdetailsabouttheestimationprocedureanddiscussesthepo-tentialbiasesthatmayariseduetotheendogeneityofsomevariables.Inthedata,anobservationisadate-ranktuple(t;k;j)thatcorrespondstoappj.Thereare13;996date-rank-apptuplesinthedata.AppsareuniquelyidentiedinthedatabytheirIDcode.DenotedbyM=(M1;M2;:::;M100)isthevectorofrank-specicvaluationstobeestimated.Whiletheappxedeffectshelptocaptureanyunobservedcomponentsofquality,apossibleconcernisthatpricesareendogenousinthefollowingdynamicsense.Therearemorethan400apppricechangesinthedata.Manyofthesepricechangesappeartobecausedbychangesindownloadranks.If,forinstance,developerswhoseedecliningdownloadranksfortheirappstendtoreducethepriceoftheirapps,asthefolkloreontheonlinedeveloperforumssuggests,thenpricewouldbeendogenousin(7)andtheestimatedpricecoefcientwouldbebiased.Iinstrumentthepricevariableusingthelogarithmoflaggedsalesranks.Sincechangesindownloadranksdonotimmediatelytriggerpricechanges,Iuselagsofordertwoandthreeofthesalesranksaspriceinstruments.Bothpriceinstrumentsarestronglysignicantintherststage.Unitmeanpseudo-randomexponentialvariablesweregeneratedusingamul-tiplicativecongruentialrandomnumbergenerator(seeKennedyandGentle1980,pp.136-147).ThesevariablesaretheˆYsontheleft-hand-sideoftheestimatingequation:ˆY=K=ˆX(aM;a;b;e)+ˆe;(12)whereKdenotesthevectorofcurrentappranksandanasteriskdenotesparametersthataremultiples(byq)oftheparametersofinterest.ThedatamatrixˆXcontains19 Figure2:Rank-SpecicValues5.3Auto-correlatedDemandShocksAnimportantconcernforestimationisthepossibleendogeneityoftheprevious-dayrankdummiesintheestimatingequation12.Whileyesterday'sdownloadranksarenotaffectedbytheshocksthataffectappdemandstoday,demandshocksforaproductmaybeseriallycorrelated.Thiswouldcauseyesterday'srankstobecorrelatedwithtoday'sdemandshocks.Ineffect,themeasuredeffectofranksondemandcouldreectthisautocorrelationandnotadirecteffectofrankinformationondemand.Toseewhetherendogeneitycouldaffecttheresultsofestimation,theeffectofyesterday'sranksmaybeestimatedusingthemethodofinstrumentalvariables.However,giventherelativedearthofvariablesinthedata,obtainingcrediblein-strumentsforallthepastrankvariablesisimpractical.18Instead,aspecicationisusedthatrestrictsthecoefcientsMtobeproportionalwiththereciprocaloftheprevioussalesrank.Thereciprocalofpreviousranksmaybeinstrumentedusingmovementsof 18Moregranularmovementstoandfromparticularrankranges(e.g.,toandfromranks1-5,6-10,etc.)couldprovidegoodinstrumentsfortheprevious-dayrankvariables.Itturnsoutthatwhilemanyoftheseinstrumentsaresignicant,thegoodnessoftformostoftherst-stageregressionsispoor(mostrst-stageFstatisticsarelowerthan4).Notsurprisingly,giventheweakinstruments,thesecond-stageestimatesoftheeffectofpublicrankinformationondemandwereverynoisy.21 second-laggedrankstoandfromparticularrankrangesthatarenaturalbreakpointsinthewaythetoplistisdisplayed.Clearly,movementsofpastdownloadranksfromonerankrangetoanotherarecorrelatedwithcurrentranks.Becausetheappsinthebestsellerlistaredisplayedsequentially,appsdisplayedatthetopofthebest-sellerlistmayreceivemoreattentionfromconsumersthanappsatthebottomofthelist.Anappthathasjustmadethetop50(or25)ismorelikelytomaintainitstoprankingthananotherappthathasnotjustcrossedsuchathreshold.Ineffect,thein-creasedvisibilityofanappmayaffectitssubsequentsalesrank.Importantly,whilemovementsofrankstwodaysagoacrossvariousthresholdsarecorrelatedwithyes-terday'sranks,thesemovementsareunlikelytobecorrelatedwithtoday'sdemandshocks.Inprinciple,theserankmovementsaregoodinstrumentsforyesterday'sranks.TheestimatedparametersMareclosetotheestimateoftheimpactofprevioussalesrankondemandobtainedbyrestrictingtheparametersMtobeproportionalwiththereciprocalofthesalesrank.Theestimatedcoefcientonthereciprocalofsalesrankisequalto4.29,withastandarderrorof0.48.Theestimatedim-pactofsalesranksondemandcomputedusingthisestimate,bracketedbya95%condenceinterval,isdepictedinFigure2withthethinnercontinuousgreenline.Toaddressthepotentialendogeneityofpricesandprevioussalesranks,thesevariableswereinstrumentedusingthelagsofordertwoandthreeofsalesranks,aswellastwobinaryvariablesthatmeasurewhetherthetwice-laggedsalesrankofanapphasreachedthelistoftop50orthetop25appsfrombelow.Allinstrumentsarestronglysignicantintherststageregressions.FirststageresultsaresummarizedinTable6intheAppendix.Asindicatedbytheresultsofover-identicationtests,thenullhypothesisthattheinstrumentsandtheerrortermin(12)areorthogonalwasnotrejected.19Theinstrumentalvariablesestimateofthereciprocalofpastrankcoefcientwasequalto4.37,withastandarderrorof0.49;noticethatthisisonlyslightlyhigherthantheordinaryleastsquarescoefcientof4.29.20Thisndingisastrongindica-tionthatserialcorrelationisunlikelytobeacauseofconcernwhentheparametersofinterestMareestimatedbyordinaryleastsquares. 19ThemaximumvalueoftheSarganstatisticwas1.6,lowerthanthe1%c2(2)criticalvalueof9.21.ThemeanvalueoftheSarganstatisticforthe10,000simulationrunswas0.73.20TheIVcoefcientsandtheirstandarderrorsaregiveninTable5intheAppendix.22 product;italsoindicatesthatthelistsofnewlyreleasedappsmadepublicbyApplemayhavelittleeffectonconsumerchoice.However,asimpliedbythenegativeandsignicantcoefcientontheversionagevariable(VAge),demandislowerforappsthatarenotregularlyupdated.Theestimateofthepricecoefcientisnegative,asexpected,andstronglysig-nicant.Sincetheestimatedcoefcientisthetheunknownscaleparameterofthepowerlawmultipliedbythetruepricecoefcient,own-priceelasticitiesarenotidentied.Theinterpretationoftheempiricalresultsissubjecttoacaveat.Sinceappscouldreachalarge,butnitenumberofpotentialconsumers,itispossiblethatthedemandsforsomeproductsbecomesaturatedovertime.Iattempttocontrolforthissaturationeffectbyusingtheageofanappasadeterminantofdemand.Theesti-matedcoefcientsonbothappageanditssquarewerepositiveandsignicant.Inaddition,surveyevidence(seefootnote15)indicatesthatmorethanhalfofiphoneandipodtouchusersdownloadlessthanonepaidapppermonth.Additionally,thedataindicatethatthemeansurvivaltimeforanapponthemostdownloadedlistisclosetoamonth.Thesesuggestthatsaturationisnotlikelytosignicantlyaffecttheresults.Giventherelativelylargeestimatedvalueattributedbyconsumerstotheappsrankedontopofthebestsellinglist,itispuzzlingwhytopappsdonotmaintaintheirranksforlongerperiodsthanobserved.Acandidateansweristhattherearemanyfactorsotherthanrankingsthataffectconsumerchoice.Forinstance,adver-tisingbyAppleandconversionoffreelydownloadableappsintopaidonesplayanimportantroleinshapingconsumerpreferences.Withthehelpofadditionaldataonadvertisingandconversionoffreeapps,theeffectoffactorsotherthanpastapprankingsthataffectconsumerchoicemaybeidentied.6ConclusionsThemodelsofherdingandinformationcascadesofBanerjee(1992),Bikhchandani,HirshleiferandWelch(1992)andWelch(1992)haveanalyzedinteractionsbetweenconsumersthatmaygiverisetoinefcientoutcomes.Thesemodelsofbehaviorassumetheexistenceofcertainformsoflearningfromtheactionsofothers.Test-ingthisassumptionmayturnouttobecriticalforourunderstandingofeconomic24 importantcostofusingtheprocedureisadrasticreductionintherangeofempiricalmodelsofdiscreteconsumerchoicethatcanbetakentothedata.26 Variable Description Count Mean Stdev Median Min Max ID UniqueappIDnumber 452 Rank Apprankontop100list 13,996 47.86 28.35 47 1 100 L(Rank) Laggedrank 13,996 46.76 27.50 46 1 101 L2(Rank) Secondlag 13,996 46.07 26.96 45 1 100 L3(Rank) Thirdlag 13,996 46.09 27.06 45 1 100 Price PriceinUSDollars 13,996 2.72 2.25 1.99 0.99 29.99 Age Dayssincerstrelease 13,996 109.40 83.15 85 0 340 VAge Ageofcurrentversion 13,996 92.63 75.85 66 0 340 Size Appsize(megabytes) 13,996 17.20 29.11 7.8 0 412 NewVer NewVersionDummy 13,996 0.0162 0.1263 0 0 1 Table1:SummaryStatisticsNotes:Laggedrank101correspondstoapreviouslyunrankedapp.Thesizeofappsisroundedtothenearesttenthofamegabyte,sooneapp(forwhichtherearevetotalobservations)hasasizeofzero.Thesquaresofage,versionageandsizeusedintheregressionsbelowarenormalized.28 Variable Estimate Stderr t-value Variable Estimate Stderr t-value M61 0.1254 0.0252 4.9787 M85 -0.0189 0.005 -3.7812 M62 0.1142 0.0234 4.8734 M86 -0.0481 0.0098 -4.9196 M63 0.1298 0.026 5.0001 M87 0.0041 0.0036 1.1293 M64 0.1497 0.0301 4.9815 M88 -0.0061 0.0037 -1.6292 M65 0.0523 0.011 4.7531 M89 -0.0114 0.0039 -2.9459 M66 0.141 0.029 4.8551 M90 0.0555 0.0121 4.6004 M67 0.0792 0.0164 4.8328 M91 -0.0286 0.0065 -4.414 M68 0.062 0.0132 4.6888 M92 -0.05 0.0102 -4.8778 M69 0.0719 0.0151 4.7558 M93 -0.0287 0.0066 -4.3501 M70 0.055 0.0119 4.628 M94 0.0017 0.0039 0.4408 M71 0.0475 0.0103 4.6112 M95 -0.0613 0.0124 -4.9495 M72 0.0478 0.0103 4.66 M96 -0.0096 0.0037 -2.6214 M73 0.0782 0.0161 4.8609 M97 -0.1022 0.0201 -5.0721 M74 0.0204 0.0056 3.6263 M98 -0.013 0.0038 -3.3996 M75 0.0391 0.009 4.3517 M99 -0.0768 0.0153 -5.0348 M76 0.0553 0.012 4.6115 M100 -0.0697 0.0141 -4.9563 M77 -0.0052 0.0036 -1.4208 Price(a) -0.4707 0.095 -4.9572 M78 0.0603 0.0129 4.6603 Age 0.0069 0.0014 4.8745 M79 0.0327 0.0078 4.1673 Age2 0.2235 0.0427 5.2299 M80 0.0093 0.0042 2.193 Vage -0.0089 0.0018 -4.9586 M81 -0.0182 0.0048 -3.753 VAge2 -0.0147 0.0047 -3.1109 M82 0.0202 0.0057 3.5561 NewVer -0.0333 0.012 -2.7833 M83 -0.0417 0.0087 -4.8152 Size 0.0004 0.0006 0.6839 M84 0.0053 0.0037 1.4373 Size2 6.0596 1.2425 4.8769 Table2:EstimationResultsNotes:Notreportedarethecoefcientsonappdummies(417coefcientsweresignicantatthe10%condencelevel).Theestimatingequationis(12).Priceisinstrumentedusingthelogarithmsoftwice-andthrice-laggedranks;therst-stageFstatisticisequalto437.19(R2is0.95).Meansandstandarderrorsarecomputedusing10,000replications.30 Variable Estimate Stderr t-value Variable Estimate Stderr t-value M61 0.2666 0.0086 30.9159 M81 -0.0389 0.0085 -4.5635 M62 0.2426 0.0091 26.556 M82 0.0429 0.0086 4.9976 M63 0.2761 0.009 30.8259 M83 -0.0888 0.0079 -11.1993 M64 0.3183 0.0086 36.9556 M84 0.0111 0.0079 1.4143 M65 0.1113 0.0088 12.7127 M85 -0.0401 0.0078 -5.1524 M66 0.2993 0.0087 34.5094 M86 -0.1026 0.0081 -12.7142 M67 0.1684 0.009 18.693 M87 0.0084 0.0078 1.0831 M68 0.1316 0.0088 15.0381 M88 -0.0131 0.0084 -1.5608 M69 0.1527 0.0088 17.2784 M89 -0.0244 0.0076 -3.2073 M70 0.1167 0.0088 13.3079 M90 0.1178 0.0081 14.5665 M71 0.1009 0.0081 12.5227 M91 -0.0608 0.0078 -7.8078 M72 0.1016 0.0083 12.3041 M92 -0.1064 0.008 -13.3759 M73 0.1662 0.008 20.7469 M93 -0.0611 0.0078 -7.7782 M74 0.0432 0.0082 5.2984 M94 0.0033 0.0088 0.3712 M75 0.083 0.0087 9.4914 M95 -0.1305 0.0083 -15.6426 M76 0.1173 0.0081 14.5286 M96 -0.0207 0.0078 -2.6512 M77 -0.0111 0.0081 -1.3722 M97 -0.2174 0.0072 -30.2328 M78 0.1279 0.0078 16.3914 M98 -0.0283 0.0088 -3.1959 M79 0.0692 0.008 8.6572 M99 -0.1636 0.0081 -20.1672 M80 0.0195 0.0083 2.3649 M100 -0.1484 0.0081 -18.2835 Table3:Rank-DependentValuesNotes:ReportedvaluesarethemeansandstandarddeviationsoftheratiosbetweentheestimatesofMandtheestimateofafor10,000replications.Theestimatingequationis(12).ThevalueofM101wasnormalizedtozero.32 Figure3:TopAppsDisplayedontheMobileInterface34 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