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1、GIBRAT'SANDZIPF'SLAWSFOR(ALL)CITIES:COMMENTONGABAIX(1999)¤TailongLiyZhejiangSci-TechUniversityShunfengSongzUniversityofNevada,Reno¤SupportfromtheYouthResearchProjectofHumanitiesandSocialSciencesofChineseMinistryofEducation(No.10YJC790145),theZhejiangProvinci
2、alNaturalScienceFoundationofChina(No.LQ13G030018)andtheNationalNaturalScienceFoundationofChina(No.71173250)areacknowledged.ySchoolofEconomics&Management,ZhejiangSci-TechUniversity,WestDistrict,XiashaHigherEducationZone,Hangzhou310018,P.R.China.E-mailaddress:
3、m9845@163.com.zDepartmentofEconomics,UniversityofNevada,Reno,Reno,NV89557-0207,USA.1AbstractThiscommentrevisitstheseminalpaperbyGabaix[1999],whoseinsightfulexplana-tionofZipf'slawarisingfromGibrat'slawignoresanimportantstabilityproblem.Weshowthat,theoretical
4、ly,boththegrowthinhomogeneityacrosssizesandtheuppertailtruncationinempiricalexerciseshavesigni¯cantin°uencesontheshapeofcitysizedistri-butions.OuranalysisnotonlyreexaminesGibrat'sandZipf'slawsinastablesenseviaatime-varyinginhomogeneityapproachbutalsomakesafr
5、eshexplanationfortherecentdebateontheacceptanceofZipf'slawastheuppertaildistributionofcitysizes[Eeckhout2004,2009;Levy2009]inasimpleanduni¯edframework.2Wehavetosaythattherank-sizeruleisamajorembarrassmentforeconomictheory:oneofthestrongeststatisticalrelation
6、shipsweknow,lakinganyclearbasisintheory.
7、PaulKrugman[1995]IIntroductionZipf'slawforcitiesstatesthatsizesofthelargestcitiesinacountryfollowaParetodis-tribution(apowerlaw)withexponent1.AnalternativeexpressionofZipf'slawiswellknownastherank-sizerule:therthlarge
8、stcityhasasizeequaltos=rtimesthesizeofthesthlargestcity.Forthepastdecades,Zipf'slawforcitieshasbeenregardedasoneofthemostconspicuousempiricalfactsineconomics,lackinganysatisfactorysupportintheory[Krugman1995].The1999seminalpaperbyXavierGabaix[QuarterlyJourna
9、lofEco-nomics114,739-767]canlegitimatelybeconsideredoneofthemostimportanttheoreticalstudiesintheliterature.Takingadvantageoformalizedsizes,"GabaixpresentsaclearinsightonZipf'slawasthesteadysta
