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1、NBERWORKINGPAPERSERIESQUANTILEREGRESSIONUNDERMISSPECIFICATION,WITHANAPPLICATIONTOTHEU.S.WAGESTRUCTUREJoshuaAngristVictorChernozhukovIvánFernández-ValWorkingPaper10428http://www.nber.org/papers/w10428NATIONALBUREAUOFECONOMICRESEARCH1050MassachusettsAvenueCambridge,MA02138Apr
2、il2004WethankDavidAutor,GaryChamberlain,GeorgeDeltas,JinyongHahn,JerryHausman,RogerKoenker,andArtLewbelforhelpfuldiscussions,andseminarparticipantsatBYU,theUniversityofMichigan,MichiganStateUniversity,theHarvard-MITEconometricsWorkshop,theUniversityofToronto,theUniversityof
3、IllinoisatUrbana-Champaign,andthe2004WinterEconometricSocietyMeetingsforcomments.Theviewsexpressedhereinarethoseoftheauthor(s)andnotnecessarilythoseoftheNationalBureauofEconomicResearch.©2004byJoshuaAngrist,VictorChernozhukov,andIvánFernández-Val.Allrightsreserved.Shortsect
4、ionsoftext,nottoexceedtwoparagraphs,maybequotedwithoutexplicitpermissionprovidedthatfullcredit,including©notice,isgiventothesource.QuantileRegressionunderMisspecification,withanApplicationtotheU.S.WageStructureJoshuaAngrist,VictorChernozhukov,andIvánFernández-ValNBERWorking
5、PaperNo.10428April2004JELNo.J31,C13,C14ABSTRACTQuantileregression(QR)fitsalinearmodelforconditionalquantiles,justasordinaryleastsquares(OLS)fitsalinearmodelforconditionalmeans.AnattractivefeatureofOLSisthatitgivestheminimummeansquareerrorlinearapproximationtotheconditionale
6、xpectationfunctionevenwhenthelinearmodelismisspecified.EmpiricalresearchusingquantileregressionwithdiscretecovariatessuggeststhatQRmayhaveasimilarproperty,buttheexactnatureofthelinearapproximationhasremainedelusive.Inthispaper,weshowthatQRcanbeinterpretedasminimizingaweight
7、edmean-squarederrorlossfunctionforspecificationerror.Theweightingfunctionisanaveragedensityofthedependentvariablenearthetrueconditionalquantile.TheweightedleastsquaresinterpretationofQRisusedtoderiveanomittedvariablesbiasformulaandapartialquantilecorrelationconcept,similart
8、otherelationshipbetweenpartialcorrelationandOLS.Wealsoderivegeneralasymptoticresul
