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1、IVNONLINEARMODELSANDRELATEDTOPICSWenowapplythegeneralmethodsofPartIIItostudyspecificnonlinearmodelsthatoftenariseinapplications.Manynonlineareconometricmodelsareintendedtoex-plainlimiteddependentvariables.Roughly,alimiteddependentvariableisavariablewhose
2、rangeisrestrictedinsomeimportantway.Mostvariablesencounteredineconomicsarelimitedinrange,butnotallrequirespecialtreatment.Forexample,manyvariables—wage,population,andfoodconsumption,tonamejustafew—canonlytakeonpositivevalues.Ifastrictlypositivevariablet
3、akesonnumerousvalues,specialeconometricmethodsarerarelycalledfor.Often,takingthelogofthevari-ableandthenusingalinearmodelsu‰ces.Whenthevariabletobeexplained,y,isdiscreteandtakesonafinitenumberofvalues,itmakeslittlesensetotreatitasanapproximatelycontinuou
4、svariable.Dis-cretenessofydoesnotinitselfmeanthatalinearmodelforEðyjxÞisinappropriate.However,inChapter15wewillseethatlinearmodelshavecertaindrawbacksformodelingbinaryresponses,andwewilltreatnonlinearmodelssuchasprobitandlogit.Wealsocoverbasicmultinomia
5、lresponsemodelsinChapter15,includingthecasewhentheresponsehasanaturalordering.Otherkindsoflimiteddependentvariablesariseineconometricanalysis,especiallywhenmodelingchoicesbyindividuals,families,orfirms.Optimizingbehavioroftenleadstocornersolutionsforsome
6、nontrivialfractionofthepopulation.Forexample,duringanygiventime,afairlylargefractionoftheworkingagepopulationdoesnotworkoutsidethehome.Annualhoursworkedhasapopulationdistributionspreadoutoverarangeofvalues,butwithapileupatthevaluezero.Whileitcouldbethat
7、alinearmodelisappropriateformodelingexpectedhoursworked,alinearmodelwilllikelyleadtonegativepredictedhoursworkedforsomepeople.Takingthenat-urallogisnotpossiblebecauseofthecornersolutionatzero.InChapter16wewilldiscusseconometricmodelsthatarebettersuitedf
8、ordescribingthesekindsoflimiteddependentvariables.WetreattheproblemofsampleselectioninChapter17.Inmanysampleselectioncontextstheunderlyingpopulationmodelislinear,butnonlineareconometricmeth-odsarerequiredinordertocorrectfornonran
