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Micro-Econometrics:LimitedDependentVariablesandPanelDataOutlineofthecourseAndreaIchino(EuropeanUniversityinstitute,IGIERandCEPR)∗January13,2003Thecourseisintendedtointroducestudentstosomestandardmethodsspecificallyde-signedfortheanalysisofparticulartypesofmicroeconomicdata.Foreachmethodthegeneraltheoreticalbackgroundwillbeprovided,followedbythecriticaldiscussionofoneormoreappliedpapers.HouseholddatasetsfordifferentcountriesinSTATAformat(plussomedocumentation)canbedownloadedviawebforexercisesandproblemsets.Lookat:−STAGE/DataSets/DATA/courses/ichino/metricspring/Thefinalexamwillbeatakehomeexerciseinvolvingalsoaparttobeansweredatthecomputerwithrealdata.Inadditiontotheselecturenotes,thefollowingtextbooksaresuggested:J.Wooldridge,EconometricAnalysisofCrossSectionandPanelData,TheMITPress,lastedition;J.Wooldridge,IntroductoryEconometrics,SouthWesternCollegePublishing,lastedition;W.H.Greene,EconometricAnalysis,lastedition.PrenticeHall1997;;J.Johnston,J.Di-Nardo,EconometricMethods,McGraw-Hill,lastedition.Additionalreferencesarelistedattheendofthesenotes.∗Addresscorrespondenceto:AndreaIchino,EuropeanUniversityInstitute,50016SanDomenicodiFiesole,Firenze,Italia,e-mail:[e-mail]ursecanbedownloadedfrom:fit..............................122.1.6Probitmodel...............................132.1.7Logitmodel................................162.1.8Comparisonbetweenlinearprobability,probitandlogitmodels...192.1.9Maximumscoreestimator........................212.2Applications:binarychoicesmodelsfortheidentificationofsocialeffects..223Multiplechoices273.1Theory.......................................273.1.1Basicframeworkandnotation......................273.1.2Thelogitmodel..............................283.1.3IndependencefromIrrelevantAlternativesProperty(IIA).......293.1.4Whichparametersareidentifiedinthelogitmodel?..........303.1.5Themultinomiallogitmodel.......................323.1.6The(pure)ConditionalLogitmodel...................383.1.7AtestfortheIIAhypothesis.......................413.2Applicationsofmultiplechoicesmodels.....................444Paneldata454.1Examples.....................................454.2Problemsarisingincrosssectionsandsolvedbypaneldata..........464.2.1Example1:Productionfunctionsandmanagerialability.......464.2.2Example2:Returnstoschooling,abilityandtwins..........484.3Ageneralframeworkandmorenotation....................504.4Fixedeffects(within)estimators.........................524.4.1Leastsquaresdummyvariablemodel(LSDV).............524.4.2AnalysisofCovariance:usingdeviationsfromindividualspecificmeans544.4.3Aparenthesisonpartitionedregressions................554.4.4BacktotheAnalysisofCovariance...................584.4.5Firstdifferences..............................614.4.6Differences-in-Differences(DD)strategies................624.4.7Fixedeffectsestimatorsandmeasurementerror............674.4.8Fixedeffectsestimatorsandlaggeddependentvariables........7224.4.9Otherpitfallsoffixedeffectsestimation.................794.5Betweenestimator................................804.5.1OLS,“within”and“between”estimators................824.6Randomeffectsestimator.............................844.6.1GLSestimationofRandomEffectsmodels...............864.6.2FeasibleGLSestimationofrandomeffectsmodels...........874.6.3Randomeffects,within,betweenandOLSestimators.........884.7Mundlak(1978):areconciliationoffixedandrandomeffectsmodels?....904.7.1Atestforrandomorfixedeffects....................924.7.2RandomeffectsmodelsandInstrumentalVariables..........954.8Extensions.....................................1004.9PaneldataanalysisinSTATA..........................1005Paneldatawithdiscretedependentvariables1015.1Theconditionalmaximumlikelihoodapproach.................1025.2FixedeffectsconditionallogitestimationinSTATA..............1055.3Applications....................................1056References10631IntroductionInlaboreconomicsandmoregenerallyintheanalysismicro-economicdatasetswehaveoftentodealwithphenomenathatareintrinsicallydiscreteorthataremeasuredinadiscretefashion.•End-of-highschooldecision:gotocollegeordropout.•Female’sdecisiontoparticipateinthelabormarket.•Employmentorunemploymentaftertraining.•Self-employmentofwagework.•Welfareparticipation.•Consumerchoices.•Meansoftransportation.•Marriage.•Crime.•Voting.•Locationaldecisionsoffirms.•EnteringtheEU.•...Itisconvenienttodistinguishbetween:•Binarychoices:thedependentvariablecantaketwovalues.•Multiplechoices:thedependentvariablecantakemorethantwovalues.42Binarychoices2.1Theory2.1.1BasicframeworkandnotationConsiderasampleofindividualsindexedbyi={1,2,3,...N}.Foreachindividualweobservethebinaryvariab