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EssaysinNon-andSemiparametric

Econometrics

InauguraldissertationzurErlangungdesakademischenGradeseines

DoktorsderWirtschaftswissenschaftenderUniversit¨atMannheim

vorgelegtvon

ChristophRothe

April2009

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Mammen

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RichardBlundell,Ph.D.

28.05.2009

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Acknowledgements

Firstofall,IwouldliketothankmyadviserEnnoMammenforhisguidanceandsu-
pervisionduringtheprocessofwritingthisthesis.Heintroducedmetothefascinating
eldofnon-andsemiparametriceconometrics,andmyresearchhasbenetedalotfrom
hisdeepknowledgeaboutstatistics.DuringmytimeattheChairofStatistics,Ihave
receivedallthesupportIcouldeverhaveaskedfor,andIamverygratefulforthat.
IalsowishtothankRichardBlundellforadviceonmythesisandbeyond.Ibeneted
alotfromfourveryencouragingandinsightfulmonthsinLondonthatdidnotonly
broadenmyperspectiveonmyowntopicbutoneconometricsingeneral.
IwouldalsoliketothankmycolleaguesattheChairofStatistics,inparticular
KyusangYu,MelanieSchienleandChristophNagel,forallthelivelydiscussionsabout
econometrics,statisticsandessentiallyanythingelse.Thesamegoesformyfellowgrad-
uatestudentsattheCDSE,whowereimportantcontributorstothewonderfulresearch
atmosphereIexperiencedhere.
Partsofthisthesishavebeenpresentedatconferencesandseminarsoverthepast
threeyears,andIhavereceivedanumberofhelpfulsuggestionsandcommentsfromthe
respectiveaudiencesthatleadtomajorimprovements,whichisgratefullyacknowledged.
Finally,myfamilyhasalwaysbeenaninvaluablesourceofsupport.Thankyou!

ChristophRothe

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Contents

1Introduction

2NonparametricEstimationofDistributionalPolicyEects
2.1Introduction..................................
2.2ModellingFrameworkandEstimationApproach..............
2.2.1Model.................................
2.2.2ObjectsofInterest..........................
2.2.3Identication.............................
2.2.4Estimation...............................
2.3AsymptoticProperties............................
2.3.1AssumptionsandPreliminaries...................
2.3.2MainResult..............................
2.3.3Inference................................
2.4ApplicationtoObjectsofInterest......................
2.4.1Quantiles...............................
2.4.2Inequalitymeasures..........................
2.4.3TestingforStochasticDominance..................
2.5NumericalExamples.............................
2.5.1SimulationStudy...........................
2.5.2EmpiricalIllustration:TheEectofanAnti-SmokingCampaign
onInfantBirthweights........................
2.6Conclusions..................................
Appendix......................................

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55889213151618102223242527272335363

3SemiparametricEstimationofBinaryResponseModelswithEndoge-
nousRegressors49
3.1Introduction..................................49
3.2TheModel...................................52
3.3IdenticationandEstimationApproach...................54
3.3.1Identication.............................54
3.3.2TheEstimator............................56
3.4AsymptoticProperties............................57
3.4.1AssumptionsandPreliminaries...................58
3.4.2ConsistencyandAsymptoticNormality...............61
3.4.3Varianceestimation..........................63
3.5SomeExtensionsoftheStructureoftheModel...............64
3.6SimulationStudy...............................65
3.6.1Setup.................................65
3.6.2ImplementationIssues........................67
3.6.3Results.................................68
3.7AnEmpiricalApplication:Home-ownershipandIncomeinGermany..71
3.8ConcludingRemarks.............................75
Appendix......................................76

4IdenticationofUnconditionalPartialEectsinNonseparableModels85
4.1Introduction..................................85
4.2ModelandParametersofInterest......................87
4.3Identication.................................88
4.4Conclusions..................................92

Bibliography

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Chapter1

Introduction

Withimportantadvancesmadeineconometrictheoryandtherapidlyincreasingavailabil-
ityofcomputingpowerandlargedatasets,theuseofnonparametricandsemiparametric
techniqueshasgainedconsiderableimportanceforappliedeconomicresearchoverthe
pastthreedecades.Extensiveoverviewsofrecentdevelopmentsinthisareaaregivenfor
examplebyPaganandUllah(1999)orLiandRacine(2007).
Thegeneralaimofnonparametricandsemiparametrictechniquesistoweakenthe
oftenrestrictiveassumptionsthatareimposedinordertobeabletousestandardecono-
metricmethods.Inaclassicalregressionframework,forexample,itistheaimofthe
researchertoinvestigatethefunctionalrelationshipbetweenthemeanofanoutcome
variableofinterestandanumberofexplanatoryquantities.Atypical,fullyparametric
approachtothisproblemwouldbetoassumethattherelationshipcanberepresented
throughafunctionknownuptoanitenumberofparameters,whichcanbeestimated
fromthedatabymaximumlikelihoodorthemethodofleastsquares.Suchaprocedure
willofcoursebeadequatewhenthetrueunderlyingdatageneratingprocesscanbewell
approximatedbythepostulatedfunctionalform.Itwill,however,potentiallyresultin
grosslymisleadingconclusionsundermisspeci