Table Of ContentOUPCORRECTEDPROOF–FINAL,19/9/2016,SPi
Econometrics of Panel Data
OUPCORRECTEDPROOF–FINAL,19/9/2016,SPi
OUPCORRECTEDPROOF–FINAL,19/9/2016,SPi
Econometrics
of Panel Data
Methods and Applications
Erik Biørn
1
OUPCORRECTEDPROOF–FINAL,19/9/2016,SPi
3
GreatClarendonStreet,Oxford,ox26dp,
UnitedKingdom
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©ErikBiørn2017
Thefindings,interpretations,andconclusionsexpressedinthisworkareentirely
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OUPCORRECTEDPROOF–FINAL,19/9/2016,SPi
PREFACE
Panel data is a data type used with increasing frequency in empirical research in eco-
nomics, social sciences, and medicine. Panel data analysis is a core field in modern
econometricsandmultivariatestatistics,andstudiesbasedonsuchdataoccupyagrowing
part of the field in all the mentioned disciplines. A substantial literature on methods
and applications has accumulated, also synthesized in survey articles and a number of
textbooks.Whythenwriteanotherbookonpaneldataanalysis?Ihopethatsomeofmy
motivationandpartoftheanswerwillbegiveninthefollowingparagraphs.
Thetextcollectedinthisbookhasoriginated,andbeenexpandedthroughseveralyears,
partly in parallel with courses I have given at the University of Oslo for master’s and
doctoral students of economics. I have been interested in the field, both its models and
methodsandapplicationstosocialsciences,formorethanfortyyears.Thefirstdraftswere
lecturenotes,laterexpandedandsynthesizedintocoursecompendia,firstinNorwegian,
later in English. In compiling the text, I have had no ambition of giving an account of
thehistoryofpaneldataanalysisanditsvarioussubfields,someofwhichhavealonger
historythanothers.Withinsome350pagesitisimpossibletogiveacompletecoverage,
andthechoiceoftopics,andthedepthofdiscussionofeachofthem,tosomeextentreflect
mypreferences.Somereadersmaymisstopicslikecross-section-time-seriesanalysisin
continuoustime,durationanalysis,andanalysisofnon-linearpaneldatamodels(outside
thelimiteddependentvariablesfield).TopicsIgivespecificattentionto,morethanmany
comparabletexts,Ithink,arecoefficientidentificationofmodelsmixingtwo-dimensional
andindividual-specificvariables,regressionmodelswithtwo-wayrandomeffects,models
and methods for handling random coefficients and measurement errors, unbalanced
paneldata,andpaneldatainrelationtoaggregation.Problemsattheinterfacebetween
unbalanceandtruncation,andbetweenmicro-econometricsandpaneldataanalysis,are
alsodiscussed.
Itgoeswithoutsayingthatinabookdealingwithdatashowingtemporal–spatialvari-
ation,matrixalgebraisunavoidable.Althoughpaneldatahaveamatrixstructure,such
algebrashouldnotbeacorematter.Ihaveexperiencedthatmanystudentsstartingonthe
topicfeelpartsofthematrixalgebra,especiallywhenwritteninadense,compactstyle,
tobeanobstacle.Ithereforesetouttoexplainmanyofthemodelsandmethodsinsome
detailtoreaderscomingtopaneldataanalysisforthefirsttime,includingstudentsfamil-
iarwithbasicstatisticsandclassicalmultipleregressionanalysis,andappliedresearchers.
Sometechnicalmaterialisplacedinappendices.Yetsomeadvancedand‘modern’topics
arediscussed.Sinceoneofmyintentionsisthatstudentsshouldbegiventhechanceto
OUPCORRECTEDPROOF–FINAL,19/9/2016,SPi
vi PREFACE
getanacceptablegraspofbasicideaswithouthavingtobeinvolvedinextensivematrix-
algebraic exercises, most chapters start with a simple example in scalar (or elementary
vector)notation,andthenattempttotakethereadergraduallytomorecomplexcasesin
fullermatrixnotation,evenifthisnecessitatessomerepetition.
Thefirstchapterssurveyratherelementarymaterials.Ibelievethattheinitialsections
ofthefirsteightchaptersmaybeusefulforbachelorstudents,providedtheirknowledge
ofmultipleregressionanalysisandbasicmathematicalstatisticsissufficient.Chapters1–3
and5containmostlybasictopics,Chapters4and6–10containintermediateleveltopics,
andChapters11and12containsomewhatadvancedtopics.Ihave,asfaraspossible,tried
tokeepeachchapterself-contained.Yetsomeconnectionsexist.Itmayalsobehelpfulto
notethatChapter6buildsonChapters2,3,and5,thatChapters6and7expandtopicsin
Chapters2–4,thatChapters7and8aremethodologicallyrelated,thatChapter11builds
onChapters9and10,andthatChapter12buildsonChapters3and6.Eachchapterhas
aninitialsummary,somealsohaveaconcludingsection.
Somereadersmaymissexerciseswithsolutions,whichwouldhaveexpandedthesize
ofthebook.Ontheotherhand,examplesofapplications,somefrommyownresearch,
orexperiments,andillustrationsutilizingpubliclyavailabledataareincludedinseveral
chapters.Myviewofthepaneldatafieldisthatthecoretopicshave,tosomeextent,the
characterofbeingbuildingblockswhichmaybecombined,andthenumberofpotential
combinationsislarge.Notmanycombinationsarediscussedexplicitly.Certainpotential
combinations—forexample,dynamicequationswithrandomcoefficientsforunbalanced
panel data and random coefficients interacting with limited dependent variables with
measurementerrors—have(tomyknowledge)hardlybeendiscussedinanyexistingtext.
Althoughprimarilyaimingatstudentsandpractitionersofeconometrics,Ibelievethat
mybook,orpartsofit,maybeusefulalsoforstudentsandresearchersinsocialsciences
outsideeconomicsandforstudentsandresearchworkersinpsychology,politicalscience,
andmedicine,providedtheyhaveasufficientbackgroundinstatistics.Myintention,and
hope, is that the book may serve as a main text for lecturing and seminar education at
universities.Ibelievethatpartsmaybeusefulforstudents,researchers,andotherreaders
workingontheirown,interalia,withcomputerprogrammingofmodulesforpaneldata
analysis.
Duringthework,Ihavereceivedvaluablefeedbackfrommanycolleaguesandstudents,
notleastPhDstudentswritingtheirtheses,partlyundermysupervision,onappliedpanel
datatopics.Questionsfrequentlyposedduringsuchdiscussionshaveundoubtedlymade
their mark on the final text. I want to express my gratitude to the many students who
haveread,commentedon,andinotherswaysbeen‘exposedto’mynotes,sketches,and
chapter drafts. Their efforts have certainly contributed to eliminate errors. I also thank
goodcolleaguesformanylongandinterestingdiscussionsorforhavingwillinglyspent
their time in reading and commenting on drafts of preliminary versions of the various
sectionsandchapters,sometimesmorethanonce.IregretthatIhavebeenunabletotake
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PREFACE vii
alltheiradviceintoaccount.Ispecificallywanttomention(inalphabeticalorder)Jørgen
Aasness, Anne Line Bretteville-Jensen, John K. Dagsvik, Xuehui Han, Terje Skjerpen,
Thor Olav Thoresen, Knut R. Wangen, and Yngve Willassen. Needless to say, none of
themaretobeheldresponsibleforremainingerrorsorshortcomings.Thetexthasbeen
prepared by the author in the Latex document preparation software, and I feel obliged
totheconstructorsofthisexcellentscientifictextprocessor.Last,butnotleast,Iexpress
mysinceregratitudetoOxfordUniversityPress,inparticularAdamSwallowandAimee
Wright,fortheirbeliefintheprojectandforsupport,encouragement,andpatience.
ErikBiørn
Oslo,March2016
OUPCORRECTEDPROOF–FINAL,19/9/2016,SPi
OUPCORRECTEDPROOF–FINAL,19/9/2016,SPi
CONTENTS
LISTOFTABLES xvii
1 Introduction 1
1.1 Typesofpanelvariablesanddata 1
1.2 Virtuesofpaneldata:Transformations 3
1.3 Paneldataversusexperimentaldata 8
1.4 Othervirtuesofpaneldataandsomelimitations 9
1.5 Overview 11
2 Regressionanalysis:Fixedeffectsmodels 14
2.1 Simpleregressionmodel:One-wayheterogeneity 15
2.1.1 Individual-specificinterceptsandcoefficients 15
2.1.2 Individual-specificintercepts,commoncoefficient 16
2.1.3 Homogeneousbenchmarkmodel 19
2.1.4 Howaretheestimatorsrelated? 21
2.2 Multipleregressionmodel:One-wayheterogeneity 23
2.2.1 Individual-specificinterceptsandcoefficients 23
2.2.2 Individual-specificintercepts,commoncoefficients 25
2.2.3 Homogeneousbenchmarkmodel 27
2.2.4 Howaretheestimatorsrelated? 30
2.3 Simpleregressionmodel:Two-wayheterogeneity 33
2.3.1 Individual-andperiod-specificintercepts 33
2.3.2 Homogeneousbenchmarkmodel 36
2.3.3 Howaretheestimatorsrelated? 39
2.4 Multipleregressionmodel:Two-wayheterogeneity 41
2.4.1 AnexcursionintoKronecker-products:Definition 41
2.4.2 MatrixformulaewithKronecker-products:Examples 42
2.4.3 Paneldata‘operators’:Bilinearandquadraticforms 43
2.4.4 Individual-andperiod-specificintercepts 46
2.4.5 Homogeneousbenchmarkmodel 49
2.4.6 Howaretheestimatorsrelated? 50
2.5 Testingforfixedheterogeneity 53
2.5.1 One-wayinterceptandcoefficientheterogeneity 54
2.5.2 Two-wayinterceptheterogeneity 55
