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Classroom Companion: Economics Badi H. Baltagi Solutions Manual for Econometrics Fourth Edition Classroom Companion: Economics The Classroom Companion series in Economics features fundamental textbooks aimedatintroducingstudentstothecoreconcepts,empiricalmethods,theoriesand tools of the subject. The books offer a firm foundation for students preparing to movetowardsadvancedlearning.Eachbookfollowsacleardidacticstructureand presentseasyadoptionopportunitiesforlecturers. Badi H. Baltagi Solutions Manual for Econometrics Fourth Edition BadiH.Baltagi SyracuseUniversity Syracuse,NY,USA ISSN2662-2882 ISSN2662-2890 (electronic) ClassroomCompanion:Economics ISBN978-3-030-80157-1 ISBN978-3-030-80158-8 (eBook) https://doi.org/10.1007/978-3-030-80158-8 ©TheEditor(s)(ifapplicable)andTheAuthor(s),underexclusivelicensetoSpringerNatureSwitzerland AG1997,2010,2015,2022 Thisworkissubjecttocopyright.AllrightsaresolelyandexclusivelylicensedbythePublisher,whether thewhole orpart ofthematerial isconcerned, specifically therights oftranslation, reprinting, reuse ofillustrations, recitation, broadcasting, reproductiononmicrofilmsorinanyotherphysicalway,and transmissionorinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilar ordissimilarmethodologynowknownorhereafterdeveloped. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. Thepublisher,theauthors,andtheeditorsaresafetoassumethattheadviceandinformationinthisbook arebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsor theeditorsgiveawarranty,expressedorimplied,withrespecttothematerialcontainedhereinorforany errorsoromissionsthatmayhavebeenmade.Thepublisherremainsneutralwithregardtojurisdictional claimsinpublishedmapsandinstitutionalaffiliations. ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSwitzerlandAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Preface This manual provides solutions to selected exercises from each chapter of the sixth edition of Econometrics by Badi H. Baltagi.1 Eviews and Stata as well as (cid:2) SAS programs are provided for the empirical exercises. Some of the problems and solutionsare obtainedfrom EconometricTheory (ET) and these are reprinted with the permission of Cambridge University Press. I would like to thank Peter C.B. Phillips, and past editors of the Problems and Solutions section, Alberto Holly,Juan Doladoand PaoloParuolofortheirusefulservice tothe econometrics profession.I wouldalso like tothankmycolleague(fromTexasA&M)JamesM. Griffinforprovidingmanyempiricalproblemsanddatasets.Ihavealsousedthree empirical data sets from Lott and Ray (1992). The reader is encouraged to apply these econometric techniquesto their own data sets and to replicate the results of published articles. Instructors and students are encouraged to get other data sets fromtheInternetorjournalsthatprovidebackupdatasetstopublishedarticles.The JournalofAppliedEconometricsandtheAmericanEconomicReviewaretwosuch journals.Infact,theJournalofAppliedEconometricshasareplicationsectionfor whichIservedasaneditorfrom2003–2018.InmycourseIrequiremystudentsto replicateanempiricalpaper. I would like to thank my students Wei-Wen Xiong, Ming-Jang Weng, Kiseok Nam,DongLi, Gustavo Sanchez,LongLiu,Junjie Shu,and LiuTian whosolved severaloftheexercises.IwouldalsoliketothankMartinaBihn,JohannesGlaeser andJudithKrippatSpringerfortheircontinuoussupportandprofessionaleditorial help. Please report any errors, typos or suggestions to: Badi H. Baltagi, Center for Policy Research and Department of Economics, Syracuse University, Syracuse, New York 13244-1020, Telephone (315) 443-1630, Fax (315) 443-1081, or send [email protected]://pbaltagi.wix.com/badibaltagi. 1Baltagi,BadiH.,Econometrics,6thEd.,Springer-Verlag,Berlin,Heidelberg,2021. v vi Preface Data The data sets used in this text can be downloaded from the Springer website. Theaddressis:http://www.springer.com/978-3-642-54547-4.Pleasecheckthelink “Samples, Supplements, Data Sets” from the right-hand column. There is also a readmefilethatdescribesthecontentsofeachdatasetanditssource. Reference Lott,W.F.andS.Ray(1992),EconometricsProblemsandDataSets(Harcourt,BraceJovanovich: SanDiego,CA). Contents 1 WhatisEconometrics?..................................................... 1 2 AReviewofSomeBasicStatisticalConcepts............................ 5 3 SimpleLinearRegression.................................................. 31 4 MultipleRegressionAnalysis.............................................. 49 5 ViolationsoftheClassicalAssumptions.................................. 77 6 DistributedLagsandDynamicModels .................................. 123 7 TheGeneralLinearModel:TheBasics.................................. 153 8 RegressionDiagnosticsandSpecificationTests ......................... 179 9 GeneralizedLeastSquares ................................................ 215 10 SeeminglyUnrelatedRegressions......................................... 235 11 SimultaneousEquationsModel........................................... 261 12 PoolingTime-SeriesofCross-SectionData.............................. 319 13 LimitedDependentVariables ............................................. 347 14 Time-SeriesAnalysis....................................................... 409 vii 1 What is Econometrics? Thischapteremphasizesthataneconometricianhastobeacompetentmathemati- cianandstatisticianwhoisaneconomistbytraining.Itistheunificationofstatistics, economictheoryandmathematicsthatconstituteseconometrics.Eachview point, by itself is necessary but not sufficient for a real understanding of quantitative relationsinmoderneconomiclife,seeFrisch(1933).In1969,RagnarFrischshared thefirstNobelPrizeineconomicswithJanTinbergen. Econometrics aims at giving empirical content to economic relationships. The threekeyingredientsareeconomictheory,economicdata,andstatisticalmethods. Neither ‘theory without measurement’, nor ‘measurement without theory’ are sufficient for explaining economic phenomena. It is as Frisch emphasized their unionthatisthekeyforsuccessinthefuturedevelopmentofeconometrics. Econometrics provides tools for testing economic laws, such as purchasing power parity,the life cycle hypothesis,the wage curve,etc. These economic laws orhypothesesaretestablewitheconomicdata.AsHendry(1980)emphasized“The threegoldenrulesofeconometricsaretest,testandtest.” Econometricsalso providesquantitativeestimatesof price andincomeelastici- tiesofdemand,returnstoscaleinproduction,technicalefficiencyincostfunctions, wageelasticities, etc. Theseareimportantforpolicydecisionmaking.Raisingthe tax on a pack of cigarettes by 10%, how much will that reduce consumption of cigarettes?Howmuchwillitgenerateintaxrevenues?Whatistheeffectofraising minimumwageby$1perhouronunemployment?Whatistheeffectofraisingbeer taxonmotorvehiclefatality? Econometrics also provides predictions or forecasts about future interest rates, unemployment, or GNP growth. As Klein (1971) emphasized: “Econometrics shouldgiveabaseforeconomicpredictionbeyondexperienceifitistobeuseful.” LawrenceR.KleinwasawardedtheNobelPrizeineconomicsin1980. Dataineconomicsarenotgeneratedunderidealexperimentalconditionsasina physicslaboratory.Thisdatacannotbereplicatedandismostlikelymeasuredwith error. Most of the time the data collected are not ideal for the economicquestion ©TheAuthor(s),underexclusivelicensetoSpringerNatureSwitzerlandAG2022 1 B.H.Baltagi,SolutionsManualforEconometrics,ClassroomCompanion: Economics,https://doi.org/10.1007/978-3-030-80158-8_1 2 BadiBaltagi at hand. Griliches (1986, p. 1466) describes economic data as the world that we want to explain, and at the same time the source of all our trouble. The data’s imperfectionsmakesthe econometrician’sjobdifficultandsometimesimpossible, yettheseimperfectionsarewhatgiveseconometricianstheirlegitimacy. Eventhougheconomistsareincreasinglygettinginvolvedincollectingtheirdata and measuringvariablesmore accuratelyand despite the increase in data sets and datastorageandcomputationalaccuracy,someofthewarningsgivenbyGriliches (1986,p.1468)arestillvalidtoday: econometricians want too much from the data and hence tend to be disap- pointed by the answers, because the data are incomplete and imperfect. In partitisourfault,theappetitegrowswith eating.Aswegetlargersamples, wekeepaddingvariablesandexpandingourmodels,untilonthemargin,we comebacktothesameinsignificancelevels. Pesaran(1990,pp.25–26)alsosummarizessomeofthelimitationsofeconomet- rics: There is no doubt that econometrics is subject to important limitations, which stem largely from the incompleteness of the economic theory and the non-experimentalnature of economic data. But these limitations should not distract us from recognizingthe fundamentalrole that econometricshas come to play in the development of economics as a scientific discipline. It may not be possible conclusively to reject economic theories by means of econometricmethods,butitdoesnotmeanthatnothingusefulcanbelearned from attempts at testing particular formulations of a given theory against (possible)rivalalternatives.Similarly,thefactthateconometricmodellingis inevitablysubjecttotheproblemofspecificationsearchesdoesnotmeanthat the whole activity is pointless. Econometric models are important tools for forecastingandpolicyanalysis,anditisunlikelythattheywillbediscardedin thefuture.Thechallengeistorecognizetheirlimitationsandtoworktowards turningthemintomorereliableandeffectivetools.Thereseemtobenoviable alternatives. Econometricshaveexperiencedphenomenalgrowthinthepast60years.There are six volumes of the Handbook of Econometrics, most of it dealing with post 1960sresearch.Alotoftherecentgrowthreflectstherapidadvancesincomputing technology. The broad availability of micro data bases is a major advance which facilitatedthe growthofpaneldata methods(see Chap.12)andmicroeconometric methodsespeciallyonsampleselectionanddiscretechoice(seeChap.13)andthat also lead to the award of the Nobel Prize in Economics to James Heckman and Daniel McFadden in 2000. The explosion in research in time series econometrics which lead to the development of ARCH and GARCH and cointegration (see Chap.14) which also lead to the award of the Nobel Prize in Economicsto Clive GrangerandRobertEnglein2003.