讲义参考教案

IntermediateEconometrics,Spring2015

Assignment4

May16,2015

Q1.Usethedataincharls11_assign4.dta( HealthandRetirementLongitudinalStudy2011)forthisexercise.[STATA]

Followingquestionsarerelatedtoheteroskedasticity.

Estimatethemodel:

lnmedexp=β0+β1lninc+u.(1)

Anddrawtheresidualgraph(relationshipbetweenu�2andy�)formodelspecification(1).Giveyourintuitive ysis.(Hint:scatteruhat2yhat)

NowcomputetheBreusch-Pagantestforheteroskedasticity.UsetheFstatisticversionandreportthep-value.

ComputetheWhite-test(yhatversion),againusingtheFstatisticform.Howstrongistheevidencefortheheteroskedasticity.

Runthemodelspecification(1)usingrobustoptiontogeneraterobuststandarderrorsforallcoefficients.Reporttheresultsinatable(alongwiththemodelwithusualOLSstandarderrors).Andcomparetheresultsbetweentwomodelspecifications.

Q2.Usethedataincharls11_lpm_assign4.dta(HealthandRetirementLongitudinalStudy2011)to yzetheself-reportedhealthstatus.

Accordingtothedata,whatisthefractionofpeoplewhoreporttheirhealthstatusisgood?

Estimatethelinearprobabilitymodelgoodsrh=b_0+b_1lninc+b_2male+b_3urban+u

andreporttheresultsinatable.Interpretthecoefficientsforallvariablesincludingtheconstantterm.

Intheestimationinpart(ii),howmanyestimatedprobabilitiesarenegative?Howmanyarebiggerthanone?Shouldyoubeconcerned?

FollowingquestionsarerelatedtoDifference-in-Differences.

Q3. Wearestudyingthelengthoftimethataninjuredworkerreceivesworkers’

compensation.OnJuly15,1980,Kentuckyraisedthecaponweeklyearning（s周工资封顶值）

thatwerecoveredbyworkers’compensation.Anincreaseinthecaphasnoeffectonthebenefitfor eworkers,butitmakesitlesscostlyfora eworkertostayonworkers’compensation.Therefore,thecontrolgroupis eworkers,andthetreatmentgroupis eworkers.

Usingrandomsamplesbothbeforeandafterthechange,weareabletotestwhethermoregenerousworkers’compensationcausespeopletostayoutofworklonger(everythingelsefixed)withadifference-in-differencesysis.Thedependentvariableisln(durat),whereduratisthelengthoftime(inweeks)thataninjuredworkerreceivesworkers’compensation.Letafchngebethedummyvariableforobservationsafterthechangeandhighearnthedummyvariableforhighearners.Theestimatedequationis

(2)

Howtointerpretthecoefficientforhighearninequation(2)?

Pleaseinterpretthecoefficientforafchngeinequation(2).Isitsurprisingthatthecoefficientforafchngeissmallandnotstatisticallysignificant?Exin.

Interpretthecoefficientforthein ctiontermofequation(2).Isitsignificantatthe5%level?Whatdoesitimply?

Pleasesuggestsomecontrolvariable(s)ifneededinequation(2)andprovideyourreasonforaddingcontrolvariable(s)ornot.

Anotherresearcherexaminestheissueusingdifferentregressionsandthecorrespondingresultsarereportedasfollows.Pleasefillinthetwoblanksinequations

(3)and(4).Pleaseinterpretthetwocoefficients.Underwhatassumptions,equations(3)and(4)canbeusedtocapturethecausaleffectofthe.

log�(𝑑𝑑𝑑𝑑𝑑)=1.129+0.253ℎ𝑖𝑛ℎ𝑛𝑑𝑑𝑛+()𝑑𝑎𝑎ℎ𝑛𝑛𝑛∗ℎ𝑖𝑛ℎ𝑛𝑑𝑑𝑛 (3)

log(�𝑑𝑑𝑑𝑑𝑑)=1.233−0.100𝑑𝑎𝑎ℎ𝑛𝑛𝑛+()𝑑𝑎𝑎ℎ𝑛𝑛𝑛∗ℎ𝑖𝑛ℎ𝑛𝑑𝑑𝑛 (4)

Q4. In2013,aweibopostedbyLeehomWang()directedpeople’sattentionstothe

girlsatColumbiaUniversity.SomeCCERstudentsthoughtthattheyshouldalsomarrya

“ParisHilton”(美)atColumbiaUniversitysotheytriedtoapplyforColumbiaUniversity.Assumewehavedataaboutsuitors(追求者)forColumbiagirlsandnon-Columbiagirls.CouldyoupleasedesignanidentificationstrategytoevaluatetheeffectofWang’sweiboonColumbiagirls’competitivenessatthemarriagemarket?Pleasepointoutthekeyassumptionsofyourstrategyanddesignadditionalrobustcheckstojustifyyourresults.(Hint:Thisquestionishard.ItissufficienttoprovidethekeyassumptionsofDIDinthecontextandadditionaltestfortheseassumptions.)

FollowingquestionsarerelatedtoErrors-in-VariableModelandInstrumentVariable.

Q5.Supposethatsomeonewouldliketounderstandhowevisionwatchingmayaffectchilddevelopment.UsingthedatacollectedinBostonattheendof2013forchildagedbetween5and10,theregressionmodelisspecifiedasbelow:

𝑑𝑡𝑎𝑡𝑑𝑛=𝛽0+𝛽1𝑑𝑡ℎ𝑡𝑑𝑑𝑡+𝛽2𝑑𝑛𝑛+𝛽3𝑚𝑡𝑑ℎ𝑛𝑑𝑑+𝛽4𝑎𝑑𝑑ℎ𝑛𝑑𝑑+𝛽5𝑡𝑖𝑠𝑡+𝑑(5)where:tscoreisthechildscoreatastandardizedtestwhichisage-specific,tvhoursistheaveragenumberofhoursthechildspendsperweekwatchingTVduringthepastthreemonths,ageisthechild'sage,motheducandfatheducaretheyearsofeducationofthemotherandfatherofthatchildrespectively,andsibsisthenumberofsiblingsofthatchild.

Thetestsareage-specific,sofordifferentagegroupsthetestquestionsaredesigneddifferently.Theageforthesampledchildrenisrangedfrom5-10yearsold.Whyshouldwecontrolfortheagevariableintheregression?Provideyourexnation.

HowcanyoustudywhethertheeffectofTVwatchingisassociatedwithparents’education?Specifythemodifiedmodelspecificationbasedonmodel(5)andproviderelatedstatisticaltest.

ThetruenumberofhoursachildspendsperweekwatchingTVishardtomeasureprecisely.Therefore,intheactualestimation,weusereportedtimespendinwatchingTVbyparentsinsteadofthetruevalue.Supposetvhoursisanimperfectmeasureofthetruevariable𝑑𝑡ℎ𝑡𝑑𝑑𝑡∗.Doyouthinktheclassicalerror-in-variables(CEV)assumptionholdsinthiscase?Provideyourexnation.

Testswereconductedandthesurveywascollectedatendoftheyearsof2013.While,inOctober2013theDisneychannelunexpectedlystoppedtransmission