07slides.pdf - OLS Efficiency Using Qualitative Data Tyler...

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OLSEfficiency&UsingQualitativeData TylerRansom UnivofOklahoma Febfive.osf,two.osfzero.osfone.osfnine.osf one.osf/two.osftwo.osf
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Today’splan one.osf. Reviewreadingtopics one.osf.one.osf EfficiencyofOLSEstimators - TheGauss-MarkovTheorem one.osf.two.osf HowtoUseQualitativeData - DummyVariables - The“DummyVariableTrap” - LinearProbabilityModels two.osf. In-classactivity:Practicewithdummyvariables two.osf/two.osftwo.osf
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EfficiencyofOLSEstimators three.osf/two.osftwo.osf
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TheGauss-MarkovTheorem - UndertheGauss-MarkovAssumptions: - OLSestimator ˆ β zero.osf , . . . ˆ β k isthe bestlinearunbiasedestimator(BLUE) - WhatisBLUE?Workingbackwards: E: estimator—aruletocomputeanestimatefromasampleofdata U: unbiased— E ( ˆ β j )= β j , j = zero.osf , one.osf , . . . , k L: linear—theestimatorisalinearfunctionof y B: best—hasthe lowestsamplingvariance four.osf/two.osftwo.osf
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Efficiency - Ontheseconddayofclasswetalkedaboutefficiency: - Anestimatoris efficient ifithasalowersamplingvariancethanallother estimators - Thus, Var ( ˆ β j ) < Var ( ˜ β j ) forall j ,where ˜ β j isanalternativeestimator - Thisiswhatwemeanby“best” - What’ssogreataboutOLSbeingefficient? - Usuallyefficientestimatorsarenotassimpletocomputeas ˆ β j ! five.osf/two.osftwo.osf
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HowtoUseQualitativeData six.osf/two.osftwo.osf
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DescribingQualitativeInformation - Untilnow,allexampleshaveusedcontinuousvariables,numericalvalues - Howtowedescribebinaryqualitativeinformation?(e.g.Yes/No) - Aworkerbelongstoaunionordoesnot - Afirmoffersafour.osfzero.osfone.osf(k)pensionplanoritdoesnot - Canbecapturedbydefininga binaryvariable (or dummyvariable ) - Mustdecidewhichoutcomeisassignedzero.osf,andwhichisone.osf - Choosevariablenametobedescriptive seven.osf/two.osftwo.osf
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Example - toindicategender, female ,whichisone.osfifthepersonisfemale,zero.osfifmale - Thisisabetternamethan gender or sex (whatdoes gender = one.osfmean?) -------------------------------------------------------- colgpa sat hsperc athlete female sex -------------------------------------------------------- three.tosf eight.tosfone.tosfzero.tosf six.tosfsix.tosf.six.tosfsix.tosfsix.tosfsix.tosfseven.tosf
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  • Fall '08
  • STAFF
  • Regression Analysis, OLS estimators, Gauss–Markov theorem, Linear Probability Models

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