Transcription of Regression with a Binary Dependent Variable - Chapter 9
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Regression with a Binary Dependent Variable - Chapter 9
Regressionwitha Binary DependentVariableChapter9 MichaelAshCPPAL ecture22 CourseNotesIEndgameITake-home nalIDistributedFriday 19 MayIDueTuesday 23 May (Paper or emailedPDFok; no Word,Excel,etc.)IProblemSet7 IOptional,worth up to 2 percentagepointsof extracreditIDueFriday 19 MayIRegressionwitha Binary DependentVariableBinary DependentVariablesIOutcomecanbe coded1 or 0 (yes or no,approvedor denied,successor failure)Examples?IInterprettheregression as modelingtheprobability thatthedependentvariableequalsone(Y= 1).IRecallthatfor a Binary Variable ,E(Y) = Pr(Y= 1)HMDA exampleIOutcome:loandenialis coded1, loanapproval0 IKeyexplanatory Variable :blackIOtherexplanatory variables:P=I, credithistory, LTV, Probability Model(LPM)Yi= 0+ 1X1i+ 2X2i+ + kXki+ 1expressesthechangein probability thatY= 1 associatedwitha ^Yiexpressestheprobability thatYi= 1Pr(Y= 1jX1;X2; : : : ;Xk) = 0+ 1X1+ 2X2+ + kXk=^YShortcomingsof theLPMI\NonconformingPredictedProbabilit ies"Probabilitiesmustlogicallybe between0 and1, construction(always userobuststandarderrors)ProbitandLogitRe gr
Logit or Logistic Regression Logit, or logistic regression, uses a slightly di erent functional form of the CDF (the logistic function) instead of the standard normal CDF. The coe cients of the index can look di erent, but the probability results are usually very similar to the results from probit and from the LPM.
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