4. Binary dependent variable Sometimes it is not possible to quantify the y’s Ex. To work or not? To vote one or other party, etc. Some difficulties: 1.Heteroskedasticity.

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Presentation transcript:

4. Binary dependent variable Sometimes it is not possible to quantify the y’s Ex. To work or not? To vote one or other party, etc. Some difficulties: 1.Heteroskedasticity  LS inefficient 2.Individual tests of significance not applicable (lack of normality)  R 2 not representative 3.LS or GLS can be improved (non linear methods) 4.Prediction not reliable (cannot get 0 or 1) The forecasted value for β ^ X o is P(Y=1)

4.1 Linear probability model The theoretical probability that an i chooses option Y=1 is determined by a linear function In sum, it is like LS with a dummy as dependent variable Given that Y {0,1}  β is NOT the change in Y to unit changes in X β measures the change in the probability of success when X changes, all other things the same

4.2 & 4.3 Logit & Probit The LPM is easy to use yet has two serious drawbacks: 1.Prediction is not bounded between [0,1] 2.The rate of change is constant (this is common to LPM & LS!) Alternatives: Logit & Probit Non-linear functions that make for a bounded probability between [0,1] Logit: Logistic function  accumulative distribution of logistic distribution Probit: accumulative distribution of normal distribution Which one is better? Similar results

4.2 & 4.3 Logit & Probit LPM  LS or GLS Now: maximum likelihood (ML), due to the NON linear nature of the function. Before, under CLRM  LS = ML ML will account for heteroskedasticity, is consistent, and asymptotically normal Individual hypothesis tests are analogous to those of LS