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4. Binary dependent variable Sometimes it is not possible to quantify the y’s

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: Heteroskedasticity  LS inefficient Individual tests of significance not applicable (lack of normality) R 2 not representative

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4. Binary dependent variable Sometimes it is not possible to quantify the y’s

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  1. 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: • Heteroskedasticity  LS inefficient • Individual tests of significance not applicable (lack of normality) • R2 not representative • LS or GLS can be improved (non linear methods) • Prediction not reliable (cannot get 0 or 1) The forecasted value for β^Xo is P(Y=1)

  2. 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

  3. 4.2 & 4.3 Logit & Probit • The LPM is easy to use yet has two serious drawbacks: • Prediction is not bounded between [0,1] • 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. 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

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