a425_limdep

a425_limdep - Qualitative Dependent Variables APS 425 -...

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Qualitative Dependent Variables APS 425 - Advanced Managerial Data Analysis (c) Prof. G. William Schwert, 2002-2010 1 APS 425 – Winter 2010 Qualitative Dependent Variables Instructor: G. William Schwert 585-275-2470 schwert@schwert.simon.rochester.edu Topics • Linear probability model • Logit • Probit
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Qualitative Dependent Variables APS 425 - Advanced Managerial Data Analysis (c) Prof. G. William Schwert, 2002-2010 2 Dummy Dependent Variables • If the variable you are trying to explain/predict is qualitative or discrete (e.g., 0 or 1), a regression model can be used Y = 0 + 1 X + The regression model gives the conditional mean of Y given X E(Y|X) = 0 + 1 X which can often be interpreted as the probability that Y=1 given X Problems with Dummy Dependent Variables • Since Y is either 1 or 0, the residuals are either (1 - 0 - 1 X )or X (- 0 - 1 ) • Since E(u) = 0, – the probability that the residual will equal (1 - 0 - 1 X ) • has to be ( 0 + 1 X ) – and the probability that the residual will be (- 0 - 1 X ) has to be (1 X • has to be (1 - 0 - 1 ) • Therefore, the variance of the errors has to be – Var(u) = ( 0 + 1 X ) [1 - 0 - 1 X ] 2 + (1 - 0 - 1 X ) [- 0 - 1 X ] 2 = ( 0 + 1 X ) [1 - 0 - 1 X ] = E(Y| X ) [1 - E(Y| X )]
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Qualitative Dependent Variables APS 425 - Advanced Managerial Data Analysis (c) Prof. G. William Schwert, 2002-2010 3 Problems with Dummy Dependent Variables • Thus, there are a few known problems with the linear probability model – Residuals are heteroskedastic (Var(u) = E(Y| X) [1 - E(Y| X)]) – There is no restriction that the prediction from the regression is between 0 and 1 • Nevertheless, in most cases with reasonable sample sizes the linear probability model works pretty wel linear probability model works pretty well – You probably want to use White standard errors, since you know the residuals will be heteroskedastic Epidural Data (A425_epidural.wf1) • Labor & Delivery Service at a hospital question whether the use of epidural anesthetic prolongs childbirth • Collect data on:
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a425_limdep - Qualitative Dependent Variables APS 425 -...

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