a425_limdep

# a425_limdep - Qualitative Dependent Variables APS 425 -...

This preview shows pages 1–4. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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 )]
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:

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## a425_limdep - Qualitative Dependent Variables APS 425 -...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online