lect22_2010

# lect22_2010 - 1 25 Introduction to Econometrics Econ 322...

This preview shows pages 1–7. Sign up to view the full content.

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

View Full Document

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

View Full Document

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.

Unformatted text preview: 1 / 25 Introduction to Econometrics Econ 322 Fall, 2010 Lecture 22: Regression with a Binary Dependent Variable November 17, 2010 Topics Covered triangleright Topics Covered Examples of Binary Dependent Variable The Linear Probability Model Example: Probability of Getting a Loan The linear probability model: Summary Probit Regression Probit: HDMA Example Logit Regression estimation Maximum Likelihood for Probit and Logit Summary 2 / 25 1. linear probability model 2. probit model 3. logit model 4. maximum likelihood Examples of Binary Dependent Variable Topics Covered triangleright Examples of Binary Dependent Variable The Linear Probability Model Example: Probability of Getting a Loan The linear probability model: Summary Probit Regression Probit: HDMA Example Logit Regression estimation Maximum Likelihood for Probit and Logit Summary 3 / 25 square So far the dependent variable (Y) has been continuous: – district-wide average test score – traffic fatality rate – average hourly earnings square What if Y is binary? – Y = get into college, or not; X = years of education – Y = person smokes, or not; X = income – Y = mortgage application is accepted, or not; X = income, house characteristics, marital status, race – Y=decide to work, or not; X= years of education, gender, race, age , experience square What we are modeling is the probability of observing Y = 1 for example. The Linear Probability Model Topics Covered Examples of Binary Dependent Variable triangleright The Linear Probability Model Example: Probability of Getting a Loan The linear probability model: Summary Probit Regression Probit: HDMA Example Logit Regression estimation Maximum Likelihood for Probit and Logit Summary 4 / 25 square A natural starting point is the linear regression model with a single regressor: Y i = β + β 1 X i + epsilon1 i square But: – What does β 1 mean when Y is binary? Is β 1 = Δ y Δ x ? – What does the line β + β 1 X mean when Y is binary? – What does the predicted value ˆ Y mean when Y is binary? For example, what does ˆ Y = 0 . 26 mean? square In the std regression model we have E ( Y | X ) = β + β 1 X The Linear Probability Model(cont) Topics Covered Examples of Binary Dependent Variable triangleright The Linear Probability Model Example: Probability of Getting a Loan The linear probability model: Summary Probit Regression Probit: HDMA Example Logit Regression estimation Maximum Likelihood for Probit and Logit Summary 5 / 25 square when Y is binary then square Thus square when Y is a binary variable then the linear regression model is call the linear probability model square the predicted value is a probability ˆ Y = Pr ( Y = 1 | X ) square β 1 is the change in probability that Y=1 for a 1 unit change in X β 1 = Pr ( Y = 1 | X = x + Δ x )- Pr ( Y = 1 | X = x ) Δ x Example: Probability of Getting a Loan Topics Covered Examples of Binary Dependent Variable The Linear Probability Model triangleright Example: Probability of Getting a Loan...
View Full Document

{[ snackBarMessage ]}

### Page1 / 25

lect22_2010 - 1 25 Introduction to Econometrics Econ 322...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online