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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: districtwide 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 = + 1 X i + epsilon1 i square But: What does 1 mean when Y is binary? Is 1 = y x ? What does the line + 1 X mean when Y is binary? What does the predicted value Y mean when Y is binary? For example, what does Y = 0 . 26 mean? square In the std regression model we have E ( Y  X ) = + 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 Y = Pr ( Y = 1  X ) square 1 is the change in probability that Y=1 for a 1 unit change in X 1 = Pr ( Y = 1  X = x + x ) Pr ( Y = 1  X = x ) 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...
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 Fall '11
 LANDONLANE
 Econometrics

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