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lect14_103_2010_Compatibility_Mode_

lect14_103_2010_Compatibility_Mode_ - Binary Dependent...

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5/24/2010 1 Binary Dependent Variables - I So far, our dependent variables of interest have always been continuous variables, e.g. average test scores, sales, wages, etc. What happens when the dependent variable we are interested in, Y i , is a binary (dummy) variable (i.e. takes on only values 0 or 1)? Binary Dependent Variables - II • Examples: 1) Studying what determines the decision of whether or not to attend college. Y i = 1 if individual i attends college Y i = 0 if individual i doesn’t attend college 2) Studying what determines whether a website visitor purchases anything. Y i = 1 if individual i purchases something Y i = 0 if individual i doesn’t purchase anything 3) Studying what determines if a mortgage loan application is denied. Y i = 1 if individual i ’s application is denied Y i = 0 if individual i ’s application is accepted
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5/24/2010 2 Binary Dependent Variables - III First, let’s think about the expectation of a binary variable. By definition of an expectation: So the expectation of a binary variable is equal to the probability that the variable equals 1. – e.g. Y i =1 if the website visitor purchases the product; Y i =0 if the visitor does not purchase the product. Then the expected value of Y i is equal to the probability that the visitor purchases the product. The above result also holds conditional on any value of X i , , i.e. given that X i equals some particular value: [ ] ( ( ( 29 = Pr 0 *0 Pr 1 *1 = Pr 1 i i i i E Y Y Y Y = + = = [ ] ( | = Pr 1| i i i i E Y X Y X = Binary Dependent Variables - IV We will study 3 different regression models that can be used when Y i is a binary variable : – 1) Linear Probability Model – 2) Probit Model – 3) Logit Model
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5/24/2010 3 Linear Probability Model - I The Linear Probability Model (LPM) is the simplest of the above models. To preview, it essentially involves doing exactly what we did when Y i was not discrete (i.e. using the linear regression techniques that we have already learned.) • Model: Assume A1b, A2, A3, A4. Note: In models with a binary dependent variable, we will always assume A1b rather than A1. This will allow us to make more concrete statements about the estimated model. 0
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