LN+8+Binary+Dependent+Variables

# LN+8+Binary+Dependent+Variables - Empirical Methods...

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Empirical Methods II (API-202A) Kennedy School of Government Harvard University 1 Lecture Notes 8 Binary Dependent Variables I – INTRODUCTION o Up to now : use binary variables (dummies) as RHS variables in a regression. o This LN : explore the use of binary variables as LHS variable o Examples: College attendance (student attends college or not) Unemployment (worker is employed or not) Medical outcomes (patient had a heart attack or not 6 months after surgery) Mortgage application (mortgage application is denied or not) o We will study three types of regression models to study LHS binary variables: Linear Probability Model (LPM – estimated by OLS) Probit (not estimated by OLS) Logit (not estimated by OLS) o Key questions we will answer in the context of binary dependent variables: How do we interpret the predicted value: E[ Y| X 1 ,X 2 ] ? How do we interpret 1 ˆ ? How do we compute the predicted change of a one-unit increase in X 1 ?

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Empirical Methods II (API-202A) Kennedy School of Government Harvard University 2 II – LINEAR PROBABILITY MODEL (LPM) Assume our model of interest if the following: Y = 0 ˆ 1 ˆ X 1 + 2 ˆ X 2 + ˆ where Y is binary. As before, E[ Y | X 1 , X 2 ] = 0 ˆ 1 ˆ X 1 + 2 ˆ X 2 Key question : How do we interpret E[ Y| X 1 ,X 2 ]? -When Y is not binary: E(wage | female=1 educ=12) [from LN6] -When Y is binary: How do we interpret: * E(college attendance | family_income grades )? * E(mortgage denied | P/I )? [P/I : payment to income ration] E[ Y| X 1 ,X 2 ] = Pr(Y=1|X 1 ,X 2 ) = 0 ˆ 1 ˆ X 1 + 2 ˆ X 2 * Interpret Pr(Y=1 | X ) as the probability of “success” i.e. the case when the dependent variable is equal to one, in these examples, the student attending college or the mortgage was denied given certain values of the RHS variables. How do we interpret 1 ˆ ? o Hard to interpret 1 ˆ as the predicted change in Y given a one-unit increase in X 1 , holding all other variables in the regression constant. o For LPM, 1 ˆ is the predicted change in the probability of “success” when X 1 increases by one unit in the sample, holding all other variables in the regression constant.
Empirical Methods II (API-202A) Kennedy School of Government Harvard University 3 We estimate LPM just as with any OLS regression. However, the predicted values can be outside the range of 0 to 1! Graphically , eny D ˆ = 0 ˆ 1 ˆ P/I Question: What is the sing of 1 ˆ ? How do you interpret that sign?

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Empirical Methods II (API-202A) Kennedy School of Government Harvard University 4 Advantage of the LPM model: Direct extension of the OLS model, so doesn’t require learning a new method and the interpretation of the coefficients is straightforward. Drawback of the LPM model: It is possible that we could get a predicted probability for Y ˆ outside the range of the 0-1 definition of the dependent variable.
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LN+8+Binary+Dependent+Variables - Empirical Methods...

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