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# handout10_1 - Econ 139 Introduction to Econometrics Andrew...

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Econ 139: Introduction to Econometrics Andrew Sweeting 1 Department of Economics Duke University Spring 2011 Econ 139 Handout 10 (Duke) Binary Dependent Variables Spring 2011 1 / 85

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Regression with Binary Dependent Variables Up to this point, the examples we have analyzed have all involved dependent variables that took on many values (so we felt comfortable treating them as continuous). So far, we have only allowed the regressors to be dummy variables. What if the variable that you are trying to explain is binary (i.e. has only two values (say 0 and 1))? This presents a new challenge, since it°s not clear how to ±²t a line³ through data that only takes on two values. Furthermore, there are lots of examples of binary dependent variables: smoking, working, buying a hybrid car, voting for Obama. They are variously referred to as qualitative , discrete or limited dependent variables. Econ 139 Handout 10 (Duke) Binary Dependent Variables Spring 2011 2 / 85
Regression with Binary Dependent Variables Let°s look at a new example from the book: racial discrimination in the mortgage market. We have data on mortgage applicants in Boston in 1990 (2,380 black or white applicants for single family home loans). We would like to know if there is evidence of racial discrimination. Looking at the raw data we ²nd: 28% of black applicants were denied a mortgage only 9% of white applicants were denied So the probability of being denied a mortgage is 19 pp (percentage points) higher for blacks than for whites Does this indicate discrimination? Econ 139 Handout 10 (Duke) Binary Dependent Variables Spring 2011 3 / 85

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Regression with Binary Dependent Variables But this is evidence of racial discrimination only if ±everything else³is the same across the two groups: Loans are made or denied for many reasons, primarily (we hope) re´ecting an applicant°s ability to repay the debt. Some factors we could measure might include payment to income ratio, credit history, size of loan relative to home value We need to run a regression! Econ 139 Handout 10 (Duke) Binary Dependent Variables Spring 2011 4 / 85
Regression with Binary Dependent Variables Let°s ignore the discrimination issue for now and start with a single control: the payment to income ratio (the ratio of the applicant°s anticipated monthly loan payments to their monthly income). We expect that higher P / I °s will make denial more likely. Econ 139 Handout 10 (Duke) Binary Dependent Variables Spring 2011 5 / 85

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Regression with Binary Dependent Variables The line in the graph 1 is just the OLS regression line deny i = β 0 + β 1 P I i + u i Although the dependent variable is binary, there is clearly a relationship between application denial and the P / I ratio. But the line doesn°t actually hit very many of the points (cf. previous regressions) So how should you think about this regression?
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