CORNELL ECON 3120 - Omitted Variable Bias with Many Regressors (2 pages)

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Econ 3120 1st Edition Lecture 15 Outline of Current Lecture I Omitted Variable Bias with Many Regressors Current Lecture II Dummy Variables Dummy Variables Dummy variables aka binary variables indicator variables or dichotomous variables are simply variables that take on a value of 0 or 1 They indicate a single status of the observation Some examples female 1 for female 0 for male non white 1 if race is non white 0 if white urban 1 if the person lives in an urban area 0 if lives in a rural area Note that we could also define our dummy variables to indicate male white or rural but it turns out not to matter more on this below Dummy variables change the intercept of the regression equation For example suppose we want to examine the relationship between test scores and class sizes in primary schools We think that the gender of the child also has an effect on test scores so we include it in the model We therefore model the relationship as score 0 1 f emale 2clsize u 1 How do we interpret 1 1 actually represents a shift in the intercept associated with the gender of the child To see this take the conditional expectation for females and for males E score f emale 0 clsize 0 2clsize E score f emale 1 clsize 0 1 2clsize The difference between these two equations is simply a shift in the intercept from 0 to 0 1 1 score Slope 2 1 0 female male class size This interpretation easily generalizes to situations with more independent variables The coeffi cients on the continuous variables i e slope coefficients remain the same for different values of the dummy variable but the dummy variable shifts the intercept What would happen if you included the dummy variable male in the equation where male 1 if the child is a male and 0 if she is female You would therefore be running the regression score 0 1 f emale 2clsize 3male u It is not possible to run this regression because male is simply a linear combination of f emale male 1 f emale This violates Assumption MLR 3 If you tried to do