# ch6-1 - Chapter 6 Linear Regression with Multiple...

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Chapter 6 Linear Regression with Multiple Regressors (Part 1)

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Omitted Variable Bias In ch.4 and 5, we focus on the student-teacher ratio as the determinant of test score. Students from districts with small classes may have other advantages that help them perform well. Omitted factors would be important determinants and can make the OLS estimator biased: Omitted variable bias . The mean of the OLS estimator might not equal the true effect. Consider an omitted student characteristic: the percentage of students who are still learning English. The researcher find that the correlation between the student-teacher ratio and the percentage of English learners is 0.19. The OLS coefficient on the student-teacher ratio would reflect that influence.
Definition of Omitted Variable Bias Omitted variable bias occurs when: 1. the omitted variable is correlated with the included independent variable; and 2. the omitted variable is a determinant of the dependent variable. Examples: I Percentage of English learners I Time of day of the test I Parking lot space per pupil Omitted variable bias means that the first least squares assumption is incorrect.

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A Formula for Omitted Variable Bias Let the correlation between X i and u i be corr ( X i , u i ) = ρ Xu . Suppose that the second and third least square assumptions hold, but the first does not because ρ Xu 6 = 0. Then the OLS estimator has the limit: b β 1 p °! β 1 + ρ Xu σ u σ X . I b β 1 is inconsistent when there is omitted variable bias.
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