econometrics ch 6 - Introduction to Econometrics Chapter 6:...

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Unformatted text preview: Introduction to Econometrics Chapter 6: Linear Regression with Multiple Regressors Geo rey Williams gwilliams@econ.rutgers.edu October 27, 2010 Geo rey Williams gwilliams@econ.rutgers.edu Introduction to Econometrics Chapter 6: Linear Regression The Return of Other Factors Remember that our basic regression equation is: Y i = + 1 X i + u i We assumed that u i could be ignored - that while u i might have some relationship with Y i , and or with X i , that it was not important to the relationship that Y i and X i had with each other. Is this always true? Geo rey Williams gwilliams@econ.rutgers.edu Introduction to Econometrics Chapter 6: Linear Regression The example of English-learning students Consider the percentage of English-learning students in a school district. It could clearly have an impact on test scores, at the very least slowing down reading comprehension, increasing the odds of misunderstanding a question.. If districts with a high percentage of English-learning students ALSO have large class sizes, then they might have lower test scores due to the language issues, not the class size. Omitting the variable , percentage of English-learners could be biasing our results Geo rey Williams gwilliams@econ.rutgers.edu Introduction to Econometrics Chapter 6: Linear Regression Omitted Variable Bias We need two things for omitted variable bias: 1 an omitted variable that is correlated with X i 2 the same omitted variable has an in uence on Y i When both hold true, then the rst least squares assumption, E ( u i j X i ) = 0, does not hold true. Geo rey Williams gwilliams@econ.rutgers.edu Introduction to Econometrics Chapter 6: Linear Regression Several Examples 1 Percentage of English learners Correlated with X i p In uence on Y i p 2 Time of day of test Correlated with X i In uence on Y i p 3 Parking lot space per pupil Correlated with X i p In uence on Y i Geo rey Williams gwilliams@econ.rutgers.edu Introduction to Econometrics Chapter 6: Linear Regression Formal Description of Omitted Variable Bias...
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econometrics ch 6 - Introduction to Econometrics Chapter 6:...

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