Lecture 10

Lecture 10 - LECTURE 10 MULTICOLLINEARITY AND SPECIFICATION...

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LECTURE 10: MULTICOLLINEARITY AND SPECIFICATION ERROR We have assumed no perfect multicollinearity What happens if we have high multicollinearity? Theory: Under CLRM, OLS is BLUE (as long as there is no perfect multicollinearity) What are the consequences? 1. Large variances and standard errors of OLS estimators Even though the estimate may be minimum variance, it doesn’t mean small. Harder to get a precise estimate Wider confidence intervals Insignificant t-ratios Can get a high R 2 but few significant t-ratios. 2. OLS estimators and their standard errors become very sensitive to small changes in the data (i.e. they are unstable). 3. Wrong signs for regression coefficients. 4. Difficulty in assessing the individual contributions of explanatory variables.
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SPECIFICATION ERROR: INCLUDING AN IRRELEVANT VARIABLE We specify: i i 2 2 i 1 1 0 i ε ˆ X β ˆ X β ˆ β ˆ Y True model: Y i = β 0 + β 1 X 1i + ε i What will happen to our estimates? OLS estimate will still be unbiased.
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This note was uploaded on 03/20/2009 for the course ECON 103 taught by Professor Sandrablack during the Winter '07 term at UCLA.

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Lecture 10 - LECTURE 10 MULTICOLLINEARITY AND SPECIFICATION...

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