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## PowerPoint Slideshow about ' Economics 105: Statistics' - edison

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### Multicollinearity

### Multicollinearity

### Specification Bias

### Specification Bias

### Omitted Variable Bias

### Omitted Variable Bias

“Multicollinearity” typically refers to severe, but imperfect multicollinearity

Matter of degree, not existence

Consequences

Estimates of the coefficients are still unbiased

Std errors of these estimates are increased

t-statistics are smaller

Estimates are sensitive to

changes in specification (i.e., which variables are included in the model)

R2 largely unaffected

Detection

calculate all the pairwise correlation coefficients

> .7 or .8 is some cause for concern

Variance Inflation Factors (VIF) can also be calculated

Hallmark is high R2 but insignificant t-statistics

Remedy

Do nothing

Drop a variable

Transform multicollinear variables

need to have same sign and magnitudes

Get more data (i.e., increase the sample size)

- true model is (A)
- but we run (B)
- Including an irrelevant variable
- is an unbiased estimator of
- ; less efficient
- still an unbiased estimator of
- thus, t & F tests still valid

- true model is (C)
- but we run (D)
- Omitting a relevant variable
- is a biased estimator of
- is actually smaller; more efficient
- now a biased estimator of
- thus, t & F tests are incorrect

When is an unbiased estimator of ?

- b21 is the slope coefficient from a regression of the EXCLUDED variable on the INCLUDED variable

… approximately equal

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