Economics 105: Statistics

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# Economics 105: Statistics - PowerPoint PPT Presentation

Economics 105: Statistics. Go over GH 24 Unit 3 Review is due by 4:30 p.m., Thursday, May 1 st. Multicollinearity. “ Multicollinearity ” typically refers to severe, but imperfect multicollinearity Matter of degree, not existence Consequences

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### Economics 105: Statistics

Go over GH 24

Unit 3 Review is due by 4:30 p.m., Thursday, May 1st

### Multicollinearity

“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

### Multicollinearity

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)

Violation of Assumption (1)…

• 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

### Specification Bias

Violation of Assumption (1) …

• 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

### Specification Bias

When is an unbiased estimator of ?

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

### Omitted Variable Bias

Subcript c indexes 64 countries

Descriptive statistics

### Omitted Variable Bias

… approximately equal