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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

Economics 105: Statistics

Go over GH 24

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


Multicollinearity

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


Multicollinearity1

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)


Specification bias

  • 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


Specification bias1

  • 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


Omitted variable bias

Omitted Variable Bias


Omitted variable bias1

Omitted Variable Bias

Subcript c indexes 64 countries

Descriptive statistics






Omitted variable bias6

Omitted Variable Bias

… approximately equal


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