Economics 105: Statistics

1. Economics 105: Statistics Go over GH 24 Unit 3 Review is due by 4:30 p.m., Thursday, May 1st

2. 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

3. 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)

4. 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

5. 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

6. 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

7. Omitted Variable Bias Subcript c indexes 64 countries Descriptive statistics

8. Omitted Variable Bias

9. Omitted Variable Bias

10. Omitted Variable Bias

11. Omitted Variable Bias

12. Omitted Variable Bias … approximately equal