Economics 105: Statistics• RAP oral presentation schedule …

• We’ll do 8 per lab for each of the next 2 weeks. Lab Tue Apr 24, Thur Apr 26 & Tue May 1, Thur May 3

Specification Bias• Violation of Assumptions (1 & 5): well-specified model• true model is (A)

but we run (B)

• Including an irrelevant variable• is an unbiased estimator of

• ; less efficient

• estimator of , , is unbiased• t & F tests are valid

Specification Bias• Violation of Assumptions (1&5): well-specified model• true model is (C)

but we run (D)

• Omitting a relevant variable• is a biased estimator of

• is actually smaller; more efficient

• estimator of , , is now biased• t & F tests are incorrect

Omitted Variable 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• •

Omitted Variable Bias• •

Omitted Variable Bias• •

Omitted Variable Bias• •

Omitted Variable Bias• •

• • … approximately equal

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)