Let the true population model be: y = ?0+?1x+u with ?0 not= 0. Consider the following empirical
models:
! The correctly specied model: y = ?^0 + ?^1x
! The misspecied model: y = ?^x
Answer the following questions.
1. Derive the expression for the OLS estimators ?^ and ?^1.
2. Is the OLS estimator ?^ an unbiased estimator of ?1? If your answer is no, determine the
bias.
3. Derive an expression for the variances of ?^ and ?^1.
4. Compare the expressions for the variances of ?^ with the variance of ?^1 from the correctly
specified regression. Is Var(?^) > V ar( ?^1)?
5. Comment on the tradeoff between bias and variance when choosing between these estimators.
