Let the true population model be: y = ?0+?1x+u with ?0 not= 0. Consider the following empirical models: ! The correctly specied…
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.
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