(Requires Appendix material)If the Gauss-Markov conditions hold,then OLS is BLUE.In addition,assume here that X is nonrandom.Your textbook proves the Gauss-Markov theorem by using the simple regression model Yi = β0 + β1Xi + ui and assuming a linear estimator .Substitution of the simple regression model into this expression then results in two conditions for the unbiasedness of the estimator: = 0 and = 1.
The variance of the estimator is var( X1,…,Xn)= .
Different from your textbook,use the Lagrangian method to minimize the variance subject to the two constraints.Show that the resulting weights correspond to the OLS weights.

Question

(Requires Appendix material)If the Gauss-Markov conditions hold,then OLS is BLUE.In addition,assume here that X is nonrandom.Your textbook proves the Gauss-Markov theorem by using the simple regression model Yi = β0 + β1Xi + ui and assuming a linear estimator  .Substitution of the simple regression model into this expression then results in two conditions for the unbiasedness of the estimator:  = 0 and  = 1.
The variance of the estimator is var(   X1,…,Xn)=   .
Different from your textbook,use the Lagrangian method to minimize the variance subject to the two constraints.Show that the resulting weights correspond to the OLS weights.

Quizplus · Accepted Answer

The Answer of (Requires Appendix material)If the Gauss-Markov conditions hold,then OLS is BLUE.In addition,assume here that X is nonrandom.Your textbook proves the Gauss-Markov theorem by using the simple regression model Yi = β0 + β1Xi + ui and assuming a linear estimator  .Substitution of the simple regression model into this expression then results in two conditions for the unbiasedness of the estimator:  = 0 and  = 1.
The variance of the estimator is var(   X1,…,Xn)=   .
Different from your textbook,use the Lagrangian method to minimize the variance subject to the two constraints.Show that the resulting weights correspond to the OLS weights.

(Requires Appendix Material)If the Gauss-Markov Conditions Hold,then OLS Is BLUE