Consider using a partition matrix in OLS. That is, consider X = [X, X] and =...

  

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Consider using a partition matrix in OLS. That is, consider X = [X, X] and = - [1] B where X is n x r, X is n x r2, B is r x 1, 3 is r x 1, and r + r = r, the overall number of columns in X. When we take the inverse of a 2 x 2 partition matrix -(ABD C)-BD- (D-CA-B)- -1 [ ] C D B] = [ (A - BD-C)- (D-CA-B)-CA- Find the equations for 3 and 3 using the OLS estimator 3 = (X'X)-X'y 2. Newey-West estimator: Extend the linear model code we wrote in class to implement a Newey-West corrected OLS estimator with autocovariance term. The robust variance covariance matrix for this Newey-West estimator is Var(8) = (X'X)-X'X(X'X)- where 11 01 01 0 0 01 .... 01 02 000 0 You can either create a new inheriting class or you can add the functionality as an option in the least squares code that we wrote. Consider using a partition matrix in OLS. That is, consider X = [X, X] and = - [1] B where X is n x r, X is n x r2, B is r x 1, 3 is r x 1, and r + r = r, the overall number of columns in X. When we take the inverse of a 2 x 2 partition matrix -(ABD C)-BD- (D-CA-B)- -1 [ ] C D B] = [ (A - BD-C)- (D-CA-B)-CA- Find the equations for 3 and 3 using the OLS estimator 3 = (X'X)-X'y 2. Newey-West estimator: Extend the linear model code we wrote in class to implement a Newey-West corrected OLS estimator with autocovariance term. The robust variance covariance matrix for this Newey-West estimator is Var(8) = (X'X)-X'X(X'X)- where 11 01 01 0 0 01 .... 01 02 000 0 You can either create a new inheriting class or you can add the functionality as an option in the least squares code that we wrote.