The regression model to be analyzed is y X11 X22 , where X1 and X2 have K1 and K2 columns, respectively The restriction is 2 0 a Using (6 14), prove that the restricted estimator is simply b1 , 0 , where b1 is the least squares coefficient vector in the regression of y on X1 b Prove that if the res...

For the current problem R 01 where I is the last K columns Therefore RXX RN is the lower righ ...

The regression model to be analyzed is y = X11 + X22 + , where X1 and

Question:

The regression model to be analyzed is y = X1β1 + X2β2 + ε, where X1 and X2 have K1 and K2 columns, respectively. The restriction is β2 = 0.

a. Using (6-14), prove that the restricted estimator is simply [b1*, 0], where b1* is the least squares coefficient vector in the regression of y on X1. b. Prove that if the restriction is β2 = β02 for a nonzero β02, then the restricted estimator of β1 is b1* = (X'1X1) −1 X'1 (y − X2β02).