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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). |
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