The regression model to be analyzed is y = X 1 1 + X 2
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 (5-23), 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)−1X'1(y − X2β02).
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