Instead of estimating the coefficients , and B from the model y= a + x + Btz + u it is decided to use ordinary least squares on the following regression equation: y = a + Bxj + Bx + v where x is the residual from a regression of x, and x, and v is the distur- bance term.

(a) Show that the resulting estimator of B2 is identical to the regression coefficient of y on X.

(b) Obtain an expression for the bias of this estimator.

(c) Prove that the estimators of , obtained from each of the two equa- tions are identical.