1. Suppose that the true regression model includes two variables: y = Bo + B1x1 +...

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1. Suppose that the true regression model includes two variables: y = Bo + B1x1 + Bzx2 + u, where the notation is as in the curriculum. Assume that MLR.1-MLR.4 hold. Someone suggests to just include the first regressor (x1) and run this regression to estimate the coefficient on x, in the true model. a. Sketch a proof that shows that the resulting estimator of the coefficient on x, will be inconsistent in general. b. Under what conditions will the estimator be consistent? c. Suppose that you instead regress x, on x2 and obtain the residuals for this regression. Next you regress y on the residuals from the regression of x, on x2. Will this procedure lead to an inconsistent estimator of the coefficient on x1? 1. Suppose that the true regression model includes two variables: y = Bo + B1x1 + Bzx2 + u, where the notation is as in the curriculum. Assume that MLR.1-MLR.4 hold. Someone suggests to just include the first regressor (x1) and run this regression to estimate the coefficient on x, in the true model. a. Sketch a proof that shows that the resulting estimator of the coefficient on x, will be inconsistent in general. b. Under what conditions will the estimator be consistent? c. Suppose that you instead regress x, on x2 and obtain the residuals for this regression. Next you regress y on the residuals from the regression of x, on x2. Will this procedure lead to an inconsistent estimator of the coefficient on x1?

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a Sketch a proof that shows that the resulting estimator of the coefficient on X will be inconsistent in general Proof Suppose that the true regressio... View the full answer