Question

Suppose that the true relationship between the variables Y; and X; is given by: Y_{i}=\alpha+\beta X_{i}+u_{i} with u; = Wi + Zi, where Wi, Z¡ are additional variables that you

are ignoring and that end up in the error term. a) Suppose that Cov(X;,W;) > 0 and that Cov(X¡, Z¡) > 0. Is it possible that Al holds in this situation? Please explain why using both formality and intuition. b) Suppose that Cov(X¡,W;) > 0 and that Cov(X¡, Z¡) < 0. Is it possible that the regressor is uncorrelated with the error term? Can you say precisely when this is the case? c) Does Cov(X¡, u¡) = 0 imply that A1 holds?

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