Question: Consider the following model: Yi = Xi Ui Xi = Yi Vi, where E(ViUj) = 0, i,j. (a) (10 points) Find the probability limit of

Consider the following model: Yi = Xi Ui Xi = Yi Vi, where E(ViUj) = 0, i,j. (a) (10 points) Find the probability limit of the OLS estimators of the regression of Yi on Xi and the regression of Xi on Yi. Are these estimators consistent to and ? (b) (10 points) Find E(Yi|Xi) and discuss your results. (c) (20 points) Suppose now that Yi = Xi Zi Ui Xi = Yi Vi, where E(ViUj) = 0, i,j and E(Ui|Zi) = 0 and E(Vi|Zi) = 0. Based on the model, propose alternative estimators to recover the parameters and . Hint: recover first and use the fact that E(ViUj) = 0

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