2. Consider, y=X+Z+u where Euu=2I. Suppose you have ~=(XX)1Xy^=(XMZX)1XMZy (a) Explain the difference between the estimators. (b) Define MZ, and explain. (c) Find the expression for ^1=~B^. (d) What is the relation between the variance of ~ and ^ ? Find an expression. Consider the following model, with an endogenous variable. log(yi)=xi+ui (a) Suggest a method of estimation in case that E(uixi)=0. Explain and state the two conditions that the method needs to satisfy, and derive the estimator. (b) Suppose p=1,^OLS=0.50,^2SLS=0.34, and the Var(^2SLS^OLS)= 0.006 . Propose a test for endogeneity, state the null and alternative hypothesis and explain your conclusions