Part III. Consider the linear IV model Y = atXBtu where X and u are correlated. We have an instrument Z. Given a simple random sample (Xi, Yi, Zi)i=1, answer the following questions (a) Write down the formula for the IV estimator BIv. (b) Define ui = Yi - QIv - XiBIv where ary = Y - X Biv. Show that n n Cui = 0 and E Ziui = 0 i=1 i= 1 Show also cov(Zi, ui) = 0, that is, the sample covariance between Z and u is zero. (c) A friend claims that E-1 Xiui = 0 just as in the case with OLS regression. Do you agree? Explain