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2. Consider the following linear regression model: Y = X'B+U, where dim(x)=k. Suppose that there exists a random vector ZER* such that E[ZU] = 0, L" ZZ is invertible for all n, and Pr(rank( 2x ) = k) = 1. In this case, an IV estimator of B is BUV = ( 2.X)-"Z,Y). ZY Show th at this IV estim ator is equivalent to the TSLS estim ator of B, TSL5 = (XP2x) * (XPzY). TE 72 -1 -1 1 2. Consider the following linear regression model: Y = X'B+U, where dim(x)=k. Suppose that there exists a random vector ZER* such that E[ZU] = 0, L" ZZ is invertible for all n, and Pr(rank( 2x ) = k) = 1. In this case, an IV estimator of B is BUV = ( 2.X)-"Z,Y). ZY Show th at this IV estim ator is equivalent to the TSLS estim ator of B, TSL5 = (XP2x) * (XPzY). TE 72 -1 -1 1