12.4 Consider TSLS estimation with a single included endogenous variable and a single instrument. Then the predicted value from the first-stage regression is X n

i = pn 0 + pn 1Zi. Use the definition of the sample variance and covariance to show that sXn Y = pn 1sZY and s2 X

n = pn1 2 s2 Z. Use this result to fill in the steps of the derivation in Appendix 12.2 of Equation (12.4).